Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(485,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.485");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 48x^{14} + 921x^{12} + 8986x^{10} + 46812x^{8} + 125072x^{6} + 152129x^{4} + 65614x^{2} + 5041 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 485.6 | ||
Root | \(-1.35141i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.485 |
Dual form | 1089.3.b.j.485.11 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.35141i | − 0.675704i | −0.941199 | − | 0.337852i | \(-0.890300\pi\) | ||||
0.941199 | − | 0.337852i | \(-0.109700\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.17369 | 0.543424 | ||||||||
\(5\) | − 5.10469i | − 1.02094i | −0.859896 | − | 0.510469i | \(-0.829472\pi\) | ||||
0.859896 | − | 0.510469i | \(-0.170528\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.1679 | 1.88113 | 0.940565 | − | 0.339613i | \(-0.110296\pi\) | ||||
0.940565 | + | 0.339613i | \(0.110296\pi\) | |||||||
\(8\) | − 8.34318i | − 1.04290i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.89852 | −0.689852 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.67027 | 0.205405 | 0.102703 | − | 0.994712i | \(-0.467251\pi\) | ||||
0.102703 | + | 0.994712i | \(0.467251\pi\) | |||||||
\(14\) | − 17.7952i | − 1.27109i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.58027 | −0.161267 | ||||||||
\(17\) | − 17.2161i | − 1.01271i | −0.862325 | − | 0.506356i | \(-0.830992\pi\) | ||||
0.862325 | − | 0.506356i | \(-0.169008\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −30.6226 | −1.61172 | −0.805859 | − | 0.592107i | \(-0.798296\pi\) | ||||
−0.805859 | + | 0.592107i | \(0.798296\pi\) | |||||||
\(20\) | − 11.0960i | − 0.554802i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 15.5309i | − 0.675257i | −0.941279 | − | 0.337628i | \(-0.890375\pi\) | ||||
0.941279 | − | 0.337628i | \(-0.109625\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.05786 | −0.0423145 | ||||||||
\(26\) | − 3.60862i | − 0.138793i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 28.6230 | 1.02225 | ||||||||
\(29\) | 10.3828i | 0.358028i | 0.983847 | + | 0.179014i | \(0.0572908\pi\) | ||||
−0.983847 | + | 0.179014i | \(0.942709\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.8678 | 0.544124 | 0.272062 | − | 0.962280i | \(-0.412294\pi\) | ||||
0.272062 | + | 0.962280i | \(0.412294\pi\) | |||||||
\(32\) | − 29.8857i | − 0.933929i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −23.2660 | −0.684294 | ||||||||
\(35\) | − 67.2181i | − 1.92052i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.7510 | 0.506783 | 0.253391 | − | 0.967364i | \(-0.418454\pi\) | ||||
0.253391 | + | 0.967364i | \(0.418454\pi\) | |||||||
\(38\) | 41.3837i | 1.08904i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −42.5894 | −1.06473 | ||||||||
\(41\) | 13.3582i | 0.325809i | 0.986642 | + | 0.162904i | \(0.0520862\pi\) | ||||
−0.986642 | + | 0.162904i | \(0.947914\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.5356 | −0.245015 | −0.122507 | − | 0.992468i | \(-0.539093\pi\) | ||||
−0.122507 | + | 0.992468i | \(0.539093\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −20.9886 | −0.456274 | ||||||||
\(47\) | 82.2065i | 1.74907i | 0.484958 | + | 0.874537i | \(0.338835\pi\) | ||||
−0.484958 | + | 0.874537i | \(0.661165\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 124.394 | 2.53865 | ||||||||
\(50\) | 1.42960i | 0.0285921i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.80435 | 0.111622 | ||||||||
\(53\) | 62.9849i | 1.18839i | 0.804320 | + | 0.594197i | \(0.202530\pi\) | ||||
−0.804320 | + | 0.594197i | \(0.797470\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 109.862i | − 1.96183i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 14.0314 | 0.241921 | ||||||||
\(59\) | − 65.9058i | − 1.11705i | −0.829488 | − | 0.558524i | \(-0.811368\pi\) | ||||
0.829488 | − | 0.558524i | \(-0.188632\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −36.5562 | −0.599282 | −0.299641 | − | 0.954052i | \(-0.596867\pi\) | ||||
−0.299641 | + | 0.954052i | \(0.596867\pi\) | |||||||
\(62\) | − 22.7954i | − 0.367667i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −50.7089 | −0.792327 | ||||||||
\(65\) | − 13.6309i | − 0.209706i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 60.5815 | 0.904202 | 0.452101 | − | 0.891967i | \(-0.350675\pi\) | ||||
0.452101 | + | 0.891967i | \(0.350675\pi\) | |||||||
\(68\) | − 37.4225i | − 0.550331i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −90.8392 | −1.29770 | ||||||||
\(71\) | 49.1893i | 0.692807i | 0.938086 | + | 0.346404i | \(0.112597\pi\) | ||||
−0.938086 | + | 0.346404i | \(0.887403\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.37308 | −0.0873024 | −0.0436512 | − | 0.999047i | \(-0.513899\pi\) | ||||
−0.0436512 | + | 0.999047i | \(0.513899\pi\) | |||||||
\(74\) | − 25.3402i | − 0.342435i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −66.5643 | −0.875846 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −115.053 | −1.45637 | −0.728183 | − | 0.685383i | \(-0.759635\pi\) | ||||
−0.728183 | + | 0.685383i | \(0.759635\pi\) | |||||||
\(80\) | 13.1715i | 0.164644i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 18.0523 | 0.220150 | ||||||||
\(83\) | 40.4929i | 0.487867i | 0.969792 | + | 0.243933i | \(0.0784378\pi\) | ||||
−0.969792 | + | 0.243933i | \(0.921562\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −87.8828 | −1.03392 | ||||||||
\(86\) | 14.2379i | 0.165557i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 71.1308i | − 0.799222i | −0.916685 | − | 0.399611i | \(-0.869145\pi\) | ||||
0.916685 | − | 0.399611i | \(-0.130855\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 35.1619 | 0.386394 | ||||||||
\(92\) | − 33.7594i | − 0.366950i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 111.095 | 1.18186 | ||||||||
\(95\) | 156.319i | 1.64546i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.6682 | 0.192456 | 0.0962279 | − | 0.995359i | \(-0.469322\pi\) | ||||
0.0962279 | + | 0.995359i | \(0.469322\pi\) | |||||||
\(98\) | − 168.107i | − 1.71538i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.29947 | −0.0229947 | ||||||||
\(101\) | − 47.0627i | − 0.465967i | −0.972481 | − | 0.232983i | \(-0.925151\pi\) | ||||
0.972481 | − | 0.232983i | \(-0.0748488\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 111.438 | 1.08192 | 0.540960 | − | 0.841048i | \(-0.318061\pi\) | ||||
0.540960 | + | 0.841048i | \(0.318061\pi\) | |||||||
\(104\) | − 22.2785i | − 0.214217i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 85.1183 | 0.803003 | ||||||||
\(107\) | − 110.880i | − 1.03626i | −0.855301 | − | 0.518131i | \(-0.826628\pi\) | ||||
0.855301 | − | 0.518131i | \(-0.173372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −118.337 | −1.08566 | −0.542832 | − | 0.839841i | \(-0.682648\pi\) | ||||
−0.542832 | + | 0.839841i | \(0.682648\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −33.9768 | −0.303364 | ||||||||
\(113\) | − 69.3440i | − 0.613664i | −0.951764 | − | 0.306832i | \(-0.900731\pi\) | ||||
0.951764 | − | 0.306832i | \(-0.0992689\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −79.2805 | −0.689395 | ||||||||
\(116\) | 22.5691i | 0.194561i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −89.0657 | −0.754794 | ||||||||
\(119\) | − 226.700i | − 1.90504i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 49.4023i | 0.404937i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 36.6655 | 0.295690 | ||||||||
\(125\) | − 122.217i | − 0.977738i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.7748 | −0.0848412 | −0.0424206 | − | 0.999100i | \(-0.513507\pi\) | ||||
−0.0424206 | + | 0.999100i | \(0.513507\pi\) | |||||||
\(128\) | − 51.0145i | − 0.398550i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −18.4209 | −0.141699 | ||||||||
\(131\) | − 92.0724i | − 0.702843i | −0.936217 | − | 0.351421i | \(-0.885698\pi\) | ||||
0.936217 | − | 0.351421i | \(-0.114302\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −403.236 | −3.03185 | ||||||||
\(134\) | − 81.8704i | − 0.610973i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −143.637 | −1.05615 | ||||||||
\(137\) | 198.651i | 1.45001i | 0.688746 | + | 0.725003i | \(0.258162\pi\) | ||||
−0.688746 | + | 0.725003i | \(0.741838\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 59.5350 | 0.428310 | 0.214155 | − | 0.976800i | \(-0.431300\pi\) | ||||
0.214155 | + | 0.976800i | \(0.431300\pi\) | |||||||
\(140\) | − 146.112i | − 1.04365i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 66.4748 | 0.468133 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 53.0011 | 0.365525 | ||||||||
\(146\) | 8.61263i | 0.0589906i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 40.7588 | 0.275398 | ||||||||
\(149\) | 14.5644i | 0.0977477i | 0.998805 | + | 0.0488738i | \(0.0155632\pi\) | ||||
−0.998805 | + | 0.0488738i | \(0.984437\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 243.598 | 1.61323 | 0.806616 | − | 0.591076i | \(-0.201297\pi\) | ||||
0.806616 | + | 0.591076i | \(0.201297\pi\) | |||||||
\(152\) | 255.490i | 1.68086i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 86.1051i | − 0.555517i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −111.033 | −0.707218 | −0.353609 | − | 0.935393i | \(-0.615046\pi\) | ||||
−0.353609 | + | 0.935393i | \(0.615046\pi\) | |||||||
\(158\) | 155.483i | 0.984072i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −152.557 | −0.953484 | ||||||||
\(161\) | − 204.510i | − 1.27025i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 123.154 | 0.755546 | 0.377773 | − | 0.925898i | \(-0.376690\pi\) | ||||
0.377773 | + | 0.925898i | \(0.376690\pi\) | |||||||
\(164\) | 29.0365i | 0.177052i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 54.7225 | 0.329654 | ||||||||
\(167\) | − 229.010i | − 1.37132i | −0.727924 | − | 0.685658i | \(-0.759515\pi\) | ||||
0.727924 | − | 0.685658i | \(-0.240485\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −161.870 | −0.957809 | ||||||||
\(170\) | 118.766i | 0.698621i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −22.9012 | −0.133147 | ||||||||
\(173\) | 172.678i | 0.998138i | 0.866562 | + | 0.499069i | \(0.166325\pi\) | ||||
−0.866562 | + | 0.499069i | \(0.833675\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.9298 | −0.0795991 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −96.1267 | −0.540038 | ||||||||
\(179\) | 182.492i | 1.01951i | 0.860320 | + | 0.509755i | \(0.170264\pi\) | ||||
−0.860320 | + | 0.509755i | \(0.829736\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 121.741 | 0.672600 | 0.336300 | − | 0.941755i | \(-0.390824\pi\) | ||||
0.336300 | + | 0.941755i | \(0.390824\pi\) | |||||||
\(182\) | − 47.5181i | − 0.261088i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −129.577 | −0.704224 | ||||||||
\(185\) | − 95.7178i | − 0.517394i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 178.692i | 0.950488i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 211.251 | 1.11185 | ||||||||
\(191\) | 314.416i | 1.64616i | 0.567926 | + | 0.823080i | \(0.307746\pi\) | ||||
−0.567926 | + | 0.823080i | \(0.692254\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −124.391 | −0.644511 | −0.322255 | − | 0.946653i | \(-0.604441\pi\) | ||||
−0.322255 | + | 0.946653i | \(0.604441\pi\) | |||||||
\(194\) | − 25.2284i | − 0.130043i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 270.395 | 1.37956 | ||||||||
\(197\) | 193.993i | 0.984738i | 0.870387 | + | 0.492369i | \(0.163869\pi\) | ||||
−0.870387 | + | 0.492369i | \(0.836131\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −67.6934 | −0.340168 | −0.170084 | − | 0.985430i | \(-0.554404\pi\) | ||||
−0.170084 | + | 0.985430i | \(0.554404\pi\) | |||||||
\(200\) | 8.82594i | 0.0441297i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −63.6009 | −0.314856 | ||||||||
\(203\) | 136.720i | 0.673498i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 68.1892 | 0.332630 | ||||||||
\(206\) | − 150.598i | − 0.731058i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.89002 | −0.0331251 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −75.0484 | −0.355679 | −0.177840 | − | 0.984059i | \(-0.556911\pi\) | ||||
−0.177840 | + | 0.984059i | \(0.556911\pi\) | |||||||
\(212\) | 136.910i | 0.645801i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −149.844 | −0.700207 | ||||||||
\(215\) | 53.7811i | 0.250145i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 222.114 | 1.02357 | ||||||||
\(218\) | 159.922i | 0.733588i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 45.9716i | − 0.208016i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.97825 | −0.0268083 | −0.0134042 | − | 0.999910i | \(-0.504267\pi\) | ||||
−0.0134042 | + | 0.999910i | \(0.504267\pi\) | |||||||
\(224\) | − 393.533i | − 1.75684i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −93.7121 | −0.414655 | ||||||||
\(227\) | 168.380i | 0.741762i | 0.928680 | + | 0.370881i | \(0.120944\pi\) | ||||
−0.928680 | + | 0.370881i | \(0.879056\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −352.188 | −1.53794 | −0.768969 | − | 0.639287i | \(-0.779230\pi\) | ||||
−0.768969 | + | 0.639287i | \(0.779230\pi\) | |||||||
\(230\) | 107.140i | 0.465827i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 86.6257 | 0.373387 | ||||||||
\(233\) | 356.092i | 1.52829i | 0.645043 | + | 0.764146i | \(0.276840\pi\) | ||||
−0.645043 | + | 0.764146i | \(0.723160\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 419.639 | 1.78570 | ||||||||
\(236\) | − 143.259i | − 0.607030i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −306.364 | −1.28725 | ||||||||
\(239\) | 17.4384i | 0.0729639i | 0.999334 | + | 0.0364820i | \(0.0116151\pi\) | ||||
−0.999334 | + | 0.0364820i | \(0.988385\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 98.6722 | 0.409428 | 0.204714 | − | 0.978822i | \(-0.434374\pi\) | ||||
0.204714 | + | 0.978822i | \(0.434374\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −79.4620 | −0.325664 | ||||||||
\(245\) | − 634.993i | − 2.59181i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −81.7707 | −0.331055 | ||||||||
\(248\) | − 140.732i | − 0.567466i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −165.165 | −0.660661 | ||||||||
\(251\) | − 177.305i | − 0.706394i | −0.935549 | − | 0.353197i | \(-0.885094\pi\) | ||||
0.935549 | − | 0.353197i | \(-0.114906\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 14.5612i | 0.0573275i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −271.777 | −1.06163 | ||||||||
\(257\) | 115.325i | 0.448735i | 0.974505 | + | 0.224367i | \(0.0720315\pi\) | ||||
−0.974505 | + | 0.224367i | \(0.927968\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 246.911 | 0.953324 | ||||||||
\(260\) | − 29.6294i | − 0.113959i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −124.427 | −0.474914 | ||||||||
\(263\) | − 236.953i | − 0.900964i | −0.892786 | − | 0.450482i | \(-0.851252\pi\) | ||||
0.892786 | − | 0.450482i | \(-0.148748\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 321.518 | 1.21328 | ||||||||
\(266\) | 544.937i | 2.04864i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 131.686 | 0.491365 | ||||||||
\(269\) | − 528.479i | − 1.96461i | −0.187297 | − | 0.982303i | \(-0.559973\pi\) | ||||
0.187297 | − | 0.982303i | \(-0.440027\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 178.936 | 0.660280 | 0.330140 | − | 0.943932i | \(-0.392904\pi\) | ||||
0.330140 | + | 0.943932i | \(0.392904\pi\) | |||||||
\(272\) | 44.4222i | 0.163317i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 268.458 | 0.979775 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 286.215 | 1.03327 | 0.516634 | − | 0.856206i | \(-0.327185\pi\) | ||||
0.516634 | + | 0.856206i | \(0.327185\pi\) | |||||||
\(278\) | − 80.4562i | − 0.289411i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −560.813 | −2.00290 | ||||||||
\(281\) | 253.434i | 0.901902i | 0.892549 | + | 0.450951i | \(0.148915\pi\) | ||||
−0.892549 | + | 0.450951i | \(0.851085\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 283.270 | 1.00095 | 0.500477 | − | 0.865750i | \(-0.333158\pi\) | ||||
0.500477 | + | 0.865750i | \(0.333158\pi\) | |||||||
\(284\) | 106.923i | 0.376488i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 175.899i | 0.612889i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.39394 | −0.0255846 | ||||||||
\(290\) | − 71.6261i | − 0.246986i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13.8531 | −0.0474422 | ||||||||
\(293\) | 299.293i | 1.02148i | 0.859736 | + | 0.510739i | \(0.170628\pi\) | ||||
−0.859736 | + | 0.510739i | \(0.829372\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −336.429 | −1.14044 | ||||||||
\(296\) | − 156.443i | − 0.528523i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 19.6825 | 0.0660485 | ||||||||
\(299\) | − 41.4717i | − 0.138701i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −138.732 | −0.460905 | ||||||||
\(302\) | − 329.200i | − 1.09007i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 79.0148 | 0.259917 | ||||||||
\(305\) | 186.608i | 0.611829i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −111.839 | −0.364296 | −0.182148 | − | 0.983271i | \(-0.558305\pi\) | ||||
−0.182148 | + | 0.983271i | \(0.558305\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −116.363 | −0.375365 | ||||||||
\(311\) | 356.284i | 1.14561i | 0.819692 | + | 0.572805i | \(0.194145\pi\) | ||||
−0.819692 | + | 0.572805i | \(0.805855\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 338.742 | 1.08224 | 0.541121 | − | 0.840945i | \(-0.318000\pi\) | ||||
0.541121 | + | 0.840945i | \(0.318000\pi\) | |||||||
\(314\) | 150.051i | 0.477870i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −250.090 | −0.791423 | ||||||||
\(317\) | − 404.642i | − 1.27647i | −0.769840 | − | 0.638237i | \(-0.779664\pi\) | ||||
0.769840 | − | 0.638237i | \(-0.220336\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 258.853i | 0.808917i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −276.376 | −0.858311 | ||||||||
\(323\) | 527.202i | 1.63221i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.82478 | −0.00869162 | ||||||||
\(326\) | − 166.431i | − 0.510526i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 111.450 | 0.339785 | ||||||||
\(329\) | 1082.49i | 3.29024i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 634.065 | 1.91561 | 0.957803 | − | 0.287426i | \(-0.0927995\pi\) | ||||
0.957803 | + | 0.287426i | \(0.0927995\pi\) | |||||||
\(332\) | 88.0193i | 0.265118i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −309.486 | −0.926604 | ||||||||
\(335\) | − 309.250i | − 0.923134i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −237.412 | −0.704488 | −0.352244 | − | 0.935908i | \(-0.614581\pi\) | ||||
−0.352244 | + | 0.935908i | \(0.614581\pi\) | |||||||
\(338\) | 218.752i | 0.647195i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −191.030 | −0.561854 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 992.782 | 2.89441 | ||||||||
\(344\) | 87.9007i | 0.255525i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 233.358 | 0.674446 | ||||||||
\(347\) | − 487.484i | − 1.40485i | −0.711757 | − | 0.702426i | \(-0.752100\pi\) | ||||
0.711757 | − | 0.702426i | \(-0.247900\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −38.0498 | −0.109025 | −0.0545126 | − | 0.998513i | \(-0.517361\pi\) | ||||
−0.0545126 | + | 0.998513i | \(0.517361\pi\) | |||||||
\(350\) | 18.8249i | 0.0537855i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 90.5379i | 0.256481i | 0.991743 | + | 0.128241i | \(0.0409330\pi\) | ||||
−0.991743 | + | 0.128241i | \(0.959067\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 251.096 | 0.707313 | ||||||||
\(356\) | − 154.617i | − 0.434316i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 246.621 | 0.688887 | ||||||||
\(359\) | 111.987i | 0.311941i | 0.987762 | + | 0.155971i | \(0.0498505\pi\) | ||||
−0.987762 | + | 0.155971i | \(0.950150\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 576.747 | 1.59764 | ||||||||
\(362\) | − 164.521i | − 0.454478i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 76.4312 | 0.209976 | ||||||||
\(365\) | 32.5326i | 0.0891304i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 338.791 | 0.923137 | 0.461568 | − | 0.887105i | \(-0.347287\pi\) | ||||
0.461568 | + | 0.887105i | \(0.347287\pi\) | |||||||
\(368\) | 40.0740i | 0.108897i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −129.354 | −0.349605 | ||||||||
\(371\) | 829.380i | 2.23552i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 554.596 | 1.48685 | 0.743427 | − | 0.668818i | \(-0.233199\pi\) | ||||
0.743427 | + | 0.668818i | \(0.233199\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 685.864 | 1.82411 | ||||||||
\(377\) | 27.7249i | 0.0735409i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −251.309 | −0.663084 | −0.331542 | − | 0.943440i | \(-0.607569\pi\) | ||||
−0.331542 | + | 0.943440i | \(0.607569\pi\) | |||||||
\(380\) | 339.790i | 0.894184i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 424.905 | 1.11232 | ||||||||
\(383\) | 514.214i | 1.34259i | 0.741188 | + | 0.671297i | \(0.234263\pi\) | ||||
−0.741188 | + | 0.671297i | \(0.765737\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 168.102i | 0.435499i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 40.5790 | 0.104585 | ||||||||
\(389\) | − 194.151i | − 0.499102i | −0.968362 | − | 0.249551i | \(-0.919717\pi\) | ||||
0.968362 | − | 0.249551i | \(-0.0802830\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −267.382 | −0.683840 | ||||||||
\(392\) | − 1037.84i | − 2.64756i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 262.164 | 0.665392 | ||||||||
\(395\) | 587.309i | 1.48686i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −260.248 | −0.655537 | −0.327769 | − | 0.944758i | \(-0.606297\pi\) | ||||
−0.327769 | + | 0.944758i | \(0.606297\pi\) | |||||||
\(398\) | 91.4815i | 0.229853i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.72957 | 0.00682393 | ||||||||
\(401\) | 379.370i | 0.946059i | 0.881047 | + | 0.473029i | \(0.156840\pi\) | ||||
−0.881047 | + | 0.473029i | \(0.843160\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 45.0417 | 0.111766 | ||||||||
\(404\) | − 102.300i | − 0.253217i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 184.765 | 0.455085 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −682.061 | −1.66763 | −0.833815 | − | 0.552044i | \(-0.813848\pi\) | ||||
−0.833815 | + | 0.552044i | \(0.813848\pi\) | |||||||
\(410\) | − 92.1515i | − 0.224760i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 242.232 | 0.587941 | ||||||||
\(413\) | − 867.842i | − 2.10131i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 206.704 | 0.498082 | ||||||||
\(416\) | − 79.8030i | − 0.191834i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 275.319i | 0.657085i | 0.944489 | + | 0.328543i | \(0.106557\pi\) | ||||
−0.944489 | + | 0.328543i | \(0.893443\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 121.470 | 0.288527 | 0.144263 | − | 0.989539i | \(-0.453919\pi\) | ||||
0.144263 | + | 0.989539i | \(0.453919\pi\) | |||||||
\(422\) | 101.421i | 0.240334i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 525.494 | 1.23937 | ||||||||
\(425\) | 18.2123i | 0.0428524i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −481.369 | −1.12733 | ||||||||
\(428\) | − 241.019i | − 0.563130i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 72.6803 | 0.169024 | ||||||||
\(431\) | 98.7461i | 0.229109i | 0.993417 | + | 0.114555i | \(0.0365441\pi\) | ||||
−0.993417 | + | 0.114555i | \(0.963456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 559.992 | 1.29328 | 0.646642 | − | 0.762794i | \(-0.276173\pi\) | ||||
0.646642 | + | 0.762794i | \(0.276173\pi\) | |||||||
\(434\) | − 300.167i | − 0.691630i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −257.230 | −0.589976 | ||||||||
\(437\) | 475.597i | 1.08832i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 577.439 | 1.31535 | 0.657676 | − | 0.753301i | \(-0.271540\pi\) | ||||
0.657676 | + | 0.753301i | \(0.271540\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −62.1264 | −0.140558 | ||||||||
\(443\) | − 87.3800i | − 0.197246i | −0.995125 | − | 0.0986230i | \(-0.968556\pi\) | ||||
0.995125 | − | 0.0986230i | \(-0.0314438\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −363.101 | −0.815956 | ||||||||
\(446\) | 8.07906i | 0.0181145i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −667.731 | −1.49047 | ||||||||
\(449\) | − 96.2092i | − 0.214274i | −0.994244 | − | 0.107137i | \(-0.965832\pi\) | ||||
0.994244 | − | 0.107137i | \(-0.0341684\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 150.733i | − 0.333479i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 227.550 | 0.501212 | ||||||||
\(455\) | − 179.490i | − 0.394485i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 691.788 | 1.51376 | 0.756879 | − | 0.653555i | \(-0.226723\pi\) | ||||
0.756879 | + | 0.653555i | \(0.226723\pi\) | |||||||
\(458\) | 475.949i | 1.03919i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −172.332 | −0.374634 | ||||||||
\(461\) | − 70.5491i | − 0.153035i | −0.997068 | − | 0.0765175i | \(-0.975620\pi\) | ||||
0.997068 | − | 0.0765175i | \(-0.0243801\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 248.292 | 0.536267 | 0.268134 | − | 0.963382i | \(-0.413593\pi\) | ||||
0.268134 | + | 0.963382i | \(0.413593\pi\) | |||||||
\(464\) | − 26.7905i | − 0.0577381i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 481.226 | 1.03267 | ||||||||
\(467\) | − 254.158i | − 0.544235i | −0.962264 | − | 0.272118i | \(-0.912276\pi\) | ||||
0.962264 | − | 0.272118i | \(-0.0877240\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 797.732 | 1.70092 | ||||||||
\(470\) | − 567.103i | − 1.20660i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −549.864 | −1.16497 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.3946 | 0.0681991 | ||||||||
\(476\) | − 492.777i | − 1.03525i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 23.5664 | 0.0493020 | ||||||||
\(479\) | 18.2786i | 0.0381599i | 0.999818 | + | 0.0190800i | \(0.00607371\pi\) | ||||
−0.999818 | + | 0.0190800i | \(0.993926\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.0701 | 0.104096 | ||||||||
\(482\) | − 133.346i | − 0.276652i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 95.2954i | − 0.196485i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −243.375 | −0.499744 | −0.249872 | − | 0.968279i | \(-0.580389\pi\) | ||||
−0.249872 | + | 0.968279i | \(0.580389\pi\) | |||||||
\(488\) | 304.995i | 0.624990i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −858.135 | −1.75130 | ||||||||
\(491\) | 316.374i | 0.644347i | 0.946681 | + | 0.322173i | \(0.104413\pi\) | ||||
−0.946681 | + | 0.322173i | \(0.895587\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 178.752 | 0.362579 | ||||||||
\(494\) | 110.506i | 0.223696i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −43.5236 | −0.0877493 | ||||||||
\(497\) | 647.721i | 1.30326i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.8038 | 0.0537149 | 0.0268575 | − | 0.999639i | \(-0.491450\pi\) | ||||
0.0268575 | + | 0.999639i | \(0.491450\pi\) | |||||||
\(500\) | − 265.663i | − 0.531326i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −239.611 | −0.477314 | ||||||||
\(503\) | − 182.625i | − 0.363071i | −0.983384 | − | 0.181535i | \(-0.941893\pi\) | ||||
0.983384 | − | 0.181535i | \(-0.0581067\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −240.240 | −0.475723 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23.4212 | −0.0461047 | ||||||||
\(509\) | − 216.345i | − 0.425040i | −0.977157 | − | 0.212520i | \(-0.931833\pi\) | ||||
0.977157 | − | 0.212520i | \(-0.0681670\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −83.9201 | −0.164227 | ||||||||
\(512\) | 163.224i | 0.318797i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 155.851 | 0.303212 | ||||||||
\(515\) | − 568.855i | − 1.10457i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − 333.678i | − 0.644165i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −113.725 | −0.218702 | ||||||||
\(521\) | 571.189i | 1.09633i | 0.836370 | + | 0.548166i | \(0.184674\pi\) | ||||
−0.836370 | + | 0.548166i | \(0.815326\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −767.452 | −1.46740 | −0.733702 | − | 0.679472i | \(-0.762209\pi\) | ||||
−0.733702 | + | 0.679472i | \(0.762209\pi\) | |||||||
\(524\) | − 200.137i | − 0.381941i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −320.221 | −0.608785 | ||||||||
\(527\) | − 290.398i | − 0.551041i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 287.791 | 0.544028 | ||||||||
\(530\) | − 434.503i | − 0.819816i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −876.513 | −1.64758 | ||||||||
\(533\) | 35.6699i | 0.0669228i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −566.008 | −1.05796 | ||||||||
\(536\) | − 505.443i | − 0.942990i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −714.191 | −1.32749 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −205.807 | −0.380420 | −0.190210 | − | 0.981743i | \(-0.560917\pi\) | ||||
−0.190210 | + | 0.981743i | \(0.560917\pi\) | |||||||
\(542\) | − 241.815i | − 0.446154i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −514.516 | −0.945801 | ||||||||
\(545\) | 604.076i | 1.10840i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −435.348 | −0.795883 | −0.397942 | − | 0.917411i | \(-0.630275\pi\) | ||||
−0.397942 | + | 0.917411i | \(0.630275\pi\) | |||||||
\(548\) | 431.806i | 0.787968i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 317.949i | − 0.577040i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1515.01 | −2.73961 | ||||||||
\(554\) | − 386.794i | − 0.698184i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 129.411 | 0.232754 | ||||||||
\(557\) | 738.780i | 1.32636i | 0.748462 | + | 0.663178i | \(0.230793\pi\) | ||||
−0.748462 | + | 0.663178i | \(0.769207\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.1330 | −0.0503273 | ||||||||
\(560\) | 173.441i | 0.309716i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 342.493 | 0.609419 | ||||||||
\(563\) | − 65.8590i | − 0.116979i | −0.998288 | − | 0.0584893i | \(-0.981372\pi\) | ||||
0.998288 | − | 0.0584893i | \(-0.0186284\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −353.980 | −0.626513 | ||||||||
\(566\) | − 382.813i | − 0.676348i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 410.395 | 0.722527 | ||||||||
\(569\) | − 697.641i | − 1.22608i | −0.790051 | − | 0.613041i | \(-0.789946\pi\) | ||||
0.790051 | − | 0.613041i | \(-0.210054\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 256.388 | 0.449017 | 0.224508 | − | 0.974472i | \(-0.427922\pi\) | ||||
0.224508 | + | 0.974472i | \(0.427922\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 237.711 | 0.414132 | ||||||||
\(575\) | 16.4296i | 0.0285732i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 454.911 | 0.788407 | 0.394203 | − | 0.919023i | \(-0.371021\pi\) | ||||
0.394203 | + | 0.919023i | \(0.371021\pi\) | |||||||
\(578\) | 9.99223i | 0.0172876i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 115.208 | 0.198635 | ||||||||
\(581\) | 533.207i | 0.917741i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 53.1718i | 0.0910475i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 404.467 | 0.690217 | ||||||||
\(587\) | 110.294i | 0.187894i | 0.995577 | + | 0.0939470i | \(0.0299484\pi\) | ||||
−0.995577 | + | 0.0939470i | \(0.970052\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −516.538 | −0.876975 | ||||||||
\(590\) | 454.653i | 0.770598i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −48.3826 | −0.0817273 | ||||||||
\(593\) | − 250.416i | − 0.422287i | −0.977455 | − | 0.211144i | \(-0.932281\pi\) | ||||
0.977455 | − | 0.211144i | \(-0.0677188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1157.23 | −1.94493 | ||||||||
\(596\) | 31.6586i | 0.0531184i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −56.0452 | −0.0937211 | ||||||||
\(599\) | 285.443i | 0.476533i | 0.971200 | + | 0.238267i | \(0.0765792\pi\) | ||||
−0.971200 | + | 0.238267i | \(0.923421\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 223.484 | 0.371854 | 0.185927 | − | 0.982564i | \(-0.440471\pi\) | ||||
0.185927 | + | 0.982564i | \(0.440471\pi\) | |||||||
\(602\) | 187.484i | 0.311435i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 529.508 | 0.876668 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −954.863 | −1.57309 | −0.786543 | − | 0.617536i | \(-0.788131\pi\) | ||||
−0.786543 | + | 0.617536i | \(0.788131\pi\) | |||||||
\(608\) | 915.180i | 1.50523i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 252.184 | 0.413416 | ||||||||
\(611\) | 219.513i | 0.359269i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 340.137 | 0.554872 | 0.277436 | − | 0.960744i | \(-0.410515\pi\) | ||||
0.277436 | + | 0.960744i | \(0.410515\pi\) | |||||||
\(614\) | 151.140i | 0.246156i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 812.456i | 1.31678i | 0.752675 | + | 0.658392i | \(0.228763\pi\) | ||||
−0.752675 | + | 0.658392i | \(0.771237\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 913.830 | 1.47630 | 0.738150 | − | 0.674636i | \(-0.235699\pi\) | ||||
0.738150 | + | 0.674636i | \(0.235699\pi\) | |||||||
\(620\) | − 187.166i | − 0.301881i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 481.486 | 0.774093 | ||||||||
\(623\) | − 936.644i | − 1.50344i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −650.327 | −1.04052 | ||||||||
\(626\) | − 457.779i | − 0.731276i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −241.352 | −0.384319 | ||||||||
\(629\) | − 322.818i | − 0.513224i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −603.870 | −0.957005 | −0.478502 | − | 0.878086i | \(-0.658820\pi\) | ||||
−0.478502 | + | 0.878086i | \(0.658820\pi\) | |||||||
\(632\) | 959.907i | 1.51884i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −546.837 | −0.862518 | ||||||||
\(635\) | 55.0021i | 0.0866176i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 332.165 | 0.521453 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −260.413 | −0.406895 | ||||||||
\(641\) | 1077.99i | 1.68174i | 0.541241 | + | 0.840868i | \(0.317955\pi\) | ||||
−0.541241 | + | 0.840868i | \(0.682045\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 384.547 | 0.598052 | 0.299026 | − | 0.954245i | \(-0.403338\pi\) | ||||
0.299026 | + | 0.954245i | \(0.403338\pi\) | |||||||
\(644\) | − 444.542i | − 0.690282i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 712.466 | 1.10289 | ||||||||
\(647\) | − 595.205i | − 0.919946i | −0.887933 | − | 0.459973i | \(-0.847859\pi\) | ||||
0.887933 | − | 0.459973i | \(-0.152141\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.81743i | 0.00587297i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 267.699 | 0.410582 | ||||||||
\(653\) | 418.619i | 0.641071i | 0.947237 | + | 0.320535i | \(0.103863\pi\) | ||||
−0.947237 | + | 0.320535i | \(0.896137\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −470.001 | −0.717559 | ||||||||
\(656\) | − 34.4677i | − 0.0525422i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1462.88 | 2.22323 | ||||||||
\(659\) | − 1112.39i | − 1.68800i | −0.536347 | − | 0.843998i | \(-0.680196\pi\) | ||||
0.536347 | − | 0.843998i | \(-0.319804\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −736.025 | −1.11350 | −0.556751 | − | 0.830679i | \(-0.687952\pi\) | ||||
−0.556751 | + | 0.830679i | \(0.687952\pi\) | |||||||
\(662\) | − 856.882i | − 1.29438i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 337.840 | 0.508795 | ||||||||
\(665\) | 2058.40i | 3.09533i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 161.255 | 0.241761 | ||||||||
\(668\) | − 497.797i | − 0.745206i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −417.923 | −0.623765 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −545.629 | −0.810742 | −0.405371 | − | 0.914152i | \(-0.632858\pi\) | ||||
−0.405371 | + | 0.914152i | \(0.632858\pi\) | |||||||
\(674\) | 320.841i | 0.476025i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −351.855 | −0.520496 | ||||||||
\(677\) | 984.875i | 1.45476i | 0.686233 | + | 0.727382i | \(0.259263\pi\) | ||||
−0.686233 | + | 0.727382i | \(0.740737\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 245.821 | 0.362034 | ||||||||
\(680\) | 733.223i | 1.07827i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 924.817i | − 1.35405i | −0.735959 | − | 0.677026i | \(-0.763269\pi\) | ||||
0.735959 | − | 0.677026i | \(-0.236731\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1014.05 | 1.48037 | ||||||||
\(686\) | − 1341.65i | − 1.95576i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 27.1848 | 0.0395128 | ||||||||
\(689\) | 168.187i | 0.244102i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −79.1299 | −0.114515 | −0.0572575 | − | 0.998359i | \(-0.518236\pi\) | ||||
−0.0572575 | + | 0.998359i | \(0.518236\pi\) | |||||||
\(692\) | 375.349i | 0.542412i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −658.790 | −0.949265 | ||||||||
\(695\) | − 303.908i | − 0.437278i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 229.975 | 0.329950 | ||||||||
\(698\) | 51.4208i | 0.0736688i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −30.2792 | −0.0432560 | ||||||||
\(701\) | 1232.29i | 1.75790i | 0.476912 | + | 0.878951i | \(0.341756\pi\) | ||||
−0.476912 | + | 0.878951i | \(0.658244\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −574.204 | −0.816791 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 122.354 | 0.173306 | ||||||||
\(707\) | − 619.717i | − 0.876545i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −267.568 | −0.377388 | −0.188694 | − | 0.982036i | \(-0.560425\pi\) | ||||
−0.188694 | + | 0.982036i | \(0.560425\pi\) | |||||||
\(710\) | − 339.333i | − 0.477934i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −593.457 | −0.833507 | ||||||||
\(713\) | − 261.973i | − 0.367423i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 396.682i | 0.554025i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 151.340 | 0.210780 | ||||||||
\(719\) | − 686.620i | − 0.954965i | −0.878641 | − | 0.477482i | \(-0.841549\pi\) | ||||
0.878641 | − | 0.477482i | \(-0.158451\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1467.40 | 2.03523 | ||||||||
\(722\) | − 779.420i | − 1.07953i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 264.627 | 0.365507 | ||||||||
\(725\) | − 10.9836i | − 0.0151498i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1265.58 | −1.74082 | −0.870410 | − | 0.492327i | \(-0.836146\pi\) | ||||
−0.870410 | + | 0.492327i | \(0.836146\pi\) | |||||||
\(728\) | − 293.362i | − 0.402970i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 43.9648 | 0.0602258 | ||||||||
\(731\) | 181.382i | 0.248129i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −99.5964 | −0.135875 | −0.0679375 | − | 0.997690i | \(-0.521642\pi\) | ||||
−0.0679375 | + | 0.997690i | \(0.521642\pi\) | |||||||
\(734\) | − 457.845i | − 0.623767i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −464.152 | −0.630642 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 320.536 | 0.433743 | 0.216872 | − | 0.976200i | \(-0.430415\pi\) | ||||
0.216872 | + | 0.976200i | \(0.430415\pi\) | |||||||
\(740\) | − 208.061i | − 0.281164i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1120.83 | 1.51055 | ||||||||
\(743\) | 54.6611i | 0.0735681i | 0.999323 | + | 0.0367840i | \(0.0117114\pi\) | ||||
−0.999323 | + | 0.0367840i | \(0.988289\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 74.3468 | 0.0997943 | ||||||||
\(746\) | − 749.486i | − 1.00467i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1460.06i | − 1.94935i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 145.039 | 0.193128 | 0.0965641 | − | 0.995327i | \(-0.469215\pi\) | ||||
0.0965641 | + | 0.995327i | \(0.469215\pi\) | |||||||
\(752\) | − 212.115i | − 0.282068i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 37.4677 | 0.0496919 | ||||||||
\(755\) | − 1243.49i | − 1.64701i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 261.648 | 0.345638 | 0.172819 | − | 0.984954i | \(-0.444712\pi\) | ||||
0.172819 | + | 0.984954i | \(0.444712\pi\) | |||||||
\(758\) | 339.621i | 0.448049i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1304.20 | 1.71605 | ||||||||
\(761\) | − 1004.63i | − 1.32014i | −0.751204 | − | 0.660070i | \(-0.770527\pi\) | ||||
0.751204 | − | 0.660070i | \(-0.229473\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1558.26 | −2.04228 | ||||||||
\(764\) | 683.445i | 0.894562i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 694.913 | 0.907197 | ||||||||
\(767\) | − 175.986i | − 0.229448i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1067.91 | −1.38869 | −0.694347 | − | 0.719641i | \(-0.744307\pi\) | ||||
−0.694347 | + | 0.719641i | \(0.744307\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −270.387 | −0.350242 | ||||||||
\(773\) | − 177.483i | − 0.229603i | −0.993388 | − | 0.114801i | \(-0.963377\pi\) | ||||
0.993388 | − | 0.114801i | \(-0.0366232\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.8439 | −0.0230243 | ||||||||
\(776\) | − 155.752i | − 0.200712i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −262.377 | −0.337245 | ||||||||
\(779\) | − 409.062i | − 0.525112i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 361.342i | 0.462074i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −320.970 | −0.409401 | ||||||||
\(785\) | 566.790i | 0.722026i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −660.507 | −0.839271 | −0.419636 | − | 0.907693i | \(-0.637842\pi\) | ||||
−0.419636 | + | 0.907693i | \(0.637842\pi\) | |||||||
\(788\) | 421.682i | 0.535130i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 793.695 | 1.00468 | ||||||||
\(791\) | − 913.116i | − 1.15438i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −97.6148 | −0.123096 | ||||||||
\(794\) | 351.702i | 0.442949i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −147.145 | −0.184855 | ||||||||
\(797\) | − 398.568i | − 0.500086i | −0.968235 | − | 0.250043i | \(-0.919555\pi\) | ||||
0.968235 | − | 0.250043i | \(-0.0804447\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1415.27 | 1.77131 | ||||||||
\(800\) | 31.6150i | 0.0395188i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 512.683 | 0.639256 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1043.96 | −1.29684 | ||||||||
\(806\) | − 60.8697i | − 0.0755207i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −392.652 | −0.485956 | ||||||||
\(809\) | 752.975i | 0.930748i | 0.885114 | + | 0.465374i | \(0.154080\pi\) | ||||
−0.885114 | + | 0.465374i | \(0.845920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1002.83 | −1.23654 | −0.618270 | − | 0.785966i | \(-0.712166\pi\) | ||||
−0.618270 | + | 0.785966i | \(0.712166\pi\) | |||||||
\(812\) | 297.188i | 0.365995i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 628.663i | − 0.771366i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 322.629 | 0.394895 | ||||||||
\(818\) | 921.743i | 1.12683i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 148.223 | 0.180759 | ||||||||
\(821\) | 1368.74i | 1.66717i | 0.552394 | + | 0.833583i | \(0.313714\pi\) | ||||
−0.552394 | + | 0.833583i | \(0.686286\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1395.78 | −1.69597 | −0.847985 | − | 0.530019i | \(-0.822185\pi\) | ||||
−0.847985 | + | 0.530019i | \(0.822185\pi\) | |||||||
\(824\) | − 929.746i | − 1.12833i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1172.81 | −1.41987 | ||||||||
\(827\) | 202.834i | 0.245265i | 0.992452 | + | 0.122632i | \(0.0391336\pi\) | ||||
−0.992452 | + | 0.122632i | \(0.960866\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 569.961 | 0.687528 | 0.343764 | − | 0.939056i | \(-0.388298\pi\) | ||||
0.343764 | + | 0.939056i | \(0.388298\pi\) | |||||||
\(830\) | − 279.341i | − 0.336556i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −135.406 | −0.162748 | ||||||||
\(833\) | − 2141.58i | − 2.57092i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1169.02 | −1.40003 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 372.068 | 0.443995 | ||||||||
\(839\) | − 129.965i | − 0.154904i | −0.996996 | − | 0.0774522i | \(-0.975321\pi\) | ||||
0.996996 | − | 0.0774522i | \(-0.0246785\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 733.197 | 0.871816 | ||||||||
\(842\) | − 164.155i | − 0.194959i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −163.132 | −0.193285 | ||||||||
\(845\) | 826.294i | 0.977863i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 162.518i | − 0.191649i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.6122 | 0.0289555 | ||||||||
\(851\) | − 291.219i | − 0.342208i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −322.301 | −0.377844 | −0.188922 | − | 0.981992i | \(-0.560499\pi\) | ||||
−0.188922 | + | 0.981992i | \(0.560499\pi\) | |||||||
\(854\) | 650.526i | 0.761740i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −925.093 | −1.08072 | ||||||||
\(857\) | − 634.845i | − 0.740776i | −0.928877 | − | 0.370388i | \(-0.879225\pi\) | ||||
0.928877 | − | 0.370388i | \(-0.120775\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1658.25 | 1.93044 | 0.965219 | − | 0.261443i | \(-0.0841984\pi\) | ||||
0.965219 | + | 0.261443i | \(0.0841984\pi\) | |||||||
\(860\) | 116.904i | 0.135935i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 133.446 | 0.154810 | ||||||||
\(863\) | − 862.333i | − 0.999227i | −0.866249 | − | 0.499613i | \(-0.833475\pi\) | ||||
0.866249 | − | 0.499613i | \(-0.166525\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 881.467 | 1.01904 | ||||||||
\(866\) | − 756.778i | − 0.873877i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 482.809 | 0.556231 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 161.769 | 0.185728 | ||||||||
\(872\) | 987.311i | 1.13224i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 642.726 | 0.735385 | ||||||||
\(875\) | − 1609.35i | − 1.83925i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −685.376 | −0.781500 | −0.390750 | − | 0.920497i | \(-0.627784\pi\) | ||||
−0.390750 | + | 0.920497i | \(0.627784\pi\) | |||||||
\(878\) | − 780.357i | − 0.888789i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 551.003i | 0.625429i | 0.949847 | + | 0.312715i | \(0.101238\pi\) | ||||
−0.949847 | + | 0.312715i | \(0.898762\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1592.69 | −1.80373 | −0.901863 | − | 0.432022i | \(-0.857800\pi\) | ||||
−0.901863 | + | 0.432022i | \(0.857800\pi\) | |||||||
\(884\) | − 99.9282i | − 0.113041i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −118.086 | −0.133280 | ||||||||
\(887\) | 384.029i | 0.432952i | 0.976288 | + | 0.216476i | \(0.0694564\pi\) | ||||
−0.976288 | + | 0.216476i | \(0.930544\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −141.882 | −0.159597 | ||||||||
\(890\) | 490.697i | 0.551345i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.9949 | −0.0145683 | ||||||||
\(893\) | − 2517.38i | − 2.81902i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 931.566 | 1.04086 | ||||||||
\(896\) | − 671.754i | − 0.749725i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −130.018 | −0.144786 | ||||||||
\(899\) | 175.136i | 0.194812i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1084.35 | 1.20350 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −578.550 | −0.639989 | ||||||||
\(905\) | − 621.448i | − 0.686682i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1417.57 | −1.56292 | −0.781462 | − | 0.623953i | \(-0.785526\pi\) | ||||
−0.781462 | + | 0.623953i | \(0.785526\pi\) | |||||||
\(908\) | 366.007i | 0.403091i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −242.565 | −0.266555 | ||||||||
\(911\) | 874.814i | 0.960278i | 0.877192 | + | 0.480139i | \(0.159414\pi\) | ||||
−0.877192 | + | 0.480139i | \(0.840586\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − 934.888i | − 1.02285i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −765.548 | −0.835751 | ||||||||
\(917\) | − 1212.40i | − 1.32214i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1162.91 | 1.26541 | 0.632705 | − | 0.774393i | \(-0.281945\pi\) | ||||
0.632705 | + | 0.774393i | \(0.281945\pi\) | |||||||
\(920\) | 661.451i | 0.718969i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −95.3407 | −0.103406 | ||||||||
\(923\) | 131.349i | 0.142306i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.8359 | −0.0214443 | ||||||||
\(926\) | − 335.544i | − 0.362358i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 310.298 | 0.334373 | ||||||||
\(929\) | 554.284i | 0.596646i | 0.954465 | + | 0.298323i | \(0.0964273\pi\) | ||||
−0.954465 | + | 0.298323i | \(0.903573\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3809.27 | −4.09159 | ||||||||
\(932\) | 774.036i | 0.830511i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −343.471 | −0.367742 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 857.873 | 0.915553 | 0.457776 | − | 0.889067i | \(-0.348646\pi\) | ||||
0.457776 | + | 0.889067i | \(0.348646\pi\) | |||||||
\(938\) | − 1078.06i | − 1.14932i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 912.166 | 0.970390 | ||||||||
\(941\) | 337.080i | 0.358214i | 0.983830 | + | 0.179107i | \(0.0573209\pi\) | ||||
−0.983830 | + | 0.179107i | \(0.942679\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 207.464 | 0.220004 | ||||||||
\(944\) | 170.055i | 0.180143i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 405.388i | 0.428076i | 0.976825 | + | 0.214038i | \(0.0686616\pi\) | ||||
−0.976825 | + | 0.214038i | \(0.931338\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.0178 | −0.0179324 | ||||||||
\(950\) | − 43.7783i | − 0.0460824i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1891.40 | −1.98677 | ||||||||
\(953\) | 747.947i | 0.784834i | 0.919787 | + | 0.392417i | \(0.128361\pi\) | ||||
−0.919787 | + | 0.392417i | \(0.871639\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1605.00 | 1.68063 | ||||||||
\(956\) | 37.9057i | 0.0396503i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24.7019 | 0.0257848 | ||||||||
\(959\) | 2615.82i | 2.72765i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −676.476 | −0.703929 | ||||||||
\(962\) | − 67.6652i | − 0.0703380i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 214.483 | 0.222493 | ||||||||
\(965\) | 634.975i | 0.658005i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 284.479 | 0.294187 | 0.147094 | − | 0.989123i | \(-0.453008\pi\) | ||||
0.147094 | + | 0.989123i | \(0.453008\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −128.783 | −0.132766 | ||||||||
\(971\) | 1179.42i | 1.21464i | 0.794456 | + | 0.607322i | \(0.207756\pi\) | ||||
−0.794456 | + | 0.607322i | \(0.792244\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 783.952 | 0.805707 | ||||||||
\(974\) | 328.900i | 0.337679i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 94.3249 | 0.0966443 | ||||||||
\(977\) | − 13.6463i | − 0.0139676i | −0.999976 | − | 0.00698379i | \(-0.997777\pi\) | ||||
0.999976 | − | 0.00698379i | \(-0.00222303\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − 1380.28i | − 1.40845i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 427.551 | 0.435388 | ||||||||
\(983\) | 501.274i | 0.509943i | 0.966949 | + | 0.254971i | \(0.0820660\pi\) | ||||
−0.966949 | + | 0.254971i | \(0.917934\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 990.276 | 1.00536 | ||||||||
\(986\) | − 241.566i | − 0.244996i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −177.745 | −0.179903 | ||||||||
\(989\) | 163.628i | 0.165448i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 118.253 | 0.119327 | 0.0596635 | − | 0.998219i | \(-0.480997\pi\) | ||||
0.0596635 | + | 0.998219i | \(0.480997\pi\) | |||||||
\(992\) | − 504.108i | − 0.508173i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 875.335 | 0.880619 | ||||||||
\(995\) | 345.554i | 0.347290i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −495.885 | −0.497377 | −0.248689 | − | 0.968583i | \(-0.580000\pi\) | ||||
−0.248689 | + | 0.968583i | \(0.580000\pi\) | |||||||
\(998\) | − 36.2228i | − 0.0362954i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1089.3.b.j.485.6 | 16 | ||
3.2 | odd | 2 | inner | 1089.3.b.j.485.11 | 16 | ||
11.7 | odd | 10 | 99.3.l.a.71.3 | yes | 32 | ||
11.8 | odd | 10 | 99.3.l.a.53.6 | yes | 32 | ||
11.10 | odd | 2 | 1089.3.b.i.485.11 | 16 | |||
33.8 | even | 10 | 99.3.l.a.53.3 | ✓ | 32 | ||
33.29 | even | 10 | 99.3.l.a.71.6 | yes | 32 | ||
33.32 | even | 2 | 1089.3.b.i.485.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.3.l.a.53.3 | ✓ | 32 | 33.8 | even | 10 | ||
99.3.l.a.53.6 | yes | 32 | 11.8 | odd | 10 | ||
99.3.l.a.71.3 | yes | 32 | 11.7 | odd | 10 | ||
99.3.l.a.71.6 | yes | 32 | 33.29 | even | 10 | ||
1089.3.b.i.485.6 | 16 | 33.32 | even | 2 | |||
1089.3.b.i.485.11 | 16 | 11.10 | odd | 2 | |||
1089.3.b.j.485.6 | 16 | 1.1 | even | 1 | trivial | ||
1089.3.b.j.485.11 | 16 | 3.2 | odd | 2 | inner |