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lfunc_lfunctions • Show schema
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{'Lhash': '2274902914110894361638164334130', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.414213562373095, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.414213562373095, 0.0], 'a8': [0.0, 0.0], 'a9': [2.8284271247461903, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 38.647594578299724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 11], 'central_character': '4840.1', 'coefficient_field': 'CDF', 'conductor': 4840, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.414213562373095, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.414213562373095, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.0, 0], [13.0, 0]], [[1.0, 0], [5.656854249492381, 0], [17.0, 0]], [[1.0, 0], [4.82842712474619, 0], [19.0, 0]], [[1.0, 0], [-3.65685424949238, 0], [23.0, 0]], [[1.0, 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'2-4840-1.1-c1-0-104', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4840/2/a/o/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.8037020844425653e-60, 0.2538991179518023, 0.5072609663510786, 0.7595007896559309, 1.0099416341332599, 1.257774985692159, 1.5020289654548513, 1.741545798320829, 1.9749697110627387, 2.2007458485340408, 2.4171302665279755, 2.622210599507666, 2.813936626045, 2.9901596652493603, 3.148679524588423, 3.2872975689377597, 3.4038743770711544, 3.496390381731319, 3.563007843152935, 3.602132477847375, 3.612473052849081, 3.593097261791153, 3.543482226559613, 3.4635580214578323, 3.3537427006690628, 3.2149674287902066, 3.0486904718083325, 2.8568990042148763, 2.642097927463892, 2.4072851743252452, 2.155913289609819, 1.8918374251041863, 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'prelabel': '2-4840-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.216718956032975, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79458197211543779666533084517', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48067161897201629187424536431', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15289610870511843365239976533', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 38.647594578299724, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 4840, 'conductor_radical': 110, 'degree': 2, 'index': 104, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4840/2/a/o/1/2'], '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': '2-4840-1.1-c1-0-104', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4840-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.216718956032975, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79458197211543779666533084517', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2274902914110894361638164334130', 'Lhash_array': ['2274902914110894361638164334130'], 'label': '2-4840-1.1-c1-0-104', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4840/2/a/o/1/2'}