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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': 1, 'A3': 1, 'A4': -1, 'A5': 1, 'A6': 1, 'A7': 0, 'A8': -3, 'A9': 1, 'Lhash': '1096449618357840162642971150489', 'a10': [0.316227766016838, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.5773502691896257, 0], 'a4': [-0.5, 0], 'a5': [0.447213595499958, 0], 'a6': [0.40824829046386296, 0], 'a7': [0.0, 0], 'a8': [-1.0606601717798214, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.772347278393827, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 2]], [3, [1, -1]], [5, [1, -1]]], 'bad_primes': [2, 3, 5], 'central_character': '216000.1', 'coefficient_field': '1.1.1.1', 'conductor': 216000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, -1, 2], [1, -1], [1, -1], [1, 0, -2, 0, 49], [1, 0, -6, 0, 121], [1, 6, 26, 78, 169], [1, 0, 2, 0, 289], [1, 0, -10, 0, 361], [1, 0, 30, 0, 529], [1, 0, 22, 0, 841], [1, -16, 126, -496, 961], [1, -6, 82, -222, 1369], [1, -6, 90, 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'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 590987369206996510, 'z1': {'__RealLiteral__': 0, 'data': '0.864946238466998714244148432182192', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.26607927320469213703160857525802', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.68492287371980531455329544918049', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.772347278393827, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 216000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 1, 1, -1, 1, 1, 0, -3, 1, 1, 0, -1, -6, 0, 1, -1, 0, 1, 0, -1, 0, 0, 0, -3, 1, -6, 1, 0, 0, 1, 16, 5, 0, 0, 0, -1, 6, 0, -6, -3, 6, 0, 0, 0, 1, 0, 0, -1, 2, 1, 0, 6, 4, 1, 0, 0, 0, 0, 0, -1, 0, 16, 0, 7, -6, 0, -12, 0, 0, 0, 12, -3, 0, 6, 1, 0, 0, -6, -4, -1, 1, 6, 12, 0, 0, 0, 0, 0, 6, 1, 0, 0, 16, 0, 0, 5, 0, 2, 0, -1], 'euler11': [1, 0, -6, 0, 121], 'euler13': [1, 6, 26, 78, 169], 'euler17': [1, 0, 2, 0, 289], 'euler19': [1, 0, -10, 0, 361], 'euler2': [1, -1, 2, 0, 0], 'euler23': [1, 0, 30, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, -1, 0, 0, 0], 'euler31': [1, -16, 126, -496, 961], 'euler37': [1, -6, 82, -222, 1369], 'euler41': [1, -6, 90, -246, 1681], 'euler43': [1, 0, 82, 0, 1849], 'euler47': [1, 0, 78, 0, 2209], 'euler5': [1, -1, 0, 0, 0], 'euler53': [1, -4, 110, -212, 2809], 'euler59': [1, 0, -66, 0, 3481], 'euler61': [1, 0, 50, 0, 3721], 'euler67': [1, 12, 134, 804, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, -12, 162, -852, 5041], 'euler73': [1, 0, 94, 0, 5329], 'euler79': [1, 4, 126, 316, 6241], 'euler83': [1, -12, 166, -996, 6889], 'euler89': [1, -6, 66, -534, 7921], 'euler97': [1, 0, -74, 0, 9409], 'euler_factors': [[1, -1, 2, 0, 0], [1, -1, 0, 0, 0], [1, -1, 0, 0, 0], [1, 0, -2, 0, 49], [1, 0, -6, 0, 121], [1, 6, 26, 78, 169], [1, 0, 2, 0, 289], [1, 0, -10, 0, 361], [1, 0, 30, 0, 529], [1, 0, 22, 0, 841], [1, -16, 126, -496, 961], [1, -6, 82, -222, 1369], [1, -6, 90, -246, 1681], [1, 0, 82, 0, 1849], [1, 0, 78, 0, 2209], [1, -4, 110, -212, 2809], [1, 0, -66, 0, 3481], [1, 0, 50, 0, 3721], [1, 12, 134, 804, 4489], [1, -12, 162, -852, 5041], [1, 0, 94, 0, 5329], [1, 4, 126, 316, 6241], [1, -12, 166, -996, 6889], [1, -6, 66, -534, 7921], [1, 0, -74, 0, 9409]], 'index': 4, 'instance_types': ['HMF', 'ECNF', 'HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-135.1-a', 'EllipticCurve/2.2.40.1/135.1/a', 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-135.2-a', 'EllipticCurve/2.2.40.1/135.2/a'], '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': '4-60e3-1.1-c1e2-0-4', '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': '4-60e3-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9264244928355312, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 590987369206996510, 'z1': {'__RealLiteral__': 0, 'data': '0.864946238466998714244148432182192', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9494930
{'Lhash': '1096449618357840162642971150489', 'Lhash_array': ['1096449618357840162642971150489'], 'label': '4-60e3-1.1-c1e2-0-4', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.40.1/135.2/a'}
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id: 9494648
{'Lhash': '1096449618357840162642971150489', 'Lhash_array': ['1096449618357840162642971150489'], 'label': '4-60e3-1.1-c1e2-0-4', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-135.2-a'}
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id: 9494241
{'Lhash': '1096449618357840162642971150489', 'Lhash_array': ['1096449618357840162642971150489'], 'label': '4-60e3-1.1-c1e2-0-4', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.40.1/135.1/a'}
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id: 9494095
{'Lhash': '1096449618357840162642971150489', 'Lhash_array': ['1096449618357840162642971150489'], 'label': '4-60e3-1.1-c1e2-0-4', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-135.1-a'}