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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1354375582496462420,2239145659156153101', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.496491341313277, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [3, [1]], [11, [1, 1]]], 'bad_primes': [2, 3, 11], 'central_character': '431244.1', 'coefficient_field': '1.1.1.1', 'conductor': 431244, 'conductor_radical': 66, 'degree': 4, 'euler_factors': [[1, 0, -1], [1], [1, 0, 10, 0, 25], [1, 0, 10, 0, 49], [1, 1], [1, 0, 22, 0, 169], [1, 0, -2, 0, 289], [1, 0, 34, 0, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 8, 78, 248, 961], [1, -4, 78, -148, 1369], [1, 0, 46, 0, 1681], [1, 0, -14, 0, 1849], [1, -24, 238, -1128, 2209], [1, 24, 250, 1272, 2809], [1, -24, 262, -1416, 3481], [1, 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-1.7809705508135012, -1.2517354398520522, -0.6801466983933624, -0.17235125108586313, 0.1776389025671165], 'positive_zeros': ['0.72040081483209956050869656181455', '2.06078284868063780415053686863889', '2.12387935125240219535618583660340', '3.11110186957338669233243757307355', '3.78216905129380833725816829242397', '4.01426444342608389151630027273513', '4.94712570992833096255379440888773', '5.28004968616744444473082066349229', '6.03837711275371548392107302554302', '6.04977512526916981733349434592427', '6.85457054556699367962615309050230', '7.29731250016140642032626805500180', '7.61495866909191069709821054219678', '8.262955010043880759821963787459994', '8.329295392613665337579164470522152'], 'prelabel': '4-431244-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.289914778479703, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1287678232438921570, 'z1': {'__RealLiteral__': 0, 'data': '0.72040081483209956050869656181455', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.06078284868063780415053686863889', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.12387935125240219535618583660340', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.496491341313277, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 431244, 'conductor_radical': 66, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -1, 0, 0, 24, 0, -10, 0, 0, 0, -24, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 1, 0, 0, 16, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -10], 'euler11': [1, 1, 0, 0, 0], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 0, -14, 0, 1849], 'euler47': [1, -24, 238, -1128, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 24, 250, 1272, 2809], 'euler59': [1, -24, 262, -1416, 3481], 'euler61': [1, 0, 22, 0, 3721], 'euler67': [1, -16, 198, -1072, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, -24, 286, -1704, 5041], 'euler73': [1, 0, -50, 0, 5329], 'euler79': [1, 0, 154, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 10, 0, 25], [1, 0, 10, 0, 49], [1, 1, 0, 0, 0], [1, 0, 22, 0, 169], [1, 0, -2, 0, 289], [1, 0, 34, 0, 361], [1, 0, 46, 0, 529], [1, 0, 22, 0, 841], [1, 8, 78, 248, 961], [1, -4, 78, -148, 1369], [1, 0, 46, 0, 1681], [1, 0, -14, 0, 1849], [1, -24, 238, -1128, 2209], [1, 24, 250, 1272, 2809], [1, -24, 262, -1416, 3481], [1, 0, 22, 0, 3721], [1, -16, 198, -1072, 4489], [1, -24, 286, -1704, 5041], [1, 0, -50, 0, 5329], [1, 0, 154, 0, 6241], [1, 0, 22, 0, 6889], [1, 0, 178, 0, 7921], [1, -4, 198, -388, 9409]], 'index': 2, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.11.1/3564.3/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/3564.3/b'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-431244-1.1-c1e2-0-2', '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': '4-431244-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.289914778479703, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1287678232438921570, 'z1': {'__RealLiteral__': 0, 'data': '0.72040081483209956050869656181455', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9923286
{'Lhash': '1354375582496462420,2239145659156153101', 'Lhash_array': ['1354375582496462420', '2239145659156153101'], 'factors': ['2-198-1.1-c1-0-2', '2-2178-1.1-c1-0-1'], 'label': '4-431244-1.1-c1e2-0-2', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/3564.3/b'}
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id: 9923606
{'Lhash': '1354375582496462420,2239145659156153101', 'Lhash_array': ['1354375582496462420', '2239145659156153101'], 'factors': ['2-198-1.1-c1-0-2', '2-2178-1.1-c1-0-1'], 'label': '4-431244-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/3564.3/b'}