-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '714580336410120449029272817776', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.0, 2.0], 'a6': [0, 0], 'a7': [0, 2.0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.935765127447429, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, -2.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.649', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '2110919931202645794260396680907', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, -2.0]], [[1.0, 0], [0, -2.0], [-7.0, 0]], [[1.0, 0], [1.0, 0], [11.0, 0]], [[1.0, 0], [0, 0], [-13.0, 0]], [[1.0, 0], [0, -2.0], [-17.0, 0]], [[1.0, 0], [-3.0, 0], [19.0, 0]], [[1.0, 0], [0, -4.0], [-23.0, 0]], [[1.0, 0], [3.0, 0], [29.0, 0]], [[1.0, 0], [-1.0, 0], [31.0, 0]], [[1.0, 0], [0, 10.0], [-37.0, 0]], [[1.0, 0], [1.0, 0], [41.0, 0]], [[1.0, 0], [0, -10.0], [-43.0, 0]], [[1.0, 0], [0, -10.0], [-47.0, 0]], [[1.0, 0], [0, -6.0], [-53.0, 0]], [[1.0, 0], [13.0, 0], [59.0, 0]], [[1.0, 0], [10.0, 0], [61.0, 0]], [[1.0, 0], [0, 8.0], [-67.0, 0]], [[1.0, 0], [9.0, 0], [71.0, 0]], [[1.0, 0], [0, 14.0], [-73.0, 0]], [[1.0, 0], [0, 0], [79.0, 0]], [[1.0, 0], [0, -10.0], [-83.0, 0]], [[1.0, 0], [-13.0, 0], [89.0, 0]], [[1.0, 0], [0, -10.0], [-97.0, 0]], [[1.0, 0], [-1.0, 0], [101.0, 0]], [[1.0, 0], [0, 4.0], [-103.0, 0]], [[1.0, 0], [0, -12.0], [-107.0, 0]], [[1.0, 0], [-17.0, 0], [109.0, 0]], [[1.0, 0], [0, -6.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-1620-5.4-c1-0-5', 'leading_term': '1.485453649136562026671838414911354401053445562400467861', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1620/2/d/b/649/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.485453649136562, 1.3466702100081607, 1.2042213142269182, 1.0579982304319282, 0.9078848622788507, 0.7538357902789464, 0.5959508354709138, 0.4345417900473722, 0.2701878878442627, 0.10377761631748698, -0.06346456402890503, -0.2299672289691653, -0.39381676781279346, -0.5527775528451085, -0.704326843634416, -0.8457035633053243, -0.9739699033213377, -1.0860845209704026, -1.1789858689114627, -1.2496839327394922, -1.2953583560279955, -1.3134606163785372, -1.301817599538653, -1.2587336233687032, -1.1830877120682397, -1.07442273592668, -0.933022933730403, -0.7599763421712035, -0.5572187842147825, -0.3275563274373783, -0.07466352016530017, 0.19694475108182188, 0.4819692695271198, 0.7744110549326548, 1.0676842831248403, 1.3547563692068472, 1.6283129881195308, 1.8809447486594784, 2.1053511977262436, 2.2945568521301882, 2.4421330792402327, 2.542418918776899, 2.5907333982535783, 2.5835715825228176, 2.5187765467120475, 2.395679697260326, 2.215202404327148, 1.9799127562918521, 1.6940323971007478, 1.363389840622752, 0.9953183403883902, 0.5984982823725096, 0.18274610464998206, -0.24124613848006135, -0.6622143373607263, -1.0686607551698741, -1.44921721297773, -1.7930213312431031, -2.090092884861187, -2.331696510771569, -2.5106766784183123, -2.6217510434209723, -2.661749083984548, -2.629784276210682, -2.52734998284985, -2.358331669129424, -2.1289309526055002, -1.8475002505167994, -1.5242902945350123, -1.1711164068100273, -0.8009530260382305, -0.42746938223066144, -0.0645222856354226, 0.27437543502750816, 0.5765903794496834, 0.830886274278682, 1.027901981783002, 1.1605684938850336, 1.22444515611582, 1.2179578742673565, 1.1425254466543497, 1.0025643362939025, 0.8053670074654008, 0.5608542195915222, 0.28120718582357224, -0.019608972231462695, -0.3264137592551226, -0.6234503283213498, -0.8950694414236624, -1.1264297385764495, -1.3041837629853912, -1.4171185738775836, -1.4567205643219234, -1.4176363223094548, -1.2980049965151188, -1.0996425517563904, -0.8280643536691064, -0.4923394746902716, -0.10477767577448517, 0.3195421422755163, 0.7633854704452316, 1.2080938681736595, 1.6344044928250685, 2.0233219222309766, 2.3570029389726246, 2.6196129195122513, 2.798112367196518, 2.8829340336560447, 2.8685149800960636, 2.7536537296540864, 2.5416701455148587, 2.2403545335614323, 1.8617023262886603, 1.421441102175381, 0.9383671299227186, 0.4335185743799263, -0.07077856256820994, -0.551948260861893, -0.9882370646842612, -1.3597692369162409, -1.6495316442657246, -1.8442375549142027, -1.9350232198340978, -1.9179383173764373, -1.7942007830532267, -1.5701978083546968, -1.2572273472849873, -0.8709877015299491, -0.43083598975856013, 0.04115115706408717, 0.5212701835641415, 0.9853828688954384, 1.41014810484815, 1.774229517589297, 2.059415036138283, 2.251587708174316, 2.3414936139535736, 2.325262379740762, 2.204648111794432, 1.9869729671577772, 1.6847713198811665, 1.3151487431454203, 0.898885924844642, 0.45933227343558736, 0.02114650036205386, -0.39104887593159576, -0.7540259952467967, -1.0472477575591235, -1.254028183137807, -1.3624897905727806, -1.3662608428002518, -1.2648688883834835, -1.0638034093362616, -0.7742387152559315, -0.4124274954397225, 0.0012054300364153475, 0.44322174310196116, 0.8885176749205895, 1.31178623692028, 1.6890102378171101, 1.9988992020737577, 2.22418482691781, 2.352696187144087, 2.3781472637762384, 2.30058498676823, 2.1264650274622188, 1.868344009773602, 1.544199413979875, 1.1764109029323402, 0.7904577587196122, 0.4134052819981713, 0.07226721264692339, -0.2076594774221761, -0.4043873754861809, -0.5006612291663052, -0.4851208261653359, -0.3531284832141286, -0.10720424918825573, 0.24296541264322932, 0.6809544450344371, 1.1844421410852473, 1.7264329587634093, 2.2767841667101085, 2.80395410286076, 3.2768685843448844, 3.6667937580994936, 3.94910113729096, 4.104815038778391, 4.121844000140711, 3.9958154549161224, 3.7304560139381024, 3.33748681022139, 2.8360328996999202, 2.251575864041025, 1.6145076474026725, 0.9583694261160629, 0.31788026485956394, -0.27312497046861584, -0.7837215529873957, -1.1877582896065757, -1.4654404957363947, -1.6045308384838988, -1.6010892452648897, -1.4597013797185214, -1.1931771619702907, -0.8217344551752037, -0.3717162045809509, 0.12608016379054365, 0.6383564342050284, 1.1314263334054986, 1.573351683029717, 1.9359634969573387, 2.196635746113847, 2.339694505263719, 2.357368136187271, 2.250213658246382, 2.0269886558153023, 1.7039747677729546, 1.3037955831818155, 0.8538061636883815, 0.3841610746353886, -0.07430934454699986, -0.4922703613923923, -0.8439529795317761, -1.108979188394144, -1.2738138611729661, -1.3327389956166718, -1.2882776707890609, -1.1510322404942686, -0.9389414436230443, -0.6760015722391022, -0.39053481599304163, -0.1131207303027365, 0.12566790613475867, 0.2975676592206552, 0.37880299895311836, 0.351984396256445, 0.207586497332335, -0.055106058623714475, -0.42766225775986216, -0.8928134778551001, -1.4253985153127324, -1.9938912156428337, -2.562415240835697, -3.093114641809165, -3.5487216059213025, -3.895146088539735, -4.103907374230366, -4.154235487647835, -4.034690452591917, -3.744178477831962, -3.292284228332076, -2.698884745416567, -1.993060138231906, -1.2113654309210418, -0.3955734255218489, 0.4099631506730828], 'positive_zeros': ['0.56370449103362275884195960391948', '1.77428118372607824160136503158845', '3.07217952417058175831613800829971', '4.22952627523319180085593402047236', '4.97671650461894194341323598667184', '5.75704678840925281128224618963696', '6.78854792910570009001612938495557', '7.55356728093668103586015384346211', '8.440391139788530407502011339613910', '9.081867706661749262303703922302061'], 'prelabel': '2-1620-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.596632470443349, 'root_angle': -0.6475836176504333, 'root_number': '-0.4472135954999579392818347337462552470881236719223051449 - 0.89442719099991587856366946749251049417624734384461028971*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32379180882521663', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56370449103362275884195960392', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.77428118372607824160136503159', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.07217952417058175831613800830', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 12.935765127447429, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/2/d/b/649/2'], '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': '2-1620-5.4-c1-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1620-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.596632470443349, 'root_angle': -0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56370449103362275884195960392', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '714580336410120449029272817776', 'Lhash_array': ['714580336410120449029272817776'], 'label': '2-1620-5.4-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/2/d/b/649/2'}