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lfunc_lfunctions • Show schema
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{'Lhash': '1227462548384201771081463446150', 'a10': [0.7710785910513973, 0.9889629105889488], 'a2': [-0.8151032944292004, 2.434217701336572], 'a3': [1.9927157066147145, 1.1195362766485444], 'a4': [-3.6643077889554188, -2.7639097131905204], 'a5': [0.26993836537889687, -0.40715595873794536], 'a6': [-4.3494641592287895, 3.9381661394437235], 'a7': [0.3022859810358342, -0.6670411089659819], 'a8': [5.481565970842334, -3.7617842528938605], 'a9': [1.1570202616407077, 1.899661521902552], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.849294518691866, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[983, [[1.0, 0], [-18.94384456550188, -24.982609012633265]]]], 'bad_primes': [983], 'central_character': '983.2', 'coefficient_field': 'CDF', 'conductor': 983, 'conductor_radical': 983, 'conjugate': '1870619189551517222792283693063', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8151032944292004, -2.434217701336572], [-1.5967146479555487, 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[-3.7841224057064804, 0.5609349004509049], [75.60287033116114, -22.91737327203171]], [[1.0, 0], [-0.7817365546077298, 0.24243862976475086], [68.43504363720105, -46.96429284439816]], [[1.0, 0], [-5.7183736380858585, -3.7649173568146783], [35.17361942307715, 81.75461147042734]], [[1.0, 0], [5.663927909286846, -0.2901720740676606], [96.49214569927949, -9.91291169884105]], [[1.0, 0], [-3.3000054080687704, -2.391148211008802], [31.45645593962514, 95.97651473000269]], [[1.0, 0], [-5.340104685814885, -2.078019054316013], [75.90863912349604, 69.61952676095153]], [[1.0, 0], [-1.272528989309742, 6.031038717596059], [-97.8788768178778, -43.2287574754434]], [[1.0, 0], [8.743609149300232, 10.367726974553243], [-18.39322167366047, 107.43690891152625]], [[1.0, 0], [3.9092286249854493, 1.9090669928192852], [69.48108558498774, 89.11441379446767]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 34, 'label': '2-983-983.2-c1-0-34', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 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'rational': False, 'root_analytic_conductor': 2.8016592438574444, 'root_angle': -0.9036018893815583, 'root_number': '-0.9544922876980478 - 0.29823559935887456*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.451800944691', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.968297217043251410731599743750', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.09797016874898160003554125611', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80389524768495728970678328318', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.849294518691866, 'bad_primes': [983], 'central_character': '983.2', 'conductor': 983, 'conductor_radical': 983, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/983/2/c/a/2/5'], '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': '2-983-983.2-c1-0-34', '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': '2-983-983.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8016592438574444, 'root_angle': -0.45180094469077914, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.968297217043251410731599743750', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1227462548384201771081463446150', 'Lhash_array': ['1227462548384201771081463446150'], 'label': '2-983-983.2-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/983/2/c/a/2/5'}