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lfunc_lfunctions • Show schema
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{'Lhash': '3467539589354833690621909085092', 'a10': [4.002013946439463, 0.49741399842012357], 'a2': [1.302608882398979, -0.5506451665957698], 'a3': [-0.618109205827941, -1.6180052563792098], 'a4': [1.393579801009434, -1.4345505701154304], 'a5': [2.4695801500447594, 1.4258127644136982], 'a6': [-1.6961013157558158, -1.7672691721102902], 'a7': [-1.0203167421013688, 2.4410968325299285], 'a8': [1.0253610894554226, -2.6360262965742183], 'a9': [-2.235882019341504, 2.0002078880919747], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.302608882398979, 0.5506451665957698]]], [3, [[1.0, 0], [0.618109205827941, 1.6180052563792098]]], [7, [[1.0, 0], [1.0203167421013688, -2.4410968325299285]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.5', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'4.97835062783547048067097657779500', '6.35993807918435879365873370200940', '7.44210323829325234421058122434100', '9.154327536772111811281027051273289', '10.02651610105918094791428622627224', '10.89516534251911136263059904837404', '12.29351745454970497540711840639090', '13.01927105452087460574655384806812'], 'prelabel': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.3349620454011873, 'root_number': '0.4955622386979539 + 0.8685724308177598*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.167481022701', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.73540641934814965628844489332', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.61507390841455598001307839672', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.97835062783547048067097657780', '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': '168.5', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/21'], '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': '2-168-168.5-c1-0-22', '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': '2-168-168.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.16748102270059365, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.73540641934814965628844489332', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3467539589354833690621909085092', 'Lhash_array': ['3467539589354833690621909085092'], 'label': '2-168-168.5-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/5/21'}