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{'Lhash': '1659751690610483976966447760019,2315811636129081040726776639276,2584044541484474758602801041528,2706688703536928604829286564158', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8888.791674288273, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [19, [1, 4, 6, 4, 1]]], 'bad_primes': [2, 19], 'central_character': '1216.1', 'coefficient_field': '1.1.1.1', 'conductor': 2186423566336, 'conductor_radical': 38, 'degree': 8, 'euler_factors': [[1], [1, 2, 5, 10, 28, 30, 45, 54, 81], [1, 1, 2, -9, 2, -45, 50, 125, 625], [1, 1, 11, 40, 60, 280, 539, 343, 2401], [1, 7, 44, 203, 742, 2233, 5324, 9317, 14641], [1, 10, 59, 232, 852, 3016, 9971, 21970, 28561], [1, -5, 17, -114, 698, -1938, 4913, -24565, 83521], [1, 4, 6, 4, 1], [1, 8, 75, 420, 2456, 9660, 39675, 97336, 279841], [1, 10, 123, 712, 5108, 20648, 103443, 243890, 707281], [1, 6, 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'prelabel': '8-1216e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.11605662429098, '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': 2120541621010627299, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30931322109709111023474293258', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82685326359813927730044409360', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.03845171612685715089886826272', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 8888.791674288273, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 2186423566336, 'conductor_radical': 38, 'degree': 8, 'dirichlet_coefficients': [1, 0, -2, 0, -1, 0, -1, 0, -1, 0, -7, 0, -10, 0, 2, 0, 5, 0, -4, 0, 2, 0, -8, 0, -1, 0, 2, 0, -10, 0, -6, 0, 14, 0, 1, 0, -14, 0, 20, 0, -2, 0, -3, 0, 1, 0, -3, 0, -10, 0, -10, 0, -4, 0, 7, 0, 8, 0, -20, 0, 3, 0, 1, 0, 10, 0, -8, 0, 16, 0, -30, 0, 9, 0, 2, 0, 7, 0, 10, 0, -7, 0, -4, 0, -5, 0, 20, 0, -16, 0, 10, 0, 12, 0, 4, 0, -6, 0, 7, 0], 'euler11': [1, 7, 44, 203, 742, 2233, 5324, 9317, 14641], 'euler13': [1, 10, 59, 232, 852, 3016, 9971, 21970, 28561], 'euler17': [1, -5, 17, -114, 698, -1938, 4913, -24565, 83521], 'euler19': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 8, 75, 420, 2456, 9660, 39675, 97336, 279841], 'euler29': [1, 10, 123, 712, 5108, 20648, 103443, 243890, 707281], 'euler3': [1, 2, 5, 10, 28, 30, 45, 54, 81], 'euler31': [1, 6, 68, 142, 1782, 4402, 65348, 178746, 923521], 'euler37': [1, 14, 152, 1018, 7006, 37666, 208088, 709142, 1874161], 'euler41': [1, 2, 92, 54, 4694, 2214, 154652, 137842, 2825761], 'euler43': [1, 3, 140, 291, 8278, 12513, 258860, 238521, 3418801], 'euler47': [1, 3, 80, 247, 3038, 11609, 176720, 311469, 4879681], 'euler5': [1, 1, 2, -9, 2, -45, 50, 125, 625], 'euler53': [1, 4, 143, 252, 9032, 13356, 401687, 595508, 7890481], 'euler59': [1, 20, 321, 3390, 30764, 200010, 1117401, 4107580, 12117361], 'euler61': [1, -3, 178, -521, 14618, -31781, 662338, -680943, 13845841], 'euler67': [1, 8, 193, 1006, 16060, 67402, 866377, 2406104, 20151121], 'euler7': [1, 1, 11, 40, 60, 280, 539, 343, 2401], 'euler71': [1, 30, 552, 6814, 65870, 483794, 2782632, 10737330, 25411681], 'euler73': [1, -9, 245, -1662, 25114, -121326, 1305605, -3501153, 28398241], 'euler79': [1, -10, 216, -1082, 18510, -85478, 1348056, -4930390, 38950081], 'euler83': [1, 4, 216, 212, 21054, 17596, 1488024, 2287148, 47458321], 'euler89': [1, 16, 152, 224, -4082, 19936, 1203992, 11279504, 62742241], 'euler97': [1, 6, 328, 1658, 45422, 160826, 3086152, 5476038, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 5, 10, 28, 30, 45, 54, 81], [1, 1, 2, -9, 2, -45, 50, 125, 625], [1, 1, 11, 40, 60, 280, 539, 343, 2401], [1, 7, 44, 203, 742, 2233, 5324, 9317, 14641], [1, 10, 59, 232, 852, 3016, 9971, 21970, 28561], [1, -5, 17, -114, 698, -1938, 4913, -24565, 83521], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, 8, 75, 420, 2456, 9660, 39675, 97336, 279841], [1, 10, 123, 712, 5108, 20648, 103443, 243890, 707281], [1, 6, 68, 142, 1782, 4402, 65348, 178746, 923521], [1, 14, 152, 1018, 7006, 37666, 208088, 709142, 1874161], [1, 2, 92, 54, 4694, 2214, 154652, 137842, 2825761], [1, 3, 140, 291, 8278, 12513, 258860, 238521, 3418801], [1, 3, 80, 247, 3038, 11609, 176720, 311469, 4879681], [1, 4, 143, 252, 9032, 13356, 401687, 595508, 7890481], [1, 20, 321, 3390, 30764, 200010, 1117401, 4107580, 12117361], [1, -3, 178, -521, 14618, -31781, 662338, -680943, 13845841], [1, 8, 193, 1006, 16060, 67402, 866377, 2406104, 20151121], [1, 30, 552, 6814, 65870, 483794, 2782632, 10737330, 25411681], [1, -9, 245, -1662, 25114, -121326, 1305605, -3501153, 28398241], [1, -10, 216, -1082, 18510, -85478, 1348056, -4930390, 38950081], [1, 4, 216, 212, 21054, 17596, 1488024, 2287148, 47458321], [1, 16, 152, 224, -4082, 19936, 1203992, 11279504, 62742241], [1, 6, 328, 1658, 45422, 160826, 3086152, 5476038, 88529281]], 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1216/2/a/w'], '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': '8-1216e4-1.1-c1e4-0-19', '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': '8-1216e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.11605662429098, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 2120541621010627299, 'z1': {'__RealLiteral__': 0, 'data': '1.30931322109709111023474293258', 'prec': 103}}
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{'Lhash': '1659751690610483976966447760019,2315811636129081040726776639276,2584044541484474758602801041528,2706688703536928604829286564158', 'Lhash_array': ['1659751690610483976966447760019', '2315811636129081040726776639276', '2584044541484474758602801041528', '2706688703536928604829286564158'], 'label': '8-1216e4-1.1-c1e4-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/2/a/w'}