Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(440,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.440");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 440.7 | ||
Root | \(-0.382683 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.440 |
Dual form | 441.2.c.b.440.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.41421i | 1.70711i | 0.521005 | + | 0.853553i | \(0.325557\pi\) | ||||
−0.521005 | + | 0.853553i | \(0.674443\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.82843 | −1.91421 | ||||||||
\(5\) | −3.37849 | −1.51091 | −0.755454 | − | 0.655202i | \(-0.772584\pi\) | ||||
−0.755454 | + | 0.655202i | \(0.772584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 4.41421i | − 1.56066i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 8.15640i | − 2.57928i | ||||||||
\(11\) | 0.828427i | 0.249780i | 0.992171 | + | 0.124890i | \(0.0398578\pi\) | ||||
−0.992171 | + | 0.124890i | \(0.960142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.37849i | − 0.937025i | −0.883457 | − | 0.468513i | \(-0.844790\pi\) | ||||
0.883457 | − | 0.468513i | \(-0.155210\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −1.39942 | −0.339409 | −0.169704 | − | 0.985495i | \(-0.554281\pi\) | ||||
−0.169704 | + | 0.985495i | \(0.554281\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 6.75699i | − 1.55016i | −0.631864 | − | 0.775079i | \(-0.717710\pi\) | ||||
0.631864 | − | 0.775079i | \(-0.282290\pi\) | |||||||
\(20\) | 12.9343 | 2.89220 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 2.00000i | 0.417029i | 0.978019 | + | 0.208514i | \(0.0668628\pi\) | ||||
−0.978019 | + | 0.208514i | \(0.933137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.41421 | 1.28284 | ||||||||
\(26\) | 8.15640 | 1.59960 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 4.82843i | − 0.896616i | −0.893879 | − | 0.448308i | \(-0.852027\pi\) | ||||
0.893879 | − | 0.448308i | \(-0.147973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.75699i | 1.21359i | 0.794858 | + | 0.606795i | \(0.207545\pi\) | ||||
−0.794858 | + | 0.606795i | \(0.792455\pi\) | |||||||
\(32\) | − 1.58579i | − 0.280330i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 3.37849i | − 0.579407i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.58579 | −0.425101 | −0.212550 | − | 0.977150i | \(-0.568177\pi\) | ||||
−0.212550 | + | 0.977150i | \(0.568177\pi\) | |||||||
\(38\) | 16.3128 | 2.64629 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 14.9134i | 2.35801i | ||||||||
\(41\) | −8.15640 | −1.27382 | −0.636908 | − | 0.770940i | \(-0.719787\pi\) | ||||
−0.636908 | + | 0.770940i | \(0.719787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.4853 | −1.90399 | −0.951994 | − | 0.306117i | \(-0.900970\pi\) | ||||
−0.951994 | + | 0.306117i | \(0.900970\pi\) | |||||||
\(44\) | − 3.17157i | − 0.478133i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.82843 | −0.711913 | ||||||||
\(47\) | −6.75699 | −0.985608 | −0.492804 | − | 0.870140i | \(-0.664028\pi\) | ||||
−0.492804 | + | 0.870140i | \(0.664028\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 15.4853i | 2.18995i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 12.9343i | 1.79367i | ||||||||
\(53\) | − 7.07107i | − 0.971286i | −0.874157 | − | 0.485643i | \(-0.838586\pi\) | ||||
0.874157 | − | 0.485643i | \(-0.161414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2.79884i | − 0.377395i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.6569 | 1.53062 | ||||||||
\(59\) | −6.75699 | −0.879685 | −0.439842 | − | 0.898075i | \(-0.644966\pi\) | ||||
−0.439842 | + | 0.898075i | \(0.644966\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.15640i | 1.04432i | 0.852847 | + | 0.522160i | \(0.174874\pi\) | ||||
−0.852847 | + | 0.522160i | \(0.825126\pi\) | |||||||
\(62\) | −16.3128 | −2.07173 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 9.82843 | 1.22855 | ||||||||
\(65\) | 11.4142i | 1.41576i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.48528 | 1.03664 | 0.518321 | − | 0.855186i | \(-0.326557\pi\) | ||||
0.518321 | + | 0.855186i | \(0.326557\pi\) | |||||||
\(68\) | 5.35757 | 0.649701 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.82843i | 0.573029i | 0.958076 | + | 0.286514i | \(0.0924966\pi\) | ||||
−0.958076 | + | 0.286514i | \(0.907503\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.39942i | 0.163789i | 0.996641 | + | 0.0818947i | \(0.0260971\pi\) | ||||
−0.996641 | + | 0.0818947i | \(0.973903\pi\) | |||||||
\(74\) | − 6.24264i | − 0.725692i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 25.8686i | 2.96734i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.65685 | −1.08648 | −0.543240 | − | 0.839577i | \(-0.682803\pi\) | ||||
−0.543240 | + | 0.839577i | \(0.682803\pi\) | |||||||
\(80\) | −10.1355 | −1.13318 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 19.6913i | − 2.17454i | ||||||||
\(83\) | 13.5140 | 1.48335 | 0.741676 | − | 0.670759i | \(-0.234031\pi\) | ||||
0.741676 | + | 0.670759i | \(0.234031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.72792 | 0.512815 | ||||||||
\(86\) | − 30.1421i | − 3.25031i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.65685 | 0.389822 | ||||||||
\(89\) | −6.17733 | −0.654795 | −0.327398 | − | 0.944887i | \(-0.606172\pi\) | ||||
−0.327398 | + | 0.944887i | \(0.606172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 7.65685i | − 0.798282i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 16.3128i | − 1.68254i | ||||||||
\(95\) | 22.8284i | 2.34215i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1.39942i | − 0.142089i | −0.997473 | − | 0.0710447i | \(-0.977367\pi\) | ||||
0.997473 | − | 0.0710447i | \(-0.0226333\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −24.5563 | −2.45563 | ||||||||
\(101\) | −12.9343 | −1.28701 | −0.643506 | − | 0.765441i | \(-0.722521\pi\) | ||||
−0.643506 | + | 0.765441i | \(0.722521\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 2.79884i | − 0.275777i | −0.990448 | − | 0.137889i | \(-0.955968\pi\) | ||||
0.990448 | − | 0.137889i | \(-0.0440316\pi\) | |||||||
\(104\) | −14.9134 | −1.46238 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 17.0711 | 1.65809 | ||||||||
\(107\) | − 9.31371i | − 0.900390i | −0.892930 | − | 0.450195i | \(-0.851354\pi\) | ||||
0.892930 | − | 0.450195i | \(-0.148646\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.58579 | −0.247673 | −0.123837 | − | 0.992303i | \(-0.539520\pi\) | ||||
−0.123837 | + | 0.992303i | \(0.539520\pi\) | |||||||
\(110\) | 6.75699 | 0.644253 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 5.89949i | − 0.554978i | −0.960729 | − | 0.277489i | \(-0.910498\pi\) | ||||
0.960729 | − | 0.277489i | \(-0.0895022\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 6.75699i | − 0.630092i | ||||||||
\(116\) | 18.4853i | 1.71632i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 16.3128i | − 1.50172i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3137 | 0.937610 | ||||||||
\(122\) | −19.6913 | −1.78277 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 25.8686i | − 2.32307i | ||||||||
\(125\) | −4.77791 | −0.427349 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.485281 | −0.0430618 | −0.0215309 | − | 0.999768i | \(-0.506854\pi\) | ||||
−0.0215309 | + | 0.999768i | \(0.506854\pi\) | |||||||
\(128\) | 20.5563i | 1.81694i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −27.5563 | −2.41685 | ||||||||
\(131\) | 9.55582 | 0.834896 | 0.417448 | − | 0.908701i | \(-0.362925\pi\) | ||||
0.417448 | + | 0.908701i | \(0.362925\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 20.4853i | 1.76966i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.17733i | 0.529701i | ||||||||
\(137\) | − 0.828427i | − 0.0707773i | −0.999374 | − | 0.0353887i | \(-0.988733\pi\) | ||||
0.999374 | − | 0.0353887i | \(-0.0112669\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.55582i | 0.810514i | 0.914203 | + | 0.405257i | \(0.132818\pi\) | ||||
−0.914203 | + | 0.405257i | \(0.867182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.6569 | −0.978221 | ||||||||
\(143\) | 2.79884 | 0.234050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.3128i | 1.35470i | ||||||||
\(146\) | −3.37849 | −0.279606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.89949 | 0.813733 | ||||||||
\(149\) | 4.24264i | 0.347571i | 0.984784 | + | 0.173785i | \(0.0555999\pi\) | ||||
−0.984784 | + | 0.173785i | \(0.944400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.4853 | −1.01604 | −0.508019 | − | 0.861346i | \(-0.669622\pi\) | ||||
−0.508019 | + | 0.861346i | \(0.669622\pi\) | |||||||
\(152\) | −29.8268 | −2.41927 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 22.8284i | − 1.83362i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.33664i | 0.585528i | 0.956185 | + | 0.292764i | \(0.0945750\pi\) | ||||
−0.956185 | + | 0.292764i | \(0.905425\pi\) | |||||||
\(158\) | − 23.3137i | − 1.85474i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.35757i | 0.423553i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.8284 | 1.16145 | 0.580726 | − | 0.814099i | \(-0.302769\pi\) | ||||
0.580726 | + | 0.814099i | \(0.302769\pi\) | |||||||
\(164\) | 31.2262 | 2.43836 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 32.6256i | 2.53224i | ||||||||
\(167\) | −2.79884 | −0.216580 | −0.108290 | − | 0.994119i | \(-0.534538\pi\) | ||||
−0.108290 | + | 0.994119i | \(0.534538\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.58579 | 0.121984 | ||||||||
\(170\) | 11.4142i | 0.875430i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 47.7990 | 3.64464 | ||||||||
\(173\) | −8.15640 | −0.620120 | −0.310060 | − | 0.950717i | \(-0.600349\pi\) | ||||
−0.310060 | + | 0.950717i | \(0.600349\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.48528i | 0.187335i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 14.9134i | − 1.11781i | ||||||||
\(179\) | − 9.51472i | − 0.711163i | −0.934645 | − | 0.355582i | \(-0.884283\pi\) | ||||
0.934645 | − | 0.355582i | \(-0.115717\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.7122i | 1.31654i | 0.752782 | + | 0.658270i | \(0.228711\pi\) | ||||
−0.752782 | + | 0.658270i | \(0.771289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.82843 | 0.650840 | ||||||||
\(185\) | 8.73606 | 0.642288 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.15932i | − 0.0847775i | ||||||||
\(188\) | 25.8686 | 1.88666 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −55.1127 | −3.99830 | ||||||||
\(191\) | − 20.8284i | − 1.50709i | −0.657395 | − | 0.753546i | \(-0.728342\pi\) | ||||
0.657395 | − | 0.753546i | \(-0.271658\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.6569 | −1.27097 | −0.635484 | − | 0.772114i | \(-0.719199\pi\) | ||||
−0.635484 | + | 0.772114i | \(0.719199\pi\) | |||||||
\(194\) | 3.37849 | 0.242562 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.2426i | 1.15724i | 0.815597 | + | 0.578620i | \(0.196409\pi\) | ||||
−0.815597 | + | 0.578620i | \(0.803591\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.1116i | 1.35479i | 0.735620 | + | 0.677394i | \(0.236891\pi\) | ||||
−0.735620 | + | 0.677394i | \(0.763109\pi\) | |||||||
\(200\) | − 28.3137i | − 2.00208i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 31.2262i | − 2.19707i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 27.5563 | 1.92462 | ||||||||
\(206\) | 6.75699 | 0.470781 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 10.1355i | − 0.702769i | ||||||||
\(209\) | 5.59767 | 0.387199 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.31371 | 0.503496 | 0.251748 | − | 0.967793i | \(-0.418995\pi\) | ||||
0.251748 | + | 0.967793i | \(0.418995\pi\) | |||||||
\(212\) | 27.0711i | 1.85925i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 22.4853 | 1.53706 | ||||||||
\(215\) | 42.1814 | 2.87675 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 6.24264i | − 0.422805i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.7151i | 0.722414i | ||||||||
\(221\) | 4.72792i | 0.318034i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 23.0698i | − 1.54487i | −0.635095 | − | 0.772434i | \(-0.719039\pi\) | ||||
0.635095 | − | 0.772434i | \(-0.280961\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.2426 | 0.947406 | ||||||||
\(227\) | −2.79884 | −0.185765 | −0.0928826 | − | 0.995677i | \(-0.529608\pi\) | ||||
−0.0928826 | + | 0.995677i | \(0.529608\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.1146i | 0.800552i | 0.916395 | + | 0.400276i | \(0.131086\pi\) | ||||
−0.916395 | + | 0.400276i | \(0.868914\pi\) | |||||||
\(230\) | 16.3128 | 1.07563 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.3137 | −1.39931 | ||||||||
\(233\) | − 10.8284i | − 0.709394i | −0.934981 | − | 0.354697i | \(-0.884584\pi\) | ||||
0.934981 | − | 0.354697i | \(-0.115416\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.8284 | 1.48916 | ||||||||
\(236\) | 25.8686 | 1.68390 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 0.343146i | − 0.0221963i | −0.999938 | − | 0.0110981i | \(-0.996467\pi\) | ||||
0.999938 | − | 0.0110981i | \(-0.00353272\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 8.97616i | − 0.578205i | −0.957298 | − | 0.289103i | \(-0.906643\pi\) | ||||
0.957298 | − | 0.289103i | \(-0.0933569\pi\) | |||||||
\(242\) | 24.8995i | 1.60060i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 31.2262i | − 1.99905i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.8284 | −1.45254 | ||||||||
\(248\) | 29.8268 | 1.89400 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 11.5349i | − 0.729531i | ||||||||
\(251\) | 25.8686 | 1.63281 | 0.816407 | − | 0.577477i | \(-0.195963\pi\) | ||||
0.816407 | + | 0.577477i | \(0.195963\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.65685 | −0.104166 | ||||||||
\(254\) | − 1.17157i | − 0.0735110i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | −21.6704 | −1.35176 | −0.675880 | − | 0.737011i | \(-0.736236\pi\) | ||||
−0.675880 | + | 0.737011i | \(0.736236\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 43.6985i | − 2.71006i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 23.0698i | 1.42526i | ||||||||
\(263\) | 24.1421i | 1.48867i | 0.667808 | + | 0.744334i | \(0.267233\pi\) | ||||
−0.667808 | + | 0.744334i | \(0.732767\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.8896i | 1.46752i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −32.4853 | −1.98435 | ||||||||
\(269\) | 31.2262 | 1.90389 | 0.951947 | − | 0.306262i | \(-0.0990783\pi\) | ||||
0.951947 | + | 0.306262i | \(0.0990783\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.75699i | 0.410458i | 0.978714 | + | 0.205229i | \(0.0657939\pi\) | ||||
−0.978714 | + | 0.205229i | \(0.934206\pi\) | |||||||
\(272\) | −4.19825 | −0.254556 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | 5.31371i | 0.320429i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.9706 | −1.26000 | −0.630000 | − | 0.776596i | \(-0.716945\pi\) | ||||
−0.630000 | + | 0.776596i | \(0.716945\pi\) | |||||||
\(278\) | −23.0698 | −1.38363 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.8284i | 1.12321i | 0.827406 | + | 0.561605i | \(0.189816\pi\) | ||||
−0.827406 | + | 0.561605i | \(0.810184\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 29.8268i | − 1.77302i | −0.462711 | − | 0.886509i | \(-0.653123\pi\) | ||||
0.462711 | − | 0.886509i | \(-0.346877\pi\) | |||||||
\(284\) | − 18.4853i | − 1.09690i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.75699i | 0.399549i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0416 | −0.884802 | ||||||||
\(290\) | −39.3826 | −2.31263 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 5.35757i | − 0.313528i | ||||||||
\(293\) | −7.33664 | −0.428611 | −0.214306 | − | 0.976767i | \(-0.568749\pi\) | ||||
−0.214306 | + | 0.976767i | \(0.568749\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.8284 | 1.32912 | ||||||||
\(296\) | 11.4142i | 0.663438i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.2426 | −0.593340 | ||||||||
\(299\) | 6.75699 | 0.390767 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 30.1421i | − 1.73448i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 20.2710i | − 1.16262i | ||||||||
\(305\) | − 27.5563i | − 1.57787i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 12.3547i | − 0.705117i | −0.935790 | − | 0.352559i | \(-0.885312\pi\) | ||||
0.935790 | − | 0.352559i | \(-0.114688\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 55.1127 | 3.13019 | ||||||||
\(311\) | −10.7151 | −0.607600 | −0.303800 | − | 0.952736i | \(-0.598255\pi\) | ||||
−0.303800 | + | 0.952736i | \(0.598255\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 12.9343i | − 0.731091i | −0.930794 | − | 0.365545i | \(-0.880883\pi\) | ||||
0.930794 | − | 0.365545i | \(-0.119117\pi\) | |||||||
\(314\) | −17.7122 | −0.999559 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 36.9706 | 2.07976 | ||||||||
\(317\) | 23.7574i | 1.33435i | 0.744903 | + | 0.667173i | \(0.232496\pi\) | ||||
−0.744903 | + | 0.667173i | \(0.767504\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | 0.223957 | ||||||||
\(320\) | −33.2053 | −1.85623 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.45584i | 0.526137i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 21.6704i | − 1.20206i | ||||||||
\(326\) | 35.7990i | 1.98272i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 36.0041i | 1.98799i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.3431 | 0.568511 | 0.284255 | − | 0.958749i | \(-0.408254\pi\) | ||||
0.284255 | + | 0.958749i | \(0.408254\pi\) | |||||||
\(332\) | −51.7373 | −2.83945 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 6.75699i | − 0.369726i | ||||||||
\(335\) | −28.6675 | −1.56627 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.9289 | −0.704284 | −0.352142 | − | 0.935947i | \(-0.614547\pi\) | ||||
−0.352142 | + | 0.935947i | \(0.614547\pi\) | |||||||
\(338\) | 3.82843i | 0.208239i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −18.1005 | −0.981638 | ||||||||
\(341\) | −5.59767 | −0.303131 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 55.1127i | 2.97148i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 19.6913i | − 1.05861i | ||||||||
\(347\) | − 18.9706i | − 1.01839i | −0.860650 | − | 0.509197i | \(-0.829943\pi\) | ||||
0.860650 | − | 0.509197i | \(-0.170057\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.17733i | 0.330665i | 0.986238 | + | 0.165332i | \(0.0528697\pi\) | ||||
−0.986238 | + | 0.165332i | \(0.947130\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.31371 | 0.0700209 | ||||||||
\(353\) | −23.6494 | −1.25873 | −0.629367 | − | 0.777109i | \(-0.716686\pi\) | ||||
−0.629367 | + | 0.777109i | \(0.716686\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 16.3128i | − 0.865794i | ||||||||
\(356\) | 23.6494 | 1.25342 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.9706 | 1.21403 | ||||||||
\(359\) | − 1.02944i | − 0.0543316i | −0.999631 | − | 0.0271658i | \(-0.991352\pi\) | ||||
0.999631 | − | 0.0271658i | \(-0.00864821\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −26.6569 | −1.40299 | ||||||||
\(362\) | −42.7611 | −2.24747 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 4.72792i | − 0.247471i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 3.95815i | − 0.206614i | −0.994650 | − | 0.103307i | \(-0.967058\pi\) | ||||
0.994650 | − | 0.103307i | \(-0.0329424\pi\) | |||||||
\(368\) | 6.00000i | 0.312772i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.0907i | 1.09645i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.6274 | −1.17160 | −0.585802 | − | 0.810454i | \(-0.699220\pi\) | ||||
−0.585802 | + | 0.810454i | \(0.699220\pi\) | |||||||
\(374\) | 2.79884 | 0.144724 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 29.8268i | 1.53820i | ||||||||
\(377\) | −16.3128 | −0.840152 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | − 87.3970i | − 4.48337i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 50.2843 | 2.57277 | ||||||||
\(383\) | 27.0279 | 1.38106 | 0.690532 | − | 0.723302i | \(-0.257377\pi\) | ||||
0.690532 | + | 0.723302i | \(0.257377\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 42.6274i | − 2.16968i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.35757i | 0.271989i | ||||||||
\(389\) | − 13.7990i | − 0.699637i | −0.936818 | − | 0.349818i | \(-0.886243\pi\) | ||||
0.936818 | − | 0.349818i | \(-0.113757\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 2.79884i | − 0.141543i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −39.2132 | −1.97553 | ||||||||
\(395\) | 32.6256 | 1.64157 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 27.2680i | − 1.36854i | −0.729227 | − | 0.684272i | \(-0.760120\pi\) | ||||
0.729227 | − | 0.684272i | \(-0.239880\pi\) | |||||||
\(398\) | −46.1396 | −2.31277 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.2426 | 0.962132 | ||||||||
\(401\) | 10.8284i | 0.540746i | 0.962756 | + | 0.270373i | \(0.0871470\pi\) | ||||
−0.962756 | + | 0.270373i | \(0.912853\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.8284 | 1.13716 | ||||||||
\(404\) | 49.5181 | 2.46362 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 2.14214i | − 0.106182i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.7122i | 0.875813i | 0.899020 | + | 0.437907i | \(0.144280\pi\) | ||||
−0.899020 | + | 0.437907i | \(0.855720\pi\) | |||||||
\(410\) | 66.5269i | 3.28553i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.7151i | 0.527897i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −45.6569 | −2.24121 | ||||||||
\(416\) | −5.35757 | −0.262676 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13.5140i | 0.660990i | ||||||||
\(419\) | 35.4244 | 1.73060 | 0.865299 | − | 0.501256i | \(-0.167129\pi\) | ||||
0.865299 | + | 0.501256i | \(0.167129\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.3137 | −1.13624 | −0.568120 | − | 0.822946i | \(-0.692329\pi\) | ||||
−0.568120 | + | 0.822946i | \(0.692329\pi\) | |||||||
\(422\) | 17.6569i | 0.859522i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −31.2132 | −1.51585 | ||||||||
\(425\) | −8.97616 | −0.435408 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 35.6569i | 1.72354i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 101.835i | 4.91092i | ||||||||
\(431\) | − 15.4558i | − 0.744482i | −0.928136 | − | 0.372241i | \(-0.878590\pi\) | ||||
0.928136 | − | 0.372241i | \(-0.121410\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 8.15640i | − 0.391972i | −0.980607 | − | 0.195986i | \(-0.937209\pi\) | ||||
0.980607 | − | 0.195986i | \(-0.0627907\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.89949 | 0.474100 | ||||||||
\(437\) | 13.5140 | 0.646461 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 28.6675i | − 1.36822i | −0.729377 | − | 0.684112i | \(-0.760190\pi\) | ||||
0.729377 | − | 0.684112i | \(-0.239810\pi\) | |||||||
\(440\) | −12.3547 | −0.588985 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.4142 | −0.542919 | ||||||||
\(443\) | − 24.8284i | − 1.17963i | −0.807537 | − | 0.589817i | \(-0.799200\pi\) | ||||
0.807537 | − | 0.589817i | \(-0.200800\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.8701 | 0.989336 | ||||||||
\(446\) | 55.6954 | 2.63725 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.2426i | 1.14408i | 0.820225 | + | 0.572040i | \(0.193848\pi\) | ||||
−0.820225 | + | 0.572040i | \(0.806152\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 6.75699i | − 0.318174i | ||||||||
\(452\) | 22.5858i | 1.06235i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 6.75699i | − 0.317121i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.6274 | 1.33913 | 0.669567 | − | 0.742752i | \(-0.266480\pi\) | ||||
0.669567 | + | 0.742752i | \(0.266480\pi\) | |||||||
\(458\) | −29.2471 | −1.36663 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 25.8686i | 1.20613i | ||||||||
\(461\) | −21.6704 | −1.00929 | −0.504645 | − | 0.863327i | \(-0.668377\pi\) | ||||
−0.504645 | + | 0.863327i | \(0.668377\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.51472 | 0.163343 | 0.0816714 | − | 0.996659i | \(-0.473974\pi\) | ||||
0.0816714 | + | 0.996659i | \(0.473974\pi\) | |||||||
\(464\) | − 14.4853i | − 0.672462i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26.1421 | 1.21101 | ||||||||
\(467\) | 2.79884 | 0.129515 | 0.0647573 | − | 0.997901i | \(-0.479373\pi\) | ||||
0.0647573 | + | 0.997901i | \(0.479373\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 55.1127i | 2.54216i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 29.8268i | 1.37289i | ||||||||
\(473\) | − 10.3431i | − 0.475578i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 43.3407i | − 1.98861i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.828427 | 0.0378914 | ||||||||
\(479\) | 8.39651 | 0.383646 | 0.191823 | − | 0.981430i | \(-0.438560\pi\) | ||||
0.191823 | + | 0.981430i | \(0.438560\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.73606i | 0.398330i | ||||||||
\(482\) | 21.6704 | 0.987059 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −39.4853 | −1.79479 | ||||||||
\(485\) | 4.72792i | 0.214684i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.45584 | 0.428485 | 0.214243 | − | 0.976780i | \(-0.431272\pi\) | ||||
0.214243 | + | 0.976780i | \(0.431272\pi\) | |||||||
\(488\) | 36.0041 | 1.62983 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 2.68629i | − 0.121231i | −0.998161 | − | 0.0606153i | \(-0.980694\pi\) | ||||
0.998161 | − | 0.0606153i | \(-0.0193063\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.75699i | 0.304319i | ||||||||
\(494\) | − 55.1127i | − 2.47964i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.2710i | 0.910193i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.14214 | −0.0958952 | −0.0479476 | − | 0.998850i | \(-0.515268\pi\) | ||||
−0.0479476 | + | 0.998850i | \(0.515268\pi\) | |||||||
\(500\) | 18.2919 | 0.818038 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 62.4524i | 2.78739i | ||||||||
\(503\) | −32.6256 | −1.45470 | −0.727352 | − | 0.686264i | \(-0.759249\pi\) | ||||
−0.727352 | + | 0.686264i | \(0.759249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.6985 | 1.94456 | ||||||||
\(506\) | − 4.00000i | − 0.177822i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.85786 | 0.0824294 | ||||||||
\(509\) | −36.8239 | −1.63219 | −0.816095 | − | 0.577918i | \(-0.803865\pi\) | ||||
−0.816095 | + | 0.577918i | \(0.803865\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 31.2426i | − 1.38074i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 52.3169i | − 2.30760i | ||||||||
\(515\) | 9.45584i | 0.416674i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 5.59767i | − 0.246185i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 50.3848 | 2.20952 | ||||||||
\(521\) | 42.7611 | 1.87340 | 0.936699 | − | 0.350136i | \(-0.113865\pi\) | ||||
0.936699 | + | 0.350136i | \(0.113865\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 17.4721i | − 0.764003i | −0.924162 | − | 0.382001i | \(-0.875235\pi\) | ||||
0.924162 | − | 0.382001i | \(-0.124765\pi\) | |||||||
\(524\) | −36.5838 | −1.59817 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −58.2843 | −2.54131 | ||||||||
\(527\) | − 9.45584i | − 0.411903i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0000 | 0.826087 | ||||||||
\(530\) | −57.6745 | −2.50522 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.5563i | 1.19360i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.4663i | 1.36041i | ||||||||
\(536\) | − 37.4558i | − 1.61785i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 75.3867i | 3.25015i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.9706 | 0.815608 | 0.407804 | − | 0.913069i | \(-0.366295\pi\) | ||||
0.407804 | + | 0.913069i | \(0.366295\pi\) | |||||||
\(542\) | −16.3128 | −0.700695 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.21918i | 0.0951464i | ||||||||
\(545\) | 8.73606 | 0.374212 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.6274 | −1.13851 | −0.569253 | − | 0.822162i | \(-0.692768\pi\) | ||||
−0.569253 | + | 0.822162i | \(0.692768\pi\) | |||||||
\(548\) | 3.17157i | 0.135483i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −12.8284 | −0.547006 | ||||||||
\(551\) | −32.6256 | −1.38990 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 50.6274i | − 2.15095i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 36.5838i | − 1.55150i | ||||||||
\(557\) | − 10.5858i | − 0.448534i | −0.974528 | − | 0.224267i | \(-0.928001\pi\) | ||||
0.974528 | − | 0.224267i | \(-0.0719988\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 42.1814i | 1.78408i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −45.4558 | −1.91744 | ||||||||
\(563\) | −2.79884 | −0.117957 | −0.0589784 | − | 0.998259i | \(-0.518784\pi\) | ||||
−0.0589784 | + | 0.998259i | \(0.518784\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.9314i | 0.838520i | ||||||||
\(566\) | 72.0082 | 3.02673 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21.3137 | 0.894303 | ||||||||
\(569\) | 25.1127i | 1.05278i | 0.850244 | + | 0.526390i | \(0.176455\pi\) | ||||
−0.850244 | + | 0.526390i | \(0.823545\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.3137 | −0.473464 | −0.236732 | − | 0.971575i | \(-0.576076\pi\) | ||||
−0.236732 | + | 0.971575i | \(0.576076\pi\) | |||||||
\(572\) | −10.7151 | −0.448022 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.8284i | 0.534982i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 13.7541i | − 0.572590i | −0.958142 | − | 0.286295i | \(-0.907576\pi\) | ||||
0.958142 | − | 0.286295i | \(-0.0924237\pi\) | |||||||
\(578\) | − 36.3137i | − 1.51045i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 62.4524i | − 2.59319i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.85786 | 0.242608 | ||||||||
\(584\) | 6.17733 | 0.255620 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 17.7122i | − 0.731685i | ||||||||
\(587\) | 20.2710 | 0.836672 | 0.418336 | − | 0.908292i | \(-0.362613\pi\) | ||||
0.418336 | + | 0.908292i | \(0.362613\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.6569 | 1.88126 | ||||||||
\(590\) | 55.1127i | 2.26895i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.75736 | −0.318826 | ||||||||
\(593\) | 20.5111 | 0.842288 | 0.421144 | − | 0.906994i | \(-0.361629\pi\) | ||||
0.421144 | + | 0.906994i | \(0.361629\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 16.2426i | − 0.665324i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.3128i | 0.667080i | ||||||||
\(599\) | 6.48528i | 0.264981i | 0.991184 | + | 0.132491i | \(0.0422975\pi\) | ||||
−0.991184 | + | 0.132491i | \(0.957703\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 27.6076i | − 1.12614i | −0.826410 | − | 0.563069i | \(-0.809621\pi\) | ||||
0.826410 | − | 0.563069i | \(-0.190379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 47.7990 | 1.94491 | ||||||||
\(605\) | −34.8448 | −1.41664 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 23.0698i | − 0.936374i | −0.883629 | − | 0.468187i | \(-0.844907\pi\) | ||||
0.883629 | − | 0.468187i | \(-0.155093\pi\) | |||||||
\(608\) | −10.7151 | −0.434556 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 66.5269 | 2.69360 | ||||||||
\(611\) | 22.8284i | 0.923539i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.8701 | −0.439037 | −0.219519 | − | 0.975608i | \(-0.570449\pi\) | ||||
−0.219519 | + | 0.975608i | \(0.570449\pi\) | |||||||
\(614\) | 29.8268 | 1.20371 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 30.4853i | − 1.22729i | −0.789582 | − | 0.613646i | \(-0.789702\pi\) | ||||
0.789582 | − | 0.613646i | \(-0.210298\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 24.7093i | − 0.993151i | −0.867994 | − | 0.496576i | \(-0.834591\pi\) | ||||
0.867994 | − | 0.496576i | \(-0.165409\pi\) | |||||||
\(620\) | 87.3970i | 3.50995i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 25.8686i | − 1.03724i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.9289 | −0.637157 | ||||||||
\(626\) | 31.2262 | 1.24805 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 28.0878i | − 1.12083i | ||||||||
\(629\) | 3.61859 | 0.144283 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.1716 | −0.842827 | −0.421414 | − | 0.906869i | \(-0.638466\pi\) | ||||
−0.421414 | + | 0.906869i | \(0.638466\pi\) | |||||||
\(632\) | 42.6274i | 1.69563i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −57.3553 | −2.27787 | ||||||||
\(635\) | 1.63952 | 0.0650624 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.65685i | 0.382319i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 69.4495i | − 2.74523i | ||||||||
\(641\) | 7.51472i | 0.296814i | 0.988926 | + | 0.148407i | \(0.0474145\pi\) | ||||
−0.988926 | + | 0.148407i | \(0.952586\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 6.75699i | − 0.266469i | −0.991085 | − | 0.133235i | \(-0.957464\pi\) | ||||
0.991085 | − | 0.133235i | \(-0.0425364\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −22.8284 | −0.898172 | ||||||||
\(647\) | −25.8686 | −1.01700 | −0.508500 | − | 0.861062i | \(-0.669800\pi\) | ||||
−0.508500 | + | 0.861062i | \(0.669800\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 5.59767i | − 0.219728i | ||||||||
\(650\) | 52.3169 | 2.05204 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −56.7696 | −2.22327 | ||||||||
\(653\) | − 38.4853i | − 1.50605i | −0.657995 | − | 0.753023i | \(-0.728595\pi\) | ||||
0.657995 | − | 0.753023i | \(-0.271405\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.2843 | −1.26145 | ||||||||
\(656\) | −24.4692 | −0.955362 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 47.4558i | − 1.84862i | −0.381646 | − | 0.924309i | \(-0.624643\pi\) | ||||
0.381646 | − | 0.924309i | \(-0.375357\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 7.33664i | − 0.285362i | −0.989769 | − | 0.142681i | \(-0.954428\pi\) | ||||
0.989769 | − | 0.142681i | \(-0.0455724\pi\) | |||||||
\(662\) | 24.9706i | 0.970508i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 59.6536i | − 2.31501i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.65685 | 0.373915 | ||||||||
\(668\) | 10.7151 | 0.414581 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 69.2094i | − 2.67379i | ||||||||
\(671\) | −6.75699 | −0.260851 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.8995 | −1.46092 | −0.730459 | − | 0.682956i | \(-0.760694\pi\) | ||||
−0.730459 | + | 0.682956i | \(0.760694\pi\) | |||||||
\(674\) | − 31.2132i | − 1.20229i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.07107 | −0.233503 | ||||||||
\(677\) | 32.8657 | 1.26313 | 0.631566 | − | 0.775322i | \(-0.282412\pi\) | ||||
0.631566 | + | 0.775322i | \(0.282412\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 20.8701i | − 0.800330i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 13.5140i | − 0.517477i | ||||||||
\(683\) | 38.7696i | 1.48348i | 0.670690 | + | 0.741738i | \(0.265998\pi\) | ||||
−0.670690 | + | 0.741738i | \(0.734002\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.79884i | 0.106938i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −37.4558 | −1.42799 | ||||||||
\(689\) | −23.8896 | −0.910119 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.55582i | 0.363521i | 0.983343 | + | 0.181760i | \(0.0581795\pi\) | ||||
−0.983343 | + | 0.181760i | \(0.941821\pi\) | |||||||
\(692\) | 31.2262 | 1.18704 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 45.7990 | 1.73851 | ||||||||
\(695\) | − 32.2843i | − 1.22461i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.4142 | 0.432344 | ||||||||
\(698\) | −14.9134 | −0.564480 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 40.7696i | − 1.53984i | −0.638138 | − | 0.769922i | \(-0.720295\pi\) | ||||
0.638138 | − | 0.769922i | \(-0.279705\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.4721i | 0.658974i | ||||||||
\(704\) | 8.14214i | 0.306868i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 57.0948i | − 2.14879i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.7279 | −1.22912 | −0.614561 | − | 0.788869i | \(-0.710667\pi\) | ||||
−0.614561 | + | 0.788869i | \(0.710667\pi\) | |||||||
\(710\) | 39.3826 | 1.47800 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27.2680i | 1.02191i | ||||||||
\(713\) | −13.5140 | −0.506102 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.45584 | −0.353629 | ||||||||
\(716\) | 36.4264i | 1.36132i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.48528 | 0.0927499 | ||||||||
\(719\) | 13.5140 | 0.503986 | 0.251993 | − | 0.967729i | \(-0.418914\pi\) | ||||
0.251993 | + | 0.967729i | \(0.418914\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 64.3553i | − 2.39506i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 67.8100i | − 2.52014i | ||||||||
\(725\) | − 30.9706i | − 1.15022i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.3407i | 1.60742i | 0.595022 | + | 0.803710i | \(0.297143\pi\) | ||||
−0.595022 | + | 0.803710i | \(0.702857\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.4142 | 0.422459 | ||||||||
\(731\) | 17.4721 | 0.646230 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.3099i | 0.860971i | 0.902598 | + | 0.430485i | \(0.141658\pi\) | ||||
−0.902598 | + | 0.430485i | \(0.858342\pi\) | |||||||
\(734\) | 9.55582 | 0.352712 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.17157 | 0.116906 | ||||||||
\(737\) | 7.02944i | 0.258933i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.8284 | −0.692615 | −0.346307 | − | 0.938121i | \(-0.612565\pi\) | ||||
−0.346307 | + | 0.938121i | \(0.612565\pi\) | |||||||
\(740\) | −33.4454 | −1.22948 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 52.4264i | 1.92334i | 0.274212 | + | 0.961669i | \(0.411583\pi\) | ||||
−0.274212 | + | 0.961669i | \(0.588417\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 14.3337i | − 0.525147i | ||||||||
\(746\) | − 54.6274i | − 2.00005i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.43835i | 0.162282i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.6863 | 0.754853 | 0.377427 | − | 0.926039i | \(-0.376809\pi\) | ||||
0.377427 | + | 0.926039i | \(0.376809\pi\) | |||||||
\(752\) | −20.2710 | −0.739206 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 39.3826i | − 1.43423i | ||||||||
\(755\) | 42.1814 | 1.53514 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.87006 | 0.249696 | 0.124848 | − | 0.992176i | \(-0.460156\pi\) | ||||
0.124848 | + | 0.992176i | \(0.460156\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 100.770 | 3.65530 | ||||||||
\(761\) | 0.579658 | 0.0210126 | 0.0105063 | − | 0.999945i | \(-0.496656\pi\) | ||||
0.0105063 | + | 0.999945i | \(0.496656\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 79.7401i | 2.88490i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 65.2512i | 2.35762i | ||||||||
\(767\) | 22.8284i | 0.824287i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.8995i | 1.65518i | 0.561335 | + | 0.827589i | \(0.310288\pi\) | ||||
−0.561335 | + | 0.827589i | \(0.689712\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 67.5980 | 2.43290 | ||||||||
\(773\) | −18.8715 | −0.678762 | −0.339381 | − | 0.940649i | \(-0.610218\pi\) | ||||
−0.339381 | + | 0.940649i | \(0.610218\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.3407i | 1.55685i | ||||||||
\(776\) | −6.17733 | −0.221753 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.3137 | 1.19435 | ||||||||
\(779\) | 55.1127i | 1.97462i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 6.75699 | 0.241629 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 24.7868i | − 0.884679i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.5140i | 0.481721i | 0.970560 | + | 0.240861i | \(0.0774296\pi\) | ||||
−0.970560 | + | 0.240861i | \(0.922570\pi\) | |||||||
\(788\) | − 62.1838i | − 2.21520i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 78.7652i | 2.80234i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.5563 | 0.978555 | ||||||||
\(794\) | 65.8309 | 2.33625 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 73.1675i | − 2.59335i | ||||||||
\(797\) | 1.73897 | 0.0615976 | 0.0307988 | − | 0.999526i | \(-0.490195\pi\) | ||||
0.0307988 | + | 0.999526i | \(0.490195\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.45584 | 0.334524 | ||||||||
\(800\) | − 10.1716i | − 0.359619i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26.1421 | −0.923111 | ||||||||
\(803\) | −1.15932 | −0.0409114 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 55.1127i | 1.94126i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 57.0948i | 2.00859i | ||||||||
\(809\) | 32.0416i | 1.12652i | 0.826278 | + | 0.563262i | \(0.190454\pi\) | ||||
−0.826278 | + | 0.563262i | \(0.809546\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 9.55582i | − 0.335550i | −0.985825 | − | 0.167775i | \(-0.946342\pi\) | ||||
0.985825 | − | 0.167775i | \(-0.0536583\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.17157 | 0.181264 | ||||||||
\(815\) | −50.0977 | −1.75485 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 84.3629i | 2.95148i | ||||||||
\(818\) | −42.7611 | −1.49511 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −105.497 | −3.68413 | ||||||||
\(821\) | 32.2426i | 1.12528i | 0.826703 | + | 0.562638i | \(0.190213\pi\) | ||||
−0.826703 | + | 0.562638i | \(0.809787\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.9411 | 0.904251 | 0.452125 | − | 0.891954i | \(-0.350666\pi\) | ||||
0.452125 | + | 0.891954i | \(0.350666\pi\) | |||||||
\(824\) | −12.3547 | −0.430395 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.3431i | 0.985588i | 0.870146 | + | 0.492794i | \(0.164024\pi\) | ||||
−0.870146 | + | 0.492794i | \(0.835976\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.8448i | 1.21021i | 0.796146 | + | 0.605105i | \(0.206869\pi\) | ||||
−0.796146 | + | 0.605105i | \(0.793131\pi\) | |||||||
\(830\) | − 110.225i | − 3.82598i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 33.2053i | − 1.15119i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.45584 | 0.327233 | ||||||||
\(836\) | −21.4303 | −0.741181 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 85.5222i | 2.95431i | ||||||||
\(839\) | 20.2710 | 0.699831 | 0.349916 | − | 0.936781i | \(-0.386210\pi\) | ||||
0.349916 | + | 0.936781i | \(0.386210\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.68629 | 0.196079 | ||||||||
\(842\) | − 56.2843i | − 1.93968i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −28.0000 | −0.963800 | ||||||||
\(845\) | −5.35757 | −0.184306 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 21.2132i | − 0.728464i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 21.6704i | − 0.743288i | ||||||||
\(851\) | − 5.17157i | − 0.177279i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 38.8029i | − 1.32859i | −0.747472 | − | 0.664294i | \(-0.768732\pi\) | ||||
0.747472 | − | 0.664294i | \(-0.231268\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −41.1127 | −1.40520 | ||||||||
\(857\) | 19.6913 | 0.672642 | 0.336321 | − | 0.941747i | \(-0.390817\pi\) | ||||
0.336321 | + | 0.941747i | \(0.390817\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.8268i | 1.01768i | 0.860862 | + | 0.508838i | \(0.169925\pi\) | ||||
−0.860862 | + | 0.508838i | \(0.830075\pi\) | |||||||
\(860\) | −161.489 | −5.50671 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 37.3137 | 1.27091 | ||||||||
\(863\) | − 33.3137i | − 1.13401i | −0.823714 | − | 0.567006i | \(-0.808102\pi\) | ||||
0.823714 | − | 0.567006i | \(-0.191898\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27.5563 | 0.936944 | ||||||||
\(866\) | 19.6913 | 0.669138 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 8.00000i | − 0.271381i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 28.6675i | − 0.971360i | ||||||||
\(872\) | 11.4142i | 0.386534i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32.6256i | 1.10358i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.5269 | 1.09836 | 0.549178 | − | 0.835705i | \(-0.314941\pi\) | ||||
0.549178 | + | 0.835705i | \(0.314941\pi\) | |||||||
\(878\) | 69.2094 | 2.33570 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 8.39651i | − 0.283046i | ||||||||
\(881\) | −20.5111 | −0.691035 | −0.345518 | − | 0.938412i | \(-0.612297\pi\) | ||||
−0.345518 | + | 0.938412i | \(0.612297\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.4558 | −1.26049 | −0.630245 | − | 0.776397i | \(-0.717045\pi\) | ||||
−0.630245 | + | 0.776397i | \(0.717045\pi\) | |||||||
\(884\) | − 18.1005i | − 0.608786i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 59.9411 | 2.01376 | ||||||||
\(887\) | −17.9523 | −0.602780 | −0.301390 | − | 0.953501i | \(-0.597451\pi\) | ||||
−0.301390 | + | 0.953501i | \(0.597451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 50.3848i | 1.68890i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 88.3210i | 2.95721i | ||||||||
\(893\) | 45.6569i | 1.52785i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.1454i | 1.07450i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −58.5269 | −1.95307 | ||||||||
\(899\) | 32.6256 | 1.08813 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.89538i | 0.329663i | ||||||||
\(902\) | 16.3128 | 0.543157 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −26.0416 | −0.866132 | ||||||||
\(905\) | − 59.8406i | − 1.98917i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.7696 | −1.48655 | −0.743274 | − | 0.668987i | \(-0.766728\pi\) | ||||
−0.743274 | + | 0.668987i | \(0.766728\pi\) | |||||||
\(908\) | 10.7151 | 0.355594 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.5147i | 0.845340i | 0.906284 | + | 0.422670i | \(0.138907\pi\) | ||||
−0.906284 | + | 0.422670i | \(0.861093\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.1953i | 0.370512i | ||||||||
\(914\) | 69.1127i | 2.28604i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 46.3797i | − 1.53243i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.45584 | 0.311920 | 0.155960 | − | 0.987763i | \(-0.450153\pi\) | ||||
0.155960 | + | 0.987763i | \(0.450153\pi\) | |||||||
\(920\) | −29.8268 | −0.983360 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 52.3169i | − 1.72297i | ||||||||
\(923\) | 16.3128 | 0.536943 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.5858 | −0.545337 | ||||||||
\(926\) | 8.48528i | 0.278844i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.65685 | −0.251349 | ||||||||
\(929\) | 19.6913 | 0.646051 | 0.323025 | − | 0.946390i | \(-0.395300\pi\) | ||||
0.323025 | + | 0.946390i | \(0.395300\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 41.4558i | 1.35793i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.75699i | 0.221095i | ||||||||
\(935\) | 3.91674i | 0.128091i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1.73897i | − 0.0568098i | −0.999596 | − | 0.0284049i | \(-0.990957\pi\) | ||||
0.999596 | − | 0.0284049i | \(-0.00904277\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −87.3970 | −2.85057 | ||||||||
\(941\) | −14.9134 | −0.486163 | −0.243081 | − | 0.970006i | \(-0.578158\pi\) | ||||
−0.243081 | + | 0.970006i | \(0.578158\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 16.3128i | − 0.531218i | ||||||||
\(944\) | −20.2710 | −0.659763 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.9706 | 0.811863 | ||||||||
\(947\) | 22.9706i | 0.746443i | 0.927742 | + | 0.373221i | \(0.121747\pi\) | ||||
−0.927742 | + | 0.373221i | \(0.878253\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.72792 | 0.153475 | ||||||||
\(950\) | 104.634 | 3.39477 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 26.3848i | − 0.854687i | −0.904089 | − | 0.427343i | \(-0.859450\pi\) | ||||
0.904089 | − | 0.427343i | \(-0.140550\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 70.3687i | 2.27708i | ||||||||
\(956\) | 1.31371i | 0.0424884i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.2710i | 0.654925i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.6569 | −0.472802 | ||||||||
\(962\) | −21.0907 | −0.679992 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 34.3646i | 1.10681i | ||||||||
\(965\) | 59.6536 | 1.92032 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.1127 | 1.38641 | 0.693205 | − | 0.720740i | \(-0.256198\pi\) | ||||
0.693205 | + | 0.720740i | \(0.256198\pi\) | |||||||
\(968\) | − 45.5269i | − 1.46329i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.4142 | −0.366488 | ||||||||
\(971\) | −32.6256 | −1.04701 | −0.523503 | − | 0.852024i | \(-0.675375\pi\) | ||||
−0.523503 | + | 0.852024i | \(0.675375\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 22.8284i | 0.731470i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.4692i | 0.783240i | ||||||||
\(977\) | 39.1716i | 1.25321i | 0.779337 | + | 0.626605i | \(0.215556\pi\) | ||||
−0.779337 | + | 0.626605i | \(0.784444\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 5.11747i | − 0.163555i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.48528 | 0.206954 | ||||||||
\(983\) | −17.4721 | −0.557274 | −0.278637 | − | 0.960396i | \(-0.589883\pi\) | ||||
−0.278637 | + | 0.960396i | \(0.589883\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 54.8756i | − 1.74848i | ||||||||
\(986\) | −16.3128 | −0.519506 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 87.3970 | 2.78047 | ||||||||
\(989\) | − 24.9706i | − 0.794018i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 59.3970 | 1.88681 | 0.943403 | − | 0.331647i | \(-0.107604\pi\) | ||||
0.943403 | + | 0.331647i | \(0.107604\pi\) | |||||||
\(992\) | 10.7151 | 0.340206 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 64.5685i | − 2.04696i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 11.7750i | − 0.372918i | −0.982463 | − | 0.186459i | \(-0.940299\pi\) | ||||
0.982463 | − | 0.186459i | \(-0.0597011\pi\) | |||||||
\(998\) | − 5.17157i | − 0.163703i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.2.c.b.440.7 | yes | 8 | |
3.2 | odd | 2 | inner | 441.2.c.b.440.2 | yes | 8 | |
4.3 | odd | 2 | 7056.2.k.g.881.1 | 8 | |||
7.2 | even | 3 | 441.2.p.c.80.8 | 16 | |||
7.3 | odd | 6 | 441.2.p.c.215.1 | 16 | |||
7.4 | even | 3 | 441.2.p.c.215.2 | 16 | |||
7.5 | odd | 6 | 441.2.p.c.80.7 | 16 | |||
7.6 | odd | 2 | inner | 441.2.c.b.440.8 | yes | 8 | |
12.11 | even | 2 | 7056.2.k.g.881.8 | 8 | |||
21.2 | odd | 6 | 441.2.p.c.80.1 | 16 | |||
21.5 | even | 6 | 441.2.p.c.80.2 | 16 | |||
21.11 | odd | 6 | 441.2.p.c.215.7 | 16 | |||
21.17 | even | 6 | 441.2.p.c.215.8 | 16 | |||
21.20 | even | 2 | inner | 441.2.c.b.440.1 | ✓ | 8 | |
28.27 | even | 2 | 7056.2.k.g.881.7 | 8 | |||
84.83 | odd | 2 | 7056.2.k.g.881.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.c.b.440.1 | ✓ | 8 | 21.20 | even | 2 | inner | |
441.2.c.b.440.2 | yes | 8 | 3.2 | odd | 2 | inner | |
441.2.c.b.440.7 | yes | 8 | 1.1 | even | 1 | trivial | |
441.2.c.b.440.8 | yes | 8 | 7.6 | odd | 2 | inner | |
441.2.p.c.80.1 | 16 | 21.2 | odd | 6 | |||
441.2.p.c.80.2 | 16 | 21.5 | even | 6 | |||
441.2.p.c.80.7 | 16 | 7.5 | odd | 6 | |||
441.2.p.c.80.8 | 16 | 7.2 | even | 3 | |||
441.2.p.c.215.1 | 16 | 7.3 | odd | 6 | |||
441.2.p.c.215.2 | 16 | 7.4 | even | 3 | |||
441.2.p.c.215.7 | 16 | 21.11 | odd | 6 | |||
441.2.p.c.215.8 | 16 | 21.17 | even | 6 | |||
7056.2.k.g.881.1 | 8 | 4.3 | odd | 2 | |||
7056.2.k.g.881.2 | 8 | 84.83 | odd | 2 | |||
7056.2.k.g.881.7 | 8 | 28.27 | even | 2 | |||
7056.2.k.g.881.8 | 8 | 12.11 | even | 2 |