Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(9,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.j (of order \(10\), degree \(4\), 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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 16.0.6879707136000000000000.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 269.2 | ||
Root | \(-0.304260 + 0.418778i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.269 |
Dual form | 605.2.j.f.9.2 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.492303 | + | 0.159959i | −0.348111 | + | 0.113108i | −0.477853 | − | 0.878440i | \(-0.658585\pi\) |
0.129742 | + | 0.991548i | \(0.458585\pi\) | |||||||
\(3\) | 1.13551 | − | 1.56290i | 0.655589 | − | 0.902341i | −0.343736 | − | 0.939066i | \(-0.611693\pi\) |
0.999325 | + | 0.0367251i | \(0.0116926\pi\) | |||||||
\(4\) | −1.40126 | + | 1.01807i | −0.700629 | + | 0.509037i | ||||
\(5\) | −0.809764 | − | 2.08429i | −0.362137 | − | 0.932125i | ||||
\(6\) | −0.309017 | + | 0.951057i | −0.126156 | + | 0.388267i | ||||
\(7\) | 1.96677 | + | 2.70702i | 0.743368 | + | 1.02316i | 0.998418 | + | 0.0562307i | \(0.0179082\pi\) |
−0.255049 | + | 0.966928i | \(0.582092\pi\) | |||||||
\(8\) | 1.13551 | − | 1.56290i | 0.401465 | − | 0.552569i | ||||
\(9\) | −0.226216 | − | 0.696222i | −0.0754054 | − | 0.232074i | ||||
\(10\) | 0.732051 | + | 0.896575i | 0.231495 | + | 0.283522i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.34607i | 0.965926i | ||||||||
\(13\) | 4.03499 | − | 1.31105i | 1.11911 | − | 0.363619i | 0.309679 | − | 0.950841i | \(-0.399778\pi\) |
0.809426 | + | 0.587222i | \(0.199778\pi\) | |||||||
\(14\) | −1.40126 | − | 1.01807i | −0.374502 | − | 0.272092i | ||||
\(15\) | −4.17704 | − | 1.10116i | −1.07851 | − | 0.284319i | ||||
\(16\) | 0.761449 | − | 2.34350i | 0.190362 | − | 0.585875i | ||||
\(17\) | 3.67460 | + | 1.19395i | 0.891221 | + | 0.289575i | 0.718609 | − | 0.695414i | \(-0.244779\pi\) |
0.172613 | + | 0.984990i | \(0.444779\pi\) | |||||||
\(18\) | 0.222734 | + | 0.306567i | 0.0524989 | + | 0.0722585i | ||||
\(19\) | −3.39476 | − | 2.46644i | −0.778811 | − | 0.565839i | 0.125811 | − | 0.992054i | \(-0.459847\pi\) |
−0.904622 | + | 0.426215i | \(0.859847\pi\) | |||||||
\(20\) | 3.25665 | + | 2.09624i | 0.728210 | + | 0.468733i | ||||
\(21\) | 6.46410 | 1.41058 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.48477i | − | 0.726624i | −0.931668 | − | 0.363312i | \(-0.881646\pi\) | ||
0.931668 | − | 0.363312i | \(-0.118354\pi\) | |||||||
\(24\) | −1.15327 | − | 3.54939i | −0.235410 | − | 0.724516i | ||||
\(25\) | −3.68856 | + | 3.37557i | −0.737713 | + | 0.675114i | ||||
\(26\) | −1.77672 | + | 1.29087i | −0.348444 | + | 0.253160i | ||||
\(27\) | 4.16690 | + | 1.35391i | 0.801921 | + | 0.260560i | ||||
\(28\) | −5.51190 | − | 1.79092i | −1.04165 | − | 0.338453i | ||||
\(29\) | 5.60503 | − | 4.07230i | 1.04083 | − | 0.756206i | 0.0703816 | − | 0.997520i | \(-0.477578\pi\) |
0.970447 | + | 0.241314i | \(0.0775783\pi\) | |||||||
\(30\) | 2.23251 | − | 0.126049i | 0.407599 | − | 0.0230133i | ||||
\(31\) | −2.69835 | − | 8.30467i | −0.484638 | − | 1.49156i | −0.832504 | − | 0.554019i | \(-0.813093\pi\) |
0.347866 | − | 0.937544i | \(-0.386907\pi\) | |||||||
\(32\) | 5.13922i | 0.908494i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 4.04962 | − | 6.29137i | 0.684510 | − | 1.06344i | ||||
\(36\) | 1.02579 | + | 0.745282i | 0.170965 | + | 0.124214i | ||||
\(37\) | −1.05399 | − | 1.45069i | −0.173275 | − | 0.238492i | 0.713543 | − | 0.700611i | \(-0.247089\pi\) |
−0.886818 | + | 0.462119i | \(0.847089\pi\) | |||||||
\(38\) | 2.06578 | + | 0.671212i | 0.335114 | + | 0.108885i | ||||
\(39\) | 2.53275 | − | 7.79500i | 0.405565 | − | 1.24820i | ||||
\(40\) | −4.17704 | − | 1.10116i | −0.660449 | − | 0.174109i | ||||
\(41\) | −1.40126 | − | 1.01807i | −0.218840 | − | 0.158996i | 0.472964 | − | 0.881082i | \(-0.343184\pi\) |
−0.691804 | + | 0.722085i | \(0.743184\pi\) | |||||||
\(42\) | −3.18230 | + | 1.03399i | −0.491039 | + | 0.159548i | ||||
\(43\) | 6.45189i | 0.983905i | 0.870622 | + | 0.491952i | \(0.163717\pi\) | ||||
−0.870622 | + | 0.491952i | \(0.836283\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.26795 | + | 1.03528i | −0.189015 | + | 0.154330i | ||||
\(46\) | 0.557420 | + | 1.71556i | 0.0821870 | + | 0.252946i | ||||
\(47\) | 6.73156 | − | 9.26519i | 0.981899 | − | 1.35147i | 0.0460982 | − | 0.998937i | \(-0.485321\pi\) |
0.935800 | − | 0.352530i | \(-0.114679\pi\) | |||||||
\(48\) | −2.79802 | − | 3.85115i | −0.403860 | − | 0.555865i | ||||
\(49\) | −1.29668 | + | 3.99078i | −0.185240 | + | 0.570111i | ||||
\(50\) | 1.27594 | − | 2.25182i | 0.180445 | − | 0.318456i | ||||
\(51\) | 6.03859 | − | 4.38729i | 0.845571 | − | 0.614343i | ||||
\(52\) | −4.31932 | + | 5.94504i | −0.598982 | + | 0.824428i | ||||
\(53\) | 2.06578 | − | 0.671212i | 0.283757 | − | 0.0921981i | −0.163681 | − | 0.986513i | \(-0.552337\pi\) |
0.447437 | + | 0.894315i | \(0.352337\pi\) | |||||||
\(54\) | −2.26795 | −0.308629 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.46410 | 0.863802 | ||||||||
\(57\) | −7.70959 | + | 2.50500i | −1.02116 | + | 0.331795i | ||||
\(58\) | −2.10798 | + | 2.90138i | −0.276791 | + | 0.380970i | ||||
\(59\) | −1.02579 | + | 0.745282i | −0.133547 | + | 0.0970274i | −0.652553 | − | 0.757743i | \(-0.726302\pi\) |
0.519006 | + | 0.854770i | \(0.326302\pi\) | |||||||
\(60\) | 6.97418 | − | 2.70952i | 0.900363 | − | 0.349798i | ||||
\(61\) | −3.62540 | + | 11.1578i | −0.464185 | + | 1.42862i | 0.395819 | + | 0.918329i | \(0.370461\pi\) |
−0.860004 | + | 0.510287i | \(0.829539\pi\) | |||||||
\(62\) | 2.65681 | + | 3.65679i | 0.337416 | + | 0.464413i | ||||
\(63\) | 1.43977 | − | 1.98168i | 0.181394 | − | 0.249668i | ||||
\(64\) | 0.700835 | + | 2.15695i | 0.0876044 | + | 0.269618i | ||||
\(65\) | −6.00000 | − | 7.34847i | −0.744208 | − | 0.911465i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.20925i | 0.269903i | 0.990852 | + | 0.134952i | \(0.0430879\pi\) | ||||
−0.990852 | + | 0.134952i | \(0.956912\pi\) | |||||||
\(68\) | −6.36459 | + | 2.06798i | −0.771820 | + | 0.250780i | ||||
\(69\) | −5.44634 | − | 3.95700i | −0.655663 | − | 0.476367i | ||||
\(70\) | −0.987277 | + | 3.74503i | −0.118002 | + | 0.447617i | ||||
\(71\) | −2.53275 | + | 7.79500i | −0.300582 | + | 0.925097i | 0.680707 | + | 0.732556i | \(0.261673\pi\) |
−0.981289 | + | 0.192541i | \(0.938327\pi\) | |||||||
\(72\) | −1.34500 | − | 0.437016i | −0.158509 | − | 0.0515028i | ||||
\(73\) | −2.87955 | − | 3.96336i | −0.337026 | − | 0.463876i | 0.606544 | − | 0.795050i | \(-0.292555\pi\) |
−0.943570 | + | 0.331174i | \(0.892555\pi\) | |||||||
\(74\) | 0.750932 | + | 0.545584i | 0.0872941 | + | 0.0634229i | ||||
\(75\) | 1.08727 | + | 9.59787i | 0.125547 | + | 1.10827i | ||||
\(76\) | 7.26795 | 0.833691 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.24264i | 0.480384i | ||||||||
\(79\) | −0.452432 | − | 1.39244i | −0.0509026 | − | 0.156662i | 0.922374 | − | 0.386298i | \(-0.126246\pi\) |
−0.973277 | + | 0.229636i | \(0.926246\pi\) | |||||||
\(80\) | −5.50114 | + | 0.310597i | −0.615046 | + | 0.0347258i | ||||
\(81\) | 8.62433 | − | 6.26594i | 0.958259 | − | 0.696216i | ||||
\(82\) | 0.852694 | + | 0.277057i | 0.0941643 | + | 0.0305958i | ||||
\(83\) | 9.41498 | + | 3.05911i | 1.03343 | + | 0.335781i | 0.776145 | − | 0.630555i | \(-0.217173\pi\) |
0.257283 | + | 0.966336i | \(0.417173\pi\) | |||||||
\(84\) | −9.05788 | + | 6.58093i | −0.988295 | + | 0.718039i | ||||
\(85\) | −0.487015 | − | 8.62577i | −0.0528242 | − | 0.935596i | ||||
\(86\) | −1.03204 | − | 3.17629i | −0.111288 | − | 0.342508i | ||||
\(87\) | − | 13.3843i | − | 1.43494i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.464102 | −0.0491947 | −0.0245973 | − | 0.999697i | \(-0.507830\pi\) | ||||
−0.0245973 | + | 0.999697i | \(0.507830\pi\) | |||||||
\(90\) | 0.458614 | − | 0.712489i | 0.0483421 | − | 0.0751030i | ||||
\(91\) | 11.4849 | + | 8.34429i | 1.20395 | + | 0.874719i | ||||
\(92\) | 3.54775 | + | 4.88306i | 0.369878 | + | 0.509094i | ||||
\(93\) | −16.0434 | − | 5.21282i | −1.66362 | − | 0.540544i | ||||
\(94\) | −1.83192 | + | 5.63806i | −0.188948 | + | 0.581521i | ||||
\(95\) | −2.39183 | + | 9.07291i | −0.245396 | + | 0.930861i | ||||
\(96\) | 8.03209 | + | 5.83565i | 0.819771 | + | 0.595599i | ||||
\(97\) | 8.69420 | − | 2.82492i | 0.882762 | − | 0.286827i | 0.167658 | − | 0.985845i | \(-0.446379\pi\) |
0.715104 | + | 0.699018i | \(0.246379\pi\) | |||||||
\(98\) | − | 2.17209i | − | 0.219414i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.73205 | − | 8.48528i | 0.173205 | − | 0.848528i | ||||
\(101\) | 5.99255 | + | 18.4432i | 0.596281 | + | 1.83516i | 0.548243 | + | 0.836319i | \(0.315297\pi\) |
0.0480385 | + | 0.998845i | \(0.484703\pi\) | |||||||
\(102\) | −2.27103 | + | 3.12580i | −0.224865 | + | 0.309500i | ||||
\(103\) | 2.49376 | + | 3.43237i | 0.245718 | + | 0.338201i | 0.914006 | − | 0.405701i | \(-0.132973\pi\) |
−0.668288 | + | 0.743903i | \(0.732973\pi\) | |||||||
\(104\) | 2.53275 | − | 7.79500i | 0.248357 | − | 0.764363i | ||||
\(105\) | −5.23440 | − | 13.4731i | −0.510825 | − | 1.31484i | ||||
\(106\) | −0.909623 | + | 0.660880i | −0.0883504 | + | 0.0641903i | ||||
\(107\) | 1.74403 | − | 2.40046i | 0.168602 | − | 0.232061i | −0.716352 | − | 0.697739i | \(-0.754190\pi\) |
0.884954 | + | 0.465678i | \(0.154190\pi\) | |||||||
\(108\) | −7.21729 | + | 2.34504i | −0.694484 | + | 0.225651i | ||||
\(109\) | −9.19615 | −0.880832 | −0.440416 | − | 0.897794i | \(-0.645169\pi\) | ||||
−0.440416 | + | 0.897794i | \(0.645169\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.46410 | −0.328798 | ||||||||
\(112\) | 7.84150 | − | 2.54786i | 0.740952 | − | 0.240750i | ||||
\(113\) | −1.66251 | + | 2.28825i | −0.156396 | + | 0.215260i | −0.880023 | − | 0.474930i | \(-0.842473\pi\) |
0.723628 | + | 0.690190i | \(0.242473\pi\) | |||||||
\(114\) | 3.39476 | − | 2.46644i | 0.317948 | − | 0.231003i | ||||
\(115\) | −7.26328 | + | 2.82184i | −0.677304 | + | 0.263138i | ||||
\(116\) | −3.70820 | + | 11.4127i | −0.344298 | + | 1.05964i | ||||
\(117\) | −1.82556 | − | 2.51267i | −0.168773 | − | 0.232296i | ||||
\(118\) | 0.385786 | − | 0.530989i | 0.0355145 | − | 0.0488815i | ||||
\(119\) | 3.99503 | + | 12.2955i | 0.366224 | + | 1.12712i | ||||
\(120\) | −6.46410 | + | 5.27792i | −0.590089 | + | 0.481806i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 6.07296i | − | 0.549820i | ||||||
\(123\) | −3.18230 | + | 1.03399i | −0.286938 | + | 0.0932318i | ||||
\(124\) | 12.2359 | + | 8.88987i | 1.09881 | + | 0.798334i | ||||
\(125\) | 10.0226 | + | 4.95464i | 0.896444 | + | 0.443156i | ||||
\(126\) | −0.391818 | + | 1.20589i | −0.0349059 | + | 0.107429i | ||||
\(127\) | −0.852694 | − | 0.277057i | −0.0756644 | − | 0.0245848i | 0.270940 | − | 0.962596i | \(-0.412665\pi\) |
−0.346605 | + | 0.938011i | \(0.612665\pi\) | |||||||
\(128\) | −6.73156 | − | 9.26519i | −0.594991 | − | 0.818935i | ||||
\(129\) | 10.0837 | + | 7.32622i | 0.887818 | + | 0.645037i | ||||
\(130\) | 4.12927 | + | 2.65792i | 0.362161 | + | 0.233115i | ||||
\(131\) | −3.12436 | −0.272976 | −0.136488 | − | 0.990642i | \(-0.543582\pi\) | ||||
−0.136488 | + | 0.990642i | \(0.543582\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 14.0406i | − | 1.21747i | ||||||
\(134\) | −0.353390 | − | 1.08762i | −0.0305282 | − | 0.0939562i | ||||
\(135\) | −0.552263 | − | 9.78140i | −0.0475312 | − | 0.841849i | ||||
\(136\) | 6.03859 | − | 4.38729i | 0.517804 | − | 0.376207i | ||||
\(137\) | −8.43037 | − | 2.73919i | −0.720255 | − | 0.234025i | −0.0741215 | − | 0.997249i | \(-0.523615\pi\) |
−0.646134 | + | 0.763224i | \(0.723615\pi\) | |||||||
\(138\) | 3.31421 | + | 1.07685i | 0.282124 | + | 0.0916677i | ||||
\(139\) | −11.8023 | + | 8.57488i | −1.00106 | + | 0.727312i | −0.962315 | − | 0.271937i | \(-0.912336\pi\) |
−0.0387439 | + | 0.999249i | \(0.512336\pi\) | |||||||
\(140\) | 0.730523 | + | 12.9386i | 0.0617405 | + | 1.09352i | ||||
\(141\) | −6.83680 | − | 21.0415i | −0.575763 | − | 1.77202i | ||||
\(142\) | − | 4.24264i | − | 0.356034i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.80385 | −0.150321 | ||||||||
\(145\) | −13.0266 | − | 8.38494i | −1.08180 | − | 0.696332i | ||||
\(146\) | 2.05158 | + | 1.49056i | 0.169790 | + | 0.123360i | ||||
\(147\) | 4.76479 | + | 6.55817i | 0.392993 | + | 0.540909i | ||||
\(148\) | 2.95382 | + | 0.959754i | 0.242802 | + | 0.0788913i | ||||
\(149\) | 3.17297 | − | 9.76540i | 0.259940 | − | 0.800013i | −0.732876 | − | 0.680362i | \(-0.761823\pi\) |
0.992816 | − | 0.119651i | \(-0.0381775\pi\) | |||||||
\(150\) | −2.07053 | − | 4.55114i | −0.169058 | − | 0.371599i | ||||
\(151\) | −3.39476 | − | 2.46644i | −0.276262 | − | 0.200716i | 0.441024 | − | 0.897495i | \(-0.354616\pi\) |
−0.717285 | + | 0.696780i | \(0.754616\pi\) | |||||||
\(152\) | −7.70959 | + | 2.50500i | −0.625330 | + | 0.203182i | ||||
\(153\) | − | 2.82843i | − | 0.228665i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.1244 | + | 12.3490i | −1.21482 | + | 0.991894i | ||||
\(156\) | 4.38685 | + | 13.5013i | 0.351229 | + | 1.08097i | ||||
\(157\) | −12.8546 | + | 17.6928i | −1.02591 | + | 1.41204i | −0.117931 | + | 0.993022i | \(0.537626\pi\) |
−0.907977 | + | 0.419020i | \(0.862374\pi\) | |||||||
\(158\) | 0.445468 | + | 0.613134i | 0.0354395 | + | 0.0487783i | ||||
\(159\) | 1.29668 | − | 3.99078i | 0.102834 | − | 0.316489i | ||||
\(160\) | 10.7116 | − | 4.16155i | 0.846829 | − | 0.329000i | ||||
\(161\) | 9.43334 | − | 6.85373i | 0.743452 | − | 0.540149i | ||||
\(162\) | −3.24349 | + | 4.46428i | −0.254833 | + | 0.350747i | ||||
\(163\) | −4.88769 | + | 1.58811i | −0.382833 | + | 0.124390i | −0.494110 | − | 0.869399i | \(-0.664506\pi\) |
0.111277 | + | 0.993789i | \(0.464506\pi\) | |||||||
\(164\) | 3.00000 | 0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.12436 | −0.397727 | ||||||||
\(167\) | −0.492303 | + | 0.159959i | −0.0380956 | + | 0.0123780i | −0.328003 | − | 0.944677i | \(-0.606376\pi\) |
0.289907 | + | 0.957055i | \(0.406376\pi\) | |||||||
\(168\) | 7.34008 | − | 10.1027i | 0.566299 | − | 0.779444i | ||||
\(169\) | 4.04508 | − | 2.93893i | 0.311160 | − | 0.226071i | ||||
\(170\) | 1.61953 | + | 4.16859i | 0.124212 | + | 0.319716i | ||||
\(171\) | −0.949237 | + | 2.92145i | −0.0725900 | + | 0.223409i | ||||
\(172\) | −6.56850 | − | 9.04077i | −0.500844 | − | 0.689352i | ||||
\(173\) | −12.7949 | + | 17.6107i | −0.972779 | + | 1.33892i | −0.0321489 | + | 0.999483i | \(0.510235\pi\) |
−0.940630 | + | 0.339433i | \(0.889765\pi\) | |||||||
\(174\) | 2.14093 | + | 6.58911i | 0.162304 | + | 0.499519i | ||||
\(175\) | −16.3923 | − | 3.34607i | −1.23914 | − | 0.252939i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.44949i | 0.184115i | ||||||||
\(178\) | 0.228479 | − | 0.0742372i | 0.0171252 | − | 0.00556431i | ||||
\(179\) | −12.5107 | − | 9.08957i | −0.935095 | − | 0.679386i | 0.0121398 | − | 0.999926i | \(-0.496136\pi\) |
−0.947235 | + | 0.320540i | \(0.896136\pi\) | |||||||
\(180\) | 0.722737 | − | 2.74156i | 0.0538696 | − | 0.204343i | ||||
\(181\) | −5.37452 | + | 16.5411i | −0.399485 | + | 1.22949i | 0.525929 | + | 0.850529i | \(0.323718\pi\) |
−0.925413 | + | 0.378959i | \(0.876282\pi\) | |||||||
\(182\) | −6.98881 | − | 2.27080i | −0.518045 | − | 0.168323i | ||||
\(183\) | 13.3219 | + | 18.3360i | 0.984784 | + | 1.35544i | ||||
\(184\) | −5.44634 | − | 3.95700i | −0.401510 | − | 0.291714i | ||||
\(185\) | −2.17018 | + | 3.37154i | −0.159555 | + | 0.247880i | ||||
\(186\) | 8.73205 | 0.640265 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 19.8362i | 1.44670i | ||||||||
\(189\) | 4.53027 | + | 13.9427i | 0.329528 | + | 1.01418i | ||||
\(190\) | −0.273789 | − | 4.84921i | −0.0198628 | − | 0.351799i | ||||
\(191\) | 5.87989 | − | 4.27199i | 0.425454 | − | 0.309111i | −0.354374 | − | 0.935104i | \(-0.615306\pi\) |
0.779829 | + | 0.625993i | \(0.215306\pi\) | |||||||
\(192\) | 4.16690 | + | 1.35391i | 0.300720 | + | 0.0977100i | ||||
\(193\) | −14.4346 | − | 4.69008i | −1.03902 | − | 0.337599i | −0.260672 | − | 0.965428i | \(-0.583944\pi\) |
−0.778352 | + | 0.627828i | \(0.783944\pi\) | |||||||
\(194\) | −3.82831 | + | 2.78143i | −0.274857 | + | 0.199695i | ||||
\(195\) | −18.2980 | + | 1.03312i | −1.31035 | + | 0.0739830i | ||||
\(196\) | −2.24592 | − | 6.91223i | −0.160423 | − | 0.493731i | ||||
\(197\) | 17.2480i | 1.22887i | 0.788969 | + | 0.614433i | \(0.210615\pi\) | ||||
−0.788969 | + | 0.614433i | \(0.789385\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | 1.08727 | + | 9.59787i | 0.0768815 | + | 0.678672i | ||||
\(201\) | 3.45284 | + | 2.50864i | 0.243545 | + | 0.176946i | ||||
\(202\) | −5.90030 | − | 8.12107i | −0.415144 | − | 0.571397i | ||||
\(203\) | 22.0476 | + | 7.16370i | 1.54744 | + | 0.502793i | ||||
\(204\) | −3.99503 | + | 12.2955i | −0.279708 | + | 0.860854i | ||||
\(205\) | −0.987277 | + | 3.74503i | −0.0689544 | + | 0.261565i | ||||
\(206\) | −1.77672 | − | 1.29087i | −0.123790 | − | 0.0899389i | ||||
\(207\) | −2.42617 | + | 0.788310i | −0.168630 | + | 0.0547914i | ||||
\(208\) | − | 10.4543i | − | 0.724875i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.73205 | + | 5.79555i | 0.326543 | + | 0.399931i | ||||
\(211\) | −4.05565 | − | 12.4820i | −0.279202 | − | 0.859297i | −0.988077 | − | 0.153962i | \(-0.950797\pi\) |
0.708874 | − | 0.705335i | \(-0.249203\pi\) | |||||||
\(212\) | −2.21135 | + | 3.04366i | −0.151876 | + | 0.209039i | ||||
\(213\) | 9.30685 | + | 12.8098i | 0.637695 | + | 0.877711i | ||||
\(214\) | −0.474619 | + | 1.46073i | −0.0324443 | + | 0.0998532i | ||||
\(215\) | 13.4476 | − | 5.22451i | 0.917122 | − | 0.356309i | ||||
\(216\) | 6.84760 | − | 4.97507i | 0.465920 | − | 0.338511i | ||||
\(217\) | 17.1739 | − | 23.6379i | 1.16584 | − | 1.60464i | ||||
\(218\) | 4.52729 | − | 1.47101i | 0.306627 | − | 0.0996292i | ||||
\(219\) | −9.46410 | −0.639525 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.3923 | 1.10267 | ||||||||
\(222\) | 1.70539 | − | 0.554114i | 0.114458 | − | 0.0371897i | ||||
\(223\) | −0.912780 | + | 1.25633i | −0.0611243 | + | 0.0841303i | −0.838485 | − | 0.544925i | \(-0.816558\pi\) |
0.777361 | + | 0.629055i | \(0.216558\pi\) | |||||||
\(224\) | −13.9120 | + | 10.1076i | −0.929533 | + | 0.675345i | ||||
\(225\) | 3.18456 | + | 1.80445i | 0.212304 | + | 0.120297i | ||||
\(226\) | 0.452432 | − | 1.39244i | 0.0300953 | − | 0.0926240i | ||||
\(227\) | −11.8225 | − | 16.2722i | −0.784684 | − | 1.08002i | −0.994750 | − | 0.102337i | \(-0.967368\pi\) |
0.210066 | − | 0.977687i | \(-0.432632\pi\) | |||||||
\(228\) | 8.25286 | − | 11.3591i | 0.546559 | − | 0.752274i | ||||
\(229\) | 1.25825 | + | 3.87251i | 0.0831478 | + | 0.255903i | 0.983984 | − | 0.178256i | \(-0.0570456\pi\) |
−0.900836 | + | 0.434159i | \(0.857046\pi\) | |||||||
\(230\) | 3.12436 | − | 2.55103i | 0.206014 | − | 0.168210i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 13.3843i | − | 0.878720i | ||||||
\(233\) | 1.60882 | − | 0.522738i | 0.105397 | − | 0.0342457i | −0.255844 | − | 0.966718i | \(-0.582353\pi\) |
0.361241 | + | 0.932473i | \(0.382353\pi\) | |||||||
\(234\) | 1.30065 | + | 0.944980i | 0.0850263 | + | 0.0617752i | ||||
\(235\) | −24.7624 | − | 6.52793i | −1.61532 | − | 0.425835i | ||||
\(236\) | 0.678648 | − | 2.08867i | 0.0441762 | − | 0.135961i | ||||
\(237\) | −2.68999 | − | 0.874032i | −0.174734 | − | 0.0567745i | ||||
\(238\) | −3.93354 | − | 5.41405i | −0.254973 | − | 0.350941i | ||||
\(239\) | 4.57924 | + | 3.32701i | 0.296207 | + | 0.215207i | 0.725955 | − | 0.687742i | \(-0.241398\pi\) |
−0.429749 | + | 0.902948i | \(0.641398\pi\) | |||||||
\(240\) | −5.76119 | + | 8.95042i | −0.371883 | + | 0.577747i | ||||
\(241\) | 14.1244 | 0.909830 | 0.454915 | − | 0.890535i | \(-0.349670\pi\) | ||||
0.454915 | + | 0.890535i | \(0.349670\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 7.45001i | − | 0.477918i | ||||||
\(244\) | −6.27938 | − | 19.3260i | −0.401996 | − | 1.23722i | ||||
\(245\) | 9.36796 | − | 0.528920i | 0.598497 | − | 0.0337915i | ||||
\(246\) | 1.40126 | − | 1.01807i | 0.0893410 | − | 0.0649100i | ||||
\(247\) | −16.9314 | − | 5.50136i | −1.07732 | − | 0.350043i | ||||
\(248\) | −16.0434 | − | 5.21282i | −1.01876 | − | 0.331014i | ||||
\(249\) | 15.4719 | − | 11.2410i | 0.980494 | − | 0.712370i | ||||
\(250\) | −5.72667 | − | 0.835986i | −0.362187 | − | 0.0528724i | ||||
\(251\) | −1.17545 | − | 3.61767i | −0.0741940 | − | 0.228346i | 0.907082 | − | 0.420955i | \(-0.138305\pi\) |
−0.981276 | + | 0.192609i | \(0.938305\pi\) | |||||||
\(252\) | 4.24264i | 0.267261i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.464102 | 0.0291203 | ||||||||
\(255\) | −14.0342 | − | 9.03352i | −0.878858 | − | 0.565701i | ||||
\(256\) | 1.12640 | + | 0.818376i | 0.0703999 | + | 0.0511485i | ||||
\(257\) | −8.69833 | − | 11.9722i | −0.542587 | − | 0.746806i | 0.446396 | − | 0.894835i | \(-0.352707\pi\) |
−0.988983 | + | 0.148029i | \(0.952707\pi\) | |||||||
\(258\) | −6.13612 | − | 1.99374i | −0.382018 | − | 0.124125i | ||||
\(259\) | 1.85410 | − | 5.70634i | 0.115208 | − | 0.354575i | ||||
\(260\) | 15.8888 | + | 4.18866i | 0.985384 | + | 0.259770i | ||||
\(261\) | −4.10317 | − | 2.98113i | −0.253980 | − | 0.184527i | ||||
\(262\) | 1.53813 | − | 0.499769i | 0.0950260 | − | 0.0308758i | ||||
\(263\) | 6.79367i | 0.418915i | 0.977818 | + | 0.209458i | \(0.0671699\pi\) | ||||
−0.977818 | + | 0.209458i | \(0.932830\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.07180 | − | 3.76217i | −0.188699 | − | 0.231108i | ||||
\(266\) | 2.24592 | + | 6.91223i | 0.137706 | + | 0.423816i | ||||
\(267\) | −0.526994 | + | 0.725345i | −0.0322515 | + | 0.0443904i | ||||
\(268\) | −2.24918 | − | 3.09573i | −0.137391 | − | 0.189102i | ||||
\(269\) | 5.02707 | − | 15.4717i | 0.306506 | − | 0.943329i | −0.672605 | − | 0.740002i | \(-0.734825\pi\) |
0.979111 | − | 0.203327i | \(-0.0651754\pi\) | |||||||
\(270\) | 1.83650 | + | 4.72707i | 0.111766 | + | 0.287681i | ||||
\(271\) | −9.27465 | + | 6.73843i | −0.563395 | + | 0.409330i | −0.832700 | − | 0.553725i | \(-0.813206\pi\) |
0.269305 | + | 0.963055i | \(0.413206\pi\) | |||||||
\(272\) | 5.59604 | − | 7.70229i | 0.339310 | − | 0.467020i | ||||
\(273\) | 26.0826 | − | 8.47475i | 1.57859 | − | 0.512915i | ||||
\(274\) | 4.58846 | 0.277199 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.6603 | 0.701865 | ||||||||
\(277\) | 29.6606 | − | 9.63732i | 1.78213 | − | 0.579051i | 0.783055 | − | 0.621952i | \(-0.213660\pi\) |
0.999079 | + | 0.0429019i | \(0.0136603\pi\) | |||||||
\(278\) | 4.43868 | − | 6.10933i | 0.266215 | − | 0.366413i | ||||
\(279\) | −5.17148 | + | 3.75730i | −0.309609 | + | 0.224944i | ||||
\(280\) | −5.23440 | − | 13.4731i | −0.312815 | − | 0.805171i | ||||
\(281\) | −5.35233 | + | 16.4728i | −0.319293 | + | 0.982684i | 0.654658 | + | 0.755925i | \(0.272813\pi\) |
−0.973951 | + | 0.226758i | \(0.927187\pi\) | |||||||
\(282\) | 6.73156 | + | 9.26519i | 0.400858 | + | 0.551734i | ||||
\(283\) | 4.74294 | − | 6.52810i | 0.281939 | − | 0.388055i | −0.644436 | − | 0.764658i | \(-0.722908\pi\) |
0.926375 | + | 0.376603i | \(0.122908\pi\) | |||||||
\(284\) | −4.38685 | − | 13.5013i | −0.260312 | − | 0.801157i | ||||
\(285\) | 11.4641 | + | 14.0406i | 0.679075 | + | 0.831693i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 5.79555i | − | 0.342101i | ||||||
\(288\) | 3.57803 | − | 1.16257i | 0.210838 | − | 0.0685053i | ||||
\(289\) | −1.67612 | − | 1.21777i | −0.0985952 | − | 0.0716336i | ||||
\(290\) | 7.75429 | + | 2.04421i | 0.455348 | + | 0.120040i | ||||
\(291\) | 5.45732 | − | 16.7959i | 0.319914 | − | 0.984593i | ||||
\(292\) | 8.06998 | + | 2.62210i | 0.472260 | + | 0.153447i | ||||
\(293\) | 8.86138 | + | 12.1966i | 0.517687 | + | 0.712535i | 0.985192 | − | 0.171455i | \(-0.0548469\pi\) |
−0.467505 | + | 0.883991i | \(0.654847\pi\) | |||||||
\(294\) | −3.39476 | − | 2.46644i | −0.197986 | − | 0.143845i | ||||
\(295\) | 2.38404 | + | 1.53455i | 0.138804 | + | 0.0893450i | ||||
\(296\) | −3.46410 | −0.201347 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.31508i | 0.307894i | ||||||||
\(299\) | −4.56870 | − | 14.0610i | −0.264214 | − | 0.813169i | ||||
\(300\) | −11.2949 | − | 12.3422i | −0.652111 | − | 0.712576i | ||||
\(301\) | −17.4654 | + | 12.6894i | −1.00669 | + | 0.731404i | ||||
\(302\) | 2.06578 | + | 0.671212i | 0.118872 | + | 0.0386239i | ||||
\(303\) | 35.6295 | + | 11.5767i | 2.04686 | + | 0.665065i | ||||
\(304\) | −8.36503 | + | 6.07755i | −0.479767 | + | 0.348571i | ||||
\(305\) | 26.1919 | − | 1.47881i | 1.49975 | − | 0.0846765i | ||||
\(306\) | 0.452432 | + | 1.39244i | 0.0258638 | + | 0.0796007i | ||||
\(307\) | − | 7.82894i | − | 0.446821i | −0.974724 | − | 0.223411i | \(-0.928281\pi\) | ||
0.974724 | − | 0.223411i | \(-0.0717191\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.19615 | 0.466263 | ||||||||
\(310\) | 5.47044 | − | 8.49872i | 0.310700 | − | 0.482695i | ||||
\(311\) | −8.13269 | − | 5.90875i | −0.461163 | − | 0.335054i | 0.332825 | − | 0.942989i | \(-0.391998\pi\) |
−0.793987 | + | 0.607935i | \(0.791998\pi\) | |||||||
\(312\) | −9.30685 | − | 12.8098i | −0.526896 | − | 0.725211i | ||||
\(313\) | 16.3072 | + | 5.29854i | 0.921739 | + | 0.299491i | 0.731180 | − | 0.682185i | \(-0.238970\pi\) |
0.190559 | + | 0.981676i | \(0.438970\pi\) | |||||||
\(314\) | 3.49823 | − | 10.7664i | 0.197417 | − | 0.607586i | ||||
\(315\) | −5.29628 | − | 1.39622i | −0.298411 | − | 0.0786681i | ||||
\(316\) | 2.05158 | + | 1.49056i | 0.115411 | + | 0.0838508i | ||||
\(317\) | 12.0084 | − | 3.90177i | 0.674459 | − | 0.219145i | 0.0482913 | − | 0.998833i | \(-0.484622\pi\) |
0.626168 | + | 0.779688i | \(0.284622\pi\) | |||||||
\(318\) | 2.17209i | 0.121805i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.92820 | − | 3.20736i | 0.219593 | − | 0.179297i | ||||
\(321\) | −1.77130 | − | 5.45150i | −0.0988644 | − | 0.304273i | ||||
\(322\) | −3.54775 | + | 4.88306i | −0.197708 | + | 0.272122i | ||||
\(323\) | −9.52958 | − | 13.1163i | −0.530240 | − | 0.729813i | ||||
\(324\) | −5.70572 | + | 17.5604i | −0.316985 | + | 0.975578i | ||||
\(325\) | −10.4578 | + | 18.4563i | −0.580094 | + | 1.02377i | ||||
\(326\) | 2.15219 | − | 1.56366i | 0.119199 | − | 0.0866030i | ||||
\(327\) | −10.4424 | + | 14.3727i | −0.577464 | + | 0.794811i | ||||
\(328\) | −3.18230 | + | 1.03399i | −0.175713 | + | 0.0570926i | ||||
\(329\) | 38.3205 | 2.11268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.1962 | −1.00015 | −0.500075 | − | 0.865982i | \(-0.666694\pi\) | ||||
−0.500075 | + | 0.865982i | \(0.666694\pi\) | |||||||
\(332\) | −16.3072 | + | 5.29854i | −0.894975 | + | 0.290795i | ||||
\(333\) | −0.771573 | + | 1.06198i | −0.0422819 | + | 0.0581961i | ||||
\(334\) | 0.216775 | − | 0.157497i | 0.0118614 | − | 0.00861783i | ||||
\(335\) | 4.60473 | − | 1.78897i | 0.251583 | − | 0.0977421i | ||||
\(336\) | 4.92209 | − | 15.1486i | 0.268522 | − | 0.826425i | ||||
\(337\) | 10.3608 | + | 14.2605i | 0.564391 | + | 0.776817i | 0.991876 | − | 0.127205i | \(-0.0406006\pi\) |
−0.427486 | + | 0.904022i | \(0.640601\pi\) | |||||||
\(338\) | −1.52130 | + | 2.09389i | −0.0827478 | + | 0.113893i | ||||
\(339\) | 1.68850 | + | 5.19667i | 0.0917067 | + | 0.282244i | ||||
\(340\) | 9.46410 | + | 11.5911i | 0.513263 | + | 0.628616i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 1.59008i | − | 0.0859816i | ||||||
\(343\) | 8.92268 | − | 2.89915i | 0.481779 | − | 0.156540i | ||||
\(344\) | 10.0837 | + | 7.32622i | 0.543675 | + | 0.395003i | ||||
\(345\) | −3.83730 | + | 14.5560i | −0.206593 | + | 0.783670i | ||||
\(346\) | 3.48199 | − | 10.7165i | 0.187193 | − | 0.576120i | ||||
\(347\) | −4.16690 | − | 1.35391i | −0.223691 | − | 0.0726816i | 0.195027 | − | 0.980798i | \(-0.437521\pi\) |
−0.418718 | + | 0.908116i | \(0.637521\pi\) | |||||||
\(348\) | 13.6262 | + | 18.7548i | 0.730439 | + | 1.00536i | ||||
\(349\) | −5.92242 | − | 4.30289i | −0.317020 | − | 0.230328i | 0.417883 | − | 0.908501i | \(-0.362772\pi\) |
−0.734903 | + | 0.678173i | \(0.762772\pi\) | |||||||
\(350\) | 8.60522 | − | 0.974818i | 0.459968 | − | 0.0521062i | ||||
\(351\) | 18.5885 | 0.992178 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.0053i | 0.692204i | 0.938197 | + | 0.346102i | \(0.112495\pi\) | ||||
−0.938197 | + | 0.346102i | \(0.887505\pi\) | |||||||
\(354\) | −0.391818 | − | 1.20589i | −0.0208249 | − | 0.0640924i | ||||
\(355\) | 18.2980 | − | 1.03312i | 0.971158 | − | 0.0548321i | ||||
\(356\) | 0.650326 | − | 0.472490i | 0.0344672 | − | 0.0250419i | ||||
\(357\) | 23.7530 | + | 7.71781i | 1.25714 | + | 0.408470i | ||||
\(358\) | 7.61302 | + | 2.47362i | 0.402361 | + | 0.130735i | ||||
\(359\) | 28.8498 | − | 20.9606i | 1.52263 | − | 1.10626i | 0.562468 | − | 0.826819i | \(-0.309852\pi\) |
0.960164 | − | 0.279437i | \(-0.0901479\pi\) | |||||||
\(360\) | 0.178260 | + | 3.15725i | 0.00939513 | + | 0.166402i | ||||
\(361\) | −0.430246 | − | 1.32416i | −0.0226445 | − | 0.0696927i | ||||
\(362\) | − | 9.00292i | − | 0.473183i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.5885 | −1.28879 | ||||||||
\(365\) | −5.92905 | + | 9.21121i | −0.310341 | + | 0.482137i | ||||
\(366\) | −9.49143 | − | 6.89593i | −0.496125 | − | 0.360456i | ||||
\(367\) | 9.93721 | + | 13.6774i | 0.518718 | + | 0.713954i | 0.985359 | − | 0.170493i | \(-0.0545359\pi\) |
−0.466641 | + | 0.884447i | \(0.654536\pi\) | |||||||
\(368\) | −8.16655 | − | 2.65347i | −0.425711 | − | 0.138322i | ||||
\(369\) | −0.391818 | + | 1.20589i | −0.0203972 | + | 0.0627762i | ||||
\(370\) | 0.529080 | − | 2.00696i | 0.0275056 | − | 0.104337i | ||||
\(371\) | 5.87989 | + | 4.27199i | 0.305269 | + | 0.221791i | ||||
\(372\) | 27.7880 | − | 9.02886i | 1.44074 | − | 0.468125i | ||||
\(373\) | − | 0.175865i | − | 0.00910597i | −0.999990 | − | 0.00455298i | \(-0.998551\pi\) | ||
0.999990 | − | 0.00455298i | \(-0.00144926\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.1244 | − | 10.0382i | 0.987577 | − | 0.518370i | ||||
\(376\) | −6.83680 | − | 21.0415i | −0.352581 | − | 1.08513i | ||||
\(377\) | 17.2773 | − | 23.7801i | 0.889826 | − | 1.22474i | ||||
\(378\) | −4.46053 | − | 6.13939i | −0.229425 | − | 0.315776i | ||||
\(379\) | −0.452432 | + | 1.39244i | −0.0232399 | + | 0.0715250i | −0.962004 | − | 0.273036i | \(-0.911972\pi\) |
0.938764 | + | 0.344561i | \(0.111972\pi\) | |||||||
\(380\) | −5.88532 | − | 15.1485i | −0.301911 | − | 0.777104i | ||||
\(381\) | −1.40126 | + | 1.01807i | −0.0717886 | + | 0.0521575i | ||||
\(382\) | −2.21135 | + | 3.04366i | −0.113142 | + | 0.155727i | ||||
\(383\) | −36.5787 | + | 11.8852i | −1.86909 | + | 0.607303i | −0.877209 | + | 0.480109i | \(0.840597\pi\) |
−0.991878 | + | 0.127194i | \(0.959403\pi\) | |||||||
\(384\) | −22.1244 | −1.12903 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.85641 | 0.399881 | ||||||||
\(387\) | 4.49195 | − | 1.45952i | 0.228339 | − | 0.0741917i | ||||
\(388\) | −9.30685 | + | 12.8098i | −0.472483 | + | 0.650318i | ||||
\(389\) | 4.95471 | − | 3.59981i | 0.251214 | − | 0.182517i | −0.455051 | − | 0.890465i | \(-0.650379\pi\) |
0.706265 | + | 0.707948i | \(0.250379\pi\) | |||||||
\(390\) | 8.84291 | − | 3.43554i | 0.447778 | − | 0.173965i | ||||
\(391\) | 4.16064 | − | 12.8051i | 0.210412 | − | 0.647583i | ||||
\(392\) | 4.76479 | + | 6.55817i | 0.240658 | + | 0.331238i | ||||
\(393\) | −3.54775 | + | 4.88306i | −0.178960 | + | 0.246318i | ||||
\(394\) | −2.75897 | − | 8.49123i | −0.138995 | − | 0.427782i | ||||
\(395\) | −2.53590 | + | 2.07055i | −0.127595 | + | 0.104181i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.9802i | 1.65523i | 0.561298 | + | 0.827614i | \(0.310302\pi\) | ||||
−0.561298 | + | 0.827614i | \(0.689698\pi\) | |||||||
\(398\) | −0.984606 | + | 0.319918i | −0.0493538 | + | 0.0160360i | ||||
\(399\) | −21.9441 | − | 15.9433i | −1.09858 | − | 0.798163i | ||||
\(400\) | 5.10200 | + | 11.2145i | 0.255100 | + | 0.560724i | ||||
\(401\) | 0.717076 | − | 2.20693i | 0.0358091 | − | 0.110209i | −0.931554 | − | 0.363602i | \(-0.881547\pi\) |
0.967363 | + | 0.253393i | \(0.0815467\pi\) | |||||||
\(402\) | −2.10112 | − | 0.682697i | −0.104795 | − | 0.0340498i | ||||
\(403\) | −21.7757 | − | 29.9716i | −1.08472 | − | 1.49299i | ||||
\(404\) | −27.1736 | − | 19.7428i | −1.35194 | − | 0.982241i | ||||
\(405\) | −20.0437 | − | 12.9017i | −0.995981 | − | 0.641091i | ||||
\(406\) | −12.0000 | −0.595550 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − | 14.4195i | − | 0.713873i | ||||||
\(409\) | 8.07287 | + | 24.8457i | 0.399178 | + | 1.22854i | 0.925660 | + | 0.378357i | \(0.123511\pi\) |
−0.526482 | + | 0.850186i | \(0.676489\pi\) | |||||||
\(410\) | −0.113012 | − | 2.00162i | −0.00558128 | − | 0.0988528i | ||||
\(411\) | −13.8539 | + | 10.0654i | −0.683362 | + | 0.496492i | ||||
\(412\) | −6.98881 | − | 2.27080i | −0.344314 | − | 0.111874i | ||||
\(413\) | −4.03499 | − | 1.31105i | −0.198549 | − | 0.0645125i | ||||
\(414\) | 1.06831 | − | 0.776175i | 0.0525047 | − | 0.0381469i | ||||
\(415\) | −1.24782 | − | 22.1007i | −0.0612531 | − | 1.08488i | ||||
\(416\) | 6.73776 | + | 20.7367i | 0.330346 | + | 1.01670i | ||||
\(417\) | 28.1827i | 1.38011i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.3397 | 0.602836 | 0.301418 | − | 0.953492i | \(-0.402540\pi\) | ||||
0.301418 | + | 0.953492i | \(0.402540\pi\) | |||||||
\(420\) | 21.0513 | + | 13.5503i | 1.02720 | + | 0.661186i | ||||
\(421\) | 13.7958 | + | 10.0232i | 0.672367 | + | 0.488503i | 0.870817 | − | 0.491608i | \(-0.163591\pi\) |
−0.198450 | + | 0.980111i | \(0.563591\pi\) | |||||||
\(422\) | 3.99322 | + | 5.49619i | 0.194387 | + | 0.267550i | ||||
\(423\) | −7.97342 | − | 2.59072i | −0.387681 | − | 0.125965i | ||||
\(424\) | 1.29668 | − | 3.99078i | 0.0629725 | − | 0.193809i | ||||
\(425\) | −17.5843 | + | 7.99992i | −0.852962 | + | 0.388053i | ||||
\(426\) | −6.63083 | − | 4.81758i | −0.321265 | − | 0.233412i | ||||
\(427\) | −37.3349 | + | 12.1308i | −1.80676 | + | 0.587052i | ||||
\(428\) | 5.13922i | 0.248413i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.78461 | + | 4.72311i | −0.278959 | + | 0.227769i | ||||
\(431\) | −1.56727 | − | 4.82357i | −0.0754928 | − | 0.232343i | 0.906188 | − | 0.422874i | \(-0.138979\pi\) |
−0.981681 | + | 0.190531i | \(0.938979\pi\) | |||||||
\(432\) | 6.34577 | − | 8.73420i | 0.305311 | − | 0.420225i | ||||
\(433\) | −16.8915 | − | 23.2492i | −0.811754 | − | 1.11728i | −0.991050 | − | 0.133488i | \(-0.957382\pi\) |
0.179297 | − | 0.983795i | \(-0.442618\pi\) | |||||||
\(434\) | −4.67368 | + | 14.3841i | −0.224344 | + | 0.690460i | ||||
\(435\) | −27.8967 | + | 10.8381i | −1.33755 | + | 0.519647i | ||||
\(436\) | 12.8862 | − | 9.36236i | 0.617136 | − | 0.448376i | ||||
\(437\) | −8.59495 | + | 11.8299i | −0.411152 | + | 0.565903i | ||||
\(438\) | 4.65921 | − | 1.51387i | 0.222625 | − | 0.0723354i | ||||
\(439\) | −28.2487 | −1.34824 | −0.674119 | − | 0.738623i | \(-0.735476\pi\) | ||||
−0.674119 | + | 0.738623i | \(0.735476\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.07180 | 0.146276 | ||||||||
\(442\) | −8.06998 | + | 2.62210i | −0.383850 | + | 0.124720i | ||||
\(443\) | −16.2015 | + | 22.2994i | −0.769754 | + | 1.05948i | 0.226585 | + | 0.973991i | \(0.427244\pi\) |
−0.996339 | + | 0.0854846i | \(0.972756\pi\) | |||||||
\(444\) | 4.85410 | − | 3.52671i | 0.230365 | − | 0.167370i | ||||
\(445\) | 0.375813 | + | 0.967324i | 0.0178152 | + | 0.0458556i | ||||
\(446\) | 0.248403 | − | 0.764504i | 0.0117622 | − | 0.0362003i | ||||
\(447\) | −11.6594 | − | 16.0478i | −0.551471 | − | 0.759034i | ||||
\(448\) | −4.46053 | + | 6.13939i | −0.210740 | + | 0.290059i | ||||
\(449\) | −10.6662 | − | 32.8273i | −0.503371 | − | 1.54922i | −0.803492 | − | 0.595315i | \(-0.797027\pi\) |
0.300122 | − | 0.953901i | \(-0.402973\pi\) | |||||||
\(450\) | −1.85641 | − | 0.378937i | −0.0875118 | − | 0.0178633i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 4.89898i | − | 0.230429i | ||||||
\(453\) | −7.70959 | + | 2.50500i | −0.362228 | + | 0.117695i | ||||
\(454\) | 8.42312 | + | 6.11975i | 0.395316 | + | 0.287214i | ||||
\(455\) | 8.09187 | − | 30.6949i | 0.379353 | − | 1.43900i | ||||
\(456\) | −4.83928 | + | 14.8938i | −0.226620 | + | 0.697465i | ||||
\(457\) | −20.1750 | − | 6.55524i | −0.943745 | − | 0.306641i | −0.203573 | − | 0.979060i | \(-0.565256\pi\) |
−0.740171 | + | 0.672418i | \(0.765256\pi\) | |||||||
\(458\) | −1.23889 | − | 1.70518i | −0.0578893 | − | 0.0796778i | ||||
\(459\) | 13.6952 | + | 9.95015i | 0.639237 | + | 0.464433i | ||||
\(460\) | 7.30489 | − | 11.3487i | 0.340592 | − | 0.529135i | ||||
\(461\) | −33.0000 | −1.53696 | −0.768482 | − | 0.639872i | \(-0.778987\pi\) | ||||
−0.768482 | + | 0.639872i | \(0.778987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.3166i | 0.944194i | 0.881547 | + | 0.472097i | \(0.156503\pi\) | ||||
−0.881547 | + | 0.472097i | \(0.843497\pi\) | |||||||
\(464\) | −5.27548 | − | 16.2362i | −0.244908 | − | 0.753749i | ||||
\(465\) | 2.12632 | + | 37.6603i | 0.0986058 | + | 1.74646i | ||||
\(466\) | −0.708411 | + | 0.514691i | −0.0328165 | + | 0.0238426i | ||||
\(467\) | −0.588870 | − | 0.191335i | −0.0272496 | − | 0.00885394i | 0.295360 | − | 0.955386i | \(-0.404560\pi\) |
−0.322610 | + | 0.946532i | \(0.604560\pi\) | |||||||
\(468\) | 5.11616 | + | 1.66234i | 0.236495 | + | 0.0768418i | ||||
\(469\) | −5.98050 | + | 4.34509i | −0.276154 | + | 0.200638i | ||||
\(470\) | 13.2348 | − | 0.747243i | 0.610475 | − | 0.0344678i | ||||
\(471\) | 13.0556 | + | 40.1809i | 0.601569 | + | 1.85144i | ||||
\(472\) | 2.44949i | 0.112747i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.46410 | 0.0672484 | ||||||||
\(475\) | 20.8474 | − | 2.36164i | 0.956545 | − | 0.108360i | ||||
\(476\) | −18.1158 | − | 13.1619i | −0.830334 | − | 0.603273i | ||||
\(477\) | −0.934625 | − | 1.28640i | −0.0427935 | − | 0.0589003i | ||||
\(478\) | −2.78656 | − | 0.905408i | −0.127454 | − | 0.0414124i | ||||
\(479\) | −0.783636 | + | 2.41178i | −0.0358052 | + | 0.110197i | −0.967362 | − | 0.253399i | \(-0.918451\pi\) |
0.931557 | + | 0.363597i | \(0.118451\pi\) | |||||||
\(480\) | 5.65912 | − | 21.4667i | 0.258302 | − | 0.979818i | ||||
\(481\) | −6.15475 | − | 4.47169i | −0.280633 | − | 0.203892i | ||||
\(482\) | −6.95346 | + | 2.25932i | −0.316722 | + | 0.102909i | ||||
\(483\) | − | 22.5259i | − | 1.02496i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.9282 | − | 15.8338i | −0.587039 | − | 0.718974i | ||||
\(486\) | 1.19170 | + | 3.66766i | 0.0540564 | + | 0.166368i | ||||
\(487\) | 7.48128 | − | 10.2971i | 0.339009 | − | 0.466606i | −0.605142 | − | 0.796117i | \(-0.706884\pi\) |
0.944152 | + | 0.329511i | \(0.106884\pi\) | |||||||
\(488\) | 13.3219 | + | 18.3360i | 0.603054 | + | 0.830033i | ||||
\(489\) | −3.06798 | + | 9.44228i | −0.138739 | + | 0.426995i | ||||
\(490\) | −4.52727 | + | 1.75888i | −0.204521 | + | 0.0794580i | ||||
\(491\) | −32.1283 | + | 23.3426i | −1.44993 | + | 1.05344i | −0.464084 | + | 0.885791i | \(0.653617\pi\) |
−0.985847 | + | 0.167646i | \(0.946383\pi\) | |||||||
\(492\) | 3.40654 | − | 4.68870i | 0.153579 | − | 0.211383i | ||||
\(493\) | 25.4584 | − | 8.27193i | 1.14659 | − | 0.372549i | ||||
\(494\) | 9.21539 | 0.414620 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.5167 | −0.966127 | ||||||||
\(497\) | −26.0826 | + | 8.47475i | −1.16996 | + | 0.380144i | ||||
\(498\) | −5.81878 | + | 8.00886i | −0.260746 | + | 0.358886i | ||||
\(499\) | 14.2449 | − | 10.3495i | 0.637690 | − | 0.463309i | −0.221366 | − | 0.975191i | \(-0.571051\pi\) |
0.859056 | + | 0.511882i | \(0.171051\pi\) | |||||||
\(500\) | −19.0884 | + | 3.26097i | −0.853658 | + | 0.145835i | ||||
\(501\) | −0.309017 | + | 0.951057i | −0.0138059 | + | 0.0424901i | ||||
\(502\) | 1.15736 | + | 1.59297i | 0.0516555 | + | 0.0710976i | ||||
\(503\) | 4.34117 | − | 5.97510i | 0.193563 | − | 0.266417i | −0.701193 | − | 0.712971i | \(-0.747349\pi\) |
0.894756 | + | 0.446554i | \(0.147349\pi\) | |||||||
\(504\) | −1.46228 | − | 4.50045i | −0.0651353 | − | 0.200466i | ||||
\(505\) | 33.5885 | − | 27.4249i | 1.49467 | − | 1.22039i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 9.65926i | − | 0.428983i | ||||||
\(508\) | 1.47691 | − | 0.479877i | 0.0655273 | − | 0.0212911i | ||||
\(509\) | −6.53022 | − | 4.74448i | −0.289447 | − | 0.210296i | 0.433580 | − | 0.901115i | \(-0.357250\pi\) |
−0.723027 | + | 0.690819i | \(0.757250\pi\) | |||||||
\(510\) | 8.35409 | + | 2.20233i | 0.369925 | + | 0.0975208i | ||||
\(511\) | 5.06550 | − | 15.5900i | 0.224085 | − | 0.689661i | ||||
\(512\) | 21.0983 | + | 6.85527i | 0.932424 | + | 0.302963i | ||||
\(513\) | −10.8063 | − | 14.8736i | −0.477110 | − | 0.656685i | ||||
\(514\) | 6.19728 | + | 4.50258i | 0.273350 | + | 0.198600i | ||||
\(515\) | 5.13471 | − | 7.97714i | 0.226262 | − | 0.351515i | ||||
\(516\) | −21.5885 | −0.950379 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.10583i | 0.136462i | ||||||||
\(519\) | 12.9950 | + | 39.9944i | 0.570415 | + | 1.75556i | ||||
\(520\) | −18.2980 | + | 1.03312i | −0.802421 | + | 0.0453051i | ||||
\(521\) | 7.48236 | − | 5.43626i | 0.327808 | − | 0.238167i | −0.411692 | − | 0.911323i | \(-0.635062\pi\) |
0.739500 | + | 0.673156i | \(0.235062\pi\) | |||||||
\(522\) | 2.49686 | + | 0.811279i | 0.109285 | + | 0.0355087i | ||||
\(523\) | −24.3772 | − | 7.92063i | −1.06594 | − | 0.346345i | −0.277035 | − | 0.960860i | \(-0.589352\pi\) |
−0.788905 | + | 0.614515i | \(0.789352\pi\) | |||||||
\(524\) | 4.37803 | − | 3.18083i | 0.191255 | − | 0.138955i | ||||
\(525\) | −23.8433 | + | 21.8200i | −1.04061 | + | 0.952305i | ||||
\(526\) | −1.08671 | − | 3.34454i | −0.0473827 | − | 0.145829i | ||||
\(527\) | − | 33.7381i | − | 1.46965i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.8564 | 0.472018 | ||||||||
\(530\) | 2.11405 | + | 1.36077i | 0.0918284 | + | 0.0591079i | ||||
\(531\) | 0.750932 | + | 0.545584i | 0.0325877 | + | 0.0236763i | ||||
\(532\) | 14.2944 | + | 19.6745i | 0.619739 | + | 0.852998i | ||||
\(533\) | −6.98881 | − | 2.27080i | −0.302719 | − | 0.0983593i | ||||
\(534\) | 0.143415 | − | 0.441387i | 0.00620619 | − | 0.0191007i | ||||
\(535\) | −6.41551 | − | 1.69128i | −0.277367 | − | 0.0731203i | ||||
\(536\) | 3.45284 | + | 2.50864i | 0.149140 | + | 0.108357i | ||||
\(537\) | −28.4122 | + | 9.23168i | −1.22608 | + | 0.398376i | ||||
\(538\) | 8.42091i | 0.363051i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.7321 | + | 13.1440i | 0.461834 | + | 0.565629i | ||||
\(541\) | −0.805822 | − | 2.48007i | −0.0346450 | − | 0.106626i | 0.932239 | − | 0.361844i | \(-0.117853\pi\) |
−0.966884 | + | 0.255218i | \(0.917853\pi\) | |||||||
\(542\) | 3.48807 | − | 4.80091i | 0.149825 | − | 0.206217i | ||||
\(543\) | 19.7492 | + | 27.1824i | 0.847519 | + | 1.16651i | ||||
\(544\) | −6.13597 | + | 18.8846i | −0.263077 | + | 0.809669i | ||||
\(545\) | 7.44671 | + | 19.1675i | 0.318982 | + | 0.821045i | ||||
\(546\) | −11.4849 | + | 8.34429i | −0.491510 | + | 0.357103i | ||||
\(547\) | −16.8915 | + | 23.2492i | −0.722228 | + | 0.994062i | 0.277218 | + | 0.960807i | \(0.410587\pi\) |
−0.999447 | + | 0.0332552i | \(0.989413\pi\) | |||||||
\(548\) | 14.6018 | − | 4.74442i | 0.623759 | − | 0.202672i | ||||
\(549\) | 8.58846 | 0.366546 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.0718 | −1.23850 | ||||||||
\(552\) | −12.3688 | + | 4.01887i | −0.526451 | + | 0.171054i | ||||
\(553\) | 2.87955 | − | 3.96336i | 0.122451 | − | 0.168539i | ||||
\(554\) | −13.0604 | + | 9.48897i | −0.554885 | + | 0.403148i | ||||
\(555\) | 2.80510 | + | 7.22021i | 0.119070 | + | 0.306481i | ||||
\(556\) | 7.80823 | − | 24.0312i | 0.331143 | − | 1.01915i | ||||
\(557\) | 22.1018 | + | 30.4205i | 0.936482 | + | 1.28896i | 0.957277 | + | 0.289173i | \(0.0933801\pi\) |
−0.0207955 | + | 0.999784i | \(0.506620\pi\) | |||||||
\(558\) | 1.94492 | − | 2.67696i | 0.0823352 | − | 0.113325i | ||||
\(559\) | 8.45874 | + | 26.0333i | 0.357767 | + | 1.10109i | ||||
\(560\) | −11.6603 | − | 14.2808i | −0.492736 | − | 0.603475i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 8.96575i | − | 0.378198i | ||||||
\(563\) | 15.1907 | − | 4.93576i | 0.640212 | − | 0.208017i | 0.0291185 | − | 0.999576i | \(-0.490730\pi\) |
0.611093 | + | 0.791559i | \(0.290730\pi\) | |||||||
\(564\) | 31.0019 | + | 22.5242i | 1.30542 | + | 0.948441i | ||||
\(565\) | 6.11562 | + | 1.61222i | 0.257286 | + | 0.0678265i | ||||
\(566\) | −1.29074 | + | 3.97248i | −0.0542537 | + | 0.166976i | ||||
\(567\) | 33.9241 | + | 11.0226i | 1.42468 | + | 0.462906i | ||||
\(568\) | 9.30685 | + | 12.8098i | 0.390507 | + | 0.537486i | ||||
\(569\) | 24.3711 | + | 17.7067i | 1.02169 | + | 0.742301i | 0.966629 | − | 0.256181i | \(-0.0824645\pi\) |
0.0550616 | + | 0.998483i | \(0.482464\pi\) | |||||||
\(570\) | −7.88973 | − | 5.07844i | −0.330465 | − | 0.212713i | ||||
\(571\) | −19.7128 | −0.824956 | −0.412478 | − | 0.910968i | \(-0.635337\pi\) | ||||
−0.412478 | + | 0.910968i | \(0.635337\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 14.0406i | − | 0.586554i | ||||||
\(574\) | 0.927051 | + | 2.85317i | 0.0386944 | + | 0.119089i | ||||
\(575\) | 11.7631 | + | 12.8538i | 0.490554 | + | 0.536040i | ||||
\(576\) | 1.34317 | − | 0.975873i | 0.0559656 | − | 0.0406614i | ||||
\(577\) | −3.57803 | − | 1.16257i | −0.148955 | − | 0.0483986i | 0.233590 | − | 0.972335i | \(-0.424953\pi\) |
−0.382546 | + | 0.923937i | \(0.624953\pi\) | |||||||
\(578\) | 1.01995 | + | 0.331402i | 0.0424244 | + | 0.0137845i | ||||
\(579\) | −23.7208 | + | 17.2342i | −0.985802 | + | 0.716227i | ||||
\(580\) | 26.7901 | − | 1.51259i | 1.11240 | − | 0.0628067i | ||||
\(581\) | 10.2360 | + | 31.5031i | 0.424660 | + | 1.30697i | ||||
\(582\) | 9.14162i | 0.378932i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9.46410 | −0.391627 | ||||||||
\(585\) | −3.75887 | + | 5.83967i | −0.155410 | + | 0.241441i | ||||
\(586\) | −6.31345 | − | 4.58699i | −0.260806 | − | 0.189487i | ||||
\(587\) | 11.9855 | + | 16.4966i | 0.494695 | + | 0.680889i | 0.981245 | − | 0.192764i | \(-0.0617451\pi\) |
−0.486551 | + | 0.873652i | \(0.661745\pi\) | |||||||
\(588\) | −13.3534 | − | 4.33878i | −0.550685 | − | 0.178928i | ||||
\(589\) | −11.3227 | + | 34.8477i | −0.466544 | + | 1.43587i | ||||
\(590\) | −1.41913 | − | 0.374116i | −0.0584248 | − | 0.0154021i | ||||
\(591\) | 26.9569 | + | 19.5853i | 1.10886 | + | 0.805632i | ||||
\(592\) | −4.20225 | + | 1.36539i | −0.172711 | + | 0.0561173i | ||||
\(593\) | − | 0.859411i | − | 0.0352918i | −0.999844 | − | 0.0176459i | \(-0.994383\pi\) | ||
0.999844 | − | 0.0176459i | \(-0.00561715\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.3923 | − | 18.2832i | 0.917995 | − | 0.749540i | ||||
\(596\) | 5.49575 | + | 16.9142i | 0.225115 | + | 0.692831i | ||||
\(597\) | 2.27103 | − | 3.12580i | 0.0929470 | − | 0.127931i | ||||
\(598\) | 4.49837 | + | 6.19147i | 0.183952 | + | 0.253188i | ||||
\(599\) | 11.8801 | − | 36.5632i | 0.485408 | − | 1.49393i | −0.345980 | − | 0.938242i | \(-0.612454\pi\) |
0.831389 | − | 0.555692i | \(-0.187546\pi\) | |||||||
\(600\) | 16.2351 | + | 9.19922i | 0.662796 | + | 0.375557i | ||||
\(601\) | −16.1803 | + | 11.7557i | −0.660010 | + | 0.479525i | −0.866666 | − | 0.498888i | \(-0.833742\pi\) |
0.206656 | + | 0.978414i | \(0.433742\pi\) | |||||||
\(602\) | 6.56850 | − | 9.04077i | 0.267712 | − | 0.368474i | ||||
\(603\) | 1.53813 | − | 0.499769i | 0.0626375 | − | 0.0203522i | ||||
\(604\) | 7.26795 | 0.295729 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −19.3923 | −0.787759 | ||||||||
\(607\) | −34.6095 | + | 11.2453i | −1.40476 | + | 0.456433i | −0.910726 | − | 0.413011i | \(-0.864477\pi\) |
−0.494031 | + | 0.869444i | \(0.664477\pi\) | |||||||
\(608\) | 12.6756 | − | 17.4464i | 0.514061 | − | 0.707545i | ||||
\(609\) | 36.2315 | − | 26.3237i | 1.46817 | − | 1.06669i | ||||
\(610\) | −12.6578 | + | 4.91766i | −0.512500 | + | 0.199110i | ||||
\(611\) | 15.0147 | − | 46.2104i | 0.607428 | − | 1.86947i | ||||
\(612\) | 2.87955 | + | 3.96336i | 0.116399 | + | 0.160209i | ||||
\(613\) | −1.05399 | + | 1.45069i | −0.0425702 | + | 0.0585928i | −0.829771 | − | 0.558103i | \(-0.811529\pi\) |
0.787201 | + | 0.616696i | \(0.211529\pi\) | |||||||
\(614\) | 1.25231 | + | 3.85421i | 0.0505391 | + | 0.155543i | ||||
\(615\) | 4.73205 | + | 5.79555i | 0.190815 | + | 0.233699i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.0053i | 0.523575i | 0.965126 | + | 0.261787i | \(0.0843119\pi\) | ||||
−0.965126 | + | 0.261787i | \(0.915688\pi\) | |||||||
\(618\) | −4.03499 | + | 1.31105i | −0.162311 | + | 0.0527381i | ||||
\(619\) | 10.3430 | + | 7.51461i | 0.415719 | + | 0.302037i | 0.775913 | − | 0.630840i | \(-0.217290\pi\) |
−0.360194 | + | 0.932877i | \(0.617290\pi\) | |||||||
\(620\) | 8.62095 | − | 32.7018i | 0.346226 | − | 1.31334i | ||||
\(621\) | 4.71806 | − | 14.5207i | 0.189329 | − | 0.582695i | ||||
\(622\) | 4.94891 | + | 1.60800i | 0.198433 | + | 0.0644748i | ||||
\(623\) | −0.912780 | − | 1.25633i | −0.0365698 | − | 0.0503340i | ||||
\(624\) | −16.3390 | − | 11.8710i | −0.654085 | − | 0.475220i | ||||
\(625\) | 2.21102 | − | 24.9020i | 0.0884409 | − | 0.996081i | ||||
\(626\) | −8.87564 | −0.354742 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 37.8792i | − | 1.51154i | ||||||
\(629\) | −2.14093 | − | 6.58911i | −0.0853646 | − | 0.262725i | ||||
\(630\) | 2.83071 | − | 0.159824i | 0.112778 | − | 0.00636752i | ||||
\(631\) | 12.3946 | − | 9.00517i | 0.493419 | − | 0.358490i | −0.313078 | − | 0.949727i | \(-0.601360\pi\) |
0.806498 | + | 0.591237i | \(0.201360\pi\) | |||||||
\(632\) | −2.68999 | − | 0.874032i | −0.107002 | − | 0.0347671i | ||||
\(633\) | −24.1134 | − | 7.83491i | −0.958421 | − | 0.311410i | ||||
\(634\) | −5.28765 | + | 3.84170i | −0.210000 | + | 0.152574i | ||||
\(635\) | 0.113012 | + | 2.00162i | 0.00448476 | + | 0.0794317i | ||||
\(636\) | 2.24592 | + | 6.91223i | 0.0890565 | + | 0.274088i | ||||
\(637\) | 17.8028i | 0.705371i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | −13.8604 | + | 21.5332i | −0.547881 | + | 0.851173i | ||||
\(641\) | 6.35597 | + | 4.61788i | 0.251046 | + | 0.182395i | 0.706190 | − | 0.708022i | \(-0.250412\pi\) |
−0.455144 | + | 0.890418i | \(0.650412\pi\) | |||||||
\(642\) | 1.74403 | + | 2.40046i | 0.0688315 | + | 0.0947385i | ||||
\(643\) | 10.0038 | + | 3.25045i | 0.394513 | + | 0.128185i | 0.499554 | − | 0.866283i | \(-0.333497\pi\) |
−0.105041 | + | 0.994468i | \(0.533497\pi\) | |||||||
\(644\) | −6.24095 | + | 19.2077i | −0.245928 | + | 0.756889i | ||||
\(645\) | 7.10460 | − | 26.9498i | 0.279743 | − | 1.06115i | ||||
\(646\) | 6.78952 | + | 4.93287i | 0.267130 | + | 0.194081i | ||||
\(647\) | 35.5329 | − | 11.5453i | 1.39694 | − | 0.453894i | 0.488742 | − | 0.872428i | \(-0.337456\pi\) |
0.908201 | + | 0.418534i | \(0.137456\pi\) | |||||||
\(648\) | − | 20.5940i | − | 0.809010i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.19615 | − | 10.7589i | 0.0861402 | − | 0.421999i | ||||
\(651\) | −17.4424 | − | 53.6823i | −0.683622 | − | 2.10397i | ||||
\(652\) | 5.23210 | − | 7.20137i | 0.204905 | − | 0.282027i | ||||
\(653\) | 7.13919 | + | 9.82625i | 0.279378 | + | 0.384531i | 0.925528 | − | 0.378680i | \(-0.123622\pi\) |
−0.646150 | + | 0.763211i | \(0.723622\pi\) | |||||||
\(654\) | 2.84177 | − | 8.74606i | 0.111122 | − | 0.341998i | ||||
\(655\) | 2.52999 | + | 6.51208i | 0.0988549 | + | 0.254448i | ||||
\(656\) | −3.45284 | + | 2.50864i | −0.134811 | + | 0.0979458i | ||||
\(657\) | −2.10798 | + | 2.90138i | −0.0822400 | + | 0.113194i | ||||
\(658\) | −18.8653 | + | 6.12971i | −0.735446 | + | 0.238961i | ||||
\(659\) | 23.3205 | 0.908438 | 0.454219 | − | 0.890890i | \(-0.349918\pi\) | ||||
0.454219 | + | 0.890890i | \(0.349918\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.5885 | 1.15086 | 0.575429 | − | 0.817852i | \(-0.304835\pi\) | ||||
0.575429 | + | 0.817852i | \(0.304835\pi\) | |||||||
\(662\) | 8.95802 | − | 2.91064i | 0.348163 | − | 0.113125i | ||||
\(663\) | 18.6137 | − | 25.6195i | 0.722896 | − | 0.994981i | ||||
\(664\) | 15.4719 | − | 11.2410i | 0.600427 | − | 0.436236i | ||||
\(665\) | −29.2647 | + | 11.3696i | −1.13484 | + | 0.440893i | ||||
\(666\) | 0.209975 | − | 0.646235i | 0.00813635 | − | 0.0250411i | ||||
\(667\) | −14.1910 | − | 19.5322i | −0.549478 | − | 0.756291i | ||||
\(668\) | 0.526994 | − | 0.725345i | 0.0203900 | − | 0.0280644i | ||||
\(669\) | 0.927051 | + | 2.85317i | 0.0358419 | + | 0.110310i | ||||
\(670\) | −1.98076 | + | 1.61729i | −0.0765235 | + | 0.0624812i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 33.2204i | 1.28151i | ||||||||
\(673\) | −38.8118 | + | 12.6107i | −1.49608 | + | 0.486107i | −0.938873 | − | 0.344264i | \(-0.888129\pi\) |
−0.557211 | + | 0.830371i | \(0.688129\pi\) | |||||||
\(674\) | −7.38176 | − | 5.36316i | −0.284335 | − | 0.206581i | ||||
\(675\) | −19.9401 | + | 9.07170i | −0.767495 | + | 0.349170i | ||||
\(676\) | −2.67617 | + | 8.23639i | −0.102929 | + | 0.316784i | ||||
\(677\) | 19.3576 | + | 6.28967i | 0.743973 | + | 0.241732i | 0.656386 | − | 0.754425i | \(-0.272084\pi\) |
0.0875873 | + | 0.996157i | \(0.472084\pi\) | |||||||
\(678\) | −1.66251 | − | 2.28825i | −0.0638482 | − | 0.0878795i | ||||
\(679\) | 24.7466 | + | 17.9794i | 0.949687 | + | 0.689988i | ||||
\(680\) | −14.0342 | − | 9.03352i | −0.538188 | − | 0.346420i | ||||
\(681\) | −38.8564 | −1.48898 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 29.8372i | − | 1.14169i | −0.821058 | − | 0.570844i | \(-0.806616\pi\) | ||
0.821058 | − | 0.570844i | \(-0.193384\pi\) | |||||||
\(684\) | −1.64413 | − | 5.06010i | −0.0628648 | − | 0.193478i | ||||
\(685\) | 1.11732 | + | 19.7895i | 0.0426908 | + | 0.756117i | ||||
\(686\) | −3.92892 | + | 2.85452i | −0.150007 | + | 0.108986i | ||||
\(687\) | 7.48111 | + | 2.43076i | 0.285422 | + | 0.0927393i | ||||
\(688\) | 15.1200 | + | 4.91279i | 0.576445 | + | 0.187298i | ||||
\(689\) | 7.45541 | − | 5.41667i | 0.284028 | − | 0.206359i | ||||
\(690\) | −0.439251 | − | 7.77978i | −0.0167220 | − | 0.296171i | ||||
\(691\) | 11.7145 | + | 36.0536i | 0.445641 | + | 1.37154i | 0.881779 | + | 0.471663i | \(0.156346\pi\) |
−0.436138 | + | 0.899880i | \(0.643654\pi\) | |||||||
\(692\) | − | 37.7033i | − | 1.43326i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.26795 | 0.0860902 | ||||||||
\(695\) | 27.4297 | + | 17.6559i | 1.04047 | + | 0.669725i | ||||
\(696\) | −20.9183 | − | 15.1980i | −0.792905 | − | 0.576079i | ||||
\(697\) | −3.93354 | − | 5.41405i | −0.148993 | − | 0.205072i | ||||
\(698\) | 3.60391 | + | 1.17098i | 0.136410 | + | 0.0443223i | ||||
\(699\) | 1.00985 | − | 3.10800i | 0.0381961 | − | 0.117556i | ||||
\(700\) | 26.3764 | − | 11.9999i | 0.996934 | − | 0.453553i | ||||
\(701\) | −30.6265 | − | 22.2514i | −1.15675 | − | 0.840425i | −0.167383 | − | 0.985892i | \(-0.553532\pi\) |
−0.989363 | + | 0.145467i | \(0.953532\pi\) | |||||||
\(702\) | −9.15115 | + | 2.97339i | −0.345388 | + | 0.112223i | ||||
\(703\) | 7.52433i | 0.283786i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −38.3205 | + | 31.2886i | −1.44323 | + | 1.17840i | ||||
\(706\) | −2.08032 | − | 6.40256i | −0.0782938 | − | 0.240964i | ||||
\(707\) | −38.1402 | + | 52.4954i | −1.43441 | + | 1.97429i | ||||
\(708\) | −2.49376 | − | 3.43237i | −0.0937213 | − | 0.128996i | ||||
\(709\) | −0.805822 | + | 2.48007i | −0.0302633 | + | 0.0931408i | −0.965047 | − | 0.262076i | \(-0.915593\pi\) |
0.934784 | + | 0.355217i | \(0.115593\pi\) | |||||||
\(710\) | −8.84291 | + | 3.43554i | −0.331869 | + | 0.128933i | ||||
\(711\) | −0.867102 | + | 0.629986i | −0.0325189 | + | 0.0236263i | ||||
\(712\) | −0.526994 | + | 0.725345i | −0.0197499 | + | 0.0271834i | ||||
\(713\) | −28.9398 | + | 9.40313i | −1.08381 | + | 0.352150i | ||||
\(714\) | −12.9282 | −0.483826 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 26.7846 | 1.00099 | ||||||||
\(717\) | 10.3996 | − | 3.37903i | 0.388380 | − | 0.126192i | ||||
\(718\) | −10.8500 | + | 14.9337i | −0.404918 | + | 0.557322i | ||||
\(719\) | −40.6095 | + | 29.5046i | −1.51448 | + | 1.10033i | −0.550340 | + | 0.834941i | \(0.685502\pi\) |
−0.964140 | + | 0.265394i | \(0.914498\pi\) | |||||||
\(720\) | 1.46069 | + | 3.75975i | 0.0544367 | + | 0.140118i | ||||
\(721\) | −4.38685 | + | 13.5013i | −0.163375 | + | 0.502816i | ||||
\(722\) | 0.423623 | + | 0.583067i | 0.0157656 | + | 0.0216995i | ||||
\(723\) | 16.0384 | − | 22.0750i | 0.596475 | − | 0.820977i | ||||
\(724\) | −9.30894 | − | 28.6500i | −0.345964 | − | 1.06477i | ||||
\(725\) | −6.92820 | + | 33.9411i | −0.257307 | + | 1.26054i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.24504i | − | 0.305792i | −0.988242 | − | 0.152896i | \(-0.951140\pi\) | ||
0.988242 | − | 0.152896i | \(-0.0488599\pi\) | |||||||
\(728\) | 26.0826 | − | 8.47475i | 0.966685 | − | 0.314095i | ||||
\(729\) | 14.2294 | + | 10.3382i | 0.527013 | + | 0.382898i | ||||
\(730\) | 1.44547 | − | 5.48311i | 0.0534994 | − | 0.202939i | ||||
\(731\) | −7.70324 | + | 23.7081i | −0.284915 | + | 0.876877i | ||||
\(732\) | −37.3349 | − | 12.1308i | −1.37994 | − | 0.448369i | ||||
\(733\) | −5.47668 | − | 7.53800i | −0.202286 | − | 0.278423i | 0.695807 | − | 0.718229i | \(-0.255047\pi\) |
−0.898093 | + | 0.439807i | \(0.855047\pi\) | |||||||
\(734\) | −7.07994 | − | 5.14388i | −0.261325 | − | 0.189864i | ||||
\(735\) | 9.81080 | − | 15.2418i | 0.361877 | − | 0.562202i | ||||
\(736\) | 17.9090 | 0.660133 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 0.656339i | − | 0.0241602i | ||||||
\(739\) | 12.0295 | + | 37.0229i | 0.442511 | + | 1.36191i | 0.885190 | + | 0.465230i | \(0.154028\pi\) |
−0.442679 | + | 0.896680i | \(0.645972\pi\) | |||||||
\(740\) | −0.391486 | − | 6.93380i | −0.0143913 | − | 0.254892i | ||||
\(741\) | −27.8240 | + | 20.2153i | −1.02214 | + | 0.742627i | ||||
\(742\) | −3.57803 | − | 1.16257i | −0.131354 | − | 0.0426794i | ||||
\(743\) | −41.2733 | − | 13.4105i | −1.51417 | − | 0.491984i | −0.570057 | − | 0.821605i | \(-0.693079\pi\) |
−0.944113 | + | 0.329621i | \(0.893079\pi\) | |||||||
\(744\) | −26.3646 | + | 19.1550i | −0.966574 | + | 0.702257i | ||||
\(745\) | −22.9233 | + | 1.29426i | −0.839846 | + | 0.0474181i | ||||
\(746\) | 0.0281313 | + | 0.0865791i | 0.00102996 | + | 0.00316989i | ||||
\(747\) | − | 7.24693i | − | 0.265151i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.92820 | 0.362769 | ||||||||
\(750\) | −7.80928 | + | 8.00095i | −0.285155 | + | 0.292153i | ||||
\(751\) | −39.3514 | − | 28.5905i | −1.43595 | − | 1.04328i | −0.988869 | − | 0.148789i | \(-0.952462\pi\) |
−0.447084 | − | 0.894492i | \(-0.647538\pi\) | |||||||
\(752\) | −16.5872 | − | 22.8304i | −0.604874 | − | 0.832538i | ||||
\(753\) | −6.98881 | − | 2.27080i | −0.254686 | − | 0.0827526i | ||||
\(754\) | −4.70181 | + | 14.4707i | −0.171230 | + | 0.526992i | ||||
\(755\) | −2.39183 | + | 9.07291i | −0.0870475 | + | 0.330197i | ||||
\(756\) | −20.5428 | − | 14.9252i | −0.747135 | − | 0.542825i | ||||
\(757\) | 47.3387 | − | 15.3813i | 1.72056 | − | 0.559042i | 0.728522 | − | 0.685022i | \(-0.240207\pi\) |
0.992033 | + | 0.125980i | \(0.0402075\pi\) | |||||||
\(758\) | − | 0.757875i | − | 0.0275273i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.4641 | + | 14.0406i | 0.415847 | + | 0.509306i | ||||
\(761\) | −6.13597 | − | 18.8846i | −0.222429 | − | 0.684565i | −0.998542 | − | 0.0539721i | \(-0.982812\pi\) |
0.776114 | − | 0.630593i | \(-0.217188\pi\) | |||||||
\(762\) | 0.526994 | − | 0.725345i | 0.0190910 | − | 0.0262765i | ||||
\(763\) | −18.0867 | − | 24.8942i | −0.654782 | − | 0.901231i | ||||
\(764\) | −3.89005 | + | 11.9723i | −0.140737 | + | 0.433144i | ||||
\(765\) | −5.89527 | + | 2.29036i | −0.213144 | + | 0.0828081i | ||||
\(766\) | 16.1067 | − | 11.7022i | 0.581958 | − | 0.422818i | ||||
\(767\) | −3.16196 | + | 4.35207i | −0.114172 | + | 0.157144i | ||||
\(768\) | 2.55808 | − | 0.831171i | 0.0923068 | − | 0.0299923i | ||||
\(769\) | 9.85641 | 0.355431 | 0.177716 | − | 0.984082i | \(-0.443129\pi\) | ||||
0.177716 | + | 0.984082i | \(0.443129\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.5885 | −1.02959 | ||||||||
\(772\) | 25.0014 | − | 8.12345i | 0.899821 | − | 0.292369i | ||||
\(773\) | 7.07951 | − | 9.74411i | 0.254632 | − | 0.350471i | −0.662495 | − | 0.749067i | \(-0.730502\pi\) |
0.917127 | + | 0.398596i | \(0.130502\pi\) | |||||||
\(774\) | −1.97794 | + | 1.43705i | −0.0710955 | + | 0.0516539i | ||||
\(775\) | 37.9861 | + | 21.5238i | 1.36450 | + | 0.773159i | ||||
\(776\) | 5.45732 | − | 16.7959i | 0.195906 | − | 0.602938i | ||||
\(777\) | −6.81308 | − | 9.37740i | −0.244418 | − | 0.336413i | ||||
\(778\) | −1.86340 | + | 2.56475i | −0.0668060 | + | 0.0919506i | ||||
\(779\) | 2.24592 | + | 6.91223i | 0.0804684 | + | 0.247656i | ||||
\(780\) | 24.5885 | − | 20.0764i | 0.880408 | − | 0.718850i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 6.96953i | 0.249230i | ||||||||
\(783\) | 28.8692 | − | 9.38016i | 1.03170 | − | 0.335219i | ||||
\(784\) | 8.36503 | + | 6.07755i | 0.298751 | + | 0.217055i | ||||
\(785\) | 47.2863 | + | 12.4657i | 1.68772 | + | 0.444921i | ||||
\(786\) | 0.965479 | − | 2.97144i | 0.0344375 | − | 0.105988i | ||||
\(787\) | −16.5357 | − | 5.37277i | −0.589434 | − | 0.191519i | −0.000911585 | − | 1.00000i | \(-0.500290\pi\) |
−0.588522 | + | 0.808481i | \(0.700290\pi\) | |||||||
\(788\) | −17.5597 | − | 24.1689i | −0.625539 | − | 0.860980i | ||||
\(789\) | 10.6178 | + | 7.71430i | 0.378005 | + | 0.274636i | ||||
\(790\) | 0.917227 | − | 1.42498i | 0.0326335 | − | 0.0506985i | ||||
\(791\) | −9.46410 | −0.336505 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.7749i | 1.76756i | ||||||||
\(794\) | −5.27548 | − | 16.2362i | −0.187220 | − | 0.576203i | ||||
\(795\) | −9.36796 | + | 0.528920i | −0.332247 | + | 0.0187589i | ||||
\(796\) | −2.80252 | + | 2.03615i | −0.0993326 | + | 0.0721693i | ||||
\(797\) | 34.4164 | + | 11.1826i | 1.21909 | + | 0.396107i | 0.846751 | − | 0.531989i | \(-0.178555\pi\) |
0.372340 | + | 0.928096i | \(0.378555\pi\) | |||||||
\(798\) | 13.3534 | + | 4.33878i | 0.472705 | + | 0.153591i | ||||
\(799\) | 35.7980 | − | 26.0087i | 1.26644 | − | 0.920123i | ||||
\(800\) | −17.3478 | − | 18.9563i | −0.613337 | − | 0.670208i | ||||
\(801\) | 0.104987 | + | 0.323118i | 0.00370954 | + | 0.0114168i | ||||
\(802\) | 1.20118i | 0.0424153i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −7.39230 | −0.260706 | ||||||||
\(805\) | −21.9240 | − | 14.1120i | −0.772718 | − | 0.497381i | ||||
\(806\) | 15.5144 | + | 11.2719i | 0.546473 | + | 0.397036i | ||||
\(807\) | −18.4725 | − | 25.4252i | −0.650262 | − | 0.895009i | ||||
\(808\) | 35.6295 | + | 11.5767i | 1.25344 | + | 0.407268i | ||||
\(809\) | 4.49184 | − | 13.8245i | 0.157925 | − | 0.486042i | −0.840521 | − | 0.541779i | \(-0.817751\pi\) |
0.998445 | + | 0.0557371i | \(0.0177509\pi\) | |||||||
\(810\) | 11.9313 | + | 3.14537i | 0.419224 | + | 0.110517i | ||||
\(811\) | −15.3558 | − | 11.1566i | −0.539214 | − | 0.391762i | 0.284579 | − | 0.958653i | \(-0.408146\pi\) |
−0.823793 | + | 0.566891i | \(0.808146\pi\) | |||||||
\(812\) | −38.1876 | + | 12.4079i | −1.34012 | + | 0.435432i | ||||
\(813\) | 22.1469i | 0.776727i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.26795 | + | 8.90138i | 0.254585 | + | 0.311802i | ||||
\(816\) | −5.68353 | − | 17.4921i | −0.198964 | − | 0.612347i | ||||
\(817\) | 15.9132 | − | 21.9026i | 0.556732 | − | 0.766276i | ||||
\(818\) | −7.94860 | − | 10.9403i | −0.277916 | − | 0.382519i | ||||
\(819\) | 3.21140 | − | 9.88367i | 0.112215 | − | 0.345363i | ||||
\(820\) | −2.42929 | − | 6.25288i | −0.0848345 | − | 0.218360i | ||||
\(821\) | −23.6202 | + | 17.1611i | −0.824350 | + | 0.598925i | −0.917955 | − | 0.396684i | \(-0.870161\pi\) |
0.0936051 | + | 0.995609i | \(0.470161\pi\) | |||||||
\(822\) | 5.21026 | − | 7.17130i | 0.181729 | − | 0.250128i | ||||
\(823\) | −6.42581 | + | 2.08787i | −0.223990 | + | 0.0727787i | −0.418862 | − | 0.908050i | \(-0.637571\pi\) |
0.194872 | + | 0.980829i | \(0.437571\pi\) | |||||||
\(824\) | 8.19615 | 0.285526 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.19615 | 0.0764139 | ||||||||
\(827\) | 32.4118 | − | 10.5312i | 1.12707 | − | 0.366207i | 0.314608 | − | 0.949222i | \(-0.398127\pi\) |
0.812462 | + | 0.583014i | \(0.198127\pi\) | |||||||
\(828\) | 2.59713 | − | 3.57465i | 0.0902566 | − | 0.124228i | ||||
\(829\) | −8.07461 | + | 5.86654i | −0.280443 | + | 0.203754i | −0.719110 | − | 0.694896i | \(-0.755450\pi\) |
0.438668 | + | 0.898649i | \(0.355450\pi\) | |||||||
\(830\) | 4.14952 | + | 10.6807i | 0.144032 | + | 0.370731i | ||||
\(831\) | 18.6179 | − | 57.2999i | 0.645847 | − | 1.98771i | ||||
\(832\) | 5.65572 | + | 7.78444i | 0.196077 | + | 0.269877i | ||||
\(833\) | −9.52958 | + | 13.1163i | −0.330180 | + | 0.454454i | ||||
\(834\) | −4.50808 | − | 13.8744i | −0.156102 | − | 0.480433i | ||||
\(835\) | 0.732051 | + | 0.896575i | 0.0253337 | + | 0.0310273i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 38.2581i | − | 1.32239i | ||||||
\(838\) | −6.07489 | + | 1.97385i | −0.209854 | + | 0.0681856i | ||||
\(839\) | −31.3774 | − | 22.7970i | −1.08327 | − | 0.787041i | −0.105019 | − | 0.994470i | \(-0.533490\pi\) |
−0.978250 | + | 0.207430i | \(0.933490\pi\) | |||||||
\(840\) | −27.0008 | − | 7.11804i | −0.931617 | − | 0.245596i | ||||
\(841\) | 5.87132 | − | 18.0701i | 0.202459 | − | 0.623106i | ||||
\(842\) | −8.39503 | − | 2.72771i | −0.289312 | − | 0.0940031i | ||||
\(843\) | 19.6677 | + | 27.0702i | 0.677391 | + | 0.932348i | ||||
\(844\) | 18.3906 | + | 13.3616i | 0.633031 | + | 0.459924i | ||||
\(845\) | −9.40115 | − | 6.05131i | −0.323409 | − | 0.208171i | ||||
\(846\) | 4.33975 | 0.149204 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 5.35225i | − | 0.183797i | ||||||
\(849\) | −4.81710 | − | 14.8255i | −0.165322 | − | 0.508810i | ||||
\(850\) | 7.37713 | − | 6.75114i | 0.253033 | − | 0.231562i | ||||
\(851\) | −5.05531 | + | 3.67290i | −0.173294 | + | 0.125905i | ||||
\(852\) | −26.0826 | − | 8.47475i | −0.893575 | − | 0.290340i | ||||
\(853\) | 44.0952 | + | 14.3274i | 1.50979 | + | 0.490561i | 0.942856 | − | 0.333201i | \(-0.108129\pi\) |
0.566935 | + | 0.823762i | \(0.308129\pi\) | |||||||
\(854\) | 16.4396 | − | 11.9441i | 0.562553 | − | 0.408719i | ||||
\(855\) | 6.85782 | − | 0.387197i | 0.234533 | − | 0.0132418i | ||||
\(856\) | −1.77130 | − | 5.45150i | −0.0605418 | − | 0.186329i | ||||
\(857\) | 29.3195i | 1.00154i | 0.865581 | + | 0.500768i | \(0.166949\pi\) | ||||
−0.865581 | + | 0.500768i | \(0.833051\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.1962 | 0.757323 | 0.378661 | − | 0.925535i | \(-0.376384\pi\) | ||||
0.378661 | + | 0.925535i | \(0.376384\pi\) | |||||||
\(860\) | −13.5247 | + | 21.0116i | −0.461188 | + | 0.716489i | ||||
\(861\) | −9.05788 | − | 6.58093i | −0.308692 | − | 0.224278i | ||||
\(862\) | 1.54315 | + | 2.12396i | 0.0525597 | + | 0.0723423i | ||||
\(863\) | −16.2719 | − | 5.28705i | −0.553901 | − | 0.179973i | 0.0186740 | − | 0.999826i | \(-0.494056\pi\) |
−0.572575 | + | 0.819852i | \(0.694056\pi\) | |||||||
\(864\) | −6.95803 | + | 21.4146i | −0.236717 | + | 0.728540i | ||||
\(865\) | 47.0667 | + | 12.4079i | 1.60032 | + | 0.421880i | ||||
\(866\) | 12.0346 | + | 8.74368i | 0.408954 | + | 0.297122i | ||||
\(867\) | −3.80651 | + | 1.23681i | −0.129276 | + | 0.0420043i | ||||
\(868\) | 50.6071i | 1.71772i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 12.0000 | − | 9.79796i | 0.406838 | − | 0.332182i | ||||
\(871\) | 2.89644 | + | 8.91432i | 0.0981420 | + | 0.302050i | ||||
\(872\) | −10.4424 | + | 14.3727i | −0.353623 | + | 0.486720i | ||||
\(873\) | −3.93354 | − | 5.41405i | −0.133130 | − | 0.183238i | ||||
\(874\) | 2.33902 | − | 7.19876i | 0.0791184 | − | 0.243502i | ||||
\(875\) | 6.29971 | + | 36.8759i | 0.212969 | + | 1.24663i | ||||
\(876\) | 13.2617 | − | 9.63516i | 0.448070 | − | 0.325542i | ||||
\(877\) | 6.99213 | − | 9.62384i | 0.236107 | − | 0.324974i | −0.674478 | − | 0.738295i | \(-0.735631\pi\) |
0.910585 | + | 0.413321i | \(0.135631\pi\) | |||||||
\(878\) | 13.9069 | − | 4.51863i | 0.469336 | − | 0.152497i | ||||
\(879\) | 29.1244 | 0.982340 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.9090 | −0.906586 | −0.453293 | − | 0.891362i | \(-0.649751\pi\) | ||||
−0.453293 | + | 0.891362i | \(0.649751\pi\) | |||||||
\(882\) | −1.51226 | + | 0.491361i | −0.0509203 | + | 0.0165450i | ||||
\(883\) | 12.6756 | − | 17.4464i | 0.426566 | − | 0.587118i | −0.540595 | − | 0.841283i | \(-0.681801\pi\) |
0.967161 | + | 0.254165i | \(0.0818007\pi\) | |||||||
\(884\) | −22.9699 | + | 16.6886i | −0.772560 | + | 0.561298i | ||||
\(885\) | 5.10546 | − | 1.98351i | 0.171618 | − | 0.0666749i | ||||
\(886\) | 4.40904 | − | 13.5696i | 0.148125 | − | 0.455881i | ||||
\(887\) | −9.22532 | − | 12.6976i | −0.309756 | − | 0.426342i | 0.625549 | − | 0.780185i | \(-0.284875\pi\) |
−0.935305 | + | 0.353842i | \(0.884875\pi\) | |||||||
\(888\) | −3.93354 | + | 5.41405i | −0.132001 | + | 0.181684i | ||||
\(889\) | −0.927051 | − | 2.85317i | −0.0310923 | − | 0.0956922i | ||||
\(890\) | −0.339746 | − | 0.416102i | −0.0113883 | − | 0.0139478i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 2.68973i | − | 0.0900587i | ||||||
\(893\) | −45.7040 | + | 14.8501i | −1.52943 | + | 0.496941i | ||||
\(894\) | 8.30695 | + | 6.03535i | 0.277826 | + | 0.201852i | ||||
\(895\) | −8.81461 | + | 33.4364i | −0.294640 | + | 1.11766i | ||||
\(896\) | 11.8417 | − | 36.4450i | 0.395603 | − | 1.21754i | ||||
\(897\) | −27.1638 | − | 8.82604i | −0.906972 | − | 0.294693i | ||||
\(898\) | 10.5020 | + | 14.4548i | 0.350458 | + | 0.482364i | ||||
\(899\) | −48.9434 | − | 35.5595i | −1.63236 | − | 1.18598i | ||||
\(900\) | −6.29945 | + | 0.713616i | −0.209982 | + | 0.0237872i | ||||
\(901\) | 8.39230 | 0.279588 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 41.7057i | 1.38788i | ||||||||
\(904\) | 1.68850 | + | 5.19667i | 0.0561587 | + | 0.172839i | ||||
\(905\) | 38.8285 | − | 2.19228i | 1.29070 | − | 0.0728739i | ||||
\(906\) | 3.39476 | − | 2.46644i | 0.112783 | − | 0.0819419i | ||||
\(907\) | −28.6407 | − | 9.30592i | −0.950998 | − | 0.308998i | −0.207877 | − | 0.978155i | \(-0.566655\pi\) |
−0.743121 | + | 0.669157i | \(0.766655\pi\) | |||||||
\(908\) | 33.1326 | + | 10.7654i | 1.09954 | + | 0.357264i | ||||
\(909\) | 11.4849 | − | 8.34429i | 0.380931 | − | 0.276763i | ||||
\(910\) | 0.926266 | + | 16.4055i | 0.0307054 | + | 0.543839i | ||||
\(911\) | −9.34737 | − | 28.7682i | −0.309692 | − | 0.953134i | −0.977885 | − | 0.209146i | \(-0.932932\pi\) |
0.668192 | − | 0.743988i | \(-0.267068\pi\) | |||||||
\(912\) | 19.9749i | 0.661434i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 10.9808 | 0.363211 | ||||||||
\(915\) | 27.4301 | − | 42.6146i | 0.906811 | − | 1.40880i | ||||
\(916\) | −5.70564 | − | 4.14539i | −0.188520 | − | 0.136968i | ||||
\(917\) | −6.14488 | − | 8.45770i | −0.202922 | − | 0.279298i | ||||
\(918\) | −8.33381 | − | 2.70782i | −0.275057 | − | 0.0893713i | ||||
\(919\) | 5.86538 | − | 18.0518i | 0.193481 | − | 0.595473i | −0.806510 | − | 0.591220i | \(-0.798646\pi\) |
0.999991 | − | 0.00425273i | \(-0.00135369\pi\) | |||||||
\(920\) | −3.83730 | + | 14.5560i | −0.126512 | + | 0.479898i | ||||
\(921\) | −12.2359 | − | 8.88987i | −0.403185 | − | 0.292931i | ||||
\(922\) | 16.2460 | − | 5.27865i | 0.535034 | − | 0.173843i | ||||
\(923\) | 34.7733i | 1.14458i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.78461 | + | 1.79315i | 0.288836 | + | 0.0589584i | ||||
\(926\) | −3.24983 | − | 10.0019i | −0.106796 | − | 0.328684i | ||||
\(927\) | 1.82556 | − | 2.51267i | 0.0599593 | − | 0.0825268i | ||||
\(928\) | 20.9284 | + | 28.8055i | 0.687009 | + | 0.945586i | ||||
\(929\) | 13.5524 | − | 41.7099i | 0.444639 | − | 1.36846i | −0.438240 | − | 0.898858i | \(-0.644398\pi\) |
0.882879 | − | 0.469600i | \(-0.155602\pi\) | |||||||
\(930\) | −7.07090 | − | 18.2002i | −0.231864 | − | 0.596807i | ||||
\(931\) | 14.2449 | − | 10.3495i | 0.466859 | − | 0.339193i | ||||
\(932\) | −1.72219 | + | 2.37039i | −0.0564122 | + | 0.0776447i | ||||
\(933\) | −18.4696 | + | 6.00113i | −0.604666 | + | 0.196468i | ||||
\(934\) | 0.320508 | 0.0104873 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.00000 | −0.196116 | ||||||||
\(937\) | 29.6606 | − | 9.63732i | 0.968970 | − | 0.314838i | 0.218570 | − | 0.975821i | \(-0.429861\pi\) |
0.750400 | + | 0.660984i | \(0.229861\pi\) | |||||||
\(938\) | 2.24918 | − | 3.09573i | 0.0734384 | − | 0.101079i | ||||
\(939\) | 26.7982 | − | 19.4700i | 0.874525 | − | 0.635380i | ||||
\(940\) | 41.3444 | − | 16.0626i | 1.34851 | − | 0.523904i | ||||
\(941\) | −8.34346 | + | 25.6785i | −0.271989 | + | 0.837096i | 0.718011 | + | 0.696031i | \(0.245053\pi\) |
−0.990000 | + | 0.141065i | \(0.954947\pi\) | |||||||
\(942\) | −12.8546 | − | 17.6928i | −0.418825 | − | 0.576464i | ||||
\(943\) | −3.54775 | + | 4.88306i | −0.115531 | + | 0.159014i | ||||
\(944\) | 0.965479 | + | 2.97144i | 0.0314237 | + | 0.0967121i | ||||
\(945\) | 25.3923 | − | 20.7327i | 0.826012 | − | 0.674436i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 19.9749i | − | 0.649096i | −0.945869 | − | 0.324548i | \(-0.894788\pi\) | ||
0.945869 | − | 0.324548i | \(-0.105212\pi\) | |||||||
\(948\) | 4.65921 | − | 1.51387i | 0.151324 | − | 0.0491681i | ||||
\(949\) | −16.8151 | − | 12.2169i | −0.545841 | − | 0.396577i | ||||
\(950\) | −9.88548 | + | 4.49738i | −0.320727 | + | 0.145914i | ||||
\(951\) | 7.53764 | − | 23.1985i | 0.244425 | − | 0.752262i | ||||
\(952\) | 23.7530 | + | 7.71781i | 0.769839 | + | 0.250136i | ||||
\(953\) | 9.81199 | + | 13.5051i | 0.317842 | + | 0.437472i | 0.937807 | − | 0.347158i | \(-0.112853\pi\) |
−0.619965 | + | 0.784629i | \(0.712853\pi\) | |||||||
\(954\) | 0.665890 | + | 0.483797i | 0.0215590 | + | 0.0156635i | ||||
\(955\) | −13.6654 | − | 8.79612i | −0.442203 | − | 0.284636i | ||||
\(956\) | −9.80385 | −0.317079 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 1.31268i | − | 0.0424107i | ||||||
\(959\) | −9.16552 | − | 28.2086i | −0.295970 | − | 0.910902i | ||||
\(960\) | −0.552263 | − | 9.78140i | −0.0178242 | − | 0.315693i | ||||
\(961\) | −36.6070 | + | 26.5965i | −1.18087 | + | 0.857952i | ||||
\(962\) | 3.74529 | + | 1.21692i | 0.120753 | + | 0.0392350i | ||||
\(963\) | −2.06578 | − | 0.671212i | −0.0665688 | − | 0.0216295i | ||||
\(964\) | −19.7919 | + | 14.3796i | −0.637453 | + | 0.463137i | ||||
\(965\) | 1.91310 | + | 33.8838i | 0.0615847 | + | 1.09076i | ||||
\(966\) | 3.60322 | + | 11.0896i | 0.115932 | + | 0.356801i | ||||
\(967\) | 4.24264i | 0.136434i | 0.997671 | + | 0.0682171i | \(0.0217310\pi\) | ||||
−0.997671 | + | 0.0682171i | \(0.978269\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −31.3205 | −1.00616 | ||||||||
\(970\) | 8.89734 | + | 5.72702i | 0.285677 | + | 0.183884i | ||||
\(971\) | 20.1673 | + | 14.6524i | 0.647201 | + | 0.470219i | 0.862316 | − | 0.506370i | \(-0.169013\pi\) |
−0.215116 | + | 0.976589i | \(0.569013\pi\) | |||||||
\(972\) | 7.58466 | + | 10.4394i | 0.243278 | + | 0.334843i | ||||
\(973\) | −46.4248 | − | 15.0843i | −1.48831 | − | 0.483582i | ||||
\(974\) | −2.03595 | + | 6.26600i | −0.0652359 | + | 0.200775i | ||||
\(975\) | 16.9704 | + | 37.3019i | 0.543487 | + | 1.19462i | ||||
\(976\) | 23.3878 | + | 16.9923i | 0.748627 | + | 0.543909i | ||||
\(977\) | 27.6914 | − | 8.99749i | 0.885927 | − | 0.287855i | 0.169511 | − | 0.985528i | \(-0.445781\pi\) |
0.716416 | + | 0.697673i | \(0.245781\pi\) | |||||||
\(978\) | − | 5.13922i | − | 0.164334i | ||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −12.5885 | + | 10.2784i | −0.402124 | + | 0.328332i | ||||
\(981\) | 2.08032 | + | 6.40256i | 0.0664194 | + | 0.204418i | ||||
\(982\) | 12.0830 | − | 16.6309i | 0.385585 | − | 0.530712i | ||||
\(983\) | −32.9299 | − | 45.3241i | −1.05030 | − | 1.44562i | −0.888548 | − | 0.458784i | \(-0.848285\pi\) |
−0.161753 | − | 0.986831i | \(-0.551715\pi\) | |||||||
\(984\) | −1.99752 | + | 6.14773i | −0.0636785 | + | 0.195982i | ||||
\(985\) | 35.9498 | − | 13.9668i | 1.14546 | − | 0.445019i | ||||
\(986\) | −11.2101 | + | 8.14459i | −0.357001 | + | 0.259377i | ||||
\(987\) | 43.5135 | − | 59.8912i | 1.38505 | − | 1.90636i | ||||
\(988\) | 29.3261 | − | 9.52863i | 0.932988 | − | 0.303146i | ||||
\(989\) | 22.4833 | 0.714929 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.9090 | 0.632429 | 0.316215 | − | 0.948688i | \(-0.397588\pi\) | ||||
0.316215 | + | 0.948688i | \(0.397588\pi\) | |||||||
\(992\) | 42.6795 | − | 13.8674i | 1.35508 | − | 0.440291i | ||||
\(993\) | −20.6620 | + | 28.4388i | −0.655688 | + | 0.902477i | ||||
\(994\) | 11.4849 | − | 8.34429i | 0.364280 | − | 0.264665i | ||||
\(995\) | −1.61953 | − | 4.16859i | −0.0513425 | − | 0.132153i | ||||
\(996\) | −10.2360 | + | 31.5031i | −0.324340 | + | 0.998215i | ||||
\(997\) | 20.0535 | + | 27.6012i | 0.635100 | + | 0.874140i | 0.998342 | − | 0.0575549i | \(-0.0183304\pi\) |
−0.363243 | + | 0.931695i | \(0.618330\pi\) | |||||||
\(998\) | −5.35732 | + | 7.37372i | −0.169583 | + | 0.233411i | ||||
\(999\) | −2.42776 | − | 7.47189i | −0.0768110 | − | 0.236400i |
(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 | 605.2.j.f.269.2 | 16 | ||
5.4 | even | 2 | inner | 605.2.j.f.269.3 | 16 | ||
11.2 | odd | 10 | 605.2.j.e.9.2 | 16 | |||
11.3 | even | 5 | 605.2.b.d.364.3 | yes | 4 | ||
11.4 | even | 5 | inner | 605.2.j.f.124.2 | 16 | ||
11.5 | even | 5 | inner | 605.2.j.f.444.3 | 16 | ||
11.6 | odd | 10 | 605.2.j.e.444.2 | 16 | |||
11.7 | odd | 10 | 605.2.j.e.124.3 | 16 | |||
11.8 | odd | 10 | 605.2.b.e.364.2 | yes | 4 | ||
11.9 | even | 5 | inner | 605.2.j.f.9.3 | 16 | ||
11.10 | odd | 2 | 605.2.j.e.269.3 | 16 | |||
55.3 | odd | 20 | 3025.2.a.y.1.3 | 4 | |||
55.4 | even | 10 | inner | 605.2.j.f.124.3 | 16 | ||
55.8 | even | 20 | 3025.2.a.z.1.2 | 4 | |||
55.9 | even | 10 | inner | 605.2.j.f.9.2 | 16 | ||
55.14 | even | 10 | 605.2.b.d.364.2 | ✓ | 4 | ||
55.19 | odd | 10 | 605.2.b.e.364.3 | yes | 4 | ||
55.24 | odd | 10 | 605.2.j.e.9.3 | 16 | |||
55.29 | odd | 10 | 605.2.j.e.124.2 | 16 | |||
55.39 | odd | 10 | 605.2.j.e.444.3 | 16 | |||
55.47 | odd | 20 | 3025.2.a.y.1.2 | 4 | |||
55.49 | even | 10 | inner | 605.2.j.f.444.2 | 16 | ||
55.52 | even | 20 | 3025.2.a.z.1.3 | 4 | |||
55.54 | odd | 2 | 605.2.j.e.269.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.b.d.364.2 | ✓ | 4 | 55.14 | even | 10 | ||
605.2.b.d.364.3 | yes | 4 | 11.3 | even | 5 | ||
605.2.b.e.364.2 | yes | 4 | 11.8 | odd | 10 | ||
605.2.b.e.364.3 | yes | 4 | 55.19 | odd | 10 | ||
605.2.j.e.9.2 | 16 | 11.2 | odd | 10 | |||
605.2.j.e.9.3 | 16 | 55.24 | odd | 10 | |||
605.2.j.e.124.2 | 16 | 55.29 | odd | 10 | |||
605.2.j.e.124.3 | 16 | 11.7 | odd | 10 | |||
605.2.j.e.269.2 | 16 | 55.54 | odd | 2 | |||
605.2.j.e.269.3 | 16 | 11.10 | odd | 2 | |||
605.2.j.e.444.2 | 16 | 11.6 | odd | 10 | |||
605.2.j.e.444.3 | 16 | 55.39 | odd | 10 | |||
605.2.j.f.9.2 | 16 | 55.9 | even | 10 | inner | ||
605.2.j.f.9.3 | 16 | 11.9 | even | 5 | inner | ||
605.2.j.f.124.2 | 16 | 11.4 | even | 5 | inner | ||
605.2.j.f.124.3 | 16 | 55.4 | even | 10 | inner | ||
605.2.j.f.269.2 | 16 | 1.1 | even | 1 | trivial | ||
605.2.j.f.269.3 | 16 | 5.4 | even | 2 | inner | ||
605.2.j.f.444.2 | 16 | 55.49 | even | 10 | inner | ||
605.2.j.f.444.3 | 16 | 11.5 | even | 5 | inner | ||
3025.2.a.y.1.2 | 4 | 55.47 | odd | 20 | |||
3025.2.a.y.1.3 | 4 | 55.3 | odd | 20 | |||
3025.2.a.z.1.2 | 4 | 55.8 | even | 20 | |||
3025.2.a.z.1.3 | 4 | 55.52 | even | 20 |