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lfunc_lfunctions • Show schema
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{'Lhash': '540308586999190849178530167598', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.45614800334098693, 0.7900715175576873], 'a4': [0, 0], 'a5': [0.8326410544562621, 1.4421766107859704], 'a6': [0, 0], 'a7': [-0.46273757481236744, 2.604971004993485], 'a8': [0, 0], 'a9': [1.0838579980960619, 1.8772971208922709], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.496082775064236, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.46273757481236744, -2.604971004993485]]], [19, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [2, 7, 19], 'central_character': '1064.305', 'coefficient_field': 'CDF', 'conductor': 1064, 'conductor_radical': 266, 'conjugate': '2738156307430079531760653201962', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.45614800334098693, -0.7900715175576873], [-1.5, -2.598076211353316]], [[1.0, 0], [-0.8326410544562621, -1.4421766107859704], [-2.5, 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'8.801413987103246605566253757847776', '9.741340121703865168250851651083666'], 'prelabel': '2-1064-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9148040714710546, 'root_angle': -0.9238673605353872, 'root_number': '-0.97153309962613741295613288293813134576774269153987175227 - 0.2369038546137013706266963182332641485818315204811596541*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4619336802676936', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.42622832103886750384284499703', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.66484721875396313038981104333', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10676972109029697691392184153', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.496082775064236, 'bad_primes': [2, 7, 19], 'central_character': '7.4', 'conductor': 1064, 'conductor_radical': 266, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1064/2/q/n/305/3'], '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': '2-1064-7.4-c1-0-4', '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': '2-1064-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9148040714710546, 'root_angle': -0.4619336802676936, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.42622832103886750384284499703', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '540308586999190849178530167598', 'Lhash_array': ['540308586999190849178530167598'], 'label': '2-1064-7.4-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1064/2/q/n/305/3'}