Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [416,2,Mod(47,416)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(416, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("416.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 416 = 2^{5} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 416.u (of order \(4\), degree \(2\), not 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: | \(3.32177672409\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{26})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 104) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.2 | ||
Root | \(2.54951 - 2.54951i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 416.47 |
Dual form | 416.2.u.a.239.2 |
$q$-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 \(\left(\mathbb{Z}/416\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(287\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.54951 | − | 2.54951i | 1.14018 | − | 1.14018i | 0.151758 | − | 0.988418i | \(-0.451507\pi\) |
0.988418 | − | 0.151758i | \(-0.0484933\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.54951 | + | 2.54951i | 0.963624 | + | 0.963624i | 0.999361 | − | 0.0357371i | \(-0.0113779\pi\) |
−0.0357371 | + | 0.999361i | \(0.511378\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | + | 1.00000i | −0.301511 | + | 0.301511i | −0.841605 | − | 0.540094i | \(-0.818389\pi\) |
0.540094 | + | 0.841605i | \(0.318389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.54951 | − | 2.54951i | 0.707107 | − | 0.707107i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.54951 | − | 2.54951i | 0.658281 | − | 0.658281i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000i | 0.727607i | 0.931476 | + | 0.363803i | \(0.118522\pi\) | ||||
−0.931476 | + | 0.363803i | \(0.881478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | − | 2.00000i | −0.458831 | − | 0.458831i | 0.439440 | − | 0.898272i | \(-0.355177\pi\) |
−0.898272 | + | 0.439440i | \(0.855177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.54951 | + | 2.54951i | 0.556349 | + | 0.556349i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.09902 | −1.06322 | −0.531610 | − | 0.846990i | \(-0.678413\pi\) | ||||
−0.531610 | + | 0.846990i | \(0.678413\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 8.00000i | − | 1.60000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.09902i | 0.946864i | 0.880830 | + | 0.473432i | \(0.156985\pi\) | ||||
−0.880830 | + | 0.473432i | \(0.843015\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.09902 | − | 5.09902i | 0.915811 | − | 0.915811i | −0.0809104 | − | 0.996721i | \(-0.525783\pi\) |
0.996721 | + | 0.0809104i | \(0.0257828\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | + | 1.00000i | −0.174078 | + | 0.174078i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.0000 | 2.19740 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.54951 | − | 2.54951i | −0.419137 | − | 0.419137i | 0.465769 | − | 0.884906i | \(-0.345778\pi\) |
−0.884906 | + | 0.465769i | \(0.845778\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.54951 | − | 2.54951i | 0.408248 | − | 0.408248i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | + | 6.00000i | 0.937043 | + | 0.937043i | 0.998132 | − | 0.0610897i | \(-0.0194576\pi\) |
−0.0610897 | + | 0.998132i | \(0.519458\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.00000i | − | 0.152499i | −0.997089 | − | 0.0762493i | \(-0.975706\pi\) | ||
0.997089 | − | 0.0762493i | \(-0.0242945\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.09902 | + | 5.09902i | −0.760117 | + | 0.760117i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.54951 | + | 2.54951i | 0.371884 | + | 0.371884i | 0.868163 | − | 0.496279i | \(-0.165301\pi\) |
−0.496279 | + | 0.868163i | \(0.665301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.00000i | 0.857143i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.00000i | 0.420084i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.09902i | − | 0.700404i | −0.936674 | − | 0.350202i | \(-0.886113\pi\) | ||
0.936674 | − | 0.350202i | \(-0.113887\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.09902i | 0.687552i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | − | 2.00000i | −0.264906 | − | 0.264906i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | + | 8.00000i | −1.04151 | + | 1.04151i | −0.0424110 | + | 0.999100i | \(0.513504\pi\) |
−0.999100 | + | 0.0424110i | \(0.986496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.09902 | − | 5.09902i | −0.642416 | − | 0.642416i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 13.0000i | − | 1.61245i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00000 | − | 3.00000i | −0.366508 | − | 0.366508i | 0.499694 | − | 0.866202i | \(-0.333446\pi\) |
−0.866202 | + | 0.499694i | \(0.833446\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.09902 | −0.613850 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.64853 | + | 7.64853i | −0.907713 | + | 0.907713i | −0.996087 | − | 0.0883739i | \(-0.971833\pi\) |
0.0883739 | + | 0.996087i | \(0.471833\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | + | 6.00000i | −0.702247 | + | 0.702247i | −0.964892 | − | 0.262646i | \(-0.915405\pi\) |
0.262646 | + | 0.964892i | \(0.415405\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 8.00000i | − | 0.923760i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.09902 | −0.581087 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.09902i | − | 0.573685i | −0.957978 | − | 0.286842i | \(-0.907394\pi\) | ||
0.957978 | − | 0.286842i | \(-0.0926056\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.00000 | − | 5.00000i | −0.548821 | − | 0.548821i | 0.377279 | − | 0.926100i | \(-0.376860\pi\) |
−0.926100 | + | 0.377279i | \(0.876860\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.64853 | + | 7.64853i | 0.829599 | + | 0.829599i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.09902i | 0.546672i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | + | 2.00000i | −0.212000 | + | 0.212000i | −0.805116 | − | 0.593117i | \(-0.797897\pi\) |
0.593117 | + | 0.805116i | \(0.297897\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.0000 | 1.36277 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.09902 | − | 5.09902i | 0.528744 | − | 0.528744i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.1980 | −1.04630 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00000 | − | 7.00000i | −0.710742 | − | 0.710742i | 0.255948 | − | 0.966691i | \(-0.417612\pi\) |
−0.966691 | + | 0.255948i | \(0.917612\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | − | 2.00000i | 0.201008 | − | 0.201008i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.1980 | −1.01474 | −0.507371 | − | 0.861727i | \(-0.669383\pi\) | ||||
−0.507371 | + | 0.861727i | \(0.669383\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.09902 | −0.502421 | −0.251211 | − | 0.967932i | \(-0.580829\pi\) | ||||
−0.251211 | + | 0.967932i | \(0.580829\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.0000 | 1.26867 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.00000 | 0.193347 | 0.0966736 | − | 0.995316i | \(-0.469180\pi\) | ||||
0.0966736 | + | 0.995316i | \(0.469180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.54951 | + | 2.54951i | −0.244199 | + | 0.244199i | −0.818585 | − | 0.574386i | \(-0.805241\pi\) |
0.574386 | + | 0.818585i | \(0.305241\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.54951 | − | 2.54951i | −0.241989 | − | 0.241989i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.0000 | + | 13.0000i | −1.21226 | + | 1.21226i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.09902 | + | 5.09902i | −0.471405 | + | 0.471405i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.64853 | + | 7.64853i | −0.701140 | + | 0.701140i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000i | 0.818182i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.00000 | + | 6.00000i | 0.541002 | + | 0.541002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.64853 | − | 7.64853i | −0.684105 | − | 0.684105i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.2971 | 1.35739 | 0.678697 | − | 0.734418i | \(-0.262545\pi\) | ||||
0.678697 | + | 0.734418i | \(0.262545\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1.00000i | − | 0.0880451i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.00000 | −0.611593 | −0.305796 | − | 0.952097i | \(-0.598923\pi\) | ||||
−0.305796 | + | 0.952097i | \(0.598923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 10.1980i | − | 0.884282i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.7475 | + | 12.7475i | −1.09713 | + | 1.09713i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.00000 | + | 5.00000i | −0.427179 | + | 0.427179i | −0.887666 | − | 0.460487i | \(-0.847675\pi\) |
0.460487 | + | 0.887666i | \(0.347675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.0000 | 1.27228 | 0.636142 | − | 0.771572i | \(-0.280529\pi\) | ||||
0.636142 | + | 0.771572i | \(0.280529\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.54951 | + | 2.54951i | 0.214707 | + | 0.214707i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.09902i | 0.426401i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.0000 | + | 13.0000i | 1.07959 | + | 1.07959i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.00000i | 0.494872i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.1980 | − | 10.1980i | 0.835456 | − | 0.835456i | −0.152801 | − | 0.988257i | \(-0.548829\pi\) |
0.988257 | + | 0.152801i | \(0.0488294\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.64853 | − | 7.64853i | −0.622428 | − | 0.622428i | 0.323723 | − | 0.946152i | \(-0.395065\pi\) |
−0.946152 | + | 0.323723i | \(0.895065\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 26.0000i | − | 2.08837i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.1980i | 0.813892i | 0.913452 | + | 0.406946i | \(0.133406\pi\) | ||||
−0.913452 | + | 0.406946i | \(0.866594\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 5.09902i | − | 0.404379i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.0000 | − | 13.0000i | −1.02454 | − | 1.02454i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.00000 | + | 9.00000i | −0.704934 | + | 0.704934i | −0.965465 | − | 0.260531i | \(-0.916102\pi\) |
0.260531 | + | 0.965465i | \(0.416102\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.09902i | 0.396958i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.2971 | + | 15.2971i | 1.18372 | + | 1.18372i | 0.978773 | + | 0.204949i | \(0.0657030\pi\) |
0.204949 | + | 0.978773i | \(0.434297\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 13.0000i | − | 1.00000i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | + | 4.00000i | 0.305888 | + | 0.305888i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.09902 | 0.387671 | 0.193836 | − | 0.981034i | \(-0.437907\pi\) | ||||
0.193836 | + | 0.981034i | \(0.437907\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.3961 | − | 20.3961i | 1.54180 | − | 1.54180i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.00000 | + | 8.00000i | −0.601317 | + | 0.601317i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 9.00000i | − | 0.672692i | −0.941739 | − | 0.336346i | \(-0.890809\pi\) | ||
0.941739 | − | 0.336346i | \(-0.109191\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.2971 | 1.13702 | 0.568511 | − | 0.822676i | \(-0.307520\pi\) | ||||
0.568511 | + | 0.822676i | \(0.307520\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.0000 | −0.955779 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.00000 | − | 3.00000i | −0.219382 | − | 0.219382i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.7475 | − | 12.7475i | −0.927248 | − | 0.927248i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 25.4951i | − | 1.84476i | −0.386283 | − | 0.922380i | \(-0.626241\pi\) | ||
0.386283 | − | 0.922380i | \(-0.373759\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.00000 | − | 9.00000i | 0.647834 | − | 0.647834i | −0.304635 | − | 0.952469i | \(-0.598534\pi\) |
0.952469 | + | 0.304635i | \(0.0985345\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 13.0000i | − | 0.930949i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.7475 | + | 12.7475i | −0.908225 | + | 0.908225i | −0.996129 | − | 0.0879037i | \(-0.971983\pi\) |
0.0879037 | + | 0.996129i | \(0.471983\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.4951 | 1.80730 | 0.903650 | − | 0.428272i | \(-0.140878\pi\) | ||||
0.903650 | + | 0.428272i | \(0.140878\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.00000 | − | 3.00000i | −0.211604 | − | 0.211604i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.0000 | + | 13.0000i | −0.912421 | + | 0.912421i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 30.5941 | 2.13679 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.1980 | 0.708813 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.00000 | −0.481900 | −0.240950 | − | 0.970538i | \(-0.577459\pi\) | ||||
−0.240950 | + | 0.970538i | \(0.577459\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.64853 | + | 7.64853i | −0.524069 | + | 0.524069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.54951 | − | 2.54951i | −0.173875 | − | 0.173875i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.0000 | 1.76500 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.00000 | + | 6.00000i | −0.405442 | + | 0.405442i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.64853 | + | 7.64853i | 0.514496 | + | 0.514496i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.64853 | − | 7.64853i | 0.512183 | − | 0.512183i | −0.403012 | − | 0.915195i | \(-0.632037\pi\) |
0.915195 | + | 0.403012i | \(0.132037\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16.0000i | 1.06667i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.0000 | + | 12.0000i | 0.796468 | + | 0.796468i | 0.982537 | − | 0.186069i | \(-0.0595747\pi\) |
−0.186069 | + | 0.982537i | \(0.559575\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.54951 | + | 2.54951i | 0.168476 | + | 0.168476i | 0.786309 | − | 0.617833i | \(-0.211989\pi\) |
−0.617833 | + | 0.786309i | \(0.711989\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.09902 | −0.335491 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.0000i | 0.720634i | 0.932830 | + | 0.360317i | \(0.117331\pi\) | ||||
−0.932830 | + | 0.360317i | \(0.882669\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.0000 | 0.848026 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 5.09902i | − | 0.331217i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.54951 | − | 2.54951i | 0.164914 | − | 0.164914i | −0.619826 | − | 0.784740i | \(-0.712797\pi\) |
0.784740 | + | 0.619826i | \(0.212797\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0000 | + | 14.0000i | −0.901819 | + | 0.901819i | −0.995593 | − | 0.0937742i | \(-0.970107\pi\) |
0.0937742 | + | 0.995593i | \(0.470107\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.2971 | + | 15.2971i | 0.977293 | + | 0.977293i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.1980 | −0.648886 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.00000 | − | 5.00000i | −0.316862 | − | 0.316862i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.0000i | 0.631194i | 0.948893 | + | 0.315597i | \(0.102205\pi\) | ||||
−0.948893 | + | 0.315597i | \(0.897795\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.09902 | − | 5.09902i | 0.320573 | − | 0.320573i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.64853 | + | 7.64853i | 0.478969 | + | 0.478969i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.00000i | 0.187135i | 0.995613 | + | 0.0935674i | \(0.0298271\pi\) | ||||
−0.995613 | + | 0.0935674i | \(0.970173\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 13.0000i | − | 0.807781i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 10.1980i | − | 0.631243i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 20.3961i | − | 1.25768i | −0.777536 | − | 0.628838i | \(-0.783531\pi\) | ||
0.777536 | − | 0.628838i | \(-0.216469\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.0000 | − | 13.0000i | −0.798584 | − | 0.798584i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.00000 | + | 2.00000i | −0.122398 | + | 0.122398i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 20.3961i | − | 1.24357i | −0.783188 | − | 0.621785i | \(-0.786408\pi\) | ||
0.783188 | − | 0.621785i | \(-0.213592\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.64853 | − | 7.64853i | −0.464615 | − | 0.464615i | 0.435550 | − | 0.900165i | \(-0.356554\pi\) |
−0.900165 | + | 0.435550i | \(0.856554\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.0000 | 0.786796 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.00000 | + | 8.00000i | 0.482418 | + | 0.482418i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.1980 | 0.612741 | 0.306370 | − | 0.951912i | \(-0.400885\pi\) | ||||
0.306370 | + | 0.951912i | \(0.400885\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.1980 | + | 10.1980i | −0.610541 | + | 0.610541i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0000 | − | 16.0000i | 0.954480 | − | 0.954480i | −0.0445282 | − | 0.999008i | \(-0.514178\pi\) |
0.999008 | + | 0.0445282i | \(0.0141784\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 16.0000i | − | 0.951101i | −0.879688 | − | 0.475551i | \(-0.842249\pi\) | ||
0.879688 | − | 0.475551i | \(-0.157751\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.1980 | −0.604080 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 30.5941i | 1.80591i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.00000 | − | 7.00000i | −0.410347 | − | 0.410347i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.7475 | − | 12.7475i | −0.744720 | − | 0.744720i | 0.228763 | − | 0.973482i | \(-0.426532\pi\) |
−0.973482 | + | 0.228763i | \(0.926532\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 40.7922i | 2.37501i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.00000 | − | 5.00000i | 0.290129 | − | 0.290129i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.0000 | + | 13.0000i | −0.751809 | + | 0.751809i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.54951 | − | 2.54951i | 0.146951 | − | 0.146951i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.1980 | −0.585862 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0000 | − | 10.0000i | 0.570730 | − | 0.570730i | −0.361602 | − | 0.932332i | \(-0.617770\pi\) |
0.932332 | + | 0.361602i | \(0.117770\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.09902 | −0.290073 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.1980 | 0.578278 | 0.289139 | − | 0.957287i | \(-0.406631\pi\) | ||||
0.289139 | + | 0.957287i | \(0.406631\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.0000 | −1.75222 | −0.876112 | − | 0.482108i | \(-0.839871\pi\) | ||||
−0.876112 | + | 0.482108i | \(0.839871\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −26.0000 | −1.46493 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.09902 | − | 5.09902i | −0.285490 | − | 0.285490i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.00000 | 0.111629 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00000 | − | 6.00000i | 0.333849 | − | 0.333849i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.3961 | − | 20.3961i | −1.13137 | − | 1.13137i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.54951 | + | 2.54951i | −0.140988 | + | 0.140988i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.0000i | 0.716713i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.0000 | − | 21.0000i | −1.15426 | − | 1.15426i | −0.985689 | − | 0.168576i | \(-0.946083\pi\) |
−0.168576 | − | 0.985689i | \(-0.553917\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.09902 | + | 5.09902i | 0.279425 | + | 0.279425i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.2971 | −0.835768 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 17.0000i | − | 0.926049i | −0.886345 | − | 0.463025i | \(-0.846764\pi\) | ||
0.886345 | − | 0.463025i | \(-0.153236\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.00000 | 0.217250 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.1980i | 0.552255i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.54951 | − | 2.54951i | 0.137661 | − | 0.137661i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.0000 | + | 13.0000i | −0.699896 | + | 0.699896i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.00000 | 0.375780 | 0.187890 | − | 0.982190i | \(-0.439835\pi\) | ||||
0.187890 | + | 0.982190i | \(0.439835\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.9456 | − | 22.9456i | −1.22825 | − | 1.22825i | −0.964626 | − | 0.263624i | \(-0.915082\pi\) |
−0.263624 | − | 0.964626i | \(-0.584918\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.7475 | + | 12.7475i | −0.680414 | + | 0.680414i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.00000 | + | 5.00000i | 0.266123 | + | 0.266123i | 0.827536 | − | 0.561413i | \(-0.189742\pi\) |
−0.561413 | + | 0.827536i | \(0.689742\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 39.0000i | 2.06991i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.64853 | + | 7.64853i | −0.404803 | + | 0.404803i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.2971 | − | 15.2971i | −0.807348 | − | 0.807348i | 0.176884 | − | 0.984232i | \(-0.443398\pi\) |
−0.984232 | + | 0.176884i | \(0.943398\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 11.0000i | − | 0.578947i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.00000i | 0.472377i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.5941i | 1.60137i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.2971i | 0.798500i | 0.916842 | + | 0.399250i | \(0.130729\pi\) | ||||
−0.916842 | + | 0.399250i | \(0.869271\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.0000 | − | 12.0000i | −0.624695 | − | 0.624695i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.0000 | − | 13.0000i | 0.674926 | − | 0.674926i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.3961i | 1.05607i | 0.849223 | + | 0.528034i | \(0.177071\pi\) | ||||
−0.849223 | + | 0.528034i | \(0.822929\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.64853 | − | 7.64853i | −0.394968 | − | 0.394968i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.0000 | + | 13.0000i | 0.669534 | + | 0.669534i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.0000 | + | 23.0000i | 1.18143 | + | 1.18143i | 0.979374 | + | 0.202057i | \(0.0647626\pi\) |
0.202057 | + | 0.979374i | \(0.435237\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.2971 | 0.783692 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.64853 | − | 7.64853i | 0.390822 | − | 0.390822i | −0.484159 | − | 0.874980i | \(-0.660874\pi\) |
0.874980 | + | 0.484159i | \(0.160874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.0000 | + | 13.0000i | −0.662541 | + | 0.662541i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.00000i | 0.101666i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 15.2971i | − | 0.773606i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.00000 | −0.353103 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.0000 | − | 13.0000i | −0.654101 | − | 0.654101i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.1980 | + | 10.1980i | 0.511825 | + | 0.511825i | 0.915085 | − | 0.403260i | \(-0.132123\pi\) |
−0.403260 | + | 0.915085i | \(0.632123\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 10.1980i | − | 0.510541i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | − | 1.00000i | 0.0499376 | − | 0.0499376i | −0.681697 | − | 0.731635i | \(-0.738758\pi\) |
0.731635 | + | 0.681697i | \(0.238758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 26.0000i | − | 1.29515i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.54951 | − | 2.54951i | 0.126686 | − | 0.126686i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.09902 | 0.252749 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.0000 | + | 27.0000i | 1.33506 | + | 1.33506i | 0.900772 | + | 0.434292i | \(0.143001\pi\) |
0.434292 | + | 0.900772i | \(0.356999\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.00000 | + | 5.00000i | −0.246632 | + | 0.246632i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −40.7922 | −2.00725 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.4951 | −1.25151 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.0000 | 0.734553 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.00000 | −0.244266 | −0.122133 | − | 0.992514i | \(-0.538973\pi\) | ||||
−0.122133 | + | 0.992514i | \(0.538973\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.64853 | − | 7.64853i | 0.372767 | − | 0.372767i | −0.495717 | − | 0.868484i | \(-0.665095\pi\) |
0.868484 | + | 0.495717i | \(0.165095\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.09902 | − | 5.09902i | −0.247923 | − | 0.247923i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.0000 | 1.16417 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.09902i | 0.246183i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.64853 | + | 7.64853i | −0.368417 | + | 0.368417i | −0.866900 | − | 0.498483i | \(-0.833891\pi\) |
0.498483 | + | 0.866900i | \(0.333891\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 19.0000i | − | 0.913082i | −0.889702 | − | 0.456541i | \(-0.849088\pi\) | ||
0.889702 | − | 0.456541i | \(-0.150912\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.0000 | + | 13.0000i | 0.623302 | + | 0.623302i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.1980 | + | 10.1980i | 0.487838 | + | 0.487838i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 12.0000i | − | 0.571429i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.0000 | 1.47285 | 0.736427 | − | 0.676517i | \(-0.236511\pi\) | ||||
0.736427 | + | 0.676517i | \(0.236511\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.1980i | 0.483433i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.1980 | − | 10.1980i | 0.482351 | − | 0.482351i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.00000 | − | 3.00000i | 0.141579 | − | 0.141579i | −0.632765 | − | 0.774344i | \(-0.718080\pi\) |
0.774344 | + | 0.632765i | \(0.218080\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.0000 | −0.565058 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.64853 | − | 7.64853i | −0.359359 | − | 0.359359i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 33.1436 | − | 33.1436i | 1.55380 | − | 1.55380i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.00000 | − | 2.00000i | −0.0935561 | − | 0.0935561i | 0.658780 | − | 0.752336i | \(-0.271073\pi\) |
−0.752336 | + | 0.658780i | \(0.771073\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 15.0000i | − | 0.700140i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.8466 | + | 17.8466i | −0.831198 | + | 0.831198i | −0.987681 | − | 0.156483i | \(-0.949984\pi\) |
0.156483 | + | 0.987681i | \(0.449984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.4951 | + | 25.4951i | 1.18486 | + | 1.18486i | 0.978470 | + | 0.206387i | \(0.0661707\pi\) |
0.206387 | + | 0.978470i | \(0.433829\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 26.0000i | − | 1.20572i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.00000i | 0.0925490i | 0.998929 | + | 0.0462745i | \(0.0147349\pi\) | ||||
−0.998929 | + | 0.0462745i | \(0.985265\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 15.2971i | − | 0.706353i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.1980i | 0.469901i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.00000 | + | 1.00000i | 0.0459800 | + | 0.0459800i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.0000 | + | 16.0000i | −0.734130 | + | 0.734130i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.1980i | 0.466936i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.54951 | − | 2.54951i | −0.116490 | − | 0.116490i | 0.646459 | − | 0.762949i | \(-0.276249\pi\) |
−0.762949 | + | 0.646459i | \(0.776249\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.0000 | −0.592749 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.0000 | − | 13.0000i | −0.591520 | − | 0.591520i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −35.6931 | −1.62074 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.4951 | + | 25.4951i | −1.15529 | + | 1.15529i | −0.169818 | + | 0.985476i | \(0.554318\pi\) |
−0.985476 | + | 0.169818i | \(0.945682\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.00000 | + | 9.00000i | −0.406994 | + | 0.406994i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.00000i | 0.225647i | 0.993615 | + | 0.112823i | \(0.0359894\pi\) | ||||
−0.993615 | + | 0.112823i | \(0.964011\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.2971 | −0.688945 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 10.1980i | − | 0.458368i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −39.0000 | −1.74939 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.00000 | − | 2.00000i | −0.0895323 | − | 0.0895323i | 0.660922 | − | 0.750454i | \(-0.270165\pi\) |
−0.750454 | + | 0.660922i | \(0.770165\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.2971 | + | 15.2971i | 0.683422 | + | 0.683422i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 20.3961i | − | 0.909416i | −0.890641 | − | 0.454708i | \(-0.849744\pi\) | ||
0.890641 | − | 0.454708i | \(-0.150256\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.0000 | + | 26.0000i | −1.15698 | + | 1.15698i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 13.0000i | − | 0.577350i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.1980 | − | 10.1980i | 0.452020 | − | 0.452020i | −0.444004 | − | 0.896025i | \(-0.646443\pi\) |
0.896025 | + | 0.444004i | \(0.146443\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.5941 | −1.35340 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.0000 | + | 10.0000i | 0.441511 | + | 0.441511i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.0000 | + | 13.0000i | −0.572848 | + | 0.572848i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.09902 | −0.224255 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.09902 | 0.223822 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.00000 | −0.131432 | −0.0657162 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657162 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.00000 | 0.262362 | 0.131181 | − | 0.991358i | \(-0.458123\pi\) | ||||
0.131181 | + | 0.991358i | \(0.458123\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.3961 | − | 20.3961i | 0.890158 | − | 0.890158i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.2971 | + | 15.2971i | 0.666350 | + | 0.666350i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.00000 | 0.130435 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.0000 | − | 16.0000i | 0.694341 | − | 0.694341i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.5941 | 1.32518 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.09902 | − | 5.09902i | 0.220450 | − | 0.220450i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 9.00000i | − | 0.388379i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.00000 | − | 6.00000i | −0.258438 | − | 0.258438i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.8466 | − | 17.8466i | −0.767284 | − | 0.767284i | 0.210344 | − | 0.977628i | \(-0.432542\pi\) |
−0.977628 | + | 0.210344i | \(0.932542\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.2971 | 0.656460 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.0000i | 0.556859i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.0000 | −0.983409 | −0.491704 | − | 0.870762i | \(-0.663626\pi\) | ||||
−0.491704 | + | 0.870762i | \(0.663626\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.1980 | − | 10.1980i | 0.434451 | − | 0.434451i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.0000 | − | 13.0000i | 0.552816 | − | 0.552816i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.0000 | −0.551819 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.9456 | + | 22.9456i | 0.972236 | + | 0.972236i | 0.999625 | − | 0.0273891i | \(-0.00871931\pi\) |
−0.0273891 | + | 0.999625i | \(0.508719\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.54951 | − | 2.54951i | −0.107833 | − | 0.107833i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.00000 | − | 3.00000i | −0.126660 | − | 0.126660i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.00000i | 0.379305i | 0.981851 | + | 0.189652i | \(0.0607361\pi\) | ||||
−0.981851 | + | 0.189652i | \(0.939264\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.1980 | − | 10.1980i | 0.429035 | − | 0.429035i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.54951 | + | 2.54951i | 0.107069 | + | 0.107069i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 31.0000i | − | 1.29959i | −0.760111 | − | 0.649794i | \(-0.774855\pi\) | ||
0.760111 | − | 0.649794i | \(-0.225145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0000i | 0.627730i | 0.949468 | + | 0.313865i | \(0.101624\pi\) | ||||
−0.949468 | + | 0.313865i | \(0.898376\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 25.4951i | − | 1.06507i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 40.7922i | 1.70115i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0000 | + | 18.0000i | 0.749350 | + | 0.749350i | 0.974357 | − | 0.225007i | \(-0.0722406\pi\) |
−0.225007 | + | 0.974357i | \(0.572241\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.00000 | − | 9.00000i | 0.374027 | − | 0.374027i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 25.4951i | − | 1.05771i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.09902 | + | 5.09902i | 0.211180 | + | 0.211180i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 26.0000i | 1.07497i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.00000 | + | 7.00000i | 0.288921 | + | 0.288921i | 0.836653 | − | 0.547733i | \(-0.184509\pi\) |
−0.547733 | + | 0.836653i | \(0.684509\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.3961 | −0.840406 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.7475 | + | 12.7475i | −0.524364 | + | 0.524364i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.0000 | − | 29.0000i | 1.19089 | − | 1.19089i | 0.214069 | − | 0.976819i | \(-0.431328\pi\) |
0.976819 | − | 0.214069i | \(-0.0686716\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 39.0000i | 1.59884i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.4951 | 1.04344 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 30.5941i | − | 1.25004i | −0.780608 | − | 0.625021i | \(-0.785090\pi\) | ||
0.780608 | − | 0.625021i | \(-0.214910\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.0000 | 1.50926 | 0.754631 | − | 0.656150i | \(-0.227816\pi\) | ||||
0.754631 | + | 0.656150i | \(0.227816\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.00000 | + | 6.00000i | 0.244339 | + | 0.244339i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.9456 | + | 22.9456i | 0.932871 | + | 0.932871i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 10.1980i | − | 0.413926i | −0.978349 | − | 0.206963i | \(-0.933642\pi\) | ||
0.978349 | − | 0.206963i | \(-0.0663579\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.0000 | + | 13.0000i | −0.526787 | + | 0.526787i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.0000 | 0.525924 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.09902 | − | 5.09902i | 0.205947 | − | 0.205947i | −0.596595 | − | 0.802542i | \(-0.703480\pi\) |
0.802542 | + | 0.596595i | \(0.203480\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 30.5941 | 1.23367 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0000 | − | 12.0000i | −0.483102 | − | 0.483102i | 0.423019 | − | 0.906121i | \(-0.360970\pi\) |
−0.906121 | + | 0.423019i | \(0.860970\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0000 | − | 22.0000i | 0.884255 | − | 0.884255i | −0.109709 | − | 0.993964i | \(-0.534992\pi\) |
0.993964 | + | 0.109709i | \(0.0349919\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.4951 | 1.02308 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.1980 | −0.408576 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.00000 | 0.159745 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.64853 | − | 7.64853i | 0.304967 | − | 0.304967i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.8466 | + | 17.8466i | 0.710461 | + | 0.710461i | 0.966632 | − | 0.256171i | \(-0.0824610\pi\) |
−0.256171 | + | 0.966632i | \(0.582461\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.00000 | −0.278225 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 39.0000 | − | 39.0000i | 1.54767 | − | 1.54767i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.2971 | + | 15.2971i | 0.606092 | + | 0.606092i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.2971 | − | 15.2971i | 0.605142 | − | 0.605142i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.0000i | 1.57991i | 0.613168 | + | 0.789953i | \(0.289895\pi\) | ||||
−0.613168 | + | 0.789953i | \(0.710105\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.0000 | − | 15.0000i | −0.591542 | − | 0.591542i | 0.346506 | − | 0.938048i | \(-0.387368\pi\) |
−0.938048 | + | 0.346506i | \(0.887368\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.54951 | − | 2.54951i | −0.100387 | − | 0.100387i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.1980 | −0.400926 | −0.200463 | − | 0.979701i | \(-0.564245\pi\) | ||||
−0.200463 | + | 0.979701i | \(0.564245\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 16.0000i | − | 0.628055i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.0000 | 1.01902 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 30.5941i | − | 1.19724i | −0.801033 | − | 0.598620i | \(-0.795716\pi\) | ||
0.801033 | − | 0.598620i | \(-0.204284\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.8466 | + | 17.8466i | −0.697323 | + | 0.697323i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.0000 | − | 12.0000i | 0.468165 | − | 0.468165i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.0000 | −1.16863 | −0.584317 | − | 0.811525i | \(-0.698638\pi\) | ||||
−0.584317 | + | 0.811525i | \(0.698638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.09902 | − | 5.09902i | −0.198329 | − | 0.198329i | 0.600954 | − | 0.799283i | \(-0.294787\pi\) |
−0.799283 | + | 0.600954i | \(0.794787\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.64853 | + | 7.64853i | 0.297044 | + | 0.297044i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −26.0000 | − | 26.0000i | −1.00824 | − | 1.00824i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 26.0000i | − | 1.00672i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.64853 | − | 7.64853i | 0.295709 | − | 0.295709i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.0000i | 0.809491i | 0.914429 | + | 0.404745i | \(0.132640\pi\) | ||||
−0.914429 | + | 0.404745i | \(0.867360\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 40.0000i | 1.53960i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 15.2971i | − | 0.587914i | −0.955819 | − | 0.293957i | \(-0.905028\pi\) | ||
0.955819 | − | 0.293957i | \(-0.0949722\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 35.6931i | − | 1.36978i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0000 | + | 12.0000i | 0.459841 | + | 0.459841i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.0000 | + | 29.0000i | −1.10965 | + | 1.10965i | −0.116459 | + | 0.993196i | \(0.537154\pi\) |
−0.993196 | + | 0.116459i | \(0.962846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.4951i | 0.974118i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.54951 | + | 2.54951i | 0.0972699 | + | 0.0972699i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.0000 | − | 13.0000i | −0.495261 | − | 0.495261i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.00000 | − | 6.00000i | −0.228251 | − | 0.228251i | 0.583711 | − | 0.811962i | \(-0.301600\pi\) |
−0.811962 | + | 0.583711i | \(0.801600\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.1980 | 0.387391 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 38.2426 | − | 38.2426i | 1.45063 | − | 1.45063i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0000 | + | 18.0000i | −0.681799 | + | 0.681799i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.0000i | 0.416058i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.2971 | 0.577762 | 0.288881 | − | 0.957365i | \(-0.406717\pi\) | ||||
0.288881 | + | 0.957365i | \(0.406717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.1980i | 0.384626i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.0000 | 0.489608 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −26.0000 | − | 26.0000i | −0.977831 | − | 0.977831i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.1980 | − | 10.1980i | −0.382995 | − | 0.382995i | 0.489185 | − | 0.872180i | \(-0.337294\pi\) |
−0.872180 | + | 0.489185i | \(0.837294\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.1980i | 0.382456i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.0000 | + | 26.0000i | −0.973708 | + | 0.973708i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.0000 | + | 13.0000i | 0.486172 | + | 0.486172i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.54951 | − | 2.54951i | 0.0952132 | − | 0.0952132i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.4951 | −0.950807 | −0.475403 | − | 0.879768i | \(-0.657698\pi\) | ||||
−0.475403 | + | 0.879768i | \(0.657698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.0000 | − | 13.0000i | −0.484145 | − | 0.484145i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.0000 | + | 14.0000i | −0.520666 | + | 0.520666i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40.7922 | 1.51498 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.2971 | 0.567336 | 0.283668 | − | 0.958922i | \(-0.408449\pi\) | ||||
0.283668 | + | 0.958922i | \(0.408449\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.00000 | 0.110959 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.1436 | + | 33.1436i | −1.22419 | + | 1.22419i | −0.258058 | + | 0.966129i | \(0.583083\pi\) |
−0.966129 | + | 0.258058i | \(0.916917\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15.2971 | + | 15.2971i | 0.564241 | + | 0.564241i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.00000 | 0.221013 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.00000 | − | 2.00000i | 0.0735712 | − | 0.0735712i | −0.669364 | − | 0.742935i | \(-0.733433\pi\) |
0.742935 | + | 0.669364i | \(0.233433\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.1980 | −0.374634 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.64853 | − | 7.64853i | 0.280597 | − | 0.280597i | −0.552750 | − | 0.833347i | \(-0.686422\pi\) |
0.833347 | + | 0.552750i | \(0.186422\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 52.0000i | − | 1.90513i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.0000 | + | 10.0000i | 0.365881 | + | 0.365881i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.09902 | + | 5.09902i | 0.186314 | + | 0.186314i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.1980 | 0.372132 | 0.186066 | − | 0.982537i | \(-0.440426\pi\) | ||||
0.186066 | + | 0.982537i | \(0.440426\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.0000i | 0.364420i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.0000 | −1.41936 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.6931i | 1.29729i | 0.761091 | + | 0.648645i | \(0.224664\pi\) | ||||
−0.761091 | + | 0.648645i | \(0.775336\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.09902 | − | 5.09902i | 0.185083 | − | 0.185083i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.00000 | + | 4.00000i | −0.145000 | + | 0.145000i | −0.775880 | − | 0.630880i | \(-0.782694\pi\) |
0.630880 | + | 0.775880i | \(0.282694\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.0000 | −0.470632 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.2971 | − | 15.2971i | −0.553066 | − | 0.553066i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.7922i | 1.47292i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.00000 | − | 8.00000i | −0.288487 | − | 0.288487i | 0.547995 | − | 0.836482i | \(-0.315391\pi\) |
−0.836482 | + | 0.547995i | \(0.815391\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.00000i | 0.108042i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.64853 | + | 7.64853i | −0.275098 | + | 0.275098i | −0.831149 | − | 0.556050i | \(-0.812316\pi\) |
0.556050 | + | 0.831149i | \(0.312316\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.7922 | − | 40.7922i | −1.46530 | − | 1.46530i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 13.0000i | − | 0.466372i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 24.0000i | − | 0.859889i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 15.2971i | − | 0.547372i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 25.4951i | − | 0.911120i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.0000 | + | 26.0000i | 0.927980 | + | 0.927980i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.0000 | − | 30.0000i | 1.06938 | − | 1.06938i | 0.0719783 | − | 0.997406i | \(-0.477069\pi\) |
0.997406 | − | 0.0719783i | \(-0.0229312\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 20.3961i | − | 0.726120i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.1980 | + | 10.1980i | 0.362601 | + | 0.362601i | ||||
\(792\) | 0 | 0 |