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lfunc_lfunctions • Show schema
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{'Lhash': '2668804591283606437995479029033', 'a10': [0.24290431929882841, 0.4207226224035042], 'a2': [0.0, -0.18082374524677508], 'a3': [0.9130064415994333, 1.5813735444878856], 'a4': [1.9673027731549293, 0.0], 'a5': [-2.326700079291758, 1.34332091710262], 'a6': [0.2859498869484672, -0.16509324420444058], 'a7': [-2.462634433178107, -0.9671771546751619], 'a8': [0.0, -0.7173825459697912], 'a9': [-0.16716152480411908, 0.28953225403141936], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [2.462634433178107, 0.9671771546751619]]], [13, [[1.0, 0], [-1.9215308905402626, 3.0508554598177122]]]], 'bad_primes': [7, 13], 'central_character': '91.4', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '4062450073440478388156637632932', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.18082374524677508], [-2.0, 0]], [[1.0, 0], 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'9.320962546863637723493971751891376', '11.11804390652511524314278579675143', '12.07842933616434574852906421927223', '12.73310595999314207728334165160880', '13.90518716341126251498465173057206'], 'prelabel': '2-91-91.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.18587527725775804, 'root_number': '0.8342945199061347 - 0.5513190129630868*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0929376386289', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.10531560573797820735164018391', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.97848288246132326619559631352', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.28199847173491619669057323411', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '91.4', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/k/b/4/3'], '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': '2-91-91.4-c1-0-1', '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': '2-91-91.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.09293763862887902, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.10531560573797820735164018391', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2668804591283606437995479029033', 'Lhash_array': ['2668804591283606437995479029033'], 'label': '2-91-91.4-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/k/b/4/3'}