Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(241,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.68908857338\) |
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: | \( x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 241.2 | ||
Root | \(0.500000 - 0.0286340i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.241 |
Dual form | 462.2.p.b.439.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.725202 | − | 0.418696i | 0.324320 | − | 0.187246i | −0.328996 | − | 0.944331i | \(-0.606710\pi\) |
0.653317 | + | 0.757085i | \(0.273377\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.44037 | + | 1.02205i | −0.922373 | + | 0.386300i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −0.418696 | + | 0.725202i | −0.132403 | + | 0.229329i | ||||
\(11\) | −3.15670 | − | 1.01748i | −0.951780 | − | 0.306781i | ||||
\(12\) | −0.866025 | + | 0.500000i | −0.250000 | + | 0.144338i | ||||
\(13\) | 2.59370 | 0.719364 | 0.359682 | − | 0.933075i | \(-0.382885\pi\) | ||||
0.359682 | + | 0.933075i | \(0.382885\pi\) | |||||||
\(14\) | 1.60239 | − | 2.10531i | 0.428258 | − | 0.562668i | ||||
\(15\) | −0.837391 | −0.216214 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.98686 | + | 5.17339i | −0.724420 | + | 1.25473i | 0.234792 | + | 0.972046i | \(0.424559\pi\) |
−0.959212 | + | 0.282687i | \(0.908774\pi\) | |||||||
\(18\) | −0.866025 | − | 0.500000i | −0.204124 | − | 0.117851i | ||||
\(19\) | 1.55590 | + | 2.69491i | 0.356949 | + | 0.618254i | 0.987449 | − | 0.157935i | \(-0.0504837\pi\) |
−0.630501 | + | 0.776189i | \(0.717150\pi\) | |||||||
\(20\) | − | 0.837391i | − | 0.187246i | ||||||
\(21\) | 2.62445 | + | 0.335059i | 0.572702 | + | 0.0731160i | ||||
\(22\) | 3.24252 | − | 0.697189i | 0.691307 | − | 0.148641i | ||||
\(23\) | −1.43256 | − | 2.48126i | −0.298709 | − | 0.517379i | 0.677132 | − | 0.735862i | \(-0.263223\pi\) |
−0.975841 | + | 0.218483i | \(0.929889\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −2.14939 | + | 3.72285i | −0.429878 | + | 0.744570i | ||||
\(26\) | −2.24621 | + | 1.29685i | −0.440519 | + | 0.254334i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −0.335059 | + | 2.62445i | −0.0633203 | + | 0.495974i | ||||
\(29\) | 5.38769i | 1.00047i | 0.865890 | + | 0.500234i | \(0.166753\pi\) | ||||
−0.865890 | + | 0.500234i | \(0.833247\pi\) | |||||||
\(30\) | 0.725202 | − | 0.418696i | 0.132403 | − | 0.0764430i | ||||
\(31\) | −0.913399 | − | 0.527351i | −0.164051 | − | 0.0947151i | 0.415727 | − | 0.909490i | \(-0.363527\pi\) |
−0.579778 | + | 0.814775i | \(0.696861\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 2.22504 | + | 2.45951i | 0.387330 | + | 0.428146i | ||||
\(34\) | − | 5.97372i | − | 1.02448i | ||||||
\(35\) | −1.34183 | + | 1.76297i | −0.226811 | + | 0.297996i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.49467 | + | 9.51705i | 0.903319 | + | 1.56459i | 0.823158 | + | 0.567812i | \(0.192210\pi\) |
0.0801603 | + | 0.996782i | \(0.474457\pi\) | |||||||
\(38\) | −2.69491 | − | 1.55590i | −0.437171 | − | 0.252401i | ||||
\(39\) | −2.24621 | − | 1.29685i | −0.359682 | − | 0.207663i | ||||
\(40\) | 0.418696 | + | 0.725202i | 0.0662016 | + | 0.114665i | ||||
\(41\) | −11.2350 | −1.75461 | −0.877304 | − | 0.479934i | \(-0.840661\pi\) | ||||
−0.877304 | + | 0.479934i | \(0.840661\pi\) | |||||||
\(42\) | −2.44037 | + | 1.02205i | −0.376557 | + | 0.157706i | ||||
\(43\) | − | 1.27527i | − | 0.194478i | −0.995261 | − | 0.0972388i | \(-0.968999\pi\) | ||
0.995261 | − | 0.0972388i | \(-0.0310010\pi\) | |||||||
\(44\) | −2.45951 | + | 2.22504i | −0.370785 | + | 0.335438i | ||||
\(45\) | 0.725202 | + | 0.418696i | 0.108107 | + | 0.0624155i | ||||
\(46\) | 2.48126 | + | 1.43256i | 0.365842 | + | 0.211219i | ||||
\(47\) | −10.6034 | + | 6.12185i | −1.54666 | + | 0.892964i | −0.548266 | + | 0.836304i | \(0.684712\pi\) |
−0.998394 | + | 0.0566600i | \(0.981955\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 4.91081 | − | 4.98838i | 0.701544 | − | 0.712626i | ||||
\(50\) | − | 4.29878i | − | 0.607939i | ||||||
\(51\) | 5.17339 | − | 2.98686i | 0.724420 | − | 0.418244i | ||||
\(52\) | 1.29685 | − | 2.24621i | 0.179841 | − | 0.311494i | ||||
\(53\) | −2.58730 | + | 4.48134i | −0.355394 | + | 0.615560i | −0.987185 | − | 0.159579i | \(-0.948986\pi\) |
0.631792 | + | 0.775138i | \(0.282320\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −2.71526 | + | 0.583820i | −0.366125 | + | 0.0787223i | ||||
\(56\) | −1.02205 | − | 2.44037i | −0.136578 | − | 0.326108i | ||||
\(57\) | − | 3.11181i | − | 0.412169i | ||||||
\(58\) | −2.69384 | − | 4.66587i | −0.353719 | − | 0.612659i | ||||
\(59\) | −8.38751 | − | 4.84253i | −1.09196 | − | 0.630444i | −0.157863 | − | 0.987461i | \(-0.550460\pi\) |
−0.934098 | + | 0.357017i | \(0.883794\pi\) | |||||||
\(60\) | −0.418696 | + | 0.725202i | −0.0540534 | + | 0.0936232i | ||||
\(61\) | −2.03524 | − | 3.52514i | −0.260586 | − | 0.451348i | 0.705812 | − | 0.708399i | \(-0.250582\pi\) |
−0.966398 | + | 0.257051i | \(0.917249\pi\) | |||||||
\(62\) | 1.05470 | 0.133947 | ||||||||
\(63\) | −2.10531 | − | 1.60239i | −0.265244 | − | 0.201883i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.88096 | − | 1.08597i | 0.233304 | − | 0.134698i | ||||
\(66\) | −3.15670 | − | 1.01748i | −0.388563 | − | 0.125243i | ||||
\(67\) | −6.51916 | + | 11.2915i | −0.796442 | + | 1.37948i | 0.125478 | + | 0.992096i | \(0.459954\pi\) |
−0.921920 | + | 0.387381i | \(0.873380\pi\) | |||||||
\(68\) | 2.98686 | + | 5.17339i | 0.362210 | + | 0.627366i | ||||
\(69\) | 2.86511i | 0.344919i | ||||||||
\(70\) | 0.280576 | − | 2.19769i | 0.0335352 | − | 0.262674i | ||||
\(71\) | 14.0795 | 1.67093 | 0.835467 | − | 0.549541i | \(-0.185197\pi\) | ||||
0.835467 | + | 0.549541i | \(0.185197\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | 4.95659 | − | 8.58507i | 0.580125 | − | 1.00481i | −0.415339 | − | 0.909667i | \(-0.636337\pi\) |
0.995464 | − | 0.0951394i | \(-0.0303297\pi\) | |||||||
\(74\) | −9.51705 | − | 5.49467i | −1.10633 | − | 0.638743i | ||||
\(75\) | 3.72285 | − | 2.14939i | 0.429878 | − | 0.248190i | ||||
\(76\) | 3.11181 | 0.356949 | ||||||||
\(77\) | 8.74343 | − | 0.743301i | 0.996406 | − | 0.0847070i | ||||
\(78\) | 2.59370 | 0.293679 | ||||||||
\(79\) | 11.7018 | − | 6.75603i | 1.31655 | − | 0.760113i | 0.333381 | − | 0.942792i | \(-0.391810\pi\) |
0.983173 | + | 0.182680i | \(0.0584771\pi\) | |||||||
\(80\) | −0.725202 | − | 0.418696i | −0.0810801 | − | 0.0468116i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 9.72978 | − | 5.61749i | 1.07447 | − | 0.620348i | ||||
\(83\) | 2.99287 | 0.328510 | 0.164255 | − | 0.986418i | \(-0.447478\pi\) | ||||
0.164255 | + | 0.986418i | \(0.447478\pi\) | |||||||
\(84\) | 1.60239 | − | 2.10531i | 0.174836 | − | 0.229708i | ||||
\(85\) | 5.00234i | 0.542580i | ||||||||
\(86\) | 0.637637 | + | 1.10442i | 0.0687582 | + | 0.119093i | ||||
\(87\) | 2.69384 | − | 4.66587i | 0.288810 | − | 0.500234i | ||||
\(88\) | 1.01748 | − | 3.15670i | 0.108463 | − | 0.336505i | ||||
\(89\) | 7.28049 | − | 4.20339i | 0.771730 | − | 0.445559i | −0.0617614 | − | 0.998091i | \(-0.519672\pi\) |
0.833491 | + | 0.552532i | \(0.186338\pi\) | |||||||
\(90\) | −0.837391 | −0.0882688 | ||||||||
\(91\) | −6.32960 | + | 2.65091i | −0.663522 | + | 0.277891i | ||||
\(92\) | −2.86511 | −0.298709 | ||||||||
\(93\) | 0.527351 | + | 0.913399i | 0.0546838 | + | 0.0947151i | ||||
\(94\) | 6.12185 | − | 10.6034i | 0.631421 | − | 1.09365i | ||||
\(95\) | 2.25669 | + | 1.30290i | 0.231532 | + | 0.133675i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 0.786131i | 0.0798195i | 0.999203 | + | 0.0399097i | \(0.0127070\pi\) | ||||
−0.999203 | + | 0.0399097i | \(0.987293\pi\) | |||||||
\(98\) | −1.75869 | + | 6.77547i | −0.177655 | + | 0.684426i | ||||
\(99\) | −0.697189 | − | 3.24252i | −0.0700701 | − | 0.325885i | ||||
\(100\) | 2.14939 | + | 3.72285i | 0.214939 | + | 0.372285i | ||||
\(101\) | 3.36113 | − | 5.82166i | 0.334445 | − | 0.579276i | −0.648933 | − | 0.760846i | \(-0.724784\pi\) |
0.983378 | + | 0.181569i | \(0.0581177\pi\) | |||||||
\(102\) | −2.98686 | + | 5.17339i | −0.295743 | + | 0.512242i | ||||
\(103\) | −3.52596 | + | 2.03571i | −0.347423 | + | 0.200585i | −0.663550 | − | 0.748132i | \(-0.730951\pi\) |
0.316127 | + | 0.948717i | \(0.397618\pi\) | |||||||
\(104\) | 2.59370i | 0.254334i | ||||||||
\(105\) | 2.04354 | − | 0.855860i | 0.199430 | − | 0.0835234i | ||||
\(106\) | − | 5.17461i | − | 0.502602i | ||||||
\(107\) | 0.209477 | − | 0.120942i | 0.0202509 | − | 0.0116919i | −0.489840 | − | 0.871812i | \(-0.662945\pi\) |
0.510091 | + | 0.860120i | \(0.329612\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | −15.1773 | − | 8.76259i | −1.45372 | − | 0.839304i | −0.455028 | − | 0.890477i | \(-0.650371\pi\) |
−0.998690 | + | 0.0511733i | \(0.983704\pi\) | |||||||
\(110\) | 2.05957 | − | 1.86323i | 0.196372 | − | 0.177652i | ||||
\(111\) | − | 10.9893i | − | 1.04306i | ||||||
\(112\) | 2.10531 | + | 1.60239i | 0.198933 | + | 0.151412i | ||||
\(113\) | 8.08949 | 0.760995 | 0.380498 | − | 0.924782i | \(-0.375753\pi\) | ||||
0.380498 | + | 0.924782i | \(0.375753\pi\) | |||||||
\(114\) | 1.55590 | + | 2.69491i | 0.145724 | + | 0.252401i | ||||
\(115\) | −2.07779 | − | 1.19961i | −0.193755 | − | 0.111864i | ||||
\(116\) | 4.66587 | + | 2.69384i | 0.433216 | + | 0.250117i | ||||
\(117\) | 1.29685 | + | 2.24621i | 0.119894 | + | 0.207663i | ||||
\(118\) | 9.68506 | 0.891582 | ||||||||
\(119\) | 2.00155 | − | 15.6777i | 0.183482 | − | 1.43717i | ||||
\(120\) | − | 0.837391i | − | 0.0764430i | ||||||
\(121\) | 8.92949 | + | 6.42373i | 0.811771 | + | 0.583975i | ||||
\(122\) | 3.52514 | + | 2.03524i | 0.319151 | + | 0.184262i | ||||
\(123\) | 9.72978 | + | 5.61749i | 0.877304 | + | 0.506512i | ||||
\(124\) | −0.913399 | + | 0.527351i | −0.0820257 | + | 0.0473575i | ||||
\(125\) | 7.78672i | 0.696465i | ||||||||
\(126\) | 2.62445 | + | 0.335059i | 0.233805 | + | 0.0298495i | ||||
\(127\) | 12.1313i | 1.07648i | 0.842791 | + | 0.538241i | \(0.180911\pi\) | ||||
−0.842791 | + | 0.538241i | \(0.819089\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −0.637637 | + | 1.10442i | −0.0561408 | + | 0.0972388i | ||||
\(130\) | −1.08597 | + | 1.88096i | −0.0952461 | + | 0.164971i | ||||
\(131\) | −1.02224 | − | 1.77058i | −0.0893139 | − | 0.154696i | 0.817907 | − | 0.575350i | \(-0.195134\pi\) |
−0.907221 | + | 0.420654i | \(0.861801\pi\) | |||||||
\(132\) | 3.24252 | − | 0.697189i | 0.282225 | − | 0.0606825i | ||||
\(133\) | −6.55132 | − | 4.98635i | −0.568072 | − | 0.432371i | ||||
\(134\) | − | 13.0383i | − | 1.12634i | ||||||
\(135\) | −0.418696 | − | 0.725202i | −0.0360356 | − | 0.0624155i | ||||
\(136\) | −5.17339 | − | 2.98686i | −0.443615 | − | 0.256121i | ||||
\(137\) | 6.60556 | − | 11.4412i | 0.564351 | − | 0.977485i | −0.432759 | − | 0.901510i | \(-0.642460\pi\) |
0.997110 | − | 0.0759750i | \(-0.0242069\pi\) | |||||||
\(138\) | −1.43256 | − | 2.48126i | −0.121947 | − | 0.211219i | ||||
\(139\) | 6.16293 | 0.522733 | 0.261367 | − | 0.965240i | \(-0.415827\pi\) | ||||
0.261367 | + | 0.965240i | \(0.415827\pi\) | |||||||
\(140\) | 0.855860 | + | 2.04354i | 0.0723334 | + | 0.172711i | ||||
\(141\) | 12.2437 | 1.03111 | ||||||||
\(142\) | −12.1932 | + | 7.03977i | −1.02323 | + | 0.590764i | ||||
\(143\) | −8.18754 | − | 2.63903i | −0.684677 | − | 0.220687i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 2.25580 | + | 3.90716i | 0.187334 | + | 0.324472i | ||||
\(146\) | 9.91318i | 0.820421i | ||||||||
\(147\) | −6.74708 | + | 1.86466i | −0.556489 | + | 0.153795i | ||||
\(148\) | 10.9893 | 0.903319 | ||||||||
\(149\) | 3.80788 | − | 2.19848i | 0.311954 | − | 0.180107i | −0.335847 | − | 0.941917i | \(-0.609022\pi\) |
0.647800 | + | 0.761810i | \(0.275689\pi\) | |||||||
\(150\) | −2.14939 | + | 3.72285i | −0.175497 | + | 0.303969i | ||||
\(151\) | −8.86874 | − | 5.12037i | −0.721728 | − | 0.416690i | 0.0936604 | − | 0.995604i | \(-0.470143\pi\) |
−0.815388 | + | 0.578914i | \(0.803477\pi\) | |||||||
\(152\) | −2.69491 | + | 1.55590i | −0.218586 | + | 0.126200i | ||||
\(153\) | −5.97372 | −0.482947 | ||||||||
\(154\) | −7.20038 | + | 5.01543i | −0.580223 | + | 0.404155i | ||||
\(155\) | −0.883199 | −0.0709402 | ||||||||
\(156\) | −2.24621 | + | 1.29685i | −0.179841 | + | 0.103831i | ||||
\(157\) | −13.8444 | − | 7.99304i | −1.10490 | − | 0.637914i | −0.167396 | − | 0.985890i | \(-0.553536\pi\) |
−0.937504 | + | 0.347975i | \(0.886869\pi\) | |||||||
\(158\) | −6.75603 | + | 11.7018i | −0.537481 | + | 0.930944i | ||||
\(159\) | 4.48134 | − | 2.58730i | 0.355394 | − | 0.205187i | ||||
\(160\) | 0.837391 | 0.0662016 | ||||||||
\(161\) | 6.03195 | + | 4.59104i | 0.475385 | + | 0.361825i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 0.261926 | + | 0.453669i | 0.0205156 | + | 0.0355341i | 0.876101 | − | 0.482128i | \(-0.160136\pi\) |
−0.855585 | + | 0.517662i | \(0.826803\pi\) | |||||||
\(164\) | −5.61749 | + | 9.72978i | −0.438652 | + | 0.759768i | ||||
\(165\) | 2.64339 | + | 0.852026i | 0.205788 | + | 0.0663301i | ||||
\(166\) | −2.59190 | + | 1.49643i | −0.201170 | + | 0.116146i | ||||
\(167\) | −17.0544 | −1.31971 | −0.659855 | − | 0.751393i | \(-0.729382\pi\) | ||||
−0.659855 | + | 0.751393i | \(0.729382\pi\) | |||||||
\(168\) | −0.335059 | + | 2.62445i | −0.0258504 | + | 0.202481i | ||||
\(169\) | −6.27269 | −0.482515 | ||||||||
\(170\) | −2.50117 | − | 4.33216i | −0.191831 | − | 0.332261i | ||||
\(171\) | −1.55590 | + | 2.69491i | −0.118983 | + | 0.206085i | ||||
\(172\) | −1.10442 | − | 0.637637i | −0.0842112 | − | 0.0486194i | ||||
\(173\) | 3.61831 | + | 6.26710i | 0.275095 | + | 0.476479i | 0.970159 | − | 0.242469i | \(-0.0779573\pi\) |
−0.695064 | + | 0.718948i | \(0.744624\pi\) | |||||||
\(174\) | 5.38769i | 0.408440i | ||||||||
\(175\) | 1.44035 | − | 11.2819i | 0.108880 | − | 0.852833i | ||||
\(176\) | 0.697189 | + | 3.24252i | 0.0525526 | + | 0.244414i | ||||
\(177\) | 4.84253 | + | 8.38751i | 0.363987 | + | 0.630444i | ||||
\(178\) | −4.20339 | + | 7.28049i | −0.315057 | + | 0.545696i | ||||
\(179\) | −4.03318 | + | 6.98568i | −0.301454 | + | 0.522134i | −0.976466 | − | 0.215673i | \(-0.930805\pi\) |
0.675011 | + | 0.737807i | \(0.264139\pi\) | |||||||
\(180\) | 0.725202 | − | 0.418696i | 0.0540534 | − | 0.0312077i | ||||
\(181\) | − | 5.61056i | − | 0.417030i | −0.978019 | − | 0.208515i | \(-0.933137\pi\) | ||
0.978019 | − | 0.208515i | \(-0.0668630\pi\) | |||||||
\(182\) | 4.15614 | − | 5.46055i | 0.308074 | − | 0.404763i | ||||
\(183\) | 4.07048i | 0.300899i | ||||||||
\(184\) | 2.48126 | − | 1.43256i | 0.182921 | − | 0.105609i | ||||
\(185\) | 7.96950 | + | 4.60119i | 0.585929 | + | 0.338286i | ||||
\(186\) | −0.913399 | − | 0.527351i | −0.0669737 | − | 0.0386673i | ||||
\(187\) | 14.6924 | − | 13.2918i | 1.07442 | − | 0.971992i | ||||
\(188\) | 12.2437i | 0.892964i | ||||||||
\(189\) | 1.02205 | + | 2.44037i | 0.0743435 | + | 0.177511i | ||||
\(190\) | −2.60580 | −0.189045 | ||||||||
\(191\) | −5.89206 | − | 10.2053i | −0.426334 | − | 0.738433i | 0.570210 | − | 0.821499i | \(-0.306862\pi\) |
−0.996544 | + | 0.0830666i | \(0.973529\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 15.6730 | + | 9.04882i | 1.12817 | + | 0.651348i | 0.943474 | − | 0.331448i | \(-0.107537\pi\) |
0.184694 | + | 0.982796i | \(0.440870\pi\) | |||||||
\(194\) | −0.393065 | − | 0.680809i | −0.0282204 | − | 0.0488792i | ||||
\(195\) | −2.17195 | −0.155536 | ||||||||
\(196\) | −1.86466 | − | 6.74708i | −0.133190 | − | 0.481934i | ||||
\(197\) | − | 6.23110i | − | 0.443948i | −0.975053 | − | 0.221974i | \(-0.928750\pi\) | ||
0.975053 | − | 0.221974i | \(-0.0712500\pi\) | |||||||
\(198\) | 2.22504 | + | 2.45951i | 0.158127 | + | 0.174790i | ||||
\(199\) | −15.8196 | − | 9.13344i | −1.12142 | − | 0.647453i | −0.179658 | − | 0.983729i | \(-0.557499\pi\) |
−0.941763 | + | 0.336276i | \(0.890832\pi\) | |||||||
\(200\) | −3.72285 | − | 2.14939i | −0.263245 | − | 0.151985i | ||||
\(201\) | 11.2915 | − | 6.51916i | 0.796442 | − | 0.459826i | ||||
\(202\) | 6.72227i | 0.472977i | ||||||||
\(203\) | −5.50651 | − | 13.1479i | −0.386481 | − | 0.922805i | ||||
\(204\) | − | 5.97372i | − | 0.418244i | ||||||
\(205\) | −8.14763 | + | 4.70404i | −0.569055 | + | 0.328544i | ||||
\(206\) | 2.03571 | − | 3.52596i | 0.141835 | − | 0.245665i | ||||
\(207\) | 1.43256 | − | 2.48126i | 0.0995696 | − | 0.172460i | ||||
\(208\) | −1.29685 | − | 2.24621i | −0.0899205 | − | 0.155747i | ||||
\(209\) | −2.16952 | − | 10.0901i | −0.150069 | − | 0.697947i | ||||
\(210\) | −1.34183 | + | 1.76297i | −0.0925952 | + | 0.121656i | ||||
\(211\) | 10.2446i | 0.705269i | 0.935761 | + | 0.352635i | \(0.114714\pi\) | ||||
−0.935761 | + | 0.352635i | \(0.885286\pi\) | |||||||
\(212\) | 2.58730 | + | 4.48134i | 0.177697 | + | 0.307780i | ||||
\(213\) | −12.1932 | − | 7.03977i | −0.835467 | − | 0.482357i | ||||
\(214\) | −0.120942 | + | 0.209477i | −0.00826740 | + | 0.0143196i | ||||
\(215\) | −0.533952 | − | 0.924832i | −0.0364152 | − | 0.0630730i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.76801 | + | 0.353388i | 0.187905 | + | 0.0239895i | ||||
\(218\) | 17.5252 | 1.18696 | ||||||||
\(219\) | −8.58507 | + | 4.95659i | −0.580125 | + | 0.334935i | ||||
\(220\) | −0.852026 | + | 2.64339i | −0.0574436 | + | 0.178217i | ||||
\(221\) | −7.74703 | + | 13.4183i | −0.521122 | + | 0.902610i | ||||
\(222\) | 5.49467 | + | 9.51705i | 0.368778 | + | 0.638743i | ||||
\(223\) | 15.6665i | 1.04911i | 0.851377 | + | 0.524554i | \(0.175768\pi\) | ||||
−0.851377 | + | 0.524554i | \(0.824232\pi\) | |||||||
\(224\) | −2.62445 | − | 0.335059i | −0.175353 | − | 0.0223871i | ||||
\(225\) | −4.29878 | −0.286585 | ||||||||
\(226\) | −7.00571 | + | 4.04475i | −0.466013 | + | 0.269053i | ||||
\(227\) | 7.86025 | − | 13.6143i | 0.521703 | − | 0.903616i | −0.477978 | − | 0.878372i | \(-0.658630\pi\) |
0.999681 | − | 0.0252443i | \(-0.00803637\pi\) | |||||||
\(228\) | −2.69491 | − | 1.55590i | −0.178474 | − | 0.103042i | ||||
\(229\) | −2.16867 | + | 1.25208i | −0.143310 | + | 0.0827400i | −0.569940 | − | 0.821686i | \(-0.693034\pi\) |
0.426631 | + | 0.904426i | \(0.359700\pi\) | |||||||
\(230\) | 2.39922 | 0.158200 | ||||||||
\(231\) | −7.94368 | − | 3.72800i | −0.522656 | − | 0.245284i | ||||
\(232\) | −5.38769 | −0.353719 | ||||||||
\(233\) | −0.0479052 | + | 0.0276581i | −0.00313837 | + | 0.00181194i | −0.501568 | − | 0.865118i | \(-0.667243\pi\) |
0.498430 | + | 0.866930i | \(0.333910\pi\) | |||||||
\(234\) | −2.24621 | − | 1.29685i | −0.146840 | − | 0.0847779i | ||||
\(235\) | −5.12639 | + | 8.87916i | −0.334409 | + | 0.579213i | ||||
\(236\) | −8.38751 | + | 4.84253i | −0.545981 | + | 0.315222i | ||||
\(237\) | −13.5121 | −0.877702 | ||||||||
\(238\) | 6.10547 | + | 14.5781i | 0.395759 | + | 0.944957i | ||||
\(239\) | 5.74465i | 0.371591i | 0.982588 | + | 0.185795i | \(0.0594861\pi\) | ||||
−0.982588 | + | 0.185795i | \(0.940514\pi\) | |||||||
\(240\) | 0.418696 | + | 0.725202i | 0.0270267 | + | 0.0468116i | ||||
\(241\) | −3.67123 | + | 6.35875i | −0.236484 | + | 0.409603i | −0.959703 | − | 0.281016i | \(-0.909329\pi\) |
0.723219 | + | 0.690619i | \(0.242662\pi\) | |||||||
\(242\) | −10.9450 | − | 1.09837i | −0.703573 | − | 0.0706058i | ||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −4.07048 | −0.260586 | ||||||||
\(245\) | 1.47271 | − | 5.67372i | 0.0940883 | − | 0.362481i | ||||
\(246\) | −11.2350 | −0.716316 | ||||||||
\(247\) | 4.03556 | + | 6.98979i | 0.256776 | + | 0.444750i | ||||
\(248\) | 0.527351 | − | 0.913399i | 0.0334868 | − | 0.0580009i | ||||
\(249\) | −2.59190 | − | 1.49643i | −0.164255 | − | 0.0948326i | ||||
\(250\) | −3.89336 | − | 6.74349i | −0.246238 | − | 0.426496i | ||||
\(251\) | 4.20803i | 0.265608i | 0.991142 | + | 0.132804i | \(0.0423981\pi\) | ||||
−0.991142 | + | 0.132804i | \(0.957602\pi\) | |||||||
\(252\) | −2.44037 | + | 1.02205i | −0.153729 | + | 0.0643834i | ||||
\(253\) | 1.99753 | + | 9.29019i | 0.125583 | + | 0.584069i | ||||
\(254\) | −6.06567 | − | 10.5060i | −0.380594 | − | 0.659208i | ||||
\(255\) | 2.50117 | − | 4.33216i | 0.156629 | − | 0.271290i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −21.3446 | + | 12.3233i | −1.33144 | + | 0.768706i | −0.985520 | − | 0.169559i | \(-0.945766\pi\) |
−0.345918 | + | 0.938265i | \(0.612432\pi\) | |||||||
\(258\) | − | 1.27527i | − | 0.0793951i | ||||||
\(259\) | −23.1360 | − | 17.6093i | −1.43760 | − | 1.09419i | ||||
\(260\) | − | 2.17195i | − | 0.134698i | ||||||
\(261\) | −4.66587 | + | 2.69384i | −0.288810 | + | 0.166745i | ||||
\(262\) | 1.77058 | + | 1.02224i | 0.109387 | + | 0.0631545i | ||||
\(263\) | 26.3130 | + | 15.1918i | 1.62253 | + | 0.936768i | 0.986240 | + | 0.165318i | \(0.0528651\pi\) |
0.636290 | + | 0.771450i | \(0.280468\pi\) | |||||||
\(264\) | −2.45951 | + | 2.22504i | −0.151372 | + | 0.136942i | ||||
\(265\) | 4.33317i | 0.266185i | ||||||||
\(266\) | 8.16678 | + | 1.04264i | 0.500738 | + | 0.0639284i | ||||
\(267\) | −8.40678 | −0.514487 | ||||||||
\(268\) | 6.51916 | + | 11.2915i | 0.398221 | + | 0.689739i | ||||
\(269\) | 17.2977 | + | 9.98686i | 1.05466 | + | 0.608910i | 0.923951 | − | 0.382511i | \(-0.124941\pi\) |
0.130711 | + | 0.991420i | \(0.458274\pi\) | |||||||
\(270\) | 0.725202 | + | 0.418696i | 0.0441344 | + | 0.0254810i | ||||
\(271\) | −0.807639 | − | 1.39887i | −0.0490606 | − | 0.0849754i | 0.840452 | − | 0.541886i | \(-0.182289\pi\) |
−0.889513 | + | 0.456910i | \(0.848956\pi\) | |||||||
\(272\) | 5.97372 | 0.362210 | ||||||||
\(273\) | 6.80705 | + | 0.869045i | 0.411981 | + | 0.0525970i | ||||
\(274\) | 13.2111i | 0.798113i | ||||||||
\(275\) | 10.5729 | − | 9.56496i | 0.637568 | − | 0.576789i | ||||
\(276\) | 2.48126 | + | 1.43256i | 0.149354 | + | 0.0862298i | ||||
\(277\) | −4.48663 | − | 2.59035i | −0.269575 | − | 0.155639i | 0.359119 | − | 0.933292i | \(-0.383077\pi\) |
−0.628695 | + | 0.777652i | \(0.716410\pi\) | |||||||
\(278\) | −5.33726 | + | 3.08147i | −0.320107 | + | 0.184814i | ||||
\(279\) | − | 1.05470i | − | 0.0631434i | ||||||
\(280\) | −1.76297 | − | 1.34183i | −0.105358 | − | 0.0801898i | ||||
\(281\) | 25.1883i | 1.50261i | 0.659956 | + | 0.751304i | \(0.270575\pi\) | ||||
−0.659956 | + | 0.751304i | \(0.729425\pi\) | |||||||
\(282\) | −10.6034 | + | 6.12185i | −0.631421 | + | 0.364551i | ||||
\(283\) | −11.5167 | + | 19.9475i | −0.684598 | + | 1.18576i | 0.288965 | + | 0.957340i | \(0.406689\pi\) |
−0.973563 | + | 0.228419i | \(0.926644\pi\) | |||||||
\(284\) | 7.03977 | − | 12.1932i | 0.417733 | − | 0.723536i | ||||
\(285\) | −1.30290 | − | 2.25669i | −0.0771772 | − | 0.133675i | ||||
\(286\) | 8.41014 | − | 1.80830i | 0.497302 | − | 0.106927i | ||||
\(287\) | 27.4175 | − | 11.4828i | 1.61840 | − | 0.677806i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −9.34267 | − | 16.1820i | −0.549569 | − | 0.951881i | ||||
\(290\) | −3.90716 | − | 2.25580i | −0.229437 | − | 0.132465i | ||||
\(291\) | 0.393065 | − | 0.680809i | 0.0230419 | − | 0.0399097i | ||||
\(292\) | −4.95659 | − | 8.58507i | −0.290063 | − | 0.502403i | ||||
\(293\) | −4.18076 | −0.244242 | −0.122121 | − | 0.992515i | \(-0.538970\pi\) | ||||
−0.122121 | + | 0.992515i | \(0.538970\pi\) | |||||||
\(294\) | 4.91081 | − | 4.98838i | 0.286404 | − | 0.290928i | ||||
\(295\) | −8.11019 | −0.472194 | ||||||||
\(296\) | −9.51705 | + | 5.49467i | −0.553167 | + | 0.319371i | ||||
\(297\) | −1.01748 | + | 3.15670i | −0.0590399 | + | 0.183170i | ||||
\(298\) | −2.19848 | + | 3.80788i | −0.127355 | + | 0.220585i | ||||
\(299\) | −3.71563 | − | 6.43566i | −0.214880 | − | 0.372184i | ||||
\(300\) | − | 4.29878i | − | 0.248190i | ||||||
\(301\) | 1.30340 | + | 3.11214i | 0.0751267 | + | 0.179381i | ||||
\(302\) | 10.2407 | 0.589288 | ||||||||
\(303\) | −5.82166 | + | 3.36113i | −0.334445 | + | 0.193092i | ||||
\(304\) | 1.55590 | − | 2.69491i | 0.0892372 | − | 0.154563i | ||||
\(305\) | −2.95192 | − | 1.70429i | −0.169027 | − | 0.0975876i | ||||
\(306\) | 5.17339 | − | 2.98686i | 0.295743 | − | 0.170747i | ||||
\(307\) | 10.0657 | 0.574478 | 0.287239 | − | 0.957859i | \(-0.407263\pi\) | ||||
0.287239 | + | 0.957859i | \(0.407263\pi\) | |||||||
\(308\) | 3.72800 | − | 7.94368i | 0.212422 | − | 0.452633i | ||||
\(309\) | 4.07143 | 0.231615 | ||||||||
\(310\) | 0.764873 | − | 0.441599i | 0.0434418 | − | 0.0250812i | ||||
\(311\) | 1.23817 | + | 0.714858i | 0.0702102 | + | 0.0405359i | 0.534694 | − | 0.845046i | \(-0.320427\pi\) |
−0.464484 | + | 0.885582i | \(0.653760\pi\) | |||||||
\(312\) | 1.29685 | − | 2.24621i | 0.0734198 | − | 0.127167i | ||||
\(313\) | 26.3211 | − | 15.1965i | 1.48776 | − | 0.858958i | 0.487856 | − | 0.872924i | \(-0.337779\pi\) |
0.999902 | + | 0.0139662i | \(0.00444572\pi\) | |||||||
\(314\) | 15.9861 | 0.902147 | ||||||||
\(315\) | −2.19769 | − | 0.280576i | −0.123826 | − | 0.0158087i | ||||
\(316\) | − | 13.5121i | − | 0.760113i | ||||||
\(317\) | −5.42610 | − | 9.39829i | −0.304760 | − | 0.527860i | 0.672448 | − | 0.740145i | \(-0.265243\pi\) |
−0.977208 | + | 0.212284i | \(0.931910\pi\) | |||||||
\(318\) | −2.58730 | + | 4.48134i | −0.145089 | + | 0.251301i | ||||
\(319\) | 5.48184 | − | 17.0073i | 0.306924 | − | 0.952226i | ||||
\(320\) | −0.725202 | + | 0.418696i | −0.0405400 | + | 0.0234058i | ||||
\(321\) | −0.241883 | −0.0135006 | ||||||||
\(322\) | −7.51935 | − | 0.959984i | −0.419037 | − | 0.0534978i | ||||
\(323\) | −18.5891 | −1.03432 | ||||||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | −5.57488 | + | 9.65597i | −0.309239 | + | 0.535617i | ||||
\(326\) | −0.453669 | − | 0.261926i | −0.0251264 | − | 0.0145067i | ||||
\(327\) | 8.76259 | + | 15.1773i | 0.484572 | + | 0.839304i | ||||
\(328\) | − | 11.2350i | − | 0.620348i | ||||||
\(329\) | 19.6193 | − | 25.7768i | 1.08164 | − | 1.42112i | ||||
\(330\) | −2.71526 | + | 0.583820i | −0.149470 | + | 0.0321382i | ||||
\(331\) | 6.45747 | + | 11.1847i | 0.354935 | + | 0.614765i | 0.987107 | − | 0.160063i | \(-0.0511697\pi\) |
−0.632172 | + | 0.774828i | \(0.717836\pi\) | |||||||
\(332\) | 1.49643 | − | 2.59190i | 0.0821274 | − | 0.142249i | ||||
\(333\) | −5.49467 | + | 9.51705i | −0.301106 | + | 0.521531i | ||||
\(334\) | 14.7695 | − | 8.52720i | 0.808154 | − | 0.466588i | ||||
\(335\) | 10.9182i | 0.596523i | ||||||||
\(336\) | −1.02205 | − | 2.44037i | −0.0557577 | − | 0.133133i | ||||
\(337\) | 16.4809i | 0.897772i | 0.893589 | + | 0.448886i | \(0.148179\pi\) | ||||
−0.893589 | + | 0.448886i | \(0.851821\pi\) | |||||||
\(338\) | 5.43231 | − | 3.13635i | 0.295479 | − | 0.170595i | ||||
\(339\) | −7.00571 | − | 4.04475i | −0.380498 | − | 0.219680i | ||||
\(340\) | 4.33216 | + | 2.50117i | 0.234944 | + | 0.135645i | ||||
\(341\) | 2.34676 | + | 2.59405i | 0.127084 | + | 0.140476i | ||||
\(342\) | − | 3.11181i | − | 0.168267i | ||||||
\(343\) | −6.88579 | + | 17.1926i | −0.371798 | + | 0.928314i | ||||
\(344\) | 1.27527 | 0.0687582 | ||||||||
\(345\) | 1.19961 | + | 2.07779i | 0.0645849 | + | 0.111864i | ||||
\(346\) | −6.26710 | − | 3.61831i | −0.336922 | − | 0.194522i | ||||
\(347\) | 9.92748 | + | 5.73163i | 0.532935 | + | 0.307690i | 0.742211 | − | 0.670166i | \(-0.233777\pi\) |
−0.209276 | + | 0.977857i | \(0.567111\pi\) | |||||||
\(348\) | −2.69384 | − | 4.66587i | −0.144405 | − | 0.250117i | ||||
\(349\) | −20.9561 | −1.12176 | −0.560878 | − | 0.827899i | \(-0.689536\pi\) | ||||
−0.560878 | + | 0.827899i | \(0.689536\pi\) | |||||||
\(350\) | 4.39358 | + | 10.4906i | 0.234847 | + | 0.560746i | ||||
\(351\) | − | 2.59370i | − | 0.138442i | ||||||
\(352\) | −2.22504 | − | 2.45951i | −0.118595 | − | 0.131092i | ||||
\(353\) | 17.2530 | + | 9.96104i | 0.918286 | + | 0.530173i | 0.883088 | − | 0.469208i | \(-0.155460\pi\) |
0.0351983 | + | 0.999380i | \(0.488794\pi\) | |||||||
\(354\) | −8.38751 | − | 4.84253i | −0.445791 | − | 0.257378i | ||||
\(355\) | 10.2105 | − | 5.89504i | 0.541918 | − | 0.312876i | ||||
\(356\) | − | 8.40678i | − | 0.445559i | ||||||
\(357\) | −9.57226 | + | 12.5765i | −0.506618 | + | 0.665621i | ||||
\(358\) | − | 8.06636i | − | 0.426321i | ||||||
\(359\) | −3.38989 | + | 1.95715i | −0.178912 | + | 0.103295i | −0.586781 | − | 0.809746i | \(-0.699605\pi\) |
0.407870 | + | 0.913040i | \(0.366272\pi\) | |||||||
\(360\) | −0.418696 | + | 0.725202i | −0.0220672 | + | 0.0382215i | ||||
\(361\) | 4.65832 | − | 8.06845i | 0.245175 | − | 0.424655i | ||||
\(362\) | 2.80528 | + | 4.85889i | 0.147442 | + | 0.255378i | ||||
\(363\) | −4.52130 | − | 10.0279i | −0.237307 | − | 0.526326i | ||||
\(364\) | −0.869045 | + | 6.80705i | −0.0455504 | + | 0.356786i | ||||
\(365\) | − | 8.30121i | − | 0.434505i | ||||||
\(366\) | −2.03524 | − | 3.52514i | −0.106384 | − | 0.184262i | ||||
\(367\) | 10.4720 | + | 6.04600i | 0.546633 | + | 0.315599i | 0.747763 | − | 0.663966i | \(-0.231128\pi\) |
−0.201130 | + | 0.979565i | \(0.564461\pi\) | |||||||
\(368\) | −1.43256 | + | 2.48126i | −0.0746772 | + | 0.129345i | ||||
\(369\) | −5.61749 | − | 9.72978i | −0.292435 | − | 0.506512i | ||||
\(370\) | −9.20238 | −0.478409 | ||||||||
\(371\) | 1.73380 | − | 13.5805i | 0.0900145 | − | 0.705064i | ||||
\(372\) | 1.05470 | 0.0546838 | ||||||||
\(373\) | 15.3231 | − | 8.84681i | 0.793401 | − | 0.458070i | −0.0477575 | − | 0.998859i | \(-0.515207\pi\) |
0.841158 | + | 0.540789i | \(0.181874\pi\) | |||||||
\(374\) | −6.07812 | + | 18.8572i | −0.314292 | + | 0.975084i | ||||
\(375\) | 3.89336 | − | 6.74349i | 0.201052 | − | 0.348232i | ||||
\(376\) | −6.12185 | − | 10.6034i | −0.315711 | − | 0.546827i | ||||
\(377\) | 13.9741i | 0.719701i | ||||||||
\(378\) | −2.10531 | − | 1.60239i | −0.108285 | − | 0.0824183i | ||||
\(379\) | 19.6577 | 1.00975 | 0.504874 | − | 0.863193i | \(-0.331539\pi\) | ||||
0.504874 | + | 0.863193i | \(0.331539\pi\) | |||||||
\(380\) | 2.25669 | − | 1.30290i | 0.115766 | − | 0.0668374i | ||||
\(381\) | 6.06567 | − | 10.5060i | 0.310754 | − | 0.538241i | ||||
\(382\) | 10.2053 | + | 5.89206i | 0.522151 | + | 0.301464i | ||||
\(383\) | 1.18944 | − | 0.686725i | 0.0607777 | − | 0.0350900i | −0.469303 | − | 0.883037i | \(-0.655495\pi\) |
0.530081 | + | 0.847947i | \(0.322162\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 6.02954 | − | 4.19988i | 0.307294 | − | 0.214046i | ||||
\(386\) | −18.0976 | −0.921145 | ||||||||
\(387\) | 1.10442 | − | 0.637637i | 0.0561408 | − | 0.0324129i | ||||
\(388\) | 0.680809 | + | 0.393065i | 0.0345628 | + | 0.0199549i | ||||
\(389\) | −15.6896 | + | 27.1752i | −0.795496 | + | 1.37784i | 0.127027 | + | 0.991899i | \(0.459456\pi\) |
−0.922524 | + | 0.385941i | \(0.873877\pi\) | |||||||
\(390\) | 1.88096 | − | 1.08597i | 0.0952461 | − | 0.0549904i | ||||
\(391\) | 17.1154 | 0.865562 | ||||||||
\(392\) | 4.98838 | + | 4.91081i | 0.251951 | + | 0.248033i | ||||
\(393\) | 2.04449i | 0.103131i | ||||||||
\(394\) | 3.11555 | + | 5.39629i | 0.156959 | + | 0.271861i | ||||
\(395\) | 5.65744 | − | 9.79897i | 0.284657 | − | 0.493040i | ||||
\(396\) | −3.15670 | − | 1.01748i | −0.158630 | − | 0.0511301i | ||||
\(397\) | −30.5464 | + | 17.6360i | −1.53308 | + | 0.885123i | −0.533861 | + | 0.845572i | \(0.679259\pi\) |
−0.999218 | + | 0.0395508i | \(0.987407\pi\) | |||||||
\(398\) | 18.2669 | 0.915636 | ||||||||
\(399\) | 3.18044 | + | 7.59396i | 0.159221 | + | 0.380174i | ||||
\(400\) | 4.29878 | 0.214939 | ||||||||
\(401\) | −4.48309 | − | 7.76494i | −0.223875 | − | 0.387763i | 0.732106 | − | 0.681190i | \(-0.238537\pi\) |
−0.955981 | + | 0.293428i | \(0.905204\pi\) | |||||||
\(402\) | −6.51916 | + | 11.2915i | −0.325146 | + | 0.563169i | ||||
\(403\) | −2.36909 | − | 1.36779i | −0.118013 | − | 0.0681347i | ||||
\(404\) | −3.36113 | − | 5.82166i | −0.167223 | − | 0.289638i | ||||
\(405\) | 0.837391i | 0.0416103i | ||||||||
\(406\) | 11.3428 | + | 8.63320i | 0.562931 | + | 0.428459i | ||||
\(407\) | −7.66165 | − | 35.6332i | −0.379774 | − | 1.76627i | ||||
\(408\) | 2.98686 | + | 5.17339i | 0.147872 | + | 0.256121i | ||||
\(409\) | 17.9762 | − | 31.1357i | 0.888867 | − | 1.53956i | 0.0476498 | − | 0.998864i | \(-0.484827\pi\) |
0.841217 | − | 0.540698i | \(-0.181840\pi\) | |||||||
\(410\) | 4.70404 | − | 8.14763i | 0.232316 | − | 0.402383i | ||||
\(411\) | −11.4412 | + | 6.60556i | −0.564351 | + | 0.325828i | ||||
\(412\) | 4.07143i | 0.200585i | ||||||||
\(413\) | 25.4180 | + | 3.24507i | 1.25074 | + | 0.159680i | ||||
\(414\) | 2.86511i | 0.140813i | ||||||||
\(415\) | 2.17043 | − | 1.25310i | 0.106542 | − | 0.0615123i | ||||
\(416\) | 2.24621 | + | 1.29685i | 0.110130 | + | 0.0635834i | ||||
\(417\) | −5.33726 | − | 3.08147i | −0.261367 | − | 0.150900i | ||||
\(418\) | 6.92391 | + | 7.65352i | 0.338659 | + | 0.374346i | ||||
\(419\) | − | 0.724634i | − | 0.0354007i | −0.999843 | − | 0.0177004i | \(-0.994366\pi\) | ||
0.999843 | − | 0.0177004i | \(-0.00563449\pi\) | |||||||
\(420\) | 0.280576 | − | 2.19769i | 0.0136907 | − | 0.107236i | ||||
\(421\) | 3.71423 | 0.181021 | 0.0905103 | − | 0.995896i | \(-0.471150\pi\) | ||||
0.0905103 | + | 0.995896i | \(0.471150\pi\) | |||||||
\(422\) | −5.12231 | − | 8.87211i | −0.249350 | − | 0.431887i | ||||
\(423\) | −10.6034 | − | 6.12185i | −0.515553 | − | 0.297655i | ||||
\(424\) | −4.48134 | − | 2.58730i | −0.217633 | − | 0.125651i | ||||
\(425\) | −12.8398 | − | 22.2393i | −0.622824 | − | 1.07876i | ||||
\(426\) | 14.0795 | 0.682156 | ||||||||
\(427\) | 8.56963 | + | 6.52252i | 0.414714 | + | 0.315647i | ||||
\(428\) | − | 0.241883i | − | 0.0116919i | ||||||
\(429\) | 5.77110 | + | 6.37924i | 0.278632 | + | 0.307993i | ||||
\(430\) | 0.924832 | + | 0.533952i | 0.0445994 | + | 0.0257495i | ||||
\(431\) | 3.53752 | + | 2.04239i | 0.170396 | + | 0.0983784i | 0.582773 | − | 0.812635i | \(-0.301968\pi\) |
−0.412376 | + | 0.911014i | \(0.635301\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 30.3109i | − | 1.45665i | −0.685232 | − | 0.728325i | \(-0.740299\pi\) | ||
0.685232 | − | 0.728325i | \(-0.259701\pi\) | |||||||
\(434\) | −2.57386 | + | 1.07796i | −0.123549 | + | 0.0517439i | ||||
\(435\) | − | 4.51160i | − | 0.216315i | ||||||
\(436\) | −15.1773 | + | 8.76259i | −0.726859 | + | 0.419652i | ||||
\(437\) | 4.45784 | − | 7.72121i | 0.213248 | − | 0.369356i | ||||
\(438\) | 4.95659 | − | 8.58507i | 0.236835 | − | 0.410210i | ||||
\(439\) | −6.30512 | − | 10.9208i | −0.300927 | − | 0.521221i | 0.675419 | − | 0.737434i | \(-0.263963\pi\) |
−0.976346 | + | 0.216213i | \(0.930629\pi\) | |||||||
\(440\) | −0.583820 | − | 2.71526i | −0.0278325 | − | 0.129445i | ||||
\(441\) | 6.77547 | + | 1.75869i | 0.322641 | + | 0.0837473i | ||||
\(442\) | − | 15.4941i | − | 0.736978i | ||||||
\(443\) | −7.61859 | − | 13.1958i | −0.361970 | − | 0.626951i | 0.626315 | − | 0.779570i | \(-0.284562\pi\) |
−0.988285 | + | 0.152619i | \(0.951229\pi\) | |||||||
\(444\) | −9.51705 | − | 5.49467i | −0.451659 | − | 0.260766i | ||||
\(445\) | 3.51988 | − | 6.09662i | 0.166858 | − | 0.289007i | ||||
\(446\) | −7.83326 | − | 13.5676i | −0.370916 | − | 0.642445i | ||||
\(447\) | −4.39696 | −0.207969 | ||||||||
\(448\) | 2.44037 | − | 1.02205i | 0.115297 | − | 0.0482875i | ||||
\(449\) | 32.2780 | 1.52329 | 0.761647 | − | 0.647993i | \(-0.224391\pi\) | ||||
0.761647 | + | 0.647993i | \(0.224391\pi\) | |||||||
\(450\) | 3.72285 | − | 2.14939i | 0.175497 | − | 0.101323i | ||||
\(451\) | 35.4654 | + | 11.4313i | 1.67000 | + | 0.538280i | ||||
\(452\) | 4.04475 | − | 7.00571i | 0.190249 | − | 0.329521i | ||||
\(453\) | 5.12037 | + | 8.86874i | 0.240576 | + | 0.416690i | ||||
\(454\) | 15.7205i | 0.737799i | ||||||||
\(455\) | −3.48032 | + | 4.57262i | −0.163160 | + | 0.214368i | ||||
\(456\) | 3.11181 | 0.145724 | ||||||||
\(457\) | −26.2793 | + | 15.1724i | −1.22929 | + | 0.709733i | −0.966882 | − | 0.255223i | \(-0.917851\pi\) |
−0.262412 | + | 0.964956i | \(0.584518\pi\) | |||||||
\(458\) | 1.25208 | − | 2.16867i | 0.0585060 | − | 0.101335i | ||||
\(459\) | 5.17339 | + | 2.98686i | 0.241473 | + | 0.139415i | ||||
\(460\) | −2.07779 | + | 1.19961i | −0.0968773 | + | 0.0559321i | ||||
\(461\) | 4.81402 | 0.224211 | 0.112106 | − | 0.993696i | \(-0.464240\pi\) | ||||
0.112106 | + | 0.993696i | \(0.464240\pi\) | |||||||
\(462\) | 8.74343 | − | 0.743301i | 0.406781 | − | 0.0345815i | ||||
\(463\) | −33.1197 | −1.53920 | −0.769600 | − | 0.638526i | \(-0.779545\pi\) | ||||
−0.769600 | + | 0.638526i | \(0.779545\pi\) | |||||||
\(464\) | 4.66587 | − | 2.69384i | 0.216608 | − | 0.125059i | ||||
\(465\) | 0.764873 | + | 0.441599i | 0.0354701 | + | 0.0204787i | ||||
\(466\) | 0.0276581 | − | 0.0479052i | 0.00128123 | − | 0.00221916i | ||||
\(467\) | −12.4591 | + | 7.19328i | −0.576539 | + | 0.332865i | −0.759757 | − | 0.650207i | \(-0.774682\pi\) |
0.183218 | + | 0.983072i | \(0.441349\pi\) | |||||||
\(468\) | 2.59370 | 0.119894 | ||||||||
\(469\) | 4.36861 | − | 34.2184i | 0.201724 | − | 1.58006i | ||||
\(470\) | − | 10.2528i | − | 0.472925i | ||||||
\(471\) | 7.99304 | + | 13.8444i | 0.368300 | + | 0.637914i | ||||
\(472\) | 4.84253 | − | 8.38751i | 0.222896 | − | 0.386067i | ||||
\(473\) | −1.29756 | + | 4.02566i | −0.0596619 | + | 0.185100i | ||||
\(474\) | 11.7018 | − | 6.75603i | 0.537481 | − | 0.310315i | ||||
\(475\) | −13.3770 | −0.613777 | ||||||||
\(476\) | −12.5765 | − | 9.57226i | −0.576445 | − | 0.438744i | ||||
\(477\) | −5.17461 | −0.236929 | ||||||||
\(478\) | −2.87233 | − | 4.97501i | −0.131377 | − | 0.227552i | ||||
\(479\) | −3.23604 | + | 5.60499i | −0.147859 | + | 0.256099i | −0.930436 | − | 0.366455i | \(-0.880571\pi\) |
0.782577 | + | 0.622554i | \(0.213905\pi\) | |||||||
\(480\) | −0.725202 | − | 0.418696i | −0.0331008 | − | 0.0191108i | ||||
\(481\) | 14.2516 | + | 24.6844i | 0.649815 | + | 1.12551i | ||||
\(482\) | − | 7.34245i | − | 0.334440i | ||||||
\(483\) | −2.92830 | − | 6.99194i | −0.133242 | − | 0.318144i | ||||
\(484\) | 10.0279 | − | 4.52130i | 0.455812 | − | 0.205514i | ||||
\(485\) | 0.329150 | + | 0.570104i | 0.0149459 | + | 0.0258871i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 2.64048 | − | 4.57345i | 0.119652 | − | 0.207243i | −0.799978 | − | 0.600029i | \(-0.795156\pi\) |
0.919630 | + | 0.392787i | \(0.128489\pi\) | |||||||
\(488\) | 3.52514 | − | 2.03524i | 0.159576 | − | 0.0921311i | ||||
\(489\) | − | 0.523852i | − | 0.0236894i | ||||||
\(490\) | 1.56145 | + | 5.64994i | 0.0705392 | + | 0.255238i | ||||
\(491\) | 11.3633i | 0.512820i | 0.966568 | + | 0.256410i | \(0.0825398\pi\) | ||||
−0.966568 | + | 0.256410i | \(0.917460\pi\) | |||||||
\(492\) | 9.72978 | − | 5.61749i | 0.438652 | − | 0.253256i | ||||
\(493\) | −27.8726 | − | 16.0923i | −1.25532 | − | 0.724759i | ||||
\(494\) | −6.98979 | − | 4.03556i | −0.314485 | − | 0.181568i | ||||
\(495\) | −1.86323 | − | 2.05957i | −0.0837460 | − | 0.0925709i | ||||
\(496\) | 1.05470i | 0.0473575i | ||||||||
\(497\) | −34.3593 | + | 14.3901i | −1.54122 | + | 0.645482i | ||||
\(498\) | 2.99287 | 0.134114 | ||||||||
\(499\) | 14.5860 | + | 25.2638i | 0.652961 | + | 1.13096i | 0.982401 | + | 0.186785i | \(0.0598066\pi\) |
−0.329440 | + | 0.944176i | \(0.606860\pi\) | |||||||
\(500\) | 6.74349 | + | 3.89336i | 0.301578 | + | 0.174116i | ||||
\(501\) | 14.7695 | + | 8.52720i | 0.659855 | + | 0.380967i | ||||
\(502\) | −2.10401 | − | 3.64426i | −0.0939067 | − | 0.162651i | ||||
\(503\) | 22.4317 | 1.00018 | 0.500090 | − | 0.865973i | \(-0.333300\pi\) | ||||
0.500090 | + | 0.865973i | \(0.333300\pi\) | |||||||
\(504\) | 1.60239 | − | 2.10531i | 0.0713763 | − | 0.0937780i | ||||
\(505\) | − | 5.62917i | − | 0.250495i | ||||||
\(506\) | −6.37500 | − | 7.04677i | −0.283403 | − | 0.313267i | ||||
\(507\) | 5.43231 | + | 3.13635i | 0.241257 | + | 0.139290i | ||||
\(508\) | 10.5060 | + | 6.06567i | 0.466130 | + | 0.269121i | ||||
\(509\) | −23.7016 | + | 13.6841i | −1.05055 | + | 0.606537i | −0.922804 | − | 0.385269i | \(-0.874109\pi\) |
−0.127749 | + | 0.991807i | \(0.540775\pi\) | |||||||
\(510\) | 5.00234i | 0.221507i | ||||||||
\(511\) | −3.32151 | + | 26.0166i | −0.146935 | + | 1.15091i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 2.69491 | − | 1.55590i | 0.118983 | − | 0.0686948i | ||||
\(514\) | 12.3233 | − | 21.3446i | 0.543557 | − | 0.941469i | ||||
\(515\) | −1.70469 | + | 2.95261i | −0.0751176 | + | 0.130107i | ||||
\(516\) | 0.637637 | + | 1.10442i | 0.0280704 | + | 0.0486194i | ||||
\(517\) | 39.7005 | − | 8.53618i | 1.74602 | − | 0.375421i | ||||
\(518\) | 28.8410 | + | 3.68208i | 1.26720 | + | 0.161782i | ||||
\(519\) | − | 7.23663i | − | 0.317653i | ||||||
\(520\) | 1.08597 | + | 1.88096i | 0.0476231 | + | 0.0824856i | ||||
\(521\) | 30.3032 | + | 17.4955i | 1.32761 | + | 0.766493i | 0.984929 | − | 0.172960i | \(-0.0553332\pi\) |
0.342676 | + | 0.939454i | \(0.388667\pi\) | |||||||
\(522\) | 2.69384 | − | 4.66587i | 0.117906 | − | 0.204220i | ||||
\(523\) | −19.1224 | − | 33.1210i | −0.836165 | − | 1.44828i | −0.893079 | − | 0.449900i | \(-0.851459\pi\) |
0.0569142 | − | 0.998379i | \(-0.481874\pi\) | |||||||
\(524\) | −2.04449 | −0.0893139 | ||||||||
\(525\) | −6.88834 | + | 9.05026i | −0.300632 | + | 0.394986i | ||||
\(526\) | −30.3837 | −1.32479 | ||||||||
\(527\) | 5.45639 | − | 3.15025i | 0.237684 | − | 0.137227i | ||||
\(528\) | 1.01748 | − | 3.15670i | 0.0442800 | − | 0.137378i | ||||
\(529\) | 7.39556 | − | 12.8095i | 0.321546 | − | 0.556934i | ||||
\(530\) | −2.16659 | − | 3.75264i | −0.0941105 | − | 0.163004i | ||||
\(531\) | − | 9.68506i | − | 0.420296i | ||||||
\(532\) | −7.59396 | + | 3.18044i | −0.329240 | + | 0.137889i | ||||
\(533\) | −29.1402 | −1.26220 | ||||||||
\(534\) | 7.28049 | − | 4.20339i | 0.315057 | − | 0.181899i | ||||
\(535\) | 0.101275 | − | 0.175414i | 0.00437852 | − | 0.00758382i | ||||
\(536\) | −11.2915 | − | 6.51916i | −0.487719 | − | 0.281585i | ||||
\(537\) | 6.98568 | − | 4.03318i | 0.301454 | − | 0.174045i | ||||
\(538\) | −19.9737 | −0.861128 | ||||||||
\(539\) | −20.5775 | + | 10.7502i | −0.886336 | + | 0.463043i | ||||
\(540\) | −0.837391 | −0.0360356 | ||||||||
\(541\) | −2.73079 | + | 1.57662i | −0.117406 | + | 0.0677842i | −0.557553 | − | 0.830141i | \(-0.688260\pi\) |
0.440147 | + | 0.897926i | \(0.354926\pi\) | |||||||
\(542\) | 1.39887 | + | 0.807639i | 0.0600867 | + | 0.0346911i | ||||
\(543\) | −2.80528 | + | 4.85889i | −0.120386 | + | 0.208515i | ||||
\(544\) | −5.17339 | + | 2.98686i | −0.221807 | + | 0.128061i | ||||
\(545\) | −14.6754 | −0.628627 | ||||||||
\(546\) | −6.32960 | + | 2.65091i | −0.270882 | + | 0.113448i | ||||
\(547\) | 20.6313i | 0.882131i | 0.897475 | + | 0.441065i | \(0.145399\pi\) | ||||
−0.897475 | + | 0.441065i | \(0.854601\pi\) | |||||||
\(548\) | −6.60556 | − | 11.4412i | −0.282176 | − | 0.488742i | ||||
\(549\) | 2.03524 | − | 3.52514i | 0.0868620 | − | 0.150449i | ||||
\(550\) | −4.37390 | + | 13.5699i | −0.186504 | + | 0.578624i | ||||
\(551\) | −14.5193 | + | 8.38273i | −0.618543 | + | 0.357116i | ||||
\(552\) | −2.86511 | −0.121947 | ||||||||
\(553\) | −21.6516 | + | 28.4471i | −0.920722 | + | 1.20969i | ||||
\(554\) | 5.18071 | 0.220107 | ||||||||
\(555\) | −4.60119 | − | 7.96950i | −0.195310 | − | 0.338286i | ||||
\(556\) | 3.08147 | − | 5.33726i | 0.130683 | − | 0.226350i | ||||
\(557\) | −1.10046 | − | 0.635353i | −0.0466281 | − | 0.0269208i | 0.476505 | − | 0.879172i | \(-0.341904\pi\) |
−0.523133 | + | 0.852251i | \(0.675237\pi\) | |||||||
\(558\) | 0.527351 | + | 0.913399i | 0.0223246 | + | 0.0386673i | ||||
\(559\) | − | 3.30769i | − | 0.139900i | ||||||
\(560\) | 2.19769 | + | 0.280576i | 0.0928694 | + | 0.0118565i | ||||
\(561\) | −19.3699 | + | 4.16481i | −0.817798 | + | 0.175839i | ||||
\(562\) | −12.5942 | − | 21.8137i | −0.531252 | − | 0.920156i | ||||
\(563\) | −20.1729 | + | 34.9405i | −0.850187 | + | 1.47257i | 0.0308519 | + | 0.999524i | \(0.490178\pi\) |
−0.881039 | + | 0.473043i | \(0.843155\pi\) | |||||||
\(564\) | 6.12185 | − | 10.6034i | 0.257777 | − | 0.446482i | ||||
\(565\) | 5.86652 | − | 3.38704i | 0.246806 | − | 0.142494i | ||||
\(566\) | − | 23.0334i | − | 0.968168i | ||||||
\(567\) | 0.335059 | − | 2.62445i | 0.0140712 | − | 0.110217i | ||||
\(568\) | 14.0795i | 0.590764i | ||||||||
\(569\) | 2.40837 | − | 1.39047i | 0.100964 | − | 0.0582917i | −0.448668 | − | 0.893699i | \(-0.648101\pi\) |
0.549632 | + | 0.835407i | \(0.314768\pi\) | |||||||
\(570\) | 2.25669 | + | 1.30290i | 0.0945224 | + | 0.0545725i | ||||
\(571\) | 33.0674 | + | 19.0915i | 1.38383 | + | 0.798953i | 0.992610 | − | 0.121346i | \(-0.0387209\pi\) |
0.391217 | + | 0.920299i | \(0.372054\pi\) | |||||||
\(572\) | −6.37924 | + | 5.77110i | −0.266729 | + | 0.241302i | ||||
\(573\) | 11.7841i | 0.492288i | ||||||||
\(574\) | −18.0029 | + | 23.6531i | −0.751425 | + | 0.987262i | ||||
\(575\) | 12.3165 | 0.513633 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 5.92826 | + | 3.42268i | 0.246797 | + | 0.142488i | 0.618297 | − | 0.785945i | \(-0.287823\pi\) |
−0.371500 | + | 0.928433i | \(0.621156\pi\) | |||||||
\(578\) | 16.1820 | + | 9.34267i | 0.673081 | + | 0.388604i | ||||
\(579\) | −9.04882 | − | 15.6730i | −0.376056 | − | 0.651348i | ||||
\(580\) | 4.51160 | 0.187334 | ||||||||
\(581\) | −7.30370 | + | 3.05887i | −0.303009 | + | 0.126903i | ||||
\(582\) | 0.786131i | 0.0325862i | ||||||||
\(583\) | 12.7270 | − | 11.5137i | 0.527098 | − | 0.476850i | ||||
\(584\) | 8.58507 | + | 4.95659i | 0.355253 | + | 0.205105i | ||||
\(585\) | 1.88096 | + | 1.08597i | 0.0777682 | + | 0.0448995i | ||||
\(586\) | 3.62064 | − | 2.09038i | 0.149567 | − | 0.0863527i | ||||
\(587\) | − | 22.7050i | − | 0.937135i | −0.883428 | − | 0.468568i | \(-0.844770\pi\) | ||
0.883428 | − | 0.468568i | \(-0.155230\pi\) | |||||||
\(588\) | −1.75869 | + | 6.77547i | −0.0725273 | + | 0.279416i | ||||
\(589\) | − | 3.28203i | − | 0.135234i | ||||||
\(590\) | 7.02363 | − | 4.05510i | 0.289158 | − | 0.166946i | ||||
\(591\) | −3.11555 | + | 5.39629i | −0.128157 | + | 0.221974i | ||||
\(592\) | 5.49467 | − | 9.51705i | 0.225830 | − | 0.391148i | ||||
\(593\) | −5.05558 | − | 8.75652i | −0.207608 | − | 0.359587i | 0.743353 | − | 0.668900i | \(-0.233234\pi\) |
−0.950960 | + | 0.309313i | \(0.899901\pi\) | |||||||
\(594\) | −0.697189 | − | 3.24252i | −0.0286060 | − | 0.133042i | ||||
\(595\) | −5.11267 | − | 12.2076i | −0.209599 | − | 0.500461i | ||||
\(596\) | − | 4.39696i | − | 0.180107i | ||||||
\(597\) | 9.13344 | + | 15.8196i | 0.373807 | + | 0.647453i | ||||
\(598\) | 6.43566 | + | 3.71563i | 0.263174 | + | 0.151943i | ||||
\(599\) | 1.45219 | − | 2.51527i | 0.0593349 | − | 0.102771i | −0.834832 | − | 0.550505i | \(-0.814435\pi\) |
0.894167 | + | 0.447734i | \(0.147769\pi\) | |||||||
\(600\) | 2.14939 | + | 3.72285i | 0.0877484 | + | 0.151985i | ||||
\(601\) | −8.68237 | −0.354161 | −0.177081 | − | 0.984196i | \(-0.556665\pi\) | ||||
−0.177081 | + | 0.984196i | \(0.556665\pi\) | |||||||
\(602\) | −2.68485 | − | 2.04349i | −0.109426 | − | 0.0832866i | ||||
\(603\) | −13.0383 | −0.530961 | ||||||||
\(604\) | −8.86874 | + | 5.12037i | −0.360864 | + | 0.208345i | ||||
\(605\) | 9.16527 | + | 0.919765i | 0.372621 | + | 0.0373938i | ||||
\(606\) | 3.36113 | − | 5.82166i | 0.136537 | − | 0.236489i | ||||
\(607\) | 11.7341 | + | 20.3240i | 0.476272 | + | 0.824927i | 0.999630 | − | 0.0271855i | \(-0.00865449\pi\) |
−0.523359 | + | 0.852113i | \(0.675321\pi\) | |||||||
\(608\) | 3.11181i | 0.126200i | ||||||||
\(609\) | −1.80520 | + | 14.1397i | −0.0731502 | + | 0.572970i | ||||
\(610\) | 3.40859 | 0.138010 | ||||||||
\(611\) | −27.5020 | + | 15.8783i | −1.11261 | + | 0.642367i | ||||
\(612\) | −2.98686 | + | 5.17339i | −0.120737 | + | 0.209122i | ||||
\(613\) | −26.8294 | − | 15.4899i | −1.08363 | − | 0.625633i | −0.151756 | − | 0.988418i | \(-0.548493\pi\) |
−0.931873 | + | 0.362785i | \(0.881826\pi\) | |||||||
\(614\) | −8.71712 | + | 5.03283i | −0.351794 | + | 0.203108i | ||||
\(615\) | 9.40808 | 0.379370 | ||||||||
\(616\) | 0.743301 | + | 8.74343i | 0.0299485 | + | 0.352283i | ||||
\(617\) | 7.35346 | 0.296039 | 0.148020 | − | 0.988984i | \(-0.452710\pi\) | ||||
0.148020 | + | 0.988984i | \(0.452710\pi\) | |||||||
\(618\) | −3.52596 | + | 2.03571i | −0.141835 | + | 0.0818884i | ||||
\(619\) | −3.16686 | − | 1.82839i | −0.127287 | − | 0.0734892i | 0.435005 | − | 0.900428i | \(-0.356747\pi\) |
−0.562292 | + | 0.826939i | \(0.690080\pi\) | |||||||
\(620\) | −0.441599 | + | 0.764873i | −0.0177351 | + | 0.0307180i | ||||
\(621\) | −2.48126 | + | 1.43256i | −0.0995696 | + | 0.0574865i | ||||
\(622\) | −1.42972 | −0.0573264 | ||||||||
\(623\) | −13.4710 | + | 17.6989i | −0.539704 | + | 0.709091i | ||||
\(624\) | 2.59370i | 0.103831i | ||||||||
\(625\) | −7.48667 | − | 12.9673i | −0.299467 | − | 0.518692i | ||||
\(626\) | −15.1965 | + | 26.3211i | −0.607375 | + | 1.05200i | ||||
\(627\) | −3.16619 | + | 9.82304i | −0.126445 | + | 0.392294i | ||||
\(628\) | −13.8444 | + | 7.99304i | −0.552450 | + | 0.318957i | ||||
\(629\) | −65.6473 | −2.61753 | ||||||||
\(630\) | 2.04354 | − | 0.855860i | 0.0814168 | − | 0.0340983i | ||||
\(631\) | 22.5757 | 0.898724 | 0.449362 | − | 0.893350i | \(-0.351651\pi\) | ||||
0.449362 | + | 0.893350i | \(0.351651\pi\) | |||||||
\(632\) | 6.75603 | + | 11.7018i | 0.268740 | + | 0.465472i | ||||
\(633\) | 5.12231 | − | 8.87211i | 0.203594 | − | 0.352635i | ||||
\(634\) | 9.39829 | + | 5.42610i | 0.373254 | + | 0.215498i | ||||
\(635\) | 5.07934 | + | 8.79767i | 0.201567 | + | 0.349125i | ||||
\(636\) | − | 5.17461i | − | 0.205187i | ||||||
\(637\) | 12.7372 | − | 12.9384i | 0.504666 | − | 0.512638i | ||||
\(638\) | 3.75624 | + | 17.4697i | 0.148711 | + | 0.691631i | ||||
\(639\) | 7.03977 | + | 12.1932i | 0.278489 | + | 0.482357i | ||||
\(640\) | 0.418696 | − | 0.725202i | 0.0165504 | − | 0.0286661i | ||||
\(641\) | 22.2802 | − | 38.5905i | 0.880017 | − | 1.52423i | 0.0286961 | − | 0.999588i | \(-0.490864\pi\) |
0.851321 | − | 0.524646i | \(-0.175802\pi\) | |||||||
\(642\) | 0.209477 | − | 0.120942i | 0.00826740 | − | 0.00477319i | ||||
\(643\) | 14.8587i | 0.585968i | 0.956117 | + | 0.292984i | \(0.0946483\pi\) | ||||
−0.956117 | + | 0.292984i | \(0.905352\pi\) | |||||||
\(644\) | 6.99194 | − | 2.92830i | 0.275521 | − | 0.115391i | ||||
\(645\) | 1.06790i | 0.0420487i | ||||||||
\(646\) | 16.0986 | − | 9.29454i | 0.633391 | − | 0.365689i | ||||
\(647\) | 41.5179 | + | 23.9704i | 1.63224 | + | 0.942373i | 0.983401 | + | 0.181445i | \(0.0580774\pi\) |
0.648836 | + | 0.760928i | \(0.275256\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 21.5497 | + | 23.8205i | 0.845899 | + | 0.935037i | ||||
\(650\) | − | 11.1498i | − | 0.437329i | ||||||
\(651\) | −2.22048 | − | 1.69005i | −0.0870273 | − | 0.0662383i | ||||
\(652\) | 0.523852 | 0.0205156 | ||||||||
\(653\) | −12.9160 | − | 22.3711i | −0.505440 | − | 0.875448i | −0.999980 | − | 0.00629344i | \(-0.997997\pi\) |
0.494540 | − | 0.869155i | \(-0.335337\pi\) | |||||||
\(654\) | −15.1773 | − | 8.76259i | −0.593478 | − | 0.342644i | ||||
\(655\) | −1.48267 | − | 0.856019i | −0.0579326 | − | 0.0334474i | ||||
\(656\) | 5.61749 | + | 9.72978i | 0.219326 | + | 0.379884i | ||||
\(657\) | 9.91318 | 0.386750 | ||||||||
\(658\) | −4.10237 | + | 32.1330i | −0.159927 | + | 1.25267i | ||||
\(659\) | 28.7951i | 1.12170i | 0.827918 | + | 0.560850i | \(0.189525\pi\) | ||||
−0.827918 | + | 0.560850i | \(0.810475\pi\) | |||||||
\(660\) | 2.05957 | − | 1.86323i | 0.0801687 | − | 0.0725262i | ||||
\(661\) | −23.0670 | − | 13.3177i | −0.897201 | − | 0.517999i | −0.0209100 | − | 0.999781i | \(-0.506656\pi\) |
−0.876291 | + | 0.481782i | \(0.839990\pi\) | |||||||
\(662\) | −11.1847 | − | 6.45747i | −0.434705 | − | 0.250977i | ||||
\(663\) | 13.4183 | − | 7.74703i | 0.521122 | − | 0.300870i | ||||
\(664\) | 2.99287i | 0.116146i | ||||||||
\(665\) | −6.83880 | − | 0.873099i | −0.265197 | − | 0.0338573i | ||||
\(666\) | − | 10.9893i | − | 0.425829i | ||||||
\(667\) | 13.3683 | − | 7.71817i | 0.517621 | − | 0.298849i | ||||
\(668\) | −8.52720 | + | 14.7695i | −0.329927 | + | 0.571451i | ||||
\(669\) | 7.83326 | − | 13.5676i | 0.302851 | − | 0.524554i | ||||
\(670\) | −5.45909 | − | 9.45541i | −0.210903 | − | 0.365295i | ||||
\(671\) | 2.83790 | + | 13.1986i | 0.109556 | + | 0.509527i | ||||
\(672\) | 2.10531 | + | 1.60239i | 0.0812141 | + | 0.0618137i | ||||
\(673\) | − | 12.3054i | − | 0.474337i | −0.971469 | − | 0.237168i | \(-0.923781\pi\) | ||
0.971469 | − | 0.237168i | \(-0.0762193\pi\) | |||||||
\(674\) | −8.24045 | − | 14.2729i | −0.317410 | − | 0.549771i | ||||
\(675\) | 3.72285 | + | 2.14939i | 0.143293 | + | 0.0827300i | ||||
\(676\) | −3.13635 | + | 5.43231i | −0.120629 | + | 0.208935i | ||||
\(677\) | 5.73042 | + | 9.92539i | 0.220238 | + | 0.381464i | 0.954880 | − | 0.296991i | \(-0.0959832\pi\) |
−0.734642 | + | 0.678455i | \(0.762650\pi\) | |||||||
\(678\) | 8.08949 | 0.310675 | ||||||||
\(679\) | −0.803469 | − | 1.91845i | −0.0308343 | − | 0.0736233i | ||||
\(680\) | −5.00234 | −0.191831 | ||||||||
\(681\) | −13.6143 | + | 7.86025i | −0.521703 | + | 0.301205i | ||||
\(682\) | −3.32938 | − | 1.07313i | −0.127488 | − | 0.0410924i | ||||
\(683\) | 3.78001 | − | 6.54717i | 0.144638 | − | 0.250520i | −0.784600 | − | 0.620003i | \(-0.787132\pi\) |
0.929238 | + | 0.369482i | \(0.120465\pi\) | |||||||
\(684\) | 1.55590 | + | 2.69491i | 0.0594915 | + | 0.103042i | ||||
\(685\) | − | 11.0629i | − | 0.422691i | ||||||
\(686\) | −2.63304 | − | 18.3321i | −0.100530 | − | 0.699924i | ||||
\(687\) | 2.50417 | 0.0955399 | ||||||||
\(688\) | −1.10442 | + | 0.637637i | −0.0421056 | + | 0.0243097i | ||||
\(689\) | −6.71070 | + | 11.6233i | −0.255657 | + | 0.442812i | ||||
\(690\) | −2.07779 | − | 1.19961i | −0.0791000 | − | 0.0456684i | ||||
\(691\) | −16.4626 | + | 9.50471i | −0.626268 | + | 0.361576i | −0.779305 | − | 0.626644i | \(-0.784428\pi\) |
0.153037 | + | 0.988220i | \(0.451095\pi\) | |||||||
\(692\) | 7.23663 | 0.275095 | ||||||||
\(693\) | 5.01543 | + | 7.20038i | 0.190520 | + | 0.273520i | ||||
\(694\) | −11.4633 | −0.435140 | ||||||||
\(695\) | 4.46937 | − | 2.58039i | 0.169533 | − | 0.0978799i | ||||
\(696\) | 4.66587 | + | 2.69384i | 0.176860 | + | 0.102110i | ||||
\(697\) | 33.5573 | − | 58.1230i | 1.27107 | − | 2.20156i | ||||
\(698\) | 18.1485 | − | 10.4781i | 0.686932 | − | 0.396600i | ||||
\(699\) | 0.0553161 | 0.00209225 | ||||||||
\(700\) | −9.05026 | − | 6.88834i | −0.342068 | − | 0.260355i | ||||
\(701\) | 32.6349i | 1.23260i | 0.787510 | + | 0.616302i | \(0.211370\pi\) | ||||
−0.787510 | + | 0.616302i | \(0.788630\pi\) | |||||||
\(702\) | 1.29685 | + | 2.24621i | 0.0489465 | + | 0.0847779i | ||||
\(703\) | −17.0984 | + | 29.6152i | −0.644877 | + | 1.11696i | ||||
\(704\) | 3.15670 | + | 1.01748i | 0.118973 | + | 0.0383476i | ||||
\(705\) | 8.87916 | − | 5.12639i | 0.334409 | − | 0.193071i | ||||
\(706\) | −19.9221 | −0.749778 | ||||||||
\(707\) | −2.25236 | + | 17.6423i | −0.0847087 | + | 0.663505i | ||||
\(708\) | 9.68506 | 0.363987 | ||||||||
\(709\) | −7.57532 | − | 13.1208i | −0.284497 | − | 0.492764i | 0.687990 | − | 0.725720i | \(-0.258493\pi\) |
−0.972487 | + | 0.232957i | \(0.925160\pi\) | |||||||
\(710\) | −5.89504 | + | 10.2105i | −0.221237 | + | 0.383194i | ||||
\(711\) | 11.7018 | + | 6.75603i | 0.438851 | + | 0.253371i | ||||
\(712\) | 4.20339 | + | 7.28049i | 0.157529 | + | 0.272848i | ||||
\(713\) | 3.02184i | 0.113169i | ||||||||
\(714\) | 2.00155 | − | 15.6777i | 0.0749062 | − | 0.586724i | ||||
\(715\) | −7.04258 | + | 1.51426i | −0.263377 | + | 0.0566300i | ||||
\(716\) | 4.03318 | + | 6.98568i | 0.150727 | + | 0.261067i | ||||
\(717\) | 2.87233 | − | 4.97501i | 0.107269 | − | 0.185795i | ||||
\(718\) | 1.95715 | − | 3.38989i | 0.0730403 | − | 0.126510i | ||||
\(719\) | 4.46410 | − | 2.57735i | 0.166483 | − | 0.0961189i | −0.414444 | − | 0.910075i | \(-0.636024\pi\) |
0.580926 | + | 0.813956i | \(0.302690\pi\) | |||||||
\(720\) | − | 0.837391i | − | 0.0312077i | ||||||
\(721\) | 6.52403 | − | 8.57162i | 0.242968 | − | 0.319224i | ||||
\(722\) | 9.31665i | 0.346730i | ||||||||
\(723\) | 6.35875 | − | 3.67123i | 0.236484 | − | 0.136534i | ||||
\(724\) | −4.85889 | − | 2.80528i | −0.180579 | − | 0.104257i | ||||
\(725\) | −20.0575 | − | 11.5802i | −0.744919 | − | 0.430079i | ||||
\(726\) | 8.92949 | + | 6.42373i | 0.331404 | + | 0.238407i | ||||
\(727\) | − | 24.1329i | − | 0.895041i | −0.894274 | − | 0.447520i | \(-0.852307\pi\) | ||
0.894274 | − | 0.447520i | \(-0.147693\pi\) | |||||||
\(728\) | −2.65091 | − | 6.32960i | −0.0982492 | − | 0.234591i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 4.15061 | + | 7.18906i | 0.153621 | + | 0.266079i | ||||
\(731\) | 6.59750 | + | 3.80907i | 0.244017 | + | 0.140883i | ||||
\(732\) | 3.52514 | + | 2.03524i | 0.130293 | + | 0.0752247i | ||||
\(733\) | 26.0520 | + | 45.1235i | 0.962254 | + | 1.66667i | 0.716818 | + | 0.697260i | \(0.245598\pi\) |
0.245436 | + | 0.969413i | \(0.421069\pi\) | |||||||
\(734\) | −12.0920 | −0.446324 | ||||||||
\(735\) | −4.11227 | + | 4.17723i | −0.151683 | + | 0.154079i | ||||
\(736\) | − | 2.86511i | − | 0.105609i | ||||||
\(737\) | 32.0678 | − | 29.0108i | 1.18123 | − | 1.06863i | ||||
\(738\) | 9.72978 | + | 5.61749i | 0.358158 | + | 0.206783i | ||||
\(739\) | −4.80361 | − | 2.77336i | −0.176704 | − | 0.102020i | 0.409039 | − | 0.912517i | \(-0.365864\pi\) |
−0.585743 | + | 0.810497i | \(0.699197\pi\) | |||||||
\(740\) | 7.96950 | − | 4.60119i | 0.292965 | − | 0.169143i | ||||
\(741\) | − | 8.07111i | − | 0.296500i | ||||||
\(742\) | 5.28873 | + | 12.6280i | 0.194155 | + | 0.463587i | ||||
\(743\) | − | 18.2750i | − | 0.670443i | −0.942139 | − | 0.335222i | \(-0.891189\pi\) | ||
0.942139 | − | 0.335222i | \(-0.108811\pi\) | |||||||
\(744\) | −0.913399 | + | 0.527351i | −0.0334868 | + | 0.0193336i | ||||
\(745\) | 1.84099 | − | 3.18869i | 0.0674486 | − | 0.116824i | ||||
\(746\) | −8.84681 | + | 15.3231i | −0.323905 | + | 0.561019i | ||||
\(747\) | 1.49643 | + | 2.59190i | 0.0547516 | + | 0.0948326i | ||||
\(748\) | −4.16481 | − | 19.3699i | −0.152281 | − | 0.708234i | ||||
\(749\) | −0.387592 | + | 0.509239i | −0.0141623 | + | 0.0186072i | ||||
\(750\) | 7.78672i | 0.284331i | ||||||||
\(751\) | 7.35764 | + | 12.7438i | 0.268484 | + | 0.465028i | 0.968471 | − | 0.249128i | \(-0.0801440\pi\) |
−0.699986 | + | 0.714156i | \(0.746811\pi\) | |||||||
\(752\) | 10.6034 | + | 6.12185i | 0.386665 | + | 0.223241i | ||||
\(753\) | 2.10401 | − | 3.64426i | 0.0766745 | − | 0.132804i | ||||
\(754\) | −6.98704 | − | 12.1019i | −0.254453 | − | 0.440725i | ||||
\(755\) | −8.57551 | −0.312095 | ||||||||
\(756\) | 2.62445 | + | 0.335059i | 0.0954503 | + | 0.0121860i | ||||
\(757\) | −46.8890 | −1.70421 | −0.852105 | − | 0.523371i | \(-0.824674\pi\) | ||||
−0.852105 | + | 0.523371i | \(0.824674\pi\) | |||||||
\(758\) | −17.0241 | + | 9.82884i | −0.618342 | + | 0.357000i | ||||
\(759\) | 2.91518 | − | 9.04430i | 0.105814 | − | 0.328287i | ||||
\(760\) | −1.30290 | + | 2.25669i | −0.0472612 | + | 0.0818588i | ||||
\(761\) | 18.5206 | + | 32.0787i | 0.671373 | + | 1.16285i | 0.977515 | + | 0.210866i | \(0.0676283\pi\) |
−0.306142 | + | 0.951986i | \(0.599038\pi\) | |||||||
\(762\) | 12.1313i | 0.439472i | ||||||||
\(763\) | 45.9940 | + | 5.87198i | 1.66509 | + | 0.212580i | ||||
\(764\) | −11.7841 | −0.426334 | ||||||||
\(765\) | −4.33216 | + | 2.50117i | −0.156629 | + | 0.0904300i | ||||
\(766\) | −0.686725 | + | 1.18944i | −0.0248124 | + | 0.0429763i | ||||
\(767\) | −21.7547 | − | 12.5601i | −0.785518 | − | 0.453519i | ||||
\(768\) | 0.866025 | − | 0.500000i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | −10.3666 | −0.373830 | −0.186915 | − | 0.982376i | \(-0.559849\pi\) | ||||
−0.186915 | + | 0.982376i | \(0.559849\pi\) | |||||||
\(770\) | −3.12179 | + | 6.65197i | −0.112502 | + | 0.239720i | ||||
\(771\) | 24.6466 | 0.887625 | ||||||||
\(772\) | 15.6730 | − | 9.04882i | 0.564084 | − | 0.325674i | ||||
\(773\) | −18.7188 | − | 10.8073i | −0.673268 | − | 0.388712i | 0.124045 | − | 0.992277i | \(-0.460413\pi\) |
−0.797314 | + | 0.603565i | \(0.793746\pi\) | |||||||
\(774\) | −0.637637 | + | 1.10442i | −0.0229194 | + | 0.0396976i | ||||
\(775\) | 3.92650 | − | 2.26696i | 0.141044 | − | 0.0814318i | ||||
\(776\) | −0.786131 | −0.0282204 | ||||||||
\(777\) | 11.2317 | + | 26.8181i | 0.402935 | + | 0.962093i | ||||
\(778\) | − | 31.3793i | − | 1.12500i | ||||||
\(779\) | −17.4806 | − | 30.2772i | −0.626306 | − | 1.08479i | ||||
\(780\) | −1.08597 | + | 1.88096i | −0.0388841 | + | 0.0673492i | ||||
\(781\) | −44.4449 | − | 14.3256i | −1.59036 | − | 0.512610i | ||||
\(782\) | −14.8224 | + | 8.55769i | −0.530047 | + | 0.306023i | ||||
\(783\) | 5.38769 | 0.192540 | ||||||||
\(784\) | −6.77547 | − | 1.75869i | −0.241981 | − | 0.0628105i | ||||
\(785\) | −13.3866 | −0.477789 | ||||||||
\(786\) | −1.02224 | − | 1.77058i | −0.0364622 | − | 0.0631545i | ||||
\(787\) | −24.3455 | + | 42.1677i | −0.867824 | + | 1.50312i | −0.00360891 | + | 0.999993i | \(0.501149\pi\) |
−0.864215 | + | 0.503122i | \(0.832185\pi\) | |||||||
\(788\) | −5.39629 | − | 3.11555i | −0.192235 | − | 0.110987i | ||||
\(789\) | −15.1918 | − | 26.3130i | −0.540843 | − | 0.936768i | ||||
\(790\) | 11.3149i | 0.402565i | ||||||||
\(791\) | −19.7414 | + | 8.26790i | −0.701922 | + | 0.293973i | ||||
\(792\) | 3.24252 | − | 0.697189i | 0.115218 | − | 0.0247735i | ||||
\(793\) | −5.27882 | − | 9.14318i | −0.187456 | − | 0.324684i | ||||
\(794\) | 17.6360 | − | 30.5464i | 0.625877 | − | 1.08405i | ||||
\(795\) | 2.16659 | − | 3.75264i | 0.0768409 | − | 0.133092i | ||||
\(796\) | −15.8196 | + | 9.13344i | −0.560711 | + | 0.323726i | ||||
\(797\) | 36.0374i | 1.27651i | 0.769825 | + | 0.638255i | \(0.220343\pi\) | ||||
−0.769825 | + | 0.638255i | \(0.779657\pi\) | |||||||
\(798\) | −6.55132 | − | 4.98635i | −0.231914 | − | 0.176515i | ||||
\(799\) | − | 73.1405i | − | 2.58752i | ||||||
\(800\) | −3.72285 | + | 2.14939i | −0.131623 | + | 0.0759923i | ||||
\(801\) | 7.28049 | + | 4.20339i | 0.257243 | + | 0.148520i | ||||
\(802\) | 7.76494 | + | 4.48309i | 0.274190 | + | 0.158303i | ||||
\(803\) | −24.3816 | + | 22.0573i | −0.860407 | + | 0.778384i | ||||
\(804\) | − | 13.0383i | − | 0.459826i | ||||||
\(805\) | 6.29664 | + | 0.803882i | 0.221927 | + | 0.0283331i | ||||
\(806\) | 2.73559 | 0.0963569 | ||||||||
\(807\) | −9.98686 | − | 17.2977i | −0.351554 | − | 0.608910i | ||||
\(808\) | 5.82166 | + | 3.36113i | 0.204805 | + | 0.118244i | ||||
\(809\) | 25.9030 | + | 14.9551i | 0.910700 | + | 0.525793i | 0.880656 | − | 0.473756i | \(-0.157102\pi\) |
0.0300439 | + | 0.999549i | \(0.490435\pi\) | |||||||
\(810\) | −0.418696 | − | 0.725202i | −0.0147115 | − | 0.0254810i | ||||
\(811\) | 18.1295 | 0.636611 | 0.318306 | − | 0.947988i | \(-0.396886\pi\) | ||||
0.318306 | + | 0.947988i | \(0.396886\pi\) | |||||||
\(812\) | −14.1397 | − | 1.80520i | −0.496207 | − | 0.0633500i | ||||
\(813\) | 1.61528i | 0.0566503i | ||||||||
\(814\) | 24.4518 | + | 27.0284i | 0.857034 | + | 0.947345i | ||||
\(815\) | 0.379899 | + | 0.219335i | 0.0133073 | + | 0.00768296i | ||||
\(816\) | −5.17339 | − | 2.98686i | −0.181105 | − | 0.104561i | ||||
\(817\) | 3.43674 | − | 1.98420i | 0.120236 | − | 0.0694185i | ||||
\(818\) | 35.9524i | 1.25705i | ||||||||
\(819\) | −5.46055 | − | 4.15614i | −0.190807 | − | 0.145227i | ||||
\(820\) | 9.40808i | 0.328544i | ||||||||
\(821\) | −16.8684 | + | 9.73899i | −0.588712 | + | 0.339893i | −0.764588 | − | 0.644519i | \(-0.777058\pi\) |
0.175876 | + | 0.984412i | \(0.443724\pi\) | |||||||
\(822\) | 6.60556 | − | 11.4412i | 0.230395 | − | 0.399057i | ||||
\(823\) | −14.0931 | + | 24.4100i | −0.491255 | + | 0.850879i | −0.999949 | − | 0.0100686i | \(-0.996795\pi\) |
0.508694 | + | 0.860947i | \(0.330128\pi\) | |||||||
\(824\) | −2.03571 | − | 3.52596i | −0.0709174 | − | 0.122833i | ||||
\(825\) | −13.9389 | + | 2.99706i | −0.485289 | + | 0.104344i | ||||
\(826\) | −23.6351 | + | 9.89867i | −0.822372 | + | 0.344419i | ||||
\(827\) | − | 25.7981i | − | 0.897089i | −0.893761 | − | 0.448544i | \(-0.851943\pi\) | ||
0.893761 | − | 0.448544i | \(-0.148057\pi\) | |||||||
\(828\) | −1.43256 | − | 2.48126i | −0.0497848 | − | 0.0862298i | ||||
\(829\) | 31.9716 | + | 18.4588i | 1.11042 | + | 0.641100i | 0.938938 | − | 0.344087i | \(-0.111812\pi\) |
0.171480 | + | 0.985188i | \(0.445145\pi\) | |||||||
\(830\) | −1.25310 | + | 2.17043i | −0.0434958 | + | 0.0753369i | ||||
\(831\) | 2.59035 | + | 4.48663i | 0.0898584 | + | 0.155639i | ||||
\(832\) | −2.59370 | −0.0899205 | ||||||||
\(833\) | 11.1390 | + | 40.3051i | 0.385942 | + | 1.39649i | ||||
\(834\) | 6.16293 | 0.213405 | ||||||||
\(835\) | −12.3679 | + | 7.14060i | −0.428008 | + | 0.247111i | ||||
\(836\) | −9.82304 | − | 3.16619i | −0.339737 | − | 0.109505i | ||||
\(837\) | −0.527351 | + | 0.913399i | −0.0182279 | + | 0.0315717i | ||||
\(838\) | 0.362317 | + | 0.627552i | 0.0125160 | + | 0.0216784i | ||||
\(839\) | 6.71611i | 0.231866i | 0.993257 | + | 0.115933i | \(0.0369858\pi\) | ||||
−0.993257 | + | 0.115933i | \(0.963014\pi\) | |||||||
\(840\) | 0.855860 | + | 2.04354i | 0.0295300 | + | 0.0705090i | ||||
\(841\) | −0.0271771 | −0.000937142 | ||||||||
\(842\) | −3.21662 | + | 1.85712i | −0.110852 | + | 0.0640005i | ||||
\(843\) | 12.5942 | − | 21.8137i | 0.433766 | − | 0.751304i | ||||
\(844\) | 8.87211 | + | 5.12231i | 0.305390 | + | 0.176317i | ||||
\(845\) | −4.54897 | + | 2.62635i | −0.156489 | + | 0.0903492i | ||||
\(846\) | 12.2437 | 0.420947 | ||||||||
\(847\) | −28.3566 | − | 6.54985i | −0.974346 | − | 0.225055i | ||||
\(848\) | 5.17461 | 0.177697 | ||||||||
\(849\) | 19.9475 | − | 11.5167i | 0.684598 | − | 0.395253i | ||||
\(850\) | 22.2393 | + | 12.8398i | 0.762800 | + | 0.440403i | ||||
\(851\) | 15.7429 | − | 27.2674i | 0.539658 | − | 0.934716i | ||||
\(852\) | −12.1932 | + | 7.03977i | −0.417733 | + | 0.241179i | ||||
\(853\) | 39.8993 | 1.36613 | 0.683063 | − | 0.730360i | \(-0.260648\pi\) | ||||
0.683063 | + | 0.730360i | \(0.260648\pi\) | |||||||
\(854\) | −10.6828 | − | 1.36385i | −0.365557 | − | 0.0466701i | ||||
\(855\) | 2.60580i | 0.0891165i | ||||||||
\(856\) | 0.120942 | + | 0.209477i | 0.00413370 | + | 0.00715978i | ||||
\(857\) | 7.85467 | − | 13.6047i | 0.268310 | − | 0.464727i | −0.700115 | − | 0.714030i | \(-0.746868\pi\) |
0.968426 | + | 0.249303i | \(0.0802014\pi\) | |||||||
\(858\) | −8.18754 | − | 2.63903i | −0.279518 | − | 0.0900951i | ||||
\(859\) | 16.6977 | − | 9.64043i | 0.569719 | − | 0.328927i | −0.187318 | − | 0.982299i | \(-0.559980\pi\) |
0.757037 | + | 0.653372i | \(0.226646\pi\) | |||||||
\(860\) | −1.06790 | −0.0364152 | ||||||||
\(861\) | −29.4856 | − | 3.76439i | −1.00487 | − | 0.128290i | ||||
\(862\) | −4.08478 | −0.139128 | ||||||||
\(863\) | −19.0761 | − | 33.0408i | −0.649358 | − | 1.12472i | −0.983276 | − | 0.182119i | \(-0.941704\pi\) |
0.333918 | − | 0.942602i | \(-0.391629\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 5.24802 | + | 3.02995i | 0.178438 | + | 0.103021i | ||||
\(866\) | 15.1555 | + | 26.2500i | 0.515003 | + | 0.892012i | ||||
\(867\) | 18.6853i | 0.634587i | ||||||||
\(868\) | 1.69005 | − | 2.22048i | 0.0573640 | − | 0.0753679i | ||||
\(869\) | −43.8131 | + | 9.42046i | −1.48626 | + | 0.319567i | ||||
\(870\) | 2.25580 | + | 3.90716i | 0.0764788 | + | 0.132465i | ||||
\(871\) | −16.9088 | + | 29.2868i | −0.572932 | + | 0.992347i | ||||
\(872\) | 8.76259 | − | 15.1773i | 0.296739 | − | 0.513967i | ||||
\(873\) | −0.680809 | + | 0.393065i | −0.0230419 | + | 0.0133032i | ||||
\(874\) | 8.91569i | 0.301578i | ||||||||
\(875\) | −7.95845 | − | 19.0025i | −0.269045 | − | 0.642401i | ||||
\(876\) | 9.91318i | 0.334935i | ||||||||
\(877\) | 7.92511 | − | 4.57556i | 0.267612 | − | 0.154506i | −0.360190 | − | 0.932879i | \(-0.617288\pi\) |
0.627802 | + | 0.778373i | \(0.283955\pi\) | |||||||
\(878\) | 10.9208 | + | 6.30512i | 0.368559 | + | 0.212787i | ||||
\(879\) | 3.62064 | + | 2.09038i | 0.122121 | + | 0.0705067i | ||||
\(880\) | 1.86323 | + | 2.05957i | 0.0628095 | + | 0.0694282i | ||||
\(881\) | − | 47.7019i | − | 1.60712i | −0.595225 | − | 0.803559i | \(-0.702937\pi\) | ||
0.595225 | − | 0.803559i | \(-0.297063\pi\) | |||||||
\(882\) | −6.74708 | + | 1.86466i | −0.227186 | + | 0.0627864i | ||||
\(883\) | 43.7932 | 1.47376 | 0.736879 | − | 0.676025i | \(-0.236299\pi\) | ||||
0.736879 | + | 0.676025i | \(0.236299\pi\) | |||||||
\(884\) | 7.74703 | + | 13.4183i | 0.260561 | + | 0.451305i | ||||
\(885\) | 7.02363 | + | 4.05510i | 0.236097 | + | 0.136311i | ||||
\(886\) | 13.1958 | + | 7.61859i | 0.443321 | + | 0.255952i | ||||
\(887\) | −25.2896 | − | 43.8029i | −0.849142 | − | 1.47076i | −0.881975 | − | 0.471296i | \(-0.843787\pi\) |
0.0328338 | − | 0.999461i | \(-0.489547\pi\) | |||||||
\(888\) | 10.9893 | 0.368778 | ||||||||
\(889\) | −12.3989 | − | 29.6049i | −0.415845 | − | 0.992918i | ||||
\(890\) | 7.03977i | 0.235974i | ||||||||
\(891\) | 2.45951 | − | 2.22504i | 0.0823967 | − | 0.0745417i | ||||
\(892\) | 13.5676 | + | 7.83326i | 0.454277 | + | 0.262277i | ||||
\(893\) | −32.9956 | − | 19.0500i | −1.10416 | − | 0.637485i | ||||
\(894\) | 3.80788 | − | 2.19848i | 0.127355 | − | 0.0735282i | ||||
\(895\) | 6.75470i | 0.225785i | ||||||||
\(896\) | −1.60239 | + | 2.10531i | −0.0535323 | + | 0.0703335i | ||||
\(897\) | 7.43126i | 0.248123i | ||||||||
\(898\) | −27.9536 | + | 16.1390i | −0.932823 | + | 0.538566i | ||||
\(899\) | 2.84120 | − | 4.92111i | 0.0947595 | − | 0.164128i | ||||
\(900\) | −2.14939 | + | 3.72285i | −0.0716463 | + | 0.124095i | ||||
\(901\) | −15.4558 | − | 26.7703i | −0.514908 | − | 0.891847i | ||||
\(902\) | −36.4296 | + | 7.83291i | −1.21297 | + | 0.260807i | ||||
\(903\) | 0.427293 | − | 3.34689i | 0.0142194 | − | 0.111378i | ||||
\(904\) | 8.08949i | 0.269053i | ||||||||
\(905\) | −2.34912 | − | 4.06879i | −0.0780873 | − | 0.135251i | ||||
\(906\) | −8.86874 | − | 5.12037i | −0.294644 | − | 0.170113i | ||||
\(907\) | 28.9344 | − | 50.1159i | 0.960752 | − | 1.66407i | 0.240132 | − | 0.970740i | \(-0.422809\pi\) |
0.720620 | − | 0.693330i | \(-0.243857\pi\) | |||||||
\(908\) | −7.86025 | − | 13.6143i | −0.260851 | − | 0.451808i | ||||
\(909\) | 6.72227 | 0.222964 | ||||||||
\(910\) | 0.727731 | − | 5.70016i | 0.0241241 | − | 0.188959i | ||||
\(911\) | 25.4860 | 0.844389 | 0.422195 | − | 0.906505i | \(-0.361260\pi\) | ||||
0.422195 | + | 0.906505i | \(0.361260\pi\) | |||||||
\(912\) | −2.69491 | + | 1.55590i | −0.0892372 | + | 0.0515211i | ||||
\(913\) | −9.44758 | − | 3.04517i | −0.312669 | − | 0.100780i | ||||
\(914\) | 15.1724 | − | 26.2793i | 0.501857 | − | 0.869242i | ||||
\(915\) | 1.70429 | + | 2.95192i | 0.0563422 | + | 0.0975876i | ||||
\(916\) | 2.50417i | 0.0827400i | ||||||||
\(917\) | 4.30428 | + | 3.27608i | 0.142140 | + | 0.108186i | ||||
\(918\) | −5.97372 | −0.197162 | ||||||||
\(919\) | 11.2495 | − | 6.49491i | 0.371087 | − | 0.214247i | −0.302846 | − | 0.953039i | \(-0.597937\pi\) |
0.673933 | + | 0.738792i | \(0.264604\pi\) | |||||||
\(920\) | 1.19961 | − | 2.07779i | 0.0395500 | − | 0.0685026i | ||||
\(921\) | −8.71712 | − | 5.03283i | −0.287239 | − | 0.165837i | ||||
\(922\) | −4.16907 | + | 2.40701i | −0.137301 | + | 0.0792707i | ||||
\(923\) | 36.5182 | 1.20201 | ||||||||
\(924\) | −7.20038 | + | 5.01543i | −0.236875 | + | 0.164996i | ||||
\(925\) | −47.2407 | −1.55327 | ||||||||
\(926\) | 28.6825 | − | 16.5598i | 0.942564 | − | 0.544190i | ||||
\(927\) | −3.52596 | − | 2.03571i | −0.115808 | − | 0.0668616i | ||||
\(928\) | −2.69384 | + | 4.66587i | −0.0884298 | + | 0.153165i | ||||
\(929\) | −18.8834 | + | 10.9024i | −0.619545 | + | 0.357695i | −0.776692 | − | 0.629881i | \(-0.783104\pi\) |
0.157147 | + | 0.987575i | \(0.449770\pi\) | |||||||
\(930\) | −0.883199 | −0.0289612 | ||||||||
\(931\) | 21.0840 | + | 5.47272i | 0.690999 | + | 0.179361i | ||||
\(932\) | 0.0553161i | 0.00181194i | ||||||||
\(933\) | −0.714858 | − | 1.23817i | −0.0234034 | − | 0.0405359i | ||||
\(934\) | 7.19328 | − | 12.4591i | 0.235371 | − | 0.407675i | ||||
\(935\) | 5.08976 | − | 15.7909i | 0.166453 | − | 0.516417i | ||||
\(936\) | −2.24621 | + | 1.29685i | −0.0734198 | + | 0.0423889i | ||||
\(937\) | 31.2647 | 1.02137 | 0.510686 | − | 0.859767i | \(-0.329391\pi\) | ||||
0.510686 | + | 0.859767i | \(0.329391\pi\) | |||||||
\(938\) | 13.3259 | + | 31.8183i | 0.435105 | + | 1.03890i | ||||
\(939\) | −30.3930 | −0.991839 | ||||||||
\(940\) | 5.12639 | + | 8.87916i | 0.167204 | + | 0.289606i | ||||
\(941\) | 9.38779 | − | 16.2601i | 0.306033 | − | 0.530065i | −0.671458 | − | 0.741043i | \(-0.734332\pi\) |
0.977491 | + | 0.210978i | \(0.0676648\pi\) | |||||||
\(942\) | −13.8444 | − | 7.99304i | −0.451074 | − | 0.260427i | ||||
\(943\) | 16.0947 | + | 27.8769i | 0.524117 | + | 0.907797i | ||||
\(944\) | 9.68506i | 0.315222i | ||||||||
\(945\) | 1.76297 | + | 1.34183i | 0.0573494 | + | 0.0436498i | ||||
\(946\) | −0.889107 | − | 4.13510i | −0.0289074 | − | 0.134444i | ||||
\(947\) | 19.7729 | + | 34.2477i | 0.642534 | + | 1.11290i | 0.984865 | + | 0.173323i | \(0.0554503\pi\) |
−0.342331 | + | 0.939580i | \(0.611216\pi\) | |||||||
\(948\) | −6.75603 | + | 11.7018i | −0.219426 | + | 0.380056i | ||||
\(949\) | 12.8559 | − | 22.2671i | 0.417321 | − | 0.722822i | ||||
\(950\) | 11.5848 | − | 6.68848i | 0.375860 | − | 0.217003i | ||||
\(951\) | 10.8522i | 0.351907i | ||||||||
\(952\) | 15.6777 | + | 2.00155i | 0.508118 | + | 0.0648707i | ||||
\(953\) | − | 2.98673i | − | 0.0967495i | −0.998829 | − | 0.0483748i | \(-0.984596\pi\) | ||
0.998829 | − | 0.0483748i | \(-0.0154042\pi\) | |||||||
\(954\) | 4.48134 | − | 2.58730i | 0.145089 | − | 0.0837671i | ||||
\(955\) | −8.54587 | − | 4.93396i | −0.276538 | − | 0.159659i | ||||
\(956\) | 4.97501 | + | 2.87233i | 0.160903 | + | 0.0928976i | ||||
\(957\) | −13.2511 | + | 11.9878i | −0.428346 | + | 0.387512i | ||||
\(958\) | − | 6.47208i | − | 0.209104i | ||||||
\(959\) | −4.42651 | + | 34.6719i | −0.142940 | + | 1.11961i | ||||
\(960\) | 0.837391 | 0.0270267 | ||||||||
\(961\) | −14.9438 | − | 25.8834i | −0.482058 | − | 0.834949i | ||||
\(962\) | −24.6844 | − | 14.2516i | −0.795858 | − | 0.459489i | ||||
\(963\) | 0.209477 | + | 0.120942i | 0.00675030 | + | 0.00389729i | ||||
\(964\) | 3.67123 | + | 6.35875i | 0.118242 | + | 0.204802i | ||||
\(965\) | 15.1548 | 0.487850 | ||||||||
\(966\) | 6.03195 | + | 4.59104i | 0.194075 | + | 0.147714i | ||||
\(967\) | 3.61655i | 0.116300i | 0.998308 | + | 0.0581502i | \(0.0185202\pi\) | ||||
−0.998308 | + | 0.0581502i | \(0.981480\pi\) | |||||||
\(968\) | −6.42373 | + | 8.92949i | −0.206466 | + | 0.287005i | ||||
\(969\) | 16.0986 | + | 9.29454i | 0.517162 | + | 0.298584i | ||||
\(970\) | −0.570104 | − | 0.329150i | −0.0183049 | − | 0.0105684i | ||||
\(971\) | 23.9499 | − | 13.8275i | 0.768587 | − | 0.443744i | −0.0637831 | − | 0.997964i | \(-0.520317\pi\) |
0.832370 | + | 0.554220i | \(0.186983\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | −15.0398 | + | 6.29886i | −0.482155 | + | 0.201932i | ||||
\(974\) | 5.28096i | 0.169213i | ||||||||
\(975\) | 9.65597 | − | 5.57488i | 0.309239 | − | 0.178539i | ||||
\(976\) | −2.03524 | + | 3.52514i | −0.0651465 | + | 0.112837i | ||||
\(977\) | −17.4175 | + | 30.1679i | −0.557234 | + | 0.965158i | 0.440492 | + | 0.897757i | \(0.354804\pi\) |
−0.997726 | + | 0.0674010i | \(0.978529\pi\) | |||||||
\(978\) | 0.261926 | + | 0.453669i | 0.00837547 | + | 0.0145067i | ||||
\(979\) | −27.2591 | + | 5.86112i | −0.871206 | + | 0.187322i | ||||
\(980\) | −4.17723 | − | 4.11227i | −0.133437 | − | 0.131362i | ||||
\(981\) | − | 17.5252i | − | 0.559536i | ||||||
\(982\) | −5.68167 | − | 9.84094i | −0.181309 | − | 0.314037i | ||||
\(983\) | 19.2919 | + | 11.1382i | 0.615317 | + | 0.355254i | 0.775044 | − | 0.631908i | \(-0.217728\pi\) |
−0.159726 | + | 0.987161i | \(0.551061\pi\) | |||||||
\(984\) | −5.61749 | + | 9.72978i | −0.179079 | + | 0.310174i | ||||
\(985\) | −2.60894 | − | 4.51881i | −0.0831276 | − | 0.143981i | ||||
\(986\) | 32.1845 | 1.02496 | ||||||||
\(987\) | −29.8792 | + | 12.5137i | −0.951065 | + | 0.398317i | ||||
\(988\) | 8.07111 | 0.256776 | ||||||||
\(989\) | −3.16429 | + | 1.82690i | −0.100619 | + | 0.0580921i | ||||
\(990\) | 2.64339 | + | 0.852026i | 0.0840125 | + | 0.0270792i | ||||
\(991\) | −27.3088 | + | 47.3002i | −0.867493 | + | 1.50254i | −0.00294265 | + | 0.999996i | \(0.500937\pi\) |
−0.864550 | + | 0.502546i | \(0.832397\pi\) | |||||||
\(992\) | −0.527351 | − | 0.913399i | −0.0167434 | − | 0.0290005i | ||||
\(993\) | − | 12.9149i | − | 0.409843i | ||||||
\(994\) | 22.5610 | − | 29.6418i | 0.715591 | − | 0.940181i | ||||
\(995\) | −15.2965 | −0.484933 | ||||||||
\(996\) | −2.59190 | + | 1.49643i | −0.0821274 | + | 0.0474163i | ||||
\(997\) | 8.45911 | − | 14.6516i | 0.267903 | − | 0.464021i | −0.700417 | − | 0.713734i | \(-0.747003\pi\) |
0.968320 | + | 0.249712i | \(0.0803361\pi\) | |||||||
\(998\) | −25.2638 | − | 14.5860i | −0.799710 | − | 0.461713i | ||||
\(999\) | 9.51705 | − | 5.49467i | 0.301106 | − | 0.173844i |
(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 | 462.2.p.b.241.2 | yes | 16 | |
3.2 | odd | 2 | 1386.2.bk.b.703.7 | 16 | |||
7.3 | odd | 6 | 3234.2.e.a.2155.4 | 16 | |||
7.4 | even | 3 | 3234.2.e.b.2155.5 | 16 | |||
7.5 | odd | 6 | 462.2.p.a.439.6 | yes | 16 | ||
11.10 | odd | 2 | 462.2.p.a.241.6 | ✓ | 16 | ||
21.5 | even | 6 | 1386.2.bk.a.901.3 | 16 | |||
33.32 | even | 2 | 1386.2.bk.a.703.3 | 16 | |||
77.10 | even | 6 | 3234.2.e.b.2155.12 | 16 | |||
77.32 | odd | 6 | 3234.2.e.a.2155.13 | 16 | |||
77.54 | even | 6 | inner | 462.2.p.b.439.2 | yes | 16 | |
231.131 | odd | 6 | 1386.2.bk.b.901.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.p.a.241.6 | ✓ | 16 | 11.10 | odd | 2 | ||
462.2.p.a.439.6 | yes | 16 | 7.5 | odd | 6 | ||
462.2.p.b.241.2 | yes | 16 | 1.1 | even | 1 | trivial | |
462.2.p.b.439.2 | yes | 16 | 77.54 | even | 6 | inner | |
1386.2.bk.a.703.3 | 16 | 33.32 | even | 2 | |||
1386.2.bk.a.901.3 | 16 | 21.5 | even | 6 | |||
1386.2.bk.b.703.7 | 16 | 3.2 | odd | 2 | |||
1386.2.bk.b.901.7 | 16 | 231.131 | odd | 6 | |||
3234.2.e.a.2155.4 | 16 | 7.3 | odd | 6 | |||
3234.2.e.a.2155.13 | 16 | 77.32 | odd | 6 | |||
3234.2.e.b.2155.5 | 16 | 7.4 | even | 3 | |||
3234.2.e.b.2155.12 | 16 | 77.10 | even | 6 |