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lfunc_lfunctions • Show schema
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{'Lhash': '2483810217725925157399629698615,3472067615778810341012706001142', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2497129937801807, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1, 1]], [7, [1, -1, 7]]], 'bad_primes': [2, 5, 7], 'central_character': '140.1', 'coefficient_field': '1.1.1.1', 'conductor': 19600, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1], [1, -3, 6, -9, 9], [1, -1, 1], [1, -1, 7], [1, -2, -7, -22, 121], [1, 12, 62, 156, 169], [1, 2, -13, 34, 289], [1, 0, -19, 0, 361], [1, -9, 58, -207, 529], [1, -6, 67, -174, 841], [1, 2, -27, 62, 961], [1, 8, 27, 296, 1369], [1, -10, 107, -410, 1681], [1, -2, 87, -86, 1849], [1, 8, 17, 376, 2209], [1, 4, -37, 212, 2809], [1, -8, 5, -472, 3481], [1, 7, -12, 427, 3721], [1, -3, -58, -201, 4489], [1, -16, 206, -1136, 5041], [1, 14, 123, 1022, 5329], [1, 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'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1493831418037180751, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.95938077675247174214824466243', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.73897840237183253770951264479', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06969582227842589892302745920', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2497129937801807, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 19600, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 0, 3, 0, 1, 0, 1, 0, 3, 0, 2, 0, -12, 0, 3, 0, -2, 0, 0, 0, 3, 0, 9, 0, 0, 0, 0, 0, 6, 0, -2, 0, 6, 0, 1, 0, -8, 0, -36, 0, 10, 0, 2, 0, 3, 0, -8, 0, -6, 0, -6, 0, -4, 0, 2, 0, 0, 0, 8, 0, -7, 0, 3, 0, -12, 0, 3, 0, 27, 0, 16, 0, -14, 0, 0, 0, 2, 0, -4, 0, 0, 0, -2, 0, -2, 0, 18, 0, -13, 0, -12, 0, -6, 0, 0, 0, -20, 0, 6, 0], 'euler11': [1, -2, -7, -22, 121], 'euler13': [1, 12, 62, 156, 169], 'euler17': [1, 2, -13, 34, 289], 'euler19': [1, 0, -19, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -9, 58, -207, 529], 'euler29': [1, -6, 67, -174, 841], 'euler3': [1, -3, 6, -9, 9], 'euler31': [1, 2, -27, 62, 961], 'euler37': [1, 8, 27, 296, 1369], 'euler41': [1, -10, 107, -410, 1681], 'euler43': [1, -2, 87, -86, 1849], 'euler47': [1, 8, 17, 376, 2209], 'euler5': [1, -1, 1, 0, 0], 'euler53': [1, 4, -37, 212, 2809], 'euler59': [1, -8, 5, -472, 3481], 'euler61': [1, 7, -12, 427, 3721], 'euler67': [1, -3, -58, -201, 4489], 'euler7': [1, -1, 7, 0, 0], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, 14, 123, 1022, 5329], 'euler79': [1, 4, -63, 316, 6241], 'euler83': [1, 2, 167, 166, 6889], 'euler89': [1, 13, 80, 1157, 7921], 'euler97': [1, 20, 294, 1940, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -3, 6, -9, 9], [1, -1, 1, 0, 0], [1, -1, 7, 0, 0], [1, -2, -7, -22, 121], [1, 12, 62, 156, 169], [1, 2, -13, 34, 289], [1, 0, -19, 0, 361], [1, -9, 58, -207, 529], [1, -6, 67, -174, 841], [1, 2, -27, 62, 961], [1, 8, 27, 296, 1369], [1, -10, 107, -410, 1681], [1, -2, 87, -86, 1849], [1, 8, 17, 376, 2209], [1, 4, -37, 212, 2809], [1, -8, 5, -472, 3481], [1, 7, -12, 427, 3721], [1, -3, -58, -201, 4489], [1, -16, 206, -1136, 5041], [1, 14, 123, 1022, 5329], [1, 4, -63, 316, 6241], [1, 2, 167, 166, 6889], [1, 13, 80, 1157, 7921], [1, 20, 294, 1940, 9409]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/140/2/i/b'], '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': '4-140e2-1.1-c1e2-0-7', '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': '4-140e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.0573105637881077, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1493831418037180751, 'z1': {'__RealLiteral__': 0, 'data': '1.95938077675247174214824466243', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2483810217725925157399629698615,3472067615778810341012706001142', 'Lhash_array': ['2483810217725925157399629698615', '3472067615778810341012706001142'], 'label': '4-140e2-1.1-c1e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/140/2/i/b'}