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lfunc_lfunctions • Show schema
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{'Lhash': '1927547906171638332693528053545', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.435854125957162, 0.0], 'a4': [0.0, 0.0], 'a5': [2.3423572430150954, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.9383229289717941, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.142365890170459, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7, 23], 'central_character': '644.1', 'coefficient_field': 'CDF', 'conductor': 644, 'conductor_radical': 322, 'conjugate': '1927547906171638332693528053545', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.435854125957162, 0], [3.0, 0]], [[1.0, 0], [-2.3423572430150954, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-5.385070798009044, 0], [11.0, 0]], [[1.0, 0], [5.3233937269808385, 0], [13.0, 0]], [[1.0, 0], [-7.8875396010236765, 0], [17.0, 0]], 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'5.99291504974358417261356609866127', '7.12345781754165329060112284165586', '7.929082517893968191050195100127607', '9.165378066107544715734586675306018', '9.597790390259362621458842227693391', '10.07988906742863991427306989954445'], 'prelabel': '2-644-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2676785244320805, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52056718611942454322189858960', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81190907382411647530473884729', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67152555126827602739945331809', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.142365890170459, 'bad_primes': [2, 7, 23], 'central_character': '1.1', 'conductor': 644, 'conductor_radical': 322, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/644/2/a/d/1/3'], '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': '2-644-1.1-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-644-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2676785244320805, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52056718611942454322189858960', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1927547906171638332693528053545', 'Lhash_array': ['1927547906171638332693528053545'], 'label': '2-644-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/644/2/a/d/1/3'}