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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': -2, 'Lhash': '1475227260804999314270099097955', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.57942739416335, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]]], 'bad_primes': [2, 7], 'central_character': '1404928.1', 'coefficient_field': '1.1.1.1', 'conductor': 1404928, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, 0, 2, 0, 9], [1, 0, 2, 0, 25], [1, -1], [1, -4, 10, -44, 121], [1, 0, 22, 0, 169], [1, 0, 22, 0, 289], [1, 0, 2, 0, 361], [1, 12, 78, 276, 529], [1, -2, -22, -58, 841], [1, 0, -30, 0, 961], [1, -10, 74, -370, 1369], [1, 0, 62, 0, 1681], [1, -4, 90, -172, 1849], [1, 0, -62, 0, 2209], [1, -10, 130, -530, 2809], [1, 0, 34, 0, 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-0.15225077004906706, -0.5399212539822038], 'positive_zeros': ['1.16374911236534542788260164388036', '1.78034092513983073922801136583344', '2.51081508633609164424142946425546', '2.90735366089804934483169027143908', '3.82779271563122276431113592287873', '4.07730036325899161420861564777919', '4.39104688838354248863570972870301', '5.08361012405941074736360249976693', '5.76175796207076806488885877770755', '6.00587253425096093343995602071144', '6.21371174791133844116511861976363', '6.85998409614637159802942519472404', '7.45005912928402327913214471058627', '7.65869261167450107823750782855290'], 'prelabel': '4-112e3-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.076465650952455, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1195887799579675435, 'z1': {'__RealLiteral__': 0, 'data': '1.16374911236534542788260164388036', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.78034092513983073922801136583344', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.51081508633609164424142946425546', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.57942739416335, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 1404928, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, -20, 0, 0, 0, 0, 0, 4, 0, -20, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0], 'euler11': [1, -4, 10, -44, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 0, 22, 0, 289], 'euler19': [1, 0, 2, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 12, 78, 276, 529], 'euler29': [1, -2, -22, -58, 841], 'euler3': [1, 0, 2, 0, 9], 'euler31': [1, 0, -30, 0, 961], 'euler37': [1, -10, 74, -370, 1369], 'euler41': [1, 0, 62, 0, 1681], 'euler43': [1, -4, 90, -172, 1849], 'euler47': [1, 0, -62, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, -10, 130, -530, 2809], 'euler59': [1, 0, 34, 0, 3481], 'euler61': [1, 0, 98, 0, 3721], 'euler67': [1, 4, 102, 268, 4489], 'euler7': [1, -1, 0, 0, 0], 'euler71': [1, 20, 238, 1420, 5041], 'euler73': [1, 0, -10, 0, 5329], 'euler79': [1, 20, 254, 1580, 6241], 'euler83': [1, 0, -70, 0, 6889], 'euler89': [1, 0, -146, 0, 7921], 'euler97': [1, 0, -106, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 2, 0, 9], [1, 0, 2, 0, 25], [1, -1, 0, 0, 0], [1, -4, 10, -44, 121], [1, 0, 22, 0, 169], [1, 0, 22, 0, 289], [1, 0, 2, 0, 361], [1, 12, 78, 276, 529], [1, -2, -22, -58, 841], [1, 0, -30, 0, 961], [1, -10, 74, -370, 1369], [1, 0, 62, 0, 1681], [1, -4, 90, -172, 1849], [1, 0, -62, 0, 2209], [1, -10, 130, -530, 2809], [1, 0, 34, 0, 3481], [1, 0, 98, 0, 3721], [1, 4, 102, 268, 4489], [1, 20, 238, 1420, 5041], [1, 0, -10, 0, 5329], [1, 20, 254, 1580, 6241], [1, 0, -70, 0, 6889], [1, 0, -146, 0, 7921], [1, 0, -106, 0, 9409]], 'index': 31, 'instance_types': ['ECNF', 'BMF', 'BMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.0.7.1/28672.5/j', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.5/j', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.9/i', 'EllipticCurve/2.0.7.1/28672.9/i'], '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': '4-112e3-1.1-c1e2-0-31', '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': '4-112e3-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.076465650952455, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1195887799579675435, 'z1': {'__RealLiteral__': 0, 'data': '1.16374911236534542788260164388036', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9620757
{'Lhash': '1475227260804999314270099097955', 'Lhash_array': ['1475227260804999314270099097955'], 'label': '4-112e3-1.1-c1e2-0-31', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.9/i'}
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id: 9620552
{'Lhash': '1475227260804999314270099097955', 'Lhash_array': ['1475227260804999314270099097955'], 'label': '4-112e3-1.1-c1e2-0-31', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.9/i'}
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id: 9620450
{'Lhash': '1475227260804999314270099097955', 'Lhash_array': ['1475227260804999314270099097955'], 'label': '4-112e3-1.1-c1e2-0-31', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.5/j'}
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id: 9620432
{'Lhash': '1475227260804999314270099097955', 'Lhash_array': ['1475227260804999314270099097955'], 'label': '4-112e3-1.1-c1e2-0-31', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.5/j'}