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lfunc_lfunctions • Show schema
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{'Lhash': '1563460193510542374250137077747', 'a10': [4.859793662960084, 6.233029604971061], 'a2': [-0.6962448921899107, 2.0792599571330337], 'a3': [-2.4807618830818234, -1.393727621365128], 'a4': [-2.2418503714807754, -1.690980227133665], 'a5': [1.9917481628664904, -3.0042122085097485], 'a6': [4.625139824089924, -4.187773109194511], 'a7': [1.5369459008370496, -3.391510564274344], 'a8': [1.4609657245527494, -1.0026036147104282], 'a9': [2.6511686869793896, 4.352839193659341], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.849294518691866, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[983, [[1.0, 0], [14.281076832033769, 27.911482305989203]]]], 'bad_primes': [983], 'central_character': '983.2', 'coefficient_field': 'CDF', 'conductor': 983, 'conductor_radical': 983, 'conjugate': '978261854245261429992506800325', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6962448921899107, -2.0792599571330337], [-1.5967146479555487, 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[75.60287033116114, -22.91737327203171]], [[1.0, 0], [-14.917248926503275, 4.626261070030043], [68.43504363720105, -46.96429284439816]], [[1.0, 0], [-6.075926952804236, -4.000326717197161], [35.17361942307715, 81.75461147042734]], [[1.0, 0], [-2.8878208264716014, 0.14794767380055865], [96.49214569927949, -9.91291169884105]], [[1.0, 0], [-10.843384110115343, -7.856998795452655], [31.45645593962514, 95.97651473000269]], [[1.0, 0], [1.6000676074602533, 0.6226415345992153], [75.90863912349604, 69.61952676095153]], [[1.0, 0], [-1.664008092517794, 7.886419340286812], [-97.8788768178778, -43.2287574754434]], [[1.0, 0], [0.008494770471726318, 0.0100726667281787], [-18.39322167366047, 107.43690891152625]], [[1.0, 0], [-3.340673847653021, -1.6314139663173888], [69.48108558498774, 89.11441379446767]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 41, 'label': '2-983-983.2-c1-0-41', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/983/2/c/a/2/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9162059702709967, 0.9910313973632956, 1.0424324414403296, 1.0657794696643303, 1.054241799648705, 1.0000149600761963, 0.895986208369363, 0.7375158166953301, 0.5240783289783504, 0.2605581585053848, -0.041983994252486286, -0.3662419735947381, -0.6894268810468126, -0.9849302997068639, -1.2248555025861332, -1.3832554603660387, -1.4397761882358429, -1.3832740555236145, -1.2148815070619179, -0.9499623932942436, -0.6184463538172863, -0.2631727054143763, 0.06389424192479395, 0.3074132409438169, 0.4158727757922624, 0.3494256014018544, 0.08726640874627704, -0.36665593896286625, -0.9807464355713295, -1.6965903746876718, -2.4339424361848474, -3.0997137896252376, -3.60010717119941, -3.85439494999752, -3.808332001730678, -3.444959242344373, -2.790671868671615, 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False, 'root_analytic_conductor': 2.8016592438574444, 'root_angle': 0.15237329812197473, 'root_number': '0.8875968656159967 + 0.4606211069291748*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.076186649061', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23335262352974474444894731054', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72363126107349603710927069936', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27848740054657351992118038624', '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': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/983/2/c/a/2/10'], '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-c1-0-41', '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': 0.07618664906098736, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23335262352974474444894731054', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1563460193510542374250137077747', 'Lhash_array': ['1563460193510542374250137077747'], 'label': '2-983-983.2-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/983/2/c/a/2/10'}