-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1238562937903969951409626009350', 'a10': [0.38934523732257237, -0.025519035084742125], 'a2': [0.1305261922200516, 0.9914448613738104], 'a3': [0.0, 0.0], 'a4': [-0.9659258262890683, 0.25881904510252074], 'a5': [0.025519035084742125, -0.38934523732257237], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.3826834323650898, -0.9238795325112867], 'a9': [0.7933533402912352, 0.6087614290087207], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.1305261922200516, -0.9914448613738104]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-0.6087614290087207, -0.7933533402912352]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.227', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '1348181407903278300455154912266', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.1305261922200516, -0.9914448613738104]], [[1.0, 0], [0, 0], [-0.7933533402912352, -0.6087614290087207]], [[1.0, 0], [-0.025519035084742125, 0.38934523732257237], [-0.9914448613738104, -0.1305261922200516]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.1305261922200516, -0.9914448613738104]], [[1.0, 0], [1.0, 1.0], [0, 1.0]], [[1.0, 0], [-0.6087614290087207, -0.7933533402912352]], [[1.0, 0], [0, 0], [-0.9659258262890683, 0.25881904510252074]], [[1.0, 0], [0, 0], [0.7933533402912352, -0.6087614290087207]], [[1.0, 0], [0.32442334882145774, 0.21677275132473922], [0.3826834323650898, 0.9238795325112867]], [[1.0, 0], [0, 0], [0.7933533402912352, 0.6087614290087207]], [[1.0, 0], [-1.2933533402912352, -1.4747868327931593], [-0.1305261922200516, 0.9914448613738104]], [[1.0, 0], [-1.3826834323650898, 0.9238795325112867], [0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [-0.6072063586819179, 0.4659258262890683], [0.25881904510252074, -0.9659258262890683]], [[1.0, 0], [0, 0], [0.9659258262890683, 0.25881904510252074]], [[1.0, 0], [0.49144486137381044, -0.9965515960044903], [-0.6087614290087207, -0.7933533402912352]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [-1.7592791665803034, 0.8675804741112414], [0.6087614290087207, -0.7933533402912352]], [[1.0, 0], [0, 0], [-0.7933533402912352, 0.6087614290087207]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [-1.0897902135516373, 1.6309863136978342], [-0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [1.0, -1.7320508075688772], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.9914448613738104, -0.1305261922200516]], [[1.0, 0], [1.6593787440756738, -0.10876142900872064], [0.9914448613738104, -0.1305261922200516]], [[1.0, 0], [0.21677275132473922, -1.0897902135516373], [-0.9238795325112867, -0.3826834323650898]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-3332-476.227-c0-0-2', 'leading_term': '1.260830353557201656322400274930', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3332/1/ce/a/227/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.2608303535572016, 1.2384812954837336, 1.2225355237648543, 1.210498198138946, 1.1990636893013136, 1.1845431331817837, 1.163244856866447, 1.1317621862287988, 1.0871660949557715, 1.0271229750317186, 0.9499622694625927, 0.8547135960215461, 0.7411254870966643, 0.6096714882621709, 0.4615450392822477, 0.2986421002980228, 0.12352938028689481, -0.06060418086138275, -0.2500146577634866, -0.44049036628012417, -0.6274593753648225, -0.8061165269364299, -0.971568043064189, -1.1189906504303693, -1.2438010497775405, -1.341830554319495, -1.4094988666635584, -1.443980307868955, -1.443355400752709, -1.406740582771793, -1.3343890139835204, -1.2277559743146254, -1.089523220273467, -0.923577887969237, -0.7349430640717358, -0.5296589591454265, -0.3146156513975533, -0.09734054975474314, 0.11425403467689957, 0.3121556199724162, 0.4885589470474742, 0.6361846024176159, 0.7485960124883885, 0.8205009975719831, 0.8480236782532264, 0.8289327592596748, 0.7628131215901085, 0.6511692481384246, 0.4974512744641376, 0.3069973427181434, 0.0868893553482481, -0.15427694615028828, -0.4067025672153385, -0.6597673395816127, -0.9024702850849166, -1.123911351551105, -1.3137944508218617, -1.4629293188855348, -1.5637082358265446, -1.610533236530167, -1.600170216183997, -1.5320083395661226, -1.4082063922402197, -1.2337120932007377, -1.0161457845836637, -0.7655461232820256, -0.49398216185497706, -0.21504321300807033, 0.05677520238655464, 0.30676458570130266, 0.5207455301858487, 0.6858238786649725, 0.7911233105277384, 0.8284555538413532, 0.7928902175892995, 0.6831890739157002, 0.5020744790608217, 0.25630838268910355, -0.043433194446289465, -0.382895574619195, -0.7447854345283377, -1.1094990834798568, -1.4560118291545994, -1.7628911867666426, -2.0093879990616528, -2.1765527790811614, -2.248320250893528, -2.212503529420974, -2.0616409025577798, -1.7936428573079042, -1.412194758265506, -0.9268811972972235, -0.353011070545961, 0.28886267471339944, 0.9737186604295548, 1.673111768559929, 2.356444843874492, 2.9924110650993683, 3.5505387038792207, 4.002761190789732, 4.324930398174601, 4.498190305872706, 4.510131996184711, 4.35565924325839, 4.0375065760745725, 3.5663681022067117, 2.960614837827839, 2.245599842365133, 1.4525729807774026, 0.6172493994453288, -0.22190347365336077, -1.0255776550066913, -1.7556382989418682, -2.3771334862293623, -2.86019074383186, -3.181693489316518, -3.3266392936208073, -3.289096435284614, -3.072695058134991, -2.6906133878559646, -2.165046663702893, -1.5261752228646905, -0.8106769092959615, -0.05985598064445588, 0.682515687919757, 1.372530556765344, 1.9685233771868755, 2.4333624604852857, 2.736523652107543, 2.8558261929606363, 2.7787267832153177, 2.503091812629621, 2.037396635431058, 1.400333336906415, 0.6198427812535613, -0.26837919870907534, -1.2228198942373032, -2.198423155350746, -3.1490679889421336, -4.03010846862701, -4.800825996460468, -5.426648898231999, -5.8810072498631705, -6.146712075976765, -6.216776441821289, -6.094629803245621, -5.7937142272255056, -5.336489426808395, -4.75291053202964, -4.078475745611308, -3.3519683115187022, -2.6130367071389213, -1.8997672869020696, -1.2464039689004158, -0.6813598255364216, -0.22564614363127106, 0.10818316342300127, 0.3165082186864532, 0.4045160486822879, 0.3854853093734575, 0.27953814664449395, 0.11195047308191187, -0.08885816515488808, -0.2935122938641371, -0.473891089576757, -0.6052059863681438, -0.6677992120119963, -0.6485372082174143, -0.5417019291979411, -0.3493190626207473, -0.08090277516309673, 0.24736120726829017, 0.6139315339852619, 0.9936270151167447, 1.3596135989384546, 1.6855136203040635, 1.9474789492725133, 2.126071837538954, 2.2078110137488576, 2.1862650287414898, 2.062608304991576, 1.845595413546236, 1.5509528694982473, 1.2002319644424813, 0.8192075167512425, 0.4359427555808635, 0.0786671037003782, -0.22637075108237048, -0.4569087502873695, -0.5963799245041033, -0.6351885330761128, -0.5714512095241023, -0.4111410237623051, -0.16761832150424258, 0.1394199654407136, 0.48549481835905367, 0.843285123331633, 1.1848029379531622, 1.483633265251346, 1.7170601845385902, 1.8679077956815229, 1.9259447672331313, 1.8887339905795, 1.7618515758870783, 1.5584489813452649, 1.298184634095735, 1.0056028446324428, 0.7080839981199569, 0.43352711314057, 0.20795071498769005, 0.053208307148123093, -0.014990618192338144, 0.0114159601701522, 0.13194942532709017, 0.337395416518383, 0.6103393178947687, 0.9264056761078306, 1.2561164278592656, 1.5672298808618683, 1.827379416837111, 2.0068016292912407, 2.080930813484194, 2.03264186800263, 1.853946803535778, 1.5469897774222325, 1.1242390838286027, 0.6078378279224563, 0.02814318605787954, -0.578448245769625, -1.1722300420661846, -1.713261374695641, -2.164544821635496, -2.495047795170162, -2.682314368403998, -2.714440816669312, -2.5912341546429363, -2.3244351317687943, -1.936960914252836, -1.4612023108184804, -0.9364895208693756, -0.40591248015999915, 0.08725918351210415, 0.5032710295561036, 0.8093896975017114, 0.9829221706503962, 1.0134816171629348, 0.9042867454258253, 0.6723545007231158, 0.34753257912722535, -0.02958804582145197, -0.41074706072389555, -0.7438564045297067, -0.9773206708846455, -1.0644988640953934, -0.9679474574564316, -0.6630907230973894, -0.14099927081617422], 'positive_zeros': ['0.977053880368121569984014656509817', '2.19459518481256367512294349061894', '2.95127247097228980962300889174545', '3.97184813022316611645190348648844', '4.56234685467900187890377288372107', '5.42347637440305190712171010385015', '6.42968889500937148686319057706761', '7.21168515630980874764259205594220', '7.893031555386997958214225059610990', '9.119075198068544859131457406101784'], 'prelabel': '2-3332-476.227-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.39788361031620967, 'root_number': '0.31533353462396680965412712998006 - 0.94898090704795295435510984598518*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.19894180515810483', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.977053880368121569984014656510', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.19459518481256367512294349062', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95127247097228980962300889175', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '476.227', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/ce/a/227/1'], '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': '2-3332-476.227-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-476.227-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.19894180515810483, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.977053880368121569984014656510', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1238562937903969951409626009350', 'Lhash_array': ['1238562937903969951409626009350'], 'label': '2-3332-476.227-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/ce/a/227/1'}