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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': -5, 'A8': 0, 'A9': -2, 'Lhash': '2681966800771312252719734680086', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.8898223650461363, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.650245876577631, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1, 3]], [6361, [1, 125, 6485, 6361]]], 'bad_primes': [3, 6361], 'central_character': '57249.1', 'coefficient_field': '1.1.1.1', 'conductor': 57249, 'conductor_radical': 19083, 'degree': 4, 'euler_factors': [[1, 0, -1, 0, 4], [1, -1, 3], [1, 0, -7, 0, 25], [1, 5, 20, 35, 49], [1, 0, -13, 0, 121], [1, 4, 26, 52, 169], [1, 0, 16, 0, 289], [1, -1, 36, -19, 361], [1, 0, 43, 0, 529], [1, 0, 6, 0, 841], [1, 14, 110, 434, 961], [1, 2, 71, 74, 1369], [1, 0, -10, 0, 1681], [1, 12, 118, 516, 1849], [1, 0, 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-0.44526074347318984, -0.8294899156355683, -1.079034921755159, -1.0913852214988293], 'positive_zeros': ['2.11569875822915840641086406730237', '2.69541351369120047199854891228123', '3.43221389911543551770704413580911', '3.72609707128623372653467611045109', '5.09299787403446468950255578264082', '5.24728055883496052082717155626990', '6.32710548034214412379274702935345', '6.55535134041316075893889692379477', '7.14871835272308105238171460492164', '7.47520792151717437800393664904191', '8.364091402035647217481857053326722', '8.782024897965907841636861499858487', '9.309497741758762994499318400415101', '9.746631248281511248877325155199434'], 'prelabel': '4-57249-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.3822306845139833, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1579623777370566490, 'z1': {'__RealLiteral__': 0, 'data': '2.11569875822915840641086406730237', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.69541351369120047199854891228123', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.43221389911543551770704413580911', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.650245876577631, 'bad_primes': [3, 6361], 'central_character': '1.1', 'conductor': 57249, 'conductor_radical': 19083, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 1, 0, 0, -5, 0, -2, 0, 0, 1, -4, 0, 0, -3, 0, 0, 1, 0, -5, 0, 0, 0, 7, 0, -5, -5, 0, 0, -14, 0, 0, 0, 0, -2, -2, 0, -4, 0, 0, 0, -12, 0, 0, 0, 0, -3, 5, 0, 0, -4, 0, 0, 0, 0, 1, 0, 0, 0, 12, 0, 10, -7, 0, 0, 23, 0, 0, 0, 0, 0, -5, 0, 7, 1, 0, 0, 21, 0, 1, 0, 0, -5, 0, 0, 0, 0, 0, 0, 20, 0, -14, 0, 0, 0, -3, 0, 0, 7], 'euler11': [1, 0, -13, 0, 121], 'euler13': [1, 4, 26, 52, 169], 'euler17': [1, 0, 16, 0, 289], 'euler19': [1, -1, 36, -19, 361], 'euler2': [1, 0, -1, 0, 4], 'euler23': [1, 0, 43, 0, 529], 'euler29': [1, 0, 6, 0, 841], 'euler3': [1, -1, 3, 0, 0], 'euler31': [1, 14, 110, 434, 961], 'euler37': [1, 2, 71, 74, 1369], 'euler41': [1, 0, -10, 0, 1681], 'euler43': [1, 12, 118, 516, 1849], 'euler47': [1, 0, 13, 0, 2209], 'euler5': [1, 0, -7, 0, 25], 'euler53': [1, 0, -91, 0, 2809], 'euler59': [1, 0, -31, 0, 3481], 'euler61': [1, -12, 94, -732, 3721], 'euler67': [1, -23, 266, -1541, 4489], 'euler7': [1, 5, 20, 35, 49], 'euler71': [1, 0, -86, 0, 5041], 'euler73': [1, 5, 132, 365, 5329], 'euler79': [1, -21, 248, -1659, 6241], 'euler83': [1, 0, -128, 0, 6889], 'euler89': [1, 0, -69, 0, 7921], 'euler97': [1, 3, 124, 291, 9409], 'euler_factors': [[1, 0, -1, 0, 4], [1, -1, 3, 0, 0], [1, 0, -7, 0, 25], [1, 5, 20, 35, 49], [1, 0, -13, 0, 121], [1, 4, 26, 52, 169], [1, 0, 16, 0, 289], [1, -1, 36, -19, 361], [1, 0, 43, 0, 529], [1, 0, 6, 0, 841], [1, 14, 110, 434, 961], [1, 2, 71, 74, 1369], [1, 0, -10, 0, 1681], [1, 12, 118, 516, 1849], [1, 0, 13, 0, 2209], [1, 0, -91, 0, 2809], [1, 0, -31, 0, 3481], [1, -12, 94, -732, 3721], [1, -23, 266, -1541, 4489], [1, 0, -86, 0, 5041], [1, 5, 132, 365, 5329], [1, -21, 248, -1659, 6241], [1, 0, -128, 0, 6889], [1, 0, -69, 0, 7921], [1, 3, 124, 291, 9409]], 'index': 1, 'instance_types': ['ECNF', 'ECNF', 'BMF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.3.1/6361.2/a', 'EllipticCurve/2.0.3.1/6361.1/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/6361.2/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/6361.1/a'], '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': '4-57249-1.1-c1e2-0-1', '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': 1, 'prelabel': '4-57249-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.3822306845139833, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1579623777370566490, 'z1': {'__RealLiteral__': 0, 'data': '2.11569875822915840641086406730237', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9791565
{'Lhash': '2681966800771312252719734680086', 'Lhash_array': ['2681966800771312252719734680086'], 'label': '4-57249-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/6361.1/a'}
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id: 9791502
{'Lhash': '2681966800771312252719734680086', 'Lhash_array': ['2681966800771312252719734680086'], 'label': '4-57249-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/6361.2/a'}
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id: 9791356
{'Lhash': '2681966800771312252719734680086', 'Lhash_array': ['2681966800771312252719734680086'], 'label': '4-57249-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/6361.1/a'}
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id: 9790819
{'Lhash': '2681966800771312252719734680086', 'Lhash_array': ['2681966800771312252719734680086'], 'label': '4-57249-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/6361.2/a'}