Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(369,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.c (of order \(2\), degree \(1\), 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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 19x^{8} + 103x^{6} + 210x^{4} + 140x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.5 | ||
Root | \(-0.377861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.369 |
Dual form | 370.2.c.b.369.6 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | − | 0.377861i | − | 0.218158i | −0.994033 | − | 0.109079i | \(-0.965210\pi\) | ||
0.994033 | − | 0.109079i | \(-0.0347902\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.04797 | + | 1.97529i | −0.468665 | + | 0.883376i | ||||
\(6\) | − | 0.377861i | − | 0.154261i | ||||||
\(7\) | − | 0.631751i | − | 0.238779i | −0.992847 | − | 0.119390i | \(-0.961906\pi\) | ||
0.992847 | − | 0.119390i | \(-0.0380938\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.85722 | 0.952407 | ||||||||
\(10\) | −1.04797 | + | 1.97529i | −0.331396 | + | 0.624641i | ||||
\(11\) | 1.24789 | 0.376253 | 0.188126 | − | 0.982145i | \(-0.439759\pi\) | ||||
0.188126 | + | 0.982145i | \(0.439759\pi\) | |||||||
\(12\) | − | 0.377861i | − | 0.109079i | ||||||
\(13\) | 3.34999 | 0.929120 | 0.464560 | − | 0.885542i | \(-0.346212\pi\) | ||||
0.464560 | + | 0.885542i | \(0.346212\pi\) | |||||||
\(14\) | − | 0.631751i | − | 0.168843i | ||||||
\(15\) | 0.746385 | + | 0.395986i | 0.192716 | + | 0.102243i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.10511 | 0.753100 | 0.376550 | − | 0.926396i | \(-0.377110\pi\) | ||||
0.376550 | + | 0.926396i | \(0.377110\pi\) | |||||||
\(18\) | 2.85722 | 0.673453 | ||||||||
\(19\) | 5.97327i | 1.37036i | 0.728373 | + | 0.685181i | \(0.240277\pi\) | ||||
−0.728373 | + | 0.685181i | \(0.759723\pi\) | |||||||
\(20\) | −1.04797 | + | 1.97529i | −0.234333 | + | 0.441688i | ||||
\(21\) | −0.238714 | −0.0520917 | ||||||||
\(22\) | 1.24789 | 0.266051 | ||||||||
\(23\) | −7.60706 | −1.58618 | −0.793090 | − | 0.609104i | \(-0.791529\pi\) | ||||
−0.793090 | + | 0.609104i | \(0.791529\pi\) | |||||||
\(24\) | − | 0.377861i | − | 0.0771306i | ||||||
\(25\) | −2.80353 | − | 4.14008i | −0.560706 | − | 0.828015i | ||||
\(26\) | 3.34999 | 0.656987 | ||||||||
\(27\) | − | 2.21322i | − | 0.425934i | ||||||
\(28\) | − | 0.631751i | − | 0.119390i | ||||||
\(29\) | − | 9.57629i | − | 1.77827i | −0.457643 | − | 0.889136i | \(-0.651306\pi\) | ||
0.457643 | − | 0.889136i | \(-0.348694\pi\) | |||||||
\(30\) | 0.746385 | + | 0.395986i | 0.136271 | + | 0.0722969i | ||||
\(31\) | 7.26707i | 1.30520i | 0.757701 | + | 0.652602i | \(0.226323\pi\) | ||||
−0.757701 | + | 0.652602i | \(0.773677\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | − | 0.471529i | − | 0.0820827i | ||||||
\(34\) | 3.10511 | 0.532522 | ||||||||
\(35\) | 1.24789 | + | 0.662054i | 0.210932 | + | 0.111908i | ||||
\(36\) | 2.85722 | 0.476203 | ||||||||
\(37\) | −4.10511 | − | 4.48866i | −0.674876 | − | 0.737931i | ||||
\(38\) | 5.97327i | 0.968992i | ||||||||
\(39\) | − | 1.26583i | − | 0.202695i | ||||||
\(40\) | −1.04797 | + | 1.97529i | −0.165698 | + | 0.312321i | ||||
\(41\) | −8.45510 | −1.32046 | −0.660232 | − | 0.751061i | \(-0.729542\pi\) | ||||
−0.660232 | + | 0.751061i | \(0.729542\pi\) | |||||||
\(42\) | −0.238714 | −0.0368344 | ||||||||
\(43\) | −4.86640 | −0.742119 | −0.371059 | − | 0.928609i | \(-0.621005\pi\) | ||||
−0.371059 | + | 0.928609i | \(0.621005\pi\) | |||||||
\(44\) | 1.24789 | 0.188126 | ||||||||
\(45\) | −2.99427 | + | 5.64384i | −0.446360 | + | 0.841333i | ||||
\(46\) | −7.60706 | −1.12160 | ||||||||
\(47\) | − | 13.1187i | − | 1.91356i | −0.290815 | − | 0.956779i | \(-0.593926\pi\) | ||
0.290815 | − | 0.956779i | \(-0.406074\pi\) | |||||||
\(48\) | − | 0.377861i | − | 0.0545396i | ||||||
\(49\) | 6.60089 | 0.942984 | ||||||||
\(50\) | −2.80353 | − | 4.14008i | −0.396479 | − | 0.585495i | ||||
\(51\) | − | 1.17330i | − | 0.164295i | ||||||
\(52\) | 3.34999 | 0.464560 | ||||||||
\(53\) | 7.17340i | 0.985343i | 0.870215 | + | 0.492671i | \(0.163980\pi\) | ||||
−0.870215 | + | 0.492671i | \(0.836020\pi\) | |||||||
\(54\) | − | 2.21322i | − | 0.301181i | ||||||
\(55\) | −1.30775 | + | 2.46494i | −0.176337 | + | 0.332373i | ||||
\(56\) | − | 0.631751i | − | 0.0844213i | ||||||
\(57\) | 2.25707 | 0.298956 | ||||||||
\(58\) | − | 9.57629i | − | 1.25743i | ||||||
\(59\) | − | 4.36469i | − | 0.568234i | −0.958790 | − | 0.284117i | \(-0.908300\pi\) | ||
0.958790 | − | 0.284117i | \(-0.0917004\pi\) | |||||||
\(60\) | 0.746385 | + | 0.395986i | 0.0963579 | + | 0.0511216i | ||||
\(61\) | − | 2.14666i | − | 0.274852i | −0.990512 | − | 0.137426i | \(-0.956117\pi\) | ||
0.990512 | − | 0.137426i | \(-0.0438829\pi\) | |||||||
\(62\) | 7.26707i | 0.922919i | ||||||||
\(63\) | − | 1.80505i | − | 0.227415i | ||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.51068 | + | 6.61720i | −0.435446 | + | 0.820762i | ||||
\(66\) | − | 0.471529i | − | 0.0580412i | ||||||
\(67\) | 11.3451i | 1.38602i | 0.720926 | + | 0.693012i | \(0.243717\pi\) | ||||
−0.720926 | + | 0.693012i | \(0.756283\pi\) | |||||||
\(68\) | 3.10511 | 0.376550 | ||||||||
\(69\) | 2.87441i | 0.346038i | ||||||||
\(70\) | 1.24789 | + | 0.662054i | 0.149151 | + | 0.0791306i | ||||
\(71\) | −12.7183 | −1.50939 | −0.754694 | − | 0.656077i | \(-0.772215\pi\) | ||||
−0.754694 | + | 0.656077i | \(0.772215\pi\) | |||||||
\(72\) | 2.85722 | 0.336727 | ||||||||
\(73\) | 4.45836i | 0.521811i | 0.965364 | + | 0.260906i | \(0.0840211\pi\) | ||||
−0.965364 | + | 0.260906i | \(0.915979\pi\) | |||||||
\(74\) | −4.10511 | − | 4.48866i | −0.477209 | − | 0.521796i | ||||
\(75\) | −1.56437 | + | 1.05934i | −0.180638 | + | 0.122323i | ||||
\(76\) | 5.97327i | 0.685181i | ||||||||
\(77\) | − | 0.788355i | − | 0.0898414i | ||||||
\(78\) | − | 1.26583i | − | 0.143327i | ||||||
\(79\) | − | 8.78679i | − | 0.988592i | −0.869294 | − | 0.494296i | \(-0.835426\pi\) | ||
0.869294 | − | 0.494296i | \(-0.164574\pi\) | |||||||
\(80\) | −1.04797 | + | 1.97529i | −0.117166 | + | 0.220844i | ||||
\(81\) | 7.73537 | 0.859486 | ||||||||
\(82\) | −8.45510 | −0.933710 | ||||||||
\(83\) | 6.63185i | 0.727941i | 0.931411 | + | 0.363970i | \(0.118579\pi\) | ||||
−0.931411 | + | 0.363970i | \(0.881421\pi\) | |||||||
\(84\) | −0.238714 | −0.0260458 | ||||||||
\(85\) | −3.25406 | + | 6.13349i | −0.352952 | + | 0.665270i | ||||
\(86\) | −4.86640 | −0.524757 | ||||||||
\(87\) | −3.61851 | −0.387945 | ||||||||
\(88\) | 1.24789 | 0.133026 | ||||||||
\(89\) | − | 13.7784i | − | 1.46051i | −0.683175 | − | 0.730255i | \(-0.739401\pi\) | ||
0.683175 | − | 0.730255i | \(-0.260599\pi\) | |||||||
\(90\) | −2.99427 | + | 5.64384i | −0.315624 | + | 0.594912i | ||||
\(91\) | − | 2.11636i | − | 0.221855i | ||||||
\(92\) | −7.60706 | −0.793090 | ||||||||
\(93\) | 2.74594 | 0.284741 | ||||||||
\(94\) | − | 13.1187i | − | 1.35309i | ||||||
\(95\) | −11.7989 | − | 6.25979i | −1.21054 | − | 0.642241i | ||||
\(96\) | − | 0.377861i | − | 0.0385653i | ||||||
\(97\) | 11.0583 | 1.12280 | 0.561398 | − | 0.827546i | \(-0.310264\pi\) | ||||
0.561398 | + | 0.827546i | \(0.310264\pi\) | |||||||
\(98\) | 6.60089 | 0.666791 | ||||||||
\(99\) | 3.56550 | 0.358346 | ||||||||
\(100\) | −2.80353 | − | 4.14008i | −0.280353 | − | 0.414008i | ||||
\(101\) | 8.65314 | 0.861019 | 0.430510 | − | 0.902586i | \(-0.358334\pi\) | ||||
0.430510 | + | 0.902586i | \(0.358334\pi\) | |||||||
\(102\) | − | 1.17330i | − | 0.116174i | ||||||
\(103\) | −4.57336 | −0.450627 | −0.225313 | − | 0.974286i | \(-0.572341\pi\) | ||||
−0.225313 | + | 0.974286i | \(0.572341\pi\) | |||||||
\(104\) | 3.34999 | 0.328494 | ||||||||
\(105\) | 0.250165 | − | 0.471529i | 0.0244136 | − | 0.0460165i | ||||
\(106\) | 7.17340i | 0.696743i | ||||||||
\(107\) | 11.4715i | 1.10900i | 0.832185 | + | 0.554498i | \(0.187090\pi\) | ||||
−0.832185 | + | 0.554498i | \(0.812910\pi\) | |||||||
\(108\) | − | 2.21322i | − | 0.212967i | ||||||
\(109\) | 0.727748i | 0.0697057i | 0.999392 | + | 0.0348528i | \(0.0110962\pi\) | ||||
−0.999392 | + | 0.0348528i | \(0.988904\pi\) | |||||||
\(110\) | −1.30775 | + | 2.46494i | −0.124689 | + | 0.235023i | ||||
\(111\) | −1.69609 | + | 1.55116i | −0.160986 | + | 0.147230i | ||||
\(112\) | − | 0.631751i | − | 0.0596948i | ||||||
\(113\) | −17.9970 | −1.69301 | −0.846506 | − | 0.532379i | \(-0.821298\pi\) | ||||
−0.846506 | + | 0.532379i | \(0.821298\pi\) | |||||||
\(114\) | 2.25707 | 0.211394 | ||||||||
\(115\) | 7.97195 | − | 15.0261i | 0.743388 | − | 1.40119i | ||||
\(116\) | − | 9.57629i | − | 0.889136i | ||||||
\(117\) | 9.57166 | 0.884901 | ||||||||
\(118\) | − | 4.36469i | − | 0.401802i | ||||||
\(119\) | − | 1.96166i | − | 0.179825i | ||||||
\(120\) | 0.746385 | + | 0.395986i | 0.0681353 | + | 0.0361484i | ||||
\(121\) | −9.44277 | −0.858434 | ||||||||
\(122\) | − | 2.14666i | − | 0.194350i | ||||||
\(123\) | 3.19485i | 0.288070i | ||||||||
\(124\) | 7.26707i | 0.652602i | ||||||||
\(125\) | 11.1159 | − | 1.19911i | 0.994232 | − | 0.107252i | ||||
\(126\) | − | 1.80505i | − | 0.160807i | ||||||
\(127\) | − | 15.4830i | − | 1.37389i | −0.726707 | − | 0.686947i | \(-0.758950\pi\) | ||
0.726707 | − | 0.686947i | \(-0.241050\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.83882i | 0.161899i | ||||||||
\(130\) | −3.51068 | + | 6.61720i | −0.307907 | + | 0.580367i | ||||
\(131\) | − | 6.22121i | − | 0.543550i | −0.962361 | − | 0.271775i | \(-0.912389\pi\) | ||
0.962361 | − | 0.271775i | \(-0.0876106\pi\) | |||||||
\(132\) | − | 0.471529i | − | 0.0410413i | ||||||
\(133\) | 3.77362 | 0.327214 | ||||||||
\(134\) | 11.3451i | 0.980066i | ||||||||
\(135\) | 4.37174 | + | 2.31938i | 0.376260 | + | 0.199620i | ||||
\(136\) | 3.10511 | 0.266261 | ||||||||
\(137\) | 14.1258i | 1.20685i | 0.797419 | + | 0.603426i | \(0.206198\pi\) | ||||
−0.797419 | + | 0.603426i | \(0.793802\pi\) | |||||||
\(138\) | 2.87441i | 0.244686i | ||||||||
\(139\) | 8.43675 | 0.715596 | 0.357798 | − | 0.933799i | \(-0.383528\pi\) | ||||
0.357798 | + | 0.933799i | \(0.383528\pi\) | |||||||
\(140\) | 1.24789 | + | 0.662054i | 0.105466 | + | 0.0559538i | ||||
\(141\) | −4.95705 | −0.417459 | ||||||||
\(142\) | −12.7183 | −1.06730 | ||||||||
\(143\) | 4.18042 | 0.349584 | ||||||||
\(144\) | 2.85722 | 0.238102 | ||||||||
\(145\) | 18.9159 | + | 10.0356i | 1.57088 | + | 0.833414i | ||||
\(146\) | 4.45836i | 0.368976i | ||||||||
\(147\) | − | 2.49422i | − | 0.205720i | ||||||
\(148\) | −4.10511 | − | 4.48866i | −0.337438 | − | 0.368966i | ||||
\(149\) | 13.6447 | 1.11782 | 0.558909 | − | 0.829229i | \(-0.311220\pi\) | ||||
0.558909 | + | 0.829229i | \(0.311220\pi\) | |||||||
\(150\) | −1.56437 | + | 1.05934i | −0.127731 | + | 0.0864951i | ||||
\(151\) | −3.17741 | −0.258574 | −0.129287 | − | 0.991607i | \(-0.541269\pi\) | ||||
−0.129287 | + | 0.991607i | \(0.541269\pi\) | |||||||
\(152\) | 5.97327i | 0.484496i | ||||||||
\(153\) | 8.87199 | 0.717258 | ||||||||
\(154\) | − | 0.788355i | − | 0.0635275i | ||||||
\(155\) | −14.3546 | − | 7.61566i | −1.15299 | − | 0.611704i | ||||
\(156\) | − | 1.26583i | − | 0.101348i | ||||||
\(157\) | − | 0.215310i | − | 0.0171836i | −0.999963 | − | 0.00859180i | \(-0.997265\pi\) | ||
0.999963 | − | 0.00859180i | \(-0.00273489\pi\) | |||||||
\(158\) | − | 8.78679i | − | 0.699040i | ||||||
\(159\) | 2.71055 | 0.214961 | ||||||||
\(160\) | −1.04797 | + | 1.97529i | −0.0828491 | + | 0.156160i | ||||
\(161\) | 4.80576i | 0.378747i | ||||||||
\(162\) | 7.73537 | 0.607748 | ||||||||
\(163\) | 1.66609 | 0.130498 | 0.0652490 | − | 0.997869i | \(-0.479216\pi\) | ||||
0.0652490 | + | 0.997869i | \(0.479216\pi\) | |||||||
\(164\) | −8.45510 | −0.660232 | ||||||||
\(165\) | 0.931406 | + | 0.494147i | 0.0725099 | + | 0.0384693i | ||||
\(166\) | 6.63185i | 0.514732i | ||||||||
\(167\) | −5.92242 | −0.458290 | −0.229145 | − | 0.973392i | \(-0.573593\pi\) | ||||
−0.229145 | + | 0.973392i | \(0.573593\pi\) | |||||||
\(168\) | −0.238714 | −0.0184172 | ||||||||
\(169\) | −1.77756 | −0.136736 | ||||||||
\(170\) | −3.25406 | + | 6.13349i | −0.249575 | + | 0.470417i | ||||
\(171\) | 17.0669i | 1.30514i | ||||||||
\(172\) | −4.86640 | −0.371059 | ||||||||
\(173\) | 2.88008i | 0.218968i | 0.993989 | + | 0.109484i | \(0.0349199\pi\) | ||||
−0.993989 | + | 0.109484i | \(0.965080\pi\) | |||||||
\(174\) | −3.61851 | −0.274318 | ||||||||
\(175\) | −2.61550 | + | 1.77113i | −0.197713 | + | 0.133885i | ||||
\(176\) | 1.24789 | 0.0940632 | ||||||||
\(177\) | −1.64925 | −0.123965 | ||||||||
\(178\) | − | 13.7784i | − | 1.03274i | ||||||
\(179\) | 4.46182i | 0.333492i | 0.986000 | + | 0.166746i | \(0.0533260\pi\) | ||||
−0.986000 | + | 0.166746i | \(0.946674\pi\) | |||||||
\(180\) | −2.99427 | + | 5.64384i | −0.223180 | + | 0.420667i | ||||
\(181\) | 3.93480 | 0.292472 | 0.146236 | − | 0.989250i | \(-0.453284\pi\) | ||||
0.146236 | + | 0.989250i | \(0.453284\pi\) | |||||||
\(182\) | − | 2.11636i | − | 0.156875i | ||||||
\(183\) | −0.811140 | −0.0599612 | ||||||||
\(184\) | −7.60706 | −0.560800 | ||||||||
\(185\) | 13.1684 | − | 3.40481i | 0.968161 | − | 0.250326i | ||||
\(186\) | 2.74594 | 0.201342 | ||||||||
\(187\) | 3.87484 | 0.283356 | ||||||||
\(188\) | − | 13.1187i | − | 0.956779i | ||||||
\(189\) | −1.39820 | −0.101704 | ||||||||
\(190\) | −11.7989 | − | 6.25979i | −0.855984 | − | 0.454133i | ||||
\(191\) | 7.76296i | 0.561708i | 0.959751 | + | 0.280854i | \(0.0906177\pi\) | ||||
−0.959751 | + | 0.280854i | \(0.909382\pi\) | |||||||
\(192\) | − | 0.377861i | − | 0.0272698i | ||||||
\(193\) | 3.49189 | 0.251352 | 0.125676 | − | 0.992071i | \(-0.459890\pi\) | ||||
0.125676 | + | 0.992071i | \(0.459890\pi\) | |||||||
\(194\) | 11.0583 | 0.793937 | ||||||||
\(195\) | 2.50038 | + | 1.32655i | 0.179056 | + | 0.0949962i | ||||
\(196\) | 6.60089 | 0.471492 | ||||||||
\(197\) | − | 1.07617i | − | 0.0766736i | −0.999265 | − | 0.0383368i | \(-0.987794\pi\) | ||
0.999265 | − | 0.0383368i | \(-0.0122060\pi\) | |||||||
\(198\) | 3.56550 | 0.253389 | ||||||||
\(199\) | − | 5.71343i | − | 0.405014i | −0.979281 | − | 0.202507i | \(-0.935091\pi\) | ||
0.979281 | − | 0.202507i | \(-0.0649090\pi\) | |||||||
\(200\) | −2.80353 | − | 4.14008i | −0.198239 | − | 0.292748i | ||||
\(201\) | 4.28687 | 0.302372 | ||||||||
\(202\) | 8.65314 | 0.608833 | ||||||||
\(203\) | −6.04983 | −0.424615 | ||||||||
\(204\) | − | 1.17330i | − | 0.0821475i | ||||||
\(205\) | 8.86067 | − | 16.7013i | 0.618856 | − | 1.16647i | ||||
\(206\) | −4.57336 | −0.318641 | ||||||||
\(207\) | −21.7350 | −1.51069 | ||||||||
\(208\) | 3.34999 | 0.232280 | ||||||||
\(209\) | 7.45398i | 0.515603i | ||||||||
\(210\) | 0.250165 | − | 0.471529i | 0.0172630 | − | 0.0325386i | ||||
\(211\) | 22.8397 | 1.57235 | 0.786176 | − | 0.618003i | \(-0.212058\pi\) | ||||
0.786176 | + | 0.618003i | \(0.212058\pi\) | |||||||
\(212\) | 7.17340i | 0.492671i | ||||||||
\(213\) | 4.80576i | 0.329286i | ||||||||
\(214\) | 11.4715i | 0.784178i | ||||||||
\(215\) | 5.09983 | − | 9.61254i | 0.347805 | − | 0.655570i | ||||
\(216\) | − | 2.21322i | − | 0.150590i | ||||||
\(217\) | 4.59098 | 0.311656 | ||||||||
\(218\) | 0.727748i | 0.0492893i | ||||||||
\(219\) | 1.68464 | 0.113837 | ||||||||
\(220\) | −1.30775 | + | 2.46494i | −0.0881684 | + | 0.166186i | ||||
\(221\) | 10.4021 | 0.699720 | ||||||||
\(222\) | −1.69609 | + | 1.55116i | −0.113834 | + | 0.104107i | ||||
\(223\) | 3.32116i | 0.222401i | 0.993798 | + | 0.111201i | \(0.0354696\pi\) | ||||
−0.993798 | + | 0.111201i | \(0.964530\pi\) | |||||||
\(224\) | − | 0.631751i | − | 0.0422106i | ||||||
\(225\) | −8.01030 | − | 11.8291i | −0.534020 | − | 0.788607i | ||||
\(226\) | −17.9970 | −1.19714 | ||||||||
\(227\) | −5.62938 | −0.373635 | −0.186818 | − | 0.982395i | \(-0.559817\pi\) | ||||
−0.186818 | + | 0.982395i | \(0.559817\pi\) | |||||||
\(228\) | 2.25707 | 0.149478 | ||||||||
\(229\) | −0.973208 | −0.0643114 | −0.0321557 | − | 0.999483i | \(-0.510237\pi\) | ||||
−0.0321557 | + | 0.999483i | \(0.510237\pi\) | |||||||
\(230\) | 7.97195 | − | 15.0261i | 0.525655 | − | 0.990794i | ||||
\(231\) | −0.297889 | −0.0195997 | ||||||||
\(232\) | − | 9.57629i | − | 0.628714i | ||||||
\(233\) | 14.4150i | 0.944357i | 0.881503 | + | 0.472178i | \(0.156532\pi\) | ||||
−0.881503 | + | 0.472178i | \(0.843468\pi\) | |||||||
\(234\) | 9.57166 | 0.625719 | ||||||||
\(235\) | 25.9132 | + | 13.7480i | 1.69039 | + | 0.896819i | ||||
\(236\) | − | 4.36469i | − | 0.284117i | ||||||
\(237\) | −3.32019 | −0.215669 | ||||||||
\(238\) | − | 1.96166i | − | 0.127155i | ||||||
\(239\) | 8.43344i | 0.545514i | 0.962083 | + | 0.272757i | \(0.0879355\pi\) | ||||
−0.962083 | + | 0.272757i | \(0.912065\pi\) | |||||||
\(240\) | 0.746385 | + | 0.395986i | 0.0481789 | + | 0.0255608i | ||||
\(241\) | 18.6567i | 1.20178i | 0.799331 | + | 0.600891i | \(0.205188\pi\) | ||||
−0.799331 | + | 0.600891i | \(0.794812\pi\) | |||||||
\(242\) | −9.44277 | −0.607004 | ||||||||
\(243\) | − | 9.56255i | − | 0.613438i | ||||||
\(244\) | − | 2.14666i | − | 0.137426i | ||||||
\(245\) | −6.91752 | + | 13.0387i | −0.441944 | + | 0.833010i | ||||
\(246\) | 3.19485i | 0.203696i | ||||||||
\(247\) | 20.0104i | 1.27323i | ||||||||
\(248\) | 7.26707i | 0.461460i | ||||||||
\(249\) | 2.50592 | 0.158806 | ||||||||
\(250\) | 11.1159 | − | 1.19911i | 0.703028 | − | 0.0758385i | ||||
\(251\) | − | 25.1189i | − | 1.58549i | −0.609553 | − | 0.792746i | \(-0.708651\pi\) | ||
0.609553 | − | 0.792746i | \(-0.291349\pi\) | |||||||
\(252\) | − | 1.80505i | − | 0.113708i | ||||||
\(253\) | −9.49277 | −0.596805 | ||||||||
\(254\) | − | 15.4830i | − | 0.971490i | ||||||
\(255\) | 2.31761 | + | 1.22958i | 0.145134 | + | 0.0769994i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.3552 | 1.26973 | 0.634863 | − | 0.772625i | \(-0.281057\pi\) | ||||
0.634863 | + | 0.772625i | \(0.281057\pi\) | |||||||
\(258\) | 1.83882i | 0.114480i | ||||||||
\(259\) | −2.83571 | + | 2.59341i | −0.176203 | + | 0.161146i | ||||
\(260\) | −3.51068 | + | 6.61720i | −0.217723 | + | 0.410381i | ||||
\(261\) | − | 27.3616i | − | 1.69364i | ||||||
\(262\) | − | 6.22121i | − | 0.384348i | ||||||
\(263\) | − | 22.2211i | − | 1.37021i | −0.728443 | − | 0.685107i | \(-0.759756\pi\) | ||
0.728443 | − | 0.685107i | \(-0.240244\pi\) | |||||||
\(264\) | − | 0.471529i | − | 0.0290206i | ||||||
\(265\) | −14.1695 | − | 7.51750i | −0.870428 | − | 0.461796i | ||||
\(266\) | 3.77362 | 0.231375 | ||||||||
\(267\) | −5.20633 | −0.318622 | ||||||||
\(268\) | 11.3451i | 0.693012i | ||||||||
\(269\) | −15.8411 | −0.965850 | −0.482925 | − | 0.875662i | \(-0.660426\pi\) | ||||
−0.482925 | + | 0.875662i | \(0.660426\pi\) | |||||||
\(270\) | 4.37174 | + | 2.31938i | 0.266056 | + | 0.141153i | ||||
\(271\) | −2.00602 | −0.121857 | −0.0609285 | − | 0.998142i | \(-0.519406\pi\) | ||||
−0.0609285 | + | 0.998142i | \(0.519406\pi\) | |||||||
\(272\) | 3.10511 | 0.188275 | ||||||||
\(273\) | −0.799690 | −0.0483994 | ||||||||
\(274\) | 14.1258i | 0.853373i | ||||||||
\(275\) | −3.49849 | − | 5.16636i | −0.210967 | − | 0.311543i | ||||
\(276\) | 2.87441i | 0.173019i | ||||||||
\(277\) | 11.5671 | 0.695000 | 0.347500 | − | 0.937680i | \(-0.387031\pi\) | ||||
0.347500 | + | 0.937680i | \(0.387031\pi\) | |||||||
\(278\) | 8.43675 | 0.506003 | ||||||||
\(279\) | 20.7636i | 1.24309i | ||||||||
\(280\) | 1.24789 | + | 0.662054i | 0.0745757 | + | 0.0395653i | ||||
\(281\) | − | 14.2909i | − | 0.852521i | −0.904600 | − | 0.426261i | \(-0.859831\pi\) | ||
0.904600 | − | 0.426261i | \(-0.140169\pi\) | |||||||
\(282\) | −4.95705 | −0.295188 | ||||||||
\(283\) | 12.3837 | 0.736137 | 0.368068 | − | 0.929799i | \(-0.380019\pi\) | ||||
0.368068 | + | 0.929799i | \(0.380019\pi\) | |||||||
\(284\) | −12.7183 | −0.754694 | ||||||||
\(285\) | −2.36533 | + | 4.45836i | −0.140110 | + | 0.264090i | ||||
\(286\) | 4.18042 | 0.247193 | ||||||||
\(287\) | 5.34152i | 0.315300i | ||||||||
\(288\) | 2.85722 | 0.168363 | ||||||||
\(289\) | −7.35829 | −0.432840 | ||||||||
\(290\) | 18.9159 | + | 10.0356i | 1.11078 | + | 0.589313i | ||||
\(291\) | − | 4.17849i | − | 0.244947i | ||||||
\(292\) | 4.45836i | 0.260906i | ||||||||
\(293\) | 27.8374i | 1.62628i | 0.582068 | + | 0.813140i | \(0.302244\pi\) | ||||
−0.582068 | + | 0.813140i | \(0.697756\pi\) | |||||||
\(294\) | − | 2.49422i | − | 0.145466i | ||||||
\(295\) | 8.62152 | + | 4.57405i | 0.501964 | + | 0.266312i | ||||
\(296\) | −4.10511 | − | 4.48866i | −0.238605 | − | 0.260898i | ||||
\(297\) | − | 2.76185i | − | 0.160259i | ||||||
\(298\) | 13.6447 | 0.790416 | ||||||||
\(299\) | −25.4836 | −1.47375 | ||||||||
\(300\) | −1.56437 | + | 1.05934i | −0.0903192 | + | 0.0611613i | ||||
\(301\) | 3.07435i | 0.177203i | ||||||||
\(302\) | −3.17741 | −0.182839 | ||||||||
\(303\) | − | 3.26968i | − | 0.187838i | ||||||
\(304\) | 5.97327i | 0.342590i | ||||||||
\(305\) | 4.24028 | + | 2.24963i | 0.242798 | + | 0.128814i | ||||
\(306\) | 8.87199 | 0.507178 | ||||||||
\(307\) | 19.9411i | 1.13810i | 0.822304 | + | 0.569049i | \(0.192688\pi\) | ||||
−0.822304 | + | 0.569049i | \(0.807312\pi\) | |||||||
\(308\) | − | 0.788355i | − | 0.0449207i | ||||||
\(309\) | 1.72810i | 0.0983080i | ||||||||
\(310\) | −14.3546 | − | 7.61566i | −0.815284 | − | 0.432540i | ||||
\(311\) | − | 4.96832i | − | 0.281727i | −0.990029 | − | 0.140864i | \(-0.955012\pi\) | ||
0.990029 | − | 0.140864i | \(-0.0449879\pi\) | |||||||
\(312\) | − | 1.26583i | − | 0.0716636i | ||||||
\(313\) | 10.0000 | 0.565233 | 0.282617 | − | 0.959233i | \(-0.408798\pi\) | ||||
0.282617 | + | 0.959233i | \(0.408798\pi\) | |||||||
\(314\) | − | 0.215310i | − | 0.0121506i | ||||||
\(315\) | 3.56550 | + | 1.89164i | 0.200893 | + | 0.106582i | ||||
\(316\) | − | 8.78679i | − | 0.494296i | ||||||
\(317\) | − | 22.9198i | − | 1.28730i | −0.765319 | − | 0.643651i | \(-0.777419\pi\) | ||
0.765319 | − | 0.643651i | \(-0.222581\pi\) | |||||||
\(318\) | 2.71055 | 0.152000 | ||||||||
\(319\) | − | 11.9502i | − | 0.669080i | ||||||
\(320\) | −1.04797 | + | 1.97529i | −0.0585832 | + | 0.110422i | ||||
\(321\) | 4.33465 | 0.241937 | ||||||||
\(322\) | 4.80576i | 0.267815i | ||||||||
\(323\) | 18.5477i | 1.03202i | ||||||||
\(324\) | 7.73537 | 0.429743 | ||||||||
\(325\) | −9.39179 | − | 13.8692i | −0.520963 | − | 0.769326i | ||||
\(326\) | 1.66609 | 0.0922760 | ||||||||
\(327\) | 0.274988 | 0.0152069 | ||||||||
\(328\) | −8.45510 | −0.466855 | ||||||||
\(329\) | −8.28775 | −0.456918 | ||||||||
\(330\) | 0.931406 | + | 0.494147i | 0.0512722 | + | 0.0272019i | ||||
\(331\) | 5.54265i | 0.304651i | 0.988330 | + | 0.152326i | \(0.0486763\pi\) | ||||
−0.988330 | + | 0.152326i | \(0.951324\pi\) | |||||||
\(332\) | 6.63185i | 0.363970i | ||||||||
\(333\) | −11.7292 | − | 12.8251i | −0.642757 | − | 0.702811i | ||||
\(334\) | −5.92242 | −0.324060 | ||||||||
\(335\) | −22.4098 | − | 11.8893i | −1.22438 | − | 0.649581i | ||||
\(336\) | −0.238714 | −0.0130229 | ||||||||
\(337\) | − | 25.6348i | − | 1.39642i | −0.715894 | − | 0.698209i | \(-0.753981\pi\) | ||
0.715894 | − | 0.698209i | \(-0.246019\pi\) | |||||||
\(338\) | −1.77756 | −0.0966867 | ||||||||
\(339\) | 6.80035i | 0.369344i | ||||||||
\(340\) | −3.25406 | + | 6.13349i | −0.176476 | + | 0.332635i | ||||
\(341\) | 9.06851i | 0.491087i | ||||||||
\(342\) | 17.0669i | 0.922875i | ||||||||
\(343\) | − | 8.59237i | − | 0.463945i | ||||||
\(344\) | −4.86640 | −0.262379 | ||||||||
\(345\) | −5.67779 | − | 3.01229i | −0.305682 | − | 0.162176i | ||||
\(346\) | 2.88008i | 0.154834i | ||||||||
\(347\) | −19.6225 | −1.05339 | −0.526696 | − | 0.850054i | \(-0.676569\pi\) | ||||
−0.526696 | + | 0.850054i | \(0.676569\pi\) | |||||||
\(348\) | −3.61851 | −0.193972 | ||||||||
\(349\) | −15.6263 | −0.836459 | −0.418230 | − | 0.908341i | \(-0.637349\pi\) | ||||
−0.418230 | + | 0.908341i | \(0.637349\pi\) | |||||||
\(350\) | −2.61550 | + | 1.77113i | −0.139804 | + | 0.0946709i | ||||
\(351\) | − | 7.41425i | − | 0.395744i | ||||||
\(352\) | 1.24789 | 0.0665128 | ||||||||
\(353\) | −23.5724 | −1.25463 | −0.627316 | − | 0.778765i | \(-0.715847\pi\) | ||||
−0.627316 | + | 0.778765i | \(0.715847\pi\) | |||||||
\(354\) | −1.64925 | −0.0876564 | ||||||||
\(355\) | 13.3284 | − | 25.1224i | 0.707398 | − | 1.33336i | ||||
\(356\) | − | 13.7784i | − | 0.730255i | ||||||
\(357\) | −0.741234 | −0.0392302 | ||||||||
\(358\) | 4.46182i | 0.235815i | ||||||||
\(359\) | −9.34905 | −0.493424 | −0.246712 | − | 0.969089i | \(-0.579350\pi\) | ||||
−0.246712 | + | 0.969089i | \(0.579350\pi\) | |||||||
\(360\) | −2.99427 | + | 5.64384i | −0.157812 | + | 0.297456i | ||||
\(361\) | −16.6799 | −0.877891 | ||||||||
\(362\) | 3.93480 | 0.206809 | ||||||||
\(363\) | 3.56806i | 0.187274i | ||||||||
\(364\) | − | 2.11636i | − | 0.110927i | ||||||
\(365\) | −8.80654 | − | 4.67221i | −0.460955 | − | 0.244555i | ||||
\(366\) | −0.811140 | −0.0423990 | ||||||||
\(367\) | 12.2379i | 0.638811i | 0.947618 | + | 0.319406i | \(0.103483\pi\) | ||||
−0.947618 | + | 0.319406i | \(0.896517\pi\) | |||||||
\(368\) | −7.60706 | −0.396545 | ||||||||
\(369\) | −24.1581 | −1.25762 | ||||||||
\(370\) | 13.1684 | − | 3.40481i | 0.684594 | − | 0.177008i | ||||
\(371\) | 4.53180 | 0.235280 | ||||||||
\(372\) | 2.74594 | 0.142371 | ||||||||
\(373\) | − | 10.1918i | − | 0.527712i | −0.964562 | − | 0.263856i | \(-0.915006\pi\) | ||
0.964562 | − | 0.263856i | \(-0.0849943\pi\) | |||||||
\(374\) | 3.87484 | 0.200363 | ||||||||
\(375\) | −0.453098 | − | 4.20025i | −0.0233979 | − | 0.216900i | ||||
\(376\) | − | 13.1187i | − | 0.676545i | ||||||
\(377\) | − | 32.0805i | − | 1.65223i | ||||||
\(378\) | −1.39820 | −0.0719157 | ||||||||
\(379\) | 20.7538 | 1.06605 | 0.533025 | − | 0.846099i | \(-0.321055\pi\) | ||||
0.533025 | + | 0.846099i | \(0.321055\pi\) | |||||||
\(380\) | −11.7989 | − | 6.25979i | −0.605272 | − | 0.321120i | ||||
\(381\) | −5.85042 | −0.299726 | ||||||||
\(382\) | 7.76296i | 0.397188i | ||||||||
\(383\) | −17.7328 | −0.906103 | −0.453052 | − | 0.891484i | \(-0.649665\pi\) | ||||
−0.453052 | + | 0.891484i | \(0.649665\pi\) | |||||||
\(384\) | − | 0.377861i | − | 0.0192826i | ||||||
\(385\) | 1.55723 | + | 0.826171i | 0.0793638 | + | 0.0421056i | ||||
\(386\) | 3.49189 | 0.177732 | ||||||||
\(387\) | −13.9044 | −0.706799 | ||||||||
\(388\) | 11.0583 | 0.561398 | ||||||||
\(389\) | 10.9054i | 0.552923i | 0.961025 | + | 0.276462i | \(0.0891619\pi\) | ||||
−0.961025 | + | 0.276462i | \(0.910838\pi\) | |||||||
\(390\) | 2.50038 | + | 1.32655i | 0.126612 | + | 0.0671725i | ||||
\(391\) | −23.6208 | −1.19455 | ||||||||
\(392\) | 6.60089 | 0.333395 | ||||||||
\(393\) | −2.35075 | −0.118580 | ||||||||
\(394\) | − | 1.07617i | − | 0.0542164i | ||||||
\(395\) | 17.3565 | + | 9.20827i | 0.873298 | + | 0.463319i | ||||
\(396\) | 3.56550 | 0.179173 | ||||||||
\(397\) | 23.0106i | 1.15487i | 0.816437 | + | 0.577435i | \(0.195946\pi\) | ||||
−0.816437 | + | 0.577435i | \(0.804054\pi\) | |||||||
\(398\) | − | 5.71343i | − | 0.286388i | ||||||
\(399\) | − | 1.42590i | − | 0.0713844i | ||||||
\(400\) | −2.80353 | − | 4.14008i | −0.140176 | − | 0.207004i | ||||
\(401\) | − | 16.5769i | − | 0.827809i | −0.910320 | − | 0.413904i | \(-0.864165\pi\) | ||
0.910320 | − | 0.413904i | \(-0.135835\pi\) | |||||||
\(402\) | 4.28687 | 0.213810 | ||||||||
\(403\) | 24.3446i | 1.21269i | ||||||||
\(404\) | 8.65314 | 0.430510 | ||||||||
\(405\) | −8.10642 | + | 15.2796i | −0.402811 | + | 0.759249i | ||||
\(406\) | −6.04983 | −0.300248 | ||||||||
\(407\) | −5.12273 | − | 5.60135i | −0.253924 | − | 0.277649i | ||||
\(408\) | − | 1.17330i | − | 0.0580870i | ||||||
\(409\) | 5.05401i | 0.249905i | 0.992163 | + | 0.124952i | \(0.0398778\pi\) | ||||
−0.992163 | + | 0.124952i | \(0.960122\pi\) | |||||||
\(410\) | 8.86067 | − | 16.7013i | 0.437597 | − | 0.824817i | ||||
\(411\) | 5.33760 | 0.263285 | ||||||||
\(412\) | −4.57336 | −0.225313 | ||||||||
\(413\) | −2.75740 | −0.135683 | ||||||||
\(414\) | −21.7350 | −1.06822 | ||||||||
\(415\) | −13.0998 | − | 6.94997i | −0.643045 | − | 0.341161i | ||||
\(416\) | 3.34999 | 0.164247 | ||||||||
\(417\) | − | 3.18792i | − | 0.156113i | ||||||
\(418\) | 7.45398i | 0.364586i | ||||||||
\(419\) | −24.2194 | −1.18319 | −0.591597 | − | 0.806234i | \(-0.701502\pi\) | ||||
−0.591597 | + | 0.806234i | \(0.701502\pi\) | |||||||
\(420\) | 0.250165 | − | 0.471529i | 0.0122068 | − | 0.0230083i | ||||
\(421\) | 20.8487i | 1.01611i | 0.861326 | + | 0.508053i | \(0.169635\pi\) | ||||
−0.861326 | + | 0.508053i | \(0.830365\pi\) | |||||||
\(422\) | 22.8397 | 1.11182 | ||||||||
\(423\) | − | 37.4830i | − | 1.82249i | ||||||
\(424\) | 7.17340i | 0.348371i | ||||||||
\(425\) | −8.70527 | − | 12.8554i | −0.422267 | − | 0.623578i | ||||
\(426\) | 4.80576i | 0.232840i | ||||||||
\(427\) | −1.35616 | −0.0656290 | ||||||||
\(428\) | 11.4715i | 0.554498i | ||||||||
\(429\) | − | 1.57962i | − | 0.0762647i | ||||||
\(430\) | 5.09983 | − | 9.61254i | 0.245935 | − | 0.463558i | ||||
\(431\) | 28.2298i | 1.35978i | 0.733314 | + | 0.679890i | \(0.237973\pi\) | ||||
−0.733314 | + | 0.679890i | \(0.762027\pi\) | |||||||
\(432\) | − | 2.21322i | − | 0.106483i | ||||||
\(433\) | 30.3997i | 1.46091i | 0.682958 | + | 0.730457i | \(0.260693\pi\) | ||||
−0.682958 | + | 0.730457i | \(0.739307\pi\) | |||||||
\(434\) | 4.59098 | 0.220374 | ||||||||
\(435\) | 3.79208 | − | 7.14759i | 0.181816 | − | 0.342701i | ||||
\(436\) | 0.727748i | 0.0348528i | ||||||||
\(437\) | − | 45.4390i | − | 2.17364i | ||||||
\(438\) | 1.68464 | 0.0804952 | ||||||||
\(439\) | 33.7591i | 1.61123i | 0.592438 | + | 0.805616i | \(0.298166\pi\) | ||||
−0.592438 | + | 0.805616i | \(0.701834\pi\) | |||||||
\(440\) | −1.30775 | + | 2.46494i | −0.0623444 | + | 0.117512i | ||||
\(441\) | 18.8602 | 0.898105 | ||||||||
\(442\) | 10.4021 | 0.494777 | ||||||||
\(443\) | − | 15.5413i | − | 0.738388i | −0.929352 | − | 0.369194i | \(-0.879634\pi\) | ||
0.929352 | − | 0.369194i | \(-0.120366\pi\) | |||||||
\(444\) | −1.69609 | + | 1.55116i | −0.0804929 | + | 0.0736149i | ||||
\(445\) | 27.2164 | + | 14.4393i | 1.29018 | + | 0.684490i | ||||
\(446\) | 3.32116i | 0.157261i | ||||||||
\(447\) | − | 5.15580i | − | 0.243861i | ||||||
\(448\) | − | 0.631751i | − | 0.0298474i | ||||||
\(449\) | 14.2184i | 0.671006i | 0.942039 | + | 0.335503i | \(0.108906\pi\) | ||||
−0.942039 | + | 0.335503i | \(0.891094\pi\) | |||||||
\(450\) | −8.01030 | − | 11.8291i | −0.377609 | − | 0.557630i | ||||
\(451\) | −10.5510 | −0.496829 | ||||||||
\(452\) | −17.9970 | −0.846506 | ||||||||
\(453\) | 1.20062i | 0.0564100i | ||||||||
\(454\) | −5.62938 | −0.264200 | ||||||||
\(455\) | 4.18042 | + | 2.21788i | 0.195981 | + | 0.103976i | ||||
\(456\) | 2.25707 | 0.105697 | ||||||||
\(457\) | −9.17031 | −0.428969 | −0.214484 | − | 0.976727i | \(-0.568807\pi\) | ||||
−0.214484 | + | 0.976727i | \(0.568807\pi\) | |||||||
\(458\) | −0.973208 | −0.0454750 | ||||||||
\(459\) | − | 6.87228i | − | 0.320771i | ||||||
\(460\) | 7.97195 | − | 15.0261i | 0.371694 | − | 0.700597i | ||||
\(461\) | 10.3300i | 0.481114i | 0.970635 | + | 0.240557i | \(0.0773301\pi\) | ||||
−0.970635 | + | 0.240557i | \(0.922670\pi\) | |||||||
\(462\) | −0.297889 | −0.0138590 | ||||||||
\(463\) | 25.8049 | 1.19926 | 0.599629 | − | 0.800278i | \(-0.295315\pi\) | ||||
0.599629 | + | 0.800278i | \(0.295315\pi\) | |||||||
\(464\) | − | 9.57629i | − | 0.444568i | ||||||
\(465\) | −2.87766 | + | 5.42403i | −0.133448 | + | 0.251533i | ||||
\(466\) | 14.4150i | 0.667761i | ||||||||
\(467\) | 34.4582 | 1.59454 | 0.797268 | − | 0.603625i | \(-0.206278\pi\) | ||||
0.797268 | + | 0.603625i | \(0.206278\pi\) | |||||||
\(468\) | 9.57166 | 0.442450 | ||||||||
\(469\) | 7.16727 | 0.330954 | ||||||||
\(470\) | 25.9132 | + | 13.7480i | 1.19529 | + | 0.634147i | ||||
\(471\) | −0.0813572 | −0.00374874 | ||||||||
\(472\) | − | 4.36469i | − | 0.200901i | ||||||
\(473\) | −6.07273 | −0.279224 | ||||||||
\(474\) | −3.32019 | −0.152501 | ||||||||
\(475\) | 24.7298 | − | 16.7462i | 1.13468 | − | 0.768369i | ||||
\(476\) | − | 1.96166i | − | 0.0899124i | ||||||
\(477\) | 20.4960i | 0.938448i | ||||||||
\(478\) | 8.43344i | 0.385737i | ||||||||
\(479\) | 29.6039i | 1.35264i | 0.736610 | + | 0.676318i | \(0.236426\pi\) | ||||
−0.736610 | + | 0.676318i | \(0.763574\pi\) | |||||||
\(480\) | 0.746385 | + | 0.395986i | 0.0340676 | + | 0.0180742i | ||||
\(481\) | −13.7521 | − | 15.0370i | −0.627041 | − | 0.685627i | ||||
\(482\) | 18.6567i | 0.849789i | ||||||||
\(483\) | 1.81591 | 0.0826268 | ||||||||
\(484\) | −9.44277 | −0.429217 | ||||||||
\(485\) | −11.5887 | + | 21.8433i | −0.526216 | + | 0.991852i | ||||
\(486\) | − | 9.56255i | − | 0.433766i | ||||||
\(487\) | 27.0961 | 1.22784 | 0.613920 | − | 0.789369i | \(-0.289592\pi\) | ||||
0.613920 | + | 0.789369i | \(0.289592\pi\) | |||||||
\(488\) | − | 2.14666i | − | 0.0971749i | ||||||
\(489\) | − | 0.629549i | − | 0.0284692i | ||||||
\(490\) | −6.91752 | + | 13.0387i | −0.312502 | + | 0.589027i | ||||
\(491\) | 2.46033 | 0.111033 | 0.0555166 | − | 0.998458i | \(-0.482319\pi\) | ||||
0.0555166 | + | 0.998458i | \(0.482319\pi\) | |||||||
\(492\) | 3.19485i | 0.144035i | ||||||||
\(493\) | − | 29.7354i | − | 1.33922i | ||||||
\(494\) | 20.0104i | 0.900310i | ||||||||
\(495\) | −3.73653 | + | 7.04289i | −0.167944 | + | 0.316554i | ||||
\(496\) | 7.26707i | 0.326301i | ||||||||
\(497\) | 8.03482i | 0.360411i | ||||||||
\(498\) | 2.50592 | 0.112293 | ||||||||
\(499\) | − | 31.4091i | − | 1.40606i | −0.711158 | − | 0.703032i | \(-0.751829\pi\) | ||
0.711158 | − | 0.703032i | \(-0.248171\pi\) | |||||||
\(500\) | 11.1159 | − | 1.19911i | 0.497116 | − | 0.0536259i | ||||
\(501\) | 2.23785i | 0.0999798i | ||||||||
\(502\) | − | 25.1189i | − | 1.12111i | ||||||
\(503\) | −1.78145 | −0.0794311 | −0.0397156 | − | 0.999211i | \(-0.512645\pi\) | ||||
−0.0397156 | + | 0.999211i | \(0.512645\pi\) | |||||||
\(504\) | − | 1.80505i | − | 0.0804034i | ||||||
\(505\) | −9.06821 | + | 17.0924i | −0.403530 | + | 0.760604i | ||||
\(506\) | −9.49277 | −0.422005 | ||||||||
\(507\) | 0.671672i | 0.0298300i | ||||||||
\(508\) | − | 15.4830i | − | 0.686947i | ||||||
\(509\) | 21.2370 | 0.941314 | 0.470657 | − | 0.882316i | \(-0.344017\pi\) | ||||
0.470657 | + | 0.882316i | \(0.344017\pi\) | |||||||
\(510\) | 2.31761 | + | 1.22958i | 0.102625 | + | 0.0544468i | ||||
\(511\) | 2.81657 | 0.124598 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 13.2201 | 0.583683 | ||||||||
\(514\) | 20.3552 | 0.897831 | ||||||||
\(515\) | 4.79274 | − | 9.03371i | 0.211193 | − | 0.398073i | ||||
\(516\) | 1.83882i | 0.0809496i | ||||||||
\(517\) | − | 16.3707i | − | 0.719982i | ||||||
\(518\) | −2.83571 | + | 2.59341i | −0.124594 | + | 0.113948i | ||||
\(519\) | 1.08827 | 0.0477698 | ||||||||
\(520\) | −3.51068 | + | 6.61720i | −0.153954 | + | 0.290183i | ||||
\(521\) | 2.52950 | 0.110819 | 0.0554097 | − | 0.998464i | \(-0.482354\pi\) | ||||
0.0554097 | + | 0.998464i | \(0.482354\pi\) | |||||||
\(522\) | − | 27.3616i | − | 1.19758i | ||||||
\(523\) | 1.60848 | 0.0703338 | 0.0351669 | − | 0.999381i | \(-0.488804\pi\) | ||||
0.0351669 | + | 0.999381i | \(0.488804\pi\) | |||||||
\(524\) | − | 6.22121i | − | 0.271775i | ||||||
\(525\) | 0.669242 | + | 0.988294i | 0.0292081 | + | 0.0431327i | ||||
\(526\) | − | 22.2211i | − | 0.968887i | ||||||
\(527\) | 22.5651i | 0.982950i | ||||||||
\(528\) | − | 0.471529i | − | 0.0205207i | ||||||
\(529\) | 34.8673 | 1.51597 | ||||||||
\(530\) | −14.1695 | − | 7.51750i | −0.615486 | − | 0.326539i | ||||
\(531\) | − | 12.4709i | − | 0.541190i | ||||||
\(532\) | 3.77362 | 0.163607 | ||||||||
\(533\) | −28.3245 | −1.22687 | ||||||||
\(534\) | −5.20633 | −0.225300 | ||||||||
\(535\) | −22.6596 | − | 12.0218i | −0.979660 | − | 0.519748i | ||||
\(536\) | 11.3451i | 0.490033i | ||||||||
\(537\) | 1.68595 | 0.0727541 | ||||||||
\(538\) | −15.8411 | −0.682959 | ||||||||
\(539\) | 8.23719 | 0.354801 | ||||||||
\(540\) | 4.37174 | + | 2.31938i | 0.188130 | + | 0.0998102i | ||||
\(541\) | − | 3.12463i | − | 0.134338i | −0.997742 | − | 0.0671692i | \(-0.978603\pi\) | ||
0.997742 | − | 0.0671692i | \(-0.0213967\pi\) | |||||||
\(542\) | −2.00602 | −0.0861660 | ||||||||
\(543\) | − | 1.48681i | − | 0.0638051i | ||||||
\(544\) | 3.10511 | 0.133131 | ||||||||
\(545\) | −1.43751 | − | 0.762657i | −0.0615763 | − | 0.0326686i | ||||
\(546\) | −0.799690 | −0.0342236 | ||||||||
\(547\) | −5.44201 | −0.232683 | −0.116342 | − | 0.993209i | \(-0.537117\pi\) | ||||
−0.116342 | + | 0.993209i | \(0.537117\pi\) | |||||||
\(548\) | 14.1258i | 0.603426i | ||||||||
\(549\) | − | 6.13349i | − | 0.261771i | ||||||
\(550\) | −3.49849 | − | 5.16636i | −0.149176 | − | 0.220294i | ||||
\(551\) | 57.2017 | 2.43688 | ||||||||
\(552\) | 2.87441i | 0.122343i | ||||||||
\(553\) | −5.55106 | −0.236055 | ||||||||
\(554\) | 11.5671 | 0.491440 | ||||||||
\(555\) | −1.28654 | − | 4.97583i | −0.0546108 | − | 0.211212i | ||||
\(556\) | 8.43675 | 0.357798 | ||||||||
\(557\) | 36.3451 | 1.53999 | 0.769995 | − | 0.638050i | \(-0.220259\pi\) | ||||
0.769995 | + | 0.638050i | \(0.220259\pi\) | |||||||
\(558\) | 20.7636i | 0.878995i | ||||||||
\(559\) | −16.3024 | −0.689517 | ||||||||
\(560\) | 1.24789 | + | 0.662054i | 0.0527330 | + | 0.0279769i | ||||
\(561\) | − | 1.46415i | − | 0.0618165i | ||||||
\(562\) | − | 14.2909i | − | 0.602824i | ||||||
\(563\) | 38.4949 | 1.62237 | 0.811184 | − | 0.584791i | \(-0.198823\pi\) | ||||
0.811184 | + | 0.584791i | \(0.198823\pi\) | |||||||
\(564\) | −4.95705 | −0.208729 | ||||||||
\(565\) | 18.8602 | − | 35.5492i | 0.793456 | − | 1.49557i | ||||
\(566\) | 12.3837 | 0.520527 | ||||||||
\(567\) | − | 4.88683i | − | 0.205228i | ||||||
\(568\) | −12.7183 | −0.533649 | ||||||||
\(569\) | 41.2793i | 1.73052i | 0.501324 | + | 0.865260i | \(0.332846\pi\) | ||||
−0.501324 | + | 0.865260i | \(0.667154\pi\) | |||||||
\(570\) | −2.36533 | + | 4.45836i | −0.0990728 | + | 0.186740i | ||||
\(571\) | −26.0635 | −1.09072 | −0.545362 | − | 0.838200i | \(-0.683608\pi\) | ||||
−0.545362 | + | 0.838200i | \(0.683608\pi\) | |||||||
\(572\) | 4.18042 | 0.174792 | ||||||||
\(573\) | 2.93332 | 0.122541 | ||||||||
\(574\) | 5.34152i | 0.222951i | ||||||||
\(575\) | 21.3266 | + | 31.4938i | 0.889381 | + | 1.31338i | ||||
\(576\) | 2.85722 | 0.119051 | ||||||||
\(577\) | −11.8411 | −0.492952 | −0.246476 | − | 0.969149i | \(-0.579273\pi\) | ||||
−0.246476 | + | 0.969149i | \(0.579273\pi\) | |||||||
\(578\) | −7.35829 | −0.306064 | ||||||||
\(579\) | − | 1.31945i | − | 0.0548344i | ||||||
\(580\) | 18.9159 | + | 10.0356i | 0.785441 | + | 0.416707i | ||||
\(581\) | 4.18968 | 0.173817 | ||||||||
\(582\) | − | 4.17849i | − | 0.173204i | ||||||
\(583\) | 8.95162i | 0.370738i | ||||||||
\(584\) | 4.45836i | 0.184488i | ||||||||
\(585\) | −10.0308 | + | 18.9068i | −0.414722 | + | 0.781700i | ||||
\(586\) | 27.8374i | 1.14995i | ||||||||
\(587\) | 26.7315 | 1.10333 | 0.551663 | − | 0.834067i | \(-0.313994\pi\) | ||||
0.551663 | + | 0.834067i | \(0.313994\pi\) | |||||||
\(588\) | − | 2.49422i | − | 0.102860i | ||||||
\(589\) | −43.4082 | −1.78860 | ||||||||
\(590\) | 8.62152 | + | 4.57405i | 0.354942 | + | 0.188311i | ||||
\(591\) | −0.406641 | −0.0167270 | ||||||||
\(592\) | −4.10511 | − | 4.48866i | −0.168719 | − | 0.184483i | ||||
\(593\) | 22.6119i | 0.928560i | 0.885688 | + | 0.464280i | \(0.153687\pi\) | ||||
−0.885688 | + | 0.464280i | \(0.846313\pi\) | |||||||
\(594\) | − | 2.76185i | − | 0.113320i | ||||||
\(595\) | 3.87484 | + | 2.05575i | 0.158853 | + | 0.0842776i | ||||
\(596\) | 13.6447 | 0.558909 | ||||||||
\(597\) | −2.15888 | −0.0883572 | ||||||||
\(598\) | −25.4836 | −1.04210 | ||||||||
\(599\) | 14.3406 | 0.585942 | 0.292971 | − | 0.956121i | \(-0.405356\pi\) | ||||
0.292971 | + | 0.956121i | \(0.405356\pi\) | |||||||
\(600\) | −1.56437 | + | 1.05934i | −0.0638653 | + | 0.0432476i | ||||
\(601\) | 15.0845 | 0.615308 | 0.307654 | − | 0.951498i | \(-0.400456\pi\) | ||||
0.307654 | + | 0.951498i | \(0.400456\pi\) | |||||||
\(602\) | 3.07435i | 0.125301i | ||||||||
\(603\) | 32.4154i | 1.32006i | ||||||||
\(604\) | −3.17741 | −0.129287 | ||||||||
\(605\) | 9.89572 | − | 18.6522i | 0.402318 | − | 0.758320i | ||||
\(606\) | − | 3.26968i | − | 0.132822i | ||||||
\(607\) | −41.5964 | −1.68835 | −0.844174 | − | 0.536070i | \(-0.819908\pi\) | ||||
−0.844174 | + | 0.536070i | \(0.819908\pi\) | |||||||
\(608\) | 5.97327i | 0.242248i | ||||||||
\(609\) | 2.28599i | 0.0926332i | ||||||||
\(610\) | 4.24028 | + | 2.24963i | 0.171684 | + | 0.0910850i | ||||
\(611\) | − | 43.9475i | − | 1.77793i | ||||||
\(612\) | 8.87199 | 0.358629 | ||||||||
\(613\) | − | 30.4369i | − | 1.22934i | −0.788786 | − | 0.614668i | \(-0.789290\pi\) | ||
0.788786 | − | 0.614668i | \(-0.210710\pi\) | |||||||
\(614\) | 19.9411i | 0.804756i | ||||||||
\(615\) | −6.31076 | − | 3.34810i | −0.254474 | − | 0.135009i | ||||
\(616\) | − | 0.788355i | − | 0.0317637i | ||||||
\(617\) | − | 39.8195i | − | 1.60307i | −0.597946 | − | 0.801536i | \(-0.704016\pi\) | ||
0.597946 | − | 0.801536i | \(-0.295984\pi\) | |||||||
\(618\) | 1.72810i | 0.0695142i | ||||||||
\(619\) | 39.4011 | 1.58367 | 0.791833 | − | 0.610738i | \(-0.209127\pi\) | ||||
0.791833 | + | 0.610738i | \(0.209127\pi\) | |||||||
\(620\) | −14.3546 | − | 7.61566i | −0.576493 | − | 0.305852i | ||||
\(621\) | 16.8361i | 0.675608i | ||||||||
\(622\) | − | 4.96832i | − | 0.199211i | ||||||
\(623\) | −8.70453 | −0.348740 | ||||||||
\(624\) | − | 1.26583i | − | 0.0506738i | ||||||
\(625\) | −9.28046 | + | 23.2136i | −0.371218 | + | 0.928546i | ||||
\(626\) | 10.0000 | 0.399680 | ||||||||
\(627\) | 2.81657 | 0.112483 | ||||||||
\(628\) | − | 0.215310i | − | 0.00859180i | ||||||
\(629\) | −12.7468 | − | 13.9378i | −0.508249 | − | 0.555736i | ||||
\(630\) | 3.56550 | + | 1.89164i | 0.142053 | + | 0.0753646i | ||||
\(631\) | − | 0.114985i | − | 0.00457750i | −0.999997 | − | 0.00228875i | \(-0.999271\pi\) | ||
0.999997 | − | 0.00228875i | \(-0.000728532\pi\) | |||||||
\(632\) | − | 8.78679i | − | 0.349520i | ||||||
\(633\) | − | 8.63024i | − | 0.343021i | ||||||
\(634\) | − | 22.9198i | − | 0.910260i | ||||||
\(635\) | 30.5834 | + | 16.2257i | 1.21366 | + | 0.643897i | ||||
\(636\) | 2.71055 | 0.107480 | ||||||||
\(637\) | 22.1129 | 0.876146 | ||||||||
\(638\) | − | 11.9502i | − | 0.473111i | ||||||
\(639\) | −36.3391 | −1.43755 | ||||||||
\(640\) | −1.04797 | + | 1.97529i | −0.0414246 | + | 0.0780801i | ||||
\(641\) | 34.9774 | 1.38153 | 0.690763 | − | 0.723081i | \(-0.257275\pi\) | ||||
0.690763 | + | 0.723081i | \(0.257275\pi\) | |||||||
\(642\) | 4.33465 | 0.171075 | ||||||||
\(643\) | 25.2868 | 0.997216 | 0.498608 | − | 0.866828i | \(-0.333845\pi\) | ||||
0.498608 | + | 0.866828i | \(0.333845\pi\) | |||||||
\(644\) | 4.80576i | 0.189374i | ||||||||
\(645\) | −3.63220 | − | 1.92703i | −0.143018 | − | 0.0758766i | ||||
\(646\) | 18.5477i | 0.729748i | ||||||||
\(647\) | −23.5824 | −0.927120 | −0.463560 | − | 0.886066i | \(-0.653428\pi\) | ||||
−0.463560 | + | 0.886066i | \(0.653428\pi\) | |||||||
\(648\) | 7.73537 | 0.303874 | ||||||||
\(649\) | − | 5.44665i | − | 0.213800i | ||||||
\(650\) | −9.39179 | − | 13.8692i | −0.368376 | − | 0.543995i | ||||
\(651\) | − | 1.73475i | − | 0.0679903i | ||||||
\(652\) | 1.66609 | 0.0652490 | ||||||||
\(653\) | 9.89261 | 0.387128 | 0.193564 | − | 0.981088i | \(-0.437995\pi\) | ||||
0.193564 | + | 0.981088i | \(0.437995\pi\) | |||||||
\(654\) | 0.274988 | 0.0107529 | ||||||||
\(655\) | 12.2887 | + | 6.51963i | 0.480159 | + | 0.254743i | ||||
\(656\) | −8.45510 | −0.330116 | ||||||||
\(657\) | 12.7385i | 0.496977i | ||||||||
\(658\) | −8.28775 | −0.323090 | ||||||||
\(659\) | −25.4137 | −0.989976 | −0.494988 | − | 0.868900i | \(-0.664827\pi\) | ||||
−0.494988 | + | 0.868900i | \(0.664827\pi\) | |||||||
\(660\) | 0.931406 | + | 0.494147i | 0.0362549 | + | 0.0192347i | ||||
\(661\) | 28.4574i | 1.10687i | 0.832894 | + | 0.553433i | \(0.186682\pi\) | ||||
−0.832894 | + | 0.553433i | \(0.813318\pi\) | |||||||
\(662\) | 5.54265i | 0.215421i | ||||||||
\(663\) | − | 3.93055i | − | 0.152650i | ||||||
\(664\) | 6.63185i | 0.257366i | ||||||||
\(665\) | −3.95463 | + | 7.45398i | −0.153354 | + | 0.289053i | ||||
\(666\) | −11.7292 | − | 12.8251i | −0.454498 | − | 0.496962i | ||||
\(667\) | 72.8474i | 2.82066i | ||||||||
\(668\) | −5.92242 | −0.229145 | ||||||||
\(669\) | 1.25494 | 0.0485186 | ||||||||
\(670\) | −22.4098 | − | 11.8893i | −0.865767 | − | 0.459323i | ||||
\(671\) | − | 2.67880i | − | 0.103414i | ||||||
\(672\) | −0.238714 | −0.00920860 | ||||||||
\(673\) | − | 20.4187i | − | 0.787082i | −0.919307 | − | 0.393541i | \(-0.871250\pi\) | ||
0.919307 | − | 0.393541i | \(-0.128750\pi\) | |||||||
\(674\) | − | 25.6348i | − | 0.987416i | ||||||
\(675\) | −9.16288 | + | 6.20481i | −0.352680 | + | 0.238823i | ||||
\(676\) | −1.77756 | −0.0683678 | ||||||||
\(677\) | 18.5163i | 0.711641i | 0.934554 | + | 0.355821i | \(0.115799\pi\) | ||||
−0.934554 | + | 0.355821i | \(0.884201\pi\) | |||||||
\(678\) | 6.80035i | 0.261166i | ||||||||
\(679\) | − | 6.98607i | − | 0.268101i | ||||||
\(680\) | −3.25406 | + | 6.13349i | −0.124787 | + | 0.235209i | ||||
\(681\) | 2.12713i | 0.0815116i | ||||||||
\(682\) | 9.06851i | 0.347251i | ||||||||
\(683\) | 32.0667 | 1.22700 | 0.613499 | − | 0.789695i | \(-0.289761\pi\) | ||||
0.613499 | + | 0.789695i | \(0.289761\pi\) | |||||||
\(684\) | 17.0669i | 0.652571i | ||||||||
\(685\) | −27.9026 | − | 14.8034i | −1.06610 | − | 0.565609i | ||||
\(686\) | − | 8.59237i | − | 0.328058i | ||||||
\(687\) | 0.367738i | 0.0140301i | ||||||||
\(688\) | −4.86640 | −0.185530 | ||||||||
\(689\) | 24.0308i | 0.915502i | ||||||||
\(690\) | −5.67779 | − | 3.01229i | −0.216150 | − | 0.114676i | ||||
\(691\) | −6.57629 | −0.250174 | −0.125087 | − | 0.992146i | \(-0.539921\pi\) | ||||
−0.125087 | + | 0.992146i | \(0.539921\pi\) | |||||||
\(692\) | 2.88008i | 0.109484i | ||||||||
\(693\) | − | 2.25251i | − | 0.0855656i | ||||||
\(694\) | −19.6225 | −0.744860 | ||||||||
\(695\) | −8.84144 | + | 16.6650i | −0.335375 | + | 0.632140i | ||||
\(696\) | −3.61851 | −0.137159 | ||||||||
\(697\) | −26.2540 | −0.994442 | ||||||||
\(698\) | −15.6263 | −0.591466 | ||||||||
\(699\) | 5.44686 | 0.206019 | ||||||||
\(700\) | −2.61550 | + | 1.77113i | −0.0988565 | + | 0.0669425i | ||||
\(701\) | − | 9.62168i | − | 0.363406i | −0.983353 | − | 0.181703i | \(-0.941839\pi\) | ||
0.983353 | − | 0.181703i | \(-0.0581609\pi\) | |||||||
\(702\) | − | 7.41425i | − | 0.279833i | ||||||
\(703\) | 26.8120 | − | 24.5209i | 1.01123 | − | 0.924824i | ||||
\(704\) | 1.24789 | 0.0470316 | ||||||||
\(705\) | 5.19482 | − | 9.79160i | 0.195648 | − | 0.368773i | ||||
\(706\) | −23.5724 | −0.887159 | ||||||||
\(707\) | − | 5.46663i | − | 0.205594i | ||||||
\(708\) | −1.64925 | −0.0619825 | ||||||||
\(709\) | − | 8.65759i | − | 0.325142i | −0.986697 | − | 0.162571i | \(-0.948021\pi\) | ||
0.986697 | − | 0.162571i | \(-0.0519787\pi\) | |||||||
\(710\) | 13.3284 | − | 25.1224i | 0.500206 | − | 0.942826i | ||||
\(711\) | − | 25.1058i | − | 0.941541i | ||||||
\(712\) | − | 13.7784i | − | 0.516368i | ||||||
\(713\) | − | 55.2810i | − | 2.07029i | ||||||
\(714\) | −0.741234 | −0.0277400 | ||||||||
\(715\) | −4.38094 | + | 8.25753i | −0.163838 | + | 0.308814i | ||||
\(716\) | 4.46182i | 0.166746i | ||||||||
\(717\) | 3.18667 | 0.119008 | ||||||||
\(718\) | −9.34905 | −0.348904 | ||||||||
\(719\) | 51.5303 | 1.92176 | 0.960878 | − | 0.276972i | \(-0.0893310\pi\) | ||||
0.960878 | + | 0.276972i | \(0.0893310\pi\) | |||||||
\(720\) | −2.99427 | + | 5.64384i | −0.111590 | + | 0.210333i | ||||
\(721\) | 2.88923i | 0.107600i | ||||||||
\(722\) | −16.6799 | −0.620763 | ||||||||
\(723\) | 7.04964 | 0.262179 | ||||||||
\(724\) | 3.93480 | 0.146236 | ||||||||
\(725\) | −39.6466 | + | 26.8474i | −1.47244 | + | 0.997087i | ||||
\(726\) | 3.56806i | 0.132423i | ||||||||
\(727\) | −11.3224 | −0.419924 | −0.209962 | − | 0.977710i | \(-0.567334\pi\) | ||||
−0.209962 | + | 0.977710i | \(0.567334\pi\) | |||||||
\(728\) | − | 2.11636i | − | 0.0784375i | ||||||
\(729\) | 19.5928 | 0.725660 | ||||||||
\(730\) | −8.80654 | − | 4.67221i | −0.325945 | − | 0.172926i | ||||
\(731\) | −15.1107 | −0.558890 | ||||||||
\(732\) | −0.811140 | −0.0299806 | ||||||||
\(733\) | 2.74231i | 0.101290i | 0.998717 | + | 0.0506448i | \(0.0161276\pi\) | ||||
−0.998717 | + | 0.0506448i | \(0.983872\pi\) | |||||||
\(734\) | 12.2379i | 0.451708i | ||||||||
\(735\) | 4.92680 | + | 2.61386i | 0.181728 | + | 0.0964137i | ||||
\(736\) | −7.60706 | −0.280400 | ||||||||
\(737\) | 14.1574i | 0.521495i | ||||||||
\(738\) | −24.1581 | −0.889272 | ||||||||
\(739\) | 8.18878 | 0.301229 | 0.150614 | − | 0.988593i | \(-0.451875\pi\) | ||||
0.150614 | + | 0.988593i | \(0.451875\pi\) | |||||||
\(740\) | 13.1684 | − | 3.40481i | 0.484081 | − | 0.125163i | ||||
\(741\) | 7.56115 | 0.277766 | ||||||||
\(742\) | 4.53180 | 0.166368 | ||||||||
\(743\) | − | 22.1217i | − | 0.811567i | −0.913969 | − | 0.405784i | \(-0.866999\pi\) | ||
0.913969 | − | 0.405784i | \(-0.133001\pi\) | |||||||
\(744\) | 2.74594 | 0.100671 | ||||||||
\(745\) | −14.2992 | + | 26.9522i | −0.523882 | + | 0.987453i | ||||
\(746\) | − | 10.1918i | − | 0.373149i | ||||||
\(747\) | 18.9487i | 0.693296i | ||||||||
\(748\) | 3.87484 | 0.141678 | ||||||||
\(749\) | 7.24715 | 0.264805 | ||||||||
\(750\) | −0.453098 | − | 4.20025i | −0.0165448 | − | 0.153371i | ||||
\(751\) | −19.0818 | −0.696306 | −0.348153 | − | 0.937438i | \(-0.613191\pi\) | ||||
−0.348153 | + | 0.937438i | \(0.613191\pi\) | |||||||
\(752\) | − | 13.1187i | − | 0.478390i | ||||||
\(753\) | −9.49146 | −0.345888 | ||||||||
\(754\) | − | 32.0805i | − | 1.16830i | ||||||
\(755\) | 3.32982 | − | 6.27630i | 0.121185 | − | 0.228418i | ||||
\(756\) | −1.39820 | −0.0508521 | ||||||||
\(757\) | −31.2209 | −1.13474 | −0.567372 | − | 0.823462i | \(-0.692040\pi\) | ||||
−0.567372 | + | 0.823462i | \(0.692040\pi\) | |||||||
\(758\) | 20.7538 | 0.753811 | ||||||||
\(759\) | 3.58695i | 0.130198i | ||||||||
\(760\) | −11.7989 | − | 6.25979i | −0.427992 | − | 0.227066i | ||||
\(761\) | −29.3163 | −1.06271 | −0.531357 | − | 0.847148i | \(-0.678318\pi\) | ||||
−0.531357 | + | 0.847148i | \(0.678318\pi\) | |||||||
\(762\) | −5.85042 | −0.211939 | ||||||||
\(763\) | 0.459756 | 0.0166443 | ||||||||
\(764\) | 7.76296i | 0.280854i | ||||||||
\(765\) | −9.29756 | + | 17.5247i | −0.336154 | + | 0.633608i | ||||
\(766\) | −17.7328 | −0.640712 | ||||||||
\(767\) | − | 14.6217i | − | 0.527958i | ||||||
\(768\) | − | 0.377861i | − | 0.0136349i | ||||||
\(769\) | − | 29.0289i | − | 1.04681i | −0.852084 | − | 0.523404i | \(-0.824662\pi\) | ||
0.852084 | − | 0.523404i | \(-0.175338\pi\) | |||||||
\(770\) | 1.55723 | + | 0.826171i | 0.0561187 | + | 0.0297731i | ||||
\(771\) | − | 7.69146i | − | 0.277001i | ||||||
\(772\) | 3.49189 | 0.125676 | ||||||||
\(773\) | 43.4153i | 1.56154i | 0.624819 | + | 0.780769i | \(0.285173\pi\) | ||||
−0.624819 | + | 0.780769i | \(0.714827\pi\) | |||||||
\(774\) | −13.9044 | −0.499782 | ||||||||
\(775\) | 30.0862 | − | 20.3734i | 1.08073 | − | 0.731836i | ||||
\(776\) | 11.0583 | 0.396969 | ||||||||
\(777\) | 0.979948 | + | 1.07151i | 0.0351554 | + | 0.0384401i | ||||
\(778\) | 10.9054i | 0.390976i | ||||||||
\(779\) | − | 50.5046i | − | 1.80951i | ||||||
\(780\) | 2.50038 | + | 1.32655i | 0.0895280 | + | 0.0474981i | ||||
\(781\) | −15.8711 | −0.567912 | ||||||||
\(782\) | −23.6208 | −0.844676 | ||||||||
\(783\) | −21.1944 | −0.757426 | ||||||||
\(784\) | 6.60089 | 0.235746 | ||||||||
\(785\) | 0.425299 | + | 0.225638i | 0.0151796 | + | 0.00805336i | ||||
\(786\) | −2.35075 | −0.0838486 | ||||||||
\(787\) | 18.9119i | 0.674136i | 0.941480 | + | 0.337068i | \(0.109435\pi\) | ||||
−0.941480 | + | 0.337068i | \(0.890565\pi\) | |||||||
\(788\) | − | 1.07617i | − | 0.0383368i | ||||||
\(789\) | −8.39650 | −0.298923 | ||||||||
\(790\) | 17.3565 | + | 9.20827i | 0.617515 | + | 0.327616i | ||||
\(791\) | 11.3696i | 0.404256i | ||||||||
\(792\) | 3.56550 | 0.126694 | ||||||||
\(793\) | − | 7.19130i | − | 0.255371i | ||||||
\(794\) | 23.0106i | 0.816616i | ||||||||
\(795\) | −2.84057 | + | 5.35412i | −0.100745 | + | 0.189891i | ||||
\(796\) | − | 5.71343i | − | 0.202507i | ||||||
\(797\) | −6.65779 | −0.235831 | −0.117916 | − | 0.993024i | \(-0.537621\pi\) | ||||
−0.117916 | + | 0.993024i | \(0.537621\pi\) | |||||||
\(798\) | − | 1.42590i | − | 0.0504764i | ||||||
\(799\) | − | 40.7350i | − | 1.44110i | ||||||
\(800\) | −2.80353 | − | 4.14008i | −0.0991197 | − | 0.146374i | ||||
\(801\) | − | 39.3680i | − | 1.39100i | ||||||
\(802\) | − | 16.5769i | − | 0.585349i | ||||||
\(803\) | 5.56354i | 0.196333i | ||||||||
\(804\) | 4.28687 | 0.151186 | ||||||||
\(805\) | −9.49277 | − | 5.03628i | −0.334576 | − | 0.177506i | ||||
\(806\) | 24.3446i | 0.857503i | ||||||||
\(807\) | 5.98574i | 0.210708i | ||||||||
\(808\) | 8.65314 | 0.304416 | ||||||||
\(809\) | − | 35.3855i | − | 1.24409i | −0.782982 | − | 0.622044i | \(-0.786302\pi\) | ||
0.782982 | − | 0.622044i | \(-0.213698\pi\) | |||||||
\(810\) | −8.10642 | + | 15.2796i | −0.284831 | + | 0.536870i | ||||
\(811\) | 34.1205 | 1.19813 | 0.599067 | − | 0.800699i | \(-0.295538\pi\) | ||||
0.599067 | + | 0.800699i | \(0.295538\pi\) | |||||||
\(812\) | −6.04983 | −0.212307 | ||||||||
\(813\) | 0.757997i | 0.0265841i | ||||||||
\(814\) | −5.12273 | − | 5.60135i | −0.179551 | − | 0.196327i | ||||
\(815\) | −1.74600 | + | 3.29100i | −0.0611599 | + | 0.115279i | ||||
\(816\) | − | 1.17330i | − | 0.0410737i | ||||||
\(817\) | − | 29.0683i | − | 1.01697i | ||||||
\(818\) | 5.05401i | 0.176709i | ||||||||
\(819\) | − | 6.04691i | − | 0.211296i | ||||||
\(820\) | 8.86067 | − | 16.7013i | 0.309428 | − | 0.583233i | ||||
\(821\) | −50.1981 | −1.75193 | −0.875963 | − | 0.482378i | \(-0.839773\pi\) | ||||
−0.875963 | + | 0.482378i | \(0.839773\pi\) | |||||||
\(822\) | 5.33760 | 0.186170 | ||||||||
\(823\) | 47.6713i | 1.66172i | 0.556483 | + | 0.830859i | \(0.312150\pi\) | ||||
−0.556483 | + | 0.830859i | \(0.687850\pi\) | |||||||
\(824\) | −4.57336 | −0.159321 | ||||||||
\(825\) | −1.95217 | + | 1.32195i | −0.0679657 | + | 0.0460242i | ||||
\(826\) | −2.75740 | −0.0959420 | ||||||||
\(827\) | 3.77813 | 0.131378 | 0.0656892 | − | 0.997840i | \(-0.479075\pi\) | ||||
0.0656892 | + | 0.997840i | \(0.479075\pi\) | |||||||
\(828\) | −21.7350 | −0.755345 | ||||||||
\(829\) | − | 11.9862i | − | 0.416297i | −0.978097 | − | 0.208149i | \(-0.933256\pi\) | ||
0.978097 | − | 0.208149i | \(-0.0667438\pi\) | |||||||
\(830\) | −13.0998 | − | 6.94997i | −0.454702 | − | 0.241237i | ||||
\(831\) | − | 4.37076i | − | 0.151620i | ||||||
\(832\) | 3.34999 | 0.116140 | ||||||||
\(833\) | 20.4965 | 0.710162 | ||||||||
\(834\) | − | 3.18792i | − | 0.110389i | ||||||
\(835\) | 6.20650 | − | 11.6985i | 0.214785 | − | 0.404843i | ||||
\(836\) | 7.45398i | 0.257801i | ||||||||
\(837\) | 16.0836 | 0.555931 | ||||||||
\(838\) | −24.2194 | −0.836644 | ||||||||
\(839\) | −54.1303 | −1.86879 | −0.934393 | − | 0.356243i | \(-0.884058\pi\) | ||||
−0.934393 | + | 0.356243i | \(0.884058\pi\) | |||||||
\(840\) | 0.250165 | − | 0.471529i | 0.00863150 | − | 0.0162693i | ||||
\(841\) | −62.7053 | −2.16225 | ||||||||
\(842\) | 20.8487i | 0.718495i | ||||||||
\(843\) | −5.39996 | −0.185985 | ||||||||
\(844\) | 22.8397 | 0.786176 | ||||||||
\(845\) | 1.86283 | − | 3.51120i | 0.0640833 | − | 0.120789i | ||||
\(846\) | − | 37.4830i | − | 1.28869i | ||||||
\(847\) | 5.96548i | 0.204976i | ||||||||
\(848\) | 7.17340i | 0.246336i | ||||||||
\(849\) | − | 4.67933i | − | 0.160594i | ||||||
\(850\) | −8.70527 | − | 12.8554i | −0.298588 | − | 0.440936i | ||||
\(851\) | 31.2278 | + | 34.1455i | 1.07048 | + | 1.17049i | ||||
\(852\) | 4.80576i | 0.164643i | ||||||||
\(853\) | −54.7590 | −1.87491 | −0.937457 | − | 0.348101i | \(-0.886827\pi\) | ||||
−0.937457 | + | 0.348101i | \(0.886827\pi\) | |||||||
\(854\) | −1.35616 | −0.0464067 | ||||||||
\(855\) | −33.7121 | − | 17.8856i | −1.15293 | − | 0.611675i | ||||
\(856\) | 11.4715i | 0.392089i | ||||||||
\(857\) | 13.8273 | 0.472331 | 0.236165 | − | 0.971713i | \(-0.424109\pi\) | ||||
0.236165 | + | 0.971713i | \(0.424109\pi\) | |||||||
\(858\) | − | 1.57962i | − | 0.0539273i | ||||||
\(859\) | 27.9420i | 0.953368i | 0.879075 | + | 0.476684i | \(0.158161\pi\) | ||||
−0.879075 | + | 0.476684i | \(0.841839\pi\) | |||||||
\(860\) | 5.09983 | − | 9.61254i | 0.173903 | − | 0.327785i | ||||
\(861\) | 2.01835 | 0.0687852 | ||||||||
\(862\) | 28.2298i | 0.961510i | ||||||||
\(863\) | − | 0.665448i | − | 0.0226521i | −0.999936 | − | 0.0113261i | \(-0.996395\pi\) | ||
0.999936 | − | 0.0113261i | \(-0.00360527\pi\) | |||||||
\(864\) | − | 2.21322i | − | 0.0752951i | ||||||
\(865\) | −5.68899 | − | 3.01823i | −0.193431 | − | 0.102623i | ||||
\(866\) | 30.3997i | 1.03302i | ||||||||
\(867\) | 2.78041i | 0.0944277i | ||||||||
\(868\) | 4.59098 | 0.155828 | ||||||||
\(869\) | − | 10.9650i | − | 0.371961i | ||||||
\(870\) | 3.79208 | − | 7.14759i | 0.128563 | − | 0.242326i | ||||
\(871\) | 38.0059i | 1.28778i | ||||||||
\(872\) | 0.727748i | 0.0246447i | ||||||||
\(873\) | 31.5959 | 1.06936 | ||||||||
\(874\) | − | 45.4390i | − | 1.53700i | ||||||
\(875\) | −0.757540 | − | 7.02245i | −0.0256095 | − | 0.237402i | ||||
\(876\) | 1.68464 | 0.0569187 | ||||||||
\(877\) | 2.04026i | 0.0688948i | 0.999407 | + | 0.0344474i | \(0.0109671\pi\) | ||||
−0.999407 | + | 0.0344474i | \(0.989033\pi\) | |||||||
\(878\) | 33.7591i | 1.13931i | ||||||||
\(879\) | 10.5187 | 0.354786 | ||||||||
\(880\) | −1.30775 | + | 2.46494i | −0.0440842 | + | 0.0830932i | ||||
\(881\) | 19.5251 | 0.657816 | 0.328908 | − | 0.944362i | \(-0.393319\pi\) | ||||
0.328908 | + | 0.944362i | \(0.393319\pi\) | |||||||
\(882\) | 18.8602 | 0.635056 | ||||||||
\(883\) | −21.6799 | −0.729586 | −0.364793 | − | 0.931089i | \(-0.618860\pi\) | ||||
−0.364793 | + | 0.931089i | \(0.618860\pi\) | |||||||
\(884\) | 10.4021 | 0.349860 | ||||||||
\(885\) | 1.72836 | − | 3.25774i | 0.0580981 | − | 0.109508i | ||||
\(886\) | − | 15.5413i | − | 0.522119i | ||||||
\(887\) | 35.0252i | 1.17603i | 0.808850 | + | 0.588015i | \(0.200090\pi\) | ||||
−0.808850 | + | 0.588015i | \(0.799910\pi\) | |||||||
\(888\) | −1.69609 | + | 1.55116i | −0.0569171 | + | 0.0520536i | ||||
\(889\) | −9.78140 | −0.328058 | ||||||||
\(890\) | 27.2164 | + | 14.4393i | 0.912294 | + | 0.484008i | ||||
\(891\) | 9.65290 | 0.323384 | ||||||||
\(892\) | 3.32116i | 0.111201i | ||||||||
\(893\) | 78.3615 | 2.62227 | ||||||||
\(894\) | − | 5.15580i | − | 0.172436i | ||||||
\(895\) | −8.81339 | − | 4.67585i | −0.294599 | − | 0.156296i | ||||
\(896\) | − | 0.631751i | − | 0.0211053i | ||||||
\(897\) | 9.62925i | 0.321511i | ||||||||
\(898\) | 14.2184i | 0.474473i | ||||||||
\(899\) | 69.5916 | 2.32101 | ||||||||
\(900\) | −8.01030 | − | 11.8291i | −0.267010 | − | 0.394304i | ||||
\(901\) | 22.2742i | 0.742062i | ||||||||
\(902\) | −10.5510 | −0.351311 | ||||||||
\(903\) | 1.16168 | 0.0386582 | ||||||||
\(904\) | −17.9970 | −0.598570 | ||||||||
\(905\) | −4.12355 | + | 7.77237i | −0.137071 | + | 0.258362i | ||||
\(906\) | 1.20062i | 0.0398879i | ||||||||
\(907\) | −19.4042 | −0.644307 | −0.322153 | − | 0.946688i | \(-0.604407\pi\) | ||||
−0.322153 | + | 0.946688i | \(0.604407\pi\) | |||||||
\(908\) | −5.62938 | −0.186818 | ||||||||
\(909\) | 24.7239 | 0.820041 | ||||||||
\(910\) | 4.18042 | + | 2.21788i | 0.138580 | + | 0.0735219i | ||||
\(911\) | − | 7.46474i | − | 0.247318i | −0.992325 | − | 0.123659i | \(-0.960537\pi\) | ||
0.992325 | − | 0.123659i | \(-0.0394629\pi\) | |||||||
\(912\) | 2.25707 | 0.0747389 | ||||||||
\(913\) | 8.27583i | 0.273890i | ||||||||
\(914\) | −9.17031 | −0.303327 | ||||||||
\(915\) | 0.850049 | − | 1.60224i | 0.0281017 | − | 0.0529683i | ||||
\(916\) | −0.973208 | −0.0321557 | ||||||||
\(917\) | −3.93025 | −0.129788 | ||||||||
\(918\) | − | 6.87228i | − | 0.226819i | ||||||
\(919\) | − | 27.8014i | − | 0.917083i | −0.888673 | − | 0.458541i | \(-0.848372\pi\) | ||
0.888673 | − | 0.458541i | \(-0.151628\pi\) | |||||||
\(920\) | 7.97195 | − | 15.0261i | 0.262827 | − | 0.495397i | ||||
\(921\) | 7.53496 | 0.248285 | ||||||||
\(922\) | 10.3300i | 0.340199i | ||||||||
\(923\) | −42.6063 | −1.40240 | ||||||||
\(924\) | −0.297889 | −0.00979983 | ||||||||
\(925\) | −7.07460 | + | 29.5796i | −0.232611 | + | 0.972570i | ||||
\(926\) | 25.8049 | 0.848003 | ||||||||
\(927\) | −13.0671 | −0.429180 | ||||||||
\(928\) | − | 9.57629i | − | 0.314357i | ||||||
\(929\) | 19.4503 | 0.638145 | 0.319072 | − | 0.947730i | \(-0.396629\pi\) | ||||
0.319072 | + | 0.947730i | \(0.396629\pi\) | |||||||
\(930\) | −2.87766 | + | 5.42403i | −0.0943622 | + | 0.177861i | ||||
\(931\) | 39.4289i | 1.29223i | ||||||||
\(932\) | 14.4150i | 0.472178i | ||||||||
\(933\) | −1.87733 | −0.0614611 | ||||||||
\(934\) | 34.4582 | 1.12751 | ||||||||
\(935\) | −4.06070 | + | 7.65392i | −0.132799 | + | 0.250310i | ||||
\(936\) | 9.57166 | 0.312860 | ||||||||
\(937\) | − | 14.2786i | − | 0.466463i | −0.972421 | − | 0.233231i | \(-0.925070\pi\) | ||
0.972421 | − | 0.233231i | \(-0.0749299\pi\) | |||||||
\(938\) | 7.16727 | 0.234020 | ||||||||
\(939\) | − | 3.77861i | − | 0.123310i | ||||||
\(940\) | 25.9132 | + | 13.7480i | 0.845196 | + | 0.448409i | ||||
\(941\) | −18.0266 | −0.587649 | −0.293825 | − | 0.955859i | \(-0.594928\pi\) | ||||
−0.293825 | + | 0.955859i | \(0.594928\pi\) | |||||||
\(942\) | −0.0813572 | −0.00265076 | ||||||||
\(943\) | 64.3184 | 2.09450 | ||||||||
\(944\) | − | 4.36469i | − | 0.142058i | ||||||
\(945\) | 1.46527 | − | 2.76185i | 0.0476652 | − | 0.0898430i | ||||
\(946\) | −6.07273 | −0.197441 | ||||||||
\(947\) | 20.7621 | 0.674679 | 0.337339 | − | 0.941383i | \(-0.390473\pi\) | ||||
0.337339 | + | 0.941383i | \(0.390473\pi\) | |||||||
\(948\) | −3.32019 | −0.107835 | ||||||||
\(949\) | 14.9354i | 0.484825i | ||||||||
\(950\) | 24.7298 | − | 16.7462i | 0.802340 | − | 0.543319i | ||||
\(951\) | −8.66049 | −0.280836 | ||||||||
\(952\) | − | 1.96166i | − | 0.0635776i | ||||||
\(953\) | − | 40.9858i | − | 1.32766i | −0.747883 | − | 0.663831i | \(-0.768929\pi\) | ||
0.747883 | − | 0.663831i | \(-0.231071\pi\) | |||||||
\(954\) | 20.4960i | 0.663583i | ||||||||
\(955\) | −15.3341 | − | 8.13533i | −0.496199 | − | 0.263253i | ||||
\(956\) | 8.43344i | 0.272757i | ||||||||
\(957\) | −4.51550 | −0.145965 | ||||||||
\(958\) | 29.6039i | 0.956458i | ||||||||
\(959\) | 8.92401 | 0.288171 | ||||||||
\(960\) | 0.746385 | + | 0.395986i | 0.0240895 | + | 0.0127804i | ||||
\(961\) | −21.8103 | −0.703560 | ||||||||
\(962\) | −13.7521 | − | 15.0370i | −0.443385 | − | 0.484811i | ||||
\(963\) | 32.7767i | 1.05622i | ||||||||
\(964\) | 18.6567i | 0.600891i | ||||||||
\(965\) | −3.65939 | + | 6.89749i | −0.117800 | + | 0.222038i | ||||
\(966\) | 1.81591 | 0.0584260 | ||||||||
\(967\) | −25.1227 | −0.807892 | −0.403946 | − | 0.914783i | \(-0.632362\pi\) | ||||
−0.403946 | + | 0.914783i | \(0.632362\pi\) | |||||||
\(968\) | −9.44277 | −0.303502 | ||||||||
\(969\) | 7.00844 | 0.225144 | ||||||||
\(970\) | −11.5887 | + | 21.8433i | −0.372091 | + | 0.701345i | ||||
\(971\) | −10.0012 | −0.320953 | −0.160476 | − | 0.987040i | \(-0.551303\pi\) | ||||
−0.160476 | + | 0.987040i | \(0.551303\pi\) | |||||||
\(972\) | − | 9.56255i | − | 0.306719i | ||||||
\(973\) | − | 5.32992i | − | 0.170869i | ||||||
\(974\) | 27.0961 | 0.868214 | ||||||||
\(975\) | −5.24064 | + | 3.54879i | −0.167835 | + | 0.113652i | ||||
\(976\) | − | 2.14666i | − | 0.0687130i | ||||||
\(977\) | 49.4636 | 1.58248 | 0.791240 | − | 0.611505i | \(-0.209436\pi\) | ||||
0.791240 | + | 0.611505i | \(0.209436\pi\) | |||||||
\(978\) | − | 0.629549i | − | 0.0201308i | ||||||
\(979\) | − | 17.1940i | − | 0.549521i | ||||||
\(980\) | −6.91752 | + | 13.0387i | −0.220972 | + | 0.416505i | ||||
\(981\) | 2.07934i | 0.0663882i | ||||||||
\(982\) | 2.46033 | 0.0785123 | ||||||||
\(983\) | − | 36.4329i | − | 1.16203i | −0.813894 | − | 0.581014i | \(-0.802656\pi\) | ||
0.813894 | − | 0.581014i | \(-0.197344\pi\) | |||||||
\(984\) | 3.19485i | 0.101848i | ||||||||
\(985\) | 2.12574 | + | 1.12779i | 0.0677316 | + | 0.0359343i | ||||
\(986\) | − | 29.7354i | − | 0.946969i | ||||||
\(987\) | 3.13162i | 0.0996805i | ||||||||
\(988\) | 20.0104i | 0.636615i | ||||||||
\(989\) | 37.0190 | 1.17713 | ||||||||
\(990\) | −3.73653 | + | 7.04289i | −0.118755 | + | 0.223838i | ||||
\(991\) | − | 49.5991i | − | 1.57557i | −0.615953 | − | 0.787783i | \(-0.711229\pi\) | ||
0.615953 | − | 0.787783i | \(-0.288771\pi\) | |||||||
\(992\) | 7.26707i | 0.230730i | ||||||||
\(993\) | 2.09435 | 0.0664622 | ||||||||
\(994\) | 8.03482i | 0.254849i | ||||||||
\(995\) | 11.2857 | + | 5.98749i | 0.357780 | + | 0.189816i | ||||
\(996\) | 2.50592 | 0.0794031 | ||||||||
\(997\) | −3.21866 | −0.101936 | −0.0509680 | − | 0.998700i | \(-0.516231\pi\) | ||||
−0.0509680 | + | 0.998700i | \(0.516231\pi\) | |||||||
\(998\) | − | 31.4091i | − | 0.994238i | ||||||
\(999\) | −9.93437 | + | 9.08550i | −0.314310 | + | 0.287452i |
(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 | 370.2.c.b.369.5 | yes | 10 | |
3.2 | odd | 2 | 3330.2.e.c.739.7 | 10 | |||
5.2 | odd | 4 | 1850.2.d.i.1701.15 | 20 | |||
5.3 | odd | 4 | 1850.2.d.i.1701.6 | 20 | |||
5.4 | even | 2 | 370.2.c.a.369.6 | yes | 10 | ||
15.14 | odd | 2 | 3330.2.e.d.739.3 | 10 | |||
37.36 | even | 2 | 370.2.c.a.369.5 | ✓ | 10 | ||
111.110 | odd | 2 | 3330.2.e.d.739.4 | 10 | |||
185.73 | odd | 4 | 1850.2.d.i.1701.16 | 20 | |||
185.147 | odd | 4 | 1850.2.d.i.1701.5 | 20 | |||
185.184 | even | 2 | inner | 370.2.c.b.369.6 | yes | 10 | |
555.554 | odd | 2 | 3330.2.e.c.739.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.c.a.369.5 | ✓ | 10 | 37.36 | even | 2 | ||
370.2.c.a.369.6 | yes | 10 | 5.4 | even | 2 | ||
370.2.c.b.369.5 | yes | 10 | 1.1 | even | 1 | trivial | |
370.2.c.b.369.6 | yes | 10 | 185.184 | even | 2 | inner | |
1850.2.d.i.1701.5 | 20 | 185.147 | odd | 4 | |||
1850.2.d.i.1701.6 | 20 | 5.3 | odd | 4 | |||
1850.2.d.i.1701.15 | 20 | 5.2 | odd | 4 | |||
1850.2.d.i.1701.16 | 20 | 185.73 | odd | 4 | |||
3330.2.e.c.739.7 | 10 | 3.2 | odd | 2 | |||
3330.2.e.c.739.8 | 10 | 555.554 | odd | 2 | |||
3330.2.e.d.739.3 | 10 | 15.14 | odd | 2 | |||
3330.2.e.d.739.4 | 10 | 111.110 | odd | 2 |