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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 2, 'Lhash': '980135838895849071416122392918', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.57942739416335, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 1]]], 'bad_primes': [2, 7], 'central_character': '1404928.1', 'coefficient_field': '1.1.1.1', 'conductor': 1404928, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, 0, -2, 0, 9], [1, 0, -8, 0, 25], [1, 1], [1, 2, 14, 22, 121], [1, 0, -4, 0, 169], [1, 0, -22, 0, 289], [1, 0, 14, 0, 361], [1, -10, 70, -230, 529], [1, -2, 10, -58, 841], [1, 0, -46, 0, 961], [1, -14, 122, -518, 1369], [1, 0, -46, 0, 1681], [1, -10, 110, -430, 1849], [1, 0, -82, 0, 2209], [1, 12, 126, 636, 2809], [1, 0, -10, 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0.11939676248408027, -1.5817337968364633, -3.061673461844026], 'positive_zeros': ['0.77319084511093529052384267548014', '1.26103728277585432803082203041269', '2.31791429746176536021089701497589', '2.82615218690483214852746848369891', '3.14862666538970933031940528536860', '3.84201900946707902233181584977731', '4.56183285338164699412778357896297', '4.72880283260889052388768004860456', '5.16868759832305841168491244921503', '5.88398018806554165474694775789285', '6.19005107657214767311200944848411', '6.69712286046205447338284334904435', '7.14920768061793573827449106437726', '7.44919334704313709548073621308320', '7.81104757783730404177131587981532'], 'prelabel': '4-112e3-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.076465650952455, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 890396053678206202, 'z1': {'__RealLiteral__': 0, 'data': '0.77319084511093529052384267548014', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.26103728277585432803082203041269', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.31791429746176536021089701497589', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.57942739416335, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 1404928, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -1, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 1, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 2, 0, 4, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0], 'euler11': [1, 2, 14, 22, 121], 'euler13': [1, 0, -4, 0, 169], 'euler17': [1, 0, -22, 0, 289], 'euler19': [1, 0, 14, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -10, 70, -230, 529], 'euler29': [1, -2, 10, -58, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 0, -46, 0, 961], 'euler37': [1, -14, 122, -518, 1369], 'euler41': [1, 0, -46, 0, 1681], 'euler43': [1, -10, 110, -430, 1849], 'euler47': [1, 0, -82, 0, 2209], 'euler5': [1, 0, -8, 0, 25], 'euler53': [1, 12, 126, 636, 2809], 'euler59': [1, 0, -10, 0, 3481], 'euler61': [1, 0, -48, 0, 3721], 'euler67': [1, -8, 6, -536, 4489], 'euler7': [1, 1, 0, 0, 0], 'euler71': [1, 8, 142, 568, 5041], 'euler73': [1, 0, -26, 0, 5329], 'euler79': [1, -4, 158, -316, 6241], 'euler83': [1, 0, -34, 0, 6889], 'euler89': [1, 0, 38, 0, 7921], 'euler97': [1, 0, -6, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -2, 0, 9], [1, 0, -8, 0, 25], [1, 1, 0, 0, 0], [1, 2, 14, 22, 121], [1, 0, -4, 0, 169], [1, 0, -22, 0, 289], [1, 0, 14, 0, 361], [1, -10, 70, -230, 529], [1, -2, 10, -58, 841], [1, 0, -46, 0, 961], [1, -14, 122, -518, 1369], [1, 0, -46, 0, 1681], [1, -10, 110, -430, 1849], [1, 0, -82, 0, 2209], [1, 12, 126, 636, 2809], [1, 0, -10, 0, 3481], [1, 0, -48, 0, 3721], [1, -8, 6, -536, 4489], [1, 8, 142, 568, 5041], [1, 0, -26, 0, 5329], [1, -4, 158, -316, 6241], [1, 0, -34, 0, 6889], [1, 0, 38, 0, 7921], [1, 0, -6, 0, 9409]], 'index': 9, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.7.1/28672.8/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.8/d', 'EllipticCurve/2.0.7.1/28672.6/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.6/d'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-112e3-1.1-c1e2-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-112e3-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.076465650952455, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 890396053678206202, 'z1': {'__RealLiteral__': 0, 'data': '0.77319084511093529052384267548014', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9620436
{'Lhash': '980135838895849071416122392918', 'Lhash_array': ['980135838895849071416122392918'], 'label': '4-112e3-1.1-c1e2-0-9', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.6/d'}
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id: 9620281
{'Lhash': '980135838895849071416122392918', 'Lhash_array': ['980135838895849071416122392918'], 'label': '4-112e3-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.6/d'}
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id: 9619794
{'Lhash': '980135838895849071416122392918', 'Lhash_array': ['980135838895849071416122392918'], 'label': '4-112e3-1.1-c1e2-0-9', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.8/d'}
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id: 9619792
{'Lhash': '980135838895849071416122392918', 'Lhash_array': ['980135838895849071416122392918'], 'label': '4-112e3-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.8/d'}