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'8.302147952705361882193863854074705', '8.387361065421477009127377174460279', '8.536369759493712591970660613849824', '8.622440126044797827118706350252588', '8.768357939163126364910945396664227', '9.265677000862623320034465975495736', '9.326942655554410349488623302761024', '9.935290020569122213739987438420698', '10.25696943349034234137116405243418', '10.54397566200736196196048454036072', '10.69380714326108650488253231074235', '10.90414473034916737584421224430619', '11.32360421178795386961626160751914', '11.61865458042174095040592607421450', '11.67379482032757640573734427078438', '11.99553861310626440190086689808539', '12.17674600461428497912601104499336', '12.59387178164138923123330030975897', '12.91837495169102241744881554198935', '13.18153866567090037113711101745882', '13.18642218246635535579533856888204', '13.39856948619495352602979483992062', '13.90200077274478395209904132357454', '14.38064540906110877033278196374836'], 'prelabel': '8-124e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.24876507304381038, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e4-0', 'trace_hash': 193505020699476273, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52908883261400833847866302720', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76326840611427196538532991642', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.23664863338373525323008173673', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.4666120133608898e-05, 'bad_primes': [2, 31], 'central_character': '1.1', 'conductor': 236421376, 'conductor_radical': 62, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, -2, -2, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 3, -2, 0, 0, 4, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -6, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6], 'euler11': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler13': [1, -2, 1, -2, 4, -2, 1, -2, 1], 'euler17': [1, 2, 1, 2, 4, 2, 1, 2, 1], 'euler19': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler2': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler23': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler29': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler3': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler31': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler37': [1, 2, 1, 2, 4, 2, 1, 2, 1], 'euler41': [1, 2, 1, 2, 4, 2, 1, 2, 1], 'euler43': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler47': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler5': [1, 2, 1, 2, 4, 2, 1, 2, 1], 'euler53': [1, -2, 1, -2, 4, -2, 1, -2, 1], 'euler59': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler61': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler67': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler7': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler71': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler73': [1, 2, 1, 2, 4, 2, 1, 2, 1], 'euler79': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler83': [1, 0, 1, 0, 0, 0, 1, 0, 1], 'euler89': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler97': [1, 0, 4, 0, 6, 0, 4, 0, 1], 'euler_factors': [[1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 2, 1, 2, 4, 2, 1, 2, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, -2, 1, -2, 4, -2, 1, -2, 1], [1, 2, 1, 2, 4, 2, 1, 2, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 2, 1, 2, 4, 2, 1, 2, 1], [1, 2, 1, 2, 4, 2, 1, 2, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, -2, 1, -2, 4, -2, 1, -2, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 2, 1, 2, 4, 2, 1, 2, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 1, 0, 0, 0, 1, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 1]], 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/124/1/i/a', 'ArtinRepresentation/2.124.16t60.a'], 'is_instance_Artin': True, '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': '8-124e4-1.1-c0e4-0-0', 'motivic_weight': 0, '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': [0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '8-124e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.24876507304381038, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e4-0', 'trace_hash': 193505020699476273, 'z1': {'__RealLiteral__': 0, 'data': '1.52908883261400833847866302720', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24602826
{'Lhash': '1938350376465430267780267985387,3502858853602459619986102002595,4595848658436332310998490858476,5003332414951637055700844143287', 'Lhash_array': ['1938350376465430267780267985387', '3502858853602459619986102002595', '4595848658436332310998490858476', '5003332414951637055700844143287'], 'label': '8-124e4-1.1-c0e4-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.124.16t60.a'}
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id: 19803711
{'Lhash': '1938350376465430267780267985387,3502858853602459619986102002595,4595848658436332310998490858476,5003332414951637055700844143287', 'Lhash_array': ['1938350376465430267780267985387', '3502858853602459619986102002595', '4595848658436332310998490858476', '5003332414951637055700844143287'], 'label': '8-124e4-1.1-c0e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/124/1/i/a'}