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{'Lhash': '1687319630395736584374998922770,2389457104567973298649699098775,2402296382581682748024857918831,2693544356730857712287613850123', 'a10': 4, 'a2': 1, 'a3': 1, 'a4': -2, 'a5': 4, 'a6': 1, 'a7': -11, 'a8': -1, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43153.62199339725, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, -4, 6, -4, 1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '1805.1', 'coefficient_field': '1.1.1.1', 'conductor': 10614726900625, 'conductor_radical': 95, 'degree': 8, 'euler_factors': [[1, -1, 3, -4, 8, -8, 12, -8, 16], [1, -1, 4, 2, 7, 6, 36, -27, 81], [1, -4, 6, -4, 1], [1, 11, 68, 284, 873, 1988, 3332, 3773, 2401], [1, 0, 35, -10, 527, -110, 4235, 0, 14641], [1, 2, 20, 100, 253, 1300, 3380, 4394, 28561], [1, 7, 43, 101, 448, 1717, 12427, 34391, 83521], [1], [1, 11, 94, 478, 2557, 10994, 49726, 133837, 279841], [1, 15, 165, 1255, 7772, 36395, 138765, 365835, 707281], [1, 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'6.83046747953375593739316353040469', '6.84554802373447528433998608220240', '7.50522270546496593451649728009730', '7.62295373388420760953512645529133', '7.81763782162645497217339050140069', '8.019298720659268070585920877513595', '8.189230799826952465039978745125463', '8.425522885301920951853493430878208', '8.978258552152199066108734871589823', '8.997441775051851374421843156592593', '9.114036470987235002310880227192909', '9.114956210668691486951519915612581'], 'prelabel': '8-1805e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.7964453854679796, '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': 1446804386403023538, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33106049103116382791208280700', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.88494929449626927902308617843', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.89507769897254834967821868741', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 43153.62199339725, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 10614726900625, 'conductor_radical': 95, 'degree': 8, 'dirichlet_coefficients': [1, 1, 1, -2, 4, 1, -11, -1, -3, 4, 0, -2, -2, -11, 4, 1, -7, -3, 0, -8, -11, 0, -11, -1, 10, -2, -9, 22, -15, 4, -1, -4, 0, -7, -44, 6, -11, 0, -2, -4, 22, -11, -26, 0, -12, -11, -26, 1, 53, 10, -7, 4, -16, -9, 0, 11, 0, -15, -10, -8, 2, -1, 33, 1, -8, 0, 3, 14, -11, -44, 18, 3, -24, -11, 10, 0, 0, -2, 30, 4, -6, 22, -12, 22, -28, -26, -15, 0, 9, -12, 22, 22, -1, -26, 0, -4, 19, 53, 0, -20], 'euler11': [1, 0, 35, -10, 527, -110, 4235, 0, 14641], 'euler13': [1, 2, 20, 100, 253, 1300, 3380, 4394, 28561], 'euler17': [1, 7, 43, 101, 448, 1717, 12427, 34391, 83521], 'euler19': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler2': [1, -1, 3, -4, 8, -8, 12, -8, 16], 'euler23': [1, 11, 94, 478, 2557, 10994, 49726, 133837, 279841], 'euler29': [1, 15, 165, 1255, 7772, 36395, 138765, 365835, 707281], 'euler3': [1, -1, 4, 2, 7, 6, 36, -27, 81], 'euler31': [1, 1, 64, 96, 2705, 2976, 61504, 29791, 923521], 'euler37': [1, 11, 178, 1204, 10333, 44548, 243682, 557183, 1874161], 'euler41': [1, -22, 264, -2100, 14225, -86100, 443784, -1516262, 2825761], 'euler43': [1, 26, 397, 4042, 30823, 173806, 734053, 2067182, 3418801], 'euler47': [1, 26, 388, 3904, 30373, 183488, 857092, 2699398, 4879681], 'euler5': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler53': [1, 16, 237, 2012, 17613, 106636, 665733, 2382032, 7890481], 'euler59': [1, 10, 195, 1420, 16877, 83780, 678795, 2053790, 12117361], 'euler61': [1, -2, 113, 566, 4600, 34526, 420473, -453962, 13845841], 'euler67': [1, -3, 158, -524, 14583, -35108, 709262, -902289, 20151121], 'euler7': [1, 11, 68, 284, 873, 1988, 3332, 3773, 2401], 'euler71': [1, -18, 384, -4000, 44465, -284000, 1935744, -6442398, 25411681], 'euler73': [1, 24, 442, 5168, 51803, 377264, 2355418, 9336408, 28398241], 'euler79': [1, -30, 637, -8570, 90548, -677030, 3975517, -14791170, 38950081], 'euler83': [1, 12, 327, 2692, 40508, 223436, 2252703, 6861444, 47458321], 'euler89': [1, -9, 356, -2390, 47525, -212710, 2819876, -6344721, 62742241], 'euler97': [1, -19, 340, -4300, 46303, -417100, 3199060, -17340787, 88529281], 'euler_factors': [[1, -1, 3, -4, 8, -8, 12, -8, 16], [1, -1, 4, 2, 7, 6, 36, -27, 81], [1, -4, 6, -4, 1, 0, 0, 0, 0], [1, 11, 68, 284, 873, 1988, 3332, 3773, 2401], [1, 0, 35, -10, 527, -110, 4235, 0, 14641], [1, 2, 20, 100, 253, 1300, 3380, 4394, 28561], [1, 7, 43, 101, 448, 1717, 12427, 34391, 83521], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 11, 94, 478, 2557, 10994, 49726, 133837, 279841], [1, 15, 165, 1255, 7772, 36395, 138765, 365835, 707281], [1, 1, 64, 96, 2705, 2976, 61504, 29791, 923521], [1, 11, 178, 1204, 10333, 44548, 243682, 557183, 1874161], [1, -22, 264, -2100, 14225, -86100, 443784, -1516262, 2825761], [1, 26, 397, 4042, 30823, 173806, 734053, 2067182, 3418801], [1, 26, 388, 3904, 30373, 183488, 857092, 2699398, 4879681], [1, 16, 237, 2012, 17613, 106636, 665733, 2382032, 7890481], [1, 10, 195, 1420, 16877, 83780, 678795, 2053790, 12117361], [1, -2, 113, 566, 4600, 34526, 420473, -453962, 13845841], [1, -3, 158, -524, 14583, -35108, 709262, -902289, 20151121], [1, -18, 384, -4000, 44465, -284000, 1935744, -6442398, 25411681], [1, 24, 442, 5168, 51803, 377264, 2355418, 9336408, 28398241], [1, -30, 637, -8570, 90548, -677030, 3975517, -14791170, 38950081], [1, 12, 327, 2692, 40508, 223436, 2252703, 6861444, 47458321], [1, -9, 356, -2390, 47525, -212710, 2819876, -6344721, 62742241], [1, -19, 340, -4300, 46303, -417100, 3199060, -17340787, 88529281]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1805/2/a/n'], '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': '8-1805e4-1.1-c1e4-0-7', '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': '8-1805e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1446804386403023538, 'z1': {'__RealLiteral__': 0, 'data': '1.33106049103116382791208280700', 'prec': 103}}
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lfunc_instances • Show schema
Hide schema
{'Lhash': '1687319630395736584374998922770,2389457104567973298649699098775,2402296382581682748024857918831,2693544356730857712287613850123', 'Lhash_array': ['1687319630395736584374998922770', '2389457104567973298649699098775', '2402296382581682748024857918831', '2693544356730857712287613850123'], 'label': '8-1805e4-1.1-c1e4-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1805/2/a/n'}