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lfunc_lfunctions • Show schema
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{'Lhash': '1990972607956240888907830756954,2737469944039504274676626871753', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1992652640772627, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 2, 1]]], 'bad_primes': [2, 7], 'central_character': '224.1', 'coefficient_field': '1.1.1.1', 'conductor': 50176, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, -2, 2, -6, 9], [1, -2, 6, -10, 25], [1, 2, 1], [1, -4, 6, -44, 121], [1, -6, 30, -78, 169], [1, 0, 14, 0, 289], [1, 2, 34, 38, 361], [1, 8, 62, 184, 529], [1, 0, 38, 0, 841], [1, 4, 46, 124, 961], [1, 0, 54, 0, 1369], [1, 8, 78, 328, 1681], [1, 4, 70, 172, 1849], [1, 12, 110, 564, 2209], [1, 20, 206, 1060, 2809], [1, -14, 162, -826, 3481], [1, -18, 198, -1098, 3721], [1, 8, 150, 536, 4489], [1, 8, 78, 568, 5041], [1, -12, 102, -876, 5329], [1, 8, 94, 632, 6241], [1, 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['1.57060045378259883863154228778104', '2.15948301807031587246528686001402', '3.45664727824938054196263640485645', '3.48053718942393294634255816721724', '4.29668658677344589822753768805552', '5.23651453418504227026658067373822', '6.11868239118300673563659650682405', '6.36402485764266418077390521555085', '6.71752546290169180092862320997385', '7.62017593248943357078401779318853', '8.356816000659126457280838882807068', '8.524978190737606320675831669004439', '9.042883762049257040898170081216646', '9.572373527065341565451768546361134', '10.12554122039553452308402962481415', '10.13066451433255203489171863316473', '11.14940950384920267977657764595422', '11.47458123413300220597019137644520', '12.05972195931707119663777641651720', '12.69184392290246865848785566472929'], 'prelabel': '4-224e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3374038302908668, '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': 673948960568800778, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57060045378259883863154228778', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.15948301807031587246528686001', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.45664727824938054196263640486', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1992652640772627, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 50176, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, 2, 0, -2, 0, 2, 0, 4, 0, 6, 0, 4, 0, 0, 0, -2, 0, -4, 0, -8, 0, -2, 0, 6, 0, 0, 0, -4, 0, 8, 0, -4, 0, 0, 0, 12, 0, -8, 0, -4, 0, 4, 0, -12, 0, 3, 0, 0, 0, -20, 0, 8, 0, -4, 0, 14, 0, 18, 0, -4, 0, 12, 0, -8, 0, -16, 0, -8, 0, 12, 0, -4, 0, -8, 0, -8, 0, 11, 0, 14, 0, 0, 0, 0, 0, -12, 0, -12, 0, -8, 0, -4, 0, 16, 0, 8, 0], 'euler11': [1, -4, 6, -44, 121], 'euler13': [1, -6, 30, -78, 169], 'euler17': [1, 0, 14, 0, 289], 'euler19': [1, 2, 34, 38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 8, 62, 184, 529], 'euler29': [1, 0, 38, 0, 841], 'euler3': [1, -2, 2, -6, 9], 'euler31': [1, 4, 46, 124, 961], 'euler37': [1, 0, 54, 0, 1369], 'euler41': [1, 8, 78, 328, 1681], 'euler43': [1, 4, 70, 172, 1849], 'euler47': [1, 12, 110, 564, 2209], 'euler5': [1, -2, 6, -10, 25], 'euler53': [1, 20, 206, 1060, 2809], 'euler59': [1, -14, 162, -826, 3481], 'euler61': [1, -18, 198, -1098, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, 8, 78, 568, 5041], 'euler73': [1, -12, 102, -876, 5329], 'euler79': [1, 8, 94, 632, 6241], 'euler83': [1, -14, 210, -1162, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, -16, 238, -1552, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 2, -6, 9], [1, -2, 6, -10, 25], [1, 2, 1, 0, 0], [1, -4, 6, -44, 121], [1, -6, 30, -78, 169], [1, 0, 14, 0, 289], [1, 2, 34, 38, 361], [1, 8, 62, 184, 529], [1, 0, 38, 0, 841], [1, 4, 46, 124, 961], [1, 0, 54, 0, 1369], [1, 8, 78, 328, 1681], [1, 4, 70, 172, 1849], [1, 12, 110, 564, 2209], [1, 20, 206, 1060, 2809], [1, -14, 162, -826, 3481], [1, -18, 198, -1098, 3721], [1, 8, 150, 536, 4489], [1, 8, 78, 568, 5041], [1, -12, 102, -876, 5329], [1, 8, 94, 632, 6241], [1, -14, 210, -1162, 6889], [1, 12, 214, 1068, 7921], [1, -16, 238, -1552, 9409]], 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/224/2/a/d'], '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': '4-224e2-1.1-c1e2-0-14', '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': '4-224e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3374038302908668, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 673948960568800778, 'z1': {'__RealLiteral__': 0, 'data': '1.57060045378259883863154228778', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1990972607956240888907830756954,2737469944039504274676626871753', 'Lhash_array': ['1990972607956240888907830756954', '2737469944039504274676626871753'], 'label': '4-224e2-1.1-c1e2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/224/2/a/d'}