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lfunc_lfunctions • Show schema
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{'Lhash': '4417188442791416792016157967156', 'a10': -92, 'a2': 1, 'a3': 9, 'a4': -31, 'a5': -92, 'a6': 9, 'a7': -26, 'a8': -63, 'a9': 81, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.292666053828362, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -9]], [11, [1, -121]]], 'bad_primes': [3, 11], 'central_character': '33.1', 'coefficient_field': '1.1.1.1', 'conductor': 33, 'conductor_radical': 33, 'degree': 2, 'euler_factors': [[1, -1, 32], [1, -9], [1, 92, 3125], [1, 26, 16807], [1, -121], [1, 692, 371293], [1, 1442, 1419857], [1, -2160, 2476099], [1, 1582, 6436343], [1, 5526, 20511149], [1, -4792, 28629151], [1, 10194, 69343957], [1, 10622, 115856201], [1, -8580, 147008443], [1, 2362, 229345007], [1, 30804, 418195493], [1, -6416, 714924299], [1, -42096, 844596301], [1, 28444, 1350125107], [1, -45690, 1804229351], [1, 18374, 2073071593], [1, 105214, 3077056399], [1, -62292, 3939040643], [1, 72246, 5584059449], [1, 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1]], [[[1, -166554, 18424351793], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-33-1.1-c5-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/33/6/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-2.029304482383099e-120, 0.22967480456341247, 0.4578052750454347, 0.6827990237068892, 0.9029706335549659, 1.116502768521572, 1.3214162367866606, 1.5155516643518543, 1.6965651545403453, 1.8619399530257896, 2.0090157011763363, 2.1350363347251626, 2.237217061202542, 2.312830121047555, 2.359308201291384, 2.374363432169969, 2.3561188712885843, 2.303248294765751, 2.2151190115628667, 2.0919313512872826, 1.9348475153833935, 1.746101705724254, 1.529082939282964, 1.2883818113096521, 1.0297927672804206, 0.7602642604566118, 0.4877905638914416, 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'12.65131546278528974072539142567865', '13.97906495770982178781141224416591', '15.04545088187470708793847680822382'], 'prelabel': '2-33-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.300579503913821, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 1030489472908256755, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.48454727351222856936721607244', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.69833549041135197409722948204', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.31976147177241080382725337192', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.292666053828362, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 33, 'conductor_radical': 33, 'degree': 2, 'dirichlet_coefficients': [1, 1, 9, -31, -92, 9, -26, -63, 81, -92, 121, -279, -692, -26, -828, 929, -1442, 81, 2160, 2852, -234, 121, -1582, -567, 5339, -692, 729, 806, -5526, -828, 4792, 2945, 1089, -1442, 2392, -2511, -10194, 2160, -6228, 5796, -10622, -234, 8580, -3751, -7452, -1582, -2362, 8361, -16131, 5339, -12978, 21452, -30804, 729, -11132, 1638, 19440, -5526, 6416, 25668, 42096, 4792, -2106, -26783, 63664, 1089, -28444, 44702, -14238, 2392, 45690, -5103, -18374, -10194, 48051, -66960, -3146, -6228, -105214, -85468, 6561, -10622, 62292, 7254, 132664, 8580, -49734, -7623, -72246, -7452, 17992, 49042, 43128, -2362, -198720, 26505, 79262, -16131, 9801, -165509], 'euler11': [1, -121, 0], 'euler13': [1, 692, 371293], 'euler17': [1, 1442, 1419857], 'euler19': [1, -2160, 2476099], 'euler2': [1, -1, 32], 'euler23': [1, 1582, 6436343], 'euler29': [1, 5526, 20511149], 'euler3': [1, -9, 0], 'euler31': [1, -4792, 28629151], 'euler37': [1, 10194, 69343957], 'euler41': [1, 10622, 115856201], 'euler43': [1, -8580, 147008443], 'euler47': [1, 2362, 229345007], 'euler5': [1, 92, 3125], 'euler53': [1, 30804, 418195493], 'euler59': [1, -6416, 714924299], 'euler61': [1, -42096, 844596301], 'euler67': [1, 28444, 1350125107], 'euler7': [1, 26, 16807], 'euler71': [1, -45690, 1804229351], 'euler73': [1, 18374, 2073071593], 'euler79': [1, 105214, 3077056399], 'euler83': [1, -62292, 3939040643], 'euler89': [1, 72246, 5584059449], 'euler97': [1, -79262, 8587340257], 'euler_factors': [[1, -1, 32], [1, -9, 0], [1, 92, 3125], [1, 26, 16807], [1, -121, 0], [1, 692, 371293], [1, 1442, 1419857], [1, -2160, 2476099], [1, 1582, 6436343], [1, 5526, 20511149], [1, -4792, 28629151], [1, 10194, 69343957], [1, 10622, 115856201], [1, -8580, 147008443], [1, 2362, 229345007], [1, 30804, 418195493], [1, -6416, 714924299], [1, -42096, 844596301], [1, 28444, 1350125107], [1, -45690, 1804229351], [1, 18374, 2073071593], [1, 105214, 3077056399], [1, -62292, 3939040643], [1, 72246, 5584059449], [1, -79262, 8587340257]], 'index': 6, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/33/6/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/33/6/a/b'], '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': '2-33-1.1-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-33-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.300579503913821, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 1030489472908256755, 'z1': {'__RealLiteral__': 0, 'data': '3.48454727351222856936721607244', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10205626
{'Lhash': '4417188442791416792016157967156', 'Lhash_array': ['4417188442791416792016157967156'], 'label': '2-33-1.1-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/33/6/a/b'}
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id: 24550095
{'Lhash': '4417188442791416792016157967156', 'Lhash_array': ['4417188442791416792016157967156'], 'label': '2-33-1.1-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/33/6/a/b/1/1'}