Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(49,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.i (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 199.6 | ||
Character | \(\chi\) | \(=\) | 375.199 |
Dual form | 375.2.i.d.49.6 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{3}{10}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.26995 | + | 1.74793i | 0.897987 | + | 1.23597i | 0.971106 | + | 0.238650i | \(0.0767048\pi\) |
−0.0731189 | + | 0.997323i | \(0.523295\pi\) | |||||||
\(3\) | −0.951057 | − | 0.309017i | −0.549093 | − | 0.178411i | ||||
\(4\) | −0.824463 | + | 2.53744i | −0.412232 | + | 1.26872i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.667650 | − | 2.05481i | −0.272567 | − | 0.838875i | ||||
\(7\) | 3.16056i | 1.19458i | 0.802026 | + | 0.597290i | \(0.203756\pi\) | ||||
−0.802026 | + | 0.597290i | \(0.796244\pi\) | |||||||
\(8\) | −1.37265 | + | 0.446002i | −0.485307 | + | 0.157686i | ||||
\(9\) | 0.809017 | + | 0.587785i | 0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.24455 | + | 0.904220i | −0.375247 | + | 0.272633i | −0.759383 | − | 0.650644i | \(-0.774499\pi\) |
0.384137 | + | 0.923276i | \(0.374499\pi\) | |||||||
\(12\) | 1.56822 | − | 2.15847i | 0.452707 | − | 0.623097i | ||||
\(13\) | −3.08084 | + | 4.24041i | −0.854471 | + | 1.17608i | 0.128389 | + | 0.991724i | \(0.459019\pi\) |
−0.982860 | + | 0.184355i | \(0.940981\pi\) | |||||||
\(14\) | −5.52444 | + | 4.01374i | −1.47647 | + | 1.07272i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.79417 | + | 1.30354i | 0.448542 | + | 0.325885i | ||||
\(17\) | 1.22751 | − | 0.398843i | 0.297716 | − | 0.0967337i | −0.156351 | − | 0.987702i | \(-0.549973\pi\) |
0.454066 | + | 0.890968i | \(0.349973\pi\) | |||||||
\(18\) | 2.16056i | 0.509249i | ||||||||
\(19\) | −1.68287 | − | 5.17933i | −0.386076 | − | 1.18822i | −0.935696 | − | 0.352806i | \(-0.885228\pi\) |
0.549620 | − | 0.835415i | \(-0.314772\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.976667 | − | 3.00587i | 0.213126 | − | 0.655935i | ||||
\(22\) | −3.16103 | − | 1.02708i | −0.673933 | − | 0.218974i | ||||
\(23\) | 3.78677 | + | 5.21204i | 0.789596 | + | 1.08679i | 0.994158 | + | 0.107932i | \(0.0344230\pi\) |
−0.204562 | + | 0.978854i | \(0.565577\pi\) | |||||||
\(24\) | 1.44329 | 0.294611 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −11.3244 | −2.22090 | ||||||||
\(27\) | −0.587785 | − | 0.809017i | −0.113119 | − | 0.155695i | ||||
\(28\) | −8.01972 | − | 2.60577i | −1.51558 | − | 0.492443i | ||||
\(29\) | 0.730396 | − | 2.24793i | 0.135631 | − | 0.417430i | −0.860056 | − | 0.510199i | \(-0.829572\pi\) |
0.995688 | + | 0.0927690i | \(0.0295718\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.37989 | − | 4.24687i | −0.247836 | − | 0.762760i | −0.995157 | − | 0.0982974i | \(-0.968660\pi\) |
0.747321 | − | 0.664463i | \(-0.231340\pi\) | |||||||
\(32\) | 7.67809i | 1.35731i | ||||||||
\(33\) | 1.46306 | − | 0.475377i | 0.254686 | − | 0.0827525i | ||||
\(34\) | 2.25602 | + | 1.63910i | 0.386905 | + | 0.281103i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.15847 | + | 1.56822i | −0.359745 | + | 0.261370i | ||||
\(37\) | 3.50174 | − | 4.81973i | 0.575682 | − | 0.792358i | −0.417532 | − | 0.908662i | \(-0.637105\pi\) |
0.993214 | + | 0.116304i | \(0.0371048\pi\) | |||||||
\(38\) | 6.91596 | − | 9.51901i | 1.12192 | − | 1.54419i | ||||
\(39\) | 4.24041 | − | 3.08084i | 0.679009 | − | 0.493329i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.90269 | + | 5.01510i | 1.07802 | + | 0.783227i | 0.977336 | − | 0.211692i | \(-0.0678974\pi\) |
0.100683 | + | 0.994919i | \(0.467897\pi\) | |||||||
\(42\) | 6.49436 | − | 2.11015i | 1.00210 | − | 0.325603i | ||||
\(43\) | − | 8.48426i | − | 1.29384i | −0.762559 | − | 0.646919i | \(-0.776057\pi\) | ||
0.762559 | − | 0.646919i | \(-0.223943\pi\) | |||||||
\(44\) | −1.26831 | − | 3.90347i | −0.191206 | − | 0.588470i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.30129 | + | 13.2380i | −0.634191 | + | 1.95184i | ||||
\(47\) | −0.716212 | − | 0.232712i | −0.104470 | − | 0.0339445i | 0.256315 | − | 0.966593i | \(-0.417491\pi\) |
−0.360786 | + | 0.932649i | \(0.617491\pi\) | |||||||
\(48\) | −1.30354 | − | 1.79417i | −0.188150 | − | 0.258966i | ||||
\(49\) | −2.98914 | −0.427020 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.29068 | −0.180732 | ||||||||
\(52\) | −8.21974 | − | 11.3135i | −1.13987 | − | 1.56890i | ||||
\(53\) | 9.27271 | + | 3.01289i | 1.27371 | + | 0.413852i | 0.866359 | − | 0.499422i | \(-0.166454\pi\) |
0.407346 | + | 0.913274i | \(0.366454\pi\) | |||||||
\(54\) | 0.667650 | − | 2.05481i | 0.0908556 | − | 0.279625i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.40962 | − | 4.33836i | −0.188368 | − | 0.579737i | ||||
\(57\) | 5.44587i | 0.721324i | ||||||||
\(58\) | 4.85678 | − | 1.57806i | 0.637727 | − | 0.207210i | ||||
\(59\) | 3.32724 | + | 2.41738i | 0.433170 | + | 0.314717i | 0.782915 | − | 0.622128i | \(-0.213732\pi\) |
−0.349745 | + | 0.936845i | \(0.613732\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.65159 | − | 6.28574i | 1.10772 | − | 0.804807i | 0.125419 | − | 0.992104i | \(-0.459973\pi\) |
0.982303 | + | 0.187297i | \(0.0599726\pi\) | |||||||
\(62\) | 5.67084 | − | 7.80525i | 0.720198 | − | 0.991267i | ||||
\(63\) | −1.85773 | + | 2.55695i | −0.234052 | + | 0.322145i | ||||
\(64\) | −9.83243 | + | 7.14368i | −1.22905 | + | 0.892960i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.68893 | + | 1.95362i | 0.330984 | + | 0.240474i | ||||
\(67\) | −1.80572 | + | 0.586713i | −0.220604 | + | 0.0716785i | −0.417233 | − | 0.908799i | \(-0.637000\pi\) |
0.196630 | + | 0.980478i | \(0.437000\pi\) | |||||||
\(68\) | 3.44357i | 0.417594i | ||||||||
\(69\) | −1.99082 | − | 6.12712i | −0.239667 | − | 0.737619i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0219023 | + | 0.0674084i | −0.00259933 | + | 0.00799990i | −0.952348 | − | 0.305014i | \(-0.901339\pi\) |
0.949748 | + | 0.313014i | \(0.101339\pi\) | |||||||
\(72\) | −1.37265 | − | 0.446002i | −0.161769 | − | 0.0525619i | ||||
\(73\) | −2.35774 | − | 3.24515i | −0.275952 | − | 0.379816i | 0.648436 | − | 0.761270i | \(-0.275424\pi\) |
−0.924388 | + | 0.381454i | \(0.875424\pi\) | |||||||
\(74\) | 12.8716 | 1.49629 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 14.5297 | 1.66667 | ||||||||
\(77\) | −2.85784 | − | 3.93348i | −0.325681 | − | 0.448262i | ||||
\(78\) | 10.7702 | + | 3.49944i | 1.21948 | + | 0.396234i | ||||
\(79\) | −0.500141 | + | 1.53928i | −0.0562703 | + | 0.173182i | −0.975242 | − | 0.221143i | \(-0.929021\pi\) |
0.918971 | + | 0.394325i | \(0.129021\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 18.4343i | 2.03573i | ||||||||
\(83\) | −12.5053 | + | 4.06322i | −1.37263 | + | 0.445996i | −0.900241 | − | 0.435392i | \(-0.856610\pi\) |
−0.472393 | + | 0.881388i | \(0.656610\pi\) | |||||||
\(84\) | 6.82198 | + | 4.95646i | 0.744339 | + | 0.540794i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.8299 | − | 10.7745i | 1.59915 | − | 1.16185i | ||||
\(87\) | −1.38930 | + | 1.91220i | −0.148948 | + | 0.205010i | ||||
\(88\) | 1.30506 | − | 1.79626i | 0.139119 | − | 0.191481i | ||||
\(89\) | 5.88638 | − | 4.27671i | 0.623955 | − | 0.453330i | −0.230345 | − | 0.973109i | \(-0.573986\pi\) |
0.854301 | + | 0.519779i | \(0.173986\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.4021 | − | 9.73718i | −1.40492 | − | 1.02073i | ||||
\(92\) | −16.3473 | + | 5.31155i | −1.70432 | + | 0.553768i | ||||
\(93\) | 4.46542i | 0.463043i | ||||||||
\(94\) | −0.502787 | − | 1.54742i | −0.0518585 | − | 0.159604i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.37266 | − | 7.30230i | 0.242159 | − | 0.745288i | ||||
\(97\) | −9.69499 | − | 3.15009i | −0.984377 | − | 0.319843i | −0.227771 | − | 0.973715i | \(-0.573144\pi\) |
−0.756606 | + | 0.653871i | \(0.773144\pi\) | |||||||
\(98\) | −3.79604 | − | 5.22480i | −0.383458 | − | 0.527785i | ||||
\(99\) | −1.53835 | −0.154610 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.08759 | 0.108219 | 0.0541096 | − | 0.998535i | \(-0.482768\pi\) | ||||
0.0541096 | + | 0.998535i | \(0.482768\pi\) | |||||||
\(102\) | −1.63910 | − | 2.25602i | −0.162295 | − | 0.223380i | ||||
\(103\) | −4.69590 | − | 1.52579i | −0.462701 | − | 0.150341i | 0.0683845 | − | 0.997659i | \(-0.478216\pi\) |
−0.531085 | + | 0.847319i | \(0.678216\pi\) | |||||||
\(104\) | 2.33769 | − | 7.19468i | 0.229230 | − | 0.705497i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.50952 | + | 20.0343i | 0.632261 | + | 1.94590i | ||||
\(107\) | − | 15.3059i | − | 1.47967i | −0.672786 | − | 0.739837i | \(-0.734902\pi\) | ||
0.672786 | − | 0.739837i | \(-0.265098\pi\) | |||||||
\(108\) | 2.53744 | − | 0.824463i | 0.244165 | − | 0.0793340i | ||||
\(109\) | 5.38724 | + | 3.91406i | 0.516004 | + | 0.374899i | 0.815097 | − | 0.579325i | \(-0.196684\pi\) |
−0.299092 | + | 0.954224i | \(0.596684\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.81973 | + | 3.50174i | −0.457468 | + | 0.332370i | ||||
\(112\) | −4.11991 | + | 5.67058i | −0.389295 | + | 0.535819i | ||||
\(113\) | −5.27328 | + | 7.25804i | −0.496068 | + | 0.682779i | −0.981493 | − | 0.191499i | \(-0.938665\pi\) |
0.485425 | + | 0.874278i | \(0.338665\pi\) | |||||||
\(114\) | −9.51901 | + | 6.91596i | −0.891537 | + | 0.647739i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.10179 | + | 3.70667i | 0.473689 | + | 0.344155i | ||||
\(117\) | −4.98490 | + | 1.61969i | −0.460854 | + | 0.149741i | ||||
\(118\) | 8.88573i | 0.817998i | ||||||||
\(119\) | 1.26057 | + | 3.87963i | 0.115556 | + | 0.355645i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.66789 | + | 8.21092i | −0.242536 | + | 0.746448i | ||||
\(122\) | 21.9741 | + | 7.13981i | 1.98944 | + | 0.646408i | ||||
\(123\) | −5.01510 | − | 6.90269i | −0.452196 | − | 0.622395i | ||||
\(124\) | 11.9138 | 1.06989 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.82858 | −0.608338 | ||||||||
\(127\) | 5.88870 | + | 8.10511i | 0.522538 | + | 0.719212i | 0.985970 | − | 0.166920i | \(-0.0533823\pi\) |
−0.463432 | + | 0.886132i | \(0.653382\pi\) | |||||||
\(128\) | −10.3687 | − | 3.36899i | −0.916471 | − | 0.297780i | ||||
\(129\) | −2.62178 | + | 8.06901i | −0.230835 | + | 0.710437i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.97111 | − | 6.06645i | −0.172217 | − | 0.530029i | 0.827279 | − | 0.561792i | \(-0.189888\pi\) |
−0.999495 | + | 0.0317631i | \(0.989888\pi\) | |||||||
\(132\) | 4.10435i | 0.357238i | ||||||||
\(133\) | 16.3696 | − | 5.31880i | 1.41942 | − | 0.461199i | ||||
\(134\) | −3.31870 | − | 2.41117i | −0.286692 | − | 0.208294i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.50707 | + | 1.09495i | −0.129230 | + | 0.0938910i | ||||
\(137\) | 5.39429 | − | 7.42461i | 0.460866 | − | 0.634327i | −0.513822 | − | 0.857897i | \(-0.671771\pi\) |
0.974688 | + | 0.223570i | \(0.0717710\pi\) | |||||||
\(138\) | 8.18154 | − | 11.2609i | 0.696459 | − | 0.958594i | ||||
\(139\) | −7.49586 | + | 5.44606i | −0.635790 | + | 0.461929i | −0.858401 | − | 0.512979i | \(-0.828542\pi\) |
0.222611 | + | 0.974907i | \(0.428542\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.609247 | + | 0.442644i | 0.0513078 | + | 0.0372773i | ||||
\(142\) | −0.145640 | + | 0.0473213i | −0.0122218 | + | 0.00397111i | ||||
\(143\) | − | 8.06317i | − | 0.674276i | ||||||
\(144\) | 0.685311 | + | 2.10917i | 0.0571093 | + | 0.175764i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.67809 | − | 8.24232i | 0.221641 | − | 0.682140i | ||||
\(147\) | 2.84284 | + | 0.923695i | 0.234473 | + | 0.0761850i | ||||
\(148\) | 9.34270 | + | 12.8591i | 0.767965 | + | 1.05701i | ||||
\(149\) | 10.0817 | 0.825928 | 0.412964 | − | 0.910747i | \(-0.364494\pi\) | ||||
0.412964 | + | 0.910747i | \(0.364494\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7375 | 0.873804 | 0.436902 | − | 0.899509i | \(-0.356076\pi\) | ||||
0.436902 | + | 0.899509i | \(0.356076\pi\) | |||||||
\(152\) | 4.61999 | + | 6.35887i | 0.374731 | + | 0.515773i | ||||
\(153\) | 1.22751 | + | 0.398843i | 0.0992385 | + | 0.0322446i | ||||
\(154\) | 3.24615 | − | 9.99061i | 0.261582 | − | 0.805067i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.32137 | + | 13.2998i | 0.345987 | + | 1.06484i | ||||
\(157\) | − | 17.4417i | − | 1.39200i | −0.718041 | − | 0.696001i | \(-0.754961\pi\) | ||
0.718041 | − | 0.696001i | \(-0.245039\pi\) | |||||||
\(158\) | −3.32570 | + | 1.08058i | −0.264578 | + | 0.0859667i | ||||
\(159\) | −7.88784 | − | 5.73085i | −0.625546 | − | 0.454486i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.4730 | + | 11.9683i | −1.29825 | + | 0.943235i | ||||
\(162\) | −1.26995 | + | 1.74793i | −0.0997763 | + | 0.137330i | ||||
\(163\) | −9.55586 | + | 13.1525i | −0.748473 | + | 1.03018i | 0.249613 | + | 0.968346i | \(0.419697\pi\) |
−0.998086 | + | 0.0618392i | \(0.980303\pi\) | |||||||
\(164\) | −18.4165 | + | 13.3804i | −1.43809 | + | 1.04483i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −22.9832 | − | 16.6983i | −1.78385 | − | 1.29604i | ||||
\(167\) | −10.8331 | + | 3.51989i | −0.838290 | + | 0.272377i | −0.696533 | − | 0.717525i | \(-0.745275\pi\) |
−0.141757 | + | 0.989902i | \(0.545275\pi\) | |||||||
\(168\) | 4.56162i | 0.351936i | ||||||||
\(169\) | −4.47230 | − | 13.7643i | −0.344023 | − | 1.05879i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.68287 | − | 5.17933i | 0.128692 | − | 0.396074i | ||||
\(172\) | 21.5283 | + | 6.99496i | 1.64152 | + | 0.533361i | ||||
\(173\) | −5.55954 | − | 7.65205i | −0.422684 | − | 0.581775i | 0.543571 | − | 0.839363i | \(-0.317072\pi\) |
−0.966255 | + | 0.257589i | \(0.917072\pi\) | |||||||
\(174\) | −5.10672 | −0.387140 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.41162 | −0.257161 | ||||||||
\(177\) | −2.41738 | − | 3.32724i | −0.181702 | − | 0.250091i | ||||
\(178\) | 14.9508 | + | 4.85780i | 1.12061 | + | 0.364107i | ||||
\(179\) | −1.26001 | + | 3.87790i | −0.0941773 | + | 0.289848i | −0.987038 | − | 0.160484i | \(-0.948694\pi\) |
0.892861 | + | 0.450332i | \(0.148694\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.43633 | − | 10.5759i | −0.255421 | − | 0.786104i | −0.993747 | − | 0.111660i | \(-0.964383\pi\) |
0.738326 | − | 0.674444i | \(-0.235617\pi\) | |||||||
\(182\) | − | 35.7916i | − | 2.65305i | ||||||
\(183\) | −10.1705 | + | 3.30461i | −0.751829 | + | 0.244284i | ||||
\(184\) | −7.52251 | − | 5.46542i | −0.554567 | − | 0.402916i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.80525 | + | 5.67084i | −0.572308 | + | 0.415806i | ||||
\(187\) | −1.16706 | + | 1.60632i | −0.0853440 | + | 0.117466i | ||||
\(188\) | 1.18098 | − | 1.62548i | 0.0861319 | − | 0.118550i | ||||
\(189\) | 2.55695 | − | 1.85773i | 0.185990 | − | 0.135130i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.92164 | − | 2.12270i | −0.211403 | − | 0.153593i | 0.477046 | − | 0.878879i | \(-0.341708\pi\) |
−0.688448 | + | 0.725286i | \(0.741708\pi\) | |||||||
\(192\) | 11.5587 | − | 3.75565i | 0.834178 | − | 0.271041i | ||||
\(193\) | − | 17.0562i | − | 1.22774i | −0.789409 | − | 0.613868i | \(-0.789613\pi\) | ||
0.789409 | − | 0.613868i | \(-0.210387\pi\) | |||||||
\(194\) | −6.80596 | − | 20.9466i | −0.488640 | − | 1.50388i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.46443 | − | 7.58475i | 0.176031 | − | 0.541768i | ||||
\(197\) | 4.18963 | + | 1.36129i | 0.298498 | + | 0.0969880i | 0.454437 | − | 0.890779i | \(-0.349840\pi\) |
−0.155939 | + | 0.987767i | \(0.549840\pi\) | |||||||
\(198\) | −1.95362 | − | 2.68893i | −0.138838 | − | 0.191094i | ||||
\(199\) | −16.5956 | −1.17643 | −0.588214 | − | 0.808705i | \(-0.700169\pi\) | ||||
−0.588214 | + | 0.808705i | \(0.700169\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.89864 | 0.133920 | ||||||||
\(202\) | 1.38118 | + | 1.90103i | 0.0971795 | + | 0.133756i | ||||
\(203\) | 7.10471 | + | 2.30846i | 0.498653 | + | 0.162022i | ||||
\(204\) | 1.06412 | − | 3.27503i | 0.0745034 | − | 0.229298i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.29656 | − | 10.1458i | −0.229682 | − | 0.706889i | ||||
\(207\) | 6.44244i | 0.447780i | ||||||||
\(208\) | −11.0551 | + | 3.59202i | −0.766532 | + | 0.249061i | ||||
\(209\) | 6.77768 | + | 4.92427i | 0.468822 | + | 0.340619i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.0035 | + | 10.9007i | −1.03288 | + | 0.750434i | −0.968884 | − | 0.247516i | \(-0.920386\pi\) |
−0.0640001 | + | 0.997950i | \(0.520386\pi\) | |||||||
\(212\) | −15.2900 | + | 21.0449i | −1.05012 | + | 1.44537i | ||||
\(213\) | 0.0416607 | − | 0.0573410i | 0.00285454 | − | 0.00392894i | ||||
\(214\) | 26.7536 | − | 19.4376i | 1.82884 | − | 1.32873i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.16765 | + | 0.848347i | 0.0794485 | + | 0.0577227i | ||||
\(217\) | 13.4225 | − | 4.36123i | 0.911178 | − | 0.296060i | ||||
\(218\) | 14.3872i | 0.974422i | ||||||||
\(219\) | 1.23954 | + | 3.81490i | 0.0837601 | + | 0.257787i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.09051 | + | 6.43393i | −0.140623 | + | 0.432793i | ||||
\(222\) | −12.2416 | − | 3.97753i | −0.821601 | − | 0.266954i | ||||
\(223\) | 0.453510 | + | 0.624203i | 0.0303693 | + | 0.0417997i | 0.823932 | − | 0.566689i | \(-0.191776\pi\) |
−0.793562 | + | 0.608489i | \(0.791776\pi\) | |||||||
\(224\) | −24.2671 | −1.62141 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.3833 | −1.28936 | ||||||||
\(227\) | 6.71919 | + | 9.24817i | 0.445968 | + | 0.613823i | 0.971525 | − | 0.236936i | \(-0.0761430\pi\) |
−0.525557 | + | 0.850758i | \(0.676143\pi\) | |||||||
\(228\) | −13.8186 | − | 4.48992i | −0.915157 | − | 0.297352i | ||||
\(229\) | −3.15962 | + | 9.72432i | −0.208794 | + | 0.642601i | 0.790743 | + | 0.612149i | \(0.209695\pi\) |
−0.999536 | + | 0.0304520i | \(0.990305\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.50246 | + | 4.62409i | 0.0988544 | + | 0.304242i | ||||
\(232\) | 3.41139i | 0.223969i | ||||||||
\(233\) | 21.4206 | − | 6.95997i | 1.40331 | − | 0.455963i | 0.493050 | − | 0.870001i | \(-0.335882\pi\) |
0.910260 | + | 0.414038i | \(0.135882\pi\) | |||||||
\(234\) | −9.16166 | − | 6.65634i | −0.598917 | − | 0.435138i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.87715 | + | 6.44963i | −0.577853 | + | 0.419835i | ||||
\(237\) | 0.951325 | − | 1.30939i | 0.0617952 | − | 0.0850538i | ||||
\(238\) | −5.18047 | + | 7.13030i | −0.335800 | + | 0.462189i | ||||
\(239\) | −0.476571 | + | 0.346249i | −0.0308268 | + | 0.0223970i | −0.603092 | − | 0.797672i | \(-0.706065\pi\) |
0.572265 | + | 0.820069i | \(0.306065\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.22110 | − | 0.887185i | −0.0786583 | − | 0.0571486i | 0.547761 | − | 0.836635i | \(-0.315480\pi\) |
−0.626419 | + | 0.779486i | \(0.715480\pi\) | |||||||
\(242\) | −17.7402 | + | 5.76414i | −1.14038 | + | 0.370533i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 8.81677 | + | 27.1352i | 0.564436 | + | 1.73715i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.69652 | − | 17.5321i | 0.363197 | − | 1.11780i | ||||
\(247\) | 27.1472 | + | 8.82065i | 1.72733 | + | 0.561244i | ||||
\(248\) | 3.78823 | + | 5.21405i | 0.240553 | + | 0.331093i | ||||
\(249\) | 13.1488 | 0.833274 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.8953 | 0.750823 | 0.375412 | − | 0.926858i | \(-0.377501\pi\) | ||||
0.375412 | + | 0.926858i | \(0.377501\pi\) | |||||||
\(252\) | −4.95646 | − | 6.82198i | −0.312228 | − | 0.429744i | ||||
\(253\) | −9.42567 | − | 3.06258i | −0.592587 | − | 0.192543i | ||||
\(254\) | −6.68882 | + | 20.5861i | −0.419694 | + | 1.29169i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.232398 | + | 0.715248i | 0.0145249 | + | 0.0447030i | ||||
\(257\) | 18.0492i | 1.12588i | 0.826498 | + | 0.562939i | \(0.190329\pi\) | ||||
−0.826498 | + | 0.562939i | \(0.809671\pi\) | |||||||
\(258\) | −17.4336 | + | 5.66451i | −1.08537 | + | 0.352657i | ||||
\(259\) | 15.2330 | + | 11.0674i | 0.946534 | + | 0.687698i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.91220 | − | 1.38930i | 0.118362 | − | 0.0859953i | ||||
\(262\) | 8.10053 | − | 11.1494i | 0.500453 | − | 0.688814i | ||||
\(263\) | −11.2306 | + | 15.4576i | −0.692509 | + | 0.953157i | 0.307490 | + | 0.951551i | \(0.400511\pi\) |
−0.999999 | + | 0.00160518i | \(0.999489\pi\) | |||||||
\(264\) | −1.79626 | + | 1.30506i | −0.110552 | + | 0.0803206i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 30.0854 | + | 21.8583i | 1.84465 | + | 1.34022i | ||||
\(267\) | −6.91986 | + | 2.24840i | −0.423489 | + | 0.137600i | ||||
\(268\) | − | 5.06562i | − | 0.309432i | ||||||
\(269\) | 6.86791 | + | 21.1372i | 0.418744 | + | 1.28876i | 0.908859 | + | 0.417103i | \(0.136955\pi\) |
−0.490115 | + | 0.871658i | \(0.663045\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.24546 | − | 19.2216i | 0.379385 | − | 1.16763i | −0.561088 | − | 0.827756i | \(-0.689617\pi\) |
0.940472 | − | 0.339870i | \(-0.110383\pi\) | |||||||
\(272\) | 2.72227 | + | 0.884520i | 0.165062 | + | 0.0536319i | ||||
\(273\) | 9.73718 | + | 13.4021i | 0.589321 | + | 0.811130i | ||||
\(274\) | 19.8281 | 1.19786 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 17.1885 | 1.03463 | ||||||||
\(277\) | −9.42882 | − | 12.9777i | −0.566523 | − | 0.779752i | 0.425615 | − | 0.904904i | \(-0.360058\pi\) |
−0.992137 | + | 0.125153i | \(0.960058\pi\) | |||||||
\(278\) | −19.0387 | − | 6.18604i | −1.14186 | − | 0.371014i | ||||
\(279\) | 1.37989 | − | 4.24687i | 0.0826120 | − | 0.254253i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.58742 | + | 7.96327i | 0.154353 | + | 0.475049i | 0.998095 | − | 0.0617001i | \(-0.0196522\pi\) |
−0.843742 | + | 0.536749i | \(0.819652\pi\) | |||||||
\(282\) | 1.62705i | 0.0968896i | ||||||||
\(283\) | 1.07465 | − | 0.349174i | 0.0638811 | − | 0.0207562i | −0.276902 | − | 0.960898i | \(-0.589308\pi\) |
0.340783 | + | 0.940142i | \(0.389308\pi\) | |||||||
\(284\) | −0.152987 | − | 0.111151i | −0.00907810 | − | 0.00659563i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.0939 | − | 10.2398i | 0.833387 | − | 0.605491i | ||||
\(287\) | −15.8505 | + | 21.8164i | −0.935626 | + | 1.28778i | ||||
\(288\) | −4.51307 | + | 6.21171i | −0.265935 | + | 0.366028i | ||||
\(289\) | −12.4056 | + | 9.01318i | −0.729740 | + | 0.530187i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.24705 | + | 5.99183i | 0.483451 | + | 0.351247i | ||||
\(292\) | 10.1782 | − | 3.30711i | 0.595636 | − | 0.193534i | ||||
\(293\) | − | 2.37857i | − | 0.138958i | −0.997583 | − | 0.0694789i | \(-0.977866\pi\) | ||
0.997583 | − | 0.0694789i | \(-0.0221337\pi\) | |||||||
\(294\) | 1.99570 | + | 6.14212i | 0.116391 | + | 0.358216i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.65706 | + | 8.17760i | −0.154439 | + | 0.475313i | ||||
\(297\) | 1.46306 | + | 0.475377i | 0.0848953 | + | 0.0275842i | ||||
\(298\) | 12.8032 | + | 17.6222i | 0.741672 | + | 1.02082i | ||||
\(299\) | −33.7676 | −1.95283 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.8150 | 1.54559 | ||||||||
\(302\) | 13.6360 | + | 18.7684i | 0.784665 | + | 1.08000i | ||||
\(303\) | −1.03436 | − | 0.336084i | −0.0594224 | − | 0.0193075i | ||||
\(304\) | 3.73212 | − | 11.4863i | 0.214052 | − | 0.658783i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.861724 | + | 2.65212i | 0.0492615 | + | 0.151611i | ||||
\(307\) | − | 2.89366i | − | 0.165150i | −0.996585 | − | 0.0825748i | \(-0.973686\pi\) | ||
0.996585 | − | 0.0825748i | \(-0.0263143\pi\) | |||||||
\(308\) | 12.3371 | − | 4.00858i | 0.702974 | − | 0.228410i | ||||
\(309\) | 3.99457 | + | 2.90222i | 0.227243 | + | 0.165102i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.78079 | − | 4.19999i | 0.327799 | − | 0.238160i | −0.411697 | − | 0.911321i | \(-0.635064\pi\) |
0.739496 | + | 0.673161i | \(0.235064\pi\) | |||||||
\(312\) | −4.44656 | + | 6.12016i | −0.251737 | + | 0.346486i | ||||
\(313\) | 13.5378 | − | 18.6331i | 0.765200 | − | 1.05321i | −0.231563 | − | 0.972820i | \(-0.574384\pi\) |
0.996764 | − | 0.0803879i | \(-0.0256159\pi\) | |||||||
\(314\) | 30.4869 | − | 22.1500i | 1.72048 | − | 1.25000i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.49347 | − | 2.53815i | −0.196523 | − | 0.142782i | ||||
\(317\) | −19.7582 | + | 6.41981i | −1.10973 | + | 0.360573i | −0.805839 | − | 0.592135i | \(-0.798285\pi\) |
−0.303890 | + | 0.952707i | \(0.598285\pi\) | |||||||
\(318\) | − | 21.0653i | − | 1.18128i | ||||||
\(319\) | 1.12361 | + | 3.45810i | 0.0629098 | + | 0.193617i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.72978 | + | 14.5568i | −0.263990 | + | 0.812479i | ||||
\(322\) | −41.8395 | − | 13.5945i | −2.33163 | − | 0.757591i | ||||
\(323\) | −4.13148 | − | 5.68650i | −0.229882 | − | 0.316405i | ||||
\(324\) | −2.66802 | −0.148223 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −35.1251 | −1.94540 | ||||||||
\(327\) | −3.91406 | − | 5.38724i | −0.216448 | − | 0.297915i | ||||
\(328\) | −11.7118 | − | 3.80538i | −0.646673 | − | 0.210117i | ||||
\(329\) | 0.735499 | − | 2.26363i | 0.0405494 | − | 0.124798i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.94869 | − | 18.3082i | −0.326969 | − | 1.00631i | −0.970544 | − | 0.240925i | \(-0.922549\pi\) |
0.643574 | − | 0.765383i | \(-0.277451\pi\) | |||||||
\(332\) | − | 35.0814i | − | 1.92534i | ||||||
\(333\) | 5.66593 | − | 1.84097i | 0.310491 | − | 0.100885i | ||||
\(334\) | −19.9099 | − | 14.4654i | −1.08942 | − | 0.791513i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.67058 | − | 4.11991i | 0.309355 | − | 0.224760i | ||||
\(337\) | −12.7587 | + | 17.5609i | −0.695012 | + | 0.956602i | 0.304979 | + | 0.952359i | \(0.401351\pi\) |
−0.999991 | + | 0.00424305i | \(0.998649\pi\) | |||||||
\(338\) | 18.3795 | − | 25.2972i | 0.999712 | − | 1.37599i | ||||
\(339\) | 7.25804 | − | 5.27328i | 0.394203 | − | 0.286405i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.55745 | + | 4.03773i | 0.300953 | + | 0.218655i | ||||
\(342\) | 11.1903 | − | 3.63594i | 0.605100 | − | 0.196609i | ||||
\(343\) | 12.6766i | 0.684470i | ||||||||
\(344\) | 3.78400 | + | 11.6460i | 0.204020 | + | 0.627908i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.31493 | − | 19.4354i | 0.339493 | − | 1.04485i | ||||
\(347\) | 1.63100 | + | 0.529944i | 0.0875567 | + | 0.0284489i | 0.352468 | − | 0.935824i | \(-0.385343\pi\) |
−0.264911 | + | 0.964273i | \(0.585343\pi\) | |||||||
\(348\) | −3.70667 | − | 5.10179i | −0.198698 | − | 0.273485i | ||||
\(349\) | 15.5553 | 0.832654 | 0.416327 | − | 0.909215i | \(-0.363317\pi\) | ||||
0.416327 | + | 0.909215i | \(0.363317\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.24144 | 0.279767 | ||||||||
\(352\) | −6.94268 | − | 9.55579i | −0.370046 | − | 0.509325i | ||||
\(353\) | 14.7923 | + | 4.80632i | 0.787316 | + | 0.255814i | 0.674961 | − | 0.737854i | \(-0.264161\pi\) |
0.112355 | + | 0.993668i | \(0.464161\pi\) | |||||||
\(354\) | 2.74584 | − | 8.45083i | 0.145940 | − | 0.449157i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.99877 | + | 18.4623i | 0.317934 | + | 0.978501i | ||||
\(357\) | − | 4.07928i | − | 0.215899i | ||||||
\(358\) | −8.37844 | + | 2.72232i | −0.442814 | + | 0.143879i | ||||
\(359\) | −19.8509 | − | 14.4225i | −1.04769 | − | 0.761191i | −0.0759181 | − | 0.997114i | \(-0.524189\pi\) |
−0.971772 | + | 0.235923i | \(0.924189\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.62214 | + | 6.26435i | −0.453797 | + | 0.329703i | ||||
\(362\) | 14.1221 | − | 19.4373i | 0.742239 | − | 1.02160i | ||||
\(363\) | 5.07463 | − | 6.98463i | 0.266349 | − | 0.366598i | ||||
\(364\) | 35.7570 | − | 25.9790i | 1.87418 | − | 1.36167i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −18.6923 | − | 13.5807i | −0.977060 | − | 0.709876i | ||||
\(367\) | 26.7311 | − | 8.68548i | 1.39535 | − | 0.453378i | 0.487669 | − | 0.873029i | \(-0.337847\pi\) |
0.907686 | + | 0.419651i | \(0.137847\pi\) | |||||||
\(368\) | 14.2875i | 0.744786i | ||||||||
\(369\) | 2.63659 | + | 8.11460i | 0.137256 | + | 0.422429i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.52241 | + | 29.3070i | −0.494379 | + | 1.52154i | ||||
\(372\) | −11.3307 | − | 3.68158i | −0.587471 | − | 0.190881i | ||||
\(373\) | 5.70637 | + | 7.85414i | 0.295464 | + | 0.406672i | 0.930779 | − | 0.365581i | \(-0.119130\pi\) |
−0.635315 | + | 0.772253i | \(0.719130\pi\) | |||||||
\(374\) | −4.28984 | −0.221823 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.08690 | 0.0560527 | ||||||||
\(377\) | 7.28191 | + | 10.0227i | 0.375037 | + | 0.516195i | ||||
\(378\) | 6.49436 | + | 2.11015i | 0.334034 | + | 0.108534i | ||||
\(379\) | 6.88071 | − | 21.1767i | 0.353438 | − | 1.08777i | −0.603471 | − | 0.797385i | \(-0.706216\pi\) |
0.956909 | − | 0.290387i | \(-0.0937839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.09587 | − | 9.52812i | −0.158606 | − | 0.488141i | ||||
\(382\) | − | 7.80253i | − | 0.399212i | ||||||
\(383\) | 12.9628 | − | 4.21189i | 0.662371 | − | 0.215217i | 0.0415099 | − | 0.999138i | \(-0.486783\pi\) |
0.620861 | + | 0.783921i | \(0.286783\pi\) | |||||||
\(384\) | 8.82014 | + | 6.40820i | 0.450101 | + | 0.327017i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 29.8131 | − | 21.6605i | 1.51745 | − | 1.10249i | ||||
\(387\) | 4.98692 | − | 6.86391i | 0.253500 | − | 0.348912i | ||||
\(388\) | 15.9863 | − | 22.0033i | 0.811582 | − | 1.11705i | ||||
\(389\) | 15.5577 | − | 11.3034i | 0.788808 | − | 0.573103i | −0.118801 | − | 0.992918i | \(-0.537905\pi\) |
0.907610 | + | 0.419815i | \(0.137905\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.72710 | + | 4.88752i | 0.340204 | + | 0.247173i | ||||
\(392\) | 4.10305 | − | 1.33316i | 0.207236 | − | 0.0673349i | ||||
\(393\) | 6.37865i | 0.321760i | ||||||||
\(394\) | 2.94115 | + | 9.05194i | 0.148173 | + | 0.456030i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.26831 | − | 3.90347i | 0.0637352 | − | 0.196157i | ||||
\(397\) | −21.1402 | − | 6.86887i | −1.06100 | − | 0.344739i | −0.274022 | − | 0.961723i | \(-0.588354\pi\) |
−0.786975 | + | 0.616984i | \(0.788354\pi\) | |||||||
\(398\) | −21.0755 | − | 29.0079i | −1.05642 | − | 1.45403i | ||||
\(399\) | −17.2120 | −0.861678 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.71728 | 0.235570 | 0.117785 | − | 0.993039i | \(-0.462421\pi\) | ||||
0.117785 | + | 0.993039i | \(0.462421\pi\) | |||||||
\(402\) | 2.41117 | + | 3.31870i | 0.120258 | + | 0.165522i | ||||
\(403\) | 22.2597 | + | 7.23261i | 1.10883 | + | 0.360282i | ||||
\(404\) | −0.896678 | + | 2.75969i | −0.0446114 | + | 0.137300i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.98757 | + | 15.3502i | 0.247529 | + | 0.761815i | ||||
\(407\) | 9.16474i | 0.454279i | ||||||||
\(408\) | 1.77166 | − | 0.575648i | 0.0877104 | − | 0.0284988i | ||||
\(409\) | −10.0971 | − | 7.33597i | −0.499269 | − | 0.362740i | 0.309469 | − | 0.950910i | \(-0.399849\pi\) |
−0.808738 | + | 0.588169i | \(0.799849\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.42461 | + | 5.39429i | −0.366229 | + | 0.266081i | ||||
\(412\) | 7.74319 | − | 10.6576i | 0.381480 | − | 0.525062i | ||||
\(413\) | −7.64029 | + | 10.5160i | −0.375954 | + | 0.517456i | ||||
\(414\) | −11.2609 | + | 8.18154i | −0.553444 | + | 0.402101i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −32.5583 | − | 23.6550i | −1.59630 | − | 1.15978i | ||||
\(417\) | 8.81191 | − | 2.86316i | 0.431521 | − | 0.140210i | ||||
\(418\) | 18.1005i | 0.885322i | ||||||||
\(419\) | −10.7996 | − | 33.2379i | −0.527597 | − | 1.62378i | −0.759123 | − | 0.650947i | \(-0.774372\pi\) |
0.231527 | − | 0.972829i | \(-0.425628\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.2247 | + | 37.6239i | −0.595797 | + | 1.83368i | −0.0450804 | + | 0.998983i | \(0.514354\pi\) |
−0.550717 | + | 0.834692i | \(0.685646\pi\) | |||||||
\(422\) | −38.1073 | − | 12.3818i | −1.85503 | − | 0.602737i | ||||
\(423\) | −0.442644 | − | 0.609247i | −0.0215221 | − | 0.0296226i | ||||
\(424\) | −14.0720 | −0.683396 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.153135 | 0.00741940 | ||||||||
\(427\) | 19.8665 | + | 27.3439i | 0.961406 | + | 1.32326i | ||||
\(428\) | 38.8377 | + | 12.6191i | 1.87729 | + | 0.609969i | ||||
\(429\) | −2.49166 | + | 7.66853i | −0.120298 | + | 0.370240i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.34429 | − | 13.3703i | −0.209257 | − | 0.644027i | −0.999512 | − | 0.0312481i | \(-0.990052\pi\) |
0.790255 | − | 0.612778i | \(-0.209948\pi\) | |||||||
\(432\) | − | 2.21771i | − | 0.106700i | ||||||
\(433\) | 0.522775 | − | 0.169860i | 0.0251230 | − | 0.00816294i | −0.296429 | − | 0.955055i | \(-0.595796\pi\) |
0.321552 | + | 0.946892i | \(0.395796\pi\) | |||||||
\(434\) | 24.6689 | + | 17.9230i | 1.18415 | + | 0.860333i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.3733 | + | 10.4428i | −0.688355 | + | 0.500119i | ||||
\(437\) | 20.6223 | − | 28.3841i | 0.986497 | − | 1.35780i | ||||
\(438\) | −5.09404 | + | 7.01134i | −0.243402 | + | 0.335015i | ||||
\(439\) | −2.40583 | + | 1.74794i | −0.114824 | + | 0.0834245i | −0.643715 | − | 0.765265i | \(-0.722608\pi\) |
0.528891 | + | 0.848690i | \(0.322608\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.41826 | − | 1.75697i | −0.115155 | − | 0.0836653i | ||||
\(442\) | −13.9009 | + | 4.51667i | −0.661198 | + | 0.214836i | ||||
\(443\) | − | 36.6893i | − | 1.74316i | −0.490253 | − | 0.871580i | \(-0.663095\pi\) | ||
0.490253 | − | 0.871580i | \(-0.336905\pi\) | |||||||
\(444\) | −4.91175 | − | 15.1168i | −0.233101 | − | 0.717412i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.515130 | + | 1.58541i | −0.0243921 | + | 0.0750712i | ||||
\(447\) | −9.58830 | − | 3.11543i | −0.453511 | − | 0.147355i | ||||
\(448\) | −22.5780 | − | 31.0760i | −1.06671 | − | 1.46820i | ||||
\(449\) | 17.8432 | 0.842071 | 0.421036 | − | 0.907044i | \(-0.361667\pi\) | ||||
0.421036 | + | 0.907044i | \(0.361667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.1255 | −0.618056 | ||||||||
\(452\) | −14.0692 | − | 19.3646i | −0.661759 | − | 0.910834i | ||||
\(453\) | −10.2120 | − | 3.31807i | −0.479800 | − | 0.155896i | ||||
\(454\) | −7.63215 | + | 23.4893i | −0.358195 | + | 1.10241i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.42887 | − | 7.47530i | −0.113742 | − | 0.350063i | ||||
\(457\) | 24.1784i | 1.13102i | 0.824742 | + | 0.565509i | \(0.191320\pi\) | ||||
−0.824742 | + | 0.565509i | \(0.808680\pi\) | |||||||
\(458\) | −21.0100 | + | 6.82655i | −0.981731 | + | 0.318984i | ||||
\(459\) | −1.04418 | − | 0.758645i | −0.0487384 | − | 0.0354105i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.2470 | − | 21.9757i | 1.40874 | − | 1.02351i | 0.415240 | − | 0.909712i | \(-0.363698\pi\) |
0.993504 | − | 0.113800i | \(-0.0363024\pi\) | |||||||
\(462\) | −6.17454 | + | 8.49852i | −0.287266 | + | 0.395387i | ||||
\(463\) | 12.0093 | − | 16.5294i | 0.558120 | − | 0.768186i | −0.432966 | − | 0.901410i | \(-0.642533\pi\) |
0.991086 | + | 0.133224i | \(0.0425331\pi\) | |||||||
\(464\) | 4.24072 | − | 3.08106i | 0.196870 | − | 0.143035i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 39.3685 | + | 28.6029i | 1.82371 | + | 1.32500i | ||||
\(467\) | 29.6848 | − | 9.64517i | 1.37365 | − | 0.446325i | 0.473072 | − | 0.881024i | \(-0.343145\pi\) |
0.900576 | + | 0.434699i | \(0.143145\pi\) | |||||||
\(468\) | − | 13.9843i | − | 0.646422i | ||||||
\(469\) | −1.85434 | − | 5.70708i | −0.0856256 | − | 0.263529i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.38979 | + | 16.5881i | −0.248348 | + | 0.764338i | ||||
\(472\) | −5.64532 | − | 1.83427i | −0.259847 | − | 0.0844293i | ||||
\(473\) | 7.67164 | + | 10.5591i | 0.352742 | + | 0.485508i | ||||
\(474\) | 3.49684 | 0.160615 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10.8836 | −0.498849 | ||||||||
\(477\) | 5.73085 | + | 7.88784i | 0.262398 | + | 0.361159i | ||||
\(478\) | −1.21044 | − | 0.393295i | −0.0553641 | − | 0.0179889i | ||||
\(479\) | −3.42915 | + | 10.5538i | −0.156682 | + | 0.482217i | −0.998327 | − | 0.0578133i | \(-0.981587\pi\) |
0.841646 | + | 0.540030i | \(0.181587\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.64933 | + | 29.6976i | 0.439972 | + | 1.35409i | ||||
\(482\) | − | 3.26108i | − | 0.148538i | ||||||
\(483\) | 19.3651 | − | 6.29211i | 0.881144 | − | 0.286301i | ||||
\(484\) | −18.6351 | − | 13.5392i | −0.847051 | − | 0.615418i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.74793 | − | 1.26995i | 0.0792877 | − | 0.0576059i | ||||
\(487\) | −4.19504 | + | 5.77397i | −0.190095 | + | 0.261644i | −0.893417 | − | 0.449228i | \(-0.851699\pi\) |
0.703322 | + | 0.710871i | \(0.251699\pi\) | |||||||
\(488\) | −9.07218 | + | 12.4868i | −0.410678 | + | 0.565250i | ||||
\(489\) | 13.1525 | − | 9.55586i | 0.594777 | − | 0.432131i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.85201 | − | 4.25173i | −0.264097 | − | 0.191878i | 0.447854 | − | 0.894107i | \(-0.352188\pi\) |
−0.711951 | + | 0.702229i | \(0.752188\pi\) | |||||||
\(492\) | 21.6499 | − | 7.03448i | 0.976053 | − | 0.317139i | ||||
\(493\) | − | 3.05067i | − | 0.137395i | ||||||
\(494\) | 19.0575 | + | 58.6531i | 0.857439 | + | 2.63893i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.06020 | − | 9.41834i | 0.137407 | − | 0.422896i | ||||
\(497\) | −0.213048 | − | 0.0692236i | −0.00955652 | − | 0.00310510i | ||||
\(498\) | 16.6983 | + | 22.9832i | 0.748269 | + | 1.02990i | ||||
\(499\) | −16.0169 | −0.717014 | −0.358507 | − | 0.933527i | \(-0.616714\pi\) | ||||
−0.358507 | + | 0.933527i | \(0.616714\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.3906 | 0.508894 | ||||||||
\(502\) | 15.1063 | + | 20.7921i | 0.674229 | + | 0.927997i | ||||
\(503\) | −32.1422 | − | 10.4436i | −1.43315 | − | 0.465659i | −0.513396 | − | 0.858152i | \(-0.671613\pi\) |
−0.919755 | + | 0.392492i | \(0.871613\pi\) | |||||||
\(504\) | 1.40962 | − | 4.33836i | 0.0627894 | − | 0.193246i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.61690 | − | 20.3647i | −0.294157 | − | 0.905322i | ||||
\(507\) | 14.4727i | 0.642753i | ||||||||
\(508\) | −25.4212 | + | 8.25985i | −1.12788 | + | 0.366472i | ||||
\(509\) | −29.4701 | − | 21.4113i | −1.30624 | − | 0.949038i | −0.306243 | − | 0.951953i | \(-0.599072\pi\) |
−0.999996 | + | 0.00291563i | \(0.999072\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.2565 | − | 7.45178i | 0.453720 | − | 0.329647i | ||||
\(512\) | −13.7715 | + | 18.9548i | −0.608619 | + | 0.837692i | ||||
\(513\) | −3.20100 | + | 4.40581i | −0.141328 | + | 0.194521i | ||||
\(514\) | −31.5487 | + | 22.9215i | −1.39156 | + | 1.01102i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −18.3130 | − | 13.3052i | −0.806187 | − | 0.585729i | ||||
\(517\) | 1.10179 | − | 0.357992i | 0.0484565 | − | 0.0157445i | ||||
\(518\) | 40.6813i | 1.78743i | ||||||||
\(519\) | 2.92282 | + | 8.99552i | 0.128298 | + | 0.394860i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.87972 | − | 24.2513i | 0.345217 | − | 1.06247i | −0.616251 | − | 0.787550i | \(-0.711349\pi\) |
0.961468 | − | 0.274918i | \(-0.0886507\pi\) | |||||||
\(522\) | 4.85678 | + | 1.57806i | 0.212576 | + | 0.0690700i | ||||
\(523\) | 4.13315 | + | 5.68880i | 0.180730 | + | 0.248754i | 0.889764 | − | 0.456420i | \(-0.150869\pi\) |
−0.709034 | + | 0.705174i | \(0.750869\pi\) | |||||||
\(524\) | 17.0184 | 0.743450 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −41.2811 | −1.79994 | ||||||||
\(527\) | −3.38767 | − | 4.66273i | −0.147569 | − | 0.203112i | ||||
\(528\) | 3.24465 | + | 1.05425i | 0.141205 | + | 0.0458803i | ||||
\(529\) | −5.71836 | + | 17.5993i | −0.248624 | + | 0.765187i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.27089 | + | 3.91141i | 0.0551521 | + | 0.169741i | ||||
\(532\) | 45.9220i | 1.99097i | ||||||||
\(533\) | −42.5322 | + | 13.8195i | −1.84227 | + | 0.598590i | ||||
\(534\) | −12.7179 | − | 9.24008i | −0.550357 | − | 0.399858i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.21695 | − | 1.61071i | 0.0957577 | − | 0.0695721i | ||||
\(537\) | 2.39667 | − | 3.29874i | 0.103424 | − | 0.142351i | ||||
\(538\) | −28.2246 | + | 38.8478i | −1.21685 | + | 1.67485i | ||||
\(539\) | 3.72014 | − | 2.70284i | 0.160238 | − | 0.116420i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.9629 | + | 15.9570i | 0.944258 | + | 0.686044i | 0.949442 | − | 0.313943i | \(-0.101650\pi\) |
−0.00518365 | + | 0.999987i | \(0.501650\pi\) | |||||||
\(542\) | 41.5293 | − | 13.4937i | 1.78384 | − | 0.579604i | ||||
\(543\) | 11.1202i | 0.477214i | ||||||||
\(544\) | 3.06235 | + | 9.42496i | 0.131297 | + | 0.404092i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.0602 | + | 34.0398i | −0.473333 | + | 1.45677i | ||||
\(547\) | −41.9196 | − | 13.6205i | −1.79235 | − | 0.582371i | −0.792723 | − | 0.609582i | \(-0.791337\pi\) |
−0.999630 | + | 0.0272113i | \(0.991337\pi\) | |||||||
\(548\) | 14.3921 | + | 19.8090i | 0.614799 | + | 0.846198i | ||||
\(549\) | 10.6939 | 0.456407 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.8719 | −0.548363 | ||||||||
\(552\) | 5.46542 | + | 7.52251i | 0.232624 | + | 0.320179i | ||||
\(553\) | −4.86497 | − | 1.58073i | −0.206880 | − | 0.0672193i | ||||
\(554\) | 10.7099 | − | 32.9618i | 0.455022 | − | 1.40041i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.63897 | − | 23.5103i | −0.323965 | − | 0.997061i | ||||
\(557\) | 9.85667i | 0.417641i | 0.977954 | + | 0.208820i | \(0.0669624\pi\) | ||||
−0.977954 | + | 0.208820i | \(0.933038\pi\) | |||||||
\(558\) | 9.17562 | − | 2.98134i | 0.388435 | − | 0.126210i | ||||
\(559\) | 35.9768 | + | 26.1386i | 1.52165 | + | 1.10555i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.60632 | − | 1.16706i | 0.0678190 | − | 0.0492734i | ||||
\(562\) | −10.6334 | + | 14.6356i | −0.448541 | + | 0.617363i | ||||
\(563\) | −7.28367 | + | 10.0251i | −0.306970 | + | 0.422508i | −0.934433 | − | 0.356138i | \(-0.884093\pi\) |
0.627463 | + | 0.778646i | \(0.284093\pi\) | |||||||
\(564\) | −1.62548 | + | 1.18098i | −0.0684451 | + | 0.0497283i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.97507 | + | 1.43497i | 0.0830185 | + | 0.0603165i | ||||
\(567\) | −3.00587 | + | 0.976667i | −0.126235 | + | 0.0410161i | ||||
\(568\) | − | 0.102297i | − | 0.00429228i | ||||||
\(569\) | 3.62037 | + | 11.1424i | 0.151774 | + | 0.467112i | 0.997820 | − | 0.0659983i | \(-0.0210232\pi\) |
−0.846046 | + | 0.533110i | \(0.821023\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.95523 | − | 27.5614i | 0.374765 | − | 1.15341i | −0.568872 | − | 0.822426i | \(-0.692620\pi\) |
0.943637 | − | 0.330982i | \(-0.107380\pi\) | |||||||
\(572\) | 20.4598 | + | 6.64779i | 0.855467 | + | 0.277958i | ||||
\(573\) | 2.12270 | + | 2.92164i | 0.0886769 | + | 0.122053i | ||||
\(574\) | −58.2628 | −2.43184 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.1535 | −0.506398 | ||||||||
\(577\) | −19.2808 | − | 26.5377i | −0.802668 | − | 1.10478i | −0.992414 | − | 0.122945i | \(-0.960766\pi\) |
0.189745 | − | 0.981833i | \(-0.439234\pi\) | |||||||
\(578\) | −31.5088 | − | 10.2378i | −1.31059 | − | 0.425838i | ||||
\(579\) | −5.27067 | + | 16.2215i | −0.219042 | + | 0.674141i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.8420 | − | 39.5237i | −0.532777 | − | 1.63972i | ||||
\(582\) | 22.0246i | 0.912947i | ||||||||
\(583\) | −14.2647 | + | 4.63488i | −0.590783 | + | 0.191957i | ||||
\(584\) | 4.68371 | + | 3.40291i | 0.193813 | + | 0.140813i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.15758 | − | 3.02066i | 0.171748 | − | 0.124782i | ||||
\(587\) | −10.9560 | + | 15.0797i | −0.452203 | + | 0.622405i | −0.972869 | − | 0.231356i | \(-0.925684\pi\) |
0.520666 | + | 0.853761i | \(0.325684\pi\) | |||||||
\(588\) | −4.68763 | + | 6.45197i | −0.193315 | + | 0.266075i | ||||
\(589\) | −19.6738 | + | 14.2938i | −0.810644 | + | 0.588967i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.56391 | − | 2.58933i | −0.146600 | − | 0.106511i | ||||
\(592\) | 12.5654 | − | 4.08275i | 0.516435 | − | 0.167800i | ||||
\(593\) | 1.55882i | 0.0640129i | 0.999488 | + | 0.0320064i | \(0.0101897\pi\) | ||||
−0.999488 | + | 0.0320064i | \(0.989810\pi\) | |||||||
\(594\) | 1.02708 | + | 3.16103i | 0.0421416 | + | 0.129698i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.31202 | + | 25.5818i | −0.340474 | + | 1.04787i | ||||
\(597\) | 15.7833 | + | 5.12831i | 0.645969 | + | 0.209888i | ||||
\(598\) | −42.8830 | − | 59.0234i | −1.75362 | − | 2.41365i | ||||
\(599\) | 31.5470 | 1.28898 | 0.644489 | − | 0.764614i | \(-0.277070\pi\) | ||||
0.644489 | + | 0.764614i | \(0.277070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.3999 | −1.32162 | −0.660809 | − | 0.750554i | \(-0.729787\pi\) | ||||
−0.660809 | + | 0.750554i | \(0.729787\pi\) | |||||||
\(602\) | 34.0536 | + | 46.8707i | 1.38792 | + | 1.91031i | ||||
\(603\) | −1.80572 | − | 0.586713i | −0.0735345 | − | 0.0238928i | ||||
\(604\) | −8.85266 | + | 27.2457i | −0.360210 | + | 1.10861i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.726129 | − | 2.23480i | −0.0294970 | − | 0.0907824i | ||||
\(607\) | − | 24.8410i | − | 1.00827i | −0.863626 | − | 0.504133i | \(-0.831812\pi\) | ||
0.863626 | − | 0.504133i | \(-0.168188\pi\) | |||||||
\(608\) | 39.7674 | − | 12.9212i | 1.61278 | − | 0.524024i | ||||
\(609\) | −6.04363 | − | 4.39095i | −0.244900 | − | 0.177930i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.19333 | − | 2.32009i | 0.129188 | − | 0.0938607i | ||||
\(612\) | −2.02408 | + | 2.78590i | −0.0818185 | + | 0.112614i | ||||
\(613\) | −2.31915 | + | 3.19204i | −0.0936697 | + | 0.128925i | −0.853280 | − | 0.521454i | \(-0.825390\pi\) |
0.759610 | + | 0.650379i | \(0.225390\pi\) | |||||||
\(614\) | 5.05791 | − | 3.67478i | 0.204120 | − | 0.148302i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.67717 | + | 4.12471i | 0.228740 | + | 0.166189i | ||||
\(617\) | −16.6264 | + | 5.40225i | −0.669354 | + | 0.217486i | −0.623929 | − | 0.781481i | \(-0.714464\pi\) |
−0.0454257 | + | 0.998968i | \(0.514464\pi\) | |||||||
\(618\) | 10.6679i | 0.429126i | ||||||||
\(619\) | 4.44581 | + | 13.6828i | 0.178692 | + | 0.549958i | 0.999783 | − | 0.0208398i | \(-0.00663400\pi\) |
−0.821091 | + | 0.570798i | \(0.806634\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.99082 | − | 6.12712i | 0.0798890 | − | 0.245873i | ||||
\(622\) | 14.6826 | + | 4.77066i | 0.588718 | + | 0.191286i | ||||
\(623\) | 13.5168 | + | 18.6043i | 0.541539 | + | 0.745364i | ||||
\(624\) | 11.6240 | 0.465333 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 49.7617 | 1.98888 | ||||||||
\(627\) | −4.92427 | − | 6.77768i | −0.196656 | − | 0.270674i | ||||
\(628\) | 44.2573 | + | 14.3801i | 1.76606 | + | 0.573827i | ||||
\(629\) | 2.37611 | − | 7.31292i | 0.0947418 | − | 0.291585i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.46214 | − | 16.8107i | −0.217444 | − | 0.669225i | −0.998971 | − | 0.0453529i | \(-0.985559\pi\) |
0.781527 | − | 0.623872i | \(-0.214441\pi\) | |||||||
\(632\) | − | 2.33596i | − | 0.0929194i | ||||||
\(633\) | 17.6377 | − | 5.73083i | 0.701035 | − | 0.227780i | ||||
\(634\) | −36.3132 | − | 26.3831i | −1.44218 | − | 1.04781i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 21.0449 | − | 15.2900i | 0.834485 | − | 0.606289i | ||||
\(637\) | 9.20905 | − | 12.6752i | 0.364876 | − | 0.502209i | ||||
\(638\) | −4.61760 | + | 6.35559i | −0.182813 | + | 0.251620i | ||||
\(639\) | −0.0573410 | + | 0.0416607i | −0.00226837 | + | 0.00164807i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.21774 | + | 1.61128i | 0.0875954 | + | 0.0636417i | 0.630721 | − | 0.776010i | \(-0.282759\pi\) |
−0.543126 | + | 0.839651i | \(0.682759\pi\) | |||||||
\(642\) | −31.4507 | + | 10.2190i | −1.24126 | + | 0.403310i | ||||
\(643\) | 20.9276i | 0.825303i | 0.910889 | + | 0.412651i | \(0.135397\pi\) | ||||
−0.910889 | + | 0.412651i | \(0.864603\pi\) | |||||||
\(644\) | −16.7875 | − | 51.6665i | −0.661519 | − | 2.03595i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.69284 | − | 14.4431i | 0.184637 | − | 0.568256i | ||||
\(647\) | 1.75629 | + | 0.570653i | 0.0690469 | + | 0.0224347i | 0.343337 | − | 0.939212i | \(-0.388443\pi\) |
−0.274290 | + | 0.961647i | \(0.588443\pi\) | |||||||
\(648\) | −0.848347 | − | 1.16765i | −0.0333262 | − | 0.0458696i | ||||
\(649\) | −6.32678 | −0.248348 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.1132 | −0.553141 | ||||||||
\(652\) | −25.4952 | − | 35.0912i | −0.998470 | − | 1.37428i | ||||
\(653\) | −17.5121 | − | 5.69002i | −0.685300 | − | 0.222667i | −0.0543858 | − | 0.998520i | \(-0.517320\pi\) |
−0.630914 | + | 0.775853i | \(0.717320\pi\) | |||||||
\(654\) | 4.44588 | − | 13.6830i | 0.173848 | − | 0.535048i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.84721 | + | 17.9959i | 0.228295 | + | 0.702620i | ||||
\(657\) | − | 4.01123i | − | 0.156493i | ||||||
\(658\) | 4.89071 | − | 1.58909i | 0.190660 | − | 0.0619491i | ||||
\(659\) | −10.8246 | − | 7.86455i | −0.421668 | − | 0.306360i | 0.356641 | − | 0.934242i | \(-0.383922\pi\) |
−0.778308 | + | 0.627882i | \(0.783922\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.7001 | + | 23.0315i | −1.23299 | + | 0.895820i | −0.997111 | − | 0.0759628i | \(-0.975797\pi\) |
−0.235879 | + | 0.971782i | \(0.575797\pi\) | |||||||
\(662\) | 24.4469 | − | 33.6483i | 0.950155 | − | 1.30778i | ||||
\(663\) | 3.97639 | − | 5.47303i | 0.154430 | − | 0.212555i | ||||
\(664\) | 15.3532 | − | 11.1548i | 0.595821 | − | 0.432890i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.4133 | + | 7.56571i | 0.403507 | + | 0.293165i | ||||
\(667\) | 14.4821 | − | 4.70553i | 0.560751 | − | 0.182199i | ||||
\(668\) | − | 30.3903i | − | 1.17584i | ||||||
\(669\) | −0.238424 | − | 0.733794i | −0.00921801 | − | 0.0283701i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.08365 | + | 15.6459i | −0.196252 | + | 0.604002i | ||||
\(672\) | 23.0794 | + | 7.49894i | 0.890305 | + | 0.289278i | ||||
\(673\) | −11.3978 | − | 15.6877i | −0.439353 | − | 0.604718i | 0.530715 | − | 0.847550i | \(-0.321923\pi\) |
−0.970068 | + | 0.242832i | \(0.921923\pi\) | |||||||
\(674\) | −46.8981 | −1.80645 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 38.6133 | 1.48513 | ||||||||
\(677\) | −26.8522 | − | 36.9588i | −1.03201 | − | 1.42044i | −0.903425 | − | 0.428746i | \(-0.858956\pi\) |
−0.128587 | − | 0.991698i | \(-0.541044\pi\) | |||||||
\(678\) | 18.4346 | + | 5.98977i | 0.707978 | + | 0.230036i | ||||
\(679\) | 9.95606 | − | 30.6416i | 0.382078 | − | 1.17592i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.53249 | − | 10.8719i | −0.135365 | − | 0.416611i | ||||
\(682\) | 14.8417i | 0.568319i | ||||||||
\(683\) | −11.0220 | + | 3.58128i | −0.421747 | + | 0.137034i | −0.512199 | − | 0.858867i | \(-0.671169\pi\) |
0.0904520 | + | 0.995901i | \(0.471169\pi\) | |||||||
\(684\) | 11.7548 | + | 8.54034i | 0.449455 | + | 0.326548i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −22.1577 | + | 16.0985i | −0.845987 | + | 0.614645i | ||||
\(687\) | 6.00996 | − | 8.27200i | 0.229294 | − | 0.315596i | ||||
\(688\) | 11.0596 | − | 15.2222i | 0.421642 | − | 0.580340i | ||||
\(689\) | −41.3436 | + | 30.0379i | −1.57507 | + | 1.14435i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.5091 | + | 12.7211i | 0.666077 | + | 0.483934i | 0.868710 | − | 0.495321i | \(-0.164950\pi\) |
−0.202632 | + | 0.979255i | \(0.564950\pi\) | |||||||
\(692\) | 24.0002 | − | 7.79815i | 0.912352 | − | 0.296441i | ||||
\(693\) | − | 4.86205i | − | 0.184694i | ||||||
\(694\) | 1.14498 | + | 3.52388i | 0.0434627 | + | 0.133764i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.05418 | − | 3.24442i | 0.0399585 | − | 0.122980i | ||||
\(697\) | 10.4734 | + | 3.40301i | 0.396707 | + | 0.128898i | ||||
\(698\) | 19.7543 | + | 27.1895i | 0.747713 | + | 1.02914i | ||||
\(699\) | −22.5229 | −0.851896 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.61904 | −0.325537 | −0.162768 | − | 0.986664i | \(-0.552042\pi\) | ||||
−0.162768 | + | 0.986664i | \(0.552042\pi\) | |||||||
\(702\) | 6.65634 | + | 9.16166i | 0.251227 | + | 0.345785i | ||||
\(703\) | −30.8559 | − | 10.0257i | −1.16375 | − | 0.378126i | ||||
\(704\) | 5.77751 | − | 17.7814i | 0.217748 | − | 0.670160i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.3843 | + | 31.9597i | 0.390820 | + | 1.20282i | ||||
\(707\) | 3.43739i | 0.129276i | ||||||||
\(708\) | 10.4357 | − | 3.39077i | 0.392198 | − | 0.127433i | ||||
\(709\) | 12.9443 | + | 9.40460i | 0.486134 | + | 0.353197i | 0.803696 | − | 0.595041i | \(-0.202864\pi\) |
−0.317562 | + | 0.948238i | \(0.602864\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.30939 | + | 0.951325i | −0.0491058 | + | 0.0356775i | ||||
\(712\) | −6.17255 | + | 8.49579i | −0.231326 | + | 0.318393i | ||||
\(713\) | 16.9095 | − | 23.2740i | 0.633267 | − | 0.871617i | ||||
\(714\) | 7.13030 | − | 5.18047i | 0.266845 | − | 0.193874i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.80110 | − | 6.39437i | −0.328913 | − | 0.238969i | ||||
\(717\) | 0.560243 | − | 0.182034i | 0.0209226 | − | 0.00679818i | ||||
\(718\) | − | 53.0138i | − | 1.97846i | ||||||
\(719\) | 15.0132 | + | 46.2060i | 0.559899 | + | 1.72319i | 0.682642 | + | 0.730753i | \(0.260831\pi\) |
−0.122743 | + | 0.992438i | \(0.539169\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.82235 | − | 14.8417i | 0.179594 | − | 0.552733i | ||||
\(722\) | −21.8993 | − | 7.11551i | −0.815007 | − | 0.264812i | ||||
\(723\) | 0.887185 | + | 1.22110i | 0.0329948 | + | 0.0454134i | ||||
\(724\) | 29.6689 | 1.10264 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 18.6531 | 0.692283 | ||||||||
\(727\) | 14.9490 | + | 20.5756i | 0.554429 | + | 0.763106i | 0.990605 | − | 0.136755i | \(-0.0436675\pi\) |
−0.436176 | + | 0.899861i | \(0.643667\pi\) | |||||||
\(728\) | 22.7392 | + | 7.38842i | 0.842772 | + | 0.273833i | ||||
\(729\) | −0.309017 | + | 0.951057i | −0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.38389 | − | 10.4145i | −0.125158 | − | 0.385196i | ||||
\(732\) | − | 28.5317i | − | 1.05456i | ||||||
\(733\) | 17.7077 | − | 5.75358i | 0.654049 | − | 0.212513i | 0.0368505 | − | 0.999321i | \(-0.488267\pi\) |
0.617199 | + | 0.786807i | \(0.288267\pi\) | |||||||
\(734\) | 49.1287 | + | 35.6941i | 1.81337 | + | 1.31749i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −40.0185 | + | 29.0752i | −1.47510 | + | 1.07172i | ||||
\(737\) | 1.71679 | − | 2.36296i | 0.0632389 | − | 0.0870408i | ||||
\(738\) | −10.8354 | + | 14.9137i | −0.398857 | + | 0.548980i | ||||
\(739\) | 37.9326 | − | 27.5596i | 1.39537 | − | 1.01380i | 0.400121 | − | 0.916462i | \(-0.368968\pi\) |
0.995252 | − | 0.0973351i | \(-0.0310319\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.0927 | − | 16.7779i | −0.848333 | − | 0.616350i | ||||
\(742\) | −63.3194 | + | 20.5737i | −2.32453 | + | 0.755286i | ||||
\(743\) | − | 42.7061i | − | 1.56674i | −0.621558 | − | 0.783368i | \(-0.713500\pi\) | ||
0.621558 | − | 0.783368i | \(-0.286500\pi\) | |||||||
\(744\) | −1.99159 | − | 6.12948i | −0.0730152 | − | 0.224718i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.48171 | + | 19.9487i | −0.237312 | + | 0.730372i | ||||
\(747\) | −12.5053 | − | 4.06322i | −0.457545 | − | 0.148665i | ||||
\(748\) | −3.11374 | − | 4.28570i | −0.113850 | − | 0.156701i | ||||
\(749\) | 48.3751 | 1.76759 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.64893 | −0.0966608 | −0.0483304 | − | 0.998831i | \(-0.515390\pi\) | ||||
−0.0483304 | + | 0.998831i | \(0.515390\pi\) | |||||||
\(752\) | −0.981657 | − | 1.35113i | −0.0357973 | − | 0.0492708i | ||||
\(753\) | −11.3131 | − | 3.67584i | −0.412272 | − | 0.133955i | ||||
\(754\) | −8.27133 | + | 25.4565i | −0.301224 | + | 0.927072i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.60577 | + | 8.01972i | 0.0947708 | + | 0.291674i | ||||
\(757\) | − | 52.9153i | − | 1.92324i | −0.274383 | − | 0.961620i | \(-0.588474\pi\) | ||
0.274383 | − | 0.961620i | \(-0.411526\pi\) | |||||||
\(758\) | 45.7534 | − | 14.8662i | 1.66184 | − | 0.539964i | ||||
\(759\) | 8.01795 | + | 5.82538i | 0.291033 | + | 0.211448i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.0808 | + | 29.8470i | −1.48918 | + | 1.08195i | −0.514728 | + | 0.857354i | \(0.672107\pi\) |
−0.974451 | + | 0.224598i | \(0.927893\pi\) | |||||||
\(762\) | 12.7229 | − | 17.5116i | 0.460902 | − | 0.634377i | ||||
\(763\) | −12.3706 | + | 17.0267i | −0.447847 | + | 0.616408i | ||||
\(764\) | 7.79499 | − | 5.66339i | 0.282013 | − | 0.204894i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.8242 | + | 17.3093i | 0.860803 | + | 0.625410i | ||||
\(767\) | −20.5014 | + | 6.66131i | −0.740263 | + | 0.240526i | ||||
\(768\) | − | 0.752056i | − | 0.0271375i | ||||||
\(769\) | −7.59580 | − | 23.3775i | −0.273912 | − | 0.843013i | −0.989505 | − | 0.144496i | \(-0.953844\pi\) |
0.715594 | − | 0.698517i | \(-0.246156\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.57751 | − | 17.1658i | 0.200869 | − | 0.618212i | ||||
\(772\) | 43.2791 | + | 14.0622i | 1.55765 | + | 0.506111i | ||||
\(773\) | 11.7623 | + | 16.1894i | 0.423061 | + | 0.582293i | 0.966343 | − | 0.257257i | \(-0.0828186\pi\) |
−0.543282 | + | 0.839550i | \(0.682819\pi\) | |||||||
\(774\) | 18.3308 | 0.658885 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.7128 | 0.528159 | ||||||||
\(777\) | −11.0674 | − | 15.2330i | −0.397042 | − | 0.546482i | ||||
\(778\) | 39.5149 | + | 12.8392i | 1.41668 | + | 0.460307i | ||||
\(779\) | 14.3586 | − | 44.1911i | 0.514449 | − | 1.58331i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0336934 | − | 0.103698i | −0.00120565 | − | 0.00371060i | ||||
\(782\) | 17.9654i | 0.642441i | ||||||||
\(783\) | −2.24793 | + | 0.730396i | −0.0803344 | + | 0.0261022i | ||||
\(784\) | −5.36302 | − | 3.89646i | −0.191536 | − | 0.139159i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11.1494 | + | 8.10053i | −0.397687 | + | 0.288936i | ||||
\(787\) | −5.28579 | + | 7.27526i | −0.188418 | + | 0.259335i | −0.892767 | − | 0.450519i | \(-0.851239\pi\) |
0.704349 | + | 0.709854i | \(0.251239\pi\) | |||||||
\(788\) | −6.90838 | + | 9.50857i | −0.246101 | + | 0.338729i | ||||
\(789\) | 15.4576 | − | 11.2306i | 0.550305 | − | 0.399820i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.9395 | − | 16.6665i | −0.815634 | − | 0.592593i | ||||
\(792\) | 2.11162 | − | 0.686108i | 0.0750333 | − | 0.0243798i | ||||
\(793\) | 56.0517i | 1.99045i | ||||||||
\(794\) | −14.8406 | − | 45.6747i | −0.526674 | − | 1.62093i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.6824 | − | 42.1102i | 0.484961 | − | 1.49256i | ||||
\(797\) | 35.9084 | + | 11.6674i | 1.27194 | + | 0.413279i | 0.865735 | − | 0.500502i | \(-0.166851\pi\) |
0.406207 | + | 0.913781i | \(0.366851\pi\) | |||||||
\(798\) | −21.8583 | − | 30.0854i | −0.773776 | − | 1.06501i | ||||
\(799\) | −0.971976 | −0.0343860 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.27597 | 0.257084 | ||||||||
\(802\) | 5.99069 | + | 8.24547i | 0.211538 | + | 0.291158i | ||||
\(803\) | 5.86866 | + | 1.90684i | 0.207100 | + | 0.0672910i | ||||
\(804\) | −1.56536 | + | 4.81769i | −0.0552061 | + | 0.169907i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15.6265 | + | 48.0934i | 0.550420 | + | 1.69402i | ||||
\(807\) | − | 22.2250i | − | 0.782358i | ||||||
\(808\) | −1.49289 | + | 0.485068i | −0.0525195 | + | 0.0170646i | ||||
\(809\) | −39.5610 | − | 28.7428i | −1.39089 | − | 1.01054i | −0.995767 | − | 0.0919140i | \(-0.970702\pi\) |
−0.395124 | − | 0.918628i | \(-0.629298\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.6069 | − | 10.6125i | 0.512916 | − | 0.372655i | −0.301013 | − | 0.953620i | \(-0.597325\pi\) |
0.813929 | + | 0.580965i | \(0.197325\pi\) | |||||||
\(812\) | −11.7151 | + | 16.1245i | −0.411121 | + | 0.565860i | ||||
\(813\) | −11.8796 | + | 16.3508i | −0.416635 | + | 0.573449i | ||||
\(814\) | −16.0193 | + | 11.6387i | −0.561477 | + | 0.407937i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.31570 | − | 1.68246i | −0.0810658 | − | 0.0588978i | ||||
\(817\) | −43.9428 | + | 14.2779i | −1.53736 | + | 0.499520i | ||||
\(818\) | − | 26.9653i | − | 0.942819i | ||||||
\(819\) | −5.11914 | − | 15.7551i | −0.178877 | − | 0.550527i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.6393 | − | 48.1327i | 0.545814 | − | 1.67984i | −0.173232 | − | 0.984881i | \(-0.555421\pi\) |
0.719046 | − | 0.694962i | \(-0.244579\pi\) | |||||||
\(822\) | −18.8577 | − | 6.12723i | −0.657737 | − | 0.213712i | ||||
\(823\) | 15.7568 | + | 21.6873i | 0.549246 | + | 0.755972i | 0.989910 | − | 0.141700i | \(-0.0452568\pi\) |
−0.440664 | + | 0.897672i | \(0.645257\pi\) | |||||||
\(824\) | 7.12635 | 0.248258 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.0839 | −0.977163 | ||||||||
\(827\) | −12.5580 | − | 17.2845i | −0.436683 | − | 0.601042i | 0.532788 | − | 0.846249i | \(-0.321144\pi\) |
−0.969471 | + | 0.245206i | \(0.921144\pi\) | |||||||
\(828\) | −16.3473 | − | 5.31155i | −0.568107 | − | 0.184589i | ||||
\(829\) | 14.8675 | − | 45.7575i | 0.516370 | − | 1.58922i | −0.264405 | − | 0.964412i | \(-0.585176\pi\) |
0.780775 | − | 0.624812i | \(-0.214824\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.95702 | + | 15.2561i | 0.171957 | + | 0.529230i | ||||
\(832\) | − | 63.7021i | − | 2.20847i | ||||||
\(833\) | −3.66921 | + | 1.19220i | −0.127130 | + | 0.0413072i | ||||
\(834\) | 16.1953 | + | 11.7665i | 0.560796 | + | 0.407442i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −18.0830 | + | 13.1380i | −0.625412 | + | 0.454389i | ||||
\(837\) | −2.62471 | + | 3.61260i | −0.0907232 | + | 0.124870i | ||||
\(838\) | 44.3825 | − | 61.0873i | 1.53317 | − | 2.11022i | ||||
\(839\) | −33.8606 | + | 24.6012i | −1.16900 | + | 0.849327i | −0.990889 | − | 0.134684i | \(-0.956998\pi\) |
−0.178110 | + | 0.984011i | \(0.556998\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.9418 | + | 13.7620i | 0.653165 | + | 0.474552i | ||||
\(842\) | −81.2886 | + | 26.4123i | −2.80139 | + | 0.910227i | ||||
\(843\) | − | 8.37308i | − | 0.288384i | ||||||
\(844\) | −15.2900 | − | 47.0577i | −0.526302 | − | 1.61979i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.502787 | − | 1.54742i | 0.0172862 | − | 0.0532014i | ||||
\(847\) | −25.9511 | − | 8.43203i | −0.891691 | − | 0.289728i | ||||
\(848\) | 12.7094 | + | 17.4930i | 0.436442 | + | 0.600711i | ||||
\(849\) | −1.12995 | −0.0387798 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.3809 | 1.31568 | ||||||||
\(852\) | 0.111151 | + | 0.152987i | 0.00380799 | + | 0.00524124i | ||||
\(853\) | −55.3537 | − | 17.9855i | −1.89527 | − | 0.615812i | −0.973819 | − | 0.227327i | \(-0.927002\pi\) |
−0.921455 | − | 0.388485i | \(-0.872998\pi\) | |||||||
\(854\) | −22.5658 | + | 69.4504i | −0.772186 | + | 2.37654i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.82646 | + | 21.0097i | 0.233324 | + | 0.718096i | ||||
\(857\) | 3.22045i | 0.110008i | 0.998486 | + | 0.0550042i | \(0.0175172\pi\) | ||||
−0.998486 | + | 0.0550042i | \(0.982483\pi\) | |||||||
\(858\) | −16.5683 | + | 5.38337i | −0.565633 | + | 0.183785i | ||||
\(859\) | 40.0003 | + | 29.0619i | 1.36479 | + | 0.991580i | 0.998124 | + | 0.0612288i | \(0.0195019\pi\) |
0.366669 | + | 0.930351i | \(0.380498\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.8164 | − | 15.8505i | 0.743500 | − | 0.540184i | ||||
\(862\) | 17.8534 | − | 24.5731i | 0.608089 | − | 0.836963i | ||||
\(863\) | 12.6329 | − | 17.3878i | 0.430030 | − | 0.591886i | −0.537930 | − | 0.842990i | \(-0.680793\pi\) |
0.967960 | + | 0.251104i | \(0.0807935\pi\) | |||||||
\(864\) | 6.21171 | − | 4.51307i | 0.211327 | − | 0.153538i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.960798 | + | 0.698061i | 0.0326493 | + | 0.0237211i | ||||
\(867\) | 14.5836 | − | 4.73851i | 0.495286 | − | 0.160928i | ||||
\(868\) | 37.6544i | 1.27807i | ||||||||
\(869\) | −0.769392 | − | 2.36795i | −0.0260999 | − | 0.0803271i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.07522 | − | 9.46456i | 0.104200 | − | 0.320694i | ||||
\(872\) | −9.14051 | − | 2.96993i | −0.309537 | − | 0.100575i | ||||
\(873\) | −5.99183 | − | 8.24705i | −0.202793 | − | 0.279120i | ||||
\(874\) | 75.8026 | 2.56406 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.7020 | −0.361588 | ||||||||
\(877\) | 9.03971 | + | 12.4421i | 0.305249 | + | 0.420140i | 0.933892 | − | 0.357554i | \(-0.116389\pi\) |
−0.628643 | + | 0.777694i | \(0.716389\pi\) | |||||||
\(878\) | −6.11054 | − | 1.98544i | −0.206221 | − | 0.0670052i | ||||
\(879\) | −0.735020 | + | 2.26216i | −0.0247916 | + | 0.0763007i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.84891 | + | 18.0011i | 0.197055 | + | 0.606472i | 0.999946 | + | 0.0103472i | \(0.00329367\pi\) |
−0.802892 | + | 0.596125i | \(0.796706\pi\) | |||||||
\(882\) | − | 6.45821i | − | 0.217459i | ||||||
\(883\) | −6.00790 | + | 1.95208i | −0.202182 | + | 0.0656928i | −0.408357 | − | 0.912822i | \(-0.633898\pi\) |
0.206175 | + | 0.978515i | \(0.433898\pi\) | |||||||
\(884\) | −14.6021 | − | 10.6091i | −0.491123 | − | 0.356822i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 64.1303 | − | 46.5934i | 2.15450 | − | 1.56534i | ||||
\(887\) | −0.0424138 | + | 0.0583776i | −0.00142412 | + | 0.00196013i | −0.809728 | − | 0.586805i | \(-0.800386\pi\) |
0.808304 | + | 0.588765i | \(0.200386\pi\) | |||||||
\(888\) | 5.05404 | − | 6.95628i | 0.169602 | − | 0.233438i | ||||
\(889\) | −25.6167 | + | 18.6116i | −0.859156 | + | 0.624213i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.24455 | − | 0.904220i | −0.0416941 | − | 0.0302925i | ||||
\(892\) | −1.95778 | + | 0.636120i | −0.0655512 | + | 0.0212989i | ||||
\(893\) | 4.10113i | 0.137239i | ||||||||
\(894\) | −6.73107 | − | 20.7161i | −0.225121 | − | 0.692850i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 10.6479 | − | 32.7709i | 0.355721 | − | 1.09480i | ||||
\(897\) | 32.1149 | + | 10.4348i | 1.07229 | + | 0.348407i | ||||
\(898\) | 22.6599 | + | 31.1886i | 0.756169 | + | 1.04078i | ||||
\(899\) | −10.5545 | −0.352013 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.5840 | 0.419235 | ||||||||
\(902\) | −16.6687 | − | 22.9425i | −0.555006 | − | 0.763901i | ||||
\(903\) | −25.5026 | − | 8.28629i | −0.848673 | − | 0.275751i | ||||
\(904\) | 4.00128 | − | 12.3147i | 0.133081 | − | 0.409580i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.16888 | − | 22.0635i | −0.238170 | − | 0.733012i | ||||
\(907\) | 25.4951i | 0.846550i | 0.906001 | + | 0.423275i | \(0.139120\pi\) | ||||
−0.906001 | + | 0.423275i | \(0.860880\pi\) | |||||||
\(908\) | −29.0064 | + | 9.42474i | −0.962610 | + | 0.312771i | ||||
\(909\) | 0.879879 | + | 0.639269i | 0.0291837 | + | 0.0212032i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.87851 | + | 2.09136i | −0.0953692 | + | 0.0692898i | −0.634448 | − | 0.772966i | \(-0.718773\pi\) |
0.539079 | + | 0.842255i | \(0.318773\pi\) | |||||||
\(912\) | −7.09891 | + | 9.77081i | −0.235068 | + | 0.323544i | ||||
\(913\) | 11.8894 | − | 16.3644i | 0.393483 | − | 0.541583i | ||||
\(914\) | −42.2621 | + | 30.7052i | −1.39791 | + | 1.01564i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.0698 | − | 16.0347i | −0.729208 | − | 0.529801i | ||||
\(917\) | 19.1734 | − | 6.22981i | 0.633161 | − | 0.205727i | ||||
\(918\) | − | 2.78860i | − | 0.0920375i | ||||||
\(919\) | −2.46277 | − | 7.57962i | −0.0812392 | − | 0.250029i | 0.902185 | − | 0.431350i | \(-0.141963\pi\) |
−0.983424 | + | 0.181321i | \(0.941963\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.894189 | + | 2.75203i | −0.0294645 | + | 0.0906825i | ||||
\(922\) | 76.8241 | + | 24.9617i | 2.53007 | + | 0.822068i | ||||
\(923\) | −0.218362 | − | 0.300549i | −0.00718747 | − | 0.00989270i | ||||
\(924\) | −12.9720 | −0.426749 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 44.1434 | 1.45064 | ||||||||
\(927\) | −2.90222 | − | 3.99457i | −0.0953216 | − | 0.131199i | ||||
\(928\) | 17.2598 | + | 5.60805i | 0.566581 | + | 0.184093i | ||||
\(929\) | −15.0004 | + | 46.1666i | −0.492149 | + | 1.51468i | 0.329205 | + | 0.944258i | \(0.393219\pi\) |
−0.821354 | + | 0.570419i | \(0.806781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.03032 | + | 15.4817i | 0.164862 | + | 0.507394i | ||||
\(932\) | 60.0916i | 1.96837i | ||||||||
\(933\) | −6.79573 | + | 2.20807i | −0.222482 | + | 0.0722888i | ||||
\(934\) | 54.5571 | + | 39.6381i | 1.78516 | + | 1.29700i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.12016 | − | 4.44656i | 0.200044 | − | 0.145340i | ||||
\(937\) | −18.6502 | + | 25.6698i | −0.609274 | + | 0.838594i | −0.996518 | − | 0.0833833i | \(-0.973427\pi\) |
0.387243 | + | 0.921978i | \(0.373427\pi\) | |||||||
\(938\) | 7.62066 | − | 10.4889i | 0.248823 | − | 0.342476i | ||||
\(939\) | −18.6331 | + | 13.5378i | −0.608070 | + | 0.441789i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.1752 | − | 24.1032i | −1.08148 | − | 0.785742i | −0.103541 | − | 0.994625i | \(-0.533017\pi\) |
−0.977941 | + | 0.208883i | \(0.933017\pi\) | |||||||
\(942\) | −35.8395 | + | 11.6450i | −1.16771 | + | 0.379414i | ||||
\(943\) | 54.9681i | 1.79001i | ||||||||
\(944\) | 2.81848 | + | 8.67439i | 0.0917337 | + | 0.282327i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.71401 | + | 26.8190i | −0.283317 | + | 0.871960i | ||||
\(947\) | 9.33737 | + | 3.03389i | 0.303424 | + | 0.0985883i | 0.456772 | − | 0.889584i | \(-0.349006\pi\) |
−0.153348 | + | 0.988172i | \(0.549006\pi\) | |||||||
\(948\) | 2.53815 | + | 3.49347i | 0.0824353 | + | 0.113463i | ||||
\(949\) | 21.0246 | 0.682487 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.7750 | 0.673674 | ||||||||
\(952\) | −3.46065 | − | 4.76317i | −0.112160 | − | 0.154375i | ||||
\(953\) | 50.5123 | + | 16.4125i | 1.63626 | + | 0.531652i | 0.975697 | − | 0.219123i | \(-0.0703197\pi\) |
0.660558 | + | 0.750775i | \(0.270320\pi\) | |||||||
\(954\) | −6.50952 | + | 20.0343i | −0.210754 | + | 0.648633i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.485670 | − | 1.49474i | −0.0157077 | − | 0.0483433i | ||||
\(957\) | − | 3.63606i | − | 0.117537i | ||||||
\(958\) | −22.8022 | + | 7.40888i | −0.736705 | + | 0.239370i | ||||
\(959\) | 23.4659 | + | 17.0490i | 0.757754 | + | 0.550540i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.94773 | − | 6.50090i | 0.288636 | − | 0.209707i | ||||
\(962\) | −39.6552 | + | 54.5807i | −1.27853 | + | 1.75975i | ||||
\(963\) | 8.99657 | − | 12.3827i | 0.289910 | − | 0.399027i | ||||
\(964\) | 3.25793 | − | 2.36703i | 0.104931 | − | 0.0762368i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 35.5908 | + | 25.8583i | 1.14512 | + | 0.831976i | ||||
\(967\) | −2.32754 | + | 0.756262i | −0.0748485 | + | 0.0243198i | −0.346202 | − | 0.938160i | \(-0.612529\pi\) |
0.271353 | + | 0.962480i | \(0.412529\pi\) | |||||||
\(968\) | − | 12.4606i | − | 0.400500i | ||||||
\(969\) | 2.17205 | + | 6.68488i | 0.0697763 | + | 0.214749i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.8230 | + | 45.6205i | −0.475693 | + | 1.46403i | 0.369328 | + | 0.929299i | \(0.379588\pi\) |
−0.845021 | + | 0.534734i | \(0.820412\pi\) | |||||||
\(972\) | 2.53744 | + | 0.824463i | 0.0813883 | + | 0.0264447i | ||||
\(973\) | −17.2126 | − | 23.6911i | −0.551811 | − | 0.759502i | ||||
\(974\) | −15.4200 | −0.494088 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 23.7161 | 0.759134 | ||||||||
\(977\) | 13.9276 | + | 19.1696i | 0.445582 | + | 0.613291i | 0.971441 | − | 0.237280i | \(-0.0762560\pi\) |
−0.525859 | + | 0.850572i | \(0.676256\pi\) | |||||||
\(978\) | 33.4060 | + | 10.8543i | 1.06820 | + | 0.347081i | ||||
\(979\) | −3.45883 | + | 10.6452i | −0.110545 | + | 0.340221i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.05774 | + | 6.33308i | 0.0656987 | + | 0.202200i | ||||
\(982\) | − | 15.6284i | − | 0.498721i | ||||||
\(983\) | −12.3167 | + | 4.00193i | −0.392841 | + | 0.127642i | −0.498775 | − | 0.866731i | \(-0.666217\pi\) |
0.105934 | + | 0.994373i | \(0.466217\pi\) | |||||||
\(984\) | 9.96261 | + | 7.23826i | 0.317597 | + | 0.230747i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.33236 | − | 3.87419i | 0.169817 | − | 0.123379i | ||||
\(987\) | −1.39900 | + | 1.92556i | −0.0445307 | + | 0.0612913i | ||||
\(988\) | −44.7637 | + | 61.6119i | −1.42412 | + | 1.96014i | ||||
\(989\) | 44.2203 | − | 32.1279i | 1.40612 | − | 1.02161i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.9986 | − | 26.1545i | −1.14353 | − | 0.830826i | −0.155926 | − | 0.987769i | \(-0.549836\pi\) |
−0.987608 | + | 0.156943i | \(0.949836\pi\) | |||||||
\(992\) | 32.6079 | − | 10.5949i | 1.03530 | − | 0.336389i | ||||
\(993\) | 19.2504i | 0.610891i | ||||||||
\(994\) | −0.149562 | − | 0.460303i | −0.00474381 | − | 0.0145999i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.8407 | + | 33.3644i | −0.343502 | + | 1.05719i | ||||
\(997\) | 52.8324 | + | 17.1663i | 1.67322 | + | 0.543662i | 0.983577 | − | 0.180488i | \(-0.0577678\pi\) |
0.689642 | + | 0.724150i | \(0.257768\pi\) | |||||||
\(998\) | −20.3406 | − | 27.9964i | −0.643869 | − | 0.886209i | ||||
\(999\) | −5.95751 | −0.188487 |
(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 | 375.2.i.d.199.6 | 24 | ||
5.2 | odd | 4 | 75.2.g.c.61.1 | yes | 12 | ||
5.3 | odd | 4 | 375.2.g.c.301.3 | 12 | |||
5.4 | even | 2 | inner | 375.2.i.d.199.1 | 24 | ||
15.2 | even | 4 | 225.2.h.d.136.3 | 12 | |||
25.3 | odd | 20 | 1875.2.a.k.1.2 | 6 | |||
25.4 | even | 10 | 1875.2.b.f.1249.10 | 12 | |||
25.9 | even | 10 | inner | 375.2.i.d.49.6 | 24 | ||
25.12 | odd | 20 | 75.2.g.c.16.1 | ✓ | 12 | ||
25.13 | odd | 20 | 375.2.g.c.76.3 | 12 | |||
25.16 | even | 5 | inner | 375.2.i.d.49.1 | 24 | ||
25.21 | even | 5 | 1875.2.b.f.1249.3 | 12 | |||
25.22 | odd | 20 | 1875.2.a.j.1.5 | 6 | |||
75.47 | even | 20 | 5625.2.a.p.1.2 | 6 | |||
75.53 | even | 20 | 5625.2.a.q.1.5 | 6 | |||
75.62 | even | 20 | 225.2.h.d.91.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.16.1 | ✓ | 12 | 25.12 | odd | 20 | ||
75.2.g.c.61.1 | yes | 12 | 5.2 | odd | 4 | ||
225.2.h.d.91.3 | 12 | 75.62 | even | 20 | |||
225.2.h.d.136.3 | 12 | 15.2 | even | 4 | |||
375.2.g.c.76.3 | 12 | 25.13 | odd | 20 | |||
375.2.g.c.301.3 | 12 | 5.3 | odd | 4 | |||
375.2.i.d.49.1 | 24 | 25.16 | even | 5 | inner | ||
375.2.i.d.49.6 | 24 | 25.9 | even | 10 | inner | ||
375.2.i.d.199.1 | 24 | 5.4 | even | 2 | inner | ||
375.2.i.d.199.6 | 24 | 1.1 | even | 1 | trivial | ||
1875.2.a.j.1.5 | 6 | 25.22 | odd | 20 | |||
1875.2.a.k.1.2 | 6 | 25.3 | odd | 20 | |||
1875.2.b.f.1249.3 | 12 | 25.21 | even | 5 | |||
1875.2.b.f.1249.10 | 12 | 25.4 | even | 10 | |||
5625.2.a.p.1.2 | 6 | 75.47 | even | 20 | |||
5625.2.a.q.1.5 | 6 | 75.53 | even | 20 |