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lfunc_lfunctions • Show schema
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{'Lhash': '645022500514546976766932657161', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-5.132444468702838, 0], 'a6': [0, 0], 'a7': [0, -4.025159310547453], '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': '1169096416447892737592979444856', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.132444468702838, 0], [25.0, 0]], [[1.0, 0], [0, 4.025159310547453], [-49.0, 0]], [[1.0, 0], [0, -4.303437580862017], [-121.0, 0]], [[1.0, 0], [18.486200670659763, 0], [169.0, 0]], [[1.0, 0], [-23.575067935211006, 0], [289.0, 0]], [[1.0, 0], [0, 21.725930297517984], [-361.0, 0]], [[1.0, 0], [0, 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'4.42440376470844223053004505402806', '5.43824642711047093483108303013641', '6.35886962063375280997929912650576', '7.70421198423827178803559074306366', '7.86398681236203862030943953239409', '8.986195124270759377742121339299105', '9.901339445783881738409123761902819'], 'prelabel': '2-864-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8520402760828, 'root_angle': -0.25, 'root_number': '0.7071067811865475244008443621048490392848359376884740366 - 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.125', 'prec': 20}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50883303364382608112728411481', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.32465771174988980256254098090', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42332582492648342278803055291', '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': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/864/3/g/b/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-c2-0-9', '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': -0.125, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.50883303364382608112728411481', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '645022500514546976766932657161', 'Lhash_array': ['645022500514546976766932657161'], 'label': '2-864-4.3-c2-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/864/3/g/b/703/3'}