Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,4,Mod(559,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.559");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.d (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: | \(54.8717763053\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 2763 x^{18} + 2652899 x^{16} + 1161420105 x^{14} + 247831438280 x^{12} + 26461073949176 x^{10} + \cdots + 34\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 559.5 | ||
Root | \(-2.45273i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.559 |
Dual form | 930.4.d.c.559.15 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.00000i | − | 0.707107i | ||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 1.65380 | + | 11.0573i | 0.147920 | + | 0.988999i | ||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | − | 2.45273i | − | 0.132435i | −0.997805 | − | 0.0662175i | \(-0.978907\pi\) | ||
0.997805 | − | 0.0662175i | \(-0.0210931\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 22.1147 | − | 3.30759i | 0.699328 | − | 0.104595i | ||||
\(11\) | −35.2532 | −0.966295 | −0.483147 | − | 0.875539i | \(-0.660506\pi\) | ||||
−0.483147 | + | 0.875539i | \(0.660506\pi\) | |||||||
\(12\) | − | 12.0000i | − | 0.288675i | ||||||
\(13\) | − | 31.1443i | − | 0.664452i | −0.943200 | − | 0.332226i | \(-0.892200\pi\) | ||
0.943200 | − | 0.332226i | \(-0.107800\pi\) | |||||||
\(14\) | −4.90546 | −0.0936457 | ||||||||
\(15\) | −33.1720 | + | 4.96139i | −0.570999 | + | 0.0854017i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − | 47.1144i | − | 0.672172i | −0.941831 | − | 0.336086i | \(-0.890897\pi\) | ||
0.941831 | − | 0.336086i | \(-0.109103\pi\) | |||||||
\(18\) | 18.0000i | 0.235702i | ||||||||
\(19\) | 118.399 | 1.42961 | 0.714806 | − | 0.699323i | \(-0.246515\pi\) | ||||
0.714806 | + | 0.699323i | \(0.246515\pi\) | |||||||
\(20\) | −6.61519 | − | 44.2294i | −0.0739601 | − | 0.494500i | ||||
\(21\) | 7.35819 | 0.0764614 | ||||||||
\(22\) | 70.5064i | 0.683273i | ||||||||
\(23\) | 57.1501i | 0.518114i | 0.965862 | + | 0.259057i | \(0.0834117\pi\) | ||||
−0.965862 | + | 0.259057i | \(0.916588\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | −119.530 | + | 36.5732i | −0.956239 | + | 0.292586i | ||||
\(26\) | −62.2886 | −0.469839 | ||||||||
\(27\) | − | 27.0000i | − | 0.192450i | ||||||
\(28\) | 9.81092i | 0.0662175i | ||||||||
\(29\) | −298.374 | −1.91058 | −0.955288 | − | 0.295676i | \(-0.904455\pi\) | ||||
−0.955288 | + | 0.295676i | \(0.904455\pi\) | |||||||
\(30\) | 9.92278 | + | 66.3441i | 0.0603881 | + | 0.403757i | ||||
\(31\) | −31.0000 | −0.179605 | ||||||||
\(32\) | − | 32.0000i | − | 0.176777i | ||||||
\(33\) | − | 105.760i | − | 0.557890i | ||||||
\(34\) | −94.2289 | −0.475298 | ||||||||
\(35\) | 27.1207 | − | 4.05632i | 0.130978 | − | 0.0195898i | ||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 82.3944i | 0.366096i | 0.983104 | + | 0.183048i | \(0.0585964\pi\) | ||||
−0.983104 | + | 0.183048i | \(0.941404\pi\) | |||||||
\(38\) | − | 236.798i | − | 1.01089i | ||||||
\(39\) | 93.4329 | 0.383622 | ||||||||
\(40\) | −88.4588 | + | 13.2304i | −0.349664 | + | 0.0522977i | ||||
\(41\) | −25.0717 | −0.0955009 | −0.0477505 | − | 0.998859i | \(-0.515205\pi\) | ||||
−0.0477505 | + | 0.998859i | \(0.515205\pi\) | |||||||
\(42\) | − | 14.7164i | − | 0.0540664i | ||||||
\(43\) | − | 264.775i | − | 0.939018i | −0.882928 | − | 0.469509i | \(-0.844431\pi\) | ||
0.882928 | − | 0.469509i | \(-0.155569\pi\) | |||||||
\(44\) | 141.013 | 0.483147 | ||||||||
\(45\) | −14.8842 | − | 99.5161i | −0.0493067 | − | 0.329666i | ||||
\(46\) | 114.300 | 0.366362 | ||||||||
\(47\) | − | 344.703i | − | 1.06979i | −0.844919 | − | 0.534894i | \(-0.820352\pi\) | ||
0.844919 | − | 0.534894i | \(-0.179648\pi\) | |||||||
\(48\) | 48.0000i | 0.144338i | ||||||||
\(49\) | 336.984 | 0.982461 | ||||||||
\(50\) | 73.1465 | + | 239.060i | 0.206889 | + | 0.676163i | ||||
\(51\) | 141.343 | 0.388079 | ||||||||
\(52\) | 124.577i | 0.332226i | ||||||||
\(53\) | − | 422.169i | − | 1.09414i | −0.837087 | − | 0.547069i | \(-0.815743\pi\) | ||
0.837087 | − | 0.547069i | \(-0.184257\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | −58.3016 | − | 389.807i | −0.142934 | − | 0.955665i | ||||
\(56\) | 19.6218 | 0.0468228 | ||||||||
\(57\) | 355.198i | 0.825387i | ||||||||
\(58\) | 596.749i | 1.35098i | ||||||||
\(59\) | −43.3724 | −0.0957051 | −0.0478526 | − | 0.998854i | \(-0.515238\pi\) | ||||
−0.0478526 | + | 0.998854i | \(0.515238\pi\) | |||||||
\(60\) | 132.688 | − | 19.8456i | 0.285500 | − | 0.0427009i | ||||
\(61\) | 96.2068 | 0.201935 | 0.100967 | − | 0.994890i | \(-0.467806\pi\) | ||||
0.100967 | + | 0.994890i | \(0.467806\pi\) | |||||||
\(62\) | 62.0000i | 0.127000i | ||||||||
\(63\) | 22.0746i | 0.0441450i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 344.373 | − | 51.5064i | 0.657143 | − | 0.0982858i | ||||
\(66\) | −211.519 | −0.394488 | ||||||||
\(67\) | 706.568i | 1.28837i | 0.764868 | + | 0.644186i | \(0.222804\pi\) | ||||
−0.764868 | + | 0.644186i | \(0.777196\pi\) | |||||||
\(68\) | 188.458i | 0.336086i | ||||||||
\(69\) | −171.450 | −0.299133 | ||||||||
\(70\) | −8.11264 | − | 54.2414i | −0.0138521 | − | 0.0926155i | ||||
\(71\) | 1110.36 | 1.85600 | 0.928000 | − | 0.372580i | \(-0.121527\pi\) | ||||
0.928000 | + | 0.372580i | \(0.121527\pi\) | |||||||
\(72\) | − | 72.0000i | − | 0.117851i | ||||||
\(73\) | 94.3706i | 0.151305i | 0.997134 | + | 0.0756524i | \(0.0241039\pi\) | ||||
−0.997134 | + | 0.0756524i | \(0.975896\pi\) | |||||||
\(74\) | 164.789 | 0.258869 | ||||||||
\(75\) | −109.720 | − | 358.590i | −0.168924 | − | 0.552085i | ||||
\(76\) | −473.597 | −0.714806 | ||||||||
\(77\) | 86.4666i | 0.127971i | ||||||||
\(78\) | − | 186.866i | − | 0.271261i | ||||||
\(79\) | 607.265 | 0.864843 | 0.432422 | − | 0.901672i | \(-0.357659\pi\) | ||||
0.432422 | + | 0.901672i | \(0.357659\pi\) | |||||||
\(80\) | 26.4608 | + | 176.918i | 0.0369800 | + | 0.247250i | ||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 50.1434i | 0.0675294i | ||||||||
\(83\) | − | 604.212i | − | 0.799047i | −0.916723 | − | 0.399523i | \(-0.869176\pi\) | ||
0.916723 | − | 0.399523i | \(-0.130824\pi\) | |||||||
\(84\) | −29.4328 | −0.0382307 | ||||||||
\(85\) | 520.961 | − | 77.9177i | 0.664778 | − | 0.0994278i | ||||
\(86\) | −529.549 | −0.663986 | ||||||||
\(87\) | − | 895.123i | − | 1.10307i | ||||||
\(88\) | − | 282.026i | − | 0.341637i | ||||||
\(89\) | 391.745 | 0.466572 | 0.233286 | − | 0.972408i | \(-0.425052\pi\) | ||||
0.233286 | + | 0.972408i | \(0.425052\pi\) | |||||||
\(90\) | −199.032 | + | 29.7684i | −0.233109 | + | 0.0348651i | ||||
\(91\) | −76.3886 | −0.0879967 | ||||||||
\(92\) | − | 228.600i | − | 0.259057i | ||||||
\(93\) | − | 93.0000i | − | 0.103695i | ||||||
\(94\) | −689.405 | −0.756454 | ||||||||
\(95\) | 195.808 | + | 1309.18i | 0.211468 | + | 1.41389i | ||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | − | 1048.85i | − | 1.09788i | −0.835861 | − | 0.548942i | \(-0.815031\pi\) | ||
0.835861 | − | 0.548942i | \(-0.184969\pi\) | |||||||
\(98\) | − | 673.968i | − | 0.694705i | ||||||
\(99\) | 317.279 | 0.322098 | ||||||||
\(100\) | 478.120 | − | 146.293i | 0.478120 | − | 0.146293i | ||||
\(101\) | 1284.24 | 1.26521 | 0.632605 | − | 0.774474i | \(-0.281986\pi\) | ||||
0.632605 | + | 0.774474i | \(0.281986\pi\) | |||||||
\(102\) | − | 282.687i | − | 0.274413i | ||||||
\(103\) | − | 1975.76i | − | 1.89007i | −0.326970 | − | 0.945035i | \(-0.606028\pi\) | ||
0.326970 | − | 0.945035i | \(-0.393972\pi\) | |||||||
\(104\) | 249.154 | 0.234919 | ||||||||
\(105\) | 12.1690 | + | 81.3621i | 0.0113102 | + | 0.0756202i | ||||
\(106\) | −844.338 | −0.773673 | ||||||||
\(107\) | − | 1618.89i | − | 1.46266i | −0.682026 | − | 0.731328i | \(-0.738901\pi\) | ||
0.682026 | − | 0.731328i | \(-0.261099\pi\) | |||||||
\(108\) | 108.000i | 0.0962250i | ||||||||
\(109\) | 2039.14 | 1.79187 | 0.895936 | − | 0.444182i | \(-0.146506\pi\) | ||||
0.895936 | + | 0.444182i | \(0.146506\pi\) | |||||||
\(110\) | −779.614 | + | 116.603i | −0.675757 | + | 0.101070i | ||||
\(111\) | −247.183 | −0.211366 | ||||||||
\(112\) | − | 39.2437i | − | 0.0331087i | ||||||
\(113\) | − | 895.966i | − | 0.745888i | −0.927854 | − | 0.372944i | \(-0.878348\pi\) | ||
0.927854 | − | 0.372944i | \(-0.121652\pi\) | |||||||
\(114\) | 710.395 | 0.583637 | ||||||||
\(115\) | −631.928 | + | 94.5146i | −0.512414 | + | 0.0766394i | ||||
\(116\) | 1193.50 | 0.955288 | ||||||||
\(117\) | 280.299i | 0.221484i | ||||||||
\(118\) | 86.7447i | 0.0676737i | ||||||||
\(119\) | −115.559 | −0.0890191 | ||||||||
\(120\) | −39.6911 | − | 265.376i | −0.0301941 | − | 0.201879i | ||||
\(121\) | −88.2119 | −0.0662749 | ||||||||
\(122\) | − | 192.414i | − | 0.142789i | ||||||
\(123\) | − | 75.2150i | − | 0.0551375i | ||||||
\(124\) | 124.000 | 0.0898027 | ||||||||
\(125\) | −602.081 | − | 1261.20i | −0.430814 | − | 0.902441i | ||||
\(126\) | 44.1491 | 0.0312152 | ||||||||
\(127\) | 920.890i | 0.643431i | 0.946836 | + | 0.321716i | \(0.104260\pi\) | ||||
−0.946836 | + | 0.321716i | \(0.895740\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | 794.324 | 0.542142 | ||||||||
\(130\) | −103.013 | − | 688.747i | −0.0694986 | − | 0.464670i | ||||
\(131\) | −2612.31 | −1.74228 | −0.871141 | − | 0.491034i | \(-0.836619\pi\) | ||||
−0.871141 | + | 0.491034i | \(0.836619\pi\) | |||||||
\(132\) | 423.038i | 0.278945i | ||||||||
\(133\) | − | 290.401i | − | 0.189331i | ||||||
\(134\) | 1413.14 | 0.911017 | ||||||||
\(135\) | 298.548 | − | 44.6525i | 0.190333 | − | 0.0284672i | ||||
\(136\) | 376.916 | 0.237649 | ||||||||
\(137\) | 2194.36i | 1.36845i | 0.729273 | + | 0.684223i | \(0.239859\pi\) | ||||
−0.729273 | + | 0.684223i | \(0.760141\pi\) | |||||||
\(138\) | 342.900i | 0.211519i | ||||||||
\(139\) | 783.660 | 0.478196 | 0.239098 | − | 0.970995i | \(-0.423148\pi\) | ||||
0.239098 | + | 0.970995i | \(0.423148\pi\) | |||||||
\(140\) | −108.483 | + | 16.2253i | −0.0654891 | + | 0.00979490i | ||||
\(141\) | 1034.11 | 0.617642 | ||||||||
\(142\) | − | 2220.73i | − | 1.31239i | ||||||
\(143\) | 1097.94i | 0.642056i | ||||||||
\(144\) | −144.000 | −0.0833333 | ||||||||
\(145\) | −493.451 | − | 3299.23i | −0.282613 | − | 1.88956i | ||||
\(146\) | 188.741 | 0.106989 | ||||||||
\(147\) | 1010.95i | 0.567224i | ||||||||
\(148\) | − | 329.578i | − | 0.183048i | ||||||
\(149\) | −256.065 | −0.140790 | −0.0703949 | − | 0.997519i | \(-0.522426\pi\) | ||||
−0.0703949 | + | 0.997519i | \(0.522426\pi\) | |||||||
\(150\) | −717.179 | + | 219.439i | −0.390383 | + | 0.119448i | ||||
\(151\) | −3553.83 | −1.91528 | −0.957638 | − | 0.287973i | \(-0.907019\pi\) | ||||
−0.957638 | + | 0.287973i | \(0.907019\pi\) | |||||||
\(152\) | 947.193i | 0.505444i | ||||||||
\(153\) | 424.030i | 0.224057i | ||||||||
\(154\) | 172.933 | 0.0904893 | ||||||||
\(155\) | −51.2677 | − | 342.778i | −0.0265672 | − | 0.177630i | ||||
\(156\) | −373.732 | −0.191811 | ||||||||
\(157\) | − | 345.400i | − | 0.175579i | −0.996139 | − | 0.0877896i | \(-0.972020\pi\) | ||
0.996139 | − | 0.0877896i | \(-0.0279803\pi\) | |||||||
\(158\) | − | 1214.53i | − | 0.611537i | ||||||
\(159\) | 1266.51 | 0.631701 | ||||||||
\(160\) | 353.835 | − | 52.9215i | 0.174832 | − | 0.0261488i | ||||
\(161\) | 140.174 | 0.0686164 | ||||||||
\(162\) | − | 162.000i | − | 0.0785674i | ||||||
\(163\) | − | 1410.83i | − | 0.677945i | −0.940796 | − | 0.338972i | \(-0.889921\pi\) | ||
0.940796 | − | 0.338972i | \(-0.110079\pi\) | |||||||
\(164\) | 100.287 | 0.0477505 | ||||||||
\(165\) | 1169.42 | − | 174.905i | 0.551753 | − | 0.0825232i | ||||
\(166\) | −1208.42 | −0.565011 | ||||||||
\(167\) | − | 1809.73i | − | 0.838569i | −0.907855 | − | 0.419285i | \(-0.862281\pi\) | ||
0.907855 | − | 0.419285i | \(-0.137719\pi\) | |||||||
\(168\) | 58.8655i | 0.0270332i | ||||||||
\(169\) | 1227.03 | 0.558503 | ||||||||
\(170\) | −155.835 | − | 1041.92i | −0.0703061 | − | 0.470069i | ||||
\(171\) | −1065.59 | −0.476537 | ||||||||
\(172\) | 1059.10i | 0.469509i | ||||||||
\(173\) | − | 3916.63i | − | 1.72125i | −0.509243 | − | 0.860623i | \(-0.670075\pi\) | ||
0.509243 | − | 0.860623i | \(-0.329925\pi\) | |||||||
\(174\) | −1790.25 | −0.779990 | ||||||||
\(175\) | 89.7043 | + | 293.175i | 0.0387486 | + | 0.126640i | ||||
\(176\) | −564.051 | −0.241574 | ||||||||
\(177\) | − | 130.117i | − | 0.0552554i | ||||||
\(178\) | − | 783.490i | − | 0.329916i | ||||||
\(179\) | −265.024 | −0.110664 | −0.0553320 | − | 0.998468i | \(-0.517622\pi\) | ||||
−0.0553320 | + | 0.998468i | \(0.517622\pi\) | |||||||
\(180\) | 59.5367 | + | 398.065i | 0.0246534 | + | 0.164833i | ||||
\(181\) | 2535.64 | 1.04128 | 0.520642 | − | 0.853775i | \(-0.325693\pi\) | ||||
0.520642 | + | 0.853775i | \(0.325693\pi\) | |||||||
\(182\) | 152.777i | 0.0622231i | ||||||||
\(183\) | 288.620i | 0.116587i | ||||||||
\(184\) | −457.201 | −0.183181 | ||||||||
\(185\) | −911.064 | + | 136.264i | −0.362069 | + | 0.0541530i | ||||
\(186\) | −186.000 | −0.0733236 | ||||||||
\(187\) | 1660.93i | 0.649516i | ||||||||
\(188\) | 1378.81i | 0.534894i | ||||||||
\(189\) | −66.2237 | −0.0254871 | ||||||||
\(190\) | 2618.36 | − | 391.617i | 0.999768 | − | 0.149531i | ||||
\(191\) | −634.288 | −0.240290 | −0.120145 | − | 0.992756i | \(-0.538336\pi\) | ||||
−0.120145 | + | 0.992756i | \(0.538336\pi\) | |||||||
\(192\) | − | 192.000i | − | 0.0721688i | ||||||
\(193\) | − | 4931.48i | − | 1.83925i | −0.392796 | − | 0.919626i | \(-0.628492\pi\) | ||
0.392796 | − | 0.919626i | \(-0.371508\pi\) | |||||||
\(194\) | −2097.70 | −0.776321 | ||||||||
\(195\) | 154.519 | + | 1033.12i | 0.0567454 | + | 0.379401i | ||||
\(196\) | −1347.94 | −0.491230 | ||||||||
\(197\) | 4890.76i | 1.76879i | 0.466737 | + | 0.884396i | \(0.345430\pi\) | ||||
−0.466737 | + | 0.884396i | \(0.654570\pi\) | |||||||
\(198\) | − | 634.558i | − | 0.227758i | ||||||
\(199\) | 2738.39 | 0.975474 | 0.487737 | − | 0.872991i | \(-0.337823\pi\) | ||||
0.487737 | + | 0.872991i | \(0.337823\pi\) | |||||||
\(200\) | −292.586 | − | 956.239i | −0.103445 | − | 0.338082i | ||||
\(201\) | −2119.70 | −0.743842 | ||||||||
\(202\) | − | 2568.47i | − | 0.894639i | ||||||
\(203\) | 731.832i | 0.253027i | ||||||||
\(204\) | −565.373 | −0.194039 | ||||||||
\(205\) | −41.4635 | − | 277.226i | −0.0141265 | − | 0.0944504i | ||||
\(206\) | −3951.51 | −1.33648 | ||||||||
\(207\) | − | 514.351i | − | 0.172705i | ||||||
\(208\) | − | 498.309i | − | 0.166113i | ||||||
\(209\) | −4173.95 | −1.38143 | ||||||||
\(210\) | 162.724 | − | 24.3379i | 0.0534716 | − | 0.00799750i | ||||
\(211\) | 5556.03 | 1.81276 | 0.906381 | − | 0.422460i | \(-0.138833\pi\) | ||||
0.906381 | + | 0.422460i | \(0.138833\pi\) | |||||||
\(212\) | 1688.68i | 0.547069i | ||||||||
\(213\) | 3331.09i | 1.07156i | ||||||||
\(214\) | −3237.78 | −1.03425 | ||||||||
\(215\) | 2927.71 | − | 437.884i | 0.928688 | − | 0.138900i | ||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 76.0346i | 0.0237860i | ||||||||
\(218\) | − | 4078.28i | − | 1.26705i | ||||||
\(219\) | −283.112 | −0.0873559 | ||||||||
\(220\) | 233.207 | + | 1559.23i | 0.0714672 | + | 0.477832i | ||||
\(221\) | −1467.35 | −0.446626 | ||||||||
\(222\) | 494.366i | 0.149458i | ||||||||
\(223\) | 6505.89i | 1.95366i | 0.214014 | + | 0.976831i | \(0.431346\pi\) | ||||
−0.214014 | + | 0.976831i | \(0.568654\pi\) | |||||||
\(224\) | −78.4874 | −0.0234114 | ||||||||
\(225\) | 1075.77 | − | 329.159i | 0.318746 | − | 0.0975286i | ||||
\(226\) | −1791.93 | −0.527423 | ||||||||
\(227\) | − | 1721.52i | − | 0.503354i | −0.967811 | − | 0.251677i | \(-0.919018\pi\) | ||
0.967811 | − | 0.251677i | \(-0.0809821\pi\) | |||||||
\(228\) | − | 1420.79i | − | 0.412694i | ||||||
\(229\) | −2074.96 | −0.598764 | −0.299382 | − | 0.954133i | \(-0.596781\pi\) | ||||
−0.299382 | + | 0.954133i | \(0.596781\pi\) | |||||||
\(230\) | 189.029 | + | 1263.86i | 0.0541923 | + | 0.362331i | ||||
\(231\) | −259.400 | −0.0738842 | ||||||||
\(232\) | − | 2386.99i | − | 0.675491i | ||||||
\(233\) | − | 4235.01i | − | 1.19075i | −0.803448 | − | 0.595375i | \(-0.797003\pi\) | ||
0.803448 | − | 0.595375i | \(-0.202997\pi\) | |||||||
\(234\) | 560.598 | 0.156613 | ||||||||
\(235\) | 3811.50 | − | 570.068i | 1.05802 | − | 0.158243i | ||||
\(236\) | 173.489 | 0.0478526 | ||||||||
\(237\) | 1821.79i | 0.499318i | ||||||||
\(238\) | 231.118i | 0.0629460i | ||||||||
\(239\) | −6106.61 | −1.65274 | −0.826368 | − | 0.563131i | \(-0.809597\pi\) | ||||
−0.826368 | + | 0.563131i | \(0.809597\pi\) | |||||||
\(240\) | −530.753 | + | 79.3823i | −0.142750 | + | 0.0213504i | ||||
\(241\) | −3008.74 | −0.804190 | −0.402095 | − | 0.915598i | \(-0.631718\pi\) | ||||
−0.402095 | + | 0.915598i | \(0.631718\pi\) | |||||||
\(242\) | 176.424i | 0.0468635i | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | −384.827 | −0.100967 | ||||||||
\(245\) | 557.303 | + | 3726.15i | 0.145326 | + | 0.971653i | ||||
\(246\) | −150.430 | −0.0389881 | ||||||||
\(247\) | − | 3687.46i | − | 0.949909i | ||||||
\(248\) | − | 248.000i | − | 0.0635001i | ||||||
\(249\) | 1812.64 | 0.461330 | ||||||||
\(250\) | −2522.40 | + | 1204.16i | −0.638122 | + | 0.304632i | ||||
\(251\) | −4410.77 | −1.10918 | −0.554592 | − | 0.832122i | \(-0.687126\pi\) | ||||
−0.554592 | + | 0.832122i | \(0.687126\pi\) | |||||||
\(252\) | − | 88.2983i | − | 0.0220725i | ||||||
\(253\) | − | 2014.72i | − | 0.500650i | ||||||
\(254\) | 1841.78 | 0.454975 | ||||||||
\(255\) | 233.753 | + | 1562.88i | 0.0574047 | + | 0.383810i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 4828.05i | 1.17185i | 0.810365 | + | 0.585925i | \(0.199269\pi\) | ||||
−0.810365 | + | 0.585925i | \(0.800731\pi\) | |||||||
\(258\) | − | 1588.65i | − | 0.383352i | ||||||
\(259\) | 202.091 | 0.0484839 | ||||||||
\(260\) | −1377.49 | + | 206.026i | −0.328571 | + | 0.0491429i | ||||
\(261\) | 2685.37 | 0.636859 | ||||||||
\(262\) | 5224.63i | 1.23198i | ||||||||
\(263\) | 4853.47i | 1.13794i | 0.822359 | + | 0.568970i | \(0.192658\pi\) | ||||
−0.822359 | + | 0.568970i | \(0.807342\pi\) | |||||||
\(264\) | 846.077 | 0.197244 | ||||||||
\(265\) | 4668.07 | − | 698.182i | 1.08210 | − | 0.161845i | ||||
\(266\) | −580.803 | −0.133877 | ||||||||
\(267\) | 1175.23i | 0.269375i | ||||||||
\(268\) | − | 2826.27i | − | 0.644186i | ||||||
\(269\) | 1124.63 | 0.254906 | 0.127453 | − | 0.991845i | \(-0.459320\pi\) | ||||
0.127453 | + | 0.991845i | \(0.459320\pi\) | |||||||
\(270\) | −89.3051 | − | 597.097i | −0.0201294 | − | 0.134586i | ||||
\(271\) | −2424.69 | −0.543503 | −0.271751 | − | 0.962367i | \(-0.587603\pi\) | ||||
−0.271751 | + | 0.962367i | \(0.587603\pi\) | |||||||
\(272\) | − | 753.831i | − | 0.168043i | ||||||
\(273\) | − | 229.166i | − | 0.0508049i | ||||||
\(274\) | 4388.73 | 0.967638 | ||||||||
\(275\) | 4213.81 | − | 1289.32i | 0.924009 | − | 0.282724i | ||||
\(276\) | 685.801 | 0.149567 | ||||||||
\(277\) | − | 5668.85i | − | 1.22963i | −0.788671 | − | 0.614816i | \(-0.789230\pi\) | ||
0.788671 | − | 0.614816i | \(-0.210770\pi\) | |||||||
\(278\) | − | 1567.32i | − | 0.338135i | ||||||
\(279\) | 279.000 | 0.0598684 | ||||||||
\(280\) | 32.4506 | + | 216.966i | 0.00692604 | + | 0.0463078i | ||||
\(281\) | −3211.25 | −0.681733 | −0.340866 | − | 0.940112i | \(-0.610720\pi\) | ||||
−0.340866 | + | 0.940112i | \(0.610720\pi\) | |||||||
\(282\) | − | 2068.22i | − | 0.436739i | ||||||
\(283\) | 1030.37i | 0.216428i | 0.994128 | + | 0.108214i | \(0.0345132\pi\) | ||||
−0.994128 | + | 0.108214i | \(0.965487\pi\) | |||||||
\(284\) | −4441.46 | −0.928000 | ||||||||
\(285\) | −3927.54 | + | 587.425i | −0.816307 | + | 0.122091i | ||||
\(286\) | 2195.87 | 0.454002 | ||||||||
\(287\) | 61.4941i | 0.0126477i | ||||||||
\(288\) | 288.000i | 0.0589256i | ||||||||
\(289\) | 2693.23 | 0.548184 | ||||||||
\(290\) | −6598.46 | + | 986.901i | −1.33612 | + | 0.199837i | ||||
\(291\) | 3146.55 | 0.633864 | ||||||||
\(292\) | − | 377.483i | − | 0.0756524i | ||||||
\(293\) | − | 899.072i | − | 0.179264i | −0.995975 | − | 0.0896320i | \(-0.971431\pi\) | ||
0.995975 | − | 0.0896320i | \(-0.0285691\pi\) | |||||||
\(294\) | 2021.90 | 0.401088 | ||||||||
\(295\) | −71.7291 | − | 479.583i | −0.0141567 | − | 0.0946523i | ||||
\(296\) | −659.155 | −0.129435 | ||||||||
\(297\) | 951.836i | 0.185963i | ||||||||
\(298\) | 512.130i | 0.0995534i | ||||||||
\(299\) | 1779.90 | 0.344262 | ||||||||
\(300\) | 438.879 | + | 1434.36i | 0.0844622 | + | 0.276042i | ||||
\(301\) | −649.421 | −0.124359 | ||||||||
\(302\) | 7107.67i | 1.35431i | ||||||||
\(303\) | 3852.71i | 0.730470i | ||||||||
\(304\) | 1894.39 | 0.357403 | ||||||||
\(305\) | 159.107 | + | 1063.79i | 0.0298702 | + | 0.199713i | ||||
\(306\) | 848.060 | 0.158433 | ||||||||
\(307\) | − | 7269.78i | − | 1.35149i | −0.737135 | − | 0.675746i | \(-0.763822\pi\) | ||
0.737135 | − | 0.675746i | \(-0.236178\pi\) | |||||||
\(308\) | − | 345.866i | − | 0.0639856i | ||||||
\(309\) | 5927.27 | 1.09123 | ||||||||
\(310\) | −685.556 | + | 102.535i | −0.125603 | + | 0.0187859i | ||||
\(311\) | −3473.70 | −0.633362 | −0.316681 | − | 0.948532i | \(-0.602568\pi\) | ||||
−0.316681 | + | 0.948532i | \(0.602568\pi\) | |||||||
\(312\) | 747.463i | 0.135631i | ||||||||
\(313\) | − | 3467.92i | − | 0.626257i | −0.949711 | − | 0.313128i | \(-0.898623\pi\) | ||
0.949711 | − | 0.313128i | \(-0.101377\pi\) | |||||||
\(314\) | −690.800 | −0.124153 | ||||||||
\(315\) | −244.086 | + | 36.5069i | −0.0436594 | + | 0.00652993i | ||||
\(316\) | −2429.06 | −0.432422 | ||||||||
\(317\) | − | 1696.27i | − | 0.300542i | −0.988645 | − | 0.150271i | \(-0.951985\pi\) | ||
0.988645 | − | 0.150271i | \(-0.0480147\pi\) | |||||||
\(318\) | − | 2533.01i | − | 0.446680i | ||||||
\(319\) | 10518.7 | 1.84618 | ||||||||
\(320\) | −105.843 | − | 707.670i | −0.0184900 | − | 0.123625i | ||||
\(321\) | 4856.67 | 0.844465 | ||||||||
\(322\) | − | 280.347i | − | 0.0485191i | ||||||
\(323\) | − | 5578.31i | − | 0.960946i | ||||||
\(324\) | −324.000 | −0.0555556 | ||||||||
\(325\) | 1139.05 | + | 3722.68i | 0.194409 | + | 0.635375i | ||||
\(326\) | −2821.67 | −0.479379 | ||||||||
\(327\) | 6117.42i | 1.03454i | ||||||||
\(328\) | − | 200.573i | − | 0.0337647i | ||||||
\(329\) | −845.462 | −0.141677 | ||||||||
\(330\) | −349.810 | − | 2338.84i | −0.0583527 | − | 0.390148i | ||||
\(331\) | 5986.62 | 0.994122 | 0.497061 | − | 0.867715i | \(-0.334412\pi\) | ||||
0.497061 | + | 0.867715i | \(0.334412\pi\) | |||||||
\(332\) | 2416.85i | 0.399523i | ||||||||
\(333\) | − | 741.550i | − | 0.122032i | ||||||
\(334\) | −3619.46 | −0.592958 | ||||||||
\(335\) | −7812.77 | + | 1168.52i | −1.27420 | + | 0.190576i | ||||
\(336\) | 117.731 | 0.0191153 | ||||||||
\(337\) | 2762.05i | 0.446464i | 0.974765 | + | 0.223232i | \(0.0716608\pi\) | ||||
−0.974765 | + | 0.223232i | \(0.928339\pi\) | |||||||
\(338\) | − | 2454.06i | − | 0.394922i | ||||||
\(339\) | 2687.90 | 0.430639 | ||||||||
\(340\) | −2083.84 | + | 311.671i | −0.332389 | + | 0.0497139i | ||||
\(341\) | 1092.85 | 0.173552 | ||||||||
\(342\) | 2131.19i | 0.336963i | ||||||||
\(343\) | − | 1667.82i | − | 0.262547i | ||||||
\(344\) | 2118.20 | 0.331993 | ||||||||
\(345\) | −283.544 | − | 1895.78i | −0.0442478 | − | 0.295842i | ||||
\(346\) | −7833.25 | −1.21710 | ||||||||
\(347\) | 348.734i | 0.0539511i | 0.999636 | + | 0.0269756i | \(0.00858763\pi\) | ||||
−0.999636 | + | 0.0269756i | \(0.991412\pi\) | |||||||
\(348\) | 3580.49i | 0.551536i | ||||||||
\(349\) | −3247.11 | −0.498034 | −0.249017 | − | 0.968499i | \(-0.580108\pi\) | ||||
−0.249017 | + | 0.968499i | \(0.580108\pi\) | |||||||
\(350\) | 586.349 | − | 179.409i | 0.0895477 | − | 0.0273994i | ||||
\(351\) | −840.896 | −0.127874 | ||||||||
\(352\) | 1128.10i | 0.170818i | ||||||||
\(353\) | 8034.97i | 1.21150i | 0.795656 | + | 0.605749i | \(0.207126\pi\) | ||||
−0.795656 | + | 0.605749i | \(0.792874\pi\) | |||||||
\(354\) | −260.234 | −0.0390714 | ||||||||
\(355\) | 1836.32 | + | 12277.7i | 0.274540 | + | 1.83558i | ||||
\(356\) | −1566.98 | −0.233286 | ||||||||
\(357\) | − | 346.677i | − | 0.0513952i | ||||||
\(358\) | 530.049i | 0.0782512i | ||||||||
\(359\) | −5821.40 | −0.855826 | −0.427913 | − | 0.903820i | \(-0.640751\pi\) | ||||
−0.427913 | + | 0.903820i | \(0.640751\pi\) | |||||||
\(360\) | 796.129 | − | 119.073i | 0.116555 | − | 0.0174326i | ||||
\(361\) | 7159.37 | 1.04379 | ||||||||
\(362\) | − | 5071.27i | − | 0.736299i | ||||||
\(363\) | − | 264.636i | − | 0.0382639i | ||||||
\(364\) | 305.554 | 0.0439984 | ||||||||
\(365\) | −1043.49 | + | 156.070i | −0.149640 | + | 0.0223810i | ||||
\(366\) | 577.241 | 0.0824395 | ||||||||
\(367\) | − | 5139.43i | − | 0.730997i | −0.930812 | − | 0.365499i | \(-0.880898\pi\) | ||
0.930812 | − | 0.365499i | \(-0.119102\pi\) | |||||||
\(368\) | 914.401i | 0.129528i | ||||||||
\(369\) | 225.645 | 0.0318336 | ||||||||
\(370\) | 272.527 | + | 1822.13i | 0.0382919 | + | 0.256021i | ||||
\(371\) | −1035.47 | −0.144902 | ||||||||
\(372\) | 372.000i | 0.0518476i | ||||||||
\(373\) | − | 895.837i | − | 0.124356i | −0.998065 | − | 0.0621779i | \(-0.980195\pi\) | ||
0.998065 | − | 0.0621779i | \(-0.0198046\pi\) | |||||||
\(374\) | 3321.87 | 0.459277 | ||||||||
\(375\) | 3783.60 | − | 1806.24i | 0.521024 | − | 0.248731i | ||||
\(376\) | 2757.62 | 0.378227 | ||||||||
\(377\) | 9292.66i | 1.26949i | ||||||||
\(378\) | 132.447i | 0.0180221i | ||||||||
\(379\) | −14266.0 | −1.93350 | −0.966748 | − | 0.255732i | \(-0.917684\pi\) | ||||
−0.966748 | + | 0.255732i | \(0.917684\pi\) | |||||||
\(380\) | −783.233 | − | 5236.72i | −0.105734 | − | 0.706943i | ||||
\(381\) | −2762.67 | −0.371485 | ||||||||
\(382\) | 1268.58i | 0.169911i | ||||||||
\(383\) | − | 7255.84i | − | 0.968032i | −0.875059 | − | 0.484016i | \(-0.839178\pi\) | ||
0.875059 | − | 0.484016i | \(-0.160822\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | −956.091 | + | 142.998i | −0.126563 | + | 0.0189295i | ||||
\(386\) | −9862.96 | −1.30055 | ||||||||
\(387\) | 2382.97i | 0.313006i | ||||||||
\(388\) | 4195.41i | 0.548942i | ||||||||
\(389\) | 4258.04 | 0.554990 | 0.277495 | − | 0.960727i | \(-0.410496\pi\) | ||||
0.277495 | + | 0.960727i | \(0.410496\pi\) | |||||||
\(390\) | 2066.24 | − | 309.038i | 0.268277 | − | 0.0401250i | ||||
\(391\) | 2692.59 | 0.348262 | ||||||||
\(392\) | 2695.87i | 0.347352i | ||||||||
\(393\) | − | 7836.94i | − | 1.00591i | ||||||
\(394\) | 9781.52 | 1.25073 | ||||||||
\(395\) | 1004.29 | + | 6714.74i | 0.127928 | + | 0.855329i | ||||
\(396\) | −1269.12 | −0.161049 | ||||||||
\(397\) | 2197.33i | 0.277786i | 0.990307 | + | 0.138893i | \(0.0443544\pi\) | ||||
−0.990307 | + | 0.138893i | \(0.955646\pi\) | |||||||
\(398\) | − | 5476.78i | − | 0.689764i | ||||||
\(399\) | 871.204 | 0.109310 | ||||||||
\(400\) | −1912.48 | + | 585.172i | −0.239060 | + | 0.0731465i | ||||
\(401\) | −1315.27 | −0.163794 | −0.0818970 | − | 0.996641i | \(-0.526098\pi\) | ||||
−0.0818970 | + | 0.996641i | \(0.526098\pi\) | |||||||
\(402\) | 4239.41i | 0.525976i | ||||||||
\(403\) | 965.474i | 0.119339i | ||||||||
\(404\) | −5136.95 | −0.632605 | ||||||||
\(405\) | 133.958 | + | 895.645i | 0.0164356 | + | 0.109889i | ||||
\(406\) | 1463.66 | 0.178917 | ||||||||
\(407\) | − | 2904.67i | − | 0.353757i | ||||||
\(408\) | 1130.75i | 0.137207i | ||||||||
\(409\) | 4484.14 | 0.542118 | 0.271059 | − | 0.962563i | \(-0.412626\pi\) | ||||
0.271059 | + | 0.962563i | \(0.412626\pi\) | |||||||
\(410\) | −554.453 | + | 82.9270i | −0.0667865 | + | 0.00998895i | ||||
\(411\) | −6583.09 | −0.790073 | ||||||||
\(412\) | 7903.03i | 0.945035i | ||||||||
\(413\) | 106.381i | 0.0126747i | ||||||||
\(414\) | −1028.70 | −0.122121 | ||||||||
\(415\) | 6680.98 | − | 999.244i | 0.790256 | − | 0.118195i | ||||
\(416\) | −996.618 | −0.117460 | ||||||||
\(417\) | 2350.98i | 0.276086i | ||||||||
\(418\) | 8347.90i | 0.976816i | ||||||||
\(419\) | 3807.12 | 0.443891 | 0.221945 | − | 0.975059i | \(-0.428759\pi\) | ||||
0.221945 | + | 0.975059i | \(0.428759\pi\) | |||||||
\(420\) | −48.6758 | − | 325.448i | −0.00565509 | − | 0.0378101i | ||||
\(421\) | 3033.45 | 0.351167 | 0.175584 | − | 0.984465i | \(-0.443819\pi\) | ||||
0.175584 | + | 0.984465i | \(0.443819\pi\) | |||||||
\(422\) | − | 11112.1i | − | 1.28182i | ||||||
\(423\) | 3102.32i | 0.356596i | ||||||||
\(424\) | 3377.35 | 0.386837 | ||||||||
\(425\) | 1723.13 | + | 5631.58i | 0.196668 | + | 0.642758i | ||||
\(426\) | 6662.19 | 0.757709 | ||||||||
\(427\) | − | 235.969i | − | 0.0267432i | ||||||
\(428\) | 6475.57i | 0.731328i | ||||||||
\(429\) | −3293.81 | −0.370691 | ||||||||
\(430\) | −875.767 | − | 5855.41i | −0.0982169 | − | 0.656681i | ||||
\(431\) | 5569.05 | 0.622393 | 0.311197 | − | 0.950346i | \(-0.399270\pi\) | ||||
0.311197 | + | 0.950346i | \(0.399270\pi\) | |||||||
\(432\) | − | 432.000i | − | 0.0481125i | ||||||
\(433\) | 11093.0i | 1.23116i | 0.788073 | + | 0.615582i | \(0.211079\pi\) | ||||
−0.788073 | + | 0.615582i | \(0.788921\pi\) | |||||||
\(434\) | 152.069 | 0.0168193 | ||||||||
\(435\) | 9897.69 | − | 1480.35i | 1.09094 | − | 0.163167i | ||||
\(436\) | −8156.56 | −0.895936 | ||||||||
\(437\) | 6766.52i | 0.740702i | ||||||||
\(438\) | 566.224i | 0.0617699i | ||||||||
\(439\) | −2915.40 | −0.316958 | −0.158479 | − | 0.987362i | \(-0.550659\pi\) | ||||
−0.158479 | + | 0.987362i | \(0.550659\pi\) | |||||||
\(440\) | 3118.46 | − | 466.413i | 0.337878 | − | 0.0505349i | ||||
\(441\) | −3032.86 | −0.327487 | ||||||||
\(442\) | 2934.69i | 0.315812i | ||||||||
\(443\) | 1390.52i | 0.149132i | 0.997216 | + | 0.0745661i | \(0.0237572\pi\) | ||||
−0.997216 | + | 0.0745661i | \(0.976243\pi\) | |||||||
\(444\) | 988.733 | 0.105683 | ||||||||
\(445\) | 647.867 | + | 4331.66i | 0.0690153 | + | 0.461439i | ||||
\(446\) | 13011.8 | 1.38145 | ||||||||
\(447\) | − | 768.195i | − | 0.0812850i | ||||||
\(448\) | 156.975i | 0.0165544i | ||||||||
\(449\) | 11386.2 | 1.19677 | 0.598383 | − | 0.801210i | \(-0.295810\pi\) | ||||
0.598383 | + | 0.801210i | \(0.295810\pi\) | |||||||
\(450\) | −658.318 | − | 2151.54i | −0.0689631 | − | 0.225388i | ||||
\(451\) | 883.857 | 0.0922820 | ||||||||
\(452\) | 3583.86i | 0.372944i | ||||||||
\(453\) | − | 10661.5i | − | 1.10579i | ||||||
\(454\) | −3443.04 | −0.355925 | ||||||||
\(455\) | −126.331 | − | 844.655i | −0.0130165 | − | 0.0870287i | ||||
\(456\) | −2841.58 | −0.291818 | ||||||||
\(457\) | 18212.5i | 1.86421i | 0.362191 | + | 0.932104i | \(0.382029\pi\) | ||||
−0.362191 | + | 0.932104i | \(0.617971\pi\) | |||||||
\(458\) | 4149.92i | 0.423390i | ||||||||
\(459\) | −1272.09 | −0.129360 | ||||||||
\(460\) | 2527.71 | − | 378.059i | 0.256207 | − | 0.0383197i | ||||
\(461\) | 8974.30 | 0.906670 | 0.453335 | − | 0.891340i | \(-0.350234\pi\) | ||||
0.453335 | + | 0.891340i | \(0.350234\pi\) | |||||||
\(462\) | 518.800i | 0.0522440i | ||||||||
\(463\) | − | 10970.1i | − | 1.10113i | −0.834792 | − | 0.550566i | \(-0.814412\pi\) | ||
0.834792 | − | 0.550566i | \(-0.185588\pi\) | |||||||
\(464\) | −4773.99 | −0.477644 | ||||||||
\(465\) | 1028.33 | − | 153.803i | 0.102554 | − | 0.0153386i | ||||
\(466\) | −8470.02 | −0.841988 | ||||||||
\(467\) | − | 4721.07i | − | 0.467805i | −0.972260 | − | 0.233903i | \(-0.924850\pi\) | ||
0.972260 | − | 0.233903i | \(-0.0751497\pi\) | |||||||
\(468\) | − | 1121.20i | − | 0.110742i | ||||||
\(469\) | 1733.02 | 0.170626 | ||||||||
\(470\) | −1140.14 | − | 7622.99i | −0.111895 | − | 0.748133i | ||||
\(471\) | 1036.20 | 0.101371 | ||||||||
\(472\) | − | 346.979i | − | 0.0338369i | ||||||
\(473\) | 9334.15i | 0.907368i | ||||||||
\(474\) | 3643.59 | 0.353071 | ||||||||
\(475\) | −14152.2 | + | 4330.24i | −1.36705 | + | 0.418284i | ||||
\(476\) | 462.236 | 0.0445096 | ||||||||
\(477\) | 3799.52i | 0.364713i | ||||||||
\(478\) | 12213.2i | 1.16866i | ||||||||
\(479\) | −18909.3 | −1.80373 | −0.901865 | − | 0.432018i | \(-0.857802\pi\) | ||||
−0.901865 | + | 0.432018i | \(0.857802\pi\) | |||||||
\(480\) | 158.765 | + | 1061.51i | 0.0150970 | + | 0.100939i | ||||
\(481\) | 2566.12 | 0.243253 | ||||||||
\(482\) | 6017.47i | 0.568648i | ||||||||
\(483\) | 420.521i | 0.0396157i | ||||||||
\(484\) | 352.848 | 0.0331375 | ||||||||
\(485\) | 11597.5 | − | 1734.59i | 1.08581 | − | 0.162399i | ||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | − | 5928.26i | − | 0.551612i | −0.961213 | − | 0.275806i | \(-0.911055\pi\) | ||
0.961213 | − | 0.275806i | \(-0.0889448\pi\) | |||||||
\(488\) | 769.654i | 0.0713947i | ||||||||
\(489\) | 4232.50 | 0.391412 | ||||||||
\(490\) | 7452.30 | − | 1114.61i | 0.687063 | − | 0.102761i | ||||
\(491\) | −16523.9 | −1.51876 | −0.759382 | − | 0.650645i | \(-0.774498\pi\) | ||||
−0.759382 | + | 0.650645i | \(0.774498\pi\) | |||||||
\(492\) | 300.860i | 0.0275687i | ||||||||
\(493\) | 14057.7i | 1.28424i | ||||||||
\(494\) | −7374.92 | −0.671687 | ||||||||
\(495\) | 524.715 | + | 3508.26i | 0.0476448 | + | 0.318555i | ||||
\(496\) | −496.000 | −0.0449013 | ||||||||
\(497\) | − | 2723.42i | − | 0.245799i | ||||||
\(498\) | − | 3625.27i | − | 0.326209i | ||||||
\(499\) | 874.688 | 0.0784698 | 0.0392349 | − | 0.999230i | \(-0.487508\pi\) | ||||
0.0392349 | + | 0.999230i | \(0.487508\pi\) | |||||||
\(500\) | 2408.32 | + | 5044.80i | 0.215407 | + | 0.451220i | ||||
\(501\) | 5429.19 | 0.484148 | ||||||||
\(502\) | 8821.54i | 0.784312i | ||||||||
\(503\) | 15289.9i | 1.35536i | 0.735359 | + | 0.677678i | \(0.237014\pi\) | ||||
−0.735359 | + | 0.677678i | \(0.762986\pi\) | |||||||
\(504\) | −176.597 | −0.0156076 | ||||||||
\(505\) | 2123.87 | + | 14200.2i | 0.187150 | + | 1.25129i | ||||
\(506\) | −4029.45 | −0.354013 | ||||||||
\(507\) | 3681.10i | 0.322452i | ||||||||
\(508\) | − | 3683.56i | − | 0.321716i | ||||||
\(509\) | −17458.2 | −1.52027 | −0.760137 | − | 0.649763i | \(-0.774868\pi\) | ||||
−0.760137 | + | 0.649763i | \(0.774868\pi\) | |||||||
\(510\) | 3125.76 | − | 467.506i | 0.271394 | − | 0.0405912i | ||||
\(511\) | 231.466 | 0.0200380 | ||||||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | − | 3196.78i | − | 0.275129i | ||||||
\(514\) | 9656.10 | 0.828623 | ||||||||
\(515\) | 21846.6 | − | 3267.50i | 1.86928 | − | 0.279579i | ||||
\(516\) | −3177.30 | −0.271071 | ||||||||
\(517\) | 12151.9i | 1.03373i | ||||||||
\(518\) | − | 404.182i | − | 0.0342833i | ||||||
\(519\) | 11749.9 | 0.993762 | ||||||||
\(520\) | 412.051 | + | 2754.99i | 0.0347493 | + | 0.232335i | ||||
\(521\) | −7380.17 | −0.620597 | −0.310298 | − | 0.950639i | \(-0.600429\pi\) | ||||
−0.310298 | + | 0.950639i | \(0.600429\pi\) | |||||||
\(522\) | − | 5370.74i | − | 0.450327i | ||||||
\(523\) | − | 7990.31i | − | 0.668053i | −0.942564 | − | 0.334027i | \(-0.891592\pi\) | ||
0.942564 | − | 0.334027i | \(-0.108408\pi\) | |||||||
\(524\) | 10449.3 | 0.871141 | ||||||||
\(525\) | −879.524 | + | 269.113i | −0.0731154 | + | 0.0223715i | ||||
\(526\) | 9706.95 | 0.804645 | ||||||||
\(527\) | 1460.55i | 0.120726i | ||||||||
\(528\) | − | 1692.15i | − | 0.139473i | ||||||
\(529\) | 8900.87 | 0.731558 | ||||||||
\(530\) | −1396.36 | − | 9336.14i | −0.114442 | − | 0.765162i | ||||
\(531\) | 390.351 | 0.0319017 | ||||||||
\(532\) | 1161.61i | 0.0946654i | ||||||||
\(533\) | 780.840i | 0.0634558i | ||||||||
\(534\) | 2350.47 | 0.190477 | ||||||||
\(535\) | 17900.6 | − | 2677.32i | 1.44657 | − | 0.216356i | ||||
\(536\) | −5652.54 | −0.455509 | ||||||||
\(537\) | − | 795.073i | − | 0.0638919i | ||||||
\(538\) | − | 2249.25i | − | 0.180246i | ||||||
\(539\) | −11879.8 | −0.949347 | ||||||||
\(540\) | −1194.19 | + | 178.610i | −0.0951665 | + | 0.0142336i | ||||
\(541\) | 5396.99 | 0.428900 | 0.214450 | − | 0.976735i | \(-0.431204\pi\) | ||||
0.214450 | + | 0.976735i | \(0.431204\pi\) | |||||||
\(542\) | 4849.37i | 0.384315i | ||||||||
\(543\) | 7606.91i | 0.601185i | ||||||||
\(544\) | −1507.66 | −0.118824 | ||||||||
\(545\) | 3372.32 | + | 22547.5i | 0.265054 | + | 1.77216i | ||||
\(546\) | −458.332 | −0.0359245 | ||||||||
\(547\) | 9629.59i | 0.752708i | 0.926476 | + | 0.376354i | \(0.122822\pi\) | ||||
−0.926476 | + | 0.376354i | \(0.877178\pi\) | |||||||
\(548\) | − | 8777.45i | − | 0.684223i | ||||||
\(549\) | −865.861 | −0.0673116 | ||||||||
\(550\) | −2578.65 | − | 8427.62i | −0.199916 | − | 0.653373i | ||||
\(551\) | −35327.3 | −2.73138 | ||||||||
\(552\) | − | 1371.60i | − | 0.105760i | ||||||
\(553\) | − | 1489.46i | − | 0.114536i | ||||||
\(554\) | −11337.7 | −0.869481 | ||||||||
\(555\) | −408.791 | − | 2733.19i | −0.0312652 | − | 0.209041i | ||||
\(556\) | −3134.64 | −0.239098 | ||||||||
\(557\) | − | 22557.4i | − | 1.71596i | −0.513684 | − | 0.857980i | \(-0.671719\pi\) | ||
0.513684 | − | 0.857980i | \(-0.328281\pi\) | |||||||
\(558\) | − | 558.000i | − | 0.0423334i | ||||||
\(559\) | −8246.22 | −0.623932 | ||||||||
\(560\) | 433.931 | − | 64.9011i | 0.0327445 | − | 0.00489745i | ||||
\(561\) | −4982.80 | −0.374998 | ||||||||
\(562\) | 6422.49i | 0.482058i | ||||||||
\(563\) | − | 19572.7i | − | 1.46517i | −0.680677 | − | 0.732584i | \(-0.738314\pi\) | ||
0.680677 | − | 0.732584i | \(-0.261686\pi\) | |||||||
\(564\) | −4136.43 | −0.308821 | ||||||||
\(565\) | 9907.00 | − | 1481.75i | 0.737683 | − | 0.110332i | ||||
\(566\) | 2060.74 | 0.153038 | ||||||||
\(567\) | − | 198.671i | − | 0.0147150i | ||||||
\(568\) | 8882.92i | 0.656195i | ||||||||
\(569\) | 20027.6 | 1.47557 | 0.737784 | − | 0.675036i | \(-0.235872\pi\) | ||||
0.737784 | + | 0.675036i | \(0.235872\pi\) | |||||||
\(570\) | 1174.85 | + | 7855.09i | 0.0863316 | + | 0.577216i | ||||
\(571\) | 2789.72 | 0.204459 | 0.102230 | − | 0.994761i | \(-0.467402\pi\) | ||||
0.102230 | + | 0.994761i | \(0.467402\pi\) | |||||||
\(572\) | − | 4391.75i | − | 0.321028i | ||||||
\(573\) | − | 1902.86i | − | 0.138732i | ||||||
\(574\) | 122.988 | 0.00894325 | ||||||||
\(575\) | −2090.16 | − | 6831.14i | −0.151593 | − | 0.495441i | ||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | − | 24541.5i | − | 1.77067i | −0.464955 | − | 0.885335i | \(-0.653929\pi\) | ||
0.464955 | − | 0.885335i | \(-0.346071\pi\) | |||||||
\(578\) | − | 5386.46i | − | 0.387625i | ||||||
\(579\) | 14794.4 | 1.06189 | ||||||||
\(580\) | 1973.80 | + | 13196.9i | 0.141306 | + | 0.944780i | ||||
\(581\) | −1481.97 | −0.105822 | ||||||||
\(582\) | − | 6293.11i | − | 0.448209i | ||||||
\(583\) | 14882.8i | 1.05726i | ||||||||
\(584\) | −754.965 | −0.0534943 | ||||||||
\(585\) | −3099.36 | + | 463.557i | −0.219048 | + | 0.0327619i | ||||
\(586\) | −1798.14 | −0.126759 | ||||||||
\(587\) | 10482.0i | 0.737030i | 0.929622 | + | 0.368515i | \(0.120134\pi\) | ||||
−0.929622 | + | 0.368515i | \(0.879866\pi\) | |||||||
\(588\) | − | 4043.81i | − | 0.283612i | ||||||
\(589\) | −3670.37 | −0.256766 | ||||||||
\(590\) | −959.167 | + | 143.458i | −0.0669293 | + | 0.0100103i | ||||
\(591\) | −14672.3 | −1.02121 | ||||||||
\(592\) | 1318.31i | 0.0915240i | ||||||||
\(593\) | − | 15003.7i | − | 1.03900i | −0.854469 | − | 0.519502i | \(-0.826118\pi\) | ||
0.854469 | − | 0.519502i | \(-0.173882\pi\) | |||||||
\(594\) | 1903.67 | 0.131496 | ||||||||
\(595\) | −191.111 | − | 1277.78i | −0.0131677 | − | 0.0880399i | ||||
\(596\) | 1024.26 | 0.0703949 | ||||||||
\(597\) | 8215.17i | 0.563190i | ||||||||
\(598\) | − | 3559.80i | − | 0.243430i | ||||||
\(599\) | 11891.8 | 0.811164 | 0.405582 | − | 0.914059i | \(-0.367069\pi\) | ||||
0.405582 | + | 0.914059i | \(0.367069\pi\) | |||||||
\(600\) | 2868.72 | − | 877.757i | 0.195192 | − | 0.0597238i | ||||
\(601\) | −20918.4 | −1.41976 | −0.709882 | − | 0.704321i | \(-0.751252\pi\) | ||||
−0.709882 | + | 0.704321i | \(0.751252\pi\) | |||||||
\(602\) | 1298.84i | 0.0879349i | ||||||||
\(603\) | − | 6359.11i | − | 0.429458i | ||||||
\(604\) | 14215.3 | 0.957638 | ||||||||
\(605\) | −145.885 | − | 975.390i | −0.00980340 | − | 0.0655459i | ||||
\(606\) | 7705.42 | 0.516520 | ||||||||
\(607\) | − | 5661.21i | − | 0.378553i | −0.981924 | − | 0.189276i | \(-0.939386\pi\) | ||
0.981924 | − | 0.189276i | \(-0.0606142\pi\) | |||||||
\(608\) | − | 3788.77i | − | 0.252722i | ||||||
\(609\) | −2195.50 | −0.146085 | ||||||||
\(610\) | 2127.58 | − | 318.213i | 0.141219 | − | 0.0211214i | ||||
\(611\) | −10735.5 | −0.710823 | ||||||||
\(612\) | − | 1696.12i | − | 0.112029i | ||||||
\(613\) | − | 7829.80i | − | 0.515893i | −0.966159 | − | 0.257947i | \(-0.916954\pi\) | ||
0.966159 | − | 0.257947i | \(-0.0830459\pi\) | |||||||
\(614\) | −14539.6 | −0.955649 | ||||||||
\(615\) | 831.679 | − | 124.390i | 0.0545309 | − | 0.00815595i | ||||
\(616\) | −691.733 | −0.0452447 | ||||||||
\(617\) | 11841.8i | 0.772662i | 0.922360 | + | 0.386331i | \(0.126258\pi\) | ||||
−0.922360 | + | 0.386331i | \(0.873742\pi\) | |||||||
\(618\) | − | 11854.5i | − | 0.771618i | ||||||
\(619\) | 21332.4 | 1.38517 | 0.692585 | − | 0.721337i | \(-0.256472\pi\) | ||||
0.692585 | + | 0.721337i | \(0.256472\pi\) | |||||||
\(620\) | 205.071 | + | 1371.11i | 0.0132836 | + | 0.0888148i | ||||
\(621\) | 1543.05 | 0.0997110 | ||||||||
\(622\) | 6947.40i | 0.447854i | ||||||||
\(623\) | − | 960.844i | − | 0.0617904i | ||||||
\(624\) | 1494.93 | 0.0959054 | ||||||||
\(625\) | 12949.8 | − | 8743.19i | 0.828787 | − | 0.559564i | ||||
\(626\) | −6935.84 | −0.442830 | ||||||||
\(627\) | − | 12521.9i | − | 0.797567i | ||||||
\(628\) | 1381.60i | 0.0877896i | ||||||||
\(629\) | 3881.97 | 0.246080 | ||||||||
\(630\) | 73.0137 | + | 488.172i | 0.00461736 | + | 0.0308718i | ||||
\(631\) | −19975.5 | −1.26024 | −0.630121 | − | 0.776497i | \(-0.716995\pi\) | ||||
−0.630121 | + | 0.776497i | \(0.716995\pi\) | |||||||
\(632\) | 4858.12i | 0.305768i | ||||||||
\(633\) | 16668.1i | 1.04660i | ||||||||
\(634\) | −3392.54 | −0.212516 | ||||||||
\(635\) | −10182.6 | + | 1522.97i | −0.636353 | + | 0.0951765i | ||||
\(636\) | −5066.03 | −0.315851 | ||||||||
\(637\) | − | 10495.1i | − | 0.652798i | ||||||
\(638\) | − | 21037.3i | − | 1.30545i | ||||||
\(639\) | −9993.28 | −0.618667 | ||||||||
\(640\) | −1415.34 | + | 211.686i | −0.0874160 | + | 0.0130744i | ||||
\(641\) | −642.218 | −0.0395727 | −0.0197863 | − | 0.999804i | \(-0.506299\pi\) | ||||
−0.0197863 | + | 0.999804i | \(0.506299\pi\) | |||||||
\(642\) | − | 9713.35i | − | 0.597127i | ||||||
\(643\) | − | 14350.3i | − | 0.880125i | −0.897967 | − | 0.440063i | \(-0.854956\pi\) | ||
0.897967 | − | 0.440063i | \(-0.145044\pi\) | |||||||
\(644\) | −560.695 | −0.0343082 | ||||||||
\(645\) | 1313.65 | + | 8783.12i | 0.0801937 | + | 0.536178i | ||||
\(646\) | −11156.6 | −0.679491 | ||||||||
\(647\) | 9666.18i | 0.587352i | 0.955905 | + | 0.293676i | \(0.0948787\pi\) | ||||
−0.955905 | + | 0.293676i | \(0.905121\pi\) | |||||||
\(648\) | 648.000i | 0.0392837i | ||||||||
\(649\) | 1529.01 | 0.0924793 | ||||||||
\(650\) | 7445.35 | − | 2278.10i | 0.449278 | − | 0.137468i | ||||
\(651\) | −228.104 | −0.0137329 | ||||||||
\(652\) | 5643.33i | 0.338972i | ||||||||
\(653\) | 3146.94i | 0.188590i | 0.995544 | + | 0.0942950i | \(0.0300597\pi\) | ||||
−0.995544 | + | 0.0942950i | \(0.969940\pi\) | |||||||
\(654\) | 12234.8 | 0.731529 | ||||||||
\(655\) | −4320.24 | − | 28885.3i | −0.257718 | − | 1.72312i | ||||
\(656\) | −401.147 | −0.0238752 | ||||||||
\(657\) | − | 849.336i | − | 0.0504349i | ||||||
\(658\) | 1690.92i | 0.100181i | ||||||||
\(659\) | −33398.3 | −1.97422 | −0.987111 | − | 0.160040i | \(-0.948838\pi\) | ||||
−0.987111 | + | 0.160040i | \(0.948838\pi\) | |||||||
\(660\) | −4677.68 | + | 699.620i | −0.275877 | + | 0.0412616i | ||||
\(661\) | −28820.2 | −1.69588 | −0.847939 | − | 0.530094i | \(-0.822157\pi\) | ||||
−0.847939 | + | 0.530094i | \(0.822157\pi\) | |||||||
\(662\) | − | 11973.2i | − | 0.702951i | ||||||
\(663\) | − | 4402.04i | − | 0.257860i | ||||||
\(664\) | 4833.69 | 0.282506 | ||||||||
\(665\) | 3211.07 | − | 480.265i | 0.187248 | − | 0.0280058i | ||||
\(666\) | −1483.10 | −0.0862897 | ||||||||
\(667\) | − | 17052.1i | − | 0.989896i | ||||||
\(668\) | 7238.92i | 0.419285i | ||||||||
\(669\) | −19517.7 | −1.12795 | ||||||||
\(670\) | 2337.04 | + | 15625.5i | 0.134758 | + | 0.900995i | ||||
\(671\) | −3391.60 | −0.195128 | ||||||||
\(672\) | − | 235.462i | − | 0.0135166i | ||||||
\(673\) | 7808.13i | 0.447223i | 0.974678 | + | 0.223612i | \(0.0717847\pi\) | ||||
−0.974678 | + | 0.223612i | \(0.928215\pi\) | |||||||
\(674\) | 5524.10 | 0.315698 | ||||||||
\(675\) | 987.477 | + | 3227.31i | 0.0563082 | + | 0.184028i | ||||
\(676\) | −4908.13 | −0.279252 | ||||||||
\(677\) | − | 21793.5i | − | 1.23721i | −0.785702 | − | 0.618606i | \(-0.787698\pi\) | ||
0.785702 | − | 0.618606i | \(-0.212302\pi\) | |||||||
\(678\) | − | 5375.79i | − | 0.304508i | ||||||
\(679\) | −2572.55 | −0.145398 | ||||||||
\(680\) | 623.342 | + | 4167.69i | 0.0351530 | + | 0.235035i | ||||
\(681\) | 5164.57 | 0.290612 | ||||||||
\(682\) | − | 2185.70i | − | 0.122720i | ||||||
\(683\) | − | 4067.07i | − | 0.227851i | −0.993489 | − | 0.113925i | \(-0.963658\pi\) | ||
0.993489 | − | 0.113925i | \(-0.0363425\pi\) | |||||||
\(684\) | 4262.37 | 0.238269 | ||||||||
\(685\) | −24263.8 | + | 3629.03i | −1.35339 | + | 0.202421i | ||||
\(686\) | −3335.64 | −0.185649 | ||||||||
\(687\) | − | 6224.87i | − | 0.345697i | ||||||
\(688\) | − | 4236.39i | − | 0.234754i | ||||||
\(689\) | −13148.2 | −0.727003 | ||||||||
\(690\) | −3791.57 | + | 567.088i | −0.209192 | + | 0.0312879i | ||||
\(691\) | −12621.9 | −0.694878 | −0.347439 | − | 0.937703i | \(-0.612949\pi\) | ||||
−0.347439 | + | 0.937703i | \(0.612949\pi\) | |||||||
\(692\) | 15666.5i | 0.860623i | ||||||||
\(693\) | − | 778.199i | − | 0.0426571i | ||||||
\(694\) | 697.469 | 0.0381492 | ||||||||
\(695\) | 1296.02 | + | 8665.20i | 0.0707348 | + | 0.472935i | ||||
\(696\) | 7160.98 | 0.389995 | ||||||||
\(697\) | 1181.24i | 0.0641931i | ||||||||
\(698\) | 6494.23i | 0.352164i | ||||||||
\(699\) | 12705.0 | 0.687480 | ||||||||
\(700\) | −358.817 | − | 1172.70i | −0.0193743 | − | 0.0633198i | ||||
\(701\) | 5058.76 | 0.272563 | 0.136282 | − | 0.990670i | \(-0.456485\pi\) | ||||
0.136282 | + | 0.990670i | \(0.456485\pi\) | |||||||
\(702\) | 1681.79i | 0.0904205i | ||||||||
\(703\) | 9755.43i | 0.523376i | ||||||||
\(704\) | 2256.20 | 0.120787 | ||||||||
\(705\) | 1710.20 | + | 11434.5i | 0.0913617 | + | 0.610848i | ||||
\(706\) | 16069.9 | 0.856658 | ||||||||
\(707\) | − | 3149.89i | − | 0.167558i | ||||||
\(708\) | 520.468i | 0.0276277i | ||||||||
\(709\) | −13023.0 | −0.689829 | −0.344915 | − | 0.938634i | \(-0.612092\pi\) | ||||
−0.344915 | + | 0.938634i | \(0.612092\pi\) | |||||||
\(710\) | 24555.4 | − | 3672.64i | 1.29795 | − | 0.194129i | ||||
\(711\) | −5465.38 | −0.288281 | ||||||||
\(712\) | 3133.96i | 0.164958i | ||||||||
\(713\) | − | 1771.65i | − | 0.0930560i | ||||||
\(714\) | −693.354 | −0.0363419 | ||||||||
\(715\) | −12140.3 | + | 1815.76i | −0.634993 | + | 0.0949731i | ||||
\(716\) | 1060.10 | 0.0553320 | ||||||||
\(717\) | − | 18319.8i | − | 0.954207i | ||||||
\(718\) | 11642.8i | 0.605161i | ||||||||
\(719\) | 17673.7 | 0.916717 | 0.458358 | − | 0.888767i | \(-0.348438\pi\) | ||||
0.458358 | + | 0.888767i | \(0.348438\pi\) | |||||||
\(720\) | −238.147 | − | 1592.26i | −0.0123267 | − | 0.0824166i | ||||
\(721\) | −4846.00 | −0.250311 | ||||||||
\(722\) | − | 14318.7i | − | 0.738072i | ||||||
\(723\) | − | 9026.21i | − | 0.464299i | ||||||
\(724\) | −10142.5 | −0.520642 | ||||||||
\(725\) | 35664.7 | − | 10912.5i | 1.82697 | − | 0.559008i | ||||
\(726\) | −529.272 | −0.0270566 | ||||||||
\(727\) | − | 26012.9i | − | 1.32705i | −0.748155 | − | 0.663524i | \(-0.769060\pi\) | ||
0.748155 | − | 0.663524i | \(-0.230940\pi\) | |||||||
\(728\) | − | 611.109i | − | 0.0311115i | ||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 312.140 | + | 2086.98i | 0.0158258 | + | 0.105812i | ||||
\(731\) | −12474.7 | −0.631182 | ||||||||
\(732\) | − | 1154.48i | − | 0.0582935i | ||||||
\(733\) | 15642.6i | 0.788229i | 0.919061 | + | 0.394115i | \(0.128949\pi\) | ||||
−0.919061 | + | 0.394115i | \(0.871051\pi\) | |||||||
\(734\) | −10278.9 | −0.516893 | ||||||||
\(735\) | −11178.5 | + | 1671.91i | −0.560984 | + | 0.0839039i | ||||
\(736\) | 1828.80 | 0.0915904 | ||||||||
\(737\) | − | 24908.8i | − | 1.24495i | ||||||
\(738\) | − | 451.290i | − | 0.0225098i | ||||||
\(739\) | −17297.5 | −0.861028 | −0.430514 | − | 0.902584i | \(-0.641668\pi\) | ||||
−0.430514 | + | 0.902584i | \(0.641668\pi\) | |||||||
\(740\) | 3644.25 | − | 545.055i | 0.181034 | − | 0.0270765i | ||||
\(741\) | 11062.4 | 0.548430 | ||||||||
\(742\) | 2070.93i | 0.102461i | ||||||||
\(743\) | 20564.7i | 1.01540i | 0.861533 | + | 0.507702i | \(0.169505\pi\) | ||||
−0.861533 | + | 0.507702i | \(0.830495\pi\) | |||||||
\(744\) | 744.000 | 0.0366618 | ||||||||
\(745\) | −423.480 | − | 2831.40i | −0.0208256 | − | 0.139241i | ||||
\(746\) | −1791.67 | −0.0879328 | ||||||||
\(747\) | 5437.91i | 0.266349i | ||||||||
\(748\) | − | 6643.74i | − | 0.324758i | ||||||
\(749\) | −3970.70 | −0.193707 | ||||||||
\(750\) | −3612.49 | − | 7567.19i | −0.175879 | − | 0.368420i | ||||
\(751\) | −27970.2 | −1.35905 | −0.679526 | − | 0.733652i | \(-0.737814\pi\) | ||||
−0.679526 | + | 0.733652i | \(0.737814\pi\) | |||||||
\(752\) | − | 5515.24i | − | 0.267447i | ||||||
\(753\) | − | 13232.3i | − | 0.640388i | ||||||
\(754\) | 18585.3 | 0.897663 | ||||||||
\(755\) | −5877.32 | − | 39296.0i | −0.283308 | − | 1.89421i | ||||
\(756\) | 264.895 | 0.0127436 | ||||||||
\(757\) | − | 16261.9i | − | 0.780780i | −0.920650 | − | 0.390390i | \(-0.872340\pi\) | ||
0.920650 | − | 0.390390i | \(-0.127660\pi\) | |||||||
\(758\) | 28532.0i | 1.36719i | ||||||||
\(759\) | 6044.17 | 0.289051 | ||||||||
\(760\) | −10473.4 | + | 1566.47i | −0.499884 | + | 0.0747654i | ||||
\(761\) | −23922.9 | −1.13956 | −0.569779 | − | 0.821798i | \(-0.692971\pi\) | ||||
−0.569779 | + | 0.821798i | \(0.692971\pi\) | |||||||
\(762\) | 5525.34i | 0.262680i | ||||||||
\(763\) | − | 5001.46i | − | 0.237307i | ||||||
\(764\) | 2537.15 | 0.120145 | ||||||||
\(765\) | −4688.65 | + | 701.260i | −0.221593 | + | 0.0331426i | ||||
\(766\) | −14511.7 | −0.684502 | ||||||||
\(767\) | 1350.80i | 0.0635915i | ||||||||
\(768\) | 768.000i | 0.0360844i | ||||||||
\(769\) | 31811.9 | 1.49176 | 0.745881 | − | 0.666079i | \(-0.232029\pi\) | ||||
0.745881 | + | 0.666079i | \(0.232029\pi\) | |||||||
\(770\) | 285.996 | + | 1912.18i | 0.0133852 | + | 0.0894939i | ||||
\(771\) | −14484.1 | −0.676568 | ||||||||
\(772\) | 19725.9i | 0.919626i | ||||||||
\(773\) | 22660.3i | 1.05438i | 0.849747 | + | 0.527190i | \(0.176754\pi\) | ||||
−0.849747 | + | 0.527190i | \(0.823246\pi\) | |||||||
\(774\) | 4765.94 | 0.221329 | ||||||||
\(775\) | 3705.43 | − | 1133.77i | 0.171746 | − | 0.0525500i | ||||
\(776\) | 8390.81 | 0.388161 | ||||||||
\(777\) | 606.274i | 0.0279922i | ||||||||
\(778\) | − | 8516.08i | − | 0.392437i | ||||||
\(779\) | −2968.47 | −0.136529 | ||||||||
\(780\) | −618.077 | − | 4132.48i | −0.0283727 | − | 0.189701i | ||||
\(781\) | −39143.9 | −1.79344 | ||||||||
\(782\) | − | 5385.19i | − | 0.246258i | ||||||
\(783\) | 8056.11i | 0.367691i | ||||||||
\(784\) | 5391.75 | 0.245615 | ||||||||
\(785\) | 3819.21 | − | 571.222i | 0.173648 | − | 0.0259717i | ||||
\(786\) | −15673.9 | −0.711283 | ||||||||
\(787\) | − | 27806.5i | − | 1.25946i | −0.776814 | − | 0.629730i | \(-0.783166\pi\) | ||
0.776814 | − | 0.629730i | \(-0.216834\pi\) | |||||||
\(788\) | − | 19563.0i | − | 0.884396i | ||||||
\(789\) | −14560.4 | −0.656990 | ||||||||
\(790\) | 13429.5 | − | 2008.59i | 0.604809 | − | 0.0904586i | ||||
\(791\) | −2197.56 | −0.0987817 | ||||||||
\(792\) | 2538.23i | 0.113879i | ||||||||
\(793\) | − | 2996.29i | − | 0.134176i | ||||||
\(794\) | 4394.66 | 0.196424 | ||||||||
\(795\) | 2094.55 | + | 14004.2i | 0.0934414 | + | 0.624752i | ||||
\(796\) | −10953.6 | −0.487737 | ||||||||
\(797\) | − | 5939.37i | − | 0.263969i | −0.991252 | − | 0.131985i | \(-0.957865\pi\) | ||
0.991252 | − | 0.131985i | \(-0.0421349\pi\) | |||||||
\(798\) | − | 1742.41i | − | 0.0772939i | ||||||
\(799\) | −16240.5 | −0.719082 | ||||||||
\(800\) | 1170.34 | + | 3824.96i | 0.0517224 | + | 0.169041i | ||||
\(801\) | −3525.70 | −0.155524 | ||||||||
\(802\) | 2630.54i | 0.115820i | ||||||||
\(803\) | − | 3326.87i | − | 0.146205i | ||||||
\(804\) | 8478.81 | 0.371921 | ||||||||
\(805\) | 231.819 | + | 1549.95i | 0.0101497 | + | 0.0678616i | ||||
\(806\) | 1930.95 | 0.0843855 | ||||||||
\(807\) | 3373.88i | 0.147170i | ||||||||
\(808\) | 10273.9i | 0.447320i | ||||||||
\(809\) | −10715.4 | −0.465678 | −0.232839 | − | 0.972515i | \(-0.574802\pi\) | ||||
−0.232839 | + | 0.972515i | \(0.574802\pi\) | |||||||
\(810\) | 1791.29 | − | 267.915i | 0.0777031 | − | 0.0116217i | ||||
\(811\) | −337.734 | −0.0146233 | −0.00731163 | − | 0.999973i | \(-0.502327\pi\) | ||||
−0.00731163 | + | 0.999973i | \(0.502327\pi\) | |||||||
\(812\) | − | 2927.33i | − | 0.126514i | ||||||
\(813\) | − | 7274.06i | − | 0.313791i | ||||||
\(814\) | −5809.33 | −0.250144 | ||||||||
\(815\) | 15600.1 | − | 2333.23i | 0.670487 | − | 0.100282i | ||||
\(816\) | 2261.49 | 0.0970197 | ||||||||
\(817\) | − | 31349.1i | − | 1.34243i | ||||||
\(818\) | − | 8968.27i | − | 0.383335i | ||||||
\(819\) | 687.497 | 0.0293322 | ||||||||
\(820\) | 165.854 | + | 1108.91i | 0.00706326 | + | 0.0472252i | ||||
\(821\) | 21168.8 | 0.899876 | 0.449938 | − | 0.893060i | \(-0.351446\pi\) | ||||
0.449938 | + | 0.893060i | \(0.351446\pi\) | |||||||
\(822\) | 13166.2i | 0.558666i | ||||||||
\(823\) | 9764.68i | 0.413579i | 0.978385 | + | 0.206789i | \(0.0663015\pi\) | ||||
−0.978385 | + | 0.206789i | \(0.933698\pi\) | |||||||
\(824\) | 15806.1 | 0.668240 | ||||||||
\(825\) | 3867.97 | + | 12641.4i | 0.163231 | + | 0.533477i | ||||
\(826\) | 212.761 | 0.00896237 | ||||||||
\(827\) | − | 29508.6i | − | 1.24077i | −0.784299 | − | 0.620383i | \(-0.786977\pi\) | ||
0.784299 | − | 0.620383i | \(-0.213023\pi\) | |||||||
\(828\) | 2057.40i | 0.0863523i | ||||||||
\(829\) | 45144.8 | 1.89137 | 0.945683 | − | 0.325089i | \(-0.105394\pi\) | ||||
0.945683 | + | 0.325089i | \(0.105394\pi\) | |||||||
\(830\) | −1998.49 | − | 13362.0i | −0.0835765 | − | 0.558796i | ||||
\(831\) | 17006.5 | 0.709928 | ||||||||
\(832\) | 1993.24i | 0.0830565i | ||||||||
\(833\) | − | 15876.8i | − | 0.660383i | ||||||
\(834\) | 4701.96 | 0.195223 | ||||||||
\(835\) | 20010.8 | − | 2992.93i | 0.829345 | − | 0.124041i | ||||
\(836\) | 16695.8 | 0.690713 | ||||||||
\(837\) | 837.000i | 0.0345651i | ||||||||
\(838\) | − | 7614.25i | − | 0.313878i | ||||||
\(839\) | 7063.92 | 0.290672 | 0.145336 | − | 0.989382i | \(-0.453574\pi\) | ||||
0.145336 | + | 0.989382i | \(0.453574\pi\) | |||||||
\(840\) | −650.897 | + | 97.3517i | −0.0267358 | + | 0.00399875i | ||||
\(841\) | 64638.3 | 2.65030 | ||||||||
\(842\) | − | 6066.91i | − | 0.248313i | ||||||
\(843\) | − | 9633.74i | − | 0.393598i | ||||||
\(844\) | −22224.1 | −0.906381 | ||||||||
\(845\) | 2029.26 | + | 13567.7i | 0.0826139 | + | 0.552360i | ||||
\(846\) | 6204.65 | 0.252151 | ||||||||
\(847\) | 216.360i | 0.00877712i | ||||||||
\(848\) | − | 6754.70i | − | 0.273535i | ||||||
\(849\) | −3091.11 | −0.124955 | ||||||||
\(850\) | 11263.2 | − | 3446.25i | 0.454498 | − | 0.139065i | ||||
\(851\) | −4708.85 | −0.189679 | ||||||||
\(852\) | − | 13324.4i | − | 0.535781i | ||||||
\(853\) | 2292.91i | 0.0920374i | 0.998941 | + | 0.0460187i | \(0.0146534\pi\) | ||||
−0.998941 | + | 0.0460187i | \(0.985347\pi\) | |||||||
\(854\) | −471.939 | −0.0189103 | ||||||||
\(855\) | −1762.27 | − | 11782.6i | −0.0704895 | − | 0.471295i | ||||
\(856\) | 12951.1 | 0.517127 | ||||||||
\(857\) | − | 17174.5i | − | 0.684562i | −0.939598 | − | 0.342281i | \(-0.888801\pi\) | ||
0.939598 | − | 0.342281i | \(-0.111199\pi\) | |||||||
\(858\) | 6587.62i | 0.262118i | ||||||||
\(859\) | −4819.24 | −0.191421 | −0.0957103 | − | 0.995409i | \(-0.530512\pi\) | ||||
−0.0957103 | + | 0.995409i | \(0.530512\pi\) | |||||||
\(860\) | −11710.8 | + | 1751.53i | −0.464344 | + | 0.0694498i | ||||
\(861\) | −184.482 | −0.00730213 | ||||||||
\(862\) | − | 11138.1i | − | 0.440099i | ||||||
\(863\) | 30921.9i | 1.21969i | 0.792521 | + | 0.609845i | \(0.208768\pi\) | ||||
−0.792521 | + | 0.609845i | \(0.791232\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 43307.5 | − | 6477.30i | 1.70231 | − | 0.254607i | ||||
\(866\) | 22185.9 | 0.870565 | ||||||||
\(867\) | 8079.69i | 0.316494i | ||||||||
\(868\) | − | 304.139i | − | 0.0118930i | ||||||
\(869\) | −21408.0 | −0.835693 | ||||||||
\(870\) | −2960.70 | − | 19795.4i | −0.115376 | − | 0.771409i | ||||
\(871\) | 22005.6 | 0.856062 | ||||||||
\(872\) | 16313.1i | 0.633523i | ||||||||
\(873\) | 9439.66i | 0.365961i | ||||||||
\(874\) | 13533.0 | 0.523755 | ||||||||
\(875\) | −3093.38 | + | 1476.74i | −0.119515 | + | 0.0570549i | ||||
\(876\) | 1132.45 | 0.0436779 | ||||||||
\(877\) | − | 1565.05i | − | 0.0602601i | −0.999546 | − | 0.0301301i | \(-0.990408\pi\) | ||
0.999546 | − | 0.0301301i | \(-0.00959215\pi\) | |||||||
\(878\) | 5830.81i | 0.224123i | ||||||||
\(879\) | 2697.22 | 0.103498 | ||||||||
\(880\) | −932.826 | − | 6236.91i | −0.0357336 | − | 0.238916i | ||||
\(881\) | −11050.9 | −0.422605 | −0.211302 | − | 0.977421i | \(-0.567770\pi\) | ||||
−0.211302 | + | 0.977421i | \(0.567770\pi\) | |||||||
\(882\) | 6065.71i | 0.231568i | ||||||||
\(883\) | 39459.8i | 1.50388i | 0.659231 | + | 0.751941i | \(0.270882\pi\) | ||||
−0.659231 | + | 0.751941i | \(0.729118\pi\) | |||||||
\(884\) | 5869.39 | 0.223313 | ||||||||
\(885\) | 1438.75 | − | 215.187i | 0.0546475 | − | 0.00817338i | ||||
\(886\) | 2781.04 | 0.105452 | ||||||||
\(887\) | 30714.7i | 1.16268i | 0.813660 | + | 0.581340i | \(0.197472\pi\) | ||||
−0.813660 | + | 0.581340i | \(0.802528\pi\) | |||||||
\(888\) | − | 1977.47i | − | 0.0747291i | ||||||
\(889\) | 2258.70 | 0.0852128 | ||||||||
\(890\) | 8663.32 | − | 1295.73i | 0.326287 | − | 0.0488012i | ||||
\(891\) | −2855.51 | −0.107366 | ||||||||
\(892\) | − | 26023.5i | − | 0.976831i | ||||||
\(893\) | − | 40812.5i | − | 1.52938i | ||||||
\(894\) | −1536.39 | −0.0574772 | ||||||||
\(895\) | −438.297 | − | 2930.47i | −0.0163694 | − | 0.109447i | ||||
\(896\) | 313.949 | 0.0117057 | ||||||||
\(897\) | 5339.70i | 0.198760i | ||||||||
\(898\) | − | 22772.4i | − | 0.846242i | ||||||
\(899\) | 9249.61 | 0.343150 | ||||||||
\(900\) | −4303.08 | + | 1316.64i | −0.159373 | + | 0.0487643i | ||||
\(901\) | −19890.3 | −0.735450 | ||||||||
\(902\) | − | 1767.71i | − | 0.0652533i | ||||||
\(903\) | − | 1948.26i | − | 0.0717986i | ||||||
\(904\) | 7167.72 | 0.263711 | ||||||||
\(905\) | 4193.43 | + | 28037.4i | 0.154027 | + | 1.02983i | ||||
\(906\) | −21323.0 | −0.781909 | ||||||||
\(907\) | − | 39300.1i | − | 1.43874i | −0.694627 | − | 0.719370i | \(-0.744431\pi\) | ||
0.694627 | − | 0.719370i | \(-0.255569\pi\) | |||||||
\(908\) | 6886.09i | 0.251677i | ||||||||
\(909\) | −11558.1 | −0.421737 | ||||||||
\(910\) | −1689.31 | + | 252.662i | −0.0615386 | + | 0.00920404i | ||||
\(911\) | 18582.8 | 0.675825 | 0.337912 | − | 0.941178i | \(-0.390279\pi\) | ||||
0.337912 | + | 0.941178i | \(0.390279\pi\) | |||||||
\(912\) | 5683.16i | 0.206347i | ||||||||
\(913\) | 21300.4i | 0.772114i | ||||||||
\(914\) | 36424.9 | 1.31819 | ||||||||
\(915\) | −3191.38 | + | 477.320i | −0.115305 | + | 0.0172456i | ||||
\(916\) | 8299.83 | 0.299382 | ||||||||
\(917\) | 6407.30i | 0.230739i | ||||||||
\(918\) | 2544.18i | 0.0914711i | ||||||||
\(919\) | 38456.3 | 1.38037 | 0.690183 | − | 0.723635i | \(-0.257530\pi\) | ||||
0.690183 | + | 0.723635i | \(0.257530\pi\) | |||||||
\(920\) | −756.117 | − | 5055.43i | −0.0270961 | − | 0.181166i | ||||
\(921\) | 21809.3 | 0.780284 | ||||||||
\(922\) | − | 17948.6i | − | 0.641113i | ||||||
\(923\) | − | 34581.5i | − | 1.23322i | ||||||
\(924\) | 1037.60 | 0.0369421 | ||||||||
\(925\) | −3013.43 | − | 9848.60i | −0.107115 | − | 0.350075i | ||||
\(926\) | −21940.2 | −0.778618 | ||||||||
\(927\) | 17781.8i | 0.630023i | ||||||||
\(928\) | 9547.98i | 0.337745i | ||||||||
\(929\) | 13511.1 | 0.477164 | 0.238582 | − | 0.971122i | \(-0.423317\pi\) | ||||
0.238582 | + | 0.971122i | \(0.423317\pi\) | |||||||
\(930\) | −307.606 | − | 2056.67i | −0.0108460 | − | 0.0725169i | ||||
\(931\) | 39898.6 | 1.40454 | ||||||||
\(932\) | 16940.0i | 0.595375i | ||||||||
\(933\) | − | 10421.1i | − | 0.365672i | ||||||
\(934\) | −9442.14 | −0.330788 | ||||||||
\(935\) | −18365.5 | + | 2746.85i | −0.642371 | + | 0.0960766i | ||||
\(936\) | −2242.39 | −0.0783064 | ||||||||
\(937\) | 7816.72i | 0.272531i | 0.990672 | + | 0.136265i | \(0.0435100\pi\) | ||||
−0.990672 | + | 0.136265i | \(0.956490\pi\) | |||||||
\(938\) | − | 3466.04i | − | 0.120651i | ||||||
\(939\) | 10403.8 | 0.361569 | ||||||||
\(940\) | −15246.0 | + | 2280.27i | −0.529010 | + | 0.0791216i | ||||
\(941\) | −32868.5 | −1.13866 | −0.569332 | − | 0.822108i | \(-0.692798\pi\) | ||||
−0.569332 | + | 0.822108i | \(0.692798\pi\) | |||||||
\(942\) | − | 2072.40i | − | 0.0716799i | ||||||
\(943\) | − | 1432.85i | − | 0.0494803i | ||||||
\(944\) | −693.958 | −0.0239263 | ||||||||
\(945\) | −109.521 | − | 732.259i | −0.00377006 | − | 0.0252067i | ||||
\(946\) | 18668.3 | 0.641606 | ||||||||
\(947\) | 2257.77i | 0.0774739i | 0.999249 | + | 0.0387370i | \(0.0123334\pi\) | ||||
−0.999249 | + | 0.0387370i | \(0.987667\pi\) | |||||||
\(948\) | − | 7287.18i | − | 0.249659i | ||||||
\(949\) | 2939.11 | 0.100535 | ||||||||
\(950\) | 8660.48 | + | 28304.5i | 0.295772 | + | 0.966651i | ||||
\(951\) | 5088.81 | 0.173518 | ||||||||
\(952\) | − | 924.472i | − | 0.0314730i | ||||||
\(953\) | 8811.68i | 0.299516i | 0.988723 | + | 0.149758i | \(0.0478494\pi\) | ||||
−0.988723 | + | 0.149758i | \(0.952151\pi\) | |||||||
\(954\) | 7599.04 | 0.257891 | ||||||||
\(955\) | −1048.98 | − | 7013.54i | −0.0355438 | − | 0.237647i | ||||
\(956\) | 24426.4 | 0.826368 | ||||||||
\(957\) | 31556.0i | 1.06589i | ||||||||
\(958\) | 37818.5i | 1.27543i | ||||||||
\(959\) | 5382.18 | 0.181230 | ||||||||
\(960\) | 2123.01 | − | 317.529i | 0.0713749 | − | 0.0106752i | ||||
\(961\) | 961.000 | 0.0322581 | ||||||||
\(962\) | − | 5132.23i | − | 0.172006i | ||||||
\(963\) | 14570.0i | 0.487552i | ||||||||
\(964\) | 12034.9 | 0.402095 | ||||||||
\(965\) | 54529.1 | − | 8155.67i | 1.81902 | − | 0.272062i | ||||
\(966\) | 841.042 | 0.0280125 | ||||||||
\(967\) | − | 12449.8i | − | 0.414020i | −0.978339 | − | 0.207010i | \(-0.933627\pi\) | ||
0.978339 | − | 0.207010i | \(-0.0663733\pi\) | |||||||
\(968\) | − | 705.696i | − | 0.0234317i | ||||||
\(969\) | 16734.9 | 0.554802 | ||||||||
\(970\) | −3469.18 | − | 23195.0i | −0.114834 | − | 0.767781i | ||||
\(971\) | −38799.1 | −1.28231 | −0.641154 | − | 0.767412i | \(-0.721544\pi\) | ||||
−0.641154 | + | 0.767412i | \(0.721544\pi\) | |||||||
\(972\) | − | 972.000i | − | 0.0320750i | ||||||
\(973\) | − | 1922.11i | − | 0.0633298i | ||||||
\(974\) | −11856.5 | −0.390049 | ||||||||
\(975\) | −11168.0 | + | 3417.14i | −0.366834 | + | 0.112242i | ||||
\(976\) | 1539.31 | 0.0504837 | ||||||||
\(977\) | 51815.4i | 1.69675i | 0.529399 | + | 0.848373i | \(0.322417\pi\) | ||||
−0.529399 | + | 0.848373i | \(0.677583\pi\) | |||||||
\(978\) | − | 8465.00i | − | 0.276770i | ||||||
\(979\) | −13810.3 | −0.450845 | ||||||||
\(980\) | −2229.21 | − | 14904.6i | −0.0726629 | − | 0.485827i | ||||
\(981\) | −18352.3 | −0.597291 | ||||||||
\(982\) | 33047.8i | 1.07393i | ||||||||
\(983\) | − | 25874.4i | − | 0.839537i | −0.907631 | − | 0.419768i | \(-0.862111\pi\) | ||
0.907631 | − | 0.419768i | \(-0.137889\pi\) | |||||||
\(984\) | 601.720 | 0.0194940 | ||||||||
\(985\) | −54078.8 | + | 8088.32i | −1.74933 | + | 0.261640i | ||||
\(986\) | 28115.5 | 0.908093 | ||||||||
\(987\) | − | 2536.39i | − | 0.0817975i | ||||||
\(988\) | 14749.8i | 0.474954i | ||||||||
\(989\) | 15131.9 | 0.486518 | ||||||||
\(990\) | 7016.52 | − | 1049.43i | 0.225252 | − | 0.0336900i | ||||
\(991\) | −56846.5 | −1.82219 | −0.911094 | − | 0.412199i | \(-0.864761\pi\) | ||||
−0.911094 | + | 0.412199i | \(0.864761\pi\) | |||||||
\(992\) | 992.000i | 0.0317500i | ||||||||
\(993\) | 17959.9i | 0.573957i | ||||||||
\(994\) | −5446.85 | −0.173806 | ||||||||
\(995\) | 4528.74 | + | 30279.3i | 0.144292 | + | 0.964743i | ||||
\(996\) | −7250.54 | −0.230665 | ||||||||
\(997\) | − | 24864.9i | − | 0.789848i | −0.918714 | − | 0.394924i | \(-0.870771\pi\) | ||
0.918714 | − | 0.394924i | \(-0.129229\pi\) | |||||||
\(998\) | − | 1749.38i | − | 0.0554865i | ||||||
\(999\) | 2224.65 | 0.0704552 |
(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 | 930.4.d.c.559.5 | ✓ | 20 | |
5.4 | even | 2 | inner | 930.4.d.c.559.15 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.4.d.c.559.5 | ✓ | 20 | 1.1 | even | 1 | trivial | |
930.4.d.c.559.15 | yes | 20 | 5.4 | even | 2 | inner |