Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,2,Mod(19,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("196.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.f (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.56506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 4x^{14} + 6x^{12} + 8x^{10} + 20x^{8} + 32x^{6} + 96x^{4} + 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.7 | ||
Root | \(-0.349313 - 1.37039i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 196.19 |
Dual form | 196.2.f.d.31.7 |
$q$-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 \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).
\(n\) | \(99\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.24165 | − | 0.676979i | 0.877981 | − | 0.478696i | ||||
\(3\) | −1.36145 | − | 2.35811i | −0.786035 | − | 1.36145i | −0.928379 | − | 0.371635i | \(-0.878797\pi\) |
0.142344 | − | 0.989817i | \(-0.454536\pi\) | |||||||
\(4\) | 1.08340 | − | 1.68114i | 0.541700 | − | 0.840572i | ||||
\(5\) | 0.937379 | + | 0.541196i | 0.419209 | + | 0.242030i | 0.694739 | − | 0.719262i | \(-0.255520\pi\) |
−0.275530 | + | 0.961292i | \(0.588853\pi\) | |||||||
\(6\) | −3.28684 | − | 2.00627i | −1.34185 | − | 0.819057i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.207107 | − | 2.82083i | 0.0732233 | − | 0.997316i | ||||
\(9\) | −2.20711 | + | 3.82282i | −0.735702 | + | 1.27427i | ||||
\(10\) | 1.53028 | + | 0.0373915i | 0.483916 | + | 0.0118242i | ||||
\(11\) | −1.80482 | + | 1.04201i | −0.544172 | + | 0.314178i | −0.746768 | − | 0.665084i | \(-0.768396\pi\) |
0.202596 | + | 0.979262i | \(0.435062\pi\) | |||||||
\(12\) | −5.43931 | − | 0.265972i | −1.57019 | − | 0.0767796i | ||||
\(13\) | 2.61313i | 0.724751i | 0.932032 | + | 0.362375i | \(0.118034\pi\) | ||||
−0.932032 | + | 0.362375i | \(0.881966\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.94725i | − | 0.760977i | ||||||
\(16\) | −1.65249 | − | 3.64270i | −0.413123 | − | 0.910675i | ||||
\(17\) | 3.86324 | − | 2.23044i | 0.936973 | − | 0.540962i | 0.0479630 | − | 0.998849i | \(-0.484727\pi\) |
0.889010 | + | 0.457887i | \(0.151394\pi\) | |||||||
\(18\) | −0.152490 | + | 6.24078i | −0.0359423 | + | 1.47097i | ||||
\(19\) | 0.563932 | − | 0.976759i | 0.129375 | − | 0.224084i | −0.794060 | − | 0.607840i | \(-0.792036\pi\) |
0.923435 | + | 0.383756i | \(0.125370\pi\) | |||||||
\(20\) | 1.92538 | − | 0.989538i | 0.430529 | − | 0.221267i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.53553 | + | 2.51564i | −0.327377 | + | 0.536336i | ||||
\(23\) | 6.16203 | + | 3.55765i | 1.28487 | + | 0.741821i | 0.977735 | − | 0.209845i | \(-0.0672959\pi\) |
0.307136 | + | 0.951665i | \(0.400629\pi\) | |||||||
\(24\) | −6.93379 | + | 3.35205i | −1.41535 | + | 0.684235i | ||||
\(25\) | −1.91421 | − | 3.31552i | −0.382843 | − | 0.663103i | ||||
\(26\) | 1.76903 | + | 3.24459i | 0.346935 | + | 0.636317i | ||||
\(27\) | 3.85077 | 0.741081 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.17157 | −0.217556 | −0.108778 | − | 0.994066i | \(-0.534694\pi\) | ||||
−0.108778 | + | 0.994066i | \(0.534694\pi\) | |||||||
\(30\) | −1.99523 | − | 3.65946i | −0.364277 | − | 0.668123i | ||||
\(31\) | 3.85077 | + | 6.66973i | 0.691619 | + | 1.19792i | 0.971307 | + | 0.237828i | \(0.0764354\pi\) |
−0.279689 | + | 0.960091i | \(0.590231\pi\) | |||||||
\(32\) | −4.51785 | − | 3.40427i | −0.798650 | − | 0.601795i | ||||
\(33\) | 4.91434 | + | 2.83730i | 0.855477 | + | 0.493910i | ||||
\(34\) | 3.28684 | − | 5.38476i | 0.563688 | − | 0.923479i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.03553 | + | 7.85211i | 0.672589 | + | 1.30868i | ||||
\(37\) | 2.00000 | − | 3.46410i | 0.328798 | − | 0.569495i | −0.653476 | − | 0.756948i | \(-0.726690\pi\) |
0.982274 | + | 0.187453i | \(0.0600231\pi\) | |||||||
\(38\) | 0.0389624 | − | 1.59457i | 0.00632053 | − | 0.258673i | ||||
\(39\) | 6.16203 | − | 3.55765i | 0.986714 | − | 0.569679i | ||||
\(40\) | 1.72076 | − | 2.53211i | 0.272076 | − | 0.400361i | ||||
\(41\) | 5.54328i | 0.865714i | 0.901462 | + | 0.432857i | \(0.142495\pi\) | ||||
−0.901462 | + | 0.432857i | \(0.857505\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.97852i | 1.21671i | 0.793664 | + | 0.608357i | \(0.208171\pi\) | ||||
−0.793664 | + | 0.608357i | \(0.791829\pi\) | |||||||
\(44\) | −0.203567 | + | 4.16307i | −0.0306888 | + | 0.627606i | ||||
\(45\) | −4.13779 | + | 2.38896i | −0.616826 | + | 0.356124i | ||||
\(46\) | 10.0595 | + | 0.245800i | 1.48320 | + | 0.0362412i | ||||
\(47\) | 2.72291 | − | 4.71621i | 0.397177 | − | 0.687930i | −0.596200 | − | 0.802836i | \(-0.703323\pi\) |
0.993376 | + | 0.114906i | \(0.0366567\pi\) | |||||||
\(48\) | −6.34009 | + | 8.85611i | −0.915113 | + | 1.27827i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.62132 | − | 2.82083i | −0.653553 | − | 0.398926i | ||||
\(51\) | −10.5192 | − | 6.07328i | −1.47299 | − | 0.850430i | ||||
\(52\) | 4.39304 | + | 2.83106i | 0.609205 | + | 0.392597i | ||||
\(53\) | 3.24264 | + | 5.61642i | 0.445411 | + | 0.771474i | 0.998081 | − | 0.0619259i | \(-0.0197243\pi\) |
−0.552670 | + | 0.833400i | \(0.686391\pi\) | |||||||
\(54\) | 4.78132 | − | 2.60689i | 0.650655 | − | 0.354753i | ||||
\(55\) | −2.25573 | −0.304162 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.07107 | −0.406773 | ||||||||
\(58\) | −1.45469 | + | 0.793130i | −0.191010 | + | 0.104143i | ||||
\(59\) | −4.41470 | − | 7.64649i | −0.574745 | − | 0.995488i | −0.996069 | − | 0.0885778i | \(-0.971768\pi\) |
0.421324 | − | 0.906910i | \(-0.361566\pi\) | |||||||
\(60\) | −4.95475 | − | 3.19305i | −0.639656 | − | 0.412221i | ||||
\(61\) | −11.3152 | − | 6.53281i | −1.44876 | − | 0.836441i | −0.450351 | − | 0.892852i | \(-0.648701\pi\) |
−0.998408 | + | 0.0564104i | \(0.982034\pi\) | |||||||
\(62\) | 9.29658 | + | 5.67459i | 1.18067 | + | 0.720674i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.91421 | − | 1.16843i | −0.989277 | − | 0.146053i | ||||
\(65\) | −1.41421 | + | 2.44949i | −0.175412 | + | 0.303822i | ||||
\(66\) | 8.02269 | + | 0.196030i | 0.987525 | + | 0.0241297i | ||||
\(67\) | −8.71442 | + | 5.03127i | −1.06464 | + | 0.614668i | −0.926711 | − | 0.375775i | \(-0.877377\pi\) |
−0.137925 | + | 0.990443i | \(0.544043\pi\) | |||||||
\(68\) | 0.435738 | − | 8.91112i | 0.0528410 | − | 1.08063i | ||||
\(69\) | − | 19.3743i | − | 2.33239i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 10.3264 | + | 7.01761i | 1.21698 | + | 0.827034i | ||||
\(73\) | −6.90282 | + | 3.98535i | −0.807914 | + | 0.466450i | −0.846231 | − | 0.532816i | \(-0.821134\pi\) |
0.0383167 | + | 0.999266i | \(0.487800\pi\) | |||||||
\(74\) | 0.138181 | − | 5.65517i | 0.0160632 | − | 0.657400i | ||||
\(75\) | −5.21222 | + | 9.02783i | −0.601856 | + | 1.04244i | ||||
\(76\) | −1.03111 | − | 2.00627i | −0.118276 | − | 0.230135i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.24264 | − | 8.58892i | 0.593612 | − | 0.972504i | ||||
\(79\) | −3.60963 | − | 2.08402i | −0.406115 | − | 0.234471i | 0.283004 | − | 0.959119i | \(-0.408669\pi\) |
−0.689119 | + | 0.724648i | \(0.742002\pi\) | |||||||
\(80\) | 0.422406 | − | 4.30891i | 0.0472264 | − | 0.481751i | ||||
\(81\) | 1.37868 | + | 2.38794i | 0.153187 | + | 0.265327i | ||||
\(82\) | 3.75268 | + | 6.88282i | 0.414414 | + | 0.760080i | ||||
\(83\) | −4.31795 | −0.473956 | −0.236978 | − | 0.971515i | \(-0.576157\pi\) | ||||
−0.236978 | + | 0.971515i | \(0.576157\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.82843 | 0.523716 | ||||||||
\(86\) | 5.40129 | + | 9.90655i | 0.582436 | + | 1.06825i | ||||
\(87\) | 1.59504 | + | 2.76269i | 0.171006 | + | 0.296192i | ||||
\(88\) | 2.56555 | + | 5.30689i | 0.273489 | + | 0.565717i | ||||
\(89\) | 3.47496 | + | 2.00627i | 0.368346 | + | 0.212664i | 0.672735 | − | 0.739883i | \(-0.265119\pi\) |
−0.304390 | + | 0.952548i | \(0.598453\pi\) | |||||||
\(90\) | −3.52043 | + | 5.76745i | −0.371085 | + | 0.607942i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.6569 | − | 6.50490i | 1.31957 | − | 0.678183i | ||||
\(93\) | 10.4853 | − | 18.1610i | 1.08727 | − | 1.88321i | ||||
\(94\) | 0.188127 | − | 7.69924i | 0.0194038 | − | 0.794116i | ||||
\(95\) | 1.05724 | − | 0.610396i | 0.108470 | − | 0.0626253i | ||||
\(96\) | −1.87678 | + | 15.2883i | −0.191548 | + | 1.56036i | ||||
\(97\) | 3.82683i | 0.388556i | 0.980946 | + | 0.194278i | \(0.0622364\pi\) | ||||
−0.980946 | + | 0.194278i | \(0.937764\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 9.19932i | − | 0.924566i | ||||||
\(100\) | −7.64772 | − | 0.373959i | −0.764772 | − | 0.0373959i | ||||
\(101\) | −0.160829 | + | 0.0928546i | −0.0160031 | + | 0.00923938i | −0.507980 | − | 0.861369i | \(-0.669608\pi\) |
0.491977 | + | 0.870608i | \(0.336274\pi\) | |||||||
\(102\) | −17.1727 | − | 0.419607i | −1.70035 | − | 0.0415472i | ||||
\(103\) | −7.70154 | + | 13.3395i | −0.758855 | + | 1.31438i | 0.184580 | + | 0.982818i | \(0.440908\pi\) |
−0.943435 | + | 0.331558i | \(0.892426\pi\) | |||||||
\(104\) | 7.37120 | + | 0.541196i | 0.722805 | + | 0.0530686i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.82843 | + | 4.77844i | 0.760364 | + | 0.464123i | ||||
\(107\) | 6.16203 | + | 3.55765i | 0.595706 | + | 0.343931i | 0.767350 | − | 0.641228i | \(-0.221575\pi\) |
−0.171645 | + | 0.985159i | \(0.554908\pi\) | |||||||
\(108\) | 4.17192 | − | 6.47370i | 0.401443 | − | 0.622932i | ||||
\(109\) | −2.82843 | − | 4.89898i | −0.270914 | − | 0.469237i | 0.698182 | − | 0.715920i | \(-0.253993\pi\) |
−0.969096 | + | 0.246683i | \(0.920659\pi\) | |||||||
\(110\) | −2.80083 | + | 1.52708i | −0.267049 | + | 0.145601i | ||||
\(111\) | −10.8916 | −1.03379 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.24264 | 0.399114 | 0.199557 | − | 0.979886i | \(-0.436050\pi\) | ||||
0.199557 | + | 0.979886i | \(0.436050\pi\) | |||||||
\(114\) | −3.81320 | + | 2.07905i | −0.357139 | + | 0.194721i | ||||
\(115\) | 3.85077 | + | 6.66973i | 0.359086 | + | 0.621955i | ||||
\(116\) | −1.26928 | + | 1.96958i | −0.117850 | + | 0.182871i | ||||
\(117\) | −9.98951 | − | 5.76745i | −0.923531 | − | 0.533201i | ||||
\(118\) | −10.6580 | − | 6.50562i | −0.981151 | − | 0.598891i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −8.31371 | − | 0.610396i | −0.758934 | − | 0.0557213i | ||||
\(121\) | −3.32843 | + | 5.76500i | −0.302584 | + | 0.524091i | ||||
\(122\) | −18.4721 | − | 0.451356i | −1.67238 | − | 0.0408638i | ||||
\(123\) | 13.0716 | − | 7.54691i | 1.17863 | − | 0.680482i | ||||
\(124\) | 15.3847 | + | 0.752284i | 1.38159 | + | 0.0675571i | ||||
\(125\) | − | 9.55582i | − | 0.854699i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.2833i | − | 1.00123i | −0.865669 | − | 0.500617i | \(-0.833106\pi\) | ||
0.865669 | − | 0.500617i | \(-0.166894\pi\) | |||||||
\(128\) | −10.6177 | + | 3.90697i | −0.938481 | + | 0.345331i | ||||
\(129\) | 18.8142 | − | 10.8624i | 1.65650 | − | 0.956380i | ||||
\(130\) | −0.0977088 | + | 3.99881i | −0.00856963 | + | 0.350719i | ||||
\(131\) | 7.93513 | − | 13.7440i | 0.693295 | − | 1.20082i | −0.277457 | − | 0.960738i | \(-0.589491\pi\) |
0.970752 | − | 0.240085i | \(-0.0771752\pi\) | |||||||
\(132\) | 10.0941 | − | 5.18779i | 0.878579 | − | 0.451539i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.41421 | + | 12.1466i | −0.640490 | + | 1.04930i | ||||
\(135\) | 3.60963 | + | 2.08402i | 0.310668 | + | 0.179364i | ||||
\(136\) | −5.49161 | − | 11.3595i | −0.470901 | − | 0.974069i | ||||
\(137\) | −0.121320 | − | 0.210133i | −0.0103651 | − | 0.0179529i | 0.860796 | − | 0.508950i | \(-0.169966\pi\) |
−0.871161 | + | 0.490997i | \(0.836633\pi\) | |||||||
\(138\) | −13.1160 | − | 24.0561i | −1.11651 | − | 2.04779i | ||||
\(139\) | −1.78855 | −0.151703 | −0.0758515 | − | 0.997119i | \(-0.524167\pi\) | ||||
−0.0758515 | + | 0.997119i | \(0.524167\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.8284 | −1.24878 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.72291 | − | 4.71621i | −0.227701 | − | 0.394389i | ||||
\(144\) | 17.5726 | + | 1.72266i | 1.46438 | + | 0.143555i | ||||
\(145\) | −1.09821 | − | 0.634051i | −0.0912012 | − | 0.0526550i | ||||
\(146\) | −5.87291 | + | 9.62148i | −0.486045 | + | 0.796279i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.65685 | − | 7.11529i | −0.300592 | − | 0.584874i | ||||
\(149\) | 0.414214 | − | 0.717439i | 0.0339337 | − | 0.0587749i | −0.848560 | − | 0.529099i | \(-0.822530\pi\) |
0.882493 | + | 0.470325i | \(0.155863\pi\) | |||||||
\(150\) | −0.360115 | + | 14.7380i | −0.0294033 | + | 1.20335i | ||||
\(151\) | −4.66687 | + | 2.69442i | −0.379784 | + | 0.219269i | −0.677724 | − | 0.735316i | \(-0.737034\pi\) |
0.297940 | + | 0.954585i | \(0.403700\pi\) | |||||||
\(152\) | −2.63848 | − | 1.79305i | −0.214009 | − | 0.145436i | ||||
\(153\) | 19.6913i | 1.59195i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.33609i | 0.669571i | ||||||||
\(156\) | 0.695020 | − | 14.2136i | 0.0556461 | − | 1.13800i | ||||
\(157\) | −17.4885 | + | 10.0970i | −1.39574 | + | 0.805830i | −0.993943 | − | 0.109900i | \(-0.964947\pi\) |
−0.401795 | + | 0.915730i | \(0.631614\pi\) | |||||||
\(158\) | −5.89274 | − | 0.143986i | −0.468802 | − | 0.0114549i | ||||
\(159\) | 8.82940 | − | 15.2930i | 0.700217 | − | 1.21281i | ||||
\(160\) | −2.39256 | − | 5.63613i | −0.189149 | − | 0.445575i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.32843 | + | 2.03166i | 0.261506 | + | 0.159622i | ||||
\(163\) | 3.29997 | + | 1.90524i | 0.258474 | + | 0.149230i | 0.623638 | − | 0.781713i | \(-0.285654\pi\) |
−0.365164 | + | 0.930943i | \(0.618987\pi\) | |||||||
\(164\) | 9.31905 | + | 6.00558i | 0.727695 | + | 0.468957i | ||||
\(165\) | 3.07107 | + | 5.31925i | 0.239082 | + | 0.414103i | ||||
\(166\) | −5.36139 | + | 2.92316i | −0.416124 | + | 0.226881i | ||||
\(167\) | 20.8489 | 1.61334 | 0.806668 | − | 0.591005i | \(-0.201269\pi\) | ||||
0.806668 | + | 0.591005i | \(0.201269\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.17157 | 0.474736 | ||||||||
\(170\) | 5.99523 | − | 3.26874i | 0.459813 | − | 0.250701i | ||||
\(171\) | 2.48932 | + | 4.31162i | 0.190363 | + | 0.329718i | ||||
\(172\) | 13.4130 | + | 8.64393i | 1.02274 | + | 0.659094i | ||||
\(173\) | 18.2651 | + | 10.5454i | 1.38867 | + | 0.801749i | 0.993165 | − | 0.116715i | \(-0.0372365\pi\) |
0.395504 | + | 0.918464i | \(0.370570\pi\) | |||||||
\(174\) | 3.85077 | + | 2.35049i | 0.291926 | + | 0.178190i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.77817 | + | 4.85249i | 0.510924 | + | 0.365770i | ||||
\(177\) | −12.0208 | + | 20.8207i | −0.903540 | + | 1.56498i | ||||
\(178\) | 5.67290 | + | 0.138614i | 0.425202 | + | 0.0103896i | ||||
\(179\) | 1.05724 | − | 0.610396i | 0.0790216 | − | 0.0456231i | −0.459969 | − | 0.887935i | \(-0.652139\pi\) |
0.538990 | + | 0.842312i | \(0.318806\pi\) | |||||||
\(180\) | −0.466705 | + | 9.54442i | −0.0347861 | + | 0.711399i | ||||
\(181\) | 6.04601i | 0.449397i | 0.974428 | + | 0.224698i | \(0.0721396\pi\) | ||||
−0.974428 | + | 0.224698i | \(0.927860\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 35.5765i | 2.62989i | ||||||||
\(184\) | 11.3117 | − | 16.6452i | 0.833912 | − | 1.22710i | ||||
\(185\) | 3.74952 | − | 2.16478i | 0.275670 | − | 0.159158i | ||||
\(186\) | 0.724434 | − | 29.6480i | 0.0531181 | − | 2.17390i | ||||
\(187\) | −4.64829 | + | 8.05107i | −0.339917 | + | 0.588753i | ||||
\(188\) | −4.97863 | − | 9.68714i | −0.363104 | − | 0.706507i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.899495 | − | 1.47363i | 0.0652562 | − | 0.106908i | ||||
\(191\) | −17.4288 | − | 10.0625i | −1.26111 | − | 0.728100i | −0.287818 | − | 0.957685i | \(-0.592930\pi\) |
−0.973289 | + | 0.229585i | \(0.926263\pi\) | |||||||
\(192\) | 8.01955 | + | 20.2533i | 0.578761 | + | 1.46166i | ||||
\(193\) | −8.70711 | − | 15.0812i | −0.626751 | − | 1.08557i | −0.988199 | − | 0.153173i | \(-0.951051\pi\) |
0.361448 | − | 0.932392i | \(-0.382282\pi\) | |||||||
\(194\) | 2.59069 | + | 4.75160i | 0.186000 | + | 0.341145i | ||||
\(195\) | 7.70154 | 0.551519 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | −6.22774 | − | 11.4223i | −0.442586 | − | 0.811751i | ||||
\(199\) | −10.8916 | − | 18.8648i | −0.772087 | − | 1.33729i | −0.936417 | − | 0.350888i | \(-0.885880\pi\) |
0.164331 | − | 0.986405i | \(-0.447454\pi\) | |||||||
\(200\) | −9.74897 | + | 4.71301i | −0.689356 | + | 0.333260i | ||||
\(201\) | 23.7285 | + | 13.6997i | 1.67368 | + | 0.966301i | ||||
\(202\) | −0.136833 | + | 0.224171i | −0.00962753 | + | 0.0157726i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −21.6066 | + | 11.1046i | −1.51276 | + | 0.777474i | ||||
\(205\) | −3.00000 | + | 5.19615i | −0.209529 | + | 0.362915i | ||||
\(206\) | −0.532104 | + | 21.7767i | −0.0370734 | + | 1.51726i | ||||
\(207\) | −27.2005 | + | 15.7042i | −1.89057 | + | 1.09152i | ||||
\(208\) | 9.51884 | − | 4.31817i | 0.660013 | − | 0.299411i | ||||
\(209\) | 2.35049i | 0.162587i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 15.9570i | − | 1.09853i | −0.835649 | − | 0.549264i | \(-0.814908\pi\) | ||
0.835649 | − | 0.549264i | \(-0.185092\pi\) | |||||||
\(212\) | 12.9551 | + | 0.633480i | 0.889759 | + | 0.0435076i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.0595 | + | 0.245800i | 0.687656 | + | 0.0168025i | ||||
\(215\) | −4.31795 | + | 7.47890i | −0.294481 | + | 0.510057i | ||||
\(216\) | 0.797521 | − | 10.8624i | 0.0542644 | − | 0.739092i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.82843 | − | 4.16804i | −0.462479 | − | 0.282295i | ||||
\(219\) | 18.7957 | + | 10.8517i | 1.27010 | + | 0.733291i | ||||
\(220\) | −2.44386 | + | 3.79220i | −0.164765 | + | 0.255670i | ||||
\(221\) | 5.82843 | + | 10.0951i | 0.392062 | + | 0.679072i | ||||
\(222\) | −13.5236 | + | 7.37340i | −0.907645 | + | 0.494870i | ||||
\(223\) | 20.8489 | 1.39614 | 0.698072 | − | 0.716027i | \(-0.254041\pi\) | ||||
0.698072 | + | 0.716027i | \(0.254041\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16.8995 | 1.12663 | ||||||||
\(226\) | 5.26788 | − | 2.87218i | 0.350414 | − | 0.191054i | ||||
\(227\) | 9.06299 | + | 15.6976i | 0.601532 | + | 1.04188i | 0.992589 | + | 0.121518i | \(0.0387761\pi\) |
−0.391057 | + | 0.920366i | \(0.627891\pi\) | |||||||
\(228\) | −3.32719 | + | 5.16291i | −0.220349 | + | 0.341922i | ||||
\(229\) | −16.3903 | − | 9.46297i | −1.08310 | − | 0.625330i | −0.151372 | − | 0.988477i | \(-0.548369\pi\) |
−0.931732 | + | 0.363146i | \(0.881702\pi\) | |||||||
\(230\) | 9.29658 | + | 5.67459i | 0.612998 | + | 0.374172i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.242641 | + | 3.30481i | −0.0159301 | + | 0.216972i | ||||
\(233\) | −3.87868 | + | 6.71807i | −0.254101 | + | 0.440115i | −0.964651 | − | 0.263531i | \(-0.915113\pi\) |
0.710550 | + | 0.703647i | \(0.248446\pi\) | |||||||
\(234\) | −16.3079 | − | 0.398476i | −1.06608 | − | 0.0260492i | ||||
\(235\) | 5.10479 | − | 2.94725i | 0.333000 | − | 0.192257i | ||||
\(236\) | −17.6377 | − | 0.862453i | −1.14812 | − | 0.0561409i | ||||
\(237\) | 11.3492i | 0.737209i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 11.2833i | − | 0.729858i | −0.931035 | − | 0.364929i | \(-0.881093\pi\) | ||
0.931035 | − | 0.364929i | \(-0.118907\pi\) | |||||||
\(240\) | −10.7360 | + | 4.87030i | −0.693003 | + | 0.314377i | ||||
\(241\) | 7.45193 | − | 4.30237i | 0.480021 | − | 0.277140i | −0.240404 | − | 0.970673i | \(-0.577280\pi\) |
0.720425 | + | 0.693533i | \(0.243947\pi\) | |||||||
\(242\) | −0.229963 | + | 9.41140i | −0.0147826 | + | 0.604988i | ||||
\(243\) | 9.53017 | − | 16.5067i | 0.611361 | − | 1.05891i | ||||
\(244\) | −23.2415 | + | 11.9448i | −1.48788 | + | 0.764686i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.1213 | − | 18.2199i | 0.709069 | − | 1.16166i | ||||
\(247\) | 2.55239 | + | 1.47363i | 0.162405 | + | 0.0937646i | ||||
\(248\) | 19.6117 | − | 9.48104i | 1.24535 | − | 0.602046i | ||||
\(249\) | 5.87868 | + | 10.1822i | 0.372546 | + | 0.645269i | ||||
\(250\) | −6.46909 | − | 11.8650i | −0.409141 | − | 0.750409i | ||||
\(251\) | −10.4244 | −0.657985 | −0.328993 | − | 0.944333i | \(-0.606709\pi\) | ||||
−0.328993 | + | 0.944333i | \(0.606709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.8284 | −0.932255 | ||||||||
\(254\) | −7.63858 | − | 14.0100i | −0.479287 | − | 0.879064i | ||||
\(255\) | −6.57368 | − | 11.3859i | −0.411659 | − | 0.713015i | ||||
\(256\) | −10.5386 | + | 12.0391i | −0.658659 | + | 0.752441i | ||||
\(257\) | −8.16186 | − | 4.71225i | −0.509123 | − | 0.293942i | 0.223350 | − | 0.974738i | \(-0.428301\pi\) |
−0.732473 | + | 0.680796i | \(0.761634\pi\) | |||||||
\(258\) | 16.0071 | − | 26.2241i | 0.996558 | − | 1.63264i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.58579 | + | 5.03127i | 0.160364 | + | 0.312026i | ||||
\(261\) | 2.58579 | − | 4.47871i | 0.160056 | − | 0.277225i | ||||
\(262\) | 0.548242 | − | 22.4372i | 0.0338705 | − | 1.38618i | ||||
\(263\) | 18.9240 | − | 10.9258i | 1.16690 | − | 0.673712i | 0.213955 | − | 0.976844i | \(-0.431365\pi\) |
0.952949 | + | 0.303131i | \(0.0980321\pi\) | |||||||
\(264\) | 9.02134 | − | 13.2749i | 0.555225 | − | 0.817015i | ||||
\(265\) | 7.01962i | 0.431212i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 10.9258i | − | 0.668647i | ||||||
\(268\) | −0.982906 | + | 20.1011i | −0.0600405 | + | 1.22787i | ||||
\(269\) | 15.0647 | − | 8.69760i | 0.918510 | − | 0.530302i | 0.0353506 | − | 0.999375i | \(-0.488745\pi\) |
0.883159 | + | 0.469073i | \(0.155412\pi\) | |||||||
\(270\) | 5.89274 | + | 0.143986i | 0.358621 | + | 0.00876272i | ||||
\(271\) | 2.72291 | − | 4.71621i | 0.165405 | − | 0.286489i | −0.771394 | − | 0.636358i | \(-0.780440\pi\) |
0.936799 | + | 0.349868i | \(0.113774\pi\) | |||||||
\(272\) | −14.5088 | − | 10.3868i | −0.879725 | − | 0.629795i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.292893 | − | 0.178781i | −0.0176943 | − | 0.0108005i | ||||
\(275\) | 6.90960 | + | 3.98926i | 0.416665 | + | 0.240562i | ||||
\(276\) | −32.5709 | − | 20.9901i | −1.96054 | − | 1.26345i | ||||
\(277\) | −12.0711 | − | 20.9077i | −0.725280 | − | 1.25622i | −0.958859 | − | 0.283884i | \(-0.908377\pi\) |
0.233578 | − | 0.972338i | \(-0.424956\pi\) | |||||||
\(278\) | −2.22076 | + | 1.21081i | −0.133192 | + | 0.0726197i | ||||
\(279\) | −33.9962 | −2.03530 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.3848 | −1.57398 | −0.786992 | − | 0.616963i | \(-0.788363\pi\) | ||||
−0.786992 | + | 0.616963i | \(0.788363\pi\) | |||||||
\(282\) | −18.4117 | + | 10.0385i | −1.09640 | + | 0.597786i | ||||
\(283\) | 6.00974 | + | 10.4092i | 0.357242 | + | 0.618762i | 0.987499 | − | 0.157625i | \(-0.0503838\pi\) |
−0.630257 | + | 0.776387i | \(0.717050\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.87875 | − | 1.66205i | −0.170523 | − | 0.0984513i | ||||
\(286\) | −6.57368 | − | 4.01254i | −0.388710 | − | 0.237267i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 22.9853 | − | 9.75735i | 1.35442 | − | 0.574957i | ||||
\(289\) | 1.44975 | − | 2.51104i | 0.0852793 | − | 0.147708i | ||||
\(290\) | −1.79283 | − | 0.0438069i | −0.105279 | − | 0.00257243i | ||||
\(291\) | 9.02408 | − | 5.21005i | 0.529001 | − | 0.305419i | ||||
\(292\) | −0.778575 | + | 15.9224i | −0.0455626 | + | 0.931786i | ||||
\(293\) | − | 23.2555i | − | 1.35860i | −0.733860 | − | 0.679300i | \(-0.762283\pi\) | ||
0.733860 | − | 0.679300i | \(-0.237717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.55688i | − | 0.556423i | ||||||
\(296\) | −9.35744 | − | 6.35911i | −0.543890 | − | 0.369616i | ||||
\(297\) | −6.94993 | + | 4.01254i | −0.403276 | + | 0.232831i | ||||
\(298\) | 0.0286182 | − | 1.17122i | 0.00165781 | − | 0.0678471i | ||||
\(299\) | −9.29658 | + | 16.1021i | −0.537635 | + | 0.931211i | ||||
\(300\) | 9.53017 | + | 18.5432i | 0.550225 | + | 1.07059i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.97056 | + | 6.50490i | −0.228480 | + | 0.374315i | ||||
\(303\) | 0.437922 | + | 0.252834i | 0.0251579 | + | 0.0145249i | ||||
\(304\) | −4.48993 | − | 0.440152i | −0.257515 | − | 0.0252444i | ||||
\(305\) | −7.07107 | − | 12.2474i | −0.404888 | − | 0.701287i | ||||
\(306\) | 13.3306 | + | 24.4497i | 0.762059 | + | 1.39770i | ||||
\(307\) | −10.4244 | −0.594954 | −0.297477 | − | 0.954729i | \(-0.596145\pi\) | ||||
−0.297477 | + | 0.954729i | \(0.596145\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 41.9411 | 2.38595 | ||||||||
\(310\) | 5.64335 | + | 10.3505i | 0.320521 | + | 0.587870i | ||||
\(311\) | −2.25573 | − | 3.90704i | −0.127911 | − | 0.221548i | 0.794956 | − | 0.606667i | \(-0.207494\pi\) |
−0.922867 | + | 0.385119i | \(0.874160\pi\) | |||||||
\(312\) | −8.75934 | − | 18.1189i | −0.495900 | − | 1.02578i | ||||
\(313\) | 8.55014 | + | 4.93642i | 0.483282 | + | 0.279023i | 0.721783 | − | 0.692119i | \(-0.243323\pi\) |
−0.238501 | + | 0.971142i | \(0.576656\pi\) | |||||||
\(314\) | −14.8792 | + | 24.3764i | −0.839683 | + | 1.37564i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.41421 | + | 3.81048i | −0.417082 | + | 0.214356i | ||||
\(317\) | 11.2426 | − | 19.4728i | 0.631450 | − | 1.09370i | −0.355806 | − | 0.934560i | \(-0.615794\pi\) |
0.987256 | − | 0.159143i | \(-0.0508731\pi\) | |||||||
\(318\) | 0.610028 | − | 24.9659i | 0.0342087 | − | 1.40002i | ||||
\(319\) | 2.11447 | − | 1.22079i | 0.118388 | − | 0.0683512i | ||||
\(320\) | −6.78627 | − | 5.37840i | −0.379364 | − | 0.300662i | ||||
\(321\) | − | 19.3743i | − | 1.08137i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.03127i | − | 0.279948i | ||||||
\(324\) | 5.50814 | + | 0.269338i | 0.306008 | + | 0.0149632i | ||||
\(325\) | 8.66386 | − | 5.00208i | 0.480584 | − | 0.277466i | ||||
\(326\) | 5.38723 | + | 0.131634i | 0.298371 | + | 0.00729054i | ||||
\(327\) | −7.70154 | + | 13.3395i | −0.425896 | + | 0.737674i | ||||
\(328\) | 15.6367 | + | 1.14805i | 0.863391 | + | 0.0633905i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.41421 | + | 4.52560i | 0.408139 | + | 0.249126i | ||||
\(331\) | 3.29997 | + | 1.90524i | 0.181383 | + | 0.104722i | 0.587942 | − | 0.808903i | \(-0.299938\pi\) |
−0.406559 | + | 0.913624i | \(0.633272\pi\) | |||||||
\(332\) | −4.67806 | + | 7.25909i | −0.256742 | + | 0.398394i | ||||
\(333\) | 8.82843 | + | 15.2913i | 0.483795 | + | 0.837957i | ||||
\(334\) | 25.8871 | − | 14.1143i | 1.41648 | − | 0.772298i | ||||
\(335\) | −10.8916 | −0.595073 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.17157 | 0.281714 | 0.140857 | − | 0.990030i | \(-0.455014\pi\) | ||||
0.140857 | + | 0.990030i | \(0.455014\pi\) | |||||||
\(338\) | 7.66295 | − | 4.17802i | 0.416809 | − | 0.227255i | ||||
\(339\) | −5.77615 | − | 10.0046i | −0.313718 | − | 0.543375i | ||||
\(340\) | 5.23112 | − | 8.11728i | 0.283697 | − | 0.440221i | ||||
\(341\) | −13.8999 | − | 8.02509i | −0.752720 | − | 0.434583i | ||||
\(342\) | 6.00974 | + | 3.66832i | 0.324970 | + | 0.198360i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 22.5061 | + | 1.65241i | 1.21345 | + | 0.0890918i | ||||
\(345\) | 10.4853 | − | 18.1610i | 0.564509 | − | 0.977758i | ||||
\(346\) | 29.8179 | + | 0.728585i | 1.60302 | + | 0.0391690i | ||||
\(347\) | −1.80482 | + | 1.04201i | −0.0968876 | + | 0.0559381i | −0.547661 | − | 0.836700i | \(-0.684482\pi\) |
0.450773 | + | 0.892638i | \(0.351148\pi\) | |||||||
\(348\) | 6.37255 | + | 0.311606i | 0.341605 | + | 0.0167038i | ||||
\(349\) | − | 5.67459i | − | 0.303754i | −0.988399 | − | 0.151877i | \(-0.951468\pi\) | ||
0.988399 | − | 0.151877i | \(-0.0485318\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.0625i | 0.537099i | ||||||||
\(352\) | 11.7012 | + | 1.43643i | 0.623674 | + | 0.0765618i | ||||
\(353\) | −24.2305 | + | 13.9895i | −1.28966 | + | 0.744586i | −0.978594 | − | 0.205801i | \(-0.934020\pi\) |
−0.311068 | + | 0.950388i | \(0.600687\pi\) | |||||||
\(354\) | −0.830525 | + | 33.9899i | −0.0441419 | + | 1.80654i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.13761 | − | 3.66832i | 0.378292 | − | 0.194421i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.899495 | − | 1.47363i | 0.0475398 | − | 0.0778835i | ||||
\(359\) | −21.4764 | − | 12.3994i | −1.13348 | − | 0.654415i | −0.188673 | − | 0.982040i | \(-0.560419\pi\) |
−0.944808 | + | 0.327625i | \(0.893752\pi\) | |||||||
\(360\) | 5.88188 | + | 12.1668i | 0.310002 | + | 0.641246i | ||||
\(361\) | 8.86396 | + | 15.3528i | 0.466524 | + | 0.808044i | ||||
\(362\) | 4.09302 | + | 7.50704i | 0.215124 | + | 0.394561i | ||||
\(363\) | 18.1260 | 0.951367 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.62742 | −0.451580 | ||||||||
\(366\) | 24.0845 | + | 44.1736i | 1.25892 | + | 2.30899i | ||||
\(367\) | 8.16872 | + | 14.1486i | 0.426404 | + | 0.738553i | 0.996550 | − | 0.0829903i | \(-0.0264470\pi\) |
−0.570147 | + | 0.821543i | \(0.693114\pi\) | |||||||
\(368\) | 2.77676 | − | 28.3254i | 0.144749 | − | 1.47656i | ||||
\(369\) | −21.1910 | − | 12.2346i | −1.10316 | − | 0.636908i | ||||
\(370\) | 3.19008 | − | 5.22625i | 0.165844 | − | 0.271700i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −19.1716 | − | 37.3029i | −0.994000 | − | 1.93407i | ||||
\(373\) | −4.07107 | + | 7.05130i | −0.210792 | + | 0.365102i | −0.951963 | − | 0.306214i | \(-0.900938\pi\) |
0.741171 | + | 0.671317i | \(0.234271\pi\) | |||||||
\(374\) | −0.321153 | + | 13.1434i | −0.0166064 | + | 0.679630i | ||||
\(375\) | −22.5336 | + | 13.0098i | −1.16363 | + | 0.671823i | ||||
\(376\) | −12.7397 | − | 8.65762i | −0.657001 | − | 0.446483i | ||||
\(377\) | − | 3.06147i | − | 0.157674i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.9356i | 1.22949i | 0.788727 | + | 0.614744i | \(0.210741\pi\) | ||||
−0.788727 | + | 0.614744i | \(0.789259\pi\) | |||||||
\(380\) | 0.119246 | − | 2.43867i | 0.00611722 | − | 0.125101i | ||||
\(381\) | −26.6073 | + | 15.3617i | −1.36313 | + | 0.787005i | ||||
\(382\) | −28.4527 | − | 0.695227i | −1.45577 | − | 0.0355709i | ||||
\(383\) | −3.38359 | + | 5.86055i | −0.172894 | + | 0.299460i | −0.939430 | − | 0.342740i | \(-0.888645\pi\) |
0.766537 | + | 0.642200i | \(0.221978\pi\) | |||||||
\(384\) | 23.6686 | + | 19.7185i | 1.20783 | + | 1.00626i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21.0208 | − | 12.8310i | −1.06993 | − | 0.653082i | ||||
\(387\) | −30.5005 | − | 17.6095i | −1.55043 | − | 0.895139i | ||||
\(388\) | 6.43346 | + | 4.14599i | 0.326609 | + | 0.210481i | ||||
\(389\) | 7.07107 | + | 12.2474i | 0.358517 | + | 0.620970i | 0.987713 | − | 0.156276i | \(-0.0499491\pi\) |
−0.629196 | + | 0.777247i | \(0.716616\pi\) | |||||||
\(390\) | 9.56263 | − | 5.21378i | 0.484223 | − | 0.264010i | ||||
\(391\) | 31.7405 | 1.60519 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −43.2132 | −2.17982 | ||||||||
\(394\) | 2.48330 | − | 1.35396i | 0.125107 | − | 0.0682114i | ||||
\(395\) | −2.25573 | − | 3.90704i | −0.113498 | − | 0.196584i | ||||
\(396\) | −15.4654 | − | 9.96654i | −0.777164 | − | 0.500837i | ||||
\(397\) | 11.0877 | + | 6.40150i | 0.556477 | + | 0.321282i | 0.751730 | − | 0.659471i | \(-0.229220\pi\) |
−0.195253 | + | 0.980753i | \(0.562553\pi\) | |||||||
\(398\) | −26.2947 | − | 16.0502i | −1.31803 | − | 0.804523i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.91421 | + | 12.4518i | −0.445711 | + | 0.622588i | ||||
\(401\) | 3.58579 | − | 6.21076i | 0.179066 | − | 0.310151i | −0.762495 | − | 0.646994i | \(-0.776026\pi\) |
0.941561 | + | 0.336843i | \(0.109359\pi\) | |||||||
\(402\) | 38.7370 | + | 0.946519i | 1.93203 | + | 0.0472081i | ||||
\(403\) | −17.4288 | + | 10.0625i | −0.868192 | + | 0.501251i | ||||
\(404\) | −0.0181400 | + | 0.370975i | −0.000902499 | + | 0.0184567i | ||||
\(405\) | 2.98454i | 0.148303i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.33609i | 0.413204i | ||||||||
\(408\) | −19.3103 | + | 28.4152i | −0.956004 | + | 1.40676i | ||||
\(409\) | −6.28710 | + | 3.62986i | −0.310877 | + | 0.179485i | −0.647319 | − | 0.762219i | \(-0.724110\pi\) |
0.336442 | + | 0.941704i | \(0.390776\pi\) | |||||||
\(410\) | −0.207272 | + | 8.48275i | −0.0102364 | + | 0.418933i | ||||
\(411\) | −0.330344 | + | 0.572172i | −0.0162947 | + | 0.0282232i | ||||
\(412\) | 14.0817 | + | 27.3994i | 0.693756 | + | 1.34987i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −23.1421 | + | 37.9133i | −1.13737 | + | 1.86334i | ||||
\(415\) | −4.04755 | − | 2.33686i | −0.198687 | − | 0.114712i | ||||
\(416\) | 8.89578 | − | 11.8057i | 0.436151 | − | 0.578823i | ||||
\(417\) | 2.43503 | + | 4.21759i | 0.119244 | + | 0.206536i | ||||
\(418\) | 1.59123 | + | 2.91850i | 0.0778298 | + | 0.142748i | ||||
\(419\) | −16.5309 | −0.807589 | −0.403795 | − | 0.914850i | \(-0.632309\pi\) | ||||
−0.403795 | + | 0.914850i | \(0.632309\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.48528 | 0.316073 | 0.158037 | − | 0.987433i | \(-0.449484\pi\) | ||||
0.158037 | + | 0.987433i | \(0.449484\pi\) | |||||||
\(422\) | −10.8026 | − | 19.8131i | −0.525861 | − | 0.964487i | ||||
\(423\) | 12.0195 | + | 20.8184i | 0.584407 | + | 1.01222i | ||||
\(424\) | 16.5146 | − | 7.98375i | 0.802018 | − | 0.387725i | ||||
\(425\) | −14.7901 | − | 8.53909i | −0.717427 | − | 0.414207i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.6569 | − | 6.50490i | 0.611792 | − | 0.314426i | ||||
\(429\) | −7.41421 | + | 12.8418i | −0.357962 | + | 0.620008i | ||||
\(430\) | −0.298329 | + | 12.2094i | −0.0143867 | + | 0.588787i | ||||
\(431\) | 14.8764 | − | 8.58892i | 0.716573 | − | 0.413714i | −0.0969169 | − | 0.995292i | \(-0.530898\pi\) |
0.813490 | + | 0.581579i | \(0.197565\pi\) | |||||||
\(432\) | −6.36336 | − | 14.0272i | −0.306157 | − | 0.674884i | ||||
\(433\) | − | 15.1760i | − | 0.729313i | −0.931142 | − | 0.364657i | \(-0.881186\pi\) | ||
0.931142 | − | 0.364657i | \(-0.118814\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.45292i | 0.165555i | ||||||||
\(436\) | −11.3002 | − | 0.552560i | −0.541182 | − | 0.0264628i | ||||
\(437\) | 6.94993 | − | 4.01254i | 0.332460 | − | 0.191946i | ||||
\(438\) | 30.6841 | + | 0.749752i | 1.46615 | + | 0.0358245i | ||||
\(439\) | 8.82940 | − | 15.2930i | 0.421404 | − | 0.729894i | −0.574673 | − | 0.818383i | \(-0.694871\pi\) |
0.996077 | + | 0.0884894i | \(0.0282040\pi\) | |||||||
\(440\) | −0.467177 | + | 6.36304i | −0.0222718 | + | 0.303346i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.0711 | + | 8.58892i | 0.669292 | + | 0.408533i | ||||
\(443\) | −23.1529 | − | 13.3674i | −1.10003 | − | 0.635102i | −0.163801 | − | 0.986493i | \(-0.552375\pi\) |
−0.936229 | + | 0.351391i | \(0.885709\pi\) | |||||||
\(444\) | −11.8000 | + | 18.3104i | −0.560002 | + | 0.868972i | ||||
\(445\) | 2.17157 | + | 3.76127i | 0.102942 | + | 0.178302i | ||||
\(446\) | 25.8871 | − | 14.1143i | 1.22579 | − | 0.668329i | ||||
\(447\) | −2.25573 | −0.106692 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.2843 | 1.90113 | 0.950566 | − | 0.310522i | \(-0.100504\pi\) | ||||
0.950566 | + | 0.310522i | \(0.100504\pi\) | |||||||
\(450\) | 20.9833 | − | 11.4406i | 0.989162 | − | 0.539315i | ||||
\(451\) | −5.77615 | − | 10.0046i | −0.271988 | − | 0.471098i | ||||
\(452\) | 4.59648 | − | 7.13249i | 0.216200 | − | 0.335484i | ||||
\(453\) | 12.7074 | + | 7.33664i | 0.597048 | + | 0.344706i | ||||
\(454\) | 21.8800 | + | 13.3555i | 1.02688 | + | 0.626803i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.636039 | + | 8.66297i | −0.0297853 | + | 0.405681i | ||||
\(457\) | 12.3640 | − | 21.4150i | 0.578362 | − | 1.00175i | −0.417306 | − | 0.908766i | \(-0.637026\pi\) |
0.995667 | − | 0.0929857i | \(-0.0296411\pi\) | |||||||
\(458\) | −26.7573 | − | 0.653802i | −1.25029 | − | 0.0305501i | ||||
\(459\) | 14.8764 | − | 8.58892i | 0.694373 | − | 0.400896i | ||||
\(460\) | 15.3847 | + | 0.752284i | 0.717315 | + | 0.0350754i | ||||
\(461\) | 27.4763i | 1.27970i | 0.768501 | + | 0.639849i | \(0.221003\pi\) | ||||
−0.768501 | + | 0.639849i | \(0.778997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.60963i | 0.307175i | 0.988135 | + | 0.153588i | \(0.0490828\pi\) | ||||
−0.988135 | + | 0.153588i | \(0.950917\pi\) | |||||||
\(464\) | 1.93601 | + | 4.26769i | 0.0898771 | + | 0.198123i | ||||
\(465\) | 19.6574 | − | 11.3492i | 0.911589 | − | 0.526306i | ||||
\(466\) | −0.267980 | + | 10.9673i | −0.0124139 | + | 0.508050i | ||||
\(467\) | −3.75401 | + | 6.50214i | −0.173715 | + | 0.300883i | −0.939716 | − | 0.341956i | \(-0.888911\pi\) |
0.766001 | + | 0.642840i | \(0.222244\pi\) | |||||||
\(468\) | −20.5185 | + | 10.5454i | −0.948470 | + | 0.487459i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.34315 | − | 7.11529i | 0.200334 | − | 0.328204i | ||||
\(471\) | 47.6197 | + | 27.4932i | 2.19420 | + | 1.26682i | ||||
\(472\) | −22.4838 | + | 10.8695i | −1.03490 | + | 0.500309i | ||||
\(473\) | −8.31371 | − | 14.3998i | −0.382265 | − | 0.662102i | ||||
\(474\) | 7.68316 | + | 14.0917i | 0.352899 | + | 0.647255i | ||||
\(475\) | −4.31795 | −0.198121 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28.6274 | −1.31076 | ||||||||
\(478\) | −7.63858 | − | 14.0100i | −0.349380 | − | 0.640802i | ||||
\(479\) | 9.95727 | + | 17.2465i | 0.454959 | + | 0.788012i | 0.998686 | − | 0.0512499i | \(-0.0163205\pi\) |
−0.543727 | + | 0.839262i | \(0.682987\pi\) | |||||||
\(480\) | −10.0332 | + | 13.3152i | −0.457952 | + | 0.607755i | ||||
\(481\) | 9.05213 | + | 5.22625i | 0.412742 | + | 0.238297i | ||||
\(482\) | 6.34009 | − | 10.3868i | 0.288783 | − | 0.473108i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.08579 | + | 11.8414i | 0.276627 | + | 0.538244i | ||||
\(485\) | −2.07107 | + | 3.58719i | −0.0940423 | + | 0.162886i | ||||
\(486\) | 0.658445 | − | 26.9473i | 0.0298677 | − | 1.22236i | ||||
\(487\) | 34.4198 | − | 19.8723i | 1.55971 | − | 0.900498i | 0.562424 | − | 0.826849i | \(-0.309869\pi\) |
0.997284 | − | 0.0736490i | \(-0.0234644\pi\) | |||||||
\(488\) | −20.7714 | + | 30.5652i | −0.940279 | + | 1.38362i | ||||
\(489\) | − | 10.3756i | − | 0.469200i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.9570i | 0.720132i | 0.932927 | + | 0.360066i | \(0.117246\pi\) | ||||
−0.932927 | + | 0.360066i | \(0.882754\pi\) | |||||||
\(492\) | 1.47436 | − | 30.1516i | 0.0664692 | − | 1.35934i | ||||
\(493\) | −4.52607 | + | 2.61313i | −0.203844 | + | 0.117689i | ||||
\(494\) | 4.16680 | + | 0.101814i | 0.187473 | + | 0.00458081i | ||||
\(495\) | 4.97863 | − | 8.62325i | 0.223773 | − | 0.387586i | ||||
\(496\) | 17.9325 | − | 25.0489i | 0.805192 | − | 1.12473i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 14.1924 | + | 8.66297i | 0.635976 | + | 0.388197i | ||||
\(499\) | 15.9337 | + | 9.19932i | 0.713290 | + | 0.411818i | 0.812278 | − | 0.583271i | \(-0.198227\pi\) |
−0.0989883 | + | 0.995089i | \(0.531561\pi\) | |||||||
\(500\) | −16.0647 | − | 10.3528i | −0.718436 | − | 0.462990i | ||||
\(501\) | −28.3848 | − | 49.1639i | −1.26814 | − | 2.19648i | ||||
\(502\) | −12.9435 | + | 7.05713i | −0.577698 | + | 0.314975i | ||||
\(503\) | −20.8489 | −0.929606 | −0.464803 | − | 0.885414i | \(-0.653875\pi\) | ||||
−0.464803 | + | 0.885414i | \(0.653875\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.201010 | −0.00894483 | ||||||||
\(506\) | −18.4117 | + | 10.0385i | −0.818502 | + | 0.446267i | ||||
\(507\) | −8.40230 | − | 14.5532i | −0.373159 | − | 0.646331i | ||||
\(508\) | −18.9689 | − | 12.2244i | −0.841610 | − | 0.542368i | ||||
\(509\) | 18.2651 | + | 10.5454i | 0.809586 | + | 0.467415i | 0.846812 | − | 0.531892i | \(-0.178519\pi\) |
−0.0372260 | + | 0.999307i | \(0.511852\pi\) | |||||||
\(510\) | −15.8703 | − | 9.68714i | −0.702747 | − | 0.428954i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −4.93503 | + | 22.0827i | −0.218100 | + | 0.975927i | ||||
\(513\) | 2.17157 | − | 3.76127i | 0.0958773 | − | 0.166064i | ||||
\(514\) | −13.3243 | − | 0.325572i | −0.587709 | − | 0.0143604i | ||||
\(515\) | −14.4385 | + | 8.33609i | −0.636237 | + | 0.367332i | ||||
\(516\) | 2.12207 | − | 43.3977i | 0.0934188 | − | 1.91048i | ||||
\(517\) | 11.3492i | 0.499137i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 57.4280i | − | 2.52081i | ||||||
\(520\) | 6.61671 | + | 4.49657i | 0.290162 | + | 0.197188i | ||||
\(521\) | −15.5667 | + | 8.98743i | −0.681989 | + | 0.393746i | −0.800604 | − | 0.599194i | \(-0.795488\pi\) |
0.118615 | + | 0.992940i | \(0.462155\pi\) | |||||||
\(522\) | 0.178653 | − | 7.31153i | 0.00781945 | − | 0.320017i | ||||
\(523\) | 18.3596 | − | 31.7997i | 0.802808 | − | 1.39050i | −0.114953 | − | 0.993371i | \(-0.536672\pi\) |
0.917761 | − | 0.397133i | \(-0.129995\pi\) | |||||||
\(524\) | −14.5088 | − | 28.2304i | −0.633820 | − | 1.23325i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.1005 | − | 26.3772i | 0.702015 | − | 1.15010i | ||||
\(527\) | 29.7529 | + | 17.1778i | 1.29606 | + | 0.748278i | ||||
\(528\) | 2.21452 | − | 22.5901i | 0.0963748 | − | 0.983107i | ||||
\(529\) | 13.8137 | + | 23.9260i | 0.600596 | + | 1.04026i | ||||
\(530\) | 4.75213 | + | 8.71592i | 0.206419 | + | 0.378596i | ||||
\(531\) | 38.9749 | 1.69137 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.4853 | −0.627427 | ||||||||
\(534\) | −7.39652 | − | 13.5660i | −0.320079 | − | 0.587059i | ||||
\(535\) | 3.85077 | + | 6.66973i | 0.166483 | + | 0.288358i | ||||
\(536\) | 12.3876 | + | 25.6239i | 0.535062 | + | 1.10679i | ||||
\(537\) | −2.87875 | − | 1.66205i | −0.124227 | − | 0.0717227i | ||||
\(538\) | 12.8170 | − | 20.9979i | 0.552580 | − | 0.905282i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.41421 | − | 3.81048i | 0.319057 | − | 0.163977i | ||||
\(541\) | −11.3431 | + | 19.6469i | −0.487680 | + | 0.844686i | −0.999900 | − | 0.0141680i | \(-0.995490\pi\) |
0.512220 | + | 0.858854i | \(0.328823\pi\) | |||||||
\(542\) | 0.188127 | − | 7.69924i | 0.00808075 | − | 0.330711i | ||||
\(543\) | 14.2571 | − | 8.23136i | 0.611832 | − | 0.353241i | ||||
\(544\) | −25.0466 | − | 3.07470i | −1.07386 | − | 0.131827i | ||||
\(545\) | − | 6.12293i | − | 0.262278i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.5882i | 0.623744i | 0.950124 | + | 0.311872i | \(0.100956\pi\) | ||||
−0.950124 | + | 0.311872i | \(0.899044\pi\) | |||||||
\(548\) | −0.484702 | − | 0.0237011i | −0.0207055 | − | 0.00101246i | ||||
\(549\) | 49.9476 | − | 28.8372i | 2.13171 | − | 1.23074i | ||||
\(550\) | 11.2800 | + | 0.275620i | 0.480980 | + | 0.0117525i | ||||
\(551\) | −0.660688 | + | 1.14434i | −0.0281462 | + | 0.0487507i | ||||
\(552\) | −54.6516 | − | 4.01254i | −2.32613 | − | 0.170785i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −29.1421 | − | 17.7882i | −1.23813 | − | 0.755750i | ||||
\(555\) | −10.2096 | − | 5.89450i | −0.433372 | − | 0.250208i | ||||
\(556\) | −1.93772 | + | 3.00681i | −0.0821775 | + | 0.127517i | ||||
\(557\) | 4.17157 | + | 7.22538i | 0.176755 | + | 0.306149i | 0.940767 | − | 0.339053i | \(-0.110107\pi\) |
−0.764012 | + | 0.645202i | \(0.776773\pi\) | |||||||
\(558\) | −42.2115 | + | 23.0147i | −1.78696 | + | 0.974291i | ||||
\(559\) | −20.8489 | −0.881814 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.3137 | 1.06875 | ||||||||
\(562\) | −32.7607 | + | 17.8619i | −1.38193 | + | 0.753460i | ||||
\(563\) | −5.67940 | − | 9.83701i | −0.239358 | − | 0.414580i | 0.721172 | − | 0.692756i | \(-0.243604\pi\) |
−0.960530 | + | 0.278175i | \(0.910270\pi\) | |||||||
\(564\) | −16.0651 | + | 24.9287i | −0.676463 | + | 1.04969i | ||||
\(565\) | 3.97696 | + | 2.29610i | 0.167312 | + | 0.0965977i | ||||
\(566\) | 14.5088 | + | 8.85611i | 0.609850 | + | 0.372250i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.58579 | + | 11.4069i | −0.276091 | + | 0.478203i | −0.970410 | − | 0.241464i | \(-0.922372\pi\) |
0.694319 | + | 0.719667i | \(0.255706\pi\) | |||||||
\(570\) | −4.69958 | − | 0.114832i | −0.196844 | − | 0.00480978i | ||||
\(571\) | −35.1673 | + | 20.3039i | −1.47171 | + | 0.849691i | −0.999494 | − | 0.0317939i | \(-0.989878\pi\) |
−0.472213 | + | 0.881485i | \(0.656545\pi\) | |||||||
\(572\) | −10.8786 | − | 0.531945i | −0.454858 | − | 0.0222417i | ||||
\(573\) | 54.7987i | 2.28925i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 27.2404i | − | 1.13600i | ||||||
\(576\) | 21.9342 | − | 27.6758i | 0.913925 | − | 1.15316i | ||||
\(577\) | 33.4435 | − | 19.3086i | 1.39227 | − | 0.803828i | 0.398705 | − | 0.917079i | \(-0.369460\pi\) |
0.993566 | + | 0.113251i | \(0.0361265\pi\) | |||||||
\(578\) | 0.100164 | − | 4.09928i | 0.00416627 | − | 0.170508i | ||||
\(579\) | −23.7086 | + | 41.0645i | −0.985297 | + | 1.70658i | ||||
\(580\) | −2.25573 | + | 1.15932i | −0.0936640 | + | 0.0481380i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.67767 | − | 12.5782i | 0.318250 | − | 0.521382i | ||||
\(583\) | −11.7047 | − | 6.75773i | −0.484761 | − | 0.279877i | ||||
\(584\) | 9.81238 | + | 20.2971i | 0.406039 | + | 0.839901i | ||||
\(585\) | −6.24264 | − | 10.8126i | −0.258101 | − | 0.447045i | ||||
\(586\) | −15.7435 | − | 28.8752i | −0.650357 | − | 1.19283i | ||||
\(587\) | 1.78855 | 0.0738214 | 0.0369107 | − | 0.999319i | \(-0.488248\pi\) | ||||
0.0369107 | + | 0.999319i | \(0.488248\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.68629 | 0.357912 | ||||||||
\(590\) | −6.46980 | − | 11.8663i | −0.266358 | − | 0.488529i | ||||
\(591\) | −2.72291 | − | 4.71621i | −0.112005 | − | 0.193999i | ||||
\(592\) | −15.9237 | − | 1.56101i | −0.654459 | − | 0.0641571i | ||||
\(593\) | −30.3097 | − | 17.4993i | −1.24467 | − | 0.718611i | −0.274629 | − | 0.961550i | \(-0.588555\pi\) |
−0.970041 | + | 0.242939i | \(0.921888\pi\) | |||||||
\(594\) | −5.91299 | + | 9.68714i | −0.242613 | + | 0.397468i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.757359 | − | 1.47363i | −0.0310226 | − | 0.0603621i | ||||
\(597\) | −29.6569 | + | 51.3672i | −1.21377 | + | 2.10232i | ||||
\(598\) | −0.642306 | + | 26.2869i | −0.0262658 | + | 1.07495i | ||||
\(599\) | −36.3528 | + | 20.9883i | −1.48534 | + | 0.857560i | −0.999861 | − | 0.0166904i | \(-0.994687\pi\) |
−0.485476 | + | 0.874250i | \(0.661354\pi\) | |||||||
\(600\) | 24.3865 | + | 16.5725i | 0.995576 | + | 0.676571i | ||||
\(601\) | 6.25425i | 0.255116i | 0.991831 | + | 0.127558i | \(0.0407139\pi\) | ||||
−0.991831 | + | 0.127558i | \(0.959286\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 44.4182i | − | 1.80885i | ||||||
\(604\) | −0.526379 | + | 10.7648i | −0.0214181 | + | 0.438014i | ||||
\(605\) | −6.24000 | + | 3.60266i | −0.253692 | + | 0.146469i | ||||
\(606\) | 0.714910 | + | 0.0174685i | 0.0290412 | + | 0.000709608i | ||||
\(607\) | −7.70154 | + | 13.3395i | −0.312596 | + | 0.541432i | −0.978924 | − | 0.204227i | \(-0.934532\pi\) |
0.666328 | + | 0.745659i | \(0.267865\pi\) | |||||||
\(608\) | −5.87291 | + | 2.49307i | −0.238178 | + | 0.101108i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.0711 | − | 10.4201i | −0.691187 | − | 0.421898i | ||||
\(611\) | 12.3241 | + | 7.11529i | 0.498578 | + | 0.287854i | ||||
\(612\) | 33.1039 | + | 21.3335i | 1.33815 | + | 0.862358i | ||||
\(613\) | 15.6569 | + | 27.1185i | 0.632374 | + | 1.09530i | 0.987065 | + | 0.160321i | \(0.0512529\pi\) |
−0.354691 | + | 0.934984i | \(0.615414\pi\) | |||||||
\(614\) | −12.9435 | + | 7.05713i | −0.522358 | + | 0.284802i | ||||
\(615\) | 16.3374 | 0.658789 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.4558 | 0.622229 | 0.311114 | − | 0.950372i | \(-0.399298\pi\) | ||||
0.311114 | + | 0.950372i | \(0.399298\pi\) | |||||||
\(618\) | 52.0763 | − | 28.3932i | 2.09482 | − | 1.14214i | ||||
\(619\) | −22.2103 | − | 38.4694i | −0.892709 | − | 1.54622i | −0.836615 | − | 0.547792i | \(-0.815469\pi\) |
−0.0560944 | − | 0.998425i | \(-0.517865\pi\) | |||||||
\(620\) | 14.0142 | + | 9.03131i | 0.562822 | + | 0.362706i | ||||
\(621\) | 23.7285 | + | 13.6997i | 0.952194 | + | 0.549749i | ||||
\(622\) | −5.44581 | − | 3.32410i | −0.218357 | − | 0.133284i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −23.1421 | − | 16.5674i | −0.926427 | − | 0.663229i | ||||
\(625\) | −4.39949 | + | 7.62015i | −0.175980 | + | 0.304806i | ||||
\(626\) | 13.9581 | + | 0.341060i | 0.557880 | + | 0.0136315i | ||||
\(627\) | 5.54271 | − | 3.20009i | 0.221355 | − | 0.127799i | ||||
\(628\) | −1.97255 | + | 40.3399i | −0.0787132 | + | 1.60974i | ||||
\(629\) | − | 17.8435i | − | 0.711469i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.5667i | 0.898365i | 0.893440 | + | 0.449183i | \(0.148285\pi\) | ||||
−0.893440 | + | 0.449183i | \(0.851715\pi\) | |||||||
\(632\) | −6.62626 | + | 9.75056i | −0.263578 | + | 0.387856i | ||||
\(633\) | −37.6284 | + | 21.7248i | −1.49559 | + | 0.863482i | ||||
\(634\) | 0.776760 | − | 31.7895i | 0.0308491 | − | 1.26252i | ||||
\(635\) | 6.10650 | − | 10.5768i | 0.242329 | − | 0.419726i | ||||
\(636\) | −16.1439 | − | 31.4119i | −0.640148 | − | 1.24556i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.79899 | − | 2.94725i | 0.0712227 | − | 0.116683i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −12.0672 | − | 2.08394i | −0.477000 | − | 0.0823751i | ||||
\(641\) | 0.727922 | + | 1.26080i | 0.0287512 | + | 0.0497985i | 0.880043 | − | 0.474894i | \(-0.157514\pi\) |
−0.851292 | + | 0.524693i | \(0.824180\pi\) | |||||||
\(642\) | −13.1160 | − | 24.0561i | −0.517646 | − | 0.949419i | ||||
\(643\) | −6.84734 | −0.270033 | −0.135016 | − | 0.990843i | \(-0.543109\pi\) | ||||
−0.135016 | + | 0.990843i | \(0.543109\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23.5147 | 0.925891 | ||||||||
\(646\) | −3.40606 | − | 6.24709i | −0.134010 | − | 0.245788i | ||||
\(647\) | −4.78512 | − | 8.28808i | −0.188123 | − | 0.325838i | 0.756502 | − | 0.653992i | \(-0.226907\pi\) |
−0.944624 | + | 0.328154i | \(0.893574\pi\) | |||||||
\(648\) | 7.02153 | − | 3.39447i | 0.275832 | − | 0.133347i | ||||
\(649\) | 15.9354 | + | 9.20033i | 0.625521 | + | 0.361145i | ||||
\(650\) | 7.37120 | − | 12.0761i | 0.289122 | − | 0.473663i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.77817 | − | 3.48359i | 0.265454 | − | 0.136428i | ||||
\(653\) | −7.89949 | + | 13.6823i | −0.309131 | + | 0.535431i | −0.978173 | − | 0.207794i | \(-0.933372\pi\) |
0.669041 | + | 0.743225i | \(0.266705\pi\) | |||||||
\(654\) | −0.532104 | + | 21.7767i | −0.0208069 | + | 0.851538i | ||||
\(655\) | 14.8764 | − | 8.58892i | 0.581271 | − | 0.335597i | ||||
\(656\) | 20.1925 | − | 9.16021i | 0.788385 | − | 0.357646i | ||||
\(657\) | − | 35.1843i | − | 1.37267i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.5452i | 1.18987i | 0.803773 | + | 0.594936i | \(0.202823\pi\) | ||||
−0.803773 | + | 0.594936i | \(0.797177\pi\) | |||||||
\(660\) | 12.2696 | + | 0.599962i | 0.477594 | + | 0.0233535i | ||||
\(661\) | 10.8603 | − | 6.27018i | 0.422416 | − | 0.243882i | −0.273695 | − | 0.961817i | \(-0.588246\pi\) |
0.696110 | + | 0.717935i | \(0.254912\pi\) | |||||||
\(662\) | 5.38723 | + | 0.131634i | 0.209381 | + | 0.00511611i | ||||
\(663\) | 15.8703 | − | 27.4881i | 0.616350 | − | 1.06755i | ||||
\(664\) | −0.894276 | + | 12.1802i | −0.0347046 | + | 0.472684i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 21.3137 | + | 13.0098i | 0.825889 | + | 0.504119i | ||||
\(667\) | −7.21926 | − | 4.16804i | −0.279531 | − | 0.161387i | ||||
\(668\) | 22.5877 | − | 35.0500i | 0.873944 | − | 1.35612i | ||||
\(669\) | −28.3848 | − | 49.1639i | −1.09742 | − | 1.90079i | ||||
\(670\) | −13.5236 | + | 7.37340i | −0.522462 | + | 0.284859i | ||||
\(671\) | 27.2291 | 1.05117 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.3848 | −1.01706 | −0.508529 | − | 0.861045i | \(-0.669811\pi\) | ||||
−0.508529 | + | 0.861045i | \(0.669811\pi\) | |||||||
\(674\) | 6.42129 | − | 3.50104i | 0.247339 | − | 0.134855i | ||||
\(675\) | −7.37120 | − | 12.7673i | −0.283717 | − | 0.491413i | ||||
\(676\) | 6.68628 | − | 10.3753i | 0.257165 | − | 0.399050i | ||||
\(677\) | 34.7221 | + | 20.0468i | 1.33448 | + | 0.770461i | 0.985982 | − | 0.166850i | \(-0.0533596\pi\) |
0.348495 | + | 0.937311i | \(0.386693\pi\) | |||||||
\(678\) | −13.9449 | − | 8.51189i | −0.535550 | − | 0.326897i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.00000 | − | 13.6202i | 0.0383482 | − | 0.522311i | ||||
\(681\) | 24.6777 | − | 42.7430i | 0.945650 | − | 1.63791i | ||||
\(682\) | −22.6916 | − | 0.554458i | −0.868906 | − | 0.0212313i | ||||
\(683\) | −36.3528 | + | 20.9883i | −1.39100 | + | 0.803096i | −0.993426 | − | 0.114473i | \(-0.963482\pi\) |
−0.397576 | + | 0.917569i | \(0.630149\pi\) | |||||||
\(684\) | 9.94539 | + | 0.486311i | 0.380271 | + | 0.0185946i | ||||
\(685\) | − | 0.262632i | − | 0.0100347i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 51.5335i | 1.96613i | ||||||||
\(688\) | 29.0634 | − | 13.1844i | 1.10803 | − | 0.502652i | ||||
\(689\) | −14.6764 | + | 8.47343i | −0.559127 | + | 0.322812i | ||||
\(690\) | 0.724434 | − | 29.6480i | 0.0275787 | − | 1.12868i | ||||
\(691\) | −2.48932 | + | 4.31162i | −0.0946981 | + | 0.164022i | −0.909483 | − | 0.415742i | \(-0.863522\pi\) |
0.814784 | + | 0.579764i | \(0.196855\pi\) | |||||||
\(692\) | 37.5167 | − | 19.2814i | 1.42617 | − | 0.732970i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.53553 | + | 2.51564i | −0.0582881 | + | 0.0954923i | ||||
\(695\) | −1.67655 | − | 0.967957i | −0.0635952 | − | 0.0367167i | ||||
\(696\) | 8.12344 | − | 3.92717i | 0.307918 | − | 0.148859i | ||||
\(697\) | 12.3640 | + | 21.4150i | 0.468318 | + | 0.811151i | ||||
\(698\) | −3.84158 | − | 7.04587i | −0.145406 | − | 0.266690i | ||||
\(699\) | 21.1226 | 0.798928 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0000 | 0.604312 | 0.302156 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302156 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(702\) | 6.81213 | + | 12.4942i | 0.257107 | + | 0.471562i | ||||
\(703\) | −2.25573 | − | 3.90704i | −0.0850764 | − | 0.147357i | ||||
\(704\) | 15.5012 | − | 6.13790i | 0.584224 | − | 0.231331i | ||||
\(705\) | −13.8999 | − | 8.02509i | −0.523499 | − | 0.302242i | ||||
\(706\) | −20.6153 | + | 33.7737i | −0.775867 | + | 1.27109i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 21.9792 | + | 42.7658i | 0.826028 | + | 1.60724i | ||||
\(709\) | 0.686292 | − | 1.18869i | 0.0257742 | − | 0.0446423i | −0.852851 | − | 0.522155i | \(-0.825128\pi\) |
0.878625 | + | 0.477513i | \(0.158462\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.9337 | − | 9.19932i | 0.597560 | − | 0.345001i | ||||
\(712\) | 6.37905 | − | 9.38679i | 0.239065 | − | 0.351785i | ||||
\(713\) | 54.7987i | 2.05223i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5.89450i | − | 0.220442i | ||||||
\(716\) | 0.119246 | − | 2.43867i | 0.00445645 | − | 0.0911374i | ||||
\(717\) | −26.6073 | + | 15.3617i | −0.993668 | + | 0.573694i | ||||
\(718\) | −35.0603 | − | 0.856682i | −1.30844 | − | 0.0319711i | ||||
\(719\) | −5.91299 | + | 10.2416i | −0.220517 | + | 0.381947i | −0.954965 | − | 0.296718i | \(-0.904108\pi\) |
0.734448 | + | 0.678665i | \(0.237441\pi\) | |||||||
\(720\) | 15.5399 | + | 11.1250i | 0.579138 | + | 0.414605i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 21.3995 | + | 13.0622i | 0.796407 | + | 0.486123i | ||||
\(723\) | −20.2909 | − | 11.7150i | −0.754626 | − | 0.435684i | ||||
\(724\) | 10.1642 | + | 6.55025i | 0.377750 | + | 0.243438i | ||||
\(725\) | 2.24264 | + | 3.88437i | 0.0832896 | + | 0.144262i | ||||
\(726\) | 22.5062 | − | 12.2709i | 0.835282 | − | 0.455416i | ||||
\(727\) | −38.1207 | −1.41382 | −0.706909 | − | 0.707305i | \(-0.749911\pi\) | ||||
−0.706909 | + | 0.707305i | \(0.749911\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.6274 | −1.61583 | ||||||||
\(730\) | −10.7123 | + | 5.84058i | −0.396478 | + | 0.216169i | ||||
\(731\) | 17.7956 | + | 30.8230i | 0.658196 | + | 1.14003i | ||||
\(732\) | 59.8092 | + | 38.5435i | 2.21061 | + | 1.42461i | ||||
\(733\) | −2.03559 | − | 1.17525i | −0.0751861 | − | 0.0434087i | 0.461936 | − | 0.886913i | \(-0.347155\pi\) |
−0.537122 | + | 0.843505i | \(0.680488\pi\) | |||||||
\(734\) | 19.7210 | + | 12.0376i | 0.727916 | + | 0.444317i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.7279 | − | 37.0501i | −0.579739 | − | 1.36568i | ||||
\(737\) | 10.4853 | − | 18.1610i | 0.386230 | − | 0.668971i | ||||
\(738\) | −34.5944 | − | 0.845296i | −1.27344 | − | 0.0311158i | ||||
\(739\) | 45.3769 | − | 26.1984i | 1.66922 | − | 0.963723i | 0.701156 | − | 0.713008i | \(-0.252668\pi\) |
0.968061 | − | 0.250715i | \(-0.0806657\pi\) | |||||||
\(740\) | 0.422911 | − | 8.64880i | 0.0155465 | − | 0.317936i | ||||
\(741\) | − | 8.02509i | − | 0.294809i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 17.8930i | − | 0.656429i | −0.944603 | − | 0.328215i | \(-0.893553\pi\) | ||
0.944603 | − | 0.328215i | \(-0.106447\pi\) | |||||||
\(744\) | −49.0577 | − | 33.3385i | −1.79854 | − | 1.22225i | ||||
\(745\) | 0.776550 | − | 0.448342i | 0.0284506 | − | 0.0164260i | ||||
\(746\) | −0.281272 | + | 11.5113i | −0.0102981 | + | 0.421458i | ||||
\(747\) | 9.53017 | − | 16.5067i | 0.348691 | − | 0.603950i | ||||
\(748\) | 8.49906 | + | 16.5370i | 0.310756 | + | 0.604652i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −19.1716 | + | 31.4084i | −0.700047 | + | 1.14687i | ||||
\(751\) | 11.8861 | + | 6.86246i | 0.433731 | + | 0.250415i | 0.700935 | − | 0.713225i | \(-0.252766\pi\) |
−0.267204 | + | 0.963640i | \(0.586100\pi\) | |||||||
\(752\) | −21.6793 | − | 2.12524i | −0.790564 | − | 0.0774995i | ||||
\(753\) | 14.1924 | + | 24.5819i | 0.517199 | + | 0.895816i | ||||
\(754\) | −2.07255 | − | 3.80128i | −0.0754778 | − | 0.138434i | ||||
\(755\) | −5.83283 | −0.212279 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.2843 | 0.446479 | 0.223240 | − | 0.974764i | \(-0.428337\pi\) | ||||
0.223240 | + | 0.974764i | \(0.428337\pi\) | |||||||
\(758\) | 16.2039 | + | 29.7197i | 0.588551 | + | 1.07947i | ||||
\(759\) | 20.1882 | + | 34.9670i | 0.732785 | + | 1.26922i | ||||
\(760\) | −1.50286 | − | 3.10871i | −0.0545146 | − | 0.112765i | ||||
\(761\) | −22.5166 | − | 13.0000i | −0.816227 | − | 0.471249i | 0.0328870 | − | 0.999459i | \(-0.489530\pi\) |
−0.849113 | + | 0.528210i | \(0.822863\pi\) | |||||||
\(762\) | −22.6374 | + | 37.0865i | −0.820068 | + | 1.34350i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −35.7990 | + | 18.3986i | −1.29516 | + | 0.665639i | ||||
\(765\) | −10.6569 | + | 18.4582i | −0.385299 | + | 0.667358i | ||||
\(766\) | −0.233774 | + | 9.56739i | −0.00844661 | + | 0.345684i | ||||
\(767\) | 19.9812 | − | 11.5362i | 0.721481 | − | 0.416547i | ||||
\(768\) | 42.7371 | + | 8.46041i | 1.54214 | + | 0.305289i | ||||
\(769\) | − | 46.1940i | − | 1.66580i | −0.553425 | − | 0.832899i | \(-0.686680\pi\) | ||
0.553425 | − | 0.832899i | \(-0.313320\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.6620i | 0.924196i | ||||||||
\(772\) | −34.7869 | − | 1.70101i | −1.25201 | − | 0.0612208i | ||||
\(773\) | 45.8764 | − | 26.4867i | 1.65006 | − | 0.952662i | 0.673014 | − | 0.739630i | \(-0.264999\pi\) |
0.977045 | − | 0.213032i | \(-0.0683339\pi\) | |||||||
\(774\) | −49.7922 | − | 1.21665i | −1.78974 | − | 0.0437315i | ||||
\(775\) | 14.7424 | − | 25.5346i | 0.529562 | − | 0.917229i | ||||
\(776\) | 10.7949 | + | 0.792563i | 0.387513 | + | 0.0284514i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.0711 | + | 10.4201i | 0.612027 | + | 0.373579i | ||||
\(779\) | 5.41445 | + | 3.12603i | 0.193993 | + | 0.112002i | ||||
\(780\) | 8.34385 | − | 12.9474i | 0.298758 | − | 0.463591i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 39.4107 | − | 21.4876i | 1.40932 | − | 0.768397i | ||||
\(783\) | −4.51146 | −0.161226 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.8579 | −0.780141 | ||||||||
\(786\) | −53.6558 | + | 29.2544i | −1.91384 | + | 1.04347i | ||||
\(787\) | 14.6456 | + | 25.3670i | 0.522061 | + | 0.904235i | 0.999671 | + | 0.0256635i | \(0.00816983\pi\) |
−0.477610 | + | 0.878572i | \(0.658497\pi\) | |||||||
\(788\) | 2.16680 | − | 3.36229i | 0.0771890 | − | 0.119777i | ||||
\(789\) | −51.5283 | − | 29.7499i | −1.83445 | − | 1.05912i | ||||
\(790\) | −5.44581 | − | 3.32410i | −0.193753 | − | 0.118266i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −25.9497 | − | 1.90524i | −0.922084 | − | 0.0676998i | ||||
\(793\) | 17.0711 | − | 29.5680i | 0.606211 | − | 1.04999i | ||||
\(794\) | 18.1008 | + | 0.442283i | 0.642372 | + | 0.0156960i | ||||
\(795\) | 16.5530 | − | 9.55688i | 0.587074 | − | 0.338948i | ||||
\(796\) | −43.5145 | − | 2.12778i | −1.54233 | − | 0.0754171i | ||||
\(797\) | 19.1886i | 0.679694i | 0.940481 | + | 0.339847i | \(0.110375\pi\) | ||||
−0.940481 | + | 0.339847i | \(0.889625\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 24.2931i | − | 0.859429i | ||||||
\(800\) | −2.63877 | + | 21.4955i | −0.0932947 | + | 0.759980i | ||||
\(801\) | −15.3392 | + | 8.85611i | −0.541985 | + | 0.312915i | ||||
\(802\) | 0.247744 | − | 10.1391i | 0.00874814 | − | 0.358024i | ||||
\(803\) | 8.30555 | − | 14.3856i | 0.293096 | − | 0.507658i | ||||
\(804\) | 48.7386 | − | 25.0489i | 1.71888 | − | 0.883405i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.8284 | + | 24.2931i | −0.522309 | + | 0.855689i | ||||
\(807\) | −41.0197 | − | 23.6827i | −1.44396 | − | 0.833672i | ||||
\(808\) | 0.228619 | + | 0.472902i | 0.00804278 | + | 0.0166366i | ||||
\(809\) | −24.0208 | − | 41.6053i | −0.844527 | − | 1.46276i | −0.886031 | − | 0.463625i | \(-0.846548\pi\) |
0.0415045 | − | 0.999138i | \(-0.486785\pi\) | |||||||
\(810\) | 2.02047 | + | 3.70577i | 0.0709922 | + | 0.130207i | ||||
\(811\) | −42.4386 | −1.49022 | −0.745111 | − | 0.666941i | \(-0.767603\pi\) | ||||
−0.745111 | + | 0.666941i | \(0.767603\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.8284 | −0.520056 | ||||||||
\(814\) | 5.64335 | + | 10.3505i | 0.197799 | + | 0.362785i | ||||
\(815\) | 2.06222 | + | 3.57187i | 0.0722363 | + | 0.125117i | ||||
\(816\) | −4.74023 | + | 48.3545i | −0.165941 | + | 1.69275i | ||||
\(817\) | 7.79310 | + | 4.49935i | 0.272646 | + | 0.157412i | ||||
\(818\) | −5.34906 | + | 8.76326i | −0.187025 | + | 0.306400i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.48528 | + | 10.6729i | 0.191554 | + | 0.372715i | ||||
\(821\) | 9.00000 | − | 15.5885i | 0.314102 | − | 0.544041i | −0.665144 | − | 0.746715i | \(-0.731630\pi\) |
0.979246 | + | 0.202674i | \(0.0649632\pi\) | |||||||
\(822\) | −0.0228236 | + | 0.934075i | −0.000796066 | + | 0.0325796i | ||||
\(823\) | −28.2577 | + | 16.3146i | −0.985003 | + | 0.568692i | −0.903777 | − | 0.428004i | \(-0.859217\pi\) |
−0.0812259 | + | 0.996696i | \(0.525884\pi\) | |||||||
\(824\) | 36.0334 | + | 24.4875i | 1.25528 | + | 0.853061i | ||||
\(825\) | − | 21.7248i | − | 0.756359i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17.8930i | − | 0.622199i | −0.950377 | − | 0.311100i | \(-0.899303\pi\) | ||
0.950377 | − | 0.311100i | \(-0.100697\pi\) | |||||||
\(828\) | −3.06796 | + | 62.7419i | −0.106619 | + | 2.18043i | ||||
\(829\) | 3.68290 | − | 2.12632i | 0.127912 | − | 0.0738502i | −0.434678 | − | 0.900586i | \(-0.643138\pi\) |
0.562591 | + | 0.826735i | \(0.309805\pi\) | |||||||
\(830\) | −6.60765 | − | 0.161455i | −0.229355 | − | 0.00560417i | ||||
\(831\) | −32.8684 | + | 56.9297i | −1.14019 | + | 1.97487i | ||||
\(832\) | 3.05325 | − | 20.6808i | 0.105852 | − | 0.716979i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5.87868 | + | 3.58832i | 0.203562 | + | 0.124253i | ||||
\(835\) | 19.5433 | + | 11.2833i | 0.676324 | + | 0.390476i | ||||
\(836\) | 3.95152 | + | 2.54652i | 0.136666 | + | 0.0880734i | ||||
\(837\) | 14.8284 | + | 25.6836i | 0.512545 | + | 0.887755i | ||||
\(838\) | −20.5257 | + | 11.1911i | −0.709048 | + | 0.386590i | ||||
\(839\) | 53.9108 | 1.86121 | 0.930603 | − | 0.366029i | \(-0.119283\pi\) | ||||
0.930603 | + | 0.366029i | \(0.119283\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6274 | −0.952670 | ||||||||
\(842\) | 8.05246 | − | 4.39040i | 0.277506 | − | 0.151303i | ||||
\(843\) | 35.9216 | + | 62.2181i | 1.23721 | + | 2.14290i | ||||
\(844\) | −26.8261 | − | 17.2879i | −0.923392 | − | 0.595073i | ||||
\(845\) | 5.78510 | + | 3.34003i | 0.199014 | + | 0.114901i | ||||
\(846\) | 29.0176 | + | 17.7122i | 0.997646 | + | 0.608959i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15.1005 | − | 21.0930i | 0.518553 | − | 0.724338i | ||||
\(849\) | 16.3640 | − | 28.3432i | 0.561610 | − | 0.972737i | ||||
\(850\) | −24.1450 | − | 0.589970i | −0.828166 | − | 0.0202358i | ||||
\(851\) | 24.6481 | − | 14.2306i | 0.844926 | − | 0.487818i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.61859i | 0.123898i | 0.998079 | + | 0.0619492i | \(0.0197317\pi\) | ||||
−0.998079 | + | 0.0619492i | \(0.980268\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.38883i | 0.184294i | ||||||||
\(856\) | 11.3117 | − | 16.6452i | 0.386627 | − | 0.568923i | ||||
\(857\) | −34.3809 | + | 19.8498i | −1.17443 | + | 0.678057i | −0.954719 | − | 0.297509i | \(-0.903844\pi\) |
−0.219709 | + | 0.975565i | \(0.570511\pi\) | |||||||
\(858\) | −0.512252 | + | 20.9643i | −0.0174880 | + | 0.715710i | ||||
\(859\) | −9.86051 | + | 17.0789i | −0.336436 | + | 0.582725i | −0.983760 | − | 0.179491i | \(-0.942555\pi\) |
0.647323 | + | 0.762216i | \(0.275888\pi\) | |||||||
\(860\) | 7.89505 | + | 15.3617i | 0.269219 | + | 0.523831i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.6569 | − | 20.7355i | 0.431094 | − | 0.706254i | ||||
\(863\) | 15.9337 | + | 9.19932i | 0.542389 | + | 0.313148i | 0.746047 | − | 0.665894i | \(-0.231950\pi\) |
−0.203658 | + | 0.979042i | \(0.565283\pi\) | |||||||
\(864\) | −17.3972 | − | 13.1090i | −0.591865 | − | 0.445979i | ||||
\(865\) | 11.4142 | + | 19.7700i | 0.388095 | + | 0.672200i | ||||
\(866\) | −10.2738 | − | 18.8433i | −0.349119 | − | 0.640323i | ||||
\(867\) | −7.89505 | −0.268130 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.68629 | 0.294662 | ||||||||
\(870\) | 2.33755 | + | 4.28733i | 0.0792505 | + | 0.145354i | ||||
\(871\) | −13.1474 | − | 22.7719i | −0.445481 | − | 0.771596i | ||||
\(872\) | −14.4050 | + | 6.96391i | −0.487815 | + | 0.235828i | ||||
\(873\) | −14.6293 | − | 8.44623i | −0.495127 | − | 0.285862i | ||||
\(874\) | 5.91299 | − | 9.68714i | 0.200010 | − | 0.327672i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 38.6066 | − | 19.8416i | 1.30440 | − | 0.670385i | ||||
\(877\) | 27.2132 | − | 47.1347i | 0.918925 | − | 1.59162i | 0.117873 | − | 0.993029i | \(-0.462392\pi\) |
0.801052 | − | 0.598595i | \(-0.204274\pi\) | |||||||
\(878\) | 0.610028 | − | 24.9659i | 0.0205875 | − | 0.842557i | ||||
\(879\) | −54.8389 | + | 31.6613i | −1.84967 | + | 1.06791i | ||||
\(880\) | 3.72757 | + | 8.21695i | 0.125656 | + | 0.276993i | ||||
\(881\) | − | 15.1760i | − | 0.511293i | −0.966770 | − | 0.255647i | \(-0.917712\pi\) | ||
0.966770 | − | 0.255647i | \(-0.0822883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4.67371i | − | 0.157283i | −0.996903 | − | 0.0786415i | \(-0.974942\pi\) | ||
0.996903 | − | 0.0786415i | \(-0.0250582\pi\) | |||||||
\(884\) | 23.2859 | + | 1.13864i | 0.783189 | + | 0.0382965i | ||||
\(885\) | −22.5361 | + | 13.0112i | −0.757543 | + | 0.437368i | ||||
\(886\) | −37.7973 | − | 0.923558i | −1.26983 | − | 0.0310275i | ||||
\(887\) | 8.82940 | − | 15.2930i | 0.296462 | − | 0.513488i | −0.678862 | − | 0.734266i | \(-0.737526\pi\) |
0.975324 | + | 0.220778i | \(0.0708597\pi\) | |||||||
\(888\) | −2.25573 | + | 30.7235i | −0.0756973 | + | 1.03101i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.24264 | + | 3.20009i | 0.175734 | + | 0.107267i | ||||
\(891\) | −4.97653 | − | 2.87320i | −0.166720 | − | 0.0962558i | ||||
\(892\) | 22.5877 | − | 35.0500i | 0.756291 | − | 1.17356i | ||||
\(893\) | −3.07107 | − | 5.31925i | −0.102769 | − | 0.178002i | ||||
\(894\) | −2.80083 | + | 1.52708i | −0.0936738 | + | 0.0510732i | ||||
\(895\) | 1.32138 | 0.0441687 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 50.6274 | 1.69040 | ||||||||
\(898\) | 50.0190 | − | 27.2716i | 1.66916 | − | 0.910065i | ||||
\(899\) | −4.51146 | − | 7.81407i | −0.150466 | − | 0.260614i | ||||
\(900\) | 18.3089 | − | 28.4105i | 0.610297 | − | 0.947016i | ||||
\(901\) | 25.0542 | + | 14.4650i | 0.834676 | + | 0.481901i | ||||
\(902\) | −13.9449 | − | 8.51189i | −0.464313 | − | 0.283415i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.878680 | − | 11.9678i | 0.0292245 | − | 0.398043i | ||||
\(905\) | −3.27208 | + | 5.66741i | −0.108768 | + | 0.188391i | ||||
\(906\) | 20.7450 | + | 0.506893i | 0.689205 | + | 0.0168404i | ||||
\(907\) | 20.6006 | − | 11.8937i | 0.684030 | − | 0.394925i | −0.117342 | − | 0.993092i | \(-0.537437\pi\) |
0.801372 | + | 0.598167i | \(0.204104\pi\) | |||||||
\(908\) | 36.2087 | + | 1.77054i | 1.20163 | + | 0.0587574i | ||||
\(909\) | − | 0.819760i | − | 0.0271897i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.1974i | 1.43119i | 0.698513 | + | 0.715597i | \(0.253845\pi\) | ||||
−0.698513 | + | 0.715597i | \(0.746155\pi\) | |||||||
\(912\) | 5.07491 | + | 11.1870i | 0.168047 | + | 0.370438i | ||||
\(913\) | 7.79310 | − | 4.49935i | 0.257914 | − | 0.148907i | ||||
\(914\) | 0.854233 | − | 34.9601i | 0.0282555 | − | 1.15638i | ||||
\(915\) | −19.2538 | + | 33.3486i | −0.636513 | + | 1.10247i | ||||
\(916\) | −33.6659 | + | 17.3023i | −1.11235 | + | 0.571686i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 12.6569 | − | 20.7355i | 0.417738 | − | 0.684373i | ||||
\(919\) | −42.6963 | − | 24.6507i | −1.40842 | − | 0.813151i | −0.413184 | − | 0.910648i | \(-0.635583\pi\) |
−0.995236 | + | 0.0974962i | \(0.968917\pi\) | |||||||
\(920\) | 19.6117 | − | 9.48104i | 0.646579 | − | 0.312581i | ||||
\(921\) | 14.1924 | + | 24.5819i | 0.467655 | + | 0.810002i | ||||
\(922\) | 18.6009 | + | 34.1160i | 0.612587 | + | 1.12355i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.3137 | −0.503512 | ||||||||
\(926\) | 4.47458 | + | 8.20686i | 0.147044 | + | 0.269694i | ||||
\(927\) | −33.9962 | − | 58.8832i | −1.11658 | − | 1.93398i | ||||
\(928\) | 5.29299 | + | 3.98835i | 0.173751 | + | 0.130924i | ||||
\(929\) | −14.4685 | − | 8.35338i | −0.474695 | − | 0.274065i | 0.243508 | − | 0.969899i | \(-0.421702\pi\) |
−0.718203 | + | 0.695833i | \(0.755035\pi\) | |||||||
\(930\) | 16.7245 | − | 27.3994i | 0.548416 | − | 0.898460i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.09188 | + | 13.7990i | 0.232302 | + | 0.452000i | ||||
\(933\) | −6.14214 | + | 10.6385i | −0.201084 | + | 0.348289i | ||||
\(934\) | −0.259367 | + | 10.6148i | −0.00848675 | + | 0.347326i | ||||
\(935\) | −8.71442 | + | 5.03127i | −0.284992 | + | 0.164540i | ||||
\(936\) | −18.3379 | + | 26.9843i | −0.599393 | + | 0.882009i | ||||
\(937\) | − | 53.4762i | − | 1.74699i | −0.486831 | − | 0.873496i | \(-0.661847\pi\) | ||
0.486831 | − | 0.873496i | \(-0.338153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 26.8828i | − | 0.877288i | ||||||
\(940\) | 0.575773 | − | 11.7749i | 0.0187796 | − | 0.384056i | ||||
\(941\) | 7.01655 | − | 4.05101i | 0.228733 | − | 0.132059i | −0.381254 | − | 0.924470i | \(-0.624508\pi\) |
0.609987 | + | 0.792411i | \(0.291175\pi\) | |||||||
\(942\) | 77.7394 | + | 1.89952i | 2.53289 | + | 0.0618898i | ||||
\(943\) | −19.7210 | + | 34.1578i | −0.642205 | + | 1.11233i | ||||
\(944\) | −20.5586 | + | 28.7172i | −0.669126 | + | 0.934665i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.0711 | − | 12.2513i | −0.652567 | − | 0.398324i | ||||
\(947\) | 36.6625 | + | 21.1671i | 1.19137 | + | 0.687838i | 0.958617 | − | 0.284697i | \(-0.0918931\pi\) |
0.232754 | + | 0.972536i | \(0.425226\pi\) | |||||||
\(948\) | 19.0796 | + | 12.2957i | 0.619677 | + | 0.399346i | ||||
\(949\) | −10.4142 | − | 18.0379i | −0.338060 | − | 0.585537i | ||||
\(950\) | −5.36139 | + | 2.92316i | −0.173946 | + | 0.0948398i | ||||
\(951\) | −61.2253 | −1.98537 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.6569 | 1.21983 | 0.609913 | − | 0.792469i | \(-0.291205\pi\) | ||||
0.609913 | + | 0.792469i | \(0.291205\pi\) | |||||||
\(954\) | −35.5453 | + | 19.3802i | −1.15082 | + | 0.627456i | ||||
\(955\) | −10.8916 | − | 18.8648i | −0.352445 | − | 0.610452i | ||||
\(956\) | −18.9689 | − | 12.2244i | −0.613499 | − | 0.395364i | ||||
\(957\) | −5.75751 | − | 3.32410i | −0.186114 | − | 0.107453i | ||||
\(958\) | 24.0390 | + | 14.6733i | 0.776664 | + | 0.474072i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.44365 | + | 23.3252i | −0.111143 | + | 0.752817i | ||||
\(961\) | −14.1569 | + | 24.5204i | −0.456673 | + | 0.790980i | ||||
\(962\) | 14.7777 | + | 0.361085i | 0.476451 | + | 0.0116418i | ||||
\(963\) | −27.2005 | + | 15.7042i | −0.876524 | + | 0.506061i | ||||
\(964\) | 0.840508 | − | 17.1890i | 0.0270710 | − | 0.553619i | ||||
\(965\) | − | 18.8490i | − | 0.606771i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17.8930i | − | 0.575399i | −0.957721 | − | 0.287699i | \(-0.907110\pi\) | ||
0.957721 | − | 0.287699i | \(-0.0928904\pi\) | |||||||
\(968\) | 15.5728 | + | 10.5829i | 0.500528 | + | 0.340148i | ||||
\(969\) | −11.8643 | + | 6.84984i | −0.381135 | + | 0.220049i | ||||
\(970\) | −0.143091 | + | 5.85612i | −0.00459438 | + | 0.188029i | ||||
\(971\) | 10.9884 | − | 19.0324i | 0.352634 | − | 0.610780i | −0.634076 | − | 0.773271i | \(-0.718619\pi\) |
0.986710 | + | 0.162491i | \(0.0519528\pi\) | |||||||
\(972\) | −17.4252 | − | 33.9050i | −0.558914 | − | 1.08750i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 29.2843 | − | 47.9759i | 0.938329 | − | 1.53725i | ||||
\(975\) | −23.5909 | − | 13.6202i | −0.755512 | − | 0.436195i | ||||
\(976\) | −5.09889 | + | 52.0132i | −0.163212 | + | 1.66490i | ||||
\(977\) | −27.1924 | − | 47.0986i | −0.869962 | − | 1.50682i | −0.862035 | − | 0.506849i | \(-0.830810\pi\) |
−0.00792675 | − | 0.999969i | \(-0.502523\pi\) | |||||||
\(978\) | −7.02405 | − | 12.8829i | −0.224604 | − | 0.411948i | ||||
\(979\) | −8.36223 | −0.267258 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.9706 | 0.797249 | ||||||||
\(982\) | 10.8026 | + | 19.8131i | 0.344724 | + | 0.632262i | ||||
\(983\) | −16.9981 | − | 29.4416i | −0.542156 | − | 0.939041i | −0.998780 | − | 0.0493817i | \(-0.984275\pi\) |
0.456624 | − | 0.889660i | \(-0.349058\pi\) | |||||||
\(984\) | −18.5814 | − | 38.4359i | −0.592352 | − | 1.22529i | ||||
\(985\) | 1.87476 | + | 1.08239i | 0.0597348 | + | 0.0344879i | ||||
\(986\) | −3.85077 | + | 6.30864i | −0.122633 | + | 0.200908i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.24264 | − | 2.69442i | 0.166791 | − | 0.0857208i | ||||
\(989\) | −28.3848 | + | 49.1639i | −0.902583 | + | 1.56332i | ||||
\(990\) | 0.343977 | − | 14.0775i | 0.0109323 | − | 0.447412i | ||||
\(991\) | 18.9240 | − | 10.9258i | 0.601141 | − | 0.347069i | −0.168350 | − | 0.985727i | \(-0.553844\pi\) |
0.769490 | + | 0.638659i | \(0.220510\pi\) | |||||||
\(992\) | 5.30834 | − | 43.2419i | 0.168540 | − | 1.37293i | ||||
\(993\) | − | 10.3756i | − | 0.329259i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 23.5780i | − | 0.747473i | ||||||
\(996\) | 23.4867 | + | 1.14845i | 0.744203 | + | 0.0363902i | ||||
\(997\) | 5.78510 | − | 3.34003i | 0.183216 | − | 0.105780i | −0.405587 | − | 0.914057i | \(-0.632933\pi\) |
0.588803 | + | 0.808277i | \(0.299599\pi\) | |||||||
\(998\) | 26.0118 | + | 0.635586i | 0.823390 | + | 0.0201191i | ||||
\(999\) | 7.70154 | − | 13.3395i | 0.243666 | − | 0.422042i |
(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 | 196.2.f.d.19.7 | 16 | ||
4.3 | odd | 2 | inner | 196.2.f.d.19.4 | 16 | ||
7.2 | even | 3 | 196.2.d.c.195.2 | yes | 8 | ||
7.3 | odd | 6 | inner | 196.2.f.d.31.4 | 16 | ||
7.4 | even | 3 | inner | 196.2.f.d.31.3 | 16 | ||
7.5 | odd | 6 | 196.2.d.c.195.1 | ✓ | 8 | ||
7.6 | odd | 2 | inner | 196.2.f.d.19.8 | 16 | ||
21.2 | odd | 6 | 1764.2.b.k.1567.8 | 8 | |||
21.5 | even | 6 | 1764.2.b.k.1567.7 | 8 | |||
28.3 | even | 6 | inner | 196.2.f.d.31.7 | 16 | ||
28.11 | odd | 6 | inner | 196.2.f.d.31.8 | 16 | ||
28.19 | even | 6 | 196.2.d.c.195.4 | yes | 8 | ||
28.23 | odd | 6 | 196.2.d.c.195.3 | yes | 8 | ||
28.27 | even | 2 | inner | 196.2.f.d.19.3 | 16 | ||
56.5 | odd | 6 | 3136.2.f.i.3135.7 | 8 | |||
56.19 | even | 6 | 3136.2.f.i.3135.1 | 8 | |||
56.37 | even | 6 | 3136.2.f.i.3135.2 | 8 | |||
56.51 | odd | 6 | 3136.2.f.i.3135.8 | 8 | |||
84.23 | even | 6 | 1764.2.b.k.1567.6 | 8 | |||
84.47 | odd | 6 | 1764.2.b.k.1567.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
196.2.d.c.195.1 | ✓ | 8 | 7.5 | odd | 6 | ||
196.2.d.c.195.2 | yes | 8 | 7.2 | even | 3 | ||
196.2.d.c.195.3 | yes | 8 | 28.23 | odd | 6 | ||
196.2.d.c.195.4 | yes | 8 | 28.19 | even | 6 | ||
196.2.f.d.19.3 | 16 | 28.27 | even | 2 | inner | ||
196.2.f.d.19.4 | 16 | 4.3 | odd | 2 | inner | ||
196.2.f.d.19.7 | 16 | 1.1 | even | 1 | trivial | ||
196.2.f.d.19.8 | 16 | 7.6 | odd | 2 | inner | ||
196.2.f.d.31.3 | 16 | 7.4 | even | 3 | inner | ||
196.2.f.d.31.4 | 16 | 7.3 | odd | 6 | inner | ||
196.2.f.d.31.7 | 16 | 28.3 | even | 6 | inner | ||
196.2.f.d.31.8 | 16 | 28.11 | odd | 6 | inner | ||
1764.2.b.k.1567.5 | 8 | 84.47 | odd | 6 | |||
1764.2.b.k.1567.6 | 8 | 84.23 | even | 6 | |||
1764.2.b.k.1567.7 | 8 | 21.5 | even | 6 | |||
1764.2.b.k.1567.8 | 8 | 21.2 | odd | 6 | |||
3136.2.f.i.3135.1 | 8 | 56.19 | even | 6 | |||
3136.2.f.i.3135.2 | 8 | 56.37 | even | 6 | |||
3136.2.f.i.3135.7 | 8 | 56.5 | odd | 6 | |||
3136.2.f.i.3135.8 | 8 | 56.51 | odd | 6 |