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lfunc_lfunctions • Show schema
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{'Lhash': '1986534578171202342788575189179', 'a10': [-3.6614390932605962, 0.0], 'a2': [-1.0, 0.0], 'a3': [2.0576638307369186, 0.0], 'a4': [1.0, 0.0], 'a5': [3.6614390932605962, 0.0], 'a6': [-2.0576638307369186, 0.0], 'a7': [4.214430929190476, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.2339804403229304, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.652043629638808, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]], [29, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 23, 29], 'central_character': '1334.1', 'coefficient_field': 'CDF', 'conductor': 1334, 'conductor_radical': 1334, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.0576638307369186, 0], [3.0, 0]], [[1.0, 0], [-3.6614390932605962, 0], [5.0, 0]], [[1.0, 0], [-4.214430929190476, 0], [7.0, 0]], [[1.0, 0], [3.0711360604471807, 0], [11.0, 0]], [[1.0, 0], [-3.048517237514891, 0], [13.0, 0]], [[1.0, 0], 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'4.59625102915497028247356385855791', '5.51496403373086113143247878558375', '6.38058794786585620804954206740823', '7.58231618108122537968963771478519', '8.148693918844911453750084531200784', '8.959635691093620089369674921779849', '9.254102213276291831109507619815913'], 'prelabel': '2-1334-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2637468697248577, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56709946558897551870475970795', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.12401939565870333318809052285', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01137774704123708665246071223', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.652043629638808, 'bad_primes': [2, 23, 29], 'central_character': '1.1', 'conductor': 1334, 'conductor_radical': 1334, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1334/2/a/j/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': '2-1334-1.1-c1-0-32', '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': '2-1334-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2637468697248577, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56709946558897551870475970795', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1986534578171202342788575189179', 'Lhash_array': ['1986534578171202342788575189179'], 'label': '2-1334-1.1-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1334/2/a/j/1/7'}