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lfunc_lfunctions • Show schema
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{'Lhash': '654355722000037106106696113636,2343150366998987805552476506573', 'a10': 0, 'a2': -2, 'a3': 0, 'a4': 3, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': -4, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.938966320006447, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [5, [1]], [13, [1, 6, 13]]], 'bad_primes': [2, 5, 13], 'central_character': '650.1', 'coefficient_field': '1.1.1.1', 'conductor': 422500, 'conductor_radical': 130, 'degree': 4, 'euler_factors': [[1, 2, 1], [1, 0, -2, 0, 9], [1], [1, 0, 14, 0, 49], [1, 0, -22, 0, 121], [1, 6, 13], [1, 0, 2, 0, 289], [1, 0, -38, 0, 361], [1, 0, -46, 0, 529], [1, 12, 94, 348, 841], [1, 0, -26, 0, 961], [1, -12, 110, -444, 1369], [1, 0, -82, 0, 1681], [1, 0, 14, 0, 1849], [1, 24, 238, 1128, 2209], [1, 0, -106, 0, 2809], [1, 0, 26, 0, 3481], [1, -20, 222, -1220, 3721], [1, 24, 278, 1608, 4489], [1, 0, -106, 0, 5041], [1, -12, 182, -876, 5329], [1, -16, 222, -1264, 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True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1279502349322483377, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51619564719349802105763267625', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.84841971957976754733369130889', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.94967757998084172562765226889', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.938966320006447, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 422500, 'conductor_radical': 130, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 3, 0, 0, 0, -4, 2, 0, 0, 0, -6, 0, 0, 5, 0, -4, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, -12, 0, 0, -6, 0, 0, 0, 6, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, -14, 0, 0, -18, 0, 0, 0, 0, 0, 24, 0, 0, 20, 0, 0, 7, 0, 0, -24, 0, 0, 0, 0, -8, 12, -24, 0, 0, 0, 0, 16, 0, -5, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 36, 28, 0, 0], 'euler11': [1, 0, -22, 0, 121], 'euler13': [1, 6, 13, 0, 0], 'euler17': [1, 0, 2, 0, 289], 'euler19': [1, 0, -38, 0, 361], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, 0, -46, 0, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 0, -26, 0, 961], 'euler37': [1, -12, 110, -444, 1369], 'euler41': [1, 0, -82, 0, 1681], 'euler43': [1, 0, 14, 0, 1849], 'euler47': [1, 24, 238, 1128, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -106, 0, 2809], 'euler59': [1, 0, 26, 0, 3481], 'euler61': [1, -20, 222, -1220, 3721], 'euler67': [1, 24, 278, 1608, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 0, -106, 0, 5041], 'euler73': [1, -12, 182, -876, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 24, 310, 1992, 6889], 'euler89': [1, 0, -34, 0, 7921], 'euler97': [1, -36, 518, -3492, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, 0, -2, 0, 9], [1, 0, 0, 0, 0], [1, 0, 14, 0, 49], [1, 0, -22, 0, 121], [1, 6, 13, 0, 0], [1, 0, 2, 0, 289], [1, 0, -38, 0, 361], [1, 0, -46, 0, 529], [1, 12, 94, 348, 841], [1, 0, -26, 0, 961], [1, -12, 110, -444, 1369], [1, 0, -82, 0, 1681], [1, 0, 14, 0, 1849], [1, 24, 238, 1128, 2209], [1, 0, -106, 0, 2809], [1, 0, 26, 0, 3481], [1, -20, 222, -1220, 3721], [1, 24, 278, 1608, 4489], [1, 0, -106, 0, 5041], [1, -12, 182, -876, 5329], [1, -16, 222, -1264, 6241], [1, 24, 310, 1992, 6889], [1, 0, -34, 0, 7921], [1, -36, 518, -3492, 9409]], 'index': 5, 'instance_types': ['HMF', 'ECNF', 'CMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.65.1/holomorphic/2.2.65.1-100.1-i', 'EllipticCurve/2.2.65.1/100.1/i', 'ModularForm/GL2/Q/holomorphic/650/2/c/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '4-650e2-1.1-c1e2-0-5', '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': '4-650e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2782177532850603, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1279502349322483377, 'z1': {'__RealLiteral__': 0, 'data': '0.51619564719349802105763267625', 'prec': 103}}
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lfunc_instances • Show schema
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id: 12637458
{'Lhash': '654355722000037106106696113636,2343150366998987805552476506573', 'Lhash_array': ['654355722000037106106696113636', '2343150366998987805552476506573'], 'factors': ['2-650-65.64-c1-0-1', '2-650-65.64-c1-0-16'], 'label': '4-650e2-1.1-c1e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/650/2/c/b'}
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id: 9477288
{'Lhash': '_654355722000037106106696113636', 'Lhash_array': ['_654355722000037106106696113636'], 'factors': ['4-650e2-1.1-c1e2-0-5'], 'label': '4-650e2-1.1-c1e2-0-5', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.65.1/100.1/i'}
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id: 9477248
{'Lhash': '_654355722000037106106696113636', 'Lhash_array': ['_654355722000037106106696113636'], 'factors': ['4-650e2-1.1-c1e2-0-5'], 'label': '4-650e2-1.1-c1e2-0-5', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.65.1/holomorphic/2.2.65.1-100.1-i'}