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lfunc_lfunctions • Show schema
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{'Lhash': '2787751907970887189957980587509,4426633043359181437330128086129', 'a10': -2, 'a2': 1, 'a3': 1, 'a4': 0, 'a5': -2, 'a6': 1, 'a7': 2, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.38792111500809284, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [3, [1, -1, 1]], [13, [1, -5, 13]]], 'bad_primes': [2, 3, 13], 'central_character': '78.1', 'coefficient_field': '1.1.1.1', 'conductor': 6084, 'conductor_radical': 78, 'degree': 4, 'euler_factors': [[1, -1, 1], [1, -1, 1], [1, 2, 11, 10, 25], [1, -2, -3, -14, 49], [1, 2, -7, 22, 121], [1, -5, 13], [1, 5, 8, 85, 289], [1, -2, -15, -38, 361], [1, 6, 13, 138, 529], [1, -9, 52, -261, 841], [1, 8, 78, 248, 961], [1, -11, 84, -407, 1369], [1, 5, -16, 205, 1681], [1, 10, 57, 430, 1849], [1, -4, 98, -188, 2209], [1, 2, 107, 106, 2809], [1, -8, 5, -472, 3481], [1, -11, 60, -671, 3721], [1, 2, -63, 134, 4489], [1, -14, 125, -994, 5041], [1, 26, 315, 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'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': 166219333667991443, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.19914849365351686454379623697', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.49199774966556626951947285055', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.06164971991764944799633028143', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.38792111500809284, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 6084, 'conductor_radical': 78, 'degree': 4, 'dirichlet_coefficients': [1, 1, 1, 0, -2, 1, 2, -1, 0, -2, -2, 0, 5, 2, -2, -1, -5, 0, 2, 0, 2, -2, -6, -1, -7, 5, -1, 0, 9, -2, -8, 0, -2, -5, -4, 0, 11, 2, 5, 2, -5, 2, -10, 0, 0, -6, 4, -1, 7, -7, -5, 0, -2, -1, 4, -2, 2, 9, 8, 0, 11, -8, 0, 1, -10, -2, -2, 0, -6, -4, 14, 0, -26, 11, -7, 0, -4, 5, -8, 2, -1, -5, 12, 0, 10, -10, 9, 2, -2, 0, 10, 0, -8, 4, -4, 0, 2, 7, 0, 0], 'euler11': [1, 2, -7, 22, 121], 'euler13': [1, -5, 13, 0, 0], 'euler17': [1, 5, 8, 85, 289], 'euler19': [1, -2, -15, -38, 361], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, 6, 13, 138, 529], 'euler29': [1, -9, 52, -261, 841], 'euler3': [1, -1, 1, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, -11, 84, -407, 1369], 'euler41': [1, 5, -16, 205, 1681], 'euler43': [1, 10, 57, 430, 1849], 'euler47': [1, -4, 98, -188, 2209], 'euler5': [1, 2, 11, 10, 25], 'euler53': [1, 2, 107, 106, 2809], 'euler59': [1, -8, 5, -472, 3481], 'euler61': [1, -11, 60, -671, 3721], 'euler67': [1, 2, -63, 134, 4489], 'euler7': [1, -2, -3, -14, 49], 'euler71': [1, -14, 125, -994, 5041], 'euler73': [1, 26, 315, 1898, 5329], 'euler79': [1, 8, 174, 632, 6241], 'euler83': [1, -12, 202, -996, 6889], 'euler89': [1, 2, -85, 178, 7921], 'euler97': [1, -2, -93, -194, 9409], 'euler_factors': [[1, -1, 1, 0, 0], [1, -1, 1, 0, 0], [1, 2, 11, 10, 25], [1, -2, -3, -14, 49], [1, 2, -7, 22, 121], [1, -5, 13, 0, 0], [1, 5, 8, 85, 289], [1, -2, -15, -38, 361], [1, 6, 13, 138, 529], [1, -9, 52, -261, 841], [1, 8, 78, 248, 961], [1, -11, 84, -407, 1369], [1, 5, -16, 205, 1681], [1, 10, 57, 430, 1849], [1, -4, 98, -188, 2209], [1, 2, 107, 106, 2809], [1, -8, 5, -472, 3481], [1, -11, 60, -671, 3721], [1, 2, -63, 134, 4489], [1, -14, 125, -994, 5041], [1, 26, 315, 1898, 5329], [1, 8, 174, 632, 6241], [1, -12, 202, -996, 6889], [1, 2, -85, 178, 7921], [1, -2, -93, -194, 9409]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/2/e/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': '4-78e2-1.1-c1e2-0-4', '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': '4-78e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 166219333667991443, 'z1': {'__RealLiteral__': 0, 'data': '2.19914849365351686454379623697', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2787751907970887189957980587509,4426633043359181437330128086129', 'Lhash_array': ['2787751907970887189957980587509', '4426633043359181437330128086129'], 'label': '4-78e2-1.1-c1e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/e/b'}