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lfunc_lfunctions • Show schema
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{'Lhash': '796384240847255848895225363275', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-0.5, 0.8660254037844386], 'a6': [0, 0], 'a7': [-1.0, -1.7320508075688772], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.871530254894857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 5], 'central_character': '3240.1081', 'coefficient_field': 'CDF', 'conductor': 3240, 'conductor_radical': 30, 'conjugate': '1160302431947786340009895399821', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [1.0, 1.7320508075688772], [-3.5, 6.06217782649107]], [[1.0, 0], [-1.0, -1.7320508075688772], [-5.5, 9.526279441628825]], [[1.0, 0], [2.0, -3.4641016151377544], [-6.5, -11.258330249197702]], [[1.0, 0], [-2.0, 0], [17.0, 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0.6281083132500971, 0.789548202239465, 0.858276190970925, 0.8236992555660302], 'positive_zeros': ['0.62823639313851453459713161561107', '1.87727151863891096223848118861140', '3.26061608063526723867505453473394', '3.48974079891533671451568922716254', '5.04366737560992184796880257471614', '5.39802955626714196967458616118269', '6.15890544092952890365779185306236', '7.37451708309472897532855515520696', '7.63004399668099205975332266263305', '8.742890953810567990407208661612313'], 'prelabel': '2-3240-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.086406418572434, 'root_angle': -0.22222222222222227, 'root_number': '0.7660444431189780352023926505554166739358324570803952459 - 0.6427876096865393263226434099072634329075598842056817903*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1111111111111111', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62823639313851453459713161561', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.87727151863891096223848118861', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.26061608063526723867505453473', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.871530254894857, 'bad_primes': [2, 3, 5], 'central_character': '9.4', 'conductor': 3240, 'conductor_radical': 30, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3240/2/q/d/1081/1'], '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': '2-3240-9.4-c1-0-14', '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': '2-3240-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.086406418572434, 'root_angle': -0.11111111111111113, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62823639313851453459713161561', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '796384240847255848895225363275', 'Lhash_array': ['796384240847255848895225363275'], 'label': '2-3240-9.4-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3240/2/q/d/1081/1'}