Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(94,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.94");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.f (of order \(3\), degree \(2\), 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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 94.12 | ||
Character | \(\chi\) | \(=\) | 403.94 |
Dual form | 403.2.f.c.373.12 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.137984 | + | 0.238996i | 0.0975695 | + | 0.168995i | 0.910678 | − | 0.413117i | \(-0.135560\pi\) |
−0.813109 | + | 0.582112i | \(0.802226\pi\) | |||||||
\(3\) | −0.732250 | − | 1.26829i | −0.422764 | − | 0.732250i | 0.573444 | − | 0.819245i | \(-0.305607\pi\) |
−0.996209 | + | 0.0869950i | \(0.972274\pi\) | |||||||
\(4\) | 0.961921 | − | 1.66610i | 0.480960 | − | 0.833048i | ||||
\(5\) | −1.37475 | −0.614807 | −0.307404 | − | 0.951579i | \(-0.599460\pi\) | ||||
−0.307404 | + | 0.951579i | \(0.599460\pi\) | |||||||
\(6\) | 0.202078 | − | 0.350009i | 0.0824979 | − | 0.142890i | ||||
\(7\) | 0.239780 | − | 0.415311i | 0.0906283 | − | 0.156973i | −0.817147 | − | 0.576429i | \(-0.804446\pi\) |
0.907776 | + | 0.419456i | \(0.137779\pi\) | |||||||
\(8\) | 1.08286 | 0.382847 | ||||||||
\(9\) | 0.427621 | − | 0.740662i | 0.142540 | − | 0.246887i | ||||
\(10\) | −0.189694 | − | 0.328559i | −0.0599864 | − | 0.103900i | ||||
\(11\) | 0.323908 | + | 0.561024i | 0.0976618 | + | 0.169155i | 0.910716 | − | 0.413032i | \(-0.135530\pi\) |
−0.813055 | + | 0.582187i | \(0.802197\pi\) | |||||||
\(12\) | −2.81746 | −0.813332 | ||||||||
\(13\) | −3.42483 | − | 1.12717i | −0.949878 | − | 0.312620i | ||||
\(14\) | 0.132343 | 0.0353702 | ||||||||
\(15\) | 1.00666 | + | 1.74359i | 0.259919 | + | 0.450192i | ||||
\(16\) | −1.77442 | − | 3.07339i | −0.443606 | − | 0.768348i | ||||
\(17\) | 1.17485 | − | 2.03489i | 0.284942 | − | 0.493534i | −0.687653 | − | 0.726040i | \(-0.741359\pi\) |
0.972595 | + | 0.232505i | \(0.0746922\pi\) | |||||||
\(18\) | 0.236020 | 0.0556304 | ||||||||
\(19\) | −0.704293 | + | 1.21987i | −0.161576 | + | 0.279858i | −0.935434 | − | 0.353501i | \(-0.884991\pi\) |
0.773858 | + | 0.633359i | \(0.218324\pi\) | |||||||
\(20\) | −1.32240 | + | 2.29047i | −0.295698 | + | 0.512164i | ||||
\(21\) | −0.702315 | −0.153258 | ||||||||
\(22\) | −0.0893882 | + | 0.154825i | −0.0190576 | + | 0.0330088i | ||||
\(23\) | −0.994005 | − | 1.72167i | −0.207264 | − | 0.358992i | 0.743587 | − | 0.668639i | \(-0.233123\pi\) |
−0.950852 | + | 0.309646i | \(0.899789\pi\) | |||||||
\(24\) | −0.792921 | − | 1.37338i | −0.161854 | − | 0.280340i | ||||
\(25\) | −3.11006 | −0.622012 | ||||||||
\(26\) | −0.203185 | − | 0.974052i | −0.0398478 | − | 0.191027i | ||||
\(27\) | −5.64600 | −1.08657 | ||||||||
\(28\) | −0.461299 | − | 0.798993i | −0.0871773 | − | 0.150995i | ||||
\(29\) | −0.107161 | − | 0.185608i | −0.0198993 | − | 0.0344666i | 0.855904 | − | 0.517134i | \(-0.173001\pi\) |
−0.875804 | + | 0.482668i | \(0.839668\pi\) | |||||||
\(30\) | −0.277806 | + | 0.481175i | −0.0507203 | + | 0.0878501i | ||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 1.57254 | − | 2.72372i | 0.277989 | − | 0.481490i | ||||
\(33\) | 0.474362 | − | 0.821620i | 0.0825759 | − | 0.143026i | ||||
\(34\) | 0.648441 | 0.111207 | ||||||||
\(35\) | −0.329638 | + | 0.570949i | −0.0557189 | + | 0.0965080i | ||||
\(36\) | −0.822676 | − | 1.42492i | −0.137113 | − | 0.237486i | ||||
\(37\) | −3.54620 | − | 6.14220i | −0.582991 | − | 1.00977i | −0.995123 | − | 0.0986462i | \(-0.968549\pi\) |
0.412131 | − | 0.911125i | \(-0.364785\pi\) | |||||||
\(38\) | −0.388725 | −0.0630596 | ||||||||
\(39\) | 1.07825 | + | 5.16906i | 0.172659 | + | 0.827713i | ||||
\(40\) | −1.48866 | −0.235377 | ||||||||
\(41\) | 5.27418 | + | 9.13515i | 0.823689 | + | 1.42667i | 0.902917 | + | 0.429814i | \(0.141421\pi\) |
−0.0792284 | + | 0.996856i | \(0.525246\pi\) | |||||||
\(42\) | −0.0969084 | − | 0.167850i | −0.0149533 | − | 0.0258998i | ||||
\(43\) | 4.55483 | − | 7.88920i | 0.694606 | − | 1.20309i | −0.275708 | − | 0.961241i | \(-0.588912\pi\) |
0.970313 | − | 0.241851i | \(-0.0777544\pi\) | |||||||
\(44\) | 1.24629 | 0.187886 | ||||||||
\(45\) | −0.587873 | + | 1.01823i | −0.0876349 | + | 0.151788i | ||||
\(46\) | 0.274314 | − | 0.475126i | 0.0404454 | − | 0.0700535i | ||||
\(47\) | 8.99844 | 1.31256 | 0.656279 | − | 0.754519i | \(-0.272130\pi\) | ||||
0.656279 | + | 0.754519i | \(0.272130\pi\) | |||||||
\(48\) | −2.59864 | + | 4.50098i | −0.375082 | + | 0.649661i | ||||
\(49\) | 3.38501 | + | 5.86301i | 0.483573 | + | 0.837573i | ||||
\(50\) | −0.429139 | − | 0.743291i | −0.0606894 | − | 0.105117i | ||||
\(51\) | −3.44112 | −0.481854 | ||||||||
\(52\) | −5.17239 | + | 4.62186i | −0.717281 | + | 0.640936i | ||||
\(53\) | 11.1521 | 1.53185 | 0.765926 | − | 0.642929i | \(-0.222281\pi\) | ||||
0.765926 | + | 0.642929i | \(0.222281\pi\) | |||||||
\(54\) | −0.779058 | − | 1.34937i | −0.106016 | − | 0.183626i | ||||
\(55\) | −0.445292 | − | 0.771268i | −0.0600432 | − | 0.103998i | ||||
\(56\) | 0.259647 | − | 0.449722i | 0.0346968 | − | 0.0600966i | ||||
\(57\) | 2.06287 | 0.273234 | ||||||||
\(58\) | 0.0295730 | − | 0.0512220i | 0.00388313 | − | 0.00672578i | ||||
\(59\) | 0.838771 | − | 1.45279i | 0.109199 | − | 0.189138i | −0.806247 | − | 0.591579i | \(-0.798505\pi\) |
0.915446 | + | 0.402441i | \(0.131838\pi\) | |||||||
\(60\) | 3.87331 | 0.500042 | ||||||||
\(61\) | 0.454325 | − | 0.786914i | 0.0581704 | − | 0.100754i | −0.835474 | − | 0.549530i | \(-0.814807\pi\) |
0.893644 | + | 0.448776i | \(0.148140\pi\) | |||||||
\(62\) | 0.137984 | + | 0.238996i | 0.0175240 | + | 0.0303525i | ||||
\(63\) | −0.205070 | − | 0.355192i | −0.0258364 | − | 0.0447500i | ||||
\(64\) | −6.22976 | −0.778719 | ||||||||
\(65\) | 4.70829 | + | 1.54957i | 0.583992 | + | 0.192201i | ||||
\(66\) | 0.261818 | 0.0322276 | ||||||||
\(67\) | −2.20119 | − | 3.81257i | −0.268918 | − | 0.465780i | 0.699665 | − | 0.714471i | \(-0.253333\pi\) |
−0.968583 | + | 0.248692i | \(0.919999\pi\) | |||||||
\(68\) | −2.26022 | − | 3.91481i | −0.274092 | − | 0.474741i | ||||
\(69\) | −1.45572 | + | 2.52138i | −0.175248 | + | 0.303539i | ||||
\(70\) | −0.181939 | −0.0217459 | ||||||||
\(71\) | 2.48188 | − | 4.29873i | 0.294544 | − | 0.510166i | −0.680334 | − | 0.732902i | \(-0.738165\pi\) |
0.974879 | + | 0.222736i | \(0.0714988\pi\) | |||||||
\(72\) | 0.463052 | − | 0.802030i | 0.0545712 | − | 0.0945201i | ||||
\(73\) | 6.35196 | 0.743440 | 0.371720 | − | 0.928345i | \(-0.378768\pi\) | ||||
0.371720 | + | 0.928345i | \(0.378768\pi\) | |||||||
\(74\) | 0.978638 | − | 1.69505i | 0.113764 | − | 0.197046i | ||||
\(75\) | 2.27734 | + | 3.94447i | 0.262965 | + | 0.455468i | ||||
\(76\) | 1.35495 | + | 2.34684i | 0.155423 | + | 0.269201i | ||||
\(77\) | 0.310666 | 0.0354037 | ||||||||
\(78\) | −1.08660 | + | 0.970947i | −0.123033 | + | 0.109938i | ||||
\(79\) | −2.73779 | −0.308025 | −0.154012 | − | 0.988069i | \(-0.549220\pi\) | ||||
−0.154012 | + | 0.988069i | \(0.549220\pi\) | |||||||
\(80\) | 2.43939 | + | 4.22515i | 0.272732 | + | 0.472386i | ||||
\(81\) | 2.85142 | + | 4.93880i | 0.316824 | + | 0.548755i | ||||
\(82\) | −1.45551 | + | 2.52101i | −0.160734 | + | 0.278399i | ||||
\(83\) | 6.40312 | 0.702834 | 0.351417 | − | 0.936219i | \(-0.385700\pi\) | ||||
0.351417 | + | 0.936219i | \(0.385700\pi\) | |||||||
\(84\) | −0.675571 | + | 1.17012i | −0.0737109 | + | 0.127671i | ||||
\(85\) | −1.61512 | + | 2.79747i | −0.175185 | + | 0.303428i | ||||
\(86\) | 2.51398 | 0.271089 | ||||||||
\(87\) | −0.156937 | + | 0.271823i | −0.0168254 | + | 0.0291425i | ||||
\(88\) | 0.350745 | + | 0.607509i | 0.0373896 | + | 0.0647606i | ||||
\(89\) | 2.40022 | + | 4.15730i | 0.254423 | + | 0.440673i | 0.964739 | − | 0.263210i | \(-0.0847812\pi\) |
−0.710316 | + | 0.703883i | \(0.751448\pi\) | |||||||
\(90\) | −0.324468 | −0.0342020 | ||||||||
\(91\) | −1.28933 | + | 1.15210i | −0.135159 | + | 0.120773i | ||||
\(92\) | −3.82462 | −0.398744 | ||||||||
\(93\) | −0.732250 | − | 1.26829i | −0.0759307 | − | 0.131516i | ||||
\(94\) | 1.24164 | + | 2.15059i | 0.128066 | + | 0.221816i | ||||
\(95\) | 0.968228 | − | 1.67702i | 0.0993381 | − | 0.172059i | ||||
\(96\) | −4.60597 | −0.470095 | ||||||||
\(97\) | −5.40800 | + | 9.36693i | −0.549099 | + | 0.951068i | 0.449237 | + | 0.893412i | \(0.351696\pi\) |
−0.998337 | + | 0.0576552i | \(0.981638\pi\) | |||||||
\(98\) | −0.934156 | + | 1.61801i | −0.0943640 | + | 0.163443i | ||||
\(99\) | 0.554039 | 0.0556830 | ||||||||
\(100\) | −2.99163 | + | 5.18166i | −0.299163 | + | 0.518166i | ||||
\(101\) | 3.55301 | + | 6.15399i | 0.353538 | + | 0.612345i | 0.986867 | − | 0.161538i | \(-0.0516453\pi\) |
−0.633329 | + | 0.773883i | \(0.718312\pi\) | |||||||
\(102\) | −0.474821 | − | 0.822413i | −0.0470142 | − | 0.0814311i | ||||
\(103\) | 5.08609 | 0.501147 | 0.250573 | − | 0.968098i | \(-0.419381\pi\) | ||||
0.250573 | + | 0.968098i | \(0.419381\pi\) | |||||||
\(104\) | −3.70860 | − | 1.22056i | −0.363658 | − | 0.119686i | ||||
\(105\) | 0.965508 | 0.0942239 | ||||||||
\(106\) | 1.53881 | + | 2.66529i | 0.149462 | + | 0.258876i | ||||
\(107\) | −0.960487 | − | 1.66361i | −0.0928538 | − | 0.160828i | 0.815857 | − | 0.578254i | \(-0.196266\pi\) |
−0.908711 | + | 0.417426i | \(0.862932\pi\) | |||||||
\(108\) | −5.43100 | + | 9.40677i | −0.522599 | + | 0.905167i | ||||
\(109\) | 9.77610 | 0.936380 | 0.468190 | − | 0.883628i | \(-0.344906\pi\) | ||||
0.468190 | + | 0.883628i | \(0.344906\pi\) | |||||||
\(110\) | 0.122887 | − | 0.212846i | 0.0117168 | − | 0.0202940i | ||||
\(111\) | −5.19340 | + | 8.99524i | −0.492936 | + | 0.853790i | ||||
\(112\) | −1.70189 | −0.160813 | ||||||||
\(113\) | −3.66644 | + | 6.35045i | −0.344909 | + | 0.597400i | −0.985337 | − | 0.170618i | \(-0.945424\pi\) |
0.640428 | + | 0.768018i | \(0.278757\pi\) | |||||||
\(114\) | 0.284644 | + | 0.493018i | 0.0266593 | + | 0.0461753i | ||||
\(115\) | 1.36651 | + | 2.36686i | 0.127428 | + | 0.220711i | ||||
\(116\) | −0.412322 | −0.0382831 | ||||||||
\(117\) | −2.29938 | + | 2.05464i | −0.212578 | + | 0.189952i | ||||
\(118\) | 0.462948 | 0.0426179 | ||||||||
\(119\) | −0.563410 | − | 0.975854i | −0.0516477 | − | 0.0894564i | ||||
\(120\) | 1.09007 | + | 1.88805i | 0.0995092 | + | 0.172355i | ||||
\(121\) | 5.29017 | − | 9.16284i | 0.480924 | − | 0.832985i | ||||
\(122\) | 0.250759 | 0.0227026 | ||||||||
\(123\) | 7.72403 | − | 13.3784i | 0.696453 | − | 1.20629i | ||||
\(124\) | 0.961921 | − | 1.66610i | 0.0863830 | − | 0.149620i | ||||
\(125\) | 11.1493 | 0.997225 | ||||||||
\(126\) | 0.0565928 | − | 0.0980217i | 0.00504169 | − | 0.00873246i | ||||
\(127\) | −10.0770 | − | 17.4539i | −0.894190 | − | 1.54878i | −0.834804 | − | 0.550548i | \(-0.814419\pi\) |
−0.0593868 | − | 0.998235i | \(-0.518915\pi\) | |||||||
\(128\) | −4.00469 | − | 6.93633i | −0.353968 | − | 0.613090i | ||||
\(129\) | −13.3411 | −1.17462 | ||||||||
\(130\) | 0.279328 | + | 1.33908i | 0.0244987 | + | 0.117445i | ||||
\(131\) | −0.445880 | −0.0389567 | −0.0194784 | − | 0.999810i | \(-0.506201\pi\) | ||||
−0.0194784 | + | 0.999810i | \(0.506201\pi\) | |||||||
\(132\) | −0.912598 | − | 1.58067i | −0.0794315 | − | 0.137579i | ||||
\(133\) | 0.337751 | + | 0.585002i | 0.0292867 | + | 0.0507261i | ||||
\(134\) | 0.607458 | − | 1.05215i | 0.0524764 | − | 0.0908918i | ||||
\(135\) | 7.76184 | 0.668033 | ||||||||
\(136\) | 1.27219 | − | 2.20350i | 0.109089 | − | 0.188948i | ||||
\(137\) | −10.0058 | + | 17.3305i | −0.854851 | + | 1.48065i | 0.0219326 | + | 0.999759i | \(0.493018\pi\) |
−0.876783 | + | 0.480886i | \(0.840315\pi\) | |||||||
\(138\) | −0.803465 | −0.0683955 | ||||||||
\(139\) | −5.05253 | + | 8.75123i | −0.428550 | + | 0.742270i | −0.996745 | − | 0.0806243i | \(-0.974309\pi\) |
0.568195 | + | 0.822894i | \(0.307642\pi\) | |||||||
\(140\) | 0.634171 | + | 1.09842i | 0.0535972 | + | 0.0928331i | ||||
\(141\) | −6.58910 | − | 11.4127i | −0.554903 | − | 0.961119i | ||||
\(142\) | 1.36984 | 0.114954 | ||||||||
\(143\) | −0.476961 | − | 2.28651i | −0.0398855 | − | 0.191208i | ||||
\(144\) | −3.03513 | −0.252927 | ||||||||
\(145\) | 0.147320 | + | 0.255165i | 0.0122342 | + | 0.0211903i | ||||
\(146\) | 0.876469 | + | 1.51809i | 0.0725371 | + | 0.125638i | ||||
\(147\) | 4.95735 | − | 8.58637i | 0.408875 | − | 0.708192i | ||||
\(148\) | −13.6446 | −1.12158 | ||||||||
\(149\) | −1.49818 | + | 2.59492i | −0.122736 | + | 0.212584i | −0.920846 | − | 0.389928i | \(-0.872500\pi\) |
0.798110 | + | 0.602512i | \(0.205833\pi\) | |||||||
\(150\) | −0.628474 | + | 1.08855i | −0.0513147 | + | 0.0888796i | ||||
\(151\) | 17.5705 | 1.42987 | 0.714935 | − | 0.699191i | \(-0.246456\pi\) | ||||
0.714935 | + | 0.699191i | \(0.246456\pi\) | |||||||
\(152\) | −0.762648 | + | 1.32095i | −0.0618589 | + | 0.107143i | ||||
\(153\) | −1.00478 | − | 1.74033i | −0.0812316 | − | 0.140697i | ||||
\(154\) | 0.0428670 | + | 0.0742478i | 0.00345432 | + | 0.00598306i | ||||
\(155\) | −1.37475 | −0.110423 | ||||||||
\(156\) | 9.64935 | + | 3.17575i | 0.772566 | + | 0.254264i | ||||
\(157\) | −3.11059 | −0.248252 | −0.124126 | − | 0.992266i | \(-0.539613\pi\) | ||||
−0.124126 | + | 0.992266i | \(0.539613\pi\) | |||||||
\(158\) | −0.377771 | − | 0.654319i | −0.0300539 | − | 0.0520548i | ||||
\(159\) | −8.16609 | − | 14.1441i | −0.647613 | − | 1.12170i | ||||
\(160\) | −2.16185 | + | 3.74444i | −0.170909 | + | 0.296024i | ||||
\(161\) | −0.953370 | −0.0751361 | ||||||||
\(162\) | −0.786901 | + | 1.36295i | −0.0618247 | + | 0.107084i | ||||
\(163\) | 4.83855 | − | 8.38061i | 0.378984 | − | 0.656420i | −0.611931 | − | 0.790911i | \(-0.709607\pi\) |
0.990915 | + | 0.134492i | \(0.0429401\pi\) | |||||||
\(164\) | 20.2934 | 1.58465 | ||||||||
\(165\) | −0.652130 | + | 1.12952i | −0.0507682 | + | 0.0879332i | ||||
\(166\) | 0.883530 | + | 1.53032i | 0.0685752 | + | 0.118776i | ||||
\(167\) | −4.83260 | − | 8.37032i | −0.373958 | − | 0.647714i | 0.616212 | − | 0.787580i | \(-0.288666\pi\) |
−0.990171 | + | 0.139866i | \(0.955333\pi\) | |||||||
\(168\) | −0.760506 | −0.0586743 | ||||||||
\(169\) | 10.4590 | + | 7.72073i | 0.804537 | + | 0.593902i | ||||
\(170\) | −0.891445 | −0.0683707 | ||||||||
\(171\) | 0.602342 | + | 1.04329i | 0.0460622 | + | 0.0797821i | ||||
\(172\) | −8.76278 | − | 15.1776i | −0.668156 | − | 1.15728i | ||||
\(173\) | 4.89966 | − | 8.48645i | 0.372514 | − | 0.645213i | −0.617438 | − | 0.786620i | \(-0.711829\pi\) |
0.989952 | + | 0.141407i | \(0.0451625\pi\) | |||||||
\(174\) | −0.0866194 | −0.00656660 | ||||||||
\(175\) | −0.745730 | + | 1.29164i | −0.0563719 | + | 0.0976390i | ||||
\(176\) | 1.14950 | − | 1.99099i | 0.0866468 | − | 0.150077i | ||||
\(177\) | −2.45676 | −0.184661 | ||||||||
\(178\) | −0.662385 | + | 1.14728i | −0.0496478 | + | 0.0859926i | ||||
\(179\) | −10.9139 | − | 18.9035i | −0.815745 | − | 1.41291i | −0.908792 | − | 0.417250i | \(-0.862994\pi\) |
0.0930473 | − | 0.995662i | \(-0.470339\pi\) | |||||||
\(180\) | 1.13097 | + | 1.95890i | 0.0842978 | + | 0.146008i | ||||
\(181\) | −16.4629 | −1.22368 | −0.611840 | − | 0.790982i | \(-0.709570\pi\) | ||||
−0.611840 | + | 0.790982i | \(0.709570\pi\) | |||||||
\(182\) | −0.453254 | − | 0.149173i | −0.0335974 | − | 0.0110574i | ||||
\(183\) | −1.33072 | −0.0983694 | ||||||||
\(184\) | −1.07636 | − | 1.86432i | −0.0793506 | − | 0.137439i | ||||
\(185\) | 4.87514 | + | 8.44399i | 0.358427 | + | 0.620814i | ||||
\(186\) | 0.202078 | − | 0.350009i | 0.0148171 | − | 0.0256639i | ||||
\(187\) | 1.52217 | 0.111312 | ||||||||
\(188\) | 8.65578 | − | 14.9923i | 0.631288 | − | 1.09342i | ||||
\(189\) | −1.35380 | + | 2.34485i | −0.0984743 | + | 0.170562i | ||||
\(190\) | 0.534400 | 0.0387695 | ||||||||
\(191\) | 1.19567 | − | 2.07097i | 0.0865159 | − | 0.149850i | −0.819520 | − | 0.573050i | \(-0.805760\pi\) |
0.906036 | + | 0.423200i | \(0.139093\pi\) | |||||||
\(192\) | 4.56174 | + | 7.90116i | 0.329215 | + | 0.570217i | ||||
\(193\) | 4.89518 | + | 8.47870i | 0.352363 | + | 0.610310i | 0.986663 | − | 0.162777i | \(-0.0520450\pi\) |
−0.634300 | + | 0.773087i | \(0.718712\pi\) | |||||||
\(194\) | −2.98487 | −0.214301 | ||||||||
\(195\) | −1.48233 | − | 7.10617i | −0.106152 | − | 0.508884i | ||||
\(196\) | 13.0244 | 0.930318 | ||||||||
\(197\) | −9.78152 | − | 16.9421i | −0.696904 | − | 1.20707i | −0.969535 | − | 0.244954i | \(-0.921227\pi\) |
0.272630 | − | 0.962119i | \(-0.412106\pi\) | |||||||
\(198\) | 0.0764486 | + | 0.132413i | 0.00543297 | + | 0.00941017i | ||||
\(199\) | 3.41590 | − | 5.91651i | 0.242147 | − | 0.419411i | −0.719179 | − | 0.694825i | \(-0.755482\pi\) |
0.961326 | + | 0.275415i | \(0.0888151\pi\) | |||||||
\(200\) | −3.36775 | −0.238136 | ||||||||
\(201\) | −3.22364 | + | 5.58350i | −0.227378 | + | 0.393830i | ||||
\(202\) | −0.980518 | + | 1.69831i | −0.0689890 | + | 0.119492i | ||||
\(203\) | −0.102780 | −0.00721376 | ||||||||
\(204\) | −3.31009 | + | 5.73324i | −0.231753 | + | 0.401407i | ||||
\(205\) | −7.25068 | − | 12.5586i | −0.506410 | − | 0.877127i | ||||
\(206\) | 0.701799 | + | 1.21555i | 0.0488967 | + | 0.0846915i | ||||
\(207\) | −1.70023 | −0.118174 | ||||||||
\(208\) | 2.61288 | + | 12.5259i | 0.181171 | + | 0.868518i | ||||
\(209\) | −0.912504 | −0.0631192 | ||||||||
\(210\) | 0.133225 | + | 0.230752i | 0.00919338 | + | 0.0159234i | ||||
\(211\) | 11.3270 | + | 19.6189i | 0.779781 | + | 1.35062i | 0.932068 | + | 0.362285i | \(0.118003\pi\) |
−0.152286 | + | 0.988336i | \(0.548664\pi\) | |||||||
\(212\) | 10.7274 | − | 18.5804i | 0.736760 | − | 1.27611i | ||||
\(213\) | −7.26941 | −0.498092 | ||||||||
\(214\) | 0.265064 | − | 0.459104i | 0.0181194 | − | 0.0313837i | ||||
\(215\) | −6.26176 | + | 10.8457i | −0.427048 | + | 0.739670i | ||||
\(216\) | −6.11380 | −0.415992 | ||||||||
\(217\) | 0.239780 | − | 0.415311i | 0.0162773 | − | 0.0281932i | ||||
\(218\) | 1.34895 | + | 2.33644i | 0.0913622 | + | 0.158244i | ||||
\(219\) | −4.65122 | − | 8.05614i | −0.314300 | − | 0.544384i | ||||
\(220\) | −1.71334 | −0.115514 | ||||||||
\(221\) | −6.31732 | + | 5.64493i | −0.424949 | + | 0.379719i | ||||
\(222\) | −2.86643 | −0.192382 | ||||||||
\(223\) | −4.19008 | − | 7.25744i | −0.280589 | − | 0.485994i | 0.690941 | − | 0.722911i | \(-0.257196\pi\) |
−0.971530 | + | 0.236917i | \(0.923863\pi\) | |||||||
\(224\) | −0.754128 | − | 1.30619i | −0.0503873 | − | 0.0872733i | ||||
\(225\) | −1.32993 | + | 2.30350i | −0.0886619 | + | 0.153567i | ||||
\(226\) | −2.02364 | −0.134611 | ||||||||
\(227\) | −7.33695 | + | 12.7080i | −0.486970 | + | 0.843457i | −0.999888 | − | 0.0149806i | \(-0.995231\pi\) |
0.512918 | + | 0.858438i | \(0.328565\pi\) | |||||||
\(228\) | 1.98432 | − | 3.43694i | 0.131415 | − | 0.227617i | ||||
\(229\) | −0.0186783 | −0.00123430 | −0.000617150 | − | 1.00000i | \(-0.500196\pi\) | ||||
−0.000617150 | 1.00000i | \(0.500196\pi\) | ||||||||
\(230\) | −0.377113 | + | 0.653179i | −0.0248661 | + | 0.0430694i | ||||
\(231\) | −0.227485 | − | 0.394016i | −0.0149674 | − | 0.0259243i | ||||
\(232\) | −0.116040 | − | 0.200987i | −0.00761840 | − | 0.0131954i | ||||
\(233\) | 27.1749 | 1.78029 | 0.890144 | − | 0.455680i | \(-0.150604\pi\) | ||||
0.890144 | + | 0.455680i | \(0.150604\pi\) | |||||||
\(234\) | −0.808329 | − | 0.266034i | −0.0528421 | − | 0.0173912i | ||||
\(235\) | −12.3706 | −0.806969 | ||||||||
\(236\) | −1.61366 | − | 2.79495i | −0.105040 | − | 0.181935i | ||||
\(237\) | 2.00474 | + | 3.47232i | 0.130222 | + | 0.225551i | ||||
\(238\) | 0.155483 | − | 0.269305i | 0.0100785 | − | 0.0174564i | ||||
\(239\) | 17.4218 | 1.12692 | 0.563460 | − | 0.826144i | \(-0.309470\pi\) | ||||
0.563460 | + | 0.826144i | \(0.309470\pi\) | |||||||
\(240\) | 3.57249 | − | 6.18773i | 0.230603 | − | 0.399416i | ||||
\(241\) | −2.27037 | + | 3.93240i | −0.146248 | + | 0.253308i | −0.929838 | − | 0.367970i | \(-0.880053\pi\) |
0.783590 | + | 0.621278i | \(0.213386\pi\) | |||||||
\(242\) | 2.91984 | 0.187694 | ||||||||
\(243\) | −4.29310 | + | 7.43587i | −0.275403 | + | 0.477011i | ||||
\(244\) | −0.874049 | − | 1.51390i | −0.0559553 | − | 0.0969174i | ||||
\(245\) | −4.65355 | − | 8.06018i | −0.297304 | − | 0.514946i | ||||
\(246\) | 4.26318 | 0.271810 | ||||||||
\(247\) | 3.78709 | − | 3.38400i | 0.240967 | − | 0.215319i | ||||
\(248\) | 1.08286 | 0.0687614 | ||||||||
\(249\) | −4.68868 | − | 8.12104i | −0.297133 | − | 0.514650i | ||||
\(250\) | 1.53843 | + | 2.66464i | 0.0972987 | + | 0.168526i | ||||
\(251\) | −0.0336012 | + | 0.0581989i | −0.00212089 | + | 0.00367348i | −0.867084 | − | 0.498162i | \(-0.834008\pi\) |
0.864963 | + | 0.501836i | \(0.167342\pi\) | |||||||
\(252\) | −0.789044 | −0.0497051 | ||||||||
\(253\) | 0.643932 | − | 1.11532i | 0.0404836 | − | 0.0701197i | ||||
\(254\) | 2.78094 | − | 4.81672i | 0.174491 | − | 0.302228i | ||||
\(255\) | 4.73069 | 0.296247 | ||||||||
\(256\) | −5.12459 | + | 8.87605i | −0.320287 | + | 0.554753i | ||||
\(257\) | −7.08588 | − | 12.2731i | −0.442005 | − | 0.765576i | 0.555833 | − | 0.831294i | \(-0.312399\pi\) |
−0.997838 | + | 0.0657184i | \(0.979066\pi\) | |||||||
\(258\) | −1.84086 | − | 3.18846i | −0.114607 | − | 0.198505i | ||||
\(259\) | −3.40123 | −0.211342 | ||||||||
\(260\) | 7.11074 | − | 6.35390i | 0.440990 | − | 0.394052i | ||||
\(261\) | −0.183297 | −0.0113458 | ||||||||
\(262\) | −0.0615244 | − | 0.106563i | −0.00380099 | − | 0.00658351i | ||||
\(263\) | 13.4574 | + | 23.3090i | 0.829821 | + | 1.43729i | 0.898179 | + | 0.439631i | \(0.144891\pi\) |
−0.0683581 | + | 0.997661i | \(0.521776\pi\) | |||||||
\(264\) | 0.513666 | − | 0.889696i | 0.0316140 | − | 0.0547570i | ||||
\(265\) | −15.3313 | −0.941794 | ||||||||
\(266\) | −0.0932085 | + | 0.161442i | −0.00571498 | + | 0.00989864i | ||||
\(267\) | 3.51512 | − | 6.08837i | 0.215122 | − | 0.372602i | ||||
\(268\) | −8.46947 | −0.517355 | ||||||||
\(269\) | −9.86989 | + | 17.0952i | −0.601778 | + | 1.04231i | 0.390774 | + | 0.920487i | \(0.372207\pi\) |
−0.992552 | + | 0.121823i | \(0.961126\pi\) | |||||||
\(270\) | 1.07101 | + | 1.85505i | 0.0651796 | + | 0.112894i | ||||
\(271\) | −7.77504 | − | 13.4668i | −0.472300 | − | 0.818047i | 0.527198 | − | 0.849743i | \(-0.323243\pi\) |
−0.999498 | + | 0.0316952i | \(0.989909\pi\) | |||||||
\(272\) | −8.33871 | −0.505608 | ||||||||
\(273\) | 2.40531 | + | 0.791627i | 0.145576 | + | 0.0479114i | ||||
\(274\) | −5.52255 | −0.333630 | ||||||||
\(275\) | −1.00737 | − | 1.74482i | −0.0607468 | − | 0.105217i | ||||
\(276\) | 2.80057 | + | 4.85074i | 0.168575 | + | 0.291980i | ||||
\(277\) | −6.63492 | + | 11.4920i | −0.398654 | + | 0.690489i | −0.993560 | − | 0.113307i | \(-0.963856\pi\) |
0.594906 | + | 0.803795i | \(0.297189\pi\) | |||||||
\(278\) | −2.78867 | −0.167254 | ||||||||
\(279\) | 0.427621 | − | 0.740662i | 0.0256010 | − | 0.0443423i | ||||
\(280\) | −0.356950 | + | 0.618256i | −0.0213318 | + | 0.0369478i | ||||
\(281\) | −25.0215 | −1.49266 | −0.746329 | − | 0.665577i | \(-0.768185\pi\) | ||||
−0.746329 | + | 0.665577i | \(0.768185\pi\) | |||||||
\(282\) | 1.81838 | − | 3.14953i | 0.108283 | − | 0.187552i | ||||
\(283\) | −12.6915 | − | 21.9823i | −0.754431 | − | 1.30671i | −0.945657 | − | 0.325166i | \(-0.894580\pi\) |
0.191226 | − | 0.981546i | \(-0.438754\pi\) | |||||||
\(284\) | −4.77473 | − | 8.27008i | −0.283328 | − | 0.490739i | ||||
\(285\) | −2.83594 | −0.167986 | ||||||||
\(286\) | 0.480654 | − | 0.429494i | 0.0284216 | − | 0.0253965i | ||||
\(287\) | 5.05857 | 0.298598 | ||||||||
\(288\) | −1.34490 | − | 2.32944i | −0.0792492 | − | 0.137264i | ||||
\(289\) | 5.73947 | + | 9.94105i | 0.337616 | + | 0.584768i | ||||
\(290\) | −0.0406556 | + | 0.0704175i | −0.00238738 | + | 0.00413506i | ||||
\(291\) | 15.8400 | 0.928558 | ||||||||
\(292\) | 6.11008 | − | 10.5830i | 0.357565 | − | 0.619321i | ||||
\(293\) | −1.87637 | + | 3.24996i | −0.109618 | + | 0.189865i | −0.915616 | − | 0.402055i | \(-0.868296\pi\) |
0.805997 | + | 0.591919i | \(0.201630\pi\) | |||||||
\(294\) | 2.73614 | 0.159575 | ||||||||
\(295\) | −1.15310 | + | 1.99723i | −0.0671361 | + | 0.116283i | ||||
\(296\) | −3.84002 | − | 6.65111i | −0.223197 | − | 0.386588i | ||||
\(297\) | −1.82878 | − | 3.16754i | −0.106117 | − | 0.183799i | ||||
\(298\) | −0.826900 | −0.0479010 | ||||||||
\(299\) | 1.46370 | + | 7.01684i | 0.0846477 | + | 0.405794i | ||||
\(300\) | 8.76249 | 0.505902 | ||||||||
\(301\) | −2.18432 | − | 3.78335i | −0.125902 | − | 0.218068i | ||||
\(302\) | 2.42446 | + | 4.19928i | 0.139512 | + | 0.241641i | ||||
\(303\) | 5.20338 | − | 9.01251i | 0.298926 | − | 0.517755i | ||||
\(304\) | 4.99886 | 0.286704 | ||||||||
\(305\) | −0.624584 | + | 1.08181i | −0.0357636 | + | 0.0619443i | ||||
\(306\) | 0.277287 | − | 0.480276i | 0.0158515 | − | 0.0274555i | ||||
\(307\) | −10.6024 | −0.605109 | −0.302554 | − | 0.953132i | \(-0.597839\pi\) | ||||
−0.302554 | + | 0.953132i | \(0.597839\pi\) | |||||||
\(308\) | 0.298836 | − | 0.517600i | 0.0170278 | − | 0.0294930i | ||||
\(309\) | −3.72428 | − | 6.45065i | −0.211867 | − | 0.366965i | ||||
\(310\) | −0.189694 | − | 0.328559i | −0.0107739 | − | 0.0186609i | ||||
\(311\) | 10.2239 | 0.579744 | 0.289872 | − | 0.957065i | \(-0.406387\pi\) | ||||
0.289872 | + | 0.957065i | \(0.406387\pi\) | |||||||
\(312\) | 1.16759 | + | 5.59735i | 0.0661020 | + | 0.316888i | ||||
\(313\) | 1.39017 | 0.0785773 | 0.0392886 | − | 0.999228i | \(-0.487491\pi\) | ||||
0.0392886 | + | 0.999228i | \(0.487491\pi\) | |||||||
\(314\) | −0.429212 | − | 0.743417i | −0.0242218 | − | 0.0419535i | ||||
\(315\) | 0.281920 | + | 0.488300i | 0.0158844 | + | 0.0275126i | ||||
\(316\) | −2.63353 | + | 4.56141i | −0.148148 | + | 0.256600i | ||||
\(317\) | −11.8851 | −0.667536 | −0.333768 | − | 0.942655i | \(-0.608320\pi\) | ||||
−0.333768 | + | 0.942655i | \(0.608320\pi\) | |||||||
\(318\) | 2.25358 | − | 3.90332i | 0.126375 | − | 0.218887i | ||||
\(319\) | 0.0694205 | − | 0.120240i | 0.00388680 | − | 0.00673214i | ||||
\(320\) | 8.56436 | 0.478762 | ||||||||
\(321\) | −1.40663 | + | 2.43636i | −0.0785106 | + | 0.135984i | ||||
\(322\) | −0.131550 | − | 0.227851i | −0.00733099 | − | 0.0126977i | ||||
\(323\) | 1.65487 | + | 2.86633i | 0.0920796 | + | 0.159487i | ||||
\(324\) | 10.9713 | 0.609519 | ||||||||
\(325\) | 10.6514 | + | 3.50556i | 0.590836 | + | 0.194453i | ||||
\(326\) | 2.67057 | 0.147909 | ||||||||
\(327\) | −7.15854 | − | 12.3990i | −0.395868 | − | 0.685664i | ||||
\(328\) | 5.71118 | + | 9.89205i | 0.315347 | + | 0.546197i | ||||
\(329\) | 2.15765 | − | 3.73715i | 0.118955 | − | 0.206036i | ||||
\(330\) | −0.359934 | −0.0198137 | ||||||||
\(331\) | −12.0601 | + | 20.8888i | −0.662885 | + | 1.14815i | 0.316969 | + | 0.948436i | \(0.397335\pi\) |
−0.979854 | + | 0.199714i | \(0.935999\pi\) | |||||||
\(332\) | 6.15930 | − | 10.6682i | 0.338035 | − | 0.585494i | ||||
\(333\) | −6.06572 | −0.332399 | ||||||||
\(334\) | 1.33365 | − | 2.30994i | 0.0729738 | − | 0.126394i | ||||
\(335\) | 3.02608 | + | 5.24133i | 0.165333 | + | 0.286365i | ||||
\(336\) | 1.24621 | + | 2.15849i | 0.0679861 | + | 0.117755i | ||||
\(337\) | −13.1114 | −0.714224 | −0.357112 | − | 0.934062i | \(-0.616239\pi\) | ||||
−0.357112 | + | 0.934062i | \(0.616239\pi\) | |||||||
\(338\) | −0.402045 | + | 3.56499i | −0.0218684 | + | 0.193910i | ||||
\(339\) | 10.7390 | 0.583262 | ||||||||
\(340\) | 3.10724 | + | 5.38189i | 0.168514 | + | 0.291874i | ||||
\(341\) | 0.323908 | + | 0.561024i | 0.0175406 | + | 0.0303812i | ||||
\(342\) | −0.166227 | + | 0.287914i | −0.00898854 | + | 0.0155686i | ||||
\(343\) | 6.60355 | 0.356558 | ||||||||
\(344\) | 4.93223 | − | 8.54287i | 0.265928 | − | 0.460601i | ||||
\(345\) | 2.00125 | − | 3.46627i | 0.107744 | − | 0.186618i | ||||
\(346\) | 2.70430 | 0.145384 | ||||||||
\(347\) | −4.77787 | + | 8.27552i | −0.256490 | + | 0.444253i | −0.965299 | − | 0.261147i | \(-0.915899\pi\) |
0.708809 | + | 0.705400i | \(0.249233\pi\) | |||||||
\(348\) | 0.301922 | + | 0.522945i | 0.0161847 | + | 0.0280328i | ||||
\(349\) | 3.85898 | + | 6.68394i | 0.206566 | + | 0.357783i | 0.950631 | − | 0.310325i | \(-0.100438\pi\) |
−0.744064 | + | 0.668108i | \(0.767104\pi\) | |||||||
\(350\) | −0.411596 | −0.0220007 | ||||||||
\(351\) | 19.3366 | + | 6.36399i | 1.03211 | + | 0.339685i | ||||
\(352\) | 2.03743 | 0.108595 | ||||||||
\(353\) | 13.3043 | + | 23.0437i | 0.708117 | + | 1.22649i | 0.965555 | + | 0.260200i | \(0.0837884\pi\) |
−0.257438 | + | 0.966295i | \(0.582878\pi\) | |||||||
\(354\) | −0.338994 | − | 0.587154i | −0.0180173 | − | 0.0312069i | ||||
\(355\) | −3.41196 | + | 5.90969i | −0.181088 | + | 0.313654i | ||||
\(356\) | 9.23529 | 0.489469 | ||||||||
\(357\) | −0.825113 | + | 1.42914i | −0.0436696 | + | 0.0756380i | ||||
\(358\) | 3.01190 | − | 5.21676i | 0.159184 | − | 0.275714i | ||||
\(359\) | 10.9463 | 0.577723 | 0.288862 | − | 0.957371i | \(-0.406723\pi\) | ||||
0.288862 | + | 0.957371i | \(0.406723\pi\) | |||||||
\(360\) | −0.636581 | + | 1.10259i | −0.0335508 | + | 0.0581117i | ||||
\(361\) | 8.50794 | + | 14.7362i | 0.447786 | + | 0.775589i | ||||
\(362\) | −2.27162 | − | 3.93457i | −0.119394 | − | 0.206796i | ||||
\(363\) | −15.4949 | −0.813271 | ||||||||
\(364\) | 0.679273 | + | 3.25638i | 0.0356036 | + | 0.170681i | ||||
\(365\) | −8.73235 | −0.457072 | ||||||||
\(366\) | −0.183618 | − | 0.318036i | −0.00959786 | − | 0.0166240i | ||||
\(367\) | 4.82355 | + | 8.35463i | 0.251787 | + | 0.436108i | 0.964018 | − | 0.265837i | \(-0.0856483\pi\) |
−0.712231 | + | 0.701945i | \(0.752315\pi\) | |||||||
\(368\) | −3.52757 | + | 6.10994i | −0.183888 | + | 0.318503i | ||||
\(369\) | 9.02141 | 0.469636 | ||||||||
\(370\) | −1.34538 | + | 2.33027i | −0.0699432 | + | 0.121145i | ||||
\(371\) | 2.67404 | − | 4.63157i | 0.138829 | − | 0.240459i | ||||
\(372\) | −2.81746 | −0.146079 | ||||||||
\(373\) | −11.0055 | + | 19.0621i | −0.569842 | + | 0.986996i | 0.426739 | + | 0.904375i | \(0.359662\pi\) |
−0.996581 | + | 0.0826208i | \(0.973671\pi\) | |||||||
\(374\) | 0.210035 | + | 0.363791i | 0.0108606 | + | 0.0188112i | ||||
\(375\) | −8.16408 | − | 14.1406i | −0.421591 | − | 0.730217i | ||||
\(376\) | 9.74401 | 0.502509 | ||||||||
\(377\) | 0.157797 | + | 0.756466i | 0.00812696 | + | 0.0389600i | ||||
\(378\) | −0.747210 | −0.0384324 | ||||||||
\(379\) | −10.9266 | − | 18.9255i | −0.561264 | − | 0.972138i | −0.997387 | − | 0.0722504i | \(-0.976982\pi\) |
0.436123 | − | 0.899887i | \(-0.356351\pi\) | |||||||
\(380\) | −1.86272 | − | 3.22632i | −0.0955553 | − | 0.165507i | ||||
\(381\) | −14.7578 | + | 25.5612i | −0.756064 | + | 1.30954i | ||||
\(382\) | 0.659936 | 0.0337653 | ||||||||
\(383\) | −5.62338 | + | 9.73998i | −0.287341 | + | 0.497690i | −0.973174 | − | 0.230069i | \(-0.926105\pi\) |
0.685833 | + | 0.727759i | \(0.259438\pi\) | |||||||
\(384\) | −5.86486 | + | 10.1582i | −0.299290 | + | 0.518386i | ||||
\(385\) | −0.427088 | −0.0217664 | ||||||||
\(386\) | −1.35091 | + | 2.33985i | −0.0687597 | + | 0.119095i | ||||
\(387\) | −3.89549 | − | 6.74718i | −0.198019 | − | 0.342979i | ||||
\(388\) | 10.4041 | + | 18.0205i | 0.528190 | + | 0.914852i | ||||
\(389\) | −3.48614 | −0.176754 | −0.0883771 | − | 0.996087i | \(-0.528168\pi\) | ||||
−0.0883771 | + | 0.996087i | \(0.528168\pi\) | |||||||
\(390\) | 1.49381 | − | 1.33481i | 0.0756418 | − | 0.0675907i | ||||
\(391\) | −4.67122 | −0.236234 | ||||||||
\(392\) | 3.66548 | + | 6.34880i | 0.185135 | + | 0.320663i | ||||
\(393\) | 0.326496 | + | 0.565507i | 0.0164695 | + | 0.0285261i | ||||
\(394\) | 2.69939 | − | 4.67548i | 0.135993 | − | 0.235547i | ||||
\(395\) | 3.76377 | 0.189376 | ||||||||
\(396\) | 0.532942 | − | 0.923082i | 0.0267813 | − | 0.0463866i | ||||
\(397\) | −0.602457 | + | 1.04349i | −0.0302364 | + | 0.0523710i | −0.880748 | − | 0.473586i | \(-0.842959\pi\) |
0.850511 | + | 0.525957i | \(0.176293\pi\) | |||||||
\(398\) | 1.88536 | 0.0945046 | ||||||||
\(399\) | 0.494636 | − | 0.856734i | 0.0247628 | − | 0.0428904i | ||||
\(400\) | 5.51857 | + | 9.55844i | 0.275928 | + | 0.477922i | ||||
\(401\) | 16.1824 | + | 28.0287i | 0.808108 | + | 1.39968i | 0.914173 | + | 0.405325i | \(0.132842\pi\) |
−0.106065 | + | 0.994359i | \(0.533825\pi\) | |||||||
\(402\) | −1.77924 | −0.0887406 | ||||||||
\(403\) | −3.42483 | − | 1.12717i | −0.170603 | − | 0.0561482i | ||||
\(404\) | 13.6709 | 0.680150 | ||||||||
\(405\) | −3.91999 | − | 6.78961i | −0.194786 | − | 0.337379i | ||||
\(406\) | −0.0141820 | − | 0.0245640i | −0.000703843 | − | 0.00121909i | ||||
\(407\) | 2.29728 | − | 3.97901i | 0.113872 | − | 0.197232i | ||||
\(408\) | −3.72624 | −0.184476 | ||||||||
\(409\) | 4.56787 | − | 7.91178i | 0.225867 | − | 0.391213i | −0.730712 | − | 0.682685i | \(-0.760812\pi\) |
0.956579 | + | 0.291473i | \(0.0941453\pi\) | |||||||
\(410\) | 2.00096 | − | 3.46576i | 0.0988203 | − | 0.171162i | ||||
\(411\) | 29.3069 | 1.44560 | ||||||||
\(412\) | 4.89241 | − | 8.47391i | 0.241032 | − | 0.417479i | ||||
\(413\) | −0.402241 | − | 0.696702i | −0.0197930 | − | 0.0342825i | ||||
\(414\) | −0.234605 | − | 0.406348i | −0.0115302 | − | 0.0199709i | ||||
\(415\) | −8.80270 | −0.432107 | ||||||||
\(416\) | −8.45578 | + | 7.55578i | −0.414579 | + | 0.370452i | ||||
\(417\) | 14.7988 | 0.724702 | ||||||||
\(418\) | −0.125911 | − | 0.218084i | −0.00615851 | − | 0.0106669i | ||||
\(419\) | 7.60307 | + | 13.1689i | 0.371434 | + | 0.643343i | 0.989786 | − | 0.142558i | \(-0.0455328\pi\) |
−0.618352 | + | 0.785901i | \(0.712199\pi\) | |||||||
\(420\) | 0.928742 | − | 1.60863i | 0.0453180 | − | 0.0784930i | ||||
\(421\) | 26.3139 | 1.28246 | 0.641231 | − | 0.767348i | \(-0.278424\pi\) | ||||
0.641231 | + | 0.767348i | \(0.278424\pi\) | |||||||
\(422\) | −3.12589 | + | 5.41420i | −0.152166 | + | 0.263559i | ||||
\(423\) | 3.84792 | − | 6.66480i | 0.187092 | − | 0.324054i | ||||
\(424\) | 12.0761 | 0.586466 | ||||||||
\(425\) | −3.65385 | + | 6.32865i | −0.177238 | + | 0.306984i | ||||
\(426\) | −1.00306 | − | 1.73736i | −0.0485986 | − | 0.0841752i | ||||
\(427\) | −0.217876 | − | 0.377372i | −0.0105438 | − | 0.0182623i | ||||
\(428\) | −3.69565 | −0.178636 | ||||||||
\(429\) | −2.55072 | + | 2.27923i | −0.123150 | + | 0.110042i | ||||
\(430\) | −3.45609 | −0.166668 | ||||||||
\(431\) | 9.92141 | + | 17.1844i | 0.477898 | + | 0.827743i | 0.999679 | − | 0.0253362i | \(-0.00806563\pi\) |
−0.521781 | + | 0.853079i | \(0.674732\pi\) | |||||||
\(432\) | 10.0184 | + | 17.3524i | 0.482010 | + | 0.834867i | ||||
\(433\) | −1.00617 | + | 1.74273i | −0.0483534 | + | 0.0837505i | −0.889189 | − | 0.457540i | \(-0.848731\pi\) |
0.840836 | + | 0.541290i | \(0.182064\pi\) | |||||||
\(434\) | 0.132343 | 0.00635268 | ||||||||
\(435\) | 0.215750 | − | 0.373689i | 0.0103444 | − | 0.0179170i | ||||
\(436\) | 9.40383 | − | 16.2879i | 0.450362 | − | 0.780049i | ||||
\(437\) | 2.80028 | 0.133956 | ||||||||
\(438\) | 1.28359 | − | 2.22324i | 0.0613322 | − | 0.106231i | ||||
\(439\) | −4.33545 | − | 7.50922i | −0.206920 | − | 0.358396i | 0.743823 | − | 0.668377i | \(-0.233011\pi\) |
−0.950743 | + | 0.309981i | \(0.899677\pi\) | |||||||
\(440\) | −0.482187 | − | 0.835173i | −0.0229874 | − | 0.0398153i | ||||
\(441\) | 5.79001 | 0.275715 | ||||||||
\(442\) | −2.22080 | − | 0.730902i | −0.105633 | − | 0.0347655i | ||||
\(443\) | −2.48474 | −0.118054 | −0.0590269 | − | 0.998256i | \(-0.518800\pi\) | ||||
−0.0590269 | + | 0.998256i | \(0.518800\pi\) | |||||||
\(444\) | 9.99129 | + | 17.3054i | 0.474165 | + | 0.821279i | ||||
\(445\) | −3.29970 | − | 5.71526i | −0.156421 | − | 0.270929i | ||||
\(446\) | 1.15633 | − | 2.00282i | 0.0547538 | − | 0.0948364i | ||||
\(447\) | 4.38816 | 0.207553 | ||||||||
\(448\) | −1.49377 | + | 2.58729i | −0.0705740 | + | 0.122238i | ||||
\(449\) | −5.30980 | + | 9.19685i | −0.250585 | + | 0.434026i | −0.963687 | − | 0.267034i | \(-0.913956\pi\) |
0.713102 | + | 0.701060i | \(0.247290\pi\) | |||||||
\(450\) | −0.734036 | −0.0346028 | ||||||||
\(451\) | −3.41669 | + | 5.91789i | −0.160886 | + | 0.278663i | ||||
\(452\) | 7.05364 | + | 12.2173i | 0.331775 | + | 0.574652i | ||||
\(453\) | −12.8660 | − | 22.2846i | −0.604498 | − | 1.04702i | ||||
\(454\) | −4.04953 | −0.190054 | ||||||||
\(455\) | 1.77251 | − | 1.58385i | 0.0830965 | − | 0.0742520i | ||||
\(456\) | 2.23380 | 0.104607 | ||||||||
\(457\) | −16.8487 | − | 29.1829i | −0.788150 | − | 1.36512i | −0.927099 | − | 0.374817i | \(-0.877706\pi\) |
0.138949 | − | 0.990300i | \(-0.455628\pi\) | |||||||
\(458\) | −0.00257732 | − | 0.00446404i | −0.000120430 | − | 0.000208591i | ||||
\(459\) | −6.63318 | + | 11.4890i | −0.309611 | + | 0.536261i | ||||
\(460\) | 5.25789 | 0.245151 | ||||||||
\(461\) | 3.51343 | − | 6.08543i | 0.163637 | − | 0.283427i | −0.772534 | − | 0.634974i | \(-0.781011\pi\) |
0.936170 | + | 0.351547i | \(0.114344\pi\) | |||||||
\(462\) | 0.0627787 | − | 0.108736i | 0.00292073 | − | 0.00505885i | ||||
\(463\) | −1.42217 | −0.0660939 | −0.0330469 | − | 0.999454i | \(-0.510521\pi\) | ||||
−0.0330469 | + | 0.999454i | \(0.510521\pi\) | |||||||
\(464\) | −0.380298 | + | 0.658696i | −0.0176549 | + | 0.0305792i | ||||
\(465\) | 1.00666 | + | 1.74359i | 0.0466828 | + | 0.0808569i | ||||
\(466\) | 3.74971 | + | 6.49468i | 0.173702 | + | 0.300860i | ||||
\(467\) | −15.9194 | −0.736663 | −0.368331 | − | 0.929695i | \(-0.620071\pi\) | ||||
−0.368331 | + | 0.929695i | \(0.620071\pi\) | |||||||
\(468\) | 1.21141 | + | 5.80739i | 0.0559974 | + | 0.268447i | ||||
\(469\) | −2.11120 | −0.0974863 | ||||||||
\(470\) | −1.70695 | − | 2.95652i | −0.0787356 | − | 0.136374i | ||||
\(471\) | 2.27773 | + | 3.94514i | 0.104952 | + | 0.181782i | ||||
\(472\) | 0.908268 | − | 1.57317i | 0.0418064 | − | 0.0724109i | ||||
\(473\) | 5.90138 | 0.271346 | ||||||||
\(474\) | −0.553245 | + | 0.958249i | −0.0254114 | + | 0.0440138i | ||||
\(475\) | 2.19040 | − | 3.79388i | 0.100502 | − | 0.174075i | ||||
\(476\) | −2.16782 | −0.0993619 | ||||||||
\(477\) | 4.76886 | − | 8.25990i | 0.218351 | − | 0.378195i | ||||
\(478\) | 2.40393 | + | 4.16372i | 0.109953 | + | 0.190444i | ||||
\(479\) | −5.10313 | − | 8.83888i | −0.233168 | − | 0.403859i | 0.725571 | − | 0.688148i | \(-0.241576\pi\) |
−0.958739 | + | 0.284289i | \(0.908243\pi\) | |||||||
\(480\) | 6.33206 | 0.289018 | ||||||||
\(481\) | 5.22186 | + | 25.0332i | 0.238096 | + | 1.14141i | ||||
\(482\) | −1.25310 | −0.0570773 | ||||||||
\(483\) | 0.698105 | + | 1.20915i | 0.0317649 | + | 0.0550184i | ||||
\(484\) | −10.1774 | − | 17.6279i | −0.462611 | − | 0.801266i | ||||
\(485\) | 7.43465 | − | 12.8772i | 0.337590 | − | 0.584723i | ||||
\(486\) | −2.36952 | −0.107484 | ||||||||
\(487\) | 9.28076 | − | 16.0748i | 0.420551 | − | 0.728416i | −0.575442 | − | 0.817843i | \(-0.695170\pi\) |
0.995993 | + | 0.0894261i | \(0.0285033\pi\) | |||||||
\(488\) | 0.491969 | − | 0.852115i | 0.0222704 | − | 0.0385734i | ||||
\(489\) | −14.1721 | −0.640884 | ||||||||
\(490\) | 1.28423 | − | 2.22435i | 0.0580156 | − | 0.100486i | ||||
\(491\) | −6.57495 | − | 11.3881i | −0.296723 | − | 0.513940i | 0.678661 | − | 0.734452i | \(-0.262561\pi\) |
−0.975384 | + | 0.220512i | \(0.929227\pi\) | |||||||
\(492\) | −14.8598 | − | 25.7380i | −0.669932 | − | 1.16036i | ||||
\(493\) | −0.503591 | −0.0226806 | ||||||||
\(494\) | 1.33132 | + | 0.438159i | 0.0598989 | + | 0.0197137i | ||||
\(495\) | −0.761665 | −0.0342343 | ||||||||
\(496\) | −1.77442 | − | 3.07339i | −0.0796740 | − | 0.137999i | ||||
\(497\) | −1.19021 | − | 2.06150i | −0.0533881 | − | 0.0924709i | ||||
\(498\) | 1.29393 | − | 2.24115i | 0.0579823 | − | 0.100428i | ||||
\(499\) | −2.18061 | −0.0976175 | −0.0488088 | − | 0.998808i | \(-0.515542\pi\) | ||||
−0.0488088 | + | 0.998808i | \(0.515542\pi\) | |||||||
\(500\) | 10.7248 | − | 18.5758i | 0.479626 | − | 0.830736i | ||||
\(501\) | −7.07734 | + | 12.2583i | −0.316192 | + | 0.547661i | ||||
\(502\) | −0.0185457 | −0.000827736 | ||||||||
\(503\) | −0.314336 | + | 0.544446i | −0.0140156 | + | 0.0242757i | −0.872948 | − | 0.487813i | \(-0.837795\pi\) |
0.858933 | + | 0.512089i | \(0.171128\pi\) | |||||||
\(504\) | −0.222061 | − | 0.384621i | −0.00989140 | − | 0.0171324i | ||||
\(505\) | −4.88450 | − | 8.46020i | −0.217357 | − | 0.376474i | ||||
\(506\) | 0.355409 | 0.0157999 | ||||||||
\(507\) | 2.13356 | − | 18.9186i | 0.0947546 | − | 0.840203i | ||||
\(508\) | −38.7732 | −1.72028 | ||||||||
\(509\) | −11.1164 | − | 19.2541i | −0.492725 | − | 0.853425i | 0.507240 | − | 0.861805i | \(-0.330666\pi\) |
−0.999965 | + | 0.00838010i | \(0.997332\pi\) | |||||||
\(510\) | 0.652760 | + | 1.13061i | 0.0289047 | + | 0.0500644i | ||||
\(511\) | 1.52307 | − | 2.63804i | 0.0673767 | − | 0.116700i | ||||
\(512\) | −18.8472 | −0.832937 | ||||||||
\(513\) | 3.97644 | − | 6.88740i | 0.175564 | − | 0.304086i | ||||
\(514\) | 1.95548 | − | 3.38699i | 0.0862525 | − | 0.149394i | ||||
\(515\) | −6.99210 | −0.308109 | ||||||||
\(516\) | −12.8331 | + | 22.2275i | −0.564945 | + | 0.978513i | ||||
\(517\) | 2.91466 | + | 5.04834i | 0.128187 | + | 0.222026i | ||||
\(518\) | −0.469316 | − | 0.812879i | −0.0206206 | − | 0.0357158i | ||||
\(519\) | −14.3511 | −0.629943 | ||||||||
\(520\) | 5.09840 | + | 1.67797i | 0.223580 | + | 0.0735837i | ||||
\(521\) | −13.1236 | −0.574954 | −0.287477 | − | 0.957788i | \(-0.592816\pi\) | ||||
−0.287477 | + | 0.957788i | \(0.592816\pi\) | |||||||
\(522\) | −0.0252921 | − | 0.0438073i | −0.00110701 | − | 0.00191739i | ||||
\(523\) | −10.9185 | − | 18.9114i | −0.477434 | − | 0.826939i | 0.522232 | − | 0.852803i | \(-0.325100\pi\) |
−0.999665 | + | 0.0258644i | \(0.991766\pi\) | |||||||
\(524\) | −0.428902 | + | 0.742879i | −0.0187367 | + | 0.0324528i | ||||
\(525\) | 2.18424 | 0.0953282 | ||||||||
\(526\) | −3.71382 | + | 6.43253i | −0.161930 | + | 0.280472i | ||||
\(527\) | 1.17485 | − | 2.03489i | 0.0511771 | − | 0.0886414i | ||||
\(528\) | −3.36688 | −0.146525 | ||||||||
\(529\) | 9.52391 | − | 16.4959i | 0.414083 | − | 0.717213i | ||||
\(530\) | −2.11548 | − | 3.66411i | −0.0918904 | − | 0.159159i | ||||
\(531\) | −0.717353 | − | 1.24249i | −0.0311305 | − | 0.0539195i | ||||
\(532\) | 1.29956 | 0.0563430 | ||||||||
\(533\) | −7.76636 | − | 37.2313i | −0.336398 | − | 1.61267i | ||||
\(534\) | 1.94012 | 0.0839574 | ||||||||
\(535\) | 1.32043 | + | 2.28705i | 0.0570872 | + | 0.0988779i | ||||
\(536\) | −2.38357 | − | 4.12846i | −0.102955 | − | 0.178322i | ||||
\(537\) | −15.9834 | + | 27.6841i | −0.689736 | + | 1.19466i | ||||
\(538\) | −5.44755 | −0.234861 | ||||||||
\(539\) | −2.19286 | + | 3.79815i | −0.0944532 | + | 0.163598i | ||||
\(540\) | 7.46627 | − | 12.9320i | 0.321297 | − | 0.556503i | ||||
\(541\) | −1.20030 | −0.0516048 | −0.0258024 | − | 0.999667i | \(-0.508214\pi\) | ||||
−0.0258024 | + | 0.999667i | \(0.508214\pi\) | |||||||
\(542\) | 2.14566 | − | 3.71640i | 0.0921642 | − | 0.159633i | ||||
\(543\) | 12.0550 | + | 20.8798i | 0.517328 | + | 0.896039i | ||||
\(544\) | −3.69499 | − | 6.39991i | −0.158421 | − | 0.274394i | ||||
\(545\) | −13.4397 | −0.575693 | ||||||||
\(546\) | 0.142700 | + | 0.684091i | 0.00610699 | + | 0.0292764i | ||||
\(547\) | 44.5664 | 1.90552 | 0.952761 | − | 0.303720i | \(-0.0982286\pi\) | ||||
0.952761 | + | 0.303720i | \(0.0982286\pi\) | |||||||
\(548\) | 19.2495 | + | 33.3411i | 0.822299 | + | 1.42426i | ||||
\(549\) | −0.388558 | − | 0.673002i | −0.0165833 | − | 0.0287230i | ||||
\(550\) | 0.278003 | − | 0.481515i | 0.0118541 | − | 0.0205319i | ||||
\(551\) | 0.301891 | 0.0128610 | ||||||||
\(552\) | −1.57633 | + | 2.73029i | −0.0670933 | + | 0.116209i | ||||
\(553\) | −0.656466 | + | 1.13703i | −0.0279158 | + | 0.0483516i | ||||
\(554\) | −3.66206 | −0.155586 | ||||||||
\(555\) | 7.13963 | − | 12.3662i | 0.303061 | − | 0.524916i | ||||
\(556\) | 9.72026 | + | 16.8360i | 0.412231 | + | 0.714005i | ||||
\(557\) | −1.34798 | − | 2.33476i | −0.0571156 | − | 0.0989272i | 0.836054 | − | 0.548647i | \(-0.184857\pi\) |
−0.893169 | + | 0.449720i | \(0.851524\pi\) | |||||||
\(558\) | 0.236020 | 0.00999152 | ||||||||
\(559\) | −24.4920 | + | 21.8852i | −1.03590 | + | 0.925643i | ||||
\(560\) | 2.33967 | 0.0988690 | ||||||||
\(561\) | −1.11461 | − | 1.93055i | −0.0470587 | − | 0.0815081i | ||||
\(562\) | −3.45257 | − | 5.98003i | −0.145638 | − | 0.252252i | ||||
\(563\) | 21.1399 | − | 36.6155i | 0.890942 | − | 1.54316i | 0.0521946 | − | 0.998637i | \(-0.483378\pi\) |
0.838748 | − | 0.544520i | \(-0.183288\pi\) | |||||||
\(564\) | −25.3528 | −1.06754 | ||||||||
\(565\) | 5.04043 | − | 8.73029i | 0.212053 | − | 0.367286i | ||||
\(566\) | 3.50245 | − | 6.06642i | 0.147219 | − | 0.254991i | ||||
\(567\) | 2.73485 | 0.114853 | ||||||||
\(568\) | 2.68751 | − | 4.65491i | 0.112766 | − | 0.195316i | ||||
\(569\) | −11.8065 | − | 20.4495i | −0.494956 | − | 0.857289i | 0.505027 | − | 0.863103i | \(-0.331482\pi\) |
−0.999983 | + | 0.00581474i | \(0.998149\pi\) | |||||||
\(570\) | −0.391314 | − | 0.677776i | −0.0163904 | − | 0.0283889i | ||||
\(571\) | −8.36986 | −0.350268 | −0.175134 | − | 0.984545i | \(-0.556036\pi\) | ||||
−0.175134 | + | 0.984545i | \(0.556036\pi\) | |||||||
\(572\) | −4.26835 | − | 1.40478i | −0.178469 | − | 0.0587369i | ||||
\(573\) | −3.50213 | −0.146303 | ||||||||
\(574\) | 0.698003 | + | 1.20898i | 0.0291341 | + | 0.0504617i | ||||
\(575\) | 3.09142 | + | 5.35449i | 0.128921 | + | 0.223298i | ||||
\(576\) | −2.66398 | + | 4.61414i | −0.110999 | + | 0.192256i | ||||
\(577\) | −1.70007 | −0.0707748 | −0.0353874 | − | 0.999374i | \(-0.511267\pi\) | ||||
−0.0353874 | + | 0.999374i | \(0.511267\pi\) | |||||||
\(578\) | −1.58391 | + | 2.74342i | −0.0658820 | + | 0.114111i | ||||
\(579\) | 7.16899 | − | 12.4170i | 0.297933 | − | 0.516035i | ||||
\(580\) | 0.566839 | 0.0235367 | ||||||||
\(581\) | 1.53534 | − | 2.65929i | 0.0636967 | − | 0.110326i | ||||
\(582\) | 2.18567 | + | 3.78569i | 0.0905990 | + | 0.156922i | ||||
\(583\) | 3.61223 | + | 6.25657i | 0.149603 | + | 0.259121i | ||||
\(584\) | 6.87825 | 0.284624 | ||||||||
\(585\) | 3.16108 | − | 2.82462i | 0.130694 | − | 0.116784i | ||||
\(586\) | −1.03563 | −0.0427817 | ||||||||
\(587\) | 24.1149 | + | 41.7683i | 0.995330 | + | 1.72396i | 0.581260 | + | 0.813718i | \(0.302560\pi\) |
0.414071 | + | 0.910245i | \(0.364107\pi\) | |||||||
\(588\) | −9.53715 | − | 16.5188i | −0.393305 | − | 0.681225i | ||||
\(589\) | −0.704293 | + | 1.21987i | −0.0290199 | + | 0.0502639i | ||||
\(590\) | −0.636439 | −0.0262018 | ||||||||
\(591\) | −14.3250 | + | 24.8117i | −0.589253 | + | 1.02062i | ||||
\(592\) | −12.5849 | + | 21.7977i | −0.517237 | + | 0.895881i | ||||
\(593\) | −37.2527 | −1.52978 | −0.764892 | − | 0.644159i | \(-0.777208\pi\) | ||||
−0.764892 | + | 0.644159i | \(0.777208\pi\) | |||||||
\(594\) | 0.504686 | − | 0.874142i | 0.0207075 | − | 0.0358665i | ||||
\(595\) | 0.774547 | + | 1.34156i | 0.0317534 | + | 0.0549984i | ||||
\(596\) | 2.88226 | + | 4.99222i | 0.118062 | + | 0.204489i | ||||
\(597\) | −10.0052 | −0.409484 | ||||||||
\(598\) | −1.47503 | + | 1.31803i | −0.0603183 | + | 0.0538982i | ||||
\(599\) | −7.28226 | −0.297545 | −0.148772 | − | 0.988871i | \(-0.547532\pi\) | ||||
−0.148772 | + | 0.988871i | \(0.547532\pi\) | |||||||
\(600\) | 2.46603 | + | 4.27129i | 0.100675 | + | 0.174375i | ||||
\(601\) | 4.10696 | + | 7.11347i | 0.167527 | + | 0.290165i | 0.937550 | − | 0.347852i | \(-0.113089\pi\) |
−0.770023 | + | 0.638016i | \(0.779755\pi\) | |||||||
\(602\) | 0.602802 | − | 1.04408i | 0.0245684 | − | 0.0425537i | ||||
\(603\) | −3.76510 | −0.153327 | ||||||||
\(604\) | 16.9015 | − | 29.2742i | 0.687711 | − | 1.19115i | ||||
\(605\) | −7.27266 | + | 12.5966i | −0.295676 | + | 0.512125i | ||||
\(606\) | 2.87193 | 0.116664 | ||||||||
\(607\) | 12.3260 | − | 21.3492i | 0.500296 | − | 0.866539i | −0.499704 | − | 0.866196i | \(-0.666558\pi\) |
1.00000 | 0.000342098i | \(-0.000108893\pi\) | ||||||||
\(608\) | 2.21506 | + | 3.83660i | 0.0898325 | + | 0.155595i | ||||
\(609\) | 0.0752608 | + | 0.130356i | 0.00304972 | + | 0.00528227i | ||||
\(610\) | −0.344731 | −0.0139577 | ||||||||
\(611\) | −30.8182 | − | 10.1427i | −1.24677 | − | 0.410332i | ||||
\(612\) | −3.86607 | −0.156277 | ||||||||
\(613\) | −1.42481 | − | 2.46785i | −0.0575477 | − | 0.0996755i | 0.835816 | − | 0.549009i | \(-0.184995\pi\) |
−0.893364 | + | 0.449334i | \(0.851661\pi\) | |||||||
\(614\) | −1.46296 | − | 2.53392i | −0.0590402 | − | 0.102261i | ||||
\(615\) | −10.6186 | + | 18.3920i | −0.428184 | + | 0.741637i | ||||
\(616\) | 0.336407 | 0.0135542 | ||||||||
\(617\) | −10.6162 | + | 18.3878i | −0.427392 | + | 0.740264i | −0.996640 | − | 0.0819014i | \(-0.973901\pi\) |
0.569249 | + | 0.822165i | \(0.307234\pi\) | |||||||
\(618\) | 1.02778 | − | 1.78017i | 0.0413436 | − | 0.0716091i | ||||
\(619\) | −11.0933 | −0.445878 | −0.222939 | − | 0.974832i | \(-0.571565\pi\) | ||||
−0.222939 | + | 0.974832i | \(0.571565\pi\) | |||||||
\(620\) | −1.32240 | + | 2.29047i | −0.0531089 | + | 0.0919873i | ||||
\(621\) | 5.61215 | + | 9.72053i | 0.225208 | + | 0.390072i | ||||
\(622\) | 1.41073 | + | 2.44346i | 0.0565653 | + | 0.0979740i | ||||
\(623\) | 2.30210 | 0.0922317 | ||||||||
\(624\) | 13.9733 | − | 12.4860i | 0.559379 | − | 0.499841i | ||||
\(625\) | 0.222787 | 0.00891147 | ||||||||
\(626\) | 0.191822 | + | 0.332245i | 0.00766675 | + | 0.0132792i | ||||
\(627\) | 0.668180 | + | 1.15732i | 0.0266846 | + | 0.0462190i | ||||
\(628\) | −2.99214 | + | 5.18254i | −0.119399 | + | 0.206806i | ||||
\(629\) | −16.6650 | −0.664475 | ||||||||
\(630\) | −0.0778010 | + | 0.134755i | −0.00309967 | + | 0.00536878i | ||||
\(631\) | 20.0237 | − | 34.6820i | 0.797130 | − | 1.38067i | −0.124347 | − | 0.992239i | \(-0.539684\pi\) |
0.921478 | − | 0.388431i | \(-0.126983\pi\) | |||||||
\(632\) | −2.96463 | −0.117927 | ||||||||
\(633\) | 16.5883 | − | 28.7319i | 0.659328 | − | 1.14199i | ||||
\(634\) | −1.63996 | − | 2.84050i | −0.0651312 | − | 0.112811i | ||||
\(635\) | 13.8534 | + | 23.9948i | 0.549755 | + | 0.952203i | ||||
\(636\) | −31.4205 | −1.24590 | ||||||||
\(637\) | −4.98451 | − | 23.8953i | −0.197493 | − | 0.946767i | ||||
\(638\) | 0.0383157 | 0.00151693 | ||||||||
\(639\) | −2.12261 | − | 3.67646i | −0.0839690 | − | 0.145439i | ||||
\(640\) | 5.50545 | + | 9.53572i | 0.217622 | + | 0.376932i | ||||
\(641\) | 6.82195 | − | 11.8160i | 0.269451 | − | 0.466703i | −0.699269 | − | 0.714858i | \(-0.746491\pi\) |
0.968720 | + | 0.248156i | \(0.0798244\pi\) | |||||||
\(642\) | −0.776372 | −0.0306410 | ||||||||
\(643\) | 0.680491 | − | 1.17864i | 0.0268359 | − | 0.0464812i | −0.852296 | − | 0.523061i | \(-0.824790\pi\) |
0.879131 | + | 0.476579i | \(0.158123\pi\) | |||||||
\(644\) | −0.917066 | + | 1.58841i | −0.0361375 | + | 0.0625920i | ||||
\(645\) | 18.3407 | 0.722164 | ||||||||
\(646\) | −0.456693 | + | 0.791015i | −0.0179683 | + | 0.0311221i | ||||
\(647\) | −17.2802 | − | 29.9301i | −0.679354 | − | 1.17668i | −0.975176 | − | 0.221432i | \(-0.928927\pi\) |
0.295822 | − | 0.955243i | \(-0.404407\pi\) | |||||||
\(648\) | 3.08767 | + | 5.34801i | 0.121295 | + | 0.210090i | ||||
\(649\) | 1.08674 | 0.0426582 | ||||||||
\(650\) | 0.631917 | + | 3.02936i | 0.0247858 | + | 0.118821i | ||||
\(651\) | −0.702315 | −0.0275259 | ||||||||
\(652\) | −9.30860 | − | 16.1230i | −0.364553 | − | 0.631424i | ||||
\(653\) | −7.72595 | − | 13.3817i | −0.302340 | − | 0.523668i | 0.674326 | − | 0.738434i | \(-0.264434\pi\) |
−0.976665 | + | 0.214766i | \(0.931101\pi\) | |||||||
\(654\) | 1.97553 | − | 3.42172i | 0.0772494 | − | 0.133800i | ||||
\(655\) | 0.612974 | 0.0239509 | ||||||||
\(656\) | 18.7173 | − | 32.4193i | 0.730787 | − | 1.26576i | ||||
\(657\) | 2.71623 | − | 4.70465i | 0.105970 | − | 0.183546i | ||||
\(658\) | 1.19088 | 0.0464255 | ||||||||
\(659\) | −13.3438 | + | 23.1121i | −0.519799 | + | 0.900319i | 0.479936 | + | 0.877304i | \(0.340660\pi\) |
−0.999735 | + | 0.0230154i | \(0.992673\pi\) | |||||||
\(660\) | 1.25459 | + | 2.17302i | 0.0488350 | + | 0.0845847i | ||||
\(661\) | 20.2142 | + | 35.0121i | 0.786243 | + | 1.36181i | 0.928254 | + | 0.371948i | \(0.121310\pi\) |
−0.142011 | + | 0.989865i | \(0.545357\pi\) | |||||||
\(662\) | −6.65643 | −0.258709 | ||||||||
\(663\) | 11.7853 | + | 3.87872i | 0.457702 | + | 0.150637i | ||||
\(664\) | 6.93366 | 0.269078 | ||||||||
\(665\) | −0.464323 | − | 0.804231i | −0.0180057 | − | 0.0311868i | ||||
\(666\) | −0.836973 | − | 1.44968i | −0.0324321 | − | 0.0561740i | ||||
\(667\) | −0.213037 | + | 0.368991i | −0.00824883 | + | 0.0142874i | ||||
\(668\) | −18.5943 | −0.719436 | ||||||||
\(669\) | −6.13637 | + | 10.6285i | −0.237246 | + | 0.410922i | ||||
\(670\) | −0.835103 | + | 1.44644i | −0.0322629 | + | 0.0558809i | ||||
\(671\) | 0.588637 | 0.0227241 | ||||||||
\(672\) | −1.10442 | + | 1.91291i | −0.0426039 | + | 0.0737921i | ||||
\(673\) | 6.18814 | + | 10.7182i | 0.238535 | + | 0.413155i | 0.960294 | − | 0.278989i | \(-0.0899994\pi\) |
−0.721759 | + | 0.692144i | \(0.756666\pi\) | |||||||
\(674\) | −1.80917 | − | 3.13357i | −0.0696865 | − | 0.120701i | ||||
\(675\) | 17.5594 | 0.675862 | ||||||||
\(676\) | 22.9242 | − | 9.99894i | 0.881699 | − | 0.384575i | ||||
\(677\) | 21.4334 | 0.823753 | 0.411876 | − | 0.911240i | \(-0.364874\pi\) | ||||
0.411876 | + | 0.911240i | \(0.364874\pi\) | |||||||
\(678\) | 1.48181 | + | 2.56657i | 0.0569086 | + | 0.0985685i | ||||
\(679\) | 2.59346 | + | 4.49200i | 0.0995278 | + | 0.172387i | ||||
\(680\) | −1.74894 | + | 3.02926i | −0.0670689 | + | 0.116167i | ||||
\(681\) | 21.4899 | 0.823495 | ||||||||
\(682\) | −0.0893882 | + | 0.154825i | −0.00342285 | + | 0.00592855i | ||||
\(683\) | −24.5624 | + | 42.5433i | −0.939853 | + | 1.62787i | −0.174110 | + | 0.984726i | \(0.555705\pi\) |
−0.765743 | + | 0.643147i | \(0.777628\pi\) | |||||||
\(684\) | 2.31762 | 0.0886164 | ||||||||
\(685\) | 13.7554 | − | 23.8251i | 0.525568 | − | 0.910311i | ||||
\(686\) | 0.911185 | + | 1.57822i | 0.0347892 | + | 0.0602567i | ||||
\(687\) | 0.0136772 | + | 0.0236896i | 0.000521818 | + | 0.000903815i | ||||
\(688\) | −32.3288 | −1.23253 | ||||||||
\(689\) | −38.1939 | − | 12.5702i | −1.45507 | − | 0.478888i | ||||
\(690\) | 1.10456 | 0.0420500 | ||||||||
\(691\) | 0.429641 | + | 0.744159i | 0.0163443 | + | 0.0283092i | 0.874082 | − | 0.485779i | \(-0.161464\pi\) |
−0.857738 | + | 0.514088i | \(0.828131\pi\) | |||||||
\(692\) | −9.42616 | − | 16.3266i | −0.358329 | − | 0.620644i | ||||
\(693\) | 0.132847 | − | 0.230099i | 0.00504646 | − | 0.00874072i | ||||
\(694\) | −2.63708 | −0.100102 | ||||||||
\(695\) | 6.94596 | − | 12.0308i | 0.263475 | − | 0.456353i | ||||
\(696\) | −0.169940 | + | 0.294345i | −0.00644157 | + | 0.0111571i | ||||
\(697\) | 24.7854 | 0.938815 | ||||||||
\(698\) | −1.06496 | + | 1.84456i | −0.0403092 | + | 0.0698175i | ||||
\(699\) | −19.8988 | − | 34.4658i | −0.752642 | − | 1.30361i | ||||
\(700\) | 1.43467 | + | 2.48492i | 0.0542253 | + | 0.0939210i | ||||
\(701\) | 34.0301 | 1.28530 | 0.642649 | − | 0.766161i | \(-0.277835\pi\) | ||||
0.642649 | + | 0.766161i | \(0.277835\pi\) | |||||||
\(702\) | 1.14718 | + | 5.49949i | 0.0432976 | + | 0.207565i | ||||
\(703\) | 9.99025 | 0.376790 | ||||||||
\(704\) | −2.01786 | − | 3.49504i | −0.0760511 | − | 0.131724i | ||||
\(705\) | 9.05837 | + | 15.6896i | 0.341158 | + | 0.590903i | ||||
\(706\) | −3.67157 | + | 6.35934i | −0.138181 | + | 0.239337i | ||||
\(707\) | 3.40776 | 0.128162 | ||||||||
\(708\) | −2.36321 | + | 4.09319i | −0.0888148 | + | 0.153832i | ||||
\(709\) | 23.5041 | − | 40.7103i | 0.882716 | − | 1.52891i | 0.0344058 | − | 0.999408i | \(-0.489046\pi\) |
0.848310 | − | 0.529500i | \(-0.177621\pi\) | |||||||
\(710\) | −1.88319 | −0.0706747 | ||||||||
\(711\) | −1.17074 | + | 2.02777i | −0.0439060 | + | 0.0760474i | ||||
\(712\) | 2.59909 | + | 4.50176i | 0.0974051 | + | 0.168711i | ||||
\(713\) | −0.994005 | − | 1.72167i | −0.0372258 | − | 0.0644770i | ||||
\(714\) | −0.455410 | −0.0170433 | ||||||||
\(715\) | 0.655703 | + | 3.14339i | 0.0245219 | + | 0.117556i | ||||
\(716\) | −41.9933 | −1.56936 | ||||||||
\(717\) | −12.7571 | − | 22.0959i | −0.476422 | − | 0.825186i | ||||
\(718\) | 1.51041 | + | 2.61612i | 0.0563682 | + | 0.0976326i | ||||
\(719\) | 1.56068 | − | 2.70317i | 0.0582034 | − | 0.100811i | −0.835456 | − | 0.549558i | \(-0.814796\pi\) |
0.893659 | + | 0.448747i | \(0.148129\pi\) | |||||||
\(720\) | 4.17254 | 0.155501 | ||||||||
\(721\) | 1.21954 | − | 2.11231i | 0.0454181 | − | 0.0786665i | ||||
\(722\) | −2.34792 | + | 4.06672i | −0.0873806 | + | 0.151348i | ||||
\(723\) | 6.64992 | 0.247313 | ||||||||
\(724\) | −15.8360 | + | 27.4288i | −0.588541 | + | 1.01938i | ||||
\(725\) | 0.333277 | + | 0.577253i | 0.0123776 | + | 0.0214387i | ||||
\(726\) | −2.13805 | − | 3.70321i | −0.0793505 | − | 0.137439i | ||||
\(727\) | 16.8580 | 0.625230 | 0.312615 | − | 0.949880i | \(-0.398795\pi\) | ||||
0.312615 | + | 0.949880i | \(0.398795\pi\) | |||||||
\(728\) | −1.39616 | + | 1.24756i | −0.0517452 | + | 0.0462376i | ||||
\(729\) | 29.6830 | 1.09937 | ||||||||
\(730\) | −1.20493 | − | 2.08699i | −0.0445963 | − | 0.0772431i | ||||
\(731\) | −10.7025 | − | 18.5372i | −0.395845 | − | 0.685624i | ||||
\(732\) | −1.28004 | + | 2.21710i | −0.0473118 | + | 0.0819464i | ||||
\(733\) | 18.1596 | 0.670741 | 0.335370 | − | 0.942086i | \(-0.391139\pi\) | ||||
0.335370 | + | 0.942086i | \(0.391139\pi\) | |||||||
\(734\) | −1.33115 | + | 2.30561i | −0.0491335 | + | 0.0851018i | ||||
\(735\) | −6.81511 | + | 11.8041i | −0.251379 | + | 0.435402i | ||||
\(736\) | −6.25246 | −0.230469 | ||||||||
\(737\) | 1.42596 | − | 2.46984i | 0.0525260 | − | 0.0909777i | ||||
\(738\) | 1.24481 | + | 2.15608i | 0.0458222 | + | 0.0793663i | ||||
\(739\) | −12.1064 | − | 20.9689i | −0.445341 | − | 0.771353i | 0.552735 | − | 0.833357i | \(-0.313584\pi\) |
−0.998076 | + | 0.0620039i | \(0.980251\pi\) | |||||||
\(740\) | 18.7580 | 0.689557 | ||||||||
\(741\) | −7.06500 | − | 2.32520i | −0.259539 | − | 0.0854185i | ||||
\(742\) | 1.47590 | 0.0541820 | ||||||||
\(743\) | 8.80158 | + | 15.2448i | 0.322899 | + | 0.559277i | 0.981085 | − | 0.193578i | \(-0.0620093\pi\) |
−0.658186 | + | 0.752855i | \(0.728676\pi\) | |||||||
\(744\) | −0.792921 | − | 1.37338i | −0.0290699 | − | 0.0503505i | ||||
\(745\) | 2.05962 | − | 3.56737i | 0.0754587 | − | 0.130698i | ||||
\(746\) | −6.07433 | −0.222397 | ||||||||
\(747\) | 2.73811 | − | 4.74255i | 0.100182 | − | 0.173521i | ||||
\(748\) | 1.46420 | − | 2.53608i | 0.0535366 | − | 0.0927281i | ||||
\(749\) | −0.921222 | −0.0336607 | ||||||||
\(750\) | 2.25303 | − | 3.90236i | 0.0822689 | − | 0.142494i | ||||
\(751\) | 13.6592 | + | 23.6585i | 0.498432 | + | 0.863310i | 0.999998 | − | 0.00180922i | \(-0.000575893\pi\) |
−0.501566 | + | 0.865119i | \(0.667243\pi\) | |||||||
\(752\) | −15.9671 | − | 27.6557i | −0.582258 | − | 1.00850i | ||||
\(753\) | 0.0984178 | 0.00358654 | ||||||||
\(754\) | −0.159019 | + | 0.142093i | −0.00579112 | + | 0.00517473i | ||||
\(755\) | −24.1551 | −0.879094 | ||||||||
\(756\) | 2.60449 | + | 4.51111i | 0.0947244 | + | 0.164068i | ||||
\(757\) | 8.61671 | + | 14.9246i | 0.313179 | + | 0.542443i | 0.979049 | − | 0.203626i | \(-0.0652725\pi\) |
−0.665869 | + | 0.746068i | \(0.731939\pi\) | |||||||
\(758\) | 3.01541 | − | 5.22284i | 0.109525 | − | 0.189702i | ||||
\(759\) | −1.88607 | −0.0684602 | ||||||||
\(760\) | 1.04845 | − | 1.81597i | 0.0380313 | − | 0.0658722i | ||||
\(761\) | 10.2588 | − | 17.7687i | 0.371880 | − | 0.644115i | −0.617975 | − | 0.786198i | \(-0.712047\pi\) |
0.989855 | + | 0.142083i | \(0.0453800\pi\) | |||||||
\(762\) | −8.14536 | −0.295075 | ||||||||
\(763\) | 2.34411 | − | 4.06012i | 0.0848626 | − | 0.146986i | ||||
\(764\) | −2.30029 | − | 3.98421i | −0.0832215 | − | 0.144144i | ||||
\(765\) | 1.38132 | + | 2.39252i | 0.0499417 | + | 0.0865016i | ||||
\(766\) | −3.10375 | −0.112143 | ||||||||
\(767\) | −4.51019 | + | 4.03014i | −0.162854 | + | 0.145520i | ||||
\(768\) | 15.0099 | 0.541623 | ||||||||
\(769\) | 24.5046 | + | 42.4432i | 0.883659 | + | 1.53054i | 0.847244 | + | 0.531205i | \(0.178260\pi\) |
0.0364150 | + | 0.999337i | \(0.488406\pi\) | |||||||
\(770\) | −0.0589314 | − | 0.102072i | −0.00212374 | − | 0.00367843i | ||||
\(771\) | −10.3773 | + | 17.9740i | −0.373728 | + | 0.647316i | ||||
\(772\) | 18.8351 | 0.677890 | ||||||||
\(773\) | −1.37115 | + | 2.37490i | −0.0493168 | + | 0.0854192i | −0.889630 | − | 0.456682i | \(-0.849038\pi\) |
0.840313 | + | 0.542101i | \(0.182371\pi\) | |||||||
\(774\) | 1.07503 | − | 1.86201i | 0.0386412 | − | 0.0669285i | ||||
\(775\) | −3.11006 | −0.111717 | ||||||||
\(776\) | −5.85608 | + | 10.1430i | −0.210221 | + | 0.364114i | ||||
\(777\) | 2.49055 | + | 4.31376i | 0.0893479 | + | 0.154755i | ||||
\(778\) | −0.481032 | − | 0.833171i | −0.0172458 | − | 0.0298706i | ||||
\(779\) | −14.8583 | −0.532353 | ||||||||
\(780\) | −13.2654 | − | 4.36587i | −0.474979 | − | 0.156323i | ||||
\(781\) | 3.21559 | 0.115063 | ||||||||
\(782\) | −0.644554 | − | 1.11640i | −0.0230492 | − | 0.0399224i | ||||
\(783\) | 0.605031 | + | 1.04794i | 0.0216220 | + | 0.0374505i | ||||
\(784\) | 12.0129 | − | 20.8069i | 0.429032 | − | 0.743105i | ||||
\(785\) | 4.27628 | 0.152627 | ||||||||
\(786\) | −0.0901025 | + | 0.156062i | −0.00321385 | + | 0.00556655i | ||||
\(787\) | −4.90054 | + | 8.48798i | −0.174685 | + | 0.302564i | −0.940052 | − | 0.341030i | \(-0.889224\pi\) |
0.765367 | + | 0.643594i | \(0.222558\pi\) | |||||||
\(788\) | −37.6362 | −1.34073 | ||||||||
\(789\) | 19.7084 | − | 34.1359i | 0.701637 | − | 1.21527i | ||||
\(790\) | 0.519341 | + | 0.899525i | 0.0184773 | + | 0.0320037i | ||||
\(791\) | 1.75828 | + | 3.04542i | 0.0625171 | + | 0.108283i | ||||
\(792\) | 0.599945 | 0.0213181 | ||||||||
\(793\) | −2.44297 | + | 2.18295i | −0.0867525 | + | 0.0775188i | ||||
\(794\) | −0.332518 | −0.0118006 | ||||||||
\(795\) | 11.2263 | + | 19.4446i | 0.398157 | + | 0.689628i | ||||
\(796\) | −6.57165 | − | 11.3824i | −0.232926 | − | 0.403440i | ||||
\(797\) | −14.1100 | + | 24.4393i | −0.499803 | + | 0.865685i | −1.00000 | 0.000226985i | \(-0.999928\pi\) | |
0.500197 | + | 0.865912i | \(0.333261\pi\) | |||||||
\(798\) | 0.273008 | 0.00966437 | ||||||||
\(799\) | 10.5718 | − | 18.3109i | 0.374003 | − | 0.647792i | ||||
\(800\) | −4.89070 | + | 8.47094i | −0.172912 | + | 0.299493i | ||||
\(801\) | 4.10554 | 0.145062 | ||||||||
\(802\) | −4.46582 | + | 7.73502i | −0.157693 | + | 0.273133i | ||||
\(803\) | 2.05745 | + | 3.56360i | 0.0726057 | + | 0.125757i | ||||
\(804\) | 6.20177 | + | 10.7418i | 0.218720 | + | 0.378833i | ||||
\(805\) | 1.31065 | 0.0461942 | ||||||||
\(806\) | −0.203185 | − | 0.974052i | −0.00715688 | − | 0.0343095i | ||||
\(807\) | 28.9089 | 1.01764 | ||||||||
\(808\) | 3.84740 | + | 6.66389i | 0.135351 | + | 0.234435i | ||||
\(809\) | −17.9697 | − | 31.1245i | −0.631783 | − | 1.09428i | −0.987187 | − | 0.159567i | \(-0.948990\pi\) |
0.355404 | − | 0.934713i | \(-0.384343\pi\) | |||||||
\(810\) | 1.08179 | − | 1.87372i | 0.0380103 | − | 0.0658358i | ||||
\(811\) | 10.2445 | 0.359731 | 0.179866 | − | 0.983691i | \(-0.442434\pi\) | ||||
0.179866 | + | 0.983691i | \(0.442434\pi\) | |||||||
\(812\) | −0.0988665 | + | 0.171242i | −0.00346953 | + | 0.00600941i | ||||
\(813\) | −11.3865 | + | 19.7221i | −0.399343 | + | 0.691683i | ||||
\(814\) | 1.26795 | 0.0444417 | ||||||||
\(815\) | −6.65179 | + | 11.5212i | −0.233002 | + | 0.403572i | ||||
\(816\) | 6.10602 | + | 10.5759i | 0.213753 | + | 0.370232i | ||||
\(817\) | 6.41588 | + | 11.1126i | 0.224463 | + | 0.388782i | ||||
\(818\) | 2.52118 | 0.0881508 | ||||||||
\(819\) | 0.301970 | + | 1.44762i | 0.0105517 | + | 0.0505840i | ||||
\(820\) | −27.8983 | −0.974252 | ||||||||
\(821\) | −3.92234 | − | 6.79369i | −0.136891 | − | 0.237101i | 0.789428 | − | 0.613844i | \(-0.210378\pi\) |
−0.926318 | + | 0.376742i | \(0.877044\pi\) | |||||||
\(822\) | 4.04389 | + | 7.00422i | 0.141047 | + | 0.244300i | ||||
\(823\) | −13.2367 | + | 22.9266i | −0.461402 | + | 0.799171i | −0.999031 | − | 0.0440101i | \(-0.985987\pi\) |
0.537629 | + | 0.843181i | \(0.319320\pi\) | |||||||
\(824\) | 5.50750 | 0.191863 | ||||||||
\(825\) | −1.47530 | + | 2.55529i | −0.0513632 | + | 0.0889637i | ||||
\(826\) | 0.111006 | − | 0.192268i | 0.00386238 | − | 0.00668985i | ||||
\(827\) | 44.7520 | 1.55618 | 0.778089 | − | 0.628154i | \(-0.216189\pi\) | ||||
0.778089 | + | 0.628154i | \(0.216189\pi\) | |||||||
\(828\) | −1.63549 | + | 2.83275i | −0.0568371 | + | 0.0984448i | ||||
\(829\) | −0.324838 | − | 0.562637i | −0.0112821 | − | 0.0195412i | 0.860329 | − | 0.509739i | \(-0.170258\pi\) |
−0.871611 | + | 0.490198i | \(0.836925\pi\) | |||||||
\(830\) | −1.21463 | − | 2.10381i | −0.0421605 | − | 0.0730242i | ||||
\(831\) | 19.4337 | 0.674147 | ||||||||
\(832\) | 21.3359 | + | 7.02198i | 0.739689 | + | 0.243443i | ||||
\(833\) | 15.9075 | 0.551161 | ||||||||
\(834\) | 2.04201 | + | 3.53686i | 0.0707089 | + | 0.122471i | ||||
\(835\) | 6.64362 | + | 11.5071i | 0.229912 | + | 0.398219i | ||||
\(836\) | −0.877756 | + | 1.52032i | −0.0303578 | + | 0.0525813i | ||||
\(837\) | −5.64600 | −0.195154 | ||||||||
\(838\) | −2.09821 | + | 3.63420i | −0.0724813 | + | 0.125541i | ||||
\(839\) | −17.9106 | + | 31.0221i | −0.618343 | + | 1.07100i | 0.371445 | + | 0.928455i | \(0.378862\pi\) |
−0.989788 | + | 0.142546i | \(0.954471\pi\) | |||||||
\(840\) | 1.04551 | 0.0360734 | ||||||||
\(841\) | 14.4770 | − | 25.0750i | 0.499208 | − | 0.864654i | ||||
\(842\) | 3.63091 | + | 6.28891i | 0.125129 | + | 0.216730i | ||||
\(843\) | 18.3220 | + | 31.7346i | 0.631043 | + | 1.09300i | ||||
\(844\) | 43.5826 | 1.50018 | ||||||||
\(845\) | −14.3785 | − | 10.6141i | −0.494635 | − | 0.365135i | ||||
\(846\) | 2.12381 | 0.0730181 | ||||||||
\(847\) | −2.53695 | − | 4.39413i | −0.0871707 | − | 0.150984i | ||||
\(848\) | −19.7885 | − | 34.2746i | −0.679539 | − | 1.17700i | ||||
\(849\) | −18.5867 | + | 32.1931i | −0.637893 | + | 1.10486i | ||||
\(850\) | −2.01669 | −0.0691719 | ||||||||
\(851\) | −7.04988 | + | 12.2107i | −0.241667 | + | 0.418579i | ||||
\(852\) | −6.99259 | + | 12.1115i | −0.239562 | + | 0.414934i | ||||
\(853\) | −50.3787 | −1.72494 | −0.862468 | − | 0.506112i | \(-0.831082\pi\) | ||||
−0.862468 | + | 0.506112i | \(0.831082\pi\) | |||||||
\(854\) | 0.0601269 | − | 0.104143i | 0.00205750 | − | 0.00356369i | ||||
\(855\) | −0.828069 | − | 1.43426i | −0.0283194 | − | 0.0490506i | ||||
\(856\) | −1.04007 | − | 1.80145i | −0.0355488 | − | 0.0615724i | ||||
\(857\) | 32.3249 | 1.10420 | 0.552098 | − | 0.833779i | \(-0.313827\pi\) | ||||
0.552098 | + | 0.833779i | \(0.313827\pi\) | |||||||
\(858\) | −0.896683 | − | 0.295113i | −0.0306123 | − | 0.0100750i | ||||
\(859\) | −41.7146 | −1.42329 | −0.711643 | − | 0.702542i | \(-0.752048\pi\) | ||||
−0.711643 | + | 0.702542i | \(0.752048\pi\) | |||||||
\(860\) | 12.0466 | + | 20.8654i | 0.410787 | + | 0.711504i | ||||
\(861\) | −3.70414 | − | 6.41575i | −0.126237 | − | 0.218648i | ||||
\(862\) | −2.73800 | + | 4.74235i | −0.0932565 | + | 0.161525i | ||||
\(863\) | −6.05943 | −0.206265 | −0.103133 | − | 0.994668i | \(-0.532887\pi\) | ||||
−0.103133 | + | 0.994668i | \(0.532887\pi\) | |||||||
\(864\) | −8.87856 | + | 15.3781i | −0.302055 | + | 0.523174i | ||||
\(865\) | −6.73580 | + | 11.6668i | −0.229024 | + | 0.396682i | ||||
\(866\) | −0.555341 | −0.0188713 | ||||||||
\(867\) | 8.40545 | − | 14.5587i | 0.285464 | − | 0.494438i | ||||
\(868\) | −0.461299 | − | 0.798993i | −0.0156575 | − | 0.0271196i | ||||
\(869\) | −0.886790 | − | 1.53596i | −0.0300823 | − | 0.0521040i | ||||
\(870\) | 0.119080 | 0.00403719 | ||||||||
\(871\) | 3.24130 | + | 15.5385i | 0.109827 | + | 0.526503i | ||||
\(872\) | 10.5861 | 0.358491 | ||||||||
\(873\) | 4.62515 | + | 8.01100i | 0.156538 | + | 0.271131i | ||||
\(874\) | 0.386395 | + | 0.669256i | 0.0130700 | + | 0.0226379i | ||||
\(875\) | 2.67338 | − | 4.63043i | 0.0903768 | − | 0.156537i | ||||
\(876\) | −17.8964 | −0.604664 | ||||||||
\(877\) | −10.0658 | + | 17.4345i | −0.339899 | + | 0.588723i | −0.984413 | − | 0.175870i | \(-0.943726\pi\) |
0.644514 | + | 0.764592i | \(0.277060\pi\) | |||||||
\(878\) | 1.19645 | − | 2.07231i | 0.0403782 | − | 0.0699370i | ||||
\(879\) | 5.49587 | 0.185371 | ||||||||
\(880\) | −1.58027 | + | 2.73712i | −0.0532710 | + | 0.0922681i | ||||
\(881\) | 28.9819 | + | 50.1981i | 0.976425 | + | 1.69122i | 0.675148 | + | 0.737682i | \(0.264080\pi\) |
0.301277 | + | 0.953537i | \(0.402587\pi\) | |||||||
\(882\) | 0.798930 | + | 1.38379i | 0.0269014 | + | 0.0465945i | ||||
\(883\) | 22.5446 | 0.758687 | 0.379343 | − | 0.925256i | \(-0.376150\pi\) | ||||
0.379343 | + | 0.925256i | \(0.376150\pi\) | |||||||
\(884\) | 3.32823 | + | 15.9552i | 0.111940 | + | 0.536633i | ||||
\(885\) | 3.37743 | 0.113531 | ||||||||
\(886\) | −0.342855 | − | 0.593843i | −0.0115184 | − | 0.0199505i | ||||
\(887\) | −24.8882 | − | 43.1076i | −0.835664 | − | 1.44741i | −0.893489 | − | 0.449085i | \(-0.851750\pi\) |
0.0578253 | − | 0.998327i | \(-0.481583\pi\) | |||||||
\(888\) | −5.62371 | + | 9.74055i | −0.188719 | + | 0.326871i | ||||
\(889\) | −9.66506 | −0.324156 | ||||||||
\(890\) | 0.910614 | − | 1.57723i | 0.0305238 | − | 0.0528689i | ||||
\(891\) | −1.84719 | + | 3.19943i | −0.0618832 | + | 0.107185i | ||||
\(892\) | −16.1221 | −0.539808 | ||||||||
\(893\) | −6.33754 | + | 10.9769i | −0.212078 | + | 0.367329i | ||||
\(894\) | 0.605497 | + | 1.04875i | 0.0202508 | + | 0.0350755i | ||||
\(895\) | 15.0039 | + | 25.9875i | 0.501526 | + | 0.868668i | ||||
\(896\) | −3.84098 | −0.128318 | ||||||||
\(897\) | 7.82762 | − | 6.99447i | 0.261357 | − | 0.233539i | ||||
\(898\) | −2.93067 | −0.0977979 | ||||||||
\(899\) | −0.107161 | − | 0.185608i | −0.00357402 | − | 0.00619038i | ||||
\(900\) | 2.55857 | + | 4.43158i | 0.0852857 | + | 0.147719i | ||||
\(901\) | 13.1020 | − | 22.6933i | 0.436489 | − | 0.756022i | ||||
\(902\) | −1.88580 | −0.0627902 | ||||||||
\(903\) | −3.19893 | + | 5.54071i | −0.106454 | + | 0.184383i | ||||
\(904\) | −3.97022 | + | 6.87663i | −0.132048 | + | 0.228713i | ||||
\(905\) | 22.6324 | 0.752327 | ||||||||
\(906\) | 3.55061 | − | 6.14984i | 0.117961 | − | 0.204315i | ||||
\(907\) | −2.66060 | − | 4.60829i | −0.0883437 | − | 0.153016i | 0.818467 | − | 0.574553i | \(-0.194824\pi\) |
−0.906811 | + | 0.421537i | \(0.861491\pi\) | |||||||
\(908\) | 14.1151 | + | 24.4481i | 0.468427 | + | 0.811339i | ||||
\(909\) | 6.07737 | 0.201574 | ||||||||
\(910\) | 0.623111 | + | 0.205076i | 0.0206559 | + | 0.00679820i | ||||
\(911\) | −50.5978 | −1.67638 | −0.838189 | − | 0.545380i | \(-0.816386\pi\) | ||||
−0.838189 | + | 0.545380i | \(0.816386\pi\) | |||||||
\(912\) | −3.66041 | − | 6.34002i | −0.121208 | − | 0.209939i | ||||
\(913\) | 2.07402 | + | 3.59231i | 0.0686401 | + | 0.118888i | ||||
\(914\) | 4.64972 | − | 8.05354i | 0.153799 | − | 0.266388i | ||||
\(915\) | 1.82940 | 0.0604782 | ||||||||
\(916\) | −0.0179671 | + | 0.0311199i | −0.000593649 | + | 0.00102823i | ||||
\(917\) | −0.106913 | + | 0.185179i | −0.00353058 | + | 0.00611515i | ||||
\(918\) | −3.66110 | −0.120834 | ||||||||
\(919\) | 18.1208 | − | 31.3861i | 0.597750 | − | 1.03533i | −0.395403 | − | 0.918508i | \(-0.629395\pi\) |
0.993153 | − | 0.116825i | \(-0.0372717\pi\) | |||||||
\(920\) | 1.47973 | + | 2.56297i | 0.0487853 | + | 0.0844987i | ||||
\(921\) | 7.76358 | + | 13.4469i | 0.255819 | + | 0.443091i | ||||
\(922\) | 1.93919 | 0.0638638 | ||||||||
\(923\) | −13.3454 | + | 11.9250i | −0.439269 | + | 0.392515i | ||||
\(924\) | −0.875291 | −0.0287950 | ||||||||
\(925\) | 11.0289 | + | 19.1026i | 0.362628 | + | 0.628090i | ||||
\(926\) | −0.196237 | − | 0.339893i | −0.00644875 | − | 0.0111696i | ||||
\(927\) | 2.17492 | − | 3.76707i | 0.0714337 | − | 0.123727i | ||||
\(928\) | −0.674060 | −0.0221271 | ||||||||
\(929\) | −26.9723 | + | 46.7175i | −0.884934 | + | 1.53275i | −0.0391448 | + | 0.999234i | \(0.512463\pi\) |
−0.845789 | + | 0.533517i | \(0.820870\pi\) | |||||||
\(930\) | −0.277806 | + | 0.481175i | −0.00910963 | + | 0.0157783i | ||||
\(931\) | −9.53616 | −0.312535 | ||||||||
\(932\) | 26.1401 | − | 45.2760i | 0.856248 | − | 1.48306i | ||||
\(933\) | −7.48644 | − | 12.9669i | −0.245095 | − | 0.424517i | ||||
\(934\) | −2.19663 | − | 3.80467i | −0.0718759 | − | 0.124493i | ||||
\(935\) | −2.09260 | −0.0684353 | ||||||||
\(936\) | −2.48990 | + | 2.22488i | −0.0813849 | + | 0.0727226i | ||||
\(937\) | 47.9951 | 1.56793 | 0.783966 | − | 0.620804i | \(-0.213194\pi\) | ||||
0.783966 | + | 0.620804i | \(0.213194\pi\) | |||||||
\(938\) | −0.291313 | − | 0.504568i | −0.00951169 | − | 0.0164747i | ||||
\(939\) | −1.01795 | − | 1.76315i | −0.0332197 | − | 0.0575382i | ||||
\(940\) | −11.8995 | + | 20.6106i | −0.388120 | + | 0.672244i | ||||
\(941\) | −39.2007 | −1.27791 | −0.638953 | − | 0.769246i | \(-0.720632\pi\) | ||||
−0.638953 | + | 0.769246i | \(0.720632\pi\) | |||||||
\(942\) | −0.628581 | + | 1.08873i | −0.0204803 | + | 0.0354729i | ||||
\(943\) | 10.4851 | − | 18.1608i | 0.341443 | − | 0.591396i | ||||
\(944\) | −5.95334 | −0.193765 | ||||||||
\(945\) | 1.86113 | − | 3.22358i | 0.0605427 | − | 0.104863i | ||||
\(946\) | 0.814297 | + | 1.41040i | 0.0264751 | + | 0.0458562i | ||||
\(947\) | 20.6736 | + | 35.8077i | 0.671802 | + | 1.16359i | 0.977393 | + | 0.211432i | \(0.0678126\pi\) |
−0.305591 | + | 0.952163i | \(0.598854\pi\) | |||||||
\(948\) | 7.71361 | 0.250526 | ||||||||
\(949\) | −21.7544 | − | 7.15972i | −0.706178 | − | 0.232414i | ||||
\(950\) | 1.20896 | 0.0392238 | ||||||||
\(951\) | 8.70289 | + | 15.0739i | 0.282211 | + | 0.488803i | ||||
\(952\) | −0.610091 | − | 1.05671i | −0.0197732 | − | 0.0342481i | ||||
\(953\) | 8.47178 | − | 14.6736i | 0.274428 | − | 0.475323i | −0.695563 | − | 0.718465i | \(-0.744845\pi\) |
0.969991 | + | 0.243142i | \(0.0781782\pi\) | |||||||
\(954\) | 2.63211 | 0.0852176 | ||||||||
\(955\) | −1.64375 | + | 2.84706i | −0.0531906 | + | 0.0921288i | ||||
\(956\) | 16.7583 | − | 29.0263i | 0.542004 | − | 0.938778i | ||||
\(957\) | −0.203333 | −0.00657281 | ||||||||
\(958\) | 1.40830 | − | 2.43925i | 0.0455002 | − | 0.0788086i | ||||
\(959\) | 4.79837 | + | 8.31102i | 0.154947 | + | 0.268377i | ||||
\(960\) | −6.27125 | − | 10.8621i | −0.202404 | − | 0.350573i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −5.26228 | + | 4.70218i | −0.169663 | + | 0.151604i | ||||
\(963\) | −1.64290 | −0.0529417 | ||||||||
\(964\) | 4.36784 | + | 7.56532i | 0.140679 | + | 0.243663i | ||||
\(965\) | −6.72965 | − | 11.6561i | −0.216635 | − | 0.375223i | ||||
\(966\) | −0.192655 | + | 0.333688i | −0.00619857 | + | 0.0107362i | ||||
\(967\) | 21.2770 | 0.684224 | 0.342112 | − | 0.939659i | \(-0.388858\pi\) | ||||
0.342112 | + | 0.939659i | \(0.388858\pi\) | |||||||
\(968\) | 5.72849 | − | 9.92204i | 0.184121 | − | 0.318906i | ||||
\(969\) | 2.42356 | − | 4.19773i | 0.0778560 | − | 0.134851i | ||||
\(970\) | 4.10346 | 0.131754 | ||||||||
\(971\) | −1.89724 | + | 3.28612i | −0.0608854 | + | 0.105457i | −0.894861 | − | 0.446344i | \(-0.852726\pi\) |
0.833976 | + | 0.551801i | \(0.186059\pi\) | |||||||
\(972\) | 8.25925 | + | 14.3054i | 0.264916 | + | 0.458847i | ||||
\(973\) | 2.42299 | + | 4.19674i | 0.0776775 | + | 0.134541i | ||||
\(974\) | 5.12239 | 0.164132 | ||||||||
\(975\) | −3.35344 | − | 16.0761i | −0.107396 | − | 0.514847i | ||||
\(976\) | −3.22466 | −0.103219 | ||||||||
\(977\) | −8.73096 | − | 15.1225i | −0.279328 | − | 0.483810i | 0.691890 | − | 0.722003i | \(-0.256778\pi\) |
−0.971218 | + | 0.238193i | \(0.923445\pi\) | |||||||
\(978\) | −1.95552 | − | 3.38707i | −0.0625308 | − | 0.108306i | ||||
\(979\) | −1.55490 | + | 2.69316i | −0.0496948 | + | 0.0860739i | ||||
\(980\) | −17.9054 | −0.571966 | ||||||||
\(981\) | 4.18047 | − | 7.24078i | 0.133472 | − | 0.231180i | ||||
\(982\) | 1.81448 | − | 3.14277i | 0.0579023 | − | 0.100290i | ||||
\(983\) | 34.1328 | 1.08867 | 0.544334 | − | 0.838868i | \(-0.316782\pi\) | ||||
0.544334 | + | 0.838868i | \(0.316782\pi\) | |||||||
\(984\) | 8.36402 | − | 14.4869i | 0.266635 | − | 0.461826i | ||||
\(985\) | 13.4471 | + | 23.2911i | 0.428462 | + | 0.742117i | ||||
\(986\) | −0.0694876 | − | 0.120356i | −0.00221294 | − | 0.00383292i | ||||
\(987\) | −6.31974 | −0.201160 | ||||||||
\(988\) | −1.99519 | − | 9.56479i | −0.0634756 | − | 0.304297i | ||||
\(989\) | −18.1101 | −0.575868 | ||||||||
\(990\) | −0.105098 | − | 0.182035i | −0.00334023 | − | 0.00578544i | ||||
\(991\) | −24.1200 | − | 41.7770i | −0.766196 | − | 1.32709i | −0.939612 | − | 0.342242i | \(-0.888814\pi\) |
0.173416 | − | 0.984849i | \(-0.444520\pi\) | |||||||
\(992\) | 1.57254 | − | 2.72372i | 0.0499282 | − | 0.0864782i | ||||
\(993\) | 35.3241 | 1.12098 | ||||||||
\(994\) | 0.328460 | − | 0.568909i | 0.0104181 | − | 0.0180447i | ||||
\(995\) | −4.69601 | + | 8.13373i | −0.148874 | + | 0.257857i | ||||
\(996\) | −18.0406 | −0.571637 | ||||||||
\(997\) | 11.7543 | − | 20.3591i | 0.372263 | − | 0.644778i | −0.617651 | − | 0.786453i | \(-0.711915\pi\) |
0.989913 | + | 0.141675i | \(0.0452487\pi\) | |||||||
\(998\) | −0.300890 | − | 0.521156i | −0.00952450 | − | 0.0164969i | ||||
\(999\) | 20.0218 | + | 34.6788i | 0.633463 | + | 1.09719i |
(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 | 403.2.f.c.94.12 | ✓ | 36 | |
13.3 | even | 3 | 5239.2.a.p.1.7 | 18 | |||
13.9 | even | 3 | inner | 403.2.f.c.373.12 | yes | 36 | |
13.10 | even | 6 | 5239.2.a.o.1.12 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.f.c.94.12 | ✓ | 36 | 1.1 | even | 1 | trivial | |
403.2.f.c.373.12 | yes | 36 | 13.9 | even | 3 | inner | |
5239.2.a.o.1.12 | 18 | 13.10 | even | 6 | |||
5239.2.a.p.1.7 | 18 | 13.3 | even | 3 |