Formats: - HTML - YAML - JSON - 2026-10-12T04:09:35.523896
  • lfunc_lfunctions • Show schema
    {'Lhash': '733575088181273721012828981438', 'a10': 0, 'a2': 0, 'a3': 27, 'a4': 0, 'a5': -125, 'a6': 0, 'a7': -1028, 'a8': 0, 'a9': 729, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 74.97240611618925, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[2, [1]], [3, [1, -27]], [5, [1, 125]]], 'bad_primes': [2, 3, 5], 'central_character': '240.1', 'coefficient_field': '1.1.1.1', 'conductor': 240, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1, -27], [1, 125], [1, 1028, 823543], [1, 3096, 19487171], [1, 13030, 62748517], [1, -1878, 410338673], [1, -31180, 893871739], [1, -33288, 3404825447], [1, 213054, 17249876309], [1, -172696, 27512614111], [1, -27434, 94931877133], [1, -532650, 194754273881], [1, -911908, 271818611107], [1, -732648, 506623120463], [1, -409074, 1174711139837], [1, 1508136, 2488651484819], [1, 302578, 3142742836021], [1, 1254332, 6060711605323], [1, 4781280, 9095120158391], [1, 502414, 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-1.2918107898994278, -1.226309770159103, -1.0703501250341463, -0.8312354910210735, -0.5213462051465043], 'positive_zeros': ['0.57868870811026314625490907777159', '2.45812486939073937552219476806828', '3.23781187010243431790095258036977', '4.53608779612770015106014891366150', '5.77808133587093410218856181729547', '7.26327046809883843238270533911236', '7.65133061856528015950639969010843', '9.160671784348119497256149178271691', '9.712303822604943575191740005975414', '10.73069141920775563833848045354643'], 'prelabel': '2-240-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.658660757656998, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7-0', 'trace_hash': 170915759845577931, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57868870811026314625490907777', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.45812486939073937552219476807', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.23781187010243431790095258037', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 74.97240611618925, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 240, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 27, 0, -125, 0, -1028, 0, 729, 0, -3096, 0, -13030, 0, -3375, 0, 1878, 0, 31180, 0, -27756, 0, 33288, 0, 15625, 0, 19683, 0, -213054, 0, 172696, 0, -83592, 0, 128500, 0, 27434, 0, -351810, 0, 532650, 0, 911908, 0, -91125, 0, 732648, 0, 233241, 0, 50706, 0, 409074, 0, 387000, 0, 841860, 0, -1508136, 0, -302578, 0, -749412, 0, 1628750, 0, -1254332, 0, 898776, 0, -4781280, 0, -502414, 0, 421875, 0, 3182688, 0, 1991368, 0, 531441, 0, 8099268, 0, -234750, 0, -5752458, 0, 7487970, 0, 13394840, 0, 4662792, 0, -3897500, 0, -17172574, 0, -2256984, 0], 'euler11': [1, 3096, 19487171], 'euler13': [1, 13030, 62748517], 'euler17': [1, -1878, 410338673], 'euler19': [1, -31180, 893871739], 'euler2': [1, 0, 0], 'euler23': [1, -33288, 3404825447], 'euler29': [1, 213054, 17249876309], 'euler3': [1, -27, 0], 'euler31': [1, -172696, 27512614111], 'euler37': [1, -27434, 94931877133], 'euler41': [1, -532650, 194754273881], 'euler43': [1, -911908, 271818611107], 'euler47': [1, -732648, 506623120463], 'euler5': [1, 125, 0], 'euler53': [1, -409074, 1174711139837], 'euler59': [1, 1508136, 2488651484819], 'euler61': [1, 302578, 3142742836021], 'euler67': [1, 1254332, 6060711605323], 'euler7': [1, 1028, 823543], 'euler71': [1, 4781280, 9095120158391], 'euler73': [1, 502414, 11047398519097], 'euler79': [1, -1991368, 19203908986159], 'euler83': [1, -8099268, 27136050989627], 'euler89': [1, -7487970, 44231334895529], 'euler97': [1, 17172574, 80798284478113], 'euler_factors': [[1, 0, 0], [1, -27, 0], [1, 125, 0], [1, 1028, 823543], [1, 3096, 19487171], [1, 13030, 62748517], [1, -1878, 410338673], [1, -31180, 893871739], [1, -33288, 3404825447], [1, 213054, 17249876309], [1, -172696, 27512614111], [1, -27434, 94931877133], [1, -532650, 194754273881], [1, -911908, 271818611107], [1, -732648, 506623120463], [1, -409074, 1174711139837], [1, 1508136, 2488651484819], [1, 302578, 3142742836021], [1, 1254332, 6060711605323], [1, 4781280, 9095120158391], [1, 502414, 11047398519097], [1, -1991368, 19203908986159], [1, -8099268, 27136050989627], [1, -7487970, 44231334895529], [1, 17172574, 80798284478113]], 'index': 2, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/240/8/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/240/8/a/i'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-240-1.1-c7-0-2', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-240-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.658660757656998, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 170915759845577931, 'z1': {'__RealLiteral__': 0, 'data': '0.57868870811026314625490907777', 'prec': 97}}
  • lfunc_instances • Show schema
    • id: 19994815
      {'Lhash': '733575088181273721012828981438', 'Lhash_array': ['733575088181273721012828981438'], 'factors': ['2-240-1.1-c7-0-2'], 'label': '2-240-1.1-c7-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/240/8/a/i'}
    • id: 24588346
      {'Lhash': '733575088181273721012828981438', 'Lhash_array': ['733575088181273721012828981438'], 'factors': ['2-240-1.1-c7-0-2'], 'label': '2-240-1.1-c7-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/240/8/a/i/1/1'}