Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(199,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.da (of order \(18\), degree \(6\), 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: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 199.3 | ||
Character | \(\chi\) | \(=\) | 855.199 |
Dual form | 855.2.da.b.739.3 |
$q$-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 \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.20303 | + | 0.212126i | −0.850669 | + | 0.149996i | −0.581952 | − | 0.813223i | \(-0.697711\pi\) |
−0.268717 | + | 0.963219i | \(0.586600\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.477108 | + | 0.173653i | −0.238554 | + | 0.0868266i | ||||
\(5\) | −2.06524 | − | 0.857189i | −0.923605 | − | 0.383347i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.28379 | − | 1.89590i | −1.24116 | − | 0.716583i | −0.271828 | − | 0.962346i | \(-0.587628\pi\) |
−0.969330 | + | 0.245763i | \(0.920961\pi\) | |||||||
\(8\) | 2.65299 | − | 1.53170i | 0.937972 | − | 0.541539i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.66638 | + | 0.593130i | 0.843182 | + | 0.187564i | ||||
\(11\) | −0.618663 | − | 1.07156i | −0.186534 | − | 0.323086i | 0.757558 | − | 0.652767i | \(-0.226392\pi\) |
−0.944092 | + | 0.329681i | \(0.893059\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.22146 | − | 2.64744i | 0.616123 | − | 0.734267i | −0.364275 | − | 0.931291i | \(-0.618683\pi\) |
0.980399 | + | 0.197024i | \(0.0631278\pi\) | |||||||
\(14\) | 4.35266 | + | 1.58424i | 1.16330 | + | 0.423406i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.08882 | + | 1.75273i | −0.522204 | + | 0.438181i | ||||
\(17\) | 2.96127 | − | 0.522152i | 0.718214 | − | 0.126640i | 0.197415 | − | 0.980320i | \(-0.436745\pi\) |
0.520799 | + | 0.853680i | \(0.325634\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.28612 | + | 0.793231i | −0.983302 | + | 0.181980i | ||||
\(20\) | 1.13420 | + | 0.0503361i | 0.253614 | + | 0.0112555i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.971573 | + | 1.15788i | 0.207140 | + | 0.246860i | ||||
\(23\) | −2.10267 | − | 5.77705i | −0.438438 | − | 1.20460i | −0.940508 | − | 0.339771i | \(-0.889650\pi\) |
0.502071 | − | 0.864827i | \(-0.332572\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.53045 | + | 3.54061i | 0.706091 | + | 0.708122i | ||||
\(26\) | −2.11089 | + | 3.65617i | −0.413980 | + | 0.717034i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.89595 | + | 0.334308i | 0.358302 | + | 0.0631782i | ||||
\(29\) | −0.744476 | + | 4.22213i | −0.138246 | + | 0.784031i | 0.834299 | + | 0.551313i | \(0.185873\pi\) |
−0.972544 | + | 0.232718i | \(0.925238\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.55067 | + | 4.41789i | −0.458114 | + | 0.793476i | −0.998861 | − | 0.0477088i | \(-0.984808\pi\) |
0.540748 | + | 0.841185i | \(0.318141\pi\) | |||||||
\(32\) | −1.79713 | + | 2.14174i | −0.317691 | + | 0.378610i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.45173 | + | 1.25633i | −0.591966 | + | 0.215458i | ||||
\(35\) | 5.15669 | + | 6.73032i | 0.871639 | + | 1.13763i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.13084i | 1.50110i | 0.660813 | + | 0.750550i | \(0.270211\pi\) | ||||
−0.660813 | + | 0.750550i | \(0.729789\pi\) | |||||||
\(38\) | 4.98805 | − | 1.86348i | 0.809168 | − | 0.302296i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.79202 | + | 0.889225i | −1.07391 | + | 0.140599i | ||||
\(41\) | −4.08318 | + | 3.42620i | −0.637686 | + | 0.535082i | −0.903307 | − | 0.428996i | \(-0.858868\pi\) |
0.265621 | + | 0.964078i | \(0.414423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.12092 | − | 8.57465i | 0.475935 | − | 1.30762i | −0.436979 | − | 0.899471i | \(-0.643952\pi\) |
0.912915 | − | 0.408150i | \(-0.133826\pi\) | |||||||
\(44\) | 0.481248 | + | 0.403815i | 0.0725509 | + | 0.0608774i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.75504 | + | 6.50391i | 0.553650 | + | 0.958950i | ||||
\(47\) | −7.19237 | − | 1.26821i | −1.04912 | − | 0.184987i | −0.377593 | − | 0.925972i | \(-0.623248\pi\) |
−0.671522 | + | 0.740984i | \(0.734359\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.68887 | + | 6.38931i | 0.526981 | + | 0.912758i | ||||
\(50\) | −4.99829 | − | 3.51055i | −0.706864 | − | 0.496466i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.600142 | + | 1.64888i | −0.0832248 | + | 0.228658i | ||||
\(53\) | 1.13973 | + | 3.13139i | 0.156554 | + | 0.430129i | 0.993028 | − | 0.117877i | \(-0.0376090\pi\) |
−0.836474 | + | 0.548007i | \(0.815387\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.359163 | + | 2.74333i | 0.0484295 | + | 0.369911i | ||||
\(56\) | −11.6158 | −1.55223 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 5.23727i | − | 0.687687i | ||||||
\(59\) | −0.141926 | − | 0.804901i | −0.0184772 | − | 0.104789i | 0.974174 | − | 0.225797i | \(-0.0724986\pi\) |
−0.992652 | + | 0.121008i | \(0.961387\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.01592 | + | 2.18962i | −0.770260 | + | 0.280352i | −0.697105 | − | 0.716969i | \(-0.745529\pi\) |
−0.0731548 | + | 0.997321i | \(0.523307\pi\) | |||||||
\(62\) | 2.13137 | − | 5.85590i | 0.270685 | − | 0.743700i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.43444 | − | 7.68067i | 0.554305 | − | 0.960084i | ||||
\(65\) | −6.85722 | + | 3.56338i | −0.850533 | + | 0.441983i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.995566 | − | 0.175545i | −0.121628 | − | 0.0214463i | 0.112503 | − | 0.993651i | \(-0.464113\pi\) |
−0.234131 | + | 0.972205i | \(0.575224\pi\) | |||||||
\(68\) | −1.32217 | + | 0.763357i | −0.160337 | + | 0.0925706i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.63131 | − | 7.00290i | −0.912116 | − | 0.837006i | ||||
\(71\) | 12.8546 | + | 4.67867i | 1.52555 | + | 0.555257i | 0.962528 | − | 0.271182i | \(-0.0874146\pi\) |
0.563027 | + | 0.826439i | \(0.309637\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.11096 | + | 8.47451i | 0.832275 | + | 0.991867i | 0.999982 | + | 0.00602966i | \(0.00191931\pi\) |
−0.167707 | + | 0.985837i | \(0.553636\pi\) | |||||||
\(74\) | −1.93689 | − | 10.9846i | −0.225159 | − | 1.27694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.90719 | − | 1.12275i | 0.218770 | − | 0.128789i | ||||
\(77\) | 4.69169i | 0.534668i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.06036 | − | 0.889746i | 0.119300 | − | 0.100104i | −0.581186 | − | 0.813771i | \(-0.697411\pi\) |
0.700486 | + | 0.713666i | \(0.252967\pi\) | |||||||
\(80\) | 5.81633 | − | 1.82929i | 0.650286 | − | 0.204521i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.18539 | − | 4.98796i | 0.462199 | − | 0.550828i | ||||
\(83\) | 2.18283 | + | 1.26026i | 0.239597 | + | 0.138332i | 0.614992 | − | 0.788534i | \(-0.289159\pi\) |
−0.375394 | + | 0.926865i | \(0.622493\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.56333 | − | 1.46000i | −0.711893 | − | 0.158359i | ||||
\(86\) | −1.93564 | + | 10.9776i | −0.208726 | + | 1.18374i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.28261 | − | 1.89521i | −0.349927 | − | 0.202031i | ||||
\(89\) | 2.06711 | + | 1.73451i | 0.219113 | + | 0.183858i | 0.745736 | − | 0.666241i | \(-0.232098\pi\) |
−0.526624 | + | 0.850099i | \(0.676542\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.3141 | + | 4.48197i | −1.29087 | + | 0.469838i | ||||
\(92\) | 2.00640 | + | 2.39114i | 0.209182 | + | 0.249294i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.92164 | 0.920197 | ||||||||
\(95\) | 9.53182 | + | 2.03580i | 0.977944 | + | 0.208869i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.01600 | + | 0.531802i | −0.306228 | + | 0.0539963i | −0.324651 | − | 0.945834i | \(-0.605247\pi\) |
0.0184223 | + | 0.999830i | \(0.494136\pi\) | |||||||
\(98\) | −5.79315 | − | 6.90401i | −0.585196 | − | 0.697410i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.29925 | − | 1.07618i | −0.229925 | − | 0.107618i | ||||
\(101\) | −2.85509 | − | 2.39570i | −0.284092 | − | 0.238381i | 0.489594 | − | 0.871950i | \(-0.337145\pi\) |
−0.773686 | + | 0.633569i | \(0.781589\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.4390 | + | 6.60432i | −1.12712 | + | 0.650743i | −0.943209 | − | 0.332200i | \(-0.892209\pi\) |
−0.183911 | + | 0.982943i | \(0.558876\pi\) | |||||||
\(104\) | 1.83843 | − | 10.4262i | 0.180273 | − | 1.02238i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.03538 | − | 3.52538i | −0.197693 | − | 0.342415i | ||||
\(107\) | 4.44535 | + | 2.56652i | 0.429748 | + | 0.248115i | 0.699239 | − | 0.714888i | \(-0.253522\pi\) |
−0.269491 | + | 0.963003i | \(0.586855\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.49202 | − | 0.543049i | −0.142909 | − | 0.0520147i | 0.269575 | − | 0.962979i | \(-0.413117\pi\) |
−0.412485 | + | 0.910965i | \(0.635339\pi\) | |||||||
\(110\) | −1.01402 | − | 3.22412i | −0.0966826 | − | 0.307407i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.1822 | − | 1.79540i | 0.962131 | − | 0.169650i | ||||
\(113\) | 20.0832i | 1.88927i | 0.328126 | + | 0.944634i | \(0.393583\pi\) | ||||
−0.328126 | + | 0.944634i | \(0.606417\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.609493 | + | 13.7334i | −0.0568355 | + | 1.28065i | ||||
\(116\) | −0.377991 | − | 2.14369i | −0.0350956 | − | 0.199037i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.341481 | + | 0.938212i | 0.0314359 | + | 0.0863694i | ||||
\(119\) | −10.7142 | − | 3.89963i | −0.982165 | − | 0.357479i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.73451 | − | 8.20042i | 0.430410 | − | 0.745492i | ||||
\(122\) | 6.77284 | − | 3.91030i | 0.613184 | − | 0.354022i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.449765 | − | 2.55074i | 0.0403901 | − | 0.229063i | ||||
\(125\) | −4.25627 | − | 10.3385i | −0.380692 | − | 0.924702i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.21957 | + | 2.64518i | −0.196955 | + | 0.234722i | −0.855479 | − | 0.517838i | \(-0.826737\pi\) |
0.658523 | + | 0.752560i | \(0.271181\pi\) | |||||||
\(128\) | −1.79301 | + | 4.92625i | −0.158481 | + | 0.435423i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.49353 | − | 5.74144i | 0.657226 | − | 0.503558i | ||||
\(131\) | 1.31755 | + | 7.47219i | 0.115115 | + | 0.652848i | 0.986693 | + | 0.162592i | \(0.0519856\pi\) |
−0.871579 | + | 0.490256i | \(0.836903\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.5786 | + | 5.52124i | 1.35084 | + | 0.478752i | ||||
\(134\) | 1.23493 | 0.106682 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.05643 | − | 5.92105i | 0.605084 | − | 0.507726i | ||||
\(137\) | −1.26080 | − | 3.46401i | −0.107717 | − | 0.295951i | 0.874110 | − | 0.485728i | \(-0.161446\pi\) |
−0.981827 | + | 0.189778i | \(0.939223\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.2693 | + | 11.9734i | 1.21031 | + | 1.01557i | 0.999274 | + | 0.0380898i | \(0.0121273\pi\) |
0.211033 | + | 0.977479i | \(0.432317\pi\) | |||||||
\(140\) | −3.62904 | − | 2.31562i | −0.306710 | − | 0.195705i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.4568 | − | 2.90179i | −1.38103 | − | 0.243512i | ||||
\(143\) | −4.21121 | − | 0.742550i | −0.352159 | − | 0.0620952i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.15669 | − | 8.08157i | 0.428240 | − | 0.671138i | ||||
\(146\) | −10.3523 | − | 8.68665i | −0.856766 | − | 0.718912i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.58560 | − | 4.35640i | −0.130335 | − | 0.358094i | ||||
\(149\) | 1.29297 | − | 1.08493i | 0.105924 | − | 0.0888807i | −0.588288 | − | 0.808652i | \(-0.700198\pi\) |
0.694212 | + | 0.719771i | \(0.255753\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.33890 | 0.108958 | 0.0544791 | − | 0.998515i | \(-0.482650\pi\) | ||||
0.0544791 | + | 0.998515i | \(0.482650\pi\) | |||||||
\(152\) | −10.1560 | + | 8.66948i | −0.823761 | + | 0.703188i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.995230 | − | 5.64423i | −0.0801979 | − | 0.454825i | ||||
\(155\) | 9.05472 | − | 6.93760i | 0.727292 | − | 0.557242i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.06672 | − | 5.67825i | 0.164942 | − | 0.453174i | −0.829494 | − | 0.558515i | \(-0.811371\pi\) |
0.994436 | + | 0.105341i | \(0.0335935\pi\) | |||||||
\(158\) | −1.08690 | + | 1.29532i | −0.0864692 | + | 0.103050i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.54739 | − | 2.88273i | 0.438560 | − | 0.227900i | ||||
\(161\) | −4.04795 | + | 22.9571i | −0.319023 | + | 1.80927i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.48469 | − | 4.89864i | 0.664572 | − | 0.383691i | −0.129445 | − | 0.991587i | \(-0.541319\pi\) |
0.794017 | + | 0.607896i | \(0.207986\pi\) | |||||||
\(164\) | 1.35315 | − | 2.34372i | 0.105663 | − | 0.183014i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.89334 | − | 1.05309i | −0.224567 | − | 0.0817357i | ||||
\(167\) | 1.32578 | + | 3.64255i | 0.102592 | + | 0.281869i | 0.980360 | − | 0.197217i | \(-0.0631904\pi\) |
−0.877768 | + | 0.479086i | \(0.840968\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.183403 | + | 1.04013i | 0.0141079 | + | 0.0800101i | ||||
\(170\) | 8.20556 | + | 0.364166i | 0.629338 | + | 0.0279303i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.63299i | 0.353262i | ||||||||
\(173\) | 4.66030 | − | 0.821737i | 0.354316 | − | 0.0624755i | 0.00634275 | − | 0.999980i | \(-0.497981\pi\) |
0.347973 | + | 0.937504i | \(0.386870\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.88064 | − | 18.3200i | −0.368942 | − | 1.38486i | ||||
\(176\) | 3.17042 | + | 1.15394i | 0.238979 | + | 0.0869813i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.85472 | − | 1.64817i | −0.213970 | − | 0.123536i | ||||
\(179\) | 4.68907 | + | 8.12172i | 0.350478 | + | 0.607045i | 0.986333 | − | 0.164763i | \(-0.0526859\pi\) |
−0.635855 | + | 0.771808i | \(0.719353\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.38627 | + | 19.2045i | −0.251700 | + | 1.42746i | 0.552704 | + | 0.833377i | \(0.313596\pi\) |
−0.804404 | + | 0.594083i | \(0.797515\pi\) | |||||||
\(182\) | 13.8635 | − | 8.00407i | 1.02763 | − | 0.593301i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.4271 | − | 12.1058i | −1.06358 | − | 0.892448i | ||||
\(185\) | 7.82686 | − | 18.8574i | 0.575442 | − | 1.38642i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.39154 | − | 2.85013i | −0.174887 | − | 0.208422i | ||||
\(188\) | 3.65177 | − | 0.643905i | 0.266332 | − | 0.0469616i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.8989 | − | 0.427174i | −0.863236 | − | 0.0309904i | ||||
\(191\) | −15.5024 | −1.12171 | −0.560857 | − | 0.827913i | \(-0.689528\pi\) | ||||
−0.560857 | + | 0.827913i | \(0.689528\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.7550 | − | 15.2008i | −0.918122 | − | 1.09417i | −0.995269 | − | 0.0971550i | \(-0.969026\pi\) |
0.0771477 | − | 0.997020i | \(-0.475419\pi\) | |||||||
\(194\) | 3.51552 | − | 1.27955i | 0.252400 | − | 0.0918660i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.86951 | − | 2.40781i | −0.204965 | − | 0.171986i | ||||
\(197\) | −22.4913 | − | 12.9854i | −1.60244 | − | 0.925170i | −0.990997 | − | 0.133882i | \(-0.957256\pi\) |
−0.611444 | − | 0.791288i | \(-0.709411\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.940467 | − | 5.33365i | 0.0666680 | − | 0.378093i | −0.933159 | − | 0.359465i | \(-0.882959\pi\) |
0.999826 | − | 0.0186277i | \(-0.00592971\pi\) | |||||||
\(200\) | 14.7894 | + | 3.98558i | 1.04577 | + | 0.281823i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.94294 | + | 2.27646i | 0.277424 | + | 0.160171i | ||||
\(203\) | 10.4494 | − | 12.4532i | 0.733407 | − | 0.874041i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.3697 | − | 3.57587i | 0.794091 | − | 0.249749i | ||||
\(206\) | 12.3605 | − | 10.3717i | 0.861197 | − | 0.722630i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.42363i | 0.653411i | ||||||||
\(209\) | 3.50165 | + | 4.10207i | 0.242214 | + | 0.283746i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.49375 | − | 19.8141i | −0.240520 | − | 1.36406i | −0.830671 | − | 0.556764i | \(-0.812043\pi\) |
0.590151 | − | 0.807293i | \(-0.299068\pi\) | |||||||
\(212\) | −1.08755 | − | 1.29609i | −0.0746933 | − | 0.0890160i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.89230 | − | 2.14462i | −0.402790 | − | 0.146603i | ||||
\(215\) | −13.7955 | + | 15.0335i | −0.940848 | + | 1.02528i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.7517 | − | 9.67162i | 1.13718 | − | 0.656553i | ||||
\(218\) | 1.91013 | + | 0.336808i | 0.129370 | + | 0.0228115i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.647748 | − | 1.24650i | −0.0436711 | − | 0.0840388i | ||||
\(221\) | 5.19599 | − | 8.99972i | 0.349520 | − | 0.605387i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.71080 | − | 10.1953i | 0.248493 | − | 0.682730i | −0.751249 | − | 0.660019i | \(-0.770548\pi\) |
0.999742 | − | 0.0227106i | \(-0.00722963\pi\) | |||||||
\(224\) | 9.96194 | − | 3.62585i | 0.665610 | − | 0.242262i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.26017 | − | 24.1606i | −0.283382 | − | 1.60714i | ||||
\(227\) | − | 8.78226i | − | 0.582899i | −0.956586 | − | 0.291449i | \(-0.905862\pi\) | ||
0.956586 | − | 0.291449i | \(-0.0941375\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.0824 | −1.19492 | −0.597459 | − | 0.801899i | \(-0.703823\pi\) | ||||
−0.597459 | + | 0.801899i | \(0.703823\pi\) | |||||||
\(230\) | −2.17997 | − | 16.6509i | −0.143743 | − | 1.09793i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.49197 | + | 12.3416i | 0.294912 | + | 0.810264i | ||||
\(233\) | 9.01763 | − | 24.7757i | 0.590765 | − | 1.62311i | −0.178325 | − | 0.983972i | \(-0.557068\pi\) |
0.769090 | − | 0.639141i | \(-0.220710\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.7669 | + | 8.78438i | 0.898053 | + | 0.573030i | ||||
\(236\) | 0.207488 | + | 0.359379i | 0.0135063 | + | 0.0233936i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.7166 | + | 2.41861i | 0.889117 | + | 0.156775i | ||||
\(239\) | 4.58448 | + | 7.94056i | 0.296546 | + | 0.513632i | 0.975343 | − | 0.220693i | \(-0.0708320\pi\) |
−0.678798 | + | 0.734325i | \(0.737499\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.3130 | + | 17.0446i | 1.30847 | + | 1.09794i | 0.988614 | + | 0.150474i | \(0.0480800\pi\) |
0.319859 | + | 0.947465i | \(0.396364\pi\) | |||||||
\(242\) | −3.95623 | + | 10.8696i | −0.254316 | + | 0.698727i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.49001 | − | 2.08937i | 0.159407 | − | 0.133758i | ||||
\(245\) | −2.14156 | − | 16.3575i | −0.136819 | − | 1.04504i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.42142 | + | 13.1094i | −0.472214 | + | 0.834128i | ||||
\(248\) | 15.6275i | 0.992345i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.31347 | + | 11.5346i | 0.462545 | + | 0.729513i | ||||
\(251\) | −14.0457 | + | 5.11220i | −0.886554 | + | 0.322679i | −0.744852 | − | 0.667230i | \(-0.767480\pi\) |
−0.141703 | + | 0.989909i | \(0.545258\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.88958 | + | 5.82717i | −0.307405 | + | 0.366351i | ||||
\(254\) | 2.10909 | − | 3.65306i | 0.132336 | − | 0.229213i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.96808 | + | 11.1615i | −0.123005 | + | 0.697595i | ||||
\(257\) | 10.6347 | + | 1.87519i | 0.663376 | + | 0.116971i | 0.495191 | − | 0.868784i | \(-0.335098\pi\) |
0.168185 | + | 0.985755i | \(0.446209\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.3111 | − | 29.9838i | 1.07566 | − | 1.86310i | ||||
\(260\) | 2.65284 | − | 2.89090i | 0.164522 | − | 0.179286i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.17009 | − | 8.70976i | −0.195849 | − | 0.538091i | ||||
\(263\) | −0.352998 | − | 0.420687i | −0.0217668 | − | 0.0259407i | 0.755051 | − | 0.655666i | \(-0.227612\pi\) |
−0.776818 | + | 0.629725i | \(0.783168\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.330370 | − | 7.44404i | 0.0202944 | − | 0.457284i | ||||
\(266\) | −19.9127 | − | 3.33757i | −1.22093 | − | 0.204639i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.505477 | − | 0.0891292i | 0.0308769 | − | 0.00544443i | ||||
\(269\) | 16.7970 | − | 14.0944i | 1.02413 | − | 0.859350i | 0.0339919 | − | 0.999422i | \(-0.489178\pi\) |
0.990141 | + | 0.140072i | \(0.0447335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.96664 | + | 1.80771i | 0.301702 | + | 0.109810i | 0.488435 | − | 0.872600i | \(-0.337568\pi\) |
−0.186734 | + | 0.982411i | \(0.559790\pi\) | |||||||
\(272\) | −5.27036 | + | 6.28098i | −0.319563 | + | 0.380840i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.25158 | + | 3.89985i | 0.136023 | + | 0.235599i | ||||
\(275\) | 1.60980 | − | 5.97352i | 0.0970744 | − | 0.360217i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.1027 | + | 8.71954i | −0.907433 | + | 0.523906i | −0.879604 | − | 0.475706i | \(-0.842193\pi\) |
−0.0278284 | + | 0.999613i | \(0.508859\pi\) | |||||||
\(278\) | −19.7062 | − | 11.3774i | −1.18190 | − | 0.682371i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 23.9895 | + | 9.95695i | 1.43365 | + | 0.595042i | ||||
\(281\) | −21.7859 | + | 7.92943i | −1.29964 | + | 0.473030i | −0.896879 | − | 0.442275i | \(-0.854171\pi\) |
−0.402760 | + | 0.915305i | \(0.631949\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.52409 | + | 0.797719i | −0.268929 | + | 0.0474195i | −0.306487 | − | 0.951875i | \(-0.599153\pi\) |
0.0375573 | + | 0.999294i | \(0.488042\pi\) | |||||||
\(284\) | −6.94548 | −0.412138 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.22372 | 0.308885 | ||||||||
\(287\) | 19.9040 | − | 3.50962i | 1.17490 | − | 0.207166i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.47829 | + | 2.72188i | −0.439899 | + | 0.160110i | ||||
\(290\) | −4.48933 | + | 10.8162i | −0.263622 | + | 0.635150i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.86432 | − | 2.80842i | −0.284663 | − | 0.164350i | ||||
\(293\) | 15.7033 | − | 9.06630i | 0.917396 | − | 0.529659i | 0.0345929 | − | 0.999401i | \(-0.488987\pi\) |
0.882804 | + | 0.469742i | \(0.155653\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.396842 | + | 1.78397i | −0.0231050 | + | 0.103867i | ||||
\(296\) | 13.9857 | + | 24.2240i | 0.812904 | + | 1.40799i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.32533 | + | 1.57947i | −0.0767744 | + | 0.0914962i | ||||
\(299\) | −19.9654 | − | 7.26680i | −1.15463 | − | 0.420250i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −26.5051 | + | 22.2404i | −1.52773 | + | 1.28192i | ||||
\(302\) | −1.61073 | + | 0.284016i | −0.0926873 | + | 0.0163433i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.56259 | − | 9.16930i | 0.433745 | − | 0.525895i | ||||
\(305\) | 14.3013 | + | 0.634695i | 0.818887 | + | 0.0363425i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.83731 | − | 3.38137i | −0.161934 | − | 0.192985i | 0.678976 | − | 0.734160i | \(-0.262424\pi\) |
−0.840910 | + | 0.541175i | \(0.817980\pi\) | |||||||
\(308\) | −0.814726 | − | 2.23844i | −0.0464234 | − | 0.127547i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.42142 | + | 10.2669i | −0.535101 | + | 0.583119i | ||||
\(311\) | 7.51688 | − | 13.0196i | 0.426243 | − | 0.738275i | −0.570292 | − | 0.821442i | \(-0.693170\pi\) |
0.996536 | + | 0.0831667i | \(0.0265034\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.68691 | + | 1.35541i | 0.434490 | + | 0.0766123i | 0.386615 | − | 0.922241i | \(-0.373644\pi\) |
0.0478746 | + | 0.998853i | \(0.484755\pi\) | |||||||
\(314\) | −1.28181 | + | 7.26950i | −0.0723367 | + | 0.410242i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.351398 | + | 0.608639i | −0.0197677 | + | 0.0342386i | ||||
\(317\) | −17.5037 | + | 20.8601i | −0.983107 | + | 1.17162i | 0.00205551 | + | 0.999998i | \(0.499346\pi\) |
−0.985163 | + | 0.171624i | \(0.945099\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.98483 | − | 1.81433i | 0.279097 | − | 0.101583i | ||||
\(320\) | −15.7420 | + | 12.0613i | −0.880003 | + | 0.674247i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 28.4767i | − | 1.58694i | ||||||
\(323\) | −12.2782 | + | 4.58697i | −0.683175 | + | 0.255226i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.2163 | − | 1.48132i | 0.954989 | − | 0.0821689i | ||||
\(326\) | −9.16818 | + | 7.69302i | −0.507779 | + | 0.426077i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.58471 | + | 15.3439i | −0.308364 | + | 0.847224i | ||||
\(329\) | 21.2139 | + | 17.8005i | 1.16956 | + | 0.981376i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.98999 | + | 10.3750i | 0.329240 | + | 0.570260i | 0.982361 | − | 0.186993i | \(-0.0598742\pi\) |
−0.653121 | + | 0.757253i | \(0.726541\pi\) | |||||||
\(332\) | −1.26030 | − | 0.222224i | −0.0691677 | − | 0.0121961i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.36763 | − | 4.10085i | −0.129551 | − | 0.224389i | ||||
\(335\) | 1.90561 | + | 1.21593i | 0.104115 | + | 0.0664335i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.41714 | + | 3.89355i | −0.0771963 | + | 0.212095i | −0.972288 | − | 0.233788i | \(-0.924888\pi\) |
0.895091 | + | 0.445883i | \(0.147110\pi\) | |||||||
\(338\) | −0.441278 | − | 1.21240i | −0.0240024 | − | 0.0659460i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.38495 | − | 0.443165i | 0.183575 | − | 0.0240340i | ||||
\(341\) | 6.31201 | 0.341815 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.43230i | − | 0.0773370i | ||||||
\(344\) | −4.85406 | − | 27.5287i | −0.261713 | − | 1.48425i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.43216 | + | 1.97714i | −0.292035 | + | 0.106292i | ||||
\(347\) | −3.13610 | + | 8.61637i | −0.168355 | + | 0.462551i | −0.994965 | − | 0.100224i | \(-0.968044\pi\) |
0.826610 | + | 0.562775i | \(0.190266\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.3441 | + | 28.3089i | −0.874881 | + | 1.51534i | −0.0179923 | + | 0.999838i | \(0.505727\pi\) |
−0.856889 | + | 0.515501i | \(0.827606\pi\) | |||||||
\(350\) | 9.75770 | + | 21.0042i | 0.521571 | + | 1.12272i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.40681 | + | 0.600713i | 0.181584 | + | 0.0320181i | ||||
\(353\) | −22.9238 | + | 13.2351i | −1.22011 | + | 0.704431i | −0.964941 | − | 0.262466i | \(-0.915464\pi\) |
−0.255169 | + | 0.966897i | \(0.582131\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.5373 | − | 20.6814i | −1.19615 | − | 1.09765i | ||||
\(356\) | −1.28744 | − | 0.468589i | −0.0682340 | − | 0.0248351i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.36391 | − | 8.77597i | −0.389195 | − | 0.463824i | ||||
\(359\) | 2.15533 | + | 12.2235i | 0.113754 | + | 0.645131i | 0.987360 | + | 0.158496i | \(0.0506646\pi\) |
−0.873606 | + | 0.486635i | \(0.838224\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.7416 | − | 6.79976i | 0.933767 | − | 0.357882i | ||||
\(362\) | − | 23.8219i | − | 1.25205i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.09685 | − | 4.27677i | 0.267148 | − | 0.224163i | ||||
\(365\) | −7.42159 | − | 23.5974i | −0.388464 | − | 1.23514i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.42041 | + | 4.07628i | −0.178544 | + | 0.212780i | −0.847892 | − | 0.530168i | \(-0.822129\pi\) |
0.669349 | + | 0.742948i | \(0.266573\pi\) | |||||||
\(368\) | 14.5177 | + | 8.38178i | 0.756786 | + | 0.436931i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.41578 | + | 24.3462i | −0.281553 | + | 1.26570i | ||||
\(371\) | 2.19415 | − | 12.4437i | 0.113915 | − | 0.646042i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.7186 | − | 9.65250i | −0.865657 | − | 0.499788i | 0.000245325 | − | 1.00000i | \(-0.499922\pi\) |
−0.865903 | + | 0.500212i | \(0.833255\pi\) | |||||||
\(374\) | 3.48168 | + | 2.92147i | 0.180033 | + | 0.151066i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −21.0238 | + | 7.65203i | −1.08422 | + | 0.394623i | ||||
\(377\) | 9.52401 | + | 11.3503i | 0.490511 | + | 0.584569i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.5109 | −1.05357 | −0.526787 | − | 0.849997i | \(-0.676603\pi\) | ||||
−0.526787 | + | 0.849997i | \(0.676603\pi\) | |||||||
\(380\) | −4.90123 | + | 0.683934i | −0.251428 | + | 0.0350851i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.6498 | − | 3.28846i | 0.954207 | − | 0.168252i | ||||
\(383\) | −14.6076 | − | 17.4086i | −0.746411 | − | 0.889538i | 0.250497 | − | 0.968117i | \(-0.419406\pi\) |
−0.996908 | + | 0.0785793i | \(0.974962\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.02167 | − | 9.68947i | 0.204963 | − | 0.493821i | ||||
\(386\) | 18.5690 | + | 15.5813i | 0.945139 | + | 0.793066i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.34661 | − | 0.777465i | 0.0683637 | − | 0.0394698i | ||||
\(389\) | 0.876043 | − | 4.96829i | 0.0444172 | − | 0.251902i | −0.954512 | − | 0.298173i | \(-0.903623\pi\) |
0.998929 | + | 0.0462710i | \(0.0147338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.24308 | − | 16.0095i | −0.467443 | − | 0.809635i | ||||
\(392\) | 19.5730 | + | 11.3005i | 0.988588 | + | 0.570761i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 29.8122 | + | 10.8508i | 1.50192 | + | 0.546654i | ||||
\(395\) | −2.95258 | + | 0.928613i | −0.148560 | + | 0.0467236i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.5943 | + | 3.98399i | −1.13398 | + | 0.199951i | −0.708970 | − | 0.705239i | \(-0.750840\pi\) |
−0.425008 | + | 0.905190i | \(0.639729\pi\) | |||||||
\(398\) | 6.61603i | 0.331632i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.5802 | − | 1.20777i | −0.679009 | − | 0.0603883i | ||||
\(401\) | 3.95308 | + | 22.4191i | 0.197408 | + | 1.11955i | 0.908948 | + | 0.416909i | \(0.136887\pi\) |
−0.711540 | + | 0.702645i | \(0.752002\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.02986 | + | 16.5669i | 0.300369 | + | 0.825257i | ||||
\(404\) | 1.77821 | + | 0.647214i | 0.0884691 | + | 0.0322001i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.92933 | + | 17.1981i | −0.492784 | + | 0.853527i | ||||
\(407\) | 9.78420 | − | 5.64891i | 0.484985 | − | 0.280006i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.13331 | + | 23.4412i | −0.204379 | + | 1.15909i | 0.694035 | + | 0.719941i | \(0.255831\pi\) |
−0.898414 | + | 0.439150i | \(0.855280\pi\) | |||||||
\(410\) | −12.9195 | + | 6.71367i | −0.638047 | + | 0.331564i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.31079 | − | 5.13740i | 0.212377 | − | 0.253101i | ||||
\(413\) | −1.05996 | + | 2.91221i | −0.0521571 | + | 0.143300i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.42780 | − | 4.47385i | −0.168264 | − | 0.219612i | ||||
\(416\) | 1.67786 | + | 9.51559i | 0.0822636 | + | 0.466540i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.08274 | − | 4.19211i | −0.248605 | − | 0.205043i | ||||
\(419\) | −15.9374 | −0.778593 | −0.389296 | − | 0.921113i | \(-0.627282\pi\) | ||||
−0.389296 | + | 0.921113i | \(0.627282\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.03273 | + | 1.70566i | −0.0990692 | + | 0.0831290i | −0.690977 | − | 0.722877i | \(-0.742819\pi\) |
0.591908 | + | 0.806006i | \(0.298375\pi\) | |||||||
\(422\) | 8.40616 | + | 23.0957i | 0.409206 | + | 1.12428i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.82005 | + | 6.56180i | 0.379775 | + | 0.318669i | ||||
\(425\) | 12.3034 | + | 8.64127i | 0.596801 | + | 0.419163i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.9063 | + | 4.21533i | 1.15691 | + | 0.203994i | ||||
\(428\) | −2.56660 | − | 0.452560i | −0.124061 | − | 0.0218753i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.4074 | − | 21.0121i | 0.646563 | − | 1.01329i | ||||
\(431\) | −25.5262 | − | 21.4191i | −1.22956 | − | 1.03172i | −0.998268 | − | 0.0588349i | \(-0.981261\pi\) |
−0.231288 | − | 0.972885i | \(-0.574294\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.65442 | + | 21.0303i | 0.367848 | + | 1.01065i | 0.976178 | + | 0.216970i | \(0.0696173\pi\) |
−0.608330 | + | 0.793684i | \(0.708160\pi\) | |||||||
\(434\) | −18.1012 | + | 15.1887i | −0.868885 | + | 0.729081i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.806155 | 0.0386078 | ||||||||
\(437\) | 13.5948 | + | 23.0932i | 0.650329 | + | 1.10470i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.03121 | + | 17.1909i | 0.144672 | + | 0.820475i | 0.967630 | + | 0.252373i | \(0.0812110\pi\) |
−0.822958 | + | 0.568102i | \(0.807678\pi\) | |||||||
\(440\) | 5.15482 | + | 6.72789i | 0.245747 | + | 0.320740i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.34184 | + | 11.9291i | −0.206520 | + | 0.567410i | ||||
\(443\) | −0.963275 | + | 1.14799i | −0.0457666 | + | 0.0545425i | −0.788442 | − | 0.615109i | \(-0.789112\pi\) |
0.742676 | + | 0.669651i | \(0.233556\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.78228 | − | 5.35408i | −0.131892 | − | 0.253808i | ||||
\(446\) | −2.30149 | + | 13.0524i | −0.108979 | + | 0.618050i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −29.1236 | + | 16.8145i | −1.37596 | + | 0.794410i | ||||
\(449\) | −5.99556 | + | 10.3846i | −0.282948 | + | 0.490081i | −0.972110 | − | 0.234527i | \(-0.924646\pi\) |
0.689161 | + | 0.724608i | \(0.257979\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.19747 | + | 2.25569i | 0.291827 | + | 0.106217i | ||||
\(452\) | −3.48751 | − | 9.58185i | −0.164039 | − | 0.450693i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.86295 | + | 10.5653i | 0.0874324 | + | 0.495854i | ||||
\(455\) | 29.2735 | + | 1.29917i | 1.37236 | + | 0.0609060i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 12.9472i | − | 0.605646i | −0.953047 | − | 0.302823i | \(-0.902071\pi\) | ||
0.953047 | − | 0.302823i | \(-0.0979291\pi\) | |||||||
\(458\) | 21.7536 | − | 3.83575i | 1.01648 | − | 0.179233i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.09405 | − | 6.65815i | −0.0976357 | − | 0.310438i | ||||
\(461\) | 13.0317 | + | 4.74315i | 0.606946 | + | 0.220910i | 0.627166 | − | 0.778885i | \(-0.284215\pi\) |
−0.0202204 | + | 0.999796i | \(0.506437\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.62408 | − | 2.09237i | −0.168425 | − | 0.0972405i | 0.413418 | − | 0.910541i | \(-0.364335\pi\) |
−0.581843 | + | 0.813301i | \(0.697668\pi\) | |||||||
\(464\) | −5.84517 | − | 10.1241i | −0.271355 | − | 0.470001i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.59287 | + | 31.7188i | −0.259085 | + | 1.46934i | ||||
\(467\) | −20.1800 | + | 11.6509i | −0.933820 | + | 0.539141i | −0.888018 | − | 0.459810i | \(-0.847918\pi\) |
−0.0458021 | + | 0.998951i | \(0.514584\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.93642 | + | 2.46395i | 0.135591 | + | 0.113775i | ||||
\(470\) | −18.4253 | − | 7.64753i | −0.849898 | − | 0.352754i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.60940 | − | 1.91800i | −0.0740785 | − | 0.0882833i | ||||
\(473\) | −11.1190 | + | 1.96058i | −0.511252 | + | 0.0901476i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.9404 | − | 12.3750i | −0.823164 | − | 0.567803i | ||||
\(476\) | 5.78899 | 0.265338 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.19966 | − | 8.58022i | −0.329305 | − | 0.392450i | ||||
\(479\) | −32.9992 | + | 12.0107i | −1.50777 | + | 0.548784i | −0.958059 | − | 0.286570i | \(-0.907485\pi\) |
−0.549712 | + | 0.835354i | \(0.685263\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.1733 | + | 20.2838i | 1.10221 | + | 0.924863i | ||||
\(482\) | −28.0527 | − | 16.1962i | −1.27776 | − | 0.737717i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.834846 | + | 4.73465i | −0.0379476 | + | 0.215211i | ||||
\(485\) | 6.68463 | + | 1.48698i | 0.303533 | + | 0.0675204i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.9434 | + | 16.7105i | 1.31155 | + | 0.757223i | 0.982353 | − | 0.187038i | \(-0.0598889\pi\) |
0.329196 | + | 0.944262i | \(0.393222\pi\) | |||||||
\(488\) | −12.6063 | + | 15.0236i | −0.570661 | + | 0.680088i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.04622 | + | 19.2243i | 0.273140 | + | 0.868464i | ||||
\(491\) | 13.4354 | − | 11.2737i | 0.606332 | − | 0.508773i | −0.287142 | − | 0.957888i | \(-0.592705\pi\) |
0.893474 | + | 0.449115i | \(0.148261\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.8916i | 0.580609i | ||||||||
\(494\) | 6.14733 | − | 17.3452i | 0.276582 | − | 0.780397i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.41546 | − | 13.6988i | −0.108458 | − | 0.615093i | ||||
\(497\) | −33.3414 | − | 39.7347i | −1.49557 | − | 1.78235i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.7119 | + | 11.1782i | 1.37486 | + | 0.500407i | 0.920615 | − | 0.390472i | \(-0.127688\pi\) |
0.454241 | + | 0.890879i | \(0.349910\pi\) | |||||||
\(500\) | 3.82601 | + | 4.19346i | 0.171104 | + | 0.187537i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.8129 | − | 9.12957i | 0.705764 | − | 0.407473i | ||||
\(503\) | 17.2581 | + | 3.04306i | 0.769499 | + | 0.135684i | 0.544597 | − | 0.838698i | \(-0.316683\pi\) |
0.224902 | + | 0.974381i | \(0.427794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.84288 | + | 7.39506i | 0.171006 | + | 0.329076i | ||||
\(506\) | 4.64620 | − | 8.04746i | 0.206549 | − | 0.357753i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.599632 | − | 1.64748i | 0.0266044 | − | 0.0730949i | ||||
\(509\) | −28.1903 | + | 10.2604i | −1.24951 | + | 0.454786i | −0.880237 | − | 0.474534i | \(-0.842617\pi\) |
−0.369276 | + | 0.929320i | \(0.620394\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.28411 | − | 41.3102i | −0.322230 | − | 1.82746i | ||||
\(512\) | − | 24.3299i | − | 1.07524i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.1916 | −0.581858 | ||||||||
\(515\) | 29.2855 | − | 3.83412i | 1.29047 | − | 0.168951i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.09070 | + | 8.49162i | 0.135929 | + | 0.373461i | ||||
\(518\) | −14.4654 | + | 39.7435i | −0.635575 | + | 1.74623i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.7341 | + | 19.9568i | −0.558425 | + | 0.875165i | ||||
\(521\) | −5.24373 | − | 9.08241i | −0.229732 | − | 0.397907i | 0.727997 | − | 0.685581i | \(-0.240452\pi\) |
−0.957729 | + | 0.287673i | \(0.907118\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.2610 | − | 5.68848i | −1.41067 | − | 0.248740i | −0.584152 | − | 0.811644i | \(-0.698573\pi\) |
−0.826522 | + | 0.562905i | \(0.809684\pi\) | |||||||
\(524\) | −1.92618 | − | 3.33625i | −0.0841457 | − | 0.145745i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.513906 | + | 0.431218i | 0.0224073 | + | 0.0188020i | ||||
\(527\) | −5.24641 | + | 14.4144i | −0.228537 | + | 0.627901i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.3340 | + | 9.51037i | −0.492783 | + | 0.413494i | ||||
\(530\) | 1.18163 | + | 9.02547i | 0.0513269 | + | 0.392041i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.39146 | + | 0.0710470i | −0.363816 | + | 0.00308028i | ||||
\(533\) | 18.4211i | 0.797908i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.98073 | − | 9.11100i | −0.301803 | − | 0.393903i | ||||
\(536\) | −2.91011 | + | 1.05919i | −0.125697 | + | 0.0457501i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17.2175 | + | 20.5190i | −0.742299 | + | 0.884638i | ||||
\(539\) | 4.56433 | − | 7.90565i | 0.196600 | − | 0.340521i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.56927 | − | 14.5710i | 0.110461 | − | 0.626458i | −0.878436 | − | 0.477860i | \(-0.841413\pi\) |
0.988898 | − | 0.148598i | \(-0.0474761\pi\) | |||||||
\(542\) | −6.35846 | − | 1.12117i | −0.273119 | − | 0.0481583i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.20348 | + | 7.28065i | −0.180223 | + | 0.312155i | ||||
\(545\) | 2.61588 | + | 2.40047i | 0.112052 | + | 0.102825i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.550656 | + | 1.51291i | 0.0235443 | + | 0.0646875i | 0.950908 | − | 0.309474i | \(-0.100153\pi\) |
−0.927364 | + | 0.374161i | \(0.877931\pi\) | |||||||
\(548\) | 1.20307 | + | 1.43377i | 0.0513927 | + | 0.0612475i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.669491 | + | 7.52778i | −0.0285472 | + | 0.320986i | ||||
\(551\) | −0.158216 | − | 18.6871i | −0.00674022 | − | 0.796097i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.16886 | + | 0.911410i | −0.219802 | + | 0.0387571i | ||||
\(554\) | 16.3193 | − | 13.6935i | 0.693341 | − | 0.581782i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.88722 | − | 3.23468i | −0.376902 | − | 0.137181i | ||||
\(557\) | 14.3448 | − | 17.0954i | 0.607808 | − | 0.724357i | −0.371115 | − | 0.928587i | \(-0.621025\pi\) |
0.978923 | + | 0.204230i | \(0.0654690\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.7678 | − | 27.3107i | −0.666909 | − | 1.15512i | ||||
\(560\) | −22.5678 | − | 5.02016i | −0.953663 | − | 0.212141i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24.5270 | − | 14.1607i | 1.03461 | − | 0.597333i | ||||
\(563\) | −2.09682 | − | 1.21060i | −0.0883706 | − | 0.0510208i | 0.455163 | − | 0.890408i | \(-0.349581\pi\) |
−0.543534 | + | 0.839387i | \(0.682914\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.2151 | − | 41.4767i | 0.724245 | − | 1.74494i | ||||
\(566\) | 5.27339 | − | 1.91936i | 0.221657 | − | 0.0806766i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 41.2693 | − | 7.27689i | 1.73162 | − | 0.305332i | ||||
\(569\) | 25.3556 | 1.06296 | 0.531481 | − | 0.847070i | \(-0.321636\pi\) | ||||
0.531481 | + | 0.847070i | \(0.321636\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.79252 | 0.158712 | 0.0793561 | − | 0.996846i | \(-0.474714\pi\) | ||||
0.0793561 | + | 0.996846i | \(0.474714\pi\) | |||||||
\(572\) | 2.13815 | − | 0.377013i | 0.0894005 | − | 0.0157637i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −23.2006 | + | 8.44434i | −0.968376 | + | 0.352460i | ||||
\(575\) | 13.0309 | − | 27.8403i | 0.543425 | − | 1.16102i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.8817 | − | 18.4069i | −1.32725 | − | 0.766289i | −0.342378 | − | 0.939562i | \(-0.611232\pi\) |
−0.984874 | + | 0.173274i | \(0.944566\pi\) | |||||||
\(578\) | 8.41921 | − | 4.86083i | 0.350193 | − | 0.202184i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.05691 | + | 4.75126i | −0.0438858 | + | 0.197285i | ||||
\(581\) | −4.77865 | − | 8.27687i | −0.198252 | − | 0.343382i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.65035 | − | 3.15856i | 0.109766 | − | 0.130814i | ||||
\(584\) | 31.8457 | + | 11.5909i | 1.31778 | + | 0.479634i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.9683 | + | 14.2381i | −0.700954 | + | 0.588170i | ||||
\(587\) | 27.1575 | − | 4.78860i | 1.12091 | − | 0.197647i | 0.417669 | − | 0.908599i | \(-0.362847\pi\) |
0.703240 | + | 0.710953i | \(0.251736\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.42806 | − | 20.9588i | 0.306068 | − | 0.863594i | ||||
\(590\) | 0.0989838 | − | 2.23035i | 0.00407510 | − | 0.0918220i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.0039 | − | 19.0726i | −0.657754 | − | 0.783881i | ||||
\(593\) | 2.54255 | + | 6.98559i | 0.104410 | + | 0.286864i | 0.980887 | − | 0.194580i | \(-0.0623345\pi\) |
−0.876477 | + | 0.481444i | \(0.840112\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.7846 | + | 17.2377i | 0.770093 | + | 0.706679i | ||||
\(596\) | −0.428484 | + | 0.742155i | −0.0175514 | + | 0.0303999i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 25.5604 | + | 4.50698i | 1.04524 | + | 0.184304i | ||||
\(599\) | 1.30033 | − | 7.37456i | 0.0531302 | − | 0.301316i | −0.946650 | − | 0.322262i | \(-0.895557\pi\) |
0.999781 | + | 0.0209459i | \(0.00666778\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.4586 | − | 21.5790i | 0.508199 | − | 0.880226i | −0.491756 | − | 0.870733i | \(-0.663645\pi\) |
0.999955 | − | 0.00949287i | \(-0.00302172\pi\) | |||||||
\(602\) | 27.1686 | − | 32.3783i | 1.10731 | − | 1.31964i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.638800 | + | 0.232504i | −0.0259924 | + | 0.00946046i | ||||
\(605\) | −16.8072 | + | 12.8775i | −0.683311 | + | 0.523544i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 13.5201i | − | 0.548764i | −0.961621 | − | 0.274382i | \(-0.911527\pi\) | ||
0.961621 | − | 0.274382i | \(-0.0884733\pi\) | |||||||
\(608\) | 6.00383 | − | 10.6053i | 0.243487 | − | 0.430101i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.3394 | + | 2.27011i | −0.702053 | + | 0.0919143i | ||||
\(611\) | −19.3351 | + | 16.2241i | −0.782214 | + | 0.656356i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.93380 | − | 5.31308i | 0.0781055 | − | 0.214593i | −0.894494 | − | 0.447080i | \(-0.852464\pi\) |
0.972600 | + | 0.232487i | \(0.0746862\pi\) | |||||||
\(614\) | 4.13064 | + | 3.46602i | 0.166699 | + | 0.139877i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.18627 | + | 12.4470i | 0.289543 | + | 0.501503i | ||||
\(617\) | 18.1567 | + | 3.20152i | 0.730963 | + | 0.128888i | 0.526729 | − | 0.850034i | \(-0.323418\pi\) |
0.204234 | + | 0.978922i | \(0.434530\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.49951 | − | 6.06133i | −0.140657 | − | 0.243625i | 0.787087 | − | 0.616842i | \(-0.211588\pi\) |
−0.927744 | + | 0.373216i | \(0.878255\pi\) | |||||||
\(620\) | −3.11534 | + | 4.88237i | −0.125115 | + | 0.196081i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.28121 | + | 17.2575i | −0.251854 | + | 0.691962i | ||||
\(623\) | −3.49950 | − | 9.61480i | −0.140205 | − | 0.385209i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.0718048 | + | 24.9999i | −0.00287219 | + | 0.999996i | ||||
\(626\) | −9.53508 | −0.381099 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.06803i | 0.122428i | ||||||||
\(629\) | 4.76768 | + | 27.0389i | 0.190100 | + | 1.07811i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.3690 | + | 9.59752i | −1.04973 | + | 0.382071i | −0.808562 | − | 0.588412i | \(-0.799753\pi\) |
−0.241170 | + | 0.970483i | \(0.577531\pi\) | |||||||
\(632\) | 1.45029 | − | 3.98464i | 0.0576894 | − | 0.158500i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.6325 | − | 28.8083i | 0.660560 | − | 1.14412i | ||||
\(635\) | 6.85138 | − | 3.56035i | 0.271889 | − | 0.141288i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.1100 | + | 4.42757i | 0.994893 | + | 0.175427i | ||||
\(638\) | −5.61202 | + | 3.24010i | −0.222182 | + | 0.128277i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.92573 | − | 8.63696i | 0.313292 | − | 0.341406i | ||||
\(641\) | 25.2148 | + | 9.17744i | 0.995925 | + | 0.362487i | 0.788012 | − | 0.615660i | \(-0.211111\pi\) |
0.207913 | + | 0.978147i | \(0.433333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.2770 | + | 20.5900i | 0.681339 | + | 0.811989i | 0.990279 | − | 0.139093i | \(-0.0444187\pi\) |
−0.308940 | + | 0.951082i | \(0.599974\pi\) | |||||||
\(644\) | −2.05526 | − | 11.6560i | −0.0809885 | − | 0.459309i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.7979 | − | 8.12278i | 0.542873 | − | 0.319586i | ||||
\(647\) | 8.88424i | 0.349275i | 0.984633 | + | 0.174638i | \(0.0558754\pi\) | ||||
−0.984633 | + | 0.174638i | \(0.944125\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.774692 | + | 0.650044i | −0.0304093 | + | 0.0255164i | ||||
\(650\) | −20.3975 | + | 5.43410i | −0.800054 | + | 0.213143i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.19745 | + | 3.81057i | −0.125222 | + | 0.149234i | ||||
\(653\) | −34.1303 | − | 19.7051i | −1.33562 | − | 0.771121i | −0.349465 | − | 0.936949i | \(-0.613637\pi\) |
−0.986155 | + | 0.165829i | \(0.946970\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.68402 | − | 16.5613i | 0.143947 | − | 0.647103i | ||||
\(656\) | 2.52384 | − | 14.3134i | 0.0985393 | − | 0.558844i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −29.2968 | − | 16.9145i | −1.14211 | − | 0.659397i | ||||
\(659\) | 13.2617 | + | 11.1279i | 0.516603 | + | 0.433481i | 0.863446 | − | 0.504442i | \(-0.168302\pi\) |
−0.346843 | + | 0.937923i | \(0.612746\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.3832 | + | 4.87107i | −0.520544 | + | 0.189463i | −0.588911 | − | 0.808198i | \(-0.700443\pi\) |
0.0683671 | + | 0.997660i | \(0.478221\pi\) | |||||||
\(662\) | −9.40693 | − | 11.2107i | −0.365611 | − | 0.435718i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.72138 | 0.299647 | ||||||||
\(665\) | −27.4409 | − | 24.7565i | −1.06411 | − | 0.960016i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.9569 | − | 4.57689i | 1.00505 | − | 0.177218i | ||||
\(668\) | −1.26508 | − | 1.50766i | −0.0489474 | − | 0.0583332i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.55043 | − | 1.05857i | −0.0985318 | − | 0.0408961i | ||||
\(671\) | 6.06812 | + | 5.09176i | 0.234257 | + | 0.196565i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.34892 | + | 1.93350i | −0.129091 | + | 0.0745310i | −0.563155 | − | 0.826351i | \(-0.690413\pi\) |
0.434064 | + | 0.900882i | \(0.357079\pi\) | |||||||
\(674\) | 0.878929 | − | 4.98466i | 0.0338551 | − | 0.192002i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.268125 | − | 0.464407i | −0.0103125 | − | 0.0178618i | ||||
\(677\) | 13.6054 | + | 7.85508i | 0.522898 | + | 0.301895i | 0.738119 | − | 0.674670i | \(-0.235714\pi\) |
−0.215222 | + | 0.976565i | \(0.569047\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.9122 | + | 3.97170i | 0.418771 | + | 0.152420i | ||||
\(680\) | −19.6487 | + | 6.17970i | −0.753493 | + | 0.236981i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.59353 | + | 1.33894i | −0.290771 | + | 0.0512708i | ||||
\(683\) | 11.3613i | 0.434727i | 0.976091 | + | 0.217364i | \(0.0697458\pi\) | ||||
−0.976091 | + | 0.217364i | \(0.930254\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.365462 | + | 8.23477i | −0.0139636 | + | 0.314634i | ||||
\(686\) | 0.303829 | + | 1.72310i | 0.0116002 | + | 0.0657882i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.50998 | + | 23.3810i | 0.324440 | + | 0.891392i | ||||
\(689\) | 10.8220 | + | 3.93890i | 0.412287 | + | 0.150060i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.00544 | − | 1.74147i | 0.0382487 | − | 0.0662487i | −0.846267 | − | 0.532758i | \(-0.821155\pi\) |
0.884516 | + | 0.466510i | \(0.154489\pi\) | |||||||
\(692\) | −2.08077 | + | 1.20133i | −0.0790990 | + | 0.0456679i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.94506 | − | 11.0310i | 0.0738334 | − | 0.418730i | ||||
\(695\) | −19.2061 | − | 36.9594i | −0.728531 | − | 1.40195i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.3024 | + | 12.2779i | −0.390232 | + | 0.465060i | ||||
\(698\) | 13.6574 | − | 37.5234i | 0.516940 | − | 1.42028i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.50992 | + | 7.89309i | 0.208255 | + | 0.298331i | ||||
\(701\) | −2.16414 | − | 12.2735i | −0.0817385 | − | 0.463562i | −0.998013 | − | 0.0630107i | \(-0.979930\pi\) |
0.916274 | − | 0.400551i | \(-0.131181\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.24286 | − | 39.1358i | −0.273170 | − | 1.47604i | ||||
\(704\) | −10.9737 | −0.413586 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.7704 | − | 20.7849i | 0.932248 | − | 0.782249i | ||||
\(707\) | 4.83351 | + | 13.2800i | 0.181783 | + | 0.499444i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.69839 | + | 2.26422i | 0.101340 | + | 0.0850346i | 0.692050 | − | 0.721849i | \(-0.256708\pi\) |
−0.590710 | + | 0.806884i | \(0.701152\pi\) | |||||||
\(710\) | 31.5000 | + | 20.0995i | 1.18217 | + | 0.754322i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.14076 | + | 1.43544i | 0.305088 | + | 0.0537952i | ||||
\(713\) | 30.8856 | + | 5.44596i | 1.15667 | + | 0.203953i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.06067 | + | 5.14335i | 0.301452 | + | 0.192350i | ||||
\(716\) | −3.64756 | − | 3.06066i | −0.136316 | − | 0.114382i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.18584 | − | 14.2480i | −0.193534 | − | 0.531730i | ||||
\(719\) | −18.3135 | + | 15.3668i | −0.682977 | + | 0.573086i | −0.916874 | − | 0.399176i | \(-0.869296\pi\) |
0.233898 | + | 0.972261i | \(0.424852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 50.0845 | 1.86524 | ||||||||
\(722\) | −19.9012 | + | 11.9437i | −0.740645 | + | 0.444500i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.71931 | − | 9.75067i | −0.0638975 | − | 0.362381i | ||||
\(725\) | −17.5773 | + | 12.2701i | −0.652803 | + | 0.455702i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.87402 | + | 5.14882i | −0.0695034 | + | 0.190959i | −0.969581 | − | 0.244770i | \(-0.921287\pi\) |
0.900078 | + | 0.435730i | \(0.143510\pi\) | |||||||
\(728\) | −25.8041 | + | 30.7521i | −0.956364 | + | 1.13975i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.9340 | + | 26.8140i | 0.515720 | + | 0.992429i | ||||
\(731\) | 4.76461 | − | 27.0215i | 0.176226 | − | 0.999424i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.3586 | + | 9.44464i | −0.604218 | + | 0.348846i | −0.770699 | − | 0.637199i | \(-0.780093\pi\) |
0.166481 | + | 0.986045i | \(0.446760\pi\) | |||||||
\(734\) | 3.25016 | − | 5.62944i | 0.119965 | − | 0.207786i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.1517 | + | 5.87874i | 0.595360 | + | 0.216693i | ||||
\(737\) | 0.427813 | + | 1.17541i | 0.0157587 | + | 0.0432967i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.07048 | − | 34.4274i | −0.223306 | − | 1.26643i | −0.865897 | − | 0.500223i | \(-0.833251\pi\) |
0.642590 | − | 0.766210i | \(-0.277860\pi\) | |||||||
\(740\) | −0.459611 | + | 10.3562i | −0.0168956 | + | 0.380700i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.4355i | 0.566655i | ||||||||
\(743\) | −27.2185 | + | 4.79935i | −0.998549 | + | 0.176071i | −0.648952 | − | 0.760829i | \(-0.724792\pi\) |
−0.349597 | + | 0.936900i | \(0.613681\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.60028 | + | 1.13232i | −0.131904 | + | 0.0414851i | ||||
\(746\) | 22.1605 | + | 8.06576i | 0.811354 | + | 0.295309i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.63596 | + | 0.944521i | 0.0598166 | + | 0.0345351i | ||||
\(749\) | −9.73174 | − | 16.8559i | −0.355590 | − | 0.615900i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.32641 | − | 52.8927i | 0.340326 | − | 1.93008i | −0.0261566 | − | 0.999658i | \(-0.508327\pi\) |
0.366482 | − | 0.930425i | \(-0.380562\pi\) | |||||||
\(752\) | 17.2464 | − | 9.95720i | 0.628910 | − | 0.363102i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.8653 | − | 11.6344i | −0.504946 | − | 0.423700i | ||||
\(755\) | −2.76515 | − | 1.14769i | −0.100634 | − | 0.0417687i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.7996 | − | 18.8292i | −0.574246 | − | 0.684360i | 0.398251 | − | 0.917277i | \(-0.369617\pi\) |
−0.972497 | + | 0.232917i | \(0.925173\pi\) | |||||||
\(758\) | 24.6752 | − | 4.35090i | 0.896242 | − | 0.158032i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 28.4060 | − | 9.19896i | 1.03039 | − | 0.333681i | ||||
\(761\) | 0.906887 | 0.0328746 | 0.0164373 | − | 0.999865i | \(-0.494768\pi\) | ||||
0.0164373 | + | 0.999865i | \(0.494768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.86991 | + | 4.61197i | 0.140100 | + | 0.166965i | ||||
\(764\) | 7.39632 | − | 2.69204i | 0.267589 | − | 0.0973945i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.2661 | + | 17.8444i | 0.768376 | + | 0.644744i | ||||
\(767\) | −2.44621 | − | 1.41232i | −0.0883275 | − | 0.0509959i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.70205 | + | 20.9954i | −0.133499 | + | 0.757113i | 0.842393 | + | 0.538863i | \(0.181146\pi\) |
−0.975893 | + | 0.218250i | \(0.929965\pi\) | |||||||
\(770\) | −2.78278 | + | 12.5098i | −0.100285 | + | 0.450822i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.72515 | + | 5.03747i | 0.314025 | + | 0.181302i | ||||
\(773\) | 10.6726 | − | 12.7191i | 0.383868 | − | 0.457476i | −0.539163 | − | 0.842201i | \(-0.681259\pi\) |
0.923031 | + | 0.384725i | \(0.125704\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.6470 | + | 6.56623i | −0.885347 | + | 0.235866i | ||||
\(776\) | −7.18685 | + | 6.03048i | −0.257993 | + | 0.216482i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.16282i | 0.220948i | ||||||||
\(779\) | 14.7832 | − | 17.9240i | 0.529664 | − | 0.642193i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.93917 | − | 16.6689i | −0.105172 | − | 0.596460i | ||||
\(782\) | 14.5157 | + | 17.2992i | 0.519081 | + | 0.618616i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −18.9041 | − | 6.88052i | −0.675145 | − | 0.245733i | ||||
\(785\) | −9.13561 | + | 9.95541i | −0.326064 | + | 0.355324i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.8079 | + | 20.6737i | −1.27641 | + | 0.736938i | −0.976187 | − | 0.216929i | \(-0.930396\pi\) |
−0.300228 | + | 0.953868i | \(0.597063\pi\) | |||||||
\(788\) | 12.9858 | + | 2.28974i | 0.462598 | + | 0.0815685i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.35505 | − | 1.74347i | 0.119367 | − | 0.0620297i | ||||
\(791\) | 38.0757 | − | 65.9491i | 1.35382 | − | 2.34488i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.56728 | + | 20.7909i | −0.268722 | + | 0.738308i | ||||
\(794\) | 26.3365 | − | 9.58570i | 0.934647 | − | 0.340184i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.477501 | + | 2.70804i | 0.0169246 | + | 0.0959841i | ||||
\(797\) | 22.7002i | 0.804083i | 0.915621 | + | 0.402042i | \(0.131699\pi\) | ||||
−0.915621 | + | 0.402042i | \(0.868301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.9608 | −0.776916 | ||||||||
\(800\) | −13.9278 | + | 1.19837i | −0.492420 | + | 0.0423687i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.51134 | − | 26.1322i | −0.335857 | − | 0.922760i | ||||
\(803\) | 4.68162 | − | 12.8626i | 0.165211 | − | 0.453913i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.0386 | − | 43.9421i | 0.988230 | − | 1.54876i | ||||
\(806\) | −10.7684 | − | 18.6514i | −0.379299 | − | 0.656966i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.2440 | − | 1.98262i | −0.395563 | − | 0.0697484i | ||||
\(809\) | 13.5754 | + | 23.5133i | 0.477285 | + | 0.826683i | 0.999661 | − | 0.0260328i | \(-0.00828745\pi\) |
−0.522376 | + | 0.852715i | \(0.674954\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.6710 | − | 29.0925i | −1.21746 | − | 1.02157i | −0.998953 | − | 0.0457400i | \(-0.985435\pi\) |
−0.218512 | − | 0.975834i | \(-0.570120\pi\) | |||||||
\(812\) | −2.82298 | + | 7.75609i | −0.0990673 | + | 0.272185i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.5724 | + | 8.87127i | −0.370561 | + | 0.310938i | ||||
\(815\) | −21.7220 | + | 2.84389i | −0.760889 | + | 0.0996171i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.57493 | + | 39.2275i | −0.230028 | + | 1.37240i | ||||
\(818\) | − | 29.0771i | − | 1.01666i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.80360 | + | 3.68045i | −0.167749 | + | 0.128527i | ||||
\(821\) | 13.8883 | − | 5.05494i | 0.484706 | − | 0.176419i | −0.0880966 | − | 0.996112i | \(-0.528078\pi\) |
0.572802 | + | 0.819693i | \(0.305856\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.5396 | − | 29.2452i | 0.855398 | − | 1.01942i | −0.144156 | − | 0.989555i | \(-0.546047\pi\) |
0.999554 | − | 0.0298685i | \(-0.00950886\pi\) | |||||||
\(824\) | −20.2317 | + | 35.0424i | −0.704805 | + | 1.22076i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.657401 | − | 3.72831i | 0.0228739 | − | 0.129724i | ||||
\(827\) | −44.6391 | − | 7.87107i | −1.55225 | − | 0.273704i | −0.669237 | − | 0.743049i | \(-0.733379\pi\) |
−0.883015 | + | 0.469345i | \(0.844490\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.9638 | − | 32.8463i | 0.658640 | − | 1.14080i | −0.322328 | − | 0.946628i | \(-0.604465\pi\) |
0.980968 | − | 0.194170i | \(-0.0622013\pi\) | |||||||
\(830\) | 5.07276 | + | 4.65503i | 0.176078 | + | 0.161579i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −10.4832 | − | 28.8022i | −0.363438 | − | 0.998537i | ||||
\(833\) | 14.2599 | + | 16.9943i | 0.494077 | + | 0.588818i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.384298 | − | 8.65919i | 0.0132992 | − | 0.299664i | ||||
\(836\) | −2.38300 | − | 1.34906i | −0.0824179 | − | 0.0466581i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19.1731 | − | 3.38074i | 0.662324 | − | 0.116786i | ||||
\(839\) | −5.47159 | + | 4.59121i | −0.188900 | + | 0.158506i | −0.732333 | − | 0.680946i | \(-0.761569\pi\) |
0.543433 | + | 0.839453i | \(0.317124\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.97892 | + | 3.63203i | 0.344101 | + | 0.125242i | ||||
\(842\) | 2.08361 | − | 2.48316i | 0.0718061 | − | 0.0855752i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.10767 | + | 8.84675i | 0.175813 | + | 0.304518i | ||||
\(845\) | 0.512817 | − | 2.30533i | 0.0176415 | − | 0.0793059i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31.0943 | + | 17.9523i | −1.06841 | + | 0.616849i | ||||
\(848\) | −7.86916 | − | 4.54326i | −0.270228 | − | 0.156016i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −16.6343 | − | 7.78581i | −0.570552 | − | 0.267051i | ||||
\(851\) | 52.7493 | − | 19.1992i | 1.80822 | − | 0.658139i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.2637 | − | 8.86285i | 1.72100 | − | 0.303458i | 0.776047 | − | 0.630675i | \(-0.217222\pi\) |
0.944949 | + | 0.327217i | \(0.106111\pi\) | |||||||
\(854\) | −29.6542 | −1.01474 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.7246 | 0.537456 | ||||||||
\(857\) | −13.3975 | + | 2.36234i | −0.457650 | + | 0.0806961i | −0.397721 | − | 0.917507i | \(-0.630199\pi\) |
−0.0599294 | + | 0.998203i | \(0.519088\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.1194 | + | 13.1464i | −1.23238 | + | 0.448549i | −0.874411 | − | 0.485185i | \(-0.838752\pi\) |
−0.357967 | + | 0.933734i | \(0.616530\pi\) | |||||||
\(860\) | 3.97135 | − | 9.56825i | 0.135422 | − | 0.326275i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 35.2523 | + | 20.3529i | 1.20070 | + | 0.693224i | ||||
\(863\) | −47.0645 | + | 27.1727i | −1.60210 | + | 0.924970i | −0.611028 | + | 0.791609i | \(0.709244\pi\) |
−0.991067 | + | 0.133362i | \(0.957423\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.3290 | − | 2.29768i | −0.351198 | − | 0.0781233i | ||||
\(866\) | −13.6696 | − | 23.6764i | −0.464511 | − | 0.804556i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.31288 | + | 7.52340i | −0.214273 | + | 0.255361i | ||||
\(869\) | −1.60942 | − | 0.585779i | −0.0545957 | − | 0.0198712i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.67636 | + | 2.24573i | −0.0906850 | + | 0.0760937i | ||||
\(872\) | −4.79009 | + | 0.844622i | −0.162213 | + | 0.0286025i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −21.2536 | − | 24.8979i | −0.718914 | − | 0.842184i | ||||
\(875\) | −5.62400 | + | 42.0189i | −0.190126 | + | 1.42050i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.69855 | + | 10.3665i | 0.293729 | + | 0.350053i | 0.892646 | − | 0.450759i | \(-0.148846\pi\) |
−0.598917 | + | 0.800811i | \(0.704402\pi\) | |||||||
\(878\) | −7.29327 | − | 20.0381i | −0.246136 | − | 0.676253i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.55853 | − | 5.10081i | −0.187378 | − | 0.171948i | ||||
\(881\) | −13.9789 | + | 24.2121i | −0.470960 | + | 0.815726i | −0.999448 | − | 0.0332142i | \(-0.989426\pi\) |
0.528488 | + | 0.848940i | \(0.322759\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −53.7200 | − | 9.47229i | −1.80782 | − | 0.318768i | −0.834987 | − | 0.550269i | \(-0.814525\pi\) |
−0.972835 | + | 0.231501i | \(0.925636\pi\) | |||||||
\(884\) | −0.916220 | + | 5.19614i | −0.0308158 | + | 0.174765i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.915328 | − | 1.58539i | 0.0307510 | − | 0.0532624i | ||||
\(887\) | −23.1261 | + | 27.5606i | −0.776497 | + | 0.925393i | −0.998770 | − | 0.0495912i | \(-0.984208\pi\) |
0.222272 | + | 0.974985i | \(0.428653\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.3036 | − | 4.47815i | 0.412650 | − | 0.150192i | ||||
\(890\) | 4.48289 | + | 5.85092i | 0.150267 | + | 0.196123i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.50867i | 0.184444i | ||||||||
\(893\) | 31.8333 | − | 0.269519i | 1.06526 | − | 0.00901912i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.72223 | − | 20.7927i | −0.0909940 | − | 0.695024i | ||||
\(896\) | 15.2276 | − | 12.7774i | 0.508717 | − | 0.426864i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.00998 | − | 13.7648i | 0.167185 | − | 0.459337i | ||||
\(899\) | −16.7540 | − | 14.0583i | −0.558777 | − | 0.468870i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.01012 | + | 8.67778i | 0.166911 | + | 0.289099i | ||||
\(902\) | −7.93422 | − | 1.39902i | −0.264181 | − | 0.0465822i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 30.7615 | + | 53.2804i | 1.02311 | + | 1.77208i | ||||
\(905\) | 23.4554 | − | 36.7593i | 0.779683 | − | 1.22192i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.50616 | + | 4.13814i | −0.0500112 | + | 0.137405i | −0.962183 | − | 0.272403i | \(-0.912182\pi\) |
0.912172 | + | 0.409807i | \(0.134404\pi\) | |||||||
\(908\) | 1.52507 | + | 4.19009i | 0.0506111 | + | 0.139053i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −35.4924 | + | 4.64674i | −1.17656 | + | 0.154038i | ||||
\(911\) | 14.2563 | 0.472333 | 0.236166 | − | 0.971713i | \(-0.424109\pi\) | ||||
0.236166 | + | 0.971713i | \(0.424109\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 3.11870i | − | 0.103214i | ||||||
\(914\) | 2.74645 | + | 15.5759i | 0.0908444 | + | 0.515204i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.62726 | − | 3.14006i | 0.285053 | − | 0.103751i | ||||
\(917\) | 9.83996 | − | 27.0351i | 0.324944 | − | 0.892777i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.3638 | + | 24.8789i | −0.473819 | + | 0.820678i | −0.999551 | − | 0.0299723i | \(-0.990458\pi\) |
0.525732 | + | 0.850650i | \(0.323791\pi\) | |||||||
\(920\) | 19.4185 | + | 37.3681i | 0.640209 | + | 1.23199i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.6836 | − | 2.94177i | −0.549446 | − | 0.0968821i | ||||
\(923\) | 40.9424 | − | 23.6381i | 1.34764 | − | 0.778058i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.3287 | + | 32.2360i | −1.06296 | + | 1.05991i | ||||
\(926\) | 4.80372 | + | 1.74841i | 0.157860 | + | 0.0574563i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.70479 | − | 9.18221i | −0.252922 | − | 0.301421i | ||||
\(929\) | −5.32975 | − | 30.2265i | −0.174864 | − | 0.991700i | −0.938301 | − | 0.345819i | \(-0.887601\pi\) |
0.763438 | − | 0.645881i | \(-0.223510\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.8791 | − | 24.4592i | −0.684285 | − | 0.801617i | ||||
\(932\) | 13.3866i | 0.438494i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.8056 | − | 18.2971i | 0.713502 | − | 0.598699i | ||||
\(935\) | 2.49601 | + | 7.93621i | 0.0816284 | + | 0.259542i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.4167 | − | 38.6327i | 1.05901 | − | 1.26208i | 0.0952059 | − | 0.995458i | \(-0.469649\pi\) |
0.963802 | − | 0.266619i | \(-0.0859065\pi\) | |||||||
\(938\) | −4.05526 | − | 2.34131i | −0.132409 | − | 0.0764463i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.09373 | − | 1.80044i | −0.263988 | − | 0.0587237i | ||||
\(941\) | −1.48399 | + | 8.41611i | −0.0483766 | + | 0.274357i | −0.999395 | − | 0.0347766i | \(-0.988928\pi\) |
0.951019 | + | 0.309134i | \(0.100039\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.3789 | + | 16.3846i | 0.924144 | + | 0.533555i | ||||
\(944\) | 1.70723 | + | 1.43253i | 0.0555655 | + | 0.0466250i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.9606 | − | 4.71726i | 0.421385 | − | 0.153371i | ||||
\(947\) | −13.2302 | − | 15.7671i | −0.429923 | − | 0.512362i | 0.506977 | − | 0.861959i | \(-0.330763\pi\) |
−0.936900 | + | 0.349597i | \(0.886318\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.2325 | 1.24108 | ||||||||
\(950\) | 24.2079 | + | 11.0818i | 0.785408 | + | 0.359541i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −34.3976 | + | 6.06522i | −1.11483 | + | 0.196575i | ||||
\(953\) | 38.0480 | + | 45.3438i | 1.23249 | + | 1.46883i | 0.834098 | + | 0.551617i | \(0.185989\pi\) |
0.398397 | + | 0.917213i | \(0.369567\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.0162 | + | 13.2885i | 1.03602 | + | 0.430005i | ||||
\(956\) | −3.56620 | − | 2.99239i | −0.115339 | − | 0.0967810i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37.1511 | − | 21.4492i | 1.20030 | − | 0.692993i | ||||
\(959\) | −2.42722 | + | 13.7654i | −0.0783790 | + | 0.444510i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.48818 | + | 4.30965i | 0.0802638 | + | 0.139021i | ||||
\(962\) | −33.3839 | − | 19.2742i | −1.07634 | − | 0.621425i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.6513 | − | 4.60471i | −0.407472 | − | 0.148308i | ||||
\(965\) | 13.3121 | + | 42.3267i | 0.428533 | + | 1.36254i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.8299 | + | 1.90960i | −0.348266 | + | 0.0614087i | −0.345045 | − | 0.938586i | \(-0.612136\pi\) |
−0.00322103 | + | 0.999995i | \(0.501025\pi\) | |||||||
\(968\) | − | 29.0075i | − | 0.932335i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.35722 | − | 0.370897i | −0.268334 | − | 0.0119088i | ||||
\(971\) | −5.62086 | − | 31.8775i | −0.180382 | − | 1.02300i | −0.931746 | − | 0.363109i | \(-0.881715\pi\) |
0.751365 | − | 0.659887i | \(-0.229396\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.1572 | − | 66.3713i | −0.774444 | − | 2.12777i | ||||
\(974\) | −38.3644 | − | 13.9635i | −1.22927 | − | 0.447419i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.72836 | − | 15.1180i | 0.279388 | − | 0.483914i | ||||
\(977\) | 9.61615 | − | 5.55189i | 0.307648 | − | 0.177621i | −0.338226 | − | 0.941065i | \(-0.609827\pi\) |
0.645873 | + | 0.763445i | \(0.276493\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.579780 | − | 3.28810i | 0.0185298 | − | 0.105088i | ||||
\(980\) | 3.86229 | + | 7.43242i | 0.123376 | + | 0.237420i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.7718 | + | 16.4125i | −0.439474 | + | 0.523745i | ||||
\(983\) | 4.28627 | − | 11.7764i | 0.136711 | − | 0.375610i | −0.852379 | − | 0.522925i | \(-0.824841\pi\) |
0.989090 | + | 0.147315i | \(0.0470630\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.3191 | + | 46.0973i | 1.12536 | + | 1.46878i | ||||
\(986\) | −2.73465 | − | 15.5090i | −0.0870889 | − | 0.493906i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.26434 | − | 7.54333i | 0.0402240 | − | 0.239985i | ||||
\(989\) | −56.0984 | −1.78383 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.1596 | − | 23.6287i | 0.894519 | − | 0.750591i | −0.0745922 | − | 0.997214i | \(-0.523766\pi\) |
0.969111 | + | 0.246623i | \(0.0793211\pi\) | |||||||
\(992\) | −4.87807 | − | 13.4024i | −0.154879 | − | 0.425527i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 48.5394 | + | 40.7294i | 1.53958 | + | 1.29186i | ||||
\(995\) | −6.51424 | + | 10.2091i | −0.206515 | + | 0.323651i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.1082 | + | 4.25092i | 0.763513 | + | 0.134628i | 0.541827 | − | 0.840490i | \(-0.317733\pi\) |
0.221686 | + | 0.975118i | \(0.428844\pi\) | |||||||
\(998\) | −39.3185 | − | 6.93291i | −1.24461 | − | 0.219458i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 855.2.da.b.199.3 | 48 | ||
3.2 | odd | 2 | 95.2.p.a.9.6 | yes | 48 | ||
5.4 | even | 2 | inner | 855.2.da.b.199.6 | 48 | ||
15.2 | even | 4 | 475.2.l.f.351.6 | 48 | |||
15.8 | even | 4 | 475.2.l.f.351.3 | 48 | |||
15.14 | odd | 2 | 95.2.p.a.9.3 | ✓ | 48 | ||
19.17 | even | 9 | inner | 855.2.da.b.739.6 | 48 | ||
57.17 | odd | 18 | 95.2.p.a.74.3 | yes | 48 | ||
57.32 | even | 18 | 1805.2.b.l.1084.17 | 24 | |||
57.44 | odd | 18 | 1805.2.b.k.1084.8 | 24 | |||
95.74 | even | 18 | inner | 855.2.da.b.739.3 | 48 | ||
285.17 | even | 36 | 475.2.l.f.226.6 | 48 | |||
285.32 | odd | 36 | 9025.2.a.ct.1.8 | 24 | |||
285.44 | odd | 18 | 1805.2.b.k.1084.17 | 24 | |||
285.74 | odd | 18 | 95.2.p.a.74.6 | yes | 48 | ||
285.89 | even | 18 | 1805.2.b.l.1084.8 | 24 | |||
285.158 | even | 36 | 9025.2.a.cu.1.8 | 24 | |||
285.188 | even | 36 | 475.2.l.f.226.3 | 48 | |||
285.203 | odd | 36 | 9025.2.a.ct.1.17 | 24 | |||
285.272 | even | 36 | 9025.2.a.cu.1.17 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.9.3 | ✓ | 48 | 15.14 | odd | 2 | ||
95.2.p.a.9.6 | yes | 48 | 3.2 | odd | 2 | ||
95.2.p.a.74.3 | yes | 48 | 57.17 | odd | 18 | ||
95.2.p.a.74.6 | yes | 48 | 285.74 | odd | 18 | ||
475.2.l.f.226.3 | 48 | 285.188 | even | 36 | |||
475.2.l.f.226.6 | 48 | 285.17 | even | 36 | |||
475.2.l.f.351.3 | 48 | 15.8 | even | 4 | |||
475.2.l.f.351.6 | 48 | 15.2 | even | 4 | |||
855.2.da.b.199.3 | 48 | 1.1 | even | 1 | trivial | ||
855.2.da.b.199.6 | 48 | 5.4 | even | 2 | inner | ||
855.2.da.b.739.3 | 48 | 95.74 | even | 18 | inner | ||
855.2.da.b.739.6 | 48 | 19.17 | even | 9 | inner | ||
1805.2.b.k.1084.8 | 24 | 57.44 | odd | 18 | |||
1805.2.b.k.1084.17 | 24 | 285.44 | odd | 18 | |||
1805.2.b.l.1084.8 | 24 | 285.89 | even | 18 | |||
1805.2.b.l.1084.17 | 24 | 57.32 | even | 18 | |||
9025.2.a.ct.1.8 | 24 | 285.32 | odd | 36 | |||
9025.2.a.ct.1.17 | 24 | 285.203 | odd | 36 | |||
9025.2.a.cu.1.8 | 24 | 285.158 | even | 36 | |||
9025.2.a.cu.1.17 | 24 | 285.272 | even | 36 |