Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(604,1089)]
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([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.604");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.c (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: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 11^{4} \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 604.13 | ||
Root | \(-1.95510 + 0.109518i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.604 |
Dual form | 1089.3.c.m.604.4 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.47556i | 1.23778i | 0.785478 | + | 0.618890i | \(0.212417\pi\) | ||||
−0.785478 | + | 0.618890i | \(0.787583\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.12839 | −0.532098 | ||||||||
\(5\) | 2.55350 | 0.510701 | 0.255350 | − | 0.966849i | \(-0.417809\pi\) | ||||
0.255350 | + | 0.966849i | \(0.417809\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.170400i | 0.0243428i | 0.999926 | + | 0.0121714i | \(0.00387438\pi\) | ||||
−0.999926 | + | 0.0121714i | \(0.996126\pi\) | |||||||
\(8\) | 4.63328i | 0.579160i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.32135i | 0.632135i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 19.2744i | − 1.48265i | −0.671149 | − | 0.741323i | \(-0.734199\pi\) | ||||
0.671149 | − | 0.741323i | \(-0.265801\pi\) | |||||||
\(14\) | −0.421835 | −0.0301311 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19.9835 | −1.24897 | ||||||||
\(17\) | 20.2947i | 1.19381i | 0.802313 | + | 0.596904i | \(0.203603\pi\) | ||||
−0.802313 | + | 0.596904i | \(0.796397\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.5860i | 0.767683i | 0.923399 | + | 0.383842i | \(0.125399\pi\) | ||||
−0.923399 | + | 0.383842i | \(0.874601\pi\) | |||||||
\(20\) | −5.43486 | −0.271743 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.74583 | −0.336775 | −0.168388 | − | 0.985721i | \(-0.553856\pi\) | ||||
−0.168388 | + | 0.985721i | \(0.553856\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −18.4796 | −0.739185 | ||||||||
\(26\) | 47.7149 | 1.83519 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 0.362678i | − 0.0129528i | ||||||||
\(29\) | 38.2630i | 1.31941i | 0.751523 | + | 0.659707i | \(0.229320\pi\) | ||||
−0.751523 | + | 0.659707i | \(0.770680\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −42.3732 | −1.36688 | −0.683439 | − | 0.730008i | \(-0.739517\pi\) | ||||
−0.683439 | + | 0.730008i | \(0.739517\pi\) | |||||||
\(32\) | − 30.9373i | − 0.966789i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −50.2408 | −1.47767 | ||||||||
\(35\) | 0.435117i | 0.0124319i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 51.6438 | 1.39578 | 0.697889 | − | 0.716206i | \(-0.254123\pi\) | ||||
0.697889 | + | 0.716206i | \(0.254123\pi\) | |||||||
\(38\) | −36.1085 | −0.950223 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 11.8311i | 0.295777i | ||||||||
\(41\) | 46.2448i | 1.12792i | 0.825802 | + | 0.563961i | \(0.190723\pi\) | ||||
−0.825802 | + | 0.563961i | \(0.809277\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 59.7836i | 1.39032i | 0.718857 | + | 0.695158i | \(0.244666\pi\) | ||||
−0.718857 | + | 0.695158i | \(0.755334\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 19.1753i | − 0.416853i | ||||||||
\(47\) | −34.1325 | −0.726223 | −0.363111 | − | 0.931746i | \(-0.618286\pi\) | ||||
−0.363111 | + | 0.931746i | \(0.618286\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.9710 | 0.999407 | ||||||||
\(50\) | − 45.7474i | − 0.914947i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 41.0234i | 0.788912i | ||||||||
\(53\) | 15.2253 | 0.287270 | 0.143635 | − | 0.989631i | \(-0.454121\pi\) | ||||
0.143635 | + | 0.989631i | \(0.454121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.789510 | −0.0140984 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −94.7223 | −1.63314 | ||||||||
\(59\) | 26.3418 | 0.446472 | 0.223236 | − | 0.974764i | \(-0.428338\pi\) | ||||
0.223236 | + | 0.974764i | \(0.428338\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 63.3714i | 1.03887i | 0.854508 | + | 0.519437i | \(0.173858\pi\) | ||||
−0.854508 | + | 0.519437i | \(0.826142\pi\) | |||||||
\(62\) | − 104.897i | − 1.69189i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.34707 | −0.0522979 | ||||||||
\(65\) | − 49.2172i | − 0.757188i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.91469 | −0.0435028 | −0.0217514 | − | 0.999763i | \(-0.506924\pi\) | ||||
−0.0217514 | + | 0.999763i | \(0.506924\pi\) | |||||||
\(68\) | − 43.1951i | − 0.635223i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.07716 | −0.0153880 | ||||||||
\(71\) | −96.7843 | −1.36316 | −0.681579 | − | 0.731744i | \(-0.738707\pi\) | ||||
−0.681579 | + | 0.731744i | \(0.738707\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 17.3281i | 0.237371i | 0.992932 | + | 0.118685i | \(0.0378680\pi\) | ||||
−0.992932 | + | 0.118685i | \(0.962132\pi\) | |||||||
\(74\) | 127.847i | 1.72766i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 31.0447i | − 0.408483i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 52.7777i | 0.668072i | 0.942560 | + | 0.334036i | \(0.108411\pi\) | ||||
−0.942560 | + | 0.334036i | \(0.891589\pi\) | |||||||
\(80\) | −51.0280 | −0.637850 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −114.482 | −1.39612 | ||||||||
\(83\) | − 23.4757i | − 0.282839i | −0.989950 | − | 0.141420i | \(-0.954833\pi\) | ||||
0.989950 | − | 0.141420i | \(-0.0451667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 51.8227i | 0.609679i | ||||||||
\(86\) | −147.998 | −1.72090 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −97.1861 | −1.09198 | −0.545989 | − | 0.837792i | \(-0.683846\pi\) | ||||
−0.545989 | + | 0.837792i | \(0.683846\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.28435 | 0.0360918 | ||||||||
\(92\) | 16.4862 | 0.179197 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 84.4969i | − 0.898903i | ||||||||
\(95\) | 37.2454i | 0.392057i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −50.6148 | −0.521802 | −0.260901 | − | 0.965366i | \(-0.584020\pi\) | ||||
−0.260901 | + | 0.965366i | \(0.584020\pi\) | |||||||
\(98\) | 121.230i | 1.23705i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 39.3318 | 0.393318 | ||||||||
\(101\) | 65.8066i | 0.651551i | 0.945447 | + | 0.325775i | \(0.105625\pi\) | ||||
−0.945447 | + | 0.325775i | \(0.894375\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 139.180 | 1.35127 | 0.675633 | − | 0.737238i | \(-0.263870\pi\) | ||||
0.675633 | + | 0.737238i | \(0.263870\pi\) | |||||||
\(104\) | 89.3036 | 0.858688 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 37.6912i | 0.355577i | ||||||||
\(107\) | 12.8951i | 0.120515i | 0.998183 | + | 0.0602573i | \(0.0191921\pi\) | ||||
−0.998183 | + | 0.0602573i | \(0.980808\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 117.681i | − 1.07964i | −0.841780 | − | 0.539821i | \(-0.818492\pi\) | ||||
0.841780 | − | 0.539821i | \(-0.181508\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 3.40519i | − 0.0304035i | ||||||||
\(113\) | −175.640 | −1.55433 | −0.777166 | − | 0.629295i | \(-0.783344\pi\) | ||||
−0.777166 | + | 0.629295i | \(0.783344\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19.7790 | −0.171991 | ||||||||
\(116\) | − 81.4386i | − 0.702057i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 65.2108i | 0.552634i | ||||||||
\(119\) | −3.45822 | −0.0290607 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −156.880 | −1.28590 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 90.1868 | 0.727313 | ||||||||
\(125\) | −111.025 | −0.888203 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 59.8470i | − 0.471236i | −0.971846 | − | 0.235618i | \(-0.924289\pi\) | ||||
0.971846 | − | 0.235618i | \(-0.0757114\pi\) | |||||||
\(128\) | − 132.035i | − 1.03152i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 121.840 | 0.937232 | ||||||||
\(131\) | − 27.1623i | − 0.207346i | −0.994611 | − | 0.103673i | \(-0.966940\pi\) | ||||
0.994611 | − | 0.103673i | \(-0.0330595\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.48545 | −0.0186876 | ||||||||
\(134\) | − 7.21548i | − 0.0538469i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −94.0312 | −0.691406 | ||||||||
\(137\) | 81.1683 | 0.592469 | 0.296235 | − | 0.955115i | \(-0.404269\pi\) | ||||
0.296235 | + | 0.955115i | \(0.404269\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 194.413i | − 1.39865i | −0.714802 | − | 0.699327i | \(-0.753483\pi\) | ||||
0.714802 | − | 0.699327i | \(-0.246517\pi\) | |||||||
\(140\) | − 0.926099i | − 0.00661499i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 239.595i | − 1.68729i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 97.7048i | 0.673826i | ||||||||
\(146\) | −42.8967 | −0.293813 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −109.918 | −0.742690 | ||||||||
\(149\) | − 121.294i | − 0.814055i | −0.913416 | − | 0.407027i | \(-0.866565\pi\) | ||||
0.913416 | − | 0.407027i | \(-0.133435\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 102.557i | − 0.679186i | −0.940572 | − | 0.339593i | \(-0.889711\pi\) | ||||
0.940572 | − | 0.339593i | \(-0.110289\pi\) | |||||||
\(152\) | −67.5809 | −0.444611 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −108.200 | −0.698066 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 177.331 | 1.12950 | 0.564748 | − | 0.825264i | \(-0.308974\pi\) | ||||
0.564748 | + | 0.825264i | \(0.308974\pi\) | |||||||
\(158\) | −130.654 | −0.826925 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 78.9984i | − 0.493740i | ||||||||
\(161\) | − 1.31989i | − 0.00819807i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 105.183 | 0.645294 | 0.322647 | − | 0.946519i | \(-0.395427\pi\) | ||||
0.322647 | + | 0.946519i | \(0.395427\pi\) | |||||||
\(164\) | − 98.4270i | − 0.600165i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 58.1154 | 0.350093 | ||||||||
\(167\) | − 129.407i | − 0.774891i | −0.921893 | − | 0.387446i | \(-0.873358\pi\) | ||||
0.921893 | − | 0.387446i | \(-0.126642\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −202.502 | −1.19824 | ||||||||
\(170\) | −128.290 | −0.754648 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 127.243i | − 0.739784i | ||||||||
\(173\) | − 44.7971i | − 0.258943i | −0.991583 | − | 0.129471i | \(-0.958672\pi\) | ||||
0.991583 | − | 0.129471i | \(-0.0413281\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3.14892i | − 0.0179939i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 240.590i | − 1.35163i | ||||||||
\(179\) | 317.726 | 1.77501 | 0.887504 | − | 0.460800i | \(-0.152437\pi\) | ||||
0.887504 | + | 0.460800i | \(0.152437\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 330.778 | 1.82750 | 0.913750 | − | 0.406276i | \(-0.133173\pi\) | ||||
0.913750 | + | 0.406276i | \(0.133173\pi\) | |||||||
\(182\) | 8.13061i | 0.0446737i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − 35.8886i | − 0.195047i | ||||||||
\(185\) | 131.873 | 0.712825 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 72.6472 | 0.386421 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −92.2031 | −0.485280 | ||||||||
\(191\) | 127.040 | 0.665132 | 0.332566 | − | 0.943080i | \(-0.392086\pi\) | ||||
0.332566 | + | 0.943080i | \(0.392086\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 211.396i | 1.09531i | 0.836703 | + | 0.547657i | \(0.184480\pi\) | ||||
−0.836703 | + | 0.547657i | \(0.815520\pi\) | |||||||
\(194\) | − 125.300i | − 0.645876i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −104.229 | −0.531782 | ||||||||
\(197\) | 2.87439i | 0.0145908i | 0.999973 | + | 0.00729541i | \(0.00232222\pi\) | ||||
−0.999973 | + | 0.00729541i | \(0.997678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −158.546 | −0.796713 | −0.398357 | − | 0.917231i | \(-0.630419\pi\) | ||||
−0.398357 | + | 0.917231i | \(0.630419\pi\) | |||||||
\(200\) | − 85.6212i | − 0.428106i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −162.908 | −0.806476 | ||||||||
\(203\) | −6.52001 | −0.0321183 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 118.086i | 0.576031i | ||||||||
\(206\) | 344.549i | 1.67257i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 385.170i | 1.85178i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 355.990i | 1.68715i | 0.537008 | + | 0.843577i | \(0.319554\pi\) | ||||
−0.537008 | + | 0.843577i | \(0.680446\pi\) | |||||||
\(212\) | −32.4055 | −0.152856 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −31.9225 | −0.149171 | ||||||||
\(215\) | 152.658i | 0.710036i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 7.22039i | − 0.0332737i | ||||||||
\(218\) | 291.326 | 1.33636 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 391.169 | 1.76999 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −213.373 | −0.956831 | −0.478415 | − | 0.878134i | \(-0.658789\pi\) | ||||
−0.478415 | + | 0.878134i | \(0.658789\pi\) | |||||||
\(224\) | 5.27171 | 0.0235344 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 434.806i | − 1.92392i | ||||||||
\(227\) | 176.748i | 0.778628i | 0.921105 | + | 0.389314i | \(0.127288\pi\) | ||||
−0.921105 | + | 0.389314i | \(0.872712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −62.9641 | −0.274953 | −0.137476 | − | 0.990505i | \(-0.543899\pi\) | ||||
−0.137476 | + | 0.990505i | \(0.543899\pi\) | |||||||
\(230\) | − 48.9641i | − 0.212887i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −177.283 | −0.764151 | ||||||||
\(233\) | 307.347i | 1.31909i | 0.751667 | + | 0.659543i | \(0.229250\pi\) | ||||
−0.751667 | + | 0.659543i | \(0.770750\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −87.1574 | −0.370883 | ||||||||
\(236\) | −56.0658 | −0.237567 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 8.56103i | − 0.0359707i | ||||||||
\(239\) | − 373.207i | − 1.56153i | −0.624822 | − | 0.780767i | \(-0.714829\pi\) | ||||
0.624822 | − | 0.780767i | \(-0.285171\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0743i | 0.0542501i | 0.999632 | + | 0.0271250i | \(0.00863523\pi\) | ||||
−0.999632 | + | 0.0271250i | \(0.991365\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 134.879i | − 0.552783i | ||||||||
\(245\) | 125.048 | 0.510398 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 281.136 | 1.13820 | ||||||||
\(248\) | − 196.327i | − 0.791641i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 274.850i | − 1.09940i | ||||||||
\(251\) | −138.413 | −0.551446 | −0.275723 | − | 0.961237i | \(-0.588917\pi\) | ||||
−0.275723 | + | 0.961237i | \(0.588917\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 148.155 | 0.583286 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 313.472 | 1.22450 | ||||||||
\(257\) | 287.892 | 1.12020 | 0.560102 | − | 0.828424i | \(-0.310762\pi\) | ||||
0.560102 | + | 0.828424i | \(0.310762\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.80009i | 0.0339772i | ||||||||
\(260\) | 104.754i | 0.402898i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 67.2419 | 0.256648 | ||||||||
\(263\) | − 338.296i | − 1.28629i | −0.765742 | − | 0.643147i | \(-0.777628\pi\) | ||||
0.765742 | − | 0.643147i | \(-0.222372\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 38.8779 | 0.146709 | ||||||||
\(266\) | − 6.15288i | − 0.0231311i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.20359 | 0.0231477 | ||||||||
\(269\) | 63.1555 | 0.234779 | 0.117389 | − | 0.993086i | \(-0.462547\pi\) | ||||
0.117389 | + | 0.993086i | \(0.462547\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 166.707i | 0.615153i | 0.951523 | + | 0.307577i | \(0.0995181\pi\) | ||||
−0.951523 | + | 0.307577i | \(0.900482\pi\) | |||||||
\(272\) | − 405.560i | − 1.49103i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 200.937i | 0.733346i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 42.3827i | − 0.153006i | −0.997069 | − | 0.0765030i | \(-0.975625\pi\) | ||||
0.997069 | − | 0.0765030i | \(-0.0243755\pi\) | |||||||
\(278\) | 481.280 | 1.73122 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.01602 | −0.00720006 | ||||||||
\(281\) | 142.796i | 0.508169i | 0.967182 | + | 0.254085i | \(0.0817742\pi\) | ||||
−0.967182 | + | 0.254085i | \(0.918226\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 259.085i | 0.915494i | 0.889082 | + | 0.457747i | \(0.151343\pi\) | ||||
−0.889082 | + | 0.457747i | \(0.848657\pi\) | |||||||
\(284\) | 205.995 | 0.725334 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.88011 | −0.0274568 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −122.877 | −0.425178 | ||||||||
\(290\) | −241.874 | −0.834048 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 36.8809i | − 0.126304i | ||||||||
\(293\) | 115.020i | 0.392561i | 0.980548 | + | 0.196280i | \(0.0628862\pi\) | ||||
−0.980548 | + | 0.196280i | \(0.937114\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 67.2640 | 0.228014 | ||||||||
\(296\) | 239.280i | 0.808378i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 300.271 | 1.00762 | ||||||||
\(299\) | 149.296i | 0.499318i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.1871 | −0.0338442 | ||||||||
\(302\) | 253.886 | 0.840683 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 291.479i | − 0.958813i | ||||||||
\(305\) | 161.819i | 0.530554i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.9819i | 0.0748596i | 0.999299 | + | 0.0374298i | \(0.0119171\pi\) | ||||
−0.999299 | + | 0.0374298i | \(0.988083\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 267.856i | − 0.864052i | ||||||||
\(311\) | −594.646 | −1.91205 | −0.956023 | − | 0.293291i | \(-0.905250\pi\) | ||||
−0.956023 | + | 0.293291i | \(0.905250\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −521.860 | −1.66728 | −0.833642 | − | 0.552305i | \(-0.813748\pi\) | ||||
−0.833642 | + | 0.552305i | \(0.813748\pi\) | |||||||
\(314\) | 438.993i | 1.39807i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − 112.331i | − 0.355479i | ||||||||
\(317\) | −153.642 | −0.484675 | −0.242337 | − | 0.970192i | \(-0.577914\pi\) | ||||
−0.242337 | + | 0.970192i | \(0.577914\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −8.54675 | −0.0267086 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.26746 | 0.0101474 | ||||||||
\(323\) | −296.019 | −0.916467 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 356.183i | 1.09595i | ||||||||
\(326\) | 260.386i | 0.798731i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −214.265 | −0.653247 | ||||||||
\(329\) | − 5.81617i | − 0.0176783i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 297.441 | 0.898613 | 0.449306 | − | 0.893378i | \(-0.351671\pi\) | ||||
0.449306 | + | 0.893378i | \(0.351671\pi\) | |||||||
\(332\) | 49.9654i | 0.150498i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 320.354 | 0.959144 | ||||||||
\(335\) | −7.44267 | −0.0222169 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 4.17943i | − 0.0124019i | −0.999981 | − | 0.00620094i | \(-0.998026\pi\) | ||||
0.999981 | − | 0.00620094i | \(-0.00197383\pi\) | |||||||
\(338\) | − 501.306i | − 1.48315i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − 110.299i | − 0.324409i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.6942i | 0.0486713i | ||||||||
\(344\) | −276.994 | −0.805215 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 110.898 | 0.320514 | ||||||||
\(347\) | 585.875i | 1.68840i | 0.536028 | + | 0.844200i | \(0.319924\pi\) | ||||
−0.536028 | + | 0.844200i | \(0.680076\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 231.222i | − 0.662527i | −0.943538 | − | 0.331263i | \(-0.892525\pi\) | ||||
0.943538 | − | 0.331263i | \(-0.107475\pi\) | |||||||
\(350\) | 7.79535 | 0.0222724 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 416.133 | 1.17885 | 0.589423 | − | 0.807824i | \(-0.299355\pi\) | ||||
0.589423 | + | 0.807824i | \(0.299355\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −247.139 | −0.696166 | ||||||||
\(356\) | 206.850 | 0.581040 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 786.551i | 2.19707i | ||||||||
\(359\) | 37.9041i | 0.105582i | 0.998606 | + | 0.0527912i | \(0.0168118\pi\) | ||||
−0.998606 | + | 0.0527912i | \(0.983188\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 148.249 | 0.410662 | ||||||||
\(362\) | 818.859i | 2.26204i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.99039 | −0.0192044 | ||||||||
\(365\) | 44.2473i | 0.121225i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 219.116 | 0.597047 | 0.298523 | − | 0.954402i | \(-0.403506\pi\) | ||||
0.298523 | + | 0.954402i | \(0.403506\pi\) | |||||||
\(368\) | 154.789 | 0.420622 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 326.458i | 0.882320i | ||||||||
\(371\) | 2.59439i | 0.00699298i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.9491i | 0.0481209i | 0.999711 | + | 0.0240605i | \(0.00765942\pi\) | ||||
−0.999711 | + | 0.0240605i | \(0.992341\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 158.145i | − 0.420599i | ||||||||
\(377\) | 737.496 | 1.95622 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −45.6414 | −0.120426 | −0.0602129 | − | 0.998186i | \(-0.519178\pi\) | ||||
−0.0602129 | + | 0.998186i | \(0.519178\pi\) | |||||||
\(380\) | − 79.2727i | − 0.208612i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 314.495i | 0.823286i | ||||||||
\(383\) | 28.1815 | 0.0735810 | 0.0367905 | − | 0.999323i | \(-0.488287\pi\) | ||||
0.0367905 | + | 0.999323i | \(0.488287\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −523.322 | −1.35576 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 107.728 | 0.277650 | ||||||||
\(389\) | 564.821 | 1.45198 | 0.725992 | − | 0.687704i | \(-0.241381\pi\) | ||||
0.725992 | + | 0.687704i | \(0.241381\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 157.200i | − 0.402045i | ||||||||
\(392\) | 226.896i | 0.578817i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.11572 | −0.0180602 | ||||||||
\(395\) | 134.768i | 0.341185i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.35093 | 0.0159973 | 0.00799866 | − | 0.999968i | \(-0.497454\pi\) | ||||
0.00799866 | + | 0.999968i | \(0.497454\pi\) | |||||||
\(398\) | − 392.490i | − 0.986155i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 369.288 | 0.923219 | ||||||||
\(401\) | 165.822 | 0.413521 | 0.206761 | − | 0.978392i | \(-0.433708\pi\) | ||||
0.206761 | + | 0.978392i | \(0.433708\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 816.718i | 2.02660i | ||||||||
\(404\) | − 140.062i | − 0.346689i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − 16.1407i | − 0.0397554i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 38.0311i | − 0.0929856i | −0.998919 | − | 0.0464928i | \(-0.985196\pi\) | ||||
0.998919 | − | 0.0464928i | \(-0.0148045\pi\) | |||||||
\(410\) | −292.330 | −0.712999 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −296.230 | −0.719006 | ||||||||
\(413\) | 4.48865i | 0.0108684i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 59.9452i | − 0.144446i | ||||||||
\(416\) | −596.297 | −1.43341 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 254.746 | 0.607985 | 0.303993 | − | 0.952674i | \(-0.401680\pi\) | ||||
0.303993 | + | 0.952674i | \(0.401680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 554.739 | 1.31767 | 0.658835 | − | 0.752288i | \(-0.271050\pi\) | ||||
0.658835 | + | 0.752288i | \(0.271050\pi\) | |||||||
\(422\) | −881.273 | −2.08832 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 70.5432i | 0.166375i | ||||||||
\(425\) | − 375.039i | − 0.882445i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.7985 | −0.0252892 | ||||||||
\(428\) | − 27.4457i | − 0.0641256i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −377.913 | −0.878867 | ||||||||
\(431\) | 31.4905i | 0.0730639i | 0.999332 | + | 0.0365319i | \(0.0116311\pi\) | ||||
−0.999332 | + | 0.0365319i | \(0.988369\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 633.975 | 1.46415 | 0.732073 | − | 0.681226i | \(-0.238553\pi\) | ||||
0.732073 | + | 0.681226i | \(0.238553\pi\) | |||||||
\(434\) | 17.8745 | 0.0411855 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 250.471i | 0.574475i | ||||||||
\(437\) | − 112.981i | − 0.258537i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 336.283i | − 0.766021i | −0.923744 | − | 0.383010i | \(-0.874887\pi\) | ||||
0.923744 | − | 0.383010i | \(-0.125113\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 968.361i | 2.19086i | ||||||||
\(443\) | 487.743 | 1.10100 | 0.550500 | − | 0.834835i | \(-0.314437\pi\) | ||||
0.550500 | + | 0.834835i | \(0.314437\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −248.165 | −0.557675 | ||||||||
\(446\) | − 528.218i | − 1.18435i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 0.570340i | − 0.00127308i | ||||||||
\(449\) | 668.379 | 1.48860 | 0.744298 | − | 0.667848i | \(-0.232784\pi\) | ||||
0.744298 | + | 0.667848i | \(0.232784\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 373.830 | 0.827057 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −437.551 | −0.963769 | ||||||||
\(455\) | 8.38662 | 0.0184321 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 511.486i | 1.11923i | 0.828754 | + | 0.559613i | \(0.189050\pi\) | ||||
−0.828754 | + | 0.559613i | \(0.810950\pi\) | |||||||
\(458\) | − 155.871i | − 0.340331i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 42.0975 | 0.0915162 | ||||||||
\(461\) | − 75.7082i | − 0.164226i | −0.996623 | − | 0.0821131i | \(-0.973833\pi\) | ||||
0.996623 | − | 0.0821131i | \(-0.0261669\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 292.607 | 0.631980 | 0.315990 | − | 0.948763i | \(-0.397663\pi\) | ||||
0.315990 | + | 0.948763i | \(0.397663\pi\) | |||||||
\(464\) | − 764.629i | − 1.64791i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −760.856 | −1.63274 | ||||||||
\(467\) | −774.519 | −1.65850 | −0.829249 | − | 0.558879i | \(-0.811232\pi\) | ||||
−0.829249 | + | 0.558879i | \(0.811232\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 0.496662i | − 0.00105898i | ||||||||
\(470\) | − 215.763i | − 0.459071i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 122.049i | 0.258579i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 269.543i | − 0.567460i | ||||||||
\(476\) | 7.36045 | 0.0154631 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 923.895 | 1.93283 | ||||||||
\(479\) | − 65.6365i | − 0.137028i | −0.997650 | − | 0.0685141i | \(-0.978174\pi\) | ||||
0.997650 | − | 0.0685141i | \(-0.0218258\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 995.402i | − 2.06944i | ||||||||
\(482\) | −32.3661 | −0.0671496 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −129.245 | −0.266485 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.1162 | −0.0371995 | −0.0185998 | − | 0.999827i | \(-0.505921\pi\) | ||||
−0.0185998 | + | 0.999827i | \(0.505921\pi\) | |||||||
\(488\) | −293.617 | −0.601674 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 309.563i | 0.631760i | ||||||||
\(491\) | 426.903i | 0.869455i | 0.900562 | + | 0.434728i | \(0.143155\pi\) | ||||
−0.900562 | + | 0.434728i | \(0.856845\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −776.538 | −1.57513 | ||||||||
\(494\) | 695.969i | 1.40884i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 846.766 | 1.70719 | ||||||||
\(497\) | − 16.4920i | − 0.0331832i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 285.373 | 0.571890 | 0.285945 | − | 0.958246i | \(-0.407693\pi\) | ||||
0.285945 | + | 0.958246i | \(0.407693\pi\) | |||||||
\(500\) | 236.305 | 0.472611 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 342.649i | − 0.682568i | ||||||||
\(503\) | 543.584i | 1.08068i | 0.841446 | + | 0.540342i | \(0.181705\pi\) | ||||
−0.841446 | + | 0.540342i | \(0.818295\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 168.038i | 0.332748i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 127.378i | 0.250744i | ||||||||
\(509\) | −196.501 | −0.386054 | −0.193027 | − | 0.981193i | \(-0.561830\pi\) | ||||
−0.193027 | + | 0.981193i | \(0.561830\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.95270 | −0.00577828 | ||||||||
\(512\) | 247.878i | 0.484138i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 712.695i | 1.38657i | ||||||||
\(515\) | 355.398 | 0.690093 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −21.7851 | −0.0420563 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 228.037 | 0.438533 | ||||||||
\(521\) | 573.267 | 1.10032 | 0.550160 | − | 0.835059i | \(-0.314567\pi\) | ||||
0.550160 | + | 0.835059i | \(0.314567\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 993.636i | − 1.89988i | −0.312437 | − | 0.949938i | \(-0.601145\pi\) | ||||
0.312437 | − | 0.949938i | \(-0.398855\pi\) | |||||||
\(524\) | 57.8120i | 0.110328i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 837.471 | 1.59215 | ||||||||
\(527\) | − 859.954i | − 1.63179i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −469.002 | −0.886583 | ||||||||
\(530\) | 96.2446i | 0.181594i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.29001 | 0.00994363 | ||||||||
\(533\) | 891.340 | 1.67231 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.9276i | 0.0615469i | ||||||||
\(536\) | − 13.5046i | − 0.0251951i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 156.345i | 0.290604i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 226.110i | − 0.417949i | −0.977921 | − | 0.208974i | \(-0.932987\pi\) | ||||
0.977921 | − | 0.208974i | \(-0.0670125\pi\) | |||||||
\(542\) | −412.692 | −0.761424 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 627.864 | 1.15416 | ||||||||
\(545\) | − 300.499i | − 0.551374i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 457.431i | 0.836254i | 0.908389 | + | 0.418127i | \(0.137313\pi\) | ||||
−0.908389 | + | 0.418127i | \(0.862687\pi\) | |||||||
\(548\) | −172.758 | −0.315252 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −558.104 | −1.01289 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.99331 | −0.0162628 | ||||||||
\(554\) | 104.921 | 0.189388 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 413.787i | 0.744220i | ||||||||
\(557\) | − 281.137i | − 0.504735i | −0.967631 | − | 0.252368i | \(-0.918791\pi\) | ||||
0.967631 | − | 0.252368i | \(-0.0812092\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1152.29 | 2.06135 | ||||||||
\(560\) | − 8.69517i | − 0.0155271i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −353.499 | −0.629002 | ||||||||
\(563\) | 225.243i | 0.400076i | 0.979788 | + | 0.200038i | \(0.0641066\pi\) | ||||
−0.979788 | + | 0.200038i | \(0.935893\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −448.496 | −0.793799 | ||||||||
\(566\) | −641.380 | −1.13318 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 448.428i | − 0.789487i | ||||||||
\(569\) | 148.348i | 0.260717i | 0.991467 | + | 0.130358i | \(0.0416128\pi\) | ||||
−0.991467 | + | 0.130358i | \(0.958387\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 111.405i | − 0.195106i | −0.995230 | − | 0.0975528i | \(-0.968899\pi\) | ||||
0.995230 | − | 0.0975528i | \(-0.0311015\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − 19.5077i | − 0.0339855i | ||||||||
\(575\) | 143.140 | 0.248939 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −540.605 | −0.936925 | −0.468462 | − | 0.883484i | \(-0.655192\pi\) | ||||
−0.468462 | + | 0.883484i | \(0.655192\pi\) | |||||||
\(578\) | − 304.188i | − 0.526277i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 207.954i | − 0.358541i | ||||||||
\(581\) | 4.00025 | 0.00688511 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −80.2858 | −0.137476 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −284.739 | −0.485903 | ||||||||
\(587\) | −344.226 | −0.586416 | −0.293208 | − | 0.956049i | \(-0.594723\pi\) | ||||
−0.293208 | + | 0.956049i | \(0.594723\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 618.055i | − 1.04933i | ||||||||
\(590\) | 166.516i | 0.282231i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1032.02 | −1.74328 | ||||||||
\(593\) | 723.311i | 1.21975i | 0.792498 | + | 0.609874i | \(0.208780\pi\) | ||||
−0.792498 | + | 0.609874i | \(0.791220\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.83059 | −0.0148413 | ||||||||
\(596\) | 258.161i | 0.433157i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −369.591 | −0.618046 | ||||||||
\(599\) | 283.768 | 0.473737 | 0.236868 | − | 0.971542i | \(-0.423879\pi\) | ||||
0.236868 | + | 0.971542i | \(0.423879\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 1028.06i | − 1.71059i | −0.518144 | − | 0.855294i | \(-0.673377\pi\) | ||||
0.518144 | − | 0.855294i | \(-0.326623\pi\) | |||||||
\(602\) | − 25.2188i | − 0.0418917i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 218.282i | 0.361393i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 630.478i | − 1.03868i | −0.854568 | − | 0.519339i | \(-0.826178\pi\) | ||||
0.854568 | − | 0.519339i | \(-0.173822\pi\) | |||||||
\(608\) | 451.250 | 0.742188 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −400.593 | −0.656709 | ||||||||
\(611\) | 657.882i | 1.07673i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 562.321i | 0.917325i | 0.888610 | + | 0.458663i | \(0.151671\pi\) | ||||
−0.888610 | + | 0.458663i | \(0.848329\pi\) | |||||||
\(614\) | −56.8931 | −0.0926597 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 892.792 | 1.44699 | 0.723494 | − | 0.690331i | \(-0.242535\pi\) | ||||
0.723494 | + | 0.690331i | \(0.242535\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 648.381 | 1.04746 | 0.523732 | − | 0.851883i | \(-0.324539\pi\) | ||||
0.523732 | + | 0.851883i | \(0.324539\pi\) | |||||||
\(620\) | 230.292 | 0.371439 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 1472.08i | − 2.36669i | ||||||||
\(623\) | − 16.5605i | − 0.0265819i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 178.486 | 0.285578 | ||||||||
\(626\) | − 1291.89i | − 2.06373i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −377.429 | −0.601002 | ||||||||
\(629\) | 1048.10i | 1.66629i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1019.41 | −1.61554 | −0.807772 | − | 0.589495i | \(-0.799327\pi\) | ||||
−0.807772 | + | 0.589495i | \(0.799327\pi\) | |||||||
\(632\) | −244.534 | −0.386920 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − 380.349i | − 0.599920i | ||||||||
\(635\) | − 152.820i | − 0.240661i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 943.885i | − 1.48177i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 337.152i | − 0.526800i | ||||||||
\(641\) | −436.401 | −0.680813 | −0.340406 | − | 0.940278i | \(-0.610565\pi\) | ||||
−0.340406 | + | 0.940278i | \(0.610565\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −514.698 | −0.800463 | −0.400231 | − | 0.916414i | \(-0.631070\pi\) | ||||
−0.400231 | + | 0.916414i | \(0.631070\pi\) | |||||||
\(644\) | 2.80924i | 0.00436217i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − 732.812i | − 1.13438i | ||||||||
\(647\) | −241.038 | −0.372547 | −0.186273 | − | 0.982498i | \(-0.559641\pi\) | ||||
−0.186273 | + | 0.982498i | \(0.559641\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −881.753 | −1.35654 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −223.870 | −0.343359 | ||||||||
\(653\) | 162.540 | 0.248913 | 0.124456 | − | 0.992225i | \(-0.460281\pi\) | ||||
0.124456 | + | 0.992225i | \(0.460281\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 69.3591i | − 0.105892i | ||||||||
\(656\) | − 924.133i | − 1.40874i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.3983 | 0.0218819 | ||||||||
\(659\) | − 1078.94i | − 1.63724i | −0.574332 | − | 0.818622i | \(-0.694738\pi\) | ||||
0.574332 | − | 0.818622i | \(-0.305262\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 428.584 | 0.648387 | 0.324193 | − | 0.945991i | \(-0.394907\pi\) | ||||
0.324193 | + | 0.945991i | \(0.394907\pi\) | |||||||
\(662\) | 736.332i | 1.11228i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 108.769 | 0.163809 | ||||||||
\(665\) | −6.34661 | −0.00954377 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 296.379i | − 0.444346i | ||||||||
\(668\) | 275.428i | 0.412318i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 18.4248i | − 0.0274996i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 262.693i | 0.390331i | 0.980770 | + | 0.195165i | \(0.0625244\pi\) | ||||
−0.980770 | + | 0.195165i | \(0.937476\pi\) | |||||||
\(674\) | 10.3464 | 0.0153508 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 431.004 | 0.637580 | ||||||||
\(677\) | − 149.879i | − 0.221387i | −0.993855 | − | 0.110694i | \(-0.964693\pi\) | ||||
0.993855 | − | 0.110694i | \(-0.0353073\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 8.62476i | − 0.0127021i | ||||||||
\(680\) | −240.109 | −0.353102 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 52.4276 | 0.0767608 | 0.0383804 | − | 0.999263i | \(-0.487780\pi\) | ||||
0.0383804 | + | 0.999263i | \(0.487780\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 207.264 | 0.302575 | ||||||||
\(686\) | −41.3276 | −0.0602443 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 1194.69i | − 1.73646i | ||||||||
\(689\) | − 293.459i | − 0.425920i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −196.722 | −0.284692 | −0.142346 | − | 0.989817i | \(-0.545465\pi\) | ||||
−0.142346 | + | 0.989817i | \(0.545465\pi\) | |||||||
\(692\) | 95.3458i | 0.137783i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1450.37 | −2.08987 | ||||||||
\(695\) | − 496.434i | − 0.714294i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −938.526 | −1.34652 | ||||||||
\(698\) | 572.403 | 0.820062 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.70214i | 0.00957449i | ||||||||
\(701\) | 886.407i | 1.26449i | 0.774769 | + | 0.632245i | \(0.217866\pi\) | ||||
−0.774769 | + | 0.632245i | \(0.782134\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 753.275i | 1.07152i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1030.16i | 1.45915i | ||||||||
\(707\) | −11.2134 | −0.0158606 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 310.329 | 0.437700 | 0.218850 | − | 0.975758i | \(-0.429769\pi\) | ||||
0.218850 | + | 0.975758i | \(0.429769\pi\) | |||||||
\(710\) | − 611.807i | − 0.861700i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 450.290i | − 0.632430i | ||||||||
\(713\) | 328.216 | 0.460331 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −676.246 | −0.944478 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −93.8337 | −0.130688 | ||||||||
\(719\) | −451.160 | −0.627482 | −0.313741 | − | 0.949509i | \(-0.601582\pi\) | ||||
−0.313741 | + | 0.949509i | \(0.601582\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.7163i | 0.0328937i | ||||||||
\(722\) | 366.999i | 0.508309i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −704.024 | −0.972409 | ||||||||
\(725\) | − 707.086i | − 0.975290i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −89.6851 | −0.123363 | −0.0616817 | − | 0.998096i | \(-0.519646\pi\) | ||||
−0.0616817 | + | 0.998096i | \(0.519646\pi\) | |||||||
\(728\) | 15.2173i | 0.0209029i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −109.537 | −0.150050 | ||||||||
\(731\) | −1213.29 | −1.65977 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 557.486i | 0.760554i | 0.924873 | + | 0.380277i | \(0.124171\pi\) | ||||
−0.924873 | + | 0.380277i | \(0.875829\pi\) | |||||||
\(734\) | 542.435i | 0.739012i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 239.635i | 0.325591i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 95.7304i | − 0.129541i | −0.997900 | − | 0.0647703i | \(-0.979369\pi\) | ||||
0.997900 | − | 0.0647703i | \(-0.0206315\pi\) | |||||||
\(740\) | −280.676 | −0.379292 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.42258 | −0.00865576 | ||||||||
\(743\) | − 1121.35i | − 1.50921i | −0.656177 | − | 0.754607i | \(-0.727828\pi\) | ||||
0.656177 | − | 0.754607i | \(-0.272172\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 309.725i | − 0.415738i | ||||||||
\(746\) | −44.4341 | −0.0595631 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.19732 | −0.00293367 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −255.391 | −0.340068 | −0.170034 | − | 0.985438i | \(-0.554388\pi\) | ||||
−0.170034 | + | 0.985438i | \(0.554388\pi\) | |||||||
\(752\) | 682.087 | 0.907030 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1825.71i | 2.42137i | ||||||||
\(755\) | − 261.880i | − 0.346861i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 123.853 | 0.163610 | 0.0818052 | − | 0.996648i | \(-0.473931\pi\) | ||||
0.0818052 | + | 0.996648i | \(0.473931\pi\) | |||||||
\(758\) | − 112.988i | − 0.149061i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −172.568 | −0.227063 | ||||||||
\(761\) | − 349.009i | − 0.458619i | −0.973354 | − | 0.229309i | \(-0.926353\pi\) | ||||
0.973354 | − | 0.229309i | \(-0.0736467\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.0528 | 0.0262815 | ||||||||
\(764\) | −270.391 | −0.353915 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 69.7650i | 0.0910770i | ||||||||
\(767\) | − 507.723i | − 0.661960i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 867.000i | − 1.12744i | −0.825966 | − | 0.563719i | \(-0.809370\pi\) | ||||
0.825966 | − | 0.563719i | \(-0.190630\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 449.932i | − 0.582814i | ||||||||
\(773\) | 173.732 | 0.224751 | 0.112375 | − | 0.993666i | \(-0.464154\pi\) | ||||
0.112375 | + | 0.993666i | \(0.464154\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 783.041 | 1.01038 | ||||||||
\(776\) | − 234.512i | − 0.302207i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1398.25i | 1.79723i | ||||||||
\(779\) | −674.526 | −0.865887 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 389.157 | 0.497643 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −978.612 | −1.24823 | ||||||||
\(785\) | 452.815 | 0.576834 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.2594i | 0.0575087i | 0.999587 | + | 0.0287544i | \(0.00915406\pi\) | ||||
−0.999587 | + | 0.0287544i | \(0.990846\pi\) | |||||||
\(788\) | − 6.11783i | − 0.00776374i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −333.626 | −0.422311 | ||||||||
\(791\) | − 29.9290i | − 0.0378369i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1221.44 | 1.54028 | ||||||||
\(794\) | 15.7221i | 0.0198011i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 337.448 | 0.423929 | ||||||||
\(797\) | −943.478 | −1.18379 | −0.591894 | − | 0.806016i | \(-0.701619\pi\) | ||||
−0.591894 | + | 0.806016i | \(0.701619\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 692.710i | − 0.866971i | ||||||||
\(800\) | 571.709i | 0.714636i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 410.502i | 0.511848i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 3.37034i | − 0.00418676i | ||||||||
\(806\) | −2021.83 | −2.50848 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −304.900 | −0.377352 | ||||||||
\(809\) | − 528.501i | − 0.653277i | −0.945149 | − | 0.326639i | \(-0.894084\pi\) | ||||
0.945149 | − | 0.326639i | \(-0.105916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 731.685i | 0.902201i | 0.892473 | + | 0.451101i | \(0.148968\pi\) | ||||
−0.892473 | + | 0.451101i | \(0.851032\pi\) | |||||||
\(812\) | 13.8771 | 0.0170901 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 268.585 | 0.329552 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −872.002 | −1.06732 | ||||||||
\(818\) | 94.1482 | 0.115096 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − 251.334i | − 0.306505i | ||||||||
\(821\) | − 1124.91i | − 1.37017i | −0.728463 | − | 0.685085i | \(-0.759765\pi\) | ||||
0.728463 | − | 0.685085i | \(-0.240235\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 238.410 | 0.289684 | 0.144842 | − | 0.989455i | \(-0.453733\pi\) | ||||
0.144842 | + | 0.989455i | \(0.453733\pi\) | |||||||
\(824\) | 644.861i | 0.782599i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.1119 | −0.0134527 | ||||||||
\(827\) | − 1536.19i | − 1.85755i | −0.370647 | − | 0.928774i | \(-0.620864\pi\) | ||||
0.370647 | − | 0.928774i | \(-0.379136\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1576.52 | 1.90172 | 0.950859 | − | 0.309624i | \(-0.100203\pi\) | ||||
0.950859 | + | 0.309624i | \(0.100203\pi\) | |||||||
\(830\) | 148.398 | 0.178793 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 64.5126i | 0.0775392i | ||||||||
\(833\) | 993.853i | 1.19310i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 330.441i | − 0.395738i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 630.638i | 0.752552i | ||||||||
\(839\) | 47.4743 | 0.0565844 | 0.0282922 | − | 0.999600i | \(-0.490993\pi\) | ||||
0.0282922 | + | 0.999600i | \(0.490993\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −623.058 | −0.740853 | ||||||||
\(842\) | 1373.29i | 1.63098i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − 757.685i | − 0.897731i | ||||||||
\(845\) | −517.090 | −0.611941 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −304.256 | −0.358792 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 928.431 | 1.09227 | ||||||||
\(851\) | −400.024 | −0.470063 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 743.273i | 0.871364i | 0.900101 | + | 0.435682i | \(0.143493\pi\) | ||||
−0.900101 | + | 0.435682i | \(0.856507\pi\) | |||||||
\(854\) | − 26.7323i | − 0.0313024i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −59.7464 | −0.0697972 | ||||||||
\(857\) | 572.262i | 0.667750i | 0.942617 | + | 0.333875i | \(0.108356\pi\) | ||||
−0.942617 | + | 0.333875i | \(0.891644\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −792.198 | −0.922233 | −0.461117 | − | 0.887340i | \(-0.652551\pi\) | ||||
−0.461117 | + | 0.887340i | \(0.652551\pi\) | |||||||
\(860\) | − 324.915i | − 0.377808i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −77.9566 | −0.0904369 | ||||||||
\(863\) | −1052.87 | −1.22001 | −0.610007 | − | 0.792396i | \(-0.708833\pi\) | ||||
−0.610007 | + | 0.792396i | \(0.708833\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 114.390i | − 0.132242i | ||||||||
\(866\) | 1569.44i | 1.81229i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.3678i | 0.0177049i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.1788i | 0.0644992i | ||||||||
\(872\) | 545.248 | 0.625285 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 279.690 | 0.320011 | ||||||||
\(875\) | − 18.9187i | − 0.0216214i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1419.86i | 1.61899i | 0.587124 | + | 0.809497i | \(0.300260\pi\) | ||||
−0.587124 | + | 0.809497i | \(0.699740\pi\) | |||||||
\(878\) | 832.489 | 0.948165 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −952.550 | −1.08121 | −0.540607 | − | 0.841275i | \(-0.681805\pi\) | ||||
−0.540607 | + | 0.841275i | \(0.681805\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 355.803 | 0.402948 | 0.201474 | − | 0.979494i | \(-0.435427\pi\) | ||||
0.201474 | + | 0.979494i | \(0.435427\pi\) | |||||||
\(884\) | −832.560 | −0.941810 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1207.44i | 1.36280i | ||||||||
\(887\) | 1032.34i | 1.16385i | 0.813241 | + | 0.581927i | \(0.197701\pi\) | ||||
−0.813241 | + | 0.581927i | \(0.802299\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.1979 | 0.0114712 | ||||||||
\(890\) | − 614.348i | − 0.690278i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 454.142 | 0.509128 | ||||||||
\(893\) | − 497.856i | − 0.557509i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 811.316 | 0.906498 | ||||||||
\(896\) | 22.4987 | 0.0251102 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1654.61i | 1.84255i | ||||||||
\(899\) | − 1621.33i | − 1.80348i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 308.994i | 0.342946i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − 813.787i | − 0.900207i | ||||||||
\(905\) | 844.642 | 0.933306 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1087.06 | −1.19853 | −0.599263 | − | 0.800552i | \(-0.704540\pi\) | ||||
−0.599263 | + | 0.800552i | \(0.704540\pi\) | |||||||
\(908\) | − 376.190i | − 0.414306i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 20.7616i | 0.0228149i | ||||||||
\(911\) | −400.130 | −0.439221 | −0.219610 | − | 0.975588i | \(-0.570479\pi\) | ||||
−0.219610 | + | 0.975588i | \(0.570479\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −1266.21 | −1.38536 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 134.012 | 0.146302 | ||||||||
\(917\) | 4.62846 | 0.00504739 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1347.43i | − 1.46619i | −0.680124 | − | 0.733097i | \(-0.738074\pi\) | ||||
0.680124 | − | 0.733097i | \(-0.261926\pi\) | |||||||
\(920\) | − 91.6416i | − 0.0996105i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 187.420 | 0.203276 | ||||||||
\(923\) | 1865.46i | 2.02108i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −954.357 | −1.03174 | ||||||||
\(926\) | 724.365i | 0.782252i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1183.75 | 1.27560 | ||||||||
\(929\) | 1493.12 | 1.60723 | 0.803616 | − | 0.595148i | \(-0.202907\pi\) | ||||
0.803616 | + | 0.595148i | \(0.202907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 714.290i | 0.767229i | ||||||||
\(932\) | − 654.155i | − 0.701883i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 1917.37i | − 2.05286i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 556.584i | 0.594007i | 0.954876 | + | 0.297003i | \(0.0959873\pi\) | ||||
−0.954876 | + | 0.297003i | \(0.904013\pi\) | |||||||
\(938\) | 1.22952 | 0.00131079 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 185.505 | 0.197346 | ||||||||
\(941\) | − 842.698i | − 0.895535i | −0.894150 | − | 0.447767i | \(-0.852219\pi\) | ||||
0.894150 | − | 0.447767i | \(-0.147781\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 358.204i | − 0.379856i | ||||||||
\(944\) | −526.403 | −0.557630 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −789.960 | −0.834171 | −0.417085 | − | 0.908867i | \(-0.636948\pi\) | ||||
−0.417085 | + | 0.908867i | \(0.636948\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 333.988 | 0.351937 | ||||||||
\(950\) | 667.270 | 0.702390 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 16.0229i | − 0.0168308i | ||||||||
\(953\) | 1167.43i | 1.22501i | 0.790468 | + | 0.612503i | \(0.209837\pi\) | ||||
−0.790468 | + | 0.612503i | \(0.790163\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 324.398 | 0.339683 | ||||||||
\(956\) | 794.330i | 0.830889i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 162.487 | 0.169611 | ||||||||
\(959\) | 13.8311i | 0.0144224i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 834.490 | 0.868356 | ||||||||
\(962\) | 2464.18 | 2.56151 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 27.8272i | − 0.0288664i | ||||||||
\(965\) | 539.800i | 0.559378i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 840.359i | 0.869037i | 0.900663 | + | 0.434518i | \(0.143081\pi\) | ||||
−0.900663 | + | 0.434518i | \(0.856919\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − 319.954i | − 0.329849i | ||||||||
\(971\) | −1250.52 | −1.28787 | −0.643937 | − | 0.765079i | \(-0.722700\pi\) | ||||
−0.643937 | + | 0.765079i | \(0.722700\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.1279 | 0.0340472 | ||||||||
\(974\) | − 44.8477i | − 0.0460448i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 1266.38i | − 1.29752i | ||||||||
\(977\) | −114.574 | −0.117271 | −0.0586356 | − | 0.998279i | \(-0.518675\pi\) | ||||
−0.0586356 | + | 0.998279i | \(0.518675\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −266.150 | −0.271582 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1056.82 | −1.07619 | ||||||||
\(983\) | 854.035 | 0.868804 | 0.434402 | − | 0.900719i | \(-0.356960\pi\) | ||||
0.434402 | + | 0.900719i | \(0.356960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.33977i | 0.00745154i | ||||||||
\(986\) | − 1922.36i | − 1.94966i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −598.367 | −0.605635 | ||||||||
\(989\) | − 463.073i | − 0.468224i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1236.21 | 1.24743 | 0.623716 | − | 0.781651i | \(-0.285622\pi\) | ||||
0.623716 | + | 0.781651i | \(0.285622\pi\) | |||||||
\(992\) | 1310.91i | 1.32148i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 40.8270 | 0.0410734 | ||||||||
\(995\) | −404.848 | −0.406882 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 704.988i | − 0.707109i | −0.935414 | − | 0.353555i | \(-0.884973\pi\) | ||||
0.935414 | − | 0.353555i | \(-0.115027\pi\) | |||||||
\(998\) | 706.458i | 0.707874i | ||||||||
\(999\) | 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.c.m.604.13 | 16 | ||
3.2 | odd | 2 | 363.3.c.e.241.4 | 16 | |||
11.4 | even | 5 | 99.3.k.c.28.1 | 16 | |||
11.8 | odd | 10 | 99.3.k.c.46.1 | 16 | |||
11.10 | odd | 2 | inner | 1089.3.c.m.604.4 | 16 | ||
33.2 | even | 10 | 363.3.g.a.40.4 | 16 | |||
33.5 | odd | 10 | 363.3.g.a.118.4 | 16 | |||
33.8 | even | 10 | 33.3.g.a.13.4 | ✓ | 16 | ||
33.14 | odd | 10 | 363.3.g.f.112.1 | 16 | |||
33.17 | even | 10 | 363.3.g.g.118.1 | 16 | |||
33.20 | odd | 10 | 363.3.g.g.40.1 | 16 | |||
33.26 | odd | 10 | 33.3.g.a.28.4 | yes | 16 | ||
33.29 | even | 10 | 363.3.g.f.94.1 | 16 | |||
33.32 | even | 2 | 363.3.c.e.241.13 | 16 | |||
132.59 | even | 10 | 528.3.bf.b.193.3 | 16 | |||
132.107 | odd | 10 | 528.3.bf.b.145.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.g.a.13.4 | ✓ | 16 | 33.8 | even | 10 | ||
33.3.g.a.28.4 | yes | 16 | 33.26 | odd | 10 | ||
99.3.k.c.28.1 | 16 | 11.4 | even | 5 | |||
99.3.k.c.46.1 | 16 | 11.8 | odd | 10 | |||
363.3.c.e.241.4 | 16 | 3.2 | odd | 2 | |||
363.3.c.e.241.13 | 16 | 33.32 | even | 2 | |||
363.3.g.a.40.4 | 16 | 33.2 | even | 10 | |||
363.3.g.a.118.4 | 16 | 33.5 | odd | 10 | |||
363.3.g.f.94.1 | 16 | 33.29 | even | 10 | |||
363.3.g.f.112.1 | 16 | 33.14 | odd | 10 | |||
363.3.g.g.40.1 | 16 | 33.20 | odd | 10 | |||
363.3.g.g.118.1 | 16 | 33.17 | even | 10 | |||
528.3.bf.b.145.3 | 16 | 132.107 | odd | 10 | |||
528.3.bf.b.193.3 | 16 | 132.59 | even | 10 | |||
1089.3.c.m.604.4 | 16 | 11.10 | odd | 2 | inner | ||
1089.3.c.m.604.13 | 16 | 1.1 | even | 1 | trivial |