Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(80,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.80");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.p (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 80.8 | ||
Character | \(\chi\) | \(=\) | 441.80 |
Dual form | 441.4.p.d.215.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.10847 | + | 1.79468i | −1.09901 | + | 0.634514i | −0.935961 | − | 0.352104i | \(-0.885466\pi\) |
−0.163049 | + | 0.986618i | \(0.552133\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.44173 | − | 4.22919i | 0.305216 | − | 0.528649i | ||||
\(5\) | −0.428649 | − | 0.742442i | −0.0383395 | − | 0.0664060i | 0.846219 | − | 0.532835i | \(-0.178874\pi\) |
−0.884558 | + | 0.466429i | \(0.845540\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 11.1864i | − | 0.494373i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.66489 | + | 1.53857i | 0.0842711 | + | 0.0486539i | ||||
\(11\) | 0.321369 | + | 0.185543i | 0.00880877 | + | 0.00508574i | 0.504398 | − | 0.863471i | \(-0.331714\pi\) |
−0.495589 | + | 0.868557i | \(0.665048\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 62.0038i | 1.32283i | 0.750021 | + | 0.661414i | \(0.230043\pi\) | ||||
−0.750021 | + | 0.661414i | \(0.769957\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 39.6098 | + | 68.6061i | 0.618902 | + | 1.07197i | ||||
\(17\) | 51.9931 | − | 90.0547i | 0.741775 | − | 1.28479i | −0.209911 | − | 0.977720i | \(-0.567318\pi\) |
0.951686 | − | 0.307072i | \(-0.0993491\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −61.9469 | + | 35.7650i | −0.747978 | + | 0.431845i | −0.824963 | − | 0.565187i | \(-0.808804\pi\) |
0.0769848 | + | 0.997032i | \(0.475471\pi\) | |||||||
\(20\) | −4.18657 | −0.0468073 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.33196 | −0.0129079 | ||||||||
\(23\) | −118.248 | + | 68.2704i | −1.07202 | + | 0.618929i | −0.928732 | − | 0.370753i | \(-0.879100\pi\) |
−0.143284 | + | 0.989682i | \(0.545766\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.1325 | − | 107.617i | 0.497060 | − | 0.860933i | ||||
\(26\) | −111.277 | − | 192.737i | −0.839353 | − | 1.45380i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 17.8708i | − | 0.114432i | −0.998362 | − | 0.0572161i | \(-0.981778\pi\) | ||
0.998362 | − | 0.0572161i | \(-0.0182224\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −93.2782 | − | 53.8542i | −0.540428 | − | 0.312016i | 0.204824 | − | 0.978799i | \(-0.434338\pi\) |
−0.745252 | + | 0.666783i | \(0.767671\pi\) | |||||||
\(32\) | −168.750 | − | 97.4278i | −0.932221 | − | 0.538218i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 373.243i | 1.88267i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 190.857 | + | 330.575i | 0.848020 | + | 1.46881i | 0.882972 | + | 0.469425i | \(0.155539\pi\) |
−0.0349518 | + | 0.999389i | \(0.511128\pi\) | |||||||
\(38\) | 128.373 | − | 222.349i | 0.548024 | − | 0.949205i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.30525 | + | 4.79504i | −0.0328294 | + | 0.0189540i | ||||
\(41\) | −101.733 | −0.387511 | −0.193756 | − | 0.981050i | \(-0.562067\pi\) | ||||
−0.193756 | + | 0.981050i | \(0.562067\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −326.400 | −1.15757 | −0.578785 | − | 0.815480i | \(-0.696473\pi\) | ||||
−0.578785 | + | 0.815480i | \(0.696473\pi\) | |||||||
\(44\) | 1.56939 | − | 0.906088i | 0.00537715 | − | 0.00310450i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 245.047 | − | 424.433i | 0.785438 | − | 1.36042i | ||||
\(47\) | −261.065 | − | 452.178i | −0.810218 | − | 1.40334i | −0.912711 | − | 0.408606i | \(-0.866015\pi\) |
0.102493 | − | 0.994734i | \(-0.467318\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 446.031i | 1.26157i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 262.226 | + | 151.396i | 0.699312 | + | 0.403748i | ||||
\(53\) | −268.049 | − | 154.758i | −0.694704 | − | 0.401088i | 0.110668 | − | 0.993857i | \(-0.464701\pi\) |
−0.805372 | + | 0.592770i | \(0.798034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.318131i | − | 0.000779940i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 32.0724 | + | 55.5510i | 0.0726088 | + | 0.125762i | ||||
\(59\) | 174.386 | − | 302.045i | 0.384799 | − | 0.666491i | −0.606943 | − | 0.794746i | \(-0.707604\pi\) |
0.991741 | + | 0.128255i | \(0.0409376\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 580.478 | − | 335.139i | 1.21840 | − | 0.703445i | 0.253826 | − | 0.967250i | \(-0.418311\pi\) |
0.964576 | + | 0.263805i | \(0.0849775\pi\) | |||||||
\(62\) | 386.604 | 0.791914 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 65.6495 | 0.128222 | ||||||||
\(65\) | 46.0342 | − | 26.5779i | 0.0878437 | − | 0.0507166i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 119.685 | − | 207.301i | 0.218237 | − | 0.377997i | −0.736032 | − | 0.676947i | \(-0.763303\pi\) |
0.954269 | + | 0.298949i | \(0.0966362\pi\) | |||||||
\(68\) | −253.906 | − | 439.778i | −0.452803 | − | 0.784278i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 178.563i | − | 0.298472i | −0.988802 | − | 0.149236i | \(-0.952319\pi\) | ||
0.988802 | − | 0.149236i | \(-0.0476814\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 117.414 | + | 67.7891i | 0.188251 | + | 0.108687i | 0.591163 | − | 0.806552i | \(-0.298669\pi\) |
−0.402913 | + | 0.915238i | \(0.632002\pi\) | |||||||
\(74\) | −1186.55 | − | 685.054i | −1.86397 | − | 1.07616i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 349.314i | 0.527224i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −428.404 | − | 742.018i | −0.610117 | − | 1.05675i | −0.991220 | − | 0.132221i | \(-0.957789\pi\) |
0.381103 | − | 0.924532i | \(-0.375544\pi\) | |||||||
\(80\) | 33.9574 | − | 58.8159i | 0.0474569 | − | 0.0821977i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 316.233 | − | 182.577i | 0.425879 | − | 0.245881i | ||||
\(83\) | 1241.10 | 1.64130 | 0.820651 | − | 0.571430i | \(-0.193611\pi\) | ||||
0.820651 | + | 0.571430i | \(0.193611\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −89.1472 | −0.113757 | ||||||||
\(86\) | 1014.60 | − | 585.782i | 1.27218 | − | 0.734494i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.07555 | − | 3.59496i | 0.00251426 | − | 0.00435482i | ||||
\(89\) | 282.464 | + | 489.242i | 0.336417 | + | 0.582691i | 0.983756 | − | 0.179511i | \(-0.0574515\pi\) |
−0.647339 | + | 0.762202i | \(0.724118\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 666.790i | 0.755627i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1623.03 | + | 937.055i | 1.78088 | + | 1.02819i | ||||
\(95\) | 53.1069 | + | 30.6613i | 0.0573543 | + | 0.0331135i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1730.44i | − | 1.81134i | −0.423985 | − | 0.905669i | \(-0.639369\pi\) | ||
0.423985 | − | 0.905669i | \(-0.360631\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −303.421 | − | 525.541i | −0.303421 | − | 0.525541i | ||||
\(101\) | 627.920 | − | 1087.59i | 0.618617 | − | 1.07148i | −0.371121 | − | 0.928585i | \(-0.621026\pi\) |
0.989738 | − | 0.142892i | \(-0.0456402\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1351.32 | − | 780.186i | 1.29272 | − | 0.746350i | 0.313581 | − | 0.949561i | \(-0.398471\pi\) |
0.979135 | + | 0.203211i | \(0.0651378\pi\) | |||||||
\(104\) | 693.599 | 0.653971 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1110.96 | 1.01798 | ||||||||
\(107\) | −145.139 | + | 83.7959i | −0.131132 | + | 0.0757089i | −0.564131 | − | 0.825685i | \(-0.690789\pi\) |
0.432999 | + | 0.901394i | \(0.357455\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.5542 | + | 18.2803i | −0.00927435 | + | 0.0160636i | −0.870625 | − | 0.491947i | \(-0.836285\pi\) |
0.861351 | + | 0.508010i | \(0.169619\pi\) | |||||||
\(110\) | 0.570941 | + | 0.988899i | 0.000494883 | + | 0.000857162i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1111.80i | − | 0.925573i | −0.886470 | − | 0.462787i | \(-0.846850\pi\) | ||
0.886470 | − | 0.462787i | \(-0.153150\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 101.374 | + | 58.5281i | 0.0822012 | + | 0.0474589i | ||||
\(116\) | −75.5793 | − | 43.6357i | −0.0604945 | − | 0.0349265i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1251.87i | 0.976640i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −665.431 | − | 1152.56i | −0.499948 | − | 0.865936i | ||||
\(122\) | −1202.93 | + | 2083.54i | −0.892691 | + | 1.54619i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −455.520 | + | 262.994i | −0.329894 | + | 0.190465i | ||||
\(125\) | −213.694 | −0.152907 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1725.08 | −1.20532 | −0.602662 | − | 0.797997i | \(-0.705893\pi\) | ||||
−0.602662 | + | 0.797997i | \(0.705893\pi\) | |||||||
\(128\) | 1145.93 | − | 661.603i | 0.791304 | − | 0.456859i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −95.3974 | + | 165.233i | −0.0643608 | + | 0.111476i | ||||
\(131\) | 426.358 | + | 738.474i | 0.284359 | + | 0.492525i | 0.972454 | − | 0.233097i | \(-0.0748858\pi\) |
−0.688094 | + | 0.725621i | \(0.741552\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 859.184i | 0.553897i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1007.39 | − | 581.615i | −0.635167 | − | 0.366714i | ||||
\(137\) | −264.199 | − | 152.536i | −0.164760 | − | 0.0951241i | 0.415353 | − | 0.909660i | \(-0.363658\pi\) |
−0.580113 | + | 0.814536i | \(0.696991\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1689.85i | − | 1.03116i | −0.856841 | − | 0.515581i | \(-0.827576\pi\) | ||
0.856841 | − | 0.515581i | \(-0.172424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 320.462 | + | 555.057i | 0.189384 | + | 0.328024i | ||||
\(143\) | −11.5043 | + | 19.9261i | −0.00672756 | + | 0.0116525i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.2681 | + | 7.66032i | −0.00759899 | + | 0.00438728i | ||||
\(146\) | −486.638 | −0.275852 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1864.09 | 1.03532 | ||||||||
\(149\) | −1927.91 | + | 1113.08i | −1.06000 | + | 0.611993i | −0.925433 | − | 0.378911i | \(-0.876299\pi\) |
−0.134570 | + | 0.990904i | \(0.542965\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −410.604 | + | 711.188i | −0.221288 | + | 0.383282i | −0.955199 | − | 0.295963i | \(-0.904359\pi\) |
0.733911 | + | 0.679245i | \(0.237693\pi\) | |||||||
\(152\) | 400.082 | + | 692.962i | 0.213493 | + | 0.369780i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 92.3382i | 0.0478502i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1384.34 | − | 799.250i | −0.703710 | − | 0.406287i | 0.105018 | − | 0.994470i | \(-0.466510\pi\) |
−0.808728 | + | 0.588183i | \(0.799843\pi\) | |||||||
\(158\) | 2663.36 | + | 1537.69i | 1.34105 | + | 0.774255i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 167.049i | 0.0825401i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1296.33 | + | 2245.31i | 0.622923 | + | 1.07893i | 0.988939 | + | 0.148326i | \(0.0473883\pi\) |
−0.366016 | + | 0.930609i | \(0.619278\pi\) | |||||||
\(164\) | −248.403 | + | 430.247i | −0.118275 | + | 0.204857i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3857.91 | + | 2227.37i | −1.80381 | + | 1.04143i | ||||
\(167\) | −4136.77 | −1.91685 | −0.958423 | − | 0.285352i | \(-0.907889\pi\) | ||||
−0.958423 | + | 0.285352i | \(0.907889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1647.47 | −0.749873 | ||||||||
\(170\) | 277.111 | − | 159.990i | 0.125020 | − | 0.0721806i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −796.979 | + | 1380.41i | −0.353309 | + | 0.611948i | ||||
\(173\) | −1583.86 | − | 2743.33i | −0.696063 | − | 1.20562i | −0.969821 | − | 0.243818i | \(-0.921600\pi\) |
0.273757 | − | 0.961799i | \(-0.411733\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 29.3972i | 0.0125903i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1756.06 | − | 1013.86i | −0.739451 | − | 0.426922i | ||||
\(179\) | 3110.97 | + | 1796.12i | 1.29902 | + | 0.749991i | 0.980235 | − | 0.197836i | \(-0.0633913\pi\) |
0.318787 | + | 0.947827i | \(0.396725\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 314.936i | 0.129332i | 0.997907 | + | 0.0646658i | \(0.0205981\pi\) | ||||
−0.997907 | + | 0.0646658i | \(0.979402\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 763.699 | + | 1322.77i | 0.305982 | + | 0.529976i | ||||
\(185\) | 163.622 | − | 283.401i | 0.0650254 | − | 0.112627i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 33.4179 | − | 19.2939i | 0.0130682 | − | 0.00754495i | ||||
\(188\) | −2549.80 | −0.989166 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −220.108 | −0.0840439 | ||||||||
\(191\) | −3051.20 | + | 1761.61i | −1.15590 | + | 0.667359i | −0.950318 | − | 0.311281i | \(-0.899242\pi\) |
−0.205582 | + | 0.978640i | \(0.565909\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −360.020 | + | 623.573i | −0.134274 | + | 0.232569i | −0.925320 | − | 0.379188i | \(-0.876203\pi\) |
0.791046 | + | 0.611757i | \(0.209537\pi\) | |||||||
\(194\) | 3105.58 | + | 5379.03i | 1.14932 | + | 1.99068i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3479.92i | − | 1.25855i | −0.777184 | − | 0.629274i | \(-0.783353\pi\) | ||
0.777184 | − | 0.629274i | \(-0.216647\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3381.21 | − | 1952.14i | −1.20446 | − | 0.695395i | −0.242916 | − | 0.970047i | \(-0.578104\pi\) |
−0.961544 | + | 0.274652i | \(0.911437\pi\) | |||||||
\(200\) | −1203.84 | − | 695.039i | −0.425622 | − | 0.245733i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4507.65i | 1.57009i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 43.6076 | + | 75.5305i | 0.0148570 | + | 0.0257331i | ||||
\(206\) | −2800.36 | + | 4850.37i | −0.947139 | + | 1.64049i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4253.84 | + | 2455.96i | −1.41803 | + | 0.818701i | ||||
\(209\) | −26.5437 | −0.00878502 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2913.22 | 0.950494 | 0.475247 | − | 0.879852i | \(-0.342359\pi\) | ||||
0.475247 | + | 0.879852i | \(0.342359\pi\) | |||||||
\(212\) | −1309.00 | + | 755.753i | −0.424069 | + | 0.244837i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 300.773 | − | 520.954i | 0.0960767 | − | 0.166410i | ||||
\(215\) | 139.911 | + | 242.333i | 0.0443807 | + | 0.0768696i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 75.7651i | − | 0.0235388i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.34544 | − | 0.776788i | −0.000412315 | − | 0.000238050i | ||||
\(221\) | 5583.73 | + | 3223.77i | 1.69956 | + | 0.981241i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1202.30i | − | 0.361040i | −0.983571 | − | 0.180520i | \(-0.942222\pi\) | ||
0.983571 | − | 0.180520i | \(-0.0577780\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1995.33 | + | 3456.01i | 0.587289 | + | 1.01721i | ||||
\(227\) | 2567.71 | − | 4447.40i | 0.750770 | − | 1.30037i | −0.196681 | − | 0.980468i | \(-0.563016\pi\) |
0.947450 | − | 0.319903i | \(-0.103650\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1625.94 | + | 938.735i | −0.469192 | + | 0.270888i | −0.715901 | − | 0.698202i | \(-0.753984\pi\) |
0.246710 | + | 0.969089i | \(0.420651\pi\) | |||||||
\(230\) | −420.156 | −0.120453 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −199.910 | −0.0565722 | ||||||||
\(233\) | −3016.28 | + | 1741.45i | −0.848081 | + | 0.489640i | −0.860003 | − | 0.510289i | \(-0.829538\pi\) |
0.0119216 | + | 0.999929i | \(0.496205\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −223.811 | + | 387.651i | −0.0621268 | + | 0.107607i | ||||
\(236\) | −851.605 | − | 1475.02i | −0.234893 | − | 0.406847i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2466.36i | − | 0.667514i | −0.942659 | − | 0.333757i | \(-0.891684\pi\) | ||
0.942659 | − | 0.333757i | \(-0.108316\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2112.76 | + | 1219.80i | 0.564709 | + | 0.326035i | 0.755033 | − | 0.655686i | \(-0.227621\pi\) |
−0.190324 | + | 0.981721i | \(0.560954\pi\) | |||||||
\(242\) | 4136.95 | + | 2388.47i | 1.09890 | + | 0.634448i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 3273.27i | − | 0.858810i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2217.57 | − | 3840.94i | −0.571257 | − | 0.989446i | ||||
\(248\) | −602.434 | + | 1043.45i | −0.154252 | + | 0.267173i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 664.263 | − | 383.512i | 0.168047 | − | 0.0970218i | ||||
\(251\) | −4329.06 | −1.08864 | −0.544319 | − | 0.838878i | \(-0.683212\pi\) | ||||
−0.544319 | + | 0.838878i | \(0.683212\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −50.6682 | −0.0125909 | ||||||||
\(254\) | 5362.36 | − | 3095.96i | 1.32466 | − | 0.764795i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2637.32 | + | 4567.98i | −0.643878 | + | 1.11523i | ||||
\(257\) | 1570.68 | + | 2720.50i | 0.381231 | + | 0.660312i | 0.991239 | − | 0.132084i | \(-0.0421669\pi\) |
−0.610007 | + | 0.792396i | \(0.708834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 259.584i | − | 0.0619180i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2650.64 | − | 1530.35i | −0.625028 | − | 0.360860i | ||||
\(263\) | −6663.55 | − | 3847.20i | −1.56233 | − | 0.902010i | −0.997021 | − | 0.0771283i | \(-0.975425\pi\) |
−0.565306 | − | 0.824882i | \(-0.691242\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 265.348i | 0.0615101i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −584.477 | − | 1012.34i | −0.133219 | − | 0.230741i | ||||
\(269\) | −698.723 | + | 1210.22i | −0.158371 | + | 0.274307i | −0.934281 | − | 0.356536i | \(-0.883958\pi\) |
0.775910 | + | 0.630843i | \(0.217291\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2135.91 | − | 1233.17i | 0.478772 | − | 0.276419i | −0.241133 | − | 0.970492i | \(-0.577519\pi\) |
0.719905 | + | 0.694073i | \(0.244186\pi\) | |||||||
\(272\) | 8237.73 | 1.83635 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1095.01 | 0.241430 | ||||||||
\(275\) | 39.9349 | − | 23.0564i | 0.00875697 | − | 0.00505584i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1086.42 | + | 1881.73i | −0.235655 | + | 0.408167i | −0.959463 | − | 0.281835i | \(-0.909057\pi\) |
0.723808 | + | 0.690002i | \(0.242390\pi\) | |||||||
\(278\) | 3032.74 | + | 5252.86i | 0.654287 | + | 1.13326i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4631.24i | 0.983191i | 0.870824 | + | 0.491596i | \(0.163586\pi\) | ||||
−0.870824 | + | 0.491596i | \(0.836414\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5999.60 | + | 3463.87i | 1.26021 | + | 0.727582i | 0.973115 | − | 0.230320i | \(-0.0739772\pi\) |
0.287095 | + | 0.957902i | \(0.407311\pi\) | |||||||
\(284\) | −755.176 | − | 436.001i | −0.157787 | − | 0.0910983i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 82.5863i | − | 0.0170749i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2950.06 | − | 5109.66i | −0.600460 | − | 1.04003i | ||||
\(290\) | 27.4956 | − | 47.6238i | 0.00556758 | − | 0.00964332i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 573.387 | − | 331.045i | 0.114914 | − | 0.0663457i | ||||
\(293\) | −667.366 | −0.133065 | −0.0665323 | − | 0.997784i | \(-0.521194\pi\) | ||||
−0.0665323 | + | 0.997784i | \(0.521194\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −299.002 | −0.0590120 | ||||||||
\(296\) | 3697.94 | − | 2135.00i | 0.726143 | − | 0.419239i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3995.23 | − | 6919.94i | 0.776636 | − | 1.34517i | ||||
\(299\) | −4233.02 | − | 7331.81i | −0.818736 | − | 1.41809i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 2947.61i | − | 0.561642i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4907.40 | − | 2833.29i | −0.925851 | − | 0.534540i | ||||
\(305\) | −497.642 | − | 287.314i | −0.0934260 | − | 0.0539395i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10190.1i | − | 1.89439i | −0.320658 | − | 0.947195i | \(-0.603904\pi\) | ||
0.320658 | − | 0.947195i | \(-0.396096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −165.717 | − | 287.031i | −0.0303616 | − | 0.0525879i | ||||
\(311\) | −4800.99 | + | 8315.56i | −0.875367 | + | 1.51618i | −0.0189952 | + | 0.999820i | \(0.506047\pi\) |
−0.856372 | + | 0.516360i | \(0.827287\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5683.70 | − | 3281.48i | 1.02639 | − | 0.592589i | 0.110445 | − | 0.993882i | \(-0.464772\pi\) |
0.915950 | + | 0.401293i | \(0.131439\pi\) | |||||||
\(314\) | 5737.58 | 1.03118 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4184.18 | −0.744869 | ||||||||
\(317\) | 115.552 | − | 66.7137i | 0.0204732 | − | 0.0118202i | −0.489728 | − | 0.871875i | \(-0.662904\pi\) |
0.510202 | + | 0.860055i | \(0.329571\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.31580 | − | 5.74314i | 0.000581973 | − | 0.00100801i | ||||
\(320\) | −28.1406 | − | 48.7410i | −0.00491596 | − | 0.00851470i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7438.14i | 1.28133i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6672.64 | + | 3852.45i | 1.13887 | + | 0.657525i | ||||
\(326\) | −8059.21 | − | 4652.99i | −1.36920 | − | 0.790507i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1138.02i | 0.191575i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2393.76 | − | 4146.11i | −0.397501 | − | 0.688492i | 0.595916 | − | 0.803047i | \(-0.296789\pi\) |
−0.993417 | + | 0.114555i | \(0.963456\pi\) | |||||||
\(332\) | 3030.42 | − | 5248.84i | 0.500951 | − | 0.867673i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12859.0 | − | 7424.17i | 2.10663 | − | 1.21627i | ||||
\(335\) | −205.212 | −0.0334684 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8273.70 | 1.33738 | 0.668690 | − | 0.743541i | \(-0.266855\pi\) | ||||
0.668690 | + | 0.743541i | \(0.266855\pi\) | |||||||
\(338\) | 5121.12 | − | 2956.68i | 0.824118 | − | 0.475805i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −217.673 | + | 377.021i | −0.0347205 | + | 0.0601377i | ||||
\(341\) | −19.9845 | − | 34.6142i | −0.00317367 | − | 0.00549696i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3651.24i | 0.572272i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9846.79 | + | 5685.05i | 1.52996 | + | 0.883324i | ||||
\(347\) | 3203.79 | + | 1849.71i | 0.495644 | + | 0.286160i | 0.726913 | − | 0.686730i | \(-0.240954\pi\) |
−0.231269 | + | 0.972890i | \(0.574288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 903.273i | 0.138542i | 0.997598 | + | 0.0692709i | \(0.0220673\pi\) | ||||
−0.997598 | + | 0.0692709i | \(0.977933\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −36.1540 | − | 62.6206i | −0.00547447 | − | 0.00948207i | ||||
\(353\) | 5080.80 | − | 8800.20i | 0.766073 | − | 1.32688i | −0.173605 | − | 0.984815i | \(-0.555542\pi\) |
0.939678 | − | 0.342061i | \(-0.111125\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −132.572 | + | 76.5408i | −0.0198203 | + | 0.0114433i | ||||
\(356\) | 2758.80 | 0.410719 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12893.8 | −1.90352 | ||||||||
\(359\) | 3651.25 | − | 2108.05i | 0.536784 | − | 0.309912i | −0.206991 | − | 0.978343i | \(-0.566367\pi\) |
0.743775 | + | 0.668431i | \(0.233034\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −871.225 | + | 1509.01i | −0.127019 | + | 0.220004i | ||||
\(362\) | −565.209 | − | 978.970i | −0.0820627 | − | 0.142137i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 116.231i | − | 0.0166680i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −468.678 | − | 270.591i | −0.0666615 | − | 0.0384871i | 0.466299 | − | 0.884627i | \(-0.345587\pi\) |
−0.532960 | + | 0.846140i | \(0.678921\pi\) | |||||||
\(368\) | −9367.53 | − | 5408.35i | −1.32695 | − | 0.766113i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1174.59i | 0.165038i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1120.17 | − | 1940.19i | −0.155496 | − | 0.269328i | 0.777743 | − | 0.628582i | \(-0.216364\pi\) |
−0.933240 | + | 0.359254i | \(0.883031\pi\) | |||||||
\(374\) | −69.2525 | + | 119.949i | −0.00957476 | + | 0.0165840i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5058.24 | + | 2920.38i | −0.693773 | + | 0.400550i | ||||
\(377\) | 1108.06 | 0.151374 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2922.72 | −0.396121 | −0.198060 | − | 0.980190i | \(-0.563464\pi\) | ||||
−0.198060 | + | 0.980190i | \(0.563464\pi\) | |||||||
\(380\) | 259.345 | − | 149.733i | 0.0350109 | − | 0.0202135i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6323.04 | − | 10951.8i | 0.846897 | − | 1.46687i | ||||
\(383\) | −3526.59 | − | 6108.23i | −0.470497 | − | 0.814924i | 0.528934 | − | 0.848663i | \(-0.322592\pi\) |
−0.999431 | + | 0.0337386i | \(0.989259\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 2584.48i | − | 0.340794i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7318.38 | − | 4225.27i | −0.957562 | − | 0.552849i | ||||
\(389\) | −8598.98 | − | 4964.62i | −1.12079 | − | 0.647086i | −0.179184 | − | 0.983816i | \(-0.557346\pi\) |
−0.941601 | + | 0.336730i | \(0.890679\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14198.4i | 1.83642i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6245.32 | + | 10817.2i | 0.798566 | + | 1.38316i | ||||
\(395\) | −367.270 | + | 636.131i | −0.0467832 | + | 0.0810309i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2207.29 | − | 1274.38i | 0.279044 | − | 0.161106i | −0.353946 | − | 0.935266i | \(-0.615160\pi\) |
0.632991 | + | 0.774159i | \(0.281827\pi\) | |||||||
\(398\) | 14013.9 | 1.76495 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9844.22 | 1.23053 | ||||||||
\(401\) | −4468.23 | + | 2579.74i | −0.556441 | + | 0.321261i | −0.751716 | − | 0.659487i | \(-0.770774\pi\) |
0.195275 | + | 0.980749i | \(0.437440\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3339.17 | − | 5783.61i | 0.412744 | − | 0.714893i | ||||
\(404\) | −3066.42 | − | 5311.19i | −0.377624 | − | 0.654063i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 141.649i | 0.0172513i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6922.74 | + | 3996.85i | 0.836938 | + | 0.483206i | 0.856222 | − | 0.516608i | \(-0.172805\pi\) |
−0.0192844 | + | 0.999814i | \(0.506139\pi\) | |||||||
\(410\) | −271.106 | − | 156.523i | −0.0326560 | − | 0.0188539i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 7620.01i | − | 0.911191i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −531.995 | − | 921.443i | −0.0629268 | − | 0.108992i | ||||
\(416\) | 6040.90 | − | 10463.1i | 0.711969 | − | 1.23317i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 82.5104 | − | 47.6374i | 0.00965483 | − | 0.00557422i | ||||
\(419\) | −5972.30 | −0.696338 | −0.348169 | − | 0.937432i | \(-0.613197\pi\) | ||||
−0.348169 | + | 0.937432i | \(0.613197\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12647.3 | 1.46412 | 0.732058 | − | 0.681242i | \(-0.238560\pi\) | ||||
0.732058 | + | 0.681242i | \(0.238560\pi\) | |||||||
\(422\) | −9055.66 | + | 5228.29i | −1.04460 | + | 0.603102i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1731.18 | + | 2998.50i | −0.198287 | + | 0.343443i | ||||
\(425\) | −6460.92 | − | 11190.6i | −0.737414 | − | 1.27724i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 818.426i | 0.0924302i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −869.818 | − | 502.190i | −0.0975497 | − | 0.0563203i | ||||
\(431\) | 2947.84 | + | 1701.94i | 0.329449 | + | 0.190207i | 0.655596 | − | 0.755111i | \(-0.272417\pi\) |
−0.326148 | + | 0.945319i | \(0.605751\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7413.29i | 0.822772i | 0.911461 | + | 0.411386i | \(0.134955\pi\) | ||||
−0.911461 | + | 0.411386i | \(0.865045\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 51.5407 | + | 89.2711i | 0.00566136 | + | 0.00980576i | ||||
\(437\) | 4883.39 | − | 8458.27i | 0.534563 | − | 0.925890i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4020.87 | + | 2321.45i | −0.437142 | + | 0.252384i | −0.702385 | − | 0.711797i | \(-0.747881\pi\) |
0.265242 | + | 0.964182i | \(0.414548\pi\) | |||||||
\(440\) | −3.55873 | −0.000385582 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −23142.5 | −2.49044 | ||||||||
\(443\) | −2570.90 | + | 1484.31i | −0.275727 | + | 0.159191i | −0.631487 | − | 0.775386i | \(-0.717555\pi\) |
0.355761 | + | 0.934577i | \(0.384222\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 242.156 | − | 419.426i | 0.0257961 | − | 0.0446802i | ||||
\(446\) | 2157.74 | + | 3737.31i | 0.229085 | + | 0.396786i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 8732.52i | − | 0.917847i | −0.888476 | − | 0.458923i | \(-0.848235\pi\) | ||
0.888476 | − | 0.458923i | \(-0.151765\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.6937 | − | 18.8757i | −0.00341350 | − | 0.00197078i | ||||
\(452\) | −4702.04 | − | 2714.72i | −0.489304 | − | 0.282500i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18432.8i | 1.90549i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6049.30 | + | 10477.7i | 0.619200 | + | 1.07249i | 0.989632 | + | 0.143626i | \(0.0458762\pi\) |
−0.370432 | + | 0.928859i | \(0.620790\pi\) | |||||||
\(458\) | 3369.45 | − | 5836.06i | 0.343764 | − | 0.595417i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 495.053 | − | 285.819i | 0.0501782 | − | 0.0289704i | ||||
\(461\) | −7746.32 | −0.782608 | −0.391304 | − | 0.920261i | \(-0.627976\pi\) | ||||
−0.391304 | + | 0.920261i | \(0.627976\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2573.36 | 0.258303 | 0.129152 | − | 0.991625i | \(-0.458775\pi\) | ||||
0.129152 | + | 0.991625i | \(0.458775\pi\) | |||||||
\(464\) | 1226.05 | − | 707.860i | 0.122668 | − | 0.0708223i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6250.68 | − | 10826.5i | 0.621367 | − | 1.07624i | ||||
\(467\) | −1193.94 | − | 2067.96i | −0.118306 | − | 0.204911i | 0.800791 | − | 0.598944i | \(-0.204413\pi\) |
−0.919096 | + | 0.394033i | \(0.871080\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 1606.67i | − | 0.157681i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3378.80 | − | 1950.75i | −0.329495 | − | 0.190234i | ||||
\(473\) | −104.895 | − | 60.5610i | −0.0101968 | − | 0.00588710i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8888.69i | 0.858612i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4426.32 | + | 7666.62i | 0.423547 | + | 0.733605i | ||||
\(479\) | −1453.00 | + | 2516.67i | −0.138600 | + | 0.240062i | −0.926967 | − | 0.375143i | \(-0.877593\pi\) |
0.788367 | + | 0.615205i | \(0.210927\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20496.9 | + | 11833.9i | −1.94299 | + | 1.12178i | ||||
\(482\) | −8756.60 | −0.827495 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6499.20 | −0.610368 | ||||||||
\(485\) | −1284.75 | + | 741.753i | −0.120284 | + | 0.0694459i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −132.268 | + | 229.095i | −0.0123072 | + | 0.0213168i | −0.872113 | − | 0.489304i | \(-0.837251\pi\) |
0.859806 | + | 0.510621i | \(0.170584\pi\) | |||||||
\(488\) | −3748.99 | − | 6493.45i | −0.347764 | − | 0.602346i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19788.0i | 1.81878i | 0.415943 | + | 0.909391i | \(0.363452\pi\) | ||||
−0.415943 | + | 0.909391i | \(0.636548\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1609.35 | − | 929.160i | −0.147022 | − | 0.0848829i | ||||
\(494\) | 13786.5 | + | 7959.63i | 1.25563 | + | 0.724941i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8532.61i | − | 0.772430i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5735.87 | + | 9934.82i | 0.514575 | + | 0.891270i | 0.999857 | + | 0.0169124i | \(0.00538363\pi\) |
−0.485282 | + | 0.874358i | \(0.661283\pi\) | |||||||
\(500\) | −521.783 | + | 903.755i | −0.0466697 | + | 0.0808343i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13456.8 | − | 7769.27i | 1.19642 | − | 0.690756i | ||||
\(503\) | −1261.66 | −0.111839 | −0.0559193 | − | 0.998435i | \(-0.517809\pi\) | ||||
−0.0559193 | + | 0.998435i | \(0.517809\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1076.63 | −0.0948700 | ||||||||
\(506\) | 157.501 | − | 90.9331i | 0.0138375 | − | 0.00798907i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4212.17 | + | 7295.70i | −0.367884 | + | 0.637194i | ||||
\(509\) | 4261.39 | + | 7380.94i | 0.371086 | + | 0.642740i | 0.989733 | − | 0.142929i | \(-0.0456522\pi\) |
−0.618647 | + | 0.785669i | \(0.712319\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 8346.93i | − | 0.720480i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9764.83 | − | 5637.73i | −0.837954 | − | 0.483793i | ||||
\(515\) | −1158.49 | − | 668.853i | −0.0991243 | − | 0.0572294i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 193.755i | − | 0.0164823i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −297.310 | − | 514.957i | −0.0250729 | − | 0.0434276i | ||||
\(521\) | −6608.58 | + | 11446.4i | −0.555714 | + | 0.962525i | 0.442133 | + | 0.896949i | \(0.354222\pi\) |
−0.997848 | + | 0.0655760i | \(0.979112\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7783.83 | − | 4493.99i | 0.650790 | − | 0.375734i | −0.137969 | − | 0.990437i | \(-0.544057\pi\) |
0.788759 | + | 0.614703i | \(0.210724\pi\) | |||||||
\(524\) | 4164.20 | 0.347164 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27617.9 | 2.28935 | ||||||||
\(527\) | −9699.65 | + | 5600.09i | −0.801752 | + | 0.462892i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3238.19 | − | 5608.72i | 0.266146 | − | 0.460978i | ||||
\(530\) | −476.213 | − | 824.825i | −0.0390290 | − | 0.0676002i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6307.81i | − | 0.512611i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 124.427 | + | 71.8381i | 0.0100551 | + | 0.00580529i | ||||
\(536\) | −2318.95 | − | 1338.84i | −0.186872 | − | 0.107890i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 5015.92i | − | 0.401955i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5815.74 | − | 10073.2i | −0.462178 | − | 0.800516i | 0.536891 | − | 0.843652i | \(-0.319599\pi\) |
−0.999069 | + | 0.0431356i | \(0.986265\pi\) | |||||||
\(542\) | −4426.27 | + | 7666.53i | −0.350784 | + | 0.607575i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17547.7 | + | 10131.1i | −1.38300 | + | 0.798473i | ||||
\(545\) | 18.0961 | 0.00142230 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23271.9 | −1.81908 | −0.909538 | − | 0.415622i | \(-0.863564\pi\) | ||||
−0.909538 | + | 0.415622i | \(0.863564\pi\) | |||||||
\(548\) | −1290.21 | + | 744.900i | −0.100575 | + | 0.0580667i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −82.7577 | + | 143.341i | −0.00641600 | + | 0.0111128i | ||||
\(551\) | 639.151 | + | 1107.04i | 0.0494170 | + | 0.0855927i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 7799.07i | − | 0.598106i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7146.72 | − | 4126.16i | −0.545123 | − | 0.314727i | ||||
\(557\) | 211.015 | + | 121.830i | 0.0160521 | + | 0.00926767i | 0.508005 | − | 0.861354i | \(-0.330383\pi\) |
−0.491952 | + | 0.870622i | \(0.663717\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 20238.0i | − | 1.53127i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8311.58 | − | 14396.1i | −0.623848 | − | 1.08054i | ||||
\(563\) | −4606.13 | + | 7978.05i | −0.344805 | + | 0.597220i | −0.985318 | − | 0.170727i | \(-0.945388\pi\) |
0.640513 | + | 0.767947i | \(0.278722\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −825.450 | + | 476.574i | −0.0614637 | + | 0.0354861i | ||||
\(566\) | −24866.1 | −1.84664 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1997.47 | −0.147556 | ||||||||
\(569\) | 6941.28 | − | 4007.55i | 0.511413 | − | 0.295264i | −0.222001 | − | 0.975046i | \(-0.571259\pi\) |
0.733414 | + | 0.679782i | \(0.237926\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10058.3 | + | 17421.5i | −0.737173 | + | 1.27682i | 0.216590 | + | 0.976263i | \(0.430507\pi\) |
−0.953763 | + | 0.300559i | \(0.902827\pi\) | |||||||
\(572\) | 56.1809 | + | 97.3082i | 0.00410672 | + | 0.00711304i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16967.2i | 1.23058i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10355.4 | − | 5978.68i | −0.747141 | − | 0.431362i | 0.0775191 | − | 0.996991i | \(-0.475300\pi\) |
−0.824660 | + | 0.565629i | \(0.808633\pi\) | |||||||
\(578\) | 18340.4 | + | 10588.8i | 1.31982 | + | 0.762001i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 74.8176i | 0.00535626i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −57.4284 | − | 99.4689i | −0.00407966 | − | 0.00706617i | ||||
\(584\) | 758.316 | − | 1313.44i | 0.0537317 | − | 0.0930661i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2074.49 | − | 1197.71i | 0.146239 | − | 0.0844314i | ||||
\(587\) | −5400.12 | −0.379705 | −0.189852 | − | 0.981813i | \(-0.560801\pi\) | ||||
−0.189852 | + | 0.981813i | \(0.560801\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7704.39 | 0.538971 | ||||||||
\(590\) | 929.437 | − | 536.611i | 0.0648548 | − | 0.0374439i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −15119.6 | + | 26188.0i | −1.04968 | + | 1.81811i | ||||
\(593\) | 11877.2 | + | 20571.9i | 0.822491 | + | 1.42460i | 0.903822 | + | 0.427909i | \(0.140750\pi\) |
−0.0813305 | + | 0.996687i | \(0.525917\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10871.3i | 0.747160i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 26316.5 | + | 15193.8i | 1.79960 | + | 1.03900i | ||||
\(599\) | 1263.64 | + | 729.564i | 0.0861953 | + | 0.0497649i | 0.542478 | − | 0.840070i | \(-0.317486\pi\) |
−0.456283 | + | 0.889835i | \(0.650819\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5357.92i | 0.363651i | 0.983331 | + | 0.181825i | \(0.0582006\pi\) | ||||
−0.983331 | + | 0.181825i | \(0.941799\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2005.17 | + | 3473.05i | 0.135081 | + | 0.233968i | ||||
\(605\) | −570.473 | + | 988.088i | −0.0383356 | + | 0.0663992i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8773.63 | − | 5065.46i | 0.586673 | − | 0.338716i | −0.177108 | − | 0.984191i | \(-0.556674\pi\) |
0.763781 | + | 0.645475i | \(0.223341\pi\) | |||||||
\(608\) | 13938.0 | 0.929707 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2062.54 | 0.136901 | ||||||||
\(611\) | 28036.8 | − | 16187.0i | 1.85638 | − | 1.07178i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1217.62 | − | 2108.99i | 0.0802274 | − | 0.138958i | −0.823120 | − | 0.567867i | \(-0.807769\pi\) |
0.903348 | + | 0.428909i | \(0.141102\pi\) | |||||||
\(614\) | 18287.9 | + | 31675.5i | 1.20202 | + | 2.08195i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 28047.4i | − | 1.83006i | −0.403389 | − | 0.915029i | \(-0.632168\pi\) | ||
0.403389 | − | 0.915029i | \(-0.367832\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14086.2 | − | 8132.66i | −0.914655 | − | 0.528076i | −0.0327292 | − | 0.999464i | \(-0.510420\pi\) |
−0.881926 | + | 0.471388i | \(0.843753\pi\) | |||||||
\(620\) | 390.516 | + | 225.465i | 0.0252960 | + | 0.0146046i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 34464.9i | − | 2.22173i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7674.97 | − | 13293.4i | −0.491198 | − | 0.850779i | ||||
\(626\) | −11778.4 | + | 20400.8i | −0.752012 | + | 1.30252i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6760.36 | + | 3903.10i | −0.429567 | + | 0.248010i | ||||
\(629\) | 39693.0 | 2.51616 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13662.1 | 0.861931 | 0.430966 | − | 0.902368i | \(-0.358173\pi\) | ||||
0.430966 | + | 0.902368i | \(0.358173\pi\) | |||||||
\(632\) | −8300.50 | + | 4792.30i | −0.522431 | + | 0.301625i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −239.459 | + | 414.755i | −0.0150002 | + | 0.0259811i | ||||
\(635\) | 739.454 | + | 1280.77i | 0.0462116 | + | 0.0800408i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 23.8032i | 0.00147708i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −982.404 | − | 567.191i | −0.0606764 | − | 0.0350316i | ||||
\(641\) | 23643.1 | + | 13650.3i | 1.45686 | + | 0.841117i | 0.998855 | − | 0.0478346i | \(-0.0152320\pi\) |
0.458002 | + | 0.888951i | \(0.348565\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 6857.85i | − | 0.420602i | −0.977637 | − | 0.210301i | \(-0.932556\pi\) | ||
0.977637 | − | 0.210301i | \(-0.0674445\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13349.1 | − | 23121.2i | −0.813021 | − | 1.40819i | ||||
\(647\) | −4134.32 | + | 7160.85i | −0.251216 | + | 0.435119i | −0.963861 | − | 0.266406i | \(-0.914164\pi\) |
0.712645 | + | 0.701525i | \(0.247497\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 112.084 | − | 64.7120i | 0.00677920 | − | 0.00391397i | ||||
\(650\) | −27655.6 | −1.66883 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12661.1 | 0.760504 | ||||||||
\(653\) | 10492.9 | − | 6058.07i | 0.628818 | − | 0.363048i | −0.151476 | − | 0.988461i | \(-0.548403\pi\) |
0.780294 | + | 0.625413i | \(0.215069\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 365.516 | − | 633.092i | 0.0218044 | − | 0.0377663i | ||||
\(656\) | −4029.60 | − | 6979.48i | −0.239832 | − | 0.415401i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 11814.0i | − | 0.698343i | −0.937059 | − | 0.349171i | \(-0.886463\pi\) | ||
0.937059 | − | 0.349171i | \(-0.113537\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23198.2 | + | 13393.5i | 1.36506 | + | 0.788119i | 0.990292 | − | 0.138999i | \(-0.0443886\pi\) |
0.374769 | + | 0.927118i | \(0.377722\pi\) | |||||||
\(662\) | 14881.9 | + | 8592.05i | 0.873716 | + | 0.504440i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 13883.4i | − | 0.811416i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1220.05 | + | 2113.19i | 0.0708253 | + | 0.122673i | ||||
\(668\) | −10100.9 | + | 17495.2i | −0.585051 | + | 1.01334i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 637.895 | − | 368.289i | 0.0367821 | − | 0.0212362i | ||||
\(671\) | 248.730 | 0.0143102 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3317.25 | 0.190001 | 0.0950004 | − | 0.995477i | \(-0.469715\pi\) | ||||
0.0950004 | + | 0.995477i | \(0.469715\pi\) | |||||||
\(674\) | −25718.6 | + | 14848.6i | −1.46980 | + | 0.848587i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4022.67 | + | 6967.48i | −0.228873 | + | 0.396420i | ||||
\(677\) | 14873.9 | + | 25762.4i | 0.844388 | + | 1.46252i | 0.886152 | + | 0.463395i | \(0.153369\pi\) |
−0.0417637 | + | 0.999128i | \(0.513298\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 997.235i | 0.0562385i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 124.242 | + | 71.7314i | 0.00697579 | + | 0.00402747i | ||||
\(683\) | −16830.2 | − | 9716.94i | −0.942886 | − | 0.544375i | −0.0520221 | − | 0.998646i | \(-0.516567\pi\) |
−0.890864 | + | 0.454270i | \(0.849900\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 261.537i | 0.0145881i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12928.6 | − | 22393.0i | −0.716423 | − | 1.24088i | ||||
\(689\) | 9595.58 | − | 16620.0i | 0.530570 | − | 0.918974i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2798.73 | − | 1615.85i | 0.154079 | − | 0.0889578i | −0.420978 | − | 0.907071i | \(-0.638313\pi\) |
0.575057 | + | 0.818113i | \(0.304980\pi\) | |||||||
\(692\) | −15469.5 | −0.849798 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13278.5 | −0.726290 | ||||||||
\(695\) | −1254.62 | + | 724.354i | −0.0684754 | + | 0.0395343i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5289.39 | + | 9161.49i | −0.287446 | + | 0.497871i | ||||
\(698\) | −1621.08 | − | 2807.80i | −0.0879067 | − | 0.152259i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6802.40i | − | 0.366509i | −0.983065 | − | 0.183255i | \(-0.941337\pi\) | ||
0.983065 | − | 0.183255i | \(-0.0586633\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23646.0 | − | 13652.0i | −1.26860 | − | 0.732427i | ||||
\(704\) | 21.0977 | + | 12.1808i | 0.00112948 | + | 0.000652103i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 36473.6i | 1.94433i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3508.04 | + | 6076.11i | 0.185821 | + | 0.321852i | 0.943853 | − | 0.330366i | \(-0.107172\pi\) |
−0.758032 | + | 0.652218i | \(0.773839\pi\) | |||||||
\(710\) | 274.732 | − | 475.849i | 0.0145218 | − | 0.0251525i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5472.85 | − | 3159.75i | 0.288067 | − | 0.166316i | ||||
\(713\) | 14706.6 | 0.772463 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.7253 | 0.00103173 | ||||||||
\(716\) | 15192.3 | − | 8771.27i | 0.792964 | − | 0.457818i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7566.53 | + | 13105.6i | −0.393287 | + | 0.681194i | ||||
\(719\) | 9045.55 | + | 15667.3i | 0.469182 | + | 0.812647i | 0.999379 | − | 0.0352269i | \(-0.0112154\pi\) |
−0.530197 | + | 0.847874i | \(0.677882\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 6254.26i | − | 0.322382i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1331.93 | + | 768.988i | 0.0683711 | + | 0.0394741i | ||||
\(725\) | −1923.20 | − | 1110.36i | −0.0985185 | − | 0.0568797i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 35637.5i | − | 1.81805i | −0.416745 | − | 0.909024i | \(-0.636829\pi\) | ||
0.416745 | − | 0.909024i | \(-0.363171\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 208.597 | + | 361.301i | 0.0105761 | + | 0.0183183i | ||||
\(731\) | −16970.5 | + | 29393.8i | −0.858656 | + | 1.48724i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10723.2 | + | 6191.06i | −0.540343 | + | 0.311967i | −0.745218 | − | 0.666821i | \(-0.767655\pi\) |
0.204875 | + | 0.978788i | \(0.434321\pi\) | |||||||
\(734\) | 1942.50 | 0.0976823 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26605.7 | 1.33247 | ||||||||
\(737\) | 76.9262 | − | 44.4134i | 0.00384479 | − | 0.00221979i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5933.76 | − | 10277.6i | 0.295368 | − | 0.511592i | −0.679703 | − | 0.733488i | \(-0.737891\pi\) |
0.975070 | + | 0.221896i | \(0.0712245\pi\) | |||||||
\(740\) | −799.039 | − | 1383.98i | −0.0396936 | − | 0.0687513i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6713.61i | 0.331492i | 0.986168 | + | 0.165746i | \(0.0530032\pi\) | ||||
−0.986168 | + | 0.165746i | \(0.946997\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1652.79 | + | 954.240i | 0.0812801 | + | 0.0469271i | ||||
\(746\) | 6964.03 | + | 4020.68i | 0.341784 | + | 0.197329i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 188.441i | − | 0.00921136i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13144.8 | + | 22767.5i | 0.638696 | + | 1.10625i | 0.985719 | + | 0.168397i | \(0.0538592\pi\) |
−0.347023 | + | 0.937857i | \(0.612807\pi\) | |||||||
\(752\) | 20681.5 | − | 35821.3i | 1.00289 | − | 1.73706i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3444.37 | + | 1988.61i | −0.166362 | + | 0.0960489i | ||||
\(755\) | 704.021 | 0.0339363 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37236.6 | −1.78783 | −0.893915 | − | 0.448237i | \(-0.852052\pi\) | ||||
−0.893915 | + | 0.448237i | \(0.852052\pi\) | |||||||
\(758\) | 9085.18 | − | 5245.33i | 0.435341 | − | 0.251344i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 342.989 | − | 594.075i | 0.0163704 | − | 0.0283544i | ||||
\(761\) | −6028.60 | − | 10441.8i | −0.287170 | − | 0.497393i | 0.685963 | − | 0.727636i | \(-0.259381\pi\) |
−0.973133 | + | 0.230243i | \(0.926048\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17205.5i | 0.814754i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21924.6 | + | 12658.2i | 1.03416 | + | 0.597074i | ||||
\(767\) | 18728.0 | + | 10812.6i | 0.881652 | + | 0.509022i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17232.1i | 0.808070i | 0.914744 | + | 0.404035i | \(0.132393\pi\) | ||||
−0.914744 | + | 0.404035i | \(0.867607\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1758.14 | + | 3045.19i | 0.0819649 | + | 0.141967i | ||||
\(773\) | 5556.40 | − | 9623.98i | 0.258538 | − | 0.447801i | −0.707312 | − | 0.706901i | \(-0.750093\pi\) |
0.965851 | + | 0.259100i | \(0.0834259\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11591.2 | + | 6692.20i | −0.537250 | + | 0.310182i | ||||
\(776\) | −19357.4 | −0.895477 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 35639.6 | 1.64234 | ||||||||
\(779\) | 6302.01 | − | 3638.47i | 0.289850 | − | 0.167345i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.1310 | − | 57.3845i | 0.00151795 | − | 0.00262917i | ||||
\(782\) | −25481.5 | − | 44135.2i | −1.16524 | − | 2.01825i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1370.39i | 0.0623074i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28578.1 | − | 16499.6i | −1.29441 | − | 0.747328i | −0.314978 | − | 0.949099i | \(-0.601997\pi\) |
−0.979433 | + | 0.201771i | \(0.935330\pi\) | |||||||
\(788\) | −14717.2 | − | 8497.00i | −0.665330 | − | 0.384128i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 2636.52i | − | 0.118738i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20779.9 | + | 35991.8i | 0.930537 | + | 1.61174i | ||||
\(794\) | −4574.19 | + | 7922.73i | −0.204448 | + | 0.354115i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16512.0 | + | 9533.19i | −0.735240 | + | 0.424491i | ||||
\(797\) | 17247.7 | 0.766554 | 0.383277 | − | 0.923634i | \(-0.374796\pi\) | ||||
0.383277 | + | 0.923634i | \(0.374796\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −54294.3 | −2.40400 | ||||||||
\(800\) | −20969.7 | + | 12106.9i | −0.926739 | + | 0.535053i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9259.58 | − | 16038.1i | 0.407690 | − | 0.706139i | ||||
\(803\) | 25.1555 | + | 43.5707i | 0.00110550 | + | 0.00191479i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 23970.9i | 1.04757i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12166.2 | − | 7024.15i | −0.529709 | − | 0.305828i | ||||
\(809\) | −19029.1 | − | 10986.5i | −0.826981 | − | 0.477458i | 0.0258371 | − | 0.999666i | \(-0.491775\pi\) |
−0.852818 | + | 0.522209i | \(0.825108\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30078.0i | 1.30232i | 0.758941 | + | 0.651159i | \(0.225717\pi\) | ||||
−0.758941 | + | 0.651159i | \(0.774283\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −254.213 | − | 440.311i | −0.0109462 | − | 0.0189593i | ||||
\(815\) | 1111.34 | − | 1924.90i | 0.0477652 | − | 0.0827317i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20219.4 | − | 11673.7i | 0.865837 | − | 0.499891i | ||||
\(818\) | −28692.2 | −1.22640 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 425.911 | 0.0181384 | ||||||||
\(821\) | −33411.0 | + | 19289.9i | −1.42028 | + | 0.820001i | −0.996323 | − | 0.0856788i | \(-0.972694\pi\) |
−0.423961 | + | 0.905680i | \(0.639361\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14026.1 | − | 24293.9i | 0.594068 | − | 1.02896i | −0.399610 | − | 0.916685i | \(-0.630854\pi\) |
0.993678 | − | 0.112271i | \(-0.0358124\pi\) | |||||||
\(824\) | −8727.47 | − | 15116.4i | −0.368976 | − | 0.639084i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 2038.04i | − | 0.0856948i | −0.999082 | − | 0.0428474i | \(-0.986357\pi\) | ||
0.999082 | − | 0.0428474i | \(-0.0136429\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34603.1 | − | 19978.1i | −1.44972 | − | 0.836995i | −0.451254 | − | 0.892396i | \(-0.649023\pi\) |
−0.998464 | + | 0.0554004i | \(0.982356\pi\) | |||||||
\(830\) | 3307.38 | + | 1909.52i | 0.138314 | + | 0.0798558i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4070.52i | 0.169615i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1773.22 | + | 3071.31i | 0.0734910 | + | 0.127290i | ||||
\(836\) | −64.8125 | + | 112.259i | −0.00268133 | + | 0.00464419i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18564.7 | − | 10718.3i | 0.765283 | − | 0.441836i | ||||
\(839\) | −24277.8 | −0.999004 | −0.499502 | − | 0.866313i | \(-0.666484\pi\) | ||||
−0.499502 | + | 0.866313i | \(0.666484\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24069.6 | 0.986905 | ||||||||
\(842\) | −39313.9 | + | 22697.9i | −1.60908 | + | 0.929002i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7113.28 | − | 12320.6i | 0.290106 | − | 0.502478i | ||||
\(845\) | 706.187 | + | 1223.15i | 0.0287498 | + | 0.0497961i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 24519.7i | − | 0.992937i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 40167.2 | + | 23190.5i | 1.62085 | + | 0.935798i | ||||
\(851\) | −45136.9 | − | 26059.8i | −1.81818 | − | 1.04973i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28395.8i | 1.13981i | 0.821712 | + | 0.569903i | \(0.193019\pi\) | ||||
−0.821712 | + | 0.569903i | \(0.806981\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 937.373 | + | 1623.58i | 0.0374285 | + | 0.0648280i | ||||
\(857\) | 17496.3 | − | 30304.5i | 0.697388 | − | 1.20791i | −0.271981 | − | 0.962303i | \(-0.587679\pi\) |
0.969369 | − | 0.245609i | \(-0.0789879\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8360.94 | + | 4827.19i | −0.332097 | + | 0.191737i | −0.656772 | − | 0.754089i | \(-0.728079\pi\) |
0.324675 | + | 0.945826i | \(0.394745\pi\) | |||||||
\(860\) | 1366.50 | 0.0541828 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12217.7 | −0.482757 | ||||||||
\(863\) | 36502.8 | − | 21074.9i | 1.43983 | − | 0.831284i | 0.441989 | − | 0.897021i | \(-0.354273\pi\) |
0.997837 | + | 0.0657370i | \(0.0209398\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1357.84 | + | 2351.85i | −0.0533735 | + | 0.0924456i | ||||
\(866\) | −13304.5 | − | 23044.0i | −0.522060 | − | 0.904235i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 317.949i | − | 0.0124116i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12853.4 | + | 7420.93i | 0.500025 | + | 0.288690i | ||||
\(872\) | 204.491 | + | 118.063i | 0.00794144 | + | 0.00458499i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 35056.4i | 1.35675i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 365.254 | + | 632.639i | 0.0140636 | + | 0.0243588i | 0.872972 | − | 0.487771i | \(-0.162190\pi\) |
−0.858908 | + | 0.512130i | \(0.828857\pi\) | |||||||
\(878\) | 8332.50 | − | 14432.3i | 0.320283 | − | 0.554746i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 21.8257 | − | 12.6011i | 0.000836073 | − | 0.000482707i | ||||
\(881\) | 36187.9 | 1.38388 | 0.691942 | − | 0.721953i | \(-0.256755\pi\) | ||||
0.691942 | + | 0.721953i | \(0.256755\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38996.6 | −1.48623 | −0.743115 | − | 0.669164i | \(-0.766652\pi\) | ||||
−0.743115 | + | 0.669164i | \(0.766652\pi\) | |||||||
\(884\) | 27267.9 | − | 15743.1i | 1.03746 | − | 0.598980i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5327.70 | − | 9227.85i | 0.202018 | − | 0.349905i | ||||
\(887\) | −15147.0 | − | 26235.4i | −0.573380 | − | 0.993123i | −0.996216 | − | 0.0869165i | \(-0.972299\pi\) |
0.422836 | − | 0.906206i | \(-0.361035\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1738.36i | 0.0654720i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5084.75 | − | 2935.68i | −0.190863 | − | 0.110195i | ||||
\(893\) | 32344.3 | + | 18674.0i | 1.21205 | + | 0.699778i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3079.62i | − | 0.115017i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15672.1 | + | 27144.8i | 0.582387 | + | 1.00872i | ||||
\(899\) | −962.420 | + | 1666.96i | −0.0357047 | + | 0.0618423i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27873.4 | + | 16092.7i | −1.03063 | + | 0.595034i | ||||
\(902\) | 135.503 | 0.00500196 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12437.1 | −0.457579 | ||||||||
\(905\) | 233.822 | − | 134.997i | 0.00858840 | − | 0.00495852i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26811.7 | − | 46439.3i | 0.981554 | − | 1.70010i | 0.325205 | − | 0.945644i | \(-0.394567\pi\) |
0.656349 | − | 0.754458i | \(-0.272100\pi\) | |||||||
\(908\) | −12539.3 | − | 21718.7i | −0.458293 | − | 0.793787i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29609.2i | 1.07683i | 0.842678 | + | 0.538417i | \(0.180977\pi\) | ||||
−0.842678 | + | 0.538417i | \(0.819023\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 398.850 | + | 230.276i | 0.0144578 | + | 0.00834724i | ||||
\(914\) | −37608.1 | − | 21713.1i | −1.36101 | − | 0.785782i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9168.53i | 0.330717i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22783.3 | + | 39461.8i | 0.817792 | + | 1.41646i | 0.907306 | + | 0.420472i | \(0.138135\pi\) |
−0.0895134 | + | 0.995986i | \(0.528531\pi\) | |||||||
\(920\) | 654.718 | − | 1134.00i | 0.0234624 | − | 0.0406381i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24079.2 | − | 13902.1i | 0.860094 | − | 0.496576i | ||||
\(923\) | 11071.6 | 0.394827 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 47433.8 | 1.68607 | ||||||||
\(926\) | −7999.23 | + | 4618.35i | −0.283878 | + | 0.163897i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1741.12 | + | 3015.70i | −0.0615894 | + | 0.106676i | ||||
\(929\) | 19829.7 | + | 34346.0i | 0.700313 | + | 1.21298i | 0.968357 | + | 0.249571i | \(0.0802895\pi\) |
−0.268044 | + | 0.963407i | \(0.586377\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 17008.6i | 0.597783i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7422.62 | + | 4285.45i | 0.260038 | + | 0.150133i | ||||
\(935\) | −28.6491 | − | 16.5406i | −0.00100206 | − | 0.000578540i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1645.64i | − | 0.0573753i | −0.999588 | − | 0.0286877i | \(-0.990867\pi\) | ||
0.999588 | − | 0.0286877i | \(-0.00913282\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1092.97 | + | 1893.08i | 0.0379242 | + | 0.0656866i | ||||
\(941\) | 16471.6 | − | 28529.6i | 0.570626 | − | 0.988352i | −0.425876 | − | 0.904781i | \(-0.640034\pi\) |
0.996502 | − | 0.0835710i | \(-0.0266325\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12029.7 | − | 6945.32i | 0.415418 | − | 0.239842i | ||||
\(944\) | 27629.5 | 0.952611 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 434.750 | 0.0149418 | ||||||||
\(947\) | −19826.4 | + | 11446.8i | −0.680328 | + | 0.392788i | −0.799979 | − | 0.600028i | \(-0.795156\pi\) |
0.119650 | + | 0.992816i | \(0.461823\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4203.18 | + | 7280.13i | −0.143774 | + | 0.249023i | ||||
\(950\) | −15952.3 | − | 27630.2i | −0.544802 | − | 0.943624i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 31350.3i | − | 1.06562i | −0.846234 | − | 0.532811i | \(-0.821136\pi\) | ||
0.846234 | − | 0.532811i | \(-0.178864\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2615.79 | + | 1510.22i | 0.0886333 | + | 0.0511725i | ||||
\(956\) | −10430.7 | − | 6022.18i | −0.352881 | − | 0.203736i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 10430.6i | − | 0.351773i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9094.95 | − | 15752.9i | −0.305292 | − | 0.528781i | ||||
\(962\) | 42476.0 | − | 73570.5i | 1.42358 | − | 2.46571i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10317.6 | − | 5956.85i | 0.344716 | − | 0.199022i | ||||
\(965\) | 617.289 | 0.0205920 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1272.04 | −0.0423021 | −0.0211511 | − | 0.999776i | \(-0.506733\pi\) | ||||
−0.0211511 | + | 0.999776i | \(0.506733\pi\) | |||||||
\(968\) | −12893.0 | + | 7443.77i | −0.428095 | + | 0.247161i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2662.41 | − | 4611.43i | 0.0881287 | − | 0.152643i | ||||
\(971\) | −11659.6 | − | 20195.0i | −0.385350 | − | 0.667445i | 0.606468 | − | 0.795108i | \(-0.292586\pi\) |
−0.991818 | + | 0.127663i | \(0.959253\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 949.512i | − | 0.0312365i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 45985.2 | + | 26549.5i | 1.50814 | + | 0.870728i | ||||
\(977\) | −25918.0 | − | 14963.7i | −0.848710 | − | 0.490003i | 0.0115056 | − | 0.999934i | \(-0.496338\pi\) |
−0.860215 | + | 0.509931i | \(0.829671\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 209.636i | 0.00684372i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −35513.1 | − | 61510.5i | −1.15404 | − | 1.99886i | ||||
\(983\) | −17281.3 | + | 29932.1i | −0.560720 | + | 0.971195i | 0.436714 | + | 0.899600i | \(0.356142\pi\) |
−0.997434 | + | 0.0715947i | \(0.977191\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2583.64 | + | 1491.66i | −0.0835751 | + | 0.0482521i | ||||
\(986\) | 6670.17 | 0.215438 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21658.8 | −0.697427 | ||||||||
\(989\) | 38596.1 | − | 22283.4i | 1.24093 | − | 0.716453i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11458.6 | + | 19846.9i | −0.367300 | + | 0.636183i | −0.989142 | − | 0.146960i | \(-0.953051\pi\) |
0.621842 | + | 0.783143i | \(0.286385\pi\) | |||||||
\(992\) | 10493.8 | + | 18175.8i | 0.335865 | + | 0.581736i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3347.14i | 0.106645i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28270.4 | + | 16321.9i | 0.898027 | + | 0.518476i | 0.876560 | − | 0.481294i | \(-0.159833\pi\) |
0.0214673 | + | 0.999770i | \(0.493166\pi\) | |||||||
\(998\) | −35659.6 | − | 20588.1i | −1.13105 | − | 0.653010i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.4.p.d.80.8 | 48 | ||
3.2 | odd | 2 | inner | 441.4.p.d.80.17 | 48 | ||
7.2 | even | 3 | inner | 441.4.p.d.215.17 | 48 | ||
7.3 | odd | 6 | 441.4.c.b.440.11 | ✓ | 24 | ||
7.4 | even | 3 | 441.4.c.b.440.13 | yes | 24 | ||
7.5 | odd | 6 | inner | 441.4.p.d.215.18 | 48 | ||
7.6 | odd | 2 | inner | 441.4.p.d.80.7 | 48 | ||
21.2 | odd | 6 | inner | 441.4.p.d.215.8 | 48 | ||
21.5 | even | 6 | inner | 441.4.p.d.215.7 | 48 | ||
21.11 | odd | 6 | 441.4.c.b.440.12 | yes | 24 | ||
21.17 | even | 6 | 441.4.c.b.440.14 | yes | 24 | ||
21.20 | even | 2 | inner | 441.4.p.d.80.18 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.4.c.b.440.11 | ✓ | 24 | 7.3 | odd | 6 | ||
441.4.c.b.440.12 | yes | 24 | 21.11 | odd | 6 | ||
441.4.c.b.440.13 | yes | 24 | 7.4 | even | 3 | ||
441.4.c.b.440.14 | yes | 24 | 21.17 | even | 6 | ||
441.4.p.d.80.7 | 48 | 7.6 | odd | 2 | inner | ||
441.4.p.d.80.8 | 48 | 1.1 | even | 1 | trivial | ||
441.4.p.d.80.17 | 48 | 3.2 | odd | 2 | inner | ||
441.4.p.d.80.18 | 48 | 21.20 | even | 2 | inner | ||
441.4.p.d.215.7 | 48 | 21.5 | even | 6 | inner | ||
441.4.p.d.215.8 | 48 | 21.2 | odd | 6 | inner | ||
441.4.p.d.215.17 | 48 | 7.2 | even | 3 | inner | ||
441.4.p.d.215.18 | 48 | 7.5 | odd | 6 | inner |