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lfunc_lfunctions • Show schema
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{'Lhash': '2098966543811446480284129390266,2299457854503320708601337827306', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 237.9953425354976, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -2, 1]], [7, [1, -2, 1]], [23, [1, -2, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '1932.1', 'coefficient_field': '1.1.1.1', 'conductor': 3732624, 'conductor_radical': 966, 'degree': 4, 'euler_factors': [[1], [1, -2, 1], [1, 5, 15, 25, 25], [1, -2, 1], [1, 2, 23, 22, 121], [1, 1, -5, 13, 169], [1, 10, 59, 170, 289], [1, -2, 19, -38, 361], [1, -2, 1], [1, 8, 69, 232, 841], [1, 4, 21, 124, 961], [1, 6, 63, 222, 1369], [1, 16, 141, 656, 1681], [1, 3, 27, 129, 1849], [1, 6, 58, 282, 2209], [1, -3, 107, -159, 2809], [1, 5, 123, 295, 3481], [1, -5, 27, -305, 3721], [1, -1, 73, -67, 4489], [1, -7, 93, -497, 5041], [1, 10, 151, 730, 5329], 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4.927968140365516, 4.6448926677046005, 4.258672715459355, 3.777584345871437, 3.2231891902419414], 'positive_zeros': ['1.65579264777971620514258681787088', '1.81395240462105523158445141432409', '2.79610498753449416152967632038898', '2.96681631112852332696080006067435', '3.73277189873131724902456897366029', '3.98702310368598651758968513060494', '4.25570730778494611095714411680563', '4.78549825442755682913731445418171', '5.26427202175593157361200938294762', '5.53016847591230569373791056616181', '6.66322921388635595777861013257442', '6.81623291539093492575427722249021', '7.22186441976559038444930069587891', '7.43221911252367881547037192202215', '8.056672261024702803067490546676671', '8.137659041066516298016612437904582', '8.579704083504205905857733171890844', '8.740190511858784941196779843324871'], 'prelabel': '4-1932e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.9277344195491857, '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': 1744136107648713097, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65579264777971620514258681787', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.81395240462105523158445141432', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.79610498753449416152967632039', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 237.9953425354976, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 3732624, 'conductor_radical': 966, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, -5, 0, 2, 0, 3, 0, -2, 0, -1, 0, -10, 0, -10, 0, 2, 0, 4, 0, 2, 0, 10, 0, 4, 0, -8, 0, -4, 0, -4, 0, -10, 0, -6, 0, -2, 0, -16, 0, -3, 0, -15, 0, -6, 0, 3, 0, -20, 0, 3, 0, 10, 0, 4, 0, -5, 0, 5, 0, 6, 0, 5, 0, 1, 0, 4, 0, 7, 0, -10, 0, 20, 0, -4, 0, -8, 0, 5, 0, -4, 0, 50, 0, -16, 0, -31, 0, -2, 0, -8, 0, -10, 0, -20, 0, -6, 0], 'euler11': [1, 2, 23, 22, 121], 'euler13': [1, 1, -5, 13, 169], 'euler17': [1, 10, 59, 170, 289], 'euler19': [1, -2, 19, -38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -2, 1, 0, 0], 'euler29': [1, 8, 69, 232, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 4, 21, 124, 961], 'euler37': [1, 6, 63, 222, 1369], 'euler41': [1, 16, 141, 656, 1681], 'euler43': [1, 3, 27, 129, 1849], 'euler47': [1, 6, 58, 282, 2209], 'euler5': [1, 5, 15, 25, 25], 'euler53': [1, -3, 107, -159, 2809], 'euler59': [1, 5, 123, 295, 3481], 'euler61': [1, -5, 27, -305, 3721], 'euler67': [1, -1, 73, -67, 4489], 'euler7': [1, -2, 1, 0, 0], 'euler71': [1, -7, 93, -497, 5041], 'euler73': [1, 10, 151, 730, 5329], 'euler79': [1, 8, 129, 632, 6241], 'euler83': [1, 4, 45, 332, 6889], 'euler89': [1, 31, 417, 2759, 7921], 'euler97': [1, 20, 289, 1940, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 1, 0, 0], [1, 5, 15, 25, 25], [1, -2, 1, 0, 0], [1, 2, 23, 22, 121], [1, 1, -5, 13, 169], [1, 10, 59, 170, 289], [1, -2, 19, -38, 361], [1, -2, 1, 0, 0], [1, 8, 69, 232, 841], [1, 4, 21, 124, 961], [1, 6, 63, 222, 1369], [1, 16, 141, 656, 1681], [1, 3, 27, 129, 1849], [1, 6, 58, 282, 2209], [1, -3, 107, -159, 2809], [1, 5, 123, 295, 3481], [1, -5, 27, -305, 3721], [1, -1, 73, -67, 4489], [1, -7, 93, -497, 5041], [1, 10, 151, 730, 5329], [1, 8, 129, 632, 6241], [1, 4, 45, 332, 6889], [1, 31, 417, 2759, 7921], [1, 20, 289, 1940, 9409]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1932/2/a/f'], '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': '4-1932e2-1.1-c1e2-0-8', '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': '4-1932e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.9277344195491857, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1744136107648713097, 'z1': {'__RealLiteral__': 0, 'data': '1.65579264777971620514258681787', 'prec': 103}}
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{'Lhash': '2098966543811446480284129390266,2299457854503320708601337827306', 'Lhash_array': ['2098966543811446480284129390266', '2299457854503320708601337827306'], 'label': '4-1932e2-1.1-c1e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1932/2/a/f'}