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lfunc_lfunctions • Show schema
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{'Lhash': '2307715042069671111616146001866', 'a10': [0.3211007680789601, -1.7998815376757245], 'a2': [-1.3298959734906461, 0.48101631957072566], 'a3': [1.2846282158521858, -1.1617789579074111], 'a4': [1.537246600613267, -1.279403333160796], 'a5': [-0.6464015057345192, 1.119600250021212], 'a6': [-1.1495872532069586, 2.162972294613151], 'a7': [2.4274187002655716, 1.0524440382276876], 'a8': [-1.4289641818542422, 2.440914043340657], 'a9': [0.3005393059271399, -2.984908059822418], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3298959734906461, -0.48101631957072566]]], [3, [[1.0, 0], [-1.2846282158521858, 1.1617789579074111]]], [7, [[1.0, 0], [-2.4274187002655716, -1.0524440382276876]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.107', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'4.80543825494522275007026849672311', '6.95169394975746546994009500556219', '8.092829498495045804097002617423478', '8.723814692031372697727473753095435', '9.693485835070928960320303071581366', '10.69121849853065400162200843331608', '11.53325106465660566470031693663076', '12.61658597450042786518150940334716'], 'prelabel': '2-168-168.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.04460631053341854, 'root_number': '0.9901971687762245 + 0.1396766514044099*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0223031552667', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.82046617707922609398549009913', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.64846271331490160132999193163', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.80543825494522275007026849672', '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': '168.107', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/v/a/107/4'], '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': '2-168-168.107-c1-0-12', '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': '2-168-168.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.02230315526670927, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82046617707922609398549009913', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2307715042069671111616146001866', 'Lhash_array': ['2307715042069671111616146001866'], 'label': '2-168-168.107-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/v/a/107/4'}