Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(47,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(42))
chi = DirichletCharacter(H, H._module([21, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.bp (of order \(42\), degree \(12\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(120\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{42})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{42}]$ |
Embedding invariants
Embedding label | 495.8 | ||
Character | \(\chi\) | \(=\) | 784.495 |
Dual form | 784.2.bp.c.255.8 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{29}{42}\right)\) |
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 | ||||||||
\(3\) | 1.30128 | + | 0.887199i | 0.751296 | + | 0.512225i | 0.877381 | − | 0.479795i | \(-0.159289\pi\) |
−0.126085 | + | 0.992019i | \(0.540241\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.55166 | − | 0.266160i | −1.58835 | − | 0.119030i | −0.748981 | − | 0.662592i | \(-0.769456\pi\) |
−0.839369 | + | 0.543561i | \(0.817076\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.60649 | + | 0.454131i | 0.985159 | + | 0.171645i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.189810 | − | 0.483628i | −0.0632701 | − | 0.161209i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.28740 | + | 1.29021i | 0.991187 | + | 0.389012i | 0.804853 | − | 0.593474i | \(-0.202244\pi\) |
0.186334 | + | 0.982486i | \(0.440339\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.33630 | − | 1.06566i | 0.370623 | − | 0.295562i | −0.420411 | − | 0.907334i | \(-0.638114\pi\) |
0.791035 | + | 0.611771i | \(0.209543\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.38557 | − | 3.49738i | −1.13235 | − | 0.903019i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.60104 | + | 4.95874i | 1.11592 | + | 1.20267i | 0.977196 | + | 0.212339i | \(0.0681081\pi\) |
0.138719 | + | 0.990332i | \(0.455701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.26170 | − | 2.18533i | 0.289454 | − | 0.501349i | −0.684226 | − | 0.729270i | \(-0.739860\pi\) |
0.973679 | + | 0.227922i | \(0.0731930\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.98887 | + | 2.90342i | 0.652224 | + | 0.633579i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.90853 | + | 5.29013i | −1.02350 | + | 1.10307i | −0.0288676 | + | 0.999583i | \(0.509190\pi\) |
−0.994631 | + | 0.103486i | \(0.967000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.59929 | + | 1.14541i | 1.51986 | + | 0.229082i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.23345 | − | 5.40412i | 0.237378 | − | 1.04002i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.815942 | + | 3.57488i | 0.151517 | + | 0.663838i | 0.992445 | + | 0.122691i | \(0.0391525\pi\) |
−0.840928 | + | 0.541147i | \(0.817990\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.53827 | + | 4.39641i | 0.455886 | + | 0.789618i | 0.998739 | − | 0.0502101i | \(-0.0159891\pi\) |
−0.542853 | + | 0.839828i | \(0.682656\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.13316 | + | 4.59550i | 0.545413 | + | 0.799974i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.13648 | − | 2.30666i | −1.54435 | − | 0.389897i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.30934 | − | 0.712338i | −0.379654 | − | 0.117108i | 0.0990538 | − | 0.995082i | \(-0.468418\pi\) |
−0.478708 | + | 0.877974i | \(0.658895\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.68436 | − | 0.201165i | 0.429842 | − | 0.0322122i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.85892 | + | 8.01313i | 0.602662 | + | 1.25144i | 0.949574 | + | 0.313543i | \(0.101516\pi\) |
−0.346912 | + | 0.937898i | \(0.612770\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.185940 | + | 0.386109i | −0.0283556 | + | 0.0588811i | −0.914666 | − | 0.404212i | \(-0.867546\pi\) |
0.886310 | + | 0.463093i | \(0.153260\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.545418 | + | 1.76820i | 0.0813062 | + | 0.263588i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.8599 | − | 1.93832i | 1.87581 | − | 0.282733i | 0.890693 | − | 0.454606i | \(-0.150220\pi\) |
0.985119 | + | 0.171873i | \(0.0549819\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.58753 | + | 2.36737i | 0.941076 | + | 0.338196i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.58786 | + | 10.5348i | 0.222345 | + | 1.47516i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.74376 | + | 1.15480i | −0.514245 | + | 0.158624i | −0.541007 | − | 0.841018i | \(-0.681957\pi\) |
0.0267618 | + | 0.999642i | \(0.491480\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.3323 | − | 5.45735i | −1.52805 | − | 0.735869i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.58065 | − | 1.72435i | 0.474268 | − | 0.228396i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.392828 | − | 5.24192i | −0.0511418 | − | 0.682440i | −0.962579 | − | 0.271001i | \(-0.912645\pi\) |
0.911437 | − | 0.411439i | \(-0.134974\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.85033 | − | 12.4825i | 0.492984 | − | 1.59822i | −0.277479 | − | 0.960732i | \(-0.589499\pi\) |
0.770463 | − | 0.637484i | \(-0.220025\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.275107 | − | 1.34677i | −0.0346602 | − | 0.169677i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.02972 | + | 3.42921i | −0.623861 | + | 0.425341i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.82791 | + | 5.09679i | −1.07850 | + | 0.622672i | −0.930491 | − | 0.366314i | \(-0.880620\pi\) |
−0.148009 | + | 0.988986i | \(0.547286\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.0808 | + | 2.52912i | −1.33397 | + | 0.304470i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.4127 | − | 2.60487i | −1.35444 | − | 0.309142i | −0.517146 | − | 0.855897i | \(-0.673006\pi\) |
−0.837292 | + | 0.546755i | \(0.815863\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.665073 | − | 4.41247i | 0.0778409 | − | 0.516440i | −0.915600 | − | 0.402091i | \(-0.868284\pi\) |
0.993441 | − | 0.114349i | \(-0.0364784\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.87261 | + | 8.23258i | 1.02452 | + | 0.950616i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.98262 | + | 4.85581i | 0.909704 | + | 0.553371i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.38475 | − | 3.10889i | −0.605832 | − | 0.349777i | 0.165500 | − | 0.986210i | \(-0.447076\pi\) |
−0.771332 | + | 0.636432i | \(0.780409\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.25704 | − | 4.87782i | 0.584116 | − | 0.541980i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.83732 | − | 7.31977i | 0.640729 | − | 0.803449i | −0.350365 | − | 0.936613i | \(-0.613942\pi\) |
0.991094 | + | 0.133164i | \(0.0425138\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.0215 | − | 18.8364i | −1.62931 | − | 2.04309i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.10986 | + | 5.37583i | −0.226200 | + | 0.576349i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.37597 | + | 2.89485i | −0.781851 | + | 0.306854i | −0.722489 | − | 0.691383i | \(-0.757002\pi\) |
−0.0593621 | + | 0.998237i | \(0.518907\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.96700 | − | 2.17078i | 0.415855 | − | 0.227560i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.597487 | + | 7.97291i | −0.0619565 | + | 0.826753i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.06277 | + | 7.42573i | −0.519430 | + | 0.761863i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.29761i | 0.537891i | 0.963155 | + | 0.268945i | \(0.0866751\pi\) | ||||
−0.963155 | + | 0.268945i | \(0.913325\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.83477i | − | 0.184402i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.88842 | + | 10.1035i | −0.685423 | + | 1.00533i | 0.313031 | + | 0.949743i | \(0.398656\pi\) |
−0.998454 | + | 0.0555881i | \(0.982297\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.889060 | − | 11.8637i | 0.0876017 | − | 1.16896i | −0.764157 | − | 0.645030i | \(-0.776845\pi\) |
0.851759 | − | 0.523934i | \(-0.175536\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.84266 | − | 11.1075i | −0.960546 | − | 1.08398i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.47400 | − | 0.970972i | 0.239170 | − | 0.0938674i | −0.242729 | − | 0.970094i | \(-0.578042\pi\) |
0.481899 | + | 0.876227i | \(0.339947\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.43709 | − | 6.20959i | 0.233431 | − | 0.594771i | −0.765378 | − | 0.643582i | \(-0.777448\pi\) |
0.998808 | + | 0.0488103i | \(0.0155430\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.37312 | − | 2.97580i | −0.225247 | − | 0.282451i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.36228 | − | 10.4860i | 0.786657 | − | 0.986437i | −0.213298 | − | 0.976987i | \(-0.568421\pi\) |
0.999955 | − | 0.00944959i | \(-0.00300794\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.8414 | − | 17.4823i | 1.75697 | − | 1.63023i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.769029 | − | 0.443999i | −0.0710968 | − | 0.0410478i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.74062 | + | 15.0144i | 0.892921 | + | 1.37636i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.07876 | + | 1.00094i | 0.0980691 | + | 0.0909948i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.08770 | + | 13.8510i | −0.188241 | + | 1.24890i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.32361 | − | 2.12805i | −0.833929 | − | 0.190339i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.3211 | − | 2.58396i | 1.00458 | − | 0.229289i | 0.311576 | − | 0.950221i | \(-0.399143\pi\) |
0.693006 | + | 0.720932i | \(0.256286\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.584516 | + | 0.337471i | −0.0514638 | + | 0.0297126i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.08172 | − | 2.10108i | 0.269251 | − | 0.183572i | −0.421167 | − | 0.906983i | \(-0.638379\pi\) |
0.690417 | + | 0.723411i | \(0.257427\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.28103 | − | 5.12305i | 0.371212 | − | 0.444225i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.81917 | + | 18.8653i | −0.500834 | + | 1.62366i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.624269 | + | 8.33029i | 0.0533349 | + | 0.711704i | 0.958217 | + | 0.286042i | \(0.0923397\pi\) |
−0.904882 | + | 0.425662i | \(0.860041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.6728 | + | 7.06605i | −1.24453 | + | 0.599334i | −0.936040 | − | 0.351893i | \(-0.885538\pi\) |
−0.308490 | + | 0.951228i | \(0.599824\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.4541 | + | 8.88701i | 1.55411 | + | 0.748421i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.76788 | − | 1.77916i | 0.482334 | − | 0.148780i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.94646 | − | 12.9139i | −0.161645 | − | 1.07244i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.47191 | + | 8.92507i | 0.533794 | + | 0.736127i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.30993 | + | 0.197440i | −0.107313 | + | 0.0161749i | −0.202479 | − | 0.979287i | \(-0.564900\pi\) |
0.0951660 | + | 0.995461i | \(0.469662\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.67155 | − | 21.6286i | −0.542923 | − | 1.76011i | −0.643778 | − | 0.765212i | \(-0.722634\pi\) |
0.100855 | − | 0.994901i | \(-0.467842\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.52486 | − | 3.16641i | 0.123278 | − | 0.255989i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.84491 | − | 16.2901i | −0.630118 | − | 1.30845i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.542763 | + | 0.0406744i | −0.0433172 | + | 0.00324617i | −0.0963711 | − | 0.995345i | \(-0.530724\pi\) |
0.0530539 | + | 0.998592i | \(0.483104\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.89622 | − | 1.81874i | −0.467601 | − | 0.144236i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.1964 | + | 11.5595i | −1.19765 | + | 0.911019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.28737 | + | 4.82169i | 0.257487 | + | 0.377664i | 0.933115 | − | 0.359579i | \(-0.117080\pi\) |
−0.675628 | + | 0.737243i | \(0.736127\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.90477 | − | 17.1556i | −0.771085 | − | 1.33556i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.555158 | + | 2.43231i | 0.0429594 | + | 0.188218i | 0.991855 | − | 0.127373i | \(-0.0406545\pi\) |
−0.948895 | + | 0.315591i | \(0.897797\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.24271 | + | 9.82596i | −0.172516 | + | 0.755843i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.29637 | − | 0.195396i | −0.0991359 | − | 0.0149423i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.95821 | + | 6.42142i | −0.452994 | + | 0.488212i | −0.917712 | − | 0.397247i | \(-0.869965\pi\) |
0.464717 | + | 0.885459i | \(0.346156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.2873 | + | 6.43656i | 1.45798 | + | 0.486558i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.13945 | − | 7.16973i | 0.311140 | − | 0.538910i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.64626 | − | 7.16296i | −0.496765 | − | 0.535385i | 0.434044 | − | 0.900892i | \(-0.357086\pi\) |
−0.930809 | + | 0.365507i | \(0.880896\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.59003 | + | 1.26800i | 0.118186 | + | 0.0942500i | 0.680799 | − | 0.732470i | \(-0.261633\pi\) |
−0.562613 | + | 0.826720i | \(0.690204\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.0848 | − | 12.8272i | 1.18902 | − | 0.948214i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.01241 | + | 3.14464i | 0.589084 | + | 0.231198i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.72762 | + | 22.2376i | 0.638227 | + | 1.62618i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.66916 | − | 13.5256i | 0.412370 | − | 0.983842i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.06050 | − | 0.229353i | −0.221450 | − | 0.0165954i | −0.0364569 | − | 0.999335i | \(-0.511607\pi\) |
−0.184993 | + | 0.982740i | \(0.559226\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.46724 | − | 6.45465i | −0.681467 | − | 0.464616i | 0.172455 | − | 0.985017i | \(-0.444830\pi\) |
−0.853922 | + | 0.520401i | \(0.825782\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.58748 | −0.686574 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.1900 | −1.36723 | −0.683617 | − | 0.729841i | \(-0.739594\pi\) | ||||
−0.683617 | + | 0.729841i | \(0.739594\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.245318 | + | 0.167255i | 0.0173901 | + | 0.0118564i | 0.571984 | − | 0.820265i | \(-0.306174\pi\) |
−0.554594 | + | 0.832121i | \(0.687126\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.0095 | − | 1.19974i | −1.12922 | − | 0.0846234i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.503279 | + | 9.68841i | 0.0353233 | + | 0.679993i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.5728 | − | 29.4870i | −0.808279 | − | 2.05946i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.49015 | + | 1.36978i | 0.242582 | + | 0.0952064i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.96723 | − | 5.55618i | 0.481933 | − | 0.384329i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.216716 | + | 0.172825i | 0.0149194 | + | 0.0118978i | 0.630921 | − | 0.775847i | \(-0.282677\pi\) |
−0.616002 | + | 0.787745i | \(0.711249\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.5401 | − | 13.5150i | −0.859234 | − | 0.926034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.763163 | − | 1.32184i | 0.0520473 | − | 0.0901486i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.61941 | + | 12.6119i | 0.313586 | + | 0.856150i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.78019 | − | 5.15182i | 0.323015 | − | 0.348127i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.4327 | + | 1.72321i | 0.769048 | + | 0.115915i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.36963 | + | 23.5259i | −0.359577 | + | 1.57541i | 0.394673 | + | 0.918822i | \(0.370858\pi\) |
−0.754250 | + | 0.656587i | \(0.771999\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.888470 | − | 3.89264i | −0.0592313 | − | 0.259509i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.87817 | − | 17.1095i | −0.655637 | − | 1.13560i | −0.981734 | − | 0.190260i | \(-0.939067\pi\) |
0.326097 | − | 0.945336i | \(-0.394267\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.8131 | + | 21.7268i | 0.978876 | + | 1.43575i | 0.898495 | + | 0.438983i | \(0.144661\pi\) |
0.0803806 | + | 0.996764i | \(0.474386\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.07957 | + | 13.4010i | 0.400006 | + | 0.881719i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.2835 | − | 5.63970i | −1.19779 | − | 0.369469i | −0.369212 | − | 0.929345i | \(-0.620373\pi\) |
−0.828576 | + | 0.559876i | \(0.810849\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −46.1899 | + | 3.46146i | −3.01310 | + | 0.225801i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.24888 | − | 8.82289i | −0.275994 | − | 0.573108i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.6427 | − | 24.1762i | 0.753101 | − | 1.56383i | −0.0710585 | − | 0.997472i | \(-0.522638\pi\) |
0.824159 | − | 0.566358i | \(-0.191648\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.273352 | + | 0.886186i | 0.0176082 | + | 0.0570843i | 0.963951 | − | 0.266082i | \(-0.0857290\pi\) |
−0.946342 | + | 0.323166i | \(0.895253\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.27504 | + | 0.795085i | −0.338394 | + | 0.0510047i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −22.7666 | − | 10.1614i | −1.45450 | − | 0.649190i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.642816 | − | 4.26481i | −0.0409014 | − | 0.271363i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.0901 | − | 4.34622i | 0.892924 | − | 0.275430i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.0939 | − | 13.5293i | −1.77327 | − | 0.853961i | −0.963723 | − | 0.266904i | \(-0.913999\pi\) |
−0.809545 | − | 0.587057i | \(-0.800286\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.9616 | + | 11.0577i | −1.44359 | + | 0.695194i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.83560 | − | 37.8385i | −0.177572 | − | 2.36954i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.25124 | − | 26.7499i | 0.514698 | − | 1.66861i | −0.208542 | − | 0.978013i | \(-0.566872\pi\) |
0.723240 | − | 0.690597i | \(-0.242652\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.69578 | − | 2.90544i | −0.353918 | − | 0.180535i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.57404 | − | 1.07316i | 0.0974305 | − | 0.0664270i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.0646 | + | 5.81082i | −0.620612 | + | 0.358311i | −0.777107 | − | 0.629368i | \(-0.783314\pi\) |
0.156495 | + | 0.987679i | \(0.449980\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.6039 | − | 3.10501i | 0.835682 | − | 0.190739i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.1665 | − | 2.77693i | −0.744579 | − | 0.169945i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.0717249 | + | 0.475864i | −0.00437315 | + | 0.0290139i | −0.990911 | − | 0.134519i | \(-0.957051\pi\) |
0.986538 | + | 0.163533i | \(0.0522891\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.509332 | − | 0.472591i | −0.0309397 | − | 0.0287078i | 0.664551 | − | 0.747243i | \(-0.268623\pi\) |
−0.695491 | + | 0.718535i | \(0.744813\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.08811 | + | 0.694718i | 0.428992 | + | 0.0420463i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.5040 | + | 13.5701i | 1.41735 | + | 0.818306i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.8139 | + | 10.9617i | −0.709828 | + | 0.658624i | −0.950051 | − | 0.312093i | \(-0.898970\pi\) |
0.240223 | + | 0.970718i | \(0.422779\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.64444 | − | 2.06206i | 0.0984499 | − | 0.123452i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.16927 | + | 5.22809i | 0.248718 | + | 0.311882i | 0.890481 | − | 0.455021i | \(-0.150368\pi\) |
−0.641763 | + | 0.766903i | \(0.721797\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.31133 | − | 16.0810i | 0.375169 | − | 0.955916i | −0.611216 | − | 0.791464i | \(-0.709319\pi\) |
0.986385 | − | 0.164452i | \(-0.0525856\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.1762 | + | 5.17128i | −0.780490 | + | 0.306320i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.41921 | + | 22.6386i | 0.378914 | + | 1.33631i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.14913 | + | 28.6782i | −0.126420 | + | 1.68695i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.70003 | + | 6.89368i | −0.275521 | + | 0.404115i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.46030i | − | 0.494256i | −0.968983 | − | 0.247128i | \(-0.920513\pi\) | ||
0.968983 | − | 0.247128i | \(-0.0794868\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.7221i | 1.09004i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.0273 | − | 16.1741i | 0.639868 | − | 0.938514i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.921762 | + | 12.3001i | −0.0533069 | + | 0.711331i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.659995 | + | 0.921946i | −0.0380415 | + | 0.0531401i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.9276 | + | 7.03604i | −1.02991 | + | 0.404210i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.9974 | + | 43.3087i | −0.973268 | + | 2.47985i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.47927 | − | 3.10891i | −0.141499 | − | 0.177435i | 0.706032 | − | 0.708180i | \(-0.250484\pi\) |
−0.847531 | + | 0.530745i | \(0.821912\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.6824 | − | 14.6492i | 0.664587 | − | 0.833365i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.06319 | + | 3.77009i | −0.230402 | + | 0.213782i | −0.786922 | − | 0.617052i | \(-0.788327\pi\) |
0.556520 | + | 0.830834i | \(0.312136\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.0395 | + | 6.95103i | 0.680515 | + | 0.392895i | 0.800049 | − | 0.599935i | \(-0.204807\pi\) |
−0.119534 | + | 0.992830i | \(0.538140\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.618629 | + | 4.85649i | 0.0348558 | + | 0.273632i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.1796 | + | 22.4353i | 1.35806 | + | 1.26009i | 0.935302 | + | 0.353852i | \(0.115128\pi\) |
0.422757 | + | 0.906243i | \(0.361062\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.93001 | + | 12.8048i | −0.108060 | + | 0.716929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.08081 | + | 0.931419i | 0.227769 | + | 0.0519867i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.6416 | − | 3.79834i | 0.925963 | − | 0.211345i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.3756 | − | 6.56768i | 0.631003 | − | 0.364309i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.68048 | − | 5.91825i | 0.480032 | − | 0.327280i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 34.3994 | + | 0.787883i | 1.89650 | + | 0.0434374i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.80412 | − | 22.0584i | 0.373988 | − | 1.21244i | −0.551665 | − | 0.834066i | \(-0.686007\pi\) |
0.925653 | − | 0.378374i | \(-0.123517\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.0938299 | + | 1.25207i | 0.00514185 | + | 0.0686132i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.7103 | − | 15.7524i | 1.78715 | − | 0.860648i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4737 | + | 9.85964i | 1.11528 | + | 0.537089i | 0.898430 | − | 0.439117i | \(-0.144709\pi\) |
0.216846 | + | 0.976206i | \(0.430423\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.1848 | − | 6.22619i | 1.09629 | − | 0.338160i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.67201 | + | 17.7276i | 0.144697 | + | 0.960004i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.0952 | + | 9.16212i | 0.869059 | + | 0.494708i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 40.0283 | − | 6.03330i | 2.15505 | − | 0.324822i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.30059 | + | 10.7003i | 0.177185 | + | 0.574420i | 0.999981 | + | 0.00608367i | \(0.00193650\pi\) |
−0.822796 | + | 0.568336i | \(0.807587\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.05126 | − | 4.25949i | 0.109801 | − | 0.228005i | −0.838826 | − | 0.544399i | \(-0.816758\pi\) |
0.948628 | + | 0.316394i | \(0.102472\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.11071 | − | 8.53598i | −0.219413 | − | 0.455617i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.9450 | + | 1.71949i | −1.22124 | + | 0.0915191i | −0.669701 | − | 0.742631i | \(-0.733578\pi\) |
−0.551537 | + | 0.834150i | \(0.685959\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 39.8407 | + | 12.2892i | 2.11453 | + | 0.652245i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.645428 | + | 28.1798i | −0.0341597 | + | 1.49143i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.54511 | + | 8.13319i | 0.292660 | + | 0.429253i | 0.944206 | − | 0.329356i | \(-0.106832\pi\) |
−0.651546 | + | 0.758609i | \(0.725879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.31623 | + | 10.9400i | 0.332433 | + | 0.575791i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.515736 | + | 2.25958i | 0.0270691 | + | 0.118597i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.53653 | + | 15.4946i | −0.185111 | + | 0.811023i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.1288 | + | 1.67740i | 0.580920 | + | 0.0875596i | 0.432927 | − | 0.901429i | \(-0.357481\pi\) |
0.147993 | + | 0.988988i | \(0.452719\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.14291 | − | 3.38726i | 0.163614 | − | 0.176333i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.2825 | + | 1.30980i | −0.533840 | + | 0.0680016i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.7075 | − | 22.0101i | 0.657972 | − | 1.13964i | −0.323168 | − | 0.946342i | \(-0.604748\pi\) |
0.981140 | − | 0.193299i | \(-0.0619188\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.2446 | − | 11.0411i | −0.529031 | − | 0.570160i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.89996 | + | 3.90759i | 0.252361 | + | 0.201251i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.1095 | + | 13.6444i | −0.878856 | + | 0.700864i | −0.955119 | − | 0.296224i | \(-0.904273\pi\) |
0.0762629 | + | 0.997088i | \(0.475701\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.0244 | + | 6.68158i | 0.872186 | + | 0.342308i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.98296 | − | 25.4362i | −0.510106 | − | 1.29973i | −0.921538 | − | 0.388288i | \(-0.873067\pi\) |
0.411433 | − | 0.911440i | \(-0.365029\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −27.0591 | − | 19.3709i | −1.37906 | − | 0.987230i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.222027 | + | 0.0166386i | 0.0112862 | + | 0.000845787i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.47411 | − | 6.45934i | −0.480357 | − | 0.327502i | 0.298816 | − | 0.954311i | \(-0.403408\pi\) |
−0.779173 | + | 0.626809i | \(0.784361\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −48.8167 | −2.46877 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.87426 | 0.296317 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.2973 | + | 12.4749i | 0.920639 | + | 0.627681i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2364 | + | 1.21675i | 0.814883 | + | 0.0610670i | 0.475649 | − | 0.879635i | \(-0.342213\pi\) |
0.339234 | + | 0.940702i | \(0.389832\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.1160 | − | 2.86841i | 0.506433 | − | 0.143600i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.29814 | + | 21.1433i | 0.414389 | + | 1.05585i | 0.973891 | + | 0.227017i | \(0.0728973\pi\) |
−0.559502 | + | 0.828829i | \(0.689007\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.07699 | + | 3.16998i | 0.402343 | + | 0.157908i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.9695 | + | 15.9252i | −0.992293 | + | 0.791327i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.67266 | − | 5.32127i | −0.330752 | − | 0.263766i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.6711 | − | 12.5784i | −0.577098 | − | 0.621964i | 0.375270 | − | 0.926916i | \(-0.377550\pi\) |
−0.952368 | + | 0.304952i | \(0.901360\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.57827 | + | 11.3939i | −0.324482 | + | 0.562020i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.35662 | − | 13.8414i | 0.0667548 | − | 0.681090i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.6804 | + | 24.4437i | −1.11334 | + | 1.19989i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.3624 | − | 3.82277i | −1.24200 | − | 0.187202i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.10535 | + | 4.84287i | −0.0540000 | + | 0.236590i | −0.994725 | − | 0.102582i | \(-0.967290\pi\) |
0.940725 | + | 0.339172i | \(0.110147\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.52323 | + | 19.8176i | 0.220449 | + | 0.965850i | 0.957141 | + | 0.289622i | \(0.0935295\pi\) |
−0.736692 | + | 0.676228i | \(0.763613\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.37837 | − | 5.85151i | −0.164262 | − | 0.284510i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29.2848 | + | 42.9529i | 1.42052 | + | 2.08352i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.7045 | − | 30.7868i | 0.759994 | − | 1.48988i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.08410 | + | 2.80208i | 0.438585 | + | 0.135285i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.4586 | + | 1.53316i | −0.985458 | + | 0.0738499i | −0.557699 | − | 0.830043i | \(-0.688316\pi\) |
−0.427759 | + | 0.903893i | \(0.640697\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.10273 | − | 18.9020i | −0.437449 | − | 0.908373i | −0.996837 | − | 0.0794673i | \(-0.974678\pi\) |
0.559388 | − | 0.828906i | \(-0.311036\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.92432 | − | 18.5315i | 0.427888 | − | 0.888519i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.36759 | + | 17.4013i | 0.256767 | + | 0.832417i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.4443 | − | 4.43801i | 1.40530 | − | 0.211815i | 0.597782 | − | 0.801659i | \(-0.296049\pi\) |
0.807517 | + | 0.589844i | \(0.200811\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.105452 | − | 3.63527i | −0.00502153 | − | 0.173108i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.983142 | + | 6.52272i | 0.0467105 | + | 0.309904i | 0.999970 | + | 0.00775087i | \(0.00246720\pi\) |
−0.953259 | + | 0.302153i | \(0.902295\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.9674 | − | 8.31834i | 1.27838 | − | 0.394327i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.87975 | − | 0.905241i | −0.0889092 | − | 0.0428164i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.4178 | + | 14.1668i | −1.38831 | + | 0.668575i | −0.970754 | − | 0.240077i | \(-0.922827\pi\) |
−0.417556 | + | 0.908651i | \(0.637113\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.34719 | + | 31.3211i | 0.110525 | + | 1.47485i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.5073 | − | 34.0640i | 0.493678 | − | 1.60046i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.6672 | + | 6.65403i | −0.687610 | + | 0.311946i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.4381 | + | 15.2980i | −1.04961 | + | 0.715612i | −0.959896 | − | 0.280356i | \(-0.909548\pi\) |
−0.0897138 | + | 0.995968i | \(0.528595\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 32.4728 | − | 18.7482i | 1.51570 | − | 0.875089i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.8477 | − | 4.30187i | 0.877825 | − | 0.200358i | 0.240217 | − | 0.970719i | \(-0.422781\pi\) |
0.637608 | + | 0.770361i | \(0.279924\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.95266 | + | 0.673925i | 0.137222 | + | 0.0313199i | 0.290580 | − | 0.956851i | \(-0.406152\pi\) |
−0.153358 | + | 0.988171i | \(0.549009\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.24414 | − | 28.1580i | 0.196817 | − | 1.30580i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.6095 | − | 10.7720i | −0.537223 | − | 0.498470i | 0.364253 | − | 0.931300i | \(-0.381324\pi\) |
−0.901475 | + | 0.432830i | \(0.857515\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.3244 | + | 9.27569i | −1.16937 | + | 0.428312i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.742374 | − | 0.428610i | −0.0342068 | − | 0.0197493i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.10942 | + | 1.02939i | −0.0510112 | + | 0.0473315i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.0911 | − | 15.1618i | 0.554778 | − | 0.695670i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.26910 | + | 1.59140i | 0.0581079 | + | 0.0728650i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.01058 | + | 2.57491i | −0.0461746 | + | 0.117651i | −0.952100 | − | 0.305785i | \(-0.901081\pi\) |
0.905926 | + | 0.423436i | \(0.139176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.84509 | + | 1.50909i | −0.175321 | + | 0.0688085i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −30.0304 | + | 1.55998i | −1.36643 | + | 0.0709814i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.41001 | − | 18.8153i | 0.0640253 | − | 0.854359i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.6192 | − | 31.7095i | 0.979658 | − | 1.43689i | 0.0817802 | − | 0.996650i | \(-0.473939\pi\) |
0.897878 | − | 0.440244i | \(-0.145108\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.19094i | 0.415629i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 33.8831i | − | 1.52912i | −0.644551 | − | 0.764561i | \(-0.722956\pi\) | ||
0.644551 | − | 0.764561i | \(-0.277044\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.9727 | + | 20.4942i | −0.629299 | + | 0.923011i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.488343 | + | 6.51648i | −0.0219494 | + | 0.292894i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −28.5641 | − | 11.9724i | −1.28127 | − | 0.537037i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.7013 | + | 12.0494i | −1.37438 | + | 0.539404i | −0.933634 | − | 0.358228i | \(-0.883381\pi\) |
−0.440745 | + | 0.897632i | \(0.645286\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.43552 | + | 3.65765i | −0.0641345 | + | 0.163412i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.95459 | + | 7.46682i | 0.265502 | + | 0.332929i | 0.896655 | − | 0.442729i | \(-0.145990\pi\) |
−0.631153 | + | 0.775658i | \(0.717418\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.1544 | − | 34.0506i | 1.20836 | − | 1.51523i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.6360 | + | 10.7966i | −0.516772 | + | 0.479495i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.46266 | + | 3.73122i | 0.286452 | + | 0.165383i | 0.636341 | − | 0.771408i | \(-0.280447\pi\) |
−0.349889 | + | 0.936791i | \(0.613781\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.73734 | − | 11.1990i | 0.165330 | − | 0.495415i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.2535 | − | 9.51387i | −0.452704 | − | 0.420048i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.31528 | + | 41.8991i | −0.278284 | + | 1.84630i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.7765 | + | 10.2199i | 1.96927 | + | 0.449472i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.4504 | + | 3.06996i | −0.590407 | + | 0.134756i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.39895 | + | 1.38503i | −0.105100 | + | 0.0606794i | −0.551629 | − | 0.834090i | \(-0.685993\pi\) |
0.446529 | + | 0.894769i | \(0.352660\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.4215 | − | 10.5142i | 0.674334 | − | 0.459753i | −0.177115 | − | 0.984190i | \(-0.556677\pi\) |
0.851449 | + | 0.524437i | \(0.175724\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19.3877 | + | 25.4874i | 0.846147 | + | 1.11236i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.1220 | + | 32.8146i | −0.440920 | + | 1.42943i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.17309 | − | 28.9978i | −0.0944821 | − | 1.26078i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.46058 | + | 1.18495i | −0.106780 | + | 0.0514225i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.6960 | + | 6.59564i | 0.593239 | + | 0.285689i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.04522 | + | 2.79008i | −0.391059 | + | 0.120626i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.29368 | − | 15.2176i | −0.0989797 | − | 0.656688i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.6014 | + | 16.2818i | 0.801220 | + | 0.701305i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.9373 | − | 1.64853i | 0.470231 | − | 0.0708759i | 0.0903474 | − | 0.995910i | \(-0.471202\pi\) |
0.379883 | + | 0.925034i | \(0.375964\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.944101 | + | 3.06070i | 0.0405152 | + | 0.131347i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.3084 | + | 21.4057i | −0.441565 | + | 0.916920i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.20100 | − | 17.0295i | −0.350649 | − | 0.728131i | 0.648812 | − | 0.760949i | \(-0.275266\pi\) |
−0.999461 | + | 0.0328178i | \(0.989552\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.76771 | + | 0.507170i | −0.288839 | + | 0.0216455i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.84175 | + | 2.72732i | 0.376671 | + | 0.116188i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.6234 | − | 10.5487i | −0.536803 | − | 0.448574i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.63648 | + | 11.2007i | 0.324151 | + | 0.475442i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.4347 | − | 19.8054i | −0.484502 | − | 0.839183i | 0.515339 | − | 0.856986i | \(-0.327666\pi\) |
−0.999842 | + | 0.0178037i | \(0.994333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.162990 | + | 0.714108i | 0.00689376 | + | 0.0302035i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.37210 | + | 36.6806i | −0.353470 | + | 1.54865i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.8046 | + | 1.62853i | 0.455358 | + | 0.0686342i | 0.372717 | − | 0.927945i | \(-0.378426\pi\) |
0.0826413 | + | 0.996579i | \(0.473664\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.4909 | + | 35.0169i | −1.36690 | + | 1.47317i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.9176 | − | 10.3266i | 0.668475 | − | 0.433676i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.81437 | + | 4.87463i | −0.117984 | + | 0.204355i | −0.918969 | − | 0.394330i | \(-0.870977\pi\) |
0.800984 | + | 0.598685i | \(0.204310\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.2051 | + | 23.9314i | 0.929255 | + | 1.00150i | 0.999992 | + | 0.00400343i | \(0.00127433\pi\) |
−0.0707373 | + | 0.997495i | \(0.522535\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.77909 | − | 3.01372i | −0.157874 | − | 0.125900i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −43.3607 | + | 34.5790i | −1.80826 | + | 1.44204i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.20066 | − | 1.25617i | −0.133245 | − | 0.0522949i | 0.297782 | − | 0.954634i | \(-0.403753\pi\) |
−0.431027 | + | 0.902339i | \(0.641849\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.59298 | − | 16.7986i | −0.273995 | − | 0.698128i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.5390 | − | 16.4280i | 0.769128 | − | 0.681547i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.7971 | − | 1.03395i | −0.571419 | − | 0.0428220i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.61316 | + | 1.78162i | 0.108041 | + | 0.0736609i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.50362 | 0.185884 | 0.0929421 | − | 0.995672i | \(-0.470373\pi\) | ||||
0.0929421 | + | 0.995672i | \(0.470373\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.8101 | 0.527832 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.9717 | − | 17.0254i | −1.02720 | − | 0.700331i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.1208 | − | 1.65772i | −0.908391 | − | 0.0680745i | −0.387667 | − | 0.921800i | \(-0.626719\pi\) |
−0.520724 | + | 0.853725i | \(0.674338\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.5991 | − | 55.9184i | −1.25444 | − | 2.29243i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.170839 | + | 0.435292i | 0.00699199 | + | 0.0178153i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.36118 | − | 1.71164i | −0.178193 | − | 0.0699355i | 0.274567 | − | 0.961568i | \(-0.411465\pi\) |
−0.452760 | + | 0.891632i | \(0.649561\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.4581 | − | 12.3275i | 0.630550 | − | 0.502847i | −0.255273 | − | 0.966869i | \(-0.582165\pi\) |
0.885824 | + | 0.464022i | \(0.153594\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.14058 | + | 3.30200i | 0.168617 | + | 0.134468i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.56498 | − | 3.84213i | −0.144937 | − | 0.156205i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.5186 | − | 28.6111i | 0.670470 | − | 1.16129i | −0.307301 | − | 0.951612i | \(-0.599426\pi\) |
0.977771 | − | 0.209676i | \(-0.0672409\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.94064 | + | 13.0539i | −0.321771 | + | 0.528969i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.1191 | − | 16.2945i | 0.611654 | − | 0.659207i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.3112 | + | 4.11650i | 1.10309 | + | 0.166264i | 0.675249 | − | 0.737590i | \(-0.264036\pi\) |
0.427841 | + | 0.903854i | \(0.359274\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.1014 | − | 48.6383i | 0.447650 | − | 1.96128i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.25471 | − | 18.6411i | −0.171288 | − | 0.750463i | −0.985470 | − | 0.169852i | \(-0.945671\pi\) |
0.814181 | − | 0.580611i | \(-0.197186\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.7456 | + | 30.7363i | 0.713256 | + | 1.23540i | 0.963628 | + | 0.267246i | \(0.0861136\pi\) |
−0.250373 | + | 0.968150i | \(0.580553\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.5340 | + | 33.0514i | 0.904260 | + | 1.32631i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20.5400 | + | 4.19574i | −0.822917 | + | 0.168099i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.17059 | − | 1.28646i | −0.166824 | − | 0.0514583i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.9958 | − | 1.04884i | 0.558937 | − | 0.0418866i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.09308 | − | 14.7289i | −0.282819 | − | 0.587281i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.71542 | + | 20.1743i | −0.386765 | + | 0.803126i | 0.613148 | + | 0.789968i | \(0.289903\pi\) |
−0.999913 | + | 0.0131580i | \(0.995812\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.128678 | + | 0.417165i | 0.00511451 | + | 0.0165808i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −40.8963 | + | 6.16413i | −1.62292 | + | 0.244616i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.3258 | − | 3.85658i | 0.448743 | − | 0.152803i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.906455 | + | 6.01394i | 0.0358588 | + | 0.237908i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.4722 | − | 9.70789i | 1.24308 | − | 0.383439i | 0.397654 | − | 0.917535i | \(-0.369824\pi\) |
0.845424 | + | 0.534097i | \(0.179348\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.6790 | − | 8.51375i | −0.697191 | − | 0.335749i | 0.0514960 | − | 0.998673i | \(-0.483601\pi\) |
−0.748687 | + | 0.662924i | \(0.769315\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.16582 | − | 1.04301i | 0.0852792 | − | 0.0410683i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.74351 | + | 49.9537i | 0.147173 | + | 1.96388i | 0.247386 | + | 0.968917i | \(0.420428\pi\) |
−0.100213 | + | 0.994966i | \(0.531953\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.47178 | − | 17.7391i | 0.214786 | − | 0.696320i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.17809 | + | 20.5099i | −0.202945 | + | 0.803848i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.72140 | + | 3.21899i | −0.184763 | + | 0.125969i | −0.652169 | − | 0.758073i | \(-0.726141\pi\) |
0.467407 | + | 0.884042i | \(0.345188\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.5044 | + | 6.64209i | −0.449515 | + | 0.259528i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.26023 | + | 0.515883i | −0.0881801 | + | 0.0201265i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.79992 | − | 1.32379i | −0.225933 | − | 0.0515677i | 0.108056 | − | 0.994145i | \(-0.465538\pi\) |
−0.333988 | + | 0.942577i | \(0.608395\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.58827 | + | 10.5375i | −0.0617764 | + | 0.409859i | 0.936474 | + | 0.350736i | \(0.114069\pi\) |
−0.998251 | + | 0.0591233i | \(0.981170\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.3484 | + | 12.3855i | 0.518408 | + | 0.481012i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.5683 | + | 17.0559i | −0.642491 | + | 0.661399i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.9166 | − | 13.2309i | −0.887336 | − | 0.512304i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.8595 | + | 25.8499i | −1.07711 | + | 0.999414i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.7625 | − | 36.0671i | 1.11037 | − | 1.39235i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.4019 | − | 35.6149i | −1.09481 | − | 1.37285i | −0.921678 | − | 0.387955i | \(-0.873182\pi\) |
−0.173135 | − | 0.984898i | \(-0.555390\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.5633 | − | 39.6546i | 0.599031 | − | 1.52631i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.9043 | − | 10.5592i | 1.03402 | − | 0.405822i | 0.213197 | − | 0.977009i | \(-0.431612\pi\) |
0.820820 | + | 0.571188i | \(0.193517\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.40581 | + | 13.8081i | −0.0923265 | + | 0.529908i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.32524 | − | 31.0282i | 0.0891034 | − | 1.18900i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.1617 | − | 29.5718i | 0.771466 | − | 1.13153i | −0.216413 | − | 0.976302i | \(-0.569436\pi\) |
0.987878 | − | 0.155230i | \(-0.0496120\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 29.7525i | − | 1.13678i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.4148i | 1.58008i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.77216 | + | 5.53275i | −0.143708 | + | 0.210781i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.40657 | + | 18.7694i | −0.0535085 | + | 0.714021i | 0.904352 | + | 0.426787i | \(0.140355\pi\) |
−0.957861 | + | 0.287234i | \(0.907264\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.833227 | − | 4.78231i | 0.0316517 | − | 0.181665i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 53.9935 | − | 21.1909i | 2.04809 | − | 0.803816i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.9800 | + | 56.0041i | −0.832551 | + | 2.12131i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.7884 | − | 23.5599i | −0.710642 | − | 0.891117i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.3833 | + | 13.0203i | −0.392172 | + | 0.491769i | −0.938246 | − | 0.345969i | \(-0.887550\pi\) |
0.546074 | + | 0.837737i | \(0.316122\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.47039 | + | 4.14792i | −0.168604 | + | 0.156442i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −63.1772 | − | 36.4753i | −2.37939 | − | 1.37374i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.5428 | + | 23.2063i | −0.847811 | + | 0.872761i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.980841 | + | 0.910088i | 0.0368363 | + | 0.0341791i | 0.698376 | − | 0.715731i | \(-0.253906\pi\) |
−0.661540 | + | 0.749910i | \(0.730097\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.481466 | + | 3.19432i | −0.0180564 | + | 0.119796i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.7167 | − | 8.15211i | −1.33760 | − | 0.305299i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.9591 | + | 4.78377i | −0.783825 | + | 0.178903i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 36.5995 | − | 21.1307i | 1.36683 | − | 0.789142i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.07862 | − | 5.50791i | 0.301282 | − | 0.205410i | −0.403237 | − | 0.915095i | \(-0.632115\pi\) |
0.704519 | + | 0.709685i | \(0.251163\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.70499 | − | 30.5188i | 0.286949 | − | 1.13658i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.430515 | + | 1.39570i | −0.0160110 | + | 0.0519065i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.10589 | + | 28.1011i | 0.0782106 | + | 1.04365i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.2048 | − | 12.6196i | 0.971884 | − | 0.468034i | 0.120578 | − | 0.992704i | \(-0.461525\pi\) |
0.851306 | + | 0.524669i | \(0.175811\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.9535 | − | 12.9801i | −0.998277 | − | 0.480745i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.77013 | + | 0.854472i | −0.102457 | + | 0.0316038i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.46457 | − | 42.8896i | −0.238774 | − | 1.58416i | −0.711326 | − | 0.702862i | \(-0.751905\pi\) |
0.472552 | − | 0.881303i | \(-0.343333\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20.6105 | − | 33.4214i | −0.760230 | − | 1.23277i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.5967 | + | 5.36534i | −1.31122 | + | 0.197635i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.75574 | + | 21.9016i | 0.248514 | + | 0.805662i | 0.990771 | + | 0.135547i | \(0.0432791\pi\) |
−0.742257 | + | 0.670115i | \(0.766245\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.94725 | − | 6.12002i | 0.108270 | − | 0.224825i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.34466 | − | 9.02179i | −0.159390 | − | 0.330977i | 0.805945 | − | 0.591990i | \(-0.201658\pi\) |
−0.965335 | + | 0.261013i | \(0.915943\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.70496 | − | 0.352588i | 0.172376 | − | 0.0129178i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.64803 | − | 1.43373i | −0.170063 | − | 0.0524574i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.88938 | − | 1.40731i | 0.251733 | − | 0.0514218i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.7004 | − | 15.6947i | −0.390464 | − | 0.572706i | 0.579798 | − | 0.814760i | \(-0.303131\pi\) |
−0.970263 | + | 0.242054i | \(0.922179\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.5549 | − | 42.5303i | −0.894829 | − | 1.54989i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.9384 | + | 78.5932i | 0.652845 | + | 2.86030i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.84508 | − | 12.4651i | 0.103406 | − | 0.453052i | −0.896543 | − | 0.442957i | \(-0.853929\pi\) |
0.999949 | − | 0.0100949i | \(-0.00321336\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −39.6900 | − | 5.98230i | −1.44066 | − | 0.217144i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.5297 | + | 12.4260i | −0.417950 | + | 0.450443i | −0.906571 | − | 0.422053i | \(-0.861310\pi\) |
0.488621 | + | 0.872496i | \(0.337500\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.17220 | − | 15.0785i | 0.332056 | − | 0.545877i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.25857 | + | 10.8402i | −0.226279 | + | 0.391927i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.11107 | − | 6.58616i | −0.220658 | − | 0.237813i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.2688 | − | 26.5310i | −1.19970 | − | 0.956732i | −0.199970 | − | 0.979802i | \(-0.564085\pi\) |
−0.999734 | + | 0.0230699i | \(0.992656\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 34.4696 | − | 27.4886i | 1.24139 | − | 0.989979i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.4078 | − | 8.40196i | −0.769987 | − | 0.302198i | −0.0523626 | − | 0.998628i | \(-0.516675\pi\) |
−0.717624 | + | 0.696431i | \(0.754770\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.2533 | + | 36.3169i | 0.511995 | + | 1.30454i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.83410 | − | 8.83409i | −0.173423 | − | 0.316921i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.3801 | + | 1.67716i | 0.801851 | + | 0.0600904i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.1572 | − | 23.2880i | −1.22224 | − | 0.833310i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.3255 | 0.726373 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.93853 | 0.0691892 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.56143 | + | 4.47351i | 0.233890 | + | 0.159463i | 0.674594 | − | 0.738189i | \(-0.264319\pi\) |
−0.440704 | + | 0.897652i | \(0.645271\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.2523 | − | 1.36782i | −0.649799 | − | 0.0486957i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.5582 | − | 23.5339i | 0.944299 | − | 0.836771i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.15692 | − | 20.7835i | −0.289661 | − | 0.738044i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.4573 | + | 8.02890i | 0.725545 | + | 0.284756i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.2011 | + | 16.9073i | −0.750983 | + | 0.598889i | −0.922367 | − | 0.386316i | \(-0.873748\pi\) |
0.171384 | + | 0.985204i | \(0.445176\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 68.7806 | + | 54.8507i | 2.43328 | + | 1.94048i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.80007 | + | 3.01775i | 0.0989355 | + | 0.106627i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.87936 | − | 13.6474i | 0.278056 | − | 0.481608i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 57.0492 | − | 37.0109i | 2.01072 | − | 1.30446i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.515520 | + | 0.555599i | −0.0181472 | + | 0.0195580i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.42560 | + | 1.11923i | 0.261070 | + | 0.0393500i | 0.278273 | − | 0.960502i | \(-0.410238\pi\) |
−0.0172029 | + | 0.999852i | \(0.505476\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.17813 | + | 13.9243i | −0.111599 | + | 0.488948i | 0.887978 | + | 0.459885i | \(0.152109\pi\) |
−0.999578 | + | 0.0290630i | \(0.990748\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.243502 | − | 1.06685i | −0.00853999 | − | 0.0374161i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.3923 | − | 18.0000i | −0.364026 | − | 0.630512i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.609174 | + | 0.893494i | 0.0213123 | + | 0.0312594i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.80283 | − | 1.50652i | −0.0629960 | − | 0.0526420i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.9379 | − | 8.92617i | −1.00994 | − | 0.311525i | −0.254733 | − | 0.967011i | \(-0.581988\pi\) |
−0.755207 | + | 0.655486i | \(0.772464\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.87393 | + | 0.665009i | −0.309326 | + | 0.0231808i | −0.228489 | − | 0.973547i | \(-0.573378\pi\) |
−0.0808370 | + | 0.996727i | \(0.525759\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.5460 | + | 38.5113i | 0.645690 | + | 1.34079i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.29764 | − | 15.1537i | 0.253764 | − | 0.526946i | −0.734702 | − | 0.678390i | \(-0.762678\pi\) |
0.988466 | + | 0.151444i | \(0.0483923\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.37598 | + | 14.1866i | 0.151984 | + | 0.492721i | 0.999261 | − | 0.0384305i | \(-0.0122358\pi\) |
−0.847277 | + | 0.531151i | \(0.821760\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.0984 | + | 3.78298i | −0.870654 | + | 0.131230i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.5703 | + | 43.5582i | 0.643423 | + | 1.50920i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.32435 | − | 8.78649i | −0.0458310 | − | 0.304069i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 26.8895 | − | 8.29432i | 0.929438 | − | 0.286694i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.5284 | + | 13.2570i | 0.950387 | + | 0.457682i | 0.843822 | − | 0.536623i | \(-0.180300\pi\) |
0.106565 | + | 0.994306i | \(0.466015\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0141 | − | 6.74884i | 0.483246 | − | 0.232719i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.787031 | + | 10.5022i | 0.0271068 | + | 0.361715i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.5806 | − | 34.3016i | 0.363985 | − | 1.18001i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.35721 | + | 3.09884i | 0.0809948 | + | 0.106477i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.4799 | − | 15.3265i | 0.771507 | − | 0.526005i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.1038 | − | 8.72021i | 0.517753 | − | 0.298925i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −48.2537 | + | 11.0136i | −1.65217 | + | 0.377098i | −0.944260 | − | 0.329200i | \(-0.893221\pi\) |
−0.707914 | + | 0.706298i | \(0.750364\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.55226 | + | 1.03902i | 0.155684 | + | 0.0355338i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.44894 | − | 22.8822i | 0.117814 | − | 0.781643i | −0.849413 | − | 0.527728i | \(-0.823044\pi\) |
0.967227 | − | 0.253914i | \(-0.0817180\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.9159 | − | 10.1285i | −0.372445 | − | 0.345579i | 0.471637 | − | 0.881793i | \(-0.343663\pi\) |
−0.844082 | + | 0.536214i | \(0.819854\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.7317 | + | 35.1543i | −0.399816 | + | 1.19805i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.3064 | − | 12.8786i | −0.759319 | − | 0.438393i | 0.0697325 | − | 0.997566i | \(-0.477785\pi\) |
−0.829051 | + | 0.559173i | \(0.811119\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.8707 | − | 21.2209i | 0.777625 | − | 0.721531i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −28.2399 | + | 35.4117i | −0.959078 | + | 1.20265i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.6907 | − | 17.1676i | −0.464425 | − | 0.582371i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.36527 | + | 16.2184i | −0.215679 | + | 0.549541i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.56207 | − | 1.00554i | 0.0867131 | − | 0.0340324i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.3354 | − | 9.78088i | −0.788882 | − | 0.330654i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.17044 | + | 55.6506i | −0.140826 | + | 1.87919i | 0.263621 | + | 0.964626i | \(0.415083\pi\) |
−0.404447 | + | 0.914562i | \(0.632536\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.50597 | − | 11.0092i | 0.253170 | − | 0.371332i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.9782i | 0.538319i | 0.963096 | + | 0.269159i | \(0.0867458\pi\) | ||||
−0.963096 | + | 0.269159i | \(0.913254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 14.1392i | − | 0.475822i | −0.971287 | − | 0.237911i | \(-0.923537\pi\) | ||
0.971287 | − | 0.237911i | \(-0.0764626\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.6102 | + | 24.3627i | −0.558346 | + | 0.818943i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.963813 | − | 12.8612i | 0.0323617 | − | 0.431836i | −0.957367 | − | 0.288875i | \(-0.906719\pi\) |
0.989728 | − | 0.142961i | \(-0.0456623\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.6816 | − | 1.59381i | 1.02903 | − | 0.0534545i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.5754 | − | 9.25266i | 0.789805 | − | 0.309976i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.9895 | − | 30.5487i | 0.401213 | − | 1.02227i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.6987 | + | 27.2094i | 0.725309 | + | 0.909509i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.1121 | + | 15.1881i | −0.404410 | + | 0.507115i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.6455 | + | 12.6612i | −0.455104 | + | 0.422275i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.9515 | − | 13.2511i | −0.764626 | − | 0.441457i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.67679 | + | 0.614165i | −0.0558000 | + | 0.0204381i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.30974 | − | 4.92672i | −0.176502 | − | 0.163770i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.65498 | − | 17.6147i | 0.0881573 | − | 0.584886i | −0.900518 | − | 0.434818i | \(-0.856813\pi\) |
0.988676 | − | 0.150068i | \(-0.0479492\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.19381 | + | 1.41370i | 0.205436 | + | 0.0468893i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.37522 | − | 2.13983i | 0.310615 | − | 0.0708959i | −0.0643718 | − | 0.997926i | \(-0.520504\pi\) |
0.374987 | + | 0.927030i | \(0.377647\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.6336 | − | 16.5316i | 0.947634 | − | 0.547117i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −60.5418 | + | 41.2767i | −2.00145 | + | 1.36457i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.98661 | − | 4.07693i | 0.296764 | − | 0.134632i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.44895 | − | 27.3908i | 0.278705 | − | 0.903539i | −0.702683 | − | 0.711503i | \(-0.748015\pi\) |
0.981388 | − | 0.192036i | \(-0.0615091\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.468011 | − | 6.24517i | −0.0154215 | − | 0.205785i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.0267 | + | 8.68122i | −0.593357 | + | 0.285746i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.7334 | − | 8.05840i | −0.550192 | − | 0.264959i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.90637 | + | 1.82187i | −0.193991 | + | 0.0598382i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.81476 | + | 25.3093i | 0.125158 | + | 0.830370i | 0.960024 | + | 0.279917i | \(0.0903070\pi\) |
−0.834866 | + | 0.550453i | \(0.814455\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.4850 | − | 11.4090i | 0.441952 | − | 0.373915i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.63217 | + | 1.30109i | −0.282604 | + | 0.0425958i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25.0788 | − | 81.3034i | −0.820164 | − | 2.65891i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.9204 | + | 22.6765i | −0.356754 | + | 0.740808i | −0.999685 | − | 0.0251168i | \(-0.992004\pi\) |
0.642930 | + | 0.765925i | \(0.277719\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.49989 | + | 19.7267i | 0.310017 | + | 0.643757i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.72641 | + | 0.728893i | −0.317072 | + | 0.0237612i | −0.232316 | − | 0.972640i | \(-0.574630\pi\) |
−0.0847562 | + | 0.996402i | \(0.527011\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −61.3321 | − | 18.9185i | −1.99725 | − | 0.616070i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −23.7349 | + | 46.5294i | −0.772096 | + | 1.51360i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.6860 | − | 31.8075i | −0.704700 | − | 1.03361i | −0.997009 | − | 0.0772817i | \(-0.975376\pi\) |
0.292309 | − | 0.956324i | \(-0.405576\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.81348 | − | 6.60513i | −0.123791 | − | 0.214412i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.5598 | + | 50.6468i | 0.374852 | + | 1.64233i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.52746 | − | 28.5987i | 0.211445 | − | 0.926402i | −0.752140 | − | 0.659003i | \(-0.770979\pi\) |
0.963586 | − | 0.267400i | \(-0.0861643\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.8088 | + | 1.62916i | 0.349764 | + | 0.0527185i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.8719 | + | 14.9503i | −0.448414 | + | 0.483275i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.15589 | + | 21.9963i | −0.0696174 | + | 0.710296i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.61441 | − | 4.52828i | 0.0843356 | − | 0.146074i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.939179 | − | 1.01219i | −0.0302646 | − | 0.0326175i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31.9064 | + | 25.4445i | 1.02710 | + | 0.819088i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.0616 | + | 25.5682i | −1.03103 | + | 0.822219i | −0.984267 | − | 0.176687i | \(-0.943462\pi\) |
−0.0467629 | + | 0.998906i | \(0.514891\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.0253 | + | 9.82170i | 0.803928 | + | 0.315519i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.4150 | − | 36.7287i | −0.462598 | − | 1.17868i | −0.951857 | − | 0.306542i | \(-0.900828\pi\) |
0.489259 | − | 0.872139i | \(-0.337267\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −41.4533 | + | 11.7542i | −1.32893 | + | 0.376822i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20.6297 | + | 1.54598i | 0.660678 | + | 0.0495110i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.2622 | + | 21.3142i | 1.00017 | + | 0.681901i | 0.948505 | − | 0.316763i | \(-0.102596\pi\) |
0.0516611 | + | 0.998665i | \(0.483548\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.9827 | −0.894330 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.46572 | −0.110652 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.2902 | − | 17.9243i | −0.838526 | − | 0.571697i | 0.0661444 | − | 0.997810i | \(-0.478930\pi\) |
−0.904670 | + | 0.426113i | \(0.859883\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 68.1565 | + | 5.10762i | 2.17165 | + | 0.162742i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 44.0644 | + | 31.5444i | 1.40258 | + | 1.00407i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.12988 | − | 2.87887i | −0.0359279 | − | 0.0915429i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.9420 | + | 9.39653i | 0.760542 | + | 0.298491i | 0.713737 | − | 0.700414i | \(-0.247001\pi\) |
0.0468043 | + | 0.998904i | \(0.485096\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.4243 | − | 22.6676i | 0.902017 | − | 0.719335i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.826769 | − | 0.659326i | −0.0262103 | − | 0.0209021i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.3579 | − | 17.6297i | −0.518061 | − | 0.558337i | 0.418782 | − | 0.908087i | \(-0.362457\pi\) |
−0.936843 | + | 0.349750i | \(0.886267\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.69803 | + | 11.6013i | −0.211916 | + | 0.367050i |
(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 | 784.2.bp.c.495.8 | yes | 120 | |
4.3 | odd | 2 | inner | 784.2.bp.c.495.3 | yes | 120 | |
49.10 | odd | 42 | inner | 784.2.bp.c.255.3 | ✓ | 120 | |
196.59 | even | 42 | inner | 784.2.bp.c.255.8 | yes | 120 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.2.bp.c.255.3 | ✓ | 120 | 49.10 | odd | 42 | inner | |
784.2.bp.c.255.8 | yes | 120 | 196.59 | even | 42 | inner | |
784.2.bp.c.495.3 | yes | 120 | 4.3 | odd | 2 | inner | |
784.2.bp.c.495.8 | yes | 120 | 1.1 | even | 1 | trivial |