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lfunc_lfunctions • Show schema
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{'Lhash': '95822064348953694576447293086', 'a10': [0.0, 0.0], 'a2': [-3.8447039520495934, 0.0], 'a3': [3.0, 0.0], 'a4': [6.781748478905762, 0.0], 'a5': [0.0, 0.0], 'a6': [-11.53411185614878, 0.0], 'a7': [-25.392488038895074, 0.0], 'a8': [4.683816437741446, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 110.62858126076371, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [3.8447039520495934, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [25.392488038895074, 0], [343.0, 0]], [[1.0, 0], [56.893830342337495, 0], [1331.0, 0]], [[1.0, 0], [4.981724095533982, 0], [2197.0, 0]], [[1.0, 0], [129.57529437613428, 0], [4913.0, 0]], [[1.0, 0], [-24.23575102105124, 0], [6859.0, 0]], 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'2.60248013724920657855916756528584', '3.63022760711902220773881142262435', '4.75590210515232316514367745626611', '5.90091746171820711523376563112077', '6.98841463883247691436642592262897', '7.34997874213053402451550356283822', '8.366368105495417140991069046886713', '8.828947928436027711859599787958064'], 'prelabel': '2-1875-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.51801222954051, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.07559028042246165474671089029', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.85101020484814045327414792714', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.60248013724920657855916756529', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 110.62858126076371, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/4/a/l/1/5'], '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': '2-1875-1.1-c3-0-3', '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': '2-1875-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.51801222954051, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.07559028042246165474671089029', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '95822064348953694576447293086', 'Lhash_array': ['95822064348953694576447293086'], 'label': '2-1875-1.1-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/4/a/l/1/5'}