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lfunc_lfunctions • Show schema
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{'Lhash': '2191716899132699492620789591340', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.4142135623730951, -1.0], 'a4': [0.0, 0.0], 'a5': [-1.7320508075688772, 1.4142135623730951], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, -2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.665638594042921, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.4142135623730951, 1.0]]], [5, [[1.0, 0], [1.7320508075688772, -1.4142135623730951]]]], 'bad_primes': [2, 3, 5], 'central_character': '960.959', 'coefficient_field': 'CDF', 'conductor': 960, 'conductor_radical': 30, 'conjugate': '715558642449697087783298617302', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.4142135623730951, 1.0]], [[1.0, 0], [1.7320508075688772, -1.4142135623730951]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [4.898979485566356, 0], [11.0, 0]], [[1.0, 0], [0, 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'5.68784268034844097247518107577722', '7.46915234965726146819716876722934', '7.64761827838493410703353932325862', '8.720812047839733088248734318946780', '9.264881173433288849278811985388597', '10.21375156375044352492763195471091'], 'prelabel': '2-960-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.768688966648822, 'root_angle': 0.5861338324091838, 'root_number': '-0.26730716036356506 + 0.9636113749942802*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.293066916205', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72895977703801034567059020261', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11158212028217115652841986065', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98076265085130387070085898363', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.665638594042921, 'bad_primes': [2, 3, 5], 'central_character': '60.59', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/2/o/d/959/5'], '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': '2-960-60.59-c1-0-36', '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': '2-960-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.768688966648822, 'root_angle': 0.2930669162045919, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72895977703801034567059020261', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2191716899132699492620789591340', 'Lhash_array': ['2191716899132699492620789591340'], 'label': '2-960-60.59-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/2/o/d/959/5'}