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lfunc_lfunctions • Show schema
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{'Lhash': '1018038475107845609662844970463', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.3187251868060712, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 59.88780151596032, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '7500.1', 'coefficient_field': 'CDF', 'conductor': 7500, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.3187251868060712, 0], [7.0, 0]], [[1.0, 0], [-1.5541941928875733, 0], [11.0, 0]], [[1.0, 0], [-2.428217255825342, 0], [13.0, 0]], [[1.0, 0], [1.314364624825641, 0], [17.0, 0]], [[1.0, 0], [1.0210506283385903, 0], [19.0, 0]], [[1.0, 0], [-5.007773740309257, 0], [23.0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 24, 'label': '2-7500-1.1-c1-0-24', 'leading_term': '2.5957765249206730631155901903352', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/7500/2/a/n/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [2.595776524920673, 2.5864089060596105, 2.558279431399278, 2.511315030620587, 2.445416080517819, 2.360488105593498, 2.256483225227809, 2.1334487316947177, 1.9915798316882989, 1.8312734430671387, 1.6531799856813114, 1.45825030291548, 1.2477751560991432, 1.0234151070107769, 0.7872190119800669, 0.5416297721135986, 0.2894764049233726, 0.033951917530827026, -0.22142313020121146, -0.4728510815190041, -0.7163209679676198, -0.9476845401481091, -1.1627430731532435, -1.3573431009210983, -1.5274788788904021, -1.6693990494165498, 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'6.12335925142544839542143632502974', '6.34052914492721883279625574463160', '7.30823870271713427358118048673779', '7.83951782852614459402085143155614'], 'prelabel': '2-7500-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.738720922475517, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.803090753023393581601096676886', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.82697005222597703442515736068', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.82991165368917523497163775648', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 59.88780151596032, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 7500, 'conductor_radical': 30, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7500/2/a/n/1/4'], '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': '2-7500-1.1-c1-0-24', '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': '2-7500-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.738720922475517, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.803090753023393581601096676886', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1018038475107845609662844970463', 'Lhash_array': ['1018038475107845609662844970463'], 'label': '2-7500-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7500/2/a/n/1/4'}