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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 1, 'Lhash': '705431197134190228,2066915050180543055', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.02440390618965, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [3, [1, -1]], [7, [1, -2, 1]], [13, [1, -2, 1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '894348.1', 'coefficient_field': '1.1.1.1', 'conductor': 894348, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1, 0, -1], [1, -1], [1, 0, 1, 0, 25], [1, -2, 1], [1, 0, 13, 0, 121], [1, -2, 1], [1, 0, 25, 0, 289], [1, 14, 87, 266, 361], [1, 0, -35, 0, 529], [1, 0, -23, 0, 841], [1, 8, 78, 248, 961], [1, 14, 123, 518, 1369], [1, 0, -62, 0, 1681], [1, 2, 87, 86, 1849], [1, 0, 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'data': '1.54544973372056719849266422970279', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.89338424078267539825922227518821', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.41262911451317421726904251872550', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.02440390618965, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 894348, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 1, 0, 0, 2, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, -14, 0, 2, 0, 0, 0, -1, 0, 1, 2, 0, 0, -8, 0, 0, 0, 0, 1, -14, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 1, 3, 0, 0, 2, 0, 0, 0, 0, -14, 0, 0, 0, -2, 0, 2, 1, 0, 0, 28, 0, 0, 0, 0, 0, -14, 0, -1, -14, 0, 0, -20, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, -8, 0, 0, 0, -20, 0, 0, -1], 'euler11': [1, 0, 13, 0, 121], 'euler13': [1, -2, 1, 0, 0], 'euler17': [1, 0, 25, 0, 289], 'euler19': [1, 14, 87, 266, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 0, -35, 0, 529], 'euler29': [1, 0, -23, 0, 841], 'euler3': [1, -1, 0, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, 14, 123, 518, 1369], 'euler41': [1, 0, -62, 0, 1681], 'euler43': [1, 2, 87, 86, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, 1, 0, 25], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, 2, 123, 122, 3721], 'euler67': [1, -28, 330, -1876, 4489], 'euler7': [1, -2, 1, 0, 0], 'euler71': [1, 0, -2, 0, 5041], 'euler73': [1, 14, 195, 1022, 5329], 'euler79': [1, 20, 258, 1580, 6241], 'euler83': [1, 0, 130, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, 20, 294, 1940, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, -1, 0, 0, 0], [1, 0, 1, 0, 25], [1, -2, 1, 0, 0], [1, 0, 13, 0, 121], [1, -2, 1, 0, 0], [1, 0, 25, 0, 289], [1, 14, 87, 266, 361], [1, 0, -35, 0, 529], [1, 0, -23, 0, 841], [1, 8, 78, 248, 961], [1, 14, 123, 518, 1369], [1, 0, -62, 0, 1681], [1, 2, 87, 86, 1849], [1, 0, 94, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, -26, 0, 3481], [1, 2, 123, 122, 3721], [1, -28, 330, -1876, 4489], [1, 0, -2, 0, 5041], [1, 14, 195, 1022, 5329], [1, 20, 258, 1580, 6241], [1, 0, 130, 0, 6889], [1, 0, 142, 0, 7921], [1, 20, 294, 1940, 9409]], 'index': 60, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.3.1/99372.5/k', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/99372.5/k'], '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': '4-894348-1.1-c1e2-0-60', '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': 1, 'prelabel': '4-894348-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.7479902566219083, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 466503238101039332, 'z1': {'__RealLiteral__': 0, 'data': '1.54544973372056719849266422970279', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9814298
{'Lhash': '705431197134190228,2066915050180543055', 'Lhash_array': ['705431197134190228', '2066915050180543055'], 'label': '4-894348-1.1-c1e2-0-60', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/99372.5/k'}
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id: 9813910
{'Lhash': '705431197134190228,2066915050180543055', 'Lhash_array': ['705431197134190228', '2066915050180543055'], 'label': '4-894348-1.1-c1e2-0-60', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/99372.5/k'}