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{'Lhash': '1970273474616877745337446689153,2065746918058456795242583924901', 'a10': 0, 'a2': 0, 'a3': 54, 'a4': 0, 'a5': -180, 'a6': 0, 'a7': -1032, 'a8': 0, 'a9': 2187, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3597.351474464519, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -54, 729]]], 'bad_primes': [2, 3], 'central_character': '192.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, -54, 729], [1, 180, 104190, 14062500, 6103515625], [1, 1032, 409342, 849896376, 678223072849], [1, -2840, 38824982, -55343565640, 379749833583241], [1, -340, 19403694, -21334495780, 3937376385699289], [1, -9780, 478576006, -4013112221940, 168377826559400929], [1, -32040, 1749599878, -28639650517560, 799006685782884121], [1, 11136, 289229518, 37916136177792, 11592836324538749809], [1, 304212, 57634483854, 5247619371713508, 297558232675799463481], [1, 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'1.62958698373710952628227809618', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04323680147922211300873316915', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3597.351474464519, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 54, 0, -180, 0, -1032, 0, 2187, 0, 2840, 0, 340, 0, -9720, 0, 9780, 0, 32040, 0, -55728, 0, -11136, 0, -71790, 0, 78732, 0, -304212, 0, 77640, 0, 153360, 0, 185760, 0, -1015820, 0, 18360, 0, 704100, 0, -395496, 0, -393660, 0, -1157488, 0, 655682, 0, 528120, 0, -1568580, 0, -511200, 0, 1730160, 0, 139240, 0, -2603580, 0, -2256984, 0, -61200, 0, -5289768, 0, -601344, 0, -5721760, 0, -1190700, 0, -3876660, 0, -2930880, 0, 398280, 0, 2657205, 0, -6986616, 0, -1760400, 0, -16427448, 0, -8166732, 0, -350880, 0, 4192560, 0, -5767200, 0, -10361500, 0, 6211080, 0], 'euler11': [1, -2840, 38824982, -55343565640, 379749833583241], 'euler13': [1, -340, 19403694, -21334495780, 3937376385699289], 'euler17': [1, -9780, 478576006, -4013112221940, 168377826559400929], 'euler19': [1, -32040, 1749599878, 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18885723928102, 32059758307066235064, 36732225162896895721934329], 'euler7': [1, 1032, 409342, 849896376, 678223072849], 'euler71': [1, 5721760, 24709125868142, 52040094717475288160, 82721210695570328927708881], 'euler73': [1, 1190700, 17205639157334, 13154137416688797900, 122045014039746588673695409], 'euler79': [1, -398280, 21875776506478, -7648532871007406520, 368790120348678391253573281], 'euler83': [1, 6986616, 48072352746118, 189589168020943832232, 736365263311636486061599129], 'euler89': [1, 8166732, 74896738657014, 361225458094033341228, 1956410986640441413344189841], 'euler97': [1, 10361500, 164015274574086, 837191424619967849500, 6528362774606076144776040769], 'euler_factors': [[1, 0, 0, 0, 0], [1, -54, 729, 0, 0], [1, 180, 104190, 14062500, 6103515625], [1, 1032, 409342, 849896376, 678223072849], [1, -2840, 38824982, -55343565640, 379749833583241], [1, -340, 19403694, -21334495780, 3937376385699289], [1, -9780, 478576006, -4013112221940, 168377826559400929], [1, -32040, 1749599878, -28639650517560, 799006685782884121], [1, 11136, 289229518, 37916136177792, 11592836324538749809], [1, 304212, 57634483854, 5247619371713508, 297558232675799463481], [1, -77640, 47707410382, -2136079359578040, 756943935220796320321], [1, 1015820, 447827659326, 96433699429244060, 9012061295995008299689], [1, -704100, 449624006262, -137126484239612100, 37929227194915558802161], [1, 395496, 503179893718, 107503173418374072, 73885357344138503765449], [1, 1157488, 1172277002462, 586410182458476944, 256666986187667409334369], [1, 1568580, 2748040766334, 1842628399725521460, 1379946262057143768386569], [1, -139240, 1925517532598, -346519832746197560, 6193386212891813387462761], [1, 2603580, 5065896220142, 8182382393007555180, 9876832533361318095112441], [1, 5289768, 18885723928102, 32059758307066235064, 36732225162896895721934329], [1, 5721760, 24709125868142, 52040094717475288160, 82721210695570328927708881], [1, 1190700, 17205639157334, 13154137416688797900, 122045014039746588673695409], [1, -398280, 21875776506478, -7648532871007406520, 368790120348678391253573281], [1, 6986616, 48072352746118, 189589168020943832232, 736365263311636486061599129], [1, 8166732, 74896738657014, 361225458094033341228, 1956410986640441413344189841], [1, 10361500, 164015274574086, 837191424619967849500, 6528362774606076144776040769]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/8/a/u'], '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': '4-192e2-1.1-c7e2-0-6', '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': '4-192e2-1.1-c7e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.7445416192923515, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7e2-0', 'trace_hash': 1311564255047372822, 'z1': {'__RealLiteral__': 0, 'data': '1.55427171671921840424117343047', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1970273474616877745337446689153,2065746918058456795242583924901', 'Lhash_array': ['1970273474616877745337446689153', '2065746918058456795242583924901'], 'label': '4-192e2-1.1-c7e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/8/a/u'}