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lfunc_lfunctions • Show schema
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{'Lhash': '1257211599338914818033872141420,1771432659283487730322578697710', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, '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, 2, 8, 10, 25], [1, 2, 1], [1, 0, 10, 0, 121], [1, -8, 42, -104, 169], [1, 10, 56, 170, 289], [1, -2, 1], [1, -8, 50, -184, 529], [1, -2, 56, -58, 841], [1, 0, 50, 0, 961], [1, 8, 78, 296, 1369], [1, 16, 134, 656, 1681], [1, 4, 42, 172, 1849], [1, -6, 28, -282, 2209], [1, 6, 88, 318, 2809], [1, 16, 182, 944, 3481], [1, -16, 174, -976, 3721], [1, 8, 150, 536, 4489], [1, -2, 116, -142, 5041], [1, -8, 150, -584, 5329], [1, 4, 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['0.991765080308852350426570996862470', '1.39741397114043631269220843068504', '1.96514617477119533849712532290094', '2.36450367944707923194759578219610', '3.08169825140157038054223834297773', '3.29577556059048382929893190054400', '3.61988559855993516146310733180759', '3.85537965691787464342786601358674', '4.45959312612735554465634134030136', '4.57526632988669604170397183389352', '5.20940538295844131186310197427381', '5.30764316957079062099129793117038', '6.03969934927840819380248966824615', '6.21961063699938830874031650557380', '6.52554882937912271436068041833038', '6.82340138894936012718370614380444', '7.17127843081953679290490101490507', '7.32596981093123567795109009990295'], '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': 35046403561259488, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.991765080308852350426570996862', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.39741397114043631269220843069', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.96514617477119533849712532290', '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, -2, 0, -2, 0, 0, 0, 0, 0, 8, 0, 0, 0, -10, 0, 2, 0, 0, 0, 8, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, -8, 0, 0, 0, -16, 0, -4, 0, 0, 0, 6, 0, 3, 0, 0, 0, -6, 0, 0, 0, 0, 0, -16, 0, 16, 0, 0, 0, -16, 0, -8, 0, 0, 0, 2, 0, 8, 0, 0, 0, 0, 0, -4, 0, 0, 0, -10, 0, 20, 0, 0, 0, 0, 0, -16, 0, 0, 0, -4, 0, 12, 0, 0, 0], 'euler11': [1, 0, 10, 0, 121], 'euler13': [1, -8, 42, -104, 169], 'euler17': [1, 10, 56, 170, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -8, 50, -184, 529], 'euler29': [1, -2, 56, -58, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 50, 0, 961], 'euler37': [1, 8, 78, 296, 1369], 'euler41': [1, 16, 134, 656, 1681], 'euler43': [1, 4, 42, 172, 1849], 'euler47': [1, -6, 28, -282, 2209], 'euler5': [1, 2, 8, 10, 25], 'euler53': [1, 6, 88, 318, 2809], 'euler59': [1, 16, 182, 944, 3481], 'euler61': [1, -16, 174, -976, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, -2, 116, -142, 5041], 'euler73': [1, -8, 150, -584, 5329], 'euler79': [1, 4, 150, 316, 6241], 'euler83': [1, 10, 164, 830, 6889], 'euler89': [1, 0, 70, 0, 7921], 'euler97': [1, -12, 230, -1164, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 2, 8, 10, 25], [1, 2, 1, 0, 0], [1, 0, 10, 0, 121], [1, -8, 42, -104, 169], [1, 10, 56, 170, 289], [1, -2, 1, 0, 0], [1, -8, 50, -184, 529], [1, -2, 56, -58, 841], [1, 0, 50, 0, 961], [1, 8, 78, 296, 1369], [1, 16, 134, 656, 1681], [1, 4, 42, 172, 1849], [1, -6, 28, -282, 2209], [1, 6, 88, 318, 2809], [1, 16, 182, 944, 3481], [1, -16, 174, -976, 3721], [1, 8, 150, 536, 4489], [1, -2, 116, -142, 5041], [1, -8, 150, -584, 5329], [1, 4, 150, 316, 6241], [1, 10, 164, 830, 6889], [1, 0, 70, 0, 7921], [1, -12, 230, -1164, 9409]], 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/bf'], '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-c1e2-0-12', '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': 35046403561259488, 'z1': {'__RealLiteral__': 0, 'data': '0.991765080308852350426570996862', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1257211599338914818033872141420,1771432659283487730322578697710', 'Lhash_array': ['1257211599338914818033872141420', '1771432659283487730322578697710'], 'label': '4-9576e2-1.1-c1e2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/bf'}