Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(8,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(36))
chi = DirichletCharacter(H, H._module([2, 27]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.r (of order \(36\), degree \(12\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{36})\) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{36}]$ |
Embedding invariants
Embedding label | 8.9 | ||
Character | \(\chi\) | \(=\) | 405.8 |
Dual form | 405.2.r.a.152.9 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.377486 | − | 0.264318i | 0.266923 | − | 0.186901i | −0.432451 | − | 0.901657i | \(-0.642351\pi\) |
0.699374 | + | 0.714756i | \(0.253462\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.611409 | + | 1.67983i | −0.305705 | + | 0.839916i | ||||
\(5\) | −0.538986 | − | 2.17014i | −0.241042 | − | 0.970515i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.52168 | + | 3.26325i | −0.575141 | + | 1.23339i | 0.376567 | + | 0.926389i | \(0.377104\pi\) |
−0.951708 | + | 0.307004i | \(0.900673\pi\) | |||||||
\(8\) | 0.451753 | + | 1.68596i | 0.159719 | + | 0.596078i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.777066 | − | 0.676732i | −0.245730 | − | 0.214001i | ||||
\(11\) | −2.85486 | + | 3.40229i | −0.860773 | + | 1.02583i | 0.138597 | + | 0.990349i | \(0.455741\pi\) |
−0.999370 | + | 0.0354810i | \(0.988704\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.226257 | − | 0.323128i | 0.0627524 | − | 0.0896196i | −0.786549 | − | 0.617527i | \(-0.788134\pi\) |
0.849302 | + | 0.527908i | \(0.177023\pi\) | |||||||
\(14\) | 0.288125 | + | 1.63404i | 0.0770047 | + | 0.436715i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.12266 | − | 1.78113i | −0.530666 | − | 0.445281i | ||||
\(17\) | −1.03506 | + | 3.86289i | −0.251038 | + | 0.936888i | 0.719213 | + | 0.694789i | \(0.244502\pi\) |
−0.970252 | + | 0.242098i | \(0.922164\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.05819 | + | 0.610947i | 0.242766 | + | 0.140161i | 0.616447 | − | 0.787396i | \(-0.288571\pi\) |
−0.373682 | + | 0.927557i | \(0.621905\pi\) | |||||||
\(20\) | 3.97501 | + | 0.421435i | 0.888839 | + | 0.0942357i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.178381 | + | 2.03891i | −0.0380310 | + | 0.434697i | ||||
\(23\) | 3.57786 | − | 1.66839i | 0.746036 | − | 0.347882i | −0.0121450 | − | 0.999926i | \(-0.503866\pi\) |
0.758181 | + | 0.652044i | \(0.226088\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.41899 | + | 2.33935i | −0.883798 | + | 0.467869i | ||||
\(26\) | − | 0.181780i | − | 0.0356500i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.55135 | − | 4.55135i | −0.860124 | − | 0.860124i | ||||
\(29\) | −0.885233 | + | 5.02040i | −0.164384 | + | 0.932266i | 0.785314 | + | 0.619097i | \(0.212501\pi\) |
−0.949698 | + | 0.313168i | \(0.898610\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.19946 | + | 3.34833i | 1.65227 | + | 0.601378i | 0.989121 | − | 0.147107i | \(-0.0469963\pi\) |
0.663152 | + | 0.748485i | \(0.269219\pi\) | |||||||
\(32\) | −4.74965 | − | 0.415541i | −0.839628 | − | 0.0734579i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.630312 | + | 1.73177i | 0.108098 | + | 0.296996i | ||||
\(35\) | 7.90187 | + | 1.54341i | 1.33566 | + | 0.260883i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.6220 | − | 2.84615i | −1.74624 | − | 0.467905i | −0.762426 | − | 0.647076i | \(-0.775992\pi\) |
−0.983818 | + | 0.179171i | \(0.942658\pi\) | |||||||
\(38\) | 0.560936 | − | 0.0490755i | 0.0909958 | − | 0.00796111i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.41529 | − | 1.88908i | 0.540004 | − | 0.298689i | ||||
\(41\) | 1.80826 | − | 0.318845i | 0.282403 | − | 0.0497952i | −0.0306526 | − | 0.999530i | \(-0.509759\pi\) |
0.313055 | + | 0.949735i | \(0.398647\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.218695 | − | 2.49969i | −0.0333507 | − | 0.381200i | −0.994466 | − | 0.105054i | \(-0.966498\pi\) |
0.961116 | − | 0.276146i | \(-0.0890572\pi\) | |||||||
\(44\) | −3.96979 | − | 6.87588i | −0.598469 | − | 1.03658i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.909608 | − | 1.57549i | 0.134114 | − | 0.232293i | ||||
\(47\) | −1.19000 | − | 0.554905i | −0.173579 | − | 0.0809412i | 0.333887 | − | 0.942613i | \(-0.391640\pi\) |
−0.507465 | + | 0.861672i | \(0.669418\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.83380 | − | 4.56894i | −0.547685 | − | 0.652706i | ||||
\(50\) | −1.04977 | + | 2.05109i | −0.148460 | + | 0.290068i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.404466 | + | 0.577637i | 0.0560893 | + | 0.0801039i | ||||
\(53\) | 3.53443 | − | 3.53443i | 0.485491 | − | 0.485491i | −0.421389 | − | 0.906880i | \(-0.638457\pi\) |
0.906880 | + | 0.421389i | \(0.138457\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.92217 | + | 4.36165i | 1.20307 | + | 0.588125i | ||||
\(56\) | −6.18915 | − | 1.09131i | −0.827060 | − | 0.145833i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.992822 | + | 2.12911i | 0.130364 | + | 0.279566i | ||||
\(59\) | 0.467138 | − | 0.391975i | 0.0608162 | − | 0.0510308i | −0.611873 | − | 0.790956i | \(-0.709584\pi\) |
0.672689 | + | 0.739925i | \(0.265139\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.87695 | + | 0.683152i | −0.240318 | + | 0.0874687i | −0.459372 | − | 0.888244i | \(-0.651925\pi\) |
0.219053 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(62\) | 4.35769 | − | 1.16764i | 0.553427 | − | 0.148290i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.89665 | − | 1.67238i | 0.362081 | − | 0.209048i | ||||
\(65\) | −0.823182 | − | 0.316847i | −0.102103 | − | 0.0393000i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.34241 | + | 2.34038i | 0.408341 | + | 0.285923i | 0.759645 | − | 0.650338i | \(-0.225373\pi\) |
−0.351304 | + | 0.936261i | \(0.614262\pi\) | |||||||
\(68\) | −5.85616 | − | 4.10053i | −0.710164 | − | 0.497262i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.39079 | − | 1.50600i | 0.405277 | − | 0.180001i | ||||
\(71\) | 10.9258 | − | 6.30801i | 1.29665 | − | 0.748623i | 0.316829 | − | 0.948483i | \(-0.397382\pi\) |
0.979824 | + | 0.199860i | \(0.0640487\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00309 | − | 1.07262i | 0.468526 | − | 0.125541i | −0.0168287 | − | 0.999858i | \(-0.505357\pi\) |
0.485355 | + | 0.874317i | \(0.338690\pi\) | |||||||
\(74\) | −4.76194 | + | 1.73320i | −0.553564 | + | 0.201481i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.67328 | + | 1.40404i | −0.191938 | + | 0.161055i | ||||
\(77\) | −6.75835 | − | 14.4933i | −0.770186 | − | 1.65167i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.8688 | + | 2.09278i | 1.33534 | + | 0.235457i | 0.795317 | − | 0.606193i | \(-0.207304\pi\) |
0.540023 | + | 0.841650i | \(0.318415\pi\) | |||||||
\(80\) | −2.72120 | + | 5.56647i | −0.304239 | + | 0.622350i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.598316 | − | 0.598316i | 0.0660729 | − | 0.0660729i | ||||
\(83\) | −1.54510 | − | 2.20663i | −0.169597 | − | 0.242209i | 0.725352 | − | 0.688378i | \(-0.241677\pi\) |
−0.894949 | + | 0.446169i | \(0.852788\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.94087 | + | 0.164174i | 0.969774 | + | 0.0178072i | ||||
\(86\) | −0.743269 | − | 0.885794i | −0.0801488 | − | 0.0955176i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.02584 | − | 3.27620i | −0.748957 | − | 0.349244i | ||||
\(89\) | −1.23513 | + | 2.13931i | −0.130924 | + | 0.226766i | −0.924033 | − | 0.382313i | \(-0.875128\pi\) |
0.793109 | + | 0.609079i | \(0.208461\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.710159 | + | 1.23003i | 0.0744449 | + | 0.128942i | ||||
\(92\) | 0.615070 | + | 7.03028i | 0.0641254 | + | 0.732957i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.595878 | + | 0.105069i | −0.0614601 | + | 0.0108371i | ||||
\(95\) | 0.755488 | − | 2.62571i | 0.0775114 | − | 0.269392i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.567380 | − | 0.0496393i | 0.0576087 | − | 0.00504011i | −0.0583150 | − | 0.998298i | \(-0.518573\pi\) |
0.115924 | + | 0.993258i | \(0.463017\pi\) | |||||||
\(98\) | −2.65486 | − | 0.711367i | −0.268181 | − | 0.0718589i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.22790 | − | 8.85346i | −0.122790 | − | 0.885346i | ||||
\(101\) | 5.00202 | + | 13.7429i | 0.497720 | + | 1.36747i | 0.893473 | + | 0.449117i | \(0.148261\pi\) |
−0.395753 | + | 0.918357i | \(0.629516\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.1583 | − | 1.50115i | −1.69066 | − | 0.147913i | −0.799213 | − | 0.601048i | \(-0.794750\pi\) |
−0.891442 | + | 0.453135i | \(0.850306\pi\) | |||||||
\(104\) | 0.646995 | + | 0.235487i | 0.0634431 | + | 0.0230914i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.399982 | − | 2.26841i | 0.0388497 | − | 0.220328i | ||||
\(107\) | −4.07639 | − | 4.07639i | −0.394080 | − | 0.394080i | 0.482059 | − | 0.876139i | \(-0.339889\pi\) |
−0.876139 | + | 0.482059i | \(0.839889\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.33084i | − | 0.702167i | −0.936344 | − | 0.351084i | \(-0.885813\pi\) | ||
0.936344 | − | 0.351084i | \(-0.114187\pi\) | |||||||
\(110\) | 4.52086 | − | 0.711831i | 0.431047 | − | 0.0678705i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.04228 | − | 4.21648i | 0.854415 | − | 0.398420i | ||||
\(113\) | 0.638871 | − | 7.30233i | 0.0600999 | − | 0.686945i | −0.905060 | − | 0.425284i | \(-0.860174\pi\) |
0.965160 | − | 0.261661i | \(-0.0842703\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.54904 | − | 6.86522i | −0.517451 | − | 0.640185i | ||||
\(116\) | −7.89220 | − | 4.55656i | −0.732772 | − | 0.423066i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.0727316 | − | 0.271438i | 0.00669549 | − | 0.0249879i | ||||
\(119\) | −11.0305 | − | 9.25573i | −1.01117 | − | 0.848471i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.51523 | − | 8.59327i | −0.137748 | − | 0.781206i | ||||
\(122\) | −0.527950 | + | 0.753991i | −0.0477984 | + | 0.0682632i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −11.2493 | + | 13.4064i | −1.01021 | + | 1.20393i | ||||
\(125\) | 7.45848 | + | 8.32893i | 0.667106 | + | 0.744962i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.36574 | + | 5.09700i | 0.121189 | + | 0.452285i | 0.999675 | − | 0.0254832i | \(-0.00811243\pi\) |
−0.878486 | + | 0.477769i | \(0.841446\pi\) | |||||||
\(128\) | 4.68132 | − | 10.0391i | 0.413774 | − | 0.887341i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.394488 | + | 0.0979769i | −0.0345989 | + | 0.00859314i | ||||
\(131\) | −0.242450 | + | 0.666126i | −0.0211829 | + | 0.0581997i | −0.949833 | − | 0.312756i | \(-0.898748\pi\) |
0.928650 | + | 0.370956i | \(0.120970\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.60390 | + | 2.52348i | −0.312498 | + | 0.218813i | ||||
\(134\) | 1.88032 | 0.162435 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.98028 | −0.598554 | ||||||||
\(137\) | 0.834037 | − | 0.583999i | 0.0712566 | − | 0.0498944i | −0.537405 | − | 0.843324i | \(-0.680595\pi\) |
0.608662 | + | 0.793430i | \(0.291707\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.61336 | + | 20.9175i | −0.645757 | + | 1.77420i | −0.0129201 | + | 0.999917i | \(0.504113\pi\) |
−0.632837 | + | 0.774285i | \(0.718110\pi\) | |||||||
\(140\) | −7.42394 | + | 12.3302i | −0.627437 | + | 1.04209i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.45701 | − | 5.26907i | 0.206187 | − | 0.442170i | ||||
\(143\) | 0.453445 | + | 1.69228i | 0.0379189 | + | 0.141515i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.3721 | − | 0.784852i | 0.944401 | − | 0.0651784i | ||||
\(146\) | 1.22759 | − | 1.46299i | 0.101596 | − | 0.121078i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.2754 | − | 16.1030i | 0.926835 | − | 1.32366i | ||||
\(149\) | 2.80203 | + | 15.8911i | 0.229551 | + | 1.30185i | 0.853791 | + | 0.520616i | \(0.174298\pi\) |
−0.624240 | + | 0.781233i | \(0.714591\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.91118 | + | 5.79917i | 0.562424 | + | 0.471930i | 0.879122 | − | 0.476597i | \(-0.158130\pi\) |
−0.316698 | + | 0.948526i | \(0.602574\pi\) | |||||||
\(152\) | −0.551994 | + | 2.06007i | −0.0447726 | + | 0.167094i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.38204 | − | 3.68467i | −0.514279 | − | 0.296919i | ||||
\(155\) | 2.30795 | − | 21.7688i | 0.185379 | − | 1.74851i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.125040 | + | 1.42921i | −0.00997924 | + | 0.114063i | −0.999550 | − | 0.0299812i | \(-0.990455\pi\) |
0.989571 | + | 0.144044i | \(0.0460108\pi\) | |||||||
\(158\) | 5.03345 | − | 2.34714i | 0.400440 | − | 0.186728i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.65822 | + | 10.5314i | 0.131093 | + | 0.832578i | ||||
\(161\) | 14.2142i | 1.12024i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.66882 | + | 6.66882i | 0.522343 | + | 0.522343i | 0.918278 | − | 0.395936i | \(-0.129580\pi\) |
−0.395936 | + | 0.918278i | \(0.629580\pi\) | |||||||
\(164\) | −0.569980 | + | 3.23252i | −0.0445080 | + | 0.252417i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.16651 | − | 0.424573i | −0.0905384 | − | 0.0329533i | ||||
\(167\) | 16.7028 | + | 1.46130i | 1.29250 | + | 0.113079i | 0.712578 | − | 0.701593i | \(-0.247528\pi\) |
0.579922 | + | 0.814672i | \(0.303083\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.39304 | + | 12.0698i | 0.337926 | + | 0.928445i | ||||
\(170\) | 3.41845 | − | 2.30126i | 0.262183 | − | 0.176499i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.33278 | + | 1.16096i | 0.330371 | + | 0.0885227i | ||||
\(173\) | 7.61365 | − | 0.666108i | 0.578855 | − | 0.0506432i | 0.206031 | − | 0.978545i | \(-0.433945\pi\) |
0.372824 | + | 0.927902i | \(0.378390\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.909596 | − | 17.9800i | −0.0687590 | − | 1.35916i | ||||
\(176\) | 12.1198 | − | 2.13705i | 0.913566 | − | 0.161086i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.0992144 | + | 1.13403i | 0.00743644 | + | 0.0849988i | ||||
\(179\) | −2.10555 | − | 3.64692i | −0.157376 | − | 0.272584i | 0.776545 | − | 0.630061i | \(-0.216970\pi\) |
−0.933922 | + | 0.357477i | \(0.883637\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.97345 | + | 5.15017i | −0.221015 | + | 0.382809i | −0.955116 | − | 0.296231i | \(-0.904270\pi\) |
0.734102 | + | 0.679040i | \(0.237604\pi\) | |||||||
\(182\) | 0.593194 | + | 0.276611i | 0.0439705 | + | 0.0205038i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.42915 | + | 5.27845i | 0.326521 | + | 0.389133i | ||||
\(185\) | −0.451438 | + | 24.5852i | −0.0331904 | + | 1.80754i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.1877 | − | 14.5496i | −0.745000 | − | 1.06397i | ||||
\(188\) | 1.65972 | − | 1.65972i | 0.121048 | − | 0.121048i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.408837 | − | 1.19086i | −0.0296602 | − | 0.0863938i | ||||
\(191\) | 10.6788 | + | 1.88297i | 0.772694 | + | 0.136247i | 0.546074 | − | 0.837737i | \(-0.316122\pi\) |
0.226619 | + | 0.973983i | \(0.427233\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.260068 | + | 0.557718i | 0.0187201 | + | 0.0401454i | 0.915446 | − | 0.402442i | \(-0.131838\pi\) |
−0.896725 | + | 0.442587i | \(0.854061\pi\) | |||||||
\(194\) | 0.201057 | − | 0.168707i | 0.0144351 | − | 0.0121124i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.0191 | − | 3.64664i | 0.715648 | − | 0.260475i | ||||
\(197\) | −26.5467 | + | 7.11316i | −1.89137 | + | 0.506791i | −0.892980 | + | 0.450097i | \(0.851389\pi\) |
−0.998392 | + | 0.0566946i | \(0.981944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.40020 | − | 1.38576i | 0.170146 | − | 0.0982338i | −0.412509 | − | 0.910954i | \(-0.635347\pi\) |
0.582655 | + | 0.812720i | \(0.302014\pi\) | |||||||
\(200\) | −5.94035 | − | 6.39345i | −0.420046 | − | 0.452085i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.52070 | + | 3.86564i | 0.388435 | + | 0.271985i | ||||
\(203\) | −15.0358 | − | 10.5282i | −1.05531 | − | 0.738934i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.66656 | − | 3.75232i | −0.116398 | − | 0.262073i | ||||
\(206\) | −6.87379 | + | 3.96858i | −0.478919 | + | 0.276504i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.05580 | + | 0.282900i | −0.0732065 | + | 0.0196156i | ||||
\(209\) | −5.09961 | + | 1.85611i | −0.352747 | + | 0.128389i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.7925 | + | 14.0906i | −1.15605 | + | 0.970038i | −0.999844 | − | 0.0176876i | \(-0.994370\pi\) |
−0.156202 | + | 0.987725i | \(0.549925\pi\) | |||||||
\(212\) | 3.77627 | + | 8.09823i | 0.259355 | + | 0.556189i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.61625 | − | 0.461315i | −0.178843 | − | 0.0315348i | ||||
\(215\) | −5.30681 | + | 1.82190i | −0.361921 | + | 0.124252i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.9251 | + | 24.9251i | −1.69202 | + | 1.69202i | ||||
\(218\) | −1.93768 | − | 2.76729i | −0.131236 | − | 0.187424i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.7819 | + | 12.3210i | −0.861759 | + | 0.830682i | ||||
\(221\) | 1.01402 | + | 1.20846i | 0.0682103 | + | 0.0812899i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.1077 | + | 4.71331i | 0.676863 | + | 0.315627i | 0.730479 | − | 0.682935i | \(-0.239297\pi\) |
−0.0536157 | + | 0.998562i | \(0.517075\pi\) | |||||||
\(224\) | 8.58346 | − | 14.8670i | 0.573507 | − | 0.993343i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.68897 | − | 2.92539i | −0.112349 | − | 0.194594i | ||||
\(227\) | 1.11401 | + | 12.7332i | 0.0739393 | + | 0.845130i | 0.939102 | + | 0.343639i | \(0.111660\pi\) |
−0.865163 | + | 0.501492i | \(0.832785\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.6486 | + | 2.58295i | −0.968008 | + | 0.170686i | −0.635233 | − | 0.772320i | \(-0.719096\pi\) |
−0.332775 | + | 0.943006i | \(0.607985\pi\) | |||||||
\(230\) | −3.90929 | − | 1.12481i | −0.257771 | − | 0.0741676i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.86413 | + | 0.775511i | −0.581959 | + | 0.0509148i | ||||
\(233\) | 4.81533 | + | 1.29026i | 0.315463 | + | 0.0845279i | 0.413076 | − | 0.910696i | \(-0.364454\pi\) |
−0.0976137 | + | 0.995224i | \(0.531121\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.562827 | + | 2.88154i | −0.0367148 | + | 0.187971i | ||||
\(236\) | 0.372840 | + | 1.02437i | 0.0242698 | + | 0.0666808i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.61033 | − | 0.578329i | −0.428484 | − | 0.0374875i | ||||
\(239\) | 6.83215 | + | 2.48670i | 0.441935 | + | 0.160851i | 0.553397 | − | 0.832918i | \(-0.313331\pi\) |
−0.111462 | + | 0.993769i | \(0.535553\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.42764 | − | 19.4391i | 0.220794 | − | 1.25219i | −0.649770 | − | 0.760131i | \(-0.725135\pi\) |
0.870564 | − | 0.492055i | \(-0.163754\pi\) | |||||||
\(242\) | −2.84333 | − | 2.84333i | −0.182776 | − | 0.182776i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 3.57064i | − | 0.228587i | ||||||
\(245\) | −7.84886 | + | 10.7825i | −0.501445 | + | 0.688866i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.436837 | − | 0.203700i | 0.0277953 | − | 0.0129611i | ||||
\(248\) | −1.48928 | + | 17.0226i | −0.0945696 | + | 1.08094i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.01696 | + | 1.17264i | 0.317300 | + | 0.0741643i | ||||
\(251\) | −14.7212 | − | 8.49927i | −0.929191 | − | 0.536469i | −0.0426356 | − | 0.999091i | \(-0.513575\pi\) |
−0.886556 | + | 0.462622i | \(0.846909\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.53797 | + | 16.9360i | −0.285300 | + | 1.06475i | ||||
\(254\) | 1.86278 | + | 1.56305i | 0.116881 | + | 0.0980747i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.275231 | + | 1.56091i | 0.0172019 | + | 0.0975570i | ||||
\(257\) | 8.87491 | − | 12.6747i | 0.553601 | − | 0.790625i | −0.440652 | − | 0.897678i | \(-0.645253\pi\) |
0.994253 | + | 0.107053i | \(0.0341415\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.4510 | − | 30.3313i | 1.58145 | − | 1.88469i | ||||
\(260\) | 1.03555 | − | 1.18908i | 0.0642221 | − | 0.0737439i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.0845478 | + | 0.315537i | 0.00522338 | + | 0.0194939i | ||||
\(263\) | −10.6896 | + | 22.9238i | −0.659147 | + | 1.41355i | 0.237759 | + | 0.971324i | \(0.423587\pi\) |
−0.896906 | + | 0.442221i | \(0.854191\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.57520 | − | 5.76519i | −0.588200 | − | 0.354153i | ||||
\(266\) | −0.693419 | + | 1.90515i | −0.0425163 | + | 0.116812i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.97503 | + | 4.18376i | −0.364983 | + | 0.255564i | ||||
\(269\) | 20.9181 | 1.27540 | 0.637698 | − | 0.770286i | \(-0.279887\pi\) | ||||
0.637698 | + | 0.770286i | \(0.279887\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.02125 | 0.365765 | 0.182882 | − | 0.983135i | \(-0.441457\pi\) | ||||
0.182882 | + | 0.983135i | \(0.441457\pi\) | |||||||
\(272\) | 9.07736 | − | 6.35604i | 0.550396 | − | 0.385391i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.160475 | − | 0.440902i | 0.00969467 | − | 0.0266359i | ||||
\(275\) | 4.65646 | − | 21.7132i | 0.280795 | − | 1.30936i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.52924 | − | 3.27946i | 0.0918830 | − | 0.197044i | −0.854995 | − | 0.518636i | \(-0.826440\pi\) |
0.946878 | + | 0.321592i | \(0.104218\pi\) | |||||||
\(278\) | 2.65495 | + | 9.90842i | 0.159233 | + | 0.594267i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.967565 | + | 14.0195i | 0.0578230 | + | 0.837826i | ||||
\(281\) | 15.0170 | − | 17.8966i | 0.895839 | − | 1.06762i | −0.101508 | − | 0.994835i | \(-0.532367\pi\) |
0.997348 | − | 0.0727851i | \(-0.0231887\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.0108 | − | 14.2969i | 0.595080 | − | 0.849863i | −0.402776 | − | 0.915298i | \(-0.631955\pi\) |
0.997857 | + | 0.0654355i | \(0.0208437\pi\) | |||||||
\(284\) | 3.91627 | + | 22.2103i | 0.232388 | + | 1.31794i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.618469 | + | 0.518957i | 0.0365708 | + | 0.0306866i | ||||
\(287\) | −1.71112 | + | 6.38599i | −0.101004 | + | 0.376953i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.871882 | + | 0.503381i | 0.0512872 | + | 0.0296107i | ||||
\(290\) | 4.08535 | − | 3.30212i | 0.239900 | − | 0.193907i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.645696 | + | 7.38033i | −0.0377865 | + | 0.431901i | ||||
\(293\) | −14.9428 | + | 6.96793i | −0.872966 | + | 0.407071i | −0.806861 | − | 0.590742i | \(-0.798835\pi\) |
−0.0661055 | + | 0.997813i | \(0.521057\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.10242 | − | 0.802484i | −0.0641854 | − | 0.0467224i | ||||
\(296\) | − | 19.1940i | − | 1.11563i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.25803 | + | 5.25803i | 0.304590 | + | 0.304590i | ||||
\(299\) | 0.270414 | − | 1.53359i | 0.0156384 | − | 0.0886899i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.48992 | + | 3.09008i | 0.489351 | + | 0.178109i | ||||
\(302\) | 4.14170 | + | 0.362352i | 0.238328 | + | 0.0208510i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.15801 | − | 3.18160i | −0.0664164 | − | 0.182477i | ||||
\(305\) | 2.49418 | + | 3.70502i | 0.142816 | + | 0.212149i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.6145 | + | 4.98775i | 1.06239 | + | 0.284666i | 0.747362 | − | 0.664417i | \(-0.231320\pi\) |
0.315026 | + | 0.949083i | \(0.397987\pi\) | |||||||
\(308\) | 28.4785 | − | 2.49155i | 1.62271 | − | 0.141969i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.88267 | − | 8.82744i | −0.277317 | − | 0.501365i | ||||
\(311\) | −4.11040 | + | 0.724775i | −0.233079 | + | 0.0410982i | −0.288968 | − | 0.957339i | \(-0.593312\pi\) |
0.0558883 | + | 0.998437i | \(0.482201\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.399794 | − | 4.56966i | −0.0225977 | − | 0.258293i | −0.999087 | − | 0.0427260i | \(-0.986396\pi\) |
0.976489 | − | 0.215567i | \(-0.0691598\pi\) | |||||||
\(314\) | 0.330565 | + | 0.572556i | 0.0186549 | + | 0.0323112i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.7722 | + | 18.6580i | −0.605983 | + | 1.04959i | ||||
\(317\) | −21.0570 | − | 9.81902i | −1.18268 | − | 0.551491i | −0.271072 | − | 0.962559i | \(-0.587378\pi\) |
−0.911605 | + | 0.411068i | \(0.865156\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.5537 | − | 17.3444i | −0.814849 | − | 0.971099i | ||||
\(320\) | −5.19055 | − | 5.38473i | −0.290160 | − | 0.301016i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.75708 | + | 5.36567i | 0.209374 | + | 0.299017i | ||||
\(323\) | −3.45531 | + | 3.45531i | −0.192258 | + | 0.192258i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.243917 | + | 1.95719i | −0.0135301 | + | 0.108566i | ||||
\(326\) | 4.28008 | + | 0.754693i | 0.237052 | + | 0.0417986i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.35445 | + | 2.90462i | 0.0747869 | + | 0.160381i | ||||
\(329\) | 3.62159 | − | 3.03887i | 0.199665 | − | 0.167539i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.6555 | − | 6.42608i | 0.970434 | − | 0.353209i | 0.192320 | − | 0.981332i | \(-0.438399\pi\) |
0.778114 | + | 0.628123i | \(0.216177\pi\) | |||||||
\(332\) | 4.65146 | − | 1.24635i | 0.255282 | − | 0.0684026i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.69131 | − | 3.86323i | 0.366132 | − | 0.211386i | ||||
\(335\) | 3.27744 | − | 8.51492i | 0.179065 | − | 0.465220i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.63124 | − | 4.64324i | −0.361227 | − | 0.252934i | 0.378847 | − | 0.925459i | \(-0.376321\pi\) |
−0.740074 | + | 0.672526i | \(0.765209\pi\) | |||||||
\(338\) | 4.84857 | + | 3.39501i | 0.263728 | + | 0.184664i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.74232 | + | 14.9188i | −0.311421 | + | 0.809085i | ||||
\(341\) | −37.6552 | + | 21.7402i | −2.03914 | + | 1.17730i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.60198 | + | 0.965147i | −0.194489 | + | 0.0521130i | ||||
\(344\) | 4.11560 | − | 1.49796i | 0.221898 | − | 0.0807644i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.69798 | − | 2.26387i | 0.145044 | − | 0.121707i | ||||
\(347\) | −2.42251 | − | 5.19509i | −0.130047 | − | 0.278887i | 0.830493 | − | 0.557030i | \(-0.188059\pi\) |
−0.960540 | + | 0.278143i | \(0.910281\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.63192 | + | 0.640405i | 0.194412 | + | 0.0342801i | 0.270006 | − | 0.962859i | \(-0.412974\pi\) |
−0.0755941 | + | 0.997139i | \(0.524085\pi\) | |||||||
\(350\) | −5.09580 | − | 6.54677i | −0.272382 | − | 0.349940i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14.9734 | − | 14.9734i | 0.798085 | − | 0.798085i | ||||
\(353\) | −10.0809 | − | 14.3970i | −0.536551 | − | 0.766275i | 0.455752 | − | 0.890107i | \(-0.349370\pi\) |
−0.992303 | + | 0.123832i | \(0.960482\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.5781 | − | 20.3105i | −1.03910 | − | 1.07797i | ||||
\(356\) | −2.83851 | − | 3.38281i | −0.150441 | − | 0.179288i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.75876 | − | 0.820125i | −0.0929535 | − | 0.0433449i | ||||
\(359\) | 4.06033 | − | 7.03269i | 0.214296 | − | 0.371171i | −0.738759 | − | 0.673970i | \(-0.764588\pi\) |
0.953055 | + | 0.302799i | \(0.0979210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.75349 | − | 15.1615i | −0.460710 | − | 0.797973i | ||||
\(362\) | 0.238849 | + | 2.73005i | 0.0125536 | + | 0.143488i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.50044 | + | 0.440896i | −0.131059 | + | 0.0231092i | ||||
\(365\) | −4.48535 | − | 8.10912i | −0.234774 | − | 0.424451i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.9819 | − | 1.48573i | 0.886450 | − | 0.0775543i | 0.365171 | − | 0.930940i | \(-0.381011\pi\) |
0.521279 | + | 0.853386i | \(0.325455\pi\) | |||||||
\(368\) | −10.5662 | − | 2.83121i | −0.550801 | − | 0.147587i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.32791 | + | 9.39988i | 0.328972 | + | 0.488677i | ||||
\(371\) | 6.15547 | + | 16.9120i | 0.319576 | + | 0.878028i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.1095 | + | 2.72173i | 1.61079 | + | 0.140926i | 0.856688 | − | 0.515834i | \(-0.172518\pi\) |
0.754100 | + | 0.656760i | \(0.228073\pi\) | |||||||
\(374\) | −7.69144 | − | 2.79945i | −0.397715 | − | 0.144756i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.397965 | − | 2.25697i | 0.0205235 | − | 0.116394i | ||||
\(377\) | 1.42194 | + | 1.42194i | 0.0732339 | + | 0.0732339i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 31.2281i | − | 1.60408i | −0.597269 | − | 0.802041i | \(-0.703748\pi\) | ||
0.597269 | − | 0.802041i | \(-0.296252\pi\) | |||||||
\(380\) | 3.94884 | + | 2.87448i | 0.202571 | + | 0.147458i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.52881 | − | 2.11182i | 0.231714 | − | 0.108050i | ||||
\(383\) | −2.94643 | + | 33.6778i | −0.150555 | + | 1.72086i | 0.426786 | + | 0.904353i | \(0.359646\pi\) |
−0.577341 | + | 0.816503i | \(0.695910\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −27.8099 | + | 22.4783i | −1.41732 | + | 1.14560i | ||||
\(386\) | 0.245587 | + | 0.141790i | 0.0125001 | + | 0.00721691i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.263515 | + | 0.983453i | −0.0133780 | + | 0.0499272i | ||||
\(389\) | −20.9380 | − | 17.5690i | −1.06160 | − | 0.890786i | −0.0673324 | − | 0.997731i | \(-0.521449\pi\) |
−0.994265 | + | 0.106945i | \(0.965893\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.74149 | + | 15.5478i | 0.138643 | + | 0.786284i | ||||
\(392\) | 5.97114 | − | 8.52768i | 0.301588 | − | 0.430713i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.14085 | + | 9.70188i | −0.410130 | + | 0.488774i | ||||
\(395\) | −1.85547 | − | 26.8848i | −0.0933589 | − | 1.35272i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.30445 | − | 12.3324i | −0.165846 | − | 0.618945i | −0.997931 | − | 0.0642968i | \(-0.979520\pi\) |
0.832085 | − | 0.554648i | \(-0.187147\pi\) | |||||||
\(398\) | 0.539761 | − | 1.15752i | 0.0270558 | − | 0.0580213i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.5467 | + | 2.90513i | 0.677335 | + | 0.145256i | ||||
\(401\) | 6.74752 | − | 18.5387i | 0.336955 | − | 0.925776i | −0.649298 | − | 0.760534i | \(-0.724937\pi\) |
0.986253 | − | 0.165242i | \(-0.0528406\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.16338 | − | 2.21502i | 0.157579 | − | 0.110338i | ||||
\(404\) | −26.1441 | −1.30072 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.45859 | −0.419793 | ||||||||
\(407\) | 40.0078 | − | 28.0137i | 1.98311 | − | 1.38859i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.987380 | − | 2.71280i | 0.0488228 | − | 0.134139i | −0.912885 | − | 0.408218i | \(-0.866150\pi\) |
0.961707 | + | 0.274078i | \(0.0883727\pi\) | |||||||
\(410\) | −1.62091 | − | 0.975943i | −0.0800511 | − | 0.0481984i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.0124 | − | 27.9052i | 0.641076 | − | 1.37479i | ||||
\(413\) | 0.568280 | + | 2.12085i | 0.0279632 | + | 0.104360i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.95590 | + | 4.54242i | −0.194188 | + | 0.222979i | ||||
\(416\) | −1.20891 | + | 1.44073i | −0.0592719 | + | 0.0706375i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.43443 | + | 2.04857i | −0.0701601 | + | 0.100199i | ||||
\(419\) | −3.08760 | − | 17.5106i | −0.150839 | − | 0.855451i | −0.962492 | − | 0.271310i | \(-0.912543\pi\) |
0.811653 | − | 0.584140i | \(-0.198568\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.57150 | + | 1.31864i | 0.0765901 | + | 0.0642667i | 0.680279 | − | 0.732953i | \(-0.261859\pi\) |
−0.603689 | + | 0.797220i | \(0.706303\pi\) | |||||||
\(422\) | −2.61453 | + | 9.75758i | −0.127274 | + | 0.474991i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.55561 | + | 4.36223i | 0.366933 | + | 0.211849i | ||||
\(425\) | −4.46273 | − | 19.4914i | −0.216474 | − | 0.945472i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.626811 | − | 7.16449i | 0.0303335 | − | 0.346714i | ||||
\(428\) | 9.34000 | − | 4.35531i | 0.451466 | − | 0.210522i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.52168 | + | 2.09043i | −0.0733820 | + | 0.100809i | ||||
\(431\) | − | 19.3828i | − | 0.933636i | −0.884353 | − | 0.466818i | \(-0.845400\pi\) | ||
0.884353 | − | 0.466818i | \(-0.154600\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.30954 | − | 2.30954i | −0.110989 | − | 0.110989i | 0.649431 | − | 0.760420i | \(-0.275007\pi\) |
−0.760420 | + | 0.649431i | \(0.775007\pi\) | |||||||
\(434\) | −2.82071 | + | 15.9970i | −0.135398 | + | 0.767881i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.3146 | + | 4.48214i | 0.589762 | + | 0.214656i | ||||
\(437\) | 4.80536 | + | 0.420414i | 0.229871 | + | 0.0201111i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.67858 | − | 4.61187i | −0.0801144 | − | 0.220112i | 0.893168 | − | 0.449723i | \(-0.148477\pi\) |
−0.973283 | + | 0.229610i | \(0.926255\pi\) | |||||||
\(440\) | −3.32298 | + | 17.0129i | −0.158417 | + | 0.811056i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.702196 | + | 0.188153i | 0.0334000 | + | 0.00894952i | ||||
\(443\) | −19.2540 | + | 1.68450i | −0.914783 | + | 0.0800331i | −0.534817 | − | 0.844968i | \(-0.679620\pi\) |
−0.379965 | + | 0.925001i | \(0.624064\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.30831 | + | 1.52734i | 0.251638 | + | 0.0724031i | ||||
\(446\) | 5.06133 | − | 0.892450i | 0.239661 | − | 0.0422587i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.04963 | + | 11.9973i | 0.0495903 | + | 0.566820i | ||||
\(449\) | 1.49368 | + | 2.58713i | 0.0704911 | + | 0.122094i | 0.899117 | − | 0.437709i | \(-0.144210\pi\) |
−0.828626 | + | 0.559803i | \(0.810877\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.07753 | + | 7.06249i | −0.192003 | + | 0.332560i | ||||
\(452\) | 11.8761 | + | 5.53791i | 0.558604 | + | 0.260481i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.78613 | + | 4.51214i | 0.177692 | + | 0.211765i | ||||
\(455\) | 2.28657 | − | 2.20411i | 0.107196 | − | 0.103330i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.78805 | − | 5.40989i | −0.177197 | − | 0.253064i | 0.720722 | − | 0.693224i | \(-0.243811\pi\) |
−0.897919 | + | 0.440160i | \(0.854922\pi\) | |||||||
\(458\) | −4.84692 | + | 4.84692i | −0.226482 | + | 0.226482i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.9252 | − | 5.12401i | 0.695889 | − | 0.238908i | ||||
\(461\) | −41.0394 | − | 7.23636i | −1.91140 | − | 0.337031i | −0.913791 | − | 0.406185i | \(-0.866859\pi\) |
−0.997606 | + | 0.0691537i | \(0.977970\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.30650 | + | 4.94630i | 0.107192 | + | 0.229874i | 0.952586 | − | 0.304269i | \(-0.0984122\pi\) |
−0.845394 | + | 0.534143i | \(0.820634\pi\) | |||||||
\(464\) | 10.8210 | − | 9.07991i | 0.502353 | − | 0.421524i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.15876 | − | 0.785723i | 0.100002 | − | 0.0363979i | ||||
\(467\) | 9.74812 | − | 2.61200i | 0.451089 | − | 0.120869i | −0.0261197 | − | 0.999659i | \(-0.508315\pi\) |
0.477209 | + | 0.878790i | \(0.341648\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.7233 | + | 7.34582i | −0.587509 | + | 0.339199i | ||||
\(470\) | 0.549185 | + | 1.23651i | 0.0253320 | + | 0.0570358i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.871887 | + | 0.610502i | 0.0401319 | + | 0.0281006i | ||||
\(473\) | 9.12904 | + | 6.39222i | 0.419753 | + | 0.293915i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.10535 | − | 0.224291i | −0.280133 | − | 0.0102912i | ||||
\(476\) | 22.2923 | − | 12.8704i | 1.02176 | − | 0.589916i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.23632 | − | 0.867168i | 0.148026 | − | 0.0396634i | ||||
\(479\) | −4.22629 | + | 1.53824i | −0.193104 | + | 0.0702841i | −0.436762 | − | 0.899577i | \(-0.643875\pi\) |
0.243658 | + | 0.969861i | \(0.421653\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.32297 | + | 2.78830i | −0.151514 | + | 0.127136i | ||||
\(482\) | −3.84423 | − | 8.24398i | −0.175100 | − | 0.375503i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.3617 | + | 2.70868i | 0.698258 | + | 0.123122i | ||||
\(485\) | −0.413534 | − | 1.20454i | −0.0187776 | − | 0.0546952i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.49814 | + | 2.49814i | −0.113202 | + | 0.113202i | −0.761439 | − | 0.648237i | \(-0.775507\pi\) |
0.648237 | + | 0.761439i | \(0.275507\pi\) | |||||||
\(488\) | −1.99969 | − | 2.85585i | −0.0905215 | − | 0.129278i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.112832 | + | 6.14482i | −0.00509725 | + | 0.277595i | ||||
\(491\) | −9.95960 | − | 11.8694i | −0.449471 | − | 0.535658i | 0.492964 | − | 0.870050i | \(-0.335914\pi\) |
−0.942434 | + | 0.334392i | \(0.891469\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.4770 | − | 8.61596i | −0.832162 | − | 0.388043i | ||||
\(494\) | 0.111058 | − | 0.192358i | 0.00499673 | − | 0.00865459i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.5636 | − | 23.4928i | −0.609022 | − | 1.05486i | ||||
\(497\) | 3.95907 | + | 45.2524i | 0.177589 | + | 2.02985i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.9468 | − | 2.98818i | 0.758644 | − | 0.133769i | 0.219072 | − | 0.975709i | \(-0.429697\pi\) |
0.539572 | + | 0.841939i | \(0.318586\pi\) | |||||||
\(500\) | −18.5514 | + | 7.43661i | −0.829644 | + | 0.332575i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.80354 | + | 0.682721i | −0.348289 | + | 0.0304713i | ||||
\(503\) | 38.6515 | + | 10.3567i | 1.72339 | + | 0.461780i | 0.978643 | − | 0.205569i | \(-0.0659045\pi\) |
0.744745 | + | 0.667349i | \(0.232571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.1281 | − | 18.2623i | 1.20718 | − | 0.812663i | ||||
\(506\) | 2.76346 | + | 7.59255i | 0.122851 | + | 0.337530i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.39712 | − | 0.822142i | −0.416930 | − | 0.0364766i | ||||
\(509\) | 36.9106 | + | 13.4344i | 1.63604 | + | 0.595468i | 0.986339 | − | 0.164726i | \(-0.0526738\pi\) |
0.649696 | + | 0.760194i | \(0.274896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.59118 | + | 14.6953i | −0.114627 | + | 0.650081i | ||||
\(512\) | 16.1816 | + | 16.1816i | 0.715134 | + | 0.715134i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 7.13031i | − | 0.314504i | ||||||
\(515\) | 5.99036 | + | 38.0449i | 0.263967 | + | 1.67646i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.28523 | − | 2.46454i | 0.232444 | − | 0.108390i | ||||
\(518\) | 1.59026 | − | 18.1768i | 0.0698721 | − | 0.798642i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.162318 | − | 1.53099i | 0.00711810 | − | 0.0671384i | ||||
\(521\) | 26.5294 | + | 15.3168i | 1.16227 | + | 0.671039i | 0.951848 | − | 0.306571i | \(-0.0991816\pi\) |
0.210426 | + | 0.977610i | \(0.432515\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.16084 | − | 4.33233i | 0.0507602 | − | 0.189439i | −0.935890 | − | 0.352291i | \(-0.885403\pi\) |
0.986651 | + | 0.162852i | \(0.0520693\pi\) | |||||||
\(524\) | −0.970744 | − | 0.814551i | −0.0424071 | − | 0.0355838i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.02403 | + | 11.4789i | 0.0882521 | + | 0.500503i | ||||
\(527\) | −22.4562 | + | 32.0708i | −0.978207 | + | 1.39702i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.76651 | + | 5.68051i | −0.207240 | + | 0.246979i | ||||
\(530\) | −5.13835 | + | 0.354626i | −0.223195 | + | 0.0154040i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.03556 | − | 7.59683i | −0.0882529 | − | 0.329364i | ||||
\(533\) | 0.306103 | − | 0.656441i | 0.0132588 | − | 0.0284336i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.64921 | + | 11.0435i | −0.287471 | + | 0.477450i | ||||
\(536\) | −2.43586 | + | 6.69246i | −0.105213 | + | 0.289070i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.89626 | − | 5.52902i | 0.340432 | − | 0.238373i | ||||
\(539\) | 26.4898 | 1.14100 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.96440 | 0.213436 | 0.106718 | − | 0.994289i | \(-0.465966\pi\) | ||||
0.106718 | + | 0.994289i | \(0.465966\pi\) | |||||||
\(542\) | 2.27293 | − | 1.59153i | 0.0976309 | − | 0.0683619i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.52135 | − | 17.9173i | 0.279601 | − | 0.768196i | ||||
\(545\) | −15.9089 | + | 3.95122i | −0.681464 | + | 0.169252i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.14812 | + | 13.1847i | −0.262875 | + | 0.563737i | −0.992799 | − | 0.119791i | \(-0.961777\pi\) |
0.729924 | + | 0.683528i | \(0.239555\pi\) | |||||||
\(548\) | 0.471083 | + | 1.75810i | 0.0201237 | + | 0.0751025i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.98145 | − | 9.42721i | −0.169770 | − | 0.401978i | ||||
\(551\) | −4.00394 | + | 4.77171i | −0.170574 | + | 0.203282i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.8897 | + | 35.5462i | −1.05842 | + | 1.51158i | ||||
\(554\) | −0.289556 | − | 1.64216i | −0.0123021 | − | 0.0697685i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −30.4831 | − | 25.5783i | −1.29277 | − | 1.08476i | ||||
\(557\) | 7.79233 | − | 29.0814i | 0.330171 | − | 1.23222i | −0.578838 | − | 0.815442i | \(-0.696494\pi\) |
0.909010 | − | 0.416774i | \(-0.136840\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.857203 | − | 0.494906i | −0.0362558 | − | 0.0209323i | ||||
\(560\) | −14.0240 | − | 17.3504i | −0.592622 | − | 0.733186i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.938313 | − | 10.7250i | 0.0395803 | − | 0.452405i | ||||
\(563\) | −19.4537 | + | 9.07139i | −0.819874 | + | 0.382314i | −0.786852 | − | 0.617141i | \(-0.788291\pi\) |
−0.0330215 | + | 0.999455i | \(0.510513\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.1914 | + | 2.54942i | −0.681177 | + | 0.107255i | ||||
\(566\) | − | 8.04291i | − | 0.338069i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.5708 | + | 15.5708i | 0.653338 | + | 0.653338i | ||||
\(569\) | 2.94509 | − | 16.7024i | 0.123465 | − | 0.700202i | −0.858743 | − | 0.512406i | \(-0.828754\pi\) |
0.982208 | − | 0.187796i | \(-0.0601345\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.4369 | − | 10.3502i | −1.19005 | − | 0.433142i | −0.330307 | − | 0.943873i | \(-0.607152\pi\) |
−0.859740 | + | 0.510732i | \(0.829375\pi\) | |||||||
\(572\) | −3.11998 | − | 0.272963i | −0.130453 | − | 0.0114132i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.04201 | + | 2.86290i | 0.0434927 | + | 0.119495i | ||||
\(575\) | −11.9076 | + | 15.7424i | −0.496582 | + | 0.656505i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.9807 | − | 7.49741i | −1.16485 | − | 0.312121i | −0.375950 | − | 0.926640i | \(-0.622684\pi\) |
−0.788903 | + | 0.614518i | \(0.789350\pi\) | |||||||
\(578\) | 0.462176 | − | 0.0404352i | 0.0192240 | − | 0.00168188i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.63458 | + | 19.5831i | −0.233963 | + | 0.813143i | ||||
\(581\) | 9.55194 | − | 1.68426i | 0.396281 | − | 0.0698751i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.93485 | + | 22.1155i | 0.0801334 | + | 0.915929i | ||||
\(584\) | 3.61681 | + | 6.26451i | 0.149665 | + | 0.259227i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.79893 | + | 6.57994i | −0.156932 | + | 0.271815i | ||||
\(587\) | −5.92953 | − | 2.76499i | −0.244738 | − | 0.114123i | 0.296379 | − | 0.955070i | \(-0.404221\pi\) |
−0.541117 | + | 0.840947i | \(0.681999\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.68913 | + | 9.16355i | 0.316825 | + | 0.377578i | ||||
\(590\) | −0.628259 | − | 0.0115362i | −0.0258650 | − | 0.000474939i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17.4775 | + | 24.9605i | 0.718322 | + | 1.02587i | ||||
\(593\) | −22.3175 | + | 22.3175i | −0.916469 | + | 0.916469i | −0.996771 | − | 0.0803015i | \(-0.974412\pi\) |
0.0803015 | + | 0.996771i | \(0.474412\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.1409 | + | 28.9265i | −0.579720 | + | 1.18587i | ||||
\(596\) | −28.4076 | − | 5.00902i | −1.16362 | − | 0.205177i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.303279 | − | 0.650384i | −0.0124020 | − | 0.0265962i | ||||
\(599\) | −8.78838 | + | 7.37433i | −0.359083 | + | 0.301307i | −0.804425 | − | 0.594054i | \(-0.797527\pi\) |
0.445342 | + | 0.895361i | \(0.353082\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.2326 | + | 10.6398i | −1.19242 | + | 0.434007i | −0.860574 | − | 0.509326i | \(-0.829895\pi\) |
−0.331850 | + | 0.943332i | \(0.607673\pi\) | |||||||
\(602\) | 4.02159 | − | 1.07758i | 0.163908 | − | 0.0439189i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.9672 | + | 8.06397i | −0.568317 | + | 0.328118i | ||||
\(605\) | −17.8319 | + | 7.91990i | −0.724969 | + | 0.321990i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.0216 | + | 8.41759i | 0.487940 | + | 0.341659i | 0.791517 | − | 0.611148i | \(-0.209292\pi\) |
−0.303576 | + | 0.952807i | \(0.598181\pi\) | |||||||
\(608\) | −4.77216 | − | 3.34151i | −0.193537 | − | 0.135516i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.92082 | + | 0.739334i | 0.0777718 | + | 0.0299348i | ||||
\(611\) | −0.448550 | + | 0.258971i | −0.0181464 | + | 0.0104768i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.4357 | − | 5.20779i | 0.785002 | − | 0.210341i | 0.156013 | − | 0.987755i | \(-0.450136\pi\) |
0.628989 | + | 0.777414i | \(0.283469\pi\) | |||||||
\(614\) | 8.34507 | − | 3.03736i | 0.336780 | − | 0.122578i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21.3821 | − | 17.9418i | 0.861511 | − | 0.722894i | ||||
\(617\) | −1.25995 | − | 2.70196i | −0.0507236 | − | 0.108777i | 0.879313 | − | 0.476245i | \(-0.158002\pi\) |
−0.930036 | + | 0.367468i | \(0.880225\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.1500 | − | 2.31870i | −0.528542 | − | 0.0931962i | −0.0969919 | − | 0.995285i | \(-0.530922\pi\) |
−0.431550 | + | 0.902089i | \(0.642033\pi\) | |||||||
\(620\) | 35.1568 | + | 17.1866i | 1.41193 | + | 0.690231i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.36005 | + | 1.36005i | −0.0545329 | + | 0.0545329i | ||||
\(623\) | −5.10163 | − | 7.28589i | −0.204393 | − | 0.291903i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.0549 | − | 20.6751i | 0.562196 | − | 0.827004i | ||||
\(626\) | −1.35876 | − | 1.61931i | −0.0543070 | − | 0.0647206i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.32438 | − | 1.08388i | −0.0927529 | − | 0.0432514i | ||||
\(629\) | 21.9887 | − | 38.0856i | 0.876748 | − | 1.51857i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.693777 | + | 1.20166i | 0.0276188 | + | 0.0478372i | 0.879504 | − | 0.475891i | \(-0.157874\pi\) |
−0.851886 | + | 0.523728i | \(0.824541\pi\) | |||||||
\(632\) | 1.83339 | + | 20.9557i | 0.0729283 | + | 0.833575i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.5440 | + | 1.85920i | −0.418758 | + | 0.0738383i | ||||
\(635\) | 10.3251 | − | 5.71104i | 0.409738 | − | 0.226636i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.34378 | + | 0.205054i | −0.0928638 | + | 0.00812453i | ||||
\(638\) | −10.0782 | − | 2.70046i | −0.399001 | − | 0.106912i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.3094 | − | 4.74815i | −0.960914 | − | 0.187687i | ||||
\(641\) | 6.63051 | + | 18.2172i | 0.261890 | + | 0.719536i | 0.999040 | + | 0.0438070i | \(0.0139487\pi\) |
−0.737150 | + | 0.675729i | \(0.763829\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.1928 | + | 3.60391i | 1.62449 | + | 0.142124i | 0.862705 | − | 0.505708i | \(-0.168769\pi\) |
0.761783 | + | 0.647833i | \(0.224324\pi\) | |||||||
\(644\) | −23.8775 | − | 8.69071i | −0.940906 | − | 0.342462i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.391028 | + | 2.21763i | −0.0153848 | + | 0.0872514i | ||||
\(647\) | −12.4891 | − | 12.4891i | −0.490997 | − | 0.490997i | 0.417623 | − | 0.908620i | \(-0.362863\pi\) |
−0.908620 | + | 0.417623i | \(0.862863\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.70837i | 0.106313i | ||||||||
\(650\) | 0.425247 | + | 0.803284i | 0.0166795 | + | 0.0315074i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.2799 | + | 7.12513i | −0.598407 | + | 0.279042i | ||||
\(653\) | 1.28323 | − | 14.6673i | 0.0502165 | − | 0.573977i | −0.928853 | − | 0.370449i | \(-0.879204\pi\) |
0.979069 | − | 0.203528i | \(-0.0652408\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.57626 | + | 0.167117i | 0.0615896 | + | 0.00652980i | ||||
\(656\) | −4.40623 | − | 2.54394i | −0.172034 | − | 0.0993241i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.563868 | − | 2.10438i | 0.0219819 | − | 0.0820374i | ||||
\(659\) | 21.0565 | + | 17.6685i | 0.820245 | + | 0.688268i | 0.953030 | − | 0.302877i | \(-0.0979473\pi\) |
−0.132784 | + | 0.991145i | \(0.542392\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.73362 | + | 9.83186i | 0.0674301 | + | 0.382415i | 0.999782 | + | 0.0208639i | \(0.00664165\pi\) |
−0.932352 | + | 0.361551i | \(0.882247\pi\) | |||||||
\(662\) | 4.96617 | − | 7.09243i | 0.193016 | − | 0.275655i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.02230 | − | 3.60183i | 0.117288 | − | 0.139778i | ||||
\(665\) | 7.41875 | + | 6.46084i | 0.287687 | + | 0.250541i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.20873 | + | 19.4392i | 0.201683 | + | 0.752690i | ||||
\(668\) | −12.6670 | + | 27.1644i | −0.490100 | + | 1.05102i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.01347 | − | 4.08055i | −0.0391536 | − | 0.157645i | ||||
\(671\) | 3.03414 | − | 8.33623i | 0.117132 | − | 0.321816i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.212002 | + | 0.148446i | −0.00817209 | + | 0.00572216i | −0.577655 | − | 0.816281i | \(-0.696032\pi\) |
0.569483 | + | 0.822003i | \(0.307143\pi\) | |||||||
\(674\) | −3.73049 | −0.143693 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.9612 | −0.883122 | ||||||||
\(677\) | −20.1079 | + | 14.0797i | −0.772810 | + | 0.541128i | −0.892157 | − | 0.451725i | \(-0.850809\pi\) |
0.119347 | + | 0.992853i | \(0.461920\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.701384 | + | 1.92704i | −0.0269167 | + | 0.0739529i | ||||
\(680\) | 3.76227 | + | 15.1482i | 0.144277 | + | 0.580906i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.46795 | + | 18.1596i | −0.324255 | + | 0.695366i | ||||
\(683\) | −5.75081 | − | 21.4623i | −0.220048 | − | 0.821232i | −0.984328 | − | 0.176347i | \(-0.943572\pi\) |
0.764280 | − | 0.644885i | \(-0.223095\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.71689 | − | 1.49521i | −0.0655991 | − | 0.0571289i | ||||
\(686\) | −1.10459 | + | 1.31640i | −0.0421734 | + | 0.0502603i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.98805 | + | 5.69553i | −0.152043 | + | 0.217140i | ||||
\(689\) | −0.342385 | − | 1.94176i | −0.0130438 | − | 0.0739753i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.205042 | − | 0.172050i | −0.00780016 | − | 0.00654511i | 0.638879 | − | 0.769307i | \(-0.279398\pi\) |
−0.646679 | + | 0.762762i | \(0.723843\pi\) | |||||||
\(692\) | −3.53610 | + | 13.1969i | −0.134422 | + | 0.501672i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.28762 | − | 1.32076i | −0.0868369 | − | 0.0501353i | ||||
\(695\) | 49.4974 | + | 5.24777i | 1.87754 | + | 0.199059i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.639991 | + | 7.31513i | −0.0242414 | + | 0.277080i | ||||
\(698\) | 1.54027 | − | 0.718239i | 0.0583000 | − | 0.0271857i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 30.7595 | + | 9.46517i | 1.16260 | + | 0.357750i | ||||
\(701\) | 38.5968i | 1.45778i | 0.684630 | + | 0.728891i | \(0.259964\pi\) | ||||
−0.684630 | + | 0.728891i | \(0.740036\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.50124 | − | 9.50124i | −0.358346 | − | 0.358346i | ||||
\(704\) | −2.57960 | + | 14.6297i | −0.0972225 | + | 0.551376i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.61078 | − | 2.77010i | −0.286435 | − | 0.104254i | ||||
\(707\) | −52.4582 | − | 4.58950i | −1.97289 | − | 0.172606i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.0622 | + | 44.1305i | 0.603228 | + | 1.65735i | 0.744690 | + | 0.667410i | \(0.232597\pi\) |
−0.141463 | + | 0.989944i | \(0.545181\pi\) | |||||||
\(710\) | −12.7589 | − | 2.49209i | −0.478833 | − | 0.0935264i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.16477 | − | 1.11595i | −0.156081 | − | 0.0418219i | ||||
\(713\) | 38.5007 | − | 3.36838i | 1.44186 | − | 0.126147i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.42808 | − | 1.89615i | 0.128203 | − | 0.0709120i | ||||
\(716\) | 7.41357 | − | 1.30721i | 0.277058 | − | 0.0488528i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.326154 | − | 3.72796i | −0.0121720 | − | 0.139126i | ||||
\(719\) | −0.577250 | − | 0.999826i | −0.0215278 | − | 0.0372872i | 0.855061 | − | 0.518528i | \(-0.173520\pi\) |
−0.876589 | + | 0.481241i | \(0.840186\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.0080 | − | 53.7075i | 1.15480 | − | 2.00017i | ||||
\(722\) | −7.31177 | − | 3.40954i | −0.272116 | − | 0.126890i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.83343 | − | 8.14376i | −0.253962 | − | 0.302660i | ||||
\(725\) | −7.83263 | − | 24.2560i | −0.290897 | − | 0.900844i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.7146 | − | 32.4399i | −0.842439 | − | 1.20313i | −0.977215 | − | 0.212252i | \(-0.931920\pi\) |
0.134776 | − | 0.990876i | \(-0.456969\pi\) | |||||||
\(728\) | −1.75297 | + | 1.75297i | −0.0649695 | + | 0.0649695i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.83655 | − | 1.87552i | −0.141997 | − | 0.0694160i | ||||
\(731\) | 9.88240 | + | 1.74253i | 0.365514 | + | 0.0644499i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.90113 | − | 6.22149i | −0.107156 | − | 0.229796i | 0.845417 | − | 0.534106i | \(-0.179352\pi\) |
−0.952573 | + | 0.304310i | \(0.901574\pi\) | |||||||
\(734\) | 6.01773 | − | 5.04948i | 0.222119 | − | 0.186380i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.6869 | + | 6.43750i | −0.651948 | + | 0.237290i | ||||
\(737\) | −17.5048 | + | 4.69039i | −0.644797 | + | 0.172773i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.7899 | − | 16.6218i | 1.05905 | − | 0.611444i | 0.133882 | − | 0.990997i | \(-0.457256\pi\) |
0.925170 | + | 0.379553i | \(0.123922\pi\) | |||||||
\(740\) | −41.0230 | − | 15.7900i | −1.50804 | − | 0.580450i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.79375 | + | 4.75704i | 0.249406 | + | 0.174636i | ||||
\(743\) | 13.8249 | + | 9.68027i | 0.507185 | + | 0.355135i | 0.798991 | − | 0.601343i | \(-0.205367\pi\) |
−0.291806 | + | 0.956477i | \(0.594256\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.9756 | − | 14.6459i | 1.20813 | − | 0.536583i | ||||
\(746\) | 12.4628 | − | 7.19539i | 0.456295 | − | 0.263442i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 30.6697 | − | 8.21793i | 1.12140 | − | 0.300477i | ||||
\(749\) | 19.5053 | − | 7.09934i | 0.712707 | − | 0.259404i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.1032 | − | 25.2596i | 1.09848 | − | 0.921734i | 0.101158 | − | 0.994870i | \(-0.467745\pi\) |
0.997322 | + | 0.0731359i | \(0.0233007\pi\) | |||||||
\(752\) | 1.53761 | + | 3.29741i | 0.0560708 | + | 0.120244i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.912609 | + | 0.160918i | 0.0332353 | + | 0.00586028i | ||||
\(755\) | 8.85996 | − | 18.1239i | 0.322447 | − | 0.659596i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.4181 | − | 15.4181i | 0.560380 | − | 0.560380i | −0.369036 | − | 0.929415i | \(-0.620312\pi\) |
0.929415 | + | 0.369036i | \(0.120312\pi\) | |||||||
\(758\) | −8.25417 | − | 11.7882i | −0.299805 | − | 0.428166i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.76815 | + | 0.0875537i | 0.172959 | + | 0.00317591i | ||||
\(761\) | 14.9899 | + | 17.8642i | 0.543382 | + | 0.647577i | 0.965942 | − | 0.258757i | \(-0.0833130\pi\) |
−0.422560 | + | 0.906335i | \(0.638869\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.9224 | + | 11.1552i | 0.866049 | + | 0.403845i | ||||
\(764\) | −9.69221 | + | 16.7874i | −0.350652 | + | 0.607347i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.78943 | + | 13.4917i | 0.281443 | + | 0.487474i | ||||
\(767\) | −0.0209651 | − | 0.239632i | −0.000757007 | − | 0.00865263i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.5586 | + | 7.15158i | −1.46258 | + | 0.257893i | −0.847594 | − | 0.530645i | \(-0.821950\pi\) |
−0.614987 | + | 0.788537i | \(0.710839\pi\) | |||||||
\(770\) | −4.55641 | + | 15.8359i | −0.164202 | + | 0.570685i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.09588 | + | 0.0958772i | −0.0394416 | + | 0.00345069i | ||||
\(773\) | 14.3875 | + | 3.85511i | 0.517481 | + | 0.138659i | 0.508101 | − | 0.861297i | \(-0.330348\pi\) |
0.00937966 | + | 0.999956i | \(0.497014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −48.4852 | + | 6.72450i | −1.74164 | + | 0.241551i | ||||
\(776\) | 0.340005 | + | 0.934157i | 0.0122055 | + | 0.0335343i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.5476 | − | 1.09777i | −0.449853 | − | 0.0393571i | ||||
\(779\) | 2.10828 | + | 0.767352i | 0.0755370 | + | 0.0274932i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.72994 | + | 55.1812i | −0.348165 | + | 1.97454i | ||||
\(782\) | 5.14443 | + | 5.14443i | 0.183964 | + | 0.183964i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16.5268i | 0.590243i | ||||||||
\(785\) | 3.16897 | − | 0.498971i | 0.113105 | − | 0.0178090i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.0910 | − | 6.57073i | 0.502289 | − | 0.234221i | −0.154924 | − | 0.987926i | \(-0.549513\pi\) |
0.657212 | + | 0.753705i | \(0.271735\pi\) | |||||||
\(788\) | 4.28196 | − | 48.9430i | 0.152538 | − | 1.74352i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.80657 | − | 9.65820i | −0.277745 | − | 0.343623i | ||||
\(791\) | 22.8572 | + | 13.1966i | 0.812708 | + | 0.469217i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.203926 | + | 0.761062i | −0.00724162 | + | 0.0270261i | ||||
\(794\) | −4.50706 | − | 3.78187i | −0.159950 | − | 0.134214i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.860335 | + | 4.87920i | 0.0304938 | + | 0.172939i | ||||
\(797\) | 17.3493 | − | 24.7774i | 0.614545 | − | 0.877661i | −0.384419 | − | 0.923159i | \(-0.625598\pi\) |
0.998964 | + | 0.0454973i | \(0.0144872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.37525 | − | 4.02246i | 0.119408 | − | 0.142305i | ||||
\(800\) | 21.9608 | − | 9.27482i | 0.776430 | − | 0.327914i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.35301 | − | 8.78157i | −0.0830878 | − | 0.310088i | ||||
\(803\) | −7.77889 | + | 16.6819i | −0.274511 | + | 0.588691i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30.8468 | − | 7.66127i | 1.08721 | − | 0.270024i | ||||
\(806\) | 0.608660 | − | 1.67228i | 0.0214391 | − | 0.0589035i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20.9104 | + | 14.6416i | −0.735627 | + | 0.515091i | ||||
\(809\) | −38.2730 | −1.34561 | −0.672804 | − | 0.739821i | \(-0.734910\pi\) | ||||
−0.672804 | + | 0.739821i | \(0.734910\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.0127 | 1.61572 | 0.807862 | − | 0.589371i | \(-0.200624\pi\) | ||||
0.807862 | + | 0.589371i | \(0.200624\pi\) | |||||||
\(812\) | 26.8786 | − | 18.8206i | 0.943254 | − | 0.660474i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.69781 | − | 21.1496i | 0.269808 | − | 0.741292i | ||||
\(815\) | 10.8779 | − | 18.0667i | 0.381035 | − | 0.632848i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.29576 | − | 2.77876i | 0.0453329 | − | 0.0972166i | ||||
\(818\) | −0.344322 | − | 1.28503i | −0.0120389 | − | 0.0449299i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.32222 | − | 0.505347i | 0.255703 | − | 0.0176475i | ||||
\(821\) | 30.1717 | − | 35.9573i | 1.05300 | − | 1.25492i | 0.0870458 | − | 0.996204i | \(-0.472257\pi\) |
0.965954 | − | 0.258712i | \(-0.0832982\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.1777 | + | 33.1012i | −0.807923 | + | 1.15383i | 0.177568 | + | 0.984109i | \(0.443177\pi\) |
−0.985491 | + | 0.169726i | \(0.945712\pi\) | |||||||
\(824\) | −5.22041 | − | 29.6064i | −0.181861 | − | 1.03139i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.775097 | + | 0.650383i | 0.0269691 | + | 0.0226297i | ||||
\(827\) | 10.3751 | − | 38.7205i | 0.360779 | − | 1.34645i | −0.512275 | − | 0.858821i | \(-0.671197\pi\) |
0.873054 | − | 0.487624i | \(-0.162136\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.2086 | − | 15.7089i | −0.944994 | − | 0.545593i | −0.0534718 | − | 0.998569i | \(-0.517029\pi\) |
−0.891522 | + | 0.452977i | \(0.850362\pi\) | |||||||
\(830\) | −0.292652 | + | 2.76032i | −0.0101581 | + | 0.0958119i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.114993 | − | 1.31438i | 0.00398666 | − | 0.0455678i | ||||
\(833\) | 21.6175 | − | 10.0804i | 0.749002 | − | 0.349265i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.83133 | − | 37.0349i | −0.201802 | − | 1.28165i | ||||
\(836\) | − | 9.70133i | − | 0.335527i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.79390 | − | 5.79390i | −0.200147 | − | 0.200147i | ||||
\(839\) | −4.95377 | + | 28.0942i | −0.171023 | + | 0.969920i | 0.771611 | + | 0.636094i | \(0.219451\pi\) |
−0.942635 | + | 0.333826i | \(0.891660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.83027 | + | 1.03013i | 0.0975955 | + | 0.0355219i | ||||
\(842\) | 0.941759 | + | 0.0823932i | 0.0324552 | + | 0.00283946i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.4028 | − | 36.8238i | −0.461342 | − | 1.26753i | ||||
\(845\) | 23.8253 | − | 16.0389i | 0.819615 | − | 0.551757i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.3477 | + | 8.13164i | 1.04276 | + | 0.279407i | ||||
\(848\) | −13.7977 | + | 1.20714i | −0.473814 | + | 0.0414533i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.83655 | − | 6.17815i | −0.234492 | − | 0.211909i | ||||
\(851\) | −42.7525 | + | 7.53842i | −1.46554 | + | 0.258414i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.75441 | − | 42.9131i | −0.128549 | − | 1.46932i | −0.737090 | − | 0.675795i | \(-0.763801\pi\) |
0.608541 | − | 0.793522i | \(-0.291755\pi\) | |||||||
\(854\) | −1.65709 | − | 2.87017i | −0.0567045 | − | 0.0982152i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.03113 | − | 8.71418i | 0.171961 | − | 0.297844i | ||||
\(857\) | −31.7973 | − | 14.8273i | −1.08617 | − | 0.506492i | −0.204749 | − | 0.978814i | \(-0.565638\pi\) |
−0.881426 | + | 0.472323i | \(0.843416\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.1815 | + | 24.0514i | 0.688584 | + | 0.820622i | 0.991184 | − | 0.132496i | \(-0.0422991\pi\) |
−0.302600 | + | 0.953118i | \(0.597855\pi\) | |||||||
\(860\) | 0.184145 | − | 10.0285i | 0.00627929 | − | 0.341968i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.12322 | − | 7.31672i | −0.174498 | − | 0.249209i | ||||
\(863\) | −2.26670 | + | 2.26670i | −0.0771594 | + | 0.0771594i | −0.744633 | − | 0.667474i | \(-0.767376\pi\) |
0.667474 | + | 0.744633i | \(0.267376\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.54919 | − | 16.1636i | −0.188678 | − | 0.549580i | ||||
\(866\) | −1.48227 | − | 0.261364i | −0.0503696 | − | 0.00888152i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −26.6305 | − | 57.1094i | −0.903900 | − | 1.93842i | ||||
\(869\) | −41.0040 | + | 34.4064i | −1.39096 | + | 1.16716i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.51249 | − | 0.550500i | 0.0512487 | − | 0.0186530i | ||||
\(872\) | 12.3595 | − | 3.31173i | 0.418547 | − | 0.112149i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.92508 | − | 1.11144i | 0.0651167 | − | 0.0375951i | ||||
\(875\) | −38.5288 | + | 11.6649i | −1.30251 | + | 0.394346i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.4003 | + | 22.6869i | 1.09408 | + | 0.766084i | 0.973970 | − | 0.226677i | \(-0.0727861\pi\) |
0.120111 | + | 0.992760i | \(0.461675\pi\) | |||||||
\(878\) | −1.85264 | − | 1.29723i | −0.0625236 | − | 0.0437795i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −11.1701 | − | 25.1498i | −0.376544 | − | 0.847801i | ||||
\(881\) | −12.4335 | + | 7.17846i | −0.418894 | + | 0.241848i | −0.694604 | − | 0.719392i | \(-0.744420\pi\) |
0.275710 | + | 0.961241i | \(0.411087\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.9771 | + | 11.2477i | −1.41264 | + | 0.378516i | −0.882867 | − | 0.469623i | \(-0.844390\pi\) |
−0.529774 | + | 0.848139i | \(0.677723\pi\) | |||||||
\(884\) | −2.64999 | + | 0.964518i | −0.0891289 | + | 0.0324403i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.82284 | + | 5.72505i | −0.229218 | + | 0.192337i | ||||
\(887\) | 17.3530 | + | 37.2137i | 0.582658 | + | 1.24951i | 0.947890 | + | 0.318598i | \(0.103212\pi\) |
−0.365232 | + | 0.930916i | \(0.619010\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.7110 | − | 3.29925i | −0.627547 | − | 0.110653i | ||||
\(890\) | 2.40752 | − | 0.826533i | 0.0807001 | − | 0.0277055i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.0975 | + | 14.0975i | −0.472020 | + | 0.472020i | ||||
\(893\) | −0.920226 | − | 1.31422i | −0.0307942 | − | 0.0439787i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.77946 | + | 6.53497i | −0.226612 | + | 0.218440i | ||||
\(896\) | 25.6367 | + | 30.5526i | 0.856462 | + | 1.02069i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.24767 | + | 0.581797i | 0.0416352 | + | 0.0194148i | ||||
\(899\) | −24.9536 | + | 43.2210i | −0.832250 | + | 1.44150i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.99476 | + | 17.3114i | 0.332974 | + | 0.576728i | ||||
\(902\) | 0.327536 | + | 3.74375i | 0.0109058 | + | 0.124653i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.6001 | − | 2.22173i | 0.419072 | − | 0.0738938i | ||||
\(905\) | 12.7792 | + | 3.67693i | 0.424796 | + | 0.122225i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.3504 | + | 1.86792i | −0.708928 | + | 0.0620232i | −0.435916 | − | 0.899987i | \(-0.643576\pi\) |
−0.273012 | + | 0.962011i | \(0.588020\pi\) | |||||||
\(908\) | −22.0707 | − | 5.91383i | −0.732442 | − | 0.196257i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.280560 | − | 1.43640i | 0.00930049 | − | 0.0476163i | ||||
\(911\) | −8.05314 | − | 22.1258i | −0.266813 | − | 0.733061i | −0.998668 | − | 0.0516013i | \(-0.983567\pi\) |
0.731855 | − | 0.681460i | \(-0.238655\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.9186 | + | 1.04275i | 0.394450 | + | 0.0345099i | ||||
\(914\) | −2.85987 | − | 1.04091i | −0.0945960 | − | 0.0344301i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.61738 | − | 26.1865i | 0.152563 | − | 0.865225i | ||||
\(917\) | −1.80481 | − | 1.80481i | −0.0595999 | − | 0.0595999i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.0326i | 1.32055i | 0.751023 | + | 0.660277i | \(0.229561\pi\) | ||||
−0.751023 | + | 0.660277i | \(0.770439\pi\) | |||||||
\(920\) | 9.06772 | − | 12.4569i | 0.298954 | − | 0.410691i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.4045 | + | 8.11585i | −0.573187 | + | 0.267281i | ||||
\(923\) | 0.433739 | − | 4.95766i | 0.0142767 | − | 0.163183i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 53.5966 | − | 12.2714i | 1.76224 | − | 0.403481i | ||||
\(926\) | 2.17807 | + | 1.25751i | 0.0715757 | + | 0.0413243i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.29073 | − | 23.4773i | 0.206503 | − | 0.770681i | ||||
\(929\) | −33.8872 | − | 28.4347i | −1.11180 | − | 0.932913i | −0.113641 | − | 0.993522i | \(-0.536251\pi\) |
−0.998162 | + | 0.0606092i | \(0.980696\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.26551 | − | 7.17705i | −0.0414754 | − | 0.235218i | ||||
\(932\) | −5.11156 | + | 7.30007i | −0.167435 | + | 0.239122i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.98938 | − | 3.56260i | 0.0978154 | − | 0.116572i | ||||
\(935\) | −26.0835 | + | 29.9508i | −0.853023 | + | 0.979495i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.25201 | + | 12.1366i | 0.106238 | + | 0.396487i | 0.998483 | − | 0.0550659i | \(-0.0175369\pi\) |
−0.892244 | + | 0.451553i | \(0.850870\pi\) | |||||||
\(938\) | −2.86124 | + | 6.13595i | −0.0934229 | + | 0.200346i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.49639 | − | 2.70726i | −0.146656 | − | 0.0883010i | ||||
\(941\) | 3.22172 | − | 8.85160i | 0.105025 | − | 0.288554i | −0.876038 | − | 0.482242i | \(-0.839823\pi\) |
0.981063 | + | 0.193688i | \(0.0620449\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.93775 | − | 4.15766i | 0.193360 | − | 0.135392i | ||||
\(944\) | −1.68973 | −0.0549961 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.13566 | 0.166975 | ||||||||
\(947\) | 19.4360 | − | 13.6093i | 0.631586 | − | 0.442241i | −0.213447 | − | 0.976955i | \(-0.568469\pi\) |
0.845034 | + | 0.534713i | \(0.179580\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.559131 | − | 1.53620i | 0.0181502 | − | 0.0498672i | ||||
\(950\) | −2.36397 | + | 1.52909i | −0.0766972 | + | 0.0496102i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.6218 | − | 22.7784i | 0.344253 | − | 0.738253i | ||||
\(953\) | −2.27494 | − | 8.49020i | −0.0736926 | − | 0.275025i | 0.919241 | − | 0.393695i | \(-0.128803\pi\) |
−0.992934 | + | 0.118671i | \(0.962137\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.66945 | − | 24.1894i | −0.0540221 | − | 0.782752i | ||||
\(956\) | −8.35447 | + | 9.95647i | −0.270203 | + | 0.322015i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.18878 | + | 1.69775i | −0.0384076 | + | 0.0548518i | ||||
\(959\) | 0.636599 | + | 3.61033i | 0.0205569 | + | 0.116584i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.6714 | + | 41.6793i | 1.60230 | + | 1.34449i | ||||
\(962\) | −0.517374 | + | 1.93087i | −0.0166808 | + | 0.0622536i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 30.5588 | + | 17.6431i | 0.984233 | + | 0.568247i | ||||
\(965\) | 1.07015 | − | 0.864986i | 0.0344494 | − | 0.0278449i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.885782 | − | 10.1245i | 0.0284848 | − | 0.325583i | −0.968561 | − | 0.248776i | \(-0.919972\pi\) |
0.997046 | − | 0.0768074i | \(-0.0244727\pi\) | |||||||
\(968\) | 13.8034 | − | 6.43665i | 0.443659 | − | 0.206882i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.474484 | − | 0.345391i | −0.0152348 | − | 0.0110898i | ||||
\(971\) | − | 25.3812i | − | 0.814522i | −0.913312 | − | 0.407261i | \(-0.866484\pi\) | ||
0.913312 | − | 0.407261i | \(-0.133516\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −56.6741 | − | 56.6741i | −1.81689 | − | 1.81689i | ||||
\(974\) | −0.282708 | + | 1.60332i | −0.00905856 | + | 0.0513736i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.20090 | + | 1.89297i | 0.166477 | + | 0.0605926i | ||||
\(977\) | 45.3288 | + | 3.96576i | 1.45020 | + | 0.126876i | 0.784863 | − | 0.619669i | \(-0.212733\pi\) |
0.665335 | + | 0.746545i | \(0.268289\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.75243 | − | 10.3097i | −0.119928 | − | 0.329500i | ||||
\(980\) | −13.3139 | − | 19.7773i | −0.425296 | − | 0.631762i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.89690 | − | 1.84802i | −0.220089 | − | 0.0589727i | ||||
\(983\) | 23.2285 | − | 2.03223i | 0.740875 | − | 0.0648182i | 0.289532 | − | 0.957168i | \(-0.406500\pi\) |
0.451344 | + | 0.892350i | \(0.350945\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.7448 | + | 53.7760i | 0.947748 | + | 1.71345i | ||||
\(986\) | −9.25215 | + | 1.63140i | −0.294649 | + | 0.0519545i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.0750965 | + | 0.858357i | 0.00238914 | + | 0.0273080i | ||||
\(989\) | −4.95291 | − | 8.57870i | −0.157494 | − | 0.272787i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.3804 | + | 28.3716i | −0.520339 | + | 0.901254i | 0.479381 | + | 0.877607i | \(0.340861\pi\) |
−0.999720 | + | 0.0236474i | \(0.992472\pi\) | |||||||
\(992\) | −42.3029 | − | 19.7262i | −1.34312 | − | 0.626306i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 13.4555 | + | 16.0357i | 0.426783 | + | 0.508621i | ||||
\(995\) | −4.30096 | − | 4.46186i | −0.136350 | − | 0.141451i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.0983 | + | 25.8471i | 0.573180 | + | 0.818585i | 0.996160 | − | 0.0875535i | \(-0.0279049\pi\) |
−0.422980 | + | 0.906139i | \(0.639016\pi\) | |||||||
\(998\) | 5.60735 | − | 5.60735i | 0.177498 | − | 0.177498i | ||||
\(999\) | 0 | 0 |
(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 | 405.2.r.a.8.9 | 192 | ||
3.2 | odd | 2 | 135.2.q.a.83.8 | yes | 192 | ||
5.2 | odd | 4 | inner | 405.2.r.a.332.9 | 192 | ||
15.2 | even | 4 | 135.2.q.a.2.8 | ✓ | 192 | ||
15.8 | even | 4 | 675.2.ba.b.407.9 | 192 | |||
15.14 | odd | 2 | 675.2.ba.b.218.9 | 192 | |||
27.13 | even | 9 | 135.2.q.a.68.8 | yes | 192 | ||
27.14 | odd | 18 | inner | 405.2.r.a.233.9 | 192 | ||
135.13 | odd | 36 | 675.2.ba.b.257.9 | 192 | |||
135.67 | odd | 36 | 135.2.q.a.122.8 | yes | 192 | ||
135.94 | even | 18 | 675.2.ba.b.68.9 | 192 | |||
135.122 | even | 36 | inner | 405.2.r.a.152.9 | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.q.a.2.8 | ✓ | 192 | 15.2 | even | 4 | ||
135.2.q.a.68.8 | yes | 192 | 27.13 | even | 9 | ||
135.2.q.a.83.8 | yes | 192 | 3.2 | odd | 2 | ||
135.2.q.a.122.8 | yes | 192 | 135.67 | odd | 36 | ||
405.2.r.a.8.9 | 192 | 1.1 | even | 1 | trivial | ||
405.2.r.a.152.9 | 192 | 135.122 | even | 36 | inner | ||
405.2.r.a.233.9 | 192 | 27.14 | odd | 18 | inner | ||
405.2.r.a.332.9 | 192 | 5.2 | odd | 4 | inner | ||
675.2.ba.b.68.9 | 192 | 135.94 | even | 18 | |||
675.2.ba.b.218.9 | 192 | 15.14 | odd | 2 | |||
675.2.ba.b.257.9 | 192 | 135.13 | odd | 36 | |||
675.2.ba.b.407.9 | 192 | 15.8 | even | 4 |