Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(143,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.o (of order \(12\), 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: | \(2.79476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 16.0.478584585616890104119296.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 31x^{12} + 336x^{8} - 19375x^{4} + 390625 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 157.2 | ||
Root | \(-2.23460 - 0.0811201i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.157 |
Dual form | 350.2.o.d.243.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.258819 | + | 0.965926i | −0.183013 | + | 0.683013i | ||||
\(3\) | 2.94170 | − | 0.788227i | 1.69839 | − | 0.455083i | 0.725859 | − | 0.687844i | \(-0.241443\pi\) |
0.972534 | + | 0.232761i | \(0.0747759\pi\) | |||||||
\(4\) | −0.866025 | − | 0.500000i | −0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.04547i | 1.24331i | ||||||||
\(7\) | 1.71696 | + | 2.01297i | 0.648949 | + | 0.760832i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 5.43424 | − | 3.13746i | 1.81141 | − | 1.04582i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.13746 | + | 1.97014i | −0.342957 | + | 0.594018i | −0.984980 | − | 0.172666i | \(-0.944762\pi\) |
0.642024 | + | 0.766685i | \(0.278095\pi\) | |||||||
\(12\) | −2.94170 | − | 0.788227i | −0.849196 | − | 0.227542i | ||||
\(13\) | −3.37822 | − | 3.37822i | −0.936950 | − | 0.936950i | 0.0611771 | − | 0.998127i | \(-0.480515\pi\) |
−0.998127 | + | 0.0611771i | \(0.980515\pi\) | |||||||
\(14\) | −2.38876 | + | 1.13746i | −0.638424 | + | 0.303999i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | −0.896575 | − | 3.34607i | −0.217451 | − | 0.811540i | −0.985289 | − | 0.170896i | \(-0.945334\pi\) |
0.767838 | − | 0.640644i | \(-0.221333\pi\) | |||||||
\(18\) | 1.62407 | + | 6.06110i | 0.382797 | + | 1.42862i | ||||
\(19\) | 3.70219 | + | 6.41238i | 0.849340 | + | 1.47110i | 0.881798 | + | 0.471627i | \(0.156333\pi\) |
−0.0324583 | + | 0.999473i | \(0.510334\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.63746 | + | 4.56821i | 1.44841 | + | 0.996866i | ||||
\(22\) | −1.60861 | − | 1.60861i | −0.342957 | − | 0.342957i | ||||
\(23\) | −2.89778 | − | 0.776457i | −0.604228 | − | 0.161903i | −0.0562805 | − | 0.998415i | \(-0.517924\pi\) |
−0.547948 | + | 0.836512i | \(0.684591\pi\) | |||||||
\(24\) | 1.52274 | − | 2.63746i | 0.310827 | − | 0.538369i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.13746 | − | 2.38876i | 0.811422 | − | 0.468475i | ||||
\(27\) | 7.05246 | − | 7.05246i | 1.35725 | − | 1.35725i | ||||
\(28\) | −0.480443 | − | 2.60176i | −0.0907953 | − | 0.491687i | ||||
\(29\) | − | 5.27492i | − | 0.979528i | −0.871855 | − | 0.489764i | \(-0.837083\pi\) | ||
0.871855 | − | 0.489764i | \(-0.162917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | − | 1.73205i | −0.538816 | − | 0.311086i | 0.205783 | − | 0.978598i | \(-0.434026\pi\) |
−0.744599 | + | 0.667512i | \(0.767359\pi\) | |||||||
\(32\) | −0.965926 | + | 0.258819i | −0.170753 | + | 0.0457532i | ||||
\(33\) | −1.79315 | + | 6.69213i | −0.312148 | + | 1.16495i | ||||
\(34\) | 3.46410 | 0.594089 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.27492 | −1.04582 | ||||||||
\(37\) | −0.588792 | + | 2.19740i | −0.0967968 | + | 0.361251i | −0.997286 | − | 0.0736283i | \(-0.976542\pi\) |
0.900489 | + | 0.434879i | \(0.143209\pi\) | |||||||
\(38\) | −7.15208 | + | 1.91639i | −1.16022 | + | 0.310880i | ||||
\(39\) | −12.6005 | − | 7.27492i | −2.01770 | − | 1.16492i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.19615i | 0.811503i | 0.913984 | + | 0.405751i | \(0.132990\pi\) | ||||
−0.913984 | + | 0.405751i | \(0.867010\pi\) | |||||||
\(42\) | −6.13045 | + | 5.22895i | −0.945950 | + | 0.806845i | ||||
\(43\) | 0.512711 | − | 0.512711i | 0.0781877 | − | 0.0781877i | −0.666931 | − | 0.745119i | \(-0.732393\pi\) |
0.745119 | + | 0.666931i | \(0.232393\pi\) | |||||||
\(44\) | 1.97014 | − | 1.13746i | 0.297009 | − | 0.171478i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.50000 | − | 2.59808i | 0.221163 | − | 0.383065i | ||||
\(47\) | 0.459945 | + | 0.123242i | 0.0670899 | + | 0.0179767i | 0.292208 | − | 0.956355i | \(-0.405610\pi\) |
−0.225118 | + | 0.974332i | \(0.572277\pi\) | |||||||
\(48\) | 2.15348 | + | 2.15348i | 0.310827 | + | 0.310827i | ||||
\(49\) | −1.10411 | + | 6.91238i | −0.157730 | + | 0.987482i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.27492 | − | 9.13642i | −0.738636 | − | 1.27936i | ||||
\(52\) | 1.23651 | + | 4.61474i | 0.171474 | + | 0.639949i | ||||
\(53\) | −3.31929 | − | 12.3878i | −0.455940 | − | 1.70159i | −0.685311 | − | 0.728251i | \(-0.740334\pi\) |
0.229371 | − | 0.973339i | \(-0.426333\pi\) | |||||||
\(54\) | 4.98684 | + | 8.63746i | 0.678623 | + | 1.17541i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.63746 | + | 0.209313i | 0.352445 | + | 0.0279707i | ||||
\(57\) | 15.9451 | + | 15.9451i | 2.11199 | + | 2.11199i | ||||
\(58\) | 5.09518 | + | 1.36525i | 0.669030 | + | 0.179266i | ||||
\(59\) | −5.19615 | + | 9.00000i | −0.676481 | + | 1.17170i | 0.299552 | + | 0.954080i | \(0.403163\pi\) |
−0.976034 | + | 0.217620i | \(0.930171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.08762 | + | 0.627940i | −0.139256 | + | 0.0803995i | −0.568009 | − | 0.823022i | \(-0.692286\pi\) |
0.428753 | + | 0.903422i | \(0.358953\pi\) | |||||||
\(62\) | 2.44949 | − | 2.44949i | 0.311086 | − | 0.311086i | ||||
\(63\) | 15.6460 | + | 5.55208i | 1.97121 | + | 0.699497i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.00000 | − | 3.46410i | −0.738549 | − | 0.426401i | ||||
\(67\) | −10.8907 | + | 2.91816i | −1.33051 | + | 0.356510i | −0.852907 | − | 0.522063i | \(-0.825163\pi\) |
−0.477608 | + | 0.878573i | \(0.658496\pi\) | |||||||
\(68\) | −0.896575 | + | 3.34607i | −0.108726 | + | 0.405770i | ||||
\(69\) | −9.13642 | −1.09990 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 1.62407 | − | 6.06110i | 0.191398 | − | 0.714308i | ||||
\(73\) | −0.808725 | + | 0.216697i | −0.0946541 | + | 0.0253625i | −0.305835 | − | 0.952084i | \(-0.598936\pi\) |
0.211181 | + | 0.977447i | \(0.432269\pi\) | |||||||
\(74\) | −1.97014 | − | 1.13746i | −0.229024 | − | 0.132227i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 7.40437i | − | 0.849340i | ||||||
\(77\) | −5.91880 | + | 1.09297i | −0.674510 | + | 0.124555i | ||||
\(78\) | 10.2883 | − | 10.2883i | 1.16492 | − | 1.16492i | ||||
\(79\) | 8.66025 | − | 5.00000i | 0.974355 | − | 0.562544i | 0.0737937 | − | 0.997274i | \(-0.476489\pi\) |
0.900561 | + | 0.434730i | \(0.143156\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.77492 | − | 10.0025i | 0.641657 | − | 1.11138i | ||||
\(82\) | −5.01910 | − | 1.34486i | −0.554267 | − | 0.148515i | ||||
\(83\) | −0.888041 | − | 0.888041i | −0.0974752 | − | 0.0974752i | 0.656688 | − | 0.754163i | \(-0.271957\pi\) |
−0.754163 | + | 0.656688i | \(0.771957\pi\) | |||||||
\(84\) | −3.46410 | − | 7.27492i | −0.377964 | − | 0.793759i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.362541 | + | 0.627940i | 0.0390938 | + | 0.0677125i | ||||
\(87\) | −4.15783 | − | 15.5172i | −0.445766 | − | 1.66362i | ||||
\(88\) | 0.588792 | + | 2.19740i | 0.0627654 | + | 0.234244i | ||||
\(89\) | −4.56821 | − | 7.91238i | −0.484230 | − | 0.838710i | 0.515606 | − | 0.856826i | \(-0.327567\pi\) |
−0.999836 | + | 0.0181154i | \(0.994233\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | − | 12.6005i | 0.104828 | − | 1.32089i | ||||
\(92\) | 2.12132 | + | 2.12132i | 0.221163 | + | 0.221163i | ||||
\(93\) | −10.1904 | − | 2.73050i | −1.05669 | − | 0.283139i | ||||
\(94\) | −0.238085 | + | 0.412376i | −0.0245566 | + | 0.0425333i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.63746 | + | 1.52274i | −0.269184 | + | 0.155414i | ||||
\(97\) | 1.18406 | − | 1.18406i | 0.120223 | − | 0.120223i | −0.644436 | − | 0.764658i | \(-0.722908\pi\) |
0.764658 | + | 0.644436i | \(0.222908\pi\) | |||||||
\(98\) | −6.39108 | − | 2.85554i | −0.645596 | − | 0.288453i | ||||
\(99\) | 14.2749i | 1.43468i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.91238 | − | 4.56821i | −0.787311 | − | 0.454554i | 0.0517042 | − | 0.998662i | \(-0.483535\pi\) |
−0.839015 | + | 0.544108i | \(0.816868\pi\) | |||||||
\(102\) | 10.1904 | − | 2.73050i | 1.00900 | − | 0.270360i | ||||
\(103\) | 0.108349 | − | 0.404362i | 0.0106759 | − | 0.0398430i | −0.960382 | − | 0.278685i | \(-0.910101\pi\) |
0.971058 | + | 0.238842i | \(0.0767680\pi\) | |||||||
\(104\) | −4.77753 | −0.468475 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.8248 | 1.24565 | ||||||||
\(107\) | 4.09575 | − | 15.2855i | 0.395951 | − | 1.47771i | −0.424204 | − | 0.905567i | \(-0.639446\pi\) |
0.820155 | − | 0.572142i | \(-0.193887\pi\) | |||||||
\(108\) | −9.63383 | + | 2.58138i | −0.927016 | + | 0.248393i | ||||
\(109\) | 11.9726 | + | 6.91238i | 1.14677 | + | 0.662086i | 0.948097 | − | 0.317981i | \(-0.103005\pi\) |
0.198669 | + | 0.980067i | \(0.436338\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.92820i | 0.657596i | ||||||||
\(112\) | −0.884806 | + | 2.49342i | −0.0836063 | + | 0.235606i | ||||
\(113\) | 4.24264 | − | 4.24264i | 0.399114 | − | 0.399114i | −0.478806 | − | 0.877920i | \(-0.658930\pi\) |
0.877920 | + | 0.478806i | \(0.158930\pi\) | |||||||
\(114\) | −19.5287 | + | 11.2749i | −1.82903 | + | 1.05599i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.63746 | + | 4.56821i | −0.244882 | + | 0.424148i | ||||
\(117\) | −28.9571 | − | 7.75903i | −2.67708 | − | 0.717322i | ||||
\(118\) | −7.34847 | − | 7.34847i | −0.676481 | − | 0.676481i | ||||
\(119\) | 5.19615 | − | 7.54983i | 0.476331 | − | 0.692092i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.91238 | + | 5.04438i | 0.264761 | + | 0.458580i | ||||
\(122\) | −0.325046 | − | 1.21309i | −0.0294283 | − | 0.109828i | ||||
\(123\) | 4.09575 | + | 15.2855i | 0.369301 | + | 1.37825i | ||||
\(124\) | 1.73205 | + | 3.00000i | 0.155543 | + | 0.269408i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9.41238 | + | 13.6759i | −0.838521 | + | 1.21834i | ||||
\(127\) | 6.87667 | + | 6.87667i | 0.610206 | + | 0.610206i | 0.943000 | − | 0.332794i | \(-0.107991\pi\) |
−0.332794 | + | 0.943000i | \(0.607991\pi\) | |||||||
\(128\) | 0.965926 | + | 0.258819i | 0.0853766 | + | 0.0228766i | ||||
\(129\) | 1.10411 | − | 1.91238i | 0.0972115 | − | 0.168375i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.41238 | + | 1.97014i | −0.298141 | + | 0.172132i | −0.641607 | − | 0.767033i | \(-0.721732\pi\) |
0.343467 | + | 0.939165i | \(0.388399\pi\) | |||||||
\(132\) | 4.89898 | − | 4.89898i | 0.426401 | − | 0.426401i | ||||
\(133\) | −6.55143 | + | 18.4622i | −0.568081 | + | 1.60087i | ||||
\(134\) | − | 11.2749i | − | 0.974004i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | − | 1.73205i | −0.257248 | − | 0.148522i | ||||
\(137\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(138\) | 2.36468 | − | 8.82511i | 0.201295 | − | 0.751243i | ||||
\(139\) | 21.7370 | 1.84370 | 0.921852 | − | 0.387542i | \(-0.126676\pi\) | ||||
0.921852 | + | 0.387542i | \(0.126676\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.45017 | 0.122126 | ||||||||
\(142\) | 1.55291 | − | 5.79555i | 0.130318 | − | 0.486352i | ||||
\(143\) | 10.4981 | − | 2.81297i | 0.877899 | − | 0.235232i | ||||
\(144\) | 5.43424 | + | 3.13746i | 0.452853 | + | 0.261455i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 0.837253i | − | 0.0692916i | ||||||
\(147\) | 2.20055 | + | 21.2044i | 0.181499 | + | 1.74891i | ||||
\(148\) | 1.60861 | − | 1.60861i | 0.132227 | − | 0.132227i | ||||
\(149\) | −8.50848 | + | 4.91238i | −0.697042 | + | 0.402438i | −0.806245 | − | 0.591582i | \(-0.798504\pi\) |
0.109203 | + | 0.994020i | \(0.465170\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00000 | + | 1.73205i | −0.0813788 | + | 0.140952i | −0.903842 | − | 0.427865i | \(-0.859266\pi\) |
0.822464 | + | 0.568818i | \(0.192599\pi\) | |||||||
\(152\) | 7.15208 | + | 1.91639i | 0.580110 | + | 0.155440i | ||||
\(153\) | −15.3703 | − | 15.3703i | −1.24262 | − | 1.24262i | ||||
\(154\) | 0.476171 | − | 6.00000i | 0.0383709 | − | 0.483494i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.27492 | + | 12.6005i | 0.582460 | + | 1.00885i | ||||
\(157\) | 1.45321 | + | 5.42346i | 0.115979 | + | 0.432839i | 0.999358 | − | 0.0358194i | \(-0.0114041\pi\) |
−0.883379 | + | 0.468659i | \(0.844737\pi\) | |||||||
\(158\) | 2.58819 | + | 9.65926i | 0.205905 | + | 0.768449i | ||||
\(159\) | −19.5287 | − | 33.8248i | −1.54873 | − | 2.68248i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.41238 | − | 7.16629i | −0.268933 | − | 0.564783i | ||||
\(162\) | 8.16697 | + | 8.16697i | 0.641657 | + | 0.641657i | ||||
\(163\) | 11.5911 | + | 3.10583i | 0.907886 | + | 0.243267i | 0.682400 | − | 0.730979i | \(-0.260936\pi\) |
0.225486 | + | 0.974246i | \(0.427603\pi\) | |||||||
\(164\) | 2.59808 | − | 4.50000i | 0.202876 | − | 0.351391i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.08762 | − | 0.627940i | 0.0844160 | − | 0.0487376i | ||||
\(167\) | 1.22474 | − | 1.22474i | 0.0947736 | − | 0.0947736i | −0.658130 | − | 0.752904i | \(-0.728652\pi\) |
0.752904 | + | 0.658130i | \(0.228652\pi\) | |||||||
\(168\) | 7.92361 | − | 1.46318i | 0.611319 | − | 0.112887i | ||||
\(169\) | 9.82475i | 0.755750i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 40.2371 | + | 23.2309i | 3.07701 | + | 1.77651i | ||||
\(172\) | −0.700376 | + | 0.187665i | −0.0534032 | + | 0.0143093i | ||||
\(173\) | −4.60612 | + | 17.1903i | −0.350197 | + | 1.30695i | 0.536226 | + | 0.844075i | \(0.319850\pi\) |
−0.886422 | + | 0.462877i | \(0.846817\pi\) | |||||||
\(174\) | 16.0646 | 1.21786 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.27492 | −0.171478 | ||||||||
\(177\) | −8.19149 | + | 30.5711i | −0.615710 | + | 2.29786i | ||||
\(178\) | 8.82511 | − | 2.36468i | 0.661470 | − | 0.177240i | ||||
\(179\) | 11.1066 | + | 6.41238i | 0.830143 | + | 0.479283i | 0.853902 | − | 0.520434i | \(-0.174230\pi\) |
−0.0237584 | + | 0.999718i | \(0.507563\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8.18408i | − | 0.608318i | −0.952621 | − | 0.304159i | \(-0.901625\pi\) | ||
0.952621 | − | 0.304159i | \(-0.0983754\pi\) | |||||||
\(182\) | 11.9124 | + | 4.22718i | 0.883002 | + | 0.313340i | ||||
\(183\) | −2.70451 | + | 2.70451i | −0.199923 | + | 0.199923i | ||||
\(184\) | −2.59808 | + | 1.50000i | −0.191533 | + | 0.110581i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.27492 | − | 9.13642i | 0.386776 | − | 0.669915i | ||||
\(187\) | 7.61202 | + | 2.03963i | 0.556646 | + | 0.149153i | ||||
\(188\) | −0.336703 | − | 0.336703i | −0.0245566 | − | 0.0245566i | ||||
\(189\) | 26.3052 | + | 2.08762i | 1.91342 | + | 0.151852i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5498 | + | 18.2728i | 0.763359 | + | 1.32218i | 0.941110 | + | 0.338101i | \(0.109785\pi\) |
−0.177750 | + | 0.984076i | \(0.556882\pi\) | |||||||
\(192\) | −0.788227 | − | 2.94170i | −0.0568854 | − | 0.212299i | ||||
\(193\) | −1.17758 | − | 4.39480i | −0.0847643 | − | 0.316345i | 0.910505 | − | 0.413498i | \(-0.135693\pi\) |
−0.995269 | + | 0.0971530i | \(0.969026\pi\) | |||||||
\(194\) | 0.837253 | + | 1.45017i | 0.0601113 | + | 0.104116i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.41238 | − | 5.43424i | 0.315170 | − | 0.388160i | ||||
\(197\) | −4.82583 | − | 4.82583i | −0.343826 | − | 0.343826i | 0.513978 | − | 0.857804i | \(-0.328171\pi\) |
−0.857804 | + | 0.513978i | \(0.828171\pi\) | |||||||
\(198\) | −13.7885 | − | 3.69462i | −0.979907 | − | 0.262565i | ||||
\(199\) | −3.94027 | + | 6.82475i | −0.279318 | + | 0.483794i | −0.971216 | − | 0.238202i | \(-0.923442\pi\) |
0.691897 | + | 0.721996i | \(0.256775\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −29.7371 | + | 17.1687i | −2.09750 | + | 1.21099i | ||||
\(202\) | 6.46043 | − | 6.46043i | 0.454554 | − | 0.454554i | ||||
\(203\) | 10.6183 | − | 9.05681i | 0.745256 | − | 0.635664i | ||||
\(204\) | 10.5498i | 0.738636i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.362541 | + | 0.209313i | 0.0252595 | + | 0.0145836i | ||||
\(207\) | −18.1833 | + | 4.87220i | −1.26383 | + | 0.338642i | ||||
\(208\) | 1.23651 | − | 4.61474i | 0.0857369 | − | 0.319974i | ||||
\(209\) | −16.8443 | −1.16515 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8248 | 1.15826 | 0.579132 | − | 0.815234i | \(-0.303392\pi\) | ||||
0.579132 | + | 0.815234i | \(0.303392\pi\) | |||||||
\(212\) | −3.31929 | + | 12.3878i | −0.227970 | + | 0.850795i | ||||
\(213\) | −17.6502 | + | 4.72936i | −1.20937 | + | 0.324051i | ||||
\(214\) | 13.7046 | + | 7.91238i | 0.936830 | + | 0.540879i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 9.97368i | − | 0.678623i | ||||||
\(217\) | −1.66430 | − | 9.01277i | −0.112980 | − | 0.611827i | ||||
\(218\) | −9.77558 | + | 9.77558i | −0.662086 | + | 0.662086i | ||||
\(219\) | −2.20822 | + | 1.27492i | −0.149218 | + | 0.0861509i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.27492 | + | 14.3326i | −0.556631 | + | 0.964113i | ||||
\(222\) | −6.69213 | − | 1.79315i | −0.449146 | − | 0.120348i | ||||
\(223\) | 6.16441 | + | 6.16441i | 0.412800 | + | 0.412800i | 0.882713 | − | 0.469913i | \(-0.155715\pi\) |
−0.469913 | + | 0.882713i | \(0.655715\pi\) | |||||||
\(224\) | −2.17945 | − | 1.50000i | −0.145621 | − | 0.100223i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.00000 | + | 5.19615i | 0.199557 | + | 0.345643i | ||||
\(227\) | −0.896575 | − | 3.34607i | −0.0595078 | − | 0.222086i | 0.929768 | − | 0.368146i | \(-0.120007\pi\) |
−0.989276 | + | 0.146060i | \(0.953341\pi\) | |||||||
\(228\) | −5.83633 | − | 21.7815i | −0.386520 | − | 1.44251i | ||||
\(229\) | −6.92820 | − | 12.0000i | −0.457829 | − | 0.792982i | 0.541017 | − | 0.841011i | \(-0.318039\pi\) |
−0.998846 | + | 0.0480291i | \(0.984706\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.5498 | + | 7.88054i | −1.08890 | + | 0.518502i | ||||
\(232\) | −3.72993 | − | 3.72993i | −0.244882 | − | 0.244882i | ||||
\(233\) | 18.9800 | + | 5.08567i | 1.24342 | + | 0.333173i | 0.819791 | − | 0.572663i | \(-0.194090\pi\) |
0.423628 | + | 0.905836i | \(0.360756\pi\) | |||||||
\(234\) | 14.9893 | − | 25.9622i | 0.979880 | − | 1.69720i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.00000 | − | 5.19615i | 0.585850 | − | 0.338241i | ||||
\(237\) | 21.5348 | − | 21.5348i | 1.39883 | − | 1.39883i | ||||
\(238\) | 5.94772 | + | 6.97314i | 0.385533 | + | 0.452001i | ||||
\(239\) | − | 10.5498i | − | 0.682412i | −0.939989 | − | 0.341206i | \(-0.889165\pi\) | ||
0.939989 | − | 0.341206i | \(-0.110835\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.41238 | − | 1.97014i | −0.219810 | − | 0.126908i | 0.386052 | − | 0.922477i | \(-0.373839\pi\) |
−0.605862 | + | 0.795569i | \(0.707172\pi\) | |||||||
\(242\) | −5.62628 | + | 1.50756i | −0.361671 | + | 0.0969094i | ||||
\(243\) | 1.35976 | − | 5.07468i | 0.0872284 | − | 0.325541i | ||||
\(244\) | 1.25588 | 0.0803995 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.8248 | −1.00895 | ||||||||
\(247\) | 9.15562 | − | 34.1692i | 0.582558 | − | 2.17414i | ||||
\(248\) | −3.34607 | + | 0.896575i | −0.212475 | + | 0.0569326i | ||||
\(249\) | −3.31233 | − | 1.91238i | −0.209911 | − | 0.121192i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.45203i | 0.407249i | 0.979049 | + | 0.203624i | \(0.0652721\pi\) | ||||
−0.979049 | + | 0.203624i | \(0.934728\pi\) | |||||||
\(252\) | −10.7738 | − | 12.6312i | −0.678684 | − | 0.795693i | ||||
\(253\) | 4.82583 | − | 4.82583i | 0.303397 | − | 0.303397i | ||||
\(254\) | −8.42217 | + | 4.86254i | −0.528454 | + | 0.305103i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −7.61202 | − | 2.03963i | −0.474825 | − | 0.127229i | 0.0134670 | − | 0.999909i | \(-0.495713\pi\) |
−0.488292 | + | 0.872680i | \(0.662380\pi\) | |||||||
\(258\) | 1.56145 | + | 1.56145i | 0.0972115 | + | 0.0972115i | ||||
\(259\) | −5.43424 | + | 2.58762i | −0.337667 | + | 0.160787i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.5498 | − | 28.6652i | −1.02441 | − | 1.77433i | ||||
\(262\) | −1.01982 | − | 3.80601i | −0.0630045 | − | 0.235136i | ||||
\(263\) | 0.989919 | + | 3.69443i | 0.0610410 | + | 0.227808i | 0.989707 | − | 0.143109i | \(-0.0457100\pi\) |
−0.928666 | + | 0.370917i | \(0.879043\pi\) | |||||||
\(264\) | 3.46410 | + | 6.00000i | 0.213201 | + | 0.369274i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −16.1375 | − | 11.1066i | −0.989451 | − | 0.680987i | ||||
\(267\) | −19.6751 | − | 19.6751i | −1.20409 | − | 1.20409i | ||||
\(268\) | 10.8907 | + | 2.91816i | 0.665257 | + | 0.178255i | ||||
\(269\) | −9.76436 | + | 16.9124i | −0.595344 | + | 1.03117i | 0.398154 | + | 0.917318i | \(0.369651\pi\) |
−0.993498 | + | 0.113847i | \(0.963683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.8248 | − | 9.13642i | 0.961285 | − | 0.554998i | 0.0647169 | − | 0.997904i | \(-0.479386\pi\) |
0.896568 | + | 0.442905i | \(0.146052\pi\) | |||||||
\(272\) | 2.44949 | − | 2.44949i | 0.148522 | − | 0.148522i | ||||
\(273\) | −6.99037 | − | 37.8552i | −0.423076 | − | 2.29110i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.91238 | + | 4.56821i | 0.476269 | + | 0.274974i | ||||
\(277\) | 14.5852 | − | 3.90808i | 0.876337 | − | 0.234814i | 0.207511 | − | 0.978233i | \(-0.433464\pi\) |
0.668826 | + | 0.743419i | \(0.266797\pi\) | |||||||
\(278\) | −5.62594 | + | 20.9963i | −0.337421 | + | 1.25927i | ||||
\(279\) | −21.7370 | −1.30136 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.3746 | 1.75234 | 0.876170 | − | 0.482001i | \(-0.160090\pi\) | ||||
0.876170 | + | 0.482001i | \(0.160090\pi\) | |||||||
\(282\) | −0.375330 | + | 1.40075i | −0.0223506 | + | 0.0834136i | ||||
\(283\) | −26.8797 | + | 7.20239i | −1.59783 | + | 0.428138i | −0.944387 | − | 0.328837i | \(-0.893343\pi\) |
−0.653445 | + | 0.756974i | \(0.726677\pi\) | |||||||
\(284\) | 5.19615 | + | 3.00000i | 0.308335 | + | 0.178017i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.8685i | 0.642666i | ||||||||
\(287\) | −10.4597 | + | 8.92158i | −0.617417 | + | 0.526624i | ||||
\(288\) | −4.43704 | + | 4.43704i | −0.261455 | + | 0.261455i | ||||
\(289\) | 4.33013 | − | 2.50000i | 0.254713 | − | 0.147059i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.54983 | − | 4.41644i | 0.149474 | − | 0.258896i | ||||
\(292\) | 0.808725 | + | 0.216697i | 0.0473270 | + | 0.0126812i | ||||
\(293\) | 12.5842 | + | 12.5842i | 0.735174 | + | 0.735174i | 0.971640 | − | 0.236466i | \(-0.0759891\pi\) |
−0.236466 | + | 0.971640i | \(0.575989\pi\) | |||||||
\(294\) | −21.0515 | − | 3.36254i | −1.22775 | − | 0.196107i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.13746 | + | 1.97014i | 0.0661134 | + | 0.114512i | ||||
\(297\) | 5.87242 | + | 21.9162i | 0.340752 | + | 1.27171i | ||||
\(298\) | −2.54283 | − | 9.48998i | −0.147302 | − | 0.549740i | ||||
\(299\) | 7.16629 | + | 12.4124i | 0.414437 | + | 0.717826i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.91238 | + | 0.151770i | 0.110228 | + | 0.00874785i | ||||
\(302\) | −1.41421 | − | 1.41421i | −0.0813788 | − | 0.0813788i | ||||
\(303\) | −26.8766 | − | 7.20158i | −1.54402 | − | 0.413720i | ||||
\(304\) | −3.70219 | + | 6.41238i | −0.212335 | + | 0.367775i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 18.8248 | − | 10.8685i | 1.07614 | − | 0.621309i | ||||
\(307\) | −13.2169 | + | 13.2169i | −0.754327 | + | 0.754327i | −0.975284 | − | 0.220957i | \(-0.929082\pi\) |
0.220957 | + | 0.975284i | \(0.429082\pi\) | |||||||
\(308\) | 5.67231 | + | 2.01286i | 0.323210 | + | 0.114693i | ||||
\(309\) | − | 1.27492i | − | 0.0725275i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.6495 | − | 13.0767i | −1.28434 | − | 0.741511i | −0.306698 | − | 0.951807i | \(-0.599224\pi\) |
−0.977638 | + | 0.210296i | \(0.932557\pi\) | |||||||
\(312\) | −14.0541 | + | 3.76577i | −0.795655 | + | 0.213195i | ||||
\(313\) | 2.90642 | − | 10.8469i | 0.164281 | − | 0.613104i | −0.833850 | − | 0.551991i | \(-0.813868\pi\) |
0.998131 | − | 0.0611132i | \(-0.0194651\pi\) | |||||||
\(314\) | −5.61478 | −0.316860 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | −4.65874 | + | 17.3867i | −0.261661 | + | 0.976532i | 0.702601 | + | 0.711584i | \(0.252022\pi\) |
−0.964262 | + | 0.264949i | \(0.914645\pi\) | |||||||
\(318\) | 37.7266 | − | 10.1088i | 2.11560 | − | 0.566874i | ||||
\(319\) | 10.3923 | + | 6.00000i | 0.581857 | + | 0.335936i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 48.1939i | − | 2.68992i | ||||||
\(322\) | 7.80529 | − | 1.44133i | 0.434972 | − | 0.0803222i | ||||
\(323\) | 18.1369 | − | 18.1369i | 1.00917 | − | 1.00917i | ||||
\(324\) | −10.0025 | + | 5.77492i | −0.555692 | + | 0.320829i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.00000 | + | 10.3923i | −0.332309 | + | 0.575577i | ||||
\(327\) | 40.6683 | + | 10.8970i | 2.24896 | + | 0.602608i | ||||
\(328\) | 3.67423 | + | 3.67423i | 0.202876 | + | 0.202876i | ||||
\(329\) | 0.541624 | + | 1.13746i | 0.0298607 | + | 0.0627101i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.4124 | − | 24.9630i | −0.792176 | − | 1.37209i | −0.924617 | − | 0.380898i | \(-0.875615\pi\) |
0.132441 | − | 0.991191i | \(-0.457718\pi\) | |||||||
\(332\) | 0.325046 | + | 1.21309i | 0.0178392 | + | 0.0665768i | ||||
\(333\) | 3.69462 | + | 13.7885i | 0.202464 | + | 0.755606i | ||||
\(334\) | 0.866025 | + | 1.50000i | 0.0473868 | + | 0.0820763i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.637459 | + | 8.03231i | −0.0347762 | + | 0.438199i | ||||
\(337\) | 17.1115 | + | 17.1115i | 0.932124 | + | 0.932124i | 0.997838 | − | 0.0657148i | \(-0.0209328\pi\) |
−0.0657148 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(338\) | −9.48998 | − | 2.54283i | −0.516187 | − | 0.138312i | ||||
\(339\) | 9.13642 | − | 15.8248i | 0.496222 | − | 0.859483i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.82475 | − | 3.94027i | 0.369581 | − | 0.213378i | ||||
\(342\) | −32.8535 | + | 32.8535i | −1.77651 | + | 1.77651i | ||||
\(343\) | −15.8101 | + | 9.64572i | −0.853667 | + | 0.520820i | ||||
\(344\) | − | 0.725083i | − | 0.0390938i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.4124 | − | 8.89834i | −0.828574 | − | 0.478378i | ||||
\(347\) | 26.8766 | − | 7.20158i | 1.44281 | − | 0.386601i | 0.549296 | − | 0.835628i | \(-0.314896\pi\) |
0.893518 | + | 0.449027i | \(0.148229\pi\) | |||||||
\(348\) | −4.15783 | + | 15.5172i | −0.222883 | + | 0.831811i | ||||
\(349\) | −9.13642 | −0.489062 | −0.244531 | − | 0.969642i | \(-0.578634\pi\) | ||||
−0.244531 | + | 0.969642i | \(0.578634\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −47.6495 | −2.54334 | ||||||||
\(352\) | 0.588792 | − | 2.19740i | 0.0313827 | − | 0.117122i | ||||
\(353\) | 24.3423 | − | 6.52251i | 1.29561 | − | 0.347158i | 0.455823 | − | 0.890070i | \(-0.349345\pi\) |
0.839789 | + | 0.542912i | \(0.182678\pi\) | |||||||
\(354\) | −27.4093 | − | 15.8248i | −1.45679 | − | 0.841076i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.13642i | 0.484230i | ||||||||
\(357\) | 9.33455 | − | 26.3051i | 0.494037 | − | 1.39221i | ||||
\(358\) | −9.06847 | + | 9.06847i | −0.479283 | + | 0.479283i | ||||
\(359\) | 27.4093 | − | 15.8248i | 1.44661 | − | 0.835198i | 0.448329 | − | 0.893869i | \(-0.352019\pi\) |
0.998277 | + | 0.0586703i | \(0.0186861\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9124 | + | 31.0251i | −0.942757 | + | 1.63290i | ||||
\(362\) | 7.90522 | + | 2.11820i | 0.415489 | + | 0.111330i | ||||
\(363\) | 12.5435 | + | 12.5435i | 0.658361 | + | 0.658361i | ||||
\(364\) | −7.16629 | + | 10.4124i | −0.375616 | + | 0.545757i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.91238 | − | 3.31233i | −0.0999615 | − | 0.173138i | ||||
\(367\) | 3.81789 | + | 14.2486i | 0.199292 | + | 0.743769i | 0.991114 | + | 0.133017i | \(0.0424664\pi\) |
−0.791821 | + | 0.610753i | \(0.790867\pi\) | |||||||
\(368\) | −0.776457 | − | 2.89778i | −0.0404756 | − | 0.151057i | ||||
\(369\) | 16.3027 | + | 28.2371i | 0.848685 | + | 1.46997i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.2371 | − | 27.9509i | 0.998742 | − | 1.45114i | ||||
\(372\) | 7.45986 | + | 7.45986i | 0.386776 | + | 0.386776i | ||||
\(373\) | 7.19631 | + | 1.92824i | 0.372611 | + | 0.0998407i | 0.440264 | − | 0.897868i | \(-0.354885\pi\) |
−0.0676538 | + | 0.997709i | \(0.521551\pi\) | |||||||
\(374\) | −3.94027 | + | 6.82475i | −0.203747 | + | 0.352900i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.412376 | − | 0.238085i | 0.0212667 | − | 0.0122783i | ||||
\(377\) | −17.8198 | + | 17.8198i | −0.917768 | + | 0.917768i | ||||
\(378\) | −8.82477 | + | 24.8685i | −0.453897 | + | 1.27910i | ||||
\(379\) | 3.17525i | 0.163102i | 0.996669 | + | 0.0815508i | \(0.0259873\pi\) | ||||
−0.996669 | + | 0.0815508i | \(0.974013\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 25.6495 | + | 14.8087i | 1.31406 | + | 0.758675i | ||||
\(382\) | −20.3807 | + | 5.46100i | −1.04277 | + | 0.279409i | ||||
\(383\) | 8.11386 | − | 30.2813i | 0.414599 | − | 1.54730i | −0.371039 | − | 0.928617i | \(-0.620998\pi\) |
0.785638 | − | 0.618687i | \(-0.212335\pi\) | |||||||
\(384\) | 3.04547 | 0.155414 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.54983 | 0.231580 | ||||||||
\(387\) | 1.17758 | − | 4.39480i | 0.0598599 | − | 0.223400i | ||||
\(388\) | −1.61745 | + | 0.433394i | −0.0821136 | + | 0.0220023i | ||||
\(389\) | −23.4690 | − | 13.5498i | −1.18993 | − | 0.687004i | −0.231636 | − | 0.972803i | \(-0.574408\pi\) |
−0.958290 | + | 0.285799i | \(0.907741\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.3923i | 0.525561i | ||||||||
\(392\) | 4.10706 | + | 5.66851i | 0.207438 | + | 0.286303i | ||||
\(393\) | −8.48528 | + | 8.48528i | −0.428026 | + | 0.428026i | ||||
\(394\) | 5.91041 | − | 3.41238i | 0.297762 | − | 0.171913i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.13746 | − | 12.3624i | 0.358671 | − | 0.621236i | ||||
\(397\) | −18.4589 | − | 4.94606i | −0.926428 | − | 0.248236i | −0.236097 | − | 0.971729i | \(-0.575868\pi\) |
−0.690331 | + | 0.723494i | \(0.742535\pi\) | |||||||
\(398\) | −5.57239 | − | 5.57239i | −0.279318 | − | 0.279318i | ||||
\(399\) | −4.71998 | + | 59.4743i | −0.236295 | + | 2.97744i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.04983 | − | 10.4786i | −0.302114 | − | 0.523277i | 0.674500 | − | 0.738275i | \(-0.264359\pi\) |
−0.976615 | + | 0.214997i | \(0.931026\pi\) | |||||||
\(402\) | −8.88719 | − | 33.1675i | −0.443253 | − | 1.65424i | ||||
\(403\) | 4.28341 | + | 15.9859i | 0.213372 | + | 0.796315i | ||||
\(404\) | 4.56821 | + | 7.91238i | 0.227277 | + | 0.393655i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00000 | + | 12.6005i | 0.297775 | + | 0.625354i | ||||
\(407\) | −3.65945 | − | 3.65945i | −0.181392 | − | 0.181392i | ||||
\(408\) | −10.1904 | − | 2.73050i | −0.504498 | − | 0.135180i | ||||
\(409\) | −2.35999 | + | 4.08762i | −0.116694 | + | 0.202120i | −0.918456 | − | 0.395524i | \(-0.870563\pi\) |
0.801762 | + | 0.597644i | \(0.203896\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.296014 | + | 0.296014i | −0.0145836 | + | 0.0145836i | ||||
\(413\) | −27.0383 | + | 4.99291i | −1.33047 | + | 0.245685i | ||||
\(414\) | − | 18.8248i | − | 0.925186i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.13746 | + | 2.38876i | 0.202856 | + | 0.117119i | ||||
\(417\) | 63.9437 | − | 17.1336i | 3.13133 | − | 0.839038i | ||||
\(418\) | 4.35964 | − | 16.2704i | 0.213237 | − | 0.795810i | ||||
\(419\) | −11.8208 | −0.577485 | −0.288742 | − | 0.957407i | \(-0.593237\pi\) | ||||
−0.288742 | + | 0.957407i | \(0.593237\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.1752 | 0.593385 | 0.296693 | − | 0.954973i | \(-0.404116\pi\) | ||||
0.296693 | + | 0.954973i | \(0.404116\pi\) | |||||||
\(422\) | −4.35457 | + | 16.2515i | −0.211977 | + | 0.791109i | ||||
\(423\) | 2.88612 | − | 0.773333i | 0.140328 | − | 0.0376008i | ||||
\(424\) | −11.1066 | − | 6.41238i | −0.539382 | − | 0.311412i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 18.2728i | − | 0.885322i | ||||||
\(427\) | −3.13143 | − | 1.11121i | −0.151541 | − | 0.0537752i | ||||
\(428\) | −11.1898 | + | 11.1898i | −0.540879 | + | 0.540879i | ||||
\(429\) | 28.6652 | − | 16.5498i | 1.38397 | − | 0.799034i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.72508 | − | 16.8443i | 0.468441 | − | 0.811363i | −0.530909 | − | 0.847429i | \(-0.678149\pi\) |
0.999349 | + | 0.0360659i | \(0.0114826\pi\) | |||||||
\(432\) | 9.63383 | + | 2.58138i | 0.463508 | + | 0.124197i | ||||
\(433\) | −14.1049 | − | 14.1049i | −0.677839 | − | 0.677839i | 0.281672 | − | 0.959511i | \(-0.409111\pi\) |
−0.959511 | + | 0.281672i | \(0.909111\pi\) | |||||||
\(434\) | 9.13642 | + | 0.725083i | 0.438562 | + | 0.0348051i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.91238 | − | 11.9726i | −0.331043 | − | 0.573383i | ||||
\(437\) | −5.74918 | − | 21.4562i | −0.275021 | − | 1.02639i | ||||
\(438\) | −0.659946 | − | 2.46295i | −0.0315334 | − | 0.117684i | ||||
\(439\) | −10.3923 | − | 18.0000i | −0.495998 | − | 0.859093i | 0.503992 | − | 0.863708i | \(-0.331864\pi\) |
−0.999989 | + | 0.00461537i | \(0.998531\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.6873 | + | 41.0276i | 0.747014 | + | 1.95370i | ||||
\(442\) | −11.7025 | − | 11.7025i | −0.556631 | − | 0.556631i | ||||
\(443\) | −32.6722 | − | 8.75449i | −1.55230 | − | 0.415938i | −0.622086 | − | 0.782949i | \(-0.713715\pi\) |
−0.930217 | + | 0.367010i | \(0.880381\pi\) | |||||||
\(444\) | 3.46410 | − | 6.00000i | 0.164399 | − | 0.284747i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.54983 | + | 4.35890i | −0.357495 | + | 0.206400i | ||||
\(447\) | −21.1574 | + | 21.1574i | −1.00071 | + | 1.00071i | ||||
\(448\) | 2.01297 | − | 1.71696i | 0.0951040 | − | 0.0811186i | ||||
\(449\) | − | 37.5498i | − | 1.77209i | −0.463603 | − | 0.886043i | \(-0.653444\pi\) | ||
0.463603 | − | 0.886043i | \(-0.346556\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.2371 | − | 5.91041i | −0.482048 | − | 0.278310i | ||||
\(452\) | −5.79555 | + | 1.55291i | −0.272600 | + | 0.0730429i | ||||
\(453\) | −1.57645 | + | 5.88341i | −0.0740683 | + | 0.276427i | ||||
\(454\) | 3.46410 | 0.162578 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 22.5498 | 1.05599 | ||||||||
\(457\) | 5.03407 | − | 18.7874i | 0.235484 | − | 0.878838i | −0.742446 | − | 0.669906i | \(-0.766334\pi\) |
0.977930 | − | 0.208932i | \(-0.0669989\pi\) | |||||||
\(458\) | 13.3843 | − | 3.58630i | 0.625405 | − | 0.167577i | ||||
\(459\) | −29.9210 | − | 17.2749i | −1.39659 | − | 0.806324i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.5457i | 1.70210i | 0.525082 | + | 0.851051i | \(0.324035\pi\) | ||||
−0.525082 | + | 0.851051i | \(0.675965\pi\) | |||||||
\(462\) | −3.32861 | − | 18.0255i | −0.154861 | − | 0.838624i | ||||
\(463\) | −11.6320 | + | 11.6320i | −0.540586 | + | 0.540586i | −0.923701 | − | 0.383115i | \(-0.874851\pi\) |
0.383115 | + | 0.923701i | \(0.374851\pi\) | |||||||
\(464\) | 4.56821 | − | 2.63746i | 0.212074 | − | 0.122441i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.82475 | + | 17.0170i | −0.455123 | + | 0.788296i | ||||
\(467\) | 25.5554 | + | 6.84756i | 1.18256 | + | 0.316867i | 0.795943 | − | 0.605371i | \(-0.206975\pi\) |
0.386621 | + | 0.922239i | \(0.373642\pi\) | |||||||
\(468\) | 21.1981 | + | 21.1981i | 0.979880 | + | 0.979880i | ||||
\(469\) | −24.5731 | − | 16.9124i | −1.13468 | − | 0.780941i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.54983 | + | 14.8087i | 0.393956 | + | 0.682351i | ||||
\(472\) | 2.68973 | + | 10.0382i | 0.123805 | + | 0.462045i | ||||
\(473\) | 0.426923 | + | 1.59330i | 0.0196299 | + | 0.0732599i | ||||
\(474\) | 15.2274 | + | 26.3746i | 0.699416 | + | 1.21142i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.27492 | + | 3.94027i | −0.379280 | + | 0.180602i | ||||
\(477\) | −56.9039 | − | 56.9039i | −2.60545 | − | 2.60545i | ||||
\(478\) | 10.1904 | + | 2.73050i | 0.466096 | + | 0.124890i | ||||
\(479\) | 9.13642 | − | 15.8248i | 0.417454 | − | 0.723051i | −0.578229 | − | 0.815875i | \(-0.696256\pi\) |
0.995683 | + | 0.0928234i | \(0.0295892\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.41238 | − | 5.43424i | 0.429167 | − | 0.247780i | ||||
\(482\) | 2.78619 | − | 2.78619i | 0.126908 | − | 0.126908i | ||||
\(483\) | −15.6869 | − | 18.3914i | −0.713777 | − | 0.836836i | ||||
\(484\) | − | 5.82475i | − | 0.264761i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.54983 | + | 2.62685i | 0.206385 | + | 0.119156i | ||||
\(487\) | −20.3807 | + | 5.46100i | −0.923538 | + | 0.247461i | −0.689097 | − | 0.724669i | \(-0.741993\pi\) |
−0.234441 | + | 0.972130i | \(0.575326\pi\) | |||||||
\(488\) | −0.325046 | + | 1.21309i | −0.0147141 | + | 0.0549139i | ||||
\(489\) | 36.5457 | 1.65265 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.5498 | −1.55921 | −0.779606 | − | 0.626270i | \(-0.784581\pi\) | ||||
−0.779606 | + | 0.626270i | \(0.784581\pi\) | |||||||
\(492\) | 4.09575 | − | 15.2855i | 0.184651 | − | 0.689125i | ||||
\(493\) | −17.6502 | + | 4.72936i | −0.794926 | + | 0.213000i | ||||
\(494\) | 30.6353 | + | 17.6873i | 1.37835 | + | 0.795789i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 3.46410i | − | 0.155543i | ||||||
\(497\) | −10.3017 | − | 12.0778i | −0.462097 | − | 0.541765i | ||||
\(498\) | 2.70451 | − | 2.70451i | 0.121192 | − | 0.121192i | ||||
\(499\) | −3.46410 | + | 2.00000i | −0.155074 | + | 0.0895323i | −0.575529 | − | 0.817781i | \(-0.695204\pi\) |
0.420455 | + | 0.907314i | \(0.361871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.63746 | − | 4.56821i | 0.117833 | − | 0.204093i | ||||
\(502\) | −6.23218 | − | 1.66991i | −0.278156 | − | 0.0745317i | ||||
\(503\) | 5.78702 | + | 5.78702i | 0.258031 | + | 0.258031i | 0.824253 | − | 0.566222i | \(-0.191596\pi\) |
−0.566222 | + | 0.824253i | \(0.691596\pi\) | |||||||
\(504\) | 14.9893 | − | 7.13746i | 0.667676 | − | 0.317928i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.41238 | + | 5.91041i | 0.151699 | + | 0.262750i | ||||
\(507\) | 7.74413 | + | 28.9015i | 0.343929 | + | 1.28356i | ||||
\(508\) | −2.51704 | − | 9.39371i | −0.111675 | − | 0.416778i | ||||
\(509\) | 18.9008 | + | 32.7371i | 0.837763 | + | 1.45105i | 0.891761 | + | 0.452507i | \(0.149470\pi\) |
−0.0539983 | + | 0.998541i | \(0.517197\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.82475 | − | 1.25588i | −0.0807223 | − | 0.0555569i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 71.3325 | + | 19.1135i | 3.14941 | + | 0.843881i | ||||
\(514\) | 3.94027 | − | 6.82475i | 0.173798 | − | 0.301027i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.91238 | + | 1.10411i | −0.0841877 | + | 0.0486058i | ||||
\(517\) | −0.765972 | + | 0.765972i | −0.0336874 | + | 0.0336874i | ||||
\(518\) | −1.09297 | − | 5.91880i | −0.0480223 | − | 0.260057i | ||||
\(519\) | 54.1993i | 2.37909i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.2371 | + | 5.91041i | 0.448497 | + | 0.258940i | 0.707195 | − | 0.707018i | \(-0.249960\pi\) |
−0.258698 | + | 0.965958i | \(0.583294\pi\) | |||||||
\(522\) | 31.9718 | − | 8.56682i | 1.39937 | − | 0.374960i | ||||
\(523\) | 10.5422 | − | 39.3441i | 0.460979 | − | 1.72040i | −0.208911 | − | 0.977935i | \(-0.566992\pi\) |
0.669889 | − | 0.742461i | \(-0.266341\pi\) | |||||||
\(524\) | 3.94027 | 0.172132 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.82475 | −0.166767 | ||||||||
\(527\) | −3.10583 | + | 11.5911i | −0.135292 | + | 0.504917i | ||||
\(528\) | −6.69213 | + | 1.79315i | −0.291238 | + | 0.0780369i | ||||
\(529\) | −12.1244 | − | 7.00000i | −0.527146 | − | 0.304348i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 65.2109i | 2.82991i | ||||||||
\(532\) | 14.9048 | − | 12.7130i | 0.646205 | − | 0.551178i | ||||
\(533\) | 17.5538 | − | 17.5538i | 0.760337 | − | 0.760337i | ||||
\(534\) | 24.0969 | − | 13.9124i | 1.04278 | − | 0.602047i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.63746 | + | 9.76436i | −0.243501 | + | 0.421756i | ||||
\(537\) | 37.7266 | + | 10.1088i | 1.62802 | + | 0.436228i | ||||
\(538\) | −13.8089 | − | 13.8089i | −0.595344 | − | 0.595344i | ||||
\(539\) | −12.3624 | − | 10.0378i | −0.532488 | − | 0.432358i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.9124 | + | 27.5610i | 0.684126 | + | 1.18494i | 0.973710 | + | 0.227789i | \(0.0731497\pi\) |
−0.289584 | + | 0.957153i | \(0.593517\pi\) | |||||||
\(542\) | 4.72936 | + | 17.6502i | 0.203143 | + | 0.758142i | ||||
\(543\) | −6.45091 | − | 24.0751i | −0.276835 | − | 1.03316i | ||||
\(544\) | 1.73205 | + | 3.00000i | 0.0742611 | + | 0.128624i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 38.3746 | + | 3.04547i | 1.64228 | + | 0.130334i | ||||
\(547\) | −6.94715 | − | 6.94715i | −0.297039 | − | 0.297039i | 0.542814 | − | 0.839853i | \(-0.317359\pi\) |
−0.839853 | + | 0.542814i | \(0.817359\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.94027 | + | 6.82475i | −0.168167 | + | 0.291273i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.8248 | − | 19.5287i | 1.44098 | − | 0.831952i | ||||
\(552\) | −6.46043 | + | 6.46043i | −0.274974 | + | 0.274974i | ||||
\(553\) | 24.9342 | + | 8.84806i | 1.06031 | + | 0.376258i | ||||
\(554\) | 15.0997i | 0.641523i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.8248 | − | 10.8685i | −0.798347 | − | 0.460926i | ||||
\(557\) | −41.3655 | + | 11.0839i | −1.75271 | + | 0.469638i | −0.985202 | − | 0.171397i | \(-0.945172\pi\) |
−0.767512 | + | 0.641035i | \(0.778505\pi\) | |||||||
\(558\) | 5.62594 | − | 20.9963i | 0.238165 | − | 0.888844i | ||||
\(559\) | −3.46410 | −0.146516 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | −7.60270 | + | 28.3737i | −0.320701 | + | 1.19687i | ||||
\(563\) | −18.8633 | + | 5.05441i | −0.794993 | + | 0.213018i | −0.633385 | − | 0.773837i | \(-0.718335\pi\) |
−0.161609 | + | 0.986855i | \(0.551668\pi\) | |||||||
\(564\) | −1.25588 | − | 0.725083i | −0.0528821 | − | 0.0305315i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 27.8279i | − | 1.16969i | ||||||
\(567\) | 30.0499 | − | 5.54904i | 1.26198 | − | 0.233038i | ||||
\(568\) | −4.24264 | + | 4.24264i | −0.178017 | + | 0.178017i | ||||
\(569\) | 11.1066 | − | 6.41238i | 0.465611 | − | 0.268821i | −0.248789 | − | 0.968558i | \(-0.580033\pi\) |
0.714401 | + | 0.699737i | \(0.246699\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.82475 | + | 13.5529i | −0.327456 | + | 0.567170i | −0.982006 | − | 0.188848i | \(-0.939525\pi\) |
0.654551 | + | 0.756018i | \(0.272858\pi\) | |||||||
\(572\) | −10.4981 | − | 2.81297i | −0.438949 | − | 0.117616i | ||||
\(573\) | 45.4376 | + | 45.4376i | 1.89818 | + | 1.89818i | ||||
\(574\) | −5.91041 | − | 12.4124i | −0.246696 | − | 0.518083i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.13746 | − | 5.43424i | −0.130727 | − | 0.226427i | ||||
\(577\) | 10.3255 | + | 38.5353i | 0.429857 | + | 1.60425i | 0.753083 | + | 0.657925i | \(0.228566\pi\) |
−0.323227 | + | 0.946322i | \(0.604768\pi\) | |||||||
\(578\) | 1.29410 | + | 4.82963i | 0.0538273 | + | 0.200886i | ||||
\(579\) | −6.92820 | − | 12.0000i | −0.287926 | − | 0.498703i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.262873 | − | 3.31233i | 0.0109058 | − | 0.137419i | ||||
\(582\) | 3.60601 | + | 3.60601i | 0.149474 | + | 0.149474i | ||||
\(583\) | 28.1811 | + | 7.55111i | 1.16714 | + | 0.312735i | ||||
\(584\) | −0.418627 | + | 0.725083i | −0.0173229 | + | 0.0300041i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.4124 | + | 8.89834i | −0.636679 | + | 0.367587i | ||||
\(587\) | −7.34847 | + | 7.34847i | −0.303304 | + | 0.303304i | −0.842305 | − | 0.539001i | \(-0.818802\pi\) |
0.539001 | + | 0.842305i | \(0.318802\pi\) | |||||||
\(588\) | 8.69649 | − | 19.4639i | 0.358637 | − | 0.802676i | ||||
\(589\) | − | 25.6495i | − | 1.05687i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.0000 | − | 10.3923i | −0.740421 | − | 0.427482i | ||||
\(592\) | −2.19740 | + | 0.588792i | −0.0903126 | + | 0.0241992i | ||||
\(593\) | −4.97585 | + | 18.5701i | −0.204333 | + | 0.762583i | 0.785318 | + | 0.619092i | \(0.212499\pi\) |
−0.989652 | + | 0.143491i | \(0.954167\pi\) | |||||||
\(594\) | −22.6893 | −0.930953 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.82475 | 0.402438 | ||||||||
\(597\) | −6.21166 | + | 23.1822i | −0.254226 | + | 0.948785i | ||||
\(598\) | −13.8442 | + | 3.70954i | −0.566132 | + | 0.151695i | ||||
\(599\) | 28.6652 | + | 16.5498i | 1.17123 | + | 0.676208i | 0.953969 | − | 0.299906i | \(-0.0969554\pi\) |
0.217258 | + | 0.976114i | \(0.430289\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.92820i | − | 0.282607i | −0.989966 | − | 0.141304i | \(-0.954871\pi\) | ||
0.989966 | − | 0.141304i | \(-0.0451294\pi\) | |||||||
\(602\) | −0.641557 | + | 1.80793i | −0.0261479 | + | 0.0736858i | ||||
\(603\) | −50.0272 | + | 50.0272i | −2.03727 | + | 2.03727i | ||||
\(604\) | 1.73205 | − | 1.00000i | 0.0704761 | − | 0.0406894i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.9124 | − | 24.0969i | 0.565152 | − | 0.978871i | ||||
\(607\) | −21.0519 | − | 5.64083i | −0.854469 | − | 0.228954i | −0.195109 | − | 0.980782i | \(-0.562506\pi\) |
−0.659360 | + | 0.751827i | \(0.729173\pi\) | |||||||
\(608\) | −5.23568 | − | 5.23568i | −0.212335 | − | 0.212335i | ||||
\(609\) | 24.0969 | − | 35.0120i | 0.976457 | − | 1.41876i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.13746 | − | 1.97014i | −0.0460166 | − | 0.0797032i | ||||
\(612\) | 5.62594 | + | 20.9963i | 0.227415 | + | 0.848724i | ||||
\(613\) | −9.53095 | − | 35.5700i | −0.384951 | − | 1.43666i | −0.838244 | − | 0.545296i | \(-0.816417\pi\) |
0.453292 | − | 0.891362i | \(-0.350249\pi\) | |||||||
\(614\) | −9.34574 | − | 16.1873i | −0.377163 | − | 0.653266i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.41238 | + | 4.95807i | −0.137489 | + | 0.199766i | ||||
\(617\) | 9.65166 | + | 9.65166i | 0.388561 | + | 0.388561i | 0.874174 | − | 0.485613i | \(-0.161404\pi\) |
−0.485613 | + | 0.874174i | \(0.661404\pi\) | |||||||
\(618\) | 1.23148 | + | 0.329973i | 0.0495372 | + | 0.0132735i | ||||
\(619\) | 5.43424 | − | 9.41238i | 0.218420 | − | 0.378315i | −0.735905 | − | 0.677085i | \(-0.763243\pi\) |
0.954325 | + | 0.298770i | \(0.0965762\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −25.9124 | + | 14.9605i | −1.03983 | + | 0.600345i | ||||
\(622\) | 18.4932 | − | 18.4932i | 0.741511 | − | 0.741511i | ||||
\(623\) | 8.08396 | − | 22.7809i | 0.323877 | − | 0.912697i | ||||
\(624\) | − | 14.5498i | − | 0.582460i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.72508 | + | 5.61478i | 0.388692 | + | 0.224412i | ||||
\(627\) | −49.5510 | + | 13.2772i | −1.97888 | + | 0.530239i | ||||
\(628\) | 1.45321 | − | 5.42346i | 0.0579895 | − | 0.216420i | ||||
\(629\) | 7.88054 | 0.314218 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.64950 | 0.384141 | 0.192070 | − | 0.981381i | \(-0.438480\pi\) | ||||
0.192070 | + | 0.981381i | \(0.438480\pi\) | |||||||
\(632\) | 2.58819 | − | 9.65926i | 0.102953 | − | 0.384225i | ||||
\(633\) | 49.4934 | − | 13.2617i | 1.96719 | − | 0.527106i | ||||
\(634\) | −15.5885 | − | 9.00000i | −0.619097 | − | 0.357436i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 39.0575i | 1.54873i | ||||||||
\(637\) | 27.0815 | − | 19.6216i | 1.07301 | − | 0.777436i | ||||
\(638\) | −8.48528 | + | 8.48528i | −0.335936 | + | 0.335936i | ||||
\(639\) | −32.6054 | + | 18.8248i | −1.28985 | + | 0.744696i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.5000 | − | 23.3827i | 0.533218 | − | 0.923561i | −0.466029 | − | 0.884769i | \(-0.654316\pi\) |
0.999247 | − | 0.0387913i | \(-0.0123508\pi\) | |||||||
\(642\) | 46.5517 | + | 12.4735i | 1.83725 | + | 0.492290i | ||||
\(643\) | −19.6773 | − | 19.6773i | −0.775997 | − | 0.775997i | 0.203151 | − | 0.979147i | \(-0.434882\pi\) |
−0.979147 | + | 0.203151i | \(0.934882\pi\) | |||||||
\(644\) | −0.627940 | + | 7.91238i | −0.0247443 | + | 0.311791i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.8248 | + | 22.2131i | 0.504583 | + | 0.873964i | ||||
\(647\) | −1.34486 | − | 5.01910i | −0.0528720 | − | 0.197321i | 0.934438 | − | 0.356126i | \(-0.115903\pi\) |
−0.987310 | + | 0.158805i | \(0.949236\pi\) | |||||||
\(648\) | −2.98932 | − | 11.1563i | −0.117431 | − | 0.438260i | ||||
\(649\) | −11.8208 | − | 20.4743i | −0.464008 | − | 0.803685i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | − | 25.2011i | −0.470317 | − | 0.987707i | ||||
\(652\) | −8.48528 | − | 8.48528i | −0.332309 | − | 0.332309i | ||||
\(653\) | −37.1633 | − | 9.95787i | −1.45431 | − | 0.389682i | −0.556790 | − | 0.830653i | \(-0.687967\pi\) |
−0.897521 | + | 0.440972i | \(0.854634\pi\) | |||||||
\(654\) | −21.0515 | + | 36.4622i | −0.823177 | + | 1.42579i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.50000 | + | 2.59808i | −0.175695 | + | 0.101438i | ||||
\(657\) | −3.71492 | + | 3.71492i | −0.144933 | + | 0.144933i | ||||
\(658\) | −1.23888 | + | 0.228773i | −0.0482967 | + | 0.00891850i | ||||
\(659\) | − | 1.45017i | − | 0.0564904i | −0.999601 | − | 0.0282452i | \(-0.991008\pi\) | ||
0.999601 | − | 0.0282452i | \(-0.00899193\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.9124 | − | 11.4964i | −0.774502 | − | 0.447159i | 0.0599765 | − | 0.998200i | \(-0.480897\pi\) |
−0.834478 | + | 0.551041i | \(0.814231\pi\) | |||||||
\(662\) | 27.8426 | − | 7.46039i | 1.08213 | − | 0.289956i | ||||
\(663\) | −13.0450 | + | 48.6847i | −0.506627 | + | 1.89076i | ||||
\(664\) | −1.25588 | −0.0487376 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.2749 | −0.553142 | ||||||||
\(667\) | −4.09575 | + | 15.2855i | −0.158588 | + | 0.591858i | ||||
\(668\) | −1.67303 | + | 0.448288i | −0.0647316 | + | 0.0173448i | ||||
\(669\) | 22.9928 | + | 13.2749i | 0.888954 | + | 0.513238i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.85702i | − | 0.110294i | ||||||
\(672\) | −7.59363 | − | 2.69465i | −0.292931 | − | 0.103949i | ||||
\(673\) | −29.8394 | + | 29.8394i | −1.15023 | + | 1.15023i | −0.163719 | + | 0.986507i | \(0.552349\pi\) |
−0.986507 | + | 0.163719i | \(0.947651\pi\) | |||||||
\(674\) | −20.9572 | + | 12.0997i | −0.807243 | + | 0.466062i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.91238 | − | 8.50848i | 0.188938 | − | 0.327249i | ||||
\(677\) | −8.07197 | − | 2.16288i | −0.310231 | − | 0.0831261i | 0.100345 | − | 0.994953i | \(-0.468005\pi\) |
−0.410575 | + | 0.911827i | \(0.634672\pi\) | |||||||
\(678\) | 12.9209 | + | 12.9209i | 0.496222 | + | 0.496222i | ||||
\(679\) | 4.41644 | + | 0.350497i | 0.169488 | + | 0.0134508i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.27492 | − | 9.13642i | −0.202135 | − | 0.350109i | ||||
\(682\) | 2.03963 | + | 7.61202i | 0.0781017 | + | 0.291479i | ||||
\(683\) | 2.11591 | + | 7.89668i | 0.0809630 | + | 0.302158i | 0.994519 | − | 0.104555i | \(-0.0333417\pi\) |
−0.913556 | + | 0.406713i | \(0.866675\pi\) | |||||||
\(684\) | −23.2309 | − | 40.2371i | −0.888256 | − | 1.53851i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.22508 | − | 17.7679i | −0.199495 | − | 0.678382i | ||||
\(687\) | −29.8394 | − | 29.8394i | −1.13845 | − | 1.13845i | ||||
\(688\) | 0.700376 | + | 0.187665i | 0.0267016 | + | 0.00715467i | ||||
\(689\) | −30.6353 | + | 53.0619i | −1.16711 | + | 2.02150i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.4743 | + | 18.7490i | −1.23538 | + | 0.713246i | −0.968146 | − | 0.250386i | \(-0.919443\pi\) |
−0.267233 | + | 0.963632i | \(0.586109\pi\) | |||||||
\(692\) | 12.5842 | − | 12.5842i | 0.478378 | − | 0.478378i | ||||
\(693\) | −28.7350 | + | 24.5094i | −1.09155 | + | 0.931036i | ||||
\(694\) | 27.8248i | 1.05621i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −13.9124 | − | 8.03231i | −0.527347 | − | 0.304464i | ||||
\(697\) | 17.3867 | − | 4.65874i | 0.658567 | − | 0.176462i | ||||
\(698\) | 2.36468 | − | 8.82511i | 0.0895045 | − | 0.334035i | ||||
\(699\) | 59.8421 | 2.26343 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.725083 | −0.0273860 | −0.0136930 | − | 0.999906i | \(-0.504359\pi\) | ||||
−0.0136930 | + | 0.999906i | \(0.504359\pi\) | |||||||
\(702\) | 12.3326 | − | 46.0259i | 0.465464 | − | 1.73714i | ||||
\(703\) | −16.2704 | + | 4.35964i | −0.613649 | + | 0.164427i | ||||
\(704\) | 1.97014 | + | 1.13746i | 0.0742523 | + | 0.0428696i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25.2011i | 0.948454i | ||||||||
\(707\) | −4.38953 | − | 23.7708i | −0.165085 | − | 0.893994i | ||||
\(708\) | 22.3796 | − | 22.3796i | 0.841076 | − | 0.841076i | ||||
\(709\) | −31.0251 | + | 17.9124i | −1.16517 | + | 0.672713i | −0.952538 | − | 0.304418i | \(-0.901538\pi\) |
−0.212635 | + | 0.977132i | \(0.568205\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.3746 | − | 54.3424i | 1.17664 | − | 2.03800i | ||||
\(712\) | −8.82511 | − | 2.36468i | −0.330735 | − | 0.0886202i | ||||
\(713\) | 7.34847 | + | 7.34847i | 0.275202 | + | 0.275202i | ||||
\(714\) | 22.9928 | + | 15.8248i | 0.860485 | + | 0.592226i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.41238 | − | 11.1066i | −0.239642 | − | 0.415072i | ||||
\(717\) | −8.31566 | − | 31.0345i | −0.310554 | − | 1.15900i | ||||
\(718\) | 8.19149 | + | 30.5711i | 0.305704 | + | 1.14090i | ||||
\(719\) | 6.45203 | + | 11.1752i | 0.240620 | + | 0.416766i | 0.960891 | − | 0.276926i | \(-0.0893158\pi\) |
−0.720271 | + | 0.693693i | \(0.755983\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.00000 | − | 0.476171i | 0.0372419 | − | 0.0177335i | ||||
\(722\) | −25.3319 | − | 25.3319i | −0.942757 | − | 0.942757i | ||||
\(723\) | −11.5911 | − | 3.10583i | −0.431078 | − | 0.115507i | ||||
\(724\) | −4.09204 | + | 7.08762i | −0.152080 | + | 0.263409i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −15.3625 | + | 8.86957i | −0.570157 | + | 0.329181i | ||||
\(727\) | −23.3515 | + | 23.3515i | −0.866060 | + | 0.866060i | −0.992034 | − | 0.125973i | \(-0.959795\pi\) |
0.125973 | + | 0.992034i | \(0.459795\pi\) | |||||||
\(728\) | −8.20281 | − | 9.61702i | −0.304016 | − | 0.356431i | ||||
\(729\) | 18.6495i | 0.690722i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.17525 | − | 1.25588i | −0.0804545 | − | 0.0464504i | ||||
\(732\) | 3.69443 | − | 0.989919i | 0.136550 | − | 0.0365884i | ||||
\(733\) | 9.30569 | − | 34.7293i | 0.343714 | − | 1.28276i | −0.550394 | − | 0.834905i | \(-0.685523\pi\) |
0.894108 | − | 0.447852i | \(-0.147811\pi\) | |||||||
\(734\) | −14.7512 | −0.544477 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | 0.110581 | ||||||||
\(737\) | 6.63858 | − | 24.7755i | 0.244535 | − | 0.912618i | ||||
\(738\) | −31.4944 | + | 8.43891i | −1.15933 | + | 0.310640i | ||||
\(739\) | −23.2309 | − | 13.4124i | −0.854563 | − | 0.493382i | 0.00762477 | − | 0.999971i | \(-0.497573\pi\) |
−0.862188 | + | 0.506589i | \(0.830906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 107.732i | − | 3.95765i | ||||||
\(742\) | 22.0196 | + | 25.8159i | 0.808363 | + | 0.947730i | ||||
\(743\) | −10.6066 | + | 10.6066i | −0.389118 | + | 0.389118i | −0.874373 | − | 0.485254i | \(-0.838727\pi\) |
0.485254 | + | 0.874373i | \(0.338727\pi\) | |||||||
\(744\) | −9.13642 | + | 5.27492i | −0.334958 | + | 0.193388i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.72508 | + | 6.45203i | −0.136385 | + | 0.236226i | ||||
\(747\) | −7.61202 | − | 2.03963i | −0.278509 | − | 0.0746263i | ||||
\(748\) | −5.57239 | − | 5.57239i | −0.203747 | − | 0.203747i | ||||
\(749\) | 37.8016 | − | 18.0000i | 1.38124 | − | 0.657706i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0000 | + | 34.6410i | 0.729810 | + | 1.26407i | 0.956963 | + | 0.290209i | \(0.0937250\pi\) |
−0.227153 | + | 0.973859i | \(0.572942\pi\) | |||||||
\(752\) | 0.123242 | + | 0.459945i | 0.00449417 | + | 0.0167725i | ||||
\(753\) | 5.08567 | + | 18.9800i | 0.185332 | + | 0.691668i | ||||
\(754\) | −12.6005 | − | 21.8248i | −0.458884 | − | 0.794811i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −21.7371 | − | 14.9605i | −0.790572 | − | 0.544109i | ||||
\(757\) | 4.24264 | + | 4.24264i | 0.154201 | + | 0.154201i | 0.779992 | − | 0.625790i | \(-0.215223\pi\) |
−0.625790 | + | 0.779992i | \(0.715223\pi\) | |||||||
\(758\) | −3.06705 | − | 0.821815i | −0.111400 | − | 0.0298497i | ||||
\(759\) | 10.3923 | − | 18.0000i | 0.377217 | − | 0.653359i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.5876 | + | 18.8145i | −1.18130 | + | 0.682024i | −0.956315 | − | 0.292338i | \(-0.905567\pi\) |
−0.224985 | + | 0.974362i | \(0.572233\pi\) | |||||||
\(762\) | −20.9427 | + | 20.9427i | −0.758675 | + | 0.758675i | ||||
\(763\) | 6.64201 | + | 35.9687i | 0.240457 | + | 1.30216i | ||||
\(764\) | − | 21.0997i | − | 0.763359i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.1495 | + | 15.6748i | 0.980951 | + | 0.566353i | ||||
\(767\) | 47.9577 | − | 12.8502i | 1.73165 | − | 0.463995i | ||||
\(768\) | −0.788227 | + | 2.94170i | −0.0284427 | + | 0.106150i | ||||
\(769\) | −47.4142 | −1.70980 | −0.854899 | − | 0.518794i | \(-0.826381\pi\) | ||||
−0.854899 | + | 0.518794i | \(0.826381\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0000 | −0.864339 | ||||||||
\(772\) | −1.17758 | + | 4.39480i | −0.0423822 | + | 0.158172i | ||||
\(773\) | 19.6164 | − | 5.25621i | 0.705555 | − | 0.189053i | 0.111837 | − | 0.993727i | \(-0.464326\pi\) |
0.593717 | + | 0.804674i | \(0.297660\pi\) | |||||||
\(774\) | 3.94027 | + | 2.27492i | 0.141630 | + | 0.0817702i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 1.67451i | − | 0.0601113i | ||||||
\(777\) | −13.9463 | + | 11.8954i | −0.500320 | + | 0.426746i | ||||
\(778\) | 19.1624 | − | 19.1624i | 0.687004 | − | 0.687004i | ||||
\(779\) | −33.3197 | + | 19.2371i | −1.19380 | + | 0.689242i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.82475 | − | 11.8208i | 0.244209 | − | 0.422982i | ||||
\(782\) | −10.0382 | − | 2.68973i | −0.358965 | − | 0.0961844i | ||||
\(783\) | −37.2011 | − | 37.2011i | −1.32946 | − | 1.32946i | ||||
\(784\) | −6.53835 | + | 2.50000i | −0.233512 | + | 0.0892857i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.00000 | − | 10.3923i | −0.214013 | − | 0.370681i | ||||
\(787\) | −4.18762 | − | 15.6284i | −0.149272 | − | 0.557092i | −0.999528 | − | 0.0307222i | \(-0.990219\pi\) |
0.850255 | − | 0.526370i | \(-0.176447\pi\) | |||||||
\(788\) | 1.76638 | + | 6.59220i | 0.0629245 | + | 0.234838i | ||||
\(789\) | 5.82409 | + | 10.0876i | 0.207343 | + | 0.359129i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.8248 | + | 1.25588i | 0.562663 | + | 0.0446540i | ||||
\(792\) | 10.0939 | + | 10.0939i | 0.358671 | + | 0.358671i | ||||
\(793\) | 5.79555 | + | 1.55291i | 0.205806 | + | 0.0551456i | ||||
\(794\) | 9.55505 | − | 16.5498i | 0.339096 | − | 0.587332i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.82475 | − | 3.94027i | 0.241897 | − | 0.139659i | ||||
\(797\) | −9.79796 | + | 9.79796i | −0.347062 | + | 0.347062i | −0.859014 | − | 0.511952i | \(-0.828922\pi\) |
0.511952 | + | 0.859014i | \(0.328922\pi\) | |||||||
\(798\) | −56.2261 | − | 19.9522i | −1.99038 | − | 0.706301i | ||||
\(799\) | − | 1.64950i | − | 0.0583552i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −49.6495 | − | 28.6652i | −1.75428 | − | 1.01283i | ||||
\(802\) | 11.6874 | − | 3.13162i | 0.412696 | − | 0.110582i | ||||
\(803\) | 0.492968 | − | 1.83978i | 0.0173965 | − | 0.0649245i | ||||
\(804\) | 34.3375 | 1.21099 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.5498 | −0.582943 | ||||||||
\(807\) | −15.3931 | + | 57.4477i | −0.541862 | + | 2.02226i | ||||
\(808\) | −8.82511 | + | 2.36468i | −0.310466 | + | 0.0831892i | ||||
\(809\) | 20.8709 | + | 12.0498i | 0.733783 | + | 0.423650i | 0.819804 | − | 0.572644i | \(-0.194082\pi\) |
−0.0860217 | + | 0.996293i | \(0.527415\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.2131i | − | 0.780008i | −0.920813 | − | 0.390004i | \(-0.872474\pi\) | ||
0.920813 | − | 0.390004i | \(-0.127526\pi\) | |||||||
\(812\) | −13.7241 | + | 2.53430i | −0.481621 | + | 0.0889365i | ||||
\(813\) | 39.3501 | − | 39.3501i | 1.38007 | − | 1.38007i | ||||
\(814\) | 4.48190 | − | 2.58762i | 0.157090 | − | 0.0906962i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.27492 | − | 9.13642i | 0.184659 | − | 0.319839i | ||||
\(817\) | 5.18585 | + | 1.38954i | 0.181430 | + | 0.0486140i | ||||
\(818\) | −3.33753 | − | 3.33753i | −0.116694 | − | 0.116694i | ||||
\(819\) | −34.0994 | − | 71.6117i | −1.19153 | − | 2.50232i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.09967 | + | 10.5649i | 0.212880 | + | 0.368719i | 0.952615 | − | 0.304180i | \(-0.0983824\pi\) |
−0.739735 | + | 0.672899i | \(0.765049\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.989919 | + | 3.69443i | 0.0345064 | + | 0.128780i | 0.981030 | − | 0.193854i | \(-0.0620987\pi\) |
−0.946524 | + | 0.322633i | \(0.895432\pi\) | |||||||
\(824\) | −0.209313 | − | 0.362541i | −0.00729178 | − | 0.0126297i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.17525 | − | 27.4093i | 0.0756866 | − | 0.953691i | ||||
\(827\) | 29.3267 | + | 29.3267i | 1.01979 | + | 1.01979i | 0.999800 | + | 0.0199900i | \(0.00636345\pi\) |
0.0199900 | + | 0.999800i | \(0.493637\pi\) | |||||||
\(828\) | 18.1833 | + | 4.87220i | 0.631914 | + | 0.169321i | ||||
\(829\) | 7.40437 | − | 12.8248i | 0.257165 | − | 0.445422i | −0.708317 | − | 0.705895i | \(-0.750545\pi\) |
0.965481 | + | 0.260473i | \(0.0838784\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 39.8248 | − | 22.9928i | 1.38151 | − | 0.797612i | ||||
\(832\) | −3.37822 | + | 3.37822i | −0.117119 | + | 0.117119i | ||||
\(833\) | 24.1192 | − | 2.50304i | 0.835680 | − | 0.0867252i | ||||
\(834\) | 66.1993i | 2.29230i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 14.5876 | + | 8.42217i | 0.504524 | + | 0.291287i | ||||
\(837\) | −33.3726 | + | 8.94216i | −1.15353 | + | 0.309086i | ||||
\(838\) | 3.05945 | − | 11.4180i | 0.105687 | − | 0.394429i | ||||
\(839\) | 28.6652 | 0.989631 | 0.494816 | − | 0.868998i | \(-0.335236\pi\) | ||||
0.494816 | + | 0.868998i | \(0.335236\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.17525 | 0.0405258 | ||||||||
\(842\) | −3.15119 | + | 11.7604i | −0.108597 | + | 0.405290i | ||||
\(843\) | 86.4113 | − | 23.1538i | 2.97616 | − | 0.797461i | ||||
\(844\) | −14.5707 | − | 8.41238i | −0.501543 | − | 0.289566i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.98793i | 0.102727i | ||||||||
\(847\) | −5.15377 | + | 14.5235i | −0.177086 | + | 0.499034i | ||||
\(848\) | 9.06847 | − | 9.06847i | 0.311412 | − | 0.311412i | ||||
\(849\) | −73.3949 | + | 42.3746i | −2.51891 | + | 1.45429i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.41238 | − | 5.91041i | 0.116975 | − | 0.202606i | ||||
\(852\) | 17.6502 | + | 4.72936i | 0.604686 | + | 0.162025i | ||||
\(853\) | 28.0359 | + | 28.0359i | 0.959930 | + | 0.959930i | 0.999228 | − | 0.0392974i | \(-0.0125120\pi\) |
−0.0392974 | + | 0.999228i | \(0.512512\pi\) | |||||||
\(854\) | 1.88382 | − | 2.73713i | 0.0644630 | − | 0.0936626i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.91238 | − | 13.7046i | −0.270439 | − | 0.468415i | ||||
\(857\) | −9.45872 | − | 35.3004i | −0.323104 | − | 1.20584i | −0.916204 | − | 0.400711i | \(-0.868763\pi\) |
0.593101 | − | 0.805128i | \(-0.297904\pi\) | |||||||
\(858\) | 8.56682 | + | 31.9718i | 0.292467 | + | 1.09150i | ||||
\(859\) | −14.3326 | − | 24.8248i | −0.489021 | − | 0.847010i | 0.510899 | − | 0.859641i | \(-0.329313\pi\) |
−0.999920 | + | 0.0126311i | \(0.995979\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.7371 | + | 34.4892i | −0.808959 | + | 1.17539i | ||||
\(862\) | 13.7533 | + | 13.7533i | 0.468441 | + | 0.468441i | ||||
\(863\) | −37.6711 | − | 10.0939i | −1.28234 | − | 0.343602i | −0.447593 | − | 0.894237i | \(-0.647719\pi\) |
−0.834746 | + | 0.550635i | \(0.814385\pi\) | |||||||
\(864\) | −4.98684 | + | 8.63746i | −0.169656 | + | 0.293852i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17.2749 | − | 9.97368i | 0.587026 | − | 0.338919i | ||||
\(867\) | 10.7674 | − | 10.7674i | 0.365679 | − | 0.365679i | ||||
\(868\) | −3.06506 | + | 8.63744i | −0.104035 | + | 0.293174i | ||||
\(869\) | 22.7492i | 0.771713i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.6495 | + | 26.9331i | 1.58066 | + | 0.912593i | ||||
\(872\) | 13.3537 | − | 3.57811i | 0.452213 | − | 0.121170i | ||||
\(873\) | 2.71951 | − | 10.1494i | 0.0920416 | − | 0.343504i | ||||
\(874\) | 22.2131 | 0.751370 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.54983 | 0.0861509 | ||||||||
\(877\) | 9.53095 | − | 35.5700i | 0.321837 | − | 1.20111i | −0.595616 | − | 0.803269i | \(-0.703092\pi\) |
0.917453 | − | 0.397844i | \(-0.130241\pi\) | |||||||
\(878\) | 20.0764 | − | 5.37945i | 0.677545 | − | 0.181548i | ||||
\(879\) | 46.9380 | + | 27.0997i | 1.58318 | + | 0.914049i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.9572i | 0.706067i | 0.935611 | + | 0.353034i | \(0.114850\pi\) | ||||
−0.935611 | + | 0.353034i | \(0.885150\pi\) | |||||||
\(882\) | −43.6898 | + | 4.53404i | −1.47111 | + | 0.152669i | ||||
\(883\) | 14.9197 | − | 14.9197i | 0.502089 | − | 0.502089i | −0.409998 | − | 0.912086i | \(-0.634471\pi\) |
0.912086 | + | 0.409998i | \(0.134471\pi\) | |||||||
\(884\) | 14.3326 | − | 8.27492i | 0.482057 | − | 0.278316i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.9124 | − | 29.2931i | 0.568182 | − | 0.984121i | ||||
\(887\) | 16.4371 | + | 4.40432i | 0.551905 | + | 0.147882i | 0.523985 | − | 0.851728i | \(-0.324445\pi\) |
0.0279202 | + | 0.999610i | \(0.491112\pi\) | |||||||
\(888\) | 4.89898 | + | 4.89898i | 0.164399 | + | 0.164399i | ||||
\(889\) | −2.03559 | + | 25.6495i | −0.0682715 | + | 0.860257i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.1375 | + | 22.7547i | 0.440121 | + | 0.762313i | ||||
\(892\) | −2.25633 | − | 8.42075i | −0.0755476 | − | 0.281947i | ||||
\(893\) | 0.912530 | + | 3.40561i | 0.0305367 | + | 0.113964i | ||||
\(894\) | −14.9605 | − | 25.9124i | −0.500355 | − | 0.866639i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.13746 | + | 2.38876i | 0.0379998 | + | 0.0798030i | ||||
\(897\) | 30.8649 | + | 30.8649i | 1.03055 | + | 1.03055i | ||||
\(898\) | 36.2704 | + | 9.71861i | 1.21036 | + | 0.324314i | ||||
\(899\) | −9.13642 | + | 15.8248i | −0.304717 | + | 0.527785i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38.4743 | + | 22.2131i | −1.28176 | + | 0.740026i | ||||
\(902\) | 8.35858 | − | 8.35858i | 0.278310 | − | 0.278310i | ||||
\(903\) | 5.74527 | − | 1.06093i | 0.191191 | − | 0.0353054i | ||||
\(904\) | − | 6.00000i | − | 0.199557i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.27492 | − | 3.04547i | −0.175247 | − | 0.101179i | ||||
\(907\) | 24.0751 | − | 6.45091i | 0.799402 | − | 0.214199i | 0.164081 | − | 0.986447i | \(-0.447534\pi\) |
0.635321 | + | 0.772248i | \(0.280868\pi\) | |||||||
\(908\) | −0.896575 | + | 3.34607i | −0.0297539 | + | 0.111043i | ||||
\(909\) | −57.3303 | −1.90153 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.6495 | 0.849806 | 0.424903 | − | 0.905239i | \(-0.360308\pi\) | ||||
0.424903 | + | 0.905239i | \(0.360308\pi\) | |||||||
\(912\) | −5.83633 | + | 21.7815i | −0.193260 | + | 0.721256i | ||||
\(913\) | 2.75967 | − | 0.739452i | 0.0913318 | − | 0.0244723i | ||||
\(914\) | 16.8443 | + | 9.72508i | 0.557161 | + | 0.321677i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.8564i | 0.457829i | ||||||||
\(917\) | −9.82473 | − | 3.48638i | −0.324441 | − | 0.115130i | ||||
\(918\) | 24.4304 | − | 24.4304i | 0.806324 | − | 0.806324i | ||||
\(919\) | 10.0888 | − | 5.82475i | 0.332798 | − | 0.192141i | −0.324285 | − | 0.945959i | \(-0.605124\pi\) |
0.657083 | + | 0.753819i | \(0.271790\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.4622 | + | 49.2980i | −0.937862 | + | 1.62442i | ||||
\(922\) | −35.3004 | − | 9.45872i | −1.16256 | − | 0.311506i | ||||
\(923\) | 20.2693 | + | 20.2693i | 0.667173 | + | 0.667173i | ||||
\(924\) | 18.2728 | + | 1.45017i | 0.601133 | + | 0.0477069i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.22508 | − | 14.2463i | −0.270293 | − | 0.468161i | ||||
\(927\) | −0.679878 | − | 2.53734i | −0.0223301 | − | 0.0833372i | ||||
\(928\) | 1.36525 | + | 5.09518i | 0.0448165 | + | 0.167257i | ||||
\(929\) | −6.53835 | − | 11.3248i | −0.214516 | − | 0.371553i | 0.738607 | − | 0.674137i | \(-0.235484\pi\) |
−0.953123 | + | 0.302584i | \(0.902151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −48.4124 | + | 18.5109i | −1.58665 | + | 0.606671i | ||||
\(932\) | −13.8943 | − | 13.8943i | −0.455123 | − | 0.455123i | ||||
\(933\) | −76.9355 | − | 20.6148i | −2.51876 | − | 0.674899i | ||||
\(934\) | −13.2285 | + | 22.9124i | −0.432849 | + | 0.749716i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −25.9622 | + | 14.9893i | −0.848601 | + | 0.489940i | ||||
\(937\) | −30.2300 | + | 30.2300i | −0.987572 | + | 0.987572i | −0.999924 | − | 0.0123513i | \(-0.996068\pi\) |
0.0123513 | + | 0.999924i | \(0.496068\pi\) | |||||||
\(938\) | 22.6961 | − | 19.3586i | 0.741054 | − | 0.632079i | ||||
\(939\) | − | 34.1993i | − | 1.11605i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.6495 | − | 28.6652i | −1.61853 | − | 0.934457i | −0.987301 | − | 0.158859i | \(-0.949219\pi\) |
−0.631226 | − | 0.775599i | \(-0.717448\pi\) | |||||||
\(942\) | −16.5170 | + | 4.42572i | −0.538153 | + | 0.144198i | ||||
\(943\) | 4.03459 | − | 15.0573i | 0.131384 | − | 0.490333i | ||||
\(944\) | −10.3923 | −0.338241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.64950 | −0.0536300 | ||||||||
\(947\) | −0.989919 | + | 3.69443i | −0.0321680 | + | 0.120053i | −0.980143 | − | 0.198292i | \(-0.936460\pi\) |
0.947975 | + | 0.318345i | \(0.103127\pi\) | |||||||
\(948\) | −29.4170 | + | 7.88227i | −0.955421 | + | 0.256004i | ||||
\(949\) | 3.46410 | + | 2.00000i | 0.112449 | + | 0.0649227i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 54.8185i | 1.77761i | ||||||||
\(952\) | −1.66430 | − | 9.01277i | −0.0539404 | − | 0.292106i | ||||
\(953\) | −36.2739 | + | 36.2739i | −1.17503 | + | 1.17503i | −0.194031 | + | 0.980995i | \(0.562156\pi\) |
−0.980995 | + | 0.194031i | \(0.937844\pi\) | |||||||
\(954\) | 69.6927 | − | 40.2371i | 2.25639 | − | 1.30273i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.27492 | + | 9.13642i | −0.170603 | + | 0.295493i | ||||
\(957\) | 35.3004 | + | 9.45872i | 1.14110 | + | 0.305757i | ||||
\(958\) | 12.9209 | + | 12.9209i | 0.417454 | + | 0.417454i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.50000 | − | 16.4545i | −0.306452 | − | 0.530790i | ||||
\(962\) | 2.81297 | + | 10.4981i | 0.0906937 | + | 0.338474i | ||||
\(963\) | −25.7005 | − | 95.9155i | −0.828186 | − | 3.09083i | ||||
\(964\) | 1.97014 | + | 3.41238i | 0.0634538 | + | 0.109905i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 21.8248 | − | 10.3923i | 0.702200 | − | 0.334367i | ||||
\(967\) | 17.6242 | + | 17.6242i | 0.566757 | + | 0.566757i | 0.931218 | − | 0.364462i | \(-0.118747\pi\) |
−0.364462 | + | 0.931218i | \(0.618747\pi\) | |||||||
\(968\) | 5.62628 | + | 1.50756i | 0.180835 | + | 0.0484547i | ||||
\(969\) | 39.0575 | − | 67.6495i | 1.25471 | − | 2.17322i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.76287 | − | 4.48190i | 0.249122 | − | 0.143831i | −0.370240 | − | 0.928936i | \(-0.620725\pi\) |
0.619362 | + | 0.785105i | \(0.287391\pi\) | |||||||
\(972\) | −3.71492 | + | 3.71492i | −0.119156 | + | 0.119156i | ||||
\(973\) | 37.3214 | + | 43.7559i | 1.19647 | + | 1.40275i | ||||
\(974\) | − | 21.0997i | − | 0.676077i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.08762 | − | 0.627940i | −0.0348140 | − | 0.0200999i | ||||
\(977\) | −24.7755 | + | 6.63858i | −0.792639 | + | 0.212387i | −0.632350 | − | 0.774683i | \(-0.717909\pi\) |
−0.160289 | + | 0.987070i | \(0.551243\pi\) | |||||||
\(978\) | −9.45872 | + | 35.3004i | −0.302457 | + | 1.12878i | ||||
\(979\) | 20.7846 | 0.664279 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 86.7492 | 2.76969 | ||||||||
\(982\) | 8.94216 | − | 33.3726i | 0.285356 | − | 1.06496i | ||||
\(983\) | −16.8971 | + | 4.52756i | −0.538933 | + | 0.144407i | −0.518010 | − | 0.855374i | \(-0.673327\pi\) |
−0.0209228 | + | 0.999781i | \(0.506660\pi\) | |||||||
\(984\) | 13.7046 | + | 7.91238i | 0.436888 | + | 0.252237i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 18.2728i | − | 0.581926i | ||||||
\(987\) | 2.48987 | + | 2.91914i | 0.0792535 | + | 0.0929173i | ||||
\(988\) | −25.0136 | + | 25.0136i | −0.795789 | + | 0.795789i | ||||
\(989\) | −1.88382 | + | 1.08762i | −0.0599020 | + | 0.0345844i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.8248 | + | 20.4811i | −0.375626 | + | 0.650603i | −0.990420 | − | 0.138084i | \(-0.955905\pi\) |
0.614795 | + | 0.788687i | \(0.289239\pi\) | |||||||
\(992\) | 3.34607 | + | 0.896575i | 0.106238 | + | 0.0284663i | ||||
\(993\) | −62.0734 | − | 62.0734i | −1.96984 | − | 1.96984i | ||||
\(994\) | 14.3326 | − | 6.82475i | 0.454602 | − | 0.216468i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.91238 | + | 3.31233i | 0.0605959 | + | 0.104955i | ||||
\(997\) | −5.59615 | − | 20.8851i | −0.177232 | − | 0.661438i | −0.996161 | − | 0.0875432i | \(-0.972098\pi\) |
0.818929 | − | 0.573895i | \(-0.194568\pi\) | |||||||
\(998\) | −1.03528 | − | 3.86370i | −0.0327711 | − | 0.122303i | ||||
\(999\) | 11.3446 | + | 19.6495i | 0.358929 | + | 0.621683i |
(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 | 350.2.o.d.157.2 | yes | 16 | |
5.2 | odd | 4 | inner | 350.2.o.d.143.1 | ✓ | 16 | |
5.3 | odd | 4 | inner | 350.2.o.d.143.4 | yes | 16 | |
5.4 | even | 2 | inner | 350.2.o.d.157.3 | yes | 16 | |
7.5 | odd | 6 | inner | 350.2.o.d.257.4 | yes | 16 | |
35.12 | even | 12 | inner | 350.2.o.d.243.3 | yes | 16 | |
35.19 | odd | 6 | inner | 350.2.o.d.257.1 | yes | 16 | |
35.33 | even | 12 | inner | 350.2.o.d.243.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
350.2.o.d.143.1 | ✓ | 16 | 5.2 | odd | 4 | inner | |
350.2.o.d.143.4 | yes | 16 | 5.3 | odd | 4 | inner | |
350.2.o.d.157.2 | yes | 16 | 1.1 | even | 1 | trivial | |
350.2.o.d.157.3 | yes | 16 | 5.4 | even | 2 | inner | |
350.2.o.d.243.2 | yes | 16 | 35.33 | even | 12 | inner | |
350.2.o.d.243.3 | yes | 16 | 35.12 | even | 12 | inner | |
350.2.o.d.257.1 | yes | 16 | 35.19 | odd | 6 | inner | |
350.2.o.d.257.4 | yes | 16 | 7.5 | odd | 6 | inner |