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{'Lhash': '1688906320992151635658770612165,1710909880313182716358812520832,2175653455824673445627873447495', 'a10': -15, 'a2': -3, 'a3': 1, 'a4': 6, 'a5': 5, 'a6': -3, 'a7': -1, 'a8': -10, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 49492.36667621531, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 3, 3, 1]], [11, [1]], [19, [1, -3, 3, -1]]], 'bad_primes': [2, 11, 19], 'central_character': '4598.1', 'coefficient_field': '1.1.1.1', 'conductor': 97209095192, 'conductor_radical': 418, 'degree': 6, 'euler_factors': [[1, 3, 3, 1], [1, -1, 4, -2, 12, -9, 27], [1, -5, 18, -48, 90, -125, 125], [1, 1, 14, 18, 98, 49, 343], [1], [1, 5, 40, 116, 520, 845, 2197], [1, 4, 27, 48, 459, 1156, 4913], [1, -3, 3, -1], [1, -2, 41, -124, 943, -1058, 12167], [1, 7, 68, 320, 1972, 5887, 24389], [1, 3, 68, 110, 2108, 2883, 29791], [1, 14, 127, 908, 4699, 19166, 50653], [1, -3, 98, -268, 4018, -5043, 68921], [1, -5, 62, -162, 2666, 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'7.44487620750161314651211900116108', '7.903108339144659327807809891535896', '8.006620409487818135389735778530427', '8.177443340099812555899490115066864'], 'prelabel': '6-4598e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.059308116392888, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 238118782482632393, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33231216921135747237676385657', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.34966991693543028260195209770', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.71628795460907451386955005869', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 49492.36667621531, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 97209095192, 'conductor_radical': 418, 'degree': 6, 'dirichlet_coefficients': [1, -3, 1, 6, 5, -3, -1, -10, -3, -15, 0, 6, -5, 3, 5, 15, -4, 9, 3, 30, -1, 0, 2, -10, 7, 15, -5, -6, -7, -15, -3, -21, 0, 12, -5, -18, -14, -9, -5, -50, 3, 3, 5, 0, -15, -6, 0, 15, -13, -21, -4, -30, -16, 15, 0, 10, 3, 21, -12, 30, -6, 9, 3, 28, -25, 0, 1, -24, 2, 15, -3, 30, -4, 42, 7, 18, 0, 15, -2, 75, -3, -9, -7, -6, -20, -15, -7, 0, 16, 45, 5, 12, -3, 0, 15, -21, -14, 39, 0, 42], 'euler11': [1, 0, 0, 0, 0, 0, 0], 'euler13': [1, 5, 40, 116, 520, 845, 2197], 'euler17': [1, 4, 27, 48, 459, 1156, 4913], 'euler19': [1, -3, 3, -1, 0, 0, 0], 'euler2': [1, 3, 3, 1, 0, 0, 0], 'euler23': [1, -2, 41, -124, 943, -1058, 12167], 'euler29': [1, 7, 68, 320, 1972, 5887, 24389], 'euler3': [1, -1, 4, -2, 12, -9, 27], 'euler31': [1, 3, 68, 110, 2108, 2883, 29791], 'euler37': [1, 14, 127, 908, 4699, 19166, 50653], 'euler41': [1, -3, 98, -268, 4018, -5043, 68921], 'euler43': [1, -5, 62, -162, 2666, -9245, 79507], 'euler47': [1, 0, 89, 128, 4183, 0, 103823], 'euler5': [1, -5, 18, -48, 90, -125, 125], 'euler53': [1, 16, 223, 1752, 11819, 44944, 148877], 'euler59': [1, 12, 17, -376, 1003, 41772, 205379], 'euler61': [1, 6, 195, 740, 11895, 22326, 226981], 'euler67': [1, -1, 194, -138, 12998, -4489, 300763], 'euler7': [1, 1, 14, 18, 98, 49, 343], 'euler71': [1, 3, 182, 454, 12922, 15123, 357911], 'euler73': [1, 4, 83, 528, 6059, 21316, 389017], 'euler79': [1, 2, 121, 668, 9559, 12482, 493039], 'euler83': [1, 7, 106, 54, 8798, 48223, 571787], 'euler89': [1, -16, -13, 1576, -1157, -126736, 704969], 'euler97': [1, 14, 307, 2588, 29779, 131726, 912673], 'euler_factors': [[1, 3, 3, 1, 0, 0, 0], [1, -1, 4, -2, 12, -9, 27], [1, -5, 18, -48, 90, -125, 125], [1, 1, 14, 18, 98, 49, 343], [1, 0, 0, 0, 0, 0, 0], [1, 5, 40, 116, 520, 845, 2197], [1, 4, 27, 48, 459, 1156, 4913], [1, -3, 3, -1, 0, 0, 0], [1, -2, 41, -124, 943, -1058, 12167], [1, 7, 68, 320, 1972, 5887, 24389], [1, 3, 68, 110, 2108, 2883, 29791], [1, 14, 127, 908, 4699, 19166, 50653], [1, -3, 98, -268, 4018, -5043, 68921], [1, -5, 62, -162, 2666, -9245, 79507], [1, 0, 89, 128, 4183, 0, 103823], [1, 16, 223, 1752, 11819, 44944, 148877], [1, 12, 17, -376, 1003, 41772, 205379], [1, 6, 195, 740, 11895, 22326, 226981], [1, -1, 194, -138, 12998, -4489, 300763], [1, 3, 182, 454, 12922, 15123, 357911], [1, 4, 83, 528, 6059, 21316, 389017], [1, 2, 121, 668, 9559, 12482, 493039], [1, 7, 106, 54, 8798, 48223, 571787], [1, -16, -13, 1576, -1157, -126736, 704969], [1, 14, 307, 2588, 29779, 131726, 912673]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4598/2/a/bm'], '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': '6-4598e3-1.1-c1e3-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-4598e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.059308116392888, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 238118782482632393, 'z1': {'__RealLiteral__': 0, 'data': '1.33231216921135747237676385657', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1688906320992151635658770612165,1710909880313182716358812520832,2175653455824673445627873447495', 'Lhash_array': ['1688906320992151635658770612165', '1710909880313182716358812520832', '2175653455824673445627873447495'], 'label': '6-4598e3-1.1-c1e3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4598/2/a/bm'}