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lfunc_lfunctions • Show schema
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{'Lhash': '3386688229064177016167839435382,4840779081222967821363990023867', 'a10': 1, 'a2': -1, 'a3': 0, 'a4': 2, 'a5': -1, 'a6': 0, 'a7': -2, 'a8': -5, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.08728862696352384, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[37, [1, 11, 37]]], 'bad_primes': [37], 'central_character': '37.1', 'coefficient_field': '1.1.1.1', 'conductor': 1369, 'conductor_radical': 37, 'degree': 4, 'euler_factors': [[1, 1, -1, 2, 4], [1, 0, -3, 0, 9], [1, 1, -4, 5, 25], [1, 2, -3, 14, 49], [1, 4, 26, 44, 121], [1, -2, -9, -26, 169], [1, 3, -8, 51, 289], [1, -6, 17, -114, 361], [1, 8, 62, 184, 529], [1, -18, 139, -522, 841], [1, 20, 162, 620, 961], [1, 11, 37], [1, -9, 40, -369, 1681], [1, -4, 90, -172, 1849], [1, -12, 130, -564, 2209], [1, -2, -49, -106, 2809], [1, -4, -43, -236, 3481], [1, 1, -60, 61, 3721], [1, -10, 33, -670, 4489], [1, 6, -35, 426, 5041], [1, 20, 246, 1460, 5329], [1, 10, 21, 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['2.67162594208091206392648495768560', '3.81870136798848822668749225625812', '5.42454872665064942861452531044172', '6.27178619007762406330651043689316', '7.18371500213717680724324414888897', '7.51862835549577123370251104304326', '8.778829562106292447356049750462251', '8.997337969576225080178847698983381', '10.23218905869563274534139853983770', '10.32278704395388493881457457092726', '11.18579217816029458093362187139971', '11.98519994974156085879271117346987', '12.50740797366944525930206561141473', '12.86305075480989267822374846899174', '13.88291242818527276459679165744530', '14.45606531955039221100997664344703', '15.49686103420560485601506520233859', '15.89959470749858249320840417770490', '15.92126559659218090507148212753572', '16.30070774625329966321574399971598'], 'prelabel': '4-37e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5435498941943946, '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': 1518673186804419011, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.67162594208091206392648495769', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.81870136798848822668749225626', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.42454872665064942861452531044', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.08728862696352384, 'bad_primes': [37], 'central_character': '1.1', 'conductor': 1369, 'conductor_radical': 37, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 2, -1, 0, -2, -5, 3, 1, -4, 0, 2, 2, 0, 5, -3, -3, 6, -2, 0, 4, -8, 0, 5, -2, 0, -4, 18, 0, -20, -10, 0, 3, 2, 6, -11, -6, 0, 5, 9, 0, 4, -8, -3, 8, 12, 0, 7, -5, 0, 4, 2, 0, 4, 10, 0, -18, 4, 0, -1, 20, -6, 17, -2, 0, 10, -6, 0, -2, -6, -15, -20, 11, 0, 12, 8, 0, -10, -5, 0, -9, 12, 0, 3, -4, 0, 20, -7, 3, -4, -16, 0, -12, -6, 0, 14, -7, -12, 10], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, -2, -9, -26, 169], 'euler17': [1, 3, -8, 51, 289], 'euler19': [1, -6, 17, -114, 361], 'euler2': [1, 1, -1, 2, 4], 'euler23': [1, 8, 62, 184, 529], 'euler29': [1, -18, 139, -522, 841], 'euler3': [1, 0, -3, 0, 9], 'euler31': [1, 20, 162, 620, 961], 'euler37': [1, 11, 37, 0, 0], 'euler41': [1, -9, 40, -369, 1681], 'euler43': [1, -4, 90, -172, 1849], 'euler47': [1, -12, 130, -564, 2209], 'euler5': [1, 1, -4, 5, 25], 'euler53': [1, -2, -49, -106, 2809], 'euler59': [1, -4, -43, -236, 3481], 'euler61': [1, 1, -60, 61, 3721], 'euler67': [1, -10, 33, -670, 4489], 'euler7': [1, 2, -3, 14, 49], 'euler71': [1, 6, -35, 426, 5041], 'euler73': [1, 20, 246, 1460, 5329], 'euler79': [1, 10, 21, 790, 6241], 'euler83': [1, -12, 61, -996, 6889], 'euler89': [1, 7, -40, 623, 7921], 'euler97': [1, -14, 243, -1358, 9409], 'euler_factors': [[1, 1, -1, 2, 4], [1, 0, -3, 0, 9], [1, 1, -4, 5, 25], [1, 2, -3, 14, 49], [1, 4, 26, 44, 121], [1, -2, -9, -26, 169], [1, 3, -8, 51, 289], [1, -6, 17, -114, 361], [1, 8, 62, 184, 529], [1, -18, 139, -522, 841], [1, 20, 162, 620, 961], [1, 11, 37, 0, 0], [1, -9, 40, -369, 1681], [1, -4, 90, -172, 1849], [1, -12, 130, -564, 2209], [1, -2, -49, -106, 2809], [1, -4, -43, -236, 3481], [1, 1, -60, 61, 3721], [1, -10, 33, -670, 4489], [1, 6, -35, 426, 5041], [1, 20, 246, 1460, 5329], [1, 10, 21, 790, 6241], [1, -12, 61, -996, 6889], [1, 7, -40, 623, 7921], [1, -14, 243, -1358, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/37/2/c/a'], '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': '4-37e2-1.1-c1e2-0-1', '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': '4-37e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5435498941943946, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1518673186804419011, 'z1': {'__RealLiteral__': 0, 'data': '2.67162594208091206392648495769', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3386688229064177016167839435382,4840779081222967821363990023867', 'Lhash_array': ['3386688229064177016167839435382', '4840779081222967821363990023867'], 'label': '4-37e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/37/2/c/a'}