Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(485,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.485");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.b (of order \(2\), degree \(1\), 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: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 48x^{14} + 921x^{12} + 8986x^{10} + 46812x^{8} + 125072x^{6} + 152129x^{4} + 65614x^{2} + 5041 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 485.3 | ||
Root | \(-2.99491i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.485 |
Dual form | 1089.3.b.j.485.14 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.99491i | − 1.49746i | −0.662877 | − | 0.748728i | \(-0.730665\pi\) | ||||
0.662877 | − | 0.748728i | \(-0.269335\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.96950 | −1.24238 | ||||||||
\(5\) | − 1.61173i | − 0.322345i | −0.986926 | − | 0.161173i | \(-0.948472\pi\) | ||||
0.986926 | − | 0.161173i | \(-0.0515276\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.32981 | 0.475688 | 0.237844 | − | 0.971303i | \(-0.423559\pi\) | ||||
0.237844 | + | 0.971303i | \(0.423559\pi\) | |||||||
\(8\) | 2.90358i | 0.362947i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.82698 | −0.482698 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.56350 | −0.581807 | −0.290904 | − | 0.956752i | \(-0.593956\pi\) | ||||
−0.290904 | + | 0.956752i | \(0.593956\pi\) | |||||||
\(14\) | − 9.97250i | − 0.712322i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −11.1821 | −0.698878 | ||||||||
\(17\) | − 28.3526i | − 1.66780i | −0.551917 | − | 0.833899i | \(-0.686104\pi\) | ||||
0.551917 | − | 0.833899i | \(-0.313896\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.0667 | 1.37193 | 0.685965 | − | 0.727635i | \(-0.259380\pi\) | ||||
0.685965 | + | 0.727635i | \(0.259380\pi\) | |||||||
\(20\) | 8.00948i | 0.400474i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 19.5656i | − 0.850679i | −0.905034 | − | 0.425339i | \(-0.860155\pi\) | ||||
0.905034 | − | 0.425339i | \(-0.139845\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.4023 | 0.896093 | ||||||||
\(26\) | 22.6520i | 0.871231i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −16.5475 | −0.590983 | ||||||||
\(29\) | 2.15288i | 0.0742372i | 0.999311 | + | 0.0371186i | \(0.0118179\pi\) | ||||
−0.999311 | + | 0.0371186i | \(0.988182\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.22840 | −0.297690 | −0.148845 | − | 0.988861i | \(-0.547556\pi\) | ||||
−0.148845 | + | 0.988861i | \(0.547556\pi\) | |||||||
\(32\) | 45.1036i | 1.40949i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −84.9135 | −2.49745 | ||||||||
\(35\) | − 5.36675i | − 0.153336i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −67.5342 | −1.82525 | −0.912624 | − | 0.408800i | \(-0.865948\pi\) | ||||
−0.912624 | + | 0.408800i | \(0.865948\pi\) | |||||||
\(38\) | − 78.0674i | − 2.05440i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.67977 | 0.116994 | ||||||||
\(41\) | 29.0597i | 0.708774i | 0.935099 | + | 0.354387i | \(0.115310\pi\) | ||||
−0.935099 | + | 0.354387i | \(0.884690\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.719802 | −0.0167396 | −0.00836979 | − | 0.999965i | \(-0.502664\pi\) | ||||
−0.00836979 | + | 0.999965i | \(0.502664\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −58.5973 | −1.27385 | ||||||||
\(47\) | − 24.5249i | − 0.521806i | −0.965365 | − | 0.260903i | \(-0.915980\pi\) | ||||
0.965365 | − | 0.260903i | \(-0.0840203\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −37.9123 | −0.773721 | ||||||||
\(50\) | − 67.0930i | − 1.34186i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 37.5868 | 0.722823 | ||||||||
\(53\) | − 5.79176i | − 0.109278i | −0.998506 | − | 0.0546392i | \(-0.982599\pi\) | ||||
0.998506 | − | 0.0546392i | \(-0.0174009\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.66837i | 0.172650i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.44768 | 0.111167 | ||||||||
\(59\) | − 73.9896i | − 1.25406i | −0.778994 | − | 0.627031i | \(-0.784270\pi\) | ||||
0.778994 | − | 0.627031i | \(-0.215730\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −72.1664 | −1.18306 | −0.591528 | − | 0.806284i | \(-0.701475\pi\) | ||||
−0.591528 | + | 0.806284i | \(0.701475\pi\) | |||||||
\(62\) | 27.6383i | 0.445778i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 90.3531 | 1.41177 | ||||||||
\(65\) | 12.1903i | 0.187543i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −79.8310 | −1.19151 | −0.595754 | − | 0.803167i | \(-0.703146\pi\) | ||||
−0.595754 | + | 0.803167i | \(0.703146\pi\) | |||||||
\(68\) | 140.898i | 2.07203i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −16.0730 | −0.229614 | ||||||||
\(71\) | − 107.780i | − 1.51803i | −0.651072 | − | 0.759016i | \(-0.725681\pi\) | ||||
0.651072 | − | 0.759016i | \(-0.274319\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 90.3799 | 1.23808 | 0.619041 | − | 0.785359i | \(-0.287522\pi\) | ||||
0.619041 | + | 0.785359i | \(0.287522\pi\) | |||||||
\(74\) | 202.259i | 2.73323i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −129.538 | −1.70445 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −114.802 | −1.45319 | −0.726595 | − | 0.687066i | \(-0.758898\pi\) | ||||
−0.726595 | + | 0.687066i | \(0.758898\pi\) | |||||||
\(80\) | 18.0224i | 0.225280i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 87.0314 | 1.06136 | ||||||||
\(83\) | 125.752i | 1.51509i | 0.652784 | + | 0.757544i | \(0.273601\pi\) | ||||
−0.652784 | + | 0.757544i | \(0.726399\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −45.6966 | −0.537607 | ||||||||
\(86\) | 2.15574i | 0.0250668i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 83.3041i | 0.936001i | 0.883728 | + | 0.468000i | \(0.155025\pi\) | ||||
−0.883728 | + | 0.468000i | \(0.844975\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.1850 | −0.276759 | ||||||||
\(92\) | 97.2313i | 1.05686i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −73.4499 | −0.781382 | ||||||||
\(95\) | − 42.0123i | − 0.442235i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −78.0275 | −0.804407 | −0.402203 | − | 0.915550i | \(-0.631756\pi\) | ||||
−0.402203 | + | 0.915550i | \(0.631756\pi\) | |||||||
\(98\) | 113.544i | 1.15861i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −111.328 | −1.11328 | ||||||||
\(101\) | 38.9858i | 0.385998i | 0.981199 | + | 0.192999i | \(0.0618215\pi\) | ||||
−0.981199 | + | 0.192999i | \(0.938179\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 30.1474 | 0.292694 | 0.146347 | − | 0.989233i | \(-0.453248\pi\) | ||||
0.146347 | + | 0.989233i | \(0.453248\pi\) | |||||||
\(104\) | − 21.9612i | − 0.211165i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.3458 | −0.163640 | ||||||||
\(107\) | − 49.7544i | − 0.464994i | −0.972597 | − | 0.232497i | \(-0.925310\pi\) | ||||
0.972597 | − | 0.232497i | \(-0.0746897\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 149.823 | 1.37453 | 0.687263 | − | 0.726409i | \(-0.258812\pi\) | ||||
0.687263 | + | 0.726409i | \(0.258812\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −37.2342 | −0.332448 | ||||||||
\(113\) | 127.469i | 1.12805i | 0.825759 | + | 0.564024i | \(0.190747\pi\) | ||||
−0.825759 | + | 0.564024i | \(0.809253\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −31.5344 | −0.274212 | ||||||||
\(116\) | − 10.6987i | − 0.0922305i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −221.593 | −1.87790 | ||||||||
\(119\) | − 94.4088i | − 0.793351i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 216.132i | 1.77157i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 45.8606 | 0.369843 | ||||||||
\(125\) | − 76.3996i | − 0.611197i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 237.975 | 1.87382 | 0.936910 | − | 0.349572i | \(-0.113673\pi\) | ||||
0.936910 | + | 0.349572i | \(0.113673\pi\) | |||||||
\(128\) | − 90.1853i | − 0.704573i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 36.5089 | 0.280837 | ||||||||
\(131\) | 148.535i | 1.13386i | 0.823767 | + | 0.566929i | \(0.191869\pi\) | ||||
−0.823767 | + | 0.566929i | \(0.808131\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 86.7972 | 0.652610 | ||||||||
\(134\) | 239.087i | 1.78423i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 82.3239 | 0.605322 | ||||||||
\(137\) | − 20.1586i | − 0.147143i | −0.997290 | − | 0.0735716i | \(-0.976560\pi\) | ||||
0.997290 | − | 0.0735716i | \(-0.0234397\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −148.878 | −1.07106 | −0.535532 | − | 0.844515i | \(-0.679889\pi\) | ||||
−0.535532 | + | 0.844515i | \(0.679889\pi\) | |||||||
\(140\) | 26.6701i | 0.190501i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −322.792 | −2.27319 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.46985 | 0.0239300 | ||||||||
\(146\) | − 270.680i | − 1.85397i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 335.611 | 2.26764 | ||||||||
\(149\) | − 44.8984i | − 0.301332i | −0.988585 | − | 0.150666i | \(-0.951858\pi\) | ||||
0.988585 | − | 0.150666i | \(-0.0481418\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −46.5427 | −0.308230 | −0.154115 | − | 0.988053i | \(-0.549253\pi\) | ||||
−0.154115 | + | 0.988053i | \(0.549253\pi\) | |||||||
\(152\) | 75.6866i | 0.497938i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.8737i | 0.0959591i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.1734 | 0.115754 | 0.0578769 | − | 0.998324i | \(-0.481567\pi\) | ||||
0.0578769 | + | 0.998324i | \(0.481567\pi\) | |||||||
\(158\) | 343.822i | 2.17609i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 72.6947 | 0.454342 | ||||||||
\(161\) | − 65.1498i | − 0.404657i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −139.162 | −0.853753 | −0.426876 | − | 0.904310i | \(-0.640386\pi\) | ||||
−0.426876 | + | 0.904310i | \(0.640386\pi\) | |||||||
\(164\) | − 144.412i | − 0.880564i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 376.617 | 2.26878 | ||||||||
\(167\) | − 145.214i | − 0.869544i | −0.900541 | − | 0.434772i | \(-0.856829\pi\) | ||||
0.900541 | − | 0.434772i | \(-0.143171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −111.794 | −0.661500 | ||||||||
\(170\) | 136.857i | 0.805043i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.57706 | 0.0207968 | ||||||||
\(173\) | − 290.416i | − 1.67871i | −0.543586 | − | 0.839353i | \(-0.682934\pi\) | ||||
0.543586 | − | 0.839353i | \(-0.317066\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 74.5956 | 0.426261 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 249.488 | 1.40162 | ||||||||
\(179\) | − 146.411i | − 0.817940i | −0.912548 | − | 0.408970i | \(-0.865888\pi\) | ||||
0.912548 | − | 0.408970i | \(-0.134112\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 223.461 | 1.23459 | 0.617295 | − | 0.786732i | \(-0.288228\pi\) | ||||
0.617295 | + | 0.786732i | \(0.288228\pi\) | |||||||
\(182\) | 75.4270i | 0.414434i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 56.8102 | 0.308751 | ||||||||
\(185\) | 108.847i | 0.588361i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 121.876i | 0.648279i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −125.823 | −0.662228 | ||||||||
\(191\) | 23.2178i | 0.121559i | 0.998151 | + | 0.0607795i | \(0.0193586\pi\) | ||||
−0.998151 | + | 0.0607795i | \(0.980641\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 125.437 | 0.649934 | 0.324967 | − | 0.945725i | \(-0.394647\pi\) | ||||
0.324967 | + | 0.945725i | \(0.394647\pi\) | |||||||
\(194\) | 233.685i | 1.20456i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 188.405 | 0.961252 | ||||||||
\(197\) | − 12.3847i | − 0.0628665i | −0.999506 | − | 0.0314333i | \(-0.989993\pi\) | ||||
0.999506 | − | 0.0314333i | \(-0.0100072\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 112.611 | 0.565885 | 0.282943 | − | 0.959137i | \(-0.408689\pi\) | ||||
0.282943 | + | 0.959137i | \(0.408689\pi\) | |||||||
\(200\) | 65.0469i | 0.325235i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 116.759 | 0.578016 | ||||||||
\(203\) | 7.16868i | 0.0353137i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 46.8364 | 0.228470 | ||||||||
\(206\) | − 90.2890i | − 0.438296i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 84.5754 | 0.406613 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −153.910 | −0.729433 | −0.364716 | − | 0.931119i | \(-0.618834\pi\) | ||||
−0.364716 | + | 0.931119i | \(0.618834\pi\) | |||||||
\(212\) | 28.7822i | 0.135765i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −149.010 | −0.696309 | ||||||||
\(215\) | 1.16012i | 0.00539593i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −30.7289 | −0.141608 | ||||||||
\(218\) | − 448.708i | − 2.05829i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 214.445i | 0.970337i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 282.384 | 1.26630 | 0.633148 | − | 0.774031i | \(-0.281763\pi\) | ||||
0.633148 | + | 0.774031i | \(0.281763\pi\) | |||||||
\(224\) | 150.187i | 0.670476i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 381.760 | 1.68920 | ||||||||
\(227\) | − 202.865i | − 0.893677i | −0.894615 | − | 0.446839i | \(-0.852550\pi\) | ||||
0.894615 | − | 0.446839i | \(-0.147450\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −419.120 | −1.83022 | −0.915108 | − | 0.403208i | \(-0.867895\pi\) | ||||
−0.915108 | + | 0.403208i | \(0.867895\pi\) | |||||||
\(230\) | 94.4428i | 0.410621i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.25105 | −0.0269442 | ||||||||
\(233\) | − 111.121i | − 0.476916i | −0.971153 | − | 0.238458i | \(-0.923358\pi\) | ||||
0.971153 | − | 0.238458i | \(-0.0766420\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −39.5274 | −0.168202 | ||||||||
\(236\) | 367.692i | 1.55802i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −282.746 | −1.18801 | ||||||||
\(239\) | − 314.056i | − 1.31404i | −0.753872 | − | 0.657021i | \(-0.771816\pi\) | ||||
0.753872 | − | 0.657021i | \(-0.228184\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 104.293 | 0.432753 | 0.216376 | − | 0.976310i | \(-0.430576\pi\) | ||||
0.216376 | + | 0.976310i | \(0.430576\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 358.631 | 1.46980 | ||||||||
\(245\) | 61.1043i | 0.249405i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −197.155 | −0.798199 | ||||||||
\(248\) | − 26.7954i | − 0.108046i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −228.810 | −0.915241 | ||||||||
\(251\) | 333.537i | 1.32883i | 0.747363 | + | 0.664416i | \(0.231320\pi\) | ||||
−0.747363 | + | 0.664416i | \(0.768680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − 712.714i | − 2.80596i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 91.3152 | 0.356700 | ||||||||
\(257\) | − 306.989i | − 1.19451i | −0.802052 | − | 0.597254i | \(-0.796258\pi\) | ||||
0.802052 | − | 0.597254i | \(-0.203742\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −224.876 | −0.868248 | ||||||||
\(260\) | − 60.5797i | − 0.232999i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 444.851 | 1.69790 | ||||||||
\(263\) | − 249.060i | − 0.946997i | −0.880794 | − | 0.473499i | \(-0.842991\pi\) | ||||
0.880794 | − | 0.473499i | \(-0.157009\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.33473 | −0.0352254 | ||||||||
\(266\) | − 259.950i | − 0.977255i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 396.720 | 1.48030 | ||||||||
\(269\) | − 196.927i | − 0.732071i | −0.930601 | − | 0.366035i | \(-0.880715\pi\) | ||||
0.930601 | − | 0.366035i | \(-0.119285\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 463.464 | 1.71020 | 0.855099 | − | 0.518465i | \(-0.173496\pi\) | ||||
0.855099 | + | 0.518465i | \(0.173496\pi\) | |||||||
\(272\) | 317.040i | 1.16559i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −60.3733 | −0.220340 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.4550 | 0.0846751 | 0.0423376 | − | 0.999103i | \(-0.486520\pi\) | ||||
0.0423376 | + | 0.999103i | \(0.486520\pi\) | |||||||
\(278\) | 445.876i | 1.60387i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 15.5828 | 0.0556528 | ||||||||
\(281\) | 263.447i | 0.937534i | 0.883322 | + | 0.468767i | \(0.155302\pi\) | ||||
−0.883322 | + | 0.468767i | \(0.844698\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 35.8237 | 0.126585 | 0.0632927 | − | 0.997995i | \(-0.479840\pi\) | ||||
0.0632927 | + | 0.997995i | \(0.479840\pi\) | |||||||
\(284\) | 535.614i | 1.88597i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 96.7636i | 0.337155i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −514.868 | −1.78155 | ||||||||
\(290\) | − 10.3919i | − 0.0358342i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −449.143 | −1.53816 | ||||||||
\(293\) | 114.195i | 0.389745i | 0.980829 | + | 0.194873i | \(0.0624294\pi\) | ||||
−0.980829 | + | 0.194873i | \(0.937571\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −119.251 | −0.404241 | ||||||||
\(296\) | − 196.091i | − 0.662469i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −134.467 | −0.451231 | ||||||||
\(299\) | 147.984i | 0.494931i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.39681 | −0.00796281 | ||||||||
\(302\) | 139.391i | 0.461560i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −291.479 | −0.958812 | ||||||||
\(305\) | 116.313i | 0.381353i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 224.438 | 0.731070 | 0.365535 | − | 0.930798i | \(-0.380886\pi\) | ||||
0.365535 | + | 0.930798i | \(0.380886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 44.5453 | 0.143695 | ||||||||
\(311\) | 171.175i | 0.550401i | 0.961387 | + | 0.275201i | \(0.0887442\pi\) | ||||
−0.961387 | + | 0.275201i | \(0.911256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −274.110 | −0.875749 | −0.437875 | − | 0.899036i | \(-0.644269\pi\) | ||||
−0.437875 | + | 0.899036i | \(0.644269\pi\) | |||||||
\(314\) | − 54.4276i | − 0.173336i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 570.509 | 1.80541 | ||||||||
\(317\) | − 618.549i | − 1.95126i | −0.219427 | − | 0.975629i | \(-0.570419\pi\) | ||||
0.219427 | − | 0.975629i | \(-0.429581\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − 145.625i | − 0.455077i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −195.118 | −0.605957 | ||||||||
\(323\) | − 739.057i | − 2.28810i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −169.440 | −0.521354 | ||||||||
\(326\) | 416.777i | 1.27846i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −84.3772 | −0.257248 | ||||||||
\(329\) | − 81.6633i | − 0.248217i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −160.328 | −0.484376 | −0.242188 | − | 0.970229i | \(-0.577865\pi\) | ||||
−0.242188 | + | 0.970229i | \(0.577865\pi\) | |||||||
\(332\) | − 624.926i | − 1.88231i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −434.903 | −1.30210 | ||||||||
\(335\) | 128.666i | 0.384077i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 110.004 | 0.326422 | 0.163211 | − | 0.986591i | \(-0.447815\pi\) | ||||
0.163211 | + | 0.986591i | \(0.447815\pi\) | |||||||
\(338\) | 334.812i | 0.990568i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 227.089 | 0.667910 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −289.402 | −0.843738 | ||||||||
\(344\) | − 2.09000i | − 0.00607558i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −869.771 | −2.51379 | ||||||||
\(347\) | − 221.736i | − 0.639008i | −0.947585 | − | 0.319504i | \(-0.896484\pi\) | ||||
0.947585 | − | 0.319504i | \(-0.103516\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 466.352 | 1.33625 | 0.668126 | − | 0.744049i | \(-0.267097\pi\) | ||||
0.668126 | + | 0.744049i | \(0.267097\pi\) | |||||||
\(350\) | − 223.407i | − 0.638307i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 494.404i | − 1.40058i | −0.713860 | − | 0.700289i | \(-0.753055\pi\) | ||||
0.713860 | − | 0.700289i | \(-0.246945\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −173.712 | −0.489330 | ||||||||
\(356\) | − 413.980i | − 1.16286i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −438.489 | −1.22483 | ||||||||
\(359\) | − 28.1698i | − 0.0784673i | −0.999230 | − | 0.0392336i | \(-0.987508\pi\) | ||||
0.999230 | − | 0.0392336i | \(-0.0124917\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 318.471 | 0.882191 | ||||||||
\(362\) | − 669.246i | − 1.84875i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 125.157 | 0.343838 | ||||||||
\(365\) | − 145.668i | − 0.399090i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.7976 | 0.0811925 | 0.0405962 | − | 0.999176i | \(-0.487074\pi\) | ||||
0.0405962 | + | 0.999176i | \(0.487074\pi\) | |||||||
\(368\) | 218.784i | 0.594521i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 325.986 | 0.881044 | ||||||||
\(371\) | − 19.2855i | − 0.0519824i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 313.887 | 0.841520 | 0.420760 | − | 0.907172i | \(-0.361763\pi\) | ||||
0.420760 | + | 0.907172i | \(0.361763\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 71.2099 | 0.189388 | ||||||||
\(377\) | − 16.2833i | − 0.0431917i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.4155 | −0.0828904 | −0.0414452 | − | 0.999141i | \(-0.513196\pi\) | ||||
−0.0414452 | + | 0.999141i | \(0.513196\pi\) | |||||||
\(380\) | 208.780i | 0.549422i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 69.5352 | 0.182029 | ||||||||
\(383\) | 474.897i | 1.23994i | 0.784625 | + | 0.619970i | \(0.212855\pi\) | ||||
−0.784625 | + | 0.619970i | \(0.787145\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 375.674i | − 0.973249i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 387.758 | 0.999376 | ||||||||
\(389\) | − 42.3470i | − 0.108861i | −0.998518 | − | 0.0544306i | \(-0.982666\pi\) | ||||
0.998518 | − | 0.0544306i | \(-0.0173344\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −554.735 | −1.41876 | ||||||||
\(392\) | − 110.081i | − 0.280820i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −37.0911 | −0.0941399 | ||||||||
\(395\) | 185.029i | 0.468429i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −560.270 | −1.41126 | −0.705630 | − | 0.708580i | \(-0.749336\pi\) | ||||
−0.705630 | + | 0.708580i | \(0.749336\pi\) | |||||||
\(398\) | − 337.261i | − 0.847389i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −250.504 | −0.626260 | ||||||||
\(401\) | − 565.289i | − 1.40970i | −0.709357 | − | 0.704850i | \(-0.751014\pi\) | ||||
0.709357 | − | 0.704850i | \(-0.248986\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 69.7990 | 0.173198 | ||||||||
\(404\) | − 193.740i | − 0.479555i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.4696 | 0.0528807 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −174.254 | −0.426048 | −0.213024 | − | 0.977047i | \(-0.568331\pi\) | ||||
−0.213024 | + | 0.977047i | \(0.568331\pi\) | |||||||
\(410\) | − 140.271i | − 0.342124i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −149.818 | −0.363635 | ||||||||
\(413\) | − 246.372i | − 0.596542i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 202.678 | 0.488382 | ||||||||
\(416\) | − 341.141i | − 0.820050i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 279.267i | − 0.666508i | −0.942837 | − | 0.333254i | \(-0.891853\pi\) | ||||
0.942837 | − | 0.333254i | \(-0.108147\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 387.008 | 0.919259 | 0.459630 | − | 0.888111i | \(-0.347982\pi\) | ||||
0.459630 | + | 0.888111i | \(0.347982\pi\) | |||||||
\(422\) | 460.948i | 1.09229i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 16.8168 | 0.0396623 | ||||||||
\(425\) | − 635.164i | − 1.49450i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −240.301 | −0.562765 | ||||||||
\(428\) | 247.255i | 0.577698i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.47447 | 0.00808017 | ||||||||
\(431\) | − 319.975i | − 0.742402i | −0.928552 | − | 0.371201i | \(-0.878946\pi\) | ||||
0.928552 | − | 0.371201i | \(-0.121054\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 526.145 | 1.21512 | 0.607558 | − | 0.794276i | \(-0.292149\pi\) | ||||
0.607558 | + | 0.794276i | \(0.292149\pi\) | |||||||
\(434\) | 92.0303i | 0.212051i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −744.547 | −1.70768 | ||||||||
\(437\) | − 510.010i | − 1.16707i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.7817 | −0.0518946 | −0.0259473 | − | 0.999663i | \(-0.508260\pi\) | ||||
−0.0259473 | + | 0.999663i | \(0.508260\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 642.243 | 1.45304 | ||||||||
\(443\) | − 60.0022i | − 0.135445i | −0.997704 | − | 0.0677226i | \(-0.978427\pi\) | ||||
0.997704 | − | 0.0677226i | \(-0.0215733\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 134.263 | 0.301716 | ||||||||
\(446\) | − 845.715i | − 1.89622i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 300.859 | 0.671560 | ||||||||
\(449\) | 761.224i | 1.69538i | 0.530495 | + | 0.847688i | \(0.322006\pi\) | ||||
−0.530495 | + | 0.847688i | \(0.677994\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 633.459i | − 1.40146i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −607.562 | −1.33824 | ||||||||
\(455\) | 40.5914i | 0.0892119i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 788.938 | 1.72634 | 0.863171 | − | 0.504912i | \(-0.168475\pi\) | ||||
0.863171 | + | 0.504912i | \(0.168475\pi\) | |||||||
\(458\) | 1255.23i | 2.74067i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 156.710 | 0.340675 | ||||||||
\(461\) | − 726.842i | − 1.57666i | −0.615250 | − | 0.788332i | \(-0.710945\pi\) | ||||
0.615250 | − | 0.788332i | \(-0.289055\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 301.548 | 0.651291 | 0.325646 | − | 0.945492i | \(-0.394418\pi\) | ||||
0.325646 | + | 0.945492i | \(0.394418\pi\) | |||||||
\(464\) | − 24.0736i | − 0.0518827i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −332.799 | −0.714161 | ||||||||
\(467\) | 292.485i | 0.626306i | 0.949703 | + | 0.313153i | \(0.101385\pi\) | ||||
−0.949703 | + | 0.313153i | \(0.898615\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −265.822 | −0.566785 | ||||||||
\(470\) | 118.381i | 0.251875i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 214.835 | 0.455158 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 583.954 | 1.22938 | ||||||||
\(476\) | 469.165i | 0.985640i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −940.571 | −1.96772 | ||||||||
\(479\) | 496.880i | 1.03733i | 0.854978 | + | 0.518664i | \(0.173570\pi\) | ||||
−0.854978 | + | 0.518664i | \(0.826430\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 510.795 | 1.06194 | ||||||||
\(482\) | − 312.350i | − 0.648029i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 125.759i | 0.259297i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 691.718 | 1.42037 | 0.710183 | − | 0.704017i | \(-0.248612\pi\) | ||||
0.710183 | + | 0.704017i | \(0.248612\pi\) | |||||||
\(488\) | − 209.541i | − 0.429387i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 183.002 | 0.373474 | ||||||||
\(491\) | 296.243i | 0.603346i | 0.953412 | + | 0.301673i | \(0.0975450\pi\) | ||||
−0.953412 | + | 0.301673i | \(0.902455\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 61.0396 | 0.123813 | ||||||||
\(494\) | 590.462i | 1.19527i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 103.192 | 0.208049 | ||||||||
\(497\) | − 358.888i | − 0.722109i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −134.004 | −0.268544 | −0.134272 | − | 0.990944i | \(-0.542870\pi\) | ||||
−0.134272 | + | 0.990944i | \(0.542870\pi\) | |||||||
\(500\) | 379.668i | 0.759336i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 998.914 | 1.98987 | ||||||||
\(503\) | − 190.003i | − 0.377740i | −0.982002 | − | 0.188870i | \(-0.939518\pi\) | ||||
0.982002 | − | 0.188870i | \(-0.0604824\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 62.8345 | 0.124425 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1182.62 | −2.32799 | ||||||||
\(509\) | 119.100i | 0.233989i | 0.993133 | + | 0.116995i | \(0.0373260\pi\) | ||||
−0.993133 | + | 0.116995i | \(0.962674\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 300.948 | 0.588940 | ||||||||
\(512\) | − 634.222i | − 1.23872i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −919.404 | −1.78872 | ||||||||
\(515\) | − 48.5895i | − 0.0943485i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 673.485i | 1.30016i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −35.3955 | −0.0680682 | ||||||||
\(521\) | 637.297i | 1.22322i | 0.791160 | + | 0.611609i | \(0.209478\pi\) | ||||
−0.791160 | + | 0.611609i | \(0.790522\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −129.698 | −0.247988 | −0.123994 | − | 0.992283i | \(-0.539570\pi\) | ||||
−0.123994 | + | 0.992283i | \(0.539570\pi\) | |||||||
\(524\) | − 738.147i | − 1.40868i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −745.914 | −1.41809 | ||||||||
\(527\) | 261.649i | 0.496487i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 146.187 | 0.276346 | ||||||||
\(530\) | 27.9567i | 0.0527485i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −431.339 | −0.810787 | ||||||||
\(533\) | − 219.793i | − 0.412370i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −80.1905 | −0.149889 | ||||||||
\(536\) | − 231.795i | − 0.432454i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −589.779 | −1.09624 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 493.991 | 0.913108 | 0.456554 | − | 0.889696i | \(-0.349084\pi\) | ||||
0.456554 | + | 0.889696i | \(0.349084\pi\) | |||||||
\(542\) | − 1388.03i | − 2.56095i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1278.80 | 2.35074 | ||||||||
\(545\) | − 241.474i | − 0.443072i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 106.128 | 0.194018 | 0.0970089 | − | 0.995284i | \(-0.469072\pi\) | ||||
0.0970089 | + | 0.995284i | \(0.469072\pi\) | |||||||
\(548\) | 100.178i | 0.182807i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 56.1183i | 0.101848i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −382.269 | −0.691264 | ||||||||
\(554\) | − 70.2457i | − 0.126797i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 739.849 | 1.33066 | ||||||||
\(557\) | − 827.637i | − 1.48588i | −0.669356 | − | 0.742942i | \(-0.733430\pi\) | ||||
0.669356 | − | 0.742942i | \(-0.266570\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.44422 | 0.00973921 | ||||||||
\(560\) | 60.0113i | 0.107163i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 789.001 | 1.40392 | ||||||||
\(563\) | 470.917i | 0.836442i | 0.908345 | + | 0.418221i | \(0.137346\pi\) | ||||
−0.908345 | + | 0.418221i | \(0.862654\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 205.446 | 0.363621 | ||||||||
\(566\) | − 107.289i | − 0.189556i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 312.948 | 0.550965 | ||||||||
\(569\) | 200.074i | 0.351624i | 0.984424 | + | 0.175812i | \(0.0562551\pi\) | ||||
−0.984424 | + | 0.175812i | \(0.943745\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −658.692 | −1.15358 | −0.576788 | − | 0.816894i | \(-0.695694\pi\) | ||||
−0.576788 | + | 0.816894i | \(0.695694\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 289.798 | 0.504875 | ||||||||
\(575\) | − 438.315i | − 0.762287i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −100.977 | −0.175004 | −0.0875020 | − | 0.996164i | \(-0.527888\pi\) | ||||
−0.0875020 | + | 0.996164i | \(0.527888\pi\) | |||||||
\(578\) | 1541.98i | 2.66779i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −17.2434 | −0.0297301 | ||||||||
\(581\) | 418.732i | 0.720709i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 262.425i | 0.449358i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 342.005 | 0.583627 | ||||||||
\(587\) | 349.390i | 0.595213i | 0.954689 | + | 0.297606i | \(0.0961883\pi\) | ||||
−0.954689 | + | 0.297606i | \(0.903812\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −240.554 | −0.408410 | ||||||||
\(590\) | 357.147i | 0.605333i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 755.171 | 1.27563 | ||||||||
\(593\) | − 670.238i | − 1.13025i | −0.825005 | − | 0.565125i | \(-0.808828\pi\) | ||||
0.825005 | − | 0.565125i | \(-0.191172\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −152.161 | −0.255733 | ||||||||
\(596\) | 223.123i | 0.374367i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 443.200 | 0.741138 | ||||||||
\(599\) | 771.328i | 1.28769i | 0.765155 | + | 0.643847i | \(0.222662\pi\) | ||||
−0.765155 | + | 0.643847i | \(0.777338\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 185.722 | 0.309021 | 0.154511 | − | 0.987991i | \(-0.450620\pi\) | ||||
0.154511 | + | 0.987991i | \(0.450620\pi\) | |||||||
\(602\) | 7.17823i | 0.0119240i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 231.294 | 0.382937 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 488.185 | 0.804259 | 0.402129 | − | 0.915583i | \(-0.368270\pi\) | ||||
0.402129 | + | 0.915583i | \(0.368270\pi\) | |||||||
\(608\) | 1175.70i | 1.93372i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 348.346 | 0.571059 | ||||||||
\(611\) | 185.494i | 0.303591i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −510.461 | −0.832726 | −0.416363 | − | 0.909199i | \(-0.636695\pi\) | ||||
−0.416363 | + | 0.909199i | \(0.636695\pi\) | |||||||
\(614\) | − 672.174i | − 1.09475i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1142.14i | 1.85111i | 0.378608 | + | 0.925557i | \(0.376403\pi\) | ||||
−0.378608 | + | 0.925557i | \(0.623597\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −908.213 | −1.46723 | −0.733613 | − | 0.679567i | \(-0.762168\pi\) | ||||
−0.733613 | + | 0.679567i | \(0.762168\pi\) | |||||||
\(620\) | − 73.9147i | − 0.119217i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 512.653 | 0.824202 | ||||||||
\(623\) | 277.387i | 0.445244i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 436.923 | 0.699077 | ||||||||
\(626\) | 820.934i | 1.31140i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −90.3126 | −0.143810 | ||||||||
\(629\) | 1914.77i | 3.04415i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 944.402 | 1.49668 | 0.748338 | − | 0.663318i | \(-0.230852\pi\) | ||||
0.748338 | + | 0.663318i | \(0.230852\pi\) | |||||||
\(632\) | − 333.336i | − 0.527431i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1852.50 | −2.92192 | ||||||||
\(635\) | − 383.551i | − 0.604017i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 286.750 | 0.450157 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −145.354 | −0.227116 | ||||||||
\(641\) | 359.081i | 0.560188i | 0.959973 | + | 0.280094i | \(0.0903657\pi\) | ||||
−0.959973 | + | 0.280094i | \(0.909634\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 928.146 | 1.44346 | 0.721731 | − | 0.692174i | \(-0.243347\pi\) | ||||
0.721731 | + | 0.692174i | \(0.243347\pi\) | |||||||
\(644\) | 323.762i | 0.502737i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2213.41 | −3.42633 | ||||||||
\(647\) | − 436.289i | − 0.674326i | −0.941446 | − | 0.337163i | \(-0.890533\pi\) | ||||
0.941446 | − | 0.337163i | \(-0.109467\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 507.458i | 0.780705i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 691.565 | 1.06068 | ||||||||
\(653\) | 243.417i | 0.372767i | 0.982477 | + | 0.186383i | \(0.0596767\pi\) | ||||
−0.982477 | + | 0.186383i | \(0.940323\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 239.399 | 0.365494 | ||||||||
\(656\) | − 324.948i | − 0.495347i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −244.574 | −0.371694 | ||||||||
\(659\) | − 348.053i | − 0.528153i | −0.964502 | − | 0.264076i | \(-0.914933\pi\) | ||||
0.964502 | − | 0.264076i | \(-0.0850671\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 601.901 | 0.910592 | 0.455296 | − | 0.890340i | \(-0.349533\pi\) | ||||
0.455296 | + | 0.890340i | \(0.349533\pi\) | |||||||
\(662\) | 480.170i | 0.725332i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −365.131 | −0.549897 | ||||||||
\(665\) | − 139.893i | − 0.210366i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42.1224 | 0.0631520 | ||||||||
\(668\) | 721.640i | 1.08030i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 385.343 | 0.575138 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −738.885 | −1.09790 | −0.548949 | − | 0.835856i | \(-0.684972\pi\) | ||||
−0.548949 | + | 0.835856i | \(0.684972\pi\) | |||||||
\(674\) | − 329.453i | − 0.488803i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 555.558 | 0.821832 | ||||||||
\(677\) | 42.1168i | 0.0622109i | 0.999516 | + | 0.0311055i | \(0.00990277\pi\) | ||||
−0.999516 | + | 0.0311055i | \(0.990097\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −259.817 | −0.382647 | ||||||||
\(680\) | − 132.684i | − 0.195123i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 543.110i | 0.795183i | 0.917562 | + | 0.397592i | \(0.130154\pi\) | ||||
−0.917562 | + | 0.397592i | \(0.869846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.4902 | −0.0474309 | ||||||||
\(686\) | 866.734i | 1.26346i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.04886 | 0.0116989 | ||||||||
\(689\) | 43.8059i | 0.0635790i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −428.173 | −0.619643 | −0.309821 | − | 0.950795i | \(-0.600269\pi\) | ||||
−0.309821 | + | 0.950795i | \(0.600269\pi\) | |||||||
\(692\) | 1443.22i | 2.08558i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −664.080 | −0.956887 | ||||||||
\(695\) | 239.951i | 0.345253i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 823.918 | 1.18209 | ||||||||
\(698\) | − 1396.68i | − 2.00098i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −370.703 | −0.529576 | ||||||||
\(701\) | 2.78056i | 0.00396656i | 0.999998 | + | 0.00198328i | \(0.000631299\pi\) | ||||
−0.999998 | + | 0.00198328i | \(0.999369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1760.39 | −2.50411 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1480.70 | −2.09730 | ||||||||
\(707\) | 129.816i | 0.183615i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1077.51 | 1.51976 | 0.759878 | − | 0.650065i | \(-0.225258\pi\) | ||||
0.759878 | + | 0.650065i | \(0.225258\pi\) | |||||||
\(710\) | 520.253i | 0.732751i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −241.880 | −0.339719 | ||||||||
\(713\) | 180.559i | 0.253239i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 727.591i | 1.01619i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −84.3660 | −0.117501 | ||||||||
\(719\) | − 1073.42i | − 1.49293i | −0.665424 | − | 0.746465i | \(-0.731749\pi\) | ||||
0.665424 | − | 0.746465i | \(-0.268251\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 100.385 | 0.139231 | ||||||||
\(722\) | − 953.792i | − 1.32104i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1110.49 | −1.53383 | ||||||||
\(725\) | 48.2295i | 0.0665234i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −212.371 | −0.292119 | −0.146060 | − | 0.989276i | \(-0.546659\pi\) | ||||
−0.146060 | + | 0.989276i | \(0.546659\pi\) | |||||||
\(728\) | − 73.1267i | − 0.100449i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −436.262 | −0.597620 | ||||||||
\(731\) | 20.4082i | 0.0279182i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 942.223 | 1.28543 | 0.642717 | − | 0.766104i | \(-0.277807\pi\) | ||||
0.642717 | + | 0.766104i | \(0.277807\pi\) | |||||||
\(734\) | − 89.2414i | − 0.121582i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 882.479 | 1.19902 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 720.862 | 0.975456 | 0.487728 | − | 0.872996i | \(-0.337826\pi\) | ||||
0.487728 | + | 0.872996i | \(0.337826\pi\) | |||||||
\(740\) | − 540.914i | − 0.730965i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −57.7583 | −0.0778414 | ||||||||
\(743\) | 836.564i | 1.12593i | 0.826482 | + | 0.562963i | \(0.190339\pi\) | ||||
−0.826482 | + | 0.562963i | \(0.809661\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −72.3640 | −0.0971329 | ||||||||
\(746\) | − 940.064i | − 1.26014i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 165.673i | − 0.221192i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.2668 | −0.0469598 | −0.0234799 | − | 0.999724i | \(-0.507475\pi\) | ||||
−0.0234799 | + | 0.999724i | \(0.507475\pi\) | |||||||
\(752\) | 274.238i | 0.364679i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −48.7670 | −0.0646777 | ||||||||
\(755\) | 75.0141i | 0.0993564i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 454.700 | 0.600660 | 0.300330 | − | 0.953835i | \(-0.402903\pi\) | ||||
0.300330 | + | 0.953835i | \(0.402903\pi\) | |||||||
\(758\) | 94.0866i | 0.124125i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 121.986 | 0.160508 | ||||||||
\(761\) | − 104.689i | − 0.137568i | −0.997632 | − | 0.0687840i | \(-0.978088\pi\) | ||||
0.997632 | − | 0.0687840i | \(-0.0219119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 498.884 | 0.653845 | ||||||||
\(764\) | − 115.381i | − 0.151022i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1422.28 | 1.85676 | ||||||||
\(767\) | 559.620i | 0.729622i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 93.7806 | 0.121951 | 0.0609757 | − | 0.998139i | \(-0.480579\pi\) | ||||
0.0609757 | + | 0.998139i | \(0.480579\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −623.361 | −0.807463 | ||||||||
\(773\) | 358.726i | 0.464070i | 0.972707 | + | 0.232035i | \(0.0745384\pi\) | ||||
−0.972707 | + | 0.232035i | \(0.925462\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −206.738 | −0.266758 | ||||||||
\(776\) | − 226.559i | − 0.291957i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −126.826 | −0.163015 | ||||||||
\(779\) | 757.491i | 0.972388i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1661.38i | 2.12453i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 423.938 | 0.540737 | ||||||||
\(785\) | − 29.2905i | − 0.0373127i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −276.916 | −0.351863 | −0.175931 | − | 0.984402i | \(-0.556294\pi\) | ||||
−0.175931 | + | 0.984402i | \(0.556294\pi\) | |||||||
\(788\) | 61.5458i | 0.0781038i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 554.147 | 0.701452 | ||||||||
\(791\) | 424.449i | 0.536598i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 545.830 | 0.688311 | ||||||||
\(794\) | 1677.96i | 2.11330i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −559.622 | −0.703042 | ||||||||
\(797\) | 528.612i | 0.663252i | 0.943411 | + | 0.331626i | \(0.107597\pi\) | ||||
−0.943411 | + | 0.331626i | \(0.892403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −695.343 | −0.870267 | ||||||||
\(800\) | 1010.43i | 1.26303i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1692.99 | −2.11096 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −105.004 | −0.130439 | ||||||||
\(806\) | − 209.042i | − 0.259357i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −113.198 | −0.140097 | ||||||||
\(809\) | − 1257.86i | − 1.55483i | −0.628985 | − | 0.777417i | \(-0.716529\pi\) | ||||
0.628985 | − | 0.777417i | \(-0.283471\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1041.19 | 1.28383 | 0.641916 | − | 0.766775i | \(-0.278140\pi\) | ||||
0.641916 | + | 0.766775i | \(0.278140\pi\) | |||||||
\(812\) | − 35.6248i | − 0.0438729i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 224.291i | 0.275203i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.7628 | −0.0229655 | ||||||||
\(818\) | 521.875i | 0.637989i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −232.754 | −0.283846 | ||||||||
\(821\) | 435.664i | 0.530650i | 0.964159 | + | 0.265325i | \(0.0854793\pi\) | ||||
−0.964159 | + | 0.265325i | \(0.914521\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 587.220 | 0.713512 | 0.356756 | − | 0.934198i | \(-0.383883\pi\) | ||||
0.356756 | + | 0.934198i | \(0.383883\pi\) | |||||||
\(824\) | 87.5354i | 0.106232i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −737.862 | −0.893296 | ||||||||
\(827\) | − 274.955i | − 0.332473i | −0.986086 | − | 0.166236i | \(-0.946839\pi\) | ||||
0.986086 | − | 0.166236i | \(-0.0531615\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −916.540 | −1.10560 | −0.552799 | − | 0.833315i | \(-0.686440\pi\) | ||||
−0.552799 | + | 0.833315i | \(0.686440\pi\) | |||||||
\(830\) | − 607.004i | − 0.731330i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −683.385 | −0.821376 | ||||||||
\(833\) | 1074.91i | 1.29041i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −234.045 | −0.280293 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −836.380 | −0.998067 | ||||||||
\(839\) | − 1058.83i | − 1.26202i | −0.775777 | − | 0.631008i | \(-0.782642\pi\) | ||||
0.775777 | − | 0.631008i | \(-0.217358\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 836.365 | 0.994489 | ||||||||
\(842\) | − 1159.06i | − 1.37655i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 764.858 | 0.906229 | ||||||||
\(845\) | 180.181i | 0.213232i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 64.7637i | 0.0763723i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1902.26 | −2.23795 | ||||||||
\(851\) | 1321.35i | 1.55270i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 262.534 | 0.307777 | 0.153888 | − | 0.988088i | \(-0.450820\pi\) | ||||
0.153888 | + | 0.988088i | \(0.450820\pi\) | |||||||
\(854\) | 719.680i | 0.842716i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 144.466 | 0.168768 | ||||||||
\(857\) | − 139.937i | − 0.163287i | −0.996662 | − | 0.0816437i | \(-0.973983\pi\) | ||||
0.996662 | − | 0.0816437i | \(-0.0260169\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −466.124 | −0.542635 | −0.271318 | − | 0.962490i | \(-0.587459\pi\) | ||||
−0.271318 | + | 0.962490i | \(0.587459\pi\) | |||||||
\(860\) | − 5.76524i | − 0.00670377i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −958.299 | −1.11172 | ||||||||
\(863\) | − 223.415i | − 0.258882i | −0.991587 | − | 0.129441i | \(-0.958682\pi\) | ||||
0.991587 | − | 0.129441i | \(-0.0413183\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −468.072 | −0.541123 | ||||||||
\(866\) | − 1575.76i | − 1.81958i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 152.707 | 0.175930 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 603.801 | 0.693228 | ||||||||
\(872\) | 435.023i | 0.498880i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1527.44 | −1.74764 | ||||||||
\(875\) | − 254.397i | − 0.290739i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −446.074 | −0.508637 | −0.254318 | − | 0.967121i | \(-0.581851\pi\) | ||||
−0.254318 | + | 0.967121i | \(0.581851\pi\) | |||||||
\(878\) | 68.2292i | 0.0777099i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 1631.61i | − 1.85200i | −0.377522 | − | 0.926001i | \(-0.623224\pi\) | ||||
0.377522 | − | 0.926001i | \(-0.376776\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1491.22 | 1.68881 | 0.844404 | − | 0.535707i | \(-0.179955\pi\) | ||||
0.844404 | + | 0.535707i | \(0.179955\pi\) | |||||||
\(884\) | − 1065.68i | − 1.20552i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −179.701 | −0.202823 | ||||||||
\(887\) | − 623.153i | − 0.702540i | −0.936274 | − | 0.351270i | \(-0.885750\pi\) | ||||
0.936274 | − | 0.351270i | \(-0.114250\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 792.413 | 0.891353 | ||||||||
\(890\) | − 402.107i | − 0.451806i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1403.31 | −1.57321 | ||||||||
\(893\) | − 639.282i | − 0.715881i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −235.975 | −0.263659 | ||||||||
\(896\) | − 300.300i | − 0.335157i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2279.80 | 2.53875 | ||||||||
\(899\) | − 19.8676i | − 0.0220997i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −164.211 | −0.182254 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −370.117 | −0.409422 | ||||||||
\(905\) | − 360.158i | − 0.397965i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −966.557 | −1.06566 | −0.532832 | − | 0.846221i | \(-0.678872\pi\) | ||||
−0.532832 | + | 0.846221i | \(0.678872\pi\) | |||||||
\(908\) | 1008.14i | 1.11028i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 121.568 | 0.133591 | ||||||||
\(911\) | 617.042i | 0.677324i | 0.940908 | + | 0.338662i | \(0.109974\pi\) | ||||
−0.940908 | + | 0.338662i | \(0.890026\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − 2362.80i | − 2.58512i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2082.82 | 2.27382 | ||||||||
\(917\) | 494.595i | 0.539362i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1104.16 | −1.20148 | −0.600742 | − | 0.799443i | \(-0.705128\pi\) | ||||
−0.600742 | + | 0.799443i | \(0.705128\pi\) | |||||||
\(920\) | − 91.5626i | − 0.0995246i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2176.83 | −2.36099 | ||||||||
\(923\) | 815.195i | 0.883202i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1512.92 | −1.63559 | ||||||||
\(926\) | − 903.109i | − 0.975280i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −97.1025 | −0.104636 | ||||||||
\(929\) | − 1078.61i | − 1.16104i | −0.814245 | − | 0.580521i | \(-0.802849\pi\) | ||||
0.814245 | − | 0.580521i | \(-0.197151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −988.248 | −1.06149 | ||||||||
\(932\) | 552.218i | 0.592509i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 875.967 | 0.937866 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 587.691 | 0.627205 | 0.313602 | − | 0.949554i | \(-0.398464\pi\) | ||||
0.313602 | + | 0.949554i | \(0.398464\pi\) | |||||||
\(938\) | 796.115i | 0.848736i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 196.432 | 0.208970 | ||||||||
\(941\) | − 1069.27i | − 1.13631i | −0.822921 | − | 0.568155i | \(-0.807657\pi\) | ||||
0.822921 | − | 0.568155i | \(-0.192343\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 568.572 | 0.602939 | ||||||||
\(944\) | 827.356i | 0.876437i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 435.924i | − 0.460321i | −0.973153 | − | 0.230160i | \(-0.926075\pi\) | ||||
0.973153 | − | 0.230160i | \(-0.0739251\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −683.588 | −0.720325 | ||||||||
\(950\) | − 1748.89i | − 1.84094i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 274.123 | 0.287945 | ||||||||
\(953\) | − 670.977i | − 0.704068i | −0.935987 | − | 0.352034i | \(-0.885490\pi\) | ||||
0.935987 | − | 0.352034i | \(-0.114510\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.4207 | 0.0391840 | ||||||||
\(956\) | 1560.70i | 1.63253i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1488.11 | 1.55335 | ||||||||
\(959\) | − 67.1244i | − 0.0699942i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −875.837 | −0.911380 | ||||||||
\(962\) | − 1529.79i | − 1.59021i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −518.287 | −0.537642 | ||||||||
\(965\) | − 202.171i | − 0.209503i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 940.682 | 0.972784 | 0.486392 | − | 0.873741i | \(-0.338313\pi\) | ||||
0.486392 | + | 0.873741i | \(0.338313\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 376.637 | 0.388286 | ||||||||
\(971\) | − 1077.62i | − 1.10980i | −0.831916 | − | 0.554901i | \(-0.812756\pi\) | ||||
0.831916 | − | 0.554901i | \(-0.187244\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −495.736 | −0.509492 | ||||||||
\(974\) | − 2071.64i | − 2.12694i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 806.969 | 0.826812 | ||||||||
\(977\) | − 1006.05i | − 1.02973i | −0.857270 | − | 0.514866i | \(-0.827842\pi\) | ||||
0.857270 | − | 0.514866i | \(-0.172158\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − 303.658i | − 0.309855i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 887.221 | 0.903484 | ||||||||
\(983\) | 1173.82i | 1.19412i | 0.802197 | + | 0.597060i | \(0.203665\pi\) | ||||
−0.802197 | + | 0.597060i | \(0.796335\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.9608 | −0.0202647 | ||||||||
\(986\) | − 182.808i | − 0.185404i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 979.763 | 0.991663 | ||||||||
\(989\) | 14.0834i | 0.0142400i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −989.386 | −0.998372 | −0.499186 | − | 0.866495i | \(-0.666368\pi\) | ||||
−0.499186 | + | 0.866495i | \(0.666368\pi\) | |||||||
\(992\) | − 416.234i | − 0.419591i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1074.84 | −1.08133 | ||||||||
\(995\) | − 181.499i | − 0.182411i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1465.59 | 1.47000 | 0.735000 | − | 0.678067i | \(-0.237182\pi\) | ||||
0.735000 | + | 0.678067i | \(0.237182\pi\) | |||||||
\(998\) | 401.329i | 0.402133i | ||||||||
\(999\) | 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 | 1089.3.b.j.485.3 | 16 | ||
3.2 | odd | 2 | inner | 1089.3.b.j.485.14 | 16 | ||
11.7 | odd | 10 | 99.3.l.a.71.2 | yes | 32 | ||
11.8 | odd | 10 | 99.3.l.a.53.7 | yes | 32 | ||
11.10 | odd | 2 | 1089.3.b.i.485.14 | 16 | |||
33.8 | even | 10 | 99.3.l.a.53.2 | ✓ | 32 | ||
33.29 | even | 10 | 99.3.l.a.71.7 | yes | 32 | ||
33.32 | even | 2 | 1089.3.b.i.485.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.3.l.a.53.2 | ✓ | 32 | 33.8 | even | 10 | ||
99.3.l.a.53.7 | yes | 32 | 11.8 | odd | 10 | ||
99.3.l.a.71.2 | yes | 32 | 11.7 | odd | 10 | ||
99.3.l.a.71.7 | yes | 32 | 33.29 | even | 10 | ||
1089.3.b.i.485.3 | 16 | 33.32 | even | 2 | |||
1089.3.b.i.485.14 | 16 | 11.10 | odd | 2 | |||
1089.3.b.j.485.3 | 16 | 1.1 | even | 1 | trivial | ||
1089.3.b.j.485.14 | 16 | 3.2 | odd | 2 | inner |