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  • lfunc_lfunctions • Show schema
    {'Lhash': '260043191444962546176808858642,1128161775382157713100581454586,1641375402749049237105895206888', 'a10': 0, 'a2': 4, 'a3': 2, 'a4': 7, 'a5': 0, 'a6': 8, 'a7': 0, 'a8': 7, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 374259.6031746516, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[5, [1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '9025.1', 'coefficient_field': '1.1.1.1', 'conductor': 735091890625, 'conductor_radical': 95, 'degree': 6, 'euler_factors': [[1, -4, 9, -15, 18, -16, 8], [1, -2, 8, -11, 24, -18, 27], [1], [1, 0, 14, -7, 98, 0, 343], [1, -1, 17, -35, 187, -121, 1331], [1, -5, 45, -131, 585, -845, 2197], [1, 2, 36, 81, 612, 578, 4913], [1], [1, 8, 88, 381, 2024, 4232, 12167], [1, -7, 45, -315, 1305, -5887, 24389], [1, -5, 57, -353, 1767, -4805, 29791], [1, -5, 103, -371, 3811, -6845, 50653], [1, 1, 9, -339, 369, 1681, 68921], [1, 5, 72, 137, 3096, 9245, 79507], [1, 3, 137, 269, 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'5.72227354681421957832072236859705', '5.75260015698829752360039326765698', '6.10334097807826589889646597816856', '6.24332788750761713758742705017982', '6.24721475308029850437793454343840', '6.77965047928472316027355956811544', '6.93838738851322429718444509935468', '6.95958788442853584393190562879847', '7.70203466342344005251643661100565', '7.76631157270599808473969548827880', '7.978386946338704893557362316076025'], 'prelabel': '6-95e6-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.489109954771793, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 364027837693997418, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.20513790739983402709442066685', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.889962719363712725182966712443', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.29481688602011781019288654733', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 374259.6031746516, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 735091890625, 'conductor_radical': 95, 'degree': 6, 'dirichlet_coefficients': [1, 4, 2, 7, 0, 8, 0, 7, -4, 0, 1, 14, 5, 0, 0, 7, -2, -16, 0, 0, 0, 4, -8, 14, 0, 20, -13, 0, 7, 0, 5, 14, 2, -8, 0, -28, 5, 0, 10, 0, -1, 0, -5, 7, 0, -32, -3, 14, -14, 0, -4, 35, 19, -52, 0, 0, 0, 28, -10, 0, -17, 20, 0, 28, 0, 8, -1, -14, -16, 0, 19, -28, 1, 20, 0, 0, 0, 40, -18, 0, 4, -4, -13, 0, 0, -20, 14, 7, -2, 0, 0, -56, 10, -12, 0, 28, 5, -56, -4, 0], 'euler11': [1, -1, 17, -35, 187, -121, 1331], 'euler13': [1, -5, 45, -131, 585, -845, 2197], 'euler17': [1, 2, 36, 81, 612, 578, 4913], 'euler19': [1, 0, 0, 0, 0, 0, 0], 'euler2': [1, -4, 9, -15, 18, -16, 8], 'euler23': [1, 8, 88, 381, 2024, 4232, 12167], 'euler29': [1, -7, 45, -315, 1305, -5887, 24389], 'euler3': [1, -2, 8, -11, 24, -18, 27], 'euler31': [1, -5, 57, -353, 1767, -4805, 29791], 'euler37': [1, -5, 103, -371, 3811, -6845, 50653], 'euler41': [1, 1, 9, -339, 369, 1681, 68921], 'euler43': [1, 5, 72, 137, 3096, 9245, 79507], 'euler47': [1, 3, 137, 269, 6439, 6627, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -19, 214, -1707, 11342, -53371, 148877], 'euler59': [1, 10, 145, 852, 8555, 34810, 205379], 'euler61': [1, 17, 249, 2033, 15189, 63257, 226981], 'euler67': [1, 1, 59, 693, 3953, 4489, 300763], 'euler7': [1, 0, 14, -7, 98, 0, 343], 'euler71': [1, -19, 268, -2391, 19028, -95779, 357911], 'euler73': [1, -1, 49, 317, 3577, -5329, 389017], 'euler79': [1, 18, 324, 2941, 25596, 112338, 493039], 'euler83': [1, 13, 247, 2019, 20501, 89557, 571787], 'euler89': [1, 2, 168, 75, 14952, 15842, 704969], 'euler97': [1, -5, 297, -971, 28809, -47045, 912673], 'euler_factors': [[1, -4, 9, -15, 18, -16, 8], [1, -2, 8, -11, 24, -18, 27], [1, 0, 0, 0, 0, 0, 0], [1, 0, 14, -7, 98, 0, 343], [1, -1, 17, -35, 187, -121, 1331], [1, -5, 45, -131, 585, -845, 2197], [1, 2, 36, 81, 612, 578, 4913], [1, 0, 0, 0, 0, 0, 0], [1, 8, 88, 381, 2024, 4232, 12167], [1, -7, 45, -315, 1305, -5887, 24389], [1, -5, 57, -353, 1767, -4805, 29791], [1, -5, 103, -371, 3811, -6845, 50653], [1, 1, 9, -339, 369, 1681, 68921], [1, 5, 72, 137, 3096, 9245, 79507], [1, 3, 137, 269, 6439, 6627, 103823], [1, -19, 214, -1707, 11342, -53371, 148877], [1, 10, 145, 852, 8555, 34810, 205379], [1, 17, 249, 2033, 15189, 63257, 226981], [1, 1, 59, 693, 3953, 4489, 300763], [1, -19, 268, -2391, 19028, -95779, 357911], [1, -1, 49, 317, 3577, -5329, 389017], [1, 18, 324, 2941, 25596, 112338, 493039], [1, 13, 247, 2019, 20501, 89557, 571787], [1, 2, 168, 75, 14952, 15842, 704969], [1, -5, 297, -971, 28809, -47045, 912673]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9025/2/a/be'], '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': '6-95e6-1.1-c1e3-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-95e6-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.489109954771793, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 364027837693997418, 'z1': {'__RealLiteral__': 0, 'data': '0.20513790739983402709442066685', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '260043191444962546176808858642,1128161775382157713100581454586,1641375402749049237105895206888', 'Lhash_array': ['260043191444962546176808858642', '1128161775382157713100581454586', '1641375402749049237105895206888'], 'factors': ['2-95e2-1.1-c1-0-15', '2-95e2-1.1-c1-0-247', '2-95e2-1.1-c1-0-402'], 'label': '6-95e6-1.1-c1e3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9025/2/a/be'}