Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(29,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.29");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.bb (of order \(4\), 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: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(70\) |
Relative dimension: | \(35\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 29.2 | ||
Character | \(\chi\) | \(=\) | 560.29 |
Dual form | 560.2.bb.c.309.2 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.40637 | − | 0.148759i | −0.994452 | − | 0.105189i | ||||
\(3\) | −0.279102 | + | 0.279102i | −0.161139 | + | 0.161139i | −0.783071 | − | 0.621932i | \(-0.786348\pi\) |
0.621932 | + | 0.783071i | \(0.286348\pi\) | |||||||
\(4\) | 1.95574 | + | 0.418421i | 0.977871 | + | 0.209210i | ||||
\(5\) | 2.19030 | − | 0.450071i | 0.979534 | − | 0.201278i | ||||
\(6\) | 0.434038 | − | 0.351001i | 0.177195 | − | 0.143295i | ||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.68825 | − | 0.879388i | −0.950439 | − | 0.310911i | ||||
\(9\) | 2.84420i | 0.948068i | ||||||||
\(10\) | −3.14733 | + | 0.307138i | −0.995272 | + | 0.0971254i | ||||
\(11\) | −2.35311 | + | 2.35311i | −0.709490 | + | 0.709490i | −0.966428 | − | 0.256938i | \(-0.917286\pi\) |
0.256938 | + | 0.966428i | \(0.417286\pi\) | |||||||
\(12\) | −0.662632 | + | 0.429069i | −0.191285 | + | 0.123861i | ||||
\(13\) | −2.34702 | + | 2.34702i | −0.650947 | + | 0.650947i | −0.953221 | − | 0.302274i | \(-0.902254\pi\) |
0.302274 | + | 0.953221i | \(0.402254\pi\) | |||||||
\(14\) | 1.40637 | + | 0.148759i | 0.375868 | + | 0.0397576i | ||||
\(15\) | −0.485702 | + | 0.736933i | −0.125408 | + | 0.190275i | ||||
\(16\) | 3.64985 | + | 1.63664i | 0.912462 | + | 0.409161i | ||||
\(17\) | 3.39463i | 0.823318i | 0.911338 | + | 0.411659i | \(0.135051\pi\) | ||||
−0.911338 | + | 0.411659i | \(0.864949\pi\) | |||||||
\(18\) | 0.423102 | − | 4.00000i | 0.0997261 | − | 0.942809i | ||||
\(19\) | −0.847544 | − | 0.847544i | −0.194440 | − | 0.194440i | 0.603172 | − | 0.797611i | \(-0.293903\pi\) |
−0.797611 | + | 0.603172i | \(0.793903\pi\) | |||||||
\(20\) | 4.47199 | + | 0.0362455i | 0.999967 | + | 0.00810475i | ||||
\(21\) | 0.279102 | − | 0.279102i | 0.0609050 | − | 0.0609050i | ||||
\(22\) | 3.65939 | − | 2.95929i | 0.780184 | − | 0.630923i | ||||
\(23\) | −2.16644 | −0.451734 | −0.225867 | − | 0.974158i | \(-0.572522\pi\) | ||||
−0.225867 | + | 0.974158i | \(0.572522\pi\) | |||||||
\(24\) | 0.995733 | − | 0.504856i | 0.203253 | − | 0.103053i | ||||
\(25\) | 4.59487 | − | 1.97159i | 0.918974 | − | 0.394317i | ||||
\(26\) | 3.64992 | − | 2.95163i | 0.715808 | − | 0.578863i | ||||
\(27\) | −1.63113 | − | 1.63113i | −0.313910 | − | 0.313910i | ||||
\(28\) | −1.95574 | − | 0.418421i | −0.369600 | − | 0.0790740i | ||||
\(29\) | −2.00809 | − | 2.00809i | −0.372893 | − | 0.372893i | 0.495637 | − | 0.868530i | \(-0.334935\pi\) |
−0.868530 | + | 0.495637i | \(0.834935\pi\) | |||||||
\(30\) | 0.792701 | − | 0.964147i | 0.144727 | − | 0.176028i | ||||
\(31\) | −2.92187 | −0.524784 | −0.262392 | − | 0.964961i | \(-0.584511\pi\) | ||||
−0.262392 | + | 0.964961i | \(0.584511\pi\) | |||||||
\(32\) | −4.88956 | − | 2.84467i | −0.864361 | − | 0.502872i | ||||
\(33\) | − | 1.31351i | − | 0.228653i | ||||||
\(34\) | 0.504982 | − | 4.77410i | 0.0866038 | − | 0.818751i | ||||
\(35\) | −2.19030 | + | 0.450071i | −0.370229 | + | 0.0760759i | ||||
\(36\) | −1.19007 | + | 5.56253i | −0.198346 | + | 0.927088i | ||||
\(37\) | 5.03883 | + | 5.03883i | 0.828379 | + | 0.828379i | 0.987293 | − | 0.158913i | \(-0.0507991\pi\) |
−0.158913 | + | 0.987293i | \(0.550799\pi\) | |||||||
\(38\) | 1.06588 | + | 1.31804i | 0.172908 | + | 0.213814i | ||||
\(39\) | − | 1.31011i | − | 0.209786i | ||||||
\(40\) | −6.28387 | − | 0.716224i | −0.993567 | − | 0.113245i | ||||
\(41\) | 11.0535i | 1.72627i | 0.504971 | + | 0.863136i | \(0.331503\pi\) | ||||
−0.504971 | + | 0.863136i | \(0.668497\pi\) | |||||||
\(42\) | −0.434038 | + | 0.351001i | −0.0669736 | + | 0.0541606i | ||||
\(43\) | 4.96192 | + | 4.96192i | 0.756686 | + | 0.756686i | 0.975718 | − | 0.219032i | \(-0.0702899\pi\) |
−0.219032 | + | 0.975718i | \(0.570290\pi\) | |||||||
\(44\) | −5.58667 | + | 3.61749i | −0.842222 | + | 0.545357i | ||||
\(45\) | 1.28009 | + | 6.22968i | 0.190825 | + | 0.928665i | ||||
\(46\) | 3.04682 | + | 0.322278i | 0.449228 | + | 0.0475174i | ||||
\(47\) | − | 7.39580i | − | 1.07879i | −0.842053 | − | 0.539394i | \(-0.818653\pi\) | ||
0.842053 | − | 0.539394i | \(-0.181347\pi\) | |||||||
\(48\) | −1.47547 | + | 0.561888i | −0.212966 | + | 0.0811016i | ||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.75537 | + | 2.08925i | −0.955354 | + | 0.295464i | ||||
\(51\) | −0.947446 | − | 0.947446i | −0.132669 | − | 0.132669i | ||||
\(52\) | −5.57221 | + | 3.60813i | −0.772726 | + | 0.500357i | ||||
\(53\) | −1.62915 | − | 1.62915i | −0.223781 | − | 0.223781i | 0.586307 | − | 0.810089i | \(-0.300581\pi\) |
−0.810089 | + | 0.586307i | \(0.800581\pi\) | |||||||
\(54\) | 2.05132 | + | 2.53661i | 0.279149 | + | 0.345189i | ||||
\(55\) | −4.09496 | + | 6.21310i | −0.552165 | + | 0.837774i | ||||
\(56\) | 2.68825 | + | 0.879388i | 0.359232 | + | 0.117513i | ||||
\(57\) | 0.473102 | 0.0626639 | ||||||||
\(58\) | 2.52539 | + | 3.12284i | 0.331601 | + | 0.410049i | ||||
\(59\) | −5.55555 | + | 5.55555i | −0.723271 | + | 0.723271i | −0.969270 | − | 0.245999i | \(-0.920884\pi\) |
0.245999 | + | 0.969270i | \(0.420884\pi\) | |||||||
\(60\) | −1.25826 | + | 1.23802i | −0.162440 | + | 0.159828i | ||||
\(61\) | 0.540392 | + | 0.540392i | 0.0691901 | + | 0.0691901i | 0.740855 | − | 0.671665i | \(-0.234421\pi\) |
−0.671665 | + | 0.740855i | \(0.734421\pi\) | |||||||
\(62\) | 4.10923 | + | 0.434656i | 0.521873 | + | 0.0552013i | ||||
\(63\) | − | 2.84420i | − | 0.358336i | ||||||
\(64\) | 6.45335 | + | 4.72803i | 0.806669 | + | 0.591003i | ||||
\(65\) | −4.08437 | + | 6.19702i | −0.506603 | + | 0.768646i | ||||
\(66\) | −0.195397 | + | 1.84728i | −0.0240518 | + | 0.227385i | ||||
\(67\) | 4.69437 | − | 4.69437i | 0.573508 | − | 0.573508i | −0.359599 | − | 0.933107i | \(-0.617086\pi\) |
0.933107 | + | 0.359599i | \(0.117086\pi\) | |||||||
\(68\) | −1.42038 | + | 6.63901i | −0.172247 | + | 0.805099i | ||||
\(69\) | 0.604658 | − | 0.604658i | 0.0727922 | − | 0.0727922i | ||||
\(70\) | 3.14733 | − | 0.307138i | 0.376178 | − | 0.0367100i | ||||
\(71\) | 16.1009i | 1.91082i | 0.295276 | + | 0.955412i | \(0.404589\pi\) | ||||
−0.295276 | + | 0.955412i | \(0.595411\pi\) | |||||||
\(72\) | 2.50116 | − | 7.64593i | 0.294764 | − | 0.901081i | ||||
\(73\) | 5.31323 | 0.621866 | 0.310933 | − | 0.950432i | \(-0.399359\pi\) | ||||
0.310933 | + | 0.950432i | \(0.399359\pi\) | |||||||
\(74\) | −6.33688 | − | 7.83603i | −0.736647 | − | 0.910920i | ||||
\(75\) | −0.732163 | + | 1.83271i | −0.0845429 | + | 0.211623i | ||||
\(76\) | −1.30295 | − | 2.01221i | −0.149458 | − | 0.230816i | ||||
\(77\) | 2.35311 | − | 2.35311i | 0.268162 | − | 0.268162i | ||||
\(78\) | −0.194892 | + | 1.84250i | −0.0220671 | + | 0.208622i | ||||
\(79\) | 3.05814 | 0.344068 | 0.172034 | − | 0.985091i | \(-0.444966\pi\) | ||||
0.172034 | + | 0.985091i | \(0.444966\pi\) | |||||||
\(80\) | 8.73089 | + | 1.94206i | 0.976143 | + | 0.217129i | ||||
\(81\) | −7.62211 | −0.846902 | ||||||||
\(82\) | 1.64432 | − | 15.5453i | 0.181584 | − | 1.71670i | ||||
\(83\) | −5.46375 | + | 5.46375i | −0.599725 | + | 0.599725i | −0.940239 | − | 0.340515i | \(-0.889399\pi\) |
0.340515 | + | 0.940239i | \(0.389399\pi\) | |||||||
\(84\) | 0.662632 | − | 0.429069i | 0.0722991 | − | 0.0468152i | ||||
\(85\) | 1.52782 | + | 7.43527i | 0.165716 | + | 0.806468i | ||||
\(86\) | −6.24015 | − | 7.71642i | −0.672893 | − | 0.832083i | ||||
\(87\) | 1.12092 | 0.120176 | ||||||||
\(88\) | 8.39504 | − | 4.25645i | 0.894915 | − | 0.453739i | ||||
\(89\) | − | 16.8612i | − | 1.78728i | −0.448780 | − | 0.893642i | \(-0.648141\pi\) | ||
0.448780 | − | 0.893642i | \(-0.351859\pi\) | |||||||
\(90\) | −0.873562 | − | 8.95164i | −0.0920815 | − | 0.943586i | ||||
\(91\) | 2.34702 | − | 2.34702i | 0.246035 | − | 0.246035i | ||||
\(92\) | −4.23700 | − | 0.906484i | −0.441738 | − | 0.0945075i | ||||
\(93\) | 0.815499 | − | 0.815499i | 0.0845634 | − | 0.0845634i | ||||
\(94\) | −1.10019 | + | 10.4012i | −0.113476 | + | 1.07280i | ||||
\(95\) | −2.23783 | − | 1.47492i | −0.229597 | − | 0.151324i | ||||
\(96\) | 2.15864 | − | 0.570732i | 0.220315 | − | 0.0582501i | ||||
\(97\) | 6.16712i | 0.626176i | 0.949724 | + | 0.313088i | \(0.101363\pi\) | ||||
−0.949724 | + | 0.313088i | \(0.898637\pi\) | |||||||
\(98\) | −1.40637 | − | 0.148759i | −0.142065 | − | 0.0150270i | ||||
\(99\) | −6.69273 | − | 6.69273i | −0.672645 | − | 0.672645i | ||||
\(100\) | 9.81133 | − | 1.93333i | 0.981133 | − | 0.193333i | ||||
\(101\) | 6.08324 | − | 6.08324i | 0.605305 | − | 0.605305i | −0.336410 | − | 0.941716i | \(-0.609213\pi\) |
0.941716 | + | 0.336410i | \(0.109213\pi\) | |||||||
\(102\) | 1.19152 | + | 1.47340i | 0.117978 | + | 0.145888i | ||||
\(103\) | 16.0661 | 1.58304 | 0.791519 | − | 0.611145i | \(-0.209291\pi\) | ||||
0.791519 | + | 0.611145i | \(0.209291\pi\) | |||||||
\(104\) | 8.37332 | − | 4.24543i | 0.821071 | − | 0.416299i | ||||
\(105\) | 0.485702 | − | 0.736933i | 0.0473997 | − | 0.0719173i | ||||
\(106\) | 2.04883 | + | 2.53354i | 0.199000 | + | 0.246079i | ||||
\(107\) | −12.1468 | − | 12.1468i | −1.17428 | − | 1.17428i | −0.981180 | − | 0.193097i | \(-0.938147\pi\) |
−0.193097 | − | 0.981180i | \(-0.561853\pi\) | |||||||
\(108\) | −2.50757 | − | 3.87256i | −0.241291 | − | 0.372637i | ||||
\(109\) | −4.17642 | − | 4.17642i | −0.400029 | − | 0.400029i | 0.478215 | − | 0.878243i | \(-0.341284\pi\) |
−0.878243 | + | 0.478215i | \(0.841284\pi\) | |||||||
\(110\) | 6.68328 | − | 8.12874i | 0.637226 | − | 0.775045i | ||||
\(111\) | −2.81269 | −0.266969 | ||||||||
\(112\) | −3.64985 | − | 1.63664i | −0.344878 | − | 0.154648i | ||||
\(113\) | 14.0838i | 1.32489i | 0.749111 | + | 0.662444i | \(0.230481\pi\) | ||||
−0.749111 | + | 0.662444i | \(0.769519\pi\) | |||||||
\(114\) | −0.665355 | − | 0.0703783i | −0.0623162 | − | 0.00659153i | ||||
\(115\) | −4.74517 | + | 0.975054i | −0.442489 | + | 0.0909242i | ||||
\(116\) | −3.08708 | − | 4.76754i | −0.286628 | − | 0.442655i | ||||
\(117\) | −6.67541 | − | 6.67541i | −0.617142 | − | 0.617142i | ||||
\(118\) | 8.63958 | − | 6.98670i | 0.795338 | − | 0.643178i | ||||
\(119\) | − | 3.39463i | − | 0.311185i | ||||||
\(120\) | 1.95374 | − | 1.55394i | 0.178351 | − | 0.141855i | ||||
\(121\) | − | 0.0742641i | − | 0.00675128i | ||||||
\(122\) | −0.679602 | − | 0.840378i | −0.0615283 | − | 0.0760843i | ||||
\(123\) | −3.08506 | − | 3.08506i | −0.278171 | − | 0.278171i | ||||
\(124\) | −5.71443 | − | 1.22257i | −0.513171 | − | 0.109790i | ||||
\(125\) | 9.17682 | − | 6.38640i | 0.820799 | − | 0.571217i | ||||
\(126\) | −0.423102 | + | 4.00000i | −0.0376929 | + | 0.356348i | ||||
\(127\) | 0.331675i | 0.0294314i | 0.999892 | + | 0.0147157i | \(0.00468432\pi\) | ||||
−0.999892 | + | 0.0147157i | \(0.995316\pi\) | |||||||
\(128\) | −8.37245 | − | 7.60934i | −0.740027 | − | 0.672577i | ||||
\(129\) | −2.76976 | −0.243864 | ||||||||
\(130\) | 6.66599 | − | 8.10770i | 0.584646 | − | 0.711093i | ||||
\(131\) | −4.88335 | − | 4.88335i | −0.426660 | − | 0.426660i | 0.460829 | − | 0.887489i | \(-0.347552\pi\) |
−0.887489 | + | 0.460829i | \(0.847552\pi\) | |||||||
\(132\) | 0.549601 | − | 2.56889i | 0.0478366 | − | 0.223594i | ||||
\(133\) | 0.847544 | + | 0.847544i | 0.0734914 | + | 0.0734914i | ||||
\(134\) | −7.30034 | + | 5.90367i | −0.630653 | + | 0.510000i | ||||
\(135\) | −4.30679 | − | 2.83854i | −0.370669 | − | 0.244303i | ||||
\(136\) | 2.98519 | − | 9.12560i | 0.255978 | − | 0.782514i | ||||
\(137\) | 10.8530 | 0.927237 | 0.463619 | − | 0.886035i | \(-0.346551\pi\) | ||||
0.463619 | + | 0.886035i | \(0.346551\pi\) | |||||||
\(138\) | −0.940319 | + | 0.760423i | −0.0800453 | + | 0.0647315i | ||||
\(139\) | 11.5768 | − | 11.5768i | 0.981935 | − | 0.981935i | −0.0179046 | − | 0.999840i | \(-0.505700\pi\) |
0.999840 | + | 0.0179046i | \(0.00569953\pi\) | |||||||
\(140\) | −4.47199 | − | 0.0362455i | −0.377952 | − | 0.00306331i | ||||
\(141\) | 2.06418 | + | 2.06418i | 0.173835 | + | 0.173835i | ||||
\(142\) | 2.39516 | − | 22.6438i | 0.200997 | − | 1.90022i | ||||
\(143\) | − | 11.0456i | − | 0.923680i | ||||||
\(144\) | −4.65495 | + | 10.3809i | −0.387913 | + | 0.865076i | ||||
\(145\) | −5.30212 | − | 3.49455i | −0.440317 | − | 0.290207i | ||||
\(146\) | −7.47235 | − | 0.790392i | −0.618416 | − | 0.0654133i | ||||
\(147\) | −0.279102 | + | 0.279102i | −0.0230199 | + | 0.0230199i | ||||
\(148\) | 7.74630 | + | 11.9630i | 0.636742 | + | 0.983353i | ||||
\(149\) | 9.32319 | − | 9.32319i | 0.763785 | − | 0.763785i | −0.213219 | − | 0.977004i | \(-0.568395\pi\) |
0.977004 | + | 0.213219i | \(0.0683948\pi\) | |||||||
\(150\) | 1.30232 | − | 2.46855i | 0.106334 | − | 0.201556i | ||||
\(151\) | 18.4845i | 1.50425i | 0.659023 | + | 0.752123i | \(0.270970\pi\) | ||||
−0.659023 | + | 0.752123i | \(0.729030\pi\) | |||||||
\(152\) | 1.53309 | + | 3.02373i | 0.124350 | + | 0.245257i | ||||
\(153\) | −9.65502 | −0.780562 | ||||||||
\(154\) | −3.65939 | + | 2.95929i | −0.294882 | + | 0.238467i | ||||
\(155\) | −6.39979 | + | 1.31505i | −0.514044 | + | 0.105627i | ||||
\(156\) | 0.548179 | − | 2.56225i | 0.0438894 | − | 0.205144i | ||||
\(157\) | 13.3909 | − | 13.3909i | 1.06871 | − | 1.06871i | 0.0712495 | − | 0.997459i | \(-0.477301\pi\) |
0.997459 | − | 0.0712495i | \(-0.0226987\pi\) | |||||||
\(158\) | −4.30088 | − | 0.454927i | −0.342159 | − | 0.0361921i | ||||
\(159\) | 0.909397 | 0.0721199 | ||||||||
\(160\) | −11.9899 | − | 4.03005i | −0.947888 | − | 0.318603i | ||||
\(161\) | 2.16644 | 0.170740 | ||||||||
\(162\) | 10.7195 | + | 1.13386i | 0.842203 | + | 0.0890845i | ||||
\(163\) | −3.01843 | + | 3.01843i | −0.236421 | + | 0.236421i | −0.815366 | − | 0.578945i | \(-0.803465\pi\) |
0.578945 | + | 0.815366i | \(0.303465\pi\) | |||||||
\(164\) | −4.62503 | + | 21.6179i | −0.361154 | + | 1.68807i | ||||
\(165\) | −0.591175 | − | 2.87700i | −0.0460229 | − | 0.223974i | ||||
\(166\) | 8.49683 | − | 6.87126i | 0.659482 | − | 0.533313i | ||||
\(167\) | −4.35664 | −0.337127 | −0.168563 | − | 0.985691i | \(-0.553913\pi\) | ||||
−0.168563 | + | 0.985691i | \(0.553913\pi\) | |||||||
\(168\) | −0.995733 | + | 0.504856i | −0.0768225 | + | 0.0389505i | ||||
\(169\) | 1.98298i | 0.152537i | ||||||||
\(170\) | −1.04262 | − | 10.6840i | −0.0799651 | − | 0.819426i | ||||
\(171\) | 2.41059 | − | 2.41059i | 0.184342 | − | 0.184342i | ||||
\(172\) | 7.62806 | + | 11.7804i | 0.581634 | + | 0.898247i | ||||
\(173\) | −4.72170 | + | 4.72170i | −0.358984 | + | 0.358984i | −0.863439 | − | 0.504454i | \(-0.831694\pi\) |
0.504454 | + | 0.863439i | \(0.331694\pi\) | |||||||
\(174\) | −1.57643 | − | 0.166748i | −0.119509 | − | 0.0126411i | ||||
\(175\) | −4.59487 | + | 1.97159i | −0.347340 | + | 0.149038i | ||||
\(176\) | −12.4397 | + | 4.73729i | −0.937678 | + | 0.357087i | ||||
\(177\) | − | 3.10112i | − | 0.233095i | ||||||
\(178\) | −2.50826 | + | 23.7131i | −0.188002 | + | 1.77737i | ||||
\(179\) | −1.50187 | − | 1.50187i | −0.112255 | − | 0.112255i | 0.648748 | − | 0.761003i | \(-0.275293\pi\) |
−0.761003 | + | 0.648748i | \(0.775293\pi\) | |||||||
\(180\) | −0.103090 | + | 12.7193i | −0.00768385 | + | 0.948037i | ||||
\(181\) | 15.6686 | − | 15.6686i | 1.16463 | − | 1.16463i | 0.181185 | − | 0.983449i | \(-0.442007\pi\) |
0.983449 | − | 0.181185i | \(-0.0579933\pi\) | |||||||
\(182\) | −3.64992 | + | 2.95163i | −0.270550 | + | 0.218790i | ||||
\(183\) | −0.301649 | −0.0222985 | ||||||||
\(184\) | 5.82393 | + | 1.90514i | 0.429346 | + | 0.140449i | ||||
\(185\) | 13.3044 | + | 8.76875i | 0.978160 | + | 0.644691i | ||||
\(186\) | −1.26821 | + | 1.02558i | −0.0929893 | + | 0.0751991i | ||||
\(187\) | −7.98794 | − | 7.98794i | −0.584136 | − | 0.584136i | ||||
\(188\) | 3.09456 | − | 14.4643i | 0.225694 | − | 1.05492i | ||||
\(189\) | 1.63113 | + | 1.63113i | 0.118647 | + | 0.118647i | ||||
\(190\) | 2.92781 | + | 2.40719i | 0.212406 | + | 0.174636i | ||||
\(191\) | 23.1607 | 1.67585 | 0.837925 | − | 0.545786i | \(-0.183769\pi\) | ||||
0.837925 | + | 0.545786i | \(0.183769\pi\) | |||||||
\(192\) | −3.12074 | + | 0.481542i | −0.225220 | + | 0.0347523i | ||||
\(193\) | 9.42975i | 0.678768i | 0.940648 | + | 0.339384i | \(0.110219\pi\) | ||||
−0.940648 | + | 0.339384i | \(0.889781\pi\) | |||||||
\(194\) | 0.917416 | − | 8.67323i | 0.0658666 | − | 0.622702i | ||||
\(195\) | −0.589645 | − | 2.86955i | −0.0422254 | − | 0.205493i | ||||
\(196\) | 1.95574 | + | 0.418421i | 0.139696 | + | 0.0298872i | ||||
\(197\) | −12.9007 | − | 12.9007i | −0.919137 | − | 0.919137i | 0.0778293 | − | 0.996967i | \(-0.475201\pi\) |
−0.996967 | + | 0.0778293i | \(0.975201\pi\) | |||||||
\(198\) | 8.41683 | + | 10.4080i | 0.598158 | + | 0.739668i | ||||
\(199\) | − | 5.19391i | − | 0.368186i | −0.982909 | − | 0.184093i | \(-0.941065\pi\) | ||
0.982909 | − | 0.184093i | \(-0.0589348\pi\) | |||||||
\(200\) | −14.0859 | + | 1.25944i | −0.996027 | + | 0.0890558i | ||||
\(201\) | 2.62041i | 0.184829i | ||||||||
\(202\) | −9.46022 | + | 7.65034i | −0.665619 | + | 0.538276i | ||||
\(203\) | 2.00809 | + | 2.00809i | 0.140940 | + | 0.140940i | ||||
\(204\) | −1.45653 | − | 2.24939i | −0.101977 | − | 0.157489i | ||||
\(205\) | 4.97488 | + | 24.2106i | 0.347461 | + | 1.69094i | ||||
\(206\) | −22.5948 | − | 2.38998i | −1.57425 | − | 0.166518i | ||||
\(207\) | − | 6.16181i | − | 0.428275i | ||||||
\(208\) | −12.4075 | + | 4.72503i | −0.860306 | + | 0.327622i | ||||
\(209\) | 3.98873 | 0.275906 | ||||||||
\(210\) | −0.792701 | + | 0.964147i | −0.0547016 | + | 0.0665324i | ||||
\(211\) | −11.1488 | − | 11.1488i | −0.767518 | − | 0.767518i | 0.210151 | − | 0.977669i | \(-0.432604\pi\) |
−0.977669 | + | 0.210151i | \(0.932604\pi\) | |||||||
\(212\) | −2.50453 | − | 3.86787i | −0.172012 | − | 0.265646i | ||||
\(213\) | −4.49378 | − | 4.49378i | −0.307909 | − | 0.307909i | ||||
\(214\) | 15.2759 | + | 18.8898i | 1.04424 | + | 1.29128i | ||||
\(215\) | 13.1013 | + | 8.63490i | 0.893504 | + | 0.588895i | ||||
\(216\) | 2.95048 | + | 5.81927i | 0.200755 | + | 0.395951i | ||||
\(217\) | 2.92187 | 0.198350 | ||||||||
\(218\) | 5.25230 | + | 6.49486i | 0.355731 | + | 0.439888i | ||||
\(219\) | −1.48293 | + | 1.48293i | −0.100207 | + | 0.100207i | ||||
\(220\) | −10.6084 | + | 10.4378i | −0.715217 | + | 0.703716i | ||||
\(221\) | −7.96726 | − | 7.96726i | −0.535936 | − | 0.535936i | ||||
\(222\) | 3.95568 | + | 0.418414i | 0.265488 | + | 0.0280821i | ||||
\(223\) | 8.80142i | 0.589387i | 0.955592 | + | 0.294693i | \(0.0952175\pi\) | ||||
−0.955592 | + | 0.294693i | \(0.904782\pi\) | |||||||
\(224\) | 4.88956 | + | 2.84467i | 0.326698 | + | 0.190068i | ||||
\(225\) | 5.60760 | + | 13.0688i | 0.373840 | + | 0.871250i | ||||
\(226\) | 2.09509 | − | 19.8069i | 0.139363 | − | 1.31754i | ||||
\(227\) | −0.588561 | + | 0.588561i | −0.0390642 | + | 0.0390642i | −0.726369 | − | 0.687305i | \(-0.758794\pi\) |
0.687305 | + | 0.726369i | \(0.258794\pi\) | |||||||
\(228\) | 0.925265 | + | 0.197955i | 0.0612771 | + | 0.0131099i | ||||
\(229\) | 17.3161 | − | 17.3161i | 1.14428 | − | 1.14428i | 0.156625 | − | 0.987658i | \(-0.449939\pi\) |
0.987658 | − | 0.156625i | \(-0.0500615\pi\) | |||||||
\(230\) | 6.81850 | − | 0.665396i | 0.449599 | − | 0.0438749i | ||||
\(231\) | 1.31351i | 0.0864229i | ||||||||
\(232\) | 3.63236 | + | 7.16414i | 0.238476 | + | 0.470349i | ||||
\(233\) | −17.7261 | −1.16128 | −0.580639 | − | 0.814161i | \(-0.697197\pi\) | ||||
−0.580639 | + | 0.814161i | \(0.697197\pi\) | |||||||
\(234\) | 8.39505 | + | 10.3811i | 0.548802 | + | 0.678634i | ||||
\(235\) | −3.32864 | − | 16.1991i | −0.217136 | − | 1.05671i | ||||
\(236\) | −13.1898 | + | 8.54066i | −0.858581 | + | 0.555949i | ||||
\(237\) | −0.853533 | + | 0.853533i | −0.0554429 | + | 0.0554429i | ||||
\(238\) | −0.504982 | + | 4.77410i | −0.0327331 | + | 0.309459i | ||||
\(239\) | −8.20370 | −0.530653 | −0.265327 | − | 0.964159i | \(-0.585480\pi\) | ||||
−0.265327 | + | 0.964159i | \(0.585480\pi\) | |||||||
\(240\) | −2.97884 | + | 1.89477i | −0.192283 | + | 0.122307i | ||||
\(241\) | −18.5239 | −1.19323 | −0.596614 | − | 0.802529i | \(-0.703488\pi\) | ||||
−0.596614 | + | 0.802529i | \(0.703488\pi\) | |||||||
\(242\) | −0.0110475 | + | 0.104443i | −0.000710158 | + | 0.00671383i | ||||
\(243\) | 7.02072 | − | 7.02072i | 0.450380 | − | 0.450380i | ||||
\(244\) | 0.830756 | + | 1.28298i | 0.0531837 | + | 0.0821343i | ||||
\(245\) | 2.19030 | − | 0.450071i | 0.139933 | − | 0.0287540i | ||||
\(246\) | 3.87980 | + | 4.79766i | 0.247367 | + | 0.305888i | ||||
\(247\) | 3.97841 | 0.253140 | ||||||||
\(248\) | 7.85472 | + | 2.56946i | 0.498775 | + | 0.163161i | ||||
\(249\) | − | 3.04988i | − | 0.193278i | ||||||
\(250\) | −13.8560 | + | 7.61649i | −0.876331 | + | 0.481709i | ||||
\(251\) | −2.93641 | + | 2.93641i | −0.185345 | + | 0.185345i | −0.793680 | − | 0.608335i | \(-0.791838\pi\) |
0.608335 | + | 0.793680i | \(0.291838\pi\) | |||||||
\(252\) | 1.19007 | − | 5.56253i | 0.0749676 | − | 0.350406i | ||||
\(253\) | 5.09788 | − | 5.09788i | 0.320501 | − | 0.320501i | ||||
\(254\) | 0.0493397 | − | 0.466457i | 0.00309585 | − | 0.0292681i | ||||
\(255\) | −2.50161 | − | 1.64878i | −0.156657 | − | 0.103250i | ||||
\(256\) | 10.6428 | + | 11.9470i | 0.665174 | + | 0.746688i | ||||
\(257\) | − | 1.51474i | − | 0.0944868i | −0.998883 | − | 0.0472434i | \(-0.984956\pi\) | ||
0.998883 | − | 0.0472434i | \(-0.0150436\pi\) | |||||||
\(258\) | 3.89530 | + | 0.412027i | 0.242511 | + | 0.0256517i | ||||
\(259\) | −5.03883 | − | 5.03883i | −0.313098 | − | 0.313098i | ||||
\(260\) | −10.5809 | + | 10.4108i | −0.656201 | + | 0.645649i | ||||
\(261\) | 5.71143 | − | 5.71143i | 0.353528 | − | 0.353528i | ||||
\(262\) | 6.14134 | + | 7.59423i | 0.379413 | + | 0.469173i | ||||
\(263\) | 16.5420 | 1.02003 | 0.510013 | − | 0.860167i | \(-0.329641\pi\) | ||||
0.510013 | + | 0.860167i | \(0.329641\pi\) | |||||||
\(264\) | −1.15509 | + | 3.53105i | −0.0710908 | + | 0.217321i | ||||
\(265\) | −4.30157 | − | 2.83510i | −0.264243 | − | 0.174159i | ||||
\(266\) | −1.06588 | − | 1.31804i | −0.0653532 | − | 0.0808141i | ||||
\(267\) | 4.70599 | + | 4.70599i | 0.288002 | + | 0.288002i | ||||
\(268\) | 11.1452 | − | 7.21675i | 0.680800 | − | 0.440833i | ||||
\(269\) | 7.26394 | + | 7.26394i | 0.442890 | + | 0.442890i | 0.892982 | − | 0.450092i | \(-0.148609\pi\) |
−0.450092 | + | 0.892982i | \(0.648609\pi\) | |||||||
\(270\) | 5.63467 | + | 4.63271i | 0.342915 | + | 0.281938i | ||||
\(271\) | 10.4016 | 0.631853 | 0.315927 | − | 0.948784i | \(-0.397685\pi\) | ||||
0.315927 | + | 0.948784i | \(0.397685\pi\) | |||||||
\(272\) | −5.55580 | + | 12.3899i | −0.336870 | + | 0.751247i | ||||
\(273\) | 1.31011i | 0.0792918i | ||||||||
\(274\) | −15.2634 | − | 1.61449i | −0.922093 | − | 0.0975349i | ||||
\(275\) | −6.17288 | + | 15.4516i | −0.372239 | + | 0.931767i | ||||
\(276\) | 1.43555 | − | 0.929553i | 0.0864103 | − | 0.0559525i | ||||
\(277\) | −3.02860 | − | 3.02860i | −0.181971 | − | 0.181971i | 0.610243 | − | 0.792214i | \(-0.291072\pi\) |
−0.792214 | + | 0.610243i | \(0.791072\pi\) | |||||||
\(278\) | −18.0035 | + | 14.5591i | −1.07978 | + | 0.873199i | ||||
\(279\) | − | 8.31041i | − | 0.497531i | ||||||
\(280\) | 6.28387 | + | 0.716224i | 0.375533 | + | 0.0428026i | ||||
\(281\) | 26.6477i | 1.58967i | 0.606827 | + | 0.794834i | \(0.292442\pi\) | ||||
−0.606827 | + | 0.794834i | \(0.707558\pi\) | |||||||
\(282\) | −2.59593 | − | 3.21006i | −0.154585 | − | 0.191156i | ||||
\(283\) | −1.79947 | − | 1.79947i | −0.106967 | − | 0.106967i | 0.651598 | − | 0.758565i | \(-0.274099\pi\) |
−0.758565 | + | 0.651598i | \(0.774099\pi\) | |||||||
\(284\) | −6.73694 | + | 31.4892i | −0.399764 | + | 1.86854i | ||||
\(285\) | 1.03624 | − | 0.212930i | 0.0613814 | − | 0.0126129i | ||||
\(286\) | −1.64314 | + | 15.5342i | −0.0971607 | + | 0.918556i | ||||
\(287\) | − | 11.0535i | − | 0.652470i | ||||||
\(288\) | 8.09083 | − | 13.9069i | 0.476757 | − | 0.819473i | ||||
\(289\) | 5.47650 | 0.322147 | ||||||||
\(290\) | 6.93689 | + | 5.70336i | 0.407348 | + | 0.334913i | ||||
\(291\) | −1.72125 | − | 1.72125i | −0.100902 | − | 0.100902i | ||||
\(292\) | 10.3913 | + | 2.22316i | 0.608105 | + | 0.130101i | ||||
\(293\) | −2.16307 | − | 2.16307i | −0.126368 | − | 0.126368i | 0.641094 | − | 0.767462i | \(-0.278481\pi\) |
−0.767462 | + | 0.641094i | \(0.778481\pi\) | |||||||
\(294\) | 0.434038 | − | 0.351001i | 0.0253136 | − | 0.0204708i | ||||
\(295\) | −9.66795 | + | 14.6687i | −0.562890 | + | 0.854047i | ||||
\(296\) | −9.11454 | − | 17.9767i | −0.529772 | − | 1.04488i | ||||
\(297\) | 7.67645 | 0.445433 | ||||||||
\(298\) | −14.4987 | + | 11.7249i | −0.839890 | + | 0.679206i | ||||
\(299\) | 5.08469 | − | 5.08469i | 0.294055 | − | 0.294055i | ||||
\(300\) | −2.19876 | + | 3.27795i | −0.126946 | + | 0.189253i | ||||
\(301\) | −4.96192 | − | 4.96192i | −0.286000 | − | 0.286000i | ||||
\(302\) | 2.74974 | − | 25.9960i | 0.158230 | − | 1.49590i | ||||
\(303\) | 3.39569i | 0.195077i | ||||||||
\(304\) | −1.70628 | − | 4.48054i | −0.0978618 | − | 0.256976i | ||||
\(305\) | 1.42684 | + | 0.940409i | 0.0817005 | + | 0.0538476i | ||||
\(306\) | 13.5785 | + | 1.43627i | 0.776231 | + | 0.0821063i | ||||
\(307\) | −17.9609 | + | 17.9609i | −1.02508 | + | 1.02508i | −0.0254033 | + | 0.999677i | \(0.508087\pi\) |
−0.999677 | + | 0.0254033i | \(0.991913\pi\) | |||||||
\(308\) | 5.58667 | − | 3.61749i | 0.318330 | − | 0.206125i | ||||
\(309\) | −4.48407 | + | 4.48407i | −0.255090 | + | 0.255090i | ||||
\(310\) | 9.19609 | − | 0.897417i | 0.522303 | − | 0.0509699i | ||||
\(311\) | − | 17.0625i | − | 0.967527i | −0.875199 | − | 0.483764i | \(-0.839269\pi\) | ||
0.875199 | − | 0.483764i | \(-0.160731\pi\) | |||||||
\(312\) | −1.15210 | + | 3.52191i | −0.0652248 | + | 0.199389i | ||||
\(313\) | −12.1923 | −0.689147 | −0.344574 | − | 0.938759i | \(-0.611976\pi\) | ||||
−0.344574 | + | 0.938759i | \(0.611976\pi\) | |||||||
\(314\) | −20.8245 | + | 16.8405i | −1.17520 | + | 0.950363i | ||||
\(315\) | −1.28009 | − | 6.22968i | −0.0721252 | − | 0.351002i | ||||
\(316\) | 5.98094 | + | 1.27959i | 0.336454 | + | 0.0719826i | ||||
\(317\) | −13.2752 | + | 13.2752i | −0.745611 | + | 0.745611i | −0.973652 | − | 0.228040i | \(-0.926768\pi\) |
0.228040 | + | 0.973652i | \(0.426768\pi\) | |||||||
\(318\) | −1.27895 | − | 0.135281i | −0.0717198 | − | 0.00758620i | ||||
\(319\) | 9.45053 | 0.529128 | ||||||||
\(320\) | 16.2628 | + | 7.45135i | 0.909116 | + | 0.416543i | ||||
\(321\) | 6.78039 | 0.378444 | ||||||||
\(322\) | −3.04682 | − | 0.322278i | −0.169792 | − | 0.0179599i | ||||
\(323\) | 2.87710 | − | 2.87710i | 0.160086 | − | 0.160086i | ||||
\(324\) | −14.9069 | − | 3.18925i | −0.828160 | − | 0.177180i | ||||
\(325\) | −6.15691 | + | 15.4116i | −0.341524 | + | 0.854883i | ||||
\(326\) | 4.69404 | − | 3.79600i | 0.259979 | − | 0.210241i | ||||
\(327\) | 2.33129 | 0.128921 | ||||||||
\(328\) | 9.72035 | − | 29.7147i | 0.536716 | − | 1.64072i | ||||
\(329\) | 7.39580i | 0.407744i | ||||||||
\(330\) | 0.403430 | + | 4.13406i | 0.0222081 | + | 0.227572i | ||||
\(331\) | −10.9561 | + | 10.9561i | −0.602199 | + | 0.602199i | −0.940896 | − | 0.338697i | \(-0.890014\pi\) |
0.338697 | + | 0.940896i | \(0.390014\pi\) | |||||||
\(332\) | −12.9718 | + | 8.39954i | −0.711922 | + | 0.460985i | ||||
\(333\) | −14.3315 | + | 14.3315i | −0.785360 | + | 0.785360i | ||||
\(334\) | 6.12704 | + | 0.648090i | 0.335257 | + | 0.0354619i | ||||
\(335\) | 8.16929 | − | 12.3949i | 0.446336 | − | 0.677205i | ||||
\(336\) | 1.47547 | − | 0.561888i | 0.0804934 | − | 0.0306535i | ||||
\(337\) | 0.474560i | 0.0258509i | 0.999916 | + | 0.0129255i | \(0.00411441\pi\) | ||||
−0.999916 | + | 0.0129255i | \(0.995886\pi\) | |||||||
\(338\) | 0.294987 | − | 2.78880i | 0.0160452 | − | 0.151691i | ||||
\(339\) | −3.93080 | − | 3.93080i | −0.213492 | − | 0.213492i | ||||
\(340\) | −0.123040 | + | 15.1807i | −0.00667279 | + | 0.823291i | ||||
\(341\) | 6.87549 | − | 6.87549i | 0.372329 | − | 0.372329i | ||||
\(342\) | −3.74877 | + | 3.03158i | −0.202710 | + | 0.163929i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −8.97542 | − | 17.7023i | −0.483922 | − | 0.954445i | ||||
\(345\) | 1.05225 | − | 1.59652i | 0.0566510 | − | 0.0859539i | ||||
\(346\) | 7.34285 | − | 5.93805i | 0.394754 | − | 0.319232i | ||||
\(347\) | 20.8645 | + | 20.8645i | 1.12007 | + | 1.12007i | 0.991731 | + | 0.128335i | \(0.0409634\pi\) |
0.128335 | + | 0.991731i | \(0.459037\pi\) | |||||||
\(348\) | 2.19224 | + | 0.469018i | 0.117516 | + | 0.0251420i | ||||
\(349\) | −0.488555 | − | 0.488555i | −0.0261517 | − | 0.0261517i | 0.693910 | − | 0.720062i | \(-0.255887\pi\) |
−0.720062 | + | 0.693910i | \(0.755887\pi\) | |||||||
\(350\) | 6.75537 | − | 2.08925i | 0.361090 | − | 0.111675i | ||||
\(351\) | 7.65658 | 0.408678 | ||||||||
\(352\) | 18.1995 | − | 4.81185i | 0.970038 | − | 0.256473i | ||||
\(353\) | − | 23.3169i | − | 1.24103i | −0.784194 | − | 0.620516i | \(-0.786923\pi\) | ||
0.784194 | − | 0.620516i | \(-0.213077\pi\) | |||||||
\(354\) | −0.461321 | + | 4.36132i | −0.0245189 | + | 0.231802i | ||||
\(355\) | 7.24655 | + | 35.2659i | 0.384607 | + | 1.87172i | ||||
\(356\) | 7.05508 | − | 32.9762i | 0.373918 | − | 1.74773i | ||||
\(357\) | 0.947446 | + | 0.947446i | 0.0501442 | + | 0.0501442i | ||||
\(358\) | 1.88877 | + | 2.33560i | 0.0998244 | + | 0.123440i | ||||
\(359\) | 14.5780i | 0.769397i | 0.923042 | + | 0.384699i | \(0.125695\pi\) | ||||
−0.923042 | + | 0.384699i | \(0.874305\pi\) | |||||||
\(360\) | 2.03709 | − | 17.8726i | 0.107364 | − | 0.941969i | ||||
\(361\) | − | 17.5633i | − | 0.924386i | ||||||
\(362\) | −24.3666 | + | 19.7049i | −1.28068 | + | 1.03567i | ||||
\(363\) | 0.0207272 | + | 0.0207272i | 0.00108790 | + | 0.00108790i | ||||
\(364\) | 5.57221 | − | 3.60813i | 0.292063 | − | 0.189117i | ||||
\(365\) | 11.6376 | − | 2.39133i | 0.609139 | − | 0.125168i | ||||
\(366\) | 0.424229 | + | 0.0448730i | 0.0221748 | + | 0.00234555i | ||||
\(367\) | 24.7854i | 1.29379i | 0.762580 | + | 0.646894i | \(0.223932\pi\) | ||||
−0.762580 | + | 0.646894i | \(0.776068\pi\) | |||||||
\(368\) | −7.90719 | − | 3.54570i | −0.412191 | − | 0.184832i | ||||
\(369\) | −31.4385 | −1.63662 | ||||||||
\(370\) | −17.4065 | − | 14.3112i | −0.904919 | − | 0.744006i | ||||
\(371\) | 1.62915 | + | 1.62915i | 0.0845813 | + | 0.0845813i | ||||
\(372\) | 1.93613 | − | 1.25368i | 0.100384 | − | 0.0650005i | ||||
\(373\) | −13.4261 | − | 13.4261i | −0.695176 | − | 0.695176i | 0.268190 | − | 0.963366i | \(-0.413574\pi\) |
−0.963366 | + | 0.268190i | \(0.913574\pi\) | |||||||
\(374\) | 10.0457 | + | 12.4223i | 0.519451 | + | 0.642340i | ||||
\(375\) | −0.778811 | + | 4.34372i | −0.0402176 | + | 0.224309i | ||||
\(376\) | −6.50378 | + | 19.8818i | −0.335407 | + | 1.02532i | ||||
\(377\) | 9.42607 | 0.485468 | ||||||||
\(378\) | −2.05132 | − | 2.53661i | −0.105508 | − | 0.130469i | ||||
\(379\) | 22.2169 | − | 22.2169i | 1.14121 | − | 1.14121i | 0.152978 | − | 0.988230i | \(-0.451114\pi\) |
0.988230 | − | 0.152978i | \(-0.0488863\pi\) | |||||||
\(380\) | −3.75949 | − | 3.82093i | −0.192858 | − | 0.196009i | ||||
\(381\) | −0.0925710 | − | 0.0925710i | −0.00474255 | − | 0.00474255i | ||||
\(382\) | −32.5725 | − | 3.44537i | −1.66655 | − | 0.176280i | ||||
\(383\) | − | 15.1410i | − | 0.773670i | −0.922149 | − | 0.386835i | \(-0.873568\pi\) | ||
0.922149 | − | 0.386835i | \(-0.126432\pi\) | |||||||
\(384\) | 4.46054 | − | 0.212986i | 0.227626 | − | 0.0108689i | ||||
\(385\) | 4.09496 | − | 6.21310i | 0.208699 | − | 0.316649i | ||||
\(386\) | 1.40276 | − | 13.2617i | 0.0713987 | − | 0.675002i | ||||
\(387\) | −14.1127 | + | 14.1127i | −0.717390 | + | 0.717390i | ||||
\(388\) | −2.58045 | + | 12.0613i | −0.131002 | + | 0.612319i | ||||
\(389\) | −6.59187 | + | 6.59187i | −0.334221 | + | 0.334221i | −0.854187 | − | 0.519966i | \(-0.825945\pi\) |
0.519966 | + | 0.854187i | \(0.325945\pi\) | |||||||
\(390\) | 0.402386 | + | 4.12336i | 0.0203756 | + | 0.208794i | ||||
\(391\) | − | 7.35427i | − | 0.371921i | ||||||
\(392\) | −2.68825 | − | 0.879388i | −0.135777 | − | 0.0444158i | ||||
\(393\) | 2.72590 | 0.137503 | ||||||||
\(394\) | 16.2240 | + | 20.0622i | 0.817355 | + | 1.01072i | ||||
\(395\) | 6.69827 | − | 1.37638i | 0.337027 | − | 0.0692534i | ||||
\(396\) | −10.2889 | − | 15.8896i | −0.517035 | − | 0.798484i | ||||
\(397\) | 0.462411 | − | 0.462411i | 0.0232078 | − | 0.0232078i | −0.695408 | − | 0.718615i | \(-0.744776\pi\) |
0.718615 | + | 0.695408i | \(0.244776\pi\) | |||||||
\(398\) | −0.772642 | + | 7.30455i | −0.0387291 | + | 0.366144i | ||||
\(399\) | −0.473102 | −0.0236847 | ||||||||
\(400\) | 19.9974 | + | 0.324179i | 0.999869 | + | 0.0162090i | ||||
\(401\) | −17.4581 | −0.871817 | −0.435908 | − | 0.899991i | \(-0.643573\pi\) | ||||
−0.435908 | + | 0.899991i | \(0.643573\pi\) | |||||||
\(402\) | 0.389810 | − | 3.68526i | 0.0194420 | − | 0.183804i | ||||
\(403\) | 6.85770 | − | 6.85770i | 0.341606 | − | 0.341606i | ||||
\(404\) | 14.4426 | − | 9.35190i | 0.718547 | − | 0.465274i | ||||
\(405\) | −16.6948 | + | 3.43049i | −0.829569 | + | 0.170463i | ||||
\(406\) | −2.52539 | − | 3.12284i | −0.125333 | − | 0.154984i | ||||
\(407\) | −23.7139 | −1.17545 | ||||||||
\(408\) | 1.71380 | + | 3.38014i | 0.0848456 | + | 0.167342i | ||||
\(409\) | − | 24.3263i | − | 1.20286i | −0.798926 | − | 0.601430i | \(-0.794598\pi\) | ||
0.798926 | − | 0.601430i | \(-0.205402\pi\) | |||||||
\(410\) | −3.39496 | − | 34.7891i | −0.167665 | − | 1.71811i | ||||
\(411\) | −3.02910 | + | 3.02910i | −0.149414 | + | 0.149414i | ||||
\(412\) | 31.4211 | + | 6.72237i | 1.54801 | + | 0.331188i | ||||
\(413\) | 5.55555 | − | 5.55555i | 0.273371 | − | 0.273371i | ||||
\(414\) | −0.916626 | + | 8.66577i | −0.0450497 | + | 0.425899i | ||||
\(415\) | −9.50820 | + | 14.4264i | −0.466739 | + | 0.708162i | ||||
\(416\) | 18.1524 | − | 4.79940i | 0.889996 | − | 0.235310i | ||||
\(417\) | 6.46223i | 0.316457i | ||||||||
\(418\) | −5.60962 | − | 0.593361i | −0.274376 | − | 0.0290222i | ||||
\(419\) | −6.87681 | − | 6.87681i | −0.335954 | − | 0.335954i | 0.518888 | − | 0.854842i | \(-0.326346\pi\) |
−0.854842 | + | 0.518888i | \(0.826346\pi\) | |||||||
\(420\) | 1.25826 | − | 1.23802i | 0.0613966 | − | 0.0604093i | ||||
\(421\) | −13.4535 | + | 13.4535i | −0.655685 | + | 0.655685i | −0.954356 | − | 0.298671i | \(-0.903457\pi\) |
0.298671 | + | 0.954356i | \(0.403457\pi\) | |||||||
\(422\) | 14.0209 | + | 17.3379i | 0.682526 | + | 0.843994i | ||||
\(423\) | 21.0352 | 1.02277 | ||||||||
\(424\) | 2.94691 | + | 5.81222i | 0.143114 | + | 0.282266i | ||||
\(425\) | 6.69280 | + | 15.5979i | 0.324649 | + | 0.756608i | ||||
\(426\) | 5.65142 | + | 6.98841i | 0.273812 | + | 0.338589i | ||||
\(427\) | −0.540392 | − | 0.540392i | −0.0261514 | − | 0.0261514i | ||||
\(428\) | −18.6736 | − | 28.8385i | −0.902620 | − | 1.39396i | ||||
\(429\) | 3.08285 | + | 3.08285i | 0.148841 | + | 0.148841i | ||||
\(430\) | −17.1408 | − | 14.0928i | −0.826602 | − | 0.679615i | ||||
\(431\) | 36.7314 | 1.76929 | 0.884645 | − | 0.466266i | \(-0.154401\pi\) | ||||
0.884645 | + | 0.466266i | \(0.154401\pi\) | |||||||
\(432\) | −3.28379 | − | 8.62294i | −0.157991 | − | 0.414871i | ||||
\(433\) | − | 36.4368i | − | 1.75104i | −0.483182 | − | 0.875520i | \(-0.660519\pi\) | ||
0.483182 | − | 0.875520i | \(-0.339481\pi\) | |||||||
\(434\) | −4.10923 | − | 0.434656i | −0.197249 | − | 0.0208641i | ||||
\(435\) | 2.45516 | − | 0.504496i | 0.117716 | − | 0.0241887i | ||||
\(436\) | −6.42050 | − | 9.91550i | −0.307486 | − | 0.474866i | ||||
\(437\) | 1.83616 | + | 1.83616i | 0.0878352 | + | 0.0878352i | ||||
\(438\) | 2.30614 | − | 1.86495i | 0.110192 | − | 0.0891105i | ||||
\(439\) | − | 22.3458i | − | 1.06651i | −0.845955 | − | 0.533255i | \(-0.820969\pi\) | ||
0.845955 | − | 0.533255i | \(-0.179031\pi\) | |||||||
\(440\) | 16.4720 | − | 13.1013i | 0.785272 | − | 0.624579i | ||||
\(441\) | 2.84420i | 0.135438i | ||||||||
\(442\) | 10.0197 | + | 12.3901i | 0.476589 | + | 0.589337i | ||||
\(443\) | 20.0254 | + | 20.0254i | 0.951435 | + | 0.951435i | 0.998874 | − | 0.0474395i | \(-0.0151061\pi\) |
−0.0474395 | + | 0.998874i | \(0.515106\pi\) | |||||||
\(444\) | −5.50090 | − | 1.17689i | −0.261061 | − | 0.0558527i | ||||
\(445\) | −7.58875 | − | 36.9312i | −0.359741 | − | 1.75071i | ||||
\(446\) | 1.30929 | − | 12.3780i | 0.0619968 | − | 0.586117i | ||||
\(447\) | 5.20423i | 0.246152i | ||||||||
\(448\) | −6.45335 | − | 4.72803i | −0.304892 | − | 0.223378i | ||||
\(449\) | 20.4015 | 0.962805 | 0.481403 | − | 0.876500i | \(-0.340128\pi\) | ||||
0.481403 | + | 0.876500i | \(0.340128\pi\) | |||||||
\(450\) | −5.94224 | − | 19.2137i | −0.280120 | − | 0.905741i | ||||
\(451\) | −26.0102 | − | 26.0102i | −1.22477 | − | 1.22477i | ||||
\(452\) | −5.89293 | + | 27.5442i | −0.277180 | + | 1.29557i | ||||
\(453\) | −5.15905 | − | 5.15905i | −0.242393 | − | 0.242393i | ||||
\(454\) | 0.915287 | − | 0.740179i | 0.0429566 | − | 0.0347383i | ||||
\(455\) | 4.08437 | − | 6.19702i | 0.191478 | − | 0.290521i | ||||
\(456\) | −1.27181 | − | 0.416040i | −0.0595582 | − | 0.0194829i | ||||
\(457\) | −11.8938 | −0.556368 | −0.278184 | − | 0.960528i | \(-0.589733\pi\) | ||||
−0.278184 | + | 0.960528i | \(0.589733\pi\) | |||||||
\(458\) | −26.9288 | + | 21.7769i | −1.25830 | + | 1.01757i | ||||
\(459\) | 5.53707 | − | 5.53707i | 0.258448 | − | 0.258448i | ||||
\(460\) | −9.68831 | − | 0.0785239i | −0.451720 | − | 0.00366119i | ||||
\(461\) | 18.8680 | + | 18.8680i | 0.878772 | + | 0.878772i | 0.993408 | − | 0.114636i | \(-0.0365702\pi\) |
−0.114636 | + | 0.993408i | \(0.536570\pi\) | |||||||
\(462\) | 0.195397 | − | 1.84728i | 0.00909071 | − | 0.0859434i | ||||
\(463\) | 30.6387i | 1.42390i | 0.702229 | + | 0.711951i | \(0.252188\pi\) | ||||
−0.702229 | + | 0.711951i | \(0.747812\pi\) | |||||||
\(464\) | −4.04270 | − | 10.6158i | −0.187678 | − | 0.492825i | ||||
\(465\) | 1.41916 | − | 2.15323i | 0.0658120 | − | 0.0998534i | ||||
\(466\) | 24.9295 | + | 2.63693i | 1.15483 | + | 0.122153i | ||||
\(467\) | 8.47204 | − | 8.47204i | 0.392039 | − | 0.392039i | −0.483374 | − | 0.875414i | \(-0.660589\pi\) |
0.875414 | + | 0.483374i | \(0.160589\pi\) | |||||||
\(468\) | −10.2622 | − | 15.8485i | −0.474372 | − | 0.732597i | ||||
\(469\) | −4.69437 | + | 4.69437i | −0.216766 | + | 0.216766i | ||||
\(470\) | 2.27153 | + | 23.2770i | 0.104778 | + | 1.07369i | ||||
\(471\) | 7.47483i | 0.344422i | ||||||||
\(472\) | 19.8202 | − | 10.0492i | 0.912297 | − | 0.462552i | ||||
\(473\) | −23.3519 | −1.07372 | ||||||||
\(474\) | 1.32735 | − | 1.07341i | 0.0609673 | − | 0.0493034i | ||||
\(475\) | −5.56536 | − | 2.22335i | −0.255356 | − | 0.102014i | ||||
\(476\) | 1.42038 | − | 6.63901i | 0.0651031 | − | 0.304299i | ||||
\(477\) | 4.63364 | − | 4.63364i | 0.212160 | − | 0.212160i | ||||
\(478\) | 11.5374 | + | 1.22038i | 0.527709 | + | 0.0558187i | ||||
\(479\) | 5.79127 | 0.264610 | 0.132305 | − | 0.991209i | \(-0.457762\pi\) | ||||
0.132305 | + | 0.991209i | \(0.457762\pi\) | |||||||
\(480\) | 4.47121 | − | 2.22162i | 0.204082 | − | 0.101403i | ||||
\(481\) | −23.6525 | −1.07846 | ||||||||
\(482\) | 26.0514 | + | 2.75560i | 1.18661 | + | 0.125514i | ||||
\(483\) | −0.604658 | + | 0.604658i | −0.0275129 | + | 0.0275129i | ||||
\(484\) | 0.0310736 | − | 0.145241i | 0.00141244 | − | 0.00660188i | ||||
\(485\) | 2.77564 | + | 13.5079i | 0.126035 | + | 0.613361i | ||||
\(486\) | −10.9181 | + | 8.82932i | −0.495256 | + | 0.400506i | ||||
\(487\) | −1.46355 | −0.0663197 | −0.0331599 | − | 0.999450i | \(-0.510557\pi\) | ||||
−0.0331599 | + | 0.999450i | \(0.510557\pi\) | |||||||
\(488\) | −0.977494 | − | 1.92792i | −0.0442491 | − | 0.0872729i | ||||
\(489\) | − | 1.68489i | − | 0.0761936i | ||||||
\(490\) | −3.14733 | + | 0.307138i | −0.142182 | + | 0.0138751i | ||||
\(491\) | −2.47769 | + | 2.47769i | −0.111817 | + | 0.111817i | −0.760801 | − | 0.648985i | \(-0.775194\pi\) |
0.648985 | + | 0.760801i | \(0.275194\pi\) | |||||||
\(492\) | −4.74273 | − | 7.32443i | −0.213819 | − | 0.330211i | ||||
\(493\) | 6.81673 | − | 6.81673i | 0.307010 | − | 0.307010i | ||||
\(494\) | −5.59511 | − | 0.591825i | −0.251736 | − | 0.0266275i | ||||
\(495\) | −17.6713 | − | 11.6469i | −0.794267 | − | 0.523490i | ||||
\(496\) | −10.6644 | − | 4.78207i | −0.478845 | − | 0.214721i | ||||
\(497\) | − | 16.1009i | − | 0.722224i | ||||||
\(498\) | −0.453698 | + | 4.28926i | −0.0203307 | + | 0.192206i | ||||
\(499\) | 26.8709 | + | 26.8709i | 1.20291 | + | 1.20291i | 0.973279 | + | 0.229627i | \(0.0737506\pi\) |
0.229627 | + | 0.973279i | \(0.426249\pi\) | |||||||
\(500\) | 20.6197 | − | 8.65037i | 0.922140 | − | 0.386856i | ||||
\(501\) | 1.21594 | − | 1.21594i | 0.0543244 | − | 0.0543244i | ||||
\(502\) | 4.56649 | − | 3.69285i | 0.203812 | − | 0.164820i | ||||
\(503\) | 33.7090 | 1.50301 | 0.751506 | − | 0.659726i | \(-0.229328\pi\) | ||||
0.751506 | + | 0.659726i | \(0.229328\pi\) | |||||||
\(504\) | −2.50116 | + | 7.64593i | −0.111410 | + | 0.340577i | ||||
\(505\) | 10.5863 | − | 16.0621i | 0.471083 | − | 0.714752i | ||||
\(506\) | −7.92785 | + | 6.41114i | −0.352436 | + | 0.285010i | ||||
\(507\) | −0.553453 | − | 0.553453i | −0.0245797 | − | 0.0245797i | ||||
\(508\) | −0.138780 | + | 0.648670i | −0.00615735 | + | 0.0287801i | ||||
\(509\) | −13.1713 | − | 13.1713i | −0.583808 | − | 0.583808i | 0.352139 | − | 0.935948i | \(-0.385454\pi\) |
−0.935948 | + | 0.352139i | \(0.885454\pi\) | |||||||
\(510\) | 3.27292 | + | 2.69093i | 0.144927 | + | 0.119156i | ||||
\(511\) | −5.31323 | −0.235043 | ||||||||
\(512\) | −13.1904 | − | 18.3851i | −0.582941 | − | 0.812515i | ||||
\(513\) | 2.76490i | 0.122073i | ||||||||
\(514\) | −0.225331 | + | 2.13028i | −0.00993894 | + | 0.0939626i | ||||
\(515\) | 35.1896 | − | 7.23088i | 1.55064 | − | 0.318631i | ||||
\(516\) | −5.41693 | − | 1.15892i | −0.238467 | − | 0.0510188i | ||||
\(517\) | 17.4031 | + | 17.4031i | 0.765390 | + | 0.765390i | ||||
\(518\) | 6.33688 | + | 7.83603i | 0.278427 | + | 0.344295i | ||||
\(519\) | − | 2.63567i | − | 0.115693i | ||||||
\(520\) | 16.4294 | − | 13.0674i | 0.720476 | − | 0.573043i | ||||
\(521\) | 27.9324i | 1.22374i | 0.790958 | + | 0.611871i | \(0.209583\pi\) | ||||
−0.790958 | + | 0.611871i | \(0.790417\pi\) | |||||||
\(522\) | −8.88200 | + | 7.18274i | −0.388754 | + | 0.314380i | ||||
\(523\) | 7.58361 | + | 7.58361i | 0.331608 | + | 0.331608i | 0.853197 | − | 0.521589i | \(-0.174660\pi\) |
−0.521589 | + | 0.853197i | \(0.674660\pi\) | |||||||
\(524\) | −7.50727 | − | 11.5939i | −0.327957 | − | 0.506480i | ||||
\(525\) | 0.732163 | − | 1.83271i | 0.0319542 | − | 0.0799860i | ||||
\(526\) | −23.2642 | − | 2.46078i | −1.01437 | − | 0.107295i | ||||
\(527\) | − | 9.91867i | − | 0.432064i | ||||||
\(528\) | 2.14976 | − | 4.79413i | 0.0935561 | − | 0.208638i | ||||
\(529\) | −18.3065 | −0.795936 | ||||||||
\(530\) | 5.62784 | + | 4.62710i | 0.244458 | + | 0.200988i | ||||
\(531\) | −15.8011 | − | 15.8011i | −0.685710 | − | 0.685710i | ||||
\(532\) | 1.30295 | + | 2.01221i | 0.0564899 | + | 0.0872402i | ||||
\(533\) | −25.9429 | − | 25.9429i | −1.12371 | − | 1.12371i | ||||
\(534\) | −5.91829 | − | 7.31841i | −0.256110 | − | 0.316699i | ||||
\(535\) | −32.0722 | − | 21.1383i | −1.38660 | − | 0.913888i | ||||
\(536\) | −16.7478 | + | 8.49145i | −0.723394 | + | 0.366775i | ||||
\(537\) | 0.838349 | 0.0361774 | ||||||||
\(538\) | −9.13519 | − | 11.2963i | −0.393846 | − | 0.487020i | ||||
\(539\) | −2.35311 | + | 2.35311i | −0.101356 | + | 0.101356i | ||||
\(540\) | −7.23526 | − | 7.35350i | −0.311356 | − | 0.316444i | ||||
\(541\) | −10.1790 | − | 10.1790i | −0.437631 | − | 0.437631i | 0.453583 | − | 0.891214i | \(-0.350146\pi\) |
−0.891214 | + | 0.453583i | \(0.850146\pi\) | |||||||
\(542\) | −14.6285 | − | 1.54734i | −0.628348 | − | 0.0664638i | ||||
\(543\) | 8.74623i | 0.375337i | ||||||||
\(544\) | 9.65661 | − | 16.5982i | 0.414024 | − | 0.711644i | ||||
\(545\) | −11.0273 | − | 7.26795i | −0.472359 | − | 0.311325i | ||||
\(546\) | 0.194892 | − | 1.84250i | 0.00834060 | − | 0.0788519i | ||||
\(547\) | 16.9073 | − | 16.9073i | 0.722905 | − | 0.722905i | −0.246291 | − | 0.969196i | \(-0.579212\pi\) |
0.969196 | + | 0.246291i | \(0.0792118\pi\) | |||||||
\(548\) | 21.2257 | + | 4.54113i | 0.906718 | + | 0.193988i | ||||
\(549\) | −1.53699 | + | 1.53699i | −0.0655969 | + | 0.0655969i | ||||
\(550\) | 10.9799 | − | 20.8124i | 0.468185 | − | 0.887442i | ||||
\(551\) | 3.40389i | 0.145011i | ||||||||
\(552\) | −2.15720 | + | 1.09374i | −0.0918164 | + | 0.0465527i | ||||
\(553\) | −3.05814 | −0.130046 | ||||||||
\(554\) | 3.80879 | + | 4.70985i | 0.161820 | + | 0.200102i | ||||
\(555\) | −6.16066 | + | 1.26591i | −0.261505 | + | 0.0537350i | ||||
\(556\) | 27.4853 | − | 17.7973i | 1.16564 | − | 0.754775i | ||||
\(557\) | −8.36638 | + | 8.36638i | −0.354495 | + | 0.354495i | −0.861779 | − | 0.507284i | \(-0.830649\pi\) |
0.507284 | + | 0.861779i | \(0.330649\pi\) | |||||||
\(558\) | −1.23625 | + | 11.6875i | −0.0523346 | + | 0.494771i | ||||
\(559\) | −23.2915 | −0.985124 | ||||||||
\(560\) | −8.73089 | − | 1.94206i | −0.368947 | − | 0.0820670i | ||||
\(561\) | 4.45889 | 0.188255 | ||||||||
\(562\) | 3.96409 | − | 37.4764i | 0.167215 | − | 1.58085i | ||||
\(563\) | 31.3813 | − | 31.3813i | 1.32256 | − | 1.32256i | 0.410870 | − | 0.911694i | \(-0.365225\pi\) |
0.911694 | − | 0.410870i | \(-0.134775\pi\) | |||||||
\(564\) | 3.17331 | + | 4.90070i | 0.133620 | + | 0.206357i | ||||
\(565\) | 6.33869 | + | 30.8477i | 0.266671 | + | 1.29777i | ||||
\(566\) | 2.26303 | + | 2.79840i | 0.0951221 | + | 0.117626i | ||||
\(567\) | 7.62211 | 0.320099 | ||||||||
\(568\) | 14.1589 | − | 43.2832i | 0.594095 | − | 1.81612i | ||||
\(569\) | 24.9959i | 1.04788i | 0.851754 | + | 0.523941i | \(0.175539\pi\) | ||||
−0.851754 | + | 0.523941i | \(0.824461\pi\) | |||||||
\(570\) | −1.48901 | + | 0.145307i | −0.0623676 | + | 0.00608626i | ||||
\(571\) | −10.5685 | + | 10.5685i | −0.442279 | + | 0.442279i | −0.892777 | − | 0.450498i | \(-0.851246\pi\) |
0.450498 | + | 0.892777i | \(0.351246\pi\) | |||||||
\(572\) | 4.62171 | − | 21.6023i | 0.193243 | − | 0.903239i | ||||
\(573\) | −6.46419 | + | 6.46419i | −0.270045 | + | 0.270045i | ||||
\(574\) | −1.64432 | + | 15.5453i | −0.0686324 | + | 0.648850i | ||||
\(575\) | −9.95453 | + | 4.27133i | −0.415132 | + | 0.178127i | ||||
\(576\) | −13.4475 | + | 18.3547i | −0.560311 | + | 0.764777i | ||||
\(577\) | 11.8907i | 0.495014i | 0.968886 | + | 0.247507i | \(0.0796114\pi\) | ||||
−0.968886 | + | 0.247507i | \(0.920389\pi\) | |||||||
\(578\) | −7.70198 | − | 0.814681i | −0.320360 | − | 0.0338863i | ||||
\(579\) | −2.63186 | − | 2.63186i | −0.109376 | − | 0.109376i | ||||
\(580\) | −8.90738 | − | 9.05295i | −0.369859 | − | 0.375903i | ||||
\(581\) | 5.46375 | − | 5.46375i | 0.226675 | − | 0.226675i | ||||
\(582\) | 2.16466 | + | 2.67677i | 0.0897281 | + | 0.110956i | ||||
\(583\) | 7.66715 | 0.317541 | ||||||||
\(584\) | −14.2833 | − | 4.67239i | −0.591046 | − | 0.193345i | ||||
\(585\) | −17.6256 | − | 11.6168i | −0.728729 | − | 0.480294i | ||||
\(586\) | 2.72030 | + | 3.36385i | 0.112374 | + | 0.138959i | ||||
\(587\) | 16.0540 | + | 16.0540i | 0.662620 | + | 0.662620i | 0.955997 | − | 0.293377i | \(-0.0947791\pi\) |
−0.293377 | + | 0.955997i | \(0.594779\pi\) | |||||||
\(588\) | −0.662632 | + | 0.429069i | −0.0273265 | + | 0.0176945i | ||||
\(589\) | 2.47642 | + | 2.47642i | 0.102039 | + | 0.102039i | ||||
\(590\) | 15.7788 | − | 19.1914i | 0.649603 | − | 0.790099i | ||||
\(591\) | 7.20122 | 0.296218 | ||||||||
\(592\) | 10.1442 | + | 26.6378i | 0.416924 | + | 1.09481i | ||||
\(593\) | − | 16.8255i | − | 0.690941i | −0.938430 | − | 0.345471i | \(-0.887719\pi\) | ||
0.938430 | − | 0.345471i | \(-0.112281\pi\) | |||||||
\(594\) | −10.7959 | − | 1.14194i | −0.442961 | − | 0.0468545i | ||||
\(595\) | −1.52782 | − | 7.43527i | −0.0626347 | − | 0.304816i | ||||
\(596\) | 22.1348 | − | 14.3327i | 0.906675 | − | 0.587091i | ||||
\(597\) | 1.44963 | + | 1.44963i | 0.0593293 | + | 0.0593293i | ||||
\(598\) | −7.90734 | + | 6.39455i | −0.323355 | + | 0.261492i | ||||
\(599\) | 39.0027i | 1.59361i | 0.604238 | + | 0.796804i | \(0.293478\pi\) | ||||
−0.604238 | + | 0.796804i | \(0.706522\pi\) | |||||||
\(600\) | 3.57990 | − | 4.28292i | 0.146149 | − | 0.174850i | ||||
\(601\) | 40.5397i | 1.65365i | 0.562459 | + | 0.826825i | \(0.309855\pi\) | ||||
−0.562459 | + | 0.826825i | \(0.690145\pi\) | |||||||
\(602\) | 6.24015 | + | 7.71642i | 0.254330 | + | 0.314498i | ||||
\(603\) | 13.3517 | + | 13.3517i | 0.543725 | + | 0.543725i | ||||
\(604\) | −7.73428 | + | 36.1509i | −0.314704 | + | 1.47096i | ||||
\(605\) | −0.0334241 | − | 0.162661i | −0.00135888 | − | 0.00661311i | ||||
\(606\) | 0.505140 | − | 4.77558i | 0.0205199 | − | 0.193995i | ||||
\(607\) | 25.2830i | 1.02620i | 0.858328 | + | 0.513102i | \(0.171504\pi\) | ||||
−0.858328 | + | 0.513102i | \(0.828496\pi\) | |||||||
\(608\) | 1.73313 | + | 6.55511i | 0.0702879 | + | 0.265845i | ||||
\(609\) | −1.12092 | −0.0454221 | ||||||||
\(610\) | −1.86677 | − | 1.53482i | −0.0755831 | − | 0.0621429i | ||||
\(611\) | 17.3581 | + | 17.3581i | 0.702234 | + | 0.702234i | ||||
\(612\) | −18.8827 | − | 4.03986i | −0.763288 | − | 0.163302i | ||||
\(613\) | −5.73016 | − | 5.73016i | −0.231439 | − | 0.231439i | 0.581854 | − | 0.813293i | \(-0.302327\pi\) |
−0.813293 | + | 0.581854i | \(0.802327\pi\) | |||||||
\(614\) | 27.9314 | − | 22.5877i | 1.12722 | − | 0.911567i | ||||
\(615\) | −8.14572 | − | 5.36873i | −0.328467 | − | 0.216488i | ||||
\(616\) | −8.39504 | + | 4.25645i | −0.338246 | + | 0.171497i | ||||
\(617\) | 38.7107 | 1.55844 | 0.779218 | − | 0.626753i | \(-0.215617\pi\) | ||||
0.779218 | + | 0.626753i | \(0.215617\pi\) | |||||||
\(618\) | 6.97329 | − | 5.63920i | 0.280507 | − | 0.226842i | ||||
\(619\) | −11.8179 | + | 11.8179i | −0.475001 | + | 0.475001i | −0.903529 | − | 0.428528i | \(-0.859032\pi\) |
0.428528 | + | 0.903529i | \(0.359032\pi\) | |||||||
\(620\) | −13.0666 | − | 0.105905i | −0.524767 | − | 0.00425324i | ||||
\(621\) | 3.53374 | + | 3.53374i | 0.141804 | + | 0.141804i | ||||
\(622\) | −2.53821 | + | 23.9962i | −0.101773 | + | 0.962160i | ||||
\(623\) | 16.8612i | 0.675530i | ||||||||
\(624\) | 2.14419 | − | 4.78172i | 0.0858364 | − | 0.191422i | ||||
\(625\) | 17.2257 | − | 18.1184i | 0.689028 | − | 0.724735i | ||||
\(626\) | 17.1468 | + | 1.81371i | 0.685324 | + | 0.0724905i | ||||
\(627\) | −1.11326 | + | 1.11326i | −0.0444594 | + | 0.0444594i | ||||
\(628\) | 31.7921 | − | 20.5861i | 1.26864 | − | 0.821474i | ||||
\(629\) | −17.1050 | + | 17.1050i | −0.682020 | + | 0.682020i | ||||
\(630\) | 0.873562 | + | 8.95164i | 0.0348036 | + | 0.356642i | ||||
\(631\) | − | 3.31829i | − | 0.132099i | −0.997816 | − | 0.0660495i | \(-0.978960\pi\) | ||
0.997816 | − | 0.0660495i | \(-0.0210395\pi\) | |||||||
\(632\) | −8.22105 | − | 2.68930i | −0.327016 | − | 0.106974i | ||||
\(633\) | 6.22332 | 0.247355 | ||||||||
\(634\) | 20.6447 | − | 16.6950i | 0.819905 | − | 0.663045i | ||||
\(635\) | 0.149277 | + | 0.726469i | 0.00592389 | + | 0.0288290i | ||||
\(636\) | 1.77855 | + | 0.380510i | 0.0705239 | + | 0.0150882i | ||||
\(637\) | −2.34702 | + | 2.34702i | −0.0929924 | + | 0.0929924i | ||||
\(638\) | −13.2909 | − | 1.40585i | −0.526193 | − | 0.0556583i | ||||
\(639\) | −45.7942 | −1.81159 | ||||||||
\(640\) | −21.7630 | − | 12.8986i | −0.860257 | − | 0.509861i | ||||
\(641\) | 27.1752 | 1.07336 | 0.536678 | − | 0.843787i | \(-0.319679\pi\) | ||||
0.536678 | + | 0.843787i | \(0.319679\pi\) | |||||||
\(642\) | −9.53572 | − | 1.00865i | −0.376345 | − | 0.0398081i | ||||
\(643\) | −21.5065 | + | 21.5065i | −0.848133 | + | 0.848133i | −0.989900 | − | 0.141767i | \(-0.954722\pi\) |
0.141767 | + | 0.989900i | \(0.454722\pi\) | |||||||
\(644\) | 4.23700 | + | 0.906484i | 0.166961 | + | 0.0357205i | ||||
\(645\) | −6.06662 | + | 1.24659i | −0.238873 | + | 0.0490844i | ||||
\(646\) | −4.47425 | + | 3.61826i | −0.176037 | + | 0.142359i | ||||
\(647\) | 6.44417 | 0.253347 | 0.126673 | − | 0.991944i | \(-0.459570\pi\) | ||||
0.126673 | + | 0.991944i | \(0.459570\pi\) | |||||||
\(648\) | 20.4901 | + | 6.70279i | 0.804928 | + | 0.263311i | ||||
\(649\) | − | 26.1456i | − | 1.02631i | ||||||
\(650\) | 10.9515 | − | 20.7585i | 0.429553 | − | 0.814216i | ||||
\(651\) | −0.815499 | + | 0.815499i | −0.0319619 | + | 0.0319619i | ||||
\(652\) | −7.16623 | + | 4.64029i | −0.280651 | + | 0.181728i | ||||
\(653\) | −26.3507 | + | 26.3507i | −1.03118 | + | 1.03118i | −0.0316854 | + | 0.999498i | \(0.510087\pi\) |
−0.999498 | + | 0.0316854i | \(0.989913\pi\) | |||||||
\(654\) | −3.27865 | − | 0.346801i | −0.128205 | − | 0.0135610i | ||||
\(655\) | −12.8939 | − | 8.49816i | −0.503805 | − | 0.332051i | ||||
\(656\) | −18.0907 | + | 40.3437i | −0.706324 | + | 1.57516i | ||||
\(657\) | 15.1119i | 0.589571i | ||||||||
\(658\) | 1.10019 | − | 10.4012i | 0.0428900 | − | 0.405482i | ||||
\(659\) | −23.1868 | − | 23.1868i | −0.903231 | − | 0.903231i | 0.0924832 | − | 0.995714i | \(-0.470520\pi\) |
−0.995714 | + | 0.0924832i | \(0.970520\pi\) | |||||||
\(660\) | 0.0476090 | − | 5.87402i | 0.00185318 | − | 0.228646i | ||||
\(661\) | −0.247738 | + | 0.247738i | −0.00963589 | + | 0.00963589i | −0.711908 | − | 0.702272i | \(-0.752169\pi\) |
0.702272 | + | 0.711908i | \(0.252169\pi\) | |||||||
\(662\) | 17.0381 | − | 13.7784i | 0.662203 | − | 0.535514i | ||||
\(663\) | 4.44735 | 0.172721 | ||||||||
\(664\) | 19.4927 | − | 9.88316i | 0.756462 | − | 0.383541i | ||||
\(665\) | 2.23783 | + | 1.47492i | 0.0867795 | + | 0.0571951i | ||||
\(666\) | 22.2873 | − | 18.0234i | 0.863614 | − | 0.698392i | ||||
\(667\) | 4.35042 | + | 4.35042i | 0.168449 | + | 0.168449i | ||||
\(668\) | −8.52046 | − | 1.82291i | −0.329666 | − | 0.0705304i | ||||
\(669\) | −2.45649 | − | 2.45649i | −0.0949734 | − | 0.0949734i | ||||
\(670\) | −13.3329 | + | 16.2165i | −0.515094 | + | 0.626499i | ||||
\(671\) | −2.54321 | −0.0981794 | ||||||||
\(672\) | −2.15864 | + | 0.570732i | −0.0832713 | + | 0.0220165i | ||||
\(673\) | 45.2564i | 1.74451i | 0.489056 | + | 0.872253i | \(0.337342\pi\) | ||||
−0.489056 | + | 0.872253i | \(0.662658\pi\) | |||||||
\(674\) | 0.0705951 | − | 0.667405i | 0.00271922 | − | 0.0257075i | ||||
\(675\) | −10.7107 | − | 4.27891i | −0.412256 | − | 0.164695i | ||||
\(676\) | −0.829720 | + | 3.87820i | −0.0319123 | + | 0.149161i | ||||
\(677\) | 32.0109 | + | 32.0109i | 1.23028 | + | 1.23028i | 0.963856 | + | 0.266424i | \(0.0858422\pi\) |
0.266424 | + | 0.963856i | \(0.414158\pi\) | |||||||
\(678\) | 4.94341 | + | 6.11289i | 0.189850 | + | 0.234764i | ||||
\(679\) | − | 6.16712i | − | 0.236672i | ||||||
\(680\) | 2.43131 | − | 21.3314i | 0.0932367 | − | 0.818022i | ||||
\(681\) | − | 0.328537i | − | 0.0125896i | ||||||
\(682\) | −10.6923 | + | 8.64668i | −0.409428 | + | 0.331098i | ||||
\(683\) | 27.9310 | + | 27.9310i | 1.06875 | + | 1.06875i | 0.997455 | + | 0.0712942i | \(0.0227129\pi\) |
0.0712942 | + | 0.997455i | \(0.477287\pi\) | |||||||
\(684\) | 5.72313 | − | 3.70585i | 0.218829 | − | 0.141697i | ||||
\(685\) | 23.7715 | − | 4.88464i | 0.908261 | − | 0.186632i | ||||
\(686\) | 1.40637 | + | 0.148759i | 0.0536954 | + | 0.00567966i | ||||
\(687\) | 9.66593i | 0.368778i | ||||||||
\(688\) | 9.98936 | + | 26.2312i | 0.380841 | + | 1.00005i | ||||
\(689\) | 7.64730 | 0.291339 | ||||||||
\(690\) | −1.71734 | + | 2.08877i | −0.0653781 | + | 0.0795180i | ||||
\(691\) | 8.48560 | + | 8.48560i | 0.322808 | + | 0.322808i | 0.849843 | − | 0.527036i | \(-0.176697\pi\) |
−0.527036 | + | 0.849843i | \(0.676697\pi\) | |||||||
\(692\) | −11.2101 | + | 7.25877i | −0.426144 | + | 0.275937i | ||||
\(693\) | 6.69273 | + | 6.69273i | 0.254236 | + | 0.254236i | ||||
\(694\) | −26.2394 | − | 32.4470i | −0.996034 | − | 1.23167i | ||||
\(695\) | 20.1464 | − | 30.5672i | 0.764197 | − | 1.15948i | ||||
\(696\) | −3.01332 | − | 0.985727i | −0.114220 | − | 0.0373639i | ||||
\(697\) | −37.5227 | −1.42127 | ||||||||
\(698\) | 0.614411 | + | 0.759765i | 0.0232558 | + | 0.0287575i | ||||
\(699\) | 4.94739 | − | 4.94739i | 0.187127 | − | 0.187127i | ||||
\(700\) | −9.81133 | + | 1.93333i | −0.370834 | + | 0.0730728i | ||||
\(701\) | −13.1810 | − | 13.1810i | −0.497841 | − | 0.497841i | 0.412924 | − | 0.910765i | \(-0.364507\pi\) |
−0.910765 | + | 0.412924i | \(0.864507\pi\) | |||||||
\(702\) | −10.7680 | − | 1.13899i | −0.406411 | − | 0.0429883i | ||||
\(703\) | − | 8.54127i | − | 0.322140i | ||||||
\(704\) | −26.3110 | + | 4.05989i | −0.991634 | + | 0.153013i | ||||
\(705\) | 5.45021 | + | 3.59216i | 0.205267 | + | 0.135288i | ||||
\(706\) | −3.46860 | + | 32.7921i | −0.130543 | + | 1.23415i | ||||
\(707\) | −6.08324 | + | 6.08324i | −0.228784 | + | 0.228784i | ||||
\(708\) | 1.29757 | − | 6.06500i | 0.0487658 | − | 0.227936i | ||||
\(709\) | −13.3068 | + | 13.3068i | −0.499747 | + | 0.499747i | −0.911359 | − | 0.411612i | \(-0.864966\pi\) |
0.411612 | + | 0.911359i | \(0.364966\pi\) | |||||||
\(710\) | −4.94519 | − | 50.6748i | −0.185590 | − | 1.90179i | ||||
\(711\) | 8.69799i | 0.326200i | ||||||||
\(712\) | −14.8275 | + | 45.3271i | −0.555686 | + | 1.69871i | ||||
\(713\) | 6.33007 | 0.237063 | ||||||||
\(714\) | −1.19152 | − | 1.47340i | −0.0445914 | − | 0.0551406i | ||||
\(715\) | −4.97131 | − | 24.1932i | −0.185916 | − | 0.904776i | ||||
\(716\) | −2.30886 | − | 3.56569i | −0.0862861 | − | 0.133256i | ||||
\(717\) | 2.28967 | − | 2.28967i | 0.0855091 | − | 0.0855091i | ||||
\(718\) | 2.16861 | − | 20.5020i | 0.0809319 | − | 0.765129i | ||||
\(719\) | 2.29721 | 0.0856715 | 0.0428357 | − | 0.999082i | \(-0.486361\pi\) | ||||
0.0428357 | + | 0.999082i | \(0.486361\pi\) | |||||||
\(720\) | −5.52361 | + | 24.8324i | −0.205853 | + | 0.925450i | ||||
\(721\) | −16.0661 | −0.598332 | ||||||||
\(722\) | −2.61271 | + | 24.7005i | −0.0972350 | + | 0.919258i | ||||
\(723\) | 5.17004 | − | 5.17004i | 0.192276 | − | 0.192276i | ||||
\(724\) | 37.1997 | − | 24.0876i | 1.38252 | − | 0.895208i | ||||
\(725\) | −13.1861 | − | 5.26780i | −0.489718 | − | 0.195641i | ||||
\(726\) | −0.0260667 | − | 0.0322335i | −0.000967428 | − | 0.00119630i | ||||
\(727\) | −27.4131 | −1.01670 | −0.508348 | − | 0.861152i | \(-0.669743\pi\) | ||||
−0.508348 | + | 0.861152i | \(0.669743\pi\) | |||||||
\(728\) | −8.37332 | + | 4.24543i | −0.310336 | + | 0.157346i | ||||
\(729\) | − | 18.9474i | − | 0.701754i | ||||||
\(730\) | −16.7225 | + | 1.63189i | −0.618926 | + | 0.0603990i | ||||
\(731\) | −16.8439 | + | 16.8439i | −0.622993 | + | 0.622993i | ||||
\(732\) | −0.589947 | − | 0.126216i | −0.0218051 | − | 0.00466508i | ||||
\(733\) | 13.8814 | − | 13.8814i | 0.512721 | − | 0.512721i | −0.402638 | − | 0.915359i | \(-0.631907\pi\) |
0.915359 | + | 0.402638i | \(0.131907\pi\) | |||||||
\(734\) | 3.68706 | − | 34.8574i | 0.136092 | − | 1.28661i | ||||
\(735\) | −0.485702 | + | 0.736933i | −0.0179154 | + | 0.0271822i | ||||
\(736\) | 10.5930 | + | 6.16282i | 0.390462 | + | 0.227165i | ||||
\(737\) | 22.0927i | 0.813796i | ||||||||
\(738\) | 44.2141 | + | 4.67677i | 1.62754 | + | 0.172154i | ||||
\(739\) | 36.0336 | + | 36.0336i | 1.32552 | + | 1.32552i | 0.909235 | + | 0.416283i | \(0.136667\pi\) |
0.416283 | + | 0.909235i | \(0.363333\pi\) | |||||||
\(740\) | 22.3510 | + | 22.7162i | 0.821638 | + | 0.835066i | ||||
\(741\) | −1.11038 | + | 1.11038i | −0.0407908 | + | 0.0407908i | ||||
\(742\) | −2.04883 | − | 2.53354i | −0.0752151 | − | 0.0930091i | ||||
\(743\) | −38.8070 | −1.42369 | −0.711845 | − | 0.702337i | \(-0.752140\pi\) | ||||
−0.711845 | + | 0.702337i | \(0.752140\pi\) | |||||||
\(744\) | −2.90941 | + | 1.47512i | −0.106664 | + | 0.0540807i | ||||
\(745\) | 16.2245 | − | 24.6167i | 0.594421 | − | 0.901887i | ||||
\(746\) | 16.8847 | + | 20.8792i | 0.618194 | + | 0.764444i | ||||
\(747\) | −15.5400 | − | 15.5400i | −0.568580 | − | 0.568580i | ||||
\(748\) | −12.2800 | − | 18.9647i | −0.449002 | − | 0.693416i | ||||
\(749\) | 12.1468 | + | 12.1468i | 0.443835 | + | 0.443835i | ||||
\(750\) | 1.74146 | − | 5.99301i | 0.0635892 | − | 0.218834i | ||||
\(751\) | 23.4759 | 0.856648 | 0.428324 | − | 0.903625i | \(-0.359104\pi\) | ||||
0.428324 | + | 0.903625i | \(0.359104\pi\) | |||||||
\(752\) | 12.1043 | − | 26.9936i | 0.441398 | − | 0.984354i | ||||
\(753\) | − | 1.63911i | − | 0.0597326i | ||||||
\(754\) | −13.2565 | − | 1.40222i | −0.482774 | − | 0.0510657i | ||||
\(755\) | 8.31933 | + | 40.4866i | 0.302771 | + | 1.47346i | ||||
\(756\) | 2.50757 | + | 3.87256i | 0.0911993 | + | 0.140844i | ||||
\(757\) | −22.9312 | − | 22.9312i | −0.833449 | − | 0.833449i | 0.154538 | − | 0.987987i | \(-0.450611\pi\) |
−0.987987 | + | 0.154538i | \(0.950611\pi\) | |||||||
\(758\) | −34.5502 | + | 27.9402i | −1.25492 | + | 1.01483i | ||||
\(759\) | 2.84565i | 0.103291i | ||||||||
\(760\) | 4.71882 | + | 5.93289i | 0.171170 | + | 0.215208i | ||||
\(761\) | 36.3457i | 1.31753i | 0.752348 | + | 0.658765i | \(0.228921\pi\) | ||||
−0.752348 | + | 0.658765i | \(0.771079\pi\) | |||||||
\(762\) | 0.116418 | + | 0.143960i | 0.00421738 | + | 0.00521511i | ||||
\(763\) | 4.17642 | + | 4.17642i | 0.151197 | + | 0.151197i | ||||
\(764\) | 45.2963 | + | 9.69091i | 1.63876 | + | 0.350605i | ||||
\(765\) | −21.1474 | + | 4.34545i | −0.764587 | + | 0.157110i | ||||
\(766\) | −2.25237 | + | 21.2938i | −0.0813813 | + | 0.769378i | ||||
\(767\) | − | 26.0780i | − | 0.941621i | ||||||
\(768\) | −6.30485 | − | 0.364010i | −0.227507 | − | 0.0131351i | ||||
\(769\) | −3.98219 | −0.143601 | −0.0718007 | − | 0.997419i | \(-0.522875\pi\) | ||||
−0.0718007 | + | 0.997419i | \(0.522875\pi\) | |||||||
\(770\) | −6.68328 | + | 8.12874i | −0.240849 | + | 0.292939i | ||||
\(771\) | 0.422766 | + | 0.422766i | 0.0152255 | + | 0.0152255i | ||||
\(772\) | −3.94560 | + | 18.4421i | −0.142005 | + | 0.663747i | ||||
\(773\) | −35.2651 | − | 35.2651i | −1.26840 | − | 1.26840i | −0.946916 | − | 0.321482i | \(-0.895819\pi\) |
−0.321482 | − | 0.946916i | \(-0.604181\pi\) | |||||||
\(774\) | 21.9471 | − | 17.7483i | 0.788871 | − | 0.637949i | ||||
\(775\) | −13.4256 | + | 5.76073i | −0.482263 | + | 0.206931i | ||||
\(776\) | 5.42329 | − | 16.5787i | 0.194685 | − | 0.595142i | ||||
\(777\) | 2.81269 | 0.100905 | ||||||||
\(778\) | 10.2512 | − | 8.28999i | 0.367523 | − | 0.297211i | ||||
\(779\) | 9.36836 | − | 9.36836i | 0.335656 | − | 0.335656i | ||||
\(780\) | 0.0474858 | − | 5.85882i | 0.00170026 | − | 0.209779i | ||||
\(781\) | −37.8872 | − | 37.8872i | −1.35571 | − | 1.35571i | ||||
\(782\) | −1.09402 | + | 10.3428i | −0.0391219 | + | 0.369858i | ||||
\(783\) | 6.55091i | 0.234110i | ||||||||
\(784\) | 3.64985 | + | 1.63664i | 0.130352 | + | 0.0584516i | ||||
\(785\) | 23.3032 | − | 35.3569i | 0.831729 | − | 1.26194i | ||||
\(786\) | −3.83362 | − | 0.405503i | −0.136741 | − | 0.0144638i | ||||
\(787\) | 0.963947 | − | 0.963947i | 0.0343610 | − | 0.0343610i | −0.689718 | − | 0.724079i | \(-0.742265\pi\) |
0.724079 | + | 0.689718i | \(0.242265\pi\) | |||||||
\(788\) | −19.8325 | − | 30.6284i | −0.706505 | − | 1.09109i | ||||
\(789\) | −4.61691 | + | 4.61691i | −0.164366 | + | 0.164366i | ||||
\(790\) | −9.62498 | + | 0.939271i | −0.342441 | + | 0.0334178i | ||||
\(791\) | − | 14.0838i | − | 0.500761i | ||||||
\(792\) | 12.1062 | + | 23.8772i | 0.430175 | + | 0.848440i | ||||
\(793\) | −2.53662 | −0.0900781 | ||||||||
\(794\) | −0.719108 | + | 0.581532i | −0.0255202 | + | 0.0206378i | ||||
\(795\) | 1.99186 | − | 0.409294i | 0.0706439 | − | 0.0145161i | ||||
\(796\) | 2.17324 | − | 10.1579i | 0.0770284 | − | 0.360039i | ||||
\(797\) | −6.59993 | + | 6.59993i | −0.233782 | + | 0.233782i | −0.814269 | − | 0.580488i | \(-0.802862\pi\) |
0.580488 | + | 0.814269i | \(0.302862\pi\) | |||||||
\(798\) | 0.665355 | + | 0.0703783i | 0.0235533 | + | 0.00249136i | ||||
\(799\) | 25.1060 | 0.888186 | ||||||||
\(800\) | −28.0754 | − | 3.43071i | −0.992617 | − | 0.121294i | ||||
\(801\) | 47.9567 | 1.69447 | ||||||||
\(802\) | 24.5525 | + | 2.59706i | 0.866980 | + | 0.0917052i | ||||
\(803\) | −12.5026 | + | 12.5026i | −0.441208 | + | 0.441208i | ||||
\(804\) | −1.09643 | + | 5.12484i | −0.0386682 | + | 0.180739i | ||||
\(805\) | 4.74517 | − | 0.975054i | 0.167245 | − | 0.0343661i | ||||
\(806\) | −10.6646 | + | 8.62430i | −0.375644 | + | 0.303778i | ||||
\(807\) | −4.05475 | −0.142734 | ||||||||
\(808\) | −21.7028 | + | 11.0037i | −0.763502 | + | 0.387110i | ||||
\(809\) | − | 13.0495i | − | 0.458796i | −0.973333 | − | 0.229398i | \(-0.926324\pi\) | ||
0.973333 | − | 0.229398i | \(-0.0736757\pi\) | |||||||
\(810\) | 23.9893 | − | 2.34104i | 0.842897 | − | 0.0822557i | ||||
\(811\) | −22.0720 | + | 22.0720i | −0.775053 | + | 0.775053i | −0.978985 | − | 0.203932i | \(-0.934628\pi\) |
0.203932 | + | 0.978985i | \(0.434628\pi\) | |||||||
\(812\) | 3.08708 | + | 4.76754i | 0.108335 | + | 0.167308i | ||||
\(813\) | −2.90311 | + | 2.90311i | −0.101816 | + | 0.101816i | ||||
\(814\) | 33.3504 | + | 3.52766i | 1.16893 | + | 0.123644i | ||||
\(815\) | −5.25277 | + | 7.96978i | −0.183996 | + | 0.279169i | ||||
\(816\) | −1.90740 | − | 5.00867i | −0.0667724 | − | 0.175338i | ||||
\(817\) | − | 8.41089i | − | 0.294260i | ||||||
\(818\) | −3.61877 | + | 34.2118i | −0.126527 | + | 1.19619i | ||||
\(819\) | 6.67541 | + | 6.67541i | 0.233258 | + | 0.233258i | ||||
\(820\) | −0.400641 | + | 49.4313i | −0.0139910 | + | 1.72622i | ||||
\(821\) | 2.56931 | − | 2.56931i | 0.0896695 | − | 0.0896695i | −0.660849 | − | 0.750519i | \(-0.729804\pi\) |
0.750519 | + | 0.660849i | \(0.229804\pi\) | |||||||
\(822\) | 4.71063 | − | 3.80942i | 0.164302 | − | 0.132869i | ||||
\(823\) | 12.4199 | 0.432930 | 0.216465 | − | 0.976290i | \(-0.430547\pi\) | ||||
0.216465 | + | 0.976290i | \(0.430547\pi\) | |||||||
\(824\) | −43.1896 | − | 14.1283i | −1.50458 | − | 0.492183i | ||||
\(825\) | −2.58971 | − | 6.03543i | −0.0901620 | − | 0.210127i | ||||
\(826\) | −8.63958 | + | 6.98670i | −0.300609 | + | 0.243098i | ||||
\(827\) | −12.7989 | − | 12.7989i | −0.445062 | − | 0.445062i | 0.448647 | − | 0.893709i | \(-0.351906\pi\) |
−0.893709 | + | 0.448647i | \(0.851906\pi\) | |||||||
\(828\) | 2.57823 | − | 12.0509i | 0.0895995 | − | 0.418798i | ||||
\(829\) | 14.7686 | + | 14.7686i | 0.512934 | + | 0.512934i | 0.915424 | − | 0.402491i | \(-0.131855\pi\) |
−0.402491 | + | 0.915424i | \(0.631855\pi\) | |||||||
\(830\) | 15.5181 | − | 18.8743i | 0.538641 | − | 0.655138i | ||||
\(831\) | 1.69057 | 0.0586453 | ||||||||
\(832\) | −26.2429 | + | 4.04938i | −0.909810 | + | 0.140387i | ||||
\(833\) | 3.39463i | 0.117617i | ||||||||
\(834\) | 0.961317 | − | 9.08827i | 0.0332877 | − | 0.314701i | ||||
\(835\) | −9.54237 | + | 1.96080i | −0.330227 | + | 0.0678562i | ||||
\(836\) | 7.80092 | + | 1.66897i | 0.269801 | + | 0.0577224i | ||||
\(837\) | 4.76595 | + | 4.76595i | 0.164735 | + | 0.164735i | ||||
\(838\) | 8.64834 | + | 10.6943i | 0.298752 | + | 0.369429i | ||||
\(839\) | − | 28.4351i | − | 0.981688i | −0.871247 | − | 0.490844i | \(-0.836688\pi\) | ||
0.871247 | − | 0.490844i | \(-0.163312\pi\) | |||||||
\(840\) | −1.95374 | + | 1.55394i | −0.0674103 | + | 0.0536160i | ||||
\(841\) | − | 20.9351i | − | 0.721901i | ||||||
\(842\) | 20.9219 | − | 16.9193i | 0.721018 | − | 0.583077i | ||||
\(843\) | −7.43741 | − | 7.43741i | −0.256158 | − | 0.256158i | ||||
\(844\) | −17.1393 | − | 26.4692i | −0.589961 | − | 0.911106i | ||||
\(845\) | 0.892483 | + | 4.34333i | 0.0307023 | + | 0.149415i | ||||
\(846\) | −29.5832 | − | 3.12918i | −1.01709 | − | 0.107583i | ||||
\(847\) | 0.0742641i | 0.00255174i | ||||||||
\(848\) | −3.27981 | − | 8.61250i | −0.112629 | − | 0.295754i | ||||
\(849\) | 1.00447 | 0.0344733 | ||||||||
\(850\) | −7.09221 | − | 22.9320i | −0.243261 | − | 0.786560i | ||||
\(851\) | −10.9163 | − | 10.9163i | −0.374207 | − | 0.374207i | ||||
\(852\) | −6.90839 | − | 10.6690i | −0.236677 | − | 0.365513i | ||||
\(853\) | 31.0724 | + | 31.0724i | 1.06390 | + | 1.06390i | 0.997814 | + | 0.0660853i | \(0.0210510\pi\) |
0.0660853 | + | 0.997814i | \(0.478949\pi\) | |||||||
\(854\) | 0.679602 | + | 0.840378i | 0.0232555 | + | 0.0287572i | ||||
\(855\) | 4.19499 | − | 6.36486i | 0.143466 | − | 0.217674i | ||||
\(856\) | 21.9719 | + | 43.3354i | 0.750984 | + | 1.48117i | ||||
\(857\) | −43.7236 | −1.49357 | −0.746785 | − | 0.665066i | \(-0.768403\pi\) | ||||
−0.746785 | + | 0.665066i | \(0.768403\pi\) | |||||||
\(858\) | −3.87701 | − | 4.79422i | −0.132359 | − | 0.163672i | ||||
\(859\) | −8.83027 | + | 8.83027i | −0.301285 | + | 0.301285i | −0.841516 | − | 0.540231i | \(-0.818337\pi\) |
0.540231 | + | 0.841516i | \(0.318337\pi\) | |||||||
\(860\) | 22.0098 | + | 22.3695i | 0.750528 | + | 0.762794i | ||||
\(861\) | 3.08506 | + | 3.08506i | 0.105139 | + | 0.105139i | ||||
\(862\) | −51.6579 | − | 5.46414i | −1.75947 | − | 0.186109i | ||||
\(863\) | − | 22.0584i | − | 0.750876i | −0.926848 | − | 0.375438i | \(-0.877492\pi\) | ||
0.926848 | − | 0.375438i | \(-0.122508\pi\) | |||||||
\(864\) | 3.33548 | + | 12.6155i | 0.113475 | + | 0.429189i | ||||
\(865\) | −8.21687 | + | 12.4671i | −0.279382 | + | 0.423893i | ||||
\(866\) | −5.42031 | + | 51.2435i | −0.184190 | + | 1.74133i | ||||
\(867\) | −1.52850 | + | 1.52850i | −0.0519106 | + | 0.0519106i | ||||
\(868\) | 5.71443 | + | 1.22257i | 0.193960 | + | 0.0414968i | ||||
\(869\) | −7.19615 | + | 7.19615i | −0.244113 | + | 0.244113i | ||||
\(870\) | −3.52791 | + | 0.344278i | −0.119607 | + | 0.0116721i | ||||
\(871\) | 22.0356i | 0.746646i | ||||||||
\(872\) | 7.55456 | + | 14.8999i | 0.255830 | + | 0.504576i | ||||
\(873\) | −17.5405 | −0.593657 | ||||||||
\(874\) | −2.30916 | − | 2.85545i | −0.0781087 | − | 0.0965872i | ||||
\(875\) | −9.17682 | + | 6.38640i | −0.310233 | + | 0.215900i | ||||
\(876\) | −3.52072 | + | 2.27974i | −0.118954 | + | 0.0770252i | ||||
\(877\) | 30.7374 | − | 30.7374i | 1.03793 | − | 1.03793i | 0.0386778 | − | 0.999252i | \(-0.487685\pi\) |
0.999252 | − | 0.0386778i | \(-0.0123146\pi\) | |||||||
\(878\) | −3.32415 | + | 31.4265i | −0.112185 | + | 1.06059i | ||||
\(879\) | 1.20743 | 0.0407257 | ||||||||
\(880\) | −25.1146 | + | 15.9749i | −0.846614 | + | 0.538513i | ||||
\(881\) | 18.1801 | 0.612504 | 0.306252 | − | 0.951951i | \(-0.400925\pi\) | ||||
0.306252 | + | 0.951951i | \(0.400925\pi\) | |||||||
\(882\) | 0.423102 | − | 4.00000i | 0.0142466 | − | 0.134687i | ||||
\(883\) | 14.4743 | − | 14.4743i | 0.487100 | − | 0.487100i | −0.420290 | − | 0.907390i | \(-0.638071\pi\) |
0.907390 | + | 0.420290i | \(0.138071\pi\) | |||||||
\(884\) | −12.2482 | − | 18.9156i | −0.411953 | − | 0.636200i | ||||
\(885\) | −1.39573 | − | 6.79241i | −0.0469168 | − | 0.228324i | ||||
\(886\) | −25.1841 | − | 31.1420i | −0.846076 | − | 1.04624i | ||||
\(887\) | 50.3891 | 1.69190 | 0.845950 | − | 0.533262i | \(-0.179034\pi\) | ||||
0.845950 | + | 0.533262i | \(0.179034\pi\) | |||||||
\(888\) | 7.56122 | + | 2.47345i | 0.253738 | + | 0.0830035i | ||||
\(889\) | − | 0.331675i | − | 0.0111240i | ||||||
\(890\) | 5.17871 | + | 53.0677i | 0.173591 | + | 1.77883i | ||||
\(891\) | 17.9357 | − | 17.9357i | 0.600868 | − | 0.600868i | ||||
\(892\) | −3.68270 | + | 17.2133i | −0.123306 | + | 0.576344i | ||||
\(893\) | −6.26827 | + | 6.26827i | −0.209760 | + | 0.209760i | ||||
\(894\) | 0.774178 | − | 7.31907i | 0.0258924 | − | 0.244786i | ||||
\(895\) | −3.96551 | − | 2.61361i | −0.132552 | − | 0.0873633i | ||||
\(896\) | 8.37245 | + | 7.60934i | 0.279704 | + | 0.254210i | ||||
\(897\) | 2.83829i | 0.0947677i | ||||||||
\(898\) | −28.6920 | − | 3.03491i | −0.957464 | − | 0.101276i | ||||
\(899\) | 5.86739 | + | 5.86739i | 0.195689 | + | 0.195689i | ||||
\(900\) | 5.49877 | + | 27.9054i | 0.183292 | + | 0.930181i | ||||
\(901\) | 5.53036 | − | 5.53036i | 0.184243 | − | 0.184243i | ||||
\(902\) | 32.7107 | + | 40.4492i | 1.08915 | + | 1.34681i | ||||
\(903\) | 2.76976 | 0.0921718 | ||||||||
\(904\) | 12.3851 | − | 37.8606i | 0.411922 | − | 1.25923i | ||||
\(905\) | 27.2669 | − | 41.3709i | 0.906384 | − | 1.37521i | ||||
\(906\) | 6.48806 | + | 8.02297i | 0.215551 | + | 0.266545i | ||||
\(907\) | −7.63309 | − | 7.63309i | −0.253453 | − | 0.253453i | 0.568932 | − | 0.822385i | \(-0.307357\pi\) |
−0.822385 | + | 0.568932i | \(0.807357\pi\) | |||||||
\(908\) | −1.39734 | + | 0.904807i | −0.0463723 | + | 0.0300271i | ||||
\(909\) | 17.3020 | + | 17.3020i | 0.573871 | + | 0.573871i | ||||
\(910\) | −6.66599 | + | 8.10770i | −0.220975 | + | 0.268768i | ||||
\(911\) | 27.1867 | 0.900736 | 0.450368 | − | 0.892843i | \(-0.351293\pi\) | ||||
0.450368 | + | 0.892843i | \(0.351293\pi\) | |||||||
\(912\) | 1.72675 | + | 0.774299i | 0.0571784 | + | 0.0256396i | ||||
\(913\) | − | 25.7136i | − | 0.850997i | ||||||
\(914\) | 16.7271 | + | 1.76931i | 0.553282 | + | 0.0585237i | ||||
\(915\) | −0.660702 | + | 0.135763i | −0.0218421 | + | 0.00448820i | ||||
\(916\) | 41.1113 | − | 26.6205i | 1.35836 | − | 0.879565i | ||||
\(917\) | 4.88335 | + | 4.88335i | 0.161262 | + | 0.161262i | ||||
\(918\) | −8.61084 | + | 6.96346i | −0.284200 | + | 0.229829i | ||||
\(919\) | 16.2788i | 0.536987i | 0.963282 | + | 0.268493i | \(0.0865258\pi\) | ||||
−0.963282 | + | 0.268493i | \(0.913474\pi\) | |||||||
\(920\) | 13.6136 | + | 1.55166i | 0.448829 | + | 0.0511567i | ||||
\(921\) | − | 10.0258i | − | 0.330362i | ||||||
\(922\) | −23.7286 | − | 29.3422i | −0.781460 | − | 0.966333i | ||||
\(923\) | −37.7891 | − | 37.7891i | −1.24384 | − | 1.24384i | ||||
\(924\) | −0.549601 | + | 2.56889i | −0.0180806 | + | 0.0845104i | ||||
\(925\) | 33.0873 | + | 13.2183i | 1.08790 | + | 0.434615i | ||||
\(926\) | 4.55779 | − | 43.0893i | 0.149778 | − | 1.41600i | ||||
\(927\) | 45.6952i | 1.50083i | ||||||||
\(928\) | 4.10633 | + | 15.5311i | 0.134797 | + | 0.509832i | ||||
\(929\) | 22.3311 | 0.732659 | 0.366330 | − | 0.930485i | \(-0.380614\pi\) | ||||
0.366330 | + | 0.930485i | \(0.380614\pi\) | |||||||
\(930\) | −2.31617 | + | 2.81711i | −0.0759503 | + | 0.0923768i | ||||
\(931\) | −0.847544 | − | 0.847544i | −0.0277771 | − | 0.0277771i | ||||
\(932\) | −34.6677 | − | 7.41697i | −1.13558 | − | 0.242951i | ||||
\(933\) | 4.76218 | + | 4.76218i | 0.155907 | + | 0.155907i | ||||
\(934\) | −13.1751 | + | 10.6545i | −0.431102 | + | 0.348626i | ||||
\(935\) | −21.0912 | − | 13.9009i | −0.689755 | − | 0.454607i | ||||
\(936\) | 12.0749 | + | 23.8154i | 0.394680 | + | 0.778432i | ||||
\(937\) | 16.7595 | 0.547508 | 0.273754 | − | 0.961800i | \(-0.411735\pi\) | ||||
0.273754 | + | 0.961800i | \(0.411735\pi\) | |||||||
\(938\) | 7.30034 | − | 5.90367i | 0.238364 | − | 0.192762i | ||||
\(939\) | 3.40288 | − | 3.40288i | 0.111049 | − | 0.111049i | ||||
\(940\) | 0.268065 | − | 33.0740i | 0.00874331 | − | 1.07875i | ||||
\(941\) | −6.39091 | − | 6.39091i | −0.208338 | − | 0.208338i | 0.595223 | − | 0.803561i | \(-0.297064\pi\) |
−0.803561 | + | 0.595223i | \(0.797064\pi\) | |||||||
\(942\) | 1.11195 | − | 10.5124i | 0.0362293 | − | 0.342511i | ||||
\(943\) | − | 23.9469i | − | 0.779817i | ||||||
\(944\) | −29.3694 | + | 11.1844i | −0.955891 | + | 0.364023i | ||||
\(945\) | 4.30679 | + | 2.83854i | 0.140100 | + | 0.0923378i | ||||
\(946\) | 32.8414 | + | 3.47381i | 1.06776 | + | 0.112943i | ||||
\(947\) | 5.70706 | − | 5.70706i | 0.185454 | − | 0.185454i | −0.608273 | − | 0.793728i | \(-0.708138\pi\) |
0.793728 | + | 0.608273i | \(0.208138\pi\) | |||||||
\(948\) | −2.02643 | + | 1.31215i | −0.0658152 | + | 0.0426168i | ||||
\(949\) | −12.4703 | + | 12.4703i | −0.404802 | + | 0.404802i | ||||
\(950\) | 7.49620 | + | 3.95475i | 0.243209 | + | 0.128309i | ||||
\(951\) | − | 7.41028i | − | 0.240295i | ||||||
\(952\) | −2.98519 | + | 9.12560i | −0.0967507 | + | 0.295762i | ||||
\(953\) | −34.1804 | −1.10721 | −0.553606 | − | 0.832778i | \(-0.686749\pi\) | ||||
−0.553606 | + | 0.832778i | \(0.686749\pi\) | |||||||
\(954\) | −7.20590 | + | 5.82730i | −0.233300 | + | 0.188666i | ||||
\(955\) | 50.7290 | − | 10.4240i | 1.64155 | − | 0.337312i | ||||
\(956\) | −16.0443 | − | 3.43260i | −0.518910 | − | 0.111018i | ||||
\(957\) | −2.63766 | + | 2.63766i | −0.0852634 | + | 0.0852634i | ||||
\(958\) | −8.14465 | − | 0.861505i | −0.263142 | − | 0.0278339i | ||||
\(959\) | −10.8530 | −0.350463 | ||||||||
\(960\) | −6.61865 | + | 2.45928i | −0.213616 | + | 0.0793729i | ||||
\(961\) | −22.4627 | −0.724602 | ||||||||
\(962\) | 33.2641 | + | 3.51853i | 1.07248 | + | 0.113442i | ||||
\(963\) | 34.5480 | − | 34.5480i | 1.11329 | − | 1.11329i | ||||
\(964\) | −36.2279 | − | 7.75077i | −1.16682 | − | 0.249635i | ||||
\(965\) | 4.24406 | + | 20.6540i | 0.136621 | + | 0.664877i | ||||
\(966\) | 0.940319 | − | 0.760423i | 0.0302543 | − | 0.0244662i | ||||
\(967\) | −51.3733 | −1.65206 | −0.826028 | − | 0.563630i | \(-0.809405\pi\) | ||||
−0.826028 | + | 0.563630i | \(0.809405\pi\) | |||||||
\(968\) | −0.0653069 | + | 0.199640i | −0.00209904 | + | 0.00641668i | ||||
\(969\) | 1.60600i | 0.0515923i | ||||||||
\(970\) | −1.89415 | − | 19.4099i | −0.0608176 | − | 0.623215i | ||||
\(971\) | 4.56089 | − | 4.56089i | 0.146366 | − | 0.146366i | −0.630126 | − | 0.776493i | \(-0.716997\pi\) |
0.776493 | + | 0.630126i | \(0.216997\pi\) | |||||||
\(972\) | 16.6683 | − | 10.7931i | 0.534637 | − | 0.346189i | ||||
\(973\) | −11.5768 | + | 11.5768i | −0.371137 | + | 0.371137i | ||||
\(974\) | 2.05829 | + | 0.217716i | 0.0659518 | + | 0.00697609i | ||||
\(975\) | −2.58300 | − | 6.01981i | −0.0827224 | − | 0.192788i | ||||
\(976\) | 1.08792 | + | 2.85678i | 0.0348235 | + | 0.0914433i | ||||
\(977\) | − | 0.908959i | − | 0.0290802i | −0.999894 | − | 0.0145401i | \(-0.995372\pi\) | ||
0.999894 | − | 0.0145401i | \(-0.00462842\pi\) | |||||||
\(978\) | −0.250644 | + | 2.36958i | −0.00801470 | + | 0.0757709i | ||||
\(979\) | 39.6763 | + | 39.6763i | 1.26806 | + | 1.26806i | ||||
\(980\) | 4.47199 | + | 0.0362455i | 0.142852 | + | 0.00115782i | ||||
\(981\) | 11.8786 | − | 11.8786i | 0.379254 | − | 0.379254i | ||||
\(982\) | 3.85313 | − | 3.11597i | 0.122958 | − | 0.0994346i | ||||
\(983\) | −56.8582 | −1.81349 | −0.906747 | − | 0.421675i | \(-0.861442\pi\) | ||||
−0.906747 | + | 0.421675i | \(0.861442\pi\) | |||||||
\(984\) | 5.58044 | + | 11.0064i | 0.177898 | + | 0.350870i | ||||
\(985\) | −34.0627 | − | 22.4502i | −1.08533 | − | 0.715324i | ||||
\(986\) | −10.6009 | + | 8.57278i | −0.337601 | + | 0.273013i | ||||
\(987\) | −2.06418 | − | 2.06418i | −0.0657036 | − | 0.0657036i | ||||
\(988\) | 7.78074 | + | 1.66465i | 0.247538 | + | 0.0529595i | ||||
\(989\) | −10.7497 | − | 10.7497i | −0.341821 | − | 0.341821i | ||||
\(990\) | 23.1198 | + | 19.0086i | 0.734795 | + | 0.604134i | ||||
\(991\) | −23.9059 | −0.759396 | −0.379698 | − | 0.925111i | \(-0.623972\pi\) | ||||
−0.379698 | + | 0.925111i | \(0.623972\pi\) | |||||||
\(992\) | 14.2867 | + | 8.31177i | 0.453603 | + | 0.263899i | ||||
\(993\) | − | 6.11570i | − | 0.194076i | ||||||
\(994\) | −2.39516 | + | 22.6438i | −0.0759698 | + | 0.718217i | ||||
\(995\) | −2.33763 | − | 11.3762i | −0.0741078 | − | 0.360651i | ||||
\(996\) | 1.27613 | − | 5.96478i | 0.0404358 | − | 0.189001i | ||||
\(997\) | 16.0933 | + | 16.0933i | 0.509679 | + | 0.509679i | 0.914428 | − | 0.404749i | \(-0.132641\pi\) |
−0.404749 | + | 0.914428i | \(0.632641\pi\) | |||||||
\(998\) | −33.7930 | − | 41.7876i | −1.06970 | − | 1.32276i | ||||
\(999\) | − | 16.4380i | − | 0.520074i |
(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 | 560.2.bb.c.29.2 | ✓ | 70 | |
5.4 | even | 2 | 560.2.bb.d.29.34 | yes | 70 | ||
16.5 | even | 4 | 560.2.bb.d.309.34 | yes | 70 | ||
80.69 | even | 4 | inner | 560.2.bb.c.309.2 | yes | 70 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.bb.c.29.2 | ✓ | 70 | 1.1 | even | 1 | trivial | |
560.2.bb.c.309.2 | yes | 70 | 80.69 | even | 4 | inner | |
560.2.bb.d.29.34 | yes | 70 | 5.4 | even | 2 | ||
560.2.bb.d.309.34 | yes | 70 | 16.5 | even | 4 |