Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,2,Mod(8,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, 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("105.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(0.838429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 92.12 | ||
Character | \(\chi\) | \(=\) | 105.92 |
Dual form | 105.2.j.a.8.12 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | 0.327775 | − | 0.944756i | \(-0.393701\pi\) |
0.944756 | − | 0.327775i | \(-0.106299\pi\) | |||||||
\(3\) | 0.491204 | + | 1.66094i | 0.283597 | + | 0.958944i | ||||
\(4\) | − | 4.47734i | − | 2.23867i | ||||||
\(5\) | −1.87996 | + | 1.21069i | −0.840742 | + | 0.541436i | ||||
\(6\) | 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 | ||||
\(10\) | −1.20443 | + | 5.56202i | −0.380876 | + | 1.75886i | ||||
\(11\) | 1.56870i | 0.472981i | 0.971634 | + | 0.236491i | \(0.0759973\pi\) | ||||
−0.971634 | + | 0.236491i | \(0.924003\pi\) | |||||||
\(12\) | 7.43658 | − | 2.19929i | 2.14676 | − | 0.634880i | ||||
\(13\) | 2.21881 | − | 2.21881i | 0.615386 | − | 0.615386i | −0.328958 | − | 0.944345i | \(-0.606697\pi\) |
0.944345 | + | 0.328958i | \(0.106697\pi\) | |||||||
\(14\) | −2.54506 | −0.680196 | ||||||||
\(15\) | −2.93432 | − | 2.52780i | −0.757639 | − | 0.652674i | ||||
\(16\) | −7.09187 | −1.77297 | ||||||||
\(17\) | −3.60725 | + | 3.60725i | −0.874886 | + | 0.874886i | −0.993000 | − | 0.118114i | \(-0.962315\pi\) |
0.118114 | + | 0.993000i | \(0.462315\pi\) | |||||||
\(18\) | −1.59396 | + | 7.46695i | −0.375700 | + | 1.75998i | ||||
\(19\) | − | 1.68040i | − | 0.385510i | −0.981247 | − | 0.192755i | \(-0.938258\pi\) | ||
0.981247 | − | 0.192755i | \(-0.0617423\pi\) | |||||||
\(20\) | 5.42066 | + | 8.41719i | 1.21210 | + | 1.88214i | ||||
\(21\) | 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 | \(-0.296907\pi\) |
−0.803268 | + | 0.595618i | \(0.796907\pi\) | |||||||
\(24\) | 5.21502 | − | 9.59488i | 1.06451 | − | 1.95855i | ||||
\(25\) | 2.06847 | − | 4.55208i | 0.413694 | − | 0.910416i | ||||
\(26\) | − | 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 | \(0.189388\pi\) | |||||||
\(30\) | −9.82979 | + | 0.731595i | −1.79467 | + | 0.133570i | ||||
\(31\) | 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 | ||||||||
\(35\) | 2.18542 | + | 0.473244i | 0.369403 | + | 0.0799928i | ||||
\(36\) | 7.30576 | + | 11.2714i | 1.21763 | + | 1.87857i | ||||
\(37\) | 0.440360 | + | 0.440360i | 0.0723947 | + | 0.0723947i | 0.742377 | − | 0.669982i | \(-0.233698\pi\) |
−0.669982 | + | 0.742377i | \(0.733698\pi\) | |||||||
\(38\) | −3.02410 | − | 3.02410i | −0.490574 | − | 0.490574i | ||||
\(39\) | 4.77519 | + | 2.59542i | 0.764643 | + | 0.415599i | ||||
\(40\) | 13.7790 | + | 2.98379i | 2.17865 | + | 0.471778i | ||||
\(41\) | − | 6.44292i | − | 1.00622i | −0.864224 | − | 0.503108i | \(-0.832190\pi\) | ||
0.864224 | − | 0.503108i | \(-0.167810\pi\) | |||||||
\(42\) | −1.25015 | − | 4.22719i | −0.192902 | − | 0.652270i | ||||
\(43\) | −5.47734 | + | 5.47734i | −0.835286 | + | 0.835286i | −0.988234 | − | 0.152948i | \(-0.951123\pi\) |
0.152948 | + | 0.988234i | \(0.451123\pi\) | |||||||
\(44\) | 7.02360 | 1.05885 | ||||||||
\(45\) | 2.75716 | − | 6.11539i | 0.411014 | − | 0.911629i | ||||
\(46\) | −3.58432 | −0.528480 | ||||||||
\(47\) | −3.69358 | + | 3.69358i | −0.538763 | + | 0.538763i | −0.923166 | − | 0.384402i | \(-0.874408\pi\) |
0.384402 | + | 0.923166i | \(0.374408\pi\) | |||||||
\(48\) | −3.48356 | − | 11.7792i | −0.502808 | − | 1.70018i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | −4.46958 | − | 11.9145i | −0.632095 | − | 1.68497i | ||||
\(51\) | −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 | \(-0.338751\pi\) |
−0.874410 | + | 0.485188i | \(0.838751\pi\) | |||||||
\(54\) | −13.1851 | + | 1.02033i | −1.79427 | + | 0.138849i | ||||
\(55\) | −1.89921 | − | 2.94909i | −0.256089 | − | 0.397655i | ||||
\(56\) | 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 | \(0.617630\pi\) | |||||||
\(60\) | −11.3178 | + | 13.1379i | −1.46112 | + | 1.69610i | ||||
\(61\) | 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 | ||||||
\(65\) | −1.48498 | + | 6.85754i | −0.184189 | + | 0.850574i | ||||
\(66\) | −3.30226 | + | 6.07568i | −0.406480 | + | 0.747864i | ||||
\(67\) | −3.75240 | − | 3.75240i | −0.458429 | − | 0.458429i | 0.439711 | − | 0.898139i | \(-0.355081\pi\) |
−0.898139 | + | 0.439711i | \(0.855081\pi\) | |||||||
\(68\) | 16.1509 | + | 16.1509i | 1.95858 | + | 1.95858i | ||||
\(69\) | 1.16488 | − | 2.14321i | 0.140235 | − | 0.258012i | ||||
\(70\) | 4.78460 | − | 3.08128i | 0.571869 | − | 0.368283i | ||||
\(71\) | 3.61943i | 0.429548i | 0.976664 | + | 0.214774i | \(0.0689015\pi\) | ||||
−0.976664 | + | 0.214774i | \(0.931099\pi\) | |||||||
\(72\) | 18.4981 | + | 3.94878i | 2.18003 | + | 0.465368i | ||||
\(73\) | −5.89737 | + | 5.89737i | −0.690235 | + | 0.690235i | −0.962284 | − | 0.272049i | \(-0.912299\pi\) |
0.272049 | + | 0.962284i | \(0.412299\pi\) | |||||||
\(74\) | 1.58497 | 0.184249 | ||||||||
\(75\) | 8.57677 | + | 1.19960i | 0.990360 | + | 0.138518i | ||||
\(76\) | −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 | \(0.409149\pi\) | ||||
−0.281558 | + | 0.959544i | \(0.590851\pi\) | |||||||
\(80\) | 13.3324 | − | 8.58604i | 1.49061 | − | 0.959949i | ||||
\(81\) | 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 | \(-0.330229\pi\) |
−0.861108 | + | 0.508422i | \(0.830229\pi\) | |||||||
\(84\) | −6.81359 | − | 3.70333i | −0.743423 | − | 0.404066i | ||||
\(85\) | 2.41421 | − | 11.1487i | 0.261858 | − | 1.20925i | ||||
\(86\) | 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 | \(0.333942\pi\) | |||||||
\(90\) | −6.04357 | − | 15.9673i | −0.637048 | − | 1.68310i | ||||
\(91\) | −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 | ||||||||
\(95\) | 2.03444 | + | 3.15908i | 0.208729 | + | 0.324115i | ||||
\(96\) | −8.27749 | − | 4.49899i | −0.844818 | − | 0.459176i | ||||
\(97\) | 4.39640 | + | 4.39640i | 0.446386 | + | 0.446386i | 0.894151 | − | 0.447765i | \(-0.147780\pi\) |
−0.447765 | + | 0.894151i | \(0.647780\pi\) | |||||||
\(98\) | 1.79963 | + | 1.79963i | 0.181790 | + | 0.181790i | ||||
\(99\) | −2.55968 | − | 3.94911i | −0.257258 | − | 0.396900i | ||||
\(100\) | −20.3812 | − | 9.26123i | −2.03812 | − | 0.926123i | ||||
\(101\) | − | 1.01132i | − | 0.100630i | −0.998733 | − | 0.0503152i | \(-0.983977\pi\) | ||
0.998733 | − | 0.0503152i | \(-0.0160226\pi\) | |||||||
\(102\) | −21.5647 | + | 6.37751i | −2.13522 | + | 0.631468i | ||||
\(103\) | −4.03058 | + | 4.03058i | −0.397145 | + | 0.397145i | −0.877225 | − | 0.480080i | \(-0.840608\pi\) |
0.480080 | + | 0.877225i | \(0.340608\pi\) | |||||||
\(104\) | −19.7842 | −1.94000 | ||||||||
\(105\) | 0.287457 | + | 3.86230i | 0.0280529 | + | 0.376922i | ||||
\(106\) | −10.1988 | −0.990593 | ||||||||
\(107\) | −2.81760 | + | 2.81760i | −0.272388 | + | 0.272388i | −0.830061 | − | 0.557673i | \(-0.811694\pi\) |
0.557673 | + | 0.830061i | \(0.311694\pi\) | |||||||
\(108\) | −15.1325 | + | 17.6710i | −1.45613 | + | 1.70039i | ||||
\(109\) | − | 6.42246i | − | 0.615160i | −0.951522 | − | 0.307580i | \(-0.900481\pi\) | ||
0.951522 | − | 0.307580i | \(-0.0995192\pi\) | |||||||
\(110\) | −8.72514 | − | 1.88940i | −0.831910 | − | 0.180147i | ||||
\(111\) | −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 | \(-0.320283\pi\) |
−0.844804 | + | 0.535075i | \(0.820283\pi\) | |||||||
\(114\) | 3.53739 | − | 6.50830i | 0.331307 | − | 0.609558i | ||||
\(115\) | 3.07782 | + | 0.666490i | 0.287008 | + | 0.0621505i | ||||
\(116\) | − | 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 | ||||||||
\(120\) | 1.81241 | + | 24.3517i | 0.165449 | + | 2.22300i | ||||
\(121\) | 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 | ||||||
\(125\) | 1.62252 | + | 11.0620i | 0.145123 | + | 0.989414i | ||||
\(126\) | 6.40703 | − | 4.15283i | 0.570784 | − | 0.369963i | ||||
\(127\) | 14.2818 | + | 14.2818i | 1.26730 | + | 1.26730i | 0.947476 | + | 0.319826i | \(0.103624\pi\) |
0.319826 | + | 0.947476i | \(0.396376\pi\) | |||||||
\(128\) | −8.30492 | − | 8.30492i | −0.734058 | − | 0.734058i | ||||
\(129\) | −11.7880 | − | 6.40703i | −1.03788 | − | 0.564108i | ||||
\(130\) | 9.66863 | + | 15.0134i | 0.847995 | + | 1.31677i | ||||
\(131\) | 4.89729i | 0.427878i | 0.976847 | + | 0.213939i | \(0.0686294\pi\) | ||||
−0.976847 | + | 0.213939i | \(0.931371\pi\) | |||||||
\(132\) | 3.45002 | + | 11.6658i | 0.300286 | + | 1.01538i | ||||
\(133\) | −1.18822 | + | 1.18822i | −0.103032 | + | 0.103032i | ||||
\(134\) | −13.5059 | −1.16673 | ||||||||
\(135\) | 11.5116 | + | 1.57557i | 0.990763 | + | 0.135604i | ||||
\(136\) | 32.1643 | 2.75807 | ||||||||
\(137\) | 4.55880 | − | 4.55880i | 0.389485 | − | 0.389485i | −0.485019 | − | 0.874504i | \(-0.661187\pi\) |
0.874504 | + | 0.485019i | \(0.161187\pi\) | |||||||
\(138\) | −1.76064 | − | 5.95334i | −0.149875 | − | 0.506782i | ||||
\(139\) | − | 10.2045i | − | 0.865536i | −0.901505 | − | 0.432768i | \(-0.857537\pi\) | ||
0.901505 | − | 0.432768i | \(-0.142463\pi\) | |||||||
\(140\) | 2.11887 | − | 9.78484i | 0.179077 | − | 0.826970i | ||||
\(141\) | −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 | ||||
\(145\) | −16.7684 | + | 10.7988i | −1.39254 | + | 0.896791i | ||||
\(146\) | 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 | \(0.487961\pi\) | |||||||
\(150\) | 17.5938 | − | 13.2762i | 1.43653 | − | 1.08400i | ||||
\(151\) | −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 | ||||||
\(155\) | −5.16675 | + | 3.32738i | −0.415004 | + | 0.267262i | ||||
\(156\) | 11.6205 | − | 21.3801i | 0.930389 | − | 1.71178i | ||||
\(157\) | −13.7211 | − | 13.7211i | −1.09506 | − | 1.09506i | −0.994979 | − | 0.100086i | \(-0.968088\pi\) |
−0.100086 | − | 0.994979i | \(-0.531912\pi\) | |||||||
\(158\) | 30.6967 | + | 30.6967i | 2.44210 | + | 2.44210i | ||||
\(159\) | 3.31453 | − | 6.09826i | 0.262859 | − | 0.483624i | ||||
\(160\) | 2.57411 | − | 11.8871i | 0.203501 | − | 0.939759i | ||||
\(161\) | 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 | \(-0.630777\pi\) |
0.916782 | + | 0.399387i | \(0.130777\pi\) | |||||||
\(164\) | −28.8471 | −2.25258 | ||||||||
\(165\) | 3.96536 | − | 4.60307i | 0.308703 | − | 0.358349i | ||||
\(166\) | −11.5649 | −0.897607 | ||||||||
\(167\) | 3.11442 | − | 3.11442i | 0.241001 | − | 0.241001i | −0.576263 | − | 0.817264i | \(-0.695490\pi\) |
0.817264 | + | 0.576263i | \(0.195490\pi\) | |||||||
\(168\) | −10.4722 | + | 3.09703i | −0.807946 | + | 0.238941i | ||||
\(169\) | 3.15379i | 0.242599i | ||||||||
\(170\) | −15.7189 | − | 24.4083i | −1.20558 | − | 1.87203i | ||||
\(171\) | 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 | \(-0.393960\pi\) |
−0.945022 | + | 0.327008i | \(0.893960\pi\) | |||||||
\(174\) | 34.5460 | + | 18.7764i | 2.61892 | + | 1.42344i | ||||
\(175\) | −4.68144 | + | 1.75618i | −0.353883 | + | 0.132755i | ||||
\(176\) | − | 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 | \(0.712988\pi\) | |||||||
\(180\) | −27.3807 | − | 12.3448i | −2.04084 | − | 0.920124i | ||||
\(181\) | 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 | ||||||||
\(185\) | −1.36100 | − | 0.294719i | −0.100062 | − | 0.0216681i | ||||
\(186\) | 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 | ||||
\(190\) | 9.34642 | + | 2.02393i | 0.678060 | + | 0.146831i | ||||
\(191\) | − | 12.8543i | − | 0.930108i | −0.885282 | − | 0.465054i | \(-0.846035\pi\) | ||
0.885282 | − | 0.465054i | \(-0.153965\pi\) | |||||||
\(192\) | 0.565384 | − | 0.167206i | 0.0408031 | − | 0.0120671i | ||||
\(193\) | −8.06158 | + | 8.06158i | −0.580285 | + | 0.580285i | −0.934982 | − | 0.354696i | \(-0.884584\pi\) |
0.354696 | + | 0.934982i | \(0.384584\pi\) | |||||||
\(194\) | 15.8238 | 1.13608 | ||||||||
\(195\) | −12.1194 | + | 0.902001i | −0.867887 | + | 0.0645936i | ||||
\(196\) | 4.47734 | 0.319810 | ||||||||
\(197\) | 18.7512 | − | 18.7512i | 1.33597 | − | 1.33597i | 0.436036 | − | 0.899929i | \(-0.356382\pi\) |
0.899929 | − | 0.436036i | \(-0.143618\pi\) | |||||||
\(198\) | −11.7134 | − | 2.50045i | −0.832436 | − | 0.177699i | ||||
\(199\) | − | 4.20728i | − | 0.298246i | −0.988819 | − | 0.149123i | \(-0.952355\pi\) | ||
0.988819 | − | 0.149123i | \(-0.0476451\pi\) | |||||||
\(200\) | −29.5163 | + | 11.0727i | −2.08712 | + | 0.782956i | ||||
\(201\) | 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 | ||||
\(205\) | 7.80037 | + | 12.1124i | 0.544802 | + | 0.845967i | ||||
\(206\) | 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 | ||||||||
\(210\) | 7.46803 | + | 6.43340i | 0.515343 | + | 0.443947i | ||||
\(211\) | −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 | ||||||||
\(215\) | 3.66580 | − | 16.9285i | 0.250006 | − | 1.15451i | ||||
\(216\) | 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 | ||||
\(220\) | −13.2041 | + | 8.50339i | −0.890218 | + | 0.573299i | ||||
\(221\) | 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 | \(-0.550244\pi\) |
0.987568 | + | 0.157193i | \(0.0502445\pi\) | |||||||
\(224\) | 5.43929 | 0.363428 | ||||||||
\(225\) | 2.22049 | + | 14.8347i | 0.148033 | + | 0.988982i | ||||
\(226\) | −11.8504 | −0.788279 | ||||||||
\(227\) | 8.70556 | − | 8.70556i | 0.577809 | − | 0.577809i | −0.356490 | − | 0.934299i | \(-0.616027\pi\) |
0.934299 | + | 0.356490i | \(0.116027\pi\) | |||||||
\(228\) | −3.69568 | − | 12.4964i | −0.244753 | − | 0.827597i | ||||
\(229\) | − | 4.46342i | − | 0.294951i | −0.989066 | − | 0.147476i | \(-0.952885\pi\) | ||
0.989066 | − | 0.147476i | \(-0.0471148\pi\) | |||||||
\(230\) | 6.73837 | − | 4.33950i | 0.444315 | − | 0.286138i | ||||
\(231\) | 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 | \(-0.165835\pi\) |
−0.497735 | + | 0.867329i | \(0.665835\pi\) | |||||||
\(234\) | 13.0310 | + | 20.1044i | 0.851865 | + | 1.31427i | ||||
\(235\) | 2.47199 | − | 11.4155i | 0.161255 | − | 0.744667i | ||||
\(236\) | 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 | \(0.625303\pi\) | |||||||
\(240\) | 20.8098 | + | 17.9268i | 1.34327 | + | 1.15717i | ||||
\(241\) | −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 | ||||||
\(245\) | −1.21069 | − | 1.87996i | −0.0773480 | − | 0.120106i | ||||
\(246\) | 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 | ||||
\(250\) | 22.8274 | + | 16.9875i | 1.44373 | + | 1.07439i | ||||
\(251\) | 3.19253i | 0.201511i | 0.994911 | + | 0.100755i | \(0.0321259\pi\) | ||||
−0.994911 | + | 0.100755i | \(0.967874\pi\) | |||||||
\(252\) | 2.80414 | − | 13.1360i | 0.176644 | − | 0.827493i | ||||
\(253\) | 1.56219 | − | 1.56219i | 0.0982141 | − | 0.0982141i | ||||
\(254\) | 51.4038 | 3.22536 | ||||||||
\(255\) | 19.7032 | − | 1.46644i | 1.23386 | − | 0.0918318i | ||||
\(256\) | −29.2108 | −1.82567 | ||||||||
\(257\) | −11.8118 | + | 11.8118i | −0.736799 | + | 0.736799i | −0.971957 | − | 0.235158i | \(-0.924439\pi\) |
0.235158 | + | 0.971957i | \(0.424439\pi\) | |||||||
\(258\) | −32.7443 | + | 9.68378i | −2.03857 | + | 0.602886i | ||||
\(259\) | − | 0.622763i | − | 0.0386966i | ||||||
\(260\) | 30.7035 | + | 6.64874i | 1.90415 | + | 0.412337i | ||||
\(261\) | −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 | \(-0.444366\pi\) |
−0.984765 | + | 0.173891i | \(0.944366\pi\) | |||||||
\(264\) | 15.0515 | + | 8.18080i | 0.926356 | + | 0.503493i | ||||
\(265\) | 8.75757 | + | 1.89642i | 0.537974 | + | 0.116496i | ||||
\(266\) | 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 | \(0.147559\pi\) | |||||||
\(270\) | 23.5521 | − | 17.8812i | 1.43334 | − | 1.08822i | ||||
\(271\) | 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 | ||||||
\(275\) | 7.14085 | + | 3.24481i | 0.430610 | + | 0.195669i | ||||
\(276\) | −9.59588 | − | 5.21556i | −0.577604 | − | 0.313940i | ||||
\(277\) | 16.8636 | + | 16.8636i | 1.01324 | + | 1.01324i | 0.999911 | + | 0.0133247i | \(0.00424152\pi\) |
0.0133247 | + | 0.999911i | \(0.495758\pi\) | |||||||
\(278\) | −18.3644 | − | 18.3644i | −1.10142 | − | 1.10142i | ||||
\(279\) | −6.91877 | + | 4.48452i | −0.414216 | + | 0.268481i | ||||
\(280\) | −7.63336 | − | 11.8531i | −0.456180 | − | 0.708356i | ||||
\(281\) | 24.8052i | 1.47975i | 0.672742 | + | 0.739877i | \(0.265116\pi\) | ||||
−0.672742 | + | 0.739877i | \(0.734884\pi\) | |||||||
\(282\) | −22.0808 | + | 6.53014i | −1.31489 | + | 0.388864i | ||||
\(283\) | 5.41918 | − | 5.41918i | 0.322137 | − | 0.322137i | −0.527449 | − | 0.849586i | \(-0.676852\pi\) |
0.849586 | + | 0.527449i | \(0.176852\pi\) | |||||||
\(284\) | 16.2054 | 0.961615 | ||||||||
\(285\) | −4.24771 | + | 4.93084i | −0.251613 | + | 0.292078i | ||||
\(286\) | 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 | ||||||
\(290\) | −10.7430 | + | 49.6107i | −0.630851 | + | 2.91324i | ||||
\(291\) | −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 | \(-0.365712\pi\) |
−0.912322 | + | 0.409473i | \(0.865712\pi\) | |||||||
\(294\) | −2.10509 | + | 3.87306i | −0.122771 | + | 0.225882i | ||||
\(295\) | 10.4313 | − | 6.71776i | 0.607336 | − | 0.391123i | ||||
\(296\) | − | 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 | ||||||||
\(300\) | 5.37100 | − | 38.4011i | 0.310095 | − | 2.21709i | ||||
\(301\) | 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 | ||||||||
\(305\) | −13.9242 | + | 8.96715i | −0.797296 | + | 0.513457i | ||||
\(306\) | −21.1853 | − | 32.6849i | −1.21108 | − | 1.86847i | ||||
\(307\) | −11.8525 | − | 11.8525i | −0.676457 | − | 0.676457i | 0.282740 | − | 0.959197i | \(-0.408757\pi\) |
−0.959197 | + | 0.282740i | \(0.908757\pi\) | |||||||
\(308\) | −4.96644 | − | 4.96644i | −0.282989 | − | 0.282989i | ||||
\(309\) | −8.67440 | − | 4.71471i | −0.493469 | − | 0.268211i | ||||
\(310\) | −3.31019 | + | 15.2863i | −0.188006 | + | 0.868203i | ||||
\(311\) | − | 29.2800i | − | 1.66032i | −0.557528 | − | 0.830158i | \(-0.688250\pi\) | ||
0.557528 | − | 0.830158i | \(-0.311750\pi\) | |||||||
\(312\) | −9.71807 | − | 32.8603i | −0.550177 | − | 1.86035i | ||||
\(313\) | 1.22577 | − | 1.22577i | 0.0692848 | − | 0.0692848i | −0.671615 | − | 0.740900i | \(-0.734399\pi\) |
0.740900 | + | 0.671615i | \(0.234399\pi\) | |||||||
\(314\) | −49.3859 | −2.78701 | ||||||||
\(315\) | −6.27385 | + | 2.37463i | −0.353491 | + | 0.133795i | ||||
\(316\) | 76.3710 | 4.29620 | ||||||||
\(317\) | 4.30159 | − | 4.30159i | 0.241601 | − | 0.241601i | −0.575911 | − | 0.817512i | \(-0.695353\pi\) |
0.817512 | + | 0.575911i | \(0.195353\pi\) | |||||||
\(318\) | −5.00968 | − | 16.9395i | −0.280929 | − | 0.949922i | ||||
\(319\) | 13.9921i | 0.783408i | ||||||||
\(320\) | 0.412119 | + | 0.639937i | 0.0230381 | + | 0.0357736i | ||||
\(321\) | −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 | ||||
\(325\) | −5.51066 | − | 14.6897i | −0.305676 | − | 0.814839i | ||||
\(326\) | − | 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 | ||||||||
\(330\) | −1.14765 | − | 15.4200i | −0.0631763 | − | 0.848843i | ||||
\(331\) | 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 | ||||||
\(335\) | 11.5973 | + | 2.51136i | 0.633630 | + | 0.137210i | ||||
\(336\) | −5.86588 | + | 10.7924i | −0.320010 | + | 0.588772i | ||||
\(337\) | 10.3056 | + | 10.3056i | 0.561383 | + | 0.561383i | 0.929700 | − | 0.368317i | \(-0.120066\pi\) |
−0.368317 | + | 0.929700i | \(0.620066\pi\) | |||||||
\(338\) | 5.67565 | + | 5.67565i | 0.308715 | + | 0.308715i | ||||
\(339\) | 3.85131 | − | 7.08585i | 0.209174 | − | 0.384851i | ||||
\(340\) | −49.9166 | − | 10.8092i | −2.70711 | − | 0.586214i | ||||
\(341\) | 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 | ||||||||
\(345\) | 0.404838 | + | 5.43945i | 0.0217958 | + | 0.292850i | ||||
\(346\) | −29.2573 | −1.57288 | ||||||||
\(347\) | −19.2241 | + | 19.2241i | −1.03200 | + | 1.03200i | −0.0325323 | + | 0.999471i | \(0.510357\pi\) |
−0.999471 | + | 0.0325323i | \(0.989643\pi\) | |||||||
\(348\) | 66.3310 | − | 19.6166i | 3.55571 | − | 1.05156i | ||||
\(349\) | 30.1301i | 1.61283i | 0.591353 | + | 0.806413i | \(0.298594\pi\) | ||||
−0.591353 | + | 0.806413i | \(0.701406\pi\) | |||||||
\(350\) | −5.26438 | + | 11.5853i | −0.281393 | + | 0.619262i | ||||
\(351\) | −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 | \(-0.0284863\pi\) |
−0.0893729 | + | 0.995998i | \(0.528486\pi\) | |||||||
\(354\) | −21.4905 | − | 11.6805i | −1.14221 | − | 0.620814i | ||||
\(355\) | −4.38201 | − | 6.80438i | −0.232573 | − | 0.361139i | ||||
\(356\) | − | 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 | \(0.506199\pi\) | |||||||
\(360\) | −39.5564 | + | 14.9720i | −2.08481 | + | 0.789092i | ||||
\(361\) | 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 | ||||||||
\(365\) | 3.94692 | − | 18.2267i | 0.206591 | − | 0.954028i | ||||
\(366\) | 28.6864 | + | 15.5917i | 1.49946 | + | 0.814990i | ||||
\(367\) | 23.2923 | + | 23.2923i | 1.21585 | + | 1.21585i | 0.969073 | + | 0.246776i | \(0.0793711\pi\) |
0.246776 | + | 0.969073i | \(0.420629\pi\) | |||||||
\(368\) | 7.06244 | + | 7.06244i | 0.368155 | + | 0.368155i | ||||
\(369\) | 10.5131 | + | 16.2196i | 0.547288 | + | 0.844361i | ||||
\(370\) | −2.97967 | + | 1.91890i | −0.154906 | + | 0.0997591i | ||||
\(371\) | 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 | \(-0.811937\pi\) |
0.557040 | + | 0.830485i | \(0.311937\pi\) | |||||||
\(374\) | −20.3671 | −1.05316 | ||||||||
\(375\) | −17.5763 | + | 8.12860i | −0.907635 | + | 0.419759i | ||||
\(376\) | 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 | \(0.0276961\pi\) | ||||
−0.996217 | + | 0.0869000i | \(0.972304\pi\) | |||||||
\(380\) | 14.1443 | − | 9.10888i | 0.725585 | − | 0.467276i | ||||
\(381\) | −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 | \(-0.283037\pi\) |
−0.776561 | + | 0.630043i | \(0.783037\pi\) | |||||||
\(384\) | 9.71455 | − | 17.8734i | 0.495744 | − | 0.912097i | ||||
\(385\) | −0.742378 | + | 3.42826i | −0.0378351 | + | 0.174721i | ||||
\(386\) | 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 | \(0.416661\pi\) | |||||||
\(390\) | −20.1871 | + | 23.4337i | −1.02222 | + | 1.18661i | ||||
\(391\) | 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 | ||||||
\(395\) | −20.6510 | − | 32.0668i | −1.03906 | − | 1.61346i | ||||
\(396\) | −17.6815 | + | 11.4606i | −0.888528 | + | 0.575915i | ||||
\(397\) | −24.0534 | − | 24.0534i | −1.20721 | − | 1.20721i | −0.971928 | − | 0.235280i | \(-0.924399\pi\) |
−0.235280 | − | 0.971928i | \(-0.575601\pi\) | |||||||
\(398\) | −7.57156 | − | 7.57156i | −0.379528 | − | 0.379528i | ||||
\(399\) | −2.55723 | − | 1.38991i | −0.128021 | − | 0.0695823i | ||||
\(400\) | −14.6693 | + | 32.2828i | −0.733465 | + | 1.61414i | ||||
\(401\) | − | 20.0912i | − | 1.00331i | −0.865068 | − | 0.501654i | \(-0.832725\pi\) | ||
0.865068 | − | 0.501654i | \(-0.167275\pi\) | |||||||
\(402\) | −6.63414 | − | 22.4324i | −0.330881 | − | 1.11883i | ||||
\(403\) | 6.09803 | − | 6.09803i | 0.303765 | − | 0.303765i | ||||
\(404\) | −4.52803 | −0.225278 | ||||||||
\(405\) | 3.03763 | + | 19.8940i | 0.150941 | + | 0.988543i | ||||
\(406\) | −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 | \(-0.689202\pi\) | ||
0.560008 | − | 0.828487i | \(-0.310798\pi\) | |||||||
\(410\) | 35.8356 | + | 7.76008i | 1.76980 | + | 0.383243i | ||||
\(411\) | 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 | ||||
\(415\) | 9.93061 | + | 2.15044i | 0.487475 | + | 0.105561i | ||||
\(416\) | 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 | \(0.717804\pi\) | |||||||
\(420\) | 17.2928 | − | 1.28704i | 0.843803 | − | 0.0628011i | ||||
\(421\) | 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 | ||||||||
\(425\) | 8.95900 | + | 23.8820i | 0.434576 | + | 1.15844i | ||||
\(426\) | −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 | ||||
\(430\) | −23.8679 | − | 37.0621i | −1.15101 | − | 1.78729i | ||||
\(431\) | 0.449005i | 0.0216278i | 0.999942 | + | 0.0108139i | \(0.00344224\pi\) | ||||
−0.999942 | + | 0.0108139i | \(0.996558\pi\) | |||||||
\(432\) | 27.9899 | + | 23.9691i | 1.34667 | + | 1.15321i | ||||
\(433\) | −17.7813 | + | 17.7813i | −0.854517 | + | 0.854517i | −0.990686 | − | 0.136169i | \(-0.956521\pi\) |
0.136169 | + | 0.990686i | \(0.456521\pi\) | |||||||
\(434\) | −6.99469 | −0.335756 | ||||||||
\(435\) | −26.1728 | − | 22.5468i | −1.25489 | − | 1.08104i | ||||
\(436\) | −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 | \(0.248909\pi\) | ||||
−0.709526 | + | 0.704679i | \(0.751091\pi\) | |||||||
\(440\) | −4.68067 | + | 21.6151i | −0.223142 | + | 1.03046i | ||||
\(441\) | −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 | \(-0.0748525\pi\) |
−0.232995 | + | 0.972478i | \(0.574853\pi\) | |||||||
\(444\) | 4.24325 | + | 2.30630i | 0.201376 | + | 0.109452i | ||||
\(445\) | −17.6767 | + | 11.3838i | −0.837957 | + | 0.539643i | ||||
\(446\) | − | 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 | \(0.625842\pi\) | |||||||
\(450\) | 30.6931 | + | 22.7010i | 1.44689 | + | 1.07013i | ||||
\(451\) | 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 | ||||||
\(455\) | 5.89905 | − | 3.79898i | 0.276552 | − | 0.178099i | ||||
\(456\) | −16.1232 | − | 8.76332i | −0.755040 | − | 0.410380i | ||||
\(457\) | −20.6299 | − | 20.6299i | −0.965028 | − | 0.965028i | 0.0343811 | − | 0.999409i | \(-0.489054\pi\) |
−0.999409 | + | 0.0343811i | \(0.989054\pi\) | |||||||
\(458\) | −8.03251 | − | 8.03251i | −0.375335 | − | 0.375335i | ||||
\(459\) | 26.4287 | − | 2.04518i | 1.23359 | − | 0.0954609i | ||||
\(460\) | 2.98410 | − | 13.7804i | 0.139134 | − | 0.642516i | ||||
\(461\) | − | 15.2893i | − | 0.712094i | −0.934468 | − | 0.356047i | \(-0.884124\pi\) | ||
0.934468 | − | 0.356047i | \(-0.115876\pi\) | |||||||
\(462\) | 6.63120 | − | 1.96110i | 0.308511 | − | 0.0912388i | ||||
\(463\) | 0.492195 | − | 0.492195i | 0.0228743 | − | 0.0228743i | −0.695577 | − | 0.718451i | \(-0.744851\pi\) |
0.718451 | + | 0.695577i | \(0.244851\pi\) | |||||||
\(464\) | −63.2563 | −2.93660 | ||||||||
\(465\) | −8.06451 | − | 6.94724i | −0.373983 | − | 0.322170i | ||||
\(466\) | 20.3056 | 0.940640 | ||||||||
\(467\) | 9.00044 | − | 9.00044i | 0.416491 | − | 0.416491i | −0.467501 | − | 0.883992i | \(-0.654846\pi\) |
0.883992 | + | 0.467501i | \(0.154846\pi\) | |||||||
\(468\) | 41.2192 | + | 8.79901i | 1.90536 | + | 0.406734i | ||||
\(469\) | 5.30669i | 0.245040i | ||||||||
\(470\) | −16.0951 | − | 24.9924i | −0.742410 | − | 1.15281i | ||||
\(471\) | 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 | ||||
\(475\) | −7.64932 | − | 3.47586i | −0.350975 | − | 0.159483i | ||||
\(476\) | − | 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 | \(0.325969\pi\) | |||||||
\(480\) | 21.0082 | − | 1.56356i | 0.958888 | − | 0.0713665i | ||||
\(481\) | 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 | ||||||
\(485\) | −13.5877 | − | 2.94237i | −0.616986 | − | 0.133606i | ||||
\(486\) | 31.5278 | − | 24.0830i | 1.43013 | − | 1.09243i | ||||
\(487\) | −11.4919 | − | 11.4919i | −0.520746 | − | 0.520746i | 0.397051 | − | 0.917797i | \(-0.370034\pi\) |
−0.917797 | + | 0.397051i | \(0.870034\pi\) | |||||||
\(488\) | −33.0210 | − | 33.0210i | −1.49479 | − | 1.49479i | ||||
\(489\) | 14.2163 | + | 7.72687i | 0.642884 | + | 0.349421i | ||||
\(490\) | −5.56202 | − | 1.20443i | −0.251266 | − | 0.0544108i | ||||
\(491\) | − | 0.301729i | − | 0.0136168i | −0.999977 | − | 0.00680841i | \(-0.997833\pi\) | ||
0.999977 | − | 0.00680841i | \(-0.00216720\pi\) | |||||||
\(492\) | −14.1698 | − | 47.9133i | −0.638826 | − | 2.16010i | ||||
\(493\) | −32.1750 | + | 32.1750i | −1.44909 | + | 1.44909i | ||||
\(494\) | −13.4198 | −0.603785 | ||||||||
\(495\) | 9.59323 | + | 4.32517i | 0.431183 | + | 0.194402i | ||||
\(496\) | −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 | \(0.149504\pi\) | ||||
−0.891713 | + | 0.452601i | \(0.850496\pi\) | |||||||
\(500\) | 49.5282 | − | 7.26458i | 2.21497 | − | 0.324882i | ||||
\(501\) | 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 | 0.997734 | + | 0.0672882i | \(0.0214347\pi\) |
0.0672882 | + | 0.997734i | \(0.478565\pi\) | |||||||
\(504\) | −10.2880 | − | 15.8724i | −0.458262 | − | 0.707012i | ||||
\(505\) | 1.22440 | + | 1.90124i | 0.0544850 | + | 0.0846042i | ||||
\(506\) | − | 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 | \(0.415983\pi\) | |||||||
\(510\) | 32.8194 | − | 38.0975i | 1.45327 | − | 1.68699i | ||||
\(511\) | 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 | ||||||||
\(515\) | 2.69754 | − | 12.4571i | 0.118868 | − | 0.548925i | ||||
\(516\) | −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 | ||||
\(520\) | 37.1934 | − | 23.9525i | 1.63104 | − | 1.05038i | ||||
\(521\) | 29.7872i | 1.30500i | 0.757789 | + | 0.652500i | \(0.226280\pi\) | ||||
−0.757789 | + | 0.652500i | \(0.773720\pi\) | |||||||
\(522\) | −14.2174 | + | 66.6018i | −0.622279 | + | 2.91508i | ||||
\(523\) | 17.4673 | − | 17.4673i | 0.763792 | − | 0.763792i | −0.213214 | − | 0.977006i | \(-0.568393\pi\) |
0.977006 | + | 0.213214i | \(0.0683931\pi\) | |||||||
\(524\) | 21.9268 | 0.957877 | ||||||||
\(525\) | −5.21645 | − | 6.91293i | −0.227664 | − | 0.301705i | ||||
\(526\) | −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 | ||||||
\(530\) | 19.1732 | − | 12.3475i | 0.832833 | − | 0.536343i | ||||
\(531\) | 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 | ||||
\(535\) | 1.88573 | − | 8.70821i | 0.0815272 | − | 0.376489i | ||||
\(536\) | 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 | ||||||||
\(540\) | 7.05437 | − | 51.5414i | 0.303572 | − | 2.21799i | ||||
\(541\) | −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 | ||||||
\(545\) | 7.77560 | + | 12.0739i | 0.333070 | + | 0.517191i | ||||
\(546\) | −12.1532 | − | 6.60549i | −0.520107 | − | 0.282689i | ||||
\(547\) | −25.6689 | − | 25.6689i | −1.09752 | − | 1.09752i | −0.994700 | − | 0.102823i | \(-0.967213\pi\) |
−0.102823 | − | 0.994700i | \(-0.532787\pi\) | |||||||
\(548\) | −20.4113 | − | 20.4113i | −0.871928 | − | 0.871928i | ||||
\(549\) | −18.6458 | + | 12.0856i | −0.795783 | + | 0.515801i | ||||
\(550\) | 18.6904 | − | 7.01144i | 0.796959 | − | 0.298969i | ||||
\(551\) | − | 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 | ||||||||
\(555\) | −0.179017 | − | 2.40530i | −0.00759886 | − | 0.102099i | ||||
\(556\) | −45.6891 | −1.93765 | ||||||||
\(557\) | 10.5779 | − | 10.5779i | 0.448199 | − | 0.448199i | −0.446556 | − | 0.894756i | \(-0.647350\pi\) |
0.894756 | + | 0.446556i | \(0.147350\pi\) | |||||||
\(558\) | −4.38074 | + | 20.5217i | −0.185452 | + | 0.868753i | ||||
\(559\) | 24.3063i | 1.02805i | ||||||||
\(560\) | −15.4987 | − | 3.35618i | −0.654939 | − | 0.141825i | ||||
\(561\) | 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 | \(-0.144476\pi\) |
−0.438460 | + | 0.898751i | \(0.644476\pi\) | |||||||
\(564\) | −19.3444 | + | 35.5908i | −0.814544 | + | 1.49864i | ||||
\(565\) | 10.1758 | + | 2.20354i | 0.428100 | + | 0.0927036i | ||||
\(566\) | − | 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 | \(0.843705\pi\) | |||||||
\(570\) | 1.22937 | + | 16.5180i | 0.0514927 | + | 0.691863i | ||||
\(571\) | 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 | ||||||||
\(575\) | −6.59308 | + | 2.47331i | −0.274950 | + | 0.103144i | ||||
\(576\) | 0.555438 | + | 0.856936i | 0.0231433 | + | 0.0357057i | ||||
\(577\) | 14.6975 | + | 14.6975i | 0.611865 | + | 0.611865i | 0.943432 | − | 0.331567i | \(-0.107577\pi\) |
−0.331567 | + | 0.943432i | \(0.607577\pi\) | |||||||
\(578\) | −16.2407 | − | 16.2407i | −0.675523 | − | 0.675523i | ||||
\(579\) | −17.3497 | − | 9.42991i | −0.721028 | − | 0.391894i | ||||
\(580\) | 48.3498 | + | 75.0776i | 2.00762 | + | 3.11743i | ||||
\(581\) | 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 | ||||||||
\(585\) | −7.45126 | − | 19.6865i | −0.308072 | − | 0.813936i | ||||
\(586\) | −30.9802 | −1.27978 | ||||||||
\(587\) | −4.89737 | + | 4.89737i | −0.202136 | + | 0.202136i | −0.800915 | − | 0.598779i | \(-0.795653\pi\) |
0.598779 | + | 0.800915i | \(0.295653\pi\) | |||||||
\(588\) | 2.19929 | + | 7.43658i | 0.0906971 | + | 0.306680i | ||||
\(589\) | − | 4.61831i | − | 0.190294i | ||||||
\(590\) | 6.68306 | − | 30.8620i | 0.275137 | − | 1.27057i | ||||
\(591\) | 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 | \(-0.0225904\pi\) |
−0.0709102 | + | 0.997483i | \(0.522590\pi\) | |||||||
\(594\) | −1.60059 | − | 20.6835i | −0.0656729 | − | 0.848654i | ||||
\(595\) | −9.59044 | + | 6.17623i | −0.393170 | + | 0.253201i | ||||
\(596\) | − | 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 | \(0.544493\pi\) | |||||||
\(600\) | −32.8896 | − | 43.5859i | −1.34271 | − | 1.77939i | ||||
\(601\) | −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 | ||||||||
\(605\) | −16.0533 | + | 10.3383i | −0.652658 | + | 0.420311i | ||||
\(606\) | 2.12893 | − | 3.91692i | 0.0864817 | − | 0.159114i | ||||
\(607\) | 6.30295 | + | 6.30295i | 0.255829 | + | 0.255829i | 0.823355 | − | 0.567526i | \(-0.192100\pi\) |
−0.567526 | + | 0.823355i | \(0.692100\pi\) | |||||||
\(608\) | 6.46309 | + | 6.46309i | 0.262113 | + | 0.262113i | ||||
\(609\) | 7.37760 | − | 13.5737i | 0.298956 | − | 0.550035i | ||||
\(610\) | −8.92083 | + | 41.1959i | −0.361194 | + | 1.66797i | ||||
\(611\) | 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 | \(-0.797883\pi\) |
0.593154 | + | 0.805089i | \(0.297883\pi\) | |||||||
\(614\) | −42.6601 | −1.72162 | ||||||||
\(615\) | −16.2864 | + | 18.9056i | −0.656731 | + | 0.762348i | ||||
\(616\) | −9.89062 | −0.398504 | ||||||||
\(617\) | 2.10719 | − | 2.10719i | 0.0848323 | − | 0.0848323i | −0.663417 | − | 0.748250i | \(-0.730895\pi\) |
0.748250 | + | 0.663417i | \(0.230895\pi\) | |||||||
\(618\) | −24.0954 | + | 7.12596i | −0.969261 | + | 0.286648i | ||||
\(619\) | 21.0734i | 0.847012i | 0.905893 | + | 0.423506i | \(0.139201\pi\) | ||||
−0.905893 | + | 0.423506i | \(0.860799\pi\) | |||||||
\(620\) | 14.8978 | + | 23.1333i | 0.598310 | + | 0.929055i | ||||
\(621\) | 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 | ||||
\(625\) | −16.4429 | − | 18.8317i | −0.657715 | − | 0.753267i | ||||
\(626\) | − | 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 | ||||||||
\(630\) | −7.01715 | + | 15.5641i | −0.279570 | + | 0.620087i | ||||
\(631\) | −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 | ||||||
\(635\) | −44.1399 | − | 9.55833i | −1.75164 | − | 0.379311i | ||||
\(636\) | −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 | ||||
\(640\) | 25.6675 | + | 5.55821i | 1.01460 | + | 0.219708i | ||||
\(641\) | 36.1036i | 1.42601i | 0.701161 | + | 0.713003i | \(0.252665\pi\) | ||||
−0.701161 | + | 0.713003i | \(0.747335\pi\) | |||||||
\(642\) | −16.8441 | + | 4.98144i | −0.664782 | + | 0.196602i | ||||
\(643\) | −21.0115 | + | 21.0115i | −0.828614 | + | 0.828614i | −0.987325 | − | 0.158711i | \(-0.949266\pi\) |
0.158711 | + | 0.987325i | \(0.449266\pi\) | |||||||
\(644\) | 6.30563 | 0.248477 | ||||||||
\(645\) | 29.9179 | − | 2.22667i | 1.17801 | − | 0.0876752i | ||||
\(646\) | 21.8173 | 0.858392 | ||||||||
\(647\) | −18.9025 | + | 18.9025i | −0.743133 | + | 0.743133i | −0.973180 | − | 0.230046i | \(-0.926112\pi\) |
0.230046 | + | 0.973180i | \(0.426112\pi\) | |||||||
\(648\) | −53.0112 | + | 20.2430i | −2.08248 | + | 0.795221i | ||||
\(649\) | − | 8.70428i | − | 0.341673i | ||||||
\(650\) | −36.3532 | − | 16.5189i | −1.42589 | − | 0.647925i | ||||
\(651\) | 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 | \(-0.360420\pi\) |
−0.905388 | + | 0.424585i | \(0.860420\pi\) | |||||||
\(654\) | 13.5199 | − | 24.8746i | 0.528668 | − | 0.972674i | ||||
\(655\) | −5.92909 | − | 9.20669i | −0.231669 | − | 0.359735i | ||||
\(656\) | 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 | \(0.504393\pi\) | |||||||
\(660\) | −20.6095 | − | 17.7542i | −0.802224 | − | 0.691083i | ||||
\(661\) | 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 | ||||||||
\(665\) | 0.795239 | − | 3.67237i | 0.0308381 | − | 0.142409i | ||||
\(666\) | −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 | ||||
\(670\) | 25.3904 | − | 16.3514i | 0.980918 | − | 0.631709i | ||||
\(671\) | 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 | \(-0.821785\pi\) |
0.531083 | + | 0.847320i | \(0.321785\pi\) | |||||||
\(674\) | 37.0926 | 1.42875 | ||||||||
\(675\) | −23.5489 | + | 10.9750i | −0.906397 | + | 0.422427i | ||||
\(676\) | 14.1206 | 0.543099 | ||||||||
\(677\) | −32.8605 | + | 32.8605i | −1.26293 | + | 1.26293i | −0.313264 | + | 0.949666i | \(0.601422\pi\) |
−0.949666 | + | 0.313264i | \(0.898578\pi\) | |||||||
\(678\) | −5.82098 | − | 19.6828i | −0.223554 | − | 0.755915i | ||||
\(679\) | − | 6.21744i | − | 0.238604i | ||||||
\(680\) | −60.4675 | + | 38.9409i | −2.31882 | + | 1.49332i | ||||
\(681\) | 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 | 0.995481 | + | 0.0949562i | \(0.0302711\pi\) |
0.0949562 | + | 0.995481i | \(0.469729\pi\) | |||||||
\(684\) | 18.9405 | − | 12.2766i | 0.724208 | − | 0.469408i | ||||
\(685\) | −3.05106 | + | 14.0896i | −0.116575 | + | 0.538338i | ||||
\(686\) | − | 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 | ||||||||
\(690\) | 10.5176 | + | 9.06044i | 0.400397 | + | 0.344925i | ||||
\(691\) | 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 | ||||||||
\(695\) | 12.3545 | + | 19.1840i | 0.468633 | + | 0.727692i | ||||
\(696\) | 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 | ||||
\(700\) | 7.86301 | + | 20.9604i | 0.297194 | + | 0.792227i | ||||
\(701\) | − | 4.92775i | − | 0.186118i | −0.995661 | − | 0.0930592i | \(-0.970335\pi\) | ||
0.995661 | − | 0.0930592i | \(-0.0296646\pi\) | |||||||
\(702\) | −26.9913 | + | 31.5191i | −1.01872 | + | 1.18961i | ||||
\(703\) | 0.739981 | − | 0.739981i | 0.0279089 | − | 0.0279089i | ||||
\(704\) | 0.533986 | 0.0201254 | ||||||||
\(705\) | 20.1748 | − | 1.50153i | 0.759825 | − | 0.0565509i | ||||
\(706\) | 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 | \(-0.895365\pi\) | ||
0.946456 | − | 0.322833i | \(-0.104635\pi\) | |||||||
\(710\) | −20.1313 | − | 4.35937i | −0.755516 | − | 0.163604i | ||||
\(711\) | −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 | ||||
\(715\) | −10.7574 | − | 2.32948i | −0.402305 | − | 0.0871177i | ||||
\(716\) | 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 | \(0.573392\pi\) | |||||||
\(720\) | −19.5534 | + | 43.3696i | −0.728714 | + | 1.61629i | ||||
\(721\) | 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 | ||||||
\(725\) | 18.4498 | − | 40.6025i | 0.685208 | − | 1.50794i | ||||
\(726\) | 33.0728 | + | 17.9757i | 1.22745 | + | 0.667142i | ||||
\(727\) | 5.83842 | + | 5.83842i | 0.216535 | + | 0.216535i | 0.807037 | − | 0.590501i | \(-0.201070\pi\) |
−0.590501 | + | 0.807037i | \(0.701070\pi\) | |||||||
\(728\) | 13.9895 | + | 13.9895i | 0.518486 | + | 0.518486i | ||||
\(729\) | 4.15390 | + | 26.6786i | 0.153848 | + | 0.988094i | ||||
\(730\) | −25.6983 | − | 39.9043i | −0.951136 | − | 1.47692i | ||||
\(731\) | − | 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 | \(-0.634467\pi\) |
0.912091 | + | 0.409987i | \(0.134467\pi\) | |||||||
\(734\) | 83.8351 | 3.09441 | ||||||||
\(735\) | 2.52780 | − | 2.93432i | 0.0932392 | − | 0.108234i | ||||
\(736\) | 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 | \(-0.909929\pi\) | ||
0.960231 | − | 0.279205i | \(-0.0900710\pi\) | |||||||
\(740\) | −1.31955 | + | 6.09364i | −0.0485078 | + | 0.224007i | ||||
\(741\) | 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 | 0.949729 | + | 0.313073i | \(0.101358\pi\) |
0.313073 | + | 0.949729i | \(0.398642\pi\) | |||||||
\(744\) | 14.3326 | − | 26.3700i | 0.525459 | − | 0.966770i | ||||
\(745\) | −1.73543 | + | 1.11762i | −0.0635813 | + | 0.0409463i | ||||
\(746\) | 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 | ||||||||
\(750\) | −17.0023 | + | 46.2593i | −0.620837 | + | 1.68915i | ||||
\(751\) | −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 | ||||||
\(755\) | 25.8136 | − | 16.6239i | 0.939454 | − | 0.605007i | ||||
\(756\) | 23.1956 | − | 1.79498i | 0.843615 | − | 0.0652830i | ||||
\(757\) | −1.88407 | − | 1.88407i | −0.0684777 | − | 0.0684777i | 0.672038 | − | 0.740516i | \(-0.265419\pi\) |
−0.740516 | + | 0.672038i | \(0.765419\pi\) | |||||||
\(758\) | 6.08909 | + | 6.08909i | 0.221166 | + | 0.221166i | ||||
\(759\) | 3.36206 | + | 1.82735i | 0.122035 | + | 0.0663286i | ||||
\(760\) | 5.01396 | − | 23.1542i | 0.181875 | − | 0.839892i | ||||
\(761\) | − | 35.6674i | − | 1.29294i | −0.762938 | − | 0.646472i | \(-0.776244\pi\) | ||
0.762938 | − | 0.646472i | \(-0.223756\pi\) | |||||||
\(762\) | 25.2498 | + | 85.3786i | 0.914703 | + | 3.09294i | ||||
\(763\) | −4.54137 | + | 4.54137i | −0.164409 | + | 0.164409i | ||||
\(764\) | −57.5532 | −2.08220 | ||||||||
\(765\) | 12.1140 | + | 32.0055i | 0.437981 | + | 1.15716i | ||||
\(766\) | −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 | \(-0.806105\pi\) | ||
0.820141 | − | 0.572162i | \(-0.193895\pi\) | |||||||
\(770\) | 4.83360 | + | 7.50561i | 0.174191 | + | 0.270483i | ||||
\(771\) | −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 | \(-0.290412\pi\) |
−0.790947 | + | 0.611885i | \(0.790412\pi\) | |||||||
\(774\) | −32.1683 | − | 49.6296i | −1.15627 | − | 1.78390i | ||||
\(775\) | 5.68485 | − | 12.5107i | 0.204206 | − | 0.449396i | ||||
\(776\) | − | 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 | ||||||||
\(780\) | 4.03856 | + | 54.2626i | 0.144604 | + | 1.94291i | ||||
\(781\) | −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 | ||||||
\(785\) | 42.4071 | + | 9.18310i | 1.51357 | + | 0.327759i | ||||
\(786\) | −10.3092 | + | 18.9675i | −0.367718 | + | 0.676548i | ||||
\(787\) | 18.7554 | + | 18.7554i | 0.668557 | + | 0.668557i | 0.957382 | − | 0.288825i | \(-0.0932646\pi\) |
−0.288825 | + | 0.957382i | \(0.593265\pi\) | |||||||
\(788\) | −83.9553 | − | 83.9553i | −2.99078 | − | 2.99078i | ||||
\(789\) | 15.3822 | − | 28.3011i | 0.547621 | − | 1.00754i | ||||
\(790\) | −94.8726 | − | 20.5443i | −3.37542 | − | 0.730934i | ||||
\(791\) | 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 | ||||||||
\(795\) | 1.15192 | + | 15.4773i | 0.0408544 | + | 0.548924i | ||||
\(796\) | −18.8374 | −0.667675 | ||||||||
\(797\) | 7.92792 | − | 7.92792i | 0.280821 | − | 0.280821i | −0.552615 | − | 0.833437i | \(-0.686370\pi\) |
0.833437 | + | 0.552615i | \(0.186370\pi\) | |||||||
\(798\) | −7.10338 | + | 2.10075i | −0.251457 | + | 0.0743656i | ||||
\(799\) | − | 26.6473i | − | 0.942713i | ||||||
\(800\) | 9.55238 | + | 25.4637i | 0.337728 | + | 0.900278i | ||||
\(801\) | −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 | ||||
\(805\) | −1.70507 | − | 2.64763i | −0.0600957 | − | 0.0933166i | ||||
\(806\) | − | 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 | \(0.698560\pi\) | |||||||
\(810\) | 41.2685 | + | 30.3353i | 1.45003 | + | 1.06587i | ||||
\(811\) | −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 | ||||||||
\(815\) | −4.42095 | + | 20.4157i | −0.154859 | + | 0.715132i | ||||
\(816\) | 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 | ||||
\(820\) | 54.2313 | − | 34.9249i | 1.89384 | − | 1.21963i | ||||
\(821\) | − | 32.4420i | − | 1.13223i | −0.824325 | − | 0.566116i | \(-0.808445\pi\) | ||
0.824325 | − | 0.566116i | \(-0.191555\pi\) | |||||||
\(822\) | 27.2532 | − | 8.05984i | 0.950565 | − | 0.281119i | ||||
\(823\) | −32.7235 | + | 32.7235i | −1.14067 | + | 1.14067i | −0.152341 | + | 0.988328i | \(0.548681\pi\) |
−0.988328 | + | 0.152341i | \(0.951319\pi\) | |||||||
\(824\) | 35.9390 | 1.25200 | ||||||||
\(825\) | −1.88181 | + | 13.4544i | −0.0655162 | + | 0.468422i | ||||
\(826\) | 14.1218 | 0.491361 | ||||||||
\(827\) | 36.7198 | − | 36.7198i | 1.27687 | − | 1.27687i | 0.334465 | − | 0.942408i | \(-0.391444\pi\) |
0.942408 | − | 0.334465i | \(-0.108556\pi\) | |||||||
\(828\) | 3.94919 | − | 18.5001i | 0.137244 | − | 0.642922i | ||||
\(829\) | 14.2972i | 0.496562i | 0.968688 | + | 0.248281i | \(0.0798657\pi\) | ||||
−0.968688 | + | 0.248281i | \(0.920134\pi\) | |||||||
\(830\) | 21.7414 | − | 14.0014i | 0.754656 | − | 0.485997i | ||||
\(831\) | −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 | ||||
\(835\) | −2.08438 | + | 9.62557i | −0.0721330 | + | 0.333107i | ||||
\(836\) | − | 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 | \(0.302844\pi\) | |||||||
\(840\) | 15.9377 | − | 18.5008i | 0.549903 | − | 0.638339i | ||||
\(841\) | 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 | ||||||||
\(845\) | −3.81826 | − | 5.92898i | −0.131352 | − | 0.203963i | ||||
\(846\) | −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 | ||||
\(850\) | 59.1016 | + | 26.8558i | 2.02717 | + | 0.921146i | ||||
\(851\) | − | 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 | \(-0.527729\pi\) |
0.996208 | + | 0.0870025i | \(0.0277288\pi\) | |||||||
\(854\) | −18.8504 | −0.645047 | ||||||||
\(855\) | −10.2763 | − | 4.63314i | −0.351443 | − | 0.158450i | ||||
\(856\) | 25.1234 | 0.858699 | ||||||||
\(857\) | −23.0711 | + | 23.0711i | −0.788092 | + | 0.788092i | −0.981181 | − | 0.193089i | \(-0.938149\pi\) |
0.193089 | + | 0.981181i | \(0.438149\pi\) | |||||||
\(858\) | 6.15368 | + | 20.8078i | 0.210083 | + | 0.710367i | ||||
\(859\) | 17.3242i | 0.591095i | 0.955328 | + | 0.295548i | \(0.0955021\pi\) | ||||
−0.955328 | + | 0.295548i | \(0.904498\pi\) | |||||||
\(860\) | −75.7946 | − | 16.4130i | −2.58457 | − | 0.559680i | ||||
\(861\) | −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 | \(-0.180083\pi\) |
−0.536046 | + | 0.844189i | \(0.680083\pi\) | |||||||
\(864\) | 28.1792 | − | 2.18064i | 0.958674 | − | 0.0741868i | ||||
\(865\) | 25.1229 | + | 5.44027i | 0.854204 | + | 0.184975i | ||||
\(866\) | 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 | ||||||||
\(870\) | −87.6773 | + | 6.52549i | −2.97254 | + | 0.221235i | ||||
\(871\) | −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 | ||||||||
\(875\) | 6.67471 | − | 8.96930i | 0.225646 | − | 0.303218i | ||||
\(876\) | −30.8863 | + | 56.8263i | −1.04355 | + | 1.91998i | ||||
\(877\) | 15.4630 | + | 15.4630i | 0.522148 | + | 0.522148i | 0.918220 | − | 0.396072i | \(-0.129627\pi\) |
−0.396072 | + | 0.918220i | \(0.629627\pi\) | |||||||
\(878\) | 53.1419 | + | 53.1419i | 1.79345 | + | 1.79345i | ||||
\(879\) | 10.0684 | − | 18.5243i | 0.339597 | − | 0.624810i | ||||
\(880\) | 13.4689 | + | 20.9146i | 0.454038 | + | 0.705029i | ||||
\(881\) | 3.93409i | 0.132543i | 0.997802 | + | 0.0662714i | \(0.0211103\pi\) | ||||
−0.997802 | + | 0.0662714i | \(0.978890\pi\) | |||||||
\(882\) | −7.46695 | − | 1.59396i | −0.251425 | − | 0.0536714i | ||||
\(883\) | 13.5688 | − | 13.5688i | 0.456625 | − | 0.456625i | −0.440921 | − | 0.897546i | \(-0.645348\pi\) |
0.897546 | + | 0.440921i | \(0.145348\pi\) | |||||||
\(884\) | 71.6713 | 2.41057 | ||||||||
\(885\) | 16.2817 | + | 14.0260i | 0.547304 | + | 0.471480i | ||||
\(886\) | 56.0200 | 1.88203 | ||||||||
\(887\) | −4.92491 | + | 4.92491i | −0.165362 | + | 0.165362i | −0.784937 | − | 0.619575i | \(-0.787305\pi\) |
0.619575 | + | 0.784937i | \(0.287305\pi\) | |||||||
\(888\) | 6.52168 | − | 1.92872i | 0.218853 | − | 0.0647235i | ||||
\(889\) | − | 20.1975i | − | 0.677401i | ||||||
\(890\) | −11.3250 | + | 52.2982i | −0.379614 | + | 1.75304i | ||||
\(891\) | 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 | ||||
\(895\) | 31.2035 | − | 20.0950i | 1.04302 | − | 0.671703i | ||||
\(896\) | 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 | ||||||||
\(900\) | 66.4201 | − | 9.94187i | 2.21400 | − | 0.331396i | ||||
\(901\) | 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 | ||||||||
\(905\) | −21.9075 | + | 14.1084i | −0.728229 | + | 0.468978i | ||||
\(906\) | −53.1809 | − | 28.9049i | −1.76682 | − | 0.960302i | ||||
\(907\) | −19.0317 | − | 19.0317i | −0.631938 | − | 0.631938i | 0.316616 | − | 0.948554i | \(-0.397453\pi\) |
−0.948554 | + | 0.316616i | \(0.897453\pi\) | |||||||
\(908\) | −38.9777 | − | 38.9777i | −1.29352 | − | 1.29352i | ||||
\(909\) | 1.65020 | + | 2.54594i | 0.0547336 | + | 0.0844436i | ||||
\(910\) | 3.77935 | − | 17.4529i | 0.125284 | − | 0.578557i | ||||
\(911\) | − | 17.7669i | − | 0.588644i | −0.955706 | − | 0.294322i | \(-0.904906\pi\) | ||
0.955706 | − | 0.294322i | \(-0.0950938\pi\) | |||||||
\(912\) | −19.7937 | + | 5.85377i | −0.655435 | + | 0.193838i | ||||
\(913\) | 5.04043 | − | 5.04043i | 0.166814 | − | 0.166814i | ||||
\(914\) | −74.2525 | −2.45605 | ||||||||
\(915\) | −21.7335 | − | 18.7225i | −0.718488 | − | 0.618947i | ||||
\(916\) | −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 | \(0.0447977\pi\) | ||||
−0.990113 | + | 0.140272i | \(0.955202\pi\) | |||||||
\(920\) | −10.7504 | − | 16.6932i | −0.354430 | − | 0.550359i | ||||
\(921\) | 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 | ||||
\(925\) | 2.91542 | − | 1.09368i | 0.0958586 | − | 0.0359601i | ||||
\(926\) | − | 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 | \(0.425385\pi\) | |||||||
\(930\) | −27.0156 | + | 2.01067i | −0.885876 | + | 0.0659324i | ||||
\(931\) | 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 | ||||||
\(935\) | 17.4890 | + | 3.78718i | 0.571952 | + | 0.123854i | ||||
\(936\) | 49.8054 | − | 32.2822i | 1.62794 | − | 1.05518i | ||||
\(937\) | 28.7165 | + | 28.7165i | 0.938127 | + | 0.938127i | 0.998194 | − | 0.0600678i | \(-0.0191317\pi\) |
−0.0600678 | + | 0.998194i | \(0.519132\pi\) | |||||||
\(938\) | 9.55009 | + | 9.55009i | 0.311821 | + | 0.311821i | ||||
\(939\) | 2.63804 | + | 1.43383i | 0.0860891 | + | 0.0467912i | ||||
\(940\) | −51.1112 | − | 11.0679i | −1.66706 | − | 0.360996i | ||||
\(941\) | 17.4001i | 0.567228i | 0.958939 | + | 0.283614i | \(0.0915335\pi\) | ||||
−0.958939 | + | 0.283614i | \(0.908467\pi\) | |||||||
\(942\) | −24.2586 | − | 82.0269i | −0.790387 | − | 2.67258i | ||||
\(943\) | −6.41619 | + | 6.41619i | −0.208940 | + | 0.208940i | ||||
\(944\) | 39.3508 | 1.28076 | ||||||||
\(945\) | −7.02585 | − | 9.25405i | −0.228551 | − | 0.301034i | ||||
\(946\) | −30.9259 | −1.00549 | ||||||||
\(947\) | 8.15693 | − | 8.15693i | 0.265065 | − | 0.265065i | −0.562043 | − | 0.827108i | \(-0.689985\pi\) |
0.827108 | + | 0.562043i | \(0.189985\pi\) | |||||||
\(948\) | 37.5138 | + | 126.848i | 1.21839 | + | 4.11982i | ||||
\(949\) | 26.1703i | 0.849522i | ||||||||
\(950\) | −20.0212 | + | 7.51069i | −0.649574 | + | 0.243679i | ||||
\(951\) | 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 | −0.955321 | − | 0.295569i | \(-0.904491\pi\) |
−0.295569 | − | 0.955321i | \(-0.595509\pi\) | |||||||
\(954\) | 25.6748 | − | 16.6416i | 0.831251 | − | 0.538790i | ||||
\(955\) | 15.5626 | + | 24.1656i | 0.503594 | + | 0.781981i | ||||
\(956\) | 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 | ||||||||
\(960\) | −0.860463 | + | 0.998844i | −0.0277713 | + | 0.0322375i | ||||
\(961\) | −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 | ||||||||
\(965\) | 5.39535 | − | 24.9155i | 0.173683 | − | 0.802058i | ||||
\(966\) | −2.96469 | + | 5.45461i | −0.0953874 | + | 0.175499i | ||||
\(967\) | −18.6836 | − | 18.6836i | −0.600824 | − | 0.600824i | 0.339707 | − | 0.940531i | \(-0.389672\pi\) |
−0.940531 | + | 0.339707i | \(0.889672\pi\) | |||||||
\(968\) | −38.0701 | − | 38.0701i | −1.22362 | − | 1.22362i | ||||
\(969\) | −7.09049 | + | 13.0455i | −0.227779 | + | 0.419081i | ||||
\(970\) | −29.7480 | + | 19.1577i | −0.955151 | + | 0.615115i | ||||
\(971\) | 57.4980i | 1.84520i | 0.385761 | + | 0.922599i | \(0.373939\pi\) | ||||
−0.385761 | + | 0.922599i | \(0.626061\pi\) | |||||||
\(972\) | 9.26098 | − | 69.1776i | 0.297046 | − | 2.21887i | ||||
\(973\) | −7.21569 | + | 7.21569i | −0.231324 | + | 0.231324i | ||||
\(974\) | −41.3622 | −1.32533 | ||||||||
\(975\) | 21.6919 | − | 16.3685i | 0.694696 | − | 0.524212i | ||||
\(976\) | −52.5270 | −1.68135 | ||||||||
\(977\) | 2.08515 | − | 2.08515i | 0.0667100 | − | 0.0667100i | −0.672965 | − | 0.739675i | \(-0.734979\pi\) |
0.739675 | + | 0.672965i | \(0.234979\pi\) | |||||||
\(978\) | 39.4896 | − | 11.6786i | 1.26274 | − | 0.373441i | ||||
\(979\) | 14.7501i | 0.471415i | ||||||||
\(980\) | −8.41719 | + | 5.42066i | −0.268877 | + | 0.173157i | ||||
\(981\) | 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 | \(-0.334286\pi\) |
−0.867519 | + | 0.497405i | \(0.834286\pi\) | |||||||
\(984\) | −61.8191 | − | 33.5999i | −1.97072 | − | 1.07113i | ||||
\(985\) | −12.5496 | + | 57.9532i | −0.399862 | + | 1.84654i | ||||
\(986\) | 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 | ||||||||
\(990\) | 25.0480 | − | 9.48056i | 0.796076 | − | 0.301312i | ||||
\(991\) | −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 | ||||||
\(995\) | 5.09371 | + | 7.90951i | 0.161481 | + | 0.250748i | ||||
\(996\) | −30.9612 | − | 16.8281i | −0.981044 | − | 0.533218i | ||||
\(997\) | 1.89647 | + | 1.89647i | 0.0600618 | + | 0.0600618i | 0.736500 | − | 0.676438i | \(-0.236477\pi\) |
−0.676438 | + | 0.736500i | \(0.736477\pi\) | |||||||
\(998\) | 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 | 105.2.j.a.92.12 | yes | 24 | |
3.2 | odd | 2 | inner | 105.2.j.a.92.1 | yes | 24 | |
5.2 | odd | 4 | 525.2.j.b.218.12 | 24 | |||
5.3 | odd | 4 | inner | 105.2.j.a.8.1 | ✓ | 24 | |
5.4 | even | 2 | 525.2.j.b.407.1 | 24 | |||
7.2 | even | 3 | 735.2.y.j.557.1 | 48 | |||
7.3 | odd | 6 | 735.2.y.g.422.12 | 48 | |||
7.4 | even | 3 | 735.2.y.j.422.12 | 48 | |||
7.5 | odd | 6 | 735.2.y.g.557.1 | 48 | |||
7.6 | odd | 2 | 735.2.j.h.197.12 | 24 | |||
15.2 | even | 4 | 525.2.j.b.218.1 | 24 | |||
15.8 | even | 4 | inner | 105.2.j.a.8.12 | yes | 24 | |
15.14 | odd | 2 | 525.2.j.b.407.12 | 24 | |||
21.2 | odd | 6 | 735.2.y.j.557.12 | 48 | |||
21.5 | even | 6 | 735.2.y.g.557.12 | 48 | |||
21.11 | odd | 6 | 735.2.y.j.422.1 | 48 | |||
21.17 | even | 6 | 735.2.y.g.422.1 | 48 | |||
21.20 | even | 2 | 735.2.j.h.197.1 | 24 | |||
35.3 | even | 12 | 735.2.y.g.128.12 | 48 | |||
35.13 | even | 4 | 735.2.j.h.638.1 | 24 | |||
35.18 | odd | 12 | 735.2.y.j.128.12 | 48 | |||
35.23 | odd | 12 | 735.2.y.j.263.1 | 48 | |||
35.33 | even | 12 | 735.2.y.g.263.1 | 48 | |||
105.23 | even | 12 | 735.2.y.j.263.12 | 48 | |||
105.38 | odd | 12 | 735.2.y.g.128.1 | 48 | |||
105.53 | even | 12 | 735.2.y.j.128.1 | 48 | |||
105.68 | odd | 12 | 735.2.y.g.263.12 | 48 | |||
105.83 | odd | 4 | 735.2.j.h.638.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.j.a.8.1 | ✓ | 24 | 5.3 | odd | 4 | inner | |
105.2.j.a.8.12 | yes | 24 | 15.8 | even | 4 | inner | |
105.2.j.a.92.1 | yes | 24 | 3.2 | odd | 2 | inner | |
105.2.j.a.92.12 | yes | 24 | 1.1 | even | 1 | trivial | |
525.2.j.b.218.1 | 24 | 15.2 | even | 4 | |||
525.2.j.b.218.12 | 24 | 5.2 | odd | 4 | |||
525.2.j.b.407.1 | 24 | 5.4 | even | 2 | |||
525.2.j.b.407.12 | 24 | 15.14 | odd | 2 | |||
735.2.j.h.197.1 | 24 | 21.20 | even | 2 | |||
735.2.j.h.197.12 | 24 | 7.6 | odd | 2 | |||
735.2.j.h.638.1 | 24 | 35.13 | even | 4 | |||
735.2.j.h.638.12 | 24 | 105.83 | odd | 4 | |||
735.2.y.g.128.1 | 48 | 105.38 | odd | 12 | |||
735.2.y.g.128.12 | 48 | 35.3 | even | 12 | |||
735.2.y.g.263.1 | 48 | 35.33 | even | 12 | |||
735.2.y.g.263.12 | 48 | 105.68 | odd | 12 | |||
735.2.y.g.422.1 | 48 | 21.17 | even | 6 | |||
735.2.y.g.422.12 | 48 | 7.3 | odd | 6 | |||
735.2.y.g.557.1 | 48 | 7.5 | odd | 6 | |||
735.2.y.g.557.12 | 48 | 21.5 | even | 6 | |||
735.2.y.j.128.1 | 48 | 105.53 | even | 12 | |||
735.2.y.j.128.12 | 48 | 35.18 | odd | 12 | |||
735.2.y.j.263.1 | 48 | 35.23 | odd | 12 | |||
735.2.y.j.263.12 | 48 | 105.23 | even | 12 | |||
735.2.y.j.422.1 | 48 | 21.11 | odd | 6 | |||
735.2.y.j.422.12 | 48 | 7.4 | even | 3 | |||
735.2.y.j.557.1 | 48 | 7.2 | even | 3 | |||
735.2.y.j.557.12 | 48 | 21.2 | odd | 6 |