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lfunc_lfunctions • Show schema
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{'Lhash': '636046563626010192690923148999,1462272518231157003721676900631', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': -6, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 477.2944672800165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, -8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, 2, -1, 10, 25], [1, 6, 23, 42, 49], [1, -12, 58, -132, 121], [1, -1, -12, -13, 169], [1, 2, -13, 34, 289], [1, -8, 19], [1, 0, -23, 0, 529], [1, 2, -25, 58, 841], [1, -2, 63, -62, 961], [1, 14, 123, 518, 1369], [1, 0, -41, 0, 1681], [1, 1, -42, 43, 1849], [1, 0, -47, 0, 2209], [1, 4, -37, 212, 2809], [1, -8, 5, -472, 3481], [1, -11, 60, -671, 3721], [1, -15, 158, -1005, 4489], [1, -6, -35, -426, 5041], [1, 9, 8, 657, 5329], [1, 13, 90, 1027, 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'3.68330849469412559022062920112289', '3.74982591028905006728197135365745', '3.79026423806617108421397104814910', '4.59947917396128513003517154895690', '5.18886732773353441794442939638621', '5.55342501522582746160853348767066', '6.28225212430359841448048758840156', '6.46676353902859107088307218350566', '6.74235916654225749158340644986825', '6.94953495799220625386005164377059', '7.21891069205695543263464809999722', '7.929373110075289372246179410398204', '8.343902814544177251246791840366105', '8.815751935529598399336026629236599', '9.166364681294549300852532771613959'], 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1285280845764525655, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50175226794472828149829641733', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 477.2944672800165, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, -6, 0, 0, 0, 12, 0, 1, 0, 0, 0, -2, 0, 8, 0, 0, 0, 0, 0, 5, 0, 0, 0, -2, 0, 2, 0, 0, 0, 12, 0, -14, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 13, 0, 0, 0, -4, 0, -24, 0, 0, 0, 8, 0, 11, 0, 0, 0, -2, 0, 15, 0, 0, 0, 6, 0, -9, 0, 0, 0, -72, 0, -13, 0, 0, 0, 28, 0, 4, 0, 0, 0, 12, 0, -6, 0, 0, 0, -16, 0, -10, 0, 0, 0], 'euler11': [1, -12, 58, -132, 121], 'euler13': [1, -1, -12, -13, 169], 'euler17': [1, 2, -13, 34, 289], 'euler19': [1, -8, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -23, 0, 529], 'euler29': [1, 2, -25, 58, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -2, 63, -62, 961], 'euler37': [1, 14, 123, 518, 1369], 'euler41': [1, 0, -41, 0, 1681], 'euler43': [1, 1, -42, 43, 1849], 'euler47': [1, 0, -47, 0, 2209], 'euler5': [1, 2, -1, 10, 25], 'euler53': [1, 4, -37, 212, 2809], 'euler59': [1, -8, 5, -472, 3481], 'euler61': [1, -11, 60, -671, 3721], 'euler67': [1, -15, 158, -1005, 4489], 'euler7': [1, 6, 23, 42, 49], 'euler71': [1, -6, -35, -426, 5041], 'euler73': [1, 9, 8, 657, 5329], 'euler79': [1, 13, 90, 1027, 6241], 'euler83': [1, -28, 362, -2324, 6889], 'euler89': [1, -12, 55, -1068, 7921], 'euler97': [1, 10, 3, 970, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 2, -1, 10, 25], [1, 6, 23, 42, 49], [1, -12, 58, -132, 121], [1, -1, -12, -13, 169], [1, 2, -13, 34, 289], [1, -8, 19, 0, 0], [1, 0, -23, 0, 529], [1, 2, -25, 58, 841], [1, -2, 63, -62, 961], [1, 14, 123, 518, 1369], [1, 0, -41, 0, 1681], [1, 1, -42, 43, 1849], [1, 0, -47, 0, 2209], [1, 4, -37, 212, 2809], [1, -8, 5, -472, 3481], [1, -11, 60, -671, 3721], [1, -15, 158, -1005, 4489], [1, -6, -35, -426, 5041], [1, 9, 8, 657, 5329], [1, 13, 90, 1027, 6241], [1, -28, 362, -2324, 6889], [1, -12, 55, -1068, 7921], [1, 10, 3, 970, 9409]], 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/s/e'], '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': '4-2736e2-1.1-c1e2-0-22', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1285280845764525655, 'z1': {'__RealLiteral__': 0, 'data': '0.50175226794472828149829641733', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '636046563626010192690923148999,1462272518231157003721676900631', 'Lhash_array': ['636046563626010192690923148999', '1462272518231157003721676900631'], 'label': '4-2736e2-1.1-c1e2-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/s/e'}