These directories contain zeros of various L-functions. In every case, all zeros have been found to lie on the critical line and only their imaginary parts are listed. DEGREE_1: Degree 1 L-functions consist of the Riemann zeta function and Dirichlet L-functions. For Dirichlet L-functions, real characters produce zeros in conjugate pairs, and only the zeros with positive imaginary part are listed. Complex characters come in conjugate pairs, and their respective L-functions have the same zeros, up to conjugation. So for each pair of conjugate characters, I only list the zeros (positive and negative) for one of the two conjugate L-functions. The term 'non-conjugate' below simply indicates that only one L-function from each such pair is chosen. For conductors > 4, the first column contains the conductor q, the second an index r that indicates which of the phi(q) L-functions is being considered. The last column contains the imaginary part of the zeros of the corresponding L-functions. Since most of the files only contain data for primitive and non-conjugate L-functions, not all 1 <= r <= phi(q) are represented. A lookup table that describes the characters in terms of q and r will soon be added to this web page. File Description ---------------------- ------------------------------------------------------- zeros_0001_35161820.gz The first 35,161,820 zeros of the Riemann zeta function. (much more extensive data is available elsewhere for zeta, so not much time was spent on this computation). zeros_0003_31712310.gz The first 31,712,310 zeros of the Dirichlet L-function of conductor 3. zeros_0004_32457680.gz The first 32,457,680 zeros of the Dirichlet L-function of conductor 4. zeros_0005_1000000.gz The first 10,000,000 zeros for each of the two primitive non-conjugate Dirichlet L-functions of conductor 5. zeros_0007_1000000.gz The first 10,000,000 zeros for each of the three primitive non-conjugate Dirichlet L-functions of conductor 7. zeros_0008_1000000.gz The first 10,000,000 zeros for each of the two primitive non-conjugate Dirichlet L-functions of conductor 8. zeros_0009_1000000.gz The first 10,000,000 zeros for each of the two primitive non-conjugate Dirichlet L-functions of conductor 9. zeros_0011_2000000.gz The first 2,000,000 zeros for each of the three primitive non-conjugate Dirichlet L-functions of conductor 11. zeros_0012_2000000.gz The first 2,000,000 zeros of the Dirichlet L-functions of conductor 12. zeros_0013_1000000.gz The first 1,000,000 zeros for each of the six primitive non-conjugate Dirichlet L-functions of conductor 13. zeros_0015_1000000.gz The first 1,000,000 zeros for each of the two primitive non-conjugate Dirichlet L-functions of conductor 15. zeros_0016_1000000.gz The first 1,000,000 zeros for each of the two primitive non-conjugate Dirichlet L-functions of conductor 16. zeros_0017_1000000.gz The first 1,000,000 zeros for each of the eight primitive non-conjugate Dirichlet L-functions of conductor 17. zeros_0019_1000000.gz The first 1,000,000 zeros for each of the nine primitive non-conjugate Dirichlet L-functions of conductor 19. zeros_-20000_20000_quadratic_200.gz The first 200 zeros of L(s,chi_d), chi_d Kronecker's symbol, with |d| < 20000, d a fundamental discriminant. zeros_5_20000_unitary_200.gz The first 200 zeros of L(s,chi) where chi is a generic primitive **non-real** character of conductor greater than or equal to 5 and less than or equal to 20000. ==================================================================================================== DEGREE_2: I have computed the zeros of various cusp form L-functions. These include the L-function of elliptic curves sorted by conductor, the Ramanujan tau L-function, and some twists of these. Elliptic curve L-functions: The file of the form zeros_E_N_X_m.gz contains the first m zeros of the L-function of the elliptic curve of conductor N, in isogeny class X. For example, there is only one isogeny class for conductor 11, and its first 100,000 zeros are found in the file zeros_E_00011_A_100000.gz The list of curves was obtained from John Cremona's homepage (add link). At present I have the first 100,000 zeros of the L-functions of conductors 11,14,15,17,19, the first 1000 zeros of the L-functions of conductor < 1000, and the first 100 zeros for conductors between 1000 and 8000. The latter is in the directory elliptic_conductors_1001_7998, and the rest is in the directory elliptic_conductors_11_999 Ramanujan tau: zeros_tau_284410.gz The first 284,410 zeros of the L-function whose Dirichlet coefficients are Ramanujan's tau(n) (i.e. the associated cusp form is of weight 12, level 1)