Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(218,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 218.1 | ||
Character | \(\chi\) | \(=\) | 525.218 |
Dual form | 525.2.j.b.407.1 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.79963 | − | 1.79963i | −1.27253 | − | 1.27253i | −0.944756 | − | 0.327775i | \(-0.893701\pi\) |
−0.327775 | − | 0.944756i | \(-0.606299\pi\) | |||||||
\(3\) | −0.491204 | + | 1.66094i | −0.283597 | + | 0.958944i | ||||
\(4\) | 4.47734i | 2.23867i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.87306 | − | 2.10509i | 1.58117 | − | 0.859399i | ||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 4.45829 | − | 4.45829i | 1.57624 | − | 1.57624i | ||||
\(9\) | −2.51744 | − | 1.63172i | −0.839146 | − | 0.543907i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.56870i | − | 0.472981i | −0.971634 | − | 0.236491i | \(-0.924003\pi\) | ||
0.971634 | − | 0.236491i | \(-0.0759973\pi\) | |||||||
\(12\) | −7.43658 | − | 2.19929i | −2.14676 | − | 0.634880i | ||||
\(13\) | −2.21881 | − | 2.21881i | −0.615386 | − | 0.615386i | 0.328958 | − | 0.944345i | \(-0.393303\pi\) |
−0.944345 | + | 0.328958i | \(0.893303\pi\) | |||||||
\(14\) | −2.54506 | −0.680196 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −7.09187 | −1.77297 | ||||||||
\(17\) | 3.60725 | + | 3.60725i | 0.874886 | + | 0.874886i | 0.993000 | − | 0.118114i | \(-0.0376849\pi\) |
−0.118114 | + | 0.993000i | \(0.537685\pi\) | |||||||
\(18\) | 1.59396 | + | 7.46695i | 0.375700 | + | 1.75998i | ||||
\(19\) | 1.68040i | 0.385510i | 0.981247 | + | 0.192755i | \(0.0617423\pi\) | ||||
−0.981247 | + | 0.192755i | \(0.938258\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.827127 | + | 1.52180i | 0.180494 | + | 0.332083i | ||||
\(22\) | −2.82308 | + | 2.82308i | −0.601883 | + | 0.601883i | ||||
\(23\) | 0.995850 | − | 0.995850i | 0.207649 | − | 0.207649i | −0.595618 | − | 0.803268i | \(-0.703093\pi\) |
0.803268 | + | 0.595618i | \(0.203093\pi\) | |||||||
\(24\) | 5.21502 | + | 9.59488i | 1.06451 | + | 1.95855i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.98606i | 1.56620i | ||||||||
\(27\) | 3.94676 | − | 3.37980i | 0.759555 | − | 0.650443i | ||||
\(28\) | 3.16595 | + | 3.16595i | 0.598309 | + | 0.598309i | ||||
\(29\) | 8.91955 | 1.65632 | 0.828159 | − | 0.560493i | \(-0.189388\pi\) | ||||
0.828159 | + | 0.560493i | \(0.189388\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.74834 | 0.493616 | 0.246808 | − | 0.969064i | \(-0.420618\pi\) | ||||
0.246808 | + | 0.969064i | \(0.420618\pi\) | |||||||
\(32\) | 3.84616 | + | 3.84616i | 0.679912 | + | 0.679912i | ||||
\(33\) | 2.60552 | + | 0.770553i | 0.453562 | + | 0.134136i | ||||
\(34\) | − | 12.9834i | − | 2.22664i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.30576 | − | 11.2714i | 1.21763 | − | 1.87857i | ||||
\(37\) | −0.440360 | + | 0.440360i | −0.0723947 | + | 0.0723947i | −0.742377 | − | 0.669982i | \(-0.766302\pi\) |
0.669982 | + | 0.742377i | \(0.266302\pi\) | |||||||
\(38\) | 3.02410 | − | 3.02410i | 0.490574 | − | 0.490574i | ||||
\(39\) | 4.77519 | − | 2.59542i | 0.764643 | − | 0.415599i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.44292i | 1.00622i | 0.864224 | + | 0.503108i | \(0.167810\pi\) | ||||
−0.864224 | + | 0.503108i | \(0.832190\pi\) | |||||||
\(42\) | 1.25015 | − | 4.22719i | 0.192902 | − | 0.652270i | ||||
\(43\) | 5.47734 | + | 5.47734i | 0.835286 | + | 0.835286i | 0.988234 | − | 0.152948i | \(-0.0488768\pi\) |
−0.152948 | + | 0.988234i | \(0.548877\pi\) | |||||||
\(44\) | 7.02360 | 1.05885 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.58432 | −0.528480 | ||||||||
\(47\) | 3.69358 | + | 3.69358i | 0.538763 | + | 0.538763i | 0.923166 | − | 0.384402i | \(-0.125592\pi\) |
−0.384402 | + | 0.923166i | \(0.625592\pi\) | |||||||
\(48\) | 3.48356 | − | 11.7792i | 0.502808 | − | 1.70018i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.76331 | + | 4.21952i | −1.08708 | + | 0.590851i | ||||
\(52\) | 9.93435 | − | 9.93435i | 1.37765 | − | 1.37765i | ||||
\(53\) | 2.83358 | − | 2.83358i | 0.389222 | − | 0.389222i | −0.485188 | − | 0.874410i | \(-0.661249\pi\) |
0.874410 | + | 0.485188i | \(0.161249\pi\) | |||||||
\(54\) | −13.1851 | − | 1.02033i | −1.79427 | − | 0.138849i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 6.30497i | − | 0.842537i | ||||||
\(57\) | −2.79104 | − | 0.825420i | −0.369683 | − | 0.109330i | ||||
\(58\) | −16.0519 | − | 16.0519i | −2.10772 | − | 2.10772i | ||||
\(59\) | −5.54871 | −0.722381 | −0.361191 | − | 0.932492i | \(-0.617630\pi\) | ||||
−0.361191 | + | 0.932492i | \(0.617630\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.40665 | 0.948325 | 0.474162 | − | 0.880437i | \(-0.342751\pi\) | ||||
0.474162 | + | 0.880437i | \(0.342751\pi\) | |||||||
\(62\) | −4.94599 | − | 4.94599i | −0.628141 | − | 0.628141i | ||||
\(63\) | −2.93390 | + | 0.626296i | −0.369636 | + | 0.0789058i | ||||
\(64\) | 0.340400i | 0.0425500i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.30226 | − | 6.07568i | −0.406480 | − | 0.747864i | ||||
\(67\) | 3.75240 | − | 3.75240i | 0.458429 | − | 0.458429i | −0.439711 | − | 0.898139i | \(-0.644919\pi\) |
0.898139 | + | 0.439711i | \(0.144919\pi\) | |||||||
\(68\) | −16.1509 | + | 16.1509i | −1.95858 | + | 1.95858i | ||||
\(69\) | 1.16488 | + | 2.14321i | 0.140235 | + | 0.258012i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.61943i | − | 0.429548i | −0.976664 | − | 0.214774i | \(-0.931099\pi\) | ||
0.976664 | − | 0.214774i | \(-0.0689015\pi\) | |||||||
\(72\) | −18.4981 | + | 3.94878i | −2.18003 | + | 0.465368i | ||||
\(73\) | 5.89737 | + | 5.89737i | 0.690235 | + | 0.690235i | 0.962284 | − | 0.272049i | \(-0.0877011\pi\) |
−0.272049 | + | 0.962284i | \(0.587701\pi\) | |||||||
\(74\) | 1.58497 | 0.184249 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.52372 | −0.863030 | ||||||||
\(77\) | −1.10924 | − | 1.10924i | −0.126410 | − | 0.126410i | ||||
\(78\) | −13.2644 | − | 3.92279i | −1.50189 | − | 0.444168i | ||||
\(79\) | − | 17.0572i | − | 1.91909i | −0.281558 | − | 0.959544i | \(-0.590851\pi\) | ||
0.281558 | − | 0.959544i | \(-0.409149\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.67497 | + | 8.21551i | 0.408330 | + | 0.912834i | ||||
\(82\) | 11.5949 | − | 11.5949i | 1.28044 | − | 1.28044i | ||||
\(83\) | 3.21312 | − | 3.21312i | 0.352686 | − | 0.352686i | −0.508422 | − | 0.861108i | \(-0.669771\pi\) |
0.861108 | + | 0.508422i | \(0.169771\pi\) | |||||||
\(84\) | −6.81359 | + | 3.70333i | −0.743423 | + | 0.404066i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 19.7144i | − | 2.12585i | ||||||
\(87\) | −4.38132 | + | 14.8148i | −0.469727 | + | 1.58832i | ||||
\(88\) | −6.99372 | − | 6.99372i | −0.745533 | − | 0.745533i | ||||
\(89\) | 9.40273 | 0.996688 | 0.498344 | − | 0.866979i | \(-0.333942\pi\) | ||||
0.498344 | + | 0.866979i | \(0.333942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.13787 | −0.328938 | ||||||||
\(92\) | 4.45876 | + | 4.45876i | 0.464858 | + | 0.464858i | ||||
\(93\) | −1.35000 | + | 4.56482i | −0.139988 | + | 0.473350i | ||||
\(94\) | − | 13.2941i | − | 1.37119i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.27749 | + | 4.49899i | −0.844818 | + | 0.459176i | ||||
\(97\) | −4.39640 | + | 4.39640i | −0.446386 | + | 0.446386i | −0.894151 | − | 0.447765i | \(-0.852220\pi\) |
0.447765 | + | 0.894151i | \(0.352220\pi\) | |||||||
\(98\) | −1.79963 | + | 1.79963i | −0.181790 | + | 0.181790i | ||||
\(99\) | −2.55968 | + | 3.94911i | −0.257258 | + | 0.396900i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.01132i | 0.100630i | 0.998733 | + | 0.0503152i | \(0.0160226\pi\) | ||||
−0.998733 | + | 0.0503152i | \(0.983977\pi\) | |||||||
\(102\) | 21.5647 | + | 6.37751i | 2.13522 | + | 0.631468i | ||||
\(103\) | 4.03058 | + | 4.03058i | 0.397145 | + | 0.397145i | 0.877225 | − | 0.480080i | \(-0.159392\pi\) |
−0.480080 | + | 0.877225i | \(0.659392\pi\) | |||||||
\(104\) | −19.7842 | −1.94000 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.1988 | −0.990593 | ||||||||
\(107\) | 2.81760 | + | 2.81760i | 0.272388 | + | 0.272388i | 0.830061 | − | 0.557673i | \(-0.188306\pi\) |
−0.557673 | + | 0.830061i | \(0.688306\pi\) | |||||||
\(108\) | 15.1325 | + | 17.6710i | 1.45613 | + | 1.70039i | ||||
\(109\) | 6.42246i | 0.615160i | 0.951522 | + | 0.307580i | \(0.0995192\pi\) | ||||
−0.951522 | + | 0.307580i | \(0.900481\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.515104 | − | 0.947718i | −0.0488915 | − | 0.0899534i | ||||
\(112\) | −5.01471 | + | 5.01471i | −0.473845 | + | 0.473845i | ||||
\(113\) | 3.29246 | − | 3.29246i | 0.309729 | − | 0.309729i | −0.535075 | − | 0.844804i | \(-0.679717\pi\) |
0.844804 | + | 0.535075i | \(0.179717\pi\) | |||||||
\(114\) | 3.53739 | + | 6.50830i | 0.331307 | + | 0.609558i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 39.9358i | 3.70795i | ||||||||
\(117\) | 1.96523 | + | 9.20618i | 0.181686 | + | 0.851112i | ||||
\(118\) | 9.98563 | + | 9.98563i | 0.919252 | + | 0.919252i | ||||
\(119\) | 5.10142 | 0.467646 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.53918 | 0.776289 | ||||||||
\(122\) | −13.3292 | − | 13.3292i | −1.20677 | − | 1.20677i | ||||
\(123\) | −10.7013 | − | 3.16479i | −0.964904 | − | 0.285360i | ||||
\(124\) | 12.3052i | 1.10504i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.40703 | + | 4.15283i | 0.570784 | + | 0.369963i | ||||
\(127\) | −14.2818 | + | 14.2818i | −1.26730 | + | 1.26730i | −0.319826 | + | 0.947476i | \(0.603624\pi\) |
−0.947476 | + | 0.319826i | \(0.896376\pi\) | |||||||
\(128\) | 8.30492 | − | 8.30492i | 0.734058 | − | 0.734058i | ||||
\(129\) | −11.7880 | + | 6.40703i | −1.03788 | + | 0.564108i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.89729i | − | 0.427878i | −0.976847 | − | 0.213939i | \(-0.931371\pi\) | ||
0.976847 | − | 0.213939i | \(-0.0686294\pi\) | |||||||
\(132\) | −3.45002 | + | 11.6658i | −0.300286 | + | 1.01538i | ||||
\(133\) | 1.18822 | + | 1.18822i | 0.103032 | + | 0.103032i | ||||
\(134\) | −13.5059 | −1.16673 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 32.1643 | 2.75807 | ||||||||
\(137\) | −4.55880 | − | 4.55880i | −0.389485 | − | 0.389485i | 0.485019 | − | 0.874504i | \(-0.338813\pi\) |
−0.874504 | + | 0.485019i | \(0.838813\pi\) | |||||||
\(138\) | 1.76064 | − | 5.95334i | 0.149875 | − | 0.506782i | ||||
\(139\) | 10.2045i | 0.865536i | 0.901505 | + | 0.432768i | \(0.142463\pi\) | ||||
−0.901505 | + | 0.432768i | \(0.857537\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.94911 | + | 4.32050i | −0.669435 | + | 0.363852i | ||||
\(142\) | −6.51364 | + | 6.51364i | −0.546613 | + | 0.546613i | ||||
\(143\) | −3.48065 | + | 3.48065i | −0.291066 | + | 0.291066i | ||||
\(144\) | 17.8533 | + | 11.5720i | 1.48778 | + | 0.964329i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 21.2262i | − | 1.75669i | ||||||
\(147\) | 1.66094 | + | 0.491204i | 0.136992 | + | 0.0405139i | ||||
\(148\) | −1.97164 | − | 1.97164i | −0.162068 | − | 0.162068i | ||||
\(149\) | 0.923124 | 0.0756253 | 0.0378126 | − | 0.999285i | \(-0.487961\pi\) | ||||
0.0378126 | + | 0.999285i | \(0.487961\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.7310 | −1.11741 | −0.558705 | − | 0.829366i | \(-0.688702\pi\) | ||||
−0.558705 | + | 0.829366i | \(0.688702\pi\) | |||||||
\(152\) | 7.49171 | + | 7.49171i | 0.607658 | + | 0.607658i | ||||
\(153\) | −3.19499 | − | 14.9670i | −0.258300 | − | 1.21001i | ||||
\(154\) | 3.99244i | 0.321720i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 11.6205 | + | 21.3801i | 0.930389 | + | 1.71178i | ||||
\(157\) | 13.7211 | − | 13.7211i | 1.09506 | − | 1.09506i | 0.100086 | − | 0.994979i | \(-0.468088\pi\) |
0.994979 | − | 0.100086i | \(-0.0319118\pi\) | |||||||
\(158\) | −30.6967 | + | 30.6967i | −2.44210 | + | 2.44210i | ||||
\(159\) | 3.31453 | + | 6.09826i | 0.262859 | + | 0.483624i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.40834i | − | 0.110993i | ||||||
\(162\) | 8.17128 | − | 21.3985i | 0.641997 | − | 1.68122i | ||||
\(163\) | −6.60566 | − | 6.60566i | −0.517395 | − | 0.517395i | 0.399387 | − | 0.916782i | \(-0.369223\pi\) |
−0.916782 | + | 0.399387i | \(0.869223\pi\) | |||||||
\(164\) | −28.8471 | −2.25258 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.5649 | −0.897607 | ||||||||
\(167\) | −3.11442 | − | 3.11442i | −0.241001 | − | 0.241001i | 0.576263 | − | 0.817264i | \(-0.304510\pi\) |
−0.817264 | + | 0.576263i | \(0.804510\pi\) | |||||||
\(168\) | 10.4722 | + | 3.09703i | 0.807946 | + | 0.238941i | ||||
\(169\) | − | 3.15379i | − | 0.242599i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.74195 | − | 4.23030i | 0.209682 | − | 0.323499i | ||||
\(172\) | −24.5239 | + | 24.5239i | −1.86993 | + | 1.86993i | ||||
\(173\) | 8.12870 | − | 8.12870i | 0.618013 | − | 0.618013i | −0.327008 | − | 0.945022i | \(-0.606040\pi\) |
0.945022 | + | 0.327008i | \(0.106040\pi\) | |||||||
\(174\) | 34.5460 | − | 18.7764i | 2.61892 | − | 1.42344i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.1250i | 0.838580i | ||||||||
\(177\) | 2.72555 | − | 9.21608i | 0.204865 | − | 0.692723i | ||||
\(178\) | −16.9214 | − | 16.9214i | −1.26832 | − | 1.26832i | ||||
\(179\) | −16.5980 | −1.24059 | −0.620297 | − | 0.784367i | \(-0.712988\pi\) | ||||
−0.620297 | + | 0.784367i | \(0.712988\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.6532 | 0.866174 | 0.433087 | − | 0.901352i | \(-0.357424\pi\) | ||||
0.433087 | + | 0.901352i | \(0.357424\pi\) | |||||||
\(182\) | 5.64700 | + | 5.64700i | 0.418583 | + | 0.418583i | ||||
\(183\) | −3.63818 | + | 12.3020i | −0.268942 | + | 0.909390i | ||||
\(184\) | − | 8.87958i | − | 0.654611i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.6445 | − | 5.78550i | 0.780491 | − | 0.424213i | ||||
\(187\) | 5.65869 | − | 5.65869i | 0.413805 | − | 0.413805i | ||||
\(188\) | −16.5374 | + | 16.5374i | −1.20611 | + | 1.20611i | ||||
\(189\) | 0.400905 | − | 5.18066i | 0.0291615 | − | 0.376838i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.8543i | 0.930108i | 0.885282 | + | 0.465054i | \(0.153965\pi\) | ||||
−0.885282 | + | 0.465054i | \(0.846035\pi\) | |||||||
\(192\) | −0.565384 | − | 0.167206i | −0.0408031 | − | 0.0120671i | ||||
\(193\) | 8.06158 | + | 8.06158i | 0.580285 | + | 0.580285i | 0.934982 | − | 0.354696i | \(-0.115416\pi\) |
−0.354696 | + | 0.934982i | \(0.615416\pi\) | |||||||
\(194\) | 15.8238 | 1.13608 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.47734 | 0.319810 | ||||||||
\(197\) | −18.7512 | − | 18.7512i | −1.33597 | − | 1.33597i | −0.899929 | − | 0.436036i | \(-0.856382\pi\) |
−0.436036 | − | 0.899929i | \(-0.643618\pi\) | |||||||
\(198\) | 11.7134 | − | 2.50045i | 0.832436 | − | 0.177699i | ||||
\(199\) | 4.20728i | 0.298246i | 0.988819 | + | 0.149123i | \(0.0476451\pi\) | ||||
−0.988819 | + | 0.149123i | \(0.952355\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.38931 | + | 8.07570i | 0.309598 | + | 0.569616i | ||||
\(202\) | 1.82001 | − | 1.82001i | 0.128055 | − | 0.128055i | ||||
\(203\) | 6.30707 | − | 6.30707i | 0.442670 | − | 0.442670i | ||||
\(204\) | −18.8922 | − | 34.7590i | −1.32272 | − | 2.43361i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 14.5071i | − | 1.01076i | ||||||
\(207\) | −4.13194 | + | 0.882040i | −0.287190 | + | 0.0613060i | ||||
\(208\) | 15.7355 | + | 15.7355i | 1.09106 | + | 1.09106i | ||||
\(209\) | 2.63605 | 0.182339 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.5211 | −1.48158 | −0.740788 | − | 0.671739i | \(-0.765548\pi\) | ||||
−0.740788 | + | 0.671739i | \(0.765548\pi\) | |||||||
\(212\) | 12.6869 | + | 12.6869i | 0.871338 | + | 0.871338i | ||||
\(213\) | 6.01166 | + | 1.77788i | 0.411912 | + | 0.121818i | ||||
\(214\) | − | 10.1413i | − | 0.693244i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.52769 | − | 32.6639i | 0.171988 | − | 2.22250i | ||||
\(217\) | 1.94337 | − | 1.94337i | 0.131924 | − | 0.131924i | ||||
\(218\) | 11.5581 | − | 11.5581i | 0.782810 | − | 0.782810i | ||||
\(219\) | −12.6920 | + | 6.89836i | −0.857645 | + | 0.466148i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 16.0076i | − | 1.07679i | ||||||
\(222\) | −0.778544 | + | 2.63254i | −0.0522525 | + | 0.176684i | ||||
\(223\) | −12.4001 | − | 12.4001i | −0.830375 | − | 0.830375i | 0.157193 | − | 0.987568i | \(-0.449756\pi\) |
−0.987568 | + | 0.157193i | \(0.949756\pi\) | |||||||
\(224\) | 5.43929 | 0.363428 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.8504 | −0.788279 | ||||||||
\(227\) | −8.70556 | − | 8.70556i | −0.577809 | − | 0.577809i | 0.356490 | − | 0.934299i | \(-0.383973\pi\) |
−0.934299 | + | 0.356490i | \(0.883973\pi\) | |||||||
\(228\) | 3.69568 | − | 12.4964i | 0.244753 | − | 0.827597i | ||||
\(229\) | 4.46342i | 0.294951i | 0.989066 | + | 0.147476i | \(0.0471148\pi\) | ||||
−0.989066 | + | 0.147476i | \(0.952885\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.38724 | − | 1.29752i | 0.157069 | − | 0.0853703i | ||||
\(232\) | 39.7659 | − | 39.7659i | 2.61076 | − | 2.61076i | ||||
\(233\) | −5.64161 | + | 5.64161i | −0.369594 | + | 0.369594i | −0.867329 | − | 0.497735i | \(-0.834165\pi\) |
0.497735 | + | 0.867329i | \(0.334165\pi\) | |||||||
\(234\) | 13.0310 | − | 20.1044i | 0.851865 | − | 1.31427i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 24.8435i | − | 1.61717i | ||||||
\(237\) | 28.3310 | + | 8.37859i | 1.84030 | + | 0.544248i | ||||
\(238\) | −9.18066 | − | 9.18066i | −0.595094 | − | 0.595094i | ||||
\(239\) | −11.8594 | −0.767124 | −0.383562 | − | 0.923515i | \(-0.625303\pi\) | ||||
−0.383562 | + | 0.923515i | \(0.625303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.0723 | −1.16414 | −0.582071 | − | 0.813138i | \(-0.697757\pi\) | ||||
−0.582071 | + | 0.813138i | \(0.697757\pi\) | |||||||
\(242\) | −15.3674 | − | 15.3674i | −0.987851 | − | 0.987851i | ||||
\(243\) | −15.4506 | + | 2.06841i | −0.991158 | + | 0.132689i | ||||
\(244\) | 33.1621i | 2.12298i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.5629 | + | 24.9538i | 0.864741 | + | 1.59100i | ||||
\(247\) | 3.72849 | − | 3.72849i | 0.237238 | − | 0.237238i | ||||
\(248\) | 12.2529 | − | 12.2529i | 0.778059 | − | 0.778059i | ||||
\(249\) | 3.75850 | + | 6.91510i | 0.238185 | + | 0.438226i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.19253i | − | 0.201511i | −0.994911 | − | 0.100755i | \(-0.967874\pi\) | ||
0.994911 | − | 0.100755i | \(-0.0321259\pi\) | |||||||
\(252\) | −2.80414 | − | 13.1360i | −0.176644 | − | 0.827493i | ||||
\(253\) | −1.56219 | − | 1.56219i | −0.0982141 | − | 0.0982141i | ||||
\(254\) | 51.4038 | 3.22536 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.2108 | −1.82567 | ||||||||
\(257\) | 11.8118 | + | 11.8118i | 0.736799 | + | 0.736799i | 0.971957 | − | 0.235158i | \(-0.0755607\pi\) |
−0.235158 | + | 0.971957i | \(0.575561\pi\) | |||||||
\(258\) | 32.7443 | + | 9.68378i | 2.03857 | + | 0.602886i | ||||
\(259\) | 0.622763i | 0.0386966i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.4544 | − | 14.5542i | −1.38989 | − | 0.900883i | ||||
\(262\) | −8.81331 | + | 8.81331i | −0.544488 | + | 0.544488i | ||||
\(263\) | 13.1502 | − | 13.1502i | 0.810874 | − | 0.810874i | −0.173891 | − | 0.984765i | \(-0.555634\pi\) |
0.984765 | + | 0.173891i | \(0.0556339\pi\) | |||||||
\(264\) | 15.0515 | − | 8.18080i | 0.926356 | − | 0.503493i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 4.27672i | − | 0.262223i | ||||||
\(267\) | −4.61866 | + | 15.6174i | −0.282658 | + | 0.955767i | ||||
\(268\) | 16.8008 | + | 16.8008i | 1.02627 | + | 1.02627i | ||||
\(269\) | 29.3405 | 1.78892 | 0.894461 | − | 0.447146i | \(-0.147559\pi\) | ||||
0.894461 | + | 0.447146i | \(0.147559\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.18366 | 0.193394 | 0.0966968 | − | 0.995314i | \(-0.469172\pi\) | ||||
0.0966968 | + | 0.995314i | \(0.469172\pi\) | |||||||
\(272\) | −25.5821 | − | 25.5821i | −1.55114 | − | 1.55114i | ||||
\(273\) | 1.54133 | − | 5.21181i | 0.0932858 | − | 0.315433i | ||||
\(274\) | 16.4083i | 0.991263i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.59588 | + | 5.21556i | −0.577604 | + | 0.313940i | ||||
\(277\) | −16.8636 | + | 16.8636i | −1.01324 | + | 1.01324i | −0.0133247 | + | 0.999911i | \(0.504242\pi\) |
−0.999911 | + | 0.0133247i | \(0.995758\pi\) | |||||||
\(278\) | 18.3644 | − | 18.3644i | 1.10142 | − | 1.10142i | ||||
\(279\) | −6.91877 | − | 4.48452i | −0.414216 | − | 0.268481i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.8052i | − | 1.47975i | −0.672742 | − | 0.739877i | \(-0.734884\pi\) | ||
0.672742 | − | 0.739877i | \(-0.265116\pi\) | |||||||
\(282\) | 22.0808 | + | 6.53014i | 1.31489 | + | 0.388864i | ||||
\(283\) | −5.41918 | − | 5.41918i | −0.322137 | − | 0.322137i | 0.527449 | − | 0.849586i | \(-0.323148\pi\) |
−0.849586 | + | 0.527449i | \(0.823148\pi\) | |||||||
\(284\) | 16.2054 | 0.961615 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.5277 | 0.740781 | ||||||||
\(287\) | 4.55583 | + | 4.55583i | 0.268922 | + | 0.268922i | ||||
\(288\) | −3.40661 | − | 15.9583i | −0.200736 | − | 0.940354i | ||||
\(289\) | 9.02446i | 0.530850i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.14262 | − | 9.46168i | −0.301466 | − | 0.554653i | ||||
\(292\) | −26.4045 | + | 26.4045i | −1.54521 | + | 1.54521i | ||||
\(293\) | 8.60739 | − | 8.60739i | 0.502849 | − | 0.502849i | −0.409473 | − | 0.912322i | \(-0.634288\pi\) |
0.912322 | + | 0.409473i | \(0.134288\pi\) | |||||||
\(294\) | −2.10509 | − | 3.87306i | −0.122771 | − | 0.225882i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.92650i | 0.228223i | ||||||||
\(297\) | −5.30190 | − | 6.19129i | −0.307647 | − | 0.359255i | ||||
\(298\) | −1.66128 | − | 1.66128i | −0.0962355 | − | 0.0962355i | ||||
\(299\) | −4.41920 | −0.255569 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.74612 | 0.446479 | ||||||||
\(302\) | 24.7107 | + | 24.7107i | 1.42194 | + | 1.42194i | ||||
\(303\) | −1.67975 | − | 0.496766i | −0.0964989 | − | 0.0285385i | ||||
\(304\) | − | 11.9172i | − | 0.683497i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −21.1853 | + | 32.6849i | −1.21108 | + | 1.86847i | ||||
\(307\) | 11.8525 | − | 11.8525i | 0.676457 | − | 0.676457i | −0.282740 | − | 0.959197i | \(-0.591243\pi\) |
0.959197 | + | 0.282740i | \(0.0912434\pi\) | |||||||
\(308\) | 4.96644 | − | 4.96644i | 0.282989 | − | 0.282989i | ||||
\(309\) | −8.67440 | + | 4.71471i | −0.493469 | + | 0.268211i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.2800i | 1.66032i | 0.557528 | + | 0.830158i | \(0.311750\pi\) | ||||
−0.557528 | + | 0.830158i | \(0.688250\pi\) | |||||||
\(312\) | 9.71807 | − | 32.8603i | 0.550177 | − | 1.86035i | ||||
\(313\) | −1.22577 | − | 1.22577i | −0.0692848 | − | 0.0692848i | 0.671615 | − | 0.740900i | \(-0.265601\pi\) |
−0.740900 | + | 0.671615i | \(0.765601\pi\) | |||||||
\(314\) | −49.3859 | −2.78701 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 76.3710 | 4.29620 | ||||||||
\(317\) | −4.30159 | − | 4.30159i | −0.241601 | − | 0.241601i | 0.575911 | − | 0.817512i | \(-0.304647\pi\) |
−0.817512 | + | 0.575911i | \(0.804647\pi\) | |||||||
\(318\) | 5.00968 | − | 16.9395i | 0.280929 | − | 0.949922i | ||||
\(319\) | − | 13.9921i | − | 0.783408i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.06388 | + | 3.29585i | −0.338453 | + | 0.183956i | ||||
\(322\) | −2.53450 | + | 2.53450i | −0.141242 | + | 0.141242i | ||||
\(323\) | −6.06162 | + | 6.06162i | −0.337278 | + | 0.337278i | ||||
\(324\) | −36.7836 | + | 16.4541i | −2.04353 | + | 0.914116i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 23.7755i | 1.31680i | ||||||||
\(327\) | −10.6673 | − | 3.15474i | −0.589904 | − | 0.174458i | ||||
\(328\) | 28.7244 | + | 28.7244i | 1.58604 | + | 1.58604i | ||||
\(329\) | 5.22351 | 0.287981 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.2602 | 1.82815 | 0.914074 | − | 0.405548i | \(-0.132919\pi\) | ||||
0.914074 | + | 0.405548i | \(0.132919\pi\) | |||||||
\(332\) | 14.3862 | + | 14.3862i | 0.789547 | + | 0.789547i | ||||
\(333\) | 1.82712 | − | 0.390034i | 0.100126 | − | 0.0213737i | ||||
\(334\) | 11.2096i | 0.613363i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.86588 | − | 10.7924i | −0.320010 | − | 0.588772i | ||||
\(337\) | −10.3056 | + | 10.3056i | −0.561383 | + | 0.561383i | −0.929700 | − | 0.368317i | \(-0.879934\pi\) |
0.368317 | + | 0.929700i | \(0.379934\pi\) | |||||||
\(338\) | −5.67565 | + | 5.67565i | −0.308715 | + | 0.308715i | ||||
\(339\) | 3.85131 | + | 7.08585i | 0.209174 | + | 0.384851i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.31132i | − | 0.233471i | ||||||
\(342\) | −12.5475 | + | 2.67849i | −0.678489 | + | 0.144836i | ||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 48.8391 | 2.63323 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −29.2573 | −1.57288 | ||||||||
\(347\) | 19.2241 | + | 19.2241i | 1.03200 | + | 1.03200i | 0.999471 | + | 0.0325323i | \(0.0103572\pi\) |
0.0325323 | + | 0.999471i | \(0.489643\pi\) | |||||||
\(348\) | −66.3310 | − | 19.6166i | −3.55571 | − | 1.05156i | ||||
\(349\) | − | 30.1301i | − | 1.61283i | −0.591353 | − | 0.806413i | \(-0.701406\pi\) | ||
0.591353 | − | 0.806413i | \(-0.298594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.2562 | − | 1.25799i | −0.867694 | − | 0.0671463i | ||||
\(352\) | 6.03348 | − | 6.03348i | 0.321586 | − | 0.321586i | ||||
\(353\) | −17.0339 | + | 17.0339i | −0.906625 | + | 0.906625i | −0.995998 | − | 0.0893729i | \(-0.971514\pi\) |
0.0893729 | + | 0.995998i | \(0.471514\pi\) | |||||||
\(354\) | −21.4905 | + | 11.6805i | −1.14221 | + | 0.620814i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 42.0992i | 2.23125i | ||||||||
\(357\) | −2.50584 | + | 8.47314i | −0.132623 | + | 0.448446i | ||||
\(358\) | 29.8703 | + | 29.8703i | 1.57869 | + | 1.57869i | ||||
\(359\) | −0.737982 | −0.0389492 | −0.0194746 | − | 0.999810i | \(-0.506199\pi\) | ||||
−0.0194746 | + | 0.999810i | \(0.506199\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.1763 | 0.851382 | ||||||||
\(362\) | −20.9714 | − | 20.9714i | −1.10223 | − | 1.10223i | ||||
\(363\) | −4.19448 | + | 14.1831i | −0.220153 | + | 0.744417i | ||||
\(364\) | − | 14.0493i | − | 0.736383i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 28.6864 | − | 15.5917i | 1.49946 | − | 0.814990i | ||||
\(367\) | −23.2923 | + | 23.2923i | −1.21585 | + | 1.21585i | −0.246776 | + | 0.969073i | \(0.579371\pi\) |
−0.969073 | + | 0.246776i | \(0.920629\pi\) | |||||||
\(368\) | −7.06244 | + | 7.06244i | −0.368155 | + | 0.368155i | ||||
\(369\) | 10.5131 | − | 16.2196i | 0.547288 | − | 0.844361i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4.00728i | − | 0.208048i | ||||||
\(372\) | −20.4382 | − | 6.04438i | −1.05967 | − | 0.313387i | ||||
\(373\) | 5.28110 | + | 5.28110i | 0.273445 | + | 0.273445i | 0.830485 | − | 0.557040i | \(-0.188063\pi\) |
−0.557040 | + | 0.830485i | \(0.688063\pi\) | |||||||
\(374\) | −20.3671 | −1.05316 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 32.9341 | 1.69844 | ||||||||
\(377\) | −19.7908 | − | 19.7908i | −1.01928 | − | 1.01928i | ||||
\(378\) | −10.0448 | + | 8.60180i | −0.516647 | + | 0.442429i | ||||
\(379\) | − | 3.38353i | − | 0.173800i | −0.996217 | − | 0.0869000i | \(-0.972304\pi\) | ||
0.996217 | − | 0.0869000i | \(-0.0276961\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.7059 | − | 30.7364i | −0.855868 | − | 1.57467i | ||||
\(382\) | 23.1331 | − | 23.1331i | 1.18359 | − | 1.18359i | ||||
\(383\) | 2.86741 | − | 2.86741i | 0.146518 | − | 0.146518i | −0.630043 | − | 0.776561i | \(-0.716963\pi\) |
0.776561 | + | 0.630043i | \(0.216963\pi\) | |||||||
\(384\) | 9.71455 | + | 17.8734i | 0.495744 | + | 0.912097i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 29.0157i | − | 1.47686i | ||||||
\(387\) | −4.85136 | − | 22.7263i | −0.246609 | − | 1.15524i | ||||
\(388\) | −19.6841 | − | 19.6841i | −0.999311 | − | 0.999311i | ||||
\(389\) | 10.2102 | 0.517675 | 0.258838 | − | 0.965921i | \(-0.416661\pi\) | ||||
0.258838 | + | 0.965921i | \(0.416661\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.18455 | 0.363339 | ||||||||
\(392\) | −4.45829 | − | 4.45829i | −0.225178 | − | 0.225178i | ||||
\(393\) | 8.13410 | + | 2.40557i | 0.410311 | + | 0.121345i | ||||
\(394\) | 67.4903i | 3.40011i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −17.6815 | − | 11.4606i | −0.888528 | − | 0.575915i | ||||
\(397\) | 24.0534 | − | 24.0534i | 1.20721 | − | 1.20721i | 0.235280 | − | 0.971928i | \(-0.424399\pi\) |
0.971928 | − | 0.235280i | \(-0.0756009\pi\) | |||||||
\(398\) | 7.57156 | − | 7.57156i | 0.379528 | − | 0.379528i | ||||
\(399\) | −2.55723 | + | 1.38991i | −0.128021 | + | 0.0695823i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.0912i | 1.00331i | 0.865068 | + | 0.501654i | \(0.167275\pi\) | ||||
−0.865068 | + | 0.501654i | \(0.832725\pi\) | |||||||
\(402\) | 6.63414 | − | 22.4324i | 0.330881 | − | 1.11883i | ||||
\(403\) | −6.09803 | − | 6.09803i | −0.303765 | − | 0.303765i | ||||
\(404\) | −4.52803 | −0.225278 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.7008 | −1.12662 | ||||||||
\(407\) | 0.690793 | + | 0.690793i | 0.0342413 | + | 0.0342413i | ||||
\(408\) | −15.7992 | + | 53.4229i | −0.782179 | + | 2.64483i | ||||
\(409\) | 33.5102i | 1.65697i | 0.560008 | + | 0.828487i | \(0.310798\pi\) | ||||
−0.560008 | + | 0.828487i | \(0.689202\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.81120 | − | 5.33259i | 0.483951 | − | 0.263037i | ||||
\(412\) | −18.0463 | + | 18.0463i | −0.889077 | + | 0.889077i | ||||
\(413\) | −3.92353 | + | 3.92353i | −0.193064 | + | 0.193064i | ||||
\(414\) | 9.02331 | + | 5.84862i | 0.443471 | + | 0.287444i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 17.0678i | − | 0.836817i | ||||||
\(417\) | −16.9491 | − | 5.01251i | −0.830000 | − | 0.245463i | ||||
\(418\) | −4.74391 | − | 4.74391i | −0.232032 | − | 0.232032i | ||||
\(419\) | −25.8773 | −1.26419 | −0.632093 | − | 0.774892i | \(-0.717804\pi\) | ||||
−0.632093 | + | 0.774892i | \(0.717804\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.4030 | 0.507013 | 0.253507 | − | 0.967334i | \(-0.418416\pi\) | ||||
0.253507 | + | 0.967334i | \(0.418416\pi\) | |||||||
\(422\) | 38.7301 | + | 38.7301i | 1.88535 | + | 1.88535i | ||||
\(423\) | −3.27146 | − | 15.3252i | −0.159064 | − | 0.745138i | ||||
\(424\) | − | 25.2658i | − | 1.22702i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.61923 | − | 14.0183i | −0.369153 | − | 0.679188i | ||||
\(427\) | 5.23730 | − | 5.23730i | 0.253450 | − | 0.253450i | ||||
\(428\) | −12.6154 | + | 12.6154i | −0.609786 | + | 0.609786i | ||||
\(429\) | −4.07143 | − | 7.49085i | −0.196571 | − | 0.361662i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 0.449005i | − | 0.0216278i | −0.999942 | − | 0.0108139i | \(-0.996558\pi\) | ||
0.999942 | − | 0.0108139i | \(-0.00344224\pi\) | |||||||
\(432\) | −27.9899 | + | 23.9691i | −1.34667 | + | 1.15321i | ||||
\(433\) | 17.7813 | + | 17.7813i | 0.854517 | + | 0.854517i | 0.990686 | − | 0.136169i | \(-0.0434790\pi\) |
−0.136169 | + | 0.990686i | \(0.543479\pi\) | |||||||
\(434\) | −6.99469 | −0.335756 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −28.7555 | −1.37714 | ||||||||
\(437\) | 1.67343 | + | 1.67343i | 0.0800509 | + | 0.0800509i | ||||
\(438\) | 35.2554 | + | 10.4264i | 1.68457 | + | 0.498192i | ||||
\(439\) | − | 29.5293i | − | 1.40936i | −0.709526 | − | 0.704679i | \(-0.751091\pi\) | ||
0.709526 | − | 0.704679i | \(-0.248909\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.63172 | + | 2.51744i | −0.0777010 | + | 0.119878i | ||||
\(442\) | −28.8077 | + | 28.8077i | −1.37024 | + | 1.37024i | ||||
\(443\) | −15.5643 | + | 15.5643i | −0.739483 | + | 0.739483i | −0.972478 | − | 0.232995i | \(-0.925147\pi\) |
0.232995 | + | 0.972478i | \(0.425147\pi\) | |||||||
\(444\) | 4.24325 | − | 2.30630i | 0.201376 | − | 0.109452i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 44.6313i | 2.11336i | ||||||||
\(447\) | −0.453443 | + | 1.53325i | −0.0214471 | + | 0.0725204i | ||||
\(448\) | 0.240699 | + | 0.240699i | 0.0113720 | + | 0.0113720i | ||||
\(449\) | −16.3214 | −0.770252 | −0.385126 | − | 0.922864i | \(-0.625842\pi\) | ||||
−0.385126 | + | 0.922864i | \(0.625842\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.1070 | 0.475921 | ||||||||
\(452\) | 14.7415 | + | 14.7415i | 0.693380 | + | 0.693380i | ||||
\(453\) | 6.74471 | − | 22.8063i | 0.316894 | − | 1.07153i | ||||
\(454\) | 31.3336i | 1.47056i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −16.1232 | + | 8.76332i | −0.755040 | + | 0.410380i | ||||
\(457\) | 20.6299 | − | 20.6299i | 0.965028 | − | 0.965028i | −0.0343811 | − | 0.999409i | \(-0.510946\pi\) |
0.999409 | + | 0.0343811i | \(0.0109460\pi\) | |||||||
\(458\) | 8.03251 | − | 8.03251i | 0.375335 | − | 0.375335i | ||||
\(459\) | 26.4287 | + | 2.04518i | 1.23359 | + | 0.0954609i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.2893i | 0.712094i | 0.934468 | + | 0.356047i | \(0.115876\pi\) | ||||
−0.934468 | + | 0.356047i | \(0.884124\pi\) | |||||||
\(462\) | −6.63120 | − | 1.96110i | −0.308511 | − | 0.0912388i | ||||
\(463\) | −0.492195 | − | 0.492195i | −0.0228743 | − | 0.0228743i | 0.695577 | − | 0.718451i | \(-0.255149\pi\) |
−0.718451 | + | 0.695577i | \(0.755149\pi\) | |||||||
\(464\) | −63.2563 | −2.93660 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.3056 | 0.940640 | ||||||||
\(467\) | −9.00044 | − | 9.00044i | −0.416491 | − | 0.416491i | 0.467501 | − | 0.883992i | \(-0.345154\pi\) |
−0.883992 | + | 0.467501i | \(0.845154\pi\) | |||||||
\(468\) | −41.2192 | + | 8.79901i | −1.90536 | + | 0.406734i | ||||
\(469\) | − | 5.30669i | − | 0.245040i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.0501 | + | 29.5298i | 0.739548 | + | 1.36066i | ||||
\(472\) | −24.7378 | + | 24.7378i | −1.13865 | + | 1.13865i | ||||
\(473\) | 8.59230 | − | 8.59230i | 0.395075 | − | 0.395075i | ||||
\(474\) | −35.9070 | − | 66.0637i | −1.64926 | − | 3.03441i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 22.8408i | 1.04690i | ||||||||
\(477\) | −11.7570 | + | 2.50974i | −0.538314 | + | 0.114913i | ||||
\(478\) | 21.3426 | + | 21.3426i | 0.976188 | + | 0.976188i | ||||
\(479\) | 22.7572 | 1.03980 | 0.519901 | − | 0.854226i | \(-0.325969\pi\) | ||||
0.519901 | + | 0.854226i | \(0.325969\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.95415 | 0.0891015 | ||||||||
\(482\) | 32.5235 | + | 32.5235i | 1.48141 | + | 1.48141i | ||||
\(483\) | 2.33917 | + | 0.691785i | 0.106436 | + | 0.0314773i | ||||
\(484\) | 38.2328i | 1.73785i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 31.5278 | + | 24.0830i | 1.43013 | + | 1.09243i | ||||
\(487\) | 11.4919 | − | 11.4919i | 0.520746 | − | 0.520746i | −0.397051 | − | 0.917797i | \(-0.629966\pi\) |
0.917797 | + | 0.397051i | \(0.129966\pi\) | |||||||
\(488\) | 33.0210 | − | 33.0210i | 1.49479 | − | 1.49479i | ||||
\(489\) | 14.2163 | − | 7.72687i | 0.642884 | − | 0.349421i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.301729i | 0.0136168i | 0.999977 | + | 0.00680841i | \(0.00216720\pi\) | ||||
−0.999977 | + | 0.00680841i | \(0.997833\pi\) | |||||||
\(492\) | 14.1698 | − | 47.9133i | 0.638826 | − | 2.16010i | ||||
\(493\) | 32.1750 | + | 32.1750i | 1.44909 | + | 1.44909i | ||||
\(494\) | −13.4198 | −0.603785 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19.4909 | −0.875165 | ||||||||
\(497\) | −2.55933 | − | 2.55933i | −0.114801 | − | 0.114801i | ||||
\(498\) | 5.68071 | − | 19.2085i | 0.254559 | − | 0.860754i | ||||
\(499\) | − | 20.2207i | − | 0.905202i | −0.891713 | − | 0.452601i | \(-0.850496\pi\) | ||
0.891713 | − | 0.452601i | \(-0.149504\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.70268 | − | 3.64305i | 0.299454 | − | 0.162759i | ||||
\(502\) | −5.74537 | + | 5.74537i | −0.256428 | + | 0.256428i | ||||
\(503\) | −23.8859 | + | 23.8859i | −1.06502 | + | 1.06502i | −0.0672882 | + | 0.997734i | \(0.521435\pi\) |
−0.997734 | + | 0.0672882i | \(0.978565\pi\) | |||||||
\(504\) | −10.2880 | + | 15.8724i | −0.458262 | + | 0.707012i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.62273i | 0.249961i | ||||||||
\(507\) | 5.23825 | + | 1.54915i | 0.232639 | + | 0.0688004i | ||||
\(508\) | −63.9443 | − | 63.9443i | −2.83707 | − | 2.83707i | ||||
\(509\) | 11.7721 | 0.521788 | 0.260894 | − | 0.965368i | \(-0.415983\pi\) | ||||
0.260894 | + | 0.965368i | \(0.415983\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.34014 | 0.368946 | ||||||||
\(512\) | 35.9587 | + | 35.9587i | 1.58917 | + | 1.58917i | ||||
\(513\) | 5.67942 | + | 6.63215i | 0.250752 | + | 0.292816i | ||||
\(514\) | − | 42.5137i | − | 1.87520i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −28.6864 | − | 52.7789i | −1.26285 | − | 2.32346i | ||||
\(517\) | 5.79412 | − | 5.79412i | 0.254825 | − | 0.254825i | ||||
\(518\) | 1.12074 | − | 1.12074i | 0.0492426 | − | 0.0492426i | ||||
\(519\) | 9.50842 | + | 17.4941i | 0.417373 | + | 0.767907i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 29.7872i | − | 1.30500i | −0.757789 | − | 0.652500i | \(-0.773720\pi\) | ||
0.757789 | − | 0.652500i | \(-0.226280\pi\) | |||||||
\(522\) | 14.2174 | + | 66.6018i | 0.622279 | + | 2.91508i | ||||
\(523\) | −17.4673 | − | 17.4673i | −0.763792 | − | 0.763792i | 0.213214 | − | 0.977006i | \(-0.431607\pi\) |
−0.977006 | + | 0.213214i | \(0.931607\pi\) | |||||||
\(524\) | 21.9268 | 0.957877 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −47.3309 | −2.06373 | ||||||||
\(527\) | 9.91393 | + | 9.91393i | 0.431858 | + | 0.431858i | ||||
\(528\) | −18.4780 | − | 5.46466i | −0.804151 | − | 0.237819i | ||||
\(529\) | 21.0166i | 0.913764i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.9685 | + | 9.05395i | 0.606183 | + | 0.392908i | ||||
\(532\) | −5.32007 | + | 5.32007i | −0.230654 | + | 0.230654i | ||||
\(533\) | 14.2956 | − | 14.2956i | 0.619211 | − | 0.619211i | ||||
\(534\) | 36.4174 | − | 19.7936i | 1.57593 | − | 0.856553i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 33.4586i | − | 1.44519i | ||||||
\(537\) | 8.15302 | − | 27.5683i | 0.351829 | − | 1.18966i | ||||
\(538\) | −52.8021 | − | 52.8021i | −2.27646 | − | 2.27646i | ||||
\(539\) | −1.56870 | −0.0675687 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.1117 | −0.993650 | −0.496825 | − | 0.867851i | \(-0.665501\pi\) | ||||
−0.496825 | + | 0.867851i | \(0.665501\pi\) | |||||||
\(542\) | −5.72941 | − | 5.72941i | −0.246099 | − | 0.246099i | ||||
\(543\) | −5.72409 | + | 19.3552i | −0.245644 | + | 0.830612i | ||||
\(544\) | 27.7481i | 1.18969i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −12.1532 | + | 6.60549i | −0.520107 | + | 0.282689i | ||||
\(547\) | 25.6689 | − | 25.6689i | 1.09752 | − | 1.09752i | 0.102823 | − | 0.994700i | \(-0.467213\pi\) |
0.994700 | − | 0.102823i | \(-0.0327874\pi\) | |||||||
\(548\) | 20.4113 | − | 20.4113i | 0.871928 | − | 0.871928i | ||||
\(549\) | −18.6458 | − | 12.0856i | −0.795783 | − | 0.515801i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.9884i | 0.638528i | ||||||||
\(552\) | 14.7484 | + | 4.36169i | 0.627735 | + | 0.185646i | ||||
\(553\) | −12.0613 | − | 12.0613i | −0.512898 | − | 0.512898i | ||||
\(554\) | 60.6965 | 2.57875 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −45.6891 | −1.93765 | ||||||||
\(557\) | −10.5779 | − | 10.5779i | −0.448199 | − | 0.448199i | 0.446556 | − | 0.894756i | \(-0.352650\pi\) |
−0.894756 | + | 0.446556i | \(0.852650\pi\) | |||||||
\(558\) | 4.38074 | + | 20.5217i | 0.185452 | + | 0.868753i | ||||
\(559\) | − | 24.3063i | − | 1.02805i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.61917 | + | 12.1783i | 0.279462 | + | 0.514169i | ||||
\(562\) | −44.6402 | + | 44.6402i | −1.88303 | + | 1.88303i | ||||
\(563\) | −10.9216 | + | 10.9216i | −0.460291 | + | 0.460291i | −0.898751 | − | 0.438460i | \(-0.855524\pi\) |
0.438460 | + | 0.898751i | \(0.355524\pi\) | |||||||
\(564\) | −19.3444 | − | 35.5908i | −0.814544 | − | 1.49864i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 19.5050i | 0.819858i | ||||||||
\(567\) | 8.40784 | + | 3.21064i | 0.353096 | + | 0.134834i | ||||
\(568\) | −16.1365 | − | 16.1365i | −0.677072 | − | 0.677072i | ||||
\(569\) | −42.0710 | −1.76371 | −0.881854 | − | 0.471523i | \(-0.843705\pi\) | ||||
−0.881854 | + | 0.471523i | \(0.843705\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.8342 | 0.453399 | 0.226699 | − | 0.973965i | \(-0.427207\pi\) | ||||
0.226699 | + | 0.973965i | \(0.427207\pi\) | |||||||
\(572\) | −15.5840 | − | 15.5840i | −0.651601 | − | 0.651601i | ||||
\(573\) | −21.3503 | − | 6.31411i | −0.891921 | − | 0.263776i | ||||
\(574\) | − | 16.3976i | − | 0.684424i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.555438 | − | 0.856936i | 0.0231433 | − | 0.0357057i | ||||
\(577\) | −14.6975 | + | 14.6975i | −0.611865 | + | 0.611865i | −0.943432 | − | 0.331567i | \(-0.892423\pi\) |
0.331567 | + | 0.943432i | \(0.392423\pi\) | |||||||
\(578\) | 16.2407 | − | 16.2407i | 0.675523 | − | 0.675523i | ||||
\(579\) | −17.3497 | + | 9.42991i | −0.721028 | + | 0.391894i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 4.54404i | − | 0.188519i | ||||||
\(582\) | −7.77271 | + | 26.2823i | −0.322189 | + | 1.08944i | ||||
\(583\) | −4.44503 | − | 4.44503i | −0.184094 | − | 0.184094i | ||||
\(584\) | 52.5844 | 2.17596 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −30.9802 | −1.27978 | ||||||||
\(587\) | 4.89737 | + | 4.89737i | 0.202136 | + | 0.202136i | 0.800915 | − | 0.598779i | \(-0.204347\pi\) |
−0.598779 | + | 0.800915i | \(0.704347\pi\) | |||||||
\(588\) | −2.19929 | + | 7.43658i | −0.0906971 | + | 0.306680i | ||||
\(589\) | 4.61831i | 0.190294i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 40.3552 | − | 21.9339i | 1.65999 | − | 0.902240i | ||||
\(592\) | 3.12297 | − | 3.12297i | 0.128353 | − | 0.128353i | ||||
\(593\) | −22.5635 | + | 22.5635i | −0.926573 | + | 0.926573i | −0.997483 | − | 0.0709102i | \(-0.977410\pi\) |
0.0709102 | + | 0.997483i | \(0.477410\pi\) | |||||||
\(594\) | −1.60059 | + | 20.6835i | −0.0656729 | + | 0.848654i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.13314i | 0.169300i | ||||||||
\(597\) | −6.98804 | − | 2.06664i | −0.286002 | − | 0.0845818i | ||||
\(598\) | 7.95292 | + | 7.95292i | 0.325219 | + | 0.325219i | ||||
\(599\) | −6.81971 | −0.278646 | −0.139323 | − | 0.990247i | \(-0.544493\pi\) | ||||
−0.139323 | + | 0.990247i | \(0.544493\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.46733 | −0.345390 | −0.172695 | − | 0.984975i | \(-0.555247\pi\) | ||||
−0.172695 | + | 0.984975i | \(0.555247\pi\) | |||||||
\(602\) | −13.9402 | − | 13.9402i | −0.568158 | − | 0.568158i | ||||
\(603\) | −15.5693 | + | 3.32356i | −0.634031 | + | 0.135346i | ||||
\(604\) | − | 61.4782i | − | 2.50151i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.12893 | + | 3.91692i | 0.0864817 | + | 0.159114i | ||||
\(607\) | −6.30295 | + | 6.30295i | −0.255829 | + | 0.255829i | −0.823355 | − | 0.567526i | \(-0.807900\pi\) |
0.567526 | + | 0.823355i | \(0.307900\pi\) | |||||||
\(608\) | −6.46309 | + | 6.46309i | −0.262113 | + | 0.262113i | ||||
\(609\) | 7.37760 | + | 13.5737i | 0.298956 | + | 0.550035i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 16.3907i | − | 0.663095i | ||||||
\(612\) | 67.0125 | − | 14.3051i | 2.70882 | − | 0.578248i | ||||
\(613\) | 5.24728 | + | 5.24728i | 0.211935 | + | 0.211935i | 0.805089 | − | 0.593154i | \(-0.202117\pi\) |
−0.593154 | + | 0.805089i | \(0.702117\pi\) | |||||||
\(614\) | −42.6601 | −1.72162 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.89062 | −0.398504 | ||||||||
\(617\) | −2.10719 | − | 2.10719i | −0.0848323 | − | 0.0848323i | 0.663417 | − | 0.748250i | \(-0.269105\pi\) |
−0.748250 | + | 0.663417i | \(0.769105\pi\) | |||||||
\(618\) | 24.0954 | + | 7.12596i | 0.969261 | + | 0.286648i | ||||
\(619\) | − | 21.0734i | − | 0.847012i | −0.905893 | − | 0.423506i | \(-0.860799\pi\) | ||
0.905893 | − | 0.423506i | \(-0.139201\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.564612 | − | 7.29616i | 0.0226571 | − | 0.292785i | ||||
\(622\) | 52.6932 | − | 52.6932i | 2.11280 | − | 2.11280i | ||||
\(623\) | 6.64874 | − | 6.64874i | 0.266376 | − | 0.266376i | ||||
\(624\) | −33.8650 | + | 18.4063i | −1.35569 | + | 0.736844i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.41188i | 0.176334i | ||||||||
\(627\) | −1.29484 | + | 4.37831i | −0.0517108 | + | 0.174853i | ||||
\(628\) | 61.4341 | + | 61.4341i | 2.45149 | + | 2.45149i | ||||
\(629\) | −3.17697 | −0.126674 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.6376 | −0.463287 | −0.231643 | − | 0.972801i | \(-0.574410\pi\) | ||||
−0.231643 | + | 0.972801i | \(0.574410\pi\) | |||||||
\(632\) | −76.0461 | − | 76.0461i | −3.02495 | − | 3.02495i | ||||
\(633\) | 10.5713 | − | 35.7453i | 0.420170 | − | 1.42075i | ||||
\(634\) | 15.4825i | 0.614890i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −27.3040 | + | 14.8403i | −1.08267 | + | 0.588455i | ||||
\(637\) | −2.21881 | + | 2.21881i | −0.0879123 | + | 0.0879123i | ||||
\(638\) | −25.1806 | + | 25.1806i | −0.996910 | + | 0.996910i | ||||
\(639\) | −5.90591 | + | 9.11170i | −0.233634 | + | 0.360453i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 36.1036i | − | 1.42601i | −0.701161 | − | 0.713003i | \(-0.747335\pi\) | ||
0.701161 | − | 0.713003i | \(-0.252665\pi\) | |||||||
\(642\) | 16.8441 | + | 4.98144i | 0.664782 | + | 0.196602i | ||||
\(643\) | 21.0115 | + | 21.0115i | 0.828614 | + | 0.828614i | 0.987325 | − | 0.158711i | \(-0.0507337\pi\) |
−0.158711 | + | 0.987325i | \(0.550734\pi\) | |||||||
\(644\) | 6.30563 | 0.248477 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.8173 | 0.858392 | ||||||||
\(647\) | 18.9025 | + | 18.9025i | 0.743133 | + | 0.743133i | 0.973180 | − | 0.230046i | \(-0.0738878\pi\) |
−0.230046 | + | 0.973180i | \(0.573888\pi\) | |||||||
\(648\) | 53.0112 | + | 20.2430i | 2.08248 | + | 0.795221i | ||||
\(649\) | 8.70428i | 0.341673i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.27322 | + | 4.18241i | 0.0890947 | + | 0.163921i | ||||
\(652\) | 29.5757 | − | 29.5757i | 1.15828 | − | 1.15828i | ||||
\(653\) | 12.2864 | − | 12.2864i | 0.480803 | − | 0.480803i | −0.424585 | − | 0.905388i | \(-0.639580\pi\) |
0.905388 | + | 0.424585i | \(0.139580\pi\) | |||||||
\(654\) | 13.5199 | + | 24.8746i | 0.528668 | + | 0.972674i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 45.6924i | − | 1.78399i | ||||||
\(657\) | −5.22339 | − | 24.4691i | −0.203784 | − | 0.954631i | ||||
\(658\) | −9.40038 | − | 9.40038i | −0.366465 | − | 0.366465i | ||||
\(659\) | −0.708622 | −0.0276040 | −0.0138020 | − | 0.999905i | \(-0.504393\pi\) | ||||
−0.0138020 | + | 0.999905i | \(0.504393\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.4206 | 0.677582 | 0.338791 | − | 0.940862i | \(-0.389982\pi\) | ||||
0.338791 | + | 0.940862i | \(0.389982\pi\) | |||||||
\(662\) | −59.8561 | − | 59.8561i | −2.32637 | − | 2.32637i | ||||
\(663\) | 26.5876 | + | 7.86299i | 1.03258 | + | 0.305373i | ||||
\(664\) | − | 28.6500i | − | 1.11184i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.99006 | − | 2.58623i | −0.154612 | − | 0.100214i | ||||
\(667\) | 8.88253 | − | 8.88253i | 0.343933 | − | 0.343933i | ||||
\(668\) | 13.9443 | − | 13.9443i | 0.539522 | − | 0.539522i | ||||
\(669\) | 26.6869 | − | 14.5049i | 1.03177 | − | 0.560791i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 11.6188i | − | 0.448540i | ||||||
\(672\) | −2.67181 | + | 9.03434i | −0.103067 | + | 0.348507i | ||||
\(673\) | 8.20389 | + | 8.20389i | 0.316237 | + | 0.316237i | 0.847320 | − | 0.531083i | \(-0.178215\pi\) |
−0.531083 | + | 0.847320i | \(0.678215\pi\) | |||||||
\(674\) | 37.0926 | 1.42875 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.1206 | 0.543099 | ||||||||
\(677\) | 32.8605 | + | 32.8605i | 1.26293 | + | 1.26293i | 0.949666 | + | 0.313264i | \(0.101422\pi\) |
0.313264 | + | 0.949666i | \(0.398578\pi\) | |||||||
\(678\) | 5.82098 | − | 19.6828i | 0.223554 | − | 0.755915i | ||||
\(679\) | 6.21744i | 0.238604i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.7356 | − | 10.1832i | 0.717951 | − | 0.390221i | ||||
\(682\) | −7.75878 | + | 7.75878i | −0.297099 | + | 0.297099i | ||||
\(683\) | −28.4978 | + | 28.4978i | −1.09044 | + | 1.09044i | −0.0949562 | + | 0.995481i | \(0.530271\pi\) |
−0.995481 | + | 0.0949562i | \(0.969729\pi\) | |||||||
\(684\) | 18.9405 | + | 12.2766i | 0.724208 | + | 0.469408i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.54506i | 0.0971709i | ||||||||
\(687\) | −7.41347 | − | 2.19245i | −0.282842 | − | 0.0836473i | ||||
\(688\) | −38.8446 | − | 38.8446i | −1.48093 | − | 1.48093i | ||||
\(689\) | −12.5743 | −0.479043 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.79939 | 0.220619 | 0.110310 | − | 0.993897i | \(-0.464816\pi\) | ||||
0.110310 | + | 0.993897i | \(0.464816\pi\) | |||||||
\(692\) | 36.3949 | + | 36.3949i | 1.38353 | + | 1.38353i | ||||
\(693\) | 0.982471 | + | 4.60241i | 0.0373210 | + | 0.174831i | ||||
\(694\) | − | 69.1925i | − | 2.62651i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 46.5156 | + | 85.5820i | 1.76317 | + | 3.24398i | ||||
\(697\) | −23.2412 | + | 23.2412i | −0.880324 | + | 0.880324i | ||||
\(698\) | −54.2230 | + | 54.2230i | −2.05237 | + | 2.05237i | ||||
\(699\) | −6.59919 | − | 12.1416i | −0.249604 | − | 0.459236i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.92775i | 0.186118i | 0.995661 | + | 0.0930592i | \(0.0296646\pi\) | ||||
−0.995661 | + | 0.0930592i | \(0.970335\pi\) | |||||||
\(702\) | 26.9913 | + | 31.5191i | 1.01872 | + | 1.18961i | ||||
\(703\) | −0.739981 | − | 0.739981i | −0.0279089 | − | 0.0279089i | ||||
\(704\) | 0.533986 | 0.0201254 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 61.3096 | 2.30742 | ||||||||
\(707\) | 0.715113 | + | 0.715113i | 0.0268946 | + | 0.0268946i | ||||
\(708\) | 41.2635 | + | 12.2032i | 1.55078 | + | 0.458625i | ||||
\(709\) | 17.1922i | 0.645666i | 0.946456 | + | 0.322833i | \(0.104635\pi\) | ||||
−0.946456 | + | 0.322833i | \(0.895365\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −27.8326 | + | 42.9405i | −1.04381 | + | 1.61039i | ||||
\(712\) | 41.9201 | − | 41.9201i | 1.57102 | − | 1.57102i | ||||
\(713\) | 2.73693 | − | 2.73693i | 0.102499 | − | 0.102499i | ||||
\(714\) | 19.7581 | − | 10.7389i | 0.739428 | − | 0.401895i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 74.3149i | − | 2.77728i | ||||||
\(717\) | 5.82541 | − | 19.6978i | 0.217554 | − | 0.735628i | ||||
\(718\) | 1.32809 | + | 1.32809i | 0.0495640 | + | 0.0495640i | ||||
\(719\) | −12.2556 | −0.457059 | −0.228529 | − | 0.973537i | \(-0.573392\pi\) | ||||
−0.228529 | + | 0.973537i | \(0.573392\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.70011 | 0.212283 | ||||||||
\(722\) | −29.1113 | − | 29.1113i | −1.08341 | − | 1.08341i | ||||
\(723\) | 8.87721 | − | 30.0170i | 0.330147 | − | 1.11635i | ||||
\(724\) | 52.1752i | 1.93908i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 33.0728 | − | 17.9757i | 1.22745 | − | 0.667142i | ||||
\(727\) | −5.83842 | + | 5.83842i | −0.216535 | + | 0.216535i | −0.807037 | − | 0.590501i | \(-0.798930\pi\) |
0.590501 | + | 0.807037i | \(0.298930\pi\) | |||||||
\(728\) | −13.9895 | + | 13.9895i | −0.518486 | + | 0.518486i | ||||
\(729\) | 4.15390 | − | 26.6786i | 0.153848 | − | 0.988094i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.5162i | 1.46156i | ||||||||
\(732\) | −55.0802 | − | 16.2894i | −2.03582 | − | 0.602072i | ||||
\(733\) | −13.5940 | − | 13.5940i | −0.502105 | − | 0.502105i | 0.409987 | − | 0.912091i | \(-0.365533\pi\) |
−0.912091 | + | 0.409987i | \(0.865533\pi\) | |||||||
\(734\) | 83.8351 | 3.09441 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.66040 | 0.282366 | ||||||||
\(737\) | −5.88639 | − | 5.88639i | −0.216828 | − | 0.216828i | ||||
\(738\) | −48.1090 | + | 10.2698i | −1.77092 | + | 0.378035i | ||||
\(739\) | 15.1801i | 0.558411i | 0.960231 | + | 0.279205i | \(0.0900710\pi\) | ||||
−0.960231 | + | 0.279205i | \(0.909929\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.36134 | + | 8.02424i | 0.160218 | + | 0.294778i | ||||
\(742\) | −7.21162 | + | 7.21162i | −0.264747 | + | 0.264747i | ||||
\(743\) | −34.4215 | + | 34.4215i | −1.26280 | + | 1.26280i | −0.313073 | + | 0.949729i | \(0.601358\pi\) |
−0.949729 | + | 0.313073i | \(0.898642\pi\) | |||||||
\(744\) | 14.3326 | + | 26.3700i | 0.525459 | + | 0.966770i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 19.0080i | − | 0.695934i | ||||||
\(747\) | −13.3317 | + | 2.84591i | −0.487783 | + | 0.104126i | ||||
\(748\) | 25.3359 | + | 25.3359i | 0.926371 | + | 0.926371i | ||||
\(749\) | 3.98469 | 0.145597 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.2515 | −0.811970 | −0.405985 | − | 0.913880i | \(-0.633071\pi\) | ||||
−0.405985 | + | 0.913880i | \(0.633071\pi\) | |||||||
\(752\) | −26.1944 | − | 26.1944i | −0.955210 | − | 0.955210i | ||||
\(753\) | 5.30260 | + | 1.56818i | 0.193237 | + | 0.0571478i | ||||
\(754\) | 71.2321i | 2.59412i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 23.1956 | + | 1.79498i | 0.843615 | + | 0.0652830i | ||||
\(757\) | 1.88407 | − | 1.88407i | 0.0684777 | − | 0.0684777i | −0.672038 | − | 0.740516i | \(-0.734581\pi\) |
0.740516 | + | 0.672038i | \(0.234581\pi\) | |||||||
\(758\) | −6.08909 | + | 6.08909i | −0.221166 | + | 0.221166i | ||||
\(759\) | 3.36206 | − | 1.82735i | 0.122035 | − | 0.0663286i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.6674i | 1.29294i | 0.762938 | + | 0.646472i | \(0.223756\pi\) | ||||
−0.762938 | + | 0.646472i | \(0.776244\pi\) | |||||||
\(762\) | −25.2498 | + | 85.3786i | −0.914703 | + | 3.09294i | ||||
\(763\) | 4.54137 | + | 4.54137i | 0.164409 | + | 0.164409i | ||||
\(764\) | −57.5532 | −2.08220 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.3206 | −0.372897 | ||||||||
\(767\) | 12.3115 | + | 12.3115i | 0.444543 | + | 0.444543i | ||||
\(768\) | 14.3485 | − | 48.5173i | 0.517755 | − | 1.75072i | ||||
\(769\) | 31.7331i | 1.14432i | 0.820141 | + | 0.572162i | \(0.193895\pi\) | ||||
−0.820141 | + | 0.572162i | \(0.806105\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.4207 | + | 13.8167i | −0.915503 | + | 0.497595i | ||||
\(772\) | −36.0944 | + | 36.0944i | −1.29907 | + | 1.29907i | ||||
\(773\) | 4.97844 | − | 4.97844i | 0.179062 | − | 0.179062i | −0.611885 | − | 0.790947i | \(-0.709588\pi\) |
0.790947 | + | 0.611885i | \(0.209588\pi\) | |||||||
\(774\) | −32.1683 | + | 49.6296i | −1.15627 | + | 1.78390i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 39.2008i | 1.40723i | ||||||||
\(777\) | −1.03437 | − | 0.305904i | −0.0371079 | − | 0.0109742i | ||||
\(778\) | −18.3745 | − | 18.3745i | −0.658758 | − | 0.658758i | ||||
\(779\) | −10.8267 | −0.387907 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.67781 | −0.203168 | ||||||||
\(782\) | −12.9295 | − | 12.9295i | −0.462359 | − | 0.462359i | ||||
\(783\) | 35.2034 | − | 30.1463i | 1.25807 | − | 1.07734i | ||||
\(784\) | 7.09187i | 0.253281i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.3092 | − | 18.9675i | −0.367718 | − | 0.676548i | ||||
\(787\) | −18.7554 | + | 18.7554i | −0.668557 | + | 0.668557i | −0.957382 | − | 0.288825i | \(-0.906735\pi\) |
0.288825 | + | 0.957382i | \(0.406735\pi\) | |||||||
\(788\) | 83.9553 | − | 83.9553i | 2.99078 | − | 2.99078i | ||||
\(789\) | 15.3822 | + | 28.3011i | 0.547621 | + | 1.00754i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 4.65625i | − | 0.165557i | ||||||
\(792\) | 6.19445 | + | 29.0181i | 0.220110 | + | 1.03111i | ||||
\(793\) | −16.4339 | − | 16.4339i | −0.583586 | − | 0.583586i | ||||
\(794\) | −86.5746 | −3.07242 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.8374 | −0.667675 | ||||||||
\(797\) | −7.92792 | − | 7.92792i | −0.280821 | − | 0.280821i | 0.552615 | − | 0.833437i | \(-0.313630\pi\) |
−0.833437 | + | 0.552615i | \(0.813630\pi\) | |||||||
\(798\) | 7.10338 | + | 2.10075i | 0.251457 | + | 0.0743656i | ||||
\(799\) | 26.6473i | 0.942713i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.6708 | − | 15.3426i | −0.836366 | − | 0.542105i | ||||
\(802\) | 36.1568 | − | 36.1568i | 1.27674 | − | 1.27674i | ||||
\(803\) | 9.25121 | − | 9.25121i | 0.326468 | − | 0.326468i | ||||
\(804\) | −36.1576 | + | 19.6524i | −1.27518 | + | 0.693088i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.9484i | 0.773099i | ||||||||
\(807\) | −14.4122 | + | 48.7328i | −0.507333 | + | 1.71548i | ||||
\(808\) | 4.50877 | + | 4.50877i | 0.158618 | + | 0.158618i | ||||
\(809\) | −33.2281 | −1.16824 | −0.584119 | − | 0.811668i | \(-0.698560\pi\) | ||||
−0.584119 | + | 0.811668i | \(0.698560\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.8680 | −1.75110 | −0.875550 | − | 0.483127i | \(-0.839501\pi\) | ||||
−0.875550 | + | 0.483127i | \(0.839501\pi\) | |||||||
\(812\) | 28.2389 | + | 28.2389i | 0.990991 | + | 0.990991i | ||||
\(813\) | −1.56383 | + | 5.28787i | −0.0548458 | + | 0.185454i | ||||
\(814\) | − | 2.48634i | − | 0.0871463i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 55.0564 | − | 29.9243i | 1.92736 | − | 1.04756i | ||||
\(817\) | −9.20412 | + | 9.20412i | −0.322011 | + | 0.322011i | ||||
\(818\) | 60.3060 | − | 60.3060i | 2.10855 | − | 2.10855i | ||||
\(819\) | 7.89938 | + | 5.12012i | 0.276027 | + | 0.178912i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.4420i | 1.13223i | 0.824325 | + | 0.566116i | \(0.191555\pi\) | ||||
−0.824325 | + | 0.566116i | \(0.808445\pi\) | |||||||
\(822\) | −27.2532 | − | 8.05984i | −0.950565 | − | 0.281119i | ||||
\(823\) | 32.7235 | + | 32.7235i | 1.14067 | + | 1.14067i | 0.988328 | + | 0.152341i | \(0.0486813\pi\) |
0.152341 | + | 0.988328i | \(0.451319\pi\) | |||||||
\(824\) | 35.9390 | 1.25200 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.1218 | 0.491361 | ||||||||
\(827\) | −36.7198 | − | 36.7198i | −1.27687 | − | 1.27687i | −0.942408 | − | 0.334465i | \(-0.891444\pi\) |
−0.334465 | − | 0.942408i | \(-0.608556\pi\) | |||||||
\(828\) | −3.94919 | − | 18.5001i | −0.137244 | − | 0.642922i | ||||
\(829\) | − | 14.2972i | − | 0.496562i | −0.968688 | − | 0.248281i | \(-0.920134\pi\) | ||
0.968688 | − | 0.248281i | \(-0.0798657\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.7259 | − | 36.2929i | −0.684285 | − | 1.25899i | ||||
\(832\) | 0.755282 | − | 0.755282i | 0.0261847 | − | 0.0261847i | ||||
\(833\) | 3.60725 | − | 3.60725i | 0.124984 | − | 0.124984i | ||||
\(834\) | 21.4814 | + | 39.5227i | 0.743841 | + | 1.36856i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.8025i | 0.408197i | ||||||||
\(837\) | 10.8470 | − | 9.28883i | 0.374929 | − | 0.321069i | ||||
\(838\) | 46.5695 | + | 46.5695i | 1.60872 | + | 1.60872i | ||||
\(839\) | 33.6309 | 1.16107 | 0.580534 | − | 0.814236i | \(-0.302844\pi\) | ||||
0.580534 | + | 0.814236i | \(0.302844\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.5583 | 1.74339 | ||||||||
\(842\) | −18.7216 | − | 18.7216i | −0.645190 | − | 0.645190i | ||||
\(843\) | 41.1999 | + | 12.1844i | 1.41900 | + | 0.419654i | ||||
\(844\) | − | 96.3574i | − | 3.31676i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −21.6923 | + | 33.4672i | −0.745798 | + | 1.15062i | ||||
\(847\) | 6.03811 | − | 6.03811i | 0.207472 | − | 0.207472i | ||||
\(848\) | −20.0953 | + | 20.0953i | −0.690077 | + | 0.690077i | ||||
\(849\) | 11.6629 | − | 6.33901i | 0.400268 | − | 0.217554i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.877065i | 0.0300654i | ||||||||
\(852\) | −7.96017 | + | 26.9162i | −0.272711 | + | 0.922134i | ||||
\(853\) | −26.5544 | − | 26.5544i | −0.909206 | − | 0.909206i | 0.0870025 | − | 0.996208i | \(-0.472271\pi\) |
−0.996208 | + | 0.0870025i | \(0.972271\pi\) | |||||||
\(854\) | −18.8504 | −0.645047 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25.1234 | 0.858699 | ||||||||
\(857\) | 23.0711 | + | 23.0711i | 0.788092 | + | 0.788092i | 0.981181 | − | 0.193089i | \(-0.0618506\pi\) |
−0.193089 | + | 0.981181i | \(0.561851\pi\) | |||||||
\(858\) | −6.15368 | + | 20.8078i | −0.210083 | + | 0.710367i | ||||
\(859\) | − | 17.3242i | − | 0.591095i | −0.955328 | − | 0.295548i | \(-0.904498\pi\) | ||
0.955328 | − | 0.295548i | \(-0.0955021\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.80481 | + | 5.32912i | −0.334147 | + | 0.181616i | ||||
\(862\) | −0.808044 | + | 0.808044i | −0.0275221 | + | 0.0275221i | ||||
\(863\) | −9.05228 | + | 9.05228i | −0.308143 | + | 0.308143i | −0.844189 | − | 0.536046i | \(-0.819917\pi\) |
0.536046 | + | 0.844189i | \(0.319917\pi\) | |||||||
\(864\) | 28.1792 | + | 2.18064i | 0.958674 | + | 0.0741868i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 63.9997i | − | 2.17480i | ||||||
\(867\) | −14.9891 | − | 4.43285i | −0.509056 | − | 0.150548i | ||||
\(868\) | 8.70111 | + | 8.70111i | 0.295335 | + | 0.295335i | ||||
\(869\) | −26.7577 | −0.907693 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.6517 | −0.564221 | ||||||||
\(872\) | 28.6332 | + | 28.6332i | 0.969642 | + | 0.969642i | ||||
\(873\) | 18.2413 | − | 3.89396i | 0.617376 | − | 0.131790i | ||||
\(874\) | − | 6.02310i | − | 0.203734i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −30.8863 | − | 56.8263i | −1.04355 | − | 1.91998i | ||||
\(877\) | −15.4630 | + | 15.4630i | −0.522148 | + | 0.522148i | −0.918220 | − | 0.396072i | \(-0.870373\pi\) |
0.396072 | + | 0.918220i | \(0.370373\pi\) | |||||||
\(878\) | −53.1419 | + | 53.1419i | −1.79345 | + | 1.79345i | ||||
\(879\) | 10.0684 | + | 18.5243i | 0.339597 | + | 0.624810i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.93409i | − | 0.132543i | −0.997802 | − | 0.0662714i | \(-0.978890\pi\) | ||
0.997802 | − | 0.0662714i | \(-0.0211103\pi\) | |||||||
\(882\) | 7.46695 | − | 1.59396i | 0.251425 | − | 0.0536714i | ||||
\(883\) | −13.5688 | − | 13.5688i | −0.456625 | − | 0.456625i | 0.440921 | − | 0.897546i | \(-0.354652\pi\) |
−0.897546 | + | 0.440921i | \(0.854652\pi\) | |||||||
\(884\) | 71.6713 | 2.41057 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 56.0200 | 1.88203 | ||||||||
\(887\) | 4.92491 | + | 4.92491i | 0.165362 | + | 0.165362i | 0.784937 | − | 0.619575i | \(-0.212695\pi\) |
−0.619575 | + | 0.784937i | \(0.712695\pi\) | |||||||
\(888\) | −6.52168 | − | 1.92872i | −0.218853 | − | 0.0647235i | ||||
\(889\) | 20.1975i | 0.677401i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.8877 | − | 5.76494i | 0.431753 | − | 0.193133i | ||||
\(892\) | 55.5196 | − | 55.5196i | 1.85893 | − | 1.85893i | ||||
\(893\) | −6.20669 | + | 6.20669i | −0.207699 | + | 0.207699i | ||||
\(894\) | 3.57532 | − | 1.94326i | 0.119577 | − | 0.0649923i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 11.7449i | − | 0.392371i | ||||||
\(897\) | 2.17073 | − | 7.34002i | 0.0724786 | − | 0.245076i | ||||
\(898\) | 29.3724 | + | 29.3724i | 0.980170 | + | 0.980170i | ||||
\(899\) | 24.5139 | 0.817585 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.4428 | 0.681049 | ||||||||
\(902\) | −18.1889 | − | 18.1889i | −0.605624 | − | 0.605624i | ||||
\(903\) | −3.80493 | + | 12.8658i | −0.126620 | + | 0.428148i | ||||
\(904\) | − | 29.3575i | − | 0.976416i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −53.1809 | + | 28.9049i | −1.76682 | + | 0.960302i | ||||
\(907\) | 19.0317 | − | 19.0317i | 0.631938 | − | 0.631938i | −0.316616 | − | 0.948554i | \(-0.602547\pi\) |
0.948554 | + | 0.316616i | \(0.102547\pi\) | |||||||
\(908\) | 38.9777 | − | 38.9777i | 1.29352 | − | 1.29352i | ||||
\(909\) | 1.65020 | − | 2.54594i | 0.0547336 | − | 0.0844436i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.7669i | 0.588644i | 0.955706 | + | 0.294322i | \(0.0950938\pi\) | ||||
−0.955706 | + | 0.294322i | \(0.904906\pi\) | |||||||
\(912\) | 19.7937 | + | 5.85377i | 0.655435 | + | 0.193838i | ||||
\(913\) | −5.04043 | − | 5.04043i | −0.166814 | − | 0.166814i | ||||
\(914\) | −74.2525 | −2.45605 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.9842 | −0.660298 | ||||||||
\(917\) | −3.46291 | − | 3.46291i | −0.114355 | − | 0.114355i | ||||
\(918\) | −43.8814 | − | 51.2425i | −1.44830 | − | 1.69125i | ||||
\(919\) | − | 8.50470i | − | 0.280544i | −0.990113 | − | 0.140272i | \(-0.955202\pi\) | ||
0.990113 | − | 0.140272i | \(-0.0447977\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.8643 | + | 25.5082i | 0.456843 | + | 0.840525i | ||||
\(922\) | 27.5151 | − | 27.5151i | 0.906162 | − | 0.906162i | ||||
\(923\) | −8.03083 | + | 8.03083i | −0.264338 | + | 0.264338i | ||||
\(924\) | 5.80941 | + | 10.6885i | 0.191116 | + | 0.351625i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.77154i | 0.0582164i | ||||||||
\(927\) | −3.56995 | − | 16.7235i | −0.117253 | − | 0.549273i | ||||
\(928\) | 34.3060 | + | 34.3060i | 1.12615 | + | 1.12615i | ||||
\(929\) | 14.1589 | 0.464538 | 0.232269 | − | 0.972652i | \(-0.425385\pi\) | ||||
0.232269 | + | 0.972652i | \(0.425385\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.68040 | 0.0550729 | ||||||||
\(932\) | −25.2594 | − | 25.2594i | −0.827399 | − | 0.827399i | ||||
\(933\) | −48.6323 | − | 14.3825i | −1.59215 | − | 0.470861i | ||||
\(934\) | 32.3949i | 1.05999i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 49.8054 | + | 32.2822i | 1.62794 | + | 1.05518i | ||||
\(937\) | −28.7165 | + | 28.7165i | −0.938127 | + | 0.938127i | −0.998194 | − | 0.0600678i | \(-0.980868\pi\) |
0.0600678 | + | 0.998194i | \(0.480868\pi\) | |||||||
\(938\) | −9.55009 | + | 9.55009i | −0.311821 | + | 0.311821i | ||||
\(939\) | 2.63804 | − | 1.43383i | 0.0860891 | − | 0.0467912i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 17.4001i | − | 0.567228i | −0.958939 | − | 0.283614i | \(-0.908467\pi\) | ||
0.958939 | − | 0.283614i | \(-0.0915335\pi\) | |||||||
\(942\) | 24.2586 | − | 82.0269i | 0.790387 | − | 2.67258i | ||||
\(943\) | 6.41619 | + | 6.41619i | 0.208940 | + | 0.208940i | ||||
\(944\) | 39.3508 | 1.28076 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −30.9259 | −1.00549 | ||||||||
\(947\) | −8.15693 | − | 8.15693i | −0.265065 | − | 0.265065i | 0.562043 | − | 0.827108i | \(-0.310015\pi\) |
−0.827108 | + | 0.562043i | \(0.810015\pi\) | |||||||
\(948\) | −37.5138 | + | 126.848i | −1.21839 | + | 4.11982i | ||||
\(949\) | − | 26.1703i | − | 0.849522i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.25764 | − | 5.03172i | 0.300199 | − | 0.163165i | ||||
\(952\) | 22.7436 | − | 22.7436i | 0.737124 | − | 0.737124i | ||||
\(953\) | 38.6159 | − | 38.6159i | 1.25089 | − | 1.25089i | 0.295569 | − | 0.955321i | \(-0.404491\pi\) |
0.955321 | − | 0.295569i | \(-0.0955091\pi\) | |||||||
\(954\) | 25.6748 | + | 16.6416i | 0.831251 | + | 0.538790i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 53.0987i | − | 1.71734i | ||||||
\(957\) | 23.2400 | + | 6.87298i | 0.751244 | + | 0.222172i | ||||
\(958\) | −40.9545 | − | 40.9545i | −1.32318 | − | 1.32318i | ||||
\(959\) | −6.44712 | −0.208188 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.4466 | −0.756343 | ||||||||
\(962\) | −3.51674 | − | 3.51674i | −0.113384 | − | 0.113384i | ||||
\(963\) | −2.49559 | − | 11.6907i | −0.0804194 | − | 0.376727i | ||||
\(964\) | − | 80.9159i | − | 2.60613i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.96469 | − | 5.45461i | −0.0953874 | − | 0.175499i | ||||
\(967\) | 18.6836 | − | 18.6836i | 0.600824 | − | 0.600824i | −0.339707 | − | 0.940531i | \(-0.610328\pi\) |
0.940531 | + | 0.339707i | \(0.110328\pi\) | |||||||
\(968\) | 38.0701 | − | 38.0701i | 1.22362 | − | 1.22362i | ||||
\(969\) | −7.09049 | − | 13.0455i | −0.227779 | − | 0.419081i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 57.4980i | − | 1.84520i | −0.385761 | − | 0.922599i | \(-0.626061\pi\) | ||
0.385761 | − | 0.922599i | \(-0.373939\pi\) | |||||||
\(972\) | −9.26098 | − | 69.1776i | −0.297046 | − | 2.21887i | ||||
\(973\) | 7.21569 | + | 7.21569i | 0.231324 | + | 0.231324i | ||||
\(974\) | −41.3622 | −1.32533 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −52.5270 | −1.68135 | ||||||||
\(977\) | −2.08515 | − | 2.08515i | −0.0667100 | − | 0.0667100i | 0.672965 | − | 0.739675i | \(-0.265021\pi\) |
−0.739675 | + | 0.672965i | \(0.765021\pi\) | |||||||
\(978\) | −39.4896 | − | 11.6786i | −1.26274 | − | 0.373441i | ||||
\(979\) | − | 14.7501i | − | 0.471415i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.4797 | − | 16.1681i | 0.334590 | − | 0.516209i | ||||
\(982\) | 0.543000 | − | 0.543000i | 0.0173278 | − | 0.0173278i | ||||
\(983\) | 11.6041 | − | 11.6041i | 0.370114 | − | 0.370114i | −0.497405 | − | 0.867519i | \(-0.665714\pi\) |
0.867519 | + | 0.497405i | \(0.165714\pi\) | |||||||
\(984\) | −61.8191 | + | 33.5999i | −1.97072 | + | 1.07113i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 115.806i | − | 3.68802i | ||||||
\(987\) | −2.56581 | + | 8.67592i | −0.0816706 | + | 0.276158i | ||||
\(988\) | 16.6937 | + | 16.6937i | 0.531097 | + | 0.531097i | ||||
\(989\) | 10.9092 | 0.346893 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.34125 | −0.201436 | −0.100718 | − | 0.994915i | \(-0.532114\pi\) | ||||
−0.100718 | + | 0.994915i | \(0.532114\pi\) | |||||||
\(992\) | 10.5706 | + | 10.5706i | 0.335615 | + | 0.335615i | ||||
\(993\) | −16.3376 | + | 55.2432i | −0.518457 | + | 1.75309i | ||||
\(994\) | 9.21168i | 0.292177i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −30.9612 | + | 16.8281i | −0.981044 | + | 0.533218i | ||||
\(997\) | −1.89647 | + | 1.89647i | −0.0600618 | + | 0.0600618i | −0.736500 | − | 0.676438i | \(-0.763523\pi\) |
0.676438 | + | 0.736500i | \(0.263523\pi\) | |||||||
\(998\) | −36.3897 | + | 36.3897i | −1.15190 | + | 1.15190i | ||||
\(999\) | −0.249668 | + | 3.22633i | −0.00789916 | + | 0.102076i |
(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.j.b.218.1 | 24 | ||
3.2 | odd | 2 | inner | 525.2.j.b.218.12 | 24 | ||
5.2 | odd | 4 | inner | 525.2.j.b.407.12 | 24 | ||
5.3 | odd | 4 | 105.2.j.a.92.1 | yes | 24 | ||
5.4 | even | 2 | 105.2.j.a.8.12 | yes | 24 | ||
15.2 | even | 4 | inner | 525.2.j.b.407.1 | 24 | ||
15.8 | even | 4 | 105.2.j.a.92.12 | yes | 24 | ||
15.14 | odd | 2 | 105.2.j.a.8.1 | ✓ | 24 | ||
35.3 | even | 12 | 735.2.y.g.422.1 | 48 | |||
35.4 | even | 6 | 735.2.y.j.128.1 | 48 | |||
35.9 | even | 6 | 735.2.y.j.263.12 | 48 | |||
35.13 | even | 4 | 735.2.j.h.197.1 | 24 | |||
35.18 | odd | 12 | 735.2.y.j.422.1 | 48 | |||
35.19 | odd | 6 | 735.2.y.g.263.12 | 48 | |||
35.23 | odd | 12 | 735.2.y.j.557.12 | 48 | |||
35.24 | odd | 6 | 735.2.y.g.128.1 | 48 | |||
35.33 | even | 12 | 735.2.y.g.557.12 | 48 | |||
35.34 | odd | 2 | 735.2.j.h.638.12 | 24 | |||
105.23 | even | 12 | 735.2.y.j.557.1 | 48 | |||
105.38 | odd | 12 | 735.2.y.g.422.12 | 48 | |||
105.44 | odd | 6 | 735.2.y.j.263.1 | 48 | |||
105.53 | even | 12 | 735.2.y.j.422.12 | 48 | |||
105.59 | even | 6 | 735.2.y.g.128.12 | 48 | |||
105.68 | odd | 12 | 735.2.y.g.557.1 | 48 | |||
105.74 | odd | 6 | 735.2.y.j.128.12 | 48 | |||
105.83 | odd | 4 | 735.2.j.h.197.12 | 24 | |||
105.89 | even | 6 | 735.2.y.g.263.1 | 48 | |||
105.104 | even | 2 | 735.2.j.h.638.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.j.a.8.1 | ✓ | 24 | 15.14 | odd | 2 | ||
105.2.j.a.8.12 | yes | 24 | 5.4 | even | 2 | ||
105.2.j.a.92.1 | yes | 24 | 5.3 | odd | 4 | ||
105.2.j.a.92.12 | yes | 24 | 15.8 | even | 4 | ||
525.2.j.b.218.1 | 24 | 1.1 | even | 1 | trivial | ||
525.2.j.b.218.12 | 24 | 3.2 | odd | 2 | inner | ||
525.2.j.b.407.1 | 24 | 15.2 | even | 4 | inner | ||
525.2.j.b.407.12 | 24 | 5.2 | odd | 4 | inner | ||
735.2.j.h.197.1 | 24 | 35.13 | even | 4 | |||
735.2.j.h.197.12 | 24 | 105.83 | odd | 4 | |||
735.2.j.h.638.1 | 24 | 105.104 | even | 2 | |||
735.2.j.h.638.12 | 24 | 35.34 | odd | 2 | |||
735.2.y.g.128.1 | 48 | 35.24 | odd | 6 | |||
735.2.y.g.128.12 | 48 | 105.59 | even | 6 | |||
735.2.y.g.263.1 | 48 | 105.89 | even | 6 | |||
735.2.y.g.263.12 | 48 | 35.19 | odd | 6 | |||
735.2.y.g.422.1 | 48 | 35.3 | even | 12 | |||
735.2.y.g.422.12 | 48 | 105.38 | odd | 12 | |||
735.2.y.g.557.1 | 48 | 105.68 | odd | 12 | |||
735.2.y.g.557.12 | 48 | 35.33 | even | 12 | |||
735.2.y.j.128.1 | 48 | 35.4 | even | 6 | |||
735.2.y.j.128.12 | 48 | 105.74 | odd | 6 | |||
735.2.y.j.263.1 | 48 | 105.44 | odd | 6 | |||
735.2.y.j.263.12 | 48 | 35.9 | even | 6 | |||
735.2.y.j.422.1 | 48 | 35.18 | odd | 12 | |||
735.2.y.j.422.12 | 48 | 105.53 | even | 12 | |||
735.2.y.j.557.1 | 48 | 105.23 | even | 12 | |||
735.2.y.j.557.12 | 48 | 35.23 | odd | 12 |