-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1704502250704714585708049970964', 'a10': [0.0, 0.0], 'a2': [-1.536546909413681, 0.0], 'a3': [0.0, 0.0], 'a4': [0.3609764048287347, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.4954960852765593, 0.0], 'a8': [2.5184366396165077, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.91585113697024, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '5625.1', 'coefficient_field': 'CDF', 'conductor': 5625, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.536546909413681, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.4954960852765593, 0], [7.0, 0]], [[1.0, 0], [-2.3562551626400086, 0], [11.0, 0]], [[1.0, 0], [-1.349506279130308, 0], [13.0, 0]], [[1.0, 0], [-2.1940502131394934, 0], [17.0, 0]], [[1.0, 0], [-5.710686337216502, 0], [19.0, 0]], [[1.0, 0], [8.795010018490501, 0], [23.0, 0]], [[1.0, 0], [7.90017030453212, 0], [29.0, 0]], [[1.0, 0], [3.6971703497529917, 0], [31.0, 0]], [[1.0, 0], [-9.75096795218171, 0], [37.0, 0]], [[1.0, 0], [1.8554950636901504, 0], [41.0, 0]], [[1.0, 0], [8.01874202179515, 0], [43.0, 0]], [[1.0, 0], [6.662976763385485, 0], [47.0, 0]], [[1.0, 0], [4.171526396229102, 0], [53.0, 0]], [[1.0, 0], [11.064663948324181, 0], [59.0, 0]], [[1.0, 0], [12.237223289501, 0], [61.0, 0]], [[1.0, 0], [-4.313583787651902, 0], [67.0, 0]], [[1.0, 0], [5.777502956320398, 0], [71.0, 0]], [[1.0, 0], [-6.926837135454736, 0], [73.0, 0]], [[1.0, 0], [10.668731253465024, 0], [79.0, 0]], [[1.0, 0], [0.2240029011566965, 0], [83.0, 0]], [[1.0, 0], [0.42916707525562964, 0], [89.0, 0]], [[1.0, 0], [-12.494548053591629, 0], [97.0, 0]], [[1.0, 0], [8.197668164278047, 0], [101.0, 0]], [[1.0, 0], [-2.500051844908466, 0], [103.0, 0]], [[1.0, 0], [-1.810036427416878, 0], [107.0, 0]], [[1.0, 0], [2.9477751595778576, 0], [109.0, 0]], [[1.0, 0], [13.836474438606611, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 156, 'label': '2-75e2-1.1-c1-0-156', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/5625/2/a/t/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.6894514133255834e-61, 0.11584669574162708, 0.23086644416367527, 0.34421056236995917, 0.45498890724665486, 0.5622540274713778, 0.6649907853570276, 0.7621126738177749, 0.852465629896805, 0.9348397060932796, 1.0079885378117517, 1.070656163605714, 1.1216104278428758, 1.159681927012878, 1.1838072485140014, 1.1930750881899959, 1.1867737130421556, 1.164438152348352, 1.1258954499092164, 1.071306290748286, 1.001201327926501, 0.9165105814139043, 0.8185843643260725, 0.7092043156099626, 0.5905832853309467, 0.4653530309490105, 0.3365389408295893, 0.20752130342653727, 0.08198298387276498, -0.036156251153158146, -0.14281811177000717, -0.23385579106263862, -0.3051540886936632, -0.35273771109979357, -0.3728853953550184, -0.36224712488198485, -0.31796137459392837, -0.23776905579258964, -0.12012064162886271, 0.035727144662541906, 0.2296286928155188, 0.4604844188304153, 0.7261964948238095, 1.0236483087164434, 1.3487100945928994, 1.6962725876772227, 2.060309865785431, 2.4339717553829416, 2.80970532274466, 3.1794040608975105, 3.5345824462740385, 3.8665726035468753, 4.166738913415415, 4.4267055580192, 4.63859125438041, 4.79524480934863, 4.890474669596849, 4.9192653639264154, 4.877973664909397, 4.764497449852607, 4.578410628021469, 4.321058125660524, 3.995605778406792, 3.607041059763637, 3.1621218535050275, 2.669271928022533, 2.138423354643251, 1.580807785644185, 1.0087002208130902, 0.43512058900210926, -0.12649990483968543, -0.6626792254308037, -1.1602620039919336, -1.606803291136372, -1.9909470145807324, -2.302787174367957, -2.534199766174033, -2.6791337778199575, -2.7338503654534234, -2.697100480380644, -2.570232767146376, -2.3572254554393695, -2.0646381756455674, -1.7014820798001735, -1.2790092736581637, -0.810425278867865, -0.31053095641055484, 0.20469706157144904, 0.7185759613362346, 1.2142227526979912, 1.675081325016648, 2.0854538868005386, 2.431019343000401, 2.699320960581753, 2.880206077589248, 2.9662016358531, 2.952810952711767, 2.8387193596758125, 2.625899070055227, 2.319606815623527, 1.9282713168901588, 1.4632714078450066, 0.9386094958945672, 0.3704888635939576, -0.22319303130336024, -0.8234197682128461, -1.410681318620856, -1.9656288683689946, -2.4697368084672497, -2.9059487378372006, -3.2592842879615613, -3.517384399309225, -3.670974349927067, -3.714226322207969, -3.6450065262880873, -3.464995778210146, -3.1796768297553184, -2.798186511968494, -2.333035713748216, -1.7997051850580608, -1.21612993963775, -0.602089443991679, 0.021475363800271985, 0.6331940454992132, 1.2120211698637184, 1.7379855996439117, 2.192906549696704, 2.561049238761836, 2.8296948655000764, 2.9896025732251768, 3.0353449333060847, 2.9655031399883387, 2.7827133988346753, 2.493561706539797, 2.108330138436632, 1.6406036446642605, 1.1067519655402123, 0.525306375795946, -0.08374466347546322, -0.6997134208708886, -1.301994492003795, -1.8708390289328103, -2.3880906586769886, -2.8378535386595396, -3.2070656340496835, -3.485954092760358, -3.6683543942421113, -3.751880567740087, -3.7379399847756707, -3.631592769766375, -3.441262463229645, -3.17831092799228, -2.8564963295958083, -2.491338084912569, -2.099416725189314, -1.6976394697862256, -1.302503813900304, -0.9293915147515706, -0.5919239962999194, -0.3014074279991455, -0.06639167828614485, 0.10763783095375411, 0.21842241217662917, 0.2669402806063134, 0.2572653600999286, 0.196282502927016, 0.0932735939118929, -0.04060493894549758, -0.19292756705559003, -0.35065848342305084, -0.5008316814540218, -0.6312191381011731, -0.7309545053226809, -0.7910818460871507, -0.805002573759939, -0.7687987076286843, -0.6814166164642381, -0.5447023029053304, -0.3632866560150791, -0.1443266100845218, 0.10288457526196834, 0.36741801970271815, 0.6372952774287833, 0.9001296067636765, 1.1437892969488086, 1.3570485273113881, 1.5301916125113808, 1.655538618115246, 1.7278641309059428, 1.7446862694624343, 1.7064095745232815, 1.616312908844164, 1.4803815521406962, 1.3069908916140212, 1.10645705971273, 0.8904771406348321, 0.6714877648665804, 0.46197569358513596, 0.27377708516662336, 0.11740333969540684, 0.001430633832577663, -0.0680125111171883, -0.08762993540074153, -0.05719145362281385, 0.020400292856958407, 0.1392167127078774, 0.290581583018702, 0.46350918664320573, 0.6452817270320454, 0.8221374614642262, 0.980034326218463, 1.1054488986039308, 1.1861676567475037, 1.2120268634345088, 1.1755591053984513, 1.072508532144311, 0.902183002607968, 0.6676193886452202, 0.37554781887333905, 0.03615120199587322, -0.337372594721076, -0.7294275992545118, -1.122787062189223, -1.499473713843169, -1.8417082018528992, -2.132875971432227, -2.3584604097344437, -2.5068903858635667, -2.5702534402877824, -2.5448317235797164, -2.4314261175600915, -2.235444414678236, -1.966741482295607, -1.6392123951354212, -1.2701529078877314, -0.8794146499985194, -0.48839434515316654, -0.11890651616664452, 0.20800306540673125, 0.47324097428400397, 0.660782804960738, 0.7586605849070208, 0.7597636092550069, 0.6624036212462159, 0.4706063777125606, 0.194105112997738, -0.15197340651433242, -0.5477234260292752, -0.9693523095949692, -1.3903117137466372, -1.7826154760867639, -2.118280406392438, -2.370817777987271, -2.5166985298248123, -2.536714357615489, -2.4171601454152754, -2.1507705014145095], 'positive_zeros': ['1.34461518844217315560495612468098', '1.81833072354124722810140362695360', '3.27054512884947923874444402311569', '4.05957250913183094918702471227932', '4.85751961284205216423628074471796', '5.71713002331529517582070436760191', '6.46237161335986784762771550197274', '7.51598789259072128999674878576958', '7.81476197224990602066415759723028'], 'prelabel': '2-75e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.701928911661943, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34461518844217315560495612468', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.81833072354124722810140362695', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27054512884947923874444402312', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 44.91585113697024, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 5625, 'conductor_radical': 15, 'degree': 2, 'index': 156, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5625/2/a/t/1/3'], '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': '2-75e2-1.1-c1-0-156', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-75e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.701928911661943, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34461518844217315560495612468', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1704502250704714585708049970964', 'Lhash_array': ['1704502250704714585708049970964'], 'label': '2-75e2-1.1-c1-0-156', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5625/2/a/t/1/3'}