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{'Lhash': '3079616103015734576571392539296,3646961396320455590015911318039', 'a10': 2480, 'a2': 16, 'a3': -69, 'a4': 192, 'a5': 155, 'a6': -1104, 'a7': -2238, 'a8': 2048, 'a9': 621, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 140.91187958785713, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -16, 64]], [19, [1, 13718, 47045881]]], 'bad_primes': [2, 19], 'central_character': '38.1', 'coefficient_field': '1.1.1.1', 'conductor': 1444, 'conductor_radical': 38, 'degree': 4, 'euler_factors': [[1, -16, 64], [1, 69, 4140, 150903, 4782969], [1, -155, 10178, -12109375, 6103515625], [1, 2238, 2775179, 1843089234, 678223072849], [1, 3295, 38080340, 64210228445, 379749833583241], [1, 13427, 138664758, 842524337759, 3937376385699289], [1, 32256, 1073810905, 13235884236288, 168377826559400929], [1, 13718, 47045881], [1, 82525, 5722043942, 280983220013675, 11592836324538749809], [1, 12749, 32947137104, 219918673063441, 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{'__RealLiteral__': 0, 'data': '2.87694526840743978921992319847', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.22970940818352579430758329214', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 140.91187958785713, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 1444, 'conductor_radical': 38, 'degree': 4, 'dirichlet_coefficients': [1, 16, -69, 192, 155, -1104, -2238, 2048, 621, 2480, -3295, -13248, -13427, -35808, -10695, 20480, -32256, 9936, -13718, 29760, 154422, -52720, -82525, -141312, 13847, -214832, 91908, -429696, -12749, -171120, 258944, 196608, 227355, -516096, -346890, 119232, -149260, -219488, 926463, 317440, 339130, 2470752, -83869, -632640, 96255, -1320400, 1471025, -1413120, 2233465, 221552, 2225664, -2577984, -945643, 1470528, -510725, -4583424, 946542, -203984, -969009, -2053440, -1506755, 4143104, -1389798, 1835008, -2081185, 3637680, -1848219, -6193152, 5694225, -5550240, -3417184, 1271808, -2499822, -2388160, -955443, -2633856, 7374210, 14823408, 2636926, 3174400, -3283254, 5426080, -10059354, 29649024, -4999680, -1341904, 879681, -6748160, -3506160, 1540080, 30049626, -15844800, -17867136, 23536400, -2126290, -13565952, 5893526, 35735440, -2046195, 2658624], 'euler11': [1, 3295, 38080340, 64210228445, 379749833583241], 'euler13': [1, 13427, 138664758, 842524337759, 3937376385699289], 'euler17': [1, 32256, 1073810905, 13235884236288, 168377826559400929], 'euler19': [1, 13718, 47045881, 0, 0], 'euler2': [1, -16, 64, 0, 0], 'euler23': [1, 82525, 5722043942, 280983220013675, 11592836324538749809], 'euler29': [1, 12749, 32947137104, 219918673063441, 297558232675799463481], 'euler3': [1, 69, 4140, 150903, 4782969], 'euler31': [1, -258944, 64961539758, -7124226348358784, 756943935220796320321], 'euler37': [1, 149260, 183707435838, 14169531980871580, 9012061295995008299689], 'euler41': [1, -339130, -4364095006, -66047016901263530, 37929227194915558802161], 'euler43': [1, 83869, 275614048806, 22797155094932983, 73885357344138503765449], 'euler47': [1, -1471025, 1488141383726, -745255275779084575, 256666986187667409334369], 'euler5': [1, -155, 10178, -12109375, 6103515625], 'euler53': [1, 945643, 2428814565902, 1110857366408880191, 1379946262057143768386569], 'euler59': [1, 969009, 3139777837024, 2411525686652974371, 6193386212891813387462761], 'euler61': [1, 1506755, 5925806441724, 4735343481888821855, 9876832533361318095112441], 'euler67': [1, 1848219, 11014380276458, 11201522342478469737, 36732225162896895721934329], 'euler7': [1, 2238, 2775179, 1843089234, 678223072849], 'euler71': [1, 3417184, 7686276501674, 31079699083331190944, 82721210695570328927708881], 'euler73': [1, 2499822, 17574764549507, 27616529860806100734, 122045014039746588673695409], 'euler79': [1, -2636926, 33245149452510, -50639286907236307234, 368790120348678391253573281], 'euler83': [1, 10059354, 77358130536910, 272971143066708320958, 736365263311636486061599129], 'euler89': [1, 3506160, 58485605027458, 155082137157307958640, 1956410986640441413344189841], 'euler97': [1, -5893526, 73244272821042, -476186790327155396438, 6528362774606076144776040769], 'euler_factors': [[1, -16, 64, 0, 0], [1, 69, 4140, 150903, 4782969], [1, -155, 10178, -12109375, 6103515625], [1, 2238, 2775179, 1843089234, 678223072849], [1, 3295, 38080340, 64210228445, 379749833583241], [1, 13427, 138664758, 842524337759, 3937376385699289], [1, 32256, 1073810905, 13235884236288, 168377826559400929], [1, 13718, 47045881, 0, 0], [1, 82525, 5722043942, 280983220013675, 11592836324538749809], [1, 12749, 32947137104, 219918673063441, 297558232675799463481], [1, -258944, 64961539758, -7124226348358784, 756943935220796320321], [1, 149260, 183707435838, 14169531980871580, 9012061295995008299689], [1, -339130, -4364095006, -66047016901263530, 37929227194915558802161], [1, 83869, 275614048806, 22797155094932983, 73885357344138503765449], [1, -1471025, 1488141383726, -745255275779084575, 256666986187667409334369], [1, 945643, 2428814565902, 1110857366408880191, 1379946262057143768386569], [1, 969009, 3139777837024, 2411525686652974371, 6193386212891813387462761], [1, 1506755, 5925806441724, 4735343481888821855, 9876832533361318095112441], [1, 1848219, 11014380276458, 11201522342478469737, 36732225162896895721934329], [1, 3417184, 7686276501674, 31079699083331190944, 82721210695570328927708881], [1, 2499822, 17574764549507, 27616529860806100734, 122045014039746588673695409], [1, -2636926, 33245149452510, -50639286907236307234, 368790120348678391253573281], [1, 10059354, 77358130536910, 272971143066708320958, 736365263311636486061599129], [1, 3506160, 58485605027458, 155082137157307958640, 1956410986640441413344189841], [1, -5893526, 73244272821042, -476186790327155396438, 6528362774606076144776040769]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/38/8/a/d'], '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': '4-38e2-1.1-c7e2-0-2', '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': 2, 'prelabel': '4-38e2-1.1-c7e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4453782039707384, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7e2-0', 'trace_hash': 1251148810412020623, 'z1': {'__RealLiteral__': 0, 'data': '2.42938874675819712221643987754', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3079616103015734576571392539296,3646961396320455590015911318039', 'Lhash_array': ['3079616103015734576571392539296', '3646961396320455590015911318039'], 'label': '4-38e2-1.1-c7e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/38/8/a/d'}