Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(49,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.m (of order \(6\), degree \(2\), 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: | \(2.59513806569\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(0.665665 + 1.24775i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.199 |
Dual form | 325.2.m.c.49.1 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.747754 | + | 1.29515i | −0.528742 | + | 0.915808i | 0.470696 | + | 0.882295i | \(0.344003\pi\) |
−0.999438 | + | 0.0335125i | \(0.989331\pi\) | |||||||
\(3\) | 0.0820885 | + | 0.0473938i | 0.0473938 | + | 0.0273628i | 0.523510 | − | 0.852020i | \(-0.324622\pi\) |
−0.476116 | + | 0.879383i | \(0.657956\pi\) | |||||||
\(4\) | −0.118272 | − | 0.204852i | −0.0591358 | − | 0.102426i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.122764 | + | 0.0708778i | −0.0501182 | + | 0.0289357i | ||||
\(7\) | −2.41342 | − | 4.18016i | −0.912187 | − | 1.57995i | −0.810969 | − | 0.585089i | \(-0.801059\pi\) |
−0.101218 | − | 0.994864i | \(-0.532274\pi\) | |||||||
\(8\) | −2.63726 | −0.932413 | ||||||||
\(9\) | −1.49551 | − | 2.59030i | −0.498503 | − | 0.863432i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.926118 | − | 0.534695i | −0.279235 | − | 0.161217i | 0.353842 | − | 0.935305i | \(-0.384875\pi\) |
−0.633077 | + | 0.774089i | \(0.718208\pi\) | |||||||
\(12\) | − | 0.0224214i | − | 0.00647249i | ||||||
\(13\) | −3.59030 | − | 0.331331i | −0.995769 | − | 0.0918946i | ||||
\(14\) | 7.21857 | 1.92924 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.20857 | − | 3.82535i | 0.552142 | − | 0.956337i | ||||
\(17\) | −3.08209 | + | 1.77944i | −0.747516 | + | 0.431579i | −0.824796 | − | 0.565431i | \(-0.808710\pi\) |
0.0772795 | + | 0.997009i | \(0.475377\pi\) | |||||||
\(18\) | 4.47309 | 1.05432 | ||||||||
\(19\) | −4.96410 | + | 2.86603i | −1.13884 | + | 0.657511i | −0.946144 | − | 0.323747i | \(-0.895057\pi\) |
−0.192699 | + | 0.981258i | \(0.561724\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.457524i | − | 0.0998400i | ||||||
\(22\) | 1.38502 | − | 0.799640i | 0.295287 | − | 0.170484i | ||||
\(23\) | 6.13649 | + | 3.54290i | 1.27955 | + | 0.738746i | 0.976765 | − | 0.214314i | \(-0.0687516\pi\) |
0.302781 | + | 0.953060i | \(0.402085\pi\) | |||||||
\(24\) | −0.216489 | − | 0.124990i | −0.0441906 | − | 0.0255135i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.11378 | − | 4.40221i | 0.610662 | − | 0.863344i | ||||
\(27\) | − | 0.567874i | − | 0.109287i | ||||||
\(28\) | −0.570878 | + | 0.988789i | −0.107886 | + | 0.186864i | ||||
\(29\) | 0.736543 | − | 1.27573i | 0.136773 | − | 0.236897i | −0.789501 | − | 0.613750i | \(-0.789660\pi\) |
0.926273 | + | 0.376853i | \(0.122994\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.46410i | − | 0.262960i | −0.991319 | − | 0.131480i | \(-0.958027\pi\) | ||
0.991319 | − | 0.131480i | \(-0.0419730\pi\) | |||||||
\(32\) | 0.665665 | + | 1.15297i | 0.117674 | + | 0.203818i | ||||
\(33\) | −0.0506824 | − | 0.0877845i | −0.00882268 | − | 0.0152813i | ||||
\(34\) | − | 5.32235i | − | 0.912775i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.353752 | + | 0.612717i | −0.0589587 | + | 0.102119i | ||||
\(37\) | 0.0126991 | − | 0.0219955i | 0.00208772 | − | 0.00361604i | −0.864980 | − | 0.501807i | \(-0.832669\pi\) |
0.867067 | + | 0.498191i | \(0.166002\pi\) | |||||||
\(38\) | − | 8.57233i | − | 1.39061i | ||||||
\(39\) | −0.279019 | − | 0.197356i | −0.0446788 | − | 0.0316023i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.232051 | − | 0.133975i | −0.0362402 | − | 0.0209233i | 0.481770 | − | 0.876297i | \(-0.339994\pi\) |
−0.518011 | + | 0.855374i | \(0.673327\pi\) | |||||||
\(42\) | 0.592562 | + | 0.342116i | 0.0914342 | + | 0.0527896i | ||||
\(43\) | 3.08209 | − | 1.77944i | 0.470014 | − | 0.271363i | −0.246232 | − | 0.969211i | \(-0.579192\pi\) |
0.716246 | + | 0.697848i | \(0.245859\pi\) | |||||||
\(44\) | 0.252957i | 0.0381347i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.17716 | + | 5.29844i | −1.35310 | + | 0.781212i | ||||
\(47\) | 6.51793 | 0.950738 | 0.475369 | − | 0.879787i | \(-0.342315\pi\) | ||||
0.475369 | + | 0.879787i | \(0.342315\pi\) | |||||||
\(48\) | 0.362596 | − | 0.209345i | 0.0523362 | − | 0.0302163i | ||||
\(49\) | −8.14918 | + | 14.1148i | −1.16417 | + | 2.01640i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.337339 | −0.0472368 | ||||||||
\(52\) | 0.356756 | + | 0.774668i | 0.0494732 | + | 0.107427i | ||||
\(53\) | − | 0.991015i | − | 0.136126i | −0.997681 | − | 0.0680632i | \(-0.978318\pi\) | ||
0.997681 | − | 0.0680632i | \(-0.0216820\pi\) | |||||||
\(54\) | 0.735481 | + | 0.424630i | 0.100086 | + | 0.0577848i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.36482 | + | 11.0242i | 0.850535 | + | 1.47317i | ||||
\(57\) | −0.543327 | −0.0719655 | ||||||||
\(58\) | 1.10151 | + | 1.90786i | 0.144635 | + | 0.250515i | ||||
\(59\) | 7.55440 | − | 4.36153i | 0.983499 | − | 0.567823i | 0.0801741 | − | 0.996781i | \(-0.474452\pi\) |
0.903325 | + | 0.428958i | \(0.141119\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.16867 | − | 5.48830i | −0.405707 | − | 0.702704i | 0.588697 | − | 0.808354i | \(-0.299641\pi\) |
−0.994403 | + | 0.105650i | \(0.966308\pi\) | |||||||
\(62\) | 1.89623 | + | 1.09479i | 0.240821 | + | 0.139038i | ||||
\(63\) | −7.21857 | + | 12.5029i | −0.909455 | + | 1.57522i | ||||
\(64\) | 6.84325 | 0.855406 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.151592 | 0.0186597 | ||||||||
\(67\) | 2.58658 | − | 4.48009i | 0.316001 | − | 0.547330i | −0.663649 | − | 0.748044i | \(-0.730993\pi\) |
0.979650 | + | 0.200714i | \(0.0643263\pi\) | |||||||
\(68\) | 0.729047 | + | 0.420915i | 0.0884099 | + | 0.0510435i | ||||
\(69\) | 0.335823 | + | 0.581663i | 0.0404283 | + | 0.0700240i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.72458 | + | 3.88244i | −0.798061 | + | 0.460761i | −0.842793 | − | 0.538238i | \(-0.819090\pi\) |
0.0447317 | + | 0.998999i | \(0.485757\pi\) | |||||||
\(72\) | 3.94405 | + | 6.83129i | 0.464810 | + | 0.805075i | ||||
\(73\) | −10.1088 | −1.18314 | −0.591572 | − | 0.806252i | \(-0.701493\pi\) | ||||
−0.591572 | + | 0.806252i | \(0.701493\pi\) | |||||||
\(74\) | 0.0189916 | + | 0.0328945i | 0.00220773 | + | 0.00382391i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.17422 | + | 0.677939i | 0.134693 | + | 0.0777649i | ||||
\(77\) | 5.16177i | 0.588238i | ||||||||
\(78\) | 0.464243 | − | 0.213797i | 0.0525651 | − | 0.0242077i | ||||
\(79\) | −8.78347 | −0.988218 | −0.494109 | − | 0.869400i | \(-0.664506\pi\) | ||||
−0.494109 | + | 0.869400i | \(0.664506\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.45961 | + | 7.72427i | −0.495512 | + | 0.858252i | ||||
\(82\) | 0.347034 | − | 0.200360i | 0.0383235 | − | 0.0221261i | ||||
\(83\) | −0.725474 | −0.0796311 | −0.0398155 | − | 0.999207i | \(-0.512677\pi\) | ||||
−0.0398155 | + | 0.999207i | \(0.512677\pi\) | |||||||
\(84\) | −0.0937250 | + | 0.0541121i | −0.0102262 | + | 0.00590412i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.32235i | 0.573923i | ||||||||
\(87\) | 0.120923 | − | 0.0698151i | 0.0129643 | − | 0.00748497i | ||||
\(88\) | 2.44242 | + | 1.41013i | 0.260363 | + | 0.150320i | ||||
\(89\) | −11.6970 | − | 6.75327i | −1.23988 | − | 0.715845i | −0.270810 | − | 0.962633i | \(-0.587292\pi\) |
−0.969070 | + | 0.246788i | \(0.920625\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.27987 | + | 15.8077i | 0.763138 | + | 1.65709i | ||||
\(92\) | − | 1.67610i | − | 0.174745i | ||||||
\(93\) | 0.0693893 | − | 0.120186i | 0.00719534 | − | 0.0124627i | ||||
\(94\) | −4.87381 | + | 8.44168i | −0.502695 | + | 0.870693i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.126194i | 0.0128796i | ||||||||
\(97\) | −1.71935 | − | 2.97800i | −0.174574 | − | 0.302371i | 0.765440 | − | 0.643507i | \(-0.222521\pi\) |
−0.940014 | + | 0.341137i | \(0.889188\pi\) | |||||||
\(98\) | −12.1872 | − | 21.1088i | −1.23109 | − | 2.13231i | ||||
\(99\) | 3.19856i | 0.321467i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.42763 | − | 2.47273i | 0.142055 | − | 0.246046i | −0.786215 | − | 0.617953i | \(-0.787962\pi\) |
0.928270 | + | 0.371906i | \(0.121296\pi\) | |||||||
\(102\) | 0.252246 | − | 0.436903i | 0.0249761 | − | 0.0432599i | ||||
\(103\) | − | 5.54488i | − | 0.546354i | −0.961964 | − | 0.273177i | \(-0.911926\pi\) | ||
0.961964 | − | 0.273177i | \(-0.0880744\pi\) | |||||||
\(104\) | 9.46855 | + | 0.873806i | 0.928468 | + | 0.0856838i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.28351 | + | 0.741035i | 0.124666 | + | 0.0719757i | ||||
\(107\) | 3.84611 | + | 2.22056i | 0.371818 | + | 0.214669i | 0.674252 | − | 0.738501i | \(-0.264466\pi\) |
−0.302434 | + | 0.953170i | \(0.597799\pi\) | |||||||
\(108\) | −0.116330 | + | 0.0671633i | −0.0111939 | + | 0.00646280i | ||||
\(109\) | − | 13.7804i | − | 1.31993i | −0.751298 | − | 0.659963i | \(-0.770572\pi\) | ||
0.751298 | − | 0.659963i | \(-0.229428\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.00208490 | − | 0.00120372i | 0.000197890 | − | 0.000114252i | ||||
\(112\) | −21.3208 | −2.01463 | ||||||||
\(113\) | 6.96630 | − | 4.02200i | 0.655334 | − | 0.378358i | −0.135163 | − | 0.990823i | \(-0.543156\pi\) |
0.790497 | + | 0.612466i | \(0.209822\pi\) | |||||||
\(114\) | 0.406275 | − | 0.703689i | 0.0380511 | − | 0.0659065i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.348448 | −0.0323526 | ||||||||
\(117\) | 4.51107 | + | 9.79543i | 0.417049 | + | 0.905588i | ||||
\(118\) | 13.0454i | 1.20093i | ||||||||
\(119\) | 14.8767 | + | 8.58909i | 1.36375 | + | 0.787361i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.92820 | − | 8.53590i | −0.448018 | − | 0.775991i | ||||
\(122\) | 9.47754 | 0.858056 | ||||||||
\(123\) | −0.0126991 | − | 0.0219955i | −0.00114504 | − | 0.00198327i | ||||
\(124\) | −0.299925 | + | 0.173162i | −0.0269340 | + | 0.0155504i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −10.7954 | − | 18.6982i | −0.961734 | − | 1.66577i | ||||
\(127\) | 0.611979 | + | 0.353326i | 0.0543044 | + | 0.0313526i | 0.526906 | − | 0.849923i | \(-0.323352\pi\) |
−0.472602 | + | 0.881276i | \(0.656685\pi\) | |||||||
\(128\) | −6.44840 | + | 11.1690i | −0.569963 | + | 0.987205i | ||||
\(129\) | 0.337339 | 0.0297010 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.26554 | 0.547423 | 0.273711 | − | 0.961812i | \(-0.411749\pi\) | ||||
0.273711 | + | 0.961812i | \(0.411749\pi\) | |||||||
\(132\) | −0.0119886 | + | 0.0207648i | −0.00104347 | + | 0.00180735i | ||||
\(133\) | 23.9609 | + | 13.8338i | 2.07767 | + | 1.19955i | ||||
\(134\) | 3.86825 | + | 6.70001i | 0.334166 | + | 0.578793i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.12828 | − | 4.69286i | 0.696994 | − | 0.402410i | ||||
\(137\) | −8.15290 | − | 14.1212i | −0.696549 | − | 1.20646i | −0.969656 | − | 0.244475i | \(-0.921384\pi\) |
0.273107 | − | 0.961984i | \(-0.411949\pi\) | |||||||
\(138\) | −1.00445 | −0.0855046 | ||||||||
\(139\) | −3.41264 | − | 5.91087i | −0.289456 | − | 0.501353i | 0.684224 | − | 0.729272i | \(-0.260141\pi\) |
−0.973680 | + | 0.227919i | \(0.926808\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.535047 | + | 0.308909i | 0.0450591 | + | 0.0260149i | ||||
\(142\) | − | 11.6124i | − | 0.974494i | ||||||
\(143\) | 3.14788 | + | 2.22656i | 0.263239 | + | 0.186195i | ||||
\(144\) | −13.2117 | −1.10098 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.55889 | − | 13.0924i | 0.625578 | − | 1.08353i | ||||
\(147\) | −1.33791 | + | 0.772442i | −0.110349 | + | 0.0637099i | ||||
\(148\) | −0.00600778 | −0.000493837 | ||||||||
\(149\) | 7.30887 | − | 4.21978i | 0.598766 | − | 0.345698i | −0.169790 | − | 0.985480i | \(-0.554309\pi\) |
0.768556 | + | 0.639783i | \(0.220976\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.37017i | 0.111503i | 0.998445 | + | 0.0557513i | \(0.0177554\pi\) | ||||
−0.998445 | + | 0.0557513i | \(0.982245\pi\) | |||||||
\(152\) | 13.0916 | − | 7.55846i | 1.06187 | − | 0.613072i | ||||
\(153\) | 9.21857 | + | 5.32235i | 0.745278 | + | 0.430286i | ||||
\(154\) | −6.68525 | − | 3.85973i | −0.538713 | − | 0.311026i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.00742888 | + | 0.0804993i | −0.000594787 | + | 0.00644510i | ||||
\(157\) | 11.9700i | 0.955311i | 0.878547 | + | 0.477656i | \(0.158513\pi\) | ||||
−0.878547 | + | 0.477656i | \(0.841487\pi\) | |||||||
\(158\) | 6.56787 | − | 11.3759i | 0.522512 | − | 0.905017i | ||||
\(159\) | 0.0469680 | − | 0.0813509i | 0.00372480 | − | 0.00645155i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 34.2020i | − | 2.69550i | ||||||
\(162\) | −6.66938 | − | 11.5517i | −0.523996 | − | 0.907588i | ||||
\(163\) | −11.2857 | − | 19.5474i | −0.883962 | − | 1.53107i | −0.846899 | − | 0.531754i | \(-0.821533\pi\) |
−0.0370630 | − | 0.999313i | \(-0.511800\pi\) | |||||||
\(164\) | 0.0633815i | 0.00494927i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.542476 | − | 0.939595i | 0.0421043 | − | 0.0729267i | ||||
\(167\) | −4.09850 | + | 7.09881i | −0.317152 | + | 0.549323i | −0.979893 | − | 0.199526i | \(-0.936060\pi\) |
0.662741 | + | 0.748849i | \(0.269393\pi\) | |||||||
\(168\) | 1.20661i | 0.0930922i | ||||||||
\(169\) | 12.7804 | + | 2.37915i | 0.983111 | + | 0.183012i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.8477 | + | 8.57233i | 1.13543 | + | 0.655542i | ||||
\(172\) | −0.729047 | − | 0.420915i | −0.0555893 | − | 0.0320945i | ||||
\(173\) | −7.93948 | + | 4.58386i | −0.603628 | + | 0.348505i | −0.770467 | − | 0.637479i | \(-0.779977\pi\) |
0.166840 | + | 0.985984i | \(0.446644\pi\) | |||||||
\(174\) | 0.208818i | 0.0158305i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.09079 | + | 2.36182i | −0.308355 | + | 0.178029i | ||||
\(177\) | 0.826838 | 0.0621490 | ||||||||
\(178\) | 17.4930 | − | 10.0996i | 1.31115 | − | 0.756994i | ||||
\(179\) | 5.01850 | − | 8.69229i | 0.375100 | − | 0.649693i | −0.615242 | − | 0.788338i | \(-0.710942\pi\) |
0.990342 | + | 0.138646i | \(0.0442750\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.0238 | −1.26537 | −0.632686 | − | 0.774408i | \(-0.718048\pi\) | ||||
−0.632686 | + | 0.774408i | \(0.718048\pi\) | |||||||
\(182\) | −25.9168 | − | 2.39174i | −1.92108 | − | 0.177287i | ||||
\(183\) | − | 0.600701i | − | 0.0444051i | ||||||
\(184\) | −16.1835 | − | 9.34356i | −1.19307 | − | 0.688817i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.103772 | + | 0.179739i | 0.00760895 | + | 0.0131791i | ||||
\(187\) | 3.80584 | 0.278310 | ||||||||
\(188\) | −0.770886 | − | 1.33521i | −0.0562226 | − | 0.0973804i | ||||
\(189\) | −2.37381 | + | 1.37052i | −0.172669 | + | 0.0996905i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.93870 | + | 3.35793i | 0.140280 | + | 0.242971i | 0.927602 | − | 0.373570i | \(-0.121867\pi\) |
−0.787322 | + | 0.616542i | \(0.788533\pi\) | |||||||
\(192\) | 0.561752 | + | 0.324328i | 0.0405410 | + | 0.0234063i | ||||
\(193\) | 0.626972 | − | 1.08595i | 0.0451304 | − | 0.0781681i | −0.842578 | − | 0.538575i | \(-0.818963\pi\) |
0.887708 | + | 0.460406i | \(0.152296\pi\) | |||||||
\(194\) | 5.14261 | 0.369218 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.85527 | 0.275376 | ||||||||
\(197\) | −7.64098 | + | 13.2346i | −0.544397 | + | 0.942923i | 0.454247 | + | 0.890876i | \(0.349908\pi\) |
−0.998645 | + | 0.0520479i | \(0.983425\pi\) | |||||||
\(198\) | −4.14261 | − | 2.39174i | −0.294402 | − | 0.169973i | ||||
\(199\) | 6.61480 | + | 11.4572i | 0.468911 | + | 0.812177i | 0.999368 | − | 0.0355340i | \(-0.0113132\pi\) |
−0.530458 | + | 0.847711i | \(0.677980\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.424657 | − | 0.245176i | 0.0299530 | − | 0.0172934i | ||||
\(202\) | 2.13504 | + | 3.69799i | 0.150221 | + | 0.260190i | ||||
\(203\) | −7.11035 | −0.499049 | ||||||||
\(204\) | 0.0398976 | + | 0.0691046i | 0.00279339 | + | 0.00483829i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.18144 | + | 4.14621i | 0.500355 | + | 0.288880i | ||||
\(207\) | − | 21.1937i | − | 1.47307i | ||||||
\(208\) | −9.19686 | + | 13.0024i | −0.637688 | + | 0.901552i | ||||
\(209\) | 6.12979 | 0.424007 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.40521 | − | 4.16595i | 0.165582 | − | 0.286796i | −0.771280 | − | 0.636496i | \(-0.780383\pi\) |
0.936862 | + | 0.349700i | \(0.113717\pi\) | |||||||
\(212\) | −0.203012 | + | 0.117209i | −0.0139429 | + | 0.00804994i | ||||
\(213\) | −0.736014 | −0.0504309 | ||||||||
\(214\) | −5.75189 | + | 3.32086i | −0.393191 | + | 0.227009i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.49763i | 0.101901i | ||||||||
\(217\) | −6.12019 | + | 3.53349i | −0.415465 | + | 0.239869i | ||||
\(218\) | 17.8477 | + | 10.3044i | 1.20880 | + | 0.697900i | ||||
\(219\) | −0.829815 | − | 0.479094i | −0.0560737 | − | 0.0323742i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.6552 | − | 5.36754i | 0.784013 | − | 0.361060i | ||||
\(222\) | 0.00360034i | 0.000241639i | ||||||||
\(223\) | −7.35661 | + | 12.7420i | −0.492635 | + | 0.853269i | −0.999964 | − | 0.00848317i | \(-0.997300\pi\) |
0.507329 | + | 0.861753i | \(0.330633\pi\) | |||||||
\(224\) | 3.21306 | − | 5.56518i | 0.214682 | − | 0.371839i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.0299i | 0.800214i | ||||||||
\(227\) | 7.45140 | + | 12.9062i | 0.494567 | + | 0.856615i | 0.999980 | − | 0.00626222i | \(-0.00199334\pi\) |
−0.505413 | + | 0.862877i | \(0.668660\pi\) | |||||||
\(228\) | 0.0642602 | + | 0.111302i | 0.00425573 | + | 0.00737115i | ||||
\(229\) | − | 19.3074i | − | 1.27587i | −0.770092 | − | 0.637933i | \(-0.779790\pi\) | ||
0.770092 | − | 0.637933i | \(-0.220210\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.244636 | + | 0.423722i | −0.0160959 | + | 0.0278788i | ||||
\(232\) | −1.94246 | + | 3.36444i | −0.127529 | + | 0.220886i | ||||
\(233\) | − | 21.1937i | − | 1.38845i | −0.719759 | − | 0.694224i | \(-0.755748\pi\) | ||
0.719759 | − | 0.694224i | \(-0.244252\pi\) | |||||||
\(234\) | −16.0597 | − | 1.48207i | −1.04986 | − | 0.0968860i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.78694 | − | 1.03169i | −0.116320 | − | 0.0671573i | ||||
\(237\) | −0.721022 | − | 0.416282i | −0.0468354 | − | 0.0270404i | ||||
\(238\) | −22.2483 | + | 12.8451i | −1.44214 | + | 0.832621i | ||||
\(239\) | 14.8971i | 0.963612i | 0.876278 | + | 0.481806i | \(0.160019\pi\) | ||||
−0.876278 | + | 0.481806i | \(0.839981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.13343 | + | 4.69584i | −0.523921 | + | 0.302486i | −0.738537 | − | 0.674213i | \(-0.764483\pi\) |
0.214617 | + | 0.976698i | \(0.431150\pi\) | |||||||
\(242\) | 14.7403 | 0.947544 | ||||||||
\(243\) | −2.20754 | + | 1.27453i | −0.141614 | + | 0.0817609i | ||||
\(244\) | −0.749527 | + | 1.29822i | −0.0479835 | + | 0.0831099i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.0379833 | 0.00242173 | ||||||||
\(247\) | 18.7722 | − | 8.64512i | 1.19445 | − | 0.550076i | ||||
\(248\) | 3.86122i | 0.245188i | ||||||||
\(249\) | −0.0595530 | − | 0.0343829i | −0.00377402 | − | 0.00217893i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.65817 | + | 9.80024i | 0.357140 | + | 0.618585i | 0.987482 | − | 0.157733i | \(-0.0504184\pi\) |
−0.630341 | + | 0.776318i | \(0.717085\pi\) | |||||||
\(252\) | 3.41501 | 0.215125 | ||||||||
\(253\) | −3.78874 | − | 6.56229i | −0.238196 | − | 0.412568i | ||||
\(254\) | −0.915219 | + | 0.528402i | −0.0574260 | + | 0.0331549i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.80038 | − | 4.85040i | −0.175024 | − | 0.303150i | ||||
\(257\) | −22.9773 | − | 13.2660i | −1.43329 | − | 0.827508i | −0.435917 | − | 0.899987i | \(-0.643576\pi\) |
−0.997370 | + | 0.0724788i | \(0.976909\pi\) | |||||||
\(258\) | −0.252246 | + | 0.436903i | −0.0157042 | + | 0.0272004i | ||||
\(259\) | −0.122593 | −0.00761758 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.40602 | −0.272726 | ||||||||
\(262\) | −4.68508 | + | 8.11480i | −0.289445 | + | 0.501334i | ||||
\(263\) | −12.2463 | − | 7.07038i | −0.755137 | − | 0.435979i | 0.0724100 | − | 0.997375i | \(-0.476931\pi\) |
−0.827547 | + | 0.561396i | \(0.810264\pi\) | |||||||
\(264\) | 0.133663 | + | 0.231511i | 0.00822638 | + | 0.0142485i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −35.8337 | + | 20.6886i | −2.19711 | + | 1.26850i | ||||
\(267\) | −0.640126 | − | 1.10873i | −0.0391751 | − | 0.0678532i | ||||
\(268\) | −1.22368 | −0.0747479 | ||||||||
\(269\) | 12.3872 | + | 21.4553i | 0.755264 | + | 1.30815i | 0.945243 | + | 0.326367i | \(0.105824\pi\) |
−0.189980 | + | 0.981788i | \(0.560842\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.2095 | + | 9.35856i | 0.984657 | + | 0.568492i | 0.903673 | − | 0.428224i | \(-0.140860\pi\) |
0.0809839 | + | 0.996715i | \(0.474194\pi\) | |||||||
\(272\) | 15.7201i | 0.953170i | ||||||||
\(273\) | −0.151592 | + | 1.64265i | −0.00917476 | + | 0.0994176i | ||||
\(274\) | 24.3854 | 1.47318 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.0794367 | − | 0.137588i | 0.00478152 | − | 0.00828184i | ||||
\(277\) | 19.6282 | − | 11.3323i | 1.17934 | − | 0.680893i | 0.223480 | − | 0.974709i | \(-0.428258\pi\) |
0.955862 | + | 0.293815i | \(0.0949250\pi\) | |||||||
\(278\) | 10.2073 | 0.612191 | ||||||||
\(279\) | −3.79246 | + | 2.18958i | −0.227048 | + | 0.131086i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.8384i | 1.66070i | 0.557241 | + | 0.830351i | \(0.311860\pi\) | ||||
−0.557241 | + | 0.830351i | \(0.688140\pi\) | |||||||
\(282\) | −0.800167 | + | 0.461976i | −0.0476492 | + | 0.0275103i | ||||
\(283\) | −6.85898 | − | 3.96004i | −0.407724 | − | 0.235400i | 0.282087 | − | 0.959389i | \(-0.408973\pi\) |
−0.689811 | + | 0.723989i | \(0.742307\pi\) | |||||||
\(284\) | 1.59065 | + | 0.918364i | 0.0943879 | + | 0.0544949i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.23757 | + | 2.41204i | −0.309704 | + | 0.142627i | ||||
\(287\) | 1.29335i | 0.0763439i | ||||||||
\(288\) | 1.99102 | − | 3.44854i | 0.117322 | − | 0.203207i | ||||
\(289\) | −2.16715 | + | 3.75362i | −0.127480 | + | 0.220801i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 0.325946i | − | 0.0191073i | ||||||
\(292\) | 1.19558 | + | 2.07081i | 0.0699662 | + | 0.121185i | ||||
\(293\) | −0.136485 | − | 0.236400i | −0.00797356 | − | 0.0138106i | 0.862011 | − | 0.506889i | \(-0.169205\pi\) |
−0.869985 | + | 0.493079i | \(0.835871\pi\) | |||||||
\(294\) | − | 2.31038i | − | 0.134744i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.0334909 | + | 0.0580080i | −0.00194662 | + | 0.00337165i | ||||
\(297\) | −0.303639 | + | 0.525918i | −0.0176189 | + | 0.0305169i | ||||
\(298\) | 12.6214i | 0.731139i | ||||||||
\(299\) | −20.8579 | − | 14.7533i | −1.20624 | − | 0.853204i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.8767 | − | 8.58909i | −0.857481 | − | 0.495067i | ||||
\(302\) | −1.77457 | − | 1.02455i | −0.102115 | − | 0.0589560i | ||||
\(303\) | 0.234385 | − | 0.135322i | 0.0134650 | − | 0.00777404i | ||||
\(304\) | 25.3192i | 1.45216i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −13.7864 | + | 7.95961i | −0.788119 | + | 0.455021i | ||||
\(307\) | 6.85224 | 0.391078 | 0.195539 | − | 0.980696i | \(-0.437354\pi\) | ||||
0.195539 | + | 0.980696i | \(0.437354\pi\) | |||||||
\(308\) | 1.05740 | − | 0.610491i | 0.0602510 | − | 0.0347859i | ||||
\(309\) | 0.262793 | − | 0.455171i | 0.0149498 | − | 0.0258938i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.6447 | −0.603605 | −0.301803 | − | 0.953370i | \(-0.597588\pi\) | ||||
−0.301803 | + | 0.953370i | \(0.597588\pi\) | |||||||
\(312\) | 0.735846 | + | 0.520480i | 0.0416591 | + | 0.0294664i | ||||
\(313\) | − | 17.8236i | − | 1.00745i | −0.863865 | − | 0.503724i | \(-0.831963\pi\) | ||
0.863865 | − | 0.503724i | \(-0.168037\pi\) | |||||||
\(314\) | −15.5029 | − | 8.95062i | −0.874881 | − | 0.505113i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.03883 | + | 1.79931i | 0.0584390 | + | 0.101219i | ||||
\(317\) | −8.17161 | −0.458963 | −0.229482 | − | 0.973313i | \(-0.573703\pi\) | ||||
−0.229482 | + | 0.973313i | \(0.573703\pi\) | |||||||
\(318\) | 0.0702410 | + | 0.121661i | 0.00393892 | + | 0.00682241i | ||||
\(319\) | −1.36425 | + | 0.787651i | −0.0763835 | + | 0.0441000i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.210481 | + | 0.364564i | 0.0117479 | + | 0.0203480i | ||||
\(322\) | 44.2967 | + | 25.5747i | 2.46856 | + | 1.42522i | ||||
\(323\) | 10.1999 | − | 17.6667i | 0.567536 | − | 0.983001i | ||||
\(324\) | 2.10978 | 0.117210 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 33.7556 | 1.86955 | ||||||||
\(327\) | 0.653107 | − | 1.13122i | 0.0361169 | − | 0.0625563i | ||||
\(328\) | 0.611979 | + | 0.353326i | 0.0337909 | + | 0.0195092i | ||||
\(329\) | −15.7305 | − | 27.2460i | −0.867250 | − | 1.50212i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5983 | − | 12.4698i | 1.18715 | − | 0.685400i | 0.229490 | − | 0.973311i | \(-0.426294\pi\) |
0.957657 | + | 0.287911i | \(0.0929608\pi\) | |||||||
\(332\) | 0.0858029 | + | 0.148615i | 0.00470905 | + | 0.00815631i | ||||
\(333\) | −0.0759666 | −0.00416294 | ||||||||
\(334\) | −6.12934 | − | 10.6163i | −0.335383 | − | 0.580900i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.75019 | − | 1.01047i | −0.0954807 | − | 0.0551258i | ||||
\(337\) | 19.6057i | 1.06799i | 0.845487 | + | 0.533996i | \(0.179310\pi\) | ||||
−0.845487 | + | 0.533996i | \(0.820690\pi\) | |||||||
\(338\) | −12.6380 | + | 14.7735i | −0.687415 | + | 0.803575i | ||||
\(339\) | 0.762471 | 0.0414117 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.782847 | + | 1.35593i | −0.0423936 | + | 0.0734278i | ||||
\(342\) | −22.2049 | + | 12.8200i | −1.20070 | + | 0.693225i | ||||
\(343\) | 44.8817 | 2.42339 | ||||||||
\(344\) | −8.12828 | + | 4.69286i | −0.438247 | + | 0.253022i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 13.7104i | − | 0.737076i | ||||||
\(347\) | 14.7926 | − | 8.54049i | 0.794107 | − | 0.458478i | −0.0472996 | − | 0.998881i | \(-0.515062\pi\) |
0.841406 | + | 0.540403i | \(0.181728\pi\) | |||||||
\(348\) | −0.0286036 | − | 0.0165143i | −0.00153331 | − | 0.000885259i | ||||
\(349\) | 24.5708 | + | 14.1860i | 1.31525 | + | 0.759357i | 0.982960 | − | 0.183822i | \(-0.0588469\pi\) |
0.332286 | + | 0.943179i | \(0.392180\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.188154 | + | 2.03883i | −0.0100429 | + | 0.108825i | ||||
\(352\) | − | 1.42371i | − | 0.0758840i | ||||||
\(353\) | −10.6260 | + | 18.4047i | −0.565564 | + | 0.979586i | 0.431433 | + | 0.902145i | \(0.358008\pi\) |
−0.996997 | + | 0.0774407i | \(0.975325\pi\) | |||||||
\(354\) | −0.618272 | + | 1.07088i | −0.0328608 | + | 0.0569165i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.19488i | 0.169328i | ||||||||
\(357\) | 0.814139 | + | 1.41013i | 0.0430888 | + | 0.0746320i | ||||
\(358\) | 7.50520 | + | 12.9994i | 0.396662 | + | 0.687039i | ||||
\(359\) | 32.6519i | 1.72330i | 0.507502 | + | 0.861650i | \(0.330569\pi\) | ||||
−0.507502 | + | 0.861650i | \(0.669431\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.92820 | − | 12.0000i | 0.364642 | − | 0.631579i | ||||
\(362\) | 12.7296 | − | 22.0484i | 0.669055 | − | 1.15884i | ||||
\(363\) | − | 0.934265i | − | 0.0490362i | ||||||
\(364\) | 2.37724 | − | 3.36090i | 0.124601 | − | 0.176159i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.777997 | + | 0.449176i | 0.0406665 | + | 0.0234788i | ||||
\(367\) | 5.12546 | + | 2.95918i | 0.267547 | + | 0.154468i | 0.627772 | − | 0.778397i | \(-0.283967\pi\) |
−0.360226 | + | 0.932865i | \(0.617300\pi\) | |||||||
\(368\) | 27.1057 | − | 15.6495i | 1.41298 | − | 0.815785i | ||||
\(369\) | 0.801440i | 0.0417213i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.14261 | + | 2.39174i | −0.215073 | + | 0.124173i | ||||
\(372\) | −0.0328271 | −0.00170201 | ||||||||
\(373\) | 11.5342 | − | 6.65926i | 0.597217 | − | 0.344803i | −0.170729 | − | 0.985318i | \(-0.554612\pi\) |
0.767946 | + | 0.640515i | \(0.221279\pi\) | |||||||
\(374\) | −2.84583 | + | 4.92912i | −0.147154 | + | 0.254879i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.1895 | −0.886480 | ||||||||
\(377\) | −3.06710 | + | 4.33621i | −0.157963 | + | 0.223326i | ||||
\(378\) | − | 4.09924i | − | 0.210842i | ||||||
\(379\) | 22.0131 | + | 12.7093i | 1.13074 | + | 0.652832i | 0.944120 | − | 0.329601i | \(-0.106914\pi\) |
0.186617 | + | 0.982433i | \(0.440248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0334909 | + | 0.0580080i | 0.00171579 | + | 0.00297184i | ||||
\(382\) | −5.79869 | −0.296687 | ||||||||
\(383\) | 5.41342 | + | 9.37632i | 0.276613 | + | 0.479107i | 0.970541 | − | 0.240937i | \(-0.0774547\pi\) |
−0.693928 | + | 0.720044i | \(0.744121\pi\) | |||||||
\(384\) | −1.05868 | + | 0.611228i | −0.0540254 | + | 0.0311916i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.937641 | + | 1.62404i | 0.0477247 | + | 0.0826615i | ||||
\(387\) | −9.21857 | − | 5.32235i | −0.468606 | − | 0.270550i | ||||
\(388\) | −0.406701 | + | 0.704427i | −0.0206471 | + | 0.0357618i | ||||
\(389\) | −23.0370 | −1.16802 | −0.584011 | − | 0.811746i | \(-0.698518\pi\) | ||||
−0.584011 | + | 0.811746i | \(0.698518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.2176 | −1.27531 | ||||||||
\(392\) | 21.4915 | − | 37.2244i | 1.08549 | − | 1.88012i | ||||
\(393\) | 0.514329 | + | 0.296948i | 0.0259444 | + | 0.0149790i | ||||
\(394\) | −11.4271 | − | 19.7924i | −0.575691 | − | 0.997126i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.655233 | − | 0.378299i | 0.0329267 | − | 0.0190102i | ||||
\(397\) | −10.5432 | − | 18.2614i | −0.529149 | − | 0.916512i | −0.999422 | − | 0.0339917i | \(-0.989178\pi\) |
0.470273 | − | 0.882521i | \(-0.344155\pi\) | |||||||
\(398\) | −19.7850 | −0.991731 | ||||||||
\(399\) | 1.31128 | + | 2.27120i | 0.0656459 | + | 0.113702i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.1273 | − | 9.88845i | −0.855296 | − | 0.493805i | 0.00713812 | − | 0.999975i | \(-0.497728\pi\) |
−0.862434 | + | 0.506169i | \(0.831061\pi\) | |||||||
\(402\) | 0.733324i | 0.0365749i | ||||||||
\(403\) | −0.485102 | + | 5.25656i | −0.0241646 | + | 0.261848i | ||||
\(404\) | −0.675394 | −0.0336021 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.31679 | − | 9.20895i | 0.263868 | − | 0.457033i | ||||
\(407\) | −0.0235218 | + | 0.0135803i | −0.00116593 | + | 0.000673151i | ||||
\(408\) | 0.889650 | 0.0440443 | ||||||||
\(409\) | 27.6096 | − | 15.9404i | 1.36521 | − | 0.788204i | 0.374897 | − | 0.927066i | \(-0.377678\pi\) |
0.990312 | + | 0.138862i | \(0.0443446\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1.54559i | − | 0.0762382i | ||||||
\(412\) | −1.13588 | + | 0.655802i | −0.0559609 | + | 0.0323090i | ||||
\(413\) | −36.4639 | − | 21.0524i | −1.79427 | − | 1.03592i | ||||
\(414\) | 27.4490 | + | 15.8477i | 1.34905 | + | 0.778872i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.00792 | − | 4.36004i | −0.0984465 | − | 0.213769i | ||||
\(417\) | − | 0.646952i | − | 0.0316814i | ||||||
\(418\) | −4.58358 | + | 7.93899i | −0.224190 | + | 0.388309i | ||||
\(419\) | 15.3648 | − | 26.6127i | 0.750621 | − | 1.30011i | −0.196902 | − | 0.980423i | \(-0.563088\pi\) |
0.947522 | − | 0.319690i | \(-0.103579\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.9820i | 0.876391i | 0.898880 | + | 0.438195i | \(0.144382\pi\) | ||||
−0.898880 | + | 0.438195i | \(0.855618\pi\) | |||||||
\(422\) | 3.59701 | + | 6.23021i | 0.175100 | + | 0.303282i | ||||
\(423\) | −9.74761 | − | 16.8834i | −0.473945 | − | 0.820897i | ||||
\(424\) | 2.61357i | 0.126926i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.550357 | − | 0.953247i | 0.0266649 | − | 0.0461850i | ||||
\(427\) | −15.2947 | + | 26.4911i | −0.740160 | + | 1.28200i | ||||
\(428\) | − | 1.05051i | − | 0.0507785i | ||||||
\(429\) | 0.152879 | + | 0.331965i | 0.00738107 | + | 0.0160274i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.24308 | − | 2.44974i | −0.204382 | − | 0.118000i | 0.394316 | − | 0.918975i | \(-0.370982\pi\) |
−0.598698 | + | 0.800975i | \(0.704315\pi\) | |||||||
\(432\) | −2.17232 | − | 1.25419i | −0.104516 | − | 0.0603421i | ||||
\(433\) | −16.6618 | + | 9.61972i | −0.800717 | + | 0.462294i | −0.843722 | − | 0.536781i | \(-0.819640\pi\) |
0.0430048 | + | 0.999075i | \(0.486307\pi\) | |||||||
\(434\) | − | 10.5687i | − | 0.507315i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.82296 | + | 1.62983i | −0.135195 | + | 0.0780549i | ||||
\(437\) | −40.6162 | −1.94294 | ||||||||
\(438\) | 1.24100 | − | 0.716489i | 0.0592970 | − | 0.0342352i | ||||
\(439\) | 4.27987 | − | 7.41295i | 0.204267 | − | 0.353801i | −0.745632 | − | 0.666358i | \(-0.767852\pi\) |
0.949899 | + | 0.312557i | \(0.101186\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 48.7487 | 2.32137 | ||||||||
\(442\) | −1.76346 | + | 19.1088i | −0.0838791 | + | 0.908913i | ||||
\(443\) | 37.9652i | 1.80378i | 0.431965 | + | 0.901891i | \(0.357821\pi\) | ||||
−0.431965 | + | 0.901891i | \(0.642179\pi\) | |||||||
\(444\) | −0.000493170 | 0 | 0.000284732i | −2.34048e−5 | 0 | 1.35128e-5i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.0019 | − | 19.0558i | −0.520954 | − | 0.902318i | ||||
\(447\) | 0.799965 | 0.0378370 | ||||||||
\(448\) | −16.5156 | − | 28.6059i | −0.780290 | − | 1.35150i | ||||
\(449\) | −23.1283 | + | 13.3531i | −1.09149 | + | 0.630173i | −0.933973 | − | 0.357344i | \(-0.883683\pi\) |
−0.157518 | + | 0.987516i | \(0.550349\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.143271 | + | 0.248153i | 0.00674637 | + | 0.0116851i | ||||
\(452\) | −1.64783 | − | 0.951375i | −0.0775074 | − | 0.0447489i | ||||
\(453\) | −0.0649373 | + | 0.112475i | −0.00305102 | + | 0.00528453i | ||||
\(454\) | −22.2873 | −1.04599 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.43290 | 0.0671016 | ||||||||
\(457\) | −2.13563 | + | 3.69903i | −0.0999007 | + | 0.173033i | −0.911643 | − | 0.410982i | \(-0.865186\pi\) |
0.811743 | + | 0.584015i | \(0.198519\pi\) | |||||||
\(458\) | 25.0059 | + | 14.4371i | 1.16845 | + | 0.674604i | ||||
\(459\) | 1.01050 | + | 1.75024i | 0.0471661 | + | 0.0816941i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.8767 | − | 10.3211i | 0.832603 | − | 0.480704i | −0.0221401 | − | 0.999755i | \(-0.507048\pi\) |
0.854743 | + | 0.519051i | \(0.173715\pi\) | |||||||
\(462\) | −0.365855 | − | 0.633679i | −0.0170211 | − | 0.0294814i | ||||
\(463\) | 32.1040 | 1.49200 | 0.745999 | − | 0.665947i | \(-0.231972\pi\) | ||||
0.745999 | + | 0.665947i | \(0.231972\pi\) | |||||||
\(464\) | −3.25341 | − | 5.63507i | −0.151036 | − | 0.261602i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 27.4490 | + | 15.8477i | 1.27155 | + | 0.734131i | ||||
\(467\) | − | 23.3774i | − | 1.08178i | −0.841095 | − | 0.540888i | \(-0.818088\pi\) | ||
0.841095 | − | 0.540888i | \(-0.181912\pi\) | |||||||
\(468\) | 1.47309 | − | 2.08262i | 0.0680934 | − | 0.0962694i | ||||
\(469\) | −24.9700 | −1.15301 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.567304 | + | 0.982600i | −0.0261400 | + | 0.0452758i | ||||
\(472\) | −19.9229 | + | 11.5025i | −0.917027 | + | 0.529446i | ||||
\(473\) | −3.80584 | −0.174993 | ||||||||
\(474\) | 1.07829 | − | 0.622553i | 0.0495277 | − | 0.0285948i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 4.06338i | − | 0.186245i | ||||||
\(477\) | −2.56702 | + | 1.48207i | −0.117536 | + | 0.0678594i | ||||
\(478\) | −19.2939 | − | 11.1393i | −0.882483 | − | 0.509502i | ||||
\(479\) | 4.48198 | + | 2.58767i | 0.204787 | + | 0.118234i | 0.598886 | − | 0.800834i | \(-0.295610\pi\) |
−0.394100 | + | 0.919068i | \(0.628943\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0528814 | + | 0.0747629i | −0.00241119 | + | 0.00340889i | ||||
\(482\) | − | 14.0453i | − | 0.639747i | ||||||
\(483\) | 1.62096 | − | 2.80759i | 0.0737564 | − | 0.127750i | ||||
\(484\) | −1.16573 | + | 2.01911i | −0.0529879 | + | 0.0917777i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 3.81213i | − | 0.172922i | ||||||
\(487\) | −15.3865 | − | 26.6501i | −0.697227 | − | 1.20763i | −0.969424 | − | 0.245391i | \(-0.921083\pi\) |
0.272197 | − | 0.962242i | \(-0.412250\pi\) | |||||||
\(488\) | 8.35661 | + | 14.4741i | 0.378286 | + | 0.655211i | ||||
\(489\) | − | 2.13948i | − | 0.0967508i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.8992 | − | 31.0023i | 0.807778 | − | 1.39911i | −0.106622 | − | 0.994300i | \(-0.534003\pi\) |
0.914400 | − | 0.404813i | \(-0.132663\pi\) | |||||||
\(492\) | −0.00300389 | + | 0.00520289i | −0.000135426 | + | 0.000234565i | ||||
\(493\) | 5.24255i | 0.236113i | ||||||||
\(494\) | −2.84028 | + | 30.7772i | −0.127790 | + | 1.38473i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.60070 | − | 3.23357i | −0.251479 | − | 0.145191i | ||||
\(497\) | 32.4585 | + | 18.7399i | 1.45596 | + | 0.840600i | ||||
\(498\) | 0.0890620 | − | 0.0514200i | 0.00399096 | − | 0.00230418i | ||||
\(499\) | − | 28.8971i | − | 1.29361i | −0.762655 | − | 0.646805i | \(-0.776105\pi\) | ||
0.762655 | − | 0.646805i | \(-0.223895\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.672879 | + | 0.388487i | −0.0300620 | + | 0.0173563i | ||||
\(502\) | −16.9237 | −0.755340 | ||||||||
\(503\) | 6.80974 | − | 3.93161i | 0.303631 | − | 0.175302i | −0.340442 | − | 0.940266i | \(-0.610577\pi\) |
0.644073 | + | 0.764964i | \(0.277243\pi\) | |||||||
\(504\) | 19.0373 | − | 32.9735i | 0.847988 | − | 1.46876i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 11.3322 | 0.503777 | ||||||||
\(507\) | 0.936370 | + | 0.801014i | 0.0415856 | + | 0.0355743i | ||||
\(508\) | − | 0.167154i | − | 0.00741625i | ||||||
\(509\) | −24.2585 | − | 14.0057i | −1.07524 | − | 0.620790i | −0.145631 | − | 0.989339i | \(-0.546521\pi\) |
−0.929608 | + | 0.368549i | \(0.879855\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.3968 | + | 42.2564i | 1.07925 | + | 1.86931i | ||||
\(512\) | −17.4176 | −0.769757 | ||||||||
\(513\) | 1.62754 | + | 2.81898i | 0.0718577 | + | 0.124461i | ||||
\(514\) | 34.3628 | − | 19.8394i | 1.51568 | − | 0.875076i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.0398976 | − | 0.0691046i | −0.00175639 | − | 0.00304216i | ||||
\(517\) | −6.03637 | − | 3.48510i | −0.265479 | − | 0.153275i | ||||
\(518\) | 0.0916696 | − | 0.158776i | 0.00402773 | − | 0.00697623i | ||||
\(519\) | −0.868986 | −0.0381443 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.5609 | −1.64557 | −0.822786 | − | 0.568351i | \(-0.807581\pi\) | ||||
−0.822786 | + | 0.568351i | \(0.807581\pi\) | |||||||
\(522\) | 3.29462 | − | 5.70645i | 0.144202 | − | 0.249765i | ||||
\(523\) | −39.2401 | − | 22.6553i | −1.71585 | − | 0.990647i | −0.926151 | − | 0.377154i | \(-0.876903\pi\) |
−0.789700 | − | 0.613493i | \(-0.789764\pi\) | |||||||
\(524\) | −0.741035 | − | 1.28351i | −0.0323723 | − | 0.0560704i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.3144 | − | 10.5738i | 0.798545 | − | 0.461040i | ||||
\(527\) | 2.60529 | + | 4.51249i | 0.113488 | + | 0.196567i | ||||
\(528\) | −0.447742 | −0.0194855 | ||||||||
\(529\) | 13.6043 | + | 23.5633i | 0.591491 | + | 1.02449i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.5953 | − | 13.0454i | −0.980553 | − | 0.566123i | ||||
\(532\) | − | 6.54460i | − | 0.283744i | ||||||
\(533\) | 0.788741 | + | 0.557894i | 0.0341642 | + | 0.0241651i | ||||
\(534\) | 1.91463 | 0.0828540 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.82149 | + | 11.8152i | −0.294644 | + | 0.510338i | ||||
\(537\) | 0.823922 | − | 0.475691i | 0.0355548 | − | 0.0205276i | ||||
\(538\) | −37.0504 | −1.59736 | ||||||||
\(539\) | 15.0942 | − | 8.71465i | 0.650154 | − | 0.375367i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 19.7445i | − | 0.848882i | −0.905456 | − | 0.424441i | \(-0.860471\pi\) | ||
0.905456 | − | 0.424441i | \(-0.139529\pi\) | |||||||
\(542\) | −24.2414 | + | 13.9958i | −1.04126 | + | 0.601171i | ||||
\(543\) | −1.39746 | − | 0.806824i | −0.0599708 | − | 0.0346242i | ||||
\(544\) | −4.10328 | − | 2.36903i | −0.175927 | − | 0.101571i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.01412 | − | 1.42463i | −0.0861963 | − | 0.0609685i | ||||
\(547\) | − | 11.8312i | − | 0.505867i | −0.967484 | − | 0.252934i | \(-0.918605\pi\) | ||
0.967484 | − | 0.252934i | \(-0.0813954\pi\) | |||||||
\(548\) | −1.92851 | + | 3.34028i | −0.0823820 | + | 0.142690i | ||||
\(549\) | −9.47754 | + | 16.4156i | −0.404491 | + | 0.700600i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.44381i | 0.359718i | ||||||||
\(552\) | −0.885654 | − | 1.53400i | −0.0376959 | − | 0.0652913i | ||||
\(553\) | 21.1982 | + | 36.7164i | 0.901439 | + | 1.56134i | ||||
\(554\) | 33.8952i | 1.44007i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.807237 | + | 1.39818i | −0.0342345 | + | 0.0592958i | ||||
\(557\) | 2.02310 | − | 3.50412i | 0.0857217 | − | 0.148474i | −0.819977 | − | 0.572397i | \(-0.806014\pi\) |
0.905699 | + | 0.423922i | \(0.139347\pi\) | |||||||
\(558\) | − | 6.54905i | − | 0.277244i | ||||||
\(559\) | −11.6552 | + | 5.36754i | −0.492962 | + | 0.227023i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.312415 | + | 0.180373i | 0.0131902 | + | 0.00761536i | ||||
\(562\) | −36.0549 | − | 20.8163i | −1.52088 | − | 0.878083i | ||||
\(563\) | 3.37686 | − | 1.94963i | 0.142318 | − | 0.0821671i | −0.427151 | − | 0.904181i | \(-0.640483\pi\) |
0.569468 | + | 0.822013i | \(0.307149\pi\) | |||||||
\(564\) | − | 0.146141i | − | 0.00615364i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.2577 | − | 5.92226i | 0.431162 | − | 0.248931i | ||||
\(567\) | 43.0516 | 1.80800 | ||||||||
\(568\) | 17.7345 | − | 10.2390i | 0.744123 | − | 0.429619i | ||||
\(569\) | 8.66778 | − | 15.0130i | 0.363372 | − | 0.629379i | −0.625141 | − | 0.780512i | \(-0.714959\pi\) |
0.988514 | + | 0.151133i | \(0.0482920\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.5118 | −1.23503 | −0.617515 | − | 0.786559i | \(-0.711860\pi\) | ||||
−0.617515 | + | 0.786559i | \(0.711860\pi\) | |||||||
\(572\) | 0.0838123 | − | 0.908189i | 0.00350437 | − | 0.0379733i | ||||
\(573\) | 0.367530i | 0.0153538i | ||||||||
\(574\) | −1.67508 | − | 0.967106i | −0.0699163 | − | 0.0403662i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −10.2341 | − | 17.7260i | −0.426422 | − | 0.738585i | ||||
\(577\) | 28.3684 | 1.18099 | 0.590496 | − | 0.807041i | \(-0.298932\pi\) | ||||
0.590496 | + | 0.807041i | \(0.298932\pi\) | |||||||
\(578\) | −3.24100 | − | 5.61357i | −0.134808 | − | 0.233494i | ||||
\(579\) | 0.102934 | − | 0.0594291i | 0.00427780 | − | 0.00246979i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.75087 | + | 3.03260i | 0.0726384 | + | 0.125813i | ||||
\(582\) | 0.422149 | + | 0.243728i | 0.0174986 | + | 0.0101028i | ||||
\(583\) | −0.529891 | + | 0.917797i | −0.0219458 | + | 0.0380113i | ||||
\(584\) | 26.6595 | 1.10318 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.408230 | 0.0168638 | ||||||||
\(587\) | −17.1939 | + | 29.7806i | −0.709667 | + | 1.22918i | 0.255314 | + | 0.966858i | \(0.417821\pi\) |
−0.964981 | + | 0.262320i | \(0.915512\pi\) | |||||||
\(588\) | 0.316473 | + | 0.182716i | 0.0130511 | + | 0.00753507i | ||||
\(589\) | 4.19615 | + | 7.26795i | 0.172899 | + | 0.299471i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.25447 | + | 0.724270i | −0.0516021 | + | 0.0297925i | ||||
\(592\) | −0.0560937 | − | 0.0971572i | −0.00230544 | − | 0.00399314i | ||||
\(593\) | 5.47612 | 0.224877 | 0.112439 | − | 0.993659i | \(-0.464134\pi\) | ||||
0.112439 | + | 0.993659i | \(0.464134\pi\) | |||||||
\(594\) | −0.454095 | − | 0.786515i | −0.0186317 | − | 0.0322711i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.72886 | − | 0.998159i | −0.0708170 | − | 0.0408862i | ||||
\(597\) | 1.25400i | 0.0513229i | ||||||||
\(598\) | 34.7043 | − | 15.9823i | 1.41916 | − | 0.653564i | ||||
\(599\) | −38.6039 | −1.57731 | −0.788657 | − | 0.614833i | \(-0.789223\pi\) | ||||
−0.788657 | + | 0.614833i | \(0.789223\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.28948 | + | 5.69754i | −0.134181 | + | 0.232408i | −0.925284 | − | 0.379275i | \(-0.876174\pi\) |
0.791104 | + | 0.611682i | \(0.209507\pi\) | |||||||
\(602\) | 22.2483 | − | 12.8451i | 0.906772 | − | 0.523525i | ||||
\(603\) | −15.4730 | −0.630109 | ||||||||
\(604\) | 0.280682 | − | 0.162052i | 0.0114208 | − | 0.00659379i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.404750i | 0.0164418i | ||||||||
\(607\) | −14.5201 | + | 8.38318i | −0.589352 | + | 0.340263i | −0.764841 | − | 0.644219i | \(-0.777183\pi\) |
0.175489 | + | 0.984481i | \(0.443849\pi\) | |||||||
\(608\) | −6.60886 | − | 3.81563i | −0.268025 | − | 0.154744i | ||||
\(609\) | −0.583678 | − | 0.336986i | −0.0236518 | − | 0.0136554i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.4013 | − | 2.15959i | −0.946715 | − | 0.0873677i | ||||
\(612\) | − | 2.51793i | − | 0.101781i | ||||||
\(613\) | 14.3894 | − | 24.9232i | 0.581184 | − | 1.00664i | −0.414155 | − | 0.910206i | \(-0.635923\pi\) |
0.995339 | − | 0.0964341i | \(-0.0307437\pi\) | |||||||
\(614\) | −5.12379 | + | 8.87466i | −0.206779 | + | 0.358152i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 13.6129i | − | 0.548481i | ||||||
\(617\) | 18.6645 | + | 32.3279i | 0.751406 | + | 1.30147i | 0.947141 | + | 0.320817i | \(0.103957\pi\) |
−0.195735 | + | 0.980657i | \(0.562709\pi\) | |||||||
\(618\) | 0.393009 | + | 0.680712i | 0.0158091 | + | 0.0273822i | ||||
\(619\) | − | 12.7535i | − | 0.512606i | −0.966597 | − | 0.256303i | \(-0.917496\pi\) | ||
0.966597 | − | 0.256303i | \(-0.0825045\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.01192 | − | 3.48475i | 0.0807356 | − | 0.139838i | ||||
\(622\) | 7.95961 | − | 13.7864i | 0.319151 | − | 0.552786i | ||||
\(623\) | 65.1939i | 2.61194i | ||||||||
\(624\) | −1.37119 | + | 0.631470i | −0.0548914 | + | 0.0252790i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23.0842 | + | 13.3276i | 0.922629 | + | 0.532680i | ||||
\(627\) | 0.503185 | + | 0.290514i | 0.0200953 | + | 0.0116020i | ||||
\(628\) | 2.45209 | − | 1.41571i | 0.0978489 | − | 0.0564931i | ||||
\(629\) | 0.0903896i | 0.00360407i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.8759 | − | 14.3621i | 0.990294 | − | 0.571746i | 0.0849315 | − | 0.996387i | \(-0.472933\pi\) |
0.905362 | + | 0.424641i | \(0.139600\pi\) | |||||||
\(632\) | 23.1643 | 0.921427 | ||||||||
\(633\) | 0.394880 | − | 0.227984i | 0.0156951 | − | 0.00906156i | ||||
\(634\) | 6.11035 | − | 10.5834i | 0.242673 | − | 0.420322i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.0222199 | −0.000881077 | ||||||||
\(637\) | 33.9346 | − | 47.9762i | 1.34454 | − | 1.90089i | ||||
\(638\) | − | 2.35588i | − | 0.0932701i | ||||||
\(639\) | 20.1133 | + | 11.6124i | 0.795671 | + | 0.459381i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.1985 | − | 19.3964i | −0.442315 | − | 0.766112i | 0.555546 | − | 0.831486i | \(-0.312509\pi\) |
−0.997861 | + | 0.0653739i | \(0.979176\pi\) | |||||||
\(642\) | −0.629552 | −0.0248464 | ||||||||
\(643\) | −7.08209 | − | 12.2665i | −0.279290 | − | 0.483745i | 0.691918 | − | 0.721976i | \(-0.256766\pi\) |
−0.971209 | + | 0.238231i | \(0.923433\pi\) | |||||||
\(644\) | −7.00637 | + | 4.04513i | −0.276090 | + | 0.159400i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.2540 | + | 26.4207i | 0.600160 | + | 1.03951i | ||||
\(647\) | −20.4466 | − | 11.8048i | −0.803838 | − | 0.464096i | 0.0409732 | − | 0.999160i | \(-0.486954\pi\) |
−0.844812 | + | 0.535064i | \(0.820287\pi\) | |||||||
\(648\) | 11.7612 | − | 20.3709i | 0.462022 | − | 0.800246i | ||||
\(649\) | −9.32835 | −0.366170 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.669862 | −0.0262540 | ||||||||
\(652\) | −2.66955 | + | 4.62379i | −0.104548 | + | 0.181082i | ||||
\(653\) | 28.8183 | + | 16.6383i | 1.12775 | + | 0.651105i | 0.943367 | − | 0.331750i | \(-0.107639\pi\) |
0.184380 | + | 0.982855i | \(0.440972\pi\) | |||||||
\(654\) | 0.976727 | + | 1.69174i | 0.0381930 | + | 0.0661523i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.02500 | + | 0.591784i | −0.0400195 | + | 0.0231053i | ||||
\(657\) | 15.1178 | + | 26.1848i | 0.589801 | + | 1.02156i | ||||
\(658\) | 47.0502 | 1.83421 | ||||||||
\(659\) | 11.5454 | + | 19.9972i | 0.449745 | + | 0.778982i | 0.998369 | − | 0.0570875i | \(-0.0181814\pi\) |
−0.548624 | + | 0.836069i | \(0.684848\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.6364 | + | 6.71826i | 0.452602 | + | 0.261310i | 0.708929 | − | 0.705280i | \(-0.249179\pi\) |
−0.256326 | + | 0.966590i | \(0.582512\pi\) | |||||||
\(662\) | 37.2972i | 1.44960i | ||||||||
\(663\) | 1.21114 | + | 0.111771i | 0.0470370 | + | 0.00434081i | ||||
\(664\) | 1.91326 | 0.0742491 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.0568043 | − | 0.0983879i | 0.00220112 | − | 0.00381245i | ||||
\(667\) | 9.03957 | − | 5.21900i | 0.350014 | − | 0.202080i | ||||
\(668\) | 1.93895 | 0.0750200 | ||||||||
\(669\) | −1.20779 | + | 0.697316i | −0.0466957 | + | 0.0269598i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.77708i | 0.261626i | ||||||||
\(672\) | 0.527510 | − | 0.304558i | 0.0203491 | − | 0.0117486i | ||||
\(673\) | 1.68463 | + | 0.972620i | 0.0649376 | + | 0.0374918i | 0.532117 | − | 0.846671i | \(-0.321397\pi\) |
−0.467180 | + | 0.884162i | \(0.654730\pi\) | |||||||
\(674\) | −25.3923 | − | 14.6603i | −0.978075 | − | 0.564692i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.02419 | − | 2.89949i | −0.0393919 | − | 0.111519i | ||||
\(677\) | 24.8683i | 0.955768i | 0.878423 | + | 0.477884i | \(0.158596\pi\) | ||||
−0.878423 | + | 0.477884i | \(0.841404\pi\) | |||||||
\(678\) | −0.570140 | + | 0.987512i | −0.0218961 | + | 0.0379252i | ||||
\(679\) | −8.29903 | + | 14.3743i | −0.318488 | + | 0.551637i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.41260i | 0.0541310i | ||||||||
\(682\) | −1.17075 | − | 2.02781i | −0.0448305 | − | 0.0776487i | ||||
\(683\) | 7.31107 | + | 12.6631i | 0.279750 | + | 0.484542i | 0.971323 | − | 0.237766i | \(-0.0764150\pi\) |
−0.691572 | + | 0.722307i | \(0.743082\pi\) | |||||||
\(684\) | − | 4.05545i | − | 0.155064i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −33.5605 | + | 58.1285i | −1.28135 | + | 2.21935i | ||||
\(687\) | 0.915049 | − | 1.58491i | 0.0349113 | − | 0.0604681i | ||||
\(688\) | − | 15.7201i | − | 0.599323i | ||||||
\(689\) | −0.328354 | + | 3.55804i | −0.0125093 | + | 0.135550i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.05231 | − | 1.76225i | −0.116115 | − | 0.0670393i | 0.440817 | − | 0.897597i | \(-0.354689\pi\) |
−0.556933 | + | 0.830558i | \(0.688022\pi\) | |||||||
\(692\) | 1.87803 | + | 1.08428i | 0.0713920 | + | 0.0412182i | ||||
\(693\) | 13.3705 | − | 7.71947i | 0.507904 | − | 0.293238i | ||||
\(694\) | 25.5447i | 0.969665i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.318907 | + | 0.184121i | −0.0120881 | + | 0.00697909i | ||||
\(697\) | 0.953601 | 0.0361202 | ||||||||
\(698\) | −36.7458 | + | 21.2152i | −1.39085 | + | 0.803008i | ||||
\(699\) | 1.00445 | − | 1.73976i | 0.0379919 | − | 0.0658038i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.53457 | 0.0579599 | 0.0289800 | − | 0.999580i | \(-0.490774\pi\) | ||||
0.0289800 | + | 0.999580i | \(0.490774\pi\) | |||||||
\(702\) | −2.49990 | − | 1.76823i | −0.0943526 | − | 0.0667377i | ||||
\(703\) | 0.145584i | 0.00549081i | ||||||||
\(704\) | −6.33766 | − | 3.65905i | −0.238860 | − | 0.137906i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.8912 | − | 27.5244i | −0.598075 | − | 1.03590i | ||||
\(707\) | −13.7819 | −0.518322 | ||||||||
\(708\) | −0.0977915 | − | 0.169380i | −0.00367523 | − | 0.00636568i | ||||
\(709\) | −12.1289 | + | 7.00262i | −0.455510 | + | 0.262989i | −0.710155 | − | 0.704046i | \(-0.751375\pi\) |
0.254644 | + | 0.967035i | \(0.418042\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.1357 | + | 22.7518i | 0.492629 | + | 0.853259i | ||||
\(712\) | 30.8481 | + | 17.8101i | 1.15608 | + | 0.667463i | ||||
\(713\) | 5.18717 | − | 8.98444i | 0.194261 | − | 0.336470i | ||||
\(714\) | −2.43510 | −0.0911314 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.37418 | −0.0887274 | ||||||||
\(717\) | −0.706029 | + | 1.22288i | −0.0263671 | + | 0.0456692i | ||||
\(718\) | −42.2890 | − | 24.4156i | −1.57821 | − | 0.911181i | ||||
\(719\) | −11.2381 | − | 19.4649i | −0.419109 | − | 0.725918i | 0.576741 | − | 0.816927i | \(-0.304324\pi\) |
−0.995850 | + | 0.0910091i | \(0.970991\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.1785 | + | 13.3821i | −0.863213 | + | 0.498376i | ||||
\(722\) | 10.3612 | + | 17.9461i | 0.385603 | + | 0.667884i | ||||
\(723\) | −0.890215 | −0.0331074 | ||||||||
\(724\) | 2.01344 | + | 3.48737i | 0.0748288 | + | 0.129607i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.21001 | + | 0.698600i | 0.0449077 | + | 0.0259275i | ||||
\(727\) | 10.3421i | 0.383566i | 0.981437 | + | 0.191783i | \(0.0614270\pi\) | ||||
−0.981437 | + | 0.191783i | \(0.938573\pi\) | |||||||
\(728\) | −19.1989 | − | 41.6890i | −0.711560 | − | 1.54510i | ||||
\(729\) | 26.5160 | 0.982075 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.33285 | + | 10.9688i | −0.234229 | + | 0.405696i | ||||
\(732\) | −0.123055 | + | 0.0710459i | −0.00454824 | + | 0.00262593i | ||||
\(733\) | −27.3533 | −1.01032 | −0.505159 | − | 0.863026i | \(-0.668566\pi\) | ||||
−0.505159 | + | 0.863026i | \(0.668566\pi\) | |||||||
\(734\) | −7.66516 | + | 4.42548i | −0.282926 | + | 0.163348i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.43355i | 0.347725i | ||||||||
\(737\) | −4.79096 | + | 2.76606i | −0.176477 | + | 0.101889i | ||||
\(738\) | −1.03798 | − | 0.599280i | −0.0382087 | − | 0.0220598i | ||||
\(739\) | −11.6495 | − | 6.72583i | −0.428533 | − | 0.247413i | 0.270189 | − | 0.962807i | \(-0.412914\pi\) |
−0.698721 | + | 0.715394i | \(0.746247\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.95071 | + | 0.180021i | 0.0716610 | + | 0.00661324i | ||||
\(742\) | − | 7.15372i | − | 0.262621i | ||||||
\(743\) | 8.19632 | − | 14.1964i | 0.300694 | − | 0.520817i | −0.675599 | − | 0.737269i | \(-0.736115\pi\) |
0.976293 | + | 0.216452i | \(0.0694484\pi\) | |||||||
\(744\) | −0.182998 | + | 0.316962i | −0.00670903 | + | 0.0116204i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 19.9179i | 0.729248i | ||||||||
\(747\) | 1.08495 | + | 1.87919i | 0.0396963 | + | 0.0687560i | ||||
\(748\) | −0.450122 | − | 0.779635i | −0.0164581 | − | 0.0285063i | ||||
\(749\) | − | 21.4365i | − | 0.783274i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.8328 | + | 23.9590i | −0.504764 | + | 0.874277i | 0.495221 | + | 0.868767i | \(0.335087\pi\) |
−0.999985 | + | 0.00551009i | \(0.998246\pi\) | |||||||
\(752\) | 14.3953 | − | 24.9334i | 0.524942 | − | 0.909226i | ||||
\(753\) | 1.07265i | 0.0390895i | ||||||||
\(754\) | −3.32260 | − | 7.21476i | −0.121002 | − | 0.262746i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.561508 | + | 0.324187i | 0.0204218 | + | 0.0117906i | ||||
\(757\) | −19.9167 | − | 11.4989i | −0.723885 | − | 0.417935i | 0.0922961 | − | 0.995732i | \(-0.470579\pi\) |
−0.816181 | + | 0.577797i | \(0.803913\pi\) | |||||||
\(758\) | −32.9208 | + | 19.0068i | −1.19574 | + | 0.690359i | ||||
\(759\) | − | 0.718251i | − | 0.0260709i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.63759 | − | 3.83221i | 0.240612 | − | 0.138918i | −0.374846 | − | 0.927087i | \(-0.622304\pi\) |
0.615458 | + | 0.788170i | \(0.288971\pi\) | |||||||
\(762\) | −0.100172 | −0.00362885 | ||||||||
\(763\) | −57.6045 | + | 33.2580i | −2.08542 | + | 1.20402i | ||||
\(764\) | 0.458587 | − | 0.794296i | 0.0165911 | − | 0.0287366i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.1916 | −0.585027 | ||||||||
\(767\) | −28.5676 | + | 13.1562i | −1.03152 | + | 0.475042i | ||||
\(768\) | − | 0.530882i | − | 0.0191566i | ||||||
\(769\) | −6.26219 | − | 3.61548i | −0.225820 | − | 0.130377i | 0.382822 | − | 0.923822i | \(-0.374952\pi\) |
−0.608642 | + | 0.793445i | \(0.708286\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.25745 | − | 2.17797i | −0.0452859 | − | 0.0784375i | ||||
\(772\) | −0.296612 | −0.0106753 | ||||||||
\(773\) | 16.7998 | + | 29.0981i | 0.604246 | + | 1.04658i | 0.992170 | + | 0.124893i | \(0.0398588\pi\) |
−0.387924 | + | 0.921691i | \(0.626808\pi\) | |||||||
\(774\) | 13.7864 | − | 7.95961i | 0.495544 | − | 0.286102i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.53438 | + | 7.85378i | 0.162775 | + | 0.281934i | ||||
\(777\) | −0.0100635 | − | 0.00581016i | −0.000361026 | − | 0.000208438i | ||||
\(778\) | 17.2260 | − | 29.8363i | 0.617582 | − | 1.06968i | ||||
\(779\) | 1.53590 | 0.0550293 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.30368 | 0.297129 | ||||||||
\(782\) | 18.8565 | − | 32.6605i | 0.674309 | − | 1.16794i | ||||
\(783\) | −0.724454 | − | 0.418264i | −0.0258899 | − | 0.0149475i | ||||
\(784\) | 35.9960 | + | 62.3470i | 1.28557 | + | 2.22668i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.769182 | + | 0.444088i | −0.0274358 | + | 0.0158401i | ||||
\(787\) | 1.48584 | + | 2.57355i | 0.0529645 | + | 0.0917371i | 0.891292 | − | 0.453430i | \(-0.149800\pi\) |
−0.838328 | + | 0.545167i | \(0.816466\pi\) | |||||||
\(788\) | 3.61484 | 0.128773 | ||||||||
\(789\) | −0.670185 | − | 1.16079i | −0.0238592 | − | 0.0413254i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.6252 | − | 19.4135i | −1.19557 | − | 0.690265i | ||||
\(792\) | − | 8.43544i | − | 0.299740i | ||||||
\(793\) | 9.55802 | + | 20.7545i | 0.339415 | + | 0.737013i | ||||
\(794\) | 31.5349 | 1.11913 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.56469 | − | 2.71012i | 0.0554588 | − | 0.0960575i | ||||
\(797\) | 19.5506 | − | 11.2875i | 0.692517 | − | 0.399825i | −0.112037 | − | 0.993704i | \(-0.535738\pi\) |
0.804554 | + | 0.593879i | \(0.202404\pi\) | |||||||
\(798\) | −3.92205 | −0.138839 | ||||||||
\(799\) | −20.0888 | + | 11.5983i | −0.710692 | + | 0.410318i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40.3983i | 1.42740i | ||||||||
\(802\) | 25.6140 | − | 14.7882i | 0.904462 | − | 0.522191i | ||||
\(803\) | 9.36194 | + | 5.40512i | 0.330376 | + | 0.190742i | ||||
\(804\) | −0.100450 | − | 0.0579946i | −0.00354259 | − | 0.00204531i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.44528 | − | 4.55889i | −0.227025 | − | 0.160580i | ||||
\(807\) | 2.34831i | 0.0826646i | ||||||||
\(808\) | −3.76505 | + | 6.52125i | −0.132454 | + | 0.229417i | ||||
\(809\) | 6.82921 | − | 11.8285i | 0.240102 | − | 0.415869i | −0.720641 | − | 0.693308i | \(-0.756152\pi\) |
0.960743 | + | 0.277439i | \(0.0894857\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.1147i | 0.495636i | 0.968807 | + | 0.247818i | \(0.0797135\pi\) | ||||
−0.968807 | + | 0.247818i | \(0.920287\pi\) | |||||||
\(812\) | 0.840952 | + | 1.45657i | 0.0295116 | + | 0.0511157i | ||||
\(813\) | 0.887075 | + | 1.53646i | 0.0311111 | + | 0.0538860i | ||||
\(814\) | − | 0.0406189i | − | 0.00142369i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.745035 | + | 1.29044i | −0.0260814 | + | 0.0451744i | ||||
\(817\) | −10.1999 | + | 17.6667i | −0.356848 | + | 0.618079i | ||||
\(818\) | 47.6781i | 1.66703i | ||||||||
\(819\) | 30.0594 | − | 42.4975i | 1.05036 | − | 1.48498i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.37318 | − | 0.792808i | −0.0479244 | − | 0.0276692i | 0.475846 | − | 0.879528i | \(-0.342142\pi\) |
−0.523771 | + | 0.851859i | \(0.675475\pi\) | |||||||
\(822\) | 2.00176 | + | 1.15572i | 0.0698195 | + | 0.0403103i | ||||
\(823\) | 16.0776 | − | 9.28238i | 0.560428 | − | 0.323563i | −0.192889 | − | 0.981221i | \(-0.561786\pi\) |
0.753317 | + | 0.657657i | \(0.228452\pi\) | |||||||
\(824\) | 14.6233i | 0.509427i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 54.5320 | − | 31.4840i | 1.89741 | − | 1.09547i | ||||
\(827\) | 9.01023 | 0.313316 | 0.156658 | − | 0.987653i | \(-0.449928\pi\) | ||||
0.156658 | + | 0.987653i | \(0.449928\pi\) | |||||||
\(828\) | −4.34159 | + | 2.50662i | −0.150881 | + | 0.0871110i | ||||
\(829\) | −23.5588 | + | 40.8051i | −0.818233 | + | 1.41722i | 0.0887506 | + | 0.996054i | \(0.471713\pi\) |
−0.906983 | + | 0.421167i | \(0.861621\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.14833 | 0.0745247 | ||||||||
\(832\) | −24.5693 | − | 2.26738i | −0.851787 | − | 0.0786072i | ||||
\(833\) | − | 58.0041i | − | 2.00972i | ||||||
\(834\) | 0.837898 | + | 0.483761i | 0.0290141 | + | 0.0167513i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.724980 | − | 1.25570i | −0.0250740 | − | 0.0434294i | ||||
\(837\) | −0.831425 | −0.0287383 | ||||||||
\(838\) | 22.9782 | + | 39.7994i | 0.793769 | + | 1.37485i | ||||
\(839\) | −46.3121 | + | 26.7383i | −1.59887 | + | 0.923108i | −0.607164 | + | 0.794576i | \(0.707693\pi\) |
−0.991705 | + | 0.128531i | \(0.958974\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.4150 | + | 23.2355i | 0.462586 | + | 0.801223i | ||||
\(842\) | −23.2894 | − | 13.4461i | −0.802605 | − | 0.463384i | ||||
\(843\) | −1.31937 | + | 2.28521i | −0.0454415 | + | 0.0787070i | ||||
\(844\) | −1.13787 | −0.0391672 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 29.1553 | 1.00238 | ||||||||
\(847\) | −23.7876 | + | 41.2014i | −0.817353 | + | 1.41570i | ||||
\(848\) | −3.79098 | − | 2.18872i | −0.130183 | − | 0.0751611i | ||||
\(849\) | −0.375362 | − | 0.650146i | −0.0128824 | − | 0.0223130i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.155856 | − | 0.0899835i | 0.00534268 | − | 0.00308460i | ||||
\(852\) | 0.0870495 | + | 0.150774i | 0.00298227 | + | 0.00516544i | ||||
\(853\) | −27.7756 | −0.951019 | −0.475510 | − | 0.879711i | \(-0.657736\pi\) | ||||
−0.475510 | + | 0.879711i | \(0.657736\pi\) | |||||||
\(854\) | −22.8733 | − | 39.6177i | −0.782707 | − | 1.35569i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.1432 | − | 5.85619i | −0.346688 | − | 0.200160i | ||||
\(857\) | − | 53.6917i | − | 1.83407i | −0.398801 | − | 0.917037i | \(-0.630574\pi\) | ||
0.398801 | − | 0.917037i | \(-0.369426\pi\) | |||||||
\(858\) | −0.544260 | − | 0.0502271i | −0.0185807 | − | 0.00171472i | ||||
\(859\) | −2.08958 | −0.0712955 | −0.0356477 | − | 0.999364i | \(-0.511349\pi\) | ||||
−0.0356477 | + | 0.999364i | \(0.511349\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.0612966 | + | 0.106169i | −0.00208898 | + | 0.00361823i | ||||
\(862\) | 6.34556 | − | 3.66361i | 0.216131 | − | 0.124783i | ||||
\(863\) | 1.75413 | 0.0597113 | 0.0298557 | − | 0.999554i | \(-0.490495\pi\) | ||||
0.0298557 | + | 0.999554i | \(0.490495\pi\) | |||||||
\(864\) | 0.654739 | − | 0.378014i | 0.0222747 | − | 0.0128603i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 28.7727i | − | 0.977737i | ||||||
\(867\) | −0.355797 | + | 0.205419i | −0.0120835 | + | 0.00697640i | ||||
\(868\) | 1.44769 | + | 0.835823i | 0.0491377 | + | 0.0283697i | ||||
\(869\) | 8.13453 | + | 4.69647i | 0.275945 | + | 0.159317i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.7710 | + | 15.2278i | −0.364961 | + | 0.515975i | ||||
\(872\) | 36.3426i | 1.23072i | ||||||||
\(873\) | −5.14261 | + | 8.90726i | −0.174051 | + | 0.301465i | ||||
\(874\) | 30.3709 | − | 52.6040i | 1.02731 | − | 1.77936i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.226653i | 0.00765789i | ||||||||
\(877\) | −10.7836 | − | 18.6777i | −0.364136 | − | 0.630702i | 0.624501 | − | 0.781024i | \(-0.285302\pi\) |
−0.988637 | + | 0.150322i | \(0.951969\pi\) | |||||||
\(878\) | 6.40058 | + | 11.0861i | 0.216009 | + | 0.374139i | ||||
\(879\) | − | 0.0258742i | − | 0.000872716i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.5132 | − | 21.6734i | 0.421579 | − | 0.730196i | −0.574515 | − | 0.818494i | \(-0.694809\pi\) |
0.996094 | + | 0.0882978i | \(0.0281427\pi\) | |||||||
\(882\) | −36.4520 | + | 63.1367i | −1.22740 | + | 2.12592i | ||||
\(883\) | − | 48.7832i | − | 1.64169i | −0.571154 | − | 0.820843i | \(-0.693504\pi\) | ||
0.571154 | − | 0.820843i | \(-0.306496\pi\) | |||||||
\(884\) | −2.47803 | − | 1.75277i | −0.0833452 | − | 0.0589519i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −49.1705 | − | 28.3886i | −1.65192 | − | 0.953734i | ||||
\(887\) | 29.2659 | + | 16.8967i | 0.982651 | + | 0.567334i | 0.903070 | − | 0.429494i | \(-0.141308\pi\) |
0.0795819 | + | 0.996828i | \(0.474641\pi\) | |||||||
\(888\) | −0.00549844 | + | 0.00317453i | −0.000184516 | + | 0.000106530i | ||||
\(889\) | − | 3.41090i | − | 0.114398i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.26025 | − | 4.76906i | 0.276729 | − | 0.159769i | ||||
\(892\) | 3.48031 | 0.116530 | ||||||||
\(893\) | −32.3557 | + | 18.6806i | −1.08274 | + | 0.625121i | ||||
\(894\) | −0.598177 | + | 1.03607i | −0.0200060 | + | 0.0346515i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 62.2508 | 2.07965 | ||||||||
\(897\) | −1.01298 | − | 2.19961i | −0.0338225 | − | 0.0734428i | ||||
\(898\) | − | 39.9394i | − | 1.33279i | ||||||
\(899\) | −1.86780 | − | 1.07837i | −0.0622946 | − | 0.0359658i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.76346 | + | 3.05440i | 0.0587493 | + | 0.101757i | ||||
\(902\) | −0.428526 | −0.0142683 | ||||||||
\(903\) | −0.814139 | − | 1.41013i | −0.0270929 | − | 0.0469262i | ||||
\(904\) | −18.3720 | + | 10.6071i | −0.611043 | + | 0.352786i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.0971143 | − | 0.168207i | −0.00322641 | − | 0.00558830i | ||||
\(907\) | −29.9879 | − | 17.3135i | −0.995731 | − | 0.574885i | −0.0887485 | − | 0.996054i | \(-0.528287\pi\) |
−0.906982 | + | 0.421169i | \(0.861620\pi\) | |||||||
\(908\) | 1.76258 | − | 3.05288i | 0.0584932 | − | 0.101313i | ||||
\(909\) | −8.54015 | −0.283259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.1865 | 1.03326 | 0.516628 | − | 0.856210i | \(-0.327187\pi\) | ||||
0.516628 | + | 0.856210i | \(0.327187\pi\) | |||||||
\(912\) | −1.19997 | + | 2.07842i | −0.0397351 | + | 0.0688233i | ||||
\(913\) | 0.671874 | + | 0.387907i | 0.0222358 | + | 0.0128378i | ||||
\(914\) | −3.19386 | − | 5.53192i | −0.105643 | − | 0.182980i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.95516 | + | 2.28351i | −0.130682 | + | 0.0754493i | ||||
\(917\) | −15.1214 | − | 26.1910i | −0.499352 | − | 0.864903i | ||||
\(918\) | −3.02242 | −0.0997548 | ||||||||
\(919\) | −25.9610 | − | 44.9658i | −0.856374 | − | 1.48328i | −0.875364 | − | 0.483464i | \(-0.839379\pi\) |
0.0189904 | − | 0.999820i | \(-0.493955\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.562490 | + | 0.324753i | 0.0185347 | + | 0.0107010i | ||||
\(922\) | 30.8707i | 1.01667i | ||||||||
\(923\) | 25.4296 | − | 11.7110i | 0.837026 | − | 0.385474i | ||||
\(924\) | 0.115734 | 0.00380736 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −24.0059 | + | 41.5794i | −0.788882 | + | 1.36638i | ||||
\(927\) | −14.3629 | + | 8.29242i | −0.471739 | + | 0.272359i | ||||
\(928\) | 1.96117 | 0.0643784 | ||||||||
\(929\) | 17.7462 | − | 10.2457i | 0.582232 | − | 0.336152i | −0.179788 | − | 0.983705i | \(-0.557541\pi\) |
0.762020 | + | 0.647553i | \(0.224208\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 93.4231i | − | 3.06182i | ||||||
\(932\) | −4.34159 | + | 2.50662i | −0.142213 | + | 0.0821070i | ||||
\(933\) | −0.873806 | − | 0.504492i | −0.0286071 | − | 0.0165163i | ||||
\(934\) | 30.2771 | + | 17.4805i | 0.990698 | + | 0.571980i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −11.8969 | − | 25.8331i | −0.388862 | − | 0.844382i | ||||
\(937\) | − | 39.6806i | − | 1.29631i | −0.761510 | − | 0.648154i | \(-0.775541\pi\) | ||
0.761510 | − | 0.648154i | \(-0.224459\pi\) | |||||||
\(938\) | 18.6714 | − | 32.3399i | 0.609644 | − | 1.05593i | ||||
\(939\) | 0.844727 | − | 1.46311i | 0.0275666 | − | 0.0477468i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.6189i | 0.639557i | 0.947492 | + | 0.319779i | \(0.103609\pi\) | ||||
−0.947492 | + | 0.319779i | \(0.896391\pi\) | |||||||
\(942\) | −0.848408 | − | 1.46949i | −0.0276426 | − | 0.0478784i | ||||
\(943\) | −0.949318 | − | 1.64427i | −0.0309140 | − | 0.0535447i | ||||
\(944\) | − | 38.5309i | − | 1.25408i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.84583 | − | 4.92912i | 0.0925259 | − | 0.160260i | ||||
\(947\) | 28.6062 | − | 49.5474i | 0.929576 | − | 1.61007i | 0.145544 | − | 0.989352i | \(-0.453507\pi\) |
0.784032 | − | 0.620721i | \(-0.213160\pi\) | |||||||
\(948\) | 0.196937i | 0.00639623i | ||||||||
\(949\) | 36.2936 | + | 3.34935i | 1.17814 | + | 0.108725i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.670795 | − | 0.387283i | −0.0217520 | − | 0.0125585i | ||||
\(952\) | −39.2339 | − | 22.6517i | −1.27158 | − | 0.734146i | ||||
\(953\) | 23.7958 | − | 13.7385i | 0.770820 | − | 0.445033i | −0.0623470 | − | 0.998055i | \(-0.519859\pi\) |
0.833167 | + | 0.553021i | \(0.186525\pi\) | |||||||
\(954\) | − | 4.43290i | − | 0.143520i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.05170 | − | 1.76190i | 0.0986991 | − | 0.0569840i | ||||
\(957\) | −0.149319 | −0.00482680 | ||||||||
\(958\) | −6.70283 | + | 3.86988i | −0.216559 | + | 0.125030i | ||||
\(959\) | −39.3527 | + | 68.1609i | −1.27077 | + | 2.20103i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.8564 | 0.930852 | ||||||||
\(962\) | −0.0572867 | − | 0.124393i | −0.00184700 | − | 0.00401061i | ||||
\(963\) | − | 13.2834i | − | 0.428053i | ||||||
\(964\) | 1.92391 | + | 1.11077i | 0.0619649 | + | 0.0357755i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.42416 | + | 4.19877i | 0.0779962 | + | 0.135093i | ||||
\(967\) | −10.3643 | −0.333293 | −0.166647 | − | 0.986017i | \(-0.553294\pi\) | ||||
−0.166647 | + | 0.986017i | \(0.553294\pi\) | |||||||
\(968\) | 12.9970 | + | 22.5114i | 0.417738 | + | 0.723544i | ||||
\(969\) | 1.67458 | − | 0.966821i | 0.0537953 | − | 0.0310588i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.8758 | − | 36.1579i | −0.669935 | − | 1.16036i | −0.977922 | − | 0.208971i | \(-0.932989\pi\) |
0.307987 | − | 0.951391i | \(-0.400345\pi\) | |||||||
\(972\) | 0.522180 | + | 0.301481i | 0.0167489 | + | 0.00966999i | ||||
\(973\) | −16.4723 | + | 28.5308i | −0.528077 | + | 0.914656i | ||||
\(974\) | 46.0212 | 1.47461 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.9929 | −0.896030 | ||||||||
\(977\) | 6.89691 | − | 11.9458i | 0.220652 | − | 0.382180i | −0.734354 | − | 0.678766i | \(-0.762515\pi\) |
0.955006 | + | 0.296586i | \(0.0958482\pi\) | |||||||
\(978\) | 2.77095 | + | 1.59981i | 0.0886051 | + | 0.0511562i | ||||
\(979\) | 7.22187 | + | 12.5087i | 0.230812 | + | 0.399778i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −35.6954 | + | 20.6088i | −1.13967 | + | 0.657987i | ||||
\(982\) | 26.7683 | + | 46.3641i | 0.854212 | + | 1.47954i | ||||
\(983\) | 37.9997 | 1.21200 | 0.606002 | − | 0.795463i | \(-0.292773\pi\) | ||||
0.606002 | + | 0.795463i | \(0.292773\pi\) | |||||||
\(984\) | 0.0334909 | + | 0.0580080i | 0.00106765 | + | 0.00184923i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.78988 | − | 3.92014i | −0.216234 | − | 0.124843i | ||||
\(987\) | − | 2.98211i | − | 0.0949217i | ||||||
\(988\) | −3.99119 | − | 2.82306i | −0.126977 | − | 0.0898134i | ||||
\(989\) | 25.2176 | 0.801873 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.2765 | − | 45.5122i | 0.834700 | − | 1.44574i | −0.0595748 | − | 0.998224i | \(-0.518974\pi\) |
0.894275 | − | 0.447519i | \(-0.147692\pi\) | |||||||
\(992\) | 1.68806 | − | 0.974602i | 0.0535960 | − | 0.0309436i | ||||
\(993\) | 2.36396 | 0.0750179 | ||||||||
\(994\) | −48.5419 | + | 28.0257i | −1.53966 | + | 0.888920i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.0162661i | 0.000515411i | ||||||||
\(997\) | 16.0994 | − | 9.29497i | 0.509872 | − | 0.294375i | −0.222909 | − | 0.974839i | \(-0.571555\pi\) |
0.732781 | + | 0.680465i | \(0.238222\pi\) | |||||||
\(998\) | 37.4260 | + | 21.6079i | 1.18470 | + | 0.683986i | ||||
\(999\) | −0.0124907 | − | 0.00721150i | −0.000395188 | − | 0.000228162i |
(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 | 325.2.m.c.199.1 | 8 | ||
5.2 | odd | 4 | 325.2.n.d.251.1 | 8 | |||
5.3 | odd | 4 | 65.2.m.a.56.4 | yes | 8 | ||
5.4 | even | 2 | 325.2.m.b.199.4 | 8 | |||
13.10 | even | 6 | 325.2.m.b.49.4 | 8 | |||
15.8 | even | 4 | 585.2.bu.c.316.1 | 8 | |||
20.3 | even | 4 | 1040.2.da.b.641.3 | 8 | |||
65.3 | odd | 12 | 845.2.m.g.361.1 | 8 | |||
65.7 | even | 12 | 4225.2.a.bl.1.1 | 4 | |||
65.8 | even | 4 | 845.2.e.n.191.1 | 8 | |||
65.18 | even | 4 | 845.2.e.m.191.4 | 8 | |||
65.23 | odd | 12 | 65.2.m.a.36.4 | ✓ | 8 | ||
65.28 | even | 12 | 845.2.e.m.146.4 | 8 | |||
65.32 | even | 12 | 4225.2.a.bi.1.4 | 4 | |||
65.33 | even | 12 | 845.2.a.l.1.4 | 4 | |||
65.38 | odd | 4 | 845.2.m.g.316.1 | 8 | |||
65.43 | odd | 12 | 845.2.c.g.506.7 | 8 | |||
65.48 | odd | 12 | 845.2.c.g.506.2 | 8 | |||
65.49 | even | 6 | inner | 325.2.m.c.49.1 | 8 | ||
65.58 | even | 12 | 845.2.a.m.1.1 | 4 | |||
65.62 | odd | 12 | 325.2.n.d.101.1 | 8 | |||
65.63 | even | 12 | 845.2.e.n.146.1 | 8 | |||
195.23 | even | 12 | 585.2.bu.c.361.1 | 8 | |||
195.98 | odd | 12 | 7605.2.a.cj.1.1 | 4 | |||
195.188 | odd | 12 | 7605.2.a.cf.1.4 | 4 | |||
260.23 | even | 12 | 1040.2.da.b.881.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.4 | ✓ | 8 | 65.23 | odd | 12 | ||
65.2.m.a.56.4 | yes | 8 | 5.3 | odd | 4 | ||
325.2.m.b.49.4 | 8 | 13.10 | even | 6 | |||
325.2.m.b.199.4 | 8 | 5.4 | even | 2 | |||
325.2.m.c.49.1 | 8 | 65.49 | even | 6 | inner | ||
325.2.m.c.199.1 | 8 | 1.1 | even | 1 | trivial | ||
325.2.n.d.101.1 | 8 | 65.62 | odd | 12 | |||
325.2.n.d.251.1 | 8 | 5.2 | odd | 4 | |||
585.2.bu.c.316.1 | 8 | 15.8 | even | 4 | |||
585.2.bu.c.361.1 | 8 | 195.23 | even | 12 | |||
845.2.a.l.1.4 | 4 | 65.33 | even | 12 | |||
845.2.a.m.1.1 | 4 | 65.58 | even | 12 | |||
845.2.c.g.506.2 | 8 | 65.48 | odd | 12 | |||
845.2.c.g.506.7 | 8 | 65.43 | odd | 12 | |||
845.2.e.m.146.4 | 8 | 65.28 | even | 12 | |||
845.2.e.m.191.4 | 8 | 65.18 | even | 4 | |||
845.2.e.n.146.1 | 8 | 65.63 | even | 12 | |||
845.2.e.n.191.1 | 8 | 65.8 | even | 4 | |||
845.2.m.g.316.1 | 8 | 65.38 | odd | 4 | |||
845.2.m.g.361.1 | 8 | 65.3 | odd | 12 | |||
1040.2.da.b.641.3 | 8 | 20.3 | even | 4 | |||
1040.2.da.b.881.3 | 8 | 260.23 | even | 12 | |||
4225.2.a.bi.1.4 | 4 | 65.32 | even | 12 | |||
4225.2.a.bl.1.1 | 4 | 65.7 | even | 12 | |||
7605.2.a.cf.1.4 | 4 | 195.188 | odd | 12 | |||
7605.2.a.cj.1.1 | 4 | 195.98 | odd | 12 |