Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 373.4 | ||
Character | \(\chi\) | \(=\) | 784.373 |
Dual form | 784.2.x.l.557.4 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.545265 | + | 1.30487i | 0.385560 | + | 0.922683i | ||||
\(3\) | −0.569433 | − | 0.152579i | −0.328762 | − | 0.0880916i | 0.0906624 | − | 0.995882i | \(-0.471102\pi\) |
−0.419425 | + | 0.907790i | \(0.637768\pi\) | |||||||
\(4\) | −1.40537 | + | 1.42300i | −0.702686 | + | 0.711500i | ||||
\(5\) | 1.54592 | − | 0.414228i | 0.691356 | − | 0.185248i | 0.104000 | − | 0.994577i | \(-0.466836\pi\) |
0.587356 | + | 0.809329i | \(0.300169\pi\) | |||||||
\(6\) | −0.111396 | − | 0.826233i | −0.0454772 | − | 0.337308i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.62313 | − | 1.05792i | −0.927416 | − | 0.374030i | ||||
\(9\) | −2.29710 | − | 1.32623i | −0.765701 | − | 0.442078i | ||||
\(10\) | 1.38345 | + | 1.79136i | 0.437485 | + | 0.566478i | ||||
\(11\) | 1.41182 | − | 5.26900i | 0.425681 | − | 1.58866i | −0.336750 | − | 0.941594i | \(-0.609328\pi\) |
0.762431 | − | 0.647069i | \(-0.224006\pi\) | |||||||
\(12\) | 1.01739 | − | 0.595873i | 0.293694 | − | 0.172014i | ||||
\(13\) | 4.66311 | − | 4.66311i | 1.29332 | − | 1.29332i | 0.360591 | − | 0.932724i | \(-0.382575\pi\) |
0.932724 | − | 0.360591i | \(-0.117425\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.943500 | −0.243611 | ||||||||
\(16\) | −0.0498554 | − | 3.99969i | −0.0124639 | − | 0.999922i | ||||
\(17\) | 2.66615 | + | 4.61791i | 0.646637 | + | 1.12001i | 0.983921 | + | 0.178605i | \(0.0571583\pi\) |
−0.337284 | + | 0.941403i | \(0.609508\pi\) | |||||||
\(18\) | 0.478033 | − | 3.72057i | 0.112673 | − | 0.876946i | ||||
\(19\) | −0.936730 | − | 3.49592i | −0.214901 | − | 0.802020i | −0.986202 | − | 0.165549i | \(-0.947060\pi\) |
0.771301 | − | 0.636471i | \(-0.219606\pi\) | |||||||
\(20\) | −1.58315 | + | 2.78199i | −0.354002 | + | 0.622071i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.64518 | − | 1.03075i | 1.62996 | − | 0.219757i | ||||
\(23\) | −2.25586 | − | 1.30242i | −0.470379 | − | 0.271574i | 0.246019 | − | 0.969265i | \(-0.420877\pi\) |
−0.716399 | + | 0.697691i | \(0.754211\pi\) | |||||||
\(24\) | 1.33228 | + | 1.00265i | 0.271951 | + | 0.204665i | ||||
\(25\) | −2.11185 | + | 1.21928i | −0.422370 | + | 0.243855i | ||||
\(26\) | 8.62739 | + | 3.54213i | 1.69197 | + | 0.694668i | ||||
\(27\) | 2.35625 | + | 2.35625i | 0.453461 | + | 0.453461i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.22279 | + | 1.22279i | −0.227067 | + | 0.227067i | −0.811466 | − | 0.584399i | \(-0.801330\pi\) |
0.584399 | + | 0.811466i | \(0.301330\pi\) | |||||||
\(30\) | −0.514457 | − | 1.23115i | −0.0939266 | − | 0.224775i | ||||
\(31\) | 0.416854 | + | 0.722013i | 0.0748692 | + | 0.129677i | 0.901029 | − | 0.433758i | \(-0.142813\pi\) |
−0.826160 | + | 0.563435i | \(0.809479\pi\) | |||||||
\(32\) | 5.19189 | − | 2.24594i | 0.917805 | − | 0.397031i | ||||
\(33\) | −1.60788 | + | 2.78493i | −0.279896 | + | 0.484794i | ||||
\(34\) | −4.57201 | + | 5.99696i | −0.784094 | + | 1.02847i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.11551 | − | 1.40492i | 0.852586 | − | 0.234154i | ||||
\(37\) | 6.05105 | − | 1.62137i | 0.994786 | − | 0.266552i | 0.275526 | − | 0.961294i | \(-0.411148\pi\) |
0.719260 | + | 0.694741i | \(0.244481\pi\) | |||||||
\(38\) | 4.05096 | − | 3.12852i | 0.657153 | − | 0.507512i | ||||
\(39\) | −3.36683 | + | 1.94384i | −0.539124 | + | 0.311263i | ||||
\(40\) | −4.49336 | − | 0.548881i | −0.710463 | − | 0.0867857i | ||||
\(41\) | 0.263382i | 0.0411333i | 0.999788 | + | 0.0205667i | \(0.00654703\pi\) | ||||
−0.999788 | + | 0.0205667i | \(0.993453\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.25233 | + | 1.25233i | 0.190979 | + | 0.190979i | 0.796119 | − | 0.605140i | \(-0.206883\pi\) |
−0.605140 | + | 0.796119i | \(0.706883\pi\) | |||||||
\(44\) | 5.51365 | + | 9.41394i | 0.831213 | + | 1.41920i | ||||
\(45\) | −4.10050 | − | 1.09872i | −0.611266 | − | 0.163788i | ||||
\(46\) | 0.469450 | − | 3.65377i | 0.0692166 | − | 0.538719i | ||||
\(47\) | 5.37795 | − | 9.31488i | 0.784455 | − | 1.35872i | −0.144870 | − | 0.989451i | \(-0.546276\pi\) |
0.929324 | − | 0.369265i | \(-0.120390\pi\) | |||||||
\(48\) | −0.581880 | + | 2.28516i | −0.0839872 | + | 0.329835i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.74251 | − | 2.09086i | −0.387850 | − | 0.295692i | ||||
\(51\) | −0.813598 | − | 3.03639i | −0.113927 | − | 0.425180i | ||||
\(52\) | 0.0821962 | + | 13.1890i | 0.0113986 | + | 1.82899i | ||||
\(53\) | 0.0174309 | − | 0.0650529i | 0.00239432 | − | 0.00893571i | −0.964718 | − | 0.263284i | \(-0.915194\pi\) |
0.967113 | + | 0.254348i | \(0.0818610\pi\) | |||||||
\(54\) | −1.78982 | + | 4.35939i | −0.243564 | + | 0.593237i | ||||
\(55\) | − | 8.73026i | − | 1.17719i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.13362i | 0.282605i | ||||||||
\(58\) | −2.26233 | − | 0.928839i | −0.297058 | − | 0.121963i | ||||
\(59\) | −1.32019 | + | 4.92700i | −0.171874 | + | 0.641441i | 0.825189 | + | 0.564856i | \(0.191068\pi\) |
−0.997063 | + | 0.0765850i | \(0.975598\pi\) | |||||||
\(60\) | 1.32597 | − | 1.34260i | 0.171182 | − | 0.173329i | ||||
\(61\) | 1.63393 | + | 6.09793i | 0.209204 | + | 0.780760i | 0.988127 | + | 0.153640i | \(0.0490996\pi\) |
−0.778923 | + | 0.627120i | \(0.784234\pi\) | |||||||
\(62\) | −0.714837 | + | 0.937629i | −0.0907844 | + | 0.119079i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.76162 | + | 5.55011i | 0.720203 | + | 0.693764i | ||||
\(65\) | 5.27720 | − | 9.14038i | 0.654557 | − | 1.13373i | ||||
\(66\) | −4.51069 | − | 0.579551i | −0.555228 | − | 0.0713377i | ||||
\(67\) | −12.9904 | − | 3.48077i | −1.58703 | − | 0.425244i | −0.645938 | − | 0.763390i | \(-0.723533\pi\) |
−0.941094 | + | 0.338146i | \(0.890200\pi\) | |||||||
\(68\) | −10.3182 | − | 2.69595i | −1.25127 | − | 0.326932i | ||||
\(69\) | 1.08584 | + | 1.08584i | 0.130720 | + | 0.130720i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.05301i | − | 0.243647i | −0.992552 | − | 0.121824i | \(-0.961126\pi\) | ||
0.992552 | − | 0.121824i | \(-0.0388743\pi\) | |||||||
\(72\) | 4.62255 | + | 5.90903i | 0.544773 | + | 0.696385i | ||||
\(73\) | 4.74814 | − | 2.74134i | 0.555728 | − | 0.320850i | −0.195701 | − | 0.980664i | \(-0.562698\pi\) |
0.751429 | + | 0.659814i | \(0.229365\pi\) | |||||||
\(74\) | 5.41510 | + | 7.01175i | 0.629493 | + | 0.815100i | ||||
\(75\) | 1.38859 | − | 0.372072i | 0.160341 | − | 0.0429632i | ||||
\(76\) | 6.29115 | + | 3.58011i | 0.721645 | + | 0.410667i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.37227 | − | 3.33337i | −0.495062 | − | 0.377429i | ||||
\(79\) | −2.60788 | + | 4.51698i | −0.293409 | + | 0.508200i | −0.974614 | − | 0.223893i | \(-0.928123\pi\) |
0.681204 | + | 0.732093i | \(0.261457\pi\) | |||||||
\(80\) | −1.73385 | − | 6.16254i | −0.193851 | − | 0.688993i | ||||
\(81\) | 2.99648 | + | 5.19006i | 0.332943 | + | 0.576674i | ||||
\(82\) | −0.343679 | + | 0.143613i | −0.0379530 | + | 0.0158594i | ||||
\(83\) | 5.84045 | − | 5.84045i | 0.641073 | − | 0.641073i | −0.309746 | − | 0.950819i | \(-0.600244\pi\) |
0.950819 | + | 0.309746i | \(0.100244\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.03452 | + | 6.03452i | 0.654535 | + | 0.654535i | ||||
\(86\) | −0.951279 | + | 2.31699i | −0.102579 | + | 0.249847i | ||||
\(87\) | 0.882871 | − | 0.509726i | 0.0946537 | − | 0.0546483i | ||||
\(88\) | −9.27757 | + | 12.3277i | −0.988992 | + | 1.31414i | ||||
\(89\) | −5.47892 | − | 3.16326i | −0.580764 | − | 0.335304i | 0.180673 | − | 0.983543i | \(-0.442172\pi\) |
−0.761437 | + | 0.648239i | \(0.775506\pi\) | |||||||
\(90\) | −0.802163 | − | 5.94971i | −0.0845554 | − | 0.627154i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.02367 | − | 1.37970i | 0.523754 | − | 0.143844i | ||||
\(93\) | −0.127207 | − | 0.474741i | −0.0131907 | − | 0.0492284i | ||||
\(94\) | 15.0871 | + | 1.93845i | 1.55612 | + | 0.199936i | ||||
\(95\) | −2.89622 | − | 5.01639i | −0.297146 | − | 0.514671i | ||||
\(96\) | −3.29912 | + | 0.486741i | −0.336715 | + | 0.0496778i | ||||
\(97\) | 18.8089 | 1.90976 | 0.954878 | − | 0.296999i | \(-0.0959858\pi\) | ||||
0.954878 | + | 0.296999i | \(0.0959858\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.2310 | + | 10.2310i | −1.02826 | + | 1.02826i | ||||
\(100\) | 1.23290 | − | 4.71869i | 0.123290 | − | 0.471869i | ||||
\(101\) | −1.05607 | + | 3.94130i | −0.105083 | + | 0.392174i | −0.998355 | − | 0.0573431i | \(-0.981737\pi\) |
0.893272 | + | 0.449517i | \(0.148404\pi\) | |||||||
\(102\) | 3.51847 | − | 2.71728i | 0.348380 | − | 0.269050i | ||||
\(103\) | −6.70338 | − | 3.87020i | −0.660504 | − | 0.381342i | 0.131965 | − | 0.991254i | \(-0.457871\pi\) |
−0.792469 | + | 0.609912i | \(0.791205\pi\) | |||||||
\(104\) | −17.1651 | + | 7.29876i | −1.68318 | + | 0.715703i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0943901 | − | 0.0127260i | 0.00916798 | − | 0.00123606i | ||||
\(107\) | 3.18895 | − | 0.854476i | 0.308287 | − | 0.0826053i | −0.101359 | − | 0.994850i | \(-0.532319\pi\) |
0.409646 | + | 0.912245i | \(0.365652\pi\) | |||||||
\(108\) | −6.66436 | + | 0.0415334i | −0.641279 | + | 0.00399656i | ||||
\(109\) | 6.73214 | + | 1.80387i | 0.644822 | + | 0.172779i | 0.566387 | − | 0.824140i | \(-0.308341\pi\) |
0.0784353 | + | 0.996919i | \(0.475008\pi\) | |||||||
\(110\) | 11.3919 | − | 4.76030i | 1.08617 | − | 0.453877i | ||||
\(111\) | −3.69306 | −0.350529 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.24381 | 0.493296 | 0.246648 | − | 0.969105i | \(-0.420671\pi\) | ||||
0.246648 | + | 0.969105i | \(0.420671\pi\) | |||||||
\(114\) | −2.78410 | + | 1.16339i | −0.260755 | + | 0.108961i | ||||
\(115\) | −4.02688 | − | 1.07900i | −0.375508 | − | 0.100617i | ||||
\(116\) | −0.0215540 | − | 3.45851i | −0.00200124 | − | 0.321115i | ||||
\(117\) | −16.8960 | + | 4.52728i | −1.56204 | + | 0.418547i | ||||
\(118\) | −7.14895 | + | 0.963849i | −0.658114 | + | 0.0887295i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.47492 | + | 0.998145i | 0.225929 | + | 0.0911178i | ||||
\(121\) | −16.2428 | − | 9.37781i | −1.47662 | − | 0.852528i | ||||
\(122\) | −7.06608 | + | 5.45706i | −0.639732 | + | 0.494059i | ||||
\(123\) | 0.0401866 | − | 0.149978i | 0.00362350 | − | 0.0135231i | ||||
\(124\) | −1.61326 | − | 0.421513i | −0.144875 | − | 0.0378530i | ||||
\(125\) | −8.41814 | + | 8.41814i | −0.752941 | + | 0.752941i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.6789 | −1.56875 | −0.784373 | − | 0.620290i | \(-0.787015\pi\) | ||||
−0.784373 | + | 0.620290i | \(0.787015\pi\) | |||||||
\(128\) | −4.10056 | + | 10.5444i | −0.362442 | + | 0.932006i | ||||
\(129\) | −0.522040 | − | 0.904200i | −0.0459631 | − | 0.0796104i | ||||
\(130\) | 14.8045 | + | 1.90214i | 1.29844 | + | 0.166828i | ||||
\(131\) | −0.797610 | − | 2.97672i | −0.0696875 | − | 0.260077i | 0.922289 | − | 0.386502i | \(-0.126317\pi\) |
−0.991976 | + | 0.126424i | \(0.959650\pi\) | |||||||
\(132\) | −1.70328 | − | 6.20188i | −0.148252 | − | 0.539804i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.54126 | − | 18.8487i | −0.219531 | − | 1.62828i | ||||
\(135\) | 4.61860 | + | 2.66655i | 0.397506 | + | 0.229500i | ||||
\(136\) | −2.10829 | − | 14.9339i | −0.180785 | − | 1.28057i | ||||
\(137\) | −7.40148 | + | 4.27325i | −0.632351 | + | 0.365088i | −0.781662 | − | 0.623702i | \(-0.785628\pi\) |
0.149311 | + | 0.988790i | \(0.452295\pi\) | |||||||
\(138\) | −0.824810 | + | 2.00895i | −0.0702125 | + | 0.171013i | ||||
\(139\) | −5.72549 | − | 5.72549i | −0.485629 | − | 0.485629i | 0.421295 | − | 0.906924i | \(-0.361576\pi\) |
−0.906924 | + | 0.421295i | \(0.861576\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.48364 | + | 4.48364i | −0.377591 | + | 0.377591i | ||||
\(142\) | 2.67891 | − | 1.11943i | 0.224809 | − | 0.0939408i | ||||
\(143\) | −17.9865 | − | 31.1535i | −1.50410 | − | 2.60518i | ||||
\(144\) | −5.19000 | + | 9.25382i | −0.432500 | + | 0.771151i | ||||
\(145\) | −1.38382 | + | 2.39685i | −0.114920 | + | 0.199048i | ||||
\(146\) | 6.16609 | + | 4.70095i | 0.510309 | + | 0.389054i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.19676 | + | 10.8893i | −0.509371 | + | 0.895092i | ||||
\(149\) | −0.539794 | + | 0.144637i | −0.0442217 | + | 0.0118492i | −0.280862 | − | 0.959748i | \(-0.590620\pi\) |
0.236640 | + | 0.971597i | \(0.423954\pi\) | |||||||
\(150\) | 1.24266 | + | 1.60906i | 0.101462 | + | 0.131379i | ||||
\(151\) | 3.21780 | − | 1.85780i | 0.261861 | − | 0.151185i | −0.363322 | − | 0.931663i | \(-0.618358\pi\) |
0.625183 | + | 0.780478i | \(0.285024\pi\) | |||||||
\(152\) | −1.24123 | + | 10.1612i | −0.100677 | + | 0.824186i | ||||
\(153\) | − | 14.1437i | − | 1.14345i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.943500 | + | 0.943500i | 0.0757837 | + | 0.0757837i | ||||
\(156\) | 1.96557 | − | 7.52281i | 0.157371 | − | 0.602307i | ||||
\(157\) | −5.45784 | − | 1.46242i | −0.435583 | − | 0.116714i | 0.0343627 | − | 0.999409i | \(-0.489060\pi\) |
−0.469946 | + | 0.882695i | \(0.655727\pi\) | |||||||
\(158\) | −7.31606 | − | 0.939995i | −0.582034 | − | 0.0747819i | ||||
\(159\) | −0.0198514 | + | 0.0343837i | −0.00157432 | + | 0.00272681i | ||||
\(160\) | 7.09591 | − | 5.62267i | 0.560981 | − | 0.444511i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.13848 | + | 6.73998i | −0.403717 | + | 0.529543i | ||||
\(163\) | 1.23412 | + | 4.60580i | 0.0966638 | + | 0.360754i | 0.997266 | − | 0.0738892i | \(-0.0235411\pi\) |
−0.900603 | + | 0.434643i | \(0.856874\pi\) | |||||||
\(164\) | −0.374792 | − | 0.370150i | −0.0292663 | − | 0.0289038i | ||||
\(165\) | −1.33206 | + | 4.97130i | −0.103700 | + | 0.387015i | ||||
\(166\) | 10.8056 | + | 4.43644i | 0.838679 | + | 0.344335i | ||||
\(167\) | 12.4233i | 0.961345i | 0.876900 | + | 0.480673i | \(0.159607\pi\) | ||||
−0.876900 | + | 0.480673i | \(0.840393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 30.4893i | − | 2.34533i | ||||||
\(170\) | −4.58385 | + | 11.1647i | −0.351565 | + | 0.856291i | ||||
\(171\) | −2.48464 | + | 9.27282i | −0.190005 | + | 0.709110i | ||||
\(172\) | −3.54206 | + | 0.0220747i | −0.270080 | + | 0.00168318i | ||||
\(173\) | 3.38906 | + | 12.6481i | 0.257665 | + | 0.961620i | 0.966588 | + | 0.256334i | \(0.0825147\pi\) |
−0.708923 | + | 0.705286i | \(0.750819\pi\) | |||||||
\(174\) | 1.14652 | + | 0.874097i | 0.0869178 | + | 0.0662651i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −21.1448 | − | 5.38417i | −1.59385 | − | 0.405847i | ||||
\(177\) | 1.50352 | − | 2.60417i | 0.113011 | − | 0.195741i | ||||
\(178\) | 1.14018 | − | 8.87409i | 0.0854598 | − | 0.665141i | ||||
\(179\) | 13.5991 | + | 3.64387i | 1.01644 | + | 0.272355i | 0.728319 | − | 0.685238i | \(-0.240302\pi\) |
0.288124 | + | 0.957593i | \(0.406968\pi\) | |||||||
\(180\) | 7.32621 | − | 4.29089i | 0.546063 | − | 0.319824i | ||||
\(181\) | −5.08125 | − | 5.08125i | −0.377687 | − | 0.377687i | 0.492580 | − | 0.870267i | \(-0.336054\pi\) |
−0.870267 | + | 0.492580i | \(0.836054\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.72167i | − | 0.275114i | ||||||
\(184\) | 4.53956 | + | 5.80294i | 0.334661 | + | 0.427798i | ||||
\(185\) | 8.68281 | − | 5.01302i | 0.638373 | − | 0.368565i | ||||
\(186\) | 0.550114 | − | 0.424848i | 0.0403364 | − | 0.0311513i | ||||
\(187\) | 28.0959 | − | 7.52827i | 2.05458 | − | 0.550522i | ||||
\(188\) | 5.69705 | + | 20.7437i | 0.415500 | + | 1.51289i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.96654 | − | 6.51445i | 0.360311 | − | 0.472608i | ||||
\(191\) | −10.3964 | + | 18.0070i | −0.752254 | + | 1.30294i | 0.194474 | + | 0.980908i | \(0.437700\pi\) |
−0.946728 | + | 0.322035i | \(0.895633\pi\) | |||||||
\(192\) | −2.43403 | − | 4.03952i | −0.175661 | − | 0.291527i | ||||
\(193\) | −6.67236 | − | 11.5569i | −0.480287 | − | 0.831882i | 0.519457 | − | 0.854496i | \(-0.326134\pi\) |
−0.999744 | + | 0.0226149i | \(0.992801\pi\) | |||||||
\(194\) | 10.2558 | + | 24.5432i | 0.736326 | + | 1.76210i | ||||
\(195\) | −4.39965 | + | 4.39965i | −0.315065 | + | 0.315065i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.194462 | + | 0.194462i | 0.0138549 | + | 0.0138549i | 0.714000 | − | 0.700145i | \(-0.246882\pi\) |
−0.700145 | + | 0.714000i | \(0.746882\pi\) | |||||||
\(198\) | −18.9288 | − | 7.77154i | −1.34521 | − | 0.552300i | ||||
\(199\) | 12.4710 | − | 7.20013i | 0.884045 | − | 0.510403i | 0.0120548 | − | 0.999927i | \(-0.496163\pi\) |
0.871990 | + | 0.489524i | \(0.162829\pi\) | |||||||
\(200\) | 6.82954 | − | 0.964158i | 0.482922 | − | 0.0681763i | ||||
\(201\) | 6.86608 | + | 3.96413i | 0.484296 | + | 0.279608i | ||||
\(202\) | −5.71872 | + | 0.771019i | −0.402367 | + | 0.0542487i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.46419 | + | 3.10951i | 0.382570 | + | 0.217709i | ||||
\(205\) | 0.109100 | + | 0.407167i | 0.00761987 | + | 0.0284378i | ||||
\(206\) | 1.39499 | − | 10.8573i | 0.0971935 | − | 0.756465i | ||||
\(207\) | 3.45463 | + | 5.98359i | 0.240113 | + | 0.415888i | ||||
\(208\) | −18.8835 | − | 18.4185i | −1.30933 | − | 1.27709i | ||||
\(209\) | −19.7425 | −1.36562 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.72356 | − | 7.72356i | 0.531711 | − | 0.531711i | −0.389370 | − | 0.921081i | \(-0.627307\pi\) |
0.921081 | + | 0.389370i | \(0.127307\pi\) | |||||||
\(212\) | 0.0680734 | + | 0.116228i | 0.00467530 | + | 0.00798255i | ||||
\(213\) | −0.313247 | + | 1.16905i | −0.0214633 | + | 0.0801021i | ||||
\(214\) | 2.85380 | + | 3.69525i | 0.195082 | + | 0.252602i | ||||
\(215\) | 2.45476 | + | 1.41725i | 0.167413 | + | 0.0966559i | ||||
\(216\) | −3.68804 | − | 8.67348i | −0.250939 | − | 0.590156i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.31698 | + | 9.76815i | 0.0891971 | + | 0.661583i | ||||
\(219\) | −3.12202 | + | 0.836543i | −0.210967 | + | 0.0565284i | ||||
\(220\) | 12.4232 | + | 12.2693i | 0.837569 | + | 0.827194i | ||||
\(221\) | 33.9664 | + | 9.10127i | 2.28483 | + | 0.612218i | ||||
\(222\) | −2.01369 | − | 4.81896i | −0.135150 | − | 0.323427i | ||||
\(223\) | −7.06285 | −0.472963 | −0.236482 | − | 0.971636i | \(-0.575994\pi\) | ||||
−0.236482 | + | 0.971636i | \(0.575994\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.46817 | 0.431212 | ||||||||
\(226\) | 2.85926 | + | 6.84249i | 0.190195 | + | 0.455156i | ||||
\(227\) | 16.1503 | + | 4.32747i | 1.07193 | + | 0.287224i | 0.751288 | − | 0.659975i | \(-0.229433\pi\) |
0.320647 | + | 0.947199i | \(0.396100\pi\) | |||||||
\(228\) | −3.03614 | − | 2.99853i | −0.201073 | − | 0.198583i | ||||
\(229\) | 12.8108 | − | 3.43264i | 0.846561 | − | 0.226835i | 0.190636 | − | 0.981661i | \(-0.438945\pi\) |
0.655926 | + | 0.754826i | \(0.272278\pi\) | |||||||
\(230\) | −0.787761 | − | 5.84289i | −0.0519434 | − | 0.385269i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.50115 | − | 1.91393i | 0.295515 | − | 0.125656i | ||||
\(233\) | 21.1644 | + | 12.2193i | 1.38653 | + | 0.800511i | 0.992922 | − | 0.118769i | \(-0.0378948\pi\) |
0.393604 | + | 0.919280i | \(0.371228\pi\) | |||||||
\(234\) | −15.1203 | − | 19.5786i | −0.988446 | − | 1.27989i | ||||
\(235\) | 4.45539 | − | 16.6277i | 0.290638 | − | 1.08467i | ||||
\(236\) | −5.15577 | − | 8.80290i | −0.335612 | − | 0.573020i | ||||
\(237\) | 2.17421 | − | 2.17421i | 0.141230 | − | 0.141230i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.27660 | −0.406000 | −0.203000 | − | 0.979179i | \(-0.565069\pi\) | ||||
−0.203000 | + | 0.979179i | \(0.565069\pi\) | |||||||
\(240\) | 0.0470386 | + | 3.77371i | 0.00303633 | + | 0.243592i | ||||
\(241\) | 7.50621 | + | 13.0011i | 0.483517 | + | 0.837476i | 0.999821 | − | 0.0189293i | \(-0.00602574\pi\) |
−0.516304 | + | 0.856406i | \(0.672692\pi\) | |||||||
\(242\) | 3.38017 | − | 26.3082i | 0.217286 | − | 1.69115i | ||||
\(243\) | −3.50175 | − | 13.0687i | −0.224637 | − | 0.838358i | ||||
\(244\) | −10.9736 | − | 6.24477i | −0.702515 | − | 0.399781i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.217615 | − | 0.0293396i | 0.0138746 | − | 0.00187063i | ||||
\(247\) | −20.6700 | − | 11.9338i | −1.31520 | − | 0.759330i | ||||
\(248\) | −0.329633 | − | 2.33493i | −0.0209317 | − | 0.148268i | ||||
\(249\) | −4.21688 | + | 2.43462i | −0.267234 | + | 0.154288i | ||||
\(250\) | −15.5747 | − | 6.39447i | −0.985030 | − | 0.404422i | ||||
\(251\) | 11.7926 | + | 11.7926i | 0.744339 | + | 0.744339i | 0.973410 | − | 0.229071i | \(-0.0735687\pi\) |
−0.229071 | + | 0.973410i | \(0.573569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.0473 | + | 10.0473i | −0.631671 | + | 0.631671i | ||||
\(254\) | −9.63966 | − | 23.0686i | −0.604846 | − | 1.44745i | ||||
\(255\) | −2.51551 | − | 4.35700i | −0.157528 | − | 0.272846i | ||||
\(256\) | −15.9950 | + | 0.398812i | −0.999689 | + | 0.0249258i | ||||
\(257\) | −10.1988 | + | 17.6649i | −0.636186 | + | 1.10191i | 0.350076 | + | 0.936721i | \(0.386156\pi\) |
−0.986263 | + | 0.165186i | \(0.947178\pi\) | |||||||
\(258\) | 0.895214 | − | 1.17422i | 0.0557336 | − | 0.0731039i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.59033 | + | 20.3551i | 0.346697 | + | 1.26237i | ||||
\(261\) | 4.43058 | − | 1.18717i | 0.274246 | − | 0.0734841i | ||||
\(262\) | 3.44933 | − | 2.66388i | 0.213100 | − | 0.164575i | ||||
\(263\) | −20.2176 | + | 11.6726i | −1.24667 | + | 0.719764i | −0.970443 | − | 0.241329i | \(-0.922417\pi\) |
−0.276225 | + | 0.961093i | \(0.589083\pi\) | |||||||
\(264\) | 7.16390 | − | 5.60423i | 0.440908 | − | 0.344916i | ||||
\(265\) | − | 0.107787i | − | 0.00662130i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.63723 | + | 2.63723i | 0.161396 | + | 0.161396i | ||||
\(268\) | 23.2095 | − | 13.5936i | 1.41775 | − | 0.830360i | ||||
\(269\) | −30.1489 | − | 8.07837i | −1.83821 | − | 0.492547i | −0.839502 | − | 0.543356i | \(-0.817153\pi\) |
−0.998708 | + | 0.0508094i | \(0.983820\pi\) | |||||||
\(270\) | −0.961142 | + | 7.48065i | −0.0584932 | + | 0.455258i | ||||
\(271\) | −0.731959 | + | 1.26779i | −0.0444633 | + | 0.0770127i | −0.887401 | − | 0.460999i | \(-0.847491\pi\) |
0.842937 | + | 0.538012i | \(0.180824\pi\) | |||||||
\(272\) | 18.3373 | − | 10.8940i | 1.11186 | − | 0.660546i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.61180 | − | 7.32792i | −0.580670 | − | 0.442696i | ||||
\(275\) | 3.44281 | + | 12.8487i | 0.207609 | + | 0.774808i | ||||
\(276\) | −3.07116 | + | 0.0191400i | −0.184862 | + | 0.00115209i | ||||
\(277\) | −0.509633 | + | 1.90198i | −0.0306209 | + | 0.114279i | −0.979545 | − | 0.201226i | \(-0.935507\pi\) |
0.948924 | + | 0.315505i | \(0.102174\pi\) | |||||||
\(278\) | 4.34911 | − | 10.5929i | 0.260842 | − | 0.635321i | ||||
\(279\) | − | 2.21138i | − | 0.132392i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.66742i | 0.338090i | 0.985608 | + | 0.169045i | \(0.0540683\pi\) | ||||
−0.985608 | + | 0.169045i | \(0.945932\pi\) | |||||||
\(282\) | −8.29534 | − | 3.40580i | −0.493980 | − | 0.202812i | ||||
\(283\) | −6.09854 | + | 22.7600i | −0.362520 | + | 1.35294i | 0.508231 | + | 0.861221i | \(0.330300\pi\) |
−0.870751 | + | 0.491724i | \(0.836367\pi\) | |||||||
\(284\) | 2.92143 | + | 2.88524i | 0.173355 | + | 0.171208i | ||||
\(285\) | 0.883805 | + | 3.29840i | 0.0523521 | + | 0.195381i | ||||
\(286\) | 30.8438 | − | 40.4569i | 1.82383 | − | 2.39226i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −14.9050 | − | 1.72649i | −0.878283 | − | 0.101734i | ||||
\(289\) | −5.71672 | + | 9.90165i | −0.336278 | + | 0.582450i | ||||
\(290\) | −3.88213 | − | 0.498790i | −0.227966 | − | 0.0292900i | ||||
\(291\) | −10.7104 | − | 2.86985i | −0.627856 | − | 0.168234i | ||||
\(292\) | −2.77198 | + | 10.6092i | −0.162218 | + | 0.620857i | ||||
\(293\) | 17.1121 | + | 17.1121i | 0.999698 | + | 0.999698i | 1.00000 | 0.000302098i | \(-9.61608e-5\pi\) | |
−0.000302098 | 1.00000i | \(0.500096\pi\) | ||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.16360i | 0.475303i | ||||||||
\(296\) | −17.5880 | − | 2.14844i | −1.02228 | − | 0.124875i | ||||
\(297\) | 15.7417 | − | 9.08849i | 0.913427 | − | 0.527367i | ||||
\(298\) | −0.483064 | − | 0.625496i | −0.0279831 | − | 0.0362340i | ||||
\(299\) | −16.5927 | + | 4.44599i | −0.959579 | + | 0.257118i | ||||
\(300\) | −1.42203 | + | 2.49887i | −0.0821010 | + | 0.144272i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.17874 | + | 3.18582i | 0.240459 | + | 0.183323i | ||||
\(303\) | 1.20272 | − | 2.08317i | 0.0690944 | − | 0.119675i | ||||
\(304\) | −13.9359 | + | 3.92092i | −0.799279 | + | 0.224880i | ||||
\(305\) | 5.05186 | + | 8.75008i | 0.289269 | + | 0.501028i | ||||
\(306\) | 18.4558 | − | 7.71209i | 1.05505 | − | 0.440871i | ||||
\(307\) | −9.59837 | + | 9.59837i | −0.547808 | + | 0.547808i | −0.925806 | − | 0.377998i | \(-0.876612\pi\) |
0.377998 | + | 0.925806i | \(0.376612\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.22662 | + | 3.22662i | 0.183556 | + | 0.183556i | ||||
\(310\) | −0.716688 | + | 1.74560i | −0.0407051 | + | 0.0991436i | ||||
\(311\) | 16.6161 | − | 9.59331i | 0.942213 | − | 0.543987i | 0.0515594 | − | 0.998670i | \(-0.483581\pi\) |
0.890653 | + | 0.454683i | \(0.150248\pi\) | |||||||
\(312\) | 10.8880 | − | 1.53712i | 0.616414 | − | 0.0870220i | ||||
\(313\) | −4.36445 | − | 2.51982i | −0.246693 | − | 0.142428i | 0.371556 | − | 0.928411i | \(-0.378824\pi\) |
−0.618249 | + | 0.785982i | \(0.712158\pi\) | |||||||
\(314\) | −1.06769 | − | 7.91918i | −0.0602535 | − | 0.446905i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.76262 | − | 10.0591i | −0.155409 | − | 0.565866i | ||||
\(317\) | 2.02264 | + | 7.54861i | 0.113603 | + | 0.423972i | 0.999179 | − | 0.0405232i | \(-0.0129025\pi\) |
−0.885576 | + | 0.464495i | \(0.846236\pi\) | |||||||
\(318\) | −0.0556906 | − | 0.00715533i | −0.00312297 | − | 0.000401251i | ||||
\(319\) | 4.71652 | + | 8.16926i | 0.264075 | + | 0.457391i | ||||
\(320\) | 11.2060 | + | 6.19339i | 0.626435 | + | 0.346221i | ||||
\(321\) | −1.94627 | −0.108630 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.6464 | − | 13.6464i | 0.759306 | − | 0.759306i | ||||
\(324\) | −11.5966 | − | 3.02998i | −0.644257 | − | 0.168332i | ||||
\(325\) | −4.16216 | + | 15.5334i | −0.230875 | + | 0.861638i | ||||
\(326\) | −5.33705 | + | 4.12175i | −0.295592 | + | 0.228282i | ||||
\(327\) | −3.55827 | − | 2.05437i | −0.196773 | − | 0.113607i | ||||
\(328\) | 0.278636 | − | 0.690885i | 0.0153851 | − | 0.0381477i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −7.21323 | + | 0.972515i | −0.397075 | + | 0.0535352i | ||||
\(331\) | 20.1508 | − | 5.39940i | 1.10759 | − | 0.296778i | 0.341739 | − | 0.939795i | \(-0.388984\pi\) |
0.765852 | + | 0.643017i | \(0.222318\pi\) | |||||||
\(332\) | 0.102949 | + | 16.5190i | 0.00565006 | + | 0.906597i | ||||
\(333\) | −16.0502 | − | 4.30064i | −0.879545 | − | 0.235673i | ||||
\(334\) | −16.2108 | + | 6.77400i | −0.887016 | + | 0.370657i | ||||
\(335\) | −21.5239 | −1.17598 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.7111 | 0.910311 | 0.455156 | − | 0.890412i | \(-0.349584\pi\) | ||||
0.455156 | + | 0.890412i | \(0.349584\pi\) | |||||||
\(338\) | 39.7845 | − | 16.6247i | 2.16399 | − | 0.904266i | ||||
\(339\) | −2.98600 | − | 0.800096i | −0.162177 | − | 0.0434552i | ||||
\(340\) | −17.0679 | + | 0.106370i | −0.925635 | + | 0.00576871i | ||||
\(341\) | 4.39281 | − | 1.17705i | 0.237884 | − | 0.0637408i | ||||
\(342\) | −13.4546 | + | 1.81400i | −0.727542 | + | 0.0980900i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.96017 | − | 4.60990i | −0.105685 | − | 0.248549i | ||||
\(345\) | 2.12840 | + | 1.22883i | 0.114589 | + | 0.0661582i | ||||
\(346\) | −14.6562 | + | 11.3189i | −0.787925 | + | 0.608506i | ||||
\(347\) | 2.04215 | − | 7.62139i | 0.109628 | − | 0.409138i | −0.889201 | − | 0.457517i | \(-0.848739\pi\) |
0.998829 | + | 0.0483791i | \(0.0154056\pi\) | |||||||
\(348\) | −0.515423 | + | 1.97268i | −0.0276296 | + | 0.105747i | ||||
\(349\) | −17.9789 | + | 17.9789i | −0.962388 | + | 0.962388i | −0.999318 | − | 0.0369299i | \(-0.988242\pi\) |
0.0369299 | + | 0.999318i | \(0.488242\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.9750 | 1.17294 | ||||||||
\(352\) | −4.50384 | − | 30.5270i | −0.240056 | − | 1.62709i | ||||
\(353\) | 12.5159 | + | 21.6782i | 0.666155 | + | 1.15381i | 0.978971 | + | 0.204000i | \(0.0653942\pi\) |
−0.312816 | + | 0.949814i | \(0.601272\pi\) | |||||||
\(354\) | 4.21791 | + | 0.541933i | 0.224180 | + | 0.0288034i | ||||
\(355\) | −0.850413 | − | 3.17379i | −0.0451352 | − | 0.168447i | ||||
\(356\) | 12.2012 | − | 3.35095i | 0.646664 | − | 0.177600i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.66033 | + | 19.7319i | 0.140603 | + | 1.04286i | ||||
\(359\) | 15.5806 | + | 8.99548i | 0.822314 | + | 0.474763i | 0.851214 | − | 0.524819i | \(-0.175867\pi\) |
−0.0288999 | + | 0.999582i | \(0.509200\pi\) | |||||||
\(360\) | 9.59377 | + | 7.22008i | 0.505636 | + | 0.380532i | ||||
\(361\) | 5.11046 | − | 2.95053i | 0.268972 | − | 0.155291i | ||||
\(362\) | 3.85975 | − | 9.40101i | 0.202864 | − | 0.494106i | ||||
\(363\) | 7.81836 | + | 7.81836i | 0.410357 | + | 0.410357i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.20470 | − | 6.20470i | 0.324769 | − | 0.324769i | ||||
\(366\) | 4.85629 | − | 2.02929i | 0.253842 | − | 0.106073i | ||||
\(367\) | −5.15387 | − | 8.92677i | −0.269030 | − | 0.465974i | 0.699582 | − | 0.714553i | \(-0.253370\pi\) |
−0.968612 | + | 0.248579i | \(0.920036\pi\) | |||||||
\(368\) | −5.09681 | + | 9.08767i | −0.265690 | + | 0.473728i | ||||
\(369\) | 0.349306 | − | 0.605015i | 0.0181841 | − | 0.0314958i | ||||
\(370\) | 11.2758 | + | 8.59651i | 0.586199 | + | 0.446911i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.854329 | + | 0.486174i | 0.0442949 | + | 0.0252069i | ||||
\(373\) | −21.9323 | + | 5.87673i | −1.13561 | + | 0.304286i | −0.777184 | − | 0.629273i | \(-0.783353\pi\) |
−0.358425 | + | 0.933558i | \(0.616686\pi\) | |||||||
\(374\) | 25.1431 | + | 32.5566i | 1.30012 | + | 1.68346i | ||||
\(375\) | 6.07800 | − | 3.50914i | 0.313867 | − | 0.181211i | ||||
\(376\) | −23.9614 | + | 18.7447i | −1.23572 | + | 0.966685i | ||||
\(377\) | 11.4040i | 0.587338i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.7922 | + | 15.7922i | 0.811190 | + | 0.811190i | 0.984812 | − | 0.173622i | \(-0.0555471\pi\) |
−0.173622 | + | 0.984812i | \(0.555547\pi\) | |||||||
\(380\) | 11.2086 | + | 2.92859i | 0.574988 | + | 0.150233i | ||||
\(381\) | 10.0669 | + | 2.69743i | 0.515745 | + | 0.138193i | ||||
\(382\) | −29.1656 | − | 3.74730i | −1.49224 | − | 0.191729i | ||||
\(383\) | −9.18163 | + | 15.9031i | −0.469160 | + | 0.812608i | −0.999378 | − | 0.0352526i | \(-0.988776\pi\) |
0.530219 | + | 0.847861i | \(0.322110\pi\) | |||||||
\(384\) | 3.94386 | − | 5.37870i | 0.201259 | − | 0.274481i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.4420 | − | 15.0081i | 0.582383 | − | 0.763893i | ||||
\(387\) | −1.21585 | − | 4.53762i | −0.0618052 | − | 0.230660i | ||||
\(388\) | −26.4335 | + | 26.7651i | −1.34196 | + | 1.35879i | ||||
\(389\) | 5.10801 | − | 19.0634i | 0.258987 | − | 0.966551i | −0.706842 | − | 0.707371i | \(-0.749881\pi\) |
0.965829 | − | 0.259180i | \(-0.0834523\pi\) | |||||||
\(390\) | −8.13994 | − | 3.34200i | −0.412182 | − | 0.169229i | ||||
\(391\) | − | 13.8898i | − | 0.702438i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.81674i | 0.0916426i | ||||||||
\(394\) | −0.147715 | + | 0.359781i | −0.00744175 | + | 0.0181255i | ||||
\(395\) | −2.16051 | + | 8.06314i | −0.108707 | + | 0.405701i | ||||
\(396\) | −0.180341 | − | 28.9372i | −0.00906249 | − | 1.45415i | ||||
\(397\) | −0.412931 | − | 1.54108i | −0.0207244 | − | 0.0773446i | 0.954789 | − | 0.297284i | \(-0.0960808\pi\) |
−0.975514 | + | 0.219939i | \(0.929414\pi\) | |||||||
\(398\) | 16.1952 | + | 12.3470i | 0.811793 | + | 0.618901i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.98201 | + | 8.38595i | 0.249101 | + | 0.419297i | ||||
\(401\) | 7.17349 | − | 12.4248i | 0.358227 | − | 0.620467i | −0.629438 | − | 0.777051i | \(-0.716715\pi\) |
0.987665 | + | 0.156584i | \(0.0500481\pi\) | |||||||
\(402\) | −1.42885 | + | 11.1208i | −0.0712645 | + | 0.554657i | ||||
\(403\) | 5.31066 | + | 1.42299i | 0.264543 | + | 0.0708841i | ||||
\(404\) | −4.12430 | − | 7.04177i | −0.205191 | − | 0.350341i | ||||
\(405\) | 6.78219 | + | 6.78219i | 0.337010 | + | 0.337010i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 34.1721i | − | 1.69385i | ||||||
\(408\) | −1.07808 | + | 8.82557i | −0.0533727 | + | 0.436931i | ||||
\(409\) | 33.9931 | − | 19.6259i | 1.68085 | − | 0.970438i | 0.719749 | − | 0.694234i | \(-0.244257\pi\) |
0.961099 | − | 0.276204i | \(-0.0890765\pi\) | |||||||
\(410\) | −0.471811 | + | 0.364375i | −0.0233011 | + | 0.0179952i | ||||
\(411\) | 4.86666 | − | 1.30402i | 0.240055 | − | 0.0643224i | ||||
\(412\) | 14.9280 | − | 4.09984i | 0.735451 | − | 0.201984i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.92412 | + | 7.77048i | −0.291155 | + | 0.381898i | ||||
\(415\) | 6.60959 | − | 11.4481i | 0.324452 | − | 0.561967i | ||||
\(416\) | 13.7373 | − | 34.6835i | 0.673526 | − | 1.70050i | ||||
\(417\) | 2.38669 | + | 4.13387i | 0.116877 | + | 0.202437i | ||||
\(418\) | −10.7649 | − | 25.7614i | −0.526529 | − | 1.26003i | ||||
\(419\) | −4.41473 | + | 4.41473i | −0.215673 | + | 0.215673i | −0.806672 | − | 0.590999i | \(-0.798734\pi\) |
0.590999 | + | 0.806672i | \(0.298734\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.57494 | − | 7.57494i | −0.369180 | − | 0.369180i | 0.497998 | − | 0.867178i | \(-0.334069\pi\) |
−0.867178 | + | 0.497998i | \(0.834069\pi\) | |||||||
\(422\) | 14.2896 | + | 5.86685i | 0.695608 | + | 0.285594i | ||||
\(423\) | −24.7074 | + | 14.2648i | −1.20132 | + | 0.693580i | ||||
\(424\) | −0.114544 | + | 0.152202i | −0.00556275 | + | 0.00739158i | ||||
\(425\) | −11.2610 | − | 6.50155i | −0.546239 | − | 0.315371i | ||||
\(426\) | −1.69626 | + | 0.228697i | −0.0821842 | + | 0.0110804i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.26574 | + | 5.73873i | −0.157856 | + | 0.277392i | ||||
\(429\) | 5.48872 | + | 20.4842i | 0.264998 | + | 0.988985i | ||||
\(430\) | −0.510841 | + | 3.97592i | −0.0246349 | + | 0.191736i | ||||
\(431\) | 9.26979 | + | 16.0558i | 0.446510 | + | 0.773378i | 0.998156 | − | 0.0607001i | \(-0.0193333\pi\) |
−0.551646 | + | 0.834078i | \(0.686000\pi\) | |||||||
\(432\) | 9.30681 | − | 9.54175i | 0.447774 | − | 0.459078i | ||||
\(433\) | 7.21190 | 0.346582 | 0.173291 | − | 0.984871i | \(-0.444560\pi\) | ||||
0.173291 | + | 0.984871i | \(0.444560\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.15370 | − | 1.15370i | 0.0553159 | − | 0.0553159i | ||||
\(436\) | −12.0281 | + | 7.04472i | −0.576040 | + | 0.337381i | ||||
\(437\) | −2.44003 | + | 9.10633i | −0.116723 | + | 0.435615i | ||||
\(438\) | −2.79391 | − | 3.61770i | −0.133498 | − | 0.172860i | ||||
\(439\) | 13.1302 | + | 7.58073i | 0.626671 | + | 0.361809i | 0.779462 | − | 0.626450i | \(-0.215493\pi\) |
−0.152791 | + | 0.988259i | \(0.548826\pi\) | |||||||
\(440\) | −9.23590 | + | 22.9006i | −0.440304 | + | 1.09174i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.64471 | + | 49.2843i | 0.316056 | + | 2.34422i | ||||
\(443\) | 2.89250 | − | 0.775043i | 0.137427 | − | 0.0368234i | −0.189450 | − | 0.981890i | \(-0.560670\pi\) |
0.326877 | + | 0.945067i | \(0.394004\pi\) | |||||||
\(444\) | 5.19012 | − | 5.25522i | 0.246312 | − | 0.249402i | ||||
\(445\) | −9.78027 | − | 2.62062i | −0.463629 | − | 0.124229i | ||||
\(446\) | −3.85112 | − | 9.21610i | −0.182356 | − | 0.436395i | ||||
\(447\) | 0.329445 | 0.0155822 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.29509 | 0.202698 | 0.101349 | − | 0.994851i | \(-0.467684\pi\) | ||||
0.101349 | + | 0.994851i | \(0.467684\pi\) | |||||||
\(450\) | 3.52687 | + | 8.44013i | 0.166258 | + | 0.397871i | ||||
\(451\) | 1.38776 | + | 0.371849i | 0.0653470 | + | 0.0175097i | ||||
\(452\) | −7.36950 | + | 7.46193i | −0.346632 | + | 0.350980i | ||||
\(453\) | −2.11578 | + | 0.566922i | −0.0994082 | + | 0.0266363i | ||||
\(454\) | 3.15942 | + | 23.4337i | 0.148279 | + | 1.09980i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.25719 | − | 5.59676i | 0.105703 | − | 0.262093i | ||||
\(457\) | −24.0610 | − | 13.8916i | −1.12553 | − | 0.649823i | −0.182721 | − | 0.983165i | \(-0.558490\pi\) |
−0.942806 | + | 0.333342i | \(0.891824\pi\) | |||||||
\(458\) | 11.4644 | + | 14.8447i | 0.535698 | + | 0.693648i | ||||
\(459\) | −4.59884 | + | 17.1631i | −0.214655 | + | 0.801104i | ||||
\(460\) | 7.19467 | − | 4.21385i | 0.335453 | − | 0.196472i | ||||
\(461\) | −6.50912 | + | 6.50912i | −0.303160 | + | 0.303160i | −0.842249 | − | 0.539089i | \(-0.818769\pi\) |
0.539089 | + | 0.842249i | \(0.318769\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.1018 | −1.81722 | −0.908608 | − | 0.417650i | \(-0.862854\pi\) | ||||
−0.908608 | + | 0.417650i | \(0.862854\pi\) | |||||||
\(464\) | 4.95175 | + | 4.82982i | 0.229879 | + | 0.224219i | ||||
\(465\) | −0.393302 | − | 0.681219i | −0.0182389 | − | 0.0315908i | ||||
\(466\) | −4.40436 | + | 34.2795i | −0.204028 | + | 1.58797i | ||||
\(467\) | 6.02544 | + | 22.4873i | 0.278824 | + | 1.04059i | 0.953235 | + | 0.302230i | \(0.0977311\pi\) |
−0.674411 | + | 0.738356i | \(0.735602\pi\) | |||||||
\(468\) | 17.3029 | − | 30.4055i | 0.799827 | − | 1.40550i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 24.1264 | − | 3.25282i | 1.11287 | − | 0.150041i | ||||
\(471\) | 2.88474 | + | 1.66551i | 0.132922 | + | 0.0767424i | ||||
\(472\) | 8.67538 | − | 11.5275i | 0.399317 | − | 0.530597i | ||||
\(473\) | 8.36662 | − | 4.83047i | 0.384698 | − | 0.222105i | ||||
\(474\) | 4.02258 | + | 1.65154i | 0.184763 | + | 0.0758579i | ||||
\(475\) | 6.24073 | + | 6.24073i | 0.286344 | + | 0.286344i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.126316 | + | 0.126316i | −0.00578361 | + | 0.00578361i | ||||
\(478\) | −3.42241 | − | 8.19015i | −0.156537 | − | 0.374609i | ||||
\(479\) | 18.6282 | + | 32.2650i | 0.851145 | + | 1.47423i | 0.880175 | + | 0.474649i | \(0.157425\pi\) |
−0.0290300 | + | 0.999579i | \(0.509242\pi\) | |||||||
\(480\) | −4.89855 | + | 2.11905i | −0.223587 | + | 0.0967209i | ||||
\(481\) | 20.6561 | − | 35.7774i | 0.941836 | − | 1.63131i | ||||
\(482\) | −12.8719 | + | 16.8837i | −0.586300 | + | 0.769031i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 36.1719 | − | 9.93424i | 1.64418 | − | 0.451556i | ||||
\(485\) | 29.0770 | − | 7.79117i | 1.32032 | − | 0.353779i | ||||
\(486\) | 15.1436 | − | 11.6952i | 0.686927 | − | 0.530506i | ||||
\(487\) | 33.2743 | − | 19.2110i | 1.50780 | − | 0.870531i | 0.507846 | − | 0.861448i | \(-0.330442\pi\) |
0.999959 | − | 0.00908353i | \(-0.00289142\pi\) | |||||||
\(488\) | 2.16508 | − | 17.7242i | 0.0980086 | − | 0.802338i | ||||
\(489\) | − | 2.81100i | − | 0.127118i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.52330 | + | 9.52330i | 0.429781 | + | 0.429781i | 0.888554 | − | 0.458773i | \(-0.151711\pi\) |
−0.458773 | + | 0.888554i | \(0.651711\pi\) | |||||||
\(492\) | 0.156942 | + | 0.267961i | 0.00707549 | + | 0.0120806i | ||||
\(493\) | −8.90689 | − | 2.38659i | −0.401146 | − | 0.107487i | ||||
\(494\) | 4.30147 | − | 33.4787i | 0.193532 | − | 1.50628i | ||||
\(495\) | −11.5784 | + | 20.0543i | −0.520409 | + | 0.901374i | ||||
\(496\) | 2.86704 | − | 1.70328i | 0.128734 | − | 0.0764797i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −5.47618 | − | 4.17497i | −0.245393 | − | 0.187085i | ||||
\(499\) | 3.58042 | + | 13.3623i | 0.160282 | + | 0.598180i | 0.998595 | + | 0.0529909i | \(0.0168754\pi\) |
−0.838313 | + | 0.545189i | \(0.816458\pi\) | |||||||
\(500\) | −0.148386 | − | 23.8096i | −0.00663601 | − | 1.06480i | ||||
\(501\) | 1.89554 | − | 7.07425i | 0.0846865 | − | 0.316054i | ||||
\(502\) | −8.95769 | + | 21.8178i | −0.399801 | + | 0.973777i | ||||
\(503\) | 11.0554i | 0.492938i | 0.969151 | + | 0.246469i | \(0.0792703\pi\) | ||||
−0.969151 | + | 0.246469i | \(0.920730\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.53038i | 0.290598i | ||||||||
\(506\) | −18.5889 | − | 7.63201i | −0.826379 | − | 0.339284i | ||||
\(507\) | −4.65203 | + | 17.3616i | −0.206604 | + | 0.771056i | ||||
\(508\) | 24.8454 | − | 25.1570i | 1.10234 | − | 1.11616i | ||||
\(509\) | −0.0634101 | − | 0.236650i | −0.00281060 | − | 0.0104893i | 0.964506 | − | 0.264060i | \(-0.0850617\pi\) |
−0.967317 | + | 0.253571i | \(0.918395\pi\) | |||||||
\(510\) | 4.31369 | − | 5.65814i | 0.191014 | − | 0.250546i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −9.24192 | − | 20.6540i | −0.408439 | − | 0.912786i | ||||
\(513\) | 6.03011 | − | 10.4445i | 0.266236 | − | 0.461134i | ||||
\(514\) | −28.6115 | − | 3.67611i | −1.26200 | − | 0.162146i | ||||
\(515\) | −11.9660 | − | 3.20629i | −0.527286 | − | 0.141286i | ||||
\(516\) | 2.02034 | + | 0.527875i | 0.0889404 | + | 0.0232384i | ||||
\(517\) | −41.4874 | − | 41.4874i | −1.82461 | − | 1.82461i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 7.71937i | − | 0.338843i | ||||||
\(520\) | −23.5126 | + | 18.3936i | −1.03109 | + | 0.806611i | ||||
\(521\) | −25.9687 | + | 14.9930i | −1.13771 | + | 0.656857i | −0.945862 | − | 0.324568i | \(-0.894781\pi\) |
−0.191847 | + | 0.981425i | \(0.561448\pi\) | |||||||
\(522\) | 3.96495 | + | 5.13401i | 0.173541 | + | 0.224710i | ||||
\(523\) | −2.03443 | + | 0.545124i | −0.0889594 | + | 0.0238366i | −0.303024 | − | 0.952983i | \(-0.597996\pi\) |
0.214065 | + | 0.976819i | \(0.431330\pi\) | |||||||
\(524\) | 5.35681 | + | 3.04840i | 0.234013 | + | 0.133170i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.2552 | − | 20.0166i | −1.14478 | − | 0.872766i | ||||
\(527\) | −2.22279 | + | 3.84999i | −0.0968263 | + | 0.167708i | ||||
\(528\) | 11.2190 | + | 6.29218i | 0.488245 | + | 0.273832i | ||||
\(529\) | −8.10740 | − | 14.0424i | −0.352495 | − | 0.610540i | ||||
\(530\) | 0.140648 | − | 0.0587724i | 0.00610935 | − | 0.00255291i | ||||
\(531\) | 9.56695 | − | 9.56695i | 0.415170 | − | 0.415170i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.22818 | + | 1.22818i | 0.0531983 | + | 0.0531983i | ||||
\(534\) | −2.00326 | + | 4.87923i | −0.0866894 | + | 0.211145i | ||||
\(535\) | 4.57591 | − | 2.64190i | 0.197834 | − | 0.114219i | ||||
\(536\) | 30.3932 | + | 22.8733i | 1.31279 | + | 0.987976i | ||||
\(537\) | −7.18780 | − | 4.14988i | −0.310176 | − | 0.179080i | ||||
\(538\) | −5.89790 | − | 43.7452i | −0.254277 | − | 1.88599i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −10.2854 | + | 2.82477i | −0.442611 | + | 0.121559i | ||||
\(541\) | 4.42294 | + | 16.5066i | 0.190157 | + | 0.709676i | 0.993467 | + | 0.114115i | \(0.0364034\pi\) |
−0.803310 | + | 0.595561i | \(0.796930\pi\) | |||||||
\(542\) | −2.05341 | − | 0.263830i | −0.0882016 | − | 0.0113325i | ||||
\(543\) | 2.11814 | + | 3.66873i | 0.0908982 | + | 0.157440i | ||||
\(544\) | 24.2139 | + | 17.9877i | 1.03816 | + | 0.771214i | ||||
\(545\) | 11.1545 | 0.477808 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.2663 | − | 12.2663i | 0.524468 | − | 0.524468i | −0.394449 | − | 0.918918i | \(-0.629065\pi\) |
0.918918 | + | 0.394449i | \(0.129065\pi\) | |||||||
\(548\) | 4.32101 | − | 16.5378i | 0.184584 | − | 0.706460i | ||||
\(549\) | 4.33395 | − | 16.1745i | 0.184969 | − | 0.690312i | ||||
\(550\) | −14.8887 | + | 11.4984i | −0.634856 | + | 0.490292i | ||||
\(551\) | 5.42021 | + | 3.12936i | 0.230909 | + | 0.133315i | ||||
\(552\) | −1.69957 | − | 3.99703i | −0.0723385 | − | 0.170125i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.75972 | + | 0.372076i | −0.117249 | + | 0.0158080i | ||||
\(555\) | −5.70916 | + | 1.52977i | −0.242340 | + | 0.0649349i | ||||
\(556\) | 16.1938 | − | 0.100923i | 0.686770 | − | 0.00428007i | ||||
\(557\) | 3.17901 | + | 0.851813i | 0.134699 | + | 0.0360925i | 0.325539 | − | 0.945529i | \(-0.394454\pi\) |
−0.190840 | + | 0.981621i | \(0.561121\pi\) | |||||||
\(558\) | 2.88557 | − | 1.20579i | 0.122156 | − | 0.0510451i | ||||
\(559\) | 11.6795 | 0.493992 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.1474 | −0.723964 | ||||||||
\(562\) | −7.39524 | + | 3.09024i | −0.311950 | + | 0.130354i | ||||
\(563\) | 16.4703 | + | 4.41321i | 0.694141 | + | 0.185994i | 0.588605 | − | 0.808421i | \(-0.299677\pi\) |
0.105536 | + | 0.994415i | \(0.466344\pi\) | |||||||
\(564\) | −0.0790327 | − | 12.6814i | −0.00332788 | − | 0.533984i | ||||
\(565\) | 8.10650 | − | 2.17213i | 0.341043 | − | 0.0913822i | ||||
\(566\) | −33.0242 | + | 4.45245i | −1.38811 | + | 0.187151i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.17191 | + | 5.38531i | −0.0911315 | + | 0.225963i | ||||
\(569\) | −6.92621 | − | 3.99885i | −0.290362 | − | 0.167641i | 0.347743 | − | 0.937590i | \(-0.386948\pi\) |
−0.638105 | + | 0.769949i | \(0.720281\pi\) | |||||||
\(570\) | −3.82208 | + | 2.95175i | −0.160089 | + | 0.123635i | ||||
\(571\) | 8.07146 | − | 30.1231i | 0.337780 | − | 1.26061i | −0.563044 | − | 0.826427i | \(-0.690370\pi\) |
0.900824 | − | 0.434185i | \(-0.142964\pi\) | |||||||
\(572\) | 69.6090 | + | 18.1875i | 2.91050 | + | 0.760457i | ||||
\(573\) | 8.66753 | − | 8.66753i | 0.362091 | − | 0.362091i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.35204 | 0.264899 | ||||||||
\(576\) | −5.87430 | − | 20.3904i | −0.244762 | − | 0.849601i | ||||
\(577\) | −21.7100 | − | 37.6028i | −0.903798 | − | 1.56542i | −0.822523 | − | 0.568732i | \(-0.807434\pi\) |
−0.0812747 | − | 0.996692i | \(-0.525899\pi\) | |||||||
\(578\) | −16.0375 | − | 2.06056i | −0.667072 | − | 0.0857079i | ||||
\(579\) | 2.03613 | + | 7.59893i | 0.0846185 | + | 0.315801i | ||||
\(580\) | −1.46593 | − | 5.33765i | −0.0608695 | − | 0.221634i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.09524 | − | 15.5405i | −0.0868503 | − | 0.644176i | ||||
\(583\) | −0.318155 | − | 0.183687i | −0.0131766 | − | 0.00760752i | ||||
\(584\) | −15.3551 | + | 2.16775i | −0.635399 | + | 0.0897022i | ||||
\(585\) | −24.2446 | + | 13.9976i | −1.00239 | + | 0.578730i | ||||
\(586\) | −12.9984 | + | 31.6596i | −0.536960 | + | 1.30785i | ||||
\(587\) | −18.2274 | − | 18.2274i | −0.752326 | − | 0.752326i | 0.222587 | − | 0.974913i | \(-0.428550\pi\) |
−0.974913 | + | 0.222587i | \(0.928550\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.13362 | − | 2.13362i | 0.0879143 | − | 0.0879143i | ||||
\(590\) | −10.6524 | + | 4.45132i | −0.438554 | + | 0.183258i | ||||
\(591\) | −0.0810624 | − | 0.140404i | −0.00333446 | − | 0.00577546i | ||||
\(592\) | −6.78667 | − | 24.1215i | −0.278930 | − | 0.991386i | ||||
\(593\) | 19.8757 | − | 34.4257i | 0.816197 | − | 1.41370i | −0.0922677 | − | 0.995734i | \(-0.529412\pi\) |
0.908465 | − | 0.417961i | \(-0.137255\pi\) | |||||||
\(594\) | 20.4427 | + | 15.5853i | 0.838774 | + | 0.639471i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.552793 | − | 0.971396i | 0.0226433 | − | 0.0397899i | ||||
\(597\) | −8.19998 | + | 2.19718i | −0.335603 | + | 0.0899246i | ||||
\(598\) | −14.8488 | − | 19.2270i | −0.607214 | − | 0.786252i | ||||
\(599\) | −32.5016 | + | 18.7648i | −1.32798 | + | 0.766708i | −0.984987 | − | 0.172631i | \(-0.944773\pi\) |
−0.342991 | + | 0.939339i | \(0.611440\pi\) | |||||||
\(600\) | −4.03608 | − | 0.493022i | −0.164772 | − | 0.0201276i | ||||
\(601\) | − | 3.99899i | − | 0.163122i | −0.996668 | − | 0.0815611i | \(-0.974009\pi\) | ||
0.996668 | − | 0.0815611i | \(-0.0259906\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.2240 | + | 25.2240i | 1.02720 | + | 1.02720i | ||||
\(604\) | −1.87856 | + | 7.18982i | −0.0764376 | + | 0.292550i | ||||
\(605\) | −28.9947 | − | 7.76910i | −1.17880 | − | 0.315859i | ||||
\(606\) | 3.37407 | + | 0.433513i | 0.137062 | + | 0.0176103i | ||||
\(607\) | 12.1836 | − | 21.1026i | 0.494517 | − | 0.856529i | −0.505463 | − | 0.862848i | \(-0.668678\pi\) |
0.999980 | + | 0.00631933i | \(0.00201152\pi\) | |||||||
\(608\) | −12.7151 | − | 16.0466i | −0.515663 | − | 0.650776i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.66311 | + | 11.3631i | −0.350759 | + | 0.460080i | ||||
\(611\) | −18.3584 | − | 68.5144i | −0.742700 | − | 2.77179i | ||||
\(612\) | 20.1265 | + | 19.8772i | 0.813567 | + | 0.803489i | ||||
\(613\) | −6.11872 | + | 22.8354i | −0.247133 | + | 0.922312i | 0.725167 | + | 0.688573i | \(0.241763\pi\) |
−0.972299 | + | 0.233739i | \(0.924904\pi\) | |||||||
\(614\) | −17.7583 | − | 7.29097i | −0.716666 | − | 0.294240i | ||||
\(615\) | − | 0.248501i | − | 0.0100205i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2.64202i | − | 0.106364i | −0.998585 | − | 0.0531819i | \(-0.983064\pi\) | ||
0.998585 | − | 0.0531819i | \(-0.0169363\pi\) | |||||||
\(618\) | −2.45095 | + | 5.96967i | −0.0985919 | + | 0.240136i | ||||
\(619\) | 9.87436 | − | 36.8516i | 0.396884 | − | 1.48119i | −0.421664 | − | 0.906752i | \(-0.638554\pi\) |
0.818548 | − | 0.574439i | \(-0.194780\pi\) | |||||||
\(620\) | −2.66857 | + | 0.0166310i | −0.107172 | + | 0.000667916i | ||||
\(621\) | −2.24654 | − | 8.38421i | −0.0901507 | − | 0.336447i | ||||
\(622\) | 21.5782 | + | 16.4510i | 0.865207 | + | 0.659623i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7.94260 | + | 13.3693i | 0.317959 | + | 0.535202i | ||||
\(625\) | −3.43035 | + | 5.94155i | −0.137214 | + | 0.237662i | ||||
\(626\) | 0.908252 | − | 7.06901i | 0.0363011 | − | 0.282534i | ||||
\(627\) | 11.2421 | + | 3.01230i | 0.448964 | + | 0.120300i | ||||
\(628\) | 9.75133 | − | 5.71125i | 0.389120 | − | 0.227904i | ||||
\(629\) | 23.6204 | + | 23.6204i | 0.941805 | + | 0.941805i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.9710i | 0.755223i | 0.925964 | + | 0.377611i | \(0.123254\pi\) | ||||
−0.925964 | + | 0.377611i | \(0.876746\pi\) | |||||||
\(632\) | 11.6194 | − | 9.08971i | 0.462195 | − | 0.361569i | ||||
\(633\) | −5.57650 | + | 3.21960i | −0.221646 | + | 0.127967i | ||||
\(634\) | −8.74708 | + | 6.75528i | −0.347391 | + | 0.268286i | ||||
\(635\) | −27.3301 | + | 7.32308i | −1.08456 | + | 0.290607i | ||||
\(636\) | −0.0210293 | − | 0.0765705i | −0.000833867 | − | 0.00303622i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.08807 | + | 10.6089i | −0.320210 | + | 0.420009i | ||||
\(639\) | −2.72277 | + | 4.71597i | −0.107711 | + | 0.186561i | ||||
\(640\) | −1.97134 | + | 17.9994i | −0.0779239 | + | 0.711490i | ||||
\(641\) | −15.6881 | − | 27.1726i | −0.619643 | − | 1.07325i | −0.989551 | − | 0.144184i | \(-0.953944\pi\) |
0.369908 | − | 0.929068i | \(-0.379389\pi\) | |||||||
\(642\) | −1.06123 | − | 2.53963i | −0.0418835 | − | 0.100231i | ||||
\(643\) | 13.5690 | − | 13.5690i | 0.535110 | − | 0.535110i | −0.386978 | − | 0.922089i | \(-0.626481\pi\) |
0.922089 | + | 0.386978i | \(0.126481\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.18158 | − | 1.18158i | −0.0465245 | − | 0.0465245i | ||||
\(646\) | 25.2477 | + | 10.3659i | 0.993356 | + | 0.407840i | ||||
\(647\) | 34.3455 | − | 19.8294i | 1.35026 | − | 0.779573i | 0.361974 | − | 0.932188i | \(-0.382103\pi\) |
0.988286 | + | 0.152615i | \(0.0487695\pi\) | |||||||
\(648\) | −2.36951 | − | 16.7842i | −0.0930831 | − | 0.659347i | ||||
\(649\) | 24.0965 | + | 13.9121i | 0.945871 | + | 0.546099i | ||||
\(650\) | −22.5386 | + | 3.03874i | −0.884035 | + | 0.119189i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.28845 | − | 4.71671i | −0.324601 | − | 0.184721i | ||||
\(653\) | 1.08587 | + | 4.05251i | 0.0424933 | + | 0.158587i | 0.983912 | − | 0.178652i | \(-0.0571736\pi\) |
−0.941419 | + | 0.337239i | \(0.890507\pi\) | |||||||
\(654\) | 0.740485 | − | 5.76326i | 0.0289552 | − | 0.225361i | ||||
\(655\) | −2.46608 | − | 4.27138i | −0.0963577 | − | 0.166896i | ||||
\(656\) | 1.05345 | − | 0.0131310i | 0.0411301 | − | 0.000512680i | ||||
\(657\) | −14.5426 | −0.567362 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.5078 | + | 19.5078i | −0.759915 | + | 0.759915i | −0.976307 | − | 0.216391i | \(-0.930571\pi\) |
0.216391 | + | 0.976307i | \(0.430571\pi\) | |||||||
\(660\) | −5.20213 | − | 8.88205i | −0.202492 | − | 0.345733i | ||||
\(661\) | 4.38283 | − | 16.3569i | 0.170472 | − | 0.636212i | −0.826806 | − | 0.562487i | \(-0.809845\pi\) |
0.997279 | − | 0.0737248i | \(-0.0234886\pi\) | |||||||
\(662\) | 18.0331 | + | 23.3501i | 0.700875 | + | 0.907529i | ||||
\(663\) | −17.9529 | − | 10.3651i | −0.697234 | − | 0.402548i | ||||
\(664\) | −21.4990 | + | 9.14155i | −0.834323 | + | 0.354761i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.13983 | − | 23.2884i | −0.121666 | − | 0.902407i | ||||
\(667\) | 4.35104 | − | 1.16586i | 0.168473 | − | 0.0451422i | ||||
\(668\) | −17.6784 | − | 17.4594i | −0.683997 | − | 0.675524i | ||||
\(669\) | 4.02182 | + | 1.07764i | 0.155493 | + | 0.0416641i | ||||
\(670\) | −11.7363 | − | 28.0860i | −0.453411 | − | 1.08506i | ||||
\(671\) | 34.4368 | 1.32942 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.9400 | −1.19265 | −0.596324 | − | 0.802744i | \(-0.703373\pi\) | ||||
−0.596324 | + | 0.802744i | \(0.703373\pi\) | |||||||
\(674\) | 9.11197 | + | 21.8058i | 0.350980 | + | 0.839929i | ||||
\(675\) | −7.84897 | − | 2.10313i | −0.302107 | − | 0.0809493i | ||||
\(676\) | 43.3862 | + | 42.8488i | 1.66870 | + | 1.64803i | ||||
\(677\) | 0.0168505 | − | 0.00451508i | 0.000647617 | − | 0.000173529i | −0.258495 | − | 0.966013i | \(-0.583227\pi\) |
0.259143 | + | 0.965839i | \(0.416560\pi\) | |||||||
\(678\) | −0.584138 | − | 4.33260i | −0.0224337 | − | 0.166393i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.44530 | − | 22.2133i | −0.362211 | − | 0.851843i | ||||
\(681\) | −8.53625 | − | 4.92841i | −0.327110 | − | 0.188857i | ||||
\(682\) | 3.93114 | + | 5.09024i | 0.150531 | + | 0.194915i | ||||
\(683\) | −5.17376 | + | 19.3087i | −0.197969 | + | 0.738829i | 0.793510 | + | 0.608557i | \(0.208251\pi\) |
−0.991478 | + | 0.130271i | \(0.958415\pi\) | |||||||
\(684\) | −9.70336 | − | 16.5674i | −0.371017 | − | 0.633471i | ||||
\(685\) | −9.67199 | + | 9.67199i | −0.369548 | + | 0.369548i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.81864 | −0.298300 | ||||||||
\(688\) | 4.94651 | − | 5.07138i | 0.188584 | − | 0.193345i | ||||
\(689\) | −0.222067 | − | 0.384631i | −0.00846008 | − | 0.0146533i | ||||
\(690\) | −0.442926 | + | 3.44733i | −0.0168619 | + | 0.131238i | ||||
\(691\) | 11.5428 | + | 43.0783i | 0.439109 | + | 1.63878i | 0.731038 | + | 0.682337i | \(0.239036\pi\) |
−0.291929 | + | 0.956440i | \(0.594297\pi\) | |||||||
\(692\) | −22.7612 | − | 12.9527i | −0.865250 | − | 0.492388i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.0584 | − | 1.49094i | 0.419773 | − | 0.0565954i | ||||
\(695\) | −11.2228 | − | 6.47948i | −0.425705 | − | 0.245781i | ||||
\(696\) | −2.85513 | + | 0.403072i | −0.108224 | + | 0.0152784i | ||||
\(697\) | −1.21627 | + | 0.702215i | −0.0460696 | + | 0.0265983i | ||||
\(698\) | −33.2634 | − | 13.6569i | −1.25904 | − | 0.516920i | ||||
\(699\) | −10.1873 | − | 10.1873i | −0.385319 | − | 0.385319i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.8654 | + | 16.8654i | −0.636998 | + | 0.636998i | −0.949814 | − | 0.312816i | \(-0.898728\pi\) |
0.312816 | + | 0.949814i | \(0.398728\pi\) | |||||||
\(702\) | 11.9822 | + | 28.6745i | 0.452238 | + | 1.08225i | ||||
\(703\) | −11.3364 | − | 19.6352i | −0.427560 | − | 0.740556i | ||||
\(704\) | 37.3779 | − | 22.5222i | 1.40873 | − | 0.848838i | ||||
\(705\) | −5.07410 | + | 8.78859i | −0.191102 | + | 0.330998i | ||||
\(706\) | −21.4627 | + | 28.1520i | −0.807761 | + | 1.05951i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.59273 | + | 5.79933i | 0.0598583 | + | 0.217952i | ||||
\(709\) | −29.5530 | + | 7.91870i | −1.10989 | + | 0.297393i | −0.766784 | − | 0.641905i | \(-0.778144\pi\) |
−0.343102 | + | 0.939298i | \(0.611478\pi\) | |||||||
\(710\) | 3.67768 | − | 2.84023i | 0.138021 | − | 0.106592i | ||||
\(711\) | 11.9811 | − | 6.91731i | 0.449328 | − | 0.259419i | ||||
\(712\) | 11.0255 | + | 14.0939i | 0.413196 | + | 0.528190i | ||||
\(713\) | − | 2.17168i | − | 0.0813300i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −40.7102 | − | 40.7102i | −1.52248 | − | 1.52248i | ||||
\(716\) | −24.2970 | + | 14.2305i | −0.908022 | + | 0.531819i | ||||
\(717\) | 3.57411 | + | 0.957679i | 0.133477 | + | 0.0357652i | ||||
\(718\) | −3.24237 | + | 25.2356i | −0.121004 | + | 0.941785i | ||||
\(719\) | −20.1849 | + | 34.9613i | −0.752769 | + | 1.30383i | 0.193706 | + | 0.981060i | \(0.437949\pi\) |
−0.946476 | + | 0.322775i | \(0.895384\pi\) | |||||||
\(720\) | −4.19012 | + | 16.4555i | −0.156157 | + | 0.613260i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.63661 | + | 5.05967i | 0.246989 | + | 0.188302i | ||||
\(723\) | −2.29058 | − | 8.54857i | −0.0851876 | − | 0.317925i | ||||
\(724\) | 14.3717 | − | 0.0895667i | 0.534119 | − | 0.00332872i | ||||
\(725\) | 1.09143 | − | 4.07327i | 0.0405347 | − | 0.151277i | ||||
\(726\) | −5.93887 | + | 14.4650i | −0.220412 | + | 0.536847i | ||||
\(727\) | 3.43634i | 0.127447i | 0.997968 | + | 0.0637234i | \(0.0202976\pi\) | ||||
−0.997968 | + | 0.0637234i | \(0.979702\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 10.0029i | − | 0.370476i | ||||||
\(730\) | 11.4795 | + | 4.71313i | 0.424877 | + | 0.174441i | ||||
\(731\) | −2.44425 | + | 9.12207i | −0.0904039 | + | 0.337392i | ||||
\(732\) | 5.29593 | + | 5.23033i | 0.195743 | + | 0.193319i | ||||
\(733\) | −10.0069 | − | 37.3462i | −0.369613 | − | 1.37941i | −0.861059 | − | 0.508506i | \(-0.830198\pi\) |
0.491446 | − | 0.870908i | \(-0.336469\pi\) | |||||||
\(734\) | 8.83805 | − | 11.5926i | 0.326218 | − | 0.427890i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.6373 | − | 1.69549i | −0.539540 | − | 0.0624967i | ||||
\(737\) | −36.6804 | + | 63.5323i | −1.35114 | + | 2.34024i | ||||
\(738\) | 0.979930 | + | 0.125905i | 0.0360717 | + | 0.00463463i | ||||
\(739\) | 38.7393 | + | 10.3802i | 1.42505 | + | 0.381841i | 0.887272 | − | 0.461247i | \(-0.152598\pi\) |
0.537777 | + | 0.843087i | \(0.319264\pi\) | |||||||
\(740\) | −5.06905 | + | 19.4008i | −0.186342 | + | 0.713187i | ||||
\(741\) | 9.94932 | + | 9.94932i | 0.365497 | + | 0.365497i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.1733i | 1.25370i | 0.779141 | + | 0.626848i | \(0.215656\pi\) | ||||
−0.779141 | + | 0.626848i | \(0.784344\pi\) | |||||||
\(744\) | −0.168558 | + | 1.37988i | −0.00617963 | + | 0.0505889i | ||||
\(745\) | −0.774565 | + | 0.447195i | −0.0283779 | + | 0.0163840i | ||||
\(746\) | −19.6273 | − | 25.4144i | −0.718605 | − | 0.930487i | ||||
\(747\) | −21.1619 | + | 5.67032i | −0.774274 | + | 0.207466i | ||||
\(748\) | −28.7725 | + | 50.5605i | −1.05203 | + | 1.84867i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 7.89309 | + | 6.01760i | 0.288215 | + | 0.219732i | ||||
\(751\) | −4.27895 | + | 7.41136i | −0.156141 | + | 0.270445i | −0.933474 | − | 0.358645i | \(-0.883239\pi\) |
0.777333 | + | 0.629090i | \(0.216572\pi\) | |||||||
\(752\) | −37.5248 | − | 21.0457i | −1.36839 | − | 0.767459i | ||||
\(753\) | −4.91577 | − | 8.51437i | −0.179141 | − | 0.310281i | ||||
\(754\) | −14.8808 | + | 6.21822i | −0.541926 | + | 0.226454i | ||||
\(755\) | 4.20490 | − | 4.20490i | 0.153032 | − | 0.153032i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.0492 | − | 25.0492i | −0.910428 | − | 0.910428i | 0.0858779 | − | 0.996306i | \(-0.472631\pi\) |
−0.996306 | + | 0.0858779i | \(0.972631\pi\) | |||||||
\(758\) | −11.9958 | + | 29.2177i | −0.435708 | + | 1.06123i | ||||
\(759\) | 7.25431 | − | 4.18827i | 0.263315 | − | 0.152025i | ||||
\(760\) | 2.29022 | + | 16.2226i | 0.0830751 | + | 0.588456i | ||||
\(761\) | 24.6145 | + | 14.2112i | 0.892274 | + | 0.515155i | 0.874686 | − | 0.484691i | \(-0.161068\pi\) |
0.0175884 | + | 0.999845i | \(0.494401\pi\) | |||||||
\(762\) | 1.96935 | + | 14.6069i | 0.0713421 | + | 0.529151i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −11.0132 | − | 40.1006i | −0.398445 | − | 1.45079i | ||||
\(765\) | −5.85873 | − | 21.8651i | −0.211823 | − | 0.790533i | ||||
\(766\) | −25.7578 | − | 3.30946i | −0.930669 | − | 0.119576i | ||||
\(767\) | 16.8190 | + | 29.1314i | 0.607299 | + | 1.05187i | ||||
\(768\) | 9.16895 | + | 2.21341i | 0.330856 | + | 0.0798696i | ||||
\(769\) | −12.0189 | −0.433413 | −0.216707 | − | 0.976237i | \(-0.569531\pi\) | ||||
−0.216707 | + | 0.976237i | \(0.569531\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.50286 | − | 8.50286i | 0.306223 | − | 0.306223i | ||||
\(772\) | 25.8226 | + | 6.74694i | 0.929375 | + | 0.242828i | ||||
\(773\) | 1.85543 | − | 6.92456i | 0.0667352 | − | 0.249059i | −0.924497 | − | 0.381189i | \(-0.875515\pi\) |
0.991232 | + | 0.132130i | \(0.0421815\pi\) | |||||||
\(774\) | 5.25805 | − | 4.06074i | 0.188997 | − | 0.145960i | ||||
\(775\) | −1.76066 | − | 1.01652i | −0.0632449 | − | 0.0365145i | ||||
\(776\) | −49.3382 | − | 19.8983i | −1.77114 | − | 0.714306i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.6604 | − | 3.72929i | 0.991675 | − | 0.133701i | ||||
\(779\) | 0.920763 | − | 0.246718i | 0.0329897 | − | 0.00883957i | ||||
\(780\) | −0.0775521 | − | 12.4438i | −0.00277681 | − | 0.445561i | ||||
\(781\) | −10.8173 | − | 2.89849i | −0.387074 | − | 0.103716i | ||||
\(782\) | 18.1244 | − | 7.57362i | 0.648127 | − | 0.270832i | ||||
\(783\) | −5.76241 | −0.205932 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.04315 | −0.322764 | ||||||||
\(786\) | −2.37061 | + | 0.990606i | −0.0845570 | + | 0.0353337i | ||||
\(787\) | −23.1726 | − | 6.20908i | −0.826014 | − | 0.221330i | −0.179040 | − | 0.983842i | \(-0.557299\pi\) |
−0.646974 | + | 0.762512i | \(0.723966\pi\) | |||||||
\(788\) | −0.550012 | + | 0.00342776i | −0.0195934 | + | 0.000122109i | ||||
\(789\) | 13.2936 | − | 3.56200i | 0.473263 | − | 0.126810i | ||||
\(790\) | −11.6994 | + | 1.57736i | −0.416246 | + | 0.0561199i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 37.6609 | − | 16.0137i | 1.33822 | − | 0.569023i | ||||
\(793\) | 36.0546 | + | 20.8161i | 1.28033 | + | 0.739202i | ||||
\(794\) | 1.78575 | − | 1.37912i | 0.0633740 | − | 0.0489431i | ||||
\(795\) | −0.0164460 | + | 0.0613774i | −0.000583281 | + | 0.00217683i | ||||
\(796\) | −7.28060 | + | 27.8651i | −0.258054 | + | 0.987651i | ||||
\(797\) | 35.5609 | − | 35.5609i | 1.25963 | − | 1.25963i | 0.308366 | − | 0.951268i | \(-0.400218\pi\) |
0.951268 | − | 0.308366i | \(-0.0997820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 57.3537 | 2.02903 | ||||||||
\(800\) | −8.22606 | + | 11.0734i | −0.290835 | + | 0.391505i | ||||
\(801\) | 8.39042 | + | 14.5326i | 0.296461 | + | 0.513486i | ||||
\(802\) | 20.1243 | + | 2.58564i | 0.710612 | + | 0.0913021i | ||||
\(803\) | −7.74059 | − | 28.8883i | −0.273159 | − | 1.01944i | ||||
\(804\) | −15.2904 | + | 4.19934i | −0.539249 | + | 0.148099i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.03890 | + | 7.70563i | 0.0365938 | + | 0.271419i | ||||
\(807\) | 15.9352 | + | 9.20019i | 0.560945 | + | 0.323862i | ||||
\(808\) | 6.93977 | − | 9.22130i | 0.244140 | − | 0.324404i | ||||
\(809\) | −10.2729 | + | 5.93106i | −0.361176 | + | 0.208525i | −0.669596 | − | 0.742725i | \(-0.733533\pi\) |
0.308421 | + | 0.951250i | \(0.400200\pi\) | |||||||
\(810\) | −5.15179 | + | 12.5480i | −0.181015 | + | 0.440890i | ||||
\(811\) | 20.4859 | + | 20.4859i | 0.719357 | + | 0.719357i | 0.968473 | − | 0.249117i | \(-0.0801403\pi\) |
−0.249117 | + | 0.968473i | \(0.580140\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.610240 | − | 0.610240i | 0.0214020 | − | 0.0214020i | ||||
\(814\) | 44.5901 | − | 18.6328i | 1.56288 | − | 0.653080i | ||||
\(815\) | 3.81570 | + | 6.60898i | 0.133658 | + | 0.231503i | ||||
\(816\) | −12.1041 | + | 3.40552i | −0.423727 | + | 0.119217i | ||||
\(817\) | 3.20496 | − | 5.55116i | 0.112127 | − | 0.194210i | ||||
\(818\) | 44.1445 | + | 33.6552i | 1.54347 | + | 1.17673i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.732724 | − | 0.416972i | −0.0255878 | − | 0.0145613i | ||||
\(821\) | 39.7113 | − | 10.6406i | 1.38594 | − | 0.371360i | 0.512662 | − | 0.858591i | \(-0.328659\pi\) |
0.873274 | + | 0.487230i | \(0.161993\pi\) | |||||||
\(822\) | 4.35519 | + | 5.63933i | 0.151905 | + | 0.196694i | ||||
\(823\) | −44.4787 | + | 25.6798i | −1.55043 | + | 0.895140i | −0.552322 | + | 0.833631i | \(0.686258\pi\) |
−0.998107 | + | 0.0615092i | \(0.980409\pi\) | |||||||
\(824\) | 13.4895 | + | 17.2437i | 0.469928 | + | 0.600711i | ||||
\(825\) | − | 7.84180i | − | 0.273016i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.4414 | − | 24.4414i | −0.849912 | − | 0.849912i | 0.140210 | − | 0.990122i | \(-0.455222\pi\) |
−0.990122 | + | 0.140210i | \(0.955222\pi\) | |||||||
\(828\) | −13.3697 | − | 3.49324i | −0.464629 | − | 0.121399i | ||||
\(829\) | 15.5537 | + | 4.16759i | 0.540201 | + | 0.144746i | 0.518595 | − | 0.855020i | \(-0.326455\pi\) |
0.0216062 | + | 0.999767i | \(0.493122\pi\) | |||||||
\(830\) | 18.5423 | + | 2.38239i | 0.643613 | + | 0.0826938i | ||||
\(831\) | 0.580404 | − | 1.00529i | 0.0201340 | − | 0.0348731i | ||||
\(832\) | 52.7479 | − | 0.986303i | 1.82870 | − | 0.0341939i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.09279 | + | 5.36838i | −0.141722 | + | 0.185892i | ||||
\(835\) | 5.14608 | + | 19.2054i | 0.178087 | + | 0.664632i | ||||
\(836\) | 27.7456 | − | 28.0936i | 0.959602 | − | 0.971638i | ||||
\(837\) | −0.719031 | + | 2.68346i | −0.0248533 | + | 0.0927539i | ||||
\(838\) | −8.16784 | − | 3.35345i | −0.282153 | − | 0.115843i | ||||
\(839\) | − | 35.2906i | − | 1.21837i | −0.793029 | − | 0.609184i | \(-0.791497\pi\) | ||
0.793029 | − | 0.609184i | \(-0.208503\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.0096i | 0.896881i | ||||||||
\(842\) | 5.75397 | − | 14.0147i | 0.198295 | − | 0.482977i | ||||
\(843\) | 0.864730 | − | 3.22722i | 0.0297829 | − | 0.111151i | ||||
\(844\) | 0.136142 | + | 21.8451i | 0.00468621 | + | 0.751939i | ||||
\(845\) | −12.6295 | − | 47.1339i | −0.434468 | − | 1.62146i | ||||
\(846\) | −32.0858 | − | 24.4619i | −1.10313 | − | 0.841016i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.261061 | − | 0.0664749i | −0.00896486 | − | 0.00228276i | ||||
\(849\) | 6.94542 | − | 12.0298i | 0.238366 | − | 0.412862i | ||||
\(850\) | 2.34344 | − | 18.2392i | 0.0803794 | − | 0.625600i | ||||
\(851\) | −15.7620 | − | 4.22342i | −0.540315 | − | 0.144777i | ||||
\(852\) | −1.22333 | − | 2.08870i | −0.0419107 | − | 0.0715578i | ||||
\(853\) | −6.93449 | − | 6.93449i | −0.237432 | − | 0.237432i | 0.578354 | − | 0.815786i | \(-0.303695\pi\) |
−0.815786 | + | 0.578354i | \(0.803695\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.3642i | 0.525445i | ||||||||
\(856\) | −9.26899 | − | 1.13224i | −0.316808 | − | 0.0386992i | ||||
\(857\) | −25.2698 | + | 14.5895i | −0.863200 | + | 0.498369i | −0.865083 | − | 0.501630i | \(-0.832734\pi\) |
0.00188263 | + | 0.999998i | \(0.499401\pi\) | |||||||
\(858\) | −23.7364 | + | 18.3314i | −0.810347 | + | 0.625822i | ||||
\(859\) | 2.22135 | − | 0.595210i | 0.0757916 | − | 0.0203083i | −0.220724 | − | 0.975336i | \(-0.570842\pi\) |
0.296516 | + | 0.955028i | \(0.404175\pi\) | |||||||
\(860\) | −5.46660 | + | 1.50135i | −0.186409 | + | 0.0511955i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.8962 | + | 20.8505i | −0.541426 | + | 0.710171i | ||||
\(863\) | 16.8529 | − | 29.1902i | 0.573681 | − | 0.993645i | −0.422503 | − | 0.906362i | \(-0.638848\pi\) |
0.996184 | − | 0.0872830i | \(-0.0278184\pi\) | |||||||
\(864\) | 17.5254 | + | 6.94140i | 0.596227 | + | 0.236151i | ||||
\(865\) | 10.4784 | + | 18.1491i | 0.356277 | + | 0.617090i | ||||
\(866\) | 3.93239 | + | 9.41059i | 0.133628 | + | 0.319785i | ||||
\(867\) | 4.76608 | − | 4.76608i | 0.161864 | − | 0.161864i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.1181 | + | 20.1181i | 0.682460 | + | 0.682460i | ||||
\(870\) | 2.13451 | + | 0.876360i | 0.0723666 | + | 0.0297114i | ||||
\(871\) | −76.8070 | + | 44.3445i | −2.60251 | + | 1.50256i | ||||
\(872\) | −15.7509 | − | 11.8538i | −0.533394 | − | 0.401421i | ||||
\(873\) | −43.2060 | − | 24.9450i | −1.46230 | − | 0.844260i | ||||
\(874\) | −13.2130 | + | 1.78143i | −0.446938 | + | 0.0602579i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.19720 | − | 5.61829i | 0.108024 | − | 0.189824i | ||||
\(877\) | −9.29142 | − | 34.6760i | −0.313749 | − | 1.17093i | −0.925149 | − | 0.379605i | \(-0.876060\pi\) |
0.611400 | − | 0.791322i | \(-0.290607\pi\) | |||||||
\(878\) | −2.73243 | + | 21.2667i | −0.0922150 | + | 0.717717i | ||||
\(879\) | −7.13324 | − | 12.3551i | −0.240598 | − | 0.416728i | ||||
\(880\) | −34.9183 | + | 0.435251i | −1.17710 | + | 0.0146723i | ||||
\(881\) | 13.0482 | 0.439606 | 0.219803 | − | 0.975544i | \(-0.429459\pi\) | ||||
0.219803 | + | 0.975544i | \(0.429459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.2895 | + | 24.2895i | −0.817407 | + | 0.817407i | −0.985732 | − | 0.168325i | \(-0.946164\pi\) |
0.168325 | + | 0.985732i | \(0.446164\pi\) | |||||||
\(884\) | −60.6865 | + | 35.5435i | −2.04111 | + | 1.19546i | ||||
\(885\) | 1.24560 | − | 4.64863i | 0.0418702 | − | 0.156262i | ||||
\(886\) | 2.58851 | + | 3.35173i | 0.0869627 | + | 0.112604i | ||||
\(887\) | −17.1896 | − | 9.92445i | −0.577172 | − | 0.333230i | 0.182837 | − | 0.983143i | \(-0.441472\pi\) |
−0.760009 | + | 0.649913i | \(0.774805\pi\) | |||||||
\(888\) | 9.68736 | + | 3.90695i | 0.325087 | + | 0.131109i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.91327 | − | 14.1909i | −0.0641331 | − | 0.475680i | ||||
\(891\) | 31.5770 | − | 8.46102i | 1.05787 | − | 0.283455i | ||||
\(892\) | 9.92593 | − | 10.0504i | 0.332345 | − | 0.336513i | ||||
\(893\) | −37.6018 | − | 10.0754i | −1.25830 | − | 0.337160i | ||||
\(894\) | 0.179635 | + | 0.429884i | 0.00600789 | + | 0.0143775i | ||||
\(895\) | 22.5325 | 0.753178 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.1268 | 0.338124 | ||||||||
\(898\) | 2.34196 | + | 5.60454i | 0.0781523 | + | 0.187026i | ||||
\(899\) | −1.39260 | − | 0.373145i | −0.0464457 | − | 0.0124451i | ||||
\(900\) | −9.09019 | + | 9.20421i | −0.303006 | + | 0.306807i | ||||
\(901\) | 0.346882 | − | 0.0929467i | 0.0115563 | − | 0.00309650i | ||||
\(902\) | 0.271481 | + | 2.01360i | 0.00903935 | + | 0.0670456i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.7552 | − | 5.54751i | −0.457491 | − | 0.184508i | ||||
\(905\) | −9.96000 | − | 5.75041i | −0.331082 | − | 0.191150i | ||||
\(906\) | −1.89342 | − | 2.45170i | −0.0629047 | − | 0.0814523i | ||||
\(907\) | −14.5025 | + | 54.1242i | −0.481549 | + | 1.79716i | 0.113573 | + | 0.993530i | \(0.463770\pi\) |
−0.595122 | + | 0.803635i | \(0.702896\pi\) | |||||||
\(908\) | −28.8552 | + | 16.9002i | −0.957594 | + | 0.560853i | ||||
\(909\) | 7.65297 | − | 7.65297i | 0.253833 | − | 0.253833i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.6260 | 0.385188 | 0.192594 | − | 0.981279i | \(-0.438310\pi\) | ||||
0.192594 | + | 0.981279i | \(0.438310\pi\) | |||||||
\(912\) | 8.53382 | − | 0.106373i | 0.282583 | − | 0.00352235i | ||||
\(913\) | −22.5277 | − | 39.0191i | −0.745557 | − | 1.29134i | ||||
\(914\) | 5.00715 | − | 38.9711i | 0.165622 | − | 1.28905i | ||||
\(915\) | −1.54162 | − | 5.75339i | −0.0509643 | − | 0.190201i | ||||
\(916\) | −13.1193 | + | 23.0539i | −0.433474 | + | 0.761722i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −24.9032 | + | 3.35754i | −0.821928 | + | 0.110815i | ||||
\(919\) | −36.4646 | − | 21.0528i | −1.20285 | − | 0.694468i | −0.241666 | − | 0.970360i | \(-0.577694\pi\) |
−0.961189 | + | 0.275891i | \(0.911027\pi\) | |||||||
\(920\) | 9.42153 | + | 7.09045i | 0.310619 | + | 0.233765i | ||||
\(921\) | 6.93014 | − | 4.00112i | 0.228356 | − | 0.131841i | ||||
\(922\) | −12.0427 | − | 4.94436i | −0.396607 | − | 0.162834i | ||||
\(923\) | −9.57342 | − | 9.57342i | −0.315113 | − | 0.315113i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.8020 | + | 10.8020i | −0.355167 | + | 0.355167i | ||||
\(926\) | −21.3208 | − | 51.0228i | −0.700646 | − | 1.67671i | ||||
\(927\) | 10.2656 | + | 17.7805i | 0.337165 | + | 0.583988i | ||||
\(928\) | −3.60228 | + | 9.09492i | −0.118251 | + | 0.298556i | ||||
\(929\) | −15.1619 | + | 26.2612i | −0.497447 | + | 0.861603i | −0.999996 | − | 0.00294569i | \(-0.999062\pi\) |
0.502549 | + | 0.864549i | \(0.332396\pi\) | |||||||
\(930\) | 0.674449 | − | 0.884653i | 0.0221160 | − | 0.0290089i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −47.1319 | + | 12.9443i | −1.54386 | + | 0.424005i | ||||
\(933\) | −10.9255 | + | 2.92748i | −0.357685 | + | 0.0958414i | ||||
\(934\) | −26.0575 | + | 20.1239i | −0.852628 | + | 0.658475i | ||||
\(935\) | 40.3156 | − | 23.2762i | 1.31846 | − | 0.761213i | ||||
\(936\) | 49.1100 | + | 5.99896i | 1.60521 | + | 0.196082i | ||||
\(937\) | − | 17.7772i | − | 0.580757i | −0.956912 | − | 0.290378i | \(-0.906219\pi\) | ||
0.956912 | − | 0.290378i | \(-0.0937812\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.10079 | + | 2.10079i | 0.0685567 | + | 0.0685567i | ||||
\(940\) | 17.3998 | + | 29.7082i | 0.567519 | + | 0.968975i | ||||
\(941\) | 28.9045 | + | 7.74494i | 0.942260 | + | 0.252478i | 0.697075 | − | 0.716998i | \(-0.254484\pi\) |
0.245186 | + | 0.969476i | \(0.421151\pi\) | |||||||
\(942\) | −0.600321 | + | 4.67235i | −0.0195595 | + | 0.152233i | ||||
\(943\) | 0.343034 | − | 0.594153i | 0.0111707 | − | 0.0193483i | ||||
\(944\) | 19.7723 | + | 5.03470i | 0.643533 | + | 0.163865i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.8652 | + | 8.28347i | 0.353257 | + | 0.269319i | ||||
\(947\) | 4.33732 | + | 16.1871i | 0.140944 | + | 0.526010i | 0.999902 | + | 0.0139648i | \(0.00444527\pi\) |
−0.858959 | + | 0.512045i | \(0.828888\pi\) | |||||||
\(948\) | 0.0383246 | + | 6.14948i | 0.00124472 | + | 0.199726i | ||||
\(949\) | 9.35794 | − | 34.9243i | 0.303772 | − | 1.13369i | ||||
\(950\) | −4.74049 | + | 11.5462i | −0.153802 | + | 0.374608i | ||||
\(951\) | − | 4.60704i | − | 0.149394i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.1855i | 0.459513i | 0.973248 | + | 0.229757i | \(0.0737930\pi\) | ||||
−0.973248 | + | 0.229757i | \(0.926207\pi\) | |||||||
\(954\) | −0.233701 | − | 0.0959502i | −0.00756636 | − | 0.00310650i | ||||
\(955\) | −8.61292 | + | 32.1438i | −0.278707 | + | 1.04015i | ||||
\(956\) | 8.82096 | − | 8.93160i | 0.285290 | − | 0.288869i | ||||
\(957\) | −1.43929 | − | 5.37149i | −0.0465255 | − | 0.173636i | ||||
\(958\) | −31.9444 | + | 41.9004i | −1.03208 | + | 1.35374i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5.43609 | − | 5.23653i | −0.175449 | − | 0.169008i | ||||
\(961\) | 15.1525 | − | 26.2448i | 0.488789 | − | 0.846608i | ||||
\(962\) | 57.9479 | + | 7.44536i | 1.86831 | + | 0.240048i | ||||
\(963\) | −8.45857 | − | 2.26647i | −0.272574 | − | 0.0730359i | ||||
\(964\) | −29.0496 | − | 7.59010i | −0.935625 | − | 0.244461i | ||||
\(965\) | −15.1021 | − | 15.1021i | −0.486154 | − | 0.486154i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 8.54873i | − | 0.274909i | −0.990508 | − | 0.137454i | \(-0.956108\pi\) | ||
0.990508 | − | 0.137454i | \(-0.0438920\pi\) | |||||||
\(968\) | 32.6861 | + | 41.7828i | 1.05057 | + | 1.34295i | ||||
\(969\) | −9.85287 | + | 5.68855i | −0.316520 | + | 0.182743i | ||||
\(970\) | 26.0212 | + | 33.6935i | 0.835489 | + | 1.08183i | ||||
\(971\) | 34.8458 | − | 9.33690i | 1.11825 | − | 0.299635i | 0.348077 | − | 0.937466i | \(-0.386835\pi\) |
0.770177 | + | 0.637831i | \(0.220168\pi\) | |||||||
\(972\) | 23.5180 | + | 13.3834i | 0.754341 | + | 0.429273i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 43.2111 | + | 32.9437i | 1.38457 | + | 1.05558i | ||||
\(975\) | 4.74015 | − | 8.21018i | 0.151806 | − | 0.262936i | ||||
\(976\) | 24.3084 | − | 6.83925i | 0.778091 | − | 0.218919i | ||||
\(977\) | −6.61877 | − | 11.4640i | −0.211753 | − | 0.366767i | 0.740510 | − | 0.672045i | \(-0.234584\pi\) |
−0.952263 | + | 0.305278i | \(0.901251\pi\) | |||||||
\(978\) | 3.66799 | − | 1.53274i | 0.117289 | − | 0.0490115i | ||||
\(979\) | −24.4025 | + | 24.4025i | −0.779906 | + | 0.779906i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.0721 | − | 13.0721i | −0.417359 | − | 0.417359i | ||||
\(982\) | −7.23395 | + | 17.6194i | −0.230845 | + | 0.562257i | ||||
\(983\) | 17.2541 | − | 9.96166i | 0.550320 | − | 0.317727i | −0.198931 | − | 0.980014i | \(-0.563747\pi\) |
0.749251 | + | 0.662286i | \(0.230414\pi\) | |||||||
\(984\) | −0.264079 | + | 0.350899i | −0.00841854 | + | 0.0111862i | ||||
\(985\) | 0.381174 | + | 0.220071i | 0.0121452 | + | 0.00701205i | ||||
\(986\) | −1.74242 | − | 12.9237i | −0.0554899 | − | 0.411573i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 46.0308 | − | 12.6419i | 1.46444 | − | 0.402193i | ||||
\(989\) | −1.19402 | − | 4.45615i | −0.0379677 | − | 0.141697i | ||||
\(990\) | −32.4815 | − | 4.17335i | −1.03233 | − | 0.132638i | ||||
\(991\) | −27.1797 | − | 47.0767i | −0.863392 | − | 1.49544i | −0.868635 | − | 0.495453i | \(-0.835002\pi\) |
0.00524220 | − | 0.999986i | \(-0.498331\pi\) | |||||||
\(992\) | 3.78586 | + | 2.81238i | 0.120201 | + | 0.0892931i | ||||
\(993\) | −12.2984 | −0.390278 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.2966 | − | 16.2966i | 0.516638 | − | 0.516638i | ||||
\(996\) | 2.46183 | − | 9.42216i | 0.0780061 | − | 0.298553i | ||||
\(997\) | 5.27193 | − | 19.6751i | 0.166964 | − | 0.623117i | −0.830818 | − | 0.556544i | \(-0.812127\pi\) |
0.997782 | − | 0.0665726i | \(-0.0212064\pi\) | |||||||
\(998\) | −15.4838 | + | 11.9580i | −0.490132 | + | 0.378524i | ||||
\(999\) | 18.0782 | + | 10.4374i | 0.571968 | + | 0.330226i |
(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 | 784.2.x.l.373.4 | 24 | ||
7.2 | even | 3 | 112.2.m.d.85.5 | yes | 12 | ||
7.3 | odd | 6 | 784.2.x.m.165.1 | 24 | |||
7.4 | even | 3 | inner | 784.2.x.l.165.1 | 24 | ||
7.5 | odd | 6 | 784.2.m.h.197.5 | 12 | |||
7.6 | odd | 2 | 784.2.x.m.373.4 | 24 | |||
16.13 | even | 4 | inner | 784.2.x.l.765.1 | 24 | ||
28.23 | odd | 6 | 448.2.m.d.113.4 | 12 | |||
56.37 | even | 6 | 896.2.m.g.225.4 | 12 | |||
56.51 | odd | 6 | 896.2.m.h.225.3 | 12 | |||
112.13 | odd | 4 | 784.2.x.m.765.1 | 24 | |||
112.37 | even | 12 | 896.2.m.g.673.4 | 12 | |||
112.45 | odd | 12 | 784.2.x.m.557.4 | 24 | |||
112.51 | odd | 12 | 448.2.m.d.337.4 | 12 | |||
112.61 | odd | 12 | 784.2.m.h.589.5 | 12 | |||
112.93 | even | 12 | 112.2.m.d.29.5 | ✓ | 12 | ||
112.107 | odd | 12 | 896.2.m.h.673.3 | 12 | |||
112.109 | even | 12 | inner | 784.2.x.l.557.4 | 24 | ||
224.51 | odd | 24 | 7168.2.a.bi.1.7 | 12 | |||
224.93 | even | 24 | 7168.2.a.bj.1.7 | 12 | |||
224.163 | odd | 24 | 7168.2.a.bi.1.6 | 12 | |||
224.205 | even | 24 | 7168.2.a.bj.1.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.d.29.5 | ✓ | 12 | 112.93 | even | 12 | ||
112.2.m.d.85.5 | yes | 12 | 7.2 | even | 3 | ||
448.2.m.d.113.4 | 12 | 28.23 | odd | 6 | |||
448.2.m.d.337.4 | 12 | 112.51 | odd | 12 | |||
784.2.m.h.197.5 | 12 | 7.5 | odd | 6 | |||
784.2.m.h.589.5 | 12 | 112.61 | odd | 12 | |||
784.2.x.l.165.1 | 24 | 7.4 | even | 3 | inner | ||
784.2.x.l.373.4 | 24 | 1.1 | even | 1 | trivial | ||
784.2.x.l.557.4 | 24 | 112.109 | even | 12 | inner | ||
784.2.x.l.765.1 | 24 | 16.13 | even | 4 | inner | ||
784.2.x.m.165.1 | 24 | 7.3 | odd | 6 | |||
784.2.x.m.373.4 | 24 | 7.6 | odd | 2 | |||
784.2.x.m.557.4 | 24 | 112.45 | odd | 12 | |||
784.2.x.m.765.1 | 24 | 112.13 | odd | 4 | |||
896.2.m.g.225.4 | 12 | 56.37 | even | 6 | |||
896.2.m.g.673.4 | 12 | 112.37 | even | 12 | |||
896.2.m.h.225.3 | 12 | 56.51 | odd | 6 | |||
896.2.m.h.673.3 | 12 | 112.107 | odd | 12 | |||
7168.2.a.bi.1.6 | 12 | 224.163 | odd | 24 | |||
7168.2.a.bi.1.7 | 12 | 224.51 | odd | 24 | |||
7168.2.a.bj.1.6 | 12 | 224.205 | even | 24 | |||
7168.2.a.bj.1.7 | 12 | 224.93 | even | 24 |