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lfunc_lfunctions • Show schema
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{'Lhash': '1071660102155751148637238637831', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.1451026912004223, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.6014655557952948, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.89167093819614, 0.0], 'a8': [0.0, 0.0], 'a9': [1.6014655557952948, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.701974435916174, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '3344.1', 'coefficient_field': 'CDF', 'conductor': 3344, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.1451026912004223, 0], [3.0, 0]], [[1.0, 0], [1.6014655557952948, 0], [5.0, 0]], [[1.0, 0], [2.89167093819614, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.89167093819614, 0], [13.0, 0]], [[1.0, 0], [5.746568246995717, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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'4.41151625604023429027447590391034', '5.71190213118998710536517377097578', '6.65875021716116288090863418964161', '7.07567106228648410087452310695824', '8.114986168051229965878598529773368', '8.744507718134895209416347988659780'], 'prelabel': '2-3344-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.167395324137313, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.845390758275827836033921617363', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.33974577060600775093024291230', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.12516300103931459250335527569', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.701974435916174, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 3344, 'conductor_radical': 418, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3344/2/a/q/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': '2-3344-1.1-c1-0-28', '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': '2-3344-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.167395324137313, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.845390758275827836033921617363', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1071660102155751148637238637831', 'Lhash_array': ['1071660102155751148637238637831'], 'label': '2-3344-1.1-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3344/2/a/q/1/3'}