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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -1, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '1281103270622204308104395363592', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [-0.447213595499958, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.6381058733497436, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, 1]], [331, [1, 9, 339, 331]]], 'bad_primes': [5, 331], 'central_character': '41375.1', 'coefficient_field': '1.1.1.1', 'conductor': 41375, 'conductor_radical': 1655, 'degree': 4, 'euler_factors': [[1, 0, 1, 0, 4], [1, 0, 3, 0, 9], [1, 1], [1, 0, -1, 0, 49], [1, -7, 34, -77, 121], [1, 0, 2, 0, 169], [1, 0, -12, 0, 289], [1, -8, 53, -152, 361], [1, 0, -33, 0, 529], [1, 3, 58, 87, 841], [1, -2, 62, -62, 961], [1, 0, -51, 0, 1369], [1, 1, 52, 41, 1681], [1, 0, 18, 0, 1849], [1, 0, 34, 0, 2209], [1, 0, 62, 0, 2809], [1, -5, 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-5.43689807951018, -4.503126021585387, -3.228708372085147, -1.7786396620151532, -0.3459181485075859, 0.8794338773875816], 'positive_zeros': ['1.01061228574463095034521581980628', '2.38438337170026039176009959752854', '3.52425382628233441606004274867212', '3.76313549857495181722161915381041', '4.61557275276563948105644133742824', '5.29122317955955096690201529733348', '5.82930486592205458844674091137582', '6.66540022484453257831025472625428', '6.93310706619865061972954794947991', '7.63232589238166029348888745498352', '8.410384465840586370523201176541224', '8.649679793638444255697139727111017', '9.274392963078847225722112804596194', '9.597287612587930727221694461996779', '10.01499244692265779382834373670289'], 'prelabel': '4-41375-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2744507441075994, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1419574792352509669, 'z1': {'__RealLiteral__': 0, 'data': '1.01061228574463095034521581980628', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.38438337170026039176009959752854', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.52425382628233441606004274867212', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.6381058733497436, 'bad_primes': [5, 331], 'central_character': '1.1', 'conductor': 41375, 'conductor_radical': 1655, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, -1, 0, 0, 0, -3, 0, 7, 0, 0, 0, 0, -3, 0, 0, 8, 1, 0, 0, 0, 0, 1, 0, 0, 0, -3, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, -1, 0, 0, -7, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, -7, 0, 0, 0, 5, 0, 21, 0, 0, 7, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, -8, 0, 0, -10, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -8, 0, 0, 0, -21, -1], 'euler11': [1, -7, 34, -77, 121], 'euler13': [1, 0, 2, 0, 169], 'euler17': [1, 0, -12, 0, 289], 'euler19': [1, -8, 53, -152, 361], 'euler2': [1, 0, 1, 0, 4], 'euler23': [1, 0, -33, 0, 529], 'euler29': [1, 3, 58, 87, 841], 'euler3': [1, 0, 3, 0, 9], 'euler31': [1, -2, 62, -62, 961], 'euler37': [1, 0, -51, 0, 1369], 'euler41': [1, 1, 52, 41, 1681], 'euler43': [1, 0, 18, 0, 1849], 'euler47': [1, 0, 34, 0, 2209], 'euler5': [1, 1, 0, 0, 0], 'euler53': [1, 0, 62, 0, 2809], 'euler59': [1, -5, 118, -295, 3481], 'euler61': [1, -21, 212, -1281, 3721], 'euler67': [1, 0, 8, 0, 4489], 'euler7': [1, 0, -1, 0, 49], 'euler71': [1, -24, 270, -1704, 5041], 'euler73': [1, 0, 7, 0, 5329], 'euler79': [1, 10, 174, 790, 6241], 'euler83': [1, 0, 16, 0, 6889], 'euler89': [1, -2, 10, -178, 7921], 'euler97': [1, 0, 173, 0, 9409], 'euler_factors': [[1, 0, 1, 0, 4], [1, 0, 3, 0, 9], [1, 1, 0, 0, 0], [1, 0, -1, 0, 49], [1, -7, 34, -77, 121], [1, 0, 2, 0, 169], [1, 0, -12, 0, 289], [1, -8, 53, -152, 361], [1, 0, -33, 0, 529], [1, 3, 58, 87, 841], [1, -2, 62, -62, 961], [1, 0, -51, 0, 1369], [1, 1, 52, 41, 1681], [1, 0, 18, 0, 1849], [1, 0, 34, 0, 2209], [1, 0, 62, 0, 2809], [1, -5, 118, -295, 3481], [1, -21, 212, -1281, 3721], [1, 0, 8, 0, 4489], [1, -24, 270, -1704, 5041], [1, 0, 7, 0, 5329], [1, 10, 174, 790, 6241], [1, 0, 16, 0, 6889], [1, -2, 10, -178, 7921], [1, 0, 173, 0, 9409]], 'index': 0, 'instance_types': ['HMF', 'ECNF', 'ECNF', 'HMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-1655.2-c', 'EllipticCurve/2.2.5.1/1655.1/c', 'EllipticCurve/2.2.5.1/1655.2/c', 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-1655.1-c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-41375-1.1-c1e2-0-0', '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': '4-41375-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2744507441075994, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1419574792352509669, 'z1': {'__RealLiteral__': 0, 'data': '1.01061228574463095034521581980628', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9517483
{'Lhash': '1281103270622204308104395363592', 'Lhash_array': ['1281103270622204308104395363592'], 'label': '4-41375-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-1655.1-c'}
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id: 9517291
{'Lhash': '1281103270622204308104395363592', 'Lhash_array': ['1281103270622204308104395363592'], 'label': '4-41375-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/1655.2/c'}
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id: 9517178
{'Lhash': '1281103270622204308104395363592', 'Lhash_array': ['1281103270622204308104395363592'], 'label': '4-41375-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/1655.1/c'}
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id: 9517041
{'Lhash': '1281103270622204308104395363592', 'Lhash_array': ['1281103270622204308104395363592'], 'label': '4-41375-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-1655.2-c'}