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'6.93362293875076357150746426746626', '7.09519561755741142131961778720347', '7.28482728503839421474447967925065', '7.33422428863886622626706293133494', '7.50506915351650674155870788019617', '7.60227027536356145412788662048985', '7.70467867206141201307851761679352', '7.78198352266601102032665914827163', '8.011362810765143451368702131728507', '8.088096963577961629098063731479241', '8.157699816137863667594713731008618', '8.324945006823865992465988227717383', '8.571608372290252940676374279753913', '8.653518092513455477556272873882220', '8.838918564077556610265515273473430', '8.868816175669320256015790995345153', '8.946114415799620957042032222124248', '9.107036721628647692425105054096845', '9.211251190296296087052801595829032', '9.480038383759947459258206338703226', '9.884792463777361207409099752765187', '9.914074236566597210843135056856165'], 'prelabel': '12-1690e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.673515746746758, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e6-0', 'trace_hash': 418120606924063360, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.087069049613404305233188994865', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '0.34914101344907292780115050843', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.70934924769663776858458269594', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6039248.078048942, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 23298085122481000000, 'conductor_radical': 130, 'degree': 12, 'dirichlet_coefficients': [1, 0, 0, -3, 0, 0, 0, 0, 4, 0, -12, 0, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, -8, 0, 0, 0, 4, 0, -24, 0, 0, 0, 0, -12, 0, 0, 0, 0, -4, 0, 0, 36, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 20, 0, 0, -10, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, -12, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 24], 'euler11': [1, 12, 126, 820, 4695, 19992, 75524, 219912, 568095, 1091420, 1844766, 1932612, 1771561], 'euler13': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler17': [1, 0, 0, 0, 752, 0, -50, 0, 217328, 0, 0, 0, 24137569], 'euler19': [1, -4, 30, -284, 1127, -5448, 36484, -103512, 406847, -1947956, 3909630, -9904396, 47045881], 'euler2': [1, 0, 3, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -70, 0, 2127, 0, -47860, 0, 1125183, 0, -19588870, 0, 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-4, 0, 16, 0, -62, 0, 144, 0, -324, 0, 729], [1, 0, 8, 4, 40, 0, 125, 0, 0, 0, 0, 0, 0], [1, 0, -8, 0, 88, 0, -734, 0, 4312, 0, -19208, 0, 117649], [1, 12, 126, 820, 4695, 19992, 75524, 219912, 568095, 1091420, 1844766, 1932612, 1771561], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 752, 0, -50, 0, 217328, 0, 0, 0, 24137569], [1, -4, 30, -284, 1127, -5448, 36484, -103512, 406847, -1947956, 3909630, -9904396, 47045881], [1, 0, -70, 0, 2127, 0, -47860, 0, 1125183, 0, -19588870, 0, 148035889], [1, -4, 90, -484, 4967, -21768, 187084, -631272, 4177247, -11804276, 63655290, -82044596, 594823321], [1, 24, 370, 4040, 35711, 257200, 1568924, 7973200, 34318271, 120355640, 341702770, 687099624, 887503681], [1, 0, -160, 0, 11392, 0, -506230, 0, 15595648, 0, -299865760, 0, 2565726409], [1, 4, 90, -140, 4751, 360, 327244, 14760, 7986431, -9648940, 254318490, 463424804, 4750104241], [1, 0, -84, 0, 5136, 0, -202462, 0, 9496464, 0, -287179284, 0, 6321363049], [1, 0, -216, 0, 21176, 0, 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-10, 0, 4687, 0, -11980, 0, 44099983, 0, -885292810, 0, 832972004929]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1690/2/b/a'], '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': '12-1690e6-1.1-c1e6-0-1', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-1690e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.673515746746758, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 418120606924063360, 'z1': {'__RealLiteral__': 0, 'data': '0.087069049613404305233188994865', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '110373133003733452653589191440,442588815263009610908319441522,899206999614085839582847717963,1950673684008387866766541547765,2294792109732633920646277396528,2679533624888161478825210244872', 'Lhash_array': ['110373133003733452653589191440', '442588815263009610908319441522', '899206999614085839582847717963', '1950673684008387866766541547765', '2294792109732633920646277396528', '2679533624888161478825210244872'], 'label': '12-1690e6-1.1-c1e6-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1690/2/b/a'}