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lfunc_lfunctions • Show schema
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{'Lhash': '5305896084143570770198052247723', 'a10': [-6.619216717455814, -7.813153647504138], 'a2': [0.7931937967690634, -0.4579506520841601], 'a3': [-7.598656705274825, -4.387086494269975], 'a4': [-3.580562400511385, 6.201715997356502], 'a5': [-1.993482265403309, -11.00118304808726], 'a6': [-8.036276483202188, 2.8855100934965923e-60], 'a7': [-13.880480053035425, -12.261006218793206], 'a8': [0.0, 13.886093977915419], 'a9': [24.993055816412042, 43.289242510430505], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.0650668502009224, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.993482265403309, 11.00118304808726]]], [7, [[1.0, 0], [13.880480053035425, 12.261006218793206]]]], 'bad_primes': [5, 7], 'central_character': '35.4', 'coefficient_field': 'CDF', 'conductor': 35, 'conductor_radical': 35, 'conjugate': '601753852383516541992904973110', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7931937967690634, 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'6.62069890857452638955631378717568', '9.625068749752334824224021087223528', '10.27586394306984644060738340974141', '11.52896915133507461106641505605160', '12.75191656504081715065494468413647', '14.71649405548064971561685978180648', '15.28171148865122779257316763539903', '16.38202955443804001598688460466910'], 'prelabel': '2-35-35.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4370340462915006, 'root_angle': 0.8600848325447555, 'root_number': '-0.9049404944716969 + 0.42553813162314924*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.430042416272', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.18561398794611906059357396271', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.74944042885785986858846936247', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.62069890857452638955631378718', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.0650668502009224, 'bad_primes': [5, 7], 'central_character': '35.4', 'conductor': 35, 'conductor_radical': 35, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/35/4/j/a/4/7'], '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': '2-35-35.4-c3-0-8', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-35-35.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4370340462915006, 'root_angle': 0.43004241627237777, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '4.18561398794611906059357396271', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5305896084143570770198052247723', 'Lhash_array': ['5305896084143570770198052247723'], 'label': '2-35-35.4-c3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/35/4/j/a/4/7'}