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lfunc_lfunctions • Show schema
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{'Lhash': '1111208051967119773240525235290', 'a10': [-1.1343802003081167, -1.595347903919502], 'a2': [-1.407902522530578, 0.13345593674331357], 'a3': [-1.7195850687507892, -0.20742996728858587], 'a4': [1.9643790258959293, -0.3757858999751849], 'a5': [0.6920940482867404, 1.1987420552486623], 'a6': [2.4486909165932866, 0.06255233803408344], 'a7': [-2.088625963907451, -1.6240817660732696], 'a8': [-2.7155033264689212, 0.7912279595263454], 'a9': [2.9139456173413123, 0.7133869491218338], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.407902522530578, -0.13345593674331357]]], [3, [[1.0, 0], [1.7195850687507892, 0.20742996728858587]]], [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': '2064955063834015647329539235542', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.407902522530578, -0.13345593674331357]], [[1.0, 0], [1.7195850687507892, 0.20742996728858587]], [[1.0, 0], [-0.6920940482867404, -1.1987420552486623], [-2.5, 4.330127018922194]], [[1.0, 0], [2.088625963907451, 1.6240817660732696]], [[1.0, 0], [-3.8231647347342324, -2.207305188755093], [5.5, 9.526279441628825]], [[1.0, 0], [0, -6.436085842290533], [-13.0, 0]], [[1.0, 0], [-2.5286565122637157, -1.4599205180435564], [8.5, 14.722431864335457]], [[1.0, 0], [-1.5892789885386602, -2.7527119555506347], [-9.5, 16.454482671904334]], [[1.0, 0], [-1.8469574982948067, -3.1990242264669133], [-11.5, 19.91858428704209]], [[1.0, 0], [6.678843055337619, 0], [29.0, 0]], [[1.0, 0], [2.1758021099944997, 1.25619993390868], [15.5, 26.846787517317598]], [[1.0, 0], [-5.001488723153058, 2.8876108606612956], [18.5, -32.04293994002423]], [[1.0, 0], [0, 0.49742654196943975], [-41.0, 0]], [[1.0, 0], [-0.8658976684444193, 0], [43.0, 0]], 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'3.22927083504299719977887685669198', '5.44136723556407760464455234184470', '6.18859600668768963972653150057628', '7.41249763358598796288729480173705', '8.882279749322634193129084933517283', '9.561481910181245427972484940295210', '10.57603136532822840884901658338785', '11.52028611401446250862001083465672', '12.43357492661038262208507220442342'], 'prelabel': '2-168-168.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.32148521848178907, 'root_number': '0.531881383387927 - 0.8468188672941487*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.160742609241', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.876588589763659232315218558488', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.22927083504299719977887685669', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.44136723556407760464455234184', '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': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/v/a/11/1'], '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-c1-0-1', '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': -0.16074260924089454, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.876588589763659232315218558488', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1111208051967119773240525235290', 'Lhash_array': ['1111208051967119773240525235290'], 'label': '2-168-168.11-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/v/a/11/1'}