Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(82,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.bc (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 157.6 | ||
Character | \(\chi\) | \(=\) | 525.157 |
Dual form | 525.2.bc.d.418.6 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.698503 | − | 2.60685i | 0.493916 | − | 1.84332i | −0.0421009 | − | 0.999113i | \(-0.513405\pi\) |
0.536017 | − | 0.844207i | \(-0.319928\pi\) | |||||||
\(3\) | 0.965926 | − | 0.258819i | 0.557678 | − | 0.149429i | ||||
\(4\) | −4.57570 | − | 2.64178i | −2.28785 | − | 1.32089i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.69881i | − | 1.10178i | ||||||
\(7\) | −2.58926 | − | 0.543835i | −0.978647 | − | 0.205550i | ||||
\(8\) | −6.26618 | + | 6.26618i | −2.21543 | + | 2.21543i | ||||
\(9\) | 0.866025 | − | 0.500000i | 0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.69545 | − | 2.93661i | 0.511198 | − | 0.885422i | −0.488717 | − | 0.872442i | \(-0.662535\pi\) |
0.999916 | − | 0.0129794i | \(-0.00413158\pi\) | |||||||
\(12\) | −5.10353 | − | 1.36749i | −1.47326 | − | 0.394760i | ||||
\(13\) | −4.01246 | − | 4.01246i | −1.11286 | − | 1.11286i | −0.992763 | − | 0.120093i | \(-0.961681\pi\) |
−0.120093 | − | 0.992763i | \(-0.538319\pi\) | |||||||
\(14\) | −3.22630 | + | 6.36993i | −0.862265 | + | 1.70243i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.67447 | + | 11.5605i | 1.66862 | + | 2.89013i | ||||
\(17\) | 1.00749 | + | 3.76002i | 0.244353 | + | 0.911939i | 0.973707 | + | 0.227803i | \(0.0731541\pi\) |
−0.729354 | + | 0.684137i | \(0.760179\pi\) | |||||||
\(18\) | −0.698503 | − | 2.60685i | −0.164639 | − | 0.614440i | ||||
\(19\) | 0.721181 | + | 1.24912i | 0.165450 | + | 0.286568i | 0.936815 | − | 0.349825i | \(-0.113759\pi\) |
−0.771365 | + | 0.636393i | \(0.780426\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.64178 | + | 0.144844i | −0.576484 | + | 0.0316076i | ||||
\(22\) | −6.47102 | − | 6.47102i | −1.37963 | − | 1.37963i | ||||
\(23\) | −0.739216 | − | 0.198072i | −0.154137 | − | 0.0413010i | 0.180925 | − | 0.983497i | \(-0.442091\pi\) |
−0.335063 | + | 0.942196i | \(0.608757\pi\) | |||||||
\(24\) | −4.43086 | + | 7.67447i | −0.904445 | + | 1.56655i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −13.2626 | + | 7.65716i | −2.60101 | + | 1.50169i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 10.4110 | + | 9.32868i | 1.96749 | + | 1.76296i | ||||
\(29\) | − | 5.95804i | − | 1.10638i | −0.833055 | − | 0.553190i | \(-0.813410\pi\) | ||
0.833055 | − | 0.553190i | \(-0.186590\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.17447 | + | 1.83278i | 0.570152 | + | 0.329178i | 0.757210 | − | 0.653171i | \(-0.226562\pi\) |
−0.187058 | + | 0.982349i | \(0.559895\pi\) | |||||||
\(32\) | 17.6792 | − | 4.73712i | 3.12526 | − | 0.837412i | ||||
\(33\) | 0.877631 | − | 3.27536i | 0.152776 | − | 0.570168i | ||||
\(34\) | 10.5055 | 1.80169 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.28357 | −0.880595 | ||||||||
\(37\) | 0.325192 | − | 1.21363i | 0.0534612 | − | 0.199520i | −0.934030 | − | 0.357195i | \(-0.883733\pi\) |
0.987491 | + | 0.157675i | \(0.0503998\pi\) | |||||||
\(38\) | 3.76002 | − | 1.00749i | 0.609956 | − | 0.163437i | ||||
\(39\) | −4.91424 | − | 2.83724i | −0.786908 | − | 0.454321i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.05498i | 0.164760i | 0.996601 | + | 0.0823802i | \(0.0262522\pi\) | ||||
−0.996601 | + | 0.0823802i | \(0.973748\pi\) | |||||||
\(42\) | −1.46771 | + | 6.98790i | −0.226472 | + | 1.07826i | ||||
\(43\) | 6.74494 | − | 6.74494i | 1.02859 | − | 1.02859i | 0.0290150 | − | 0.999579i | \(-0.490763\pi\) |
0.999579 | − | 0.0290150i | \(-0.00923706\pi\) | |||||||
\(44\) | −15.5158 | + | 8.95804i | −2.33909 | + | 1.35048i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.03269 | + | 1.78867i | −0.152262 | + | 0.263725i | ||||
\(47\) | −6.55073 | − | 1.75526i | −0.955522 | − | 0.256031i | −0.252818 | − | 0.967514i | \(-0.581357\pi\) |
−0.702704 | + | 0.711483i | \(0.748024\pi\) | |||||||
\(48\) | 9.43913 | + | 9.43913i | 1.36242 | + | 1.36242i | ||||
\(49\) | 6.40849 | + | 2.81626i | 0.915498 | + | 0.402322i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.94633 | + | 3.37114i | 0.272541 | + | 0.472054i | ||||
\(52\) | 7.75977 | + | 28.9599i | 1.07609 | + | 4.01601i | ||||
\(53\) | −2.94397 | − | 10.9870i | −0.404385 | − | 1.50918i | −0.805188 | − | 0.593020i | \(-0.797935\pi\) |
0.400803 | − | 0.916164i | \(-0.368731\pi\) | |||||||
\(54\) | −1.34940 | − | 2.33724i | −0.183631 | − | 0.318058i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 19.6325 | − | 12.8170i | 2.62351 | − | 1.71274i | ||||
\(57\) | 1.01990 | + | 1.01990i | 0.135090 | + | 0.135090i | ||||
\(58\) | −15.5317 | − | 4.16171i | −2.03941 | − | 0.546459i | ||||
\(59\) | 3.22630 | − | 5.58811i | 0.420028 | − | 0.727510i | −0.575913 | − | 0.817511i | \(-0.695353\pi\) |
0.995942 | + | 0.0900003i | \(0.0286868\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9254 | − | 6.30775i | 1.39885 | − | 0.807625i | 0.404576 | − | 0.914504i | \(-0.367419\pi\) |
0.994272 | + | 0.106879i | \(0.0340858\pi\) | |||||||
\(62\) | 6.99517 | − | 6.99517i | 0.888387 | − | 0.888387i | ||||
\(63\) | −2.51428 | + | 0.823652i | −0.316769 | + | 0.103770i | ||||
\(64\) | − | 22.6979i | − | 2.83724i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.92535 | − | 4.57570i | −0.975543 | − | 0.563230i | ||||
\(67\) | 0.544617 | − | 0.145930i | 0.0665355 | − | 0.0178281i | −0.225398 | − | 0.974267i | \(-0.572368\pi\) |
0.291933 | + | 0.956439i | \(0.405701\pi\) | |||||||
\(68\) | 5.32317 | − | 19.8663i | 0.645529 | − | 2.40915i | ||||
\(69\) | −0.765293 | −0.0921305 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.73985 | −0.799873 | −0.399937 | − | 0.916543i | \(-0.630968\pi\) | ||||
−0.399937 | + | 0.916543i | \(0.630968\pi\) | |||||||
\(72\) | −2.29358 | + | 8.55976i | −0.270301 | + | 1.00878i | ||||
\(73\) | 4.78910 | − | 1.28324i | 0.560522 | − | 0.150191i | 0.0325757 | − | 0.999469i | \(-0.489629\pi\) |
0.527946 | + | 0.849278i | \(0.322962\pi\) | |||||||
\(74\) | −2.93661 | − | 1.69545i | −0.341374 | − | 0.197092i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 7.62082i | − | 0.874168i | ||||||
\(77\) | −5.98699 | + | 6.68159i | −0.682281 | + | 0.761438i | ||||
\(78\) | −10.8289 | + | 10.8289i | −1.22613 | + | 1.22613i | ||||
\(79\) | −6.79587 | + | 3.92360i | −0.764595 | + | 0.441439i | −0.830943 | − | 0.556357i | \(-0.812199\pi\) |
0.0663482 | + | 0.997797i | \(0.478865\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.75018 | + | 0.736908i | 0.303706 | + | 0.0813778i | ||||
\(83\) | 1.49011 | + | 1.49011i | 0.163561 | + | 0.163561i | 0.784142 | − | 0.620581i | \(-0.213103\pi\) |
−0.620581 | + | 0.784142i | \(0.713103\pi\) | |||||||
\(84\) | 12.4707 | + | 6.31626i | 1.36066 | + | 0.689160i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −12.8717 | − | 22.2944i | −1.38799 | − | 2.40407i | ||||
\(87\) | −1.54205 | − | 5.75503i | −0.165326 | − | 0.617003i | ||||
\(88\) | 7.77732 | + | 29.0254i | 0.829065 | + | 3.09411i | ||||
\(89\) | 1.78394 | + | 3.08987i | 0.189097 | + | 0.327525i | 0.944949 | − | 0.327217i | \(-0.106111\pi\) |
−0.755853 | + | 0.654742i | \(0.772777\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.20716 | + | 12.5714i | 0.860344 | + | 1.31784i | ||||
\(92\) | 2.85917 | + | 2.85917i | 0.298089 | + | 0.298089i | ||||
\(93\) | 3.54066 | + | 0.948718i | 0.367150 | + | 0.0983775i | ||||
\(94\) | −9.15141 | + | 15.8507i | −0.943896 | + | 1.63487i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 15.8507 | − | 9.15141i | 1.61776 | − | 0.934012i | ||||
\(97\) | −1.36798 | + | 1.36798i | −0.138898 | + | 0.138898i | −0.773137 | − | 0.634239i | \(-0.781313\pi\) |
0.634239 | + | 0.773137i | \(0.281313\pi\) | |||||||
\(98\) | 11.8179 | − | 14.7388i | 1.19379 | − | 1.48884i | ||||
\(99\) | − | 3.39091i | − | 0.340799i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.1133 | + | 9.88036i | 1.70284 | + | 0.983133i | 0.942865 | + | 0.333176i | \(0.108120\pi\) |
0.759971 | + | 0.649957i | \(0.225213\pi\) | |||||||
\(102\) | 10.1476 | − | 2.71904i | 1.00476 | − | 0.269225i | ||||
\(103\) | −2.46530 | + | 9.20061i | −0.242913 | + | 0.906563i | 0.731508 | + | 0.681833i | \(0.238817\pi\) |
−0.974421 | + | 0.224730i | \(0.927850\pi\) | |||||||
\(104\) | 50.2856 | 4.93091 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −30.6979 | −2.98164 | ||||||||
\(107\) | 0.698503 | − | 2.60685i | 0.0675268 | − | 0.252014i | −0.923908 | − | 0.382614i | \(-0.875024\pi\) |
0.991435 | + | 0.130601i | \(0.0416905\pi\) | |||||||
\(108\) | −5.10353 | + | 1.36749i | −0.491088 | + | 0.131587i | ||||
\(109\) | 6.49671 | + | 3.75088i | 0.622272 | + | 0.359269i | 0.777753 | − | 0.628570i | \(-0.216359\pi\) |
−0.155481 | + | 0.987839i | \(0.549693\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.25645i | − | 0.119257i | ||||||
\(112\) | −10.9949 | − | 33.5630i | −1.03892 | − | 3.17140i | ||||
\(113\) | −2.03981 | + | 2.03981i | −0.191889 | + | 0.191889i | −0.796512 | − | 0.604623i | \(-0.793324\pi\) |
0.604623 | + | 0.796512i | \(0.293324\pi\) | |||||||
\(114\) | 3.37114 | − | 1.94633i | 0.315736 | − | 0.182291i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −15.7399 | + | 27.2622i | −1.46141 | + | 2.53123i | ||||
\(117\) | −5.48112 | − | 1.46866i | −0.506730 | − | 0.135778i | ||||
\(118\) | −12.3138 | − | 12.3138i | −1.13358 | − | 1.13358i | ||||
\(119\) | −0.563829 | − | 10.2836i | −0.0516861 | − | 0.942693i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.249123 | − | 0.431493i | −0.0226475 | − | 0.0392267i | ||||
\(122\) | −8.81197 | − | 32.8867i | −0.797798 | − | 2.97742i | ||||
\(123\) | 0.273049 | + | 1.01903i | 0.0246200 | + | 0.0918832i | ||||
\(124\) | −9.68363 | − | 16.7725i | −0.869616 | − | 1.50622i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.390906 | + | 7.12967i | 0.0348247 | + | 0.635161i | ||||
\(127\) | 5.58258 | + | 5.58258i | 0.495374 | + | 0.495374i | 0.909994 | − | 0.414621i | \(-0.136086\pi\) |
−0.414621 | + | 0.909994i | \(0.636086\pi\) | |||||||
\(128\) | −23.8117 | − | 6.38031i | −2.10467 | − | 0.563945i | ||||
\(129\) | 4.76939 | − | 8.26083i | 0.419922 | − | 0.727326i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.1762 | + | 6.45260i | −0.976472 | + | 0.563766i | −0.901203 | − | 0.433397i | \(-0.857315\pi\) |
−0.0752685 | + | 0.997163i | \(0.523981\pi\) | |||||||
\(132\) | −12.6686 | + | 12.6686i | −1.10266 | + | 1.10266i | ||||
\(133\) | −1.18801 | − | 3.62650i | −0.103013 | − | 0.314458i | ||||
\(134\) | − | 1.52167i | − | 0.131452i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −29.8741 | − | 17.2478i | −2.56168 | − | 1.47899i | ||||
\(137\) | 2.04721 | − | 0.548549i | 0.174905 | − | 0.0468657i | −0.170303 | − | 0.985392i | \(-0.554475\pi\) |
0.345209 | + | 0.938526i | \(0.387808\pi\) | |||||||
\(138\) | −0.534560 | + | 1.99500i | −0.0455047 | + | 0.169826i | ||||
\(139\) | 1.07053 | 0.0908011 | 0.0454005 | − | 0.998969i | \(-0.485544\pi\) | ||||
0.0454005 | + | 0.998969i | \(0.485544\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.78181 | −0.571132 | ||||||||
\(142\) | −4.70781 | + | 17.5698i | −0.395070 | + | 1.47442i | ||||
\(143\) | −18.5860 | + | 4.98009i | −1.55424 | + | 0.416456i | ||||
\(144\) | 11.5605 | + | 6.67447i | 0.963377 | + | 0.556206i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 13.3808i | − | 1.10740i | ||||||
\(147\) | 6.91902 | + | 1.06166i | 0.570671 | + | 0.0875640i | ||||
\(148\) | −4.69414 | + | 4.69414i | −0.385856 | + | 0.385856i | ||||
\(149\) | −7.41936 | + | 4.28357i | −0.607817 | + | 0.350923i | −0.772111 | − | 0.635488i | \(-0.780799\pi\) |
0.164293 | + | 0.986412i | \(0.447466\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.70716 | − | 13.3492i | 0.627200 | − | 1.08634i | −0.360911 | − | 0.932600i | \(-0.617534\pi\) |
0.988111 | − | 0.153742i | \(-0.0491325\pi\) | |||||||
\(152\) | −12.3463 | − | 3.30818i | −1.00142 | − | 0.268329i | ||||
\(153\) | 2.75253 | + | 2.75253i | 0.222529 | + | 0.222529i | ||||
\(154\) | 13.2360 | + | 20.2743i | 1.06658 | + | 1.63375i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 14.9907 | + | 25.9647i | 1.20022 | + | 2.07884i | ||||
\(157\) | −4.60318 | − | 17.1793i | −0.367374 | − | 1.37106i | −0.864174 | − | 0.503193i | \(-0.832159\pi\) |
0.496800 | − | 0.867865i | \(-0.334508\pi\) | |||||||
\(158\) | 5.48129 | + | 20.4564i | 0.436068 | + | 1.62743i | ||||
\(159\) | −5.68730 | − | 9.85070i | −0.451033 | − | 0.781211i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.80630 | + | 0.914872i | 0.142356 | + | 0.0721020i | ||||
\(162\) | −1.90835 | − | 1.90835i | −0.149934 | − | 0.149934i | ||||
\(163\) | −2.22680 | − | 0.596668i | −0.174416 | − | 0.0467347i | 0.170554 | − | 0.985348i | \(-0.445444\pi\) |
−0.344970 | + | 0.938614i | \(0.612111\pi\) | |||||||
\(164\) | 2.78703 | − | 4.82728i | 0.217631 | − | 0.376947i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.92535 | − | 2.84365i | 0.382281 | − | 0.220710i | ||||
\(167\) | −2.75253 | + | 2.75253i | −0.212997 | + | 0.212997i | −0.805539 | − | 0.592542i | \(-0.798124\pi\) |
0.592542 | + | 0.805539i | \(0.298124\pi\) | |||||||
\(168\) | 15.6463 | − | 17.4615i | 1.20714 | − | 1.34719i | ||||
\(169\) | 19.1996i | 1.47690i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.24912 | + | 0.721181i | 0.0955228 | + | 0.0551501i | ||||
\(172\) | −48.6815 | + | 13.0442i | −3.71193 | + | 0.994609i | ||||
\(173\) | −3.28646 | + | 12.2652i | −0.249865 | + | 0.932508i | 0.721011 | + | 0.692924i | \(0.243678\pi\) |
−0.970876 | + | 0.239584i | \(0.922989\pi\) | |||||||
\(174\) | −16.0796 | −1.21899 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 45.2650 | 3.41198 | ||||||||
\(177\) | 1.67006 | − | 6.23273i | 0.125529 | − | 0.468481i | ||||
\(178\) | 9.30090 | − | 2.49217i | 0.697132 | − | 0.186796i | ||||
\(179\) | −21.3890 | − | 12.3489i | −1.59869 | − | 0.923004i | −0.991740 | − | 0.128263i | \(-0.959060\pi\) |
−0.606949 | − | 0.794741i | \(-0.707607\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.0993i | − | 1.56830i | −0.620571 | − | 0.784150i | \(-0.713099\pi\) | ||
0.620571 | − | 0.784150i | \(-0.286901\pi\) | |||||||
\(182\) | 38.5045 | − | 12.6137i | 2.85414 | − | 0.934988i | ||||
\(183\) | 8.92051 | − | 8.92051i | 0.659423 | − | 0.659423i | ||||
\(184\) | 5.87322 | − | 3.39091i | 0.432980 | − | 0.249981i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.94633 | − | 8.56730i | 0.362683 | − | 0.628185i | ||||
\(187\) | 12.7499 | + | 3.41632i | 0.932364 | + | 0.249826i | ||||
\(188\) | 25.3372 | + | 25.3372i | 1.84790 | + | 1.84790i | ||||
\(189\) | −2.21543 | + | 1.44633i | −0.161149 | + | 0.105205i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.892661 | − | 1.54613i | −0.0645907 | − | 0.111874i | 0.831922 | − | 0.554893i | \(-0.187241\pi\) |
−0.896512 | + | 0.443019i | \(0.853908\pi\) | |||||||
\(192\) | −5.87465 | − | 21.9245i | −0.423966 | − | 1.58226i | ||||
\(193\) | 4.01578 | + | 14.9871i | 0.289062 | + | 1.07879i | 0.945820 | + | 0.324693i | \(0.105261\pi\) |
−0.656757 | + | 0.754102i | \(0.728072\pi\) | |||||||
\(194\) | 2.61058 | + | 4.52167i | 0.187429 | + | 0.324637i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21.8834 | − | 29.8162i | −1.56310 | − | 2.12973i | ||||
\(197\) | 11.7063 | + | 11.7063i | 0.834040 | + | 0.834040i | 0.988067 | − | 0.154027i | \(-0.0492243\pi\) |
−0.154027 | + | 0.988067i | \(0.549224\pi\) | |||||||
\(198\) | −8.83958 | − | 2.36856i | −0.628202 | − | 0.168326i | ||||
\(199\) | 4.86539 | − | 8.42711i | 0.344898 | − | 0.597382i | −0.640437 | − | 0.768011i | \(-0.721247\pi\) |
0.985335 | + | 0.170629i | \(0.0545800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.488290 | − | 0.281914i | 0.0344413 | − | 0.0198847i | ||||
\(202\) | 37.7103 | − | 37.7103i | 2.65329 | − | 2.65329i | ||||
\(203\) | −3.24019 | + | 15.4269i | −0.227417 | + | 1.08276i | ||||
\(204\) | − | 20.5671i | − | 1.43999i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 22.2626 | + | 12.8533i | 1.55111 | + | 0.895533i | ||||
\(207\) | −0.739216 | + | 0.198072i | −0.0513791 | + | 0.0137670i | ||||
\(208\) | 19.6051 | − | 73.1672i | 1.35937 | − | 5.07323i | ||||
\(209\) | 4.89092 | 0.338312 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.49825 | 0.240829 | 0.120415 | − | 0.992724i | \(-0.461578\pi\) | ||||
0.120415 | + | 0.992724i | \(0.461578\pi\) | |||||||
\(212\) | −15.5546 | + | 58.0507i | −1.06830 | + | 3.98694i | ||||
\(213\) | −6.51020 | + | 1.74440i | −0.446071 | + | 0.119524i | ||||
\(214\) | −6.30775 | − | 3.64178i | −0.431189 | − | 0.248947i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.86172i | 0.602964i | ||||||||
\(217\) | −7.22279 | − | 6.47193i | −0.490315 | − | 0.439344i | ||||
\(218\) | 14.3159 | − | 14.3159i | 0.969598 | − | 0.969598i | ||||
\(219\) | 4.29379 | − | 2.47902i | 0.290147 | − | 0.167517i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.0444 | − | 19.1295i | 0.742927 | − | 1.28679i | ||||
\(222\) | −3.27536 | − | 0.877631i | −0.219828 | − | 0.0589027i | ||||
\(223\) | 16.1092 | + | 16.1092i | 1.07875 | + | 1.07875i | 0.996622 | + | 0.0821283i | \(0.0261717\pi\) |
0.0821283 | + | 0.996622i | \(0.473828\pi\) | |||||||
\(224\) | −48.3521 | + | 2.65105i | −3.23066 | + | 0.177131i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.89266 | + | 6.74229i | 0.258936 | + | 0.448490i | ||||
\(227\) | 2.50303 | + | 9.34143i | 0.166132 | + | 0.620013i | 0.997893 | + | 0.0648792i | \(0.0206662\pi\) |
−0.831761 | + | 0.555134i | \(0.812667\pi\) | |||||||
\(228\) | −1.97241 | − | 7.36115i | −0.130626 | − | 0.487504i | ||||
\(229\) | 11.4598 | + | 19.8489i | 0.757285 | + | 1.31166i | 0.944231 | + | 0.329285i | \(0.106808\pi\) |
−0.186946 | + | 0.982370i | \(0.559859\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.05367 | + | 8.00347i | −0.266712 | + | 0.526589i | ||||
\(232\) | 37.3342 | + | 37.3342i | 2.45111 | + | 2.45111i | ||||
\(233\) | −2.95687 | − | 0.792290i | −0.193711 | − | 0.0519046i | 0.160659 | − | 0.987010i | \(-0.448638\pi\) |
−0.354370 | + | 0.935105i | \(0.615305\pi\) | |||||||
\(234\) | −7.65716 | + | 13.2626i | −0.500564 | + | 0.867002i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −29.5252 | + | 17.0464i | −1.92193 | + | 1.10962i | ||||
\(237\) | −5.54880 | + | 5.54880i | −0.360433 | + | 0.360433i | ||||
\(238\) | −27.2015 | − | 5.71329i | −1.76321 | − | 0.370337i | ||||
\(239\) | 5.77830i | 0.373767i | 0.982382 | + | 0.186884i | \(0.0598388\pi\) | ||||
−0.982382 | + | 0.186884i | \(0.940161\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.7725 | + | 11.4157i | 1.27366 | + | 0.735349i | 0.975675 | − | 0.219221i | \(-0.0703517\pi\) |
0.297986 | + | 0.954570i | \(0.403685\pi\) | |||||||
\(242\) | −1.29885 | + | 0.348026i | −0.0834933 | + | 0.0223720i | ||||
\(243\) | 0.258819 | − | 0.965926i | 0.0166032 | − | 0.0619642i | ||||
\(244\) | −66.6549 | −4.26714 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.84719 | 0.181530 | ||||||||
\(247\) | 2.11834 | − | 7.90576i | 0.134787 | − | 0.503032i | ||||
\(248\) | −31.3764 | + | 8.40727i | −1.99240 | + | 0.533862i | ||||
\(249\) | 1.82501 | + | 1.05367i | 0.115655 | + | 0.0667736i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.8325i | 0.809981i | 0.914321 | + | 0.404991i | \(0.132725\pi\) | ||||
−0.914321 | + | 0.404991i | \(0.867275\pi\) | |||||||
\(252\) | 13.6805 | + | 2.87339i | 0.861791 | + | 0.181007i | ||||
\(253\) | −1.83497 | + | 1.83497i | −0.115363 | + | 0.115363i | ||||
\(254\) | 18.4524 | − | 10.6535i | 1.15781 | − | 0.668460i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.5671 | + | 18.3028i | −0.660446 | + | 1.14393i | ||||
\(257\) | 23.4122 | + | 6.27328i | 1.46041 | + | 0.391317i | 0.899633 | − | 0.436648i | \(-0.143834\pi\) |
0.560781 | + | 0.827964i | \(0.310501\pi\) | |||||||
\(258\) | −18.2033 | − | 18.2033i | −1.13329 | − | 1.13329i | ||||
\(259\) | −1.50202 | + | 2.96556i | −0.0933311 | + | 0.184271i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.97902 | − | 5.15981i | −0.184397 | − | 0.319384i | ||||
\(262\) | 9.01432 | + | 33.6419i | 0.556906 | + | 2.07840i | ||||
\(263\) | 2.53977 | + | 9.47856i | 0.156609 | + | 0.584473i | 0.998962 | + | 0.0455471i | \(0.0145031\pi\) |
−0.842353 | + | 0.538926i | \(0.818830\pi\) | |||||||
\(264\) | 15.0246 | + | 26.0234i | 0.924702 | + | 1.60163i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.2836 | + | 0.563829i | −0.630526 | + | 0.0345706i | ||||
\(267\) | 2.52287 | + | 2.52287i | 0.154397 | + | 0.154397i | ||||
\(268\) | −2.87752 | − | 0.771029i | −0.175772 | − | 0.0470981i | ||||
\(269\) | 10.9812 | − | 19.0199i | 0.669533 | − | 1.15966i | −0.308502 | − | 0.951224i | \(-0.599828\pi\) |
0.978035 | − | 0.208441i | \(-0.0668389\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.9488 | + | 12.6721i | −1.33329 | + | 0.769777i | −0.985803 | − | 0.167907i | \(-0.946299\pi\) |
−0.347490 | + | 0.937684i | \(0.612966\pi\) | |||||||
\(272\) | −36.7433 | + | 36.7433i | −2.22789 | + | 2.22789i | ||||
\(273\) | 11.1812 | + | 10.0189i | 0.676719 | + | 0.606369i | ||||
\(274\) | − | 5.71994i | − | 0.345554i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.50175 | + | 2.02174i | 0.210781 | + | 0.121694i | ||||
\(277\) | −13.5087 | + | 3.61963i | −0.811657 | + | 0.217483i | −0.640696 | − | 0.767795i | \(-0.721354\pi\) |
−0.170961 | + | 0.985278i | \(0.554687\pi\) | |||||||
\(278\) | 0.747768 | − | 2.79071i | 0.0448481 | − | 0.167375i | ||||
\(279\) | 3.66557 | 0.219452 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.9161 | −1.06878 | −0.534392 | − | 0.845237i | \(-0.679459\pi\) | ||||
−0.534392 | + | 0.845237i | \(0.679459\pi\) | |||||||
\(282\) | −4.73712 | + | 17.6792i | −0.282091 | + | 1.05278i | ||||
\(283\) | 18.2310 | − | 4.88498i | 1.08372 | − | 0.290382i | 0.327601 | − | 0.944816i | \(-0.393760\pi\) |
0.756119 | + | 0.654434i | \(0.227093\pi\) | |||||||
\(284\) | 30.8396 | + | 17.8052i | 1.82999 | + | 1.05655i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 51.9294i | 3.07065i | ||||||||
\(287\) | 0.573736 | − | 2.73162i | 0.0338666 | − | 0.161242i | ||||
\(288\) | 12.9420 | − | 12.9420i | 0.762617 | − | 0.762617i | ||||
\(289\) | 1.59972 | − | 0.923596i | 0.0941009 | − | 0.0543292i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.967310 | + | 1.67543i | −0.0567047 | + | 0.0982155i | ||||
\(292\) | −25.3035 | − | 6.78006i | −1.48078 | − | 0.396773i | ||||
\(293\) | −12.6686 | − | 12.6686i | −0.740106 | − | 0.740106i | 0.232492 | − | 0.972598i | \(-0.425312\pi\) |
−0.972598 | + | 0.232492i | \(0.925312\pi\) | |||||||
\(294\) | 7.60054 | − | 17.2953i | 0.443272 | − | 1.00868i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.56713 | + | 9.64256i | 0.323583 | + | 0.560462i | ||||
\(297\) | −0.877631 | − | 3.27536i | −0.0509253 | − | 0.190056i | ||||
\(298\) | 5.98417 | + | 22.3332i | 0.346654 | + | 1.29373i | ||||
\(299\) | 2.17132 | + | 3.76083i | 0.125571 | + | 0.217495i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.1325 | + | 13.7962i | −1.21806 | + | 0.795202i | ||||
\(302\) | −29.4159 | − | 29.4159i | −1.69269 | − | 1.69269i | ||||
\(303\) | 19.0874 | + | 5.11445i | 1.09654 | + | 0.293818i | ||||
\(304\) | −9.62701 | + | 16.6745i | −0.552147 | + | 0.956347i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.09807 | − | 5.25277i | 0.520102 | − | 0.300281i | ||||
\(307\) | 8.19576 | − | 8.19576i | 0.467757 | − | 0.467757i | −0.433430 | − | 0.901187i | \(-0.642697\pi\) |
0.901187 | + | 0.433430i | \(0.142697\pi\) | |||||||
\(308\) | 45.0460 | − | 14.7566i | 2.56674 | − | 0.840837i | ||||
\(309\) | 9.52517i | 0.541868i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0899 | − | 8.71214i | −0.855668 | − | 0.494020i | 0.00689127 | − | 0.999976i | \(-0.497806\pi\) |
−0.862559 | + | 0.505956i | \(0.831140\pi\) | |||||||
\(312\) | 48.5721 | − | 13.0149i | 2.74986 | − | 0.736822i | ||||
\(313\) | −1.08089 | + | 4.03393i | −0.0610954 | + | 0.228011i | −0.989722 | − | 0.143004i | \(-0.954324\pi\) |
0.928627 | + | 0.371015i | \(0.120990\pi\) | |||||||
\(314\) | −47.9992 | −2.70875 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 41.4612 | 2.33237 | ||||||||
\(317\) | 6.03229 | − | 22.5128i | 0.338807 | − | 1.26445i | −0.560875 | − | 0.827900i | \(-0.689535\pi\) |
0.899682 | − | 0.436545i | \(-0.143798\pi\) | |||||||
\(318\) | −29.6519 | + | 7.94520i | −1.66280 | + | 0.445545i | ||||
\(319\) | −17.4964 | − | 10.1016i | −0.979613 | − | 0.565580i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 2.69881i | − | 0.150633i | ||||||
\(322\) | 3.64664 | − | 4.06971i | 0.203219 | − | 0.226796i | ||||
\(323\) | −3.97014 | + | 3.97014i | −0.220905 | + | 0.220905i | ||||
\(324\) | −4.57570 | + | 2.64178i | −0.254206 | + | 0.146766i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.11085 | + | 5.38815i | −0.172294 | + | 0.298422i | ||||
\(327\) | 7.24614 | + | 1.94160i | 0.400712 | + | 0.107371i | ||||
\(328\) | −6.61070 | − | 6.61070i | −0.365015 | − | 0.365015i | ||||
\(329\) | 16.0069 | + | 8.10734i | 0.882491 | + | 0.446972i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.06713 | − | 5.31243i | −0.168585 | − | 0.291998i | 0.769338 | − | 0.638842i | \(-0.220586\pi\) |
−0.937923 | + | 0.346845i | \(0.887253\pi\) | |||||||
\(332\) | −2.88176 | − | 10.7549i | −0.158157 | − | 0.590251i | ||||
\(333\) | −0.325192 | − | 1.21363i | −0.0178204 | − | 0.0665067i | ||||
\(334\) | 5.25277 | + | 9.09807i | 0.287419 | + | 0.497824i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −19.3070 | − | 29.5737i | −1.05328 | − | 1.61337i | ||||
\(337\) | 10.4816 | + | 10.4816i | 0.570967 | + | 0.570967i | 0.932399 | − | 0.361432i | \(-0.117712\pi\) |
−0.361432 | + | 0.932399i | \(0.617712\pi\) | |||||||
\(338\) | 50.0506 | + | 13.4110i | 2.72239 | + | 0.729463i | ||||
\(339\) | −1.44236 | + | 2.49825i | −0.0783384 | + | 0.135686i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.7643 | − | 6.21480i | 0.582922 | − | 0.336550i | ||||
\(342\) | 2.75253 | − | 2.75253i | 0.148840 | − | 0.148840i | ||||
\(343\) | −15.0616 | − | 10.7772i | −0.813251 | − | 0.581912i | ||||
\(344\) | 84.5301i | 4.55756i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 29.6780 | + | 17.1346i | 1.59550 | + | 0.921161i | ||||
\(347\) | 11.3462 | − | 3.04020i | 0.609096 | − | 0.163207i | 0.0589298 | − | 0.998262i | \(-0.481231\pi\) |
0.550166 | + | 0.835055i | \(0.314565\pi\) | |||||||
\(348\) | −8.14755 | + | 30.4071i | −0.436754 | + | 1.62999i | ||||
\(349\) | 12.3258 | 0.659786 | 0.329893 | − | 0.944018i | \(-0.392987\pi\) | ||||
0.329893 | + | 0.944018i | \(0.392987\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.67447 | −0.302881 | ||||||||
\(352\) | 16.0631 | − | 59.9484i | 0.856167 | − | 3.19526i | ||||
\(353\) | 6.32074 | − | 1.69364i | 0.336419 | − | 0.0901432i | −0.0866548 | − | 0.996238i | \(-0.527618\pi\) |
0.423074 | + | 0.906095i | \(0.360951\pi\) | |||||||
\(354\) | −15.0812 | − | 8.70716i | −0.801559 | − | 0.462781i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 18.8511i | − | 0.999106i | ||||||
\(357\) | −3.20620 | − | 9.78723i | −0.169690 | − | 0.517995i | ||||
\(358\) | −47.1321 | + | 47.1321i | −2.49101 | + | 2.49101i | ||||
\(359\) | −15.5521 | + | 8.97902i | −0.820809 | + | 0.473895i | −0.850696 | − | 0.525659i | \(-0.823819\pi\) |
0.0298861 | + | 0.999553i | \(0.490486\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.45979 | − | 14.6528i | 0.445252 | − | 0.771200i | ||||
\(362\) | −55.0027 | − | 14.7379i | −2.89088 | − | 0.774609i | ||||
\(363\) | −0.352313 | − | 0.352313i | −0.0184916 | − | 0.0184916i | ||||
\(364\) | −4.34264 | − | 79.2045i | −0.227616 | − | 4.15145i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −17.0234 | − | 29.4854i | −0.889828 | − | 1.54123i | ||||
\(367\) | 1.67283 | + | 6.24307i | 0.0873208 | + | 0.325886i | 0.995744 | − | 0.0921671i | \(-0.0293794\pi\) |
−0.908423 | + | 0.418053i | \(0.862713\pi\) | |||||||
\(368\) | −2.64406 | − | 9.86776i | −0.137831 | − | 0.514393i | ||||
\(369\) | 0.527491 | + | 0.913641i | 0.0274601 | + | 0.0475622i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.64754 | + | 30.0493i | 0.0855362 | + | 1.56008i | ||||
\(372\) | −13.6947 | − | 13.6947i | −0.710038 | − | 0.710038i | ||||
\(373\) | −21.3994 | − | 5.73395i | −1.10802 | − | 0.296893i | −0.341993 | − | 0.939702i | \(-0.611102\pi\) |
−0.766026 | + | 0.642810i | \(0.777769\pi\) | |||||||
\(374\) | 17.8117 | − | 30.8507i | 0.921019 | − | 1.59525i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 52.0468 | − | 30.0493i | 2.68411 | − | 1.54967i | ||||
\(377\) | −23.9064 | + | 23.9064i | −1.23124 | + | 1.23124i | ||||
\(378\) | 2.22288 | + | 6.78556i | 0.114333 | + | 0.349011i | ||||
\(379\) | − | 4.30211i | − | 0.220984i | −0.993877 | − | 0.110492i | \(-0.964757\pi\) | ||
0.993877 | − | 0.110492i | \(-0.0352427\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.83724 | + | 3.94748i | 0.350282 | + | 0.202236i | ||||
\(382\) | −4.65406 | + | 1.24705i | −0.238123 | + | 0.0638048i | ||||
\(383\) | 6.59463 | − | 24.6115i | 0.336970 | − | 1.25759i | −0.564748 | − | 0.825264i | \(-0.691026\pi\) |
0.901718 | − | 0.432326i | \(-0.142307\pi\) | |||||||
\(384\) | −24.6516 | −1.25800 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 41.8741 | 2.13134 | ||||||||
\(387\) | 2.46882 | − | 9.21376i | 0.125497 | − | 0.468362i | ||||
\(388\) | 9.87340 | − | 2.64557i | 0.501246 | − | 0.134308i | ||||
\(389\) | 14.8024 | + | 8.54615i | 0.750510 | + | 0.433307i | 0.825878 | − | 0.563849i | \(-0.190680\pi\) |
−0.0753681 | + | 0.997156i | \(0.524013\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.97903i | − | 0.150656i | ||||||
\(392\) | −57.8039 | + | 22.5096i | −2.91954 | + | 1.13690i | ||||
\(393\) | −9.12535 | + | 9.12535i | −0.460313 | + | 0.460313i | ||||
\(394\) | 38.6935 | − | 22.3397i | 1.94935 | − | 1.12546i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.95804 | + | 15.5158i | −0.450158 | + | 0.779697i | ||||
\(397\) | 13.0643 | + | 3.50057i | 0.655679 | + | 0.175689i | 0.571295 | − | 0.820745i | \(-0.306441\pi\) |
0.0843839 | + | 0.996433i | \(0.473108\pi\) | |||||||
\(398\) | −18.5697 | − | 18.5697i | −0.930815 | − | 0.930815i | ||||
\(399\) | −2.08613 | − | 3.19545i | −0.104437 | − | 0.159973i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5217 | − | 23.4202i | −0.675240 | − | 1.16955i | −0.976399 | − | 0.215976i | \(-0.930707\pi\) |
0.301159 | − | 0.953574i | \(-0.402627\pi\) | |||||||
\(402\) | −0.393836 | − | 1.46982i | −0.0196428 | − | 0.0733078i | ||||
\(403\) | −5.38348 | − | 20.0914i | −0.268170 | − | 1.00082i | ||||
\(404\) | −52.2036 | − | 90.4192i | −2.59722 | − | 4.49852i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 37.9523 | + | 19.2224i | 1.88354 | + | 0.953993i | ||||
\(407\) | −3.01262 | − | 3.01262i | −0.149330 | − | 0.149330i | ||||
\(408\) | −33.3203 | − | 8.92813i | −1.64960 | − | 0.442009i | ||||
\(409\) | 1.25341 | − | 2.17096i | 0.0619770 | − | 0.107347i | −0.833372 | − | 0.552712i | \(-0.813593\pi\) |
0.895349 | + | 0.445365i | \(0.146926\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.83548 | − | 1.05972i | 0.0905377 | − | 0.0522719i | ||||
\(412\) | 35.5865 | − | 35.5865i | 1.75322 | − | 1.75322i | ||||
\(413\) | −11.3927 | + | 12.7145i | −0.560599 | + | 0.625639i | ||||
\(414\) | 2.06538i | 0.101508i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −89.9444 | − | 51.9294i | −4.40989 | − | 2.54605i | ||||
\(417\) | 1.03405 | − | 0.277073i | 0.0506377 | − | 0.0135683i | ||||
\(418\) | 3.41632 | − | 12.7499i | 0.167098 | − | 0.623617i | ||||
\(419\) | −21.0422 | −1.02798 | −0.513989 | − | 0.857797i | \(-0.671833\pi\) | ||||
−0.513989 | + | 0.857797i | \(0.671833\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.0619 | −0.880282 | −0.440141 | − | 0.897929i | \(-0.645071\pi\) | ||||
−0.440141 | + | 0.897929i | \(0.645071\pi\) | |||||||
\(422\) | 2.44354 | − | 9.11940i | 0.118949 | − | 0.443925i | ||||
\(423\) | −6.55073 | + | 1.75526i | −0.318507 | + | 0.0853438i | ||||
\(424\) | 87.2941 | + | 50.3993i | 4.23938 | + | 2.44761i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 18.1896i | 0.881288i | ||||||||
\(427\) | −31.7189 | + | 10.3908i | −1.53499 | + | 0.502846i | ||||
\(428\) | −10.0829 | + | 10.0829i | −0.487374 | + | 0.487374i | ||||
\(429\) | −16.6637 | + | 9.62080i | −0.804532 | + | 0.464497i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.45979 | − | 11.1887i | 0.311157 | − | 0.538940i | −0.667456 | − | 0.744649i | \(-0.732617\pi\) |
0.978613 | + | 0.205709i | \(0.0659500\pi\) | |||||||
\(432\) | 12.8941 | + | 3.45496i | 0.620367 | + | 0.166227i | ||||
\(433\) | 22.1861 | + | 22.1861i | 1.06620 | + | 1.06620i | 0.997648 | + | 0.0685478i | \(0.0218366\pi\) |
0.0685478 | + | 0.997648i | \(0.478163\pi\) | |||||||
\(434\) | −21.9165 | + | 14.3081i | −1.05203 | + | 0.686809i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.8180 | − | 34.3258i | −0.949111 | − | 1.64391i | ||||
\(437\) | −0.285692 | − | 1.06622i | −0.0136665 | − | 0.0510041i | ||||
\(438\) | −3.46321 | − | 12.9249i | −0.165478 | − | 0.617574i | ||||
\(439\) | −4.57570 | − | 7.92535i | −0.218386 | − | 0.378256i | 0.735928 | − | 0.677059i | \(-0.236746\pi\) |
−0.954315 | + | 0.298803i | \(0.903413\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.95804 | − | 0.765293i | 0.331335 | − | 0.0364425i | ||||
\(442\) | −42.1531 | − | 42.1531i | −2.00502 | − | 2.00502i | ||||
\(443\) | −26.7986 | − | 7.18065i | −1.27324 | − | 0.341163i | −0.441967 | − | 0.897031i | \(-0.645719\pi\) |
−0.831271 | + | 0.555868i | \(0.812386\pi\) | |||||||
\(444\) | −3.31926 | + | 5.74912i | −0.157525 | + | 0.272841i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 53.2465 | − | 30.7419i | 2.52129 | − | 1.45567i | ||||
\(447\) | −6.05788 | + | 6.05788i | −0.286528 | + | 0.286528i | ||||
\(448\) | −12.3439 | + | 58.7706i | −0.583195 | + | 2.77665i | ||||
\(449\) | 28.3525i | 1.33804i | 0.743247 | + | 0.669018i | \(0.233285\pi\) | ||||
−0.743247 | + | 0.669018i | \(0.766715\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.09807 | + | 1.78867i | 0.145882 | + | 0.0842252i | ||||
\(452\) | 14.7223 | − | 3.94483i | 0.692478 | − | 0.185549i | ||||
\(453\) | 3.98952 | − | 14.8891i | 0.187444 | − | 0.699551i | ||||
\(454\) | 26.1001 | 1.22494 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.7818 | −0.598563 | ||||||||
\(457\) | −2.40189 | + | 8.96398i | −0.112356 | + | 0.419317i | −0.999076 | − | 0.0429900i | \(-0.986312\pi\) |
0.886720 | + | 0.462307i | \(0.152978\pi\) | |||||||
\(458\) | 59.7479 | − | 16.0094i | 2.79184 | − | 0.748070i | ||||
\(459\) | 3.37114 | + | 1.94633i | 0.157351 | + | 0.0908469i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.5762i | 0.632306i | 0.948708 | + | 0.316153i | \(0.102391\pi\) | ||||
−0.948708 | + | 0.316153i | \(0.897609\pi\) | |||||||
\(462\) | 18.0323 | + | 16.1577i | 0.838940 | + | 0.751727i | ||||
\(463\) | 20.5644 | − | 20.5644i | 0.955710 | − | 0.955710i | −0.0433497 | − | 0.999060i | \(-0.513803\pi\) |
0.999060 | + | 0.0433497i | \(0.0138030\pi\) | |||||||
\(464\) | 68.8781 | − | 39.7668i | 3.19758 | − | 1.84613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.13076 | + | 7.15469i | −0.191354 | + | 0.331434i | ||||
\(467\) | −36.3357 | − | 9.73612i | −1.68142 | − | 0.450534i | −0.713263 | − | 0.700896i | \(-0.752784\pi\) |
−0.968152 | + | 0.250362i | \(0.919450\pi\) | |||||||
\(468\) | 21.2001 | + | 21.2001i | 0.979975 | + | 0.979975i | ||||
\(469\) | −1.48951 | + | 0.0816672i | −0.0687793 | + | 0.00377104i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.89266 | − | 15.4025i | −0.409752 | − | 0.709712i | ||||
\(472\) | 14.7996 | + | 55.2327i | 0.681205 | + | 2.54229i | ||||
\(473\) | −8.37154 | − | 31.2430i | −0.384924 | − | 1.43655i | ||||
\(474\) | 10.5890 | + | 18.3407i | 0.486370 | + | 0.842418i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −24.5870 | + | 48.5441i | −1.12695 | + | 2.22501i | ||||
\(477\) | −8.04306 | − | 8.04306i | −0.368267 | − | 0.368267i | ||||
\(478\) | 15.0632 | + | 4.03616i | 0.688973 | + | 0.184610i | ||||
\(479\) | −11.3591 | + | 19.6745i | −0.519009 | + | 0.898950i | 0.480747 | + | 0.876859i | \(0.340365\pi\) |
−0.999756 | + | 0.0220904i | \(0.992968\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.17447 | + | 3.56483i | −0.281532 | + | 0.162542i | ||||
\(482\) | 43.5701 | − | 43.5701i | 1.98457 | − | 1.98457i | ||||
\(483\) | 1.98154 | + | 0.416193i | 0.0901632 | + | 0.0189375i | ||||
\(484\) | 2.63251i | 0.119660i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.33724 | − | 1.34940i | −0.106019 | − | 0.0612102i | ||||
\(487\) | 29.7704 | − | 7.97697i | 1.34903 | − | 0.361471i | 0.489252 | − | 0.872143i | \(-0.337270\pi\) |
0.859776 | + | 0.510672i | \(0.170603\pi\) | |||||||
\(488\) | −28.9347 | + | 107.986i | −1.30981 | + | 4.88829i | ||||
\(489\) | −2.30535 | −0.104252 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.4867 | −1.51123 | −0.755617 | − | 0.655013i | \(-0.772663\pi\) | ||||
−0.755617 | + | 0.655013i | \(0.772663\pi\) | |||||||
\(492\) | 1.44267 | − | 5.38413i | 0.0650408 | − | 0.242735i | ||||
\(493\) | 22.4024 | − | 6.00269i | 1.00895 | − | 0.270348i | ||||
\(494\) | −19.1295 | − | 11.0444i | −0.860675 | − | 0.496911i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 48.9314i | 2.19709i | ||||||||
\(497\) | 17.4512 | + | 3.66537i | 0.782793 | + | 0.164414i | ||||
\(498\) | 4.02153 | − | 4.02153i | 0.180209 | − | 0.180209i | ||||
\(499\) | −1.61577 | + | 0.932866i | −0.0723318 | + | 0.0417608i | −0.535730 | − | 0.844390i | \(-0.679963\pi\) |
0.463398 | + | 0.886150i | \(0.346630\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.94633 | + | 3.37114i | −0.0869556 | + | 0.150612i | ||||
\(502\) | 33.4524 | + | 8.96355i | 1.49306 | + | 0.400063i | ||||
\(503\) | 6.45394 | + | 6.45394i | 0.287767 | + | 0.287767i | 0.836197 | − | 0.548430i | \(-0.184774\pi\) |
−0.548430 | + | 0.836197i | \(0.684774\pi\) | |||||||
\(504\) | 10.5938 | − | 20.9161i | 0.471884 | − | 0.931676i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.50175 | + | 6.06522i | 0.155672 | + | 0.269632i | ||||
\(507\) | 4.96923 | + | 18.5454i | 0.220691 | + | 0.823632i | ||||
\(508\) | −10.7963 | − | 40.2922i | −0.479007 | − | 1.78768i | ||||
\(509\) | 11.2864 | + | 19.5486i | 0.500260 | + | 0.866476i | 1.00000 | 0.000300571i | \(9.56748e-5\pi\) | |
−0.499740 | + | 0.866176i | \(0.666571\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.0981 | + | 0.718143i | −0.579424 | + | 0.0317688i | ||||
\(512\) | 5.46881 | + | 5.46881i | 0.241689 | + | 0.241689i | ||||
\(513\) | 1.39322 | + | 0.373311i | 0.0615120 | + | 0.0164821i | ||||
\(514\) | 32.7070 | − | 56.6502i | 1.44264 | − | 2.49873i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −43.6467 | + | 25.1994i | −1.92144 | + | 1.10934i | ||||
\(517\) | −16.2610 | + | 16.2610i | −0.715157 | + | 0.715157i | ||||
\(518\) | 6.68159 | + | 5.98699i | 0.293572 | + | 0.263053i | ||||
\(519\) | 12.6979i | 0.557376i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.15281 | − | 5.28438i | −0.400992 | − | 0.231513i | 0.285920 | − | 0.958253i | \(-0.407701\pi\) |
−0.686912 | + | 0.726741i | \(0.741034\pi\) | |||||||
\(522\) | −15.5317 | + | 4.16171i | −0.679804 | + | 0.182153i | ||||
\(523\) | −3.42627 | + | 12.7870i | −0.149820 | + | 0.559137i | 0.849673 | + | 0.527310i | \(0.176799\pi\) |
−0.999493 | + | 0.0318274i | \(0.989867\pi\) | |||||||
\(524\) | 68.1855 | 2.97870 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.4832 | 1.15472 | ||||||||
\(527\) | −3.69304 | + | 13.7826i | −0.160871 | + | 0.600380i | ||||
\(528\) | 43.7227 | − | 11.7155i | 1.90278 | − | 0.509850i | ||||
\(529\) | −19.4114 | − | 11.2072i | −0.843973 | − | 0.487268i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.45260i | − | 0.280019i | ||||||
\(532\) | −4.14447 | + | 19.7322i | −0.179686 | + | 0.855502i | ||||
\(533\) | 4.23307 | − | 4.23307i | 0.183355 | − | 0.183355i | ||||
\(534\) | 8.33896 | − | 4.81450i | 0.360862 | − | 0.208344i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.49825 | + | 4.32709i | −0.107908 | + | 0.186902i | ||||
\(537\) | −23.8563 | − | 6.39229i | −1.02948 | − | 0.275847i | ||||
\(538\) | −41.9117 | − | 41.9117i | −1.80694 | − | 1.80694i | ||||
\(539\) | 19.1355 | − | 14.0444i | 0.824226 | − | 0.604935i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.67623 | − | 2.90331i | −0.0720667 | − | 0.124823i | 0.827740 | − | 0.561111i | \(-0.189626\pi\) |
−0.899807 | + | 0.436288i | \(0.856293\pi\) | |||||||
\(542\) | 17.7030 | + | 66.0686i | 0.760411 | + | 2.83789i | ||||
\(543\) | −5.46090 | − | 20.3804i | −0.234350 | − | 0.874606i | ||||
\(544\) | 35.6233 | + | 61.7014i | 1.52734 | + | 2.64543i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 33.9278 | − | 22.1496i | 1.45198 | − | 0.947914i | ||||
\(547\) | −25.3496 | − | 25.3496i | −1.08387 | − | 1.08387i | −0.996144 | − | 0.0877278i | \(-0.972039\pi\) |
−0.0877278 | − | 0.996144i | \(-0.527961\pi\) | |||||||
\(548\) | −10.8166 | − | 2.89830i | −0.462062 | − | 0.123809i | ||||
\(549\) | 6.30775 | − | 10.9254i | 0.269208 | − | 0.466283i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.44232 | − | 4.29683i | 0.317054 | − | 0.183051i | ||||
\(552\) | 4.79547 | − | 4.79547i | 0.204109 | − | 0.204109i | ||||
\(553\) | 19.7300 | − | 6.46336i | 0.839006 | − | 0.274850i | ||||
\(554\) | 37.7434i | 1.60356i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.89842 | − | 2.82811i | −0.207739 | − | 0.119938i | ||||
\(557\) | 18.2388 | − | 4.88707i | 0.772803 | − | 0.207072i | 0.149193 | − | 0.988808i | \(-0.452332\pi\) |
0.623609 | + | 0.781736i | \(0.285666\pi\) | |||||||
\(558\) | 2.56041 | − | 9.55558i | 0.108391 | − | 0.404520i | ||||
\(559\) | −54.1276 | −2.28935 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.1996 | 0.557290 | ||||||||
\(562\) | −12.5144 | + | 46.7045i | −0.527890 | + | 1.97011i | ||||
\(563\) | −33.9371 | + | 9.09342i | −1.43028 | + | 0.383242i | −0.889118 | − | 0.457678i | \(-0.848681\pi\) |
−0.541160 | + | 0.840920i | \(0.682015\pi\) | |||||||
\(564\) | 31.0316 | + | 17.9161i | 1.30666 | + | 0.754403i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 50.9376i | − | 2.14107i | ||||||
\(567\) | −1.76560 | + | 1.97044i | −0.0741484 | + | 0.0827508i | ||||
\(568\) | 42.2331 | − | 42.2331i | 1.77206 | − | 1.77206i | ||||
\(569\) | 31.8176 | − | 18.3699i | 1.33387 | − | 0.770107i | 0.347975 | − | 0.937504i | \(-0.386869\pi\) |
0.985890 | + | 0.167396i | \(0.0535359\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.5362 | + | 18.2492i | −0.440926 | + | 0.763707i | −0.997758 | − | 0.0669184i | \(-0.978683\pi\) |
0.556832 | + | 0.830625i | \(0.312017\pi\) | |||||||
\(572\) | 98.2002 | + | 26.3127i | 4.10596 | + | 1.10019i | ||||
\(573\) | −1.26241 | − | 1.26241i | −0.0527381 | − | 0.0527381i | ||||
\(574\) | −6.72015 | − | 3.40368i | −0.280494 | − | 0.142067i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.3489 | − | 19.6570i | −0.472873 | − | 0.819040i | ||||
\(577\) | −5.18335 | − | 19.3445i | −0.215786 | − | 0.805323i | −0.985888 | − | 0.167403i | \(-0.946462\pi\) |
0.770103 | − | 0.637920i | \(-0.220205\pi\) | |||||||
\(578\) | −1.29027 | − | 4.81535i | −0.0536681 | − | 0.200292i | ||||
\(579\) | 7.75789 | + | 13.4371i | 0.322407 | + | 0.558425i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.04791 | − | 4.66866i | −0.126449 | − | 0.193689i | ||||
\(582\) | 3.69192 | + | 3.69192i | 0.153035 | + | 0.153035i | ||||
\(583\) | −37.2560 | − | 9.98271i | −1.54299 | − | 0.413442i | ||||
\(584\) | −21.9684 | + | 38.0503i | −0.909058 | + | 1.57453i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −41.8741 | + | 24.1760i | −1.72980 | + | 0.998703i | ||||
\(587\) | −29.8075 | + | 29.8075i | −1.23029 | + | 1.23029i | −0.266434 | + | 0.963853i | \(0.585846\pi\) |
−0.963853 | + | 0.266434i | \(0.914154\pi\) | |||||||
\(588\) | −28.8547 | − | 23.1364i | −1.18995 | − | 0.954129i | ||||
\(589\) | 5.28708i | 0.217850i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.3372 | + | 8.27761i | 0.589755 | + | 0.340495i | ||||
\(592\) | 16.2007 | − | 4.34097i | 0.665846 | − | 0.178413i | ||||
\(593\) | 7.84014 | − | 29.2598i | 0.321956 | − | 1.20156i | −0.595381 | − | 0.803443i | \(-0.702999\pi\) |
0.917337 | − | 0.398112i | \(-0.130334\pi\) | |||||||
\(594\) | −9.15141 | −0.375487 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 45.2650 | 1.85413 | ||||||||
\(597\) | 2.51851 | − | 9.39921i | 0.103076 | − | 0.384684i | ||||
\(598\) | 11.3206 | − | 3.03334i | 0.462934 | − | 0.124043i | ||||
\(599\) | −15.5885 | − | 9.00000i | −0.636927 | − | 0.367730i | 0.146503 | − | 0.989210i | \(-0.453198\pi\) |
−0.783430 | + | 0.621480i | \(0.786532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.48584i | 0.223772i | 0.993721 | + | 0.111886i | \(0.0356892\pi\) | ||||
−0.993721 | + | 0.111886i | \(0.964311\pi\) | |||||||
\(602\) | 21.2036 | + | 64.7260i | 0.864194 | + | 2.63803i | ||||
\(603\) | 0.398687 | − | 0.398687i | 0.0162358 | − | 0.0162358i | ||||
\(604\) | −70.5314 | + | 40.7213i | −2.86988 | + | 1.65693i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 26.6652 | − | 46.1855i | 1.08320 | − | 1.87616i | ||||
\(607\) | 9.88585 | + | 2.64891i | 0.401254 | + | 0.107516i | 0.453802 | − | 0.891103i | \(-0.350067\pi\) |
−0.0525474 | + | 0.998618i | \(0.516734\pi\) | |||||||
\(608\) | 18.6671 | + | 18.6671i | 0.757052 | + | 0.757052i | ||||
\(609\) | 0.862987 | + | 15.7399i | 0.0349700 | + | 0.637811i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.2416 | + | 33.3274i | 0.778432 | + | 1.34828i | ||||
\(612\) | −5.32317 | − | 19.8663i | −0.215176 | − | 0.803049i | ||||
\(613\) | −4.80405 | − | 17.9289i | −0.194034 | − | 0.724143i | −0.992515 | − | 0.122124i | \(-0.961030\pi\) |
0.798481 | − | 0.602020i | \(-0.205637\pi\) | |||||||
\(614\) | −15.6403 | − | 27.0899i | −0.631193 | − | 1.09326i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.35246 | − | 79.3836i | −0.175365 | − | 3.19846i | ||||
\(617\) | 20.7002 | + | 20.7002i | 0.833358 | + | 0.833358i | 0.987975 | − | 0.154616i | \(-0.0494141\pi\) |
−0.154616 | + | 0.987975i | \(0.549414\pi\) | |||||||
\(618\) | 24.8307 | + | 6.65336i | 0.998837 | + | 0.267638i | ||||
\(619\) | 19.4680 | − | 33.7196i | 0.782485 | − | 1.35530i | −0.148005 | − | 0.988987i | \(-0.547285\pi\) |
0.930490 | − | 0.366317i | \(-0.119381\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.662763 | + | 0.382647i | −0.0265958 | + | 0.0153551i | ||||
\(622\) | −33.2515 | + | 33.2515i | −1.33327 | + | 1.33327i | ||||
\(623\) | −2.93869 | − | 8.97063i | −0.117736 | − | 0.359401i | ||||
\(624\) | − | 75.7482i | − | 3.03236i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.76083 | + | 5.63542i | 0.390121 | + | 0.225237i | ||||
\(627\) | 4.72426 | − | 1.26586i | 0.188669 | − | 0.0505537i | ||||
\(628\) | −24.3212 | + | 90.7680i | −0.970522 | + | 3.62204i | ||||
\(629\) | 4.89092 | 0.195014 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.0468 | −1.27576 | −0.637882 | − | 0.770134i | \(-0.720189\pi\) | ||||
−0.637882 | + | 0.770134i | \(0.720189\pi\) | |||||||
\(632\) | 17.9982 | − | 67.1701i | 0.715929 | − | 2.67188i | ||||
\(633\) | 3.37905 | − | 0.905413i | 0.134305 | − | 0.0359869i | ||||
\(634\) | −54.4739 | − | 31.4505i | −2.16344 | − | 1.24906i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 60.0985i | 2.38306i | ||||||||
\(637\) | −14.4137 | − | 37.0139i | −0.571090 | − | 1.46654i | ||||
\(638\) | −38.5546 | + | 38.5546i | −1.52639 | + | 1.52639i | ||||
\(639\) | −5.83688 | + | 3.36993i | −0.230904 | + | 0.133312i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.5881 | − | 35.6597i | 0.813182 | − | 1.40847i | −0.0974447 | − | 0.995241i | \(-0.531067\pi\) |
0.910626 | − | 0.413231i | \(-0.135600\pi\) | |||||||
\(642\) | −7.03539 | − | 1.88513i | −0.277665 | − | 0.0744000i | ||||
\(643\) | −6.68412 | − | 6.68412i | −0.263596 | − | 0.263596i | 0.562917 | − | 0.826513i | \(-0.309679\pi\) |
−0.826513 | + | 0.562917i | \(0.809679\pi\) | |||||||
\(644\) | −5.84820 | − | 8.95804i | −0.230452 | − | 0.352996i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.57640 | + | 13.1227i | 0.298090 | + | 0.516306i | ||||
\(647\) | −7.19743 | − | 26.8612i | −0.282960 | − | 1.05602i | −0.950317 | − | 0.311284i | \(-0.899241\pi\) |
0.667357 | − | 0.744738i | \(-0.267426\pi\) | |||||||
\(648\) | 2.29358 | + | 8.55976i | 0.0901004 | + | 0.336259i | ||||
\(649\) | −10.9401 | − | 18.9488i | −0.429436 | − | 0.743804i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.65174 | − | 4.38201i | −0.339088 | − | 0.171745i | ||||
\(652\) | 8.61289 | + | 8.61289i | 0.337307 | + | 0.337307i | ||||
\(653\) | 42.0596 | + | 11.2698i | 1.64592 | + | 0.441023i | 0.958466 | − | 0.285206i | \(-0.0920621\pi\) |
0.687453 | + | 0.726229i | \(0.258729\pi\) | |||||||
\(654\) | 10.1229 | − | 17.5334i | 0.395837 | − | 0.685609i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12.1961 | + | 7.04144i | −0.476179 | + | 0.274922i | ||||
\(657\) | 3.50586 | − | 3.50586i | 0.136777 | − | 0.136777i | ||||
\(658\) | 32.3155 | − | 36.0647i | 1.25979 | − | 1.40595i | ||||
\(659\) | − | 36.8357i | − | 1.43491i | −0.696603 | − | 0.717457i | \(-0.745306\pi\) | ||
0.696603 | − | 0.717457i | \(-0.254694\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.22921 | + | 3.59644i | 0.242288 | + | 0.139885i | 0.616228 | − | 0.787568i | \(-0.288660\pi\) |
−0.373940 | + | 0.927453i | \(0.621993\pi\) | |||||||
\(662\) | −15.9911 | + | 4.28480i | −0.621512 | + | 0.166534i | ||||
\(663\) | 5.71700 | − | 21.3361i | 0.222030 | − | 0.828627i | ||||
\(664\) | −18.6746 | −0.724717 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.39091 | −0.131395 | ||||||||
\(667\) | −1.18012 | + | 4.40428i | −0.0456946 | + | 0.170534i | ||||
\(668\) | 19.8663 | − | 5.32317i | 0.768651 | − | 0.205959i | ||||
\(669\) | 19.7296 | + | 11.3909i | 0.762792 | + | 0.440398i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 42.7780i | − | 1.65143i | ||||||
\(672\) | −46.0184 | + | 15.0752i | −1.77520 | + | 0.581537i | ||||
\(673\) | 14.1515 | − | 14.1515i | 0.545500 | − | 0.545500i | −0.379636 | − | 0.925136i | \(-0.623951\pi\) |
0.925136 | + | 0.379636i | \(0.123951\pi\) | |||||||
\(674\) | 34.6452 | − | 20.0024i | 1.33448 | − | 0.770465i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 50.7213 | − | 87.8519i | 1.95082 | − | 3.37892i | ||||
\(677\) | 14.7290 | + | 3.94663i | 0.566083 | + | 0.151681i | 0.530500 | − | 0.847685i | \(-0.322004\pi\) |
0.0355835 | + | 0.999367i | \(0.488671\pi\) | |||||||
\(678\) | 5.50505 | + | 5.50505i | 0.211420 | + | 0.211420i | ||||
\(679\) | 4.28602 | − | 2.79810i | 0.164482 | − | 0.107381i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.83548 | + | 8.37530i | 0.185296 | + | 0.320942i | ||||
\(682\) | −8.68211 | − | 32.4021i | −0.332455 | − | 1.24074i | ||||
\(683\) | 8.77573 | + | 32.7515i | 0.335794 | + | 1.25320i | 0.903006 | + | 0.429628i | \(0.141355\pi\) |
−0.567212 | + | 0.823572i | \(0.691978\pi\) | |||||||
\(684\) | −3.81041 | − | 6.59982i | −0.145695 | − | 0.252351i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −38.6150 | + | 31.7355i | −1.47433 | + | 1.21167i | ||||
\(687\) | 16.2066 | + | 16.2066i | 0.618320 | + | 0.618320i | ||||
\(688\) | 122.994 | + | 32.9561i | 4.68910 | + | 1.25644i | ||||
\(689\) | −32.2725 | + | 55.8975i | −1.22948 | + | 2.12953i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.7032 | + | 14.2624i | −0.939752 | + | 0.542566i | −0.889883 | − | 0.456189i | \(-0.849214\pi\) |
−0.0498697 | + | 0.998756i | \(0.515881\pi\) | |||||||
\(692\) | 47.4399 | − | 47.4399i | 1.80339 | − | 1.80339i | ||||
\(693\) | −1.84409 | + | 8.77992i | −0.0700514 | + | 0.333522i | ||||
\(694\) | − | 31.7014i | − | 1.20337i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 45.7248 | + | 26.3992i | 1.73319 | + | 1.00066i | ||||
\(697\) | −3.96675 | + | 1.06289i | −0.150251 | + | 0.0402598i | ||||
\(698\) | 8.60962 | − | 32.1315i | 0.325879 | − | 1.21620i | ||||
\(699\) | −3.06117 | −0.115784 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.52517 | −0.0953745 | −0.0476873 | − | 0.998862i | \(-0.515185\pi\) | ||||
−0.0476873 | + | 0.998862i | \(0.515185\pi\) | |||||||
\(702\) | −3.96364 | + | 14.7925i | −0.149598 | + | 0.558307i | ||||
\(703\) | 1.75050 | − | 0.469045i | 0.0660213 | − | 0.0176904i | ||||
\(704\) | −66.6549 | − | 38.4832i | −2.51215 | − | 1.45039i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 17.6602i | − | 0.664652i | ||||||
\(707\) | −38.9374 | − | 34.8896i | −1.46439 | − | 1.31216i | ||||
\(708\) | −24.1072 | + | 24.1072i | −0.906004 | + | 0.906004i | ||||
\(709\) | −8.83619 | + | 5.10158i | −0.331850 | + | 0.191594i | −0.656662 | − | 0.754185i | \(-0.728032\pi\) |
0.324812 | + | 0.945779i | \(0.394699\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.92360 | + | 6.79587i | −0.147146 | + | 0.254865i | ||||
\(712\) | −30.5401 | − | 8.18321i | −1.14454 | − | 0.306679i | ||||
\(713\) | −1.98360 | − | 1.98360i | −0.0742864 | − | 0.0742864i | ||||
\(714\) | −27.7534 | + | 1.52167i | −1.03864 | + | 0.0569469i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 65.2465 | + | 113.010i | 2.43838 | + | 4.22339i | ||||
\(717\) | 1.49554 | + | 5.58141i | 0.0558518 | + | 0.208442i | ||||
\(718\) | 12.5437 | + | 46.8139i | 0.468128 | + | 1.74708i | ||||
\(719\) | 15.2105 | + | 26.3454i | 0.567258 | + | 0.982519i | 0.996836 | + | 0.0794893i | \(0.0253290\pi\) |
−0.429578 | + | 0.903030i | \(0.641338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.3869 | − | 22.4820i | 0.424070 | − | 0.837274i | ||||
\(722\) | −32.2884 | − | 32.2884i | −1.20165 | − | 1.20165i | ||||
\(723\) | 22.0534 | + | 5.90919i | 0.820175 | + | 0.219765i | ||||
\(724\) | −55.7398 | + | 96.5442i | −2.07155 | + | 3.58804i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.16452 | + | 0.672335i | −0.0432193 | + | 0.0249527i | ||||
\(727\) | −15.0688 | + | 15.0688i | −0.558871 | + | 0.558871i | −0.928986 | − | 0.370115i | \(-0.879318\pi\) |
0.370115 | + | 0.928986i | \(0.379318\pi\) | |||||||
\(728\) | −130.202 | − | 27.3471i | −4.82562 | − | 1.01355i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.1566 | + | 18.5656i | 1.18936 | + | 0.686675i | ||||
\(732\) | −64.3837 | + | 17.2516i | −2.37969 | + | 0.637636i | ||||
\(733\) | −11.7423 | + | 43.8230i | −0.433713 | + | 1.61864i | 0.310416 | + | 0.950601i | \(0.399532\pi\) |
−0.744128 | + | 0.668037i | \(0.767135\pi\) | |||||||
\(734\) | 17.4432 | 0.643841 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.0070 | −0.516306 | ||||||||
\(737\) | 0.494834 | − | 1.84674i | 0.0182274 | − | 0.0680257i | ||||
\(738\) | 2.75018 | − | 0.736908i | 0.101235 | − | 0.0271259i | ||||
\(739\) | 31.7277 | + | 18.3180i | 1.16712 | + | 0.673839i | 0.953001 | − | 0.302968i | \(-0.0979775\pi\) |
0.214123 | + | 0.976807i | \(0.431311\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 8.18465i | − | 0.300671i | ||||||
\(742\) | 79.4847 | + | 16.6946i | 2.91797 | + | 0.612878i | ||||
\(743\) | −4.92766 | + | 4.92766i | −0.180778 | + | 0.180778i | −0.791695 | − | 0.610917i | \(-0.790801\pi\) |
0.610917 | + | 0.791695i | \(0.290801\pi\) | |||||||
\(744\) | −28.1313 | + | 16.2416i | −1.03134 | + | 0.595446i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −29.8951 | + | 51.7798i | −1.09454 | + | 1.89579i | ||||
\(747\) | 2.03553 | + | 0.545420i | 0.0744763 | + | 0.0199559i | ||||
\(748\) | −49.3145 | − | 49.3145i | −1.80312 | − | 1.80312i | ||||
\(749\) | −3.22630 | + | 6.36993i | −0.117886 | + | 0.232752i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.1745 | − | 33.2112i | −0.699686 | − | 1.21189i | −0.968575 | − | 0.248721i | \(-0.919990\pi\) |
0.268889 | − | 0.963171i | \(-0.413344\pi\) | |||||||
\(752\) | −23.4309 | − | 87.4453i | −0.854437 | − | 3.18880i | ||||
\(753\) | 3.32130 | + | 12.3953i | 0.121035 | + | 0.451708i | ||||
\(754\) | 45.6217 | + | 79.0190i | 1.66144 | + | 2.87770i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 13.9580 | − | 0.765293i | 0.507649 | − | 0.0278334i | ||||
\(757\) | 3.24686 | + | 3.24686i | 0.118009 | + | 0.118009i | 0.763645 | − | 0.645636i | \(-0.223408\pi\) |
−0.645636 | + | 0.763645i | \(0.723408\pi\) | |||||||
\(758\) | −11.2149 | − | 3.00503i | −0.407345 | − | 0.109148i | ||||
\(759\) | −1.29752 | + | 2.24737i | −0.0470969 | + | 0.0815743i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.0864 | + | 9.86481i | −0.619380 | + | 0.357599i | −0.776628 | − | 0.629960i | \(-0.783071\pi\) |
0.157248 | + | 0.987559i | \(0.449738\pi\) | |||||||
\(762\) | 15.0663 | − | 15.0663i | 0.545795 | − | 0.545795i | ||||
\(763\) | −14.7818 | − | 13.2451i | −0.535136 | − | 0.479506i | ||||
\(764\) | 9.43287i | 0.341269i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −59.5521 | − | 34.3824i | −2.15170 | − | 1.24229i | ||||
\(767\) | −35.3675 | + | 9.47668i | −1.27705 | + | 0.342183i | ||||
\(768\) | −5.46995 | + | 20.4141i | −0.197380 | + | 0.736632i | ||||
\(769\) | 39.4021 | 1.42088 | 0.710439 | − | 0.703759i | \(-0.248497\pi\) | ||||
0.710439 | + | 0.703759i | \(0.248497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.2381 | 0.872914 | ||||||||
\(772\) | 21.2176 | − | 79.1853i | 0.763640 | − | 2.84994i | ||||
\(773\) | 8.04523 | − | 2.15571i | 0.289367 | − | 0.0775356i | −0.111216 | − | 0.993796i | \(-0.535474\pi\) |
0.400583 | + | 0.916261i | \(0.368808\pi\) | |||||||
\(774\) | −22.2944 | − | 12.8717i | −0.801356 | − | 0.462663i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 17.1441i | − | 0.615436i | ||||||
\(777\) | −0.683300 | + | 3.25326i | −0.0245132 | + | 0.116710i | ||||
\(778\) | 32.6180 | − | 32.6180i | 1.16941 | − | 1.16941i | ||||
\(779\) | −1.31780 | + | 0.760833i | −0.0472151 | + | 0.0272597i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.4271 | + | 19.7923i | −0.408894 | + | 0.708225i | ||||
\(782\) | −7.76587 | − | 2.08086i | −0.277707 | − | 0.0744114i | ||||
\(783\) | −4.21297 | − | 4.21297i | −0.150559 | − | 0.150559i | ||||
\(784\) | 10.2159 | + | 92.8825i | 0.364852 | + | 3.31723i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17.4143 | + | 30.1625i | 0.621148 | + | 1.07586i | ||||
\(787\) | 2.81226 | + | 10.4955i | 0.100246 | + | 0.374124i | 0.997763 | − | 0.0668573i | \(-0.0212972\pi\) |
−0.897516 | + | 0.440981i | \(0.854631\pi\) | |||||||
\(788\) | −22.6391 | − | 84.4901i | −0.806483 | − | 3.00984i | ||||
\(789\) | 4.90646 | + | 8.49825i | 0.174675 | + | 0.302546i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.39091 | − | 4.17227i | 0.227234 | − | 0.148349i | ||||
\(792\) | 21.2480 | + | 21.2480i | 0.755016 | + | 0.755016i | ||||
\(793\) | −69.1471 | − | 18.5279i | −2.45549 | − | 0.657946i | ||||
\(794\) | 18.2509 | − | 31.6115i | 0.647701 | − | 1.12185i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −44.5252 | + | 25.7066i | −1.57815 | + | 0.911147i | ||||
\(797\) | 17.6324 | − | 17.6324i | 0.624572 | − | 0.624572i | −0.322125 | − | 0.946697i | \(-0.604397\pi\) |
0.946697 | + | 0.322125i | \(0.104397\pi\) | |||||||
\(798\) | −9.78723 | + | 3.20620i | −0.346464 | + | 0.113498i | ||||
\(799\) | − | 26.3993i | − | 0.933940i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.08987 | + | 1.78394i | 0.109175 | + | 0.0630323i | ||||
\(802\) | −70.4979 | + | 18.8898i | −2.48937 | + | 0.667024i | ||||
\(803\) | 4.35133 | − | 16.2394i | 0.153555 | − | 0.573076i | ||||
\(804\) | −2.97903 | −0.105062 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −56.1356 | −1.97729 | ||||||||
\(807\) | 5.68426 | − | 21.2140i | 0.200095 | − | 0.746767i | ||||
\(808\) | −169.147 | + | 45.3228i | −5.95057 | + | 1.59445i | ||||
\(809\) | −11.2614 | − | 6.50175i | −0.395929 | − | 0.228590i | 0.288797 | − | 0.957390i | \(-0.406745\pi\) |
−0.684726 | + | 0.728801i | \(0.740078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.6972i | 0.902349i | 0.892436 | + | 0.451175i | \(0.148995\pi\) | ||||
−0.892436 | + | 0.451175i | \(0.851005\pi\) | |||||||
\(812\) | 55.5807 | − | 62.0290i | 1.95050 | − | 2.17679i | ||||
\(813\) | −17.9211 | + | 17.9211i | −0.628520 | + | 0.628520i | ||||
\(814\) | −9.95777 | + | 5.74912i | −0.349020 | + | 0.201507i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −25.9815 | + | 45.0012i | −0.909533 | + | 1.57536i | ||||
\(817\) | 13.2896 | + | 3.56093i | 0.464944 | + | 0.124581i | ||||
\(818\) | −4.78387 | − | 4.78387i | −0.167264 | − | 0.167264i | ||||
\(819\) | 13.3933 | + | 6.78357i | 0.468000 | + | 0.237037i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.2860 | + | 31.6723i | 0.638186 | + | 1.10537i | 0.985831 | + | 0.167744i | \(0.0536483\pi\) |
−0.347644 | + | 0.937626i | \(0.613018\pi\) | |||||||
\(822\) | −1.48043 | − | 5.52504i | −0.0516359 | − | 0.192708i | ||||
\(823\) | 11.3424 | + | 42.3303i | 0.395370 | + | 1.47554i | 0.821149 | + | 0.570713i | \(0.193333\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(824\) | −42.2047 | − | 73.1007i | −1.47027 | − | 2.54658i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 25.1869 | + | 38.5802i | 0.876363 | + | 1.34238i | ||||
\(827\) | 17.7382 | + | 17.7382i | 0.616819 | + | 0.616819i | 0.944714 | − | 0.327895i | \(-0.106339\pi\) |
−0.327895 | + | 0.944714i | \(0.606339\pi\) | |||||||
\(828\) | 3.90570 | + | 1.04653i | 0.135732 | + | 0.0363694i | ||||
\(829\) | 14.9866 | − | 25.9575i | 0.520506 | − | 0.901543i | −0.479210 | − | 0.877700i | \(-0.659077\pi\) |
0.999716 | − | 0.0238423i | \(-0.00758997\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.1115 | + | 6.99260i | −0.420144 | + | 0.242571i | ||||
\(832\) | −91.0744 | + | 91.0744i | −3.15744 | + | 3.15744i | ||||
\(833\) | −4.13267 | + | 26.9334i | −0.143189 | + | 0.933187i | ||||
\(834\) | − | 2.88915i | − | 0.100043i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −22.3794 | − | 12.9207i | −0.774007 | − | 0.446873i | ||||
\(837\) | 3.54066 | − | 0.948718i | 0.122383 | − | 0.0327925i | ||||
\(838\) | −14.6980 | + | 54.8538i | −0.507735 | + | 1.89489i | ||||
\(839\) | 14.5585 | 0.502615 | 0.251308 | − | 0.967907i | \(-0.419139\pi\) | ||||
0.251308 | + | 0.967907i | \(0.419139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.49825 | −0.224077 | ||||||||
\(842\) | −12.6163 | + | 47.0846i | −0.434785 | + | 1.62264i | ||||
\(843\) | −17.3056 | + | 4.63702i | −0.596037 | + | 0.159708i | ||||
\(844\) | −16.0069 | − | 9.24161i | −0.550981 | − | 0.318109i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18.3028i | 0.629264i | ||||||||
\(847\) | 0.410381 | + | 1.25273i | 0.0141009 | + | 0.0430442i | ||||
\(848\) | 107.366 | − | 107.366i | 3.68698 | − | 3.68698i | ||||
\(849\) | 16.3455 | − | 9.43706i | 0.560975 | − | 0.323879i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.480775 | + | 0.832726i | −0.0164807 | + | 0.0285455i | ||||
\(852\) | 34.3971 | + | 9.21667i | 1.17842 | + | 0.315758i | ||||
\(853\) | 26.8710 | + | 26.8710i | 0.920046 | + | 0.920046i | 0.997032 | − | 0.0769857i | \(-0.0245296\pi\) |
−0.0769857 | + | 0.997032i | \(0.524530\pi\) | |||||||
\(854\) | 4.93148 | + | 89.9444i | 0.168752 | + | 3.07783i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.9580 | + | 20.7119i | 0.408717 | + | 0.707919i | ||||
\(857\) | 4.93665 | + | 18.4238i | 0.168633 | + | 0.629347i | 0.997549 | + | 0.0699734i | \(0.0222914\pi\) |
−0.828916 | + | 0.559373i | \(0.811042\pi\) | |||||||
\(858\) | 13.4403 | + | 50.1600i | 0.458845 | + | 1.71243i | ||||
\(859\) | −27.1174 | − | 46.9687i | −0.925233 | − | 1.60255i | −0.791186 | − | 0.611576i | \(-0.790536\pi\) |
−0.134047 | − | 0.990975i | \(-0.542797\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.152808 | − | 2.78703i | −0.00520767 | − | 0.0949818i | ||||
\(862\) | −24.6550 | − | 24.6550i | −0.839754 | − | 0.839754i | ||||
\(863\) | 30.5038 | + | 8.17346i | 1.03836 | + | 0.278228i | 0.737434 | − | 0.675419i | \(-0.236037\pi\) |
0.300927 | + | 0.953647i | \(0.402704\pi\) | |||||||
\(864\) | 9.15141 | − | 15.8507i | 0.311337 | − | 0.539252i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 73.3328 | − | 42.3387i | 2.49195 | − | 1.43873i | ||||
\(867\) | 1.30616 | − | 1.30616i | 0.0443596 | − | 0.0443596i | ||||
\(868\) | 15.9519 | + | 48.6947i | 0.541443 | + | 1.65281i | ||||
\(869\) | 26.6091i | 0.902652i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.77079 | − | 1.59972i | −0.0938846 | − | 0.0542043i | ||||
\(872\) | −64.2132 | + | 17.2059i | −2.17453 | + | 0.582665i | ||||
\(873\) | −0.500717 | + | 1.86870i | −0.0169467 | + | 0.0632459i | ||||
\(874\) | −2.97903 | −0.100767 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −26.1961 | −0.885086 | ||||||||
\(877\) | −8.62823 | + | 32.2010i | −0.291355 | + | 1.08735i | 0.652715 | + | 0.757604i | \(0.273630\pi\) |
−0.944070 | + | 0.329746i | \(0.893037\pi\) | |||||||
\(878\) | −23.8563 | + | 6.39229i | −0.805112 | + | 0.215729i | ||||
\(879\) | −15.5158 | − | 8.95804i | −0.523334 | − | 0.302147i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.6003i | 1.40155i | 0.713382 | + | 0.700775i | \(0.247162\pi\) | ||||
−0.713382 | + | 0.700775i | \(0.752838\pi\) | |||||||
\(882\) | 2.86521 | − | 18.6731i | 0.0964766 | − | 0.628757i | ||||
\(883\) | 15.0375 | − | 15.0375i | 0.506053 | − | 0.506053i | −0.407259 | − | 0.913313i | \(-0.633515\pi\) |
0.913313 | + | 0.407259i | \(0.133515\pi\) | |||||||
\(884\) | −101.072 | + | 58.3538i | −3.39941 | + | 1.96265i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −37.4377 | + | 64.8441i | −1.25775 | + | 2.17848i | ||||
\(887\) | −12.7904 | − | 3.42718i | −0.429460 | − | 0.115073i | 0.0376127 | − | 0.999292i | \(-0.488025\pi\) |
−0.467073 | + | 0.884219i | \(0.654691\pi\) | |||||||
\(888\) | 7.87312 | + | 7.87312i | 0.264204 | + | 0.264204i | ||||
\(889\) | −11.4187 | − | 17.4907i | −0.382972 | − | 0.586620i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.69545 | − | 2.93661i | −0.0567998 | − | 0.0983802i | ||||
\(892\) | −31.1539 | − | 116.268i | −1.04311 | − | 3.89293i | ||||
\(893\) | −2.53172 | − | 9.44853i | −0.0847209 | − | 0.316183i | ||||
\(894\) | 11.5605 | + | 20.0234i | 0.386642 | + | 0.669683i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 58.1846 | + | 29.4699i | 1.94381 | + | 0.984520i | ||||
\(897\) | 3.07071 | + | 3.07071i | 0.102528 | + | 0.102528i | ||||
\(898\) | 73.9106 | + | 19.8043i | 2.46643 | + | 0.660877i | ||||
\(899\) | 10.9198 | − | 18.9136i | 0.364196 | − | 0.630805i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.3454 | − | 22.1387i | 1.27747 | − | 0.737549i | ||||
\(902\) | 6.82681 | − | 6.82681i | 0.227308 | − | 0.227308i | ||||
\(903\) | −16.8417 | + | 18.7956i | −0.560457 | + | 0.625480i | ||||
\(904\) | − | 25.5636i | − | 0.850234i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −36.0269 | − | 20.8002i | −1.19691 | − | 0.691039i | ||||
\(907\) | 47.5472 | − | 12.7402i | 1.57878 | − | 0.423033i | 0.640232 | − | 0.768181i | \(-0.278838\pi\) |
0.938548 | + | 0.345149i | \(0.112171\pi\) | |||||||
\(908\) | 13.2249 | − | 49.3561i | 0.438885 | − | 1.63794i | ||||
\(909\) | 19.7607 | 0.655422 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.6594 | 1.84408 | 0.922040 | − | 0.387095i | \(-0.126521\pi\) | ||||
0.922040 | + | 0.387095i | \(0.126521\pi\) | |||||||
\(912\) | −4.98331 | + | 18.5980i | −0.165014 | + | 0.615840i | ||||
\(913\) | 6.90230 | − | 1.84947i | 0.228433 | − | 0.0612084i | ||||
\(914\) | 21.6900 | + | 12.5227i | 0.717442 | + | 0.414215i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 121.097i | − | 4.00116i | ||||||
\(917\) | 32.4473 | − | 10.6294i | 1.07150 | − | 0.351014i | ||||
\(918\) | 7.42854 | − | 7.42854i | 0.245178 | − | 0.245178i | ||||
\(919\) | −12.5459 | + | 7.24336i | −0.413850 | + | 0.238936i | −0.692443 | − | 0.721473i | \(-0.743465\pi\) |
0.278593 | + | 0.960409i | \(0.410132\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.79528 | − | 10.0377i | 0.190961 | − | 0.330754i | ||||
\(922\) | 35.3911 | + | 9.48301i | 1.16554 | + | 0.312306i | ||||
\(923\) | 27.0434 | + | 27.0434i | 0.890144 | + | 0.890144i | ||||
\(924\) | 39.6918 | − | 25.9126i | 1.30576 | − | 0.852461i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −39.2440 | − | 67.9727i | −1.28964 | − | 2.23372i | ||||
\(927\) | 2.46530 | + | 9.20061i | 0.0809710 | + | 0.302188i | ||||
\(928\) | −28.2239 | − | 105.333i | −0.926496 | − | 3.45773i | ||||
\(929\) | −22.1906 | − | 38.4353i | −0.728051 | − | 1.26102i | −0.957706 | − | 0.287749i | \(-0.907093\pi\) |
0.229655 | − | 0.973272i | \(-0.426240\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.10383 | + | 10.0360i | 0.0361766 | + | 0.328917i | ||||
\(932\) | 11.4367 | + | 11.4367i | 0.374621 | + | 0.374621i | ||||
\(933\) | −16.8306 | − | 4.50974i | −0.551008 | − | 0.147642i | ||||
\(934\) | −50.7612 | + | 87.9210i | −1.66096 | + | 2.87686i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 43.5486 | − | 25.1428i | 1.42343 | − | 0.821818i | ||||
\(937\) | 13.2536 | − | 13.2536i | 0.432975 | − | 0.432975i | −0.456664 | − | 0.889639i | \(-0.650956\pi\) |
0.889639 | + | 0.456664i | \(0.150956\pi\) | |||||||
\(938\) | −0.827535 | + | 3.93998i | −0.0270200 | + | 0.128645i | ||||
\(939\) | 4.17623i | 0.136286i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47.9804 | − | 27.7015i | −1.56412 | − | 0.903043i | −0.996833 | − | 0.0795198i | \(-0.974661\pi\) |
−0.567283 | − | 0.823523i | \(-0.692005\pi\) | |||||||
\(942\) | −46.3636 | + | 12.4231i | −1.51061 | + | 0.404766i | ||||
\(943\) | 0.208963 | − | 0.779859i | 0.00680476 | − | 0.0253957i | ||||
\(944\) | 86.1354 | 2.80347 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −87.2933 | −2.83815 | ||||||||
\(947\) | 13.6548 | − | 50.9602i | 0.443720 | − | 1.65598i | −0.275575 | − | 0.961280i | \(-0.588868\pi\) |
0.719294 | − | 0.694705i | \(-0.244465\pi\) | |||||||
\(948\) | 40.0484 | − | 10.7309i | 1.30071 | − | 0.348525i | ||||
\(949\) | −24.3650 | − | 14.0671i | −0.790921 | − | 0.456638i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 23.3070i | − | 0.755780i | ||||||
\(952\) | 67.9717 | + | 60.9056i | 2.20298 | + | 1.97396i | ||||
\(953\) | 8.29260 | − | 8.29260i | 0.268624 | − | 0.268624i | −0.559922 | − | 0.828545i | \(-0.689169\pi\) |
0.828545 | + | 0.559922i | \(0.189169\pi\) | |||||||
\(954\) | −26.5852 | + | 15.3489i | −0.860726 | + | 0.496940i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.2650 | − | 26.4398i | 0.493706 | − | 0.855124i | ||||
\(957\) | −19.5148 | − | 5.22896i | −0.630822 | − | 0.169028i | ||||
\(958\) | 43.3540 | + | 43.3540i | 1.40071 | + | 1.40071i | ||||
\(959\) | −5.59908 | + | 0.306987i | −0.180804 | + | 0.00991313i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.78181 | − | 15.2105i | −0.283284 | − | 0.490663i | ||||
\(962\) | 4.98009 | + | 18.5860i | 0.160565 | + | 0.599236i | ||||
\(963\) | −0.698503 | − | 2.60685i | −0.0225089 | − | 0.0840045i | ||||
\(964\) | −60.3155 | − | 104.470i | −1.94263 | − | 3.36474i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.46906 | − | 4.87486i | 0.0794409 | − | 0.156846i | ||||
\(967\) | 35.6264 | + | 35.6264i | 1.14567 | + | 1.14567i | 0.987396 | + | 0.158271i | \(0.0505919\pi\) |
0.158271 | + | 0.987396i | \(0.449408\pi\) | |||||||
\(968\) | 4.26486 | + | 1.14277i | 0.137078 | + | 0.0367299i | ||||
\(969\) | −2.80731 | + | 4.86241i | −0.0901839 | + | 0.156203i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.01991 | − | 2.32090i | 0.129005 | − | 0.0744811i | −0.434109 | − | 0.900861i | \(-0.642937\pi\) |
0.563114 | + | 0.826379i | \(0.309603\pi\) | |||||||
\(972\) | −3.73605 | + | 3.73605i | −0.119834 | + | 0.119834i | ||||
\(973\) | −2.77187 | − | 0.582191i | −0.0888621 | − | 0.0186642i | ||||
\(974\) | − | 83.1790i | − | 2.66523i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 145.842 | + | 84.2019i | 4.66829 | + | 2.69524i | ||||
\(977\) | −36.2863 | + | 9.72288i | −1.16090 | + | 0.311062i | −0.787325 | − | 0.616538i | \(-0.788535\pi\) |
−0.373575 | + | 0.927600i | \(0.621868\pi\) | |||||||
\(978\) | −1.61029 | + | 6.00970i | −0.0514915 | + | 0.192169i | ||||
\(979\) | 12.0983 | 0.386664 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.50175 | 0.239513 | ||||||||
\(982\) | −23.3906 | + | 87.2948i | −0.746423 | + | 2.78569i | ||||
\(983\) | −42.6564 | + | 11.4298i | −1.36053 | + | 0.364553i | −0.864011 | − | 0.503473i | \(-0.832055\pi\) |
−0.496518 | + | 0.868026i | \(0.665389\pi\) | |||||||
\(984\) | −8.09643 | − | 4.67447i | −0.258105 | − | 0.149017i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 62.5925i | − | 1.99335i | ||||||
\(987\) | 17.5598 | + | 3.68819i | 0.558936 | + | 0.117396i | ||||
\(988\) | −30.5782 | + | 30.5782i | −0.972823 | + | 0.972823i | ||||
\(989\) | −6.32196 | + | 3.64998i | −0.201027 | + | 0.116063i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.8781 | + | 22.3056i | −0.409087 | + | 0.708560i | −0.994788 | − | 0.101968i | \(-0.967486\pi\) |
0.585701 | + | 0.810528i | \(0.300819\pi\) | |||||||
\(992\) | 64.8041 | + | 17.3642i | 2.05753 | + | 0.551314i | ||||
\(993\) | −4.33758 | − | 4.33758i | −0.137649 | − | 0.137649i | ||||
\(994\) | 21.7448 | − | 42.9324i | 0.689703 | − | 1.36173i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.56713 | − | 9.64256i | −0.176401 | − | 0.305536i | ||||
\(997\) | −10.8943 | − | 40.6580i | −0.345026 | − | 1.28765i | −0.892582 | − | 0.450885i | \(-0.851109\pi\) |
0.547557 | − | 0.836769i | \(-0.315558\pi\) | |||||||
\(998\) | 1.30322 | + | 4.86368i | 0.0412527 | + | 0.153957i | ||||
\(999\) | −0.628223 | − | 1.08811i | −0.0198761 | − | 0.0344264i |
(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 | 525.2.bc.d.157.6 | yes | 24 | |
5.2 | odd | 4 | inner | 525.2.bc.d.493.6 | yes | 24 | |
5.3 | odd | 4 | inner | 525.2.bc.d.493.1 | yes | 24 | |
5.4 | even | 2 | inner | 525.2.bc.d.157.1 | yes | 24 | |
7.5 | odd | 6 | inner | 525.2.bc.d.82.1 | ✓ | 24 | |
35.12 | even | 12 | inner | 525.2.bc.d.418.1 | yes | 24 | |
35.19 | odd | 6 | inner | 525.2.bc.d.82.6 | yes | 24 | |
35.33 | even | 12 | inner | 525.2.bc.d.418.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.bc.d.82.1 | ✓ | 24 | 7.5 | odd | 6 | inner | |
525.2.bc.d.82.6 | yes | 24 | 35.19 | odd | 6 | inner | |
525.2.bc.d.157.1 | yes | 24 | 5.4 | even | 2 | inner | |
525.2.bc.d.157.6 | yes | 24 | 1.1 | even | 1 | trivial | |
525.2.bc.d.418.1 | yes | 24 | 35.12 | even | 12 | inner | |
525.2.bc.d.418.6 | yes | 24 | 35.33 | even | 12 | inner | |
525.2.bc.d.493.1 | yes | 24 | 5.3 | odd | 4 | inner | |
525.2.bc.d.493.6 | yes | 24 | 5.2 | odd | 4 | inner |