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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 4, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -1, 'Lhash': '1865105028152409852417398902735', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [1.788854381999832, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.3504806021792133, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 1]]], 'bad_primes': [2, 3], 'central_character': '36864.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 0, 1], [1, -4, 10, -20, 25], [1, 0, -6, 0, 49], [1, 0, -6, 0, 121], [1, -4, 30, -52, 169], [1, 4, 22, 68, 289], [1, 0, 26, 0, 361], [1, 0, -18, 0, 529], [1, -4, 26, -116, 841], [1, 0, -38, 0, 961], [1, -4, 62, -148, 1369], [1, 12, 102, 492, 1681], [1, 0, -22, 0, 1849], [1, 0, 14, 0, 2209], [1, -4, 106, -212, 2809], [1, 0, -6, 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'data': '1.47130844084057074366336267008299', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.28708818518850225684617667408365', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.07868749500386681033869486735477', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.3504806021792133, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, 0, 0, -1, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -12, 0, 0, 0, -4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -16, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0], 'euler11': [1, 0, -6, 0, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, 4, 22, 68, 289], 'euler19': [1, 0, 26, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -18, 0, 529], 'euler29': [1, -4, 26, -116, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, 0, -38, 0, 961], 'euler37': [1, -4, 62, -148, 1369], 'euler41': [1, 12, 102, 492, 1681], 'euler43': [1, 0, -22, 0, 1849], 'euler47': [1, 0, 14, 0, 2209], 'euler5': [1, -4, 10, -20, 25], 'euler53': [1, -4, 106, -212, 2809], 'euler59': [1, 0, -6, 0, 3481], 'euler61': [1, 12, 142, 732, 3721], 'euler67': [1, 0, 106, 0, 4489], 'euler7': [1, 0, -6, 0, 49], 'euler71': [1, 0, -114, 0, 5041], 'euler73': [1, 12, 118, 876, 5329], 'euler79': [1, 0, 58, 0, 6241], 'euler83': [1, 0, 42, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, -12, 166, -1164, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 1, 0, 0], [1, -4, 10, -20, 25], [1, 0, -6, 0, 49], [1, 0, -6, 0, 121], [1, -4, 30, -52, 169], [1, 4, 22, 68, 289], [1, 0, 26, 0, 361], [1, 0, -18, 0, 529], [1, -4, 26, -116, 841], [1, 0, -38, 0, 961], [1, -4, 62, -148, 1369], [1, 12, 102, 492, 1681], [1, 0, -22, 0, 1849], [1, 0, 14, 0, 2209], [1, -4, 106, -212, 2809], [1, 0, -6, 0, 3481], [1, 12, 142, 732, 3721], [1, 0, 106, 0, 4489], [1, 0, -114, 0, 5041], [1, 12, 118, 876, 5329], [1, 0, 58, 0, 6241], [1, 0, 42, 0, 6889], [1, -12, 214, -1068, 7921], [1, -12, 166, -1164, 9409]], 'index': 6, 'instance_types': ['ECNF', 'ECNF', 'BMF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.4.1/2304.1/d', 'EllipticCurve/2.0.4.1/2304.1/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/2304.1/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/2304.1/b'], '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': '4-192e2-1.1-c1e2-0-6', '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': '4-192e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1358681497786879494, 'z1': {'__RealLiteral__': 0, 'data': '1.47130844084057074366336267008299', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9658999
{'Lhash': '1865105028152409852417398902735', 'Lhash_array': ['1865105028152409852417398902735'], 'label': '4-192e2-1.1-c1e2-0-6', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/2304.1/b'}
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id: 9658942
{'Lhash': '1865105028152409852417398902735', 'Lhash_array': ['1865105028152409852417398902735'], 'label': '4-192e2-1.1-c1e2-0-6', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/2304.1/d'}
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id: 9658752
{'Lhash': '1865105028152409852417398902735', 'Lhash_array': ['1865105028152409852417398902735'], 'label': '4-192e2-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/2304.1/b'}
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id: 9658518
{'Lhash': '1865105028152409852417398902735', 'Lhash_array': ['1865105028152409852417398902735'], 'label': '4-192e2-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/2304.1/d'}