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lfunc_lfunctions • Show schema
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{'Lhash': '1989825712532700610629769950195', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [10.422205101855956, 0.0], 'a6': [0.0, 0.0], 'a7': [6.422205101855957, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.31346688440881, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [3.0, 0]]]], 'bad_primes': [2, 3], 'central_character': '768.1', 'coefficient_field': 'CDF', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [-10.422205101855956, 0], [125.0, 0]], [[1.0, 0], [-6.422205101855957, 0], [343.0, 0]], [[1.0, 0], [61.688820407423826, 0], [1331.0, 0]], [[1.0, 0], [-64.84441020371192, 0], [2197.0, 0]], [[1.0, 0], [75.68882040742383, 0], [4913.0, 0]], [[1.0, 0], [-10.31117959257617, 0], [6859.0, 0]], [[1.0, 0], [156.8444102037119, 0], [12167.0, 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[1295029.0, 0]], [[1.0, 0], [-921.6434857039336, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 37, 'label': '2-768-1.1-c3-0-37', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/768/4/a/e/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.517467690314382e-60, 0.2154386625996954, 0.42833517557682826, 0.6361617821099519, 0.8364201735738332, 1.0266578326600722, 1.2044862159569913, 1.3676012213541944, 1.513806250532564, 1.6410380182355513, 1.747395084047279, 1.8311688955889587, 1.8908769411976563, 1.9252974221019588, 1.9335046755232845, 1.9149044173649858, 1.8692677321421747, 1.7967626239950911, 1.6979818608997557, 1.573965798804879, 1.4262188669635907, 1.2567184330127015, 1.0679148483500267, 0.8627216020850144, 0.644494685233516, 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'6.62579326908117151843684088880450', '7.912192020414814435349601215298253', '8.534866204890713709838693015677596', '9.759808236985410230177181781194794'], 'prelabel': '2-768-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56969571282059101897698431212', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.60043023523854513975889096301', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11710082384153050518921276684', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 45.31346688440881, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/768/4/a/e/1/2'], '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': '2-768-1.1-c3-0-37', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-768-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56969571282059101897698431212', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1989825712532700610629769950195', 'Lhash_array': ['1989825712532700610629769950195'], 'label': '2-768-1.1-c3-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/4/a/e/1/2'}