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lfunc_lfunctions • Show schema
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{'Lhash': '453239612612259242740577475083,1105384810712453688617522745517', 'a10': -4, 'a2': -2, 'a3': -2, 'a4': 3, 'a5': 2, 'a6': 4, 'a7': 0, 'a8': -4, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 931.3985971344308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [3, [1, 2, 1]], [7, [1]], [13, [1, 2, 1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '3822.1', 'coefficient_field': '1.1.1.1', 'conductor': 14607684, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1, 2, 1], [1, 2, 1], [1, -2, 4, -10, 25], [1], [1, 4, 19, 44, 121], [1, 2, 1], [1, -8, 43, -136, 289], [1, 10, 63, 190, 361], [1, 10, 64, 230, 529], [1, 2, 31, 58, 841], [1, -4, 38, -124, 961], [1, -6, 76, -222, 1369], [1, -10, 100, -410, 1681], [1, 0, 58, 0, 1849], [1, 6, 103, 282, 2209], [1, 6, 115, 318, 2809], [1, 0, 55, 0, 3481], [1, -8, 75, -488, 3721], [1, 6, 31, 402, 4489], [1, -22, 235, -1562, 5041], [1, -22, 260, -1606, 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'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1004363377169995383, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35754301108732754539049450301', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.871994862396183004263668419787', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.83280741425929237456236240185', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 931.3985971344308, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 14607684, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, -2, -2, 3, 2, 4, 0, -4, 3, -4, -4, -6, -2, 0, -4, 5, 8, -6, -10, 6, 0, 8, -10, 8, 0, 4, -4, 0, -2, 8, 4, -6, 8, -16, 0, 9, 6, 20, 4, -8, 10, 0, 0, -12, 6, 20, -6, -10, 0, 0, -16, -6, -6, 8, -8, 0, 20, 4, 0, -12, 8, -8, 0, 7, -4, -16, -6, 24, 20, 0, 22, -12, 22, -12, 0, -30, 0, -8, -20, 10, 5, -20, 16, 0, 16, 0, 4, 16, -18, -12, 0, -30, -8, 12, -20, 12, 14, 0, -12, 0], 'euler11': [1, 4, 19, 44, 121], 'euler13': [1, 2, 1, 0, 0], 'euler17': [1, -8, 43, -136, 289], 'euler19': [1, 10, 63, 190, 361], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, 10, 64, 230, 529], 'euler29': [1, 2, 31, 58, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -4, 38, -124, 961], 'euler37': [1, -6, 76, -222, 1369], 'euler41': [1, -10, 100, -410, 1681], 'euler43': [1, 0, 58, 0, 1849], 'euler47': [1, 6, 103, 282, 2209], 'euler5': [1, -2, 4, -10, 25], 'euler53': [1, 6, 115, 318, 2809], 'euler59': [1, 0, 55, 0, 3481], 'euler61': [1, -8, 75, -488, 3721], 'euler67': [1, 6, 31, 402, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, -22, 235, -1562, 5041], 'euler73': [1, -22, 260, -1606, 5329], 'euler79': [1, 20, 258, 1580, 6241], 'euler83': [1, -16, 202, -1328, 6889], 'euler89': [1, 18, 196, 1602, 7921], 'euler97': [1, -14, 180, -1358, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, 2, 1, 0, 0], [1, -2, 4, -10, 25], [1, 0, 0, 0, 0], [1, 4, 19, 44, 121], [1, 2, 1, 0, 0], [1, -8, 43, -136, 289], [1, 10, 63, 190, 361], [1, 10, 64, 230, 529], [1, 2, 31, 58, 841], [1, -4, 38, -124, 961], [1, -6, 76, -222, 1369], [1, -10, 100, -410, 1681], [1, 0, 58, 0, 1849], [1, 6, 103, 282, 2209], [1, 6, 115, 318, 2809], [1, 0, 55, 0, 3481], [1, -8, 75, -488, 3721], [1, 6, 31, 402, 4489], [1, -22, 235, -1562, 5041], [1, -22, 260, -1606, 5329], [1, 20, 258, 1580, 6241], [1, -16, 202, -1328, 6889], [1, 18, 196, 1602, 7921], [1, -14, 180, -1358, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3822/2/a/bi'], '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': '4-3822e2-1.1-c1e2-0-2', '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': '4-3822e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1004363377169995383, 'z1': {'__RealLiteral__': 0, 'data': '0.35754301108732754539049450301', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '453239612612259242740577475083,1105384810712453688617522745517', 'Lhash_array': ['453239612612259242740577475083', '1105384810712453688617522745517'], 'label': '4-3822e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3822/2/a/bi'}