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lfunc_lfunctions • Show schema
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{'Lhash': '1505621650118577433465713306165', 'a10': [-1.9284369437759616, 0.0], 'a2': [-1.0, 0.0], 'a3': [0.5408445993483305, 0.0], 'a4': [1.0, 0.0], 'a5': [1.9284369437759616, 0.0], 'a6': [-0.5408445993483305, 0.0], 'a7': [2.8596310390855524, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.707487119355744, 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], [-0.5408445993483305, 0], [3.0, 0]], [[1.0, 0], [-1.9284369437759616, 0], [5.0, 0]], [[1.0, 0], [-2.8596310390855524, 0], [7.0, 0]], [[1.0, 0], [-6.290024090453582, 0], [11.0, 0]], [[1.0, 0], [5.64220678397965, 0], [13.0, 0]], [[1.0, 0], 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'4.62940135890923197611937754290891', '5.54357507738702509804684787847311', '6.40188944910318418747487939256731', '7.36265878622355428400715330340084', '8.106919157370125137377544588453189', '8.887422560326546038740093641353740', '9.763334115549973086110223778238591'], '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': '1.18772605783289451063603258964', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.15798894444054046436560488654', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.21307249614394447937254989670', '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': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1334/2/a/j/1/6'], '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-c1-0-18', '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': '1.18772605783289451063603258964', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1505621650118577433465713306165', 'Lhash_array': ['1505621650118577433465713306165'], 'label': '2-1334-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1334/2/a/j/1/6'}