-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '871172116917718949516819109719', 'a10': [0, 0], 'a2': [0, 1.4142135623730951], 'a3': [-0.8218463592949137, 2.8852328435870986], 'a4': [-2.0, 0], 'a5': [0, 0], 'a6': [-4.080335418005165, -1.1622662675018185], 'a7': [2.6457513110645907, 0], 'a8': [0, -2.8284271247461903], 'a9': [-7.6491371234273915, -4.742436216440336], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.4142135623730951]]], [3, [[1.0, 0], [0.8218463592949137, -2.8852328435870986]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.6457513110645907, 0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.701', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '1658240340464457167968684774135', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.4142135623730951]], [[1.0, 0], [0.8218463592949137, -2.8852328435870986]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.6457513110645907, 0]], [[1.0, 0], [0, -18.152522034358032], [-121.0, 0]], [[1.0, 0], [-22.54801145278525, 0], [169.0, 0]], [[1.0, 0], [0, 0.45714981607555816], [-289.0, 0]], [[1.0, 0], [-30.16265038103257, 0], [361.0, 0]], [[1.0, 0], [0, -12.397477454647426], [-529.0, 0]], [[1.0, 0], [0, -4.707208211648739], [-841.0, 0]], [[1.0, 0], [-45.266390758875104, 0], [961.0, 0]], [[1.0, 0], [32.9890872098091, 0], [1369.0, 0]], [[1.0, 0], [0, -22.942682844573206], [-1681.0, 0]], [[1.0, 0], [20.269723269115755, 0], [1849.0, 0]], [[1.0, 0], [0, 9.67333065536187], [-2209.0, 0]], [[1.0, 0], [0, 5.974651397690913], [-2809.0, 0]], [[1.0, 0], [0, -112.84803119503607], [-3481.0, 0]], [[1.0, 0], [56.38315605113386, 0], [3721.0, 0]], [[1.0, 0], [67.16844584056173, 0], [4489.0, 0]], [[1.0, 0], [0, 20.940166718747637], [-5041.0, 0]], [[1.0, 0], [-97.7885289821727, 0], [5329.0, 0]], [[1.0, 0], [-41.40470771623284, 0], [6241.0, 0]], [[1.0, 0], [0, 121.92631019521738], [-6889.0, 0]], [[1.0, 0], [0, -26.814758046063673], [-7921.0, 0]], [[1.0, 0], [151.51230559081463, 0], [9409.0, 0]], [[1.0, 0], [0, -39.32175986354265], [-10201.0, 0]], [[1.0, 0], [70.21008288349562, 0], [10609.0, 0]], [[1.0, 0], [0, 86.04094063474784], [-11449.0, 0]], [[1.0, 0], [46.444776874174885, 0], [11881.0, 0]], [[1.0, 0], [0, 60.765935051230336], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 30, 'label': '2-1050-3.2-c2-0-30', 'leading_term': '1.763209639890941440940471358252447429383165719982817365', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1050/3/e/e/701/23', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.7632096398909414, 1.6124215666052262, 1.456300186791364, 1.2965025225120954, 1.1346733640248223, 0.9724609422771768, 0.8115303935558149, 0.6535735849151757, 0.5003140745929611, 0.35350623829461664, 0.21492788438335034, 0.08636599323697391, -0.03040446553207441, -0.13364837117610595, -0.22170437957191996, -0.29302409706716875, -0.34621540472110746, -0.3800886146762987, -0.39370395063411984, -0.3864186907076151, -0.35793219683708094, -0.30832698440023243, -0.23810396283100796, -0.14821000721125402, -0.04005610583211111, 0.08447552717264312, 0.22303677979747705, 0.3728325495890739, 0.5306540423651689, 0.6929268905205864, 0.8557740851816563, 1.0150932405558464, 1.1666472021690697, 1.306166486868131, 1.4294615172783782, 1.5325421044963576, 1.6117411592110973, 1.6638391930568488, 1.6861858288305396, 1.6768142896895408, 1.6345447016074117, 1.5590720359926689, 1.4510346531710079, 1.3120596912065179, 1.1447819824734466, 0.9528337714039068, 0.7408032440898928, 0.5141607510021053, 0.27915258892070927, 0.0426632821263194, -0.18795156481777262, -0.40505861555705885, -0.6009619871668339, -0.7681348304074216, -0.8994608908428066, -0.9884788132387199, -1.029621319925383, -1.0184409927885578, -0.9518142518233771, -0.8281152770869563, -0.6473520828403462, -0.41125772972433156, -0.12333074846914027, 0.2111797699474955, 0.5853473171607073, 0.9907003750848967, 1.4174130845186537, 1.8545510320189618, 2.2903668442625342, 2.712638162273016, 3.10903858694038, 3.4675304277219254, 3.7767666313360246, 4.026488193626608, 4.207902732917456, 4.314029781283009, 4.339998769094481, 4.283286656723864, 4.143883702920131, 3.9243779269537336, 3.629951372757154, 3.2682842467083715, 2.8493662836685973, 2.385218186575909, 1.8895295558084946, 1.3772232367857868, 0.8639593227210279, 0.36559500838124565, -0.10238103993585614, -0.5254192813857912, -0.8904632238107064, -1.1864647223014269, -1.4048392623701844, -1.5398412908903654, -1.5888419922354216, -1.5524950702910405, -1.4347799995708461, -1.2429167243115065, -0.987150753735529, -0.6804128370956947, -0.33786269460653034, 0.02366859261120017, 0.3863181958303337, 0.7318896968040731, 1.0425830312688769, 1.3017271576347706, 1.494485234983309, 1.6085021857040147, 1.6344659074556684, 1.5665560826056646, 1.4027584488577425, 1.1450274222799948, 0.7992859276690955, 0.3752579651033028, -0.11386344279885963, -0.6519030215536644, -1.2203277543959337, -1.7989855795092913, -2.3669289740799084, -2.903289490499578, -3.388166045889037, -3.8034880728838463, -4.1338146539283125, -4.367032545784891, -4.494919537978183, -4.513544777913309, -4.423484354141484, -4.2298382988249, -3.9420439245823946, -3.5734896686897657, -3.1409429596696437, -2.663814608424541, -2.1632904197077414, -1.6613677033929373, -1.17983976544034, -0.7392749656328421, -0.3580383139583168, -0.05140270616796792, 0.16920625662838698, 0.29679327662918353, 0.3291729733259026, 0.2691239527888447, 0.12430556945512222, -0.09306315290516098, -0.36675143191923926, -0.6772691663835209, -1.0027911250683192, -1.320210987423005, -1.606276074552155, -1.8387486108445878, -1.9975369367212235, -2.0657404409946967, -2.030555151716511, -1.8839928288755983, -1.6233748099766325, -1.2515724042139802, -0.7769778261021305, -0.2132029197092757, 0.4214834063868683, 1.1049547309243815, 1.8122269589431526, 2.5166110016774557, 3.1909623505554703, 3.8089658363524608, 4.34639120060912, 4.782255745092027, 5.0998342999910315, 5.287463919135817, 5.339100752885316, 5.254598986839188, 5.039695947460378, 4.705702734469508, 4.268915241958012, 3.749775342282116, 3.171825509955996, 2.560511497838212, 1.9418961891799358, 1.3413529232450563, 0.7823080903791619, 0.2851004734270648, -0.13398125454911308, -0.46343100058432024, -0.6969883348813795, -0.8338076786090228, -0.8783254585938002, -0.8398340782022653, -0.7317881992081289, -0.570884176098447, -0.37596663150383, -0.1668263187031681, 0.03704004759471648, 0.21763483085732466, 0.35955800067548654, 0.45093376401152807, 0.48410983858276185, 0.45608722944738656, 0.36865435018370246, 0.22821705560460848, 0.04533458875785006, -0.16601050692580757, -0.38936389553979445, -0.6069137110442314, -0.8006982683502685, -0.9538313969729035, -1.0516676426563922, -1.082832447612826, -1.0400499907532839, -0.9207132659226115, -0.727156543730072, -0.46660870429447665, -0.1508259547128559, 0.20457706311008936, 0.5810590886261174, 0.9582906859387703, 1.3154286328704576, 1.632445400618168, 1.8914276494221336, 2.0777578511525743, 2.1810988608988033, 2.1961122710325043, 2.1228571255613433, 1.9668351670510997, 1.7386710813643922, 1.4534398417151437, 1.1296767541805728, 0.788127659464432, 0.4503154995003484, 0.13701381706165738, -0.13327333096518926, -0.3457228367109043, -0.4903969878492992, -0.5631528230675001, -0.5661846805542982, -0.5081497600328525, -0.4038520135598439, -0.2734876227744999, -0.14148399668782657, -0.03499182041434359, 0.017885600102172168, -0.00997870693627992, -0.1427666975091667, -0.399832556847821, -0.7940308369538804, -1.33037179030599, -2.0051038625735274, -2.8053000801115844, -3.708996209538754, -4.685895727048764, -5.698621766517465, -6.704461456539477, -7.657515601326305, -8.5111386202373, -9.220531927339142, -9.745340051360028, -10.052093859160971, -10.116349807911757, -9.924388182488165], 'positive_zeros': ['0.68723362475501690343582978294254', '1.42590548909866247447317292652271', '2.88176602052346747786818084582180', '3.65532070371441034488671764522503', '5.14300158844107857628155660776777', '5.91416993437269436301634464799639', '6.66662825381452027276394600716384', '8.039088070209803533868692294730341', '8.355894699366726234232258446936723', '9.219545835697895836516837119749141'], 'prelabel': '2-1050-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.9116701194523409, 'root_number': '-0.96174428119569956923578253426624462244856197006362006815 - 0.2739487864316379043235395326256665666539641281847174580*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.45583505972617044', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68723362475501690343582978294', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.42590548909866247447317292652', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.88176602052346747786818084582', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 28.61042775783118, 'bad_primes': [2, 3, 5, 7], 'central_character': '3.2', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/e/e/701/23'], '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': '2-1050-3.2-c2-0-30', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1050-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.45583505972617044, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68723362475501690343582978294', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '871172116917718949516819109719', 'Lhash_array': ['871172116917718949516819109719'], 'label': '2-1050-3.2-c2-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/e/e/701/23'}