Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [891,2,Mod(161,891)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(891, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("891.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.k (of order \(10\), degree \(4\), 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: | \(7.11467082010\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 161.5 | ||
Character | \(\chi\) | \(=\) | 891.161 |
Dual form | 891.2.k.a.404.5 |
$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(650\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.46797 | − | 1.06654i | −1.03801 | − | 0.754159i | −0.0681144 | − | 0.997678i | \(-0.521698\pi\) |
−0.969896 | + | 0.243519i | \(0.921698\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.399387 | + | 1.22919i | 0.199693 | + | 0.614593i | ||||
\(5\) | 0.706314 | + | 0.972158i | 0.315873 | + | 0.434762i | 0.937202 | − | 0.348788i | \(-0.113407\pi\) |
−0.621328 | + | 0.783550i | \(0.713407\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.60425 | + | 1.49601i | −1.74024 | + | 0.565439i | −0.994866 | − | 0.101203i | \(-0.967731\pi\) |
−0.745378 | + | 0.666643i | \(0.767731\pi\) | |||||||
\(8\) | −0.396737 | + | 1.22103i | −0.140268 | + | 0.431700i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 2.18041i | − | 0.689506i | ||||||
\(11\) | 3.30067 | − | 0.324896i | 0.995190 | − | 0.0979599i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.79861 | + | 2.47557i | −0.498844 | + | 0.686599i | −0.981988 | − | 0.188941i | \(-0.939494\pi\) |
0.483145 | + | 0.875541i | \(0.339494\pi\) | |||||||
\(14\) | 8.35446 | + | 2.71453i | 2.23282 | + | 0.725488i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.97590 | − | 2.88866i | 0.993974 | − | 0.722164i | ||||
\(17\) | 1.80866 | − | 1.31407i | 0.438664 | − | 0.318708i | −0.346440 | − | 0.938072i | \(-0.612610\pi\) |
0.785104 | + | 0.619364i | \(0.212610\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.34428 | − | 1.41154i | −0.996645 | − | 0.323830i | −0.235121 | − | 0.971966i | \(-0.575549\pi\) |
−0.761524 | + | 0.648136i | \(0.775549\pi\) | |||||||
\(20\) | −0.912871 | + | 1.25646i | −0.204124 | + | 0.280953i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.19180 | − | 3.04337i | −1.10690 | − | 0.648848i | ||||
\(23\) | − | 1.98738i | − | 0.414397i | −0.978299 | − | 0.207199i | \(-0.933565\pi\) | ||
0.978299 | − | 0.207199i | \(-0.0664346\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.09887 | − | 3.38198i | 0.219775 | − | 0.676397i | ||||
\(26\) | 5.28060 | − | 1.71577i | 1.03561 | − | 0.336490i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.67776 | − | 5.06200i | −0.695030 | − | 0.956627i | ||||
\(29\) | −0.524067 | − | 1.61291i | −0.0973167 | − | 0.299510i | 0.890534 | − | 0.454917i | \(-0.150331\pi\) |
−0.987851 | + | 0.155407i | \(0.950331\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.29749 | − | 3.12231i | −0.771852 | − | 0.560783i | 0.130671 | − | 0.991426i | \(-0.458287\pi\) |
−0.902523 | + | 0.430643i | \(0.858287\pi\) | |||||||
\(32\) | −6.34963 | −1.12247 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.05656 | −0.695694 | ||||||||
\(35\) | −4.70641 | − | 3.41941i | −0.795528 | − | 0.577985i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.344857 | + | 1.06136i | 0.0566941 | + | 0.174486i | 0.975394 | − | 0.220471i | \(-0.0707594\pi\) |
−0.918699 | + | 0.394957i | \(0.870759\pi\) | |||||||
\(38\) | 4.87179 | + | 6.70545i | 0.790309 | + | 1.08777i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.46726 | + | 0.476740i | −0.231994 | + | 0.0753793i | ||||
\(41\) | 3.28550 | − | 10.1117i | 0.513109 | − | 1.57919i | −0.273587 | − | 0.961847i | \(-0.588210\pi\) |
0.786696 | − | 0.617341i | \(-0.211790\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.79055i | − | 0.578054i | −0.957321 | − | 0.289027i | \(-0.906668\pi\) | ||
0.957321 | − | 0.289027i | \(-0.0933317\pi\) | |||||||
\(44\) | 1.71760 | + | 3.92738i | 0.258938 | + | 0.592075i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.11962 | + | 2.91741i | −0.312521 | + | 0.430149i | ||||
\(47\) | 3.10538 | + | 1.00900i | 0.452967 | + | 0.147178i | 0.526610 | − | 0.850107i | \(-0.323463\pi\) |
−0.0736436 | + | 0.997285i | \(0.523463\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.2980 | − | 9.66153i | 1.89971 | − | 1.38022i | ||||
\(50\) | −5.22014 | + | 3.79265i | −0.738239 | + | 0.536362i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.76128 | − | 1.22211i | −0.521595 | − | 0.169477i | ||||
\(53\) | −0.749954 | + | 1.03222i | −0.103014 | + | 0.141787i | −0.857412 | − | 0.514631i | \(-0.827929\pi\) |
0.754398 | + | 0.656417i | \(0.227929\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.64716 | + | 2.97930i | 0.356943 | + | 0.401728i | ||||
\(56\) | − | 6.21546i | − | 0.830575i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.950924 | + | 2.92664i | −0.124862 | + | 0.384287i | ||||
\(59\) | 0.0300536 | − | 0.00976502i | 0.00391265 | − | 0.00127130i | −0.307060 | − | 0.951690i | \(-0.599345\pi\) |
0.310973 | + | 0.950419i | \(0.399345\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.697881 | − | 0.960551i | −0.0893545 | − | 0.122986i | 0.761999 | − | 0.647578i | \(-0.224218\pi\) |
−0.851354 | + | 0.524592i | \(0.824218\pi\) | |||||||
\(62\) | 2.97851 | + | 9.16690i | 0.378271 | + | 1.16420i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.36926 | + | 0.994827i | 0.171158 | + | 0.124353i | ||||
\(65\) | −3.67703 | −0.456079 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.10554 | −0.257233 | −0.128617 | − | 0.991694i | \(-0.541054\pi\) | ||||
−0.128617 | + | 0.991694i | \(0.541054\pi\) | |||||||
\(68\) | 2.33759 | + | 1.69836i | 0.283474 | + | 0.205956i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.26192 | + | 10.0392i | 0.389874 | + | 1.19991i | ||||
\(71\) | −2.26013 | − | 3.11080i | −0.268228 | − | 0.369184i | 0.653563 | − | 0.756873i | \(-0.273274\pi\) |
−0.921790 | + | 0.387688i | \(0.873274\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.69980 | − | 2.17690i | 0.784152 | − | 0.254786i | 0.110540 | − | 0.993872i | \(-0.464742\pi\) |
0.673612 | + | 0.739085i | \(0.264742\pi\) | |||||||
\(74\) | 0.625746 | − | 1.92585i | 0.0727414 | − | 0.223875i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 5.90368i | − | 0.677198i | ||||||
\(77\) | −14.7111 | + | 6.43375i | −1.67648 | + | 0.733194i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.24604 | + | 3.09141i | −0.252700 | + | 0.347811i | −0.916454 | − | 0.400139i | \(-0.868962\pi\) |
0.663755 | + | 0.747950i | \(0.268962\pi\) | |||||||
\(80\) | 5.61646 | + | 1.82490i | 0.627940 | + | 0.204030i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −15.6076 | + | 11.3396i | −1.72357 | + | 1.25225i | ||||
\(83\) | −5.88095 | + | 4.27276i | −0.645518 | + | 0.468996i | −0.861742 | − | 0.507348i | \(-0.830626\pi\) |
0.216223 | + | 0.976344i | \(0.430626\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.55496 | + | 0.830157i | 0.277124 | + | 0.0900431i | ||||
\(86\) | −4.04278 | + | 5.56441i | −0.435945 | + | 0.600026i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.912791 | + | 4.15912i | −0.0973039 | + | 0.443364i | ||||
\(89\) | − | 10.2875i | − | 1.09048i | −0.838281 | − | 0.545238i | \(-0.816439\pi\) | ||
0.838281 | − | 0.545238i | \(-0.183561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.57775 | − | 14.0889i | 0.479879 | − | 1.47692i | ||||
\(92\) | 2.44286 | − | 0.793733i | 0.254686 | − | 0.0827524i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.48246 | − | 4.79320i | −0.359189 | − | 0.494381i | ||||
\(95\) | −1.69618 | − | 5.22031i | −0.174025 | − | 0.535593i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.7345 | − | 8.52561i | −1.19146 | − | 0.865644i | −0.198040 | − | 0.980194i | \(-0.563458\pi\) |
−0.993418 | + | 0.114549i | \(0.963458\pi\) | |||||||
\(98\) | −29.8254 | −3.01282 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.59597 | 0.459597 | ||||||||
\(101\) | −13.0136 | − | 9.45494i | −1.29490 | − | 0.940802i | −0.295011 | − | 0.955494i | \(-0.595323\pi\) |
−0.999892 | + | 0.0146921i | \(0.995323\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.643116 | − | 1.97931i | −0.0633681 | − | 0.195027i | 0.914360 | − | 0.404902i | \(-0.132694\pi\) |
−0.977728 | + | 0.209875i | \(0.932694\pi\) | |||||||
\(104\) | −2.30917 | − | 3.17830i | −0.226433 | − | 0.311658i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.20182 | − | 0.715414i | 0.213859 | − | 0.0694871i | ||||
\(107\) | 0.129361 | − | 0.398133i | 0.0125058 | − | 0.0384889i | −0.944609 | − | 0.328198i | \(-0.893559\pi\) |
0.957115 | + | 0.289709i | \(0.0935586\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.6788i | 1.40597i | 0.711205 | + | 0.702985i | \(0.248150\pi\) | ||||
−0.711205 | + | 0.702985i | \(0.751850\pi\) | |||||||
\(110\) | −0.708407 | − | 7.19682i | −0.0675440 | − | 0.686190i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −13.9846 | + | 19.2481i | −1.32142 | + | 1.81877i | ||||
\(113\) | −3.04019 | − | 0.987818i | −0.285997 | − | 0.0929261i | 0.162505 | − | 0.986708i | \(-0.448043\pi\) |
−0.448503 | + | 0.893782i | \(0.648043\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.93205 | − | 1.40371i | 0.180164 | − | 0.130897i | ||||
\(116\) | 1.77326 | − | 1.28835i | 0.164643 | − | 0.119620i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.0545326 | − | 0.0177187i | −0.00502013 | − | 0.00163114i | ||||
\(119\) | −6.36165 | + | 8.75606i | −0.583172 | + | 0.802667i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.7889 | − | 2.14475i | 0.980808 | − | 0.194977i | ||||
\(122\) | 2.15438i | 0.195048i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.12154 | − | 6.52943i | 0.190520 | − | 0.586360i | ||||
\(125\) | 9.77817 | − | 3.17712i | 0.874587 | − | 0.284170i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.1088 | − | 18.0428i | −1.16322 | − | 1.60104i | −0.698567 | − | 0.715545i | \(-0.746179\pi\) |
−0.464654 | − | 0.885492i | \(-0.653821\pi\) | |||||||
\(128\) | 2.97528 | + | 9.15696i | 0.262980 | + | 0.809368i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.39776 | + | 3.92170i | 0.473415 | + | 0.343956i | ||||
\(131\) | 15.4992 | 1.35417 | 0.677086 | − | 0.735904i | \(-0.263243\pi\) | ||||
0.677086 | + | 0.735904i | \(0.263243\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 22.1138 | 1.91751 | ||||||||
\(134\) | 3.09087 | + | 2.24565i | 0.267011 | + | 0.193995i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.886955 | + | 2.72977i | 0.0760557 | + | 0.234075i | ||||
\(137\) | 10.0751 | + | 13.8672i | 0.860773 | + | 1.18475i | 0.981385 | + | 0.192053i | \(0.0615144\pi\) |
−0.120612 | + | 0.992700i | \(0.538486\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.86040 | + | 3.20384i | −0.836348 | + | 0.271746i | −0.695717 | − | 0.718316i | \(-0.744913\pi\) |
−0.140631 | + | 0.990062i | \(0.544913\pi\) | |||||||
\(140\) | 2.32341 | − | 7.15072i | 0.196364 | − | 0.604346i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.97708i | 0.585503i | ||||||||
\(143\) | −5.13231 | + | 8.75541i | −0.429185 | + | 0.732164i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.19785 | − | 1.64870i | 0.0994759 | − | 0.136917i | ||||
\(146\) | −12.1568 | − | 3.95000i | −1.00611 | − | 0.326904i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.16688 | + | 0.847786i | −0.0959168 | + | 0.0696876i | ||||
\(149\) | −0.0327310 | + | 0.0237805i | −0.00268143 | + | 0.00194817i | −0.589125 | − | 0.808042i | \(-0.700528\pi\) |
0.586444 | + | 0.809990i | \(0.300528\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.61695 | + | 0.850299i | 0.212964 | + | 0.0691964i | 0.413556 | − | 0.910479i | \(-0.364286\pi\) |
−0.200592 | + | 0.979675i | \(0.564286\pi\) | |||||||
\(152\) | 3.44707 | − | 4.74449i | 0.279594 | − | 0.384829i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 28.4573 | + | 6.24544i | 2.29315 | + | 0.503272i | ||||
\(155\) | − | 6.38317i | − | 0.512709i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.651985 | − | 2.00660i | 0.0520341 | − | 0.160145i | −0.921663 | − | 0.387992i | \(-0.873169\pi\) |
0.973697 | + | 0.227848i | \(0.0731688\pi\) | |||||||
\(158\) | 6.59424 | − | 2.14260i | 0.524610 | − | 0.170456i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.48483 | − | 6.17284i | −0.354557 | − | 0.488006i | ||||
\(161\) | 2.97314 | + | 9.15039i | 0.234316 | + | 0.721152i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.8085 | − | 8.57941i | −0.924917 | − | 0.671991i | 0.0198264 | − | 0.999803i | \(-0.493689\pi\) |
−0.944743 | + | 0.327812i | \(0.893689\pi\) | |||||||
\(164\) | 13.7414 | 1.07302 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.1901 | 1.02375 | ||||||||
\(167\) | −0.721863 | − | 0.524464i | −0.0558594 | − | 0.0405843i | 0.559505 | − | 0.828827i | \(-0.310991\pi\) |
−0.615365 | + | 0.788243i | \(0.710991\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.12376 | + | 3.45858i | 0.0864432 | + | 0.266045i | ||||
\(170\) | −2.86520 | − | 3.94362i | −0.219751 | − | 0.302461i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.65930 | − | 1.51390i | 0.355268 | − | 0.115434i | ||||
\(173\) | 4.09368 | − | 12.5991i | 0.311237 | − | 0.957889i | −0.666039 | − | 0.745917i | \(-0.732011\pi\) |
0.977276 | − | 0.211972i | \(-0.0679885\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.2154i | 1.30136i | ||||||||
\(176\) | 12.1846 | − | 10.8263i | 0.918450 | − | 0.816060i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.9721 | + | 15.1018i | −0.822392 | + | 1.13193i | ||||
\(179\) | −19.1587 | − | 6.22502i | −1.43199 | − | 0.465280i | −0.512596 | − | 0.858630i | \(-0.671316\pi\) |
−0.919389 | + | 0.393350i | \(0.871316\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.63758 | − | 2.64286i | 0.270379 | − | 0.196442i | −0.444331 | − | 0.895863i | \(-0.646559\pi\) |
0.714710 | + | 0.699421i | \(0.246559\pi\) | |||||||
\(182\) | −21.7464 | + | 15.7997i | −1.61195 | + | 1.17115i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.42665 | + | 0.788467i | 0.178895 | + | 0.0581265i | ||||
\(185\) | −0.788232 | + | 1.08491i | −0.0579520 | + | 0.0797641i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.54285 | − | 4.92493i | 0.405333 | − | 0.360146i | ||||
\(188\) | 4.22008i | 0.307781i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.07774 | + | 9.47231i | −0.223283 | + | 0.687193i | ||||
\(191\) | 16.9040 | − | 5.49245i | 1.22313 | − | 0.397420i | 0.374910 | − | 0.927061i | \(-0.377673\pi\) |
0.848222 | + | 0.529641i | \(0.177673\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.62015 | + | 4.98270i | 0.260584 | + | 0.358663i | 0.919183 | − | 0.393831i | \(-0.128851\pi\) |
−0.658599 | + | 0.752494i | \(0.728851\pi\) | |||||||
\(194\) | 8.13295 | + | 25.0307i | 0.583912 | + | 1.79710i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 17.1869 | + | 12.4870i | 1.22763 | + | 0.891927i | ||||
\(197\) | 22.5100 | 1.60377 | 0.801886 | − | 0.597477i | \(-0.203830\pi\) | ||||
0.801886 | + | 0.597477i | \(0.203830\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.30680 | 0.659742 | 0.329871 | − | 0.944026i | \(-0.392995\pi\) | ||||
0.329871 | + | 0.944026i | \(0.392995\pi\) | |||||||
\(200\) | 3.69355 | + | 2.68352i | 0.261173 | + | 0.189753i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.01948 | + | 27.7591i | 0.634609 | + | 1.95312i | ||||
\(203\) | 4.82587 | + | 6.64224i | 0.338710 | + | 0.466194i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.1508 | − | 3.94804i | 0.848649 | − | 0.275743i | ||||
\(206\) | −1.16694 | + | 3.59147i | −0.0813046 | + | 0.250230i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.0382i | 1.04271i | ||||||||
\(209\) | −14.7976 | − | 3.24760i | −1.02357 | − | 0.224641i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.23554 | − | 11.3352i | 0.566958 | − | 0.780351i | −0.425232 | − | 0.905084i | \(-0.639808\pi\) |
0.992190 | + | 0.124734i | \(0.0398076\pi\) | |||||||
\(212\) | −1.56832 | − | 0.509577i | −0.107712 | − | 0.0349979i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.614523 | + | 0.446477i | −0.0420079 | + | 0.0305206i | ||||
\(215\) | 3.68502 | − | 2.67732i | 0.251316 | − | 0.182592i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.4577 | + | 7.94680i | 1.66030 | + | 0.539464i | ||||
\(218\) | 15.6555 | − | 21.5480i | 1.06032 | − | 1.45941i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.60487 | + | 4.44375i | −0.175620 | + | 0.299597i | ||||
\(221\) | 6.84094i | 0.460172i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.98529 | + | 15.3432i | −0.333840 | + | 1.02745i | 0.633451 | + | 0.773783i | \(0.281638\pi\) |
−0.967291 | + | 0.253671i | \(0.918362\pi\) | |||||||
\(224\) | 29.2353 | − | 9.49912i | 1.95336 | − | 0.634686i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.40936 | + | 4.69258i | 0.226787 | + | 0.312146i | ||||
\(227\) | −4.54715 | − | 13.9947i | −0.301805 | − | 0.928861i | −0.980850 | − | 0.194764i | \(-0.937606\pi\) |
0.679045 | − | 0.734097i | \(-0.262394\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.9594 | − | 13.0482i | −1.18679 | − | 0.862252i | −0.193867 | − | 0.981028i | \(-0.562103\pi\) |
−0.992921 | + | 0.118775i | \(0.962103\pi\) | |||||||
\(230\) | −4.33330 | −0.285729 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.17733 | 0.142949 | ||||||||
\(233\) | 4.18134 | + | 3.03792i | 0.273929 | + | 0.199021i | 0.716265 | − | 0.697828i | \(-0.245850\pi\) |
−0.442336 | + | 0.896849i | \(0.645850\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.21247 | + | 3.73159i | 0.0790927 | + | 0.243422i | ||||
\(236\) | 0.0240061 | + | 0.0330415i | 0.00156266 | + | 0.00215082i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.6774 | − | 6.06866i | 1.21068 | − | 0.393373i | ||||
\(239\) | −4.22278 | + | 12.9964i | −0.273149 | + | 0.840665i | 0.716555 | + | 0.697531i | \(0.245718\pi\) |
−0.989703 | + | 0.143134i | \(0.954282\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 7.05251i | − | 0.454292i | −0.973861 | − | 0.227146i | \(-0.927061\pi\) | ||
0.973861 | − | 0.227146i | \(-0.0729395\pi\) | |||||||
\(242\) | −18.1252 | − | 8.35837i | −1.16513 | − | 0.537296i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.901971 | − | 1.24146i | 0.0577428 | − | 0.0794761i | ||||
\(245\) | 18.7851 | + | 6.10364i | 1.20013 | + | 0.389947i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3080 | − | 8.21575i | 0.719512 | − | 0.522756i | ||||
\(248\) | 5.51741 | − | 4.00863i | 0.350356 | − | 0.254548i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −17.7426 | − | 5.76492i | −1.12214 | − | 0.364605i | ||||
\(251\) | 3.95496 | − | 5.44354i | 0.249635 | − | 0.343593i | −0.665748 | − | 0.746176i | \(-0.731888\pi\) |
0.915383 | + | 0.402583i | \(0.131888\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.645692 | − | 6.55969i | −0.0405943 | − | 0.412404i | ||||
\(254\) | 40.4673i | 2.53915i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.44469 | − | 19.8347i | 0.402793 | − | 1.23967i | ||||
\(257\) | 13.4589 | − | 4.37306i | 0.839543 | − | 0.272784i | 0.142483 | − | 0.989797i | \(-0.454491\pi\) |
0.697060 | + | 0.717013i | \(0.254491\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.17561 | − | 4.37086i | −0.197323 | − | 0.271592i | ||||
\(260\) | −1.46856 | − | 4.51975i | −0.0910760 | − | 0.280303i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −22.7523 | − | 16.5305i | −1.40564 | − | 1.02126i | ||||
\(263\) | 6.94583 | 0.428298 | 0.214149 | − | 0.976801i | \(-0.431302\pi\) | ||||
0.214149 | + | 0.976801i | \(0.431302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.53319 | −0.0941829 | ||||||||
\(266\) | −32.4624 | − | 23.5853i | −1.99040 | − | 1.44611i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.840926 | − | 2.58811i | −0.0513678 | − | 0.158094i | ||||
\(269\) | −4.05850 | − | 5.58605i | −0.247451 | − | 0.340587i | 0.667165 | − | 0.744910i | \(-0.267507\pi\) |
−0.914617 | + | 0.404322i | \(0.867507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.9581 | + | 4.21033i | −0.787146 | + | 0.255759i | −0.674888 | − | 0.737920i | \(-0.735808\pi\) |
−0.112258 | + | 0.993679i | \(0.535808\pi\) | |||||||
\(272\) | 3.39514 | − | 10.4492i | 0.205861 | − | 0.633575i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 31.1021i | − | 1.87895i | ||||||
\(275\) | 2.52823 | − | 11.5198i | 0.152458 | − | 0.694673i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.85079 | + | 9.42931i | −0.411624 | + | 0.566552i | −0.963614 | − | 0.267299i | \(-0.913869\pi\) |
0.551989 | + | 0.833851i | \(0.313869\pi\) | |||||||
\(278\) | 17.8918 | + | 5.81339i | 1.07308 | + | 0.348664i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.04241 | − | 4.39007i | 0.361103 | − | 0.262357i | ||||
\(281\) | 17.6693 | − | 12.8375i | 1.05406 | − | 0.765823i | 0.0810832 | − | 0.996707i | \(-0.474162\pi\) |
0.972981 | + | 0.230885i | \(0.0741621\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.3258 | − | 7.25408i | −1.32713 | − | 0.431210i | −0.442191 | − | 0.896921i | \(-0.645799\pi\) |
−0.884937 | + | 0.465711i | \(0.845799\pi\) | |||||||
\(284\) | 2.92109 | − | 4.02053i | 0.173335 | − | 0.238575i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.8721 | − | 7.37884i | 0.997667 | − | 0.436320i | ||||
\(287\) | 51.4721i | 3.03830i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.70882 | + | 11.4146i | −0.218166 | + | 0.671445i | ||||
\(290\) | −3.51681 | + | 1.14268i | −0.206514 | + | 0.0671005i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.35162 | + | 7.36588i | 0.313180 | + | 0.431055i | ||||
\(293\) | −0.524298 | − | 1.61362i | −0.0306298 | − | 0.0942689i | 0.934573 | − | 0.355772i | \(-0.115782\pi\) |
−0.965203 | + | 0.261503i | \(0.915782\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0307205 | + | 0.0223197i | 0.00178861 | + | 0.00129950i | ||||
\(296\) | −1.43277 | −0.0832781 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.0734110 | 0.00425258 | ||||||||
\(299\) | 4.91989 | + | 3.57451i | 0.284525 | + | 0.206719i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.67071 | + | 17.4527i | 0.326855 | + | 1.00595i | ||||
\(302\) | −2.93472 | − | 4.03930i | −0.168874 | − | 0.232436i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −21.3498 | + | 6.93699i | −1.22450 | + | 0.397863i | ||||
\(305\) | 0.440884 | − | 1.35690i | 0.0252449 | − | 0.0776959i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.35281i | − | 0.134282i | −0.997743 | − | 0.0671410i | \(-0.978612\pi\) | ||
0.997743 | − | 0.0671410i | \(-0.0213877\pi\) | |||||||
\(308\) | −13.7837 | − | 15.5131i | −0.785399 | − | 0.883941i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.80792 | + | 9.37029i | −0.386664 | + | 0.532197i | ||||
\(311\) | −10.0872 | − | 3.27754i | −0.571995 | − | 0.185852i | 0.00871654 | − | 0.999962i | \(-0.497225\pi\) |
−0.580711 | + | 0.814110i | \(0.697225\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.4957 | − | 14.8910i | 1.15849 | − | 0.841691i | 0.168902 | − | 0.985633i | \(-0.445978\pi\) |
0.989586 | + | 0.143942i | \(0.0459779\pi\) | |||||||
\(314\) | −3.09722 | + | 2.25026i | −0.174786 | + | 0.126990i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.69696 | − | 1.52614i | −0.264225 | − | 0.0858518i | ||||
\(317\) | −15.7600 | + | 21.6917i | −0.885168 | + | 1.21833i | 0.0897951 | + | 0.995960i | \(0.471379\pi\) |
−0.974963 | + | 0.222368i | \(0.928621\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.25380 | − | 5.15343i | −0.126189 | − | 0.288536i | ||||
\(320\) | 2.03380i | 0.113693i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.39479 | − | 16.6035i | 0.300640 | − | 0.925275i | ||||
\(323\) | −9.71216 | + | 3.15567i | −0.540399 | + | 0.175586i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.39590 | + | 8.80320i | 0.354781 | + | 0.488314i | ||||
\(326\) | 8.18427 | + | 25.1886i | 0.453285 | + | 1.39507i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.0433 | + | 8.02340i | 0.609762 | + | 0.443018i | ||||
\(329\) | −15.8074 | −0.871492 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.3237 | −0.952198 | −0.476099 | − | 0.879392i | \(-0.657950\pi\) | ||||
−0.476099 | + | 0.879392i | \(0.657950\pi\) | |||||||
\(332\) | −7.60079 | − | 5.52230i | −0.417148 | − | 0.303076i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.500309 | + | 1.53979i | 0.0273757 | + | 0.0842538i | ||||
\(335\) | −1.48717 | − | 2.04692i | −0.0812530 | − | 0.111835i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.3674 | + | 4.01842i | −0.673696 | + | 0.218897i | −0.625833 | − | 0.779957i | \(-0.715241\pi\) |
−0.0478628 | + | 0.998854i | \(0.515241\pi\) | |||||||
\(338\) | 2.03908 | − | 6.27563i | 0.110911 | − | 0.341349i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.47208i | 0.188300i | ||||||||
\(341\) | −15.1990 | − | 8.90948i | −0.823074 | − | 0.482476i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −26.8543 | + | 36.9618i | −1.45000 | + | 1.99575i | ||||
\(344\) | 4.62838 | + | 1.50385i | 0.249546 | + | 0.0810823i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.4468 | + | 14.1289i | −1.04547 | + | 0.759577i | ||||
\(347\) | −17.1967 | + | 12.4941i | −0.923168 | + | 0.670721i | −0.944310 | − | 0.329056i | \(-0.893270\pi\) |
0.0211427 | + | 0.999776i | \(0.493270\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.87430 | + | 2.88343i | 0.475030 | + | 0.154347i | 0.536740 | − | 0.843747i | \(-0.319655\pi\) |
−0.0617102 | + | 0.998094i | \(0.519655\pi\) | |||||||
\(350\) | 18.3610 | − | 25.2717i | 0.981436 | − | 1.35083i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −20.9580 | + | 2.06297i | −1.11707 | + | 0.109957i | ||||
\(353\) | 9.12141i | 0.485483i | 0.970091 | + | 0.242742i | \(0.0780468\pi\) | ||||
−0.970091 | + | 0.242742i | \(0.921953\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.42783 | − | 4.39440i | 0.0757813 | − | 0.233231i | ||||
\(356\) | 12.6453 | − | 4.10870i | 0.670199 | − | 0.217761i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 21.4851 | + | 29.5716i | 1.13552 | + | 1.56291i | ||||
\(359\) | 2.41692 | + | 7.43851i | 0.127560 | + | 0.392589i | 0.994359 | − | 0.106069i | \(-0.0338263\pi\) |
−0.866799 | + | 0.498658i | \(0.833826\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50897 | + | 1.09633i | 0.0794193 | + | 0.0577015i | ||||
\(362\) | −8.15857 | −0.428805 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 19.1462 | 1.00353 | ||||||||
\(365\) | 6.84845 | + | 4.97569i | 0.358464 | + | 0.260439i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.57224 | + | 23.3050i | 0.395268 | + | 1.21651i | 0.928753 | + | 0.370700i | \(0.120882\pi\) |
−0.533485 | + | 0.845810i | \(0.679118\pi\) | |||||||
\(368\) | −5.74086 | − | 7.90161i | −0.299263 | − | 0.411900i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.31420 | − | 0.751929i | 0.120310 | − | 0.0390909i | ||||
\(371\) | 1.90876 | − | 5.87455i | 0.0990978 | − | 0.304992i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.86129i | − | 0.148152i | −0.997253 | − | 0.0740760i | \(-0.976399\pi\) | ||
0.997253 | − | 0.0740760i | \(-0.0236007\pi\) | |||||||
\(374\) | −13.3894 | + | 1.31796i | −0.692348 | + | 0.0681501i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.46404 | + | 3.39146i | −0.127073 | + | 0.174901i | ||||
\(377\) | 4.93546 | + | 1.60363i | 0.254189 | + | 0.0825911i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.6747 | − | 17.2007i | 1.21609 | − | 0.883540i | 0.220320 | − | 0.975428i | \(-0.429290\pi\) |
0.995769 | + | 0.0918872i | \(0.0292899\pi\) | |||||||
\(380\) | 5.73931 | − | 4.16985i | 0.294420 | − | 0.213909i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −30.6725 | − | 9.96610i | −1.56934 | − | 0.509910i | ||||
\(383\) | 16.7280 | − | 23.0242i | 0.854762 | − | 1.17648i | −0.128031 | − | 0.991770i | \(-0.540866\pi\) |
0.982793 | − | 0.184709i | \(-0.0591343\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.6453 | − | 9.75724i | −0.848321 | − | 0.497275i | ||||
\(386\) | − | 11.1755i | − | 0.568818i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.79296 | − | 17.8289i | 0.294093 | − | 0.905125i | ||||
\(389\) | −13.5825 | + | 4.41321i | −0.688658 | + | 0.223759i | −0.632382 | − | 0.774657i | \(-0.717923\pi\) |
−0.0562761 | + | 0.998415i | \(0.517923\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.61155 | − | 3.59449i | −0.132072 | − | 0.181781i | ||||
\(392\) | 6.52124 | + | 20.0703i | 0.329372 | + | 1.01370i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −33.0440 | − | 24.0079i | −1.66473 | − | 1.20950i | ||||
\(395\) | −4.59175 | −0.231036 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.20687 | 0.110760 | 0.0553798 | − | 0.998465i | \(-0.482363\pi\) | ||||
0.0553798 | + | 0.998465i | \(0.482363\pi\) | |||||||
\(398\) | −13.6621 | − | 9.92609i | −0.684819 | − | 0.497550i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.40039 | − | 16.6207i | −0.270019 | − | 0.831034i | ||||
\(401\) | 18.5405 | + | 25.5188i | 0.925869 | + | 1.27435i | 0.961449 | + | 0.274983i | \(0.0886721\pi\) |
−0.0355802 | + | 0.999367i | \(0.511328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.4590 | − | 5.02293i | 0.770067 | − | 0.250210i | ||||
\(404\) | 6.42442 | − | 19.7723i | 0.319627 | − | 0.983710i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 14.8976i | − | 0.739355i | ||||||
\(407\) | 1.48309 | + | 3.39116i | 0.0735141 | + | 0.168093i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.98413 | + | 5.48368i | −0.197002 | + | 0.271150i | −0.896077 | − | 0.443898i | \(-0.853595\pi\) |
0.699075 | + | 0.715048i | \(0.253595\pi\) | |||||||
\(410\) | −22.0477 | − | 7.16375i | −1.08886 | − | 0.353792i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.17609 | − | 1.58102i | 0.107208 | − | 0.0778913i | ||||
\(413\) | −0.123766 | + | 0.0899212i | −0.00609012 | + | 0.00442473i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.30760 | − | 2.69930i | −0.407804 | − | 0.132504i | ||||
\(416\) | 11.4205 | − | 15.7189i | 0.559935 | − | 0.770685i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.2588 | + | 20.5497i | 0.893066 | + | 1.00512i | ||||
\(419\) | 28.6088i | 1.39763i | 0.715302 | + | 0.698815i | \(0.246289\pi\) | ||||
−0.715302 | + | 0.698815i | \(0.753711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.72842 | + | 5.31954i | −0.0842381 | + | 0.259258i | −0.984300 | − | 0.176504i | \(-0.943521\pi\) |
0.900062 | + | 0.435762i | \(0.143521\pi\) | |||||||
\(422\) | −24.1790 | + | 7.85624i | −1.17702 | + | 0.382436i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.962842 | − | 1.32524i | −0.0467597 | − | 0.0643592i | ||||
\(425\) | −2.45667 | − | 7.56084i | −0.119166 | − | 0.366755i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.65021 | + | 3.37858i | 0.225040 | + | 0.163501i | ||||
\(428\) | 0.541044 | 0.0261524 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.26497 | −0.398572 | ||||||||
\(431\) | −15.7825 | − | 11.4667i | −0.760216 | − | 0.552329i | 0.138760 | − | 0.990326i | \(-0.455688\pi\) |
−0.898977 | + | 0.437997i | \(0.855688\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.96921 | − | 21.4490i | −0.334919 | − | 1.03077i | −0.966762 | − | 0.255678i | \(-0.917701\pi\) |
0.631843 | − | 0.775096i | \(-0.282299\pi\) | |||||||
\(434\) | −27.4276 | − | 37.7508i | −1.31657 | − | 1.81210i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.0429 | + | 5.86250i | −0.864099 | + | 0.280763i | ||||
\(437\) | −2.80527 | + | 8.63372i | −0.134194 | + | 0.413007i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 29.9870i | − | 1.43120i | −0.698509 | − | 0.715601i | \(-0.746153\pi\) | ||
0.698509 | − | 0.715601i | \(-0.253847\pi\) | |||||||
\(440\) | −4.68804 | + | 2.05027i | −0.223494 | + | 0.0977428i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.29615 | − | 10.0423i | 0.347043 | − | 0.477663i | ||||
\(443\) | −30.0035 | − | 9.74873i | −1.42551 | − | 0.463176i | −0.508161 | − | 0.861262i | \(-0.669675\pi\) |
−0.917348 | + | 0.398086i | \(0.869675\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0011 | − | 7.26623i | 0.474098 | − | 0.344452i | ||||
\(446\) | 23.6824 | − | 17.2063i | 1.12139 | − | 0.814740i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.79270 | − | 2.53200i | −0.368171 | − | 0.119626i | ||||
\(449\) | −22.3362 | + | 30.7432i | −1.05411 | + | 1.45086i | −0.168921 | + | 0.985630i | \(0.554028\pi\) |
−0.885190 | + | 0.465229i | \(0.845972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.55911 | − | 34.4430i | 0.355944 | − | 1.62186i | ||||
\(452\) | − | 4.13148i | − | 0.194329i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.25085 | + | 25.3935i | −0.387232 | + | 1.19178i | ||||
\(455\) | 16.9300 | − | 5.50087i | 0.793688 | − | 0.257885i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.0565 | − | 31.7345i | −1.07854 | − | 1.48448i | −0.861123 | − | 0.508397i | \(-0.830238\pi\) |
−0.217413 | − | 0.976080i | \(-0.569762\pi\) | |||||||
\(458\) | 12.4473 | + | 38.3088i | 0.581624 | + | 1.79005i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.49706 | + | 1.81422i | 0.116426 | + | 0.0845885i | ||||
\(461\) | −17.5521 | −0.817482 | −0.408741 | − | 0.912650i | \(-0.634032\pi\) | ||||
−0.408741 | + | 0.912650i | \(0.634032\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.07239 | 0.235734 | 0.117867 | − | 0.993029i | \(-0.462394\pi\) | ||||
0.117867 | + | 0.993029i | \(0.462394\pi\) | |||||||
\(464\) | −6.74278 | − | 4.89892i | −0.313026 | − | 0.227427i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.89801 | − | 8.91915i | −0.134248 | − | 0.413172i | ||||
\(467\) | 9.96792 | + | 13.7197i | 0.461260 | + | 0.634870i | 0.974770 | − | 0.223214i | \(-0.0716548\pi\) |
−0.513509 | + | 0.858084i | \(0.671655\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.69445 | − | 3.14992i | 0.447648 | − | 0.145450i | ||||
\(470\) | 2.20004 | − | 6.77101i | 0.101480 | − | 0.312324i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.0405706i | 0.00186741i | ||||||||
\(473\) | −1.23154 | − | 12.5114i | −0.0566261 | − | 0.575274i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.54762 | + | 13.1412i | −0.438075 | + | 0.602958i | ||||
\(476\) | −13.3036 | − | 4.32260i | −0.609769 | − | 0.198126i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 20.0601 | − | 14.5745i | 0.917526 | − | 0.666622i | ||||
\(479\) | −14.6267 | + | 10.6269i | −0.668310 | + | 0.485556i | −0.869459 | − | 0.494005i | \(-0.835532\pi\) |
0.201149 | + | 0.979561i | \(0.435532\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.24773 | − | 1.05525i | −0.148084 | − | 0.0481153i | ||||
\(482\) | −7.52180 | + | 10.3529i | −0.342608 | + | 0.471560i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.94524 | + | 12.4050i | 0.315693 | + | 0.563862i | ||||
\(485\) | − | 17.4295i | − | 0.791435i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.03498 | + | 24.7291i | −0.364100 | + | 1.12058i | 0.586443 | + | 0.809991i | \(0.300528\pi\) |
−0.950543 | + | 0.310594i | \(0.899472\pi\) | |||||||
\(488\) | 1.44974 | − | 0.471048i | 0.0656265 | − | 0.0213234i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21.0661 | − | 28.9950i | −0.951670 | − | 1.30986i | ||||
\(491\) | −2.26569 | − | 6.97309i | −0.102249 | − | 0.314691i | 0.886826 | − | 0.462104i | \(-0.152905\pi\) |
−0.989075 | + | 0.147413i | \(0.952905\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.06733 | − | 2.22854i | −0.138146 | − | 0.100369i | ||||
\(494\) | −25.3622 | −1.14110 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −26.1057 | −1.17218 | ||||||||
\(497\) | 15.0600 | + | 10.9417i | 0.675533 | + | 0.490804i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.91064 | − | 8.95804i | −0.130298 | − | 0.401017i | 0.864531 | − | 0.502580i | \(-0.167616\pi\) |
−0.994829 | + | 0.101563i | \(0.967616\pi\) | |||||||
\(500\) | 7.81055 | + | 10.7503i | 0.349298 | + | 0.480768i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.6115 | + | 3.77281i | −0.518247 | + | 0.168389i | ||||
\(503\) | 10.3211 | − | 31.7652i | 0.460196 | − | 1.41634i | −0.404728 | − | 0.914437i | \(-0.632634\pi\) |
0.864925 | − | 0.501902i | \(-0.167366\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 19.3294i | − | 0.860149i | ||||||
\(506\) | −6.04832 | + | 10.3181i | −0.268881 | + | 0.458694i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.9424 | − | 23.3193i | 0.751699 | − | 1.03462i | ||||
\(509\) | −19.5002 | − | 6.33601i | −0.864332 | − | 0.280839i | −0.156895 | − | 0.987615i | \(-0.550149\pi\) |
−0.707437 | + | 0.706777i | \(0.750149\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.5909 | + | 20.0459i | −1.22055 | + | 0.886781i | ||||
\(512\) | −15.0364 | + | 10.9246i | −0.664521 | + | 0.482803i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −24.4213 | − | 7.93496i | −1.07718 | − | 0.349996i | ||||
\(515\) | 1.46996 | − | 2.02322i | 0.0647741 | − | 0.0891539i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.5777 | + | 2.32145i | 0.465206 | + | 0.102097i | ||||
\(518\) | 9.80320i | 0.430728i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.45881 | − | 4.48976i | 0.0639732 | − | 0.196889i | ||||
\(521\) | 12.4115 | − | 4.03273i | 0.543757 | − | 0.176677i | −0.0242430 | − | 0.999706i | \(-0.507718\pi\) |
0.568000 | + | 0.823029i | \(0.307718\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.85832 | − | 6.68690i | −0.212439 | − | 0.292398i | 0.689478 | − | 0.724307i | \(-0.257840\pi\) |
−0.901917 | + | 0.431909i | \(0.857840\pi\) | |||||||
\(524\) | 6.19018 | + | 19.0514i | 0.270419 | + | 0.832265i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.1963 | − | 7.40802i | −0.444578 | − | 0.323005i | ||||
\(527\) | −11.8756 | −0.517310 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0503 | 0.828275 | ||||||||
\(530\) | 2.25067 | + | 1.63521i | 0.0977628 | + | 0.0710289i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.83197 | + | 27.1820i | 0.382915 | + | 1.17849i | ||||
\(533\) | 19.1230 | + | 26.3205i | 0.828308 | + | 1.14007i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.478417 | − | 0.155447i | 0.0206838 | − | 0.00672057i | ||||
\(536\) | 0.835347 | − | 2.57093i | 0.0360815 | − | 0.111047i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.5287i | 0.540151i | ||||||||
\(539\) | 40.7532 | − | 36.2100i | 1.75537 | − | 1.55968i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.73469 | − | 7.89312i | 0.246554 | − | 0.339352i | −0.667747 | − | 0.744388i | \(-0.732741\pi\) |
0.914301 | + | 0.405036i | \(0.132741\pi\) | |||||||
\(542\) | 23.5125 | + | 7.63968i | 1.00995 | + | 0.328152i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −11.4843 | + | 8.34383i | −0.492385 | + | 0.357739i | ||||
\(545\) | −14.2701 | + | 10.3678i | −0.611263 | + | 0.444108i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.40406 | + | 2.40572i | 0.316575 | + | 0.102861i | 0.462994 | − | 0.886361i | \(-0.346775\pi\) |
−0.146420 | + | 0.989223i | \(0.546775\pi\) | |||||||
\(548\) | −13.0215 | + | 17.9225i | −0.556250 | + | 0.765613i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15.9978 | + | 14.2143i | −0.682147 | + | 0.606100i | ||||
\(551\) | 7.74667i | 0.330019i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.71655 | − | 17.5937i | 0.243093 | − | 0.748162i | ||||
\(554\) | 20.1135 | − | 6.53527i | 0.854541 | − | 0.277657i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.87623 | − | 10.8407i | −0.334026 | − | 0.459748i | ||||
\(557\) | −1.09093 | − | 3.35755i | −0.0462244 | − | 0.142264i | 0.925281 | − | 0.379283i | \(-0.123829\pi\) |
−0.971505 | + | 0.237019i | \(0.923829\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.38378 | + | 6.81772i | 0.396892 | + | 0.288359i | ||||
\(560\) | −28.5897 | −1.20813 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −39.6298 | −1.67168 | ||||||||
\(563\) | 1.21567 | + | 0.883235i | 0.0512343 | + | 0.0372239i | 0.613108 | − | 0.789999i | \(-0.289919\pi\) |
−0.561873 | + | 0.827223i | \(0.689919\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.18702 | − | 3.65326i | −0.0499381 | − | 0.153694i | ||||
\(566\) | 25.0367 | + | 34.4601i | 1.05237 | + | 1.44847i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.69506 | − | 1.52552i | 0.197000 | − | 0.0640093i | ||||
\(569\) | 4.58518 | − | 14.1117i | 0.192221 | − | 0.591595i | −0.807777 | − | 0.589488i | \(-0.799329\pi\) |
0.999998 | − | 0.00210682i | \(-0.000670621\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.8598i | 1.24960i | 0.780787 | + | 0.624798i | \(0.214819\pi\) | ||||
−0.780787 | + | 0.624798i | \(0.785181\pi\) | |||||||
\(572\) | −12.8118 | − | 2.81177i | −0.535688 | − | 0.117566i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 54.8972 | − | 75.5595i | 2.29136 | − | 3.15379i | ||||
\(575\) | −6.72128 | − | 2.18388i | −0.280297 | − | 0.0910740i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.6394 | + | 14.9954i | −0.859228 | + | 0.624266i | −0.927675 | − | 0.373389i | \(-0.878196\pi\) |
0.0684465 | + | 0.997655i | \(0.478196\pi\) | |||||||
\(578\) | 17.6185 | − | 12.8006i | 0.732835 | − | 0.532436i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.50496 | + | 0.813911i | 0.104013 | + | 0.0337958i | ||||
\(581\) | 20.6853 | − | 28.4708i | 0.858170 | − | 1.18117i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.13999 | + | 3.65069i | −0.0886292 | + | 0.151196i | ||||
\(584\) | 9.04432i | 0.374256i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.951344 | + | 2.92793i | −0.0392996 | + | 0.120952i | ||||
\(587\) | 22.4713 | − | 7.30137i | 0.927491 | − | 0.301360i | 0.193955 | − | 0.981011i | \(-0.437869\pi\) |
0.733536 | + | 0.679651i | \(0.237869\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.2622 | + | 19.6303i | 0.587664 | + | 0.808851i | ||||
\(590\) | −0.0212918 | − | 0.0655293i | −0.000876568 | − | 0.00269780i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.43702 | + | 3.22368i | 0.182360 | + | 0.132493i | ||||
\(593\) | 10.1681 | 0.417553 | 0.208777 | − | 0.977963i | \(-0.433052\pi\) | ||||
0.208777 | + | 0.977963i | \(0.433052\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.0056 | −0.533178 | ||||||||
\(596\) | −0.0423030 | − | 0.0307349i | −0.00173280 | − | 0.00125895i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.40988 | − | 10.4945i | −0.139441 | − | 0.429154i | ||||
\(599\) | −3.58279 | − | 4.93129i | −0.146389 | − | 0.201487i | 0.729525 | − | 0.683954i | \(-0.239741\pi\) |
−0.875914 | + | 0.482467i | \(0.839741\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.3376 | − | 4.33365i | 0.544053 | − | 0.176773i | −0.0240806 | − | 0.999710i | \(-0.507666\pi\) |
0.568133 | + | 0.822937i | \(0.307666\pi\) | |||||||
\(602\) | 10.2896 | − | 31.6680i | 0.419371 | − | 1.29069i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.55632i | 0.144705i | ||||||||
\(605\) | 9.70538 | + | 8.97363i | 0.394580 | + | 0.364830i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.497560 | + | 0.684833i | −0.0201953 | + | 0.0277965i | −0.818995 | − | 0.573800i | \(-0.805469\pi\) |
0.798800 | + | 0.601597i | \(0.205469\pi\) | |||||||
\(608\) | 27.5845 | + | 8.96276i | 1.11870 | + | 0.363488i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.09439 | + | 1.52167i | −0.0847996 | + | 0.0616105i | ||||
\(611\) | −8.08321 | + | 5.87280i | −0.327012 | + | 0.237588i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.1513 | − | 7.84724i | −0.975462 | − | 0.316947i | −0.222443 | − | 0.974946i | \(-0.571403\pi\) |
−0.753019 | + | 0.657999i | \(0.771403\pi\) | |||||||
\(614\) | −2.50937 | + | 3.45385i | −0.101270 | + | 0.139386i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.01938 | − | 20.5152i | −0.0813631 | − | 0.826581i | ||||
\(617\) | − | 10.0839i | − | 0.405962i | −0.979183 | − | 0.202981i | \(-0.934937\pi\) | ||
0.979183 | − | 0.202981i | \(-0.0650630\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.05024 | + | 24.7761i | −0.323566 | + | 0.995835i | 0.648517 | + | 0.761200i | \(0.275389\pi\) |
−0.972084 | + | 0.234635i | \(0.924611\pi\) | |||||||
\(620\) | 7.84611 | − | 2.54935i | 0.315107 | − | 0.102385i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.3121 | + | 15.5698i | 0.453574 | + | 0.624291i | ||||
\(623\) | 15.3903 | + | 47.3664i | 0.616598 | + | 1.89769i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.38931 | − | 3.18902i | −0.175573 | − | 0.127561i | ||||
\(626\) | −45.9690 | −1.83729 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.72689 | 0.108815 | ||||||||
\(629\) | 2.01842 | + | 1.46647i | 0.0804798 | + | 0.0584720i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.44605 | + | 10.6058i | 0.137185 | + | 0.422212i | 0.995923 | − | 0.0902022i | \(-0.0287513\pi\) |
−0.858739 | + | 0.512414i | \(0.828751\pi\) | |||||||
\(632\) | −2.88362 | − | 3.96897i | −0.114704 | − | 0.157877i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 46.2703 | − | 15.0341i | 1.83763 | − | 0.597081i | ||||
\(635\) | 8.28146 | − | 25.4877i | 0.328640 | − | 1.01145i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 50.2973i | 1.99285i | ||||||||
\(638\) | −2.18783 | + | 9.96884i | −0.0866172 | + | 0.394670i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.80053 | + | 9.36013i | −0.268815 | + | 0.369991i | ||||
\(641\) | −10.4988 | − | 3.41127i | −0.414679 | − | 0.134737i | 0.0942448 | − | 0.995549i | \(-0.469956\pi\) |
−0.508923 | + | 0.860812i | \(0.669956\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.7234 | + | 21.5953i | −1.17218 | + | 0.851637i | −0.991268 | − | 0.131863i | \(-0.957904\pi\) |
−0.180909 | + | 0.983500i | \(0.557904\pi\) | |||||||
\(644\) | −10.0601 | + | 7.30909i | −0.396424 | + | 0.288019i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.6228 | + | 5.72600i | 0.693360 | + | 0.225286i | ||||
\(647\) | −1.59821 | + | 2.19975i | −0.0628321 | + | 0.0864810i | −0.839277 | − | 0.543705i | \(-0.817021\pi\) |
0.776445 | + | 0.630186i | \(0.217021\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.0960246 | − | 0.0419955i | 0.00376930 | − | 0.00164847i | ||||
\(650\) | − | 19.7443i | − | 0.774436i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.82952 | − | 17.9414i | 0.228301 | − | 0.702640i | ||||
\(653\) | −42.0798 | + | 13.6726i | −1.64671 | + | 0.535048i | −0.978023 | − | 0.208496i | \(-0.933143\pi\) |
−0.668686 | + | 0.743545i | \(0.733143\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.9473 | + | 15.0677i | 0.427747 | + | 0.588743i | ||||
\(656\) | −16.1465 | − | 49.6939i | −0.630416 | − | 1.94022i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 23.2048 | + | 16.8593i | 0.904618 | + | 0.657244i | ||||
\(659\) | 9.17428 | 0.357379 | 0.178690 | − | 0.983905i | \(-0.442814\pi\) | ||||
0.178690 | + | 0.983905i | \(0.442814\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.89631 | −0.384922 | −0.192461 | − | 0.981305i | \(-0.561647\pi\) | ||||
−0.192461 | + | 0.981305i | \(0.561647\pi\) | |||||||
\(662\) | 25.4307 | + | 18.4765i | 0.988391 | + | 0.718108i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.88398 | − | 8.87599i | −0.111920 | − | 0.344455i | ||||
\(665\) | 15.6193 | + | 21.4981i | 0.605691 | + | 0.833662i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.20547 | + | 1.04152i | −0.124116 | + | 0.0403278i | ||||
\(668\) | 0.356362 | − | 1.09677i | 0.0137880 | − | 0.0424352i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.59095i | 0.177364i | ||||||||
\(671\) | −2.61556 | − | 2.94372i | −0.100972 | − | 0.113641i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.3937 | + | 14.3057i | −0.400649 | + | 0.551446i | −0.960907 | − | 0.276872i | \(-0.910702\pi\) |
0.560258 | + | 0.828318i | \(0.310702\pi\) | |||||||
\(674\) | 22.4408 | + | 7.29146i | 0.864387 | + | 0.280856i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.80243 | + | 2.76263i | −0.146247 | + | 0.106255i | ||||
\(677\) | 9.62387 | − | 6.99215i | 0.369875 | − | 0.268730i | −0.387284 | − | 0.921961i | \(-0.626587\pi\) |
0.757159 | + | 0.653230i | \(0.226587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 66.7830 | + | 21.6991i | 2.56290 | + | 0.832735i | ||||
\(680\) | −2.02729 | + | 2.79033i | −0.0777432 | + | 0.107004i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.8094 | + | 29.2892i | 0.490496 | + | 1.12154i | ||||
\(683\) | 18.2564i | 0.698561i | 0.937018 | + | 0.349280i | \(0.113574\pi\) | ||||
−0.937018 | + | 0.349280i | \(0.886426\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.36490 | + | 19.5892i | −0.243190 | + | 0.748463i | ||||
\(686\) | 78.8425 | − | 25.6175i | 3.01022 | − | 0.978080i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.9496 | − | 15.0708i | −0.417450 | − | 0.574571i | ||||
\(689\) | −1.20647 | − | 3.71312i | −0.0459627 | − | 0.141459i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.5818 | − | 10.5943i | −0.554719 | − | 0.403027i | 0.274804 | − | 0.961500i | \(-0.411387\pi\) |
−0.829522 | + | 0.558474i | \(0.811387\pi\) | |||||||
\(692\) | 17.1216 | 0.650864 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 38.5698 | 1.46409 | ||||||||
\(695\) | −10.0792 | − | 7.32295i | −0.382325 | − | 0.277775i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.34515 | − | 22.6060i | −0.278217 | − | 0.856265i | ||||
\(698\) | −9.95189 | − | 13.6976i | −0.376684 | − | 0.518462i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −21.1610 | + | 6.87562i | −0.799810 | + | 0.259874i | ||||
\(701\) | 2.60431 | − | 8.01524i | 0.0983635 | − | 0.302732i | −0.889752 | − | 0.456444i | \(-0.849123\pi\) |
0.988116 | + | 0.153712i | \(0.0491229\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.09762i | − | 0.192260i | ||||||
\(704\) | 4.84270 | + | 2.83873i | 0.182516 | + | 0.106989i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.72836 | − | 13.3899i | 0.366132 | − | 0.503937i | ||||
\(707\) | 74.0626 | + | 24.0644i | 2.78541 | + | 0.905035i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.7573 | + | 12.1749i | −0.629333 | + | 0.457237i | −0.856169 | − | 0.516696i | \(-0.827162\pi\) |
0.226836 | + | 0.973933i | \(0.427162\pi\) | |||||||
\(710\) | −6.78282 | + | 4.92801i | −0.254555 | + | 0.184945i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.5614 | + | 4.08144i | 0.470758 | + | 0.152959i | ||||
\(713\) | −6.20521 | + | 8.54074i | −0.232387 | + | 0.319853i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.1367 | + | 1.19465i | −0.453885 | + | 0.0446774i | ||||
\(716\) | − | 26.0358i | − | 0.973002i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.38552 | − | 13.4972i | 0.163666 | − | 0.503712i | ||||
\(719\) | 34.3009 | − | 11.1450i | 1.27921 | − | 0.415640i | 0.410906 | − | 0.911678i | \(-0.365212\pi\) |
0.868301 | + | 0.496038i | \(0.165212\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.92214 | + | 8.15112i | 0.220552 | + | 0.303564i | ||||
\(722\) | −1.04584 | − | 3.21875i | −0.0389220 | − | 0.119790i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.70137 | + | 3.41574i | 0.174725 | + | 0.126945i | ||||
\(725\) | −6.03072 | −0.223975 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.9857 | −0.778316 | −0.389158 | − | 0.921171i | \(-0.627234\pi\) | ||||
−0.389158 | + | 0.921171i | \(0.627234\pi\) | |||||||
\(728\) | 15.3868 | + | 11.1792i | 0.570273 | + | 0.414327i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.74653 | − | 14.6083i | −0.175677 | − | 0.540678i | ||||
\(731\) | −4.98104 | − | 6.85581i | −0.184230 | − | 0.253571i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.6350 | − | 12.5533i | 1.42701 | − | 0.463665i | 0.509191 | − | 0.860653i | \(-0.329945\pi\) |
0.917824 | + | 0.396988i | \(0.129945\pi\) | |||||||
\(734\) | 13.7399 | − | 42.2871i | 0.507149 | − | 1.56084i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.6191i | 0.465147i | ||||||||
\(737\) | −6.94971 | + | 0.684083i | −0.255996 | + | 0.0251985i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.159730 | + | 0.219850i | −0.00587578 | + | 0.00808731i | −0.811945 | − | 0.583734i | \(-0.801591\pi\) |
0.806069 | + | 0.591822i | \(0.201591\pi\) | |||||||
\(740\) | −1.64836 | − | 0.535586i | −0.0605951 | − | 0.0196885i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.06745 | + | 6.58789i | −0.332877 | + | 0.241849i | ||||
\(743\) | −16.6356 | + | 12.0864i | −0.610300 | + | 0.443409i | −0.849520 | − | 0.527557i | \(-0.823108\pi\) |
0.239220 | + | 0.970965i | \(0.423108\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.0462368 | − | 0.0150232i | −0.00169398 | − | 0.000550409i | ||||
\(746\) | −3.05169 | + | 4.20029i | −0.111730 | + | 0.153783i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.26740 | + | 4.84624i | 0.302286 | + | 0.177196i | ||||
\(749\) | 2.02663i | 0.0740514i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.1057 | + | 49.5682i | −0.587705 | + | 1.80877i | 0.000422486 | 1.00000i | \(0.499866\pi\) | |
−0.588127 | + | 0.808769i | \(0.700134\pi\) | |||||||
\(752\) | 15.2613 | − | 4.95871i | 0.556524 | − | 0.180825i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.53477 | − | 7.61795i | −0.201564 | − | 0.277430i | ||||
\(755\) | 1.02176 | + | 3.14467i | 0.0371858 | + | 0.114446i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.2153 | + | 21.9527i | 1.09819 | + | 0.797884i | 0.980764 | − | 0.195197i | \(-0.0625347\pi\) |
0.117429 | + | 0.993081i | \(0.462535\pi\) | |||||||
\(758\) | −53.0990 | −1.92864 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.04711 | 0.255625 | ||||||||
\(761\) | 36.1152 | + | 26.2392i | 1.30918 | + | 0.951171i | 1.00000 | 0.000166228i | \(5.29120e-5\pi\) | |
0.309175 | + | 0.951005i | \(0.399947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.9596 | − | 67.5847i | −0.794991 | − | 2.44673i | ||||
\(764\) | 13.5025 | + | 18.5846i | 0.488503 | + | 0.672367i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −49.1124 | + | 15.9576i | −1.77450 | + | 0.576571i | ||||
\(767\) | −0.0298807 | + | 0.0919633i | −0.00107893 | + | 0.00332060i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.3246i | 0.805047i | 0.915410 | + | 0.402524i | \(0.131867\pi\) | ||||
−0.915410 | + | 0.402524i | \(0.868133\pi\) | |||||||
\(770\) | 14.0282 | + | 32.0762i | 0.505542 | + | 1.15595i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.67883 | + | 6.43986i | −0.168395 | + | 0.231776i | ||||
\(773\) | −19.1268 | − | 6.21468i | −0.687944 | − | 0.223526i | −0.0558738 | − | 0.998438i | \(-0.517794\pi\) |
−0.632070 | + | 0.774911i | \(0.717794\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.2820 | + | 11.1030i | −0.548946 | + | 0.398832i | ||||
\(776\) | 15.0655 | − | 10.9458i | 0.540822 | − | 0.392930i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.6455 | + | 8.00781i | 0.883584 | + | 0.287094i | ||||
\(779\) | −28.5463 | + | 39.2906i | −1.02278 | + | 1.40773i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.47063 | − | 9.53343i | −0.303103 | − | 0.341133i | ||||
\(782\) | 8.06192i | 0.288294i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 24.9624 | − | 76.8265i | 0.891516 | − | 2.74380i | ||||
\(785\) | 2.41124 | − | 0.783461i | 0.0860610 | − | 0.0279629i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.4658 | − | 28.1688i | −0.729527 | − | 1.00411i | −0.999153 | − | 0.0411431i | \(-0.986900\pi\) |
0.269626 | − | 0.962965i | \(-0.413100\pi\) | |||||||
\(788\) | 8.99021 | + | 27.6690i | 0.320263 | + | 0.985668i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.74055 | + | 4.89730i | 0.239818 | + | 0.174238i | ||||
\(791\) | 15.4756 | 0.550249 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.63312 | 0.129016 | ||||||||
\(794\) | −3.23961 | − | 2.35372i | −0.114970 | − | 0.0835303i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.71701 | + | 11.4398i | 0.131746 | + | 0.405473i | ||||
\(797\) | −0.462428 | − | 0.636478i | −0.0163800 | − | 0.0225452i | 0.800748 | − | 0.599001i | \(-0.204435\pi\) |
−0.817128 | + | 0.576456i | \(0.804435\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.94247 | − | 2.25574i | 0.245607 | − | 0.0798025i | ||||
\(800\) | −6.97744 | + | 21.4743i | −0.246690 | + | 0.759233i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 57.2351i | − | 2.02104i | ||||||
\(803\) | 21.4066 | − | 9.36196i | 0.755421 | − | 0.330376i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.79565 | + | 9.35341i | −0.239515 | + | 0.329665i | ||||
\(806\) | −28.0505 | − | 9.11415i | −0.988036 | − | 0.321032i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.7078 | − | 12.1389i | 0.587777 | − | 0.427045i | ||||
\(809\) | −24.9035 | + | 18.0934i | −0.875560 | + | 0.636131i | −0.932073 | − | 0.362270i | \(-0.882002\pi\) |
0.0565132 | + | 0.998402i | \(0.482002\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.4535 | + | 13.4691i | 1.45563 | + | 0.472963i | 0.926732 | − | 0.375723i | \(-0.122606\pi\) |
0.528898 | + | 0.848686i | \(0.322606\pi\) | |||||||
\(812\) | −6.23716 | + | 8.58472i | −0.218881 | + | 0.301264i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.43968 | − | 6.55989i | 0.0504608 | − | 0.229924i | ||||
\(815\) | − | 17.5395i | − | 0.614383i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.35052 | + | 16.4672i | −0.187191 | + | 0.576115i | ||||
\(818\) | 11.6971 | − | 3.80063i | 0.408981 | − | 0.132886i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.70574 | + | 13.3588i | 0.338939 | + | 0.466510i | ||||
\(821\) | −12.0394 | − | 37.0534i | −0.420178 | − | 1.29317i | −0.907537 | − | 0.419972i | \(-0.862040\pi\) |
0.487359 | − | 0.873202i | \(-0.337960\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.4030 | − | 22.0890i | −1.05978 | − | 0.769975i | −0.0857325 | − | 0.996318i | \(-0.527323\pi\) |
−0.974048 | + | 0.226343i | \(0.927323\pi\) | |||||||
\(824\) | 2.67195 | 0.0930816 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.277589 | 0.00965857 | ||||||||
\(827\) | −36.8905 | − | 26.8025i | −1.28281 | − | 0.932015i | −0.283175 | − | 0.959068i | \(-0.591388\pi\) |
−0.999634 | + | 0.0270532i | \(0.991388\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.83146 | + | 27.1804i | 0.306729 | + | 0.944016i | 0.979026 | + | 0.203734i | \(0.0653078\pi\) |
−0.672297 | + | 0.740282i | \(0.734692\pi\) | |||||||
\(830\) | 9.31637 | + | 12.8229i | 0.323376 | + | 0.445089i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.92553 | + | 1.60040i | −0.170762 | + | 0.0554839i | ||||
\(833\) | 11.3556 | − | 34.9488i | 0.393447 | − | 1.21090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.07220i | − | 0.0371051i | ||||||
\(836\) | −1.91808 | − | 19.4861i | −0.0663382 | − | 0.673941i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30.5125 | − | 41.9968i | 1.05404 | − | 1.45076i | ||||
\(839\) | 5.41296 | + | 1.75878i | 0.186876 | + | 0.0607197i | 0.400960 | − | 0.916096i | \(-0.368677\pi\) |
−0.214084 | + | 0.976815i | \(0.568677\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.1347 | − | 15.3552i | 0.728781 | − | 0.529491i | ||||
\(842\) | 8.21078 | − | 5.96548i | 0.282962 | − | 0.205584i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17.2223 | + | 5.59587i | 0.592816 | + | 0.192618i | ||||
\(845\) | −2.56856 | + | 3.53532i | −0.0883612 | + | 0.121619i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −46.4662 | + | 26.0153i | −1.59660 | + | 0.893895i | ||||
\(848\) | 6.27037i | 0.215325i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.45764 | + | 13.7192i | −0.152896 | + | 0.470565i | ||||
\(851\) | 2.10932 | − | 0.685361i | 0.0723067 | − | 0.0234939i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.7319 | + | 20.2767i | 0.504410 | + | 0.694261i | 0.982964 | − | 0.183797i | \(-0.0588390\pi\) |
−0.478554 | + | 0.878058i | \(0.658839\pi\) | |||||||
\(854\) | −3.22297 | − | 9.91929i | −0.110288 | − | 0.339431i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.434810 | + | 0.315908i | 0.0148615 | + | 0.0107975i | ||||
\(857\) | −35.9164 | −1.22688 | −0.613440 | − | 0.789741i | \(-0.710215\pi\) | ||||
−0.613440 | + | 0.789741i | \(0.710215\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.7324 | −0.536783 | −0.268391 | − | 0.963310i | \(-0.586492\pi\) | ||||
−0.268391 | + | 0.963310i | \(0.586492\pi\) | |||||||
\(860\) | 4.76268 | + | 3.46029i | 0.162406 | + | 0.117995i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.9385 | + | 33.6654i | 0.372568 | + | 1.14665i | ||||
\(863\) | −16.0883 | − | 22.1436i | −0.547652 | − | 0.753778i | 0.442039 | − | 0.896996i | \(-0.354255\pi\) |
−0.989691 | + | 0.143217i | \(0.954255\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.1397 | − | 4.91919i | 0.514765 | − | 0.167257i | ||||
\(866\) | −12.6457 | + | 38.9194i | −0.429718 | + | 1.32254i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 33.2370i | 1.12814i | ||||||||
\(869\) | −6.40906 | + | 10.9335i | −0.217413 | + | 0.370893i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.78704 | − | 5.21242i | 0.128319 | − | 0.176616i | ||||
\(872\) | −17.9232 | − | 5.82361i | −0.606957 | − | 0.197212i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.3263 | − | 9.68210i | 0.450768 | − | 0.327502i | ||||
\(875\) | −40.2682 | + | 29.2565i | −1.36131 | + | 0.989051i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.4957 | + | 16.0821i | 1.67135 | + | 0.543055i | 0.983203 | − | 0.182516i | \(-0.0584242\pi\) |
0.688147 | + | 0.725571i | \(0.258424\pi\) | |||||||
\(878\) | −31.9824 | + | 44.0200i | −1.07935 | + | 1.48560i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 19.1310 | + | 4.19863i | 0.644906 | + | 0.141536i | ||||
\(881\) | − | 39.9758i | − | 1.34682i | −0.739270 | − | 0.673409i | \(-0.764829\pi\) | ||
0.739270 | − | 0.673409i | \(-0.235171\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.74452 | + | 17.6798i | −0.193318 | + | 0.594973i | 0.806674 | + | 0.590997i | \(0.201266\pi\) |
−0.999992 | + | 0.00397571i | \(0.998734\pi\) | |||||||
\(884\) | −8.40880 | + | 2.73218i | −0.282818 | + | 0.0918933i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33.6468 | + | 46.3108i | 1.13039 | + | 1.55584i | ||||
\(887\) | −16.8498 | − | 51.8583i | −0.565760 | − | 1.74123i | −0.665681 | − | 0.746236i | \(-0.731859\pi\) |
0.0999207 | − | 0.994995i | \(-0.468141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 87.3486 | + | 63.4625i | 2.92958 | + | 2.12846i | ||||
\(890\) | −22.4310 | −0.751890 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −20.8507 | −0.698132 | ||||||||
\(893\) | −12.0664 | − | 8.76675i | −0.403787 | − | 0.293368i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.48032 | − | 23.0221i | −0.250040 | − | 0.769543i | ||||
\(896\) | −27.3978 | − | 37.7099i | −0.915297 | − | 1.25980i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 65.5777 | − | 21.3075i | 2.18836 | − | 0.711040i | ||||
\(899\) | −2.78384 | + | 8.56777i | −0.0928461 | + | 0.285751i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.85243i | 0.0950281i | ||||||||
\(902\) | −47.8314 | + | 42.4991i | −1.59261 | + | 1.41507i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.41231 | − | 3.32027i | 0.0802324 | − | 0.110430i | ||||
\(905\) | 5.13855 | + | 1.66962i | 0.170811 | + | 0.0554999i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.0586 | − | 7.30800i | 0.333990 | − | 0.242658i | −0.408132 | − | 0.912923i | \(-0.633820\pi\) |
0.742122 | + | 0.670265i | \(0.233820\pi\) | |||||||
\(908\) | 15.3860 | − | 11.1786i | 0.510603 | − | 0.370975i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −30.7195 | − | 9.98139i | −1.01834 | − | 0.330880i | ||||
\(911\) | 26.4433 | − | 36.3961i | 0.876106 | − | 1.20586i | −0.101379 | − | 0.994848i | \(-0.532325\pi\) |
0.977484 | − | 0.211008i | \(-0.0676747\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0229 | + | 16.0137i | −0.596471 | + | 0.529976i | ||||
\(914\) | 71.1759i | 2.35429i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.86599 | − | 27.2867i | 0.292941 | − | 0.901578i | ||||
\(917\) | −71.3622 | + | 23.1870i | −2.35659 | + | 0.765702i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.6185 | + | 18.7442i | 0.449232 | + | 0.618315i | 0.972232 | − | 0.234017i | \(-0.0751872\pi\) |
−0.523000 | + | 0.852333i | \(0.675187\pi\) | |||||||
\(920\) | 0.947464 | + | 2.91599i | 0.0312370 | + | 0.0961375i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25.7659 | + | 18.7200i | 0.848555 | + | 0.616512i | ||||
\(923\) | 11.7661 | 0.387285 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.96846 | 0.130482 | ||||||||
\(926\) | −7.44610 | − | 5.40991i | −0.244694 | − | 0.177781i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.32763 | + | 10.2414i | 0.109235 | + | 0.336190i | ||||
\(929\) | −6.79920 | − | 9.35830i | −0.223075 | − | 0.307036i | 0.682781 | − | 0.730624i | \(-0.260771\pi\) |
−0.905855 | + | 0.423588i | \(0.860771\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −71.4077 | + | 23.2018i | −2.34029 | + | 0.760407i | ||||
\(932\) | −2.06420 | + | 6.35296i | −0.0676151 | + | 0.208098i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 30.7712i | − | 1.00687i | ||||||
\(935\) | 8.70280 | + | 1.90998i | 0.284612 | + | 0.0624630i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.1544 | − | 20.8582i | 0.495071 | − | 0.681407i | −0.486242 | − | 0.873824i | \(-0.661633\pi\) |
0.981313 | + | 0.192417i | \(0.0616326\pi\) | |||||||
\(938\) | −17.5907 | − | 5.71555i | −0.574356 | − | 0.186619i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.10258 | + | 2.98070i | −0.133811 | + | 0.0972197i | ||||
\(941\) | 47.8599 | − | 34.7722i | 1.56019 | − | 1.13354i | 0.624331 | − | 0.781160i | \(-0.285372\pi\) |
0.935856 | − | 0.352383i | \(-0.114628\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.0959 | − | 6.52954i | −0.654411 | − | 0.212631i | ||||
\(944\) | 0.0912824 | − | 0.125639i | 0.00297099 | − | 0.00408921i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.5361 | + | 19.6798i | −0.375069 | + | 0.639845i | ||||
\(947\) | 0.120799i | 0.00392545i | 0.999998 | + | 0.00196272i | \(0.000624755\pi\) | ||||
−0.999998 | + | 0.00196272i | \(0.999375\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.66124 | + | 20.5012i | −0.216233 | + | 0.665497i | ||||
\(950\) | 28.0312 | − | 9.10789i | 0.909453 | − | 0.295499i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.16752 | − | 11.2416i | −0.264711 | − | 0.364343i | ||||
\(953\) | 2.50261 | + | 7.70223i | 0.0810674 | + | 0.249500i | 0.983373 | − | 0.181597i | \(-0.0581267\pi\) |
−0.902306 | + | 0.431097i | \(0.858127\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.2791 | + | 12.5540i | 0.559138 | + | 0.406237i | ||||
\(956\) | −17.6615 | −0.571213 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 32.8055 | 1.05990 | ||||||||
\(959\) | −67.1337 | − | 48.7755i | −2.16786 | − | 1.57504i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.859922 | − | 2.64657i | −0.0277394 | − | 0.0853732i | ||||
\(962\) | 3.64210 | + | 5.01292i | 0.117426 | + | 0.161623i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.66885 | − | 2.81668i | 0.279205 | − | 0.0907192i | ||||
\(965\) | −2.28702 | + | 7.03871i | −0.0736216 | + | 0.226584i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 9.94567i | − | 0.319831i | −0.987131 | − | 0.159916i | \(-0.948878\pi\) | ||
0.987131 | − | 0.159916i | \(-0.0511222\pi\) | |||||||
\(968\) | −1.66154 | + | 14.0245i | −0.0534040 | + | 0.450763i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.5893 | + | 25.5860i | −0.596867 | + | 0.821518i | ||||
\(971\) | 36.6171 | + | 11.8976i | 1.17510 | + | 0.381813i | 0.830544 | − | 0.556953i | \(-0.188030\pi\) |
0.344555 | + | 0.938766i | \(0.388030\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40.6068 | − | 29.5025i | 1.30179 | − | 0.945808i | ||||
\(974\) | 38.1698 | − | 27.7320i | 1.22304 | − | 0.888589i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.54940 | − | 1.80311i | −0.177632 | − | 0.0577161i | ||||
\(977\) | −11.9388 | + | 16.4324i | −0.381956 | + | 0.525718i | −0.956101 | − | 0.293036i | \(-0.905334\pi\) |
0.574145 | + | 0.818753i | \(0.305334\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.34238 | − | 33.9558i | −0.106823 | − | 1.08523i | ||||
\(980\) | 25.5281i | 0.815464i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.11112 | + | 12.6527i | −0.131191 | + | 0.403765i | ||||
\(983\) | 9.24723 | − | 3.00461i | 0.294941 | − | 0.0958321i | −0.157809 | − | 0.987470i | \(-0.550443\pi\) |
0.452750 | + | 0.891638i | \(0.350443\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.8991 | + | 21.8833i | 0.506589 | + | 0.697260i | ||||
\(986\) | 2.12591 | + | 6.54287i | 0.0677027 | + | 0.208367i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.6150 | + | 10.6184i | 0.464964 | + | 0.337816i | ||||
\(989\) | −7.53327 | −0.239544 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.9196 | −0.728065 | −0.364032 | − | 0.931386i | \(-0.618600\pi\) | ||||
−0.364032 | + | 0.931386i | \(0.618600\pi\) | |||||||
\(992\) | 27.2875 | + | 19.8255i | 0.866378 | + | 0.629460i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.4378 | − | 32.1242i | −0.331067 | − | 1.01892i | ||||
\(995\) | 6.57352 | + | 9.04768i | 0.208395 | + | 0.286831i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.4494 | + | 6.64441i | −0.647639 | + | 0.210431i | −0.614373 | − | 0.789016i | \(-0.710591\pi\) |
−0.0332659 | + | 0.999447i | \(0.510591\pi\) | |||||||
\(998\) | −5.28139 | + | 16.2544i | −0.167179 | + | 0.514525i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 891.2.k.a.161.5 | 80 | ||
3.2 | odd | 2 | inner | 891.2.k.a.161.16 | 80 | ||
9.2 | odd | 6 | 297.2.t.a.260.8 | 80 | |||
9.4 | even | 3 | 297.2.t.a.62.8 | 80 | |||
9.5 | odd | 6 | 99.2.p.a.29.3 | ✓ | 80 | ||
9.7 | even | 3 | 99.2.p.a.95.3 | yes | 80 | ||
11.8 | odd | 10 | inner | 891.2.k.a.404.16 | 80 | ||
33.8 | even | 10 | inner | 891.2.k.a.404.5 | 80 | ||
99.41 | even | 30 | 99.2.p.a.74.3 | yes | 80 | ||
99.52 | odd | 30 | 99.2.p.a.41.3 | yes | 80 | ||
99.74 | even | 30 | 297.2.t.a.206.8 | 80 | |||
99.85 | odd | 30 | 297.2.t.a.8.8 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.p.a.29.3 | ✓ | 80 | 9.5 | odd | 6 | ||
99.2.p.a.41.3 | yes | 80 | 99.52 | odd | 30 | ||
99.2.p.a.74.3 | yes | 80 | 99.41 | even | 30 | ||
99.2.p.a.95.3 | yes | 80 | 9.7 | even | 3 | ||
297.2.t.a.8.8 | 80 | 99.85 | odd | 30 | |||
297.2.t.a.62.8 | 80 | 9.4 | even | 3 | |||
297.2.t.a.206.8 | 80 | 99.74 | even | 30 | |||
297.2.t.a.260.8 | 80 | 9.2 | odd | 6 | |||
891.2.k.a.161.5 | 80 | 1.1 | even | 1 | trivial | ||
891.2.k.a.161.16 | 80 | 3.2 | odd | 2 | inner | ||
891.2.k.a.404.5 | 80 | 33.8 | even | 10 | inner | ||
891.2.k.a.404.16 | 80 | 11.8 | odd | 10 | inner |