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lfunc_lfunctions • Show schema
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{'Lhash': '2732748481778193670472199962164', 'a10': [1.9488019128226028, 0.18472811905715808], 'a2': [0.8195274927708477, -1.1525513821920168], 'a3': [1.0394321555534851, 1.385489369862301], 'a4': [-0.6567493771854565, -1.8890950890747968], 'a5': [0.6920940482867404, 1.1987420552486623], 'a6': [2.4486909165932866, -0.06255233803408344], 'a7': [2.088625963907451, 1.6240817660732696], 'a8': [-2.7155033264689212, -0.7912279595263454], 'a9': [-0.8391615880028713, 2.8802444044248223], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8195274927708477, 1.1525513821920168]]], [3, [[1.0, 0], [-1.0394321555534851, -1.385489369862301]]], [7, [[1.0, 0], [-2.088625963907451, -1.6240817660732696]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.11', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'5.21625462379649671697834150293895', '6.79776713102920551275777684169011', '7.43365618459036817202302502156474', '8.545446668852573607565445294739887', '9.330857403114970215463095814197880', '11.16515418187029125935942099258001', '12.27076368564128719179593734066784', '13.20412555492286271405957234751722'], 'prelabel': '2-168-168.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.057960334237273065, 'root_number': '0.9344177410217224 + 0.3561790073317929*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0579603342373', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.15575844107689154384793024393', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.14204244743904919230990113874', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.21625462379649671697834150294', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.11', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/v/a/11/19'], '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': '2-168-168.11-c1-0-15', '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': '2-168-168.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.057960334237273065, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15575844107689154384793024393', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2732748481778193670472199962164', 'Lhash_array': ['2732748481778193670472199962164'], 'factors': ['2-168-168.11-c1-0-15'], 'label': '2-168-168.11-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/v/a/11/19'}