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lfunc_lfunctions • Show schema
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{'Lhash': '1650461493434044297182222377050,1721512114437725284003312230870', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5846.857224180202, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 2, 1]], [19, [1, 2, 1]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '9576.1', 'coefficient_field': '1.1.1.1', 'conductor': 91699776, 'conductor_radical': 798, 'degree': 4, 'euler_factors': [[1], [1], [1, -4, 14, -20, 25], [1, 2, 1], [1, 4, 26, 44, 121], [1, -2, 10, -26, 169], [1, 2, 18, 34, 289], [1, 2, 1], [1, -6, 38, -138, 529], [1, 10, 66, 290, 841], [1, -6, 54, -186, 961], [1, 10, 82, 370, 1369], [1, 0, 14, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 94, 0, 2209], [1, 2, 90, 106, 2809], [1, -4, 54, -236, 3481], [1, 4, 126, 244, 3721], [1, 12, 102, 804, 4489], [1, 6, -2, 426, 5041], [1, 20, 246, 1460, 5329], [1, -18, 222, 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'2.15733105751719477165458408885142', '2.26631660693678829317883843248102', '2.88819445948934469215030515990088', '2.94304353187355982524698371135352', '3.73972561851802654551471421950136', '3.83022111767345617794746055627951', '4.54971332372512253874145288966792', '4.73928513783613514319005326355436', '5.38710787028660319984339311543214', '5.49954923422036470323044211563801', '5.88257156651207040240560299792378', '5.94439462795339759171571187796902', '6.62165980050771849222973935861601', '6.64233612564993790734009632382886', '7.12478070566499264673362598198486', '7.52976781513683755530328151293528'], 'prelabel': '4-9576e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.744412214413165, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1226414015859476267, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30198454774280321651165281559', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.35803360494428203413027884755', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.15733105751719477165458408885', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5846.857224180202, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 91699776, 'conductor_radical': 798, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, -2, 0, 0, 0, -4, 0, 2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 6, 0, 2, 0, 0, 0, -10, 0, 6, 0, 0, 0, -8, 0, -10, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, -16, 0, 0, 0, 4, 0, -4, 0, 0, 0, 8, 0, -12, 0, 0, 0, -6, 0, -20, 0, 0, 0, 8, 0, 18, 0, 0, 0, 10, 0, -8, 0, 0, 0, -16, 0, -4, 0, 0, 0, -8, 0, 0, 0, 0, 0], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, -2, 10, -26, 169], 'euler17': [1, 2, 18, 34, 289], 'euler19': [1, 2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -6, 38, -138, 529], 'euler29': [1, 10, 66, 290, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -6, 54, -186, 961], 'euler37': [1, 10, 82, 370, 1369], 'euler41': [1, 0, 14, 0, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, -4, 14, -20, 25], 'euler53': [1, 2, 90, 106, 2809], 'euler59': [1, -4, 54, -236, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 12, 102, 804, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, 6, -2, 426, 5041], 'euler73': [1, 20, 246, 1460, 5329], 'euler79': [1, -18, 222, -1422, 6241], 'euler83': [1, -10, 174, -830, 6889], 'euler89': [1, 16, 174, 1424, 7921], 'euler97': [1, 0, 126, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -4, 14, -20, 25], [1, 2, 1, 0, 0], [1, 4, 26, 44, 121], [1, -2, 10, -26, 169], [1, 2, 18, 34, 289], [1, 2, 1, 0, 0], [1, -6, 38, -138, 529], [1, 10, 66, 290, 841], [1, -6, 54, -186, 961], [1, 10, 82, 370, 1369], [1, 0, 14, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 94, 0, 2209], [1, 2, 90, 106, 2809], [1, -4, 54, -236, 3481], [1, 4, 126, 244, 3721], [1, 12, 102, 804, 4489], [1, 6, -2, 426, 5041], [1, 20, 246, 1460, 5329], [1, -18, 222, -1422, 6241], [1, -10, 174, -830, 6889], [1, 16, 174, 1424, 7921], [1, 0, 126, 0, 9409]], 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/bx'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '4-9576e2-1.1-c1e2-0-21', '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': 2, 'prelabel': '4-9576e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.744412214413165, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1226414015859476267, 'z1': {'__RealLiteral__': 0, 'data': '1.30198454774280321651165281559', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1650461493434044297182222377050,1721512114437725284003312230870', 'Lhash_array': ['1650461493434044297182222377050', '1721512114437725284003312230870'], 'label': '4-9576e2-1.1-c1e2-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/bx'}