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lfunc_lfunctions • Show schema
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{'Lhash': '1809764368495086037408629430476', 'a10': [5.255837216203048, 0.0], 'a2': [0.44758990504421897, 0.0], 'a3': [-9.515185644914242, 0.0], 'a4': [-7.799663276902507, 0.0], 'a5': [11.742528499796718, 0.0], 'a6': [-4.258901039285281, 0.0], 'a7': [-2.2779704863124404, 0.0], 'a8': [-7.071769785839426, 0.0], 'a9': [63.53875785718205, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.051551991659046, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [0, 0]]]], 'bad_primes': [17], 'central_character': '289.1', 'coefficient_field': 'CDF', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.44758990504421897, 0], [8.0, 0]], [[1.0, 0], [9.515185644914242, 0], [27.0, 0]], [[1.0, 0], [-11.742528499796718, 0], [125.0, 0]], [[1.0, 0], [2.2779704863124404, 0], [343.0, 0]], [[1.0, 0], [22.68678802442717, 0], [1331.0, 0]], [[1.0, 0], [-67.40223419445718, 0], [2197.0, 0]], [[1.0, 0], 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'5.76660402676453008942502677960706', '6.37743745176777619964029315070970', '7.925889336726149091420349397718979', '9.383471077972960155094435873881786', '10.04948337090509513074947304435596', '10.89955303916345664248739244693326'], 'prelabel': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, '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': '1.42765235796776634997395105303', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.86104316188538243498343269302', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.10203093462455298518573394664', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.051551991659046, 'bad_primes': [17], 'central_character': '1.1', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/289/4/a/h/1/7'], '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': '2-17e2-1.1-c3-0-29', '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': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.42765235796776634997395105303', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1809764368495086037408629430476', 'Lhash_array': ['1809764368495086037408629430476'], 'label': '2-17e2-1.1-c3-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/289/4/a/h/1/7'}