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{'Lhash': '1468406581489063407974951704383,1852678431179917622314500740289,2000223301583858605905547054138,2448780589889174307379676688648', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': -5, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 508362.49571583833, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [11, [1, 4, 6, 4, 1]], [19, [1, 4, 6, 4, 1]]], 'bad_primes': [2, 11, 19], 'central_character': '3344.1', 'coefficient_field': '1.1.1.1', 'conductor': 125044638416896, 'conductor_radical': 418, 'degree': 8, 'euler_factors': [[1], [1, -1, 6, -2, 19, -6, 54, -27, 81], [1, 3, 16, 36, 115, 180, 400, 375, 625], [1, -3, 25, -59, 254, -413, 1225, -1029, 2401], [1, 4, 6, 4, 1], [1, 5, 29, 91, 322, 1183, 4901, 10985, 28561], [1, 0, 30, 36, 642, 612, 8670, 0, 83521], [1, 4, 6, 4, 1], [1, -8, 85, -382, 2536, -8786, 44965, -97336, 279841], [1, 1, 101, 51, 4154, 1479, 84941, 24389, 707281], [1, -7, 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'8.267559542522712190957252471006965', '8.268908911698127851980396541867661'], 'prelabel': '8-3344e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.167395324137313, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 1740478370679770895, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15836854510595399727086704546', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.46150558430403383828690775447', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.57789796433160359635634521321', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 508362.49571583833, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 125044638416896, 'conductor_radical': 418, 'degree': 8, 'dirichlet_coefficients': [1, 0, 1, 0, -3, 0, 3, 0, -5, 0, -4, 0, -5, 0, -3, 0, 0, 0, -4, 0, 3, 0, 8, 0, -7, 0, -9, 0, -1, 0, 7, 0, -4, 0, -9, 0, -16, 0, -5, 0, -7, 0, -5, 0, 15, 0, 4, 0, -16, 0, 0, 0, -18, 0, 12, 0, -4, 0, 0, 0, -6, 0, -15, 0, 15, 0, -1, 0, 8, 0, 1, 0, -6, 0, -7, 0, -12, 0, 4, 0, 4, 0, 25, 0, 0, 0, -1, 0, -14, 0, -15, 0, 7, 0, 12, 0, -36, 0, 20, 0], 'euler11': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler13': [1, 5, 29, 91, 322, 1183, 4901, 10985, 28561], 'euler17': [1, 0, 30, 36, 642, 612, 8670, 0, 83521], 'euler19': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -8, 85, -382, 2536, -8786, 44965, -97336, 279841], 'euler29': [1, 1, 101, 51, 4154, 1479, 84941, 24389, 707281], 'euler3': [1, -1, 6, -2, 19, -6, 54, -27, 81], 'euler31': [1, -7, 118, -650, 5395, -20150, 113398, -208537, 923521], 'euler37': [1, 16, 221, 1896, 13680, 70152, 302549, 810448, 1874161], 'euler41': [1, 7, 99, 381, 4244, 15621, 166419, 482447, 2825761], 'euler43': [1, 5, 153, 637, 9464, 27391, 282897, 397535, 3418801], 'euler47': [1, -4, 76, -356, 4822, -16732, 167884, -415292, 4879681], 'euler5': [1, 3, 16, 36, 115, 180, 400, 375, 625], 'euler53': [1, 18, 304, 2958, 26542, 156774, 853936, 2679786, 7890481], 'euler59': [1, 0, 213, -48, 18156, -2832, 741453, 0, 12117361], 'euler61': [1, 6, 106, 746, 10106, 45506, 394426, 1361886, 13845841], 'euler67': [1, 1, 188, -34, 16225, -2278, 843932, 300763, 20151121], 'euler7': [1, -3, 25, -59, 254, -413, 1225, -1029, 2401], 'euler71': [1, -1, 48, -306, -2731, -21726, 241968, -357911, 25411681], 'euler73': [1, 6, 176, 1186, 15006, 86578, 937904, 2334102, 28398241], 'euler79': [1, -4, 238, -680, 24922, -53720, 1485358, -1972156, 38950081], 'euler83': [1, -25, 433, -5021, 50710, -416743, 2982937, -14294675, 47458321], 'euler89': [1, 14, 341, 3364, 45484, 299396, 2701061, 9869566, 62742241], 'euler97': [1, 36, 841, 12772, 148064, 1238884, 7912969, 32856228, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 6, -2, 19, -6, 54, -27, 81], [1, 3, 16, 36, 115, 180, 400, 375, 625], [1, -3, 25, -59, 254, -413, 1225, -1029, 2401], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, 5, 29, 91, 322, 1183, 4901, 10985, 28561], [1, 0, 30, 36, 642, 612, 8670, 0, 83521], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, -8, 85, -382, 2536, -8786, 44965, -97336, 279841], [1, 1, 101, 51, 4154, 1479, 84941, 24389, 707281], [1, -7, 118, -650, 5395, -20150, 113398, -208537, 923521], [1, 16, 221, 1896, 13680, 70152, 302549, 810448, 1874161], [1, 7, 99, 381, 4244, 15621, 166419, 482447, 2825761], [1, 5, 153, 637, 9464, 27391, 282897, 397535, 3418801], [1, -4, 76, -356, 4822, -16732, 167884, -415292, 4879681], [1, 18, 304, 2958, 26542, 156774, 853936, 2679786, 7890481], [1, 0, 213, -48, 18156, -2832, 741453, 0, 12117361], [1, 6, 106, 746, 10106, 45506, 394426, 1361886, 13845841], [1, 1, 188, -34, 16225, -2278, 843932, 300763, 20151121], [1, -1, 48, -306, -2731, -21726, 241968, -357911, 25411681], [1, 6, 176, 1186, 15006, 86578, 937904, 2334102, 28398241], [1, -4, 238, -680, 24922, -53720, 1485358, -1972156, 38950081], [1, -25, 433, -5021, 50710, -416743, 2982937, -14294675, 47458321], [1, 14, 341, 3364, 45484, 299396, 2701061, 9869566, 62742241], [1, 36, 841, 12772, 148064, 1238884, 7912969, 32856228, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3344/2/a/s'], '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': '8-3344e4-1.1-c1e4-0-0', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 4, 'prelabel': '8-3344e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.167395324137313, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1740478370679770895, 'z1': {'__RealLiteral__': 0, 'data': '1.15836854510595399727086704546', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1468406581489063407974951704383,1852678431179917622314500740289,2000223301583858605905547054138,2448780589889174307379676688648', 'Lhash_array': ['1468406581489063407974951704383', '1852678431179917622314500740289', '2000223301583858605905547054138', '2448780589889174307379676688648'], 'label': '8-3344e4-1.1-c1e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3344/2/a/s'}