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 | 257.1 | ||
Root | \(0.0811201 + 2.23460i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.257 |
Dual form | 350.2.o.d.143.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965926 | + | 0.258819i | −0.683013 | + | 0.183013i | ||||
\(3\) | −0.788227 | + | 2.94170i | −0.455083 | + | 1.69839i | 0.232761 | + | 0.972534i | \(0.425224\pi\) |
−0.687844 | + | 0.725859i | \(0.741443\pi\) | |||||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 3.04547i | − | 1.24331i | ||||||
\(7\) | −2.01297 | − | 1.71696i | −0.760832 | − | 0.648949i | ||||
\(8\) | −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 | 0.642024 | − | 0.766685i | \(-0.278095\pi\) |
−0.984980 | + | 0.172666i | \(0.944762\pi\) | |||||||
\(12\) | 0.788227 | + | 2.94170i | 0.227542 | + | 0.849196i | ||||
\(13\) | −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 | ||||
\(17\) | 3.34607 | + | 0.896575i | 0.811540 | + | 0.217451i | 0.640644 | − | 0.767838i | \(-0.278667\pi\) |
0.170896 | + | 0.985289i | \(0.445334\pi\) | |||||||
\(18\) | 6.06110 | + | 1.62407i | 1.42862 | + | 0.382797i | ||||
\(19\) | −3.70219 | + | 6.41238i | −0.849340 | + | 1.47110i | 0.0324583 | + | 0.999473i | \(0.489666\pi\) |
−0.881798 | + | 0.471627i | \(0.843667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.63746 | − | 4.56821i | 1.44841 | − | 0.996866i | ||||
\(22\) | 1.60861 | + | 1.60861i | 0.342957 | + | 0.342957i | ||||
\(23\) | −0.776457 | − | 2.89778i | −0.161903 | − | 0.604228i | −0.998415 | − | 0.0562805i | \(-0.982076\pi\) |
0.836512 | − | 0.547948i | \(-0.184591\pi\) | |||||||
\(24\) | −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 | ||||
\(28\) | −2.60176 | − | 0.480443i | −0.491687 | − | 0.0907953i | ||||
\(29\) | − | 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 | −0.744599 | − | 0.667512i | \(-0.767359\pi\) |
0.205783 | + | 0.978598i | \(0.434026\pi\) | |||||||
\(32\) | −0.258819 | + | 0.965926i | −0.0457532 | + | 0.170753i | ||||
\(33\) | 6.69213 | − | 1.79315i | 1.16495 | − | 0.312148i | ||||
\(34\) | −3.46410 | −0.594089 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.27492 | −1.04582 | ||||||||
\(37\) | −2.19740 | + | 0.588792i | −0.361251 | + | 0.0967968i | −0.434879 | − | 0.900489i | \(-0.643209\pi\) |
0.0736283 | + | 0.997286i | \(0.476542\pi\) | |||||||
\(38\) | 1.91639 | − | 7.15208i | 0.310880 | − | 1.16022i | ||||
\(39\) | 12.6005 | − | 7.27492i | 2.01770 | − | 1.16492i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.19615i | − | 0.811503i | −0.913984 | − | 0.405751i | \(-0.867010\pi\) | ||
0.913984 | − | 0.405751i | \(-0.132990\pi\) | |||||||
\(42\) | −5.22895 | + | 6.13045i | −0.806845 | + | 0.945950i | ||||
\(43\) | −0.512711 | + | 0.512711i | −0.0781877 | + | 0.0781877i | −0.745119 | − | 0.666931i | \(-0.767607\pi\) |
0.666931 | + | 0.745119i | \(0.267607\pi\) | |||||||
\(44\) | −1.97014 | − | 1.13746i | −0.297009 | − | 0.171478i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.50000 | + | 2.59808i | 0.221163 | + | 0.383065i | ||||
\(47\) | −0.123242 | − | 0.459945i | −0.0179767 | − | 0.0670899i | 0.956355 | − | 0.292208i | \(-0.0943899\pi\) |
−0.974332 | + | 0.225118i | \(0.927723\pi\) | |||||||
\(48\) | 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 | ||||
\(52\) | −4.61474 | − | 1.23651i | −0.639949 | − | 0.171474i | ||||
\(53\) | −12.3878 | − | 3.31929i | −1.70159 | − | 0.455940i | −0.728251 | − | 0.685311i | \(-0.759666\pi\) |
−0.973339 | + | 0.229371i | \(0.926333\pi\) | |||||||
\(54\) | −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 | ||||
\(58\) | 1.36525 | + | 5.09518i | 0.179266 | + | 0.669030i | ||||
\(59\) | 5.19615 | + | 9.00000i | 0.676481 | + | 1.17170i | 0.976034 | + | 0.217620i | \(0.0698294\pi\) |
−0.299552 | + | 0.954080i | \(0.596837\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.08762 | − | 0.627940i | −0.139256 | − | 0.0803995i | 0.428753 | − | 0.903422i | \(-0.358953\pi\) |
−0.568009 | + | 0.823022i | \(0.692286\pi\) | |||||||
\(62\) | 2.44949 | − | 2.44949i | 0.311086 | − | 0.311086i | ||||
\(63\) | 5.55208 | + | 15.6460i | 0.699497 | + | 1.97121i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.00000 | + | 3.46410i | −0.738549 | + | 0.426401i | ||||
\(67\) | −2.91816 | + | 10.8907i | −0.356510 | + | 1.33051i | 0.522063 | + | 0.852907i | \(0.325163\pi\) |
−0.878573 | + | 0.477608i | \(0.841504\pi\) | |||||||
\(68\) | 3.34607 | − | 0.896575i | 0.405770 | − | 0.108726i | ||||
\(69\) | 9.13642 | 1.09990 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 6.06110 | − | 1.62407i | 0.714308 | − | 0.191398i | ||||
\(73\) | 0.216697 | − | 0.808725i | 0.0253625 | − | 0.0946541i | −0.952084 | − | 0.305835i | \(-0.901064\pi\) |
0.977447 | + | 0.211181i | \(0.0677310\pi\) | |||||||
\(74\) | 1.97014 | − | 1.13746i | 0.229024 | − | 0.132227i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.40437i | 0.849340i | ||||||||
\(77\) | −1.09297 | + | 5.91880i | −0.124555 | + | 0.674510i | ||||
\(78\) | −10.2883 | + | 10.2883i | −1.16492 | + | 1.16492i | ||||
\(79\) | −8.66025 | − | 5.00000i | −0.974355 | − | 0.562544i | −0.0737937 | − | 0.997274i | \(-0.523511\pi\) |
−0.900561 | + | 0.434730i | \(0.856844\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.77492 | + | 10.0025i | 0.641657 | + | 1.11138i | ||||
\(82\) | 1.34486 | + | 5.01910i | 0.148515 | + | 0.554267i | ||||
\(83\) | −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 | ||||
\(87\) | 15.5172 | + | 4.15783i | 1.66362 | + | 0.445766i | ||||
\(88\) | 2.19740 | + | 0.588792i | 0.234244 | + | 0.0627654i | ||||
\(89\) | 4.56821 | − | 7.91238i | 0.484230 | − | 0.838710i | −0.515606 | − | 0.856826i | \(-0.672433\pi\) |
0.999836 | + | 0.0181154i | \(0.00576663\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | + | 12.6005i | 0.104828 | + | 1.32089i | ||||
\(92\) | −2.12132 | − | 2.12132i | −0.221163 | − | 0.221163i | ||||
\(93\) | −2.73050 | − | 10.1904i | −0.283139 | − | 1.05669i | ||||
\(94\) | 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 | \(0.222908\pi\) | |||||||
\(98\) | −2.85554 | − | 6.39108i | −0.288453 | − | 0.645596i | ||||
\(99\) | 14.2749i | 1.43468i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.91238 | + | 4.56821i | −0.787311 | + | 0.454554i | −0.839015 | − | 0.544108i | \(-0.816868\pi\) |
0.0517042 | + | 0.998662i | \(0.483535\pi\) | |||||||
\(102\) | 2.73050 | − | 10.1904i | 0.270360 | − | 1.00900i | ||||
\(103\) | −0.404362 | + | 0.108349i | −0.0398430 | + | 0.0106759i | −0.278685 | − | 0.960382i | \(-0.589899\pi\) |
0.238842 | + | 0.971058i | \(0.423232\pi\) | |||||||
\(104\) | 4.77753 | 0.468475 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.8248 | 1.24565 | ||||||||
\(107\) | 15.2855 | − | 4.09575i | 1.47771 | − | 0.395951i | 0.572142 | − | 0.820155i | \(-0.306113\pi\) |
0.905567 | + | 0.424204i | \(0.139446\pi\) | |||||||
\(108\) | 2.58138 | − | 9.63383i | 0.248393 | − | 0.927016i | ||||
\(109\) | −11.9726 | + | 6.91238i | −1.14677 | + | 0.662086i | −0.948097 | − | 0.317981i | \(-0.896995\pi\) |
−0.198669 | + | 0.980067i | \(0.563662\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 6.92820i | − | 0.657596i | ||||||
\(112\) | −2.49342 | + | 0.884806i | −0.235606 | + | 0.0836063i | ||||
\(113\) | −4.24264 | + | 4.24264i | −0.399114 | + | 0.399114i | −0.877920 | − | 0.478806i | \(-0.841070\pi\) |
0.478806 | + | 0.877920i | \(0.341070\pi\) | |||||||
\(114\) | 19.5287 | + | 11.2749i | 1.82903 | + | 1.05599i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.63746 | − | 4.56821i | −0.244882 | − | 0.424148i | ||||
\(117\) | 7.75903 | + | 28.9571i | 0.717322 | + | 2.67708i | ||||
\(118\) | −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 | ||||
\(122\) | 1.21309 | + | 0.325046i | 0.109828 | + | 0.0294283i | ||||
\(123\) | 15.2855 | + | 4.09575i | 1.37825 | + | 0.369301i | ||||
\(124\) | −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 | 0.332794 | − | 0.943000i | \(-0.392009\pi\) |
−0.943000 | + | 0.332794i | \(0.892009\pi\) | |||||||
\(128\) | 0.258819 | + | 0.965926i | 0.0228766 | + | 0.0853766i | ||||
\(129\) | −1.10411 | − | 1.91238i | −0.0972115 | − | 0.168375i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.41238 | − | 1.97014i | −0.298141 | − | 0.172132i | 0.343467 | − | 0.939165i | \(-0.388399\pi\) |
−0.641607 | + | 0.767033i | \(0.721732\pi\) | |||||||
\(132\) | 4.89898 | − | 4.89898i | 0.426401 | − | 0.426401i | ||||
\(133\) | 18.4622 | − | 6.55143i | 1.60087 | − | 0.568081i | ||||
\(134\) | − | 11.2749i | − | 0.974004i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | + | 1.73205i | −0.257248 | + | 0.148522i | ||||
\(137\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(138\) | −8.82511 | + | 2.36468i | −0.751243 | + | 0.201295i | ||||
\(139\) | −21.7370 | −1.84370 | −0.921852 | − | 0.387542i | \(-0.873324\pi\) | ||||
−0.921852 | + | 0.387542i | \(0.873324\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.45017 | 0.122126 | ||||||||
\(142\) | 5.79555 | − | 1.55291i | 0.486352 | − | 0.130318i | ||||
\(143\) | −2.81297 | + | 10.4981i | −0.235232 | + | 0.877899i | ||||
\(144\) | −5.43424 | + | 3.13746i | −0.452853 | + | 0.261455i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.837253i | 0.0692916i | ||||||||
\(147\) | −21.2044 | − | 2.20055i | −1.74891 | − | 0.181499i | ||||
\(148\) | −1.60861 | + | 1.60861i | −0.132227 | + | 0.132227i | ||||
\(149\) | 8.50848 | + | 4.91238i | 0.697042 | + | 0.402438i | 0.806245 | − | 0.591582i | \(-0.201496\pi\) |
−0.109203 | + | 0.994020i | \(0.534830\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00000 | − | 1.73205i | −0.0813788 | − | 0.140952i | 0.822464 | − | 0.568818i | \(-0.192599\pi\) |
−0.903842 | + | 0.427865i | \(0.859266\pi\) | |||||||
\(152\) | −1.91639 | − | 7.15208i | −0.155440 | − | 0.580110i | ||||
\(153\) | −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 | ||||
\(157\) | −5.42346 | − | 1.45321i | −0.432839 | − | 0.115979i | 0.0358194 | − | 0.999358i | \(-0.488596\pi\) |
−0.468659 | + | 0.883379i | \(0.655263\pi\) | |||||||
\(158\) | 9.65926 | + | 2.58819i | 0.768449 | + | 0.205905i | ||||
\(159\) | 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 | ||||
\(163\) | 3.10583 | + | 11.5911i | 0.243267 | + | 0.907886i | 0.974246 | + | 0.225486i | \(0.0723970\pi\) |
−0.730979 | + | 0.682400i | \(0.760936\pi\) | |||||||
\(164\) | −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 | \(0.228652\pi\) | |||||||
\(168\) | −1.46318 | + | 7.92361i | −0.112887 | + | 0.611319i | ||||
\(169\) | 9.82475i | 0.755750i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 40.2371 | − | 23.2309i | 3.07701 | − | 1.77651i | ||||
\(172\) | −0.187665 | + | 0.700376i | −0.0143093 | + | 0.0534032i | ||||
\(173\) | 17.1903 | − | 4.60612i | 1.30695 | − | 0.350197i | 0.462877 | − | 0.886422i | \(-0.346817\pi\) |
0.844075 | + | 0.536226i | \(0.180150\pi\) | |||||||
\(174\) | −16.0646 | −1.21786 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.27492 | −0.171478 | ||||||||
\(177\) | −30.5711 | + | 8.19149i | −2.29786 | + | 0.615710i | ||||
\(178\) | −2.36468 | + | 8.82511i | −0.177240 | + | 0.661470i | ||||
\(179\) | −11.1066 | + | 6.41238i | −0.830143 | + | 0.479283i | −0.853902 | − | 0.520434i | \(-0.825770\pi\) |
0.0237584 | + | 0.999718i | \(0.492437\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.18408i | 0.608318i | 0.952621 | + | 0.304159i | \(0.0983754\pi\) | ||||
−0.952621 | + | 0.304159i | \(0.901625\pi\) | |||||||
\(182\) | −4.22718 | − | 11.9124i | −0.313340 | − | 0.883002i | ||||
\(183\) | 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 | ||||
\(187\) | −2.03963 | − | 7.61202i | −0.149153 | − | 0.556646i | ||||
\(188\) | −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 | −0.177750 | − | 0.984076i | \(-0.556882\pi\) |
0.941110 | − | 0.338101i | \(-0.109785\pi\) | |||||||
\(192\) | 2.94170 | + | 0.788227i | 0.212299 | + | 0.0568854i | ||||
\(193\) | −4.39480 | − | 1.17758i | −0.316345 | − | 0.0847643i | 0.0971530 | − | 0.995269i | \(-0.469026\pi\) |
−0.413498 | + | 0.910505i | \(0.635693\pi\) | |||||||
\(194\) | −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 | 0.857804 | − | 0.513978i | \(-0.171829\pi\) |
−0.513978 | + | 0.857804i | \(0.671829\pi\) | |||||||
\(198\) | −3.69462 | − | 13.7885i | −0.262565 | − | 0.979907i | ||||
\(199\) | 3.94027 | + | 6.82475i | 0.279318 | + | 0.483794i | 0.971216 | − | 0.238202i | \(-0.0765581\pi\) |
−0.691897 | + | 0.721996i | \(0.743225\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −29.7371 | − | 17.1687i | −2.09750 | − | 1.21099i | ||||
\(202\) | 6.46043 | − | 6.46043i | 0.454554 | − | 0.454554i | ||||
\(203\) | −9.05681 | + | 10.6183i | −0.635664 | + | 0.745256i | ||||
\(204\) | 10.5498i | 0.738636i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.362541 | − | 0.209313i | 0.0252595 | − | 0.0145836i | ||||
\(207\) | −4.87220 | + | 18.1833i | −0.338642 | + | 1.26383i | ||||
\(208\) | −4.61474 | + | 1.23651i | −0.319974 | + | 0.0857369i | ||||
\(209\) | 16.8443 | 1.16515 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8248 | 1.15826 | 0.579132 | − | 0.815234i | \(-0.303392\pi\) | ||||
0.579132 | + | 0.815234i | \(0.303392\pi\) | |||||||
\(212\) | −12.3878 | + | 3.31929i | −0.850795 | + | 0.227970i | ||||
\(213\) | 4.72936 | − | 17.6502i | 0.324051 | − | 1.20937i | ||||
\(214\) | −13.7046 | + | 7.91238i | −0.936830 | + | 0.540879i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.97368i | 0.678623i | ||||||||
\(217\) | 9.01277 | + | 1.66430i | 0.611827 | + | 0.112980i | ||||
\(218\) | 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 | ||||
\(222\) | 1.79315 | + | 6.69213i | 0.120348 | + | 0.449146i | ||||
\(223\) | 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 | ||||
\(227\) | 3.34607 | + | 0.896575i | 0.222086 | + | 0.0595078i | 0.368146 | − | 0.929768i | \(-0.379993\pi\) |
−0.146060 | + | 0.989276i | \(0.546659\pi\) | |||||||
\(228\) | −21.7815 | − | 5.83633i | −1.44251 | − | 0.386520i | ||||
\(229\) | 6.92820 | − | 12.0000i | 0.457829 | − | 0.792982i | −0.541017 | − | 0.841011i | \(-0.681961\pi\) |
0.998846 | + | 0.0480291i | \(0.0152940\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.5498 | − | 7.88054i | −1.08890 | − | 0.518502i | ||||
\(232\) | 3.72993 | + | 3.72993i | 0.244882 | + | 0.244882i | ||||
\(233\) | 5.08567 | + | 18.9800i | 0.333173 | + | 1.24342i | 0.905836 | + | 0.423628i | \(0.139244\pi\) |
−0.572663 | + | 0.819791i | \(0.694090\pi\) | |||||||
\(234\) | −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 | ||||
\(238\) | 6.97314 | + | 5.94772i | 0.452001 | + | 0.385533i | ||||
\(239\) | − | 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 | −0.605862 | − | 0.795569i | \(-0.707172\pi\) |
0.386052 | + | 0.922477i | \(0.373839\pi\) | |||||||
\(242\) | −1.50756 | + | 5.62628i | −0.0969094 | + | 0.361671i | ||||
\(243\) | −5.07468 | + | 1.35976i | −0.325541 | + | 0.0872284i | ||||
\(244\) | −1.25588 | −0.0803995 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.8248 | −1.00895 | ||||||||
\(247\) | 34.1692 | − | 9.15562i | 2.17414 | − | 0.582558i | ||||
\(248\) | 0.896575 | − | 3.34607i | 0.0569326 | − | 0.212475i | ||||
\(249\) | 3.31233 | − | 1.91238i | 0.209911 | − | 0.121192i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 6.45203i | − | 0.407249i | −0.979049 | − | 0.203624i | \(-0.934728\pi\) | ||
0.979049 | − | 0.203624i | \(-0.0652721\pi\) | |||||||
\(252\) | 12.6312 | + | 10.7738i | 0.795693 | + | 0.678684i | ||||
\(253\) | −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 | ||||
\(257\) | 2.03963 | + | 7.61202i | 0.127229 | + | 0.474825i | 0.999909 | − | 0.0134670i | \(-0.00428682\pi\) |
−0.872680 | + | 0.488292i | \(0.837620\pi\) | |||||||
\(258\) | 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 | ||||
\(262\) | 3.80601 | + | 1.01982i | 0.235136 | + | 0.0630045i | ||||
\(263\) | 3.69443 | + | 0.989919i | 0.227808 | + | 0.0610410i | 0.370917 | − | 0.928666i | \(-0.379043\pi\) |
−0.143109 | + | 0.989707i | \(0.545710\pi\) | |||||||
\(264\) | −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 | ||||
\(268\) | 2.91816 | + | 10.8907i | 0.178255 | + | 0.665257i | ||||
\(269\) | 9.76436 | + | 16.9124i | 0.595344 | + | 1.03117i | 0.993498 | + | 0.113847i | \(0.0363175\pi\) |
−0.398154 | + | 0.917318i | \(0.630349\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.8248 | + | 9.13642i | 0.961285 | + | 0.554998i | 0.896568 | − | 0.442905i | \(-0.146052\pi\) |
0.0647169 | + | 0.997904i | \(0.479386\pi\) | |||||||
\(272\) | 2.44949 | − | 2.44949i | 0.148522 | − | 0.148522i | ||||
\(273\) | −37.8552 | − | 6.99037i | −2.29110 | − | 0.423076i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.91238 | − | 4.56821i | 0.476269 | − | 0.274974i | ||||
\(277\) | 3.90808 | − | 14.5852i | 0.234814 | − | 0.876337i | −0.743419 | − | 0.668826i | \(-0.766797\pi\) |
0.978233 | − | 0.207511i | \(-0.0665363\pi\) | |||||||
\(278\) | 20.9963 | − | 5.62594i | 1.25927 | − | 0.337421i | ||||
\(279\) | 21.7370 | 1.30136 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.3746 | 1.75234 | 0.876170 | − | 0.482001i | \(-0.160090\pi\) | ||||
0.876170 | + | 0.482001i | \(0.160090\pi\) | |||||||
\(282\) | −1.40075 | + | 0.375330i | −0.0834136 | + | 0.0223506i | ||||
\(283\) | 7.20239 | − | 26.8797i | 0.428138 | − | 1.59783i | −0.328837 | − | 0.944387i | \(-0.606657\pi\) |
0.756974 | − | 0.653445i | \(-0.226677\pi\) | |||||||
\(284\) | −5.19615 | + | 3.00000i | −0.308335 | + | 0.178017i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 10.8685i | − | 0.642666i | ||||||
\(287\) | −8.92158 | + | 10.4597i | −0.526624 | + | 0.617417i | ||||
\(288\) | 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 | ||||
\(292\) | −0.216697 | − | 0.808725i | −0.0126812 | − | 0.0473270i | ||||
\(293\) | 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 | ||||
\(297\) | −21.9162 | − | 5.87242i | −1.27171 | − | 0.340752i | ||||
\(298\) | −9.48998 | − | 2.54283i | −0.549740 | − | 0.147302i | ||||
\(299\) | −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 | ||||
\(303\) | −7.20158 | − | 26.8766i | −0.413720 | − | 1.54402i | ||||
\(304\) | 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 | \(0.429082\pi\) | |||||||
\(308\) | 2.01286 | + | 5.67231i | 0.114693 | + | 0.323210i | ||||
\(309\) | − | 1.27492i | − | 0.0725275i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.6495 | + | 13.0767i | −1.28434 | + | 0.741511i | −0.977638 | − | 0.210296i | \(-0.932557\pi\) |
−0.306698 | + | 0.951807i | \(0.599224\pi\) | |||||||
\(312\) | −3.76577 | + | 14.0541i | −0.213195 | + | 0.795655i | ||||
\(313\) | −10.8469 | + | 2.90642i | −0.613104 | + | 0.164281i | −0.551991 | − | 0.833850i | \(-0.686132\pi\) |
−0.0611132 | + | 0.998131i | \(0.519465\pi\) | |||||||
\(314\) | 5.61478 | 0.316860 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | −17.3867 | + | 4.65874i | −0.976532 | + | 0.261661i | −0.711584 | − | 0.702601i | \(-0.752022\pi\) |
−0.264949 | + | 0.964262i | \(0.585355\pi\) | |||||||
\(318\) | −10.1088 | + | 37.7266i | −0.566874 | + | 2.11560i | ||||
\(319\) | −10.3923 | + | 6.00000i | −0.581857 | + | 0.335936i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 48.1939i | 2.68992i | ||||||||
\(322\) | 1.44133 | − | 7.80529i | 0.0803222 | − | 0.434972i | ||||
\(323\) | −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 | ||||
\(327\) | −10.8970 | − | 40.6683i | −0.602608 | − | 2.24896i | ||||
\(328\) | 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 | 0.132441 | + | 0.991191i | \(0.457718\pi\) |
−0.924617 | + | 0.380898i | \(0.875615\pi\) | |||||||
\(332\) | −1.21309 | − | 0.325046i | −0.0665768 | − | 0.0178392i | ||||
\(333\) | 13.7885 | + | 3.69462i | 0.755606 | + | 0.202464i | ||||
\(334\) | −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 | 0.0657148 | − | 0.997838i | \(-0.479067\pi\) |
−0.997838 | + | 0.0657148i | \(0.979067\pi\) | |||||||
\(338\) | −2.54283 | − | 9.48998i | −0.138312 | − | 0.516187i | ||||
\(339\) | −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 | ||||
\(343\) | 9.64572 | − | 15.8101i | 0.520820 | − | 0.853667i | ||||
\(344\) | − | 0.725083i | − | 0.0390938i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.4124 | + | 8.89834i | −0.828574 | + | 0.478378i | ||||
\(347\) | 7.20158 | − | 26.8766i | 0.386601 | − | 1.44281i | −0.449027 | − | 0.893518i | \(-0.648229\pi\) |
0.835628 | − | 0.549296i | \(-0.185104\pi\) | |||||||
\(348\) | 15.5172 | − | 4.15783i | 0.831811 | − | 0.222883i | ||||
\(349\) | 9.13642 | 0.489062 | 0.244531 | − | 0.969642i | \(-0.421366\pi\) | ||||
0.244531 | + | 0.969642i | \(0.421366\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −47.6495 | −2.54334 | ||||||||
\(352\) | 2.19740 | − | 0.588792i | 0.117122 | − | 0.0313827i | ||||
\(353\) | −6.52251 | + | 24.3423i | −0.347158 | + | 1.29561i | 0.542912 | + | 0.839789i | \(0.317322\pi\) |
−0.890070 | + | 0.455823i | \(0.849345\pi\) | |||||||
\(354\) | 27.4093 | − | 15.8248i | 1.45679 | − | 0.841076i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 9.13642i | − | 0.484230i | ||||||
\(357\) | 26.3051 | − | 9.33455i | 1.39221 | − | 0.494037i | ||||
\(358\) | 9.06847 | − | 9.06847i | 0.479283 | − | 0.479283i | ||||
\(359\) | −27.4093 | − | 15.8248i | −1.44661 | − | 0.835198i | −0.448329 | − | 0.893869i | \(-0.647981\pi\) |
−0.998277 | + | 0.0586703i | \(0.981314\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9124 | − | 31.0251i | −0.942757 | − | 1.63290i | ||||
\(362\) | −2.11820 | − | 7.90522i | −0.111330 | − | 0.415489i | ||||
\(363\) | 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 | ||||
\(367\) | −14.2486 | − | 3.81789i | −0.743769 | − | 0.199292i | −0.133017 | − | 0.991114i | \(-0.542466\pi\) |
−0.610753 | + | 0.791821i | \(0.709133\pi\) | |||||||
\(368\) | −2.89778 | − | 0.776457i | −0.151057 | − | 0.0404756i | ||||
\(369\) | −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 | ||||
\(373\) | 1.92824 | + | 7.19631i | 0.0998407 | + | 0.372611i | 0.997709 | − | 0.0676538i | \(-0.0215513\pi\) |
−0.897868 | + | 0.440264i | \(0.854885\pi\) | |||||||
\(374\) | 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 | ||||
\(378\) | 24.8685 | − | 8.82477i | 1.27910 | − | 0.453897i | ||||
\(379\) | 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 | ||||
\(382\) | −5.46100 | + | 20.3807i | −0.279409 | + | 1.04277i | ||||
\(383\) | −30.2813 | + | 8.11386i | −1.54730 | + | 0.414599i | −0.928617 | − | 0.371039i | \(-0.879002\pi\) |
−0.618687 | + | 0.785638i | \(0.712335\pi\) | |||||||
\(384\) | −3.04547 | −0.155414 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.54983 | 0.231580 | ||||||||
\(387\) | 4.39480 | − | 1.17758i | 0.223400 | − | 0.0598599i | ||||
\(388\) | 0.433394 | − | 1.61745i | 0.0220023 | − | 0.0821136i | ||||
\(389\) | 23.4690 | − | 13.5498i | 1.18993 | − | 0.687004i | 0.231636 | − | 0.972803i | \(-0.425592\pi\) |
0.958290 | + | 0.285799i | \(0.0922589\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.3923i | − | 0.525561i | ||||||
\(392\) | −5.66851 | − | 4.10706i | −0.286303 | − | 0.207438i | ||||
\(393\) | 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 | ||||
\(397\) | 4.94606 | + | 18.4589i | 0.248236 | + | 0.926428i | 0.971729 | + | 0.236097i | \(0.0758683\pi\) |
−0.723494 | + | 0.690331i | \(0.757465\pi\) | |||||||
\(398\) | −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 | −0.976615 | − | 0.214997i | \(-0.931026\pi\) |
0.674500 | + | 0.738275i | \(0.264359\pi\) | |||||||
\(402\) | 33.1675 | + | 8.88719i | 1.65424 | + | 0.443253i | ||||
\(403\) | 15.9859 | + | 4.28341i | 0.796315 | + | 0.213372i | ||||
\(404\) | −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 | ||||
\(408\) | −2.73050 | − | 10.1904i | −0.135180 | − | 0.504498i | ||||
\(409\) | 2.35999 | + | 4.08762i | 0.116694 | + | 0.202120i | 0.918456 | − | 0.395524i | \(-0.129437\pi\) |
−0.801762 | + | 0.597644i | \(0.796104\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.296014 | + | 0.296014i | −0.0145836 | + | 0.0145836i | ||||
\(413\) | 4.99291 | − | 27.0383i | 0.245685 | − | 1.33047i | ||||
\(414\) | − | 18.8248i | − | 0.925186i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.13746 | − | 2.38876i | 0.202856 | − | 0.117119i | ||||
\(417\) | 17.1336 | − | 63.9437i | 0.839038 | − | 3.13133i | ||||
\(418\) | −16.2704 | + | 4.35964i | −0.795810 | + | 0.213237i | ||||
\(419\) | 11.8208 | 0.577485 | 0.288742 | − | 0.957407i | \(-0.406763\pi\) | ||||
0.288742 | + | 0.957407i | \(0.406763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.1752 | 0.593385 | 0.296693 | − | 0.954973i | \(-0.404116\pi\) | ||||
0.296693 | + | 0.954973i | \(0.404116\pi\) | |||||||
\(422\) | −16.2515 | + | 4.35457i | −0.791109 | + | 0.211977i | ||||
\(423\) | −0.773333 | + | 2.88612i | −0.0376008 | + | 0.140328i | ||||
\(424\) | 11.1066 | − | 6.41238i | 0.539382 | − | 0.311412i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 18.2728i | 0.885322i | ||||||||
\(427\) | 1.11121 | + | 3.13143i | 0.0537752 | + | 0.151541i | ||||
\(428\) | 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 | 0.999349 | − | 0.0360659i | \(-0.0114826\pi\) |
−0.530909 | + | 0.847429i | \(0.678149\pi\) | |||||||
\(432\) | −2.58138 | − | 9.63383i | −0.124197 | − | 0.463508i | ||||
\(433\) | −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 | ||||
\(437\) | 21.4562 | + | 5.74918i | 1.02639 | + | 0.275021i | ||||
\(438\) | −2.46295 | − | 0.659946i | −0.117684 | − | 0.0315334i | ||||
\(439\) | 10.3923 | − | 18.0000i | 0.495998 | − | 0.859093i | −0.503992 | − | 0.863708i | \(-0.668136\pi\) |
0.999989 | + | 0.00461537i | \(0.00146912\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.6873 | − | 41.0276i | 0.747014 | − | 1.95370i | ||||
\(442\) | 11.7025 | + | 11.7025i | 0.556631 | + | 0.556631i | ||||
\(443\) | −8.75449 | − | 32.6722i | −0.415938 | − | 1.55230i | −0.782949 | − | 0.622086i | \(-0.786285\pi\) |
0.367010 | − | 0.930217i | \(-0.380381\pi\) | |||||||
\(444\) | −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 | ||||
\(448\) | −1.71696 | + | 2.01297i | −0.0811186 | + | 0.0951040i | ||||
\(449\) | − | 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 | ||||
\(452\) | −1.55291 | + | 5.79555i | −0.0730429 | + | 0.272600i | ||||
\(453\) | 5.88341 | − | 1.57645i | 0.276427 | − | 0.0740683i | ||||
\(454\) | −3.46410 | −0.162578 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 22.5498 | 1.05599 | ||||||||
\(457\) | 18.7874 | − | 5.03407i | 0.878838 | − | 0.235484i | 0.208932 | − | 0.977930i | \(-0.433001\pi\) |
0.669906 | + | 0.742446i | \(0.266334\pi\) | |||||||
\(458\) | −3.58630 | + | 13.3843i | −0.167577 | + | 0.625405i | ||||
\(459\) | 29.9210 | − | 17.2749i | 1.39659 | − | 0.806324i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 36.5457i | − | 1.70210i | −0.525082 | − | 0.851051i | \(-0.675965\pi\) | ||
0.525082 | − | 0.851051i | \(-0.324035\pi\) | |||||||
\(462\) | 18.0255 | + | 3.32861i | 0.838624 | + | 0.154861i | ||||
\(463\) | 11.6320 | − | 11.6320i | 0.540586 | − | 0.540586i | −0.383115 | − | 0.923701i | \(-0.625149\pi\) |
0.923701 | + | 0.383115i | \(0.125149\pi\) | |||||||
\(464\) | −4.56821 | − | 2.63746i | −0.212074 | − | 0.122441i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.82475 | − | 17.0170i | −0.455123 | − | 0.788296i | ||||
\(467\) | −6.84756 | − | 25.5554i | −0.316867 | − | 1.18256i | −0.922239 | − | 0.386621i | \(-0.873642\pi\) |
0.605371 | − | 0.795943i | \(-0.293025\pi\) | |||||||
\(468\) | 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 | ||||
\(472\) | −10.0382 | − | 2.68973i | −0.462045 | − | 0.123805i | ||||
\(473\) | 1.59330 | + | 0.426923i | 0.0732599 | + | 0.0196299i | ||||
\(474\) | −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 | ||||
\(478\) | 2.73050 | + | 10.1904i | 0.124890 | + | 0.466096i | ||||
\(479\) | −9.13642 | − | 15.8248i | −0.417454 | − | 0.723051i | 0.578229 | − | 0.815875i | \(-0.303744\pi\) |
−0.995683 | + | 0.0928234i | \(0.970411\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.41238 | + | 5.43424i | 0.429167 | + | 0.247780i | ||||
\(482\) | 2.78619 | − | 2.78619i | 0.126908 | − | 0.126908i | ||||
\(483\) | −18.3914 | − | 15.6869i | −0.836836 | − | 0.713777i | ||||
\(484\) | − | 5.82475i | − | 0.264761i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.54983 | − | 2.62685i | 0.206385 | − | 0.119156i | ||||
\(487\) | −5.46100 | + | 20.3807i | −0.247461 | + | 0.923538i | 0.724669 | + | 0.689097i | \(0.241993\pi\) |
−0.972130 | + | 0.234441i | \(0.924674\pi\) | |||||||
\(488\) | 1.21309 | − | 0.325046i | 0.0549139 | − | 0.0147141i | ||||
\(489\) | −36.5457 | −1.65265 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.5498 | −1.55921 | −0.779606 | − | 0.626270i | \(-0.784581\pi\) | ||||
−0.779606 | + | 0.626270i | \(0.784581\pi\) | |||||||
\(492\) | 15.2855 | − | 4.09575i | 0.689125 | − | 0.184651i | ||||
\(493\) | 4.72936 | − | 17.6502i | 0.213000 | − | 0.794926i | ||||
\(494\) | −30.6353 | + | 17.6873i | −1.37835 | + | 0.795789i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.46410i | 0.155543i | ||||||||
\(497\) | 12.0778 | + | 10.3017i | 0.541765 | + | 0.462097i | ||||
\(498\) | −2.70451 | + | 2.70451i | −0.121192 | + | 0.121192i | ||||
\(499\) | 3.46410 | + | 2.00000i | 0.155074 | + | 0.0895323i | 0.575529 | − | 0.817781i | \(-0.304796\pi\) |
−0.420455 | + | 0.907314i | \(0.638129\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.63746 | + | 4.56821i | 0.117833 | + | 0.204093i | ||||
\(502\) | 1.66991 | + | 6.23218i | 0.0745317 | + | 0.278156i | ||||
\(503\) | 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 | ||||
\(507\) | −28.9015 | − | 7.74413i | −1.28356 | − | 0.343929i | ||||
\(508\) | −9.39371 | − | 2.51704i | −0.416778 | − | 0.111675i | ||||
\(509\) | −18.9008 | + | 32.7371i | −0.837763 | + | 1.45105i | 0.0539983 | + | 0.998541i | \(0.482803\pi\) |
−0.891761 | + | 0.452507i | \(0.850530\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.82475 | + | 1.25588i | −0.0807223 | + | 0.0555569i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 19.1135 | + | 71.3325i | 0.843881 | + | 3.14941i | ||||
\(514\) | −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 | ||||
\(518\) | −5.91880 | − | 1.09297i | −0.260057 | − | 0.0480223i | ||||
\(519\) | 54.1993i | 2.37909i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.2371 | − | 5.91041i | 0.448497 | − | 0.258940i | −0.258698 | − | 0.965958i | \(-0.583294\pi\) |
0.707195 | + | 0.707018i | \(0.249960\pi\) | |||||||
\(522\) | 8.56682 | − | 31.9718i | 0.374960 | − | 1.39937i | ||||
\(523\) | −39.3441 | + | 10.5422i | −1.72040 | + | 0.460979i | −0.977935 | − | 0.208911i | \(-0.933008\pi\) |
−0.742461 | + | 0.669889i | \(0.766341\pi\) | |||||||
\(524\) | −3.94027 | −0.172132 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.82475 | −0.166767 | ||||||||
\(527\) | −11.5911 | + | 3.10583i | −0.504917 | + | 0.135292i | ||||
\(528\) | 1.79315 | − | 6.69213i | 0.0780369 | − | 0.291238i | ||||
\(529\) | 12.1244 | − | 7.00000i | 0.527146 | − | 0.304348i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 65.2109i | − | 2.82991i | ||||||
\(532\) | 12.7130 | − | 14.9048i | 0.551178 | − | 0.646205i | ||||
\(533\) | −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 | ||||
\(537\) | −10.1088 | − | 37.7266i | −0.436228 | − | 1.62802i | ||||
\(538\) | −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 | −0.289584 | − | 0.957153i | \(-0.593517\pi\) |
0.973710 | − | 0.227789i | \(-0.0731497\pi\) | |||||||
\(542\) | −17.6502 | − | 4.72936i | −0.758142 | − | 0.203143i | ||||
\(543\) | −24.0751 | − | 6.45091i | −1.03316 | − | 0.276835i | ||||
\(544\) | −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 | 0.839853 | − | 0.542814i | \(-0.182641\pi\) |
−0.542814 | + | 0.839853i | \(0.682641\pi\) | |||||||
\(548\) | 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 | ||||
\(553\) | 8.84806 | + | 24.9342i | 0.376258 | + | 1.06031i | ||||
\(554\) | 15.0997i | 0.641523i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.8248 | + | 10.8685i | −0.798347 | + | 0.460926i | ||||
\(557\) | −11.0839 | + | 41.3655i | −0.469638 | + | 1.75271i | 0.171397 | + | 0.985202i | \(0.445172\pi\) |
−0.641035 | + | 0.767512i | \(0.721495\pi\) | |||||||
\(558\) | −20.9963 | + | 5.62594i | −0.888844 | + | 0.238165i | ||||
\(559\) | 3.46410 | 0.146516 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | −28.3737 | + | 7.60270i | −1.19687 | + | 0.320701i | ||||
\(563\) | 5.05441 | − | 18.8633i | 0.213018 | − | 0.794993i | −0.773837 | − | 0.633385i | \(-0.781665\pi\) |
0.986855 | − | 0.161609i | \(-0.0516683\pi\) | |||||||
\(564\) | 1.25588 | − | 0.725083i | 0.0528821 | − | 0.0305315i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 27.8279i | 1.16969i | ||||||||
\(567\) | 5.54904 | − | 30.0499i | 0.233038 | − | 1.26198i | ||||
\(568\) | 4.24264 | − | 4.24264i | 0.178017 | − | 0.178017i | ||||
\(569\) | −11.1066 | − | 6.41238i | −0.465611 | − | 0.268821i | 0.248789 | − | 0.968558i | \(-0.419967\pi\) |
−0.714401 | + | 0.699737i | \(0.753301\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.82475 | − | 13.5529i | −0.327456 | − | 0.567170i | 0.654551 | − | 0.756018i | \(-0.272858\pi\) |
−0.982006 | + | 0.188848i | \(0.939525\pi\) | |||||||
\(572\) | 2.81297 | + | 10.4981i | 0.117616 | + | 0.438949i | ||||
\(573\) | 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 | ||||
\(577\) | −38.5353 | − | 10.3255i | −1.60425 | − | 0.429857i | −0.657925 | − | 0.753083i | \(-0.728566\pi\) |
−0.946322 | + | 0.323227i | \(0.895232\pi\) | |||||||
\(578\) | 4.82963 | + | 1.29410i | 0.200886 | + | 0.0538273i | ||||
\(579\) | 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 | ||||
\(583\) | 7.55111 | + | 28.1811i | 0.312735 | + | 1.16714i | ||||
\(584\) | 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 | \(0.318802\pi\) | |||||||
\(588\) | −19.4639 | + | 8.69649i | −0.802676 | + | 0.358637i | ||||
\(589\) | − | 25.6495i | − | 1.05687i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.0000 | + | 10.3923i | −0.740421 | + | 0.427482i | ||||
\(592\) | −0.588792 | + | 2.19740i | −0.0241992 | + | 0.0903126i | ||||
\(593\) | 18.5701 | − | 4.97585i | 0.762583 | − | 0.204333i | 0.143491 | − | 0.989652i | \(-0.454167\pi\) |
0.619092 | + | 0.785318i | \(0.287501\pi\) | |||||||
\(594\) | 22.6893 | 0.930953 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.82475 | 0.402438 | ||||||||
\(597\) | −23.1822 | + | 6.21166i | −0.948785 | + | 0.254226i | ||||
\(598\) | 3.70954 | − | 13.8442i | 0.151695 | − | 0.566132i | ||||
\(599\) | −28.6652 | + | 16.5498i | −1.17123 | + | 0.676208i | −0.953969 | − | 0.299906i | \(-0.903045\pi\) |
−0.217258 | + | 0.976114i | \(0.569711\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.92820i | 0.282607i | 0.989966 | + | 0.141304i | \(0.0451294\pi\) | ||||
−0.989966 | + | 0.141304i | \(0.954871\pi\) | |||||||
\(602\) | −1.80793 | + | 0.641557i | −0.0736858 | + | 0.0261479i | ||||
\(603\) | 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 | ||||
\(607\) | 5.64083 | + | 21.0519i | 0.228954 | + | 0.854469i | 0.980782 | + | 0.195109i | \(0.0625060\pi\) |
−0.751827 | + | 0.659360i | \(0.770827\pi\) | |||||||
\(608\) | −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 | ||||
\(612\) | −20.9963 | − | 5.62594i | −0.848724 | − | 0.227415i | ||||
\(613\) | −35.5700 | − | 9.53095i | −1.43666 | − | 0.384951i | −0.545296 | − | 0.838244i | \(-0.683583\pi\) |
−0.891362 | + | 0.453292i | \(0.850249\pi\) | |||||||
\(614\) | 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 | 0.485613 | − | 0.874174i | \(-0.338596\pi\) |
−0.874174 | + | 0.485613i | \(0.838596\pi\) | |||||||
\(618\) | 0.329973 | + | 1.23148i | 0.0132735 | + | 0.0495372i | ||||
\(619\) | −5.43424 | − | 9.41238i | −0.218420 | − | 0.378315i | 0.735905 | − | 0.677085i | \(-0.236757\pi\) |
−0.954325 | + | 0.298770i | \(0.903424\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −25.9124 | − | 14.9605i | −1.03983 | − | 0.600345i | ||||
\(622\) | 18.4932 | − | 18.4932i | 0.741511 | − | 0.741511i | ||||
\(623\) | −22.7809 | + | 8.08396i | −0.912697 | + | 0.323877i | ||||
\(624\) | − | 14.5498i | − | 0.582460i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.72508 | − | 5.61478i | 0.388692 | − | 0.224412i | ||||
\(627\) | −13.2772 | + | 49.5510i | −0.530239 | + | 1.97888i | ||||
\(628\) | −5.42346 | + | 1.45321i | −0.216420 | + | 0.0579895i | ||||
\(629\) | −7.88054 | −0.314218 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.64950 | 0.384141 | 0.192070 | − | 0.981381i | \(-0.438480\pi\) | ||||
0.192070 | + | 0.981381i | \(0.438480\pi\) | |||||||
\(632\) | 9.65926 | − | 2.58819i | 0.384225 | − | 0.102953i | ||||
\(633\) | −13.2617 | + | 49.4934i | −0.527106 | + | 1.96719i | ||||
\(634\) | 15.5885 | − | 9.00000i | 0.619097 | − | 0.357436i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 39.0575i | − | 1.54873i | ||||||
\(637\) | 19.6216 | − | 27.0815i | 0.777436 | − | 1.07301i | ||||
\(638\) | 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 | 0.999247 | + | 0.0387913i | \(0.0123508\pi\) |
−0.466029 | + | 0.884769i | \(0.654316\pi\) | |||||||
\(642\) | −12.4735 | − | 46.5517i | −0.492290 | − | 1.83725i | ||||
\(643\) | −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 | ||||
\(647\) | 5.01910 | + | 1.34486i | 0.197321 | + | 0.0528720i | 0.356126 | − | 0.934438i | \(-0.384097\pi\) |
−0.158805 | + | 0.987310i | \(0.550764\pi\) | |||||||
\(648\) | −11.1563 | − | 2.98932i | −0.438260 | − | 0.117431i | ||||
\(649\) | 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 | ||||
\(653\) | −9.95787 | − | 37.1633i | −0.389682 | − | 1.45431i | −0.830653 | − | 0.556790i | \(-0.812033\pi\) |
0.440972 | − | 0.897521i | \(-0.354634\pi\) | |||||||
\(654\) | 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 | ||||
\(658\) | 0.228773 | − | 1.23888i | 0.00891850 | − | 0.0482967i | ||||
\(659\) | − | 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 | −0.834478 | − | 0.551041i | \(-0.814231\pi\) |
0.0599765 | + | 0.998200i | \(0.480897\pi\) | |||||||
\(662\) | 7.46039 | − | 27.8426i | 0.289956 | − | 1.08213i | ||||
\(663\) | 48.6847 | − | 13.0450i | 1.89076 | − | 0.506627i | ||||
\(664\) | 1.25588 | 0.0487376 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.2749 | −0.553142 | ||||||||
\(667\) | −15.2855 | + | 4.09575i | −0.591858 | + | 0.158588i | ||||
\(668\) | 0.448288 | − | 1.67303i | 0.0173448 | − | 0.0647316i | ||||
\(669\) | −22.9928 | + | 13.2749i | −0.888954 | + | 0.513238i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.85702i | 0.110294i | ||||||||
\(672\) | 2.69465 | + | 7.59363i | 0.103949 | + | 0.292931i | ||||
\(673\) | 29.8394 | − | 29.8394i | 1.15023 | − | 1.15023i | 0.163719 | − | 0.986507i | \(-0.447651\pi\) |
0.986507 | − | 0.163719i | \(-0.0523490\pi\) | |||||||
\(674\) | 20.9572 | + | 12.0997i | 0.807243 | + | 0.466062i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.91238 | + | 8.50848i | 0.188938 | + | 0.327249i | ||||
\(677\) | 2.16288 | + | 8.07197i | 0.0831261 | + | 0.310231i | 0.994953 | − | 0.100345i | \(-0.0319945\pi\) |
−0.911827 | + | 0.410575i | \(0.865328\pi\) | |||||||
\(678\) | 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 | ||||
\(682\) | −7.61202 | − | 2.03963i | −0.291479 | − | 0.0781017i | ||||
\(683\) | 7.89668 | + | 2.11591i | 0.302158 | + | 0.0809630i | 0.406713 | − | 0.913556i | \(-0.366675\pi\) |
−0.104555 | + | 0.994519i | \(0.533342\pi\) | |||||||
\(684\) | 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 | ||||
\(688\) | 0.187665 | + | 0.700376i | 0.00715467 | + | 0.0267016i | ||||
\(689\) | 30.6353 | + | 53.0619i | 1.16711 | + | 2.02150i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.4743 | − | 18.7490i | −1.23538 | − | 0.713246i | −0.267233 | − | 0.963632i | \(-0.586109\pi\) |
−0.968146 | + | 0.250386i | \(0.919443\pi\) | |||||||
\(692\) | 12.5842 | − | 12.5842i | 0.478378 | − | 0.478378i | ||||
\(693\) | 24.5094 | − | 28.7350i | 0.931036 | − | 1.09155i | ||||
\(694\) | 27.8248i | 1.05621i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −13.9124 | + | 8.03231i | −0.527347 | + | 0.304464i | ||||
\(697\) | 4.65874 | − | 17.3867i | 0.176462 | − | 0.658567i | ||||
\(698\) | −8.82511 | + | 2.36468i | −0.334035 | + | 0.0895045i | ||||
\(699\) | −59.8421 | −2.26343 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.725083 | −0.0273860 | −0.0136930 | − | 0.999906i | \(-0.504359\pi\) | ||||
−0.0136930 | + | 0.999906i | \(0.504359\pi\) | |||||||
\(702\) | 46.0259 | − | 12.3326i | 1.73714 | − | 0.465464i | ||||
\(703\) | 4.35964 | − | 16.2704i | 0.164427 | − | 0.613649i | ||||
\(704\) | −1.97014 | + | 1.13746i | −0.0742523 | + | 0.0428696i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 25.2011i | − | 0.948454i | ||||||
\(707\) | 23.7708 | + | 4.38953i | 0.893994 | + | 0.165085i | ||||
\(708\) | −22.3796 | + | 22.3796i | −0.841076 | + | 0.841076i | ||||
\(709\) | 31.0251 | + | 17.9124i | 1.16517 | + | 0.672713i | 0.952538 | − | 0.304418i | \(-0.0984620\pi\) |
0.212635 | + | 0.977132i | \(0.431795\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.3746 | + | 54.3424i | 1.17664 | + | 2.03800i | ||||
\(712\) | 2.36468 | + | 8.82511i | 0.0886202 | + | 0.330735i | ||||
\(713\) | 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 | ||||
\(717\) | 31.0345 | + | 8.31566i | 1.15900 | + | 0.310554i | ||||
\(718\) | 30.5711 | + | 8.19149i | 1.14090 | + | 0.305704i | ||||
\(719\) | −6.45203 | + | 11.1752i | −0.240620 | + | 0.416766i | −0.960891 | − | 0.276926i | \(-0.910684\pi\) |
0.720271 | + | 0.693693i | \(0.244017\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.00000 | + | 0.476171i | 0.0372419 | + | 0.0177335i | ||||
\(722\) | 25.3319 | + | 25.3319i | 0.942757 | + | 0.942757i | ||||
\(723\) | −3.10583 | − | 11.5911i | −0.115507 | − | 0.431078i | ||||
\(724\) | 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 | \(0.459795\pi\) | |||||||
\(728\) | −9.61702 | − | 8.20281i | −0.356431 | − | 0.304016i | ||||
\(729\) | 18.6495i | 0.690722i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.17525 | + | 1.25588i | −0.0804545 | + | 0.0464504i | ||||
\(732\) | 0.989919 | − | 3.69443i | 0.0365884 | − | 0.136550i | ||||
\(733\) | −34.7293 | + | 9.30569i | −1.28276 | + | 0.343714i | −0.834905 | − | 0.550394i | \(-0.814477\pi\) |
−0.447852 | + | 0.894108i | \(0.647811\pi\) | |||||||
\(734\) | 14.7512 | 0.544477 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | 0.110581 | ||||||||
\(737\) | 24.7755 | − | 6.63858i | 0.912618 | − | 0.244535i | ||||
\(738\) | 8.43891 | − | 31.4944i | 0.310640 | − | 1.15933i | ||||
\(739\) | 23.2309 | − | 13.4124i | 0.854563 | − | 0.493382i | −0.00762477 | − | 0.999971i | \(-0.502427\pi\) |
0.862188 | + | 0.506589i | \(0.169094\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 107.732i | 3.95765i | ||||||||
\(742\) | −25.8159 | − | 22.0196i | −0.947730 | − | 0.808363i | ||||
\(743\) | 10.6066 | − | 10.6066i | 0.389118 | − | 0.389118i | −0.485254 | − | 0.874373i | \(-0.661273\pi\) |
0.874373 | + | 0.485254i | \(0.161273\pi\) | |||||||
\(744\) | 9.13642 | + | 5.27492i | 0.334958 | + | 0.193388i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.72508 | − | 6.45203i | −0.136385 | − | 0.236226i | ||||
\(747\) | 2.03963 | + | 7.61202i | 0.0746263 | + | 0.278509i | ||||
\(748\) | −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 | −0.227153 | − | 0.973859i | \(-0.572942\pi\) |
0.956963 | − | 0.290209i | \(-0.0937250\pi\) | |||||||
\(752\) | −0.459945 | − | 0.123242i | −0.0167725 | − | 0.00449417i | ||||
\(753\) | 18.9800 | + | 5.08567i | 0.691668 | + | 0.185332i | ||||
\(754\) | 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 | 0.625790 | − | 0.779992i | \(-0.284777\pi\) |
−0.779992 | + | 0.625790i | \(0.784777\pi\) | |||||||
\(758\) | −0.821815 | − | 3.06705i | −0.0298497 | − | 0.111400i | ||||
\(759\) | −10.3923 | − | 18.0000i | −0.377217 | − | 0.653359i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.5876 | − | 18.8145i | −1.18130 | − | 0.682024i | −0.224985 | − | 0.974362i | \(-0.572233\pi\) |
−0.956315 | + | 0.292338i | \(0.905567\pi\) | |||||||
\(762\) | −20.9427 | + | 20.9427i | −0.758675 | + | 0.758675i | ||||
\(763\) | 35.9687 | + | 6.64201i | 1.30216 | + | 0.240457i | ||||
\(764\) | − | 21.0997i | − | 0.763359i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.1495 | − | 15.6748i | 0.980951 | − | 0.566353i | ||||
\(767\) | 12.8502 | − | 47.9577i | 0.463995 | − | 1.73165i | ||||
\(768\) | 2.94170 | − | 0.788227i | 0.106150 | − | 0.0284427i | ||||
\(769\) | 47.4142 | 1.70980 | 0.854899 | − | 0.518794i | \(-0.173619\pi\) | ||||
0.854899 | + | 0.518794i | \(0.173619\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0000 | −0.864339 | ||||||||
\(772\) | −4.39480 | + | 1.17758i | −0.158172 | + | 0.0423822i | ||||
\(773\) | −5.25621 | + | 19.6164i | −0.189053 | + | 0.705555i | 0.804674 | + | 0.593717i | \(0.202340\pi\) |
−0.993727 | + | 0.111837i | \(0.964326\pi\) | |||||||
\(774\) | −3.94027 | + | 2.27492i | −0.141630 | + | 0.0817702i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.67451i | 0.0601113i | ||||||||
\(777\) | −11.8954 | + | 13.9463i | −0.426746 | + | 0.500320i | ||||
\(778\) | −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 | ||||
\(782\) | 2.68973 | + | 10.0382i | 0.0961844 | + | 0.358965i | ||||
\(783\) | −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 | ||||
\(787\) | 15.6284 | + | 4.18762i | 0.557092 | + | 0.149272i | 0.526370 | − | 0.850255i | \(-0.323553\pi\) |
0.0307222 | + | 0.999528i | \(0.490219\pi\) | |||||||
\(788\) | 6.59220 | + | 1.76638i | 0.234838 | + | 0.0629245i | ||||
\(789\) | −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 | ||||
\(793\) | 1.55291 | + | 5.79555i | 0.0551456 | + | 0.205806i | ||||
\(794\) | −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 | \(0.328922\pi\) | |||||||
\(798\) | −19.9522 | − | 56.2261i | −0.706301 | − | 1.99038i | ||||
\(799\) | − | 1.64950i | − | 0.0583552i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −49.6495 | + | 28.6652i | −1.75428 | + | 1.01283i | ||||
\(802\) | 3.13162 | − | 11.6874i | 0.110582 | − | 0.412696i | ||||
\(803\) | −1.83978 | + | 0.492968i | −0.0649245 | + | 0.0173965i | ||||
\(804\) | −34.3375 | −1.21099 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.5498 | −0.582943 | ||||||||
\(807\) | −57.4477 | + | 15.3931i | −2.02226 | + | 0.541862i | ||||
\(808\) | 2.36468 | − | 8.82511i | 0.0831892 | − | 0.310466i | ||||
\(809\) | −20.8709 | + | 12.0498i | −0.733783 | + | 0.423650i | −0.819804 | − | 0.572644i | \(-0.805918\pi\) |
0.0860217 | + | 0.996293i | \(0.472585\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.2131i | 0.780008i | 0.920813 | + | 0.390004i | \(0.127526\pi\) | ||||
−0.920813 | + | 0.390004i | \(0.872474\pi\) | |||||||
\(812\) | −2.53430 | + | 13.7241i | −0.0889365 | + | 0.481621i | ||||
\(813\) | −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 | ||||
\(817\) | −1.38954 | − | 5.18585i | −0.0486140 | − | 0.181430i | ||||
\(818\) | −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 | −0.739735 | − | 0.672899i | \(-0.765049\pi\) |
0.952615 | + | 0.304180i | \(0.0983824\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.69443 | + | 0.989919i | 0.128780 | + | 0.0345064i | 0.322633 | − | 0.946524i | \(-0.395432\pi\) |
−0.193854 | + | 0.981030i | \(0.562099\pi\) | |||||||
\(824\) | 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 | \(-0.993637\pi\) |
−0.0199900 | − | 0.999800i | \(-0.506363\pi\) | |||||||
\(828\) | 4.87220 | + | 18.1833i | 0.169321 | + | 0.631914i | ||||
\(829\) | −7.40437 | − | 12.8248i | −0.257165 | − | 0.445422i | 0.708317 | − | 0.705895i | \(-0.249455\pi\) |
−0.965481 | + | 0.260473i | \(0.916122\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 39.8248 | + | 22.9928i | 1.38151 | + | 0.797612i | ||||
\(832\) | −3.37822 | + | 3.37822i | −0.117119 | + | 0.117119i | ||||
\(833\) | −2.50304 | + | 24.1192i | −0.0867252 | + | 0.835680i | ||||
\(834\) | 66.1993i | 2.29230i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 14.5876 | − | 8.42217i | 0.504524 | − | 0.291287i | ||||
\(837\) | −8.94216 | + | 33.3726i | −0.309086 | + | 1.15353i | ||||
\(838\) | −11.4180 | + | 3.05945i | −0.394429 | + | 0.105687i | ||||
\(839\) | −28.6652 | −0.989631 | −0.494816 | − | 0.868998i | \(-0.664764\pi\) | ||||
−0.494816 | + | 0.868998i | \(0.664764\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.17525 | 0.0405258 | ||||||||
\(842\) | −11.7604 | + | 3.15119i | −0.405290 | + | 0.108597i | ||||
\(843\) | −23.1538 | + | 86.4113i | −0.797461 | + | 2.97616i | ||||
\(844\) | 14.5707 | − | 8.41238i | 0.501543 | − | 0.289566i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 2.98793i | − | 0.102727i | ||||||
\(847\) | −14.5235 | + | 5.15377i | −0.499034 | + | 0.177086i | ||||
\(848\) | −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 | ||||
\(852\) | −4.72936 | − | 17.6502i | −0.162025 | − | 0.604686i | ||||
\(853\) | 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 | ||||
\(857\) | 35.3004 | + | 9.45872i | 1.20584 | + | 0.323104i | 0.805128 | − | 0.593101i | \(-0.202096\pi\) |
0.400711 | + | 0.916204i | \(0.368763\pi\) | |||||||
\(858\) | 31.9718 | + | 8.56682i | 1.09150 | + | 0.292467i | ||||
\(859\) | 14.3326 | − | 24.8248i | 0.489021 | − | 0.847010i | −0.510899 | − | 0.859641i | \(-0.670687\pi\) |
0.999920 | + | 0.0126311i | \(0.00402073\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.7371 | − | 34.4892i | −0.808959 | − | 1.17539i | ||||
\(862\) | −13.7533 | − | 13.7533i | −0.468441 | − | 0.468441i | ||||
\(863\) | −10.0939 | − | 37.6711i | −0.343602 | − | 1.28234i | −0.894237 | − | 0.447593i | \(-0.852281\pi\) |
0.550635 | − | 0.834746i | \(-0.314385\pi\) | |||||||
\(864\) | 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 | ||||
\(868\) | 8.63744 | − | 3.06506i | 0.293174 | − | 0.104035i | ||||
\(869\) | 22.7492i | 0.771713i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.6495 | − | 26.9331i | 1.58066 | − | 0.912593i | ||||
\(872\) | 3.57811 | − | 13.3537i | 0.121170 | − | 0.452213i | ||||
\(873\) | −10.1494 | + | 2.71951i | −0.343504 | + | 0.0920416i | ||||
\(874\) | −22.2131 | −0.751370 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.54983 | 0.0861509 | ||||||||
\(877\) | 35.5700 | − | 9.53095i | 1.20111 | − | 0.321837i | 0.397844 | − | 0.917453i | \(-0.369759\pi\) |
0.803269 | + | 0.595616i | \(0.203092\pi\) | |||||||
\(878\) | −5.37945 | + | 20.0764i | −0.181548 | + | 0.677545i | ||||
\(879\) | −46.9380 | + | 27.0997i | −1.58318 | + | 0.914049i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 20.9572i | − | 0.706067i | −0.935611 | − | 0.353034i | \(-0.885150\pi\) | ||
0.935611 | − | 0.353034i | \(-0.114850\pi\) | |||||||
\(882\) | −4.53404 | + | 43.6898i | −0.152669 | + | 1.47111i | ||||
\(883\) | −14.9197 | + | 14.9197i | −0.502089 | + | 0.502089i | −0.912086 | − | 0.409998i | \(-0.865529\pi\) |
0.409998 | + | 0.912086i | \(0.365529\pi\) | |||||||
\(884\) | −14.3326 | − | 8.27492i | −0.482057 | − | 0.278316i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.9124 | + | 29.2931i | 0.568182 | + | 0.984121i | ||||
\(887\) | −4.40432 | − | 16.4371i | −0.147882 | − | 0.551905i | −0.999610 | − | 0.0279202i | \(-0.991112\pi\) |
0.851728 | − | 0.523985i | \(-0.175555\pi\) | |||||||
\(888\) | 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 | ||||
\(892\) | 8.42075 | + | 2.25633i | 0.281947 | + | 0.0755476i | ||||
\(893\) | 3.40561 | + | 0.912530i | 0.113964 | + | 0.0305367i | ||||
\(894\) | 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 | ||||
\(898\) | 9.71861 | + | 36.2704i | 0.324314 | + | 1.21036i | ||||
\(899\) | 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 | ||||
\(903\) | −1.06093 | + | 5.74527i | −0.0353054 | + | 0.191191i | ||||
\(904\) | − | 6.00000i | − | 0.199557i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.27492 | + | 3.04547i | −0.175247 | + | 0.101179i | ||||
\(907\) | 6.45091 | − | 24.0751i | 0.214199 | − | 0.799402i | −0.772248 | − | 0.635321i | \(-0.780868\pi\) |
0.986447 | − | 0.164081i | \(-0.0524657\pi\) | |||||||
\(908\) | 3.34607 | − | 0.896575i | 0.111043 | − | 0.0297539i | ||||
\(909\) | 57.3303 | 1.90153 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.6495 | 0.849806 | 0.424903 | − | 0.905239i | \(-0.360308\pi\) | ||||
0.424903 | + | 0.905239i | \(0.360308\pi\) | |||||||
\(912\) | −21.7815 | + | 5.83633i | −0.721256 | + | 0.193260i | ||||
\(913\) | −0.739452 | + | 2.75967i | −0.0244723 | + | 0.0913318i | ||||
\(914\) | −16.8443 | + | 9.72508i | −0.557161 | + | 0.321677i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 13.8564i | − | 0.457829i | ||||||
\(917\) | 3.48638 | + | 9.82473i | 0.115130 | + | 0.324441i | ||||
\(918\) | −24.4304 | + | 24.4304i | −0.806324 | + | 0.806324i | ||||
\(919\) | −10.0888 | − | 5.82475i | −0.332798 | − | 0.192141i | 0.324285 | − | 0.945959i | \(-0.394876\pi\) |
−0.657083 | + | 0.753819i | \(0.728210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.4622 | − | 49.2980i | −0.937862 | − | 1.62442i | ||||
\(922\) | 9.45872 | + | 35.3004i | 0.311506 | + | 1.16256i | ||||
\(923\) | 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 | ||||
\(927\) | 2.53734 | + | 0.679878i | 0.0833372 | + | 0.0223301i | ||||
\(928\) | 5.09518 | + | 1.36525i | 0.167257 | + | 0.0448165i | ||||
\(929\) | 6.53835 | − | 11.3248i | 0.214516 | − | 0.371553i | −0.738607 | − | 0.674137i | \(-0.764516\pi\) |
0.953123 | + | 0.302584i | \(0.0978492\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −48.4124 | − | 18.5109i | −1.58665 | − | 0.606671i | ||||
\(932\) | 13.8943 | + | 13.8943i | 0.455123 | + | 0.455123i | ||||
\(933\) | −20.6148 | − | 76.9355i | −0.674899 | − | 2.51876i | ||||
\(934\) | 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 | \(0.496068\pi\) | |||||||
\(938\) | −19.3586 | + | 22.6961i | −0.632079 | + | 0.741054i | ||||
\(939\) | − | 34.1993i | − | 1.11605i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.6495 | + | 28.6652i | −1.61853 | + | 0.934457i | −0.631226 | + | 0.775599i | \(0.717448\pi\) |
−0.987301 | + | 0.158859i | \(0.949219\pi\) | |||||||
\(942\) | −4.42572 | + | 16.5170i | −0.144198 | + | 0.538153i | ||||
\(943\) | −15.0573 | + | 4.03459i | −0.490333 | + | 0.131384i | ||||
\(944\) | 10.3923 | 0.338241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.64950 | −0.0536300 | ||||||||
\(947\) | −3.69443 | + | 0.989919i | −0.120053 | + | 0.0321680i | −0.318345 | − | 0.947975i | \(-0.603127\pi\) |
0.198292 | + | 0.980143i | \(0.436460\pi\) | |||||||
\(948\) | 7.88227 | − | 29.4170i | 0.256004 | − | 0.955421i | ||||
\(949\) | −3.46410 | + | 2.00000i | −0.112449 | + | 0.0649227i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 54.8185i | − | 1.77761i | ||||||
\(952\) | 9.01277 | + | 1.66430i | 0.292106 | + | 0.0539404i | ||||
\(953\) | 36.2739 | − | 36.2739i | 1.17503 | − | 1.17503i | 0.194031 | − | 0.980995i | \(-0.437844\pi\) |
0.980995 | − | 0.194031i | \(-0.0621561\pi\) | |||||||
\(954\) | −69.6927 | − | 40.2371i | −2.25639 | − | 1.30273i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.27492 | − | 9.13642i | −0.170603 | − | 0.295493i | ||||
\(957\) | −9.45872 | − | 35.3004i | −0.305757 | − | 1.14110i | ||||
\(958\) | 12.9209 | + | 12.9209i | 0.417454 | + | 0.417454i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.50000 | + | 16.4545i | −0.306452 | + | 0.530790i | ||||
\(962\) | −10.4981 | − | 2.81297i | −0.338474 | − | 0.0906937i | ||||
\(963\) | −95.9155 | − | 25.7005i | −3.09083 | − | 0.828186i | ||||
\(964\) | −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 | 0.364462 | − | 0.931218i | \(-0.381253\pi\) |
−0.931218 | + | 0.364462i | \(0.881253\pi\) | |||||||
\(968\) | 1.50756 | + | 5.62628i | 0.0484547 | + | 0.180835i | ||||
\(969\) | −39.0575 | − | 67.6495i | −1.25471 | − | 2.17322i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.76287 | + | 4.48190i | 0.249122 | + | 0.143831i | 0.619362 | − | 0.785105i | \(-0.287391\pi\) |
−0.370240 | + | 0.928936i | \(0.620725\pi\) | |||||||
\(972\) | −3.71492 | + | 3.71492i | −0.119156 | + | 0.119156i | ||||
\(973\) | 43.7559 | + | 37.3214i | 1.40275 | + | 1.19647i | ||||
\(974\) | − | 21.0997i | − | 0.676077i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.08762 | + | 0.627940i | −0.0348140 | + | 0.0200999i | ||||
\(977\) | −6.63858 | + | 24.7755i | −0.212387 | + | 0.792639i | 0.774683 | + | 0.632350i | \(0.217909\pi\) |
−0.987070 | + | 0.160289i | \(0.948757\pi\) | |||||||
\(978\) | 35.3004 | − | 9.45872i | 1.12878 | − | 0.302457i | ||||
\(979\) | −20.7846 | −0.664279 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 86.7492 | 2.76969 | ||||||||
\(982\) | 33.3726 | − | 8.94216i | 1.06496 | − | 0.285356i | ||||
\(983\) | 4.52756 | − | 16.8971i | 0.144407 | − | 0.538933i | −0.855374 | − | 0.518010i | \(-0.826673\pi\) |
0.999781 | − | 0.0209228i | \(-0.00666042\pi\) | |||||||
\(984\) | −13.7046 | + | 7.91238i | −0.436888 | + | 0.252237i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.2728i | 0.581926i | ||||||||
\(987\) | −2.91914 | − | 2.48987i | −0.0929173 | − | 0.0792535i | ||||
\(988\) | 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 | 0.614795 | − | 0.788687i | \(-0.289239\pi\) |
−0.990420 | + | 0.138084i | \(0.955905\pi\) | |||||||
\(992\) | −0.896575 | − | 3.34607i | −0.0284663 | − | 0.106238i | ||||
\(993\) | −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 | ||||
\(997\) | 20.8851 | + | 5.59615i | 0.661438 | + | 0.177232i | 0.573895 | − | 0.818929i | \(-0.305432\pi\) |
0.0875432 | + | 0.996161i | \(0.472098\pi\) | |||||||
\(998\) | −3.86370 | − | 1.03528i | −0.122303 | − | 0.0327711i | ||||
\(999\) | −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.257.1 | yes | 16 | |
5.2 | odd | 4 | inner | 350.2.o.d.243.2 | yes | 16 | |
5.3 | odd | 4 | inner | 350.2.o.d.243.3 | yes | 16 | |
5.4 | even | 2 | inner | 350.2.o.d.257.4 | yes | 16 | |
7.3 | odd | 6 | inner | 350.2.o.d.157.3 | yes | 16 | |
35.3 | even | 12 | inner | 350.2.o.d.143.1 | ✓ | 16 | |
35.17 | even | 12 | inner | 350.2.o.d.143.4 | yes | 16 | |
35.24 | odd | 6 | inner | 350.2.o.d.157.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
350.2.o.d.143.1 | ✓ | 16 | 35.3 | even | 12 | inner | |
350.2.o.d.143.4 | yes | 16 | 35.17 | even | 12 | inner | |
350.2.o.d.157.2 | yes | 16 | 35.24 | odd | 6 | inner | |
350.2.o.d.157.3 | yes | 16 | 7.3 | odd | 6 | inner | |
350.2.o.d.243.2 | yes | 16 | 5.2 | odd | 4 | inner | |
350.2.o.d.243.3 | yes | 16 | 5.3 | odd | 4 | inner | |
350.2.o.d.257.1 | yes | 16 | 1.1 | even | 1 | trivial | |
350.2.o.d.257.4 | yes | 16 | 5.4 | even | 2 | inner |