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lfunc_lfunctions • Show schema
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{'Lhash': '85786416971092257195045435177', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-3.2251192601336025, 0], 'a6': [0, 0], 'a7': [0, -6.572207324149796], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.542294840729653, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '864.703', 'coefficient_field': 'CDF', 'conductor': 864, 'conductor_radical': 6, 'conjugate': '1644048474418727990668717049881', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.2251192601336025, 0], [25.0, 0]], [[1.0, 0], [0, 6.572207324149796], [-49.0, 0]], [[1.0, 0], [0, 13.890328550739019], [-121.0, 0]], [[1.0, 0], [19.08648097344565, 0], [169.0, 0]], [[1.0, 0], [-23.08648097344565, 0], [289.0, 0]], [[1.0, 0], [0, -18.84254336568047], [-361.0, 0]], [[1.0, 0], [0, -13.594653168566797], 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'2.98221448016273932571701956809148', '4.38546630451603118447707997951716', '5.07466926079232097632451182300321', '6.13754550632315883880790827788449', '7.40691492920769303004553246621271', '7.67615580715718365189238026873181', '8.912433701349676765847585849123186', '9.656983234125201467481967138386548'], 'prelabel': '2-864-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8520402760828, 'root_angle': -0.75, 'root_number': '-0.7071067811865475244008443621048490392848359376884740366 - 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.375', 'prec': 20}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.06767355054748300774396075447', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.02914806623947508199937396665', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98221448016273932571701956809', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.542294840729653, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 864, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/864/3/g/c/703/3'], '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': '2-864-4.3-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-864-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8520402760828, 'root_angle': -0.375, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.06767355054748300774396075447', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '85786416971092257195045435177', 'Lhash_array': ['85786416971092257195045435177'], 'label': '2-864-4.3-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/864/3/g/c/703/3'}