Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [880,2,Mod(49,880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(880, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("880.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 880 = 2^{4} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 880.cd (of order \(10\), degree \(4\), 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: | \(7.02683537787\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 8 x^{14} + 10 x^{13} - 109 x^{12} + 280 x^{11} - 198 x^{10} - 1168 x^{9} + \cdots + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 110) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 609.4 | ||
Root | \(1.19237 + 1.89162i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 880.609 |
Dual form | 880.2.cd.b.289.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(177\) | \(321\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.53884 | + | 0.500000i | 0.888451 | + | 0.288675i | 0.717462 | − | 0.696598i | \(-0.245304\pi\) |
0.170989 | + | 0.985273i | \(0.445304\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.829496 | − | 2.07652i | −0.370962 | − | 0.928648i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.76878 | + | 1.54947i | −1.80243 | + | 0.585645i | −0.999939 | − | 0.0110184i | \(-0.996493\pi\) |
−0.802491 | + | 0.596664i | \(0.796493\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.309017 | − | 0.224514i | −0.103006 | − | 0.0748380i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.969425 | + | 3.17178i | 0.292293 | + | 0.956329i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.37249 | + | 1.88906i | −0.380659 | + | 0.523932i | −0.955759 | − | 0.294151i | \(-0.904963\pi\) |
0.575100 | + | 0.818083i | \(0.304963\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.238203 | − | 3.61018i | −0.0615037 | − | 0.932146i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.0359433 | − | 0.0494717i | −0.00871753 | − | 0.0119986i | 0.804636 | − | 0.593768i | \(-0.202360\pi\) |
−0.813354 | + | 0.581770i | \(0.802360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.636930 | + | 1.96027i | −0.146122 | + | 0.449717i | −0.997154 | − | 0.0753974i | \(-0.975977\pi\) |
0.851032 | + | 0.525114i | \(0.175977\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.11314 | −1.77043 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.91525i | 0.816387i | 0.912896 | + | 0.408193i | \(0.133841\pi\) | ||||
−0.912896 | + | 0.408193i | \(0.866159\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.62387 | + | 3.44493i | −0.724775 | + | 0.688986i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.21644 | − | 4.42705i | −0.619004 | − | 0.851986i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.27844 | + | 3.93464i | 0.237401 | + | 0.730644i | 0.996794 | + | 0.0800122i | \(0.0254959\pi\) |
−0.759393 | + | 0.650632i | \(0.774504\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.18170 | − | 5.21781i | −1.28987 | − | 0.937147i | −0.290069 | − | 0.957006i | \(-0.593678\pi\) |
−0.999803 | + | 0.0198592i | \(0.993678\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0941007 | + | 5.36559i | −0.0163808 | + | 0.934029i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.17320 | + | 8.61720i | 1.21249 | + | 1.45657i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.33385 | + | 1.40815i | −0.712481 | + | 0.231499i | −0.642760 | − | 0.766067i | \(-0.722211\pi\) |
−0.0697209 | + | 0.997567i | \(0.522211\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.05657 | + | 2.22073i | −0.489443 | + | 0.355601i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.41525 | + | 4.35570i | −0.221025 | + | 0.680246i | 0.777646 | + | 0.628703i | \(0.216414\pi\) |
−0.998671 | + | 0.0515429i | \(0.983586\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.61803i | 0.551745i | 0.961194 | + | 0.275873i | \(0.0889668\pi\) | ||||
−0.961194 | + | 0.275873i | \(0.911033\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.209880 | + | 0.827913i | −0.0312870 | + | 0.123418i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.44260 | − | 2.74317i | −1.23148 | − | 0.400132i | −0.380229 | − | 0.924892i | \(-0.624155\pi\) |
−0.851250 | + | 0.524760i | \(0.824155\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.6773 | − | 10.6637i | 2.09676 | − | 1.52338i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0305752 | − | 0.0941007i | −0.00428138 | − | 0.0131767i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.30598 | + | 1.79753i | −0.179391 | + | 0.246910i | −0.889237 | − | 0.457446i | \(-0.848764\pi\) |
0.709847 | + | 0.704356i | \(0.248764\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.78214 | − | 4.64401i | 0.779664 | − | 0.626199i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.96027 | + | 2.69808i | −0.259644 | + | 0.357370i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.599137 | + | 1.84396i | 0.0780011 | + | 0.240063i | 0.982452 | − | 0.186515i | \(-0.0597192\pi\) |
−0.904451 | + | 0.426577i | \(0.859719\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.84211 | − | 5.69763i | 1.00408 | − | 0.729506i | 0.0411202 | − | 0.999154i | \(-0.486907\pi\) |
0.962959 | + | 0.269648i | \(0.0869073\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.82151 | + | 0.591846i | 0.229489 | + | 0.0745655i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.06115 | + | 1.28302i | 0.627758 | + | 0.159139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.49573i | − | 0.304902i | −0.988311 | − | 0.152451i | \(-0.951283\pi\) | ||
0.988311 | − | 0.152451i | \(-0.0487167\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.95763 | + | 6.02495i | −0.235670 | + | 0.725319i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.13254 | − | 5.18210i | 0.846477 | − | 0.615002i | −0.0776953 | − | 0.996977i | \(-0.524756\pi\) |
0.924172 | + | 0.381975i | \(0.124756\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.13205 | − | 1.66751i | 0.600662 | − | 0.195167i | 0.00712611 | − | 0.999975i | \(-0.497732\pi\) |
0.593535 | + | 0.804808i | \(0.297732\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.29903 | + | 3.48927i | −0.842820 | + | 0.402906i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.53757 | − | 13.6235i | −1.08691 | − | 1.55254i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.38417 | + | 3.91183i | 0.605766 | + | 0.440115i | 0.847921 | − | 0.530123i | \(-0.177854\pi\) |
−0.242155 | + | 0.970238i | \(0.577854\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.38197 | − | 7.33094i | −0.264663 | − | 0.814549i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.49620 | − | 8.94125i | −0.713050 | − | 0.981429i | −0.999726 | − | 0.0234017i | \(-0.992550\pi\) |
0.286676 | − | 0.958028i | \(-0.407450\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0729142 | + | 0.115674i | −0.00790865 | + | 0.0125466i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.69401i | 0.717673i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.09017 | −0.645557 | −0.322778 | − | 0.946475i | \(-0.604617\pi\) | ||||
−0.322778 | + | 0.946475i | \(0.604617\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.61803 | − | 11.1352i | 0.379273 | − | 1.16728i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.44260 | − | 11.6202i | −0.875456 | − | 1.20496i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.59887 | − | 0.303437i | 0.471834 | − | 0.0311320i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.29216 | + | 5.90765i | −0.435802 | + | 0.599831i | −0.969273 | − | 0.245988i | \(-0.920888\pi\) |
0.533470 | + | 0.845819i | \(0.320888\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.412541 | − | 1.19778i | 0.0414620 | − | 0.120382i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.179498 | + | 0.130413i | 0.0178608 | + | 0.0129766i | 0.596680 | − | 0.802479i | \(-0.296486\pi\) |
−0.578819 | + | 0.815456i | \(0.696486\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.538341 | + | 0.174918i | −0.0530443 | + | 0.0172351i | −0.335419 | − | 0.942069i | \(-0.608878\pi\) |
0.282375 | + | 0.959304i | \(0.408878\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.72982 | + | 16.8471i | 0.656763 | + | 1.64411i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.12087 | + | 0.689113i | 0.205033 | + | 0.0666191i | 0.409733 | − | 0.912206i | \(-0.365622\pi\) |
−0.204700 | + | 0.978825i | \(0.565622\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.86288 | −0.753127 | −0.376563 | − | 0.926391i | \(-0.622894\pi\) | ||||
−0.376563 | + | 0.926391i | \(0.622894\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.37319 | −0.699832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.9469 | + | 3.88177i | 1.12387 | + | 0.365166i | 0.811242 | − | 0.584710i | \(-0.198792\pi\) |
0.312624 | + | 0.949877i | \(0.398792\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.13010 | − | 3.24769i | 0.758136 | − | 0.302848i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.848243 | − | 0.275611i | 0.0784200 | − | 0.0254802i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.248061 | + | 0.180227i | 0.0227397 | + | 0.0165214i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.12043 | + | 6.14961i | −0.829130 | + | 0.559056i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.35570 | + | 5.99511i | −0.392740 | + | 0.540560i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.1595 | + | 4.66749i | 0.908689 | + | 0.417473i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.50112 | + | 11.7008i | 0.754353 | + | 1.03828i | 0.997663 | + | 0.0683289i | \(0.0217667\pi\) |
−0.243310 | + | 0.969949i | \(0.578233\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.80902 | + | 5.56758i | −0.159275 | + | 0.490198i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.3256 | −1.33900 | −0.669502 | − | 0.742810i | \(-0.733493\pi\) | ||||
−0.669502 | + | 0.742810i | \(0.733493\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 10.3350i | − | 0.896159i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.52484 | + | 10.3512i | −0.561569 | + | 0.890892i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.649130 | + | 0.893451i | 0.0554589 | + | 0.0763326i | 0.835846 | − | 0.548964i | \(-0.184978\pi\) |
−0.780387 | + | 0.625297i | \(0.784978\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.06115 | − | 9.42125i | −0.259643 | − | 0.799100i | −0.992879 | − | 0.119126i | \(-0.961991\pi\) |
0.733236 | − | 0.679974i | \(-0.238009\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.6202 | − | 8.44260i | −0.978600 | − | 0.710995i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.32222 | − | 2.52192i | −0.612315 | − | 0.210894i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.10990 | − | 5.91848i | 0.590445 | − | 0.491503i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 27.9179 | − | 9.07108i | 2.30263 | − | 0.748170i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.11314 | − | 5.16800i | 0.582731 | − | 0.423379i | −0.256977 | − | 0.966418i | \(-0.582726\pi\) |
0.839708 | + | 0.543039i | \(0.182726\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.67177 | + | 20.5336i | −0.542941 | + | 1.67100i | 0.182894 | + | 0.983133i | \(0.441453\pi\) |
−0.725835 | + | 0.687868i | \(0.758547\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0233574i | 0.00188833i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.87770 | + | 19.2411i | −0.391786 | + | 1.54548i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.24760 | + | 1.05521i | 0.259186 | + | 0.0842148i | 0.435728 | − | 0.900078i | \(-0.356491\pi\) |
−0.176542 | + | 0.984293i | \(0.556491\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.90847 | + | 2.11313i | −0.230657 | + | 0.167582i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.06657 | − | 18.6710i | −0.478113 | − | 1.47148i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2336 | − | 14.0853i | 0.801554 | − | 1.10324i | −0.191019 | − | 0.981586i | \(-0.561179\pi\) |
0.992572 | − | 0.121657i | \(-0.0388209\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.2198 | − | 4.25533i | 0.873461 | − | 0.331277i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.94321 | + | 2.67460i | −0.150370 | + | 0.206967i | −0.877556 | − | 0.479473i | \(-0.840828\pi\) |
0.727186 | + | 0.686440i | \(0.240828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.33237 | + | 7.17831i | 0.179413 | + | 0.552178i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.636930 | − | 0.462757i | 0.0487073 | − | 0.0353879i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.87758 | − | 1.58482i | −0.370836 | − | 0.120492i | 0.117670 | − | 0.993053i | \(-0.462458\pi\) |
−0.488505 | + | 0.872561i | \(0.662458\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.9436 | − | 22.0432i | 0.902855 | − | 1.66631i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.13712i | 0.235801i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.46201 | + | 13.7327i | −0.333507 | + | 1.02643i | 0.633947 | + | 0.773377i | \(0.281434\pi\) |
−0.967453 | + | 0.253051i | \(0.918566\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.63223 | + | 6.99822i | −0.715958 | + | 0.520174i | −0.885090 | − | 0.465419i | \(-0.845903\pi\) |
0.169132 | + | 0.985593i | \(0.445903\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.9166 | − | 4.84669i | 1.10267 | − | 0.358278i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.51898 | + | 7.83128i | 0.479285 | + | 0.575767i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.122069 | − | 0.161963i | 0.00892658 | − | 0.0118439i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 22.1981 | + | 16.1279i | 1.61467 | + | 1.17313i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.25026 | − | 10.0033i | −0.235181 | − | 0.723812i | −0.997097 | − | 0.0761369i | \(-0.975741\pi\) |
0.761917 | − | 0.647675i | \(-0.224259\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.86174 | + | 3.93885i | 0.205993 | + | 0.283525i | 0.899496 | − | 0.436929i | \(-0.143934\pi\) |
−0.693503 | + | 0.720453i | \(0.743934\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.14680 | + | 4.50494i | 0.511793 | + | 0.322606i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 15.9760i | − | 1.13824i | −0.822253 | − | 0.569122i | \(-0.807283\pi\) | ||
0.822253 | − | 0.569122i | \(-0.192717\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.7076 | 1.18437 | 0.592184 | − | 0.805803i | \(-0.298266\pi\) | ||||
0.592184 | + | 0.805803i | \(0.298266\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.24787 | − | 3.84054i | 0.0880177 | − | 0.270891i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.1932 | − | 16.7825i | −0.855797 | − | 1.17790i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.2186 | − | 0.674234i | 0.713701 | − | 0.0470906i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.879029 | − | 1.20988i | 0.0610967 | − | 0.0840924i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.83501 | − | 0.119871i | −0.472788 | − | 0.00829167i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7388 | − | 9.25526i | −0.876974 | − | 0.637159i | 0.0554754 | − | 0.998460i | \(-0.482333\pi\) |
−0.932449 | + | 0.361301i | \(0.882333\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.5669 | − | 4.40815i | 0.929589 | − | 0.302042i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.51292 | − | 3.00114i | 0.512377 | − | 0.204676i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 42.3328 | + | 13.7548i | 2.87374 | + | 0.933735i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.73117 | 0.589998 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.142787 | 0.00960488 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.8432 | + | 4.49794i | 0.927011 | + | 0.301204i | 0.733340 | − | 0.679862i | \(-0.237961\pi\) |
0.193671 | + | 0.981067i | \(0.437961\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.89327 | − | 0.250932i | 0.126218 | − | 0.0167288i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.35512 | + | 3.03966i | −0.620921 | + | 0.201749i | −0.602549 | − | 0.798082i | \(-0.705848\pi\) |
−0.0183719 | + | 0.999831i | \(0.505848\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.5785 | − | 9.13881i | −0.831210 | − | 0.603909i | 0.0886913 | − | 0.996059i | \(-0.471732\pi\) |
−0.919901 | + | 0.392150i | \(0.871732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.86508 | − | 25.7331i | −0.517484 | − | 1.69312i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.2217 | + | 20.9509i | −0.997206 | + | 1.37254i | −0.0701824 | + | 0.997534i | \(0.522358\pi\) |
−0.927024 | + | 0.375002i | \(0.877642\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.30686 | + | 19.8067i | 0.0852501 | + | 1.29204i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.32947 | + | 8.71177i | 0.411143 | + | 0.565890i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.17911 | − | 19.0173i | 0.399693 | − | 1.23013i | −0.525552 | − | 0.850761i | \(-0.676141\pi\) |
0.925246 | − | 0.379369i | \(-0.123859\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.01381 | 0.580630 | 0.290315 | − | 0.956931i | \(-0.406240\pi\) | ||||
0.290315 | + | 0.956931i | \(0.406240\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.94427i | 0.253025i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −34.3181 | − | 21.6323i | −2.19251 | − | 1.38203i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.82890 | − | 3.89364i | −0.179998 | − | 0.247747i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.52599 | − | 17.0073i | −0.350196 | − | 1.07779i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.06115 | + | 0.770971i | 0.0669792 | + | 0.0486632i | 0.620771 | − | 0.783992i | \(-0.286820\pi\) |
−0.553792 | + | 0.832655i | \(0.686820\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.4183 | + | 3.79554i | −0.780734 | + | 0.238624i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.170040 | + | 0.141546i | −0.0106483 | + | 0.00886397i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.24551 | + | 1.37945i | −0.264827 | + | 0.0860477i | −0.438421 | − | 0.898770i | \(-0.644462\pi\) |
0.173594 | + | 0.984817i | \(0.444462\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.4853 | − | 13.4304i | 1.14862 | − | 0.834522i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.488321 | − | 1.50290i | 0.0302263 | − | 0.0930271i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.1791i | 0.874320i | 0.899384 | + | 0.437160i | \(0.144016\pi\) | ||||
−0.899384 | + | 0.437160i | \(0.855984\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.81592 | + | 1.22086i | 0.295840 | + | 0.0749966i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.37181 | − | 3.04508i | −0.573545 | − | 0.186356i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.8847 | + | 18.8063i | −1.57822 | + | 1.14664i | −0.659516 | + | 0.751691i | \(0.729239\pi\) |
−0.918702 | + | 0.394952i | \(0.870761\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.327988 | − | 1.00944i | −0.0199238 | − | 0.0613192i | 0.940600 | − | 0.339516i | \(-0.110263\pi\) |
−0.960524 | + | 0.278197i | \(0.910263\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.1352 | − | 15.3262i | 0.673931 | − | 0.927586i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.4396 | − | 8.15454i | −0.870744 | − | 0.491737i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.89892 | + | 5.36641i | −0.234264 | + | 0.322436i | −0.909923 | − | 0.414778i | \(-0.863859\pi\) |
0.675659 | + | 0.737214i | \(0.263859\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.04780 | + | 3.22478i | 0.0627299 | + | 0.193063i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.6582 | + | 9.19674i | −0.755126 | + | 0.548631i | −0.897412 | − | 0.441194i | \(-0.854555\pi\) |
0.142285 | + | 0.989826i | \(0.454555\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.3993 | + | 6.95305i | 1.27205 | + | 0.413316i | 0.865775 | − | 0.500433i | \(-0.166826\pi\) |
0.406280 | + | 0.913749i | \(0.366826\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.22866 | + | 1.83249i | 0.428189 | + | 0.108548i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 22.9643i | − | 1.35554i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.25213 | − | 16.1644i | 0.308949 | − | 0.950847i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.55877 | + | 6.94485i | −0.560345 | + | 0.407115i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.2985 | − | 5.62063i | 1.01059 | − | 0.328360i | 0.243500 | − | 0.969901i | \(-0.421704\pi\) |
0.767089 | + | 0.641540i | \(0.221704\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.33203 | − | 2.77367i | 0.193998 | − | 0.161490i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.9236 | − | 14.4935i | 0.633849 | − | 0.841001i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.39616 | − | 5.37363i | −0.427731 | − | 0.310765i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.60604 | − | 17.2536i | −0.323127 | − | 0.994482i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.211013 | + | 0.290435i | 0.0121224 | + | 0.0166850i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.3362 | − | 11.5581i | −1.04993 | − | 0.661817i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.3820i | 0.706676i | 0.935496 | + | 0.353338i | \(0.114953\pi\) | ||||
−0.935496 | + | 0.353338i | \(0.885047\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.915880 | −0.0521026 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.90784 | + | 8.94941i | −0.164889 | + | 0.507475i | −0.999028 | − | 0.0440788i | \(-0.985965\pi\) |
0.834140 | + | 0.551553i | \(0.185965\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.95297 | − | 12.3227i | −0.506052 | − | 0.696520i | 0.477196 | − | 0.878797i | \(-0.341653\pi\) |
−0.983247 | + | 0.182277i | \(0.941653\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.281959 | − | 4.27334i | −0.0158866 | − | 0.240776i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.90964 | − | 10.8867i | 0.444250 | − | 0.611457i | −0.526900 | − | 0.849927i | \(-0.676646\pi\) |
0.971150 | + | 0.238470i | \(0.0766459\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.2405 | + | 7.86928i | −0.629346 | + | 0.440595i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.91913 | + | 2.12087i | 0.162930 | + | 0.118376i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.119871 | − | 0.0389485i | 0.00666982 | − | 0.00216715i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.53398 | − | 11.5738i | −0.0850900 | − | 0.642001i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.0997 | − | 3.93144i | −0.669116 | − | 0.217409i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 44.5114 | 2.45399 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.82236 | 0.210096 | 0.105048 | − | 0.994467i | \(-0.466500\pi\) | ||||
0.105048 | + | 0.994467i | \(0.466500\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.65538 | + | 0.537867i | 0.0907145 | + | 0.0294749i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.18244 | + | 2.07020i | −0.283147 | + | 0.113107i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.00338 | + | 2.92538i | −0.490445 | + | 0.159355i | −0.543791 | − | 0.839221i | \(-0.683012\pi\) |
0.0533455 | + | 0.998576i | \(0.483012\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.4434 | + | 11.9469i | 0.893086 | + | 0.648865i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.58765 | − | 27.8371i | 0.519201 | − | 1.50746i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −32.8390 | + | 45.1989i | −1.77314 | + | 2.44051i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.1348 | − | 0.932624i | 0.760991 | − | 0.0502108i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.72341 | + | 13.3831i | 0.521980 | + | 0.718444i | 0.985882 | − | 0.167443i | \(-0.0535510\pi\) |
−0.463902 | + | 0.885887i | \(0.653551\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.03161 | + | 27.7964i | −0.483451 | + | 1.48791i | 0.350761 | + | 0.936465i | \(0.385923\pi\) |
−0.834212 | + | 0.551444i | \(0.814077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.7775 | 0.682012 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.9200i | 1.48603i | 0.669272 | + | 0.743017i | \(0.266606\pi\) | ||||
−0.669272 | + | 0.743017i | \(0.733394\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.6771 | − | 10.5123i | −0.885131 | − | 0.557937i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.291613 | + | 0.401371i | 0.0154338 | + | 0.0212428i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.25768 | + | 16.1815i | 0.277490 | + | 0.854025i | 0.988550 | + | 0.150894i | \(0.0482152\pi\) |
−0.711060 | + | 0.703131i | \(0.751785\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.9343 | + | 8.67081i | 0.628123 | + | 0.456358i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.1097 | + | 4.90307i | −0.898027 | + | 0.257344i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.71963 | − | 9.27363i | −0.404064 | − | 0.485404i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.9983 | − | 9.09719i | 1.46150 | − | 0.474870i | 0.532971 | − | 0.846133i | \(-0.321075\pi\) |
0.928527 | + | 0.371264i | \(0.121075\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.41525 | − | 1.02824i | 0.0736751 | − | 0.0535281i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.44273 | − | 10.5956i | 0.178738 | − | 0.550098i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0743i | 0.832297i | 0.909297 | + | 0.416149i | \(0.136620\pi\) | ||||
−0.909297 | + | 0.416149i | \(0.863380\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.3000 | + | 12.2623i | 0.686812 | + | 0.633220i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.18743 | − | 2.98518i | −0.473177 | − | 0.153744i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.6618 | + | 10.6524i | −0.753125 | + | 0.547178i | −0.896794 | − | 0.442448i | \(-0.854110\pi\) |
0.143669 | + | 0.989626i | \(0.454110\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.23149 | + | 22.2562i | 0.370480 | + | 1.14022i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.76587 | − | 10.6888i | 0.396817 | − | 0.546172i | −0.563124 | − | 0.826372i | \(-0.690401\pi\) |
0.959942 | + | 0.280200i | \(0.0904008\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.3780 | + | 31.1056i | −1.03856 | + | 1.58529i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.812299 | − | 1.11803i | 0.0412915 | − | 0.0568329i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.19653 | + | 25.2263i | 0.415580 | + | 1.27902i | 0.911731 | + | 0.410788i | \(0.134746\pi\) |
−0.496150 | + | 0.868237i | \(0.665254\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.193694 | − | 0.140727i | 0.00979553 | − | 0.00711687i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.5837 | − | 7.66280i | −1.18964 | − | 0.386537i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.65684 | − | 14.4252i | 0.183996 | − | 0.725810i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.3246i | 1.52195i | 0.648783 | + | 0.760974i | \(0.275278\pi\) | ||||
−0.648783 | + | 0.760974i | \(0.724722\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.16751 | − | 15.9039i | 0.258699 | − | 0.796193i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.7565 | + | 11.4478i | −0.786844 | + | 0.571676i | −0.907025 | − | 0.421076i | \(-0.861652\pi\) |
0.120181 | + | 0.992752i | \(0.461652\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.7136 | − | 6.40532i | 0.982002 | − | 0.319072i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.2470 | + | 11.0272i | −0.658249 | + | 0.547945i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.66771 | − | 12.3809i | −0.429642 | − | 0.613701i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.9197 | − | 16.6521i | −1.13330 | − | 0.823394i | −0.147132 | − | 0.989117i | \(-0.547004\pi\) |
−0.986172 | + | 0.165723i | \(0.947004\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.552183 | + | 1.69944i | 0.0272372 | + | 0.0838274i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.71431 | − | 7.86508i | −0.281183 | − | 0.387015i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.1781 | + | 20.9062i | −0.646888 | + | 1.02625i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 16.0284i | − | 0.784914i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.4826 | −0.756374 | −0.378187 | − | 0.925729i | \(-0.623452\pi\) | ||||
−0.378187 | + | 0.925729i | \(0.623452\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.63964 | − | 20.4347i | 0.323596 | − | 0.995927i | −0.648474 | − | 0.761237i | \(-0.724592\pi\) |
0.972070 | − | 0.234690i | \(-0.0754076\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.99303 | + | 2.74317i | 0.0969043 | + | 0.133377i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.300680 | + | 0.0554570i | 0.0145851 | + | 0.00269006i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.5690 | + | 39.3219i | −1.38255 | + | 1.90292i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.0068 | − | 7.54195i | −0.483132 | − | 0.364129i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.3896 | + | 15.5404i | 1.03030 | + | 0.748557i | 0.968369 | − | 0.249523i | \(-0.0802739\pi\) |
0.0619316 | + | 0.998080i | \(0.480274\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.2725 | − | 10.1611i | 1.50286 | − | 0.488309i | 0.562010 | − | 0.827130i | \(-0.310028\pi\) |
0.940851 | + | 0.338821i | \(0.110028\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.9002 | − | 5.55265i | 0.666466 | − | 0.266229i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.67495 | − | 2.49374i | −0.367143 | − | 0.119292i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.1796 | −0.581299 | −0.290649 | − | 0.956830i | \(-0.593871\pi\) | ||||
−0.290649 | + | 0.956830i | \(0.593871\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.92969 | −0.329985 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.7961 | − | 5.13247i | −0.750496 | − | 0.243851i | −0.0913015 | − | 0.995823i | \(-0.529103\pi\) |
−0.659195 | + | 0.751972i | \(0.729103\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.05177 | + | 12.6464i | 0.239477 | + | 0.599495i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.5300 | − | 4.39616i | 0.639947 | − | 0.207931i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.33928 | − | 3.15267i | −0.204783 | − | 0.148784i | 0.480667 | − | 0.876903i | \(-0.340395\pi\) |
−0.685450 | + | 0.728119i | \(0.740395\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.1873 | − | 0.266353i | −0.715143 | − | 0.0125421i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.5336 | + | 28.2621i | −0.964753 | + | 1.32787i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −26.1235 | + | 1.72365i | −1.22469 | + | 0.0808061i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.12330 | + | 2.92247i | 0.0993237 | + | 0.136707i | 0.855786 | − | 0.517330i | \(-0.173074\pi\) |
−0.756462 | + | 0.654037i | \(0.773074\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.103404 | + | 0.318246i | −0.00482650 | + | 0.0148544i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −40.6625 | −1.89384 | −0.946922 | − | 0.321464i | \(-0.895825\pi\) | ||||
−0.946922 | + | 0.321464i | \(0.895825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.11880i | − | 0.0984690i | −0.998787 | − | 0.0492345i | \(-0.984322\pi\) | ||
0.998787 | − | 0.0492345i | \(-0.0156782\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.1266 | + | 27.1702i | −0.794225 | + | 1.25999i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.08494 | − | 11.1280i | −0.374126 | − | 0.514941i | 0.579890 | − | 0.814695i | \(-0.303095\pi\) |
−0.954017 | + | 0.299754i | \(0.903095\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.86707 | + | 11.9016i | 0.178565 | + | 0.549565i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.46993 | + | 3.24760i | 0.205964 | + | 0.149641i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.4756 | + | 3.50741i | −0.527650 | + | 0.161271i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.44484 | − | 9.29795i | −0.203943 | − | 0.426619i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.807142 | − | 0.262256i | 0.0369565 | − | 0.0120079i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.4118 | + | 18.4628i | −1.16110 | + | 0.843586i | −0.989916 | − | 0.141654i | \(-0.954758\pi\) |
−0.171180 | + | 0.985240i | \(0.554758\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.28806 | − | 10.1196i | 0.149922 | − | 0.461414i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 31.7650i | − | 1.44536i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.8277 | + | 4.01238i | 0.718698 | + | 0.182193i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.14274 | + | 2.32082i | 0.323668 | + | 0.105166i | 0.466344 | − | 0.884603i | \(-0.345571\pi\) |
−0.142676 | + | 0.989769i | \(0.545571\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.7905 | − | 16.5582i | 1.03062 | − | 0.748789i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.48008 | − | 10.7106i | −0.157054 | − | 0.483361i | 0.841310 | − | 0.540554i | \(-0.181785\pi\) |
−0.998363 | + | 0.0571923i | \(0.981785\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.148702 | − | 0.204671i | 0.00669719 | − | 0.00921790i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.82943 | + | 0.136907i | −0.127173 | + | 0.00615353i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.9840 | + | 35.7640i | −1.16554 | + | 1.60423i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.33753 | − | 25.6603i | −0.373239 | − | 1.14871i | −0.944659 | − | 0.328054i | \(-0.893607\pi\) |
0.571420 | − | 0.820658i | \(-0.306393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.32760 | + | 3.14419i | −0.193343 | + | 0.140472i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.5818 | − | 9.93662i | −1.36357 | − | 0.443052i | −0.466339 | − | 0.884606i | \(-0.654427\pi\) |
−0.897235 | + | 0.441554i | \(0.854427\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.121913 | − | 0.480909i | 0.00542504 | − | 0.0214002i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.2125i | 0.542375i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.64048 | + | 11.2043i | −0.161362 | + | 0.496620i | −0.998750 | − | 0.0499888i | \(-0.984081\pi\) |
0.837388 | + | 0.546609i | \(0.184081\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.8899 | + | 15.9039i | −0.968352 | + | 0.703549i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.7269 | − | 3.48537i | 0.473603 | − | 0.153883i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.809772 | + | 0.972783i | 0.0356828 | + | 0.0428659i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.516268 | − | 29.4374i | 0.0227054 | − | 1.29465i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.71341 | − | 4.87758i | −0.294686 | − | 0.214102i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.718847 | + | 2.21238i | 0.0314933 | + | 0.0969263i | 0.965568 | − | 0.260152i | \(-0.0837728\pi\) |
−0.934074 | + | 0.357079i | \(0.883773\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.901612 | − | 1.24096i | −0.0394248 | − | 0.0542635i | 0.788850 | − | 0.614586i | \(-0.210677\pi\) |
−0.828274 | + | 0.560323i | \(0.810677\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 29.4010 | − | 27.9492i | 1.28316 | − | 1.21980i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.542836i | 0.0236463i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.67080 | 0.333513 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.228850 | − | 0.704328i | 0.00993125 | − | 0.0305652i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.28578 | − | 8.65163i | −0.272267 | − | 0.374744i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.328298 | − | 4.97565i | −0.0141935 | − | 0.215116i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.7327 | + | 18.9014i | −0.592608 | + | 0.815655i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 48.0515 | + | 36.2156i | 2.06972 | + | 1.55992i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.4927 | + | 9.07650i | 0.537104 | + | 0.390229i | 0.823008 | − | 0.568029i | \(-0.192294\pi\) |
−0.285904 | + | 0.958258i | \(0.592294\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.3216 | + | 5.95305i | −0.786255 | + | 0.255470i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.52222 | + | 16.3274i | 0.279381 | + | 0.699390i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.1261 | + | 3.29017i | 0.432960 | + | 0.140677i | 0.517385 | − | 0.855752i | \(-0.326905\pi\) |
−0.0844251 | + | 0.996430i | \(0.526905\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.70254 | −0.158021 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.52724 | −0.363272 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.7372 | − | 10.3120i | −1.34960 | − | 0.438513i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.11603 | + | 15.3106i | 0.259611 | + | 0.649898i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.2595 | + | 10.4818i | −1.36688 | + | 0.444126i | −0.898334 | − | 0.439313i | \(-0.855222\pi\) |
−0.468545 | + | 0.883439i | \(0.655222\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.83470 | − | 4.96570i | −0.289077 | − | 0.210027i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.268827 | − | 0.188201i | 0.0113499 | − | 0.00794587i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.789857 | − | 1.08714i | 0.0332885 | − | 0.0458177i | −0.792048 | − | 0.610458i | \(-0.790985\pi\) |
0.825337 | + | 0.564641i | \(0.190985\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.84930 | − | 28.0278i | −0.0778006 | − | 1.17914i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.7182 | + | 31.2689i | 0.954073 | + | 1.31317i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.70595 | − | 29.8718i | 0.406894 | − | 1.25229i | −0.512409 | − | 0.858742i | \(-0.671247\pi\) |
0.919303 | − | 0.393550i | \(-0.128753\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.25361 | −0.387252 | −0.193626 | − | 0.981075i | \(-0.562025\pi\) | ||||
−0.193626 | + | 0.981075i | \(0.562025\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 17.0186i | − | 0.710962i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.4878 | − | 14.1884i | −0.562479 | − | 0.591696i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.4998 | − | 35.0975i | −1.06157 | − | 1.46113i | −0.878327 | − | 0.478060i | \(-0.841340\pi\) |
−0.183244 | − | 0.983068i | \(-0.558660\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.43434 | + | 7.49214i | 0.101168 | + | 0.311363i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.8332 | + | 32.5732i | 1.85999 | + | 1.35136i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.96744 | − | 2.39973i | −0.288562 | − | 0.0993865i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.27592 | − | 1.53277i | −0.0527530 | − | 0.0633724i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.05524 | + | 0.992708i | −0.126103 | + | 0.0409734i | −0.371389 | − | 0.928477i | \(-0.621118\pi\) |
0.245285 | + | 0.969451i | \(0.421118\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.8026 | − | 10.7547i | 0.609929 | − | 0.443139i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.98801 | − | 24.5846i | 0.328583 | − | 1.01127i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 0.0315027i | − | 0.00129366i | −1.00000 | 0.000646829i | \(-0.999794\pi\) | |||
1.00000 | 0.000646829i | \(-0.000205892\pi\) | ||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.168479 | − | 0.664600i | 0.00690696 | − | 0.0272460i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.7103 | + | 8.35379i | 1.05225 | + | 0.341898i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.50993 | − | 6.18283i | 0.347706 | − | 0.252623i | −0.400200 | − | 0.916428i | \(-0.631059\pi\) |
0.747906 | + | 0.663804i | \(0.231059\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.45305 | + | 22.9381i | 0.304016 | + | 0.935665i | 0.980043 | + | 0.198788i | \(0.0637005\pi\) |
−0.676026 | + | 0.736877i | \(0.736300\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.560327 | + | 0.771224i | −0.0228183 | + | 0.0314067i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.3352 | + | 13.8377i | 0.826742 | + | 0.562582i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.46340 | + | 2.01420i | −0.0593975 | + | 0.0817537i | −0.837682 | − | 0.546158i | \(-0.816090\pi\) |
0.778285 | + | 0.627911i | \(0.216090\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.3722 | − | 31.9223i | −0.420302 | − | 1.29356i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.7694 | − | 12.1836i | 0.678415 | − | 0.492898i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.7338 | + | 11.6106i | 1.44328 | + | 0.468949i | 0.922917 | − | 0.384999i | \(-0.125798\pi\) |
0.520359 | + | 0.853948i | \(0.325798\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.0620 | + | 4.07178i | 0.647682 | + | 0.164190i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 45.5803i | − | 1.83499i | −0.397744 | − | 0.917496i | \(-0.630207\pi\) | ||
0.397744 | − | 0.917496i | \(-0.369793\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.77382 | − | 5.45924i | 0.0712957 | − | 0.219425i | −0.909059 | − | 0.416667i | \(-0.863198\pi\) |
0.980355 | + | 0.197241i | \(0.0631982\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.3330 | − | 12.5932i | 0.695550 | − | 0.505347i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.0427 | − | 9.43655i | 1.16357 | − | 0.378067i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.26491 | − | 24.9680i | 0.0505964 | − | 0.998719i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.4581 | − | 3.60197i | −0.417655 | − | 0.143849i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.225437 | + | 0.163789i | 0.00898875 | + | 0.00653071i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.70103 | − | 11.3906i | −0.147336 | − | 0.453453i | 0.849968 | − | 0.526834i | \(-0.176621\pi\) |
−0.997304 | + | 0.0733811i | \(0.976621\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.9753 | − | 20.6118i | −0.595216 | − | 0.819245i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.2453 | − | 27.3585i | 0.684358 | − | 1.08569i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 42.3621i | 1.67845i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.36753 | −0.133217 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.8526 | + | 33.4007i | −0.428650 | + | 1.31925i | 0.470805 | + | 0.882237i | \(0.343964\pi\) |
−0.899455 | + | 0.437013i | \(0.856036\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.9529 | − | 28.8392i | −0.826302 | − | 1.13731i | −0.988600 | − | 0.150565i | \(-0.951891\pi\) |
0.162298 | − | 0.986742i | \(-0.448109\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.0618 | − | 0.861826i | 0.514307 | − | 0.0339344i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.8476 | − | 16.3068i | 0.465778 | − | 0.641088i | −0.509917 | − | 0.860224i | \(-0.670324\pi\) |
0.975694 | + | 0.219136i | \(0.0703238\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.26781 | + | 3.68791i | −0.206780 | + | 0.144763i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 58.2661 | + | 42.3328i | 2.28363 | + | 1.65915i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.1905 | + | 7.53504i | −0.907513 | + | 0.294869i | −0.725334 | − | 0.688397i | \(-0.758315\pi\) |
−0.182178 | + | 0.983266i | \(0.558315\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.7125 | + | 31.8239i | 0.496720 | + | 1.24346i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.96027 | − | 0.636930i | −0.0764774 | − | 0.0248490i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.98788 | −0.272209 | −0.136104 | − | 0.990694i | \(-0.543458\pi\) | ||||
−0.136104 | + | 0.990694i | \(0.543458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.61827 | −0.140735 | −0.0703673 | − | 0.997521i | \(-0.522417\pi\) | ||||
−0.0703673 | + | 0.997521i | \(0.522417\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.219726 | + | 0.0713934i | 0.00853346 | + | 0.00277269i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −21.4609 | + | 8.57285i | −0.832216 | + | 0.332441i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.4051 | + | 5.00542i | −0.596488 | + | 0.193811i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.0536 | + | 13.8432i | 0.736653 | + | 0.535210i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.6740 | + | 19.3501i | 0.991133 | + | 0.747001i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.68377 | − | 6.44665i | 0.180546 | − | 0.248500i | −0.709146 | − | 0.705062i | \(-0.750919\pi\) |
0.889692 | + | 0.456562i | \(0.150919\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 26.9069 | + | 4.96266i | 1.03565 | + | 0.191013i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.48443 | + | 11.6778i | 0.326083 | + | 0.448815i | 0.940312 | − | 0.340313i | \(-0.110533\pi\) |
−0.614229 | + | 0.789128i | \(0.710533\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.3146 | − | 34.8229i | 0.434216 | − | 1.33638i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.9159 | −0.609898 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.6723i | 1.13538i | 0.823242 | + | 0.567690i | \(0.192163\pi\) | ||||
−0.823242 | + | 0.567690i | \(0.807837\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.31682 | − | 2.08904i | 0.0503130 | − | 0.0798183i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.7869 | − | 20.3524i | −0.564156 | − | 0.776493i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.60321 | − | 4.93417i | −0.0610774 | − | 0.187977i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.1812 | + | 19.0218i | 0.995980 | + | 0.723622i | 0.961223 | − | 0.275774i | \(-0.0889341\pi\) |
0.0347577 | + | 0.999396i | \(0.488934\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.111386 | + | 6.35120i | −0.00423121 | + | 0.241262i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.0242 | + | 14.1714i | −0.645765 | + | 0.537553i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.266353 | − | 0.0865432i | 0.0100888 | − | 0.00327806i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −33.8992 | + | 24.6292i | −1.28219 | + | 0.931562i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.86089 | − | 18.0380i | 0.221363 | − | 0.681284i | −0.777278 | − | 0.629157i | \(-0.783400\pi\) |
0.998640 | − | 0.0521266i | \(-0.0165999\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9.39242i | − | 0.354242i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.89228 | + | 31.1328i | −0.297241 | + | 1.17253i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.05806 | − | 0.343785i | −0.0397925 | − | 0.0129294i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.78617 | − | 4.93044i | 0.254860 | − | 0.185167i | −0.453018 | − | 0.891501i | \(-0.649653\pi\) |
0.707878 | + | 0.706335i | \(0.249653\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.785540 | − | 2.41764i | −0.0294600 | − | 0.0906687i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.4290 | − | 28.1182i | 0.765074 | − | 1.05303i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.836934 | + | 17.2967i | 0.0312995 | + | 0.646859i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.0173 | − | 26.1751i | 0.710216 | − | 0.977528i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.33218 | + | 7.17771i | 0.0869756 | + | 0.267684i | 0.985079 | − | 0.172100i | \(-0.0550552\pi\) |
−0.898104 | + | 0.439783i | \(0.855055\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.29620 | − | 1.66829i | 0.0855150 | − | 0.0621303i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.8708 | + | 4.50690i | 0.515861 | + | 0.167614i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.1875 | − | 9.85449i | −0.675466 | − | 0.365987i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 24.2826i | − | 0.900593i | −0.892879 | − | 0.450297i | \(-0.851318\pi\) | ||
0.892879 | − | 0.450297i | \(-0.148682\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.11803 | + | 28.0624i | −0.337705 | + | 1.03935i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.178990 | − | 0.130044i | 0.00662019 | − | 0.00480985i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.3541 | − | 6.61345i | 0.751796 | − | 0.244273i | 0.0920424 | − | 0.995755i | \(-0.470660\pi\) |
0.659754 | + | 0.751482i | \(0.270660\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −41.9941 | − | 50.4477i | −1.54897 | − | 1.86079i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.91593 | − | 2.41943i | 0.291587 | − | 0.0891207i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.4419 | − | 20.6642i | −1.04625 | − | 0.760147i | −0.0747558 | − | 0.997202i | \(-0.523818\pi\) |
−0.971496 | + | 0.237055i | \(0.923818\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.40640 | − | 7.40615i | −0.0884015 | − | 0.272072i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.0435 | + | 27.5875i | 0.735324 | + | 1.01209i | 0.998874 | + | 0.0474407i | \(0.0151065\pi\) |
−0.263550 | + | 0.964646i | \(0.584893\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.6318 | − | 10.4837i | −0.609341 | − | 0.384095i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.22148i | 0.154456i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.1817 | −0.408572 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.0690 | − | 34.0669i | 0.403914 | − | 1.24312i | −0.517884 | − | 0.855451i | \(-0.673280\pi\) |
0.921799 | − | 0.387669i | \(-0.126720\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.24746 | + | 1.71698i | 0.0454599 | + | 0.0625701i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 48.1727 | − | 3.17847i | 1.75318 | − | 0.115676i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.2408 | − | 19.6008i | 0.517592 | − | 0.712404i | −0.467584 | − | 0.883948i | \(-0.654876\pi\) |
0.985176 | + | 0.171544i | \(0.0548756\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21.0076 | − | 0.368428i | −0.762528 | − | 0.0133731i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.62191 | − | 6.26419i | −0.312544 | − | 0.227077i | 0.420443 | − | 0.907319i | \(-0.361875\pi\) |
−0.732987 | + | 0.680242i | \(0.761875\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 37.4964 | − | 12.1833i | 1.35746 | − | 0.441065i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0485020 | − | 0.0193748i | 0.00175359 | − | 0.000700499i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.30566 | − | 1.39899i | −0.155468 | − | 0.0505147i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.8297 | −0.931444 | −0.465722 | − | 0.884931i | \(-0.654205\pi\) | ||||
−0.465722 | + | 0.884931i | \(0.654205\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.22289 | −0.260126 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.4679 | + | 3.72614i | 0.412471 | + | 0.134020i | 0.507899 | − | 0.861416i | \(-0.330422\pi\) |
−0.0954286 | + | 0.995436i | \(0.530422\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 44.0006 | − | 5.83177i | 1.58055 | − | 0.209484i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 35.1612 | − | 11.4246i | 1.26140 | − | 0.409854i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.63693 | − | 5.54855i | −0.273621 | − | 0.198798i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.3510 | + | 17.5992i | 0.835563 | + | 0.629750i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.3068 | − | 18.3153i | 0.475547 | − | 0.654534i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.502707 | − | 7.61899i | −0.0179424 | − | 0.271933i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.6725 | − | 14.6895i | −0.380435 | − | 0.523624i | 0.575265 | − | 0.817967i | \(-0.304899\pi\) |
−0.955700 | + | 0.294343i | \(0.904899\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.08954 | + | 21.8194i | −0.252394 | + | 0.776790i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −62.9867 | −2.23955 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.6342i | 0.803762i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.80051 | + | 4.28666i | 0.241189 | + | 0.152032i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.946725 | − | 1.30306i | −0.0335347 | − | 0.0461566i | 0.791920 | − | 0.610624i | \(-0.209081\pi\) |
−0.825455 | + | 0.564468i | \(0.809081\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.167746 | + | 0.516268i | 0.00593441 | + | 0.0182642i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.88197 | + | 1.36733i | 0.0664960 | + | 0.0483122i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.2641 | + | 14.6612i | 0.362213 | + | 0.517384i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −33.7385 | + | 28.0849i | −1.18913 | + | 0.989862i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −49.2356 | + | 15.9976i | −1.73318 | + | 0.563143i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.7273 | − | 15.0593i | 0.728733 | − | 0.529455i | −0.160429 | − | 0.987047i | \(-0.551288\pi\) |
0.889162 | + | 0.457592i | \(0.151288\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.5506 | + | 41.7045i | −0.475827 | + | 1.46444i | 0.369012 | + | 0.929424i | \(0.379696\pi\) |
−0.844839 | + | 0.535020i | \(0.820304\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1.71737i | − | 0.0602306i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −37.7370 | − | 9.56650i | −1.32187 | − | 0.335100i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.09233 | − | 2.30444i | −0.248129 | − | 0.0806220i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.61803 | + | 2.62866i | −0.126424 | + | 0.0918527i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.43938 | − | 16.7407i | −0.189836 | − | 0.584254i | 0.810163 | − | 0.586205i | \(-0.199379\pi\) |
−0.999998 | + | 0.00195152i | \(0.999379\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.43854 | + | 10.2383i | −0.259291 | + | 0.356884i | −0.918738 | − | 0.394867i | \(-0.870791\pi\) |
0.659447 | + | 0.751751i | \(0.270791\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18.1431 | − | 19.7684i | −0.631660 | − | 0.688246i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.19856 | + | 7.15520i | −0.180772 | + | 0.248811i | −0.889780 | − | 0.456389i | \(-0.849143\pi\) |
0.709009 | + | 0.705200i | \(0.249143\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.6571 | − | 35.8767i | −0.404866 | − | 1.24605i | −0.921007 | − | 0.389546i | \(-0.872632\pi\) |
0.516141 | − | 0.856504i | \(-0.327368\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.68303 | + | 6.30859i | −0.301211 | + | 0.218843i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.05510 | − | 0.342823i | −0.0365571 | − | 0.0118781i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.16576 | + | 1.81655i | 0.247981 | + | 0.0628643i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 48.5765i | 1.67905i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.8934 | + | 36.6041i | −0.410606 | + | 1.26372i | 0.505517 | + | 0.862817i | \(0.331302\pi\) |
−0.916123 | + | 0.400898i | \(0.868698\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.61452 | − | 6.98536i | 0.331535 | − | 0.240874i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.0774 | + | 7.82321i | −0.829269 | + | 0.269446i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.9712 | − | 10.7976i | 0.446223 | − | 0.371449i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.9647 | − | 43.4580i | 1.16704 | − | 1.49324i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.4536 | + | 21.3993i | 1.01084 | + | 0.734421i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.51328 | − | 16.9681i | −0.188993 | − | 0.581660i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.9122 | + | 41.1706i | 1.02417 | + | 1.40965i | 0.909237 | + | 0.416280i | \(0.136666\pi\) |
0.114936 | + | 0.993373i | \(0.463334\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.48926 | − | 0.938744i | −0.0509315 | − | 0.0321044i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.5197i | 0.393506i | 0.980453 | + | 0.196753i | \(0.0630397\pi\) | ||||
−0.980453 | + | 0.196753i | \(0.936960\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.9497 | 0.817153 | 0.408577 | − | 0.912724i | \(-0.366025\pi\) | ||||
0.408577 | + | 0.912724i | \(0.366025\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.4821 | − | 35.3384i | 0.391310 | − | 1.20433i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.5170 | + | 32.3684i | 0.800530 | + | 1.10183i | 0.992716 | + | 0.120476i | \(0.0384421\pi\) |
−0.192187 | + | 0.981358i | \(0.561558\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.755018 | + | 11.4430i | 0.0256714 | + | 0.389074i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.1644 | − | 22.2484i | 0.548972 | − | 0.755595i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.18793 | + | 20.8696i | −0.243834 | + | 0.707954i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.71460 | + | 3.42536i | 0.159748 | + | 0.116064i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.65270 | − | 0.861914i | 0.0897802 | − | 0.0291714i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −55.6804 | − | 6.51646i | −1.88234 | − | 0.220297i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.7104 | − | 8.02891i | −0.834413 | − | 0.271117i | −0.139510 | − | 0.990221i | \(-0.544553\pi\) |
−0.694903 | + | 0.719104i | \(0.744553\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29.4300 | 0.992648 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.1372 | 0.846893 | 0.423446 | − | 0.905921i | \(-0.360820\pi\) | ||||
0.423446 | + | 0.905921i | \(0.360820\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.3431 | + | 13.4332i | 1.39131 | + | 0.452063i | 0.906369 | − | 0.422486i | \(-0.138843\pi\) |
0.484937 | + | 0.874549i | \(0.338843\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.51430 | − | 2.60223i | 0.218976 | − | 0.0874731i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.2078 | + | 8.84036i | −0.913549 | + | 0.296830i | −0.727818 | − | 0.685770i | \(-0.759465\pi\) |
−0.185731 | + | 0.982601i | \(0.559465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −58.6701 | − | 42.6263i | −1.96773 | − | 1.42964i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.9430 | − | 14.6619i | 0.701617 | − | 0.491191i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.7547 | − | 14.8026i | 0.359892 | − | 0.495349i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.2174 | − | 2.12573i | 1.07691 | − | 0.0710553i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.69471 | − | 11.9672i | −0.290308 | − | 0.399575i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.3488 | − | 34.9281i | 0.378504 | − | 1.16492i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.135868 | 0.00452643 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 29.3536i | − | 0.976827i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.5219 | + | 14.1965i | 0.748652 | + | 0.471908i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.0438 | − | 38.5990i | −0.931179 | − | 1.28166i | −0.959398 | − | 0.282056i | \(-0.908983\pi\) |
0.0282187 | − | 0.999602i | \(-0.491017\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.0261885 | − | 0.0805998i | −0.000868617 | − | 0.00267333i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.3003 | + | 29.2799i | 1.33521 | + | 0.970085i | 0.999606 | + | 0.0280809i | \(0.00893959\pi\) |
0.335602 | + | 0.942004i | \(0.391060\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.0621 | − | 29.2724i | 0.730150 | − | 0.968775i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −22.4375 | − | 26.9543i | −0.741761 | − | 0.891081i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 73.0845 | − | 23.7466i | 2.41346 | − | 0.784182i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.7058 | − | 25.2153i | 1.14484 | − | 0.831775i | 0.157053 | − | 0.987590i | \(-0.449801\pi\) |
0.987786 | + | 0.155815i | \(0.0498005\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.19098 | + | 19.0539i | −0.204000 | + | 0.627847i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.5862i | 0.677602i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.8543 | − | 20.0328i | 0.356889 | − | 0.658674i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.205628 | + | 0.0668126i | 0.00675371 | + | 0.00219441i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.20719 | + | 2.33016i | −0.105224 | + | 0.0764500i | −0.639153 | − | 0.769079i | \(-0.720715\pi\) |
0.533929 | + | 0.845529i | \(0.320715\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.5553 | + | 35.5635i | 0.378709 | + | 1.16555i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.94941 | + | 12.3178i | −0.292991 | + | 0.403267i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.437576 | − | 0.119131i | −0.0143103 | − | 0.00389601i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.24563 | − | 1.71446i | 0.0406929 | − | 0.0560090i | −0.788186 | − | 0.615437i | \(-0.788979\pi\) |
0.828879 | + | 0.559429i | \(0.188979\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.61585 | − | 23.4392i | −0.248534 | − | 0.764909i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.08118 | + | 2.96515i | −0.133043 | + | 0.0966612i | −0.652316 | − | 0.757947i | \(-0.726203\pi\) |
0.519274 | + | 0.854608i | \(0.326203\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.0537 | − | 5.54107i | −0.555344 | − | 0.180442i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.0766 | − | 59.4728i | 0.490442 | − | 1.93465i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 0.986192i | − | 0.0320470i | −0.999872 | − | 0.0160235i | \(-0.994899\pi\) | ||
0.999872 | − | 0.0160235i | \(-0.00510065\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.89364 | + | 11.9834i | −0.126393 | + | 0.388998i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.6150 | − | 12.7981i | 0.571206 | − | 0.415006i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.8386 | + | 7.09580i | −0.707422 | + | 0.229855i | −0.640562 | − | 0.767907i | \(-0.721298\pi\) |
−0.0668608 | + | 0.997762i | \(0.521298\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.0759 | + | 15.0469i | −0.584924 | + | 0.486907i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.2320 | + | 6.48934i | −0.686331 | + | 0.209770i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.47994 | − | 3.25486i | −0.144665 | − | 0.105105i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.7718 | + | 45.4628i | 0.476508 | + | 1.46654i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.500670 | − | 0.689113i | −0.0161339 | − | 0.0222064i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.80530 | − | 9.20972i | 0.186879 | − | 0.296472i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.1267i | 0.647231i | 0.946189 | + | 0.323616i | \(0.104898\pi\) | ||||
−0.946189 | + | 0.323616i | \(0.895102\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.203937 | 0.00655141 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.77852 | − | 20.8621i | 0.217533 | − | 0.669498i | −0.781431 | − | 0.623991i | \(-0.785510\pi\) |
0.998964 | − | 0.0455060i | \(-0.0144900\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.1959 | + | 40.1847i | 0.935978 | + | 1.28826i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.42637 | − | 18.5773i | 0.109732 | − | 0.594950i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.7133 | + | 47.7788i | −1.11058 | + | 1.52858i | −0.290015 | + | 0.957022i | \(0.593660\pi\) |
−0.820562 | + | 0.571557i | \(0.806340\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.90396 | − | 19.3167i | −0.188691 | − | 0.617365i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.42976 | + | 1.76533i | 0.0775763 | + | 0.0563625i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.9751 | − | 14.9382i | 1.46638 | − | 0.476455i | 0.536367 | − | 0.843985i | \(-0.319796\pi\) |
0.930012 | + | 0.367530i | \(0.119796\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.1745 | + | 13.2520i | −1.05703 | + | 0.422245i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 68.4960 | + | 22.2557i | 2.18025 | + | 0.708406i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.1655 | −0.450437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.0154 | 1.74762 | 0.873811 | − | 0.486266i | \(-0.161641\pi\) | ||||
0.873811 | + | 0.486266i | \(0.161641\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.88201 | + | 1.91118i | 0.186660 | + | 0.0606495i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.8589 | − | 34.6936i | −0.439356 | − | 1.09986i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.8457 | + | 7.09810i | −0.691861 | + | 0.224799i | −0.633781 | − | 0.773513i | \(-0.718498\pi\) |
−0.0580799 | + | 0.998312i | \(0.518498\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.1736 | + | 14.6569i | 0.638263 | + | 0.463725i |
(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 | 880.2.cd.b.609.4 | 16 | ||
4.3 | odd | 2 | 110.2.j.b.59.2 | ✓ | 16 | ||
5.4 | even | 2 | inner | 880.2.cd.b.609.2 | 16 | ||
11.3 | even | 5 | inner | 880.2.cd.b.289.2 | 16 | ||
12.11 | even | 2 | 990.2.ba.h.829.3 | 16 | |||
20.3 | even | 4 | 550.2.h.n.301.1 | 8 | |||
20.7 | even | 4 | 550.2.h.j.301.2 | 8 | |||
20.19 | odd | 2 | 110.2.j.b.59.4 | yes | 16 | ||
44.3 | odd | 10 | 110.2.j.b.69.4 | yes | 16 | ||
44.27 | odd | 10 | 1210.2.b.k.969.1 | 8 | |||
44.39 | even | 10 | 1210.2.b.l.969.5 | 8 | |||
55.14 | even | 10 | inner | 880.2.cd.b.289.4 | 16 | ||
60.59 | even | 2 | 990.2.ba.h.829.1 | 16 | |||
132.47 | even | 10 | 990.2.ba.h.289.1 | 16 | |||
220.3 | even | 20 | 550.2.h.n.201.1 | 8 | |||
220.27 | even | 20 | 6050.2.a.di.1.2 | 4 | |||
220.39 | even | 10 | 1210.2.b.l.969.3 | 8 | |||
220.47 | even | 20 | 550.2.h.j.201.2 | 8 | |||
220.83 | odd | 20 | 6050.2.a.dl.1.4 | 4 | |||
220.127 | odd | 20 | 6050.2.a.da.1.1 | 4 | |||
220.159 | odd | 10 | 1210.2.b.k.969.7 | 8 | |||
220.179 | odd | 10 | 110.2.j.b.69.2 | yes | 16 | ||
220.203 | even | 20 | 6050.2.a.dd.1.3 | 4 | |||
660.179 | even | 10 | 990.2.ba.h.289.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
110.2.j.b.59.2 | ✓ | 16 | 4.3 | odd | 2 | ||
110.2.j.b.59.4 | yes | 16 | 20.19 | odd | 2 | ||
110.2.j.b.69.2 | yes | 16 | 220.179 | odd | 10 | ||
110.2.j.b.69.4 | yes | 16 | 44.3 | odd | 10 | ||
550.2.h.j.201.2 | 8 | 220.47 | even | 20 | |||
550.2.h.j.301.2 | 8 | 20.7 | even | 4 | |||
550.2.h.n.201.1 | 8 | 220.3 | even | 20 | |||
550.2.h.n.301.1 | 8 | 20.3 | even | 4 | |||
880.2.cd.b.289.2 | 16 | 11.3 | even | 5 | inner | ||
880.2.cd.b.289.4 | 16 | 55.14 | even | 10 | inner | ||
880.2.cd.b.609.2 | 16 | 5.4 | even | 2 | inner | ||
880.2.cd.b.609.4 | 16 | 1.1 | even | 1 | trivial | ||
990.2.ba.h.289.1 | 16 | 132.47 | even | 10 | |||
990.2.ba.h.289.3 | 16 | 660.179 | even | 10 | |||
990.2.ba.h.829.1 | 16 | 60.59 | even | 2 | |||
990.2.ba.h.829.3 | 16 | 12.11 | even | 2 | |||
1210.2.b.k.969.1 | 8 | 44.27 | odd | 10 | |||
1210.2.b.k.969.7 | 8 | 220.159 | odd | 10 | |||
1210.2.b.l.969.3 | 8 | 220.39 | even | 10 | |||
1210.2.b.l.969.5 | 8 | 44.39 | even | 10 | |||
6050.2.a.da.1.1 | 4 | 220.127 | odd | 20 | |||
6050.2.a.dd.1.3 | 4 | 220.203 | even | 20 | |||
6050.2.a.di.1.2 | 4 | 220.27 | even | 20 | |||
6050.2.a.dl.1.4 | 4 | 220.83 | odd | 20 |