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lfunc_lfunctions • Show schema
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{'Lhash': '145489991133180834887118195923,3301732962266724602252627002621', 'a10': 2340, 'a2': -6, 'a3': 27, 'a4': 128, 'a5': -390, 'a6': -162, 'a7': 0, 'a8': -2088, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2108.7013892063746, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -27, 729]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '147.1', 'coefficient_field': '1.1.1.1', 'conductor': 21609, 'conductor_radical': 21, 'degree': 4, 'euler_factors': [[1, 6, -92, 768, 16384], [1, -27, 729], [1, 390, 73975, 30468750, 6103515625], [1], [1, -948, -18588467, -18473838108, 379749833583241], [1, 10196, 151486638, 639783879332, 3937376385699289], [1, 28386, 395426323, 11647873571778, 168377826559400929], [1, -8620, -819567339, -7705174390180, 799006685782884121], [1, -15288, -3171102503, -52052971433736, 11592836324538749809], [1, -73020, 35832732718, -1259585968083180, 297558232675799463481], [1, -276808, 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'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7e2-0', 'trace_hash': 494381502365336998, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.11477136610591801454738830990', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.13688477795705688288287603548', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.28500547319412939676208910363', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 2108.7013892063746, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 21609, 'conductor_radical': 21, 'degree': 4, 'dirichlet_coefficients': [1, -6, 27, 128, -390, -162, 0, -2088, 0, 2340, 948, 3456, -10196, 0, -10530, 12528, -28386, 0, 8620, -49920, 0, -5688, 15288, -56376, 78125, 61176, -19683, 0, 73020, 63180, 276808, -267264, 25596, 170316, 0, 0, -268526, -51720, -275292, 814320, -1259436, 0, 1371544, 121344, 0, -91728, -583296, 338256, 0, -468750, -766422, -1305088, 428058, 118098, -369720, 0, 232740, -438120, -1306380, -1347840, -300662, -1660848, 0, 2262592, 3976440, -153576, 507244, -3633408, 412776, 0, 11121264, 0, -1369082, 1611156, 2109375, 1103360, 0, 1651752, 6913720, -4885920, -531441, 7556616, -8753496, 0, 11070540, -8229264, 1971540, -1979424, 8528310, 0, 0, 1956864, 7473816, 3499776, -3361800, -7216128, -17653628, 0, 0, 10000000], 'euler11': [1, -948, -18588467, -18473838108, 379749833583241], 'euler13': [1, 10196, 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3251124526737845220, 6193386212891813387462761], 'euler61': [1, 300662, -3052345197777, 944903346563745902, 9876832533361318095112441], 'euler67': [1, -507244, -5803415129787, -3074259597530459812, 36732225162896895721934329], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, -11121264, 49110868556206, -101149232393188126224, 82721210695570328927708881], 'euler73': [1, 1369082, -9173012996373, 15124794459322358954, 122045014039746588673695409], 'euler79': [1, -6913720, 28595615252241, -132770449635787201480, 368790120348678391253573281], 'euler83': [1, 8753496, 73428025034758, 237535313793495985992, 736365263311636486061599129], 'euler89': [1, -8528310, 28500736560571, -377218535702888925990, 1956410986640441413344189841], 'euler97': [1, 17653628, 239509214346822, 1426382857214781043964, 6528362774606076144776040769], 'euler_factors': [[1, 6, -92, 768, 16384], [1, -27, 729, 0, 0], [1, 390, 73975, 30468750, 6103515625], [1, 0, 0, 0, 0], [1, -948, -18588467, -18473838108, 379749833583241], [1, 10196, 151486638, 639783879332, 3937376385699289], [1, 28386, 395426323, 11647873571778, 168377826559400929], [1, -8620, -819567339, -7705174390180, 799006685782884121], [1, -15288, -3171102503, -52052971433736, 11592836324538749809], [1, -73020, 35832732718, -1259585968083180, 297558232675799463481], [1, -276808, 49110054753, -7615711686837688, 756943935220796320321], [1, 268526, -22825664457, 25491677239015958, 9012061295995008299689], [1, 1259436, 786053307286, 245280543679591116, 37929227194915558802161], [1, -1371544, 1013920458198, -372811185152139208, 73885357344138503765449], [1, 583296, -166388896847, 295511239673586048, 256666986187667409334369], [1, -428058, -991477488473, -502844501096346546, 1379946262057143768386569], [1, 1306380, -782022780419, 3251124526737845220, 6193386212891813387462761], [1, 300662, -3052345197777, 944903346563745902, 9876832533361318095112441], [1, -507244, -5803415129787, -3074259597530459812, 36732225162896895721934329], [1, -11121264, 49110868556206, -101149232393188126224, 82721210695570328927708881], [1, 1369082, -9173012996373, 15124794459322358954, 122045014039746588673695409], [1, -6913720, 28595615252241, -132770449635787201480, 368790120348678391253573281], [1, 8753496, 73428025034758, 237535313793495985992, 736365263311636486061599129], [1, -8528310, 28500736560571, -377218535702888925990, 1956410986640441413344189841], [1, 17653628, 239509214346822, 1426382857214781043964, 6528362774606076144776040769]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/8/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': '4-147e2-1.1-c7e2-0-0', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7, 7], 'order_of_vanishing': 0, 'prelabel': '4-147e2-1.1-c7e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.776473916880808, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7e2-0', 'trace_hash': 494381502365336998, 'z1': {'__RealLiteral__': 0, 'data': '0.11477136610591801454738830990', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '145489991133180834887118195923,3301732962266724602252627002621', 'Lhash_array': ['145489991133180834887118195923', '3301732962266724602252627002621'], 'label': '4-147e2-1.1-c7e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/8/e/b'}