Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(491,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.q (of order \(6\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 491.10 | ||
Character | \(\chi\) | \(=\) | 637.491 |
Dual form | 637.2.q.j.589.10 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.489742 | − | 0.282753i | 0.346300 | − | 0.199936i | −0.316754 | − | 0.948508i | \(-0.602593\pi\) |
0.663054 | + | 0.748571i | \(0.269260\pi\) | |||||||
\(3\) | 1.54556 | + | 2.67698i | 0.892328 | + | 1.54556i | 0.837077 | + | 0.547085i | \(0.184262\pi\) |
0.0552505 | + | 0.998473i | \(0.482404\pi\) | |||||||
\(4\) | −0.840102 | + | 1.45510i | −0.420051 | + | 0.727550i | ||||
\(5\) | − | 1.80514i | − | 0.807283i | −0.914917 | − | 0.403642i | \(-0.867744\pi\) | ||
0.914917 | − | 0.403642i | \(-0.132256\pi\) | |||||||
\(6\) | 1.51385 | + | 0.874021i | 0.618026 | + | 0.356818i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.08118i | 0.735806i | ||||||||
\(9\) | −3.27749 | + | 5.67679i | −1.09250 | + | 1.89226i | ||||
\(10\) | −0.510408 | − | 0.884053i | −0.161405 | − | 0.279562i | ||||
\(11\) | 3.10412 | − | 1.79216i | 0.935927 | − | 0.540358i | 0.0472456 | − | 0.998883i | \(-0.484956\pi\) |
0.888681 | + | 0.458526i | \(0.151622\pi\) | |||||||
\(12\) | −5.19370 | −1.49929 | ||||||||
\(13\) | −0.328042 | + | 3.59060i | −0.0909825 | + | 0.995852i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.83233 | − | 2.78995i | 1.24770 | − | 0.720361i | ||||
\(16\) | −1.09175 | − | 1.89096i | −0.272936 | − | 0.472740i | ||||
\(17\) | −3.07459 | + | 5.32535i | −0.745699 | + | 1.29159i | 0.204169 | + | 0.978936i | \(0.434551\pi\) |
−0.949868 | + | 0.312652i | \(0.898783\pi\) | |||||||
\(18\) | 3.70688i | 0.873720i | ||||||||
\(19\) | −2.17438 | − | 1.25538i | −0.498836 | − | 0.288003i | 0.229397 | − | 0.973333i | \(-0.426325\pi\) |
−0.728233 | + | 0.685330i | \(0.759658\pi\) | |||||||
\(20\) | 2.62666 | + | 1.51650i | 0.587339 | + | 0.339100i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.01348 | − | 1.75540i | 0.216074 | − | 0.374252i | ||||
\(23\) | 2.06593 | + | 3.57829i | 0.430775 | + | 0.746125i | 0.996940 | − | 0.0781674i | \(-0.0249069\pi\) |
−0.566165 | + | 0.824292i | \(0.691574\pi\) | |||||||
\(24\) | −5.57127 | + | 3.21657i | −1.13723 | + | 0.656581i | ||||
\(25\) | 1.74147 | 0.348294 | ||||||||
\(26\) | 0.854595 | + | 1.85122i | 0.167600 | + | 0.363054i | ||||
\(27\) | −10.9889 | −2.11481 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.55567 | − | 4.42655i | −0.474576 | − | 0.821989i | 0.525001 | − | 0.851102i | \(-0.324065\pi\) |
−0.999576 | + | 0.0291130i | \(0.990732\pi\) | |||||||
\(30\) | 1.57773 | − | 2.73271i | 0.288053 | − | 0.498922i | ||||
\(31\) | − | 4.55318i | − | 0.817775i | −0.912585 | − | 0.408888i | \(-0.865917\pi\) | ||
0.912585 | − | 0.408888i | \(-0.134083\pi\) | |||||||
\(32\) | −4.67405 | − | 2.69856i | −0.826263 | − | 0.477043i | ||||
\(33\) | 9.59518 | + | 5.53978i | 1.67031 | + | 0.964352i | ||||
\(34\) | 3.47740i | 0.596369i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.50686 | − | 9.53816i | −0.917809 | − | 1.58969i | ||||
\(37\) | 10.1511 | − | 5.86074i | 1.66883 | − | 0.963500i | 0.700561 | − | 0.713592i | \(-0.252933\pi\) |
0.968270 | − | 0.249908i | \(-0.0804004\pi\) | |||||||
\(38\) | −1.41984 | −0.230329 | ||||||||
\(39\) | −10.1190 | + | 4.67131i | −1.62033 | + | 0.748008i | ||||
\(40\) | 3.75681 | 0.594004 | ||||||||
\(41\) | 1.61635 | − | 0.933202i | 0.252432 | − | 0.145742i | −0.368445 | − | 0.929649i | \(-0.620110\pi\) |
0.620877 | + | 0.783908i | \(0.286777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.711568 | + | 1.23247i | −0.108513 | + | 0.187950i | −0.915168 | − | 0.403072i | \(-0.867942\pi\) |
0.806655 | + | 0.591023i | \(0.201276\pi\) | |||||||
\(44\) | 6.02240i | 0.907911i | ||||||||
\(45\) | 10.2474 | + | 5.91634i | 1.52759 | + | 0.881955i | ||||
\(46\) | 2.02354 | + | 1.16829i | 0.298355 | + | 0.172255i | ||||
\(47\) | 8.86595i | 1.29323i | 0.762816 | + | 0.646616i | \(0.223816\pi\) | ||||
−0.762816 | + | 0.646616i | \(0.776184\pi\) | |||||||
\(48\) | 3.37471 | − | 5.84517i | 0.487098 | − | 0.843678i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.852870 | − | 0.492405i | 0.120614 | − | 0.0696366i | ||||
\(51\) | −19.0078 | −2.66163 | ||||||||
\(52\) | −4.94909 | − | 3.49380i | −0.686315 | − | 0.484503i | ||||
\(53\) | 2.02920 | 0.278732 | 0.139366 | − | 0.990241i | \(-0.455494\pi\) | ||||
0.139366 | + | 0.990241i | \(0.455494\pi\) | |||||||
\(54\) | −5.38171 | + | 3.10713i | −0.732358 | + | 0.422827i | ||||
\(55\) | −3.23511 | − | 5.60337i | −0.436222 | − | 0.755558i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.76102i | − | 1.02797i | ||||||
\(58\) | −2.50324 | − | 1.44524i | −0.328691 | − | 0.189770i | ||||
\(59\) | −7.88734 | − | 4.55376i | −1.02684 | − | 0.592849i | −0.110766 | − | 0.993847i | \(-0.535330\pi\) |
−0.916079 | + | 0.400997i | \(0.868664\pi\) | |||||||
\(60\) | 9.37536i | 1.21035i | ||||||||
\(61\) | 2.73920 | − | 4.74444i | 0.350719 | − | 0.607463i | −0.635656 | − | 0.771972i | \(-0.719271\pi\) |
0.986376 | + | 0.164509i | \(0.0526038\pi\) | |||||||
\(62\) | −1.28742 | − | 2.22988i | −0.163503 | − | 0.283195i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.31488 | 0.164360 | ||||||||
\(65\) | 6.48153 | + | 0.592162i | 0.803935 | + | 0.0734486i | ||||
\(66\) | 6.26555 | 0.771236 | ||||||||
\(67\) | 6.07998 | − | 3.51028i | 0.742788 | − | 0.428849i | −0.0802944 | − | 0.996771i | \(-0.525586\pi\) |
0.823082 | + | 0.567923i | \(0.192253\pi\) | |||||||
\(68\) | −5.16594 | − | 8.94768i | −0.626463 | − | 1.08507i | ||||
\(69\) | −6.38601 | + | 11.0609i | −0.768785 | + | 1.33158i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.89200 | + | 2.24705i | 0.461896 | + | 0.266676i | 0.712841 | − | 0.701326i | \(-0.247408\pi\) |
−0.250945 | + | 0.968001i | \(0.580741\pi\) | |||||||
\(72\) | −11.8144 | − | 6.82104i | −1.39234 | − | 0.803867i | ||||
\(73\) | 9.35564i | 1.09499i | 0.836807 | + | 0.547497i | \(0.184419\pi\) | ||||
−0.836807 | + | 0.547497i | \(0.815581\pi\) | |||||||
\(74\) | 3.31428 | − | 5.74050i | 0.385277 | − | 0.667320i | ||||
\(75\) | 2.69154 | + | 4.66188i | 0.310792 | + | 0.538308i | ||||
\(76\) | 3.65339 | − | 2.10929i | 0.419073 | − | 0.241952i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.63486 | + | 5.14890i | −0.411567 | + | 0.582999i | ||||
\(79\) | 5.20970 | 0.586137 | 0.293069 | − | 0.956091i | \(-0.405324\pi\) | ||||
0.293069 | + | 0.956091i | \(0.405324\pi\) | |||||||
\(80\) | −3.41345 | + | 1.97075i | −0.381635 | + | 0.220337i | ||||
\(81\) | −7.15145 | − | 12.3867i | −0.794605 | − | 1.37630i | ||||
\(82\) | 0.527731 | − | 0.914056i | 0.0582781 | − | 0.100941i | ||||
\(83\) | − | 9.42491i | − | 1.03452i | −0.855829 | − | 0.517259i | \(-0.826952\pi\) | ||
0.855829 | − | 0.517259i | \(-0.173048\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.61301 | + | 5.55007i | 1.04268 | + | 0.601990i | ||||
\(86\) | 0.804791i | 0.0867829i | ||||||||
\(87\) | 7.89986 | − | 13.6830i | 0.846954 | − | 1.46697i | ||||
\(88\) | 3.72981 | + | 6.46021i | 0.397599 | + | 0.688661i | ||||
\(89\) | 0.308000 | − | 0.177824i | 0.0326479 | − | 0.0188493i | −0.483587 | − | 0.875296i | \(-0.660666\pi\) |
0.516235 | + | 0.856447i | \(0.327333\pi\) | |||||||
\(90\) | 6.69144 | 0.705340 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.94235 | −0.723790 | ||||||||
\(93\) | 12.1888 | − | 7.03720i | 1.26392 | − | 0.729723i | ||||
\(94\) | 2.50687 | + | 4.34203i | 0.258564 | + | 0.447846i | ||||
\(95\) | −2.26613 | + | 3.92505i | −0.232500 | + | 0.402702i | ||||
\(96\) | − | 16.6831i | − | 1.70272i | ||||||
\(97\) | 9.18293 | + | 5.30176i | 0.932385 | + | 0.538313i | 0.887565 | − | 0.460682i | \(-0.152395\pi\) |
0.0448198 | + | 0.998995i | \(0.485729\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 23.4952i | 2.36136i | ||||||||
\(100\) | −1.46301 | + | 2.53401i | −0.146301 | + | 0.253401i | ||||
\(101\) | 1.71254 | + | 2.96620i | 0.170404 | + | 0.295148i | 0.938561 | − | 0.345113i | \(-0.112159\pi\) |
−0.768157 | + | 0.640261i | \(0.778826\pi\) | |||||||
\(102\) | −9.30894 | + | 5.37452i | −0.921722 | + | 0.532157i | ||||
\(103\) | 12.9558 | 1.27658 | 0.638288 | − | 0.769798i | \(-0.279643\pi\) | ||||
0.638288 | + | 0.769798i | \(0.279643\pi\) | |||||||
\(104\) | −7.47266 | − | 0.682713i | −0.732755 | − | 0.0669455i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.993783 | − | 0.573761i | 0.0965248 | − | 0.0557286i | ||||
\(107\) | 9.08482 | + | 15.7354i | 0.878263 | + | 1.52120i | 0.853246 | + | 0.521508i | \(0.174630\pi\) |
0.0250164 | + | 0.999687i | \(0.492036\pi\) | |||||||
\(108\) | 9.23177 | − | 15.9899i | 0.888328 | − | 1.53863i | ||||
\(109\) | − | 13.9294i | − | 1.33420i | −0.744970 | − | 0.667098i | \(-0.767536\pi\) | ||
0.744970 | − | 0.667098i | \(-0.232464\pi\) | |||||||
\(110\) | −3.16873 | − | 1.82947i | −0.302127 | − | 0.174433i | ||||
\(111\) | 31.3782 | + | 18.1162i | 2.97829 | + | 1.71952i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.06404 | − | 8.77118i | 0.476385 | − | 0.825123i | −0.523249 | − | 0.852180i | \(-0.675280\pi\) |
0.999634 | + | 0.0270569i | \(0.00861353\pi\) | |||||||
\(114\) | −2.19445 | − | 3.80090i | −0.205529 | − | 0.355987i | ||||
\(115\) | 6.45931 | − | 3.72928i | 0.602334 | − | 0.347758i | ||||
\(116\) | 8.58808 | 0.797383 | ||||||||
\(117\) | −19.3079 | − | 13.6304i | −1.78502 | − | 1.26013i | ||||
\(118\) | −5.15035 | −0.474128 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.80637 | + | 10.0569i | 0.530047 | + | 0.918068i | ||||
\(121\) | 0.923697 | − | 1.59989i | 0.0839725 | − | 0.145445i | ||||
\(122\) | − | 3.09807i | − | 0.280486i | ||||||
\(123\) | 4.99633 | + | 2.88463i | 0.450504 | + | 0.260099i | ||||
\(124\) | 6.62533 | + | 3.82513i | 0.594972 | + | 0.343507i | ||||
\(125\) | − | 12.1693i | − | 1.08845i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.05109 | + | 5.28465i | 0.270741 | + | 0.468937i | 0.969052 | − | 0.246858i | \(-0.0793980\pi\) |
−0.698311 | + | 0.715795i | \(0.746065\pi\) | |||||||
\(128\) | 9.99205 | − | 5.76891i | 0.883181 | − | 0.509905i | ||||
\(129\) | −4.39908 | −0.387317 | ||||||||
\(130\) | 3.34171 | − | 1.54266i | 0.293088 | − | 0.135301i | ||||
\(131\) | −5.97266 | −0.521833 | −0.260917 | − | 0.965361i | \(-0.584025\pi\) | ||||
−0.260917 | + | 0.965361i | \(0.584025\pi\) | |||||||
\(132\) | −16.1219 | + | 9.30796i | −1.40323 | + | 0.810154i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.98508 | − | 3.43826i | 0.171485 | − | 0.297020i | ||||
\(135\) | 19.8365i | 1.70725i | ||||||||
\(136\) | −11.0830 | − | 6.39877i | −0.950359 | − | 0.548690i | ||||
\(137\) | −3.12407 | − | 1.80368i | −0.266907 | − | 0.154099i | 0.360574 | − | 0.932731i | \(-0.382581\pi\) |
−0.627481 | + | 0.778632i | \(0.715914\pi\) | |||||||
\(138\) | 7.22265i | 0.614833i | ||||||||
\(139\) | 6.45833 | − | 11.1862i | 0.547789 | − | 0.948798i | −0.450637 | − | 0.892707i | \(-0.648803\pi\) |
0.998426 | − | 0.0560906i | \(-0.0178636\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −23.7340 | + | 13.7028i | −1.99876 | + | 1.15399i | ||||
\(142\) | 2.54144 | 0.213273 | ||||||||
\(143\) | 5.41665 | + | 11.7335i | 0.452963 | + | 0.981208i | ||||
\(144\) | 14.3128 | 1.19273 | ||||||||
\(145\) | −7.99054 | + | 4.61334i | −0.663578 | + | 0.383117i | ||||
\(146\) | 2.64533 | + | 4.58185i | 0.218929 | + | 0.379197i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 19.6945i | 1.61888i | ||||||||
\(149\) | 1.90020 | + | 1.09708i | 0.155670 | + | 0.0898763i | 0.575812 | − | 0.817582i | \(-0.304686\pi\) |
−0.420141 | + | 0.907459i | \(0.638019\pi\) | |||||||
\(150\) | 2.63632 | + | 1.52208i | 0.215255 | + | 0.124277i | ||||
\(151\) | 1.94893i | 0.158602i | 0.996851 | + | 0.0793009i | \(0.0252688\pi\) | ||||
−0.996851 | + | 0.0793009i | \(0.974731\pi\) | |||||||
\(152\) | 2.61266 | − | 4.52526i | 0.211915 | − | 0.367047i | ||||
\(153\) | −20.1539 | − | 34.9076i | −1.62935 | − | 2.82211i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.21913 | −0.660176 | ||||||||
\(156\) | 1.70375 | − | 18.6485i | 0.136409 | − | 1.49307i | ||||
\(157\) | −18.3508 | −1.46455 | −0.732275 | − | 0.681009i | \(-0.761541\pi\) | ||||
−0.732275 | + | 0.681009i | \(0.761541\pi\) | |||||||
\(158\) | 2.55141 | − | 1.47306i | 0.202979 | − | 0.117190i | ||||
\(159\) | 3.13624 | + | 5.43213i | 0.248720 | + | 0.430796i | ||||
\(160\) | −4.87128 | + | 8.43731i | −0.385109 | + | 0.667028i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.00473 | − | 4.04418i | −0.550344 | − | 0.317741i | ||||
\(163\) | −19.1044 | − | 11.0299i | −1.49637 | − | 0.863931i | −0.496380 | − | 0.868105i | \(-0.665338\pi\) |
−0.999991 | + | 0.00417469i | \(0.998671\pi\) | |||||||
\(164\) | 3.13594i | 0.244876i | ||||||||
\(165\) | 10.0001 | − | 17.3206i | 0.778505 | − | 1.34841i | ||||
\(166\) | −2.66492 | − | 4.61578i | −0.206838 | − | 0.358254i | ||||
\(167\) | −2.45846 | + | 1.41939i | −0.190241 | + | 0.109836i | −0.592096 | − | 0.805868i | \(-0.701699\pi\) |
0.401854 | + | 0.915704i | \(0.368366\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7848 | − | 2.35573i | −0.983444 | − | 0.181210i | ||||
\(170\) | 6.27719 | 0.481439 | ||||||||
\(171\) | 14.2530 | − | 8.22898i | 1.08995 | − | 0.629286i | ||||
\(172\) | −1.19558 | − | 2.07080i | −0.0911621 | − | 0.157897i | ||||
\(173\) | 1.76411 | − | 3.05553i | 0.134123 | − | 0.232308i | −0.791139 | − | 0.611636i | \(-0.790512\pi\) |
0.925262 | + | 0.379329i | \(0.123845\pi\) | |||||||
\(174\) | − | 8.93483i | − | 0.677347i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.77781 | − | 3.91317i | −0.510897 | − | 0.294967i | ||||
\(177\) | − | 28.1524i | − | 2.11606i | ||||||
\(178\) | 0.100560 | − | 0.174176i | 0.00753732 | − | 0.0130550i | ||||
\(179\) | −3.34735 | − | 5.79778i | −0.250193 | − | 0.433346i | 0.713386 | − | 0.700771i | \(-0.247161\pi\) |
−0.963579 | + | 0.267425i | \(0.913827\pi\) | |||||||
\(180\) | −17.2177 | + | 9.94065i | −1.28333 | + | 0.740932i | ||||
\(181\) | 12.5317 | 0.931476 | 0.465738 | − | 0.884923i | \(-0.345789\pi\) | ||||
0.465738 | + | 0.884923i | \(0.345789\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.9344 | 1.25183 | ||||||||
\(184\) | −7.44704 | + | 4.29955i | −0.549003 | + | 0.316967i | ||||
\(185\) | −10.5795 | − | 18.3242i | −0.777817 | − | 1.34722i | ||||
\(186\) | 3.97957 | − | 6.89282i | 0.291797 | − | 0.505406i | ||||
\(187\) | 22.0407i | 1.61178i | ||||||||
\(188\) | −12.9008 | − | 7.44830i | −0.940890 | − | 0.543223i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.56302i | 0.185941i | ||||||||
\(191\) | −1.51821 | + | 2.62961i | −0.109854 | + | 0.190272i | −0.915711 | − | 0.401838i | \(-0.868372\pi\) |
0.805857 | + | 0.592110i | \(0.201705\pi\) | |||||||
\(192\) | 2.03222 | + | 3.51991i | 0.146663 | + | 0.254028i | ||||
\(193\) | −23.3350 | + | 13.4725i | −1.67969 | + | 0.969769i | −0.717833 | + | 0.696215i | \(0.754866\pi\) |
−0.961857 | + | 0.273554i | \(0.911801\pi\) | |||||||
\(194\) | 5.99635 | 0.430513 | ||||||||
\(195\) | 8.43237 | + | 18.2662i | 0.603855 | + | 1.30807i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.05315 | + | 4.64949i | −0.573763 | + | 0.331262i | −0.758651 | − | 0.651497i | \(-0.774141\pi\) |
0.184888 | + | 0.982760i | \(0.440808\pi\) | |||||||
\(198\) | 6.64333 | + | 11.5066i | 0.472121 | + | 0.817738i | ||||
\(199\) | 8.69242 | − | 15.0557i | 0.616190 | − | 1.06727i | −0.373985 | − | 0.927435i | \(-0.622009\pi\) |
0.990175 | − | 0.139837i | \(-0.0446578\pi\) | |||||||
\(200\) | 3.62430i | 0.256277i | ||||||||
\(201\) | 18.7939 | + | 10.8507i | 1.32562 | + | 0.765347i | ||||
\(202\) | 1.67740 | + | 0.968450i | 0.118022 | + | 0.0681399i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 15.9685 | − | 27.6583i | 1.11802 | − | 1.93647i | ||||
\(205\) | −1.68456 | − | 2.91774i | −0.117655 | − | 0.203784i | ||||
\(206\) | 6.34501 | − | 3.66329i | 0.442078 | − | 0.255234i | ||||
\(207\) | −27.0842 | −1.88248 | ||||||||
\(208\) | 7.14781 | − | 3.29971i | 0.495612 | − | 0.228793i | ||||
\(209\) | −8.99936 | −0.622499 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.9118 | − | 18.8998i | −0.751199 | − | 1.30112i | −0.947242 | − | 0.320520i | \(-0.896142\pi\) |
0.196042 | − | 0.980595i | \(-0.437191\pi\) | |||||||
\(212\) | −1.70473 | + | 2.95268i | −0.117082 | + | 0.202791i | ||||
\(213\) | 13.8918i | 0.951849i | ||||||||
\(214\) | 8.89844 | + | 5.13751i | 0.608285 | + | 0.351193i | ||||
\(215\) | 2.22479 | + | 1.28448i | 0.151729 | + | 0.0876009i | ||||
\(216\) | − | 22.8698i | − | 1.55609i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.93858 | − | 6.82182i | −0.266754 | − | 0.462032i | ||||
\(219\) | −25.0449 | + | 14.4597i | −1.69238 | + | 0.977094i | ||||
\(220\) | 10.8713 | 0.732941 | ||||||||
\(221\) | −18.1126 | − | 12.7866i | −1.21839 | − | 0.860118i | ||||
\(222\) | 20.4896 | 1.37517 | ||||||||
\(223\) | 1.65573 | − | 0.955937i | 0.110876 | − | 0.0640143i | −0.443536 | − | 0.896256i | \(-0.646276\pi\) |
0.554413 | + | 0.832242i | \(0.312943\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.70765 | + | 9.88594i | −0.380510 | + | 0.659063i | ||||
\(226\) | − | 5.72749i | − | 0.380987i | ||||||
\(227\) | −8.95012 | − | 5.16735i | −0.594040 | − | 0.342969i | 0.172653 | − | 0.984983i | \(-0.444766\pi\) |
−0.766693 | + | 0.642013i | \(0.778099\pi\) | |||||||
\(228\) | 11.2931 | + | 6.52005i | 0.747901 | + | 0.431801i | ||||
\(229\) | 6.10394i | 0.403360i | 0.979451 | + | 0.201680i | \(0.0646401\pi\) | ||||
−0.979451 | + | 0.201680i | \(0.935360\pi\) | |||||||
\(230\) | 2.10893 | − | 3.65278i | 0.139059 | − | 0.240857i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.21242 | − | 5.31879i | 0.604825 | − | 0.349196i | ||||
\(233\) | −7.12776 | −0.466955 | −0.233478 | − | 0.972362i | \(-0.575011\pi\) | ||||
−0.233478 | + | 0.972362i | \(0.575011\pi\) | |||||||
\(234\) | −13.3099 | − | 1.21601i | −0.870096 | − | 0.0794932i | ||||
\(235\) | 16.0043 | 1.04400 | ||||||||
\(236\) | 13.2523 | − | 7.65124i | 0.862654 | − | 0.498054i | ||||
\(237\) | 8.05189 | + | 13.9463i | 0.523027 | + | 0.905909i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.32349i | − | 0.473717i | −0.971544 | − | 0.236859i | \(-0.923882\pi\) | ||
0.971544 | − | 0.236859i | \(-0.0761178\pi\) | |||||||
\(240\) | −10.5514 | − | 6.09183i | −0.681087 | − | 0.393226i | ||||
\(241\) | 0.227850 | + | 0.131549i | 0.0146771 | + | 0.00847383i | 0.507321 | − | 0.861757i | \(-0.330636\pi\) |
−0.492643 | + | 0.870231i | \(0.663969\pi\) | |||||||
\(242\) | − | 1.04471i | − | 0.0671566i | ||||||
\(243\) | 5.62264 | − | 9.73869i | 0.360692 | − | 0.624737i | ||||
\(244\) | 4.60242 | + | 7.97163i | 0.294640 | + | 0.510331i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.26255 | 0.208013 | ||||||||
\(247\) | 5.22084 | − | 7.39549i | 0.332194 | − | 0.470564i | ||||
\(248\) | 9.47596 | 0.601724 | ||||||||
\(249\) | 25.2303 | − | 14.5667i | 1.59891 | − | 0.923130i | ||||
\(250\) | −3.44090 | − | 5.95982i | −0.217622 | − | 0.376932i | ||||
\(251\) | −6.64096 | + | 11.5025i | −0.419173 | + | 0.726030i | −0.995857 | − | 0.0909383i | \(-0.971013\pi\) |
0.576683 | + | 0.816968i | \(0.304347\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.8257 | + | 7.40495i | 0.806348 | + | 0.465545i | ||||
\(254\) | 2.98850 | + | 1.72541i | 0.187515 | + | 0.108262i | ||||
\(255\) | 34.3118i | 2.14869i | ||||||||
\(256\) | 1.94747 | − | 3.37312i | 0.121717 | − | 0.210820i | ||||
\(257\) | −8.70718 | − | 15.0813i | −0.543139 | − | 0.940745i | −0.998721 | − | 0.0505509i | \(-0.983902\pi\) |
0.455582 | − | 0.890194i | \(-0.349431\pi\) | |||||||
\(258\) | −2.15441 | + | 1.24385i | −0.134128 | + | 0.0774388i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.30680 | + | 8.93379i | −0.391131 | + | 0.554050i | ||||
\(261\) | 33.5047 | 2.07389 | ||||||||
\(262\) | −2.92506 | + | 1.68878i | −0.180711 | + | 0.104333i | ||||
\(263\) | 6.36382 | + | 11.0225i | 0.392410 | + | 0.679674i | 0.992767 | − | 0.120058i | \(-0.0383081\pi\) |
−0.600357 | + | 0.799732i | \(0.704975\pi\) | |||||||
\(264\) | −11.5293 | + | 19.9693i | −0.709577 | + | 1.22902i | ||||
\(265\) | − | 3.66299i | − | 0.225015i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.952063 | + | 0.549674i | 0.0582653 | + | 0.0336395i | ||||
\(268\) | 11.7960i | 0.720553i | ||||||||
\(269\) | 1.08082 | − | 1.87203i | 0.0658985 | − | 0.114140i | −0.831194 | − | 0.555983i | \(-0.812342\pi\) |
0.897092 | + | 0.441843i | \(0.145675\pi\) | |||||||
\(270\) | 5.60881 | + | 9.71475i | 0.341341 | + | 0.591221i | ||||
\(271\) | −5.04864 | + | 2.91483i | −0.306683 | + | 0.177063i | −0.645441 | − | 0.763810i | \(-0.723326\pi\) |
0.338758 | + | 0.940873i | \(0.389993\pi\) | |||||||
\(272\) | 13.4267 | 0.814113 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.03999 | −0.123240 | ||||||||
\(275\) | 5.40572 | − | 3.12100i | 0.325977 | − | 0.188203i | ||||
\(276\) | −10.7298 | − | 18.5846i | −0.645858 | − | 1.11866i | ||||
\(277\) | −5.82366 | + | 10.0869i | −0.349910 | + | 0.606062i | −0.986233 | − | 0.165361i | \(-0.947121\pi\) |
0.636323 | + | 0.771423i | \(0.280455\pi\) | |||||||
\(278\) | − | 7.30445i | − | 0.438092i | ||||||
\(279\) | 25.8474 | + | 14.9230i | 1.54744 | + | 0.893418i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.7940i | − | 1.47908i | −0.673110 | − | 0.739542i | \(-0.735042\pi\) | ||
0.673110 | − | 0.739542i | \(-0.264958\pi\) | |||||||
\(282\) | −7.74903 | + | 13.4217i | −0.461448 | + | 0.799251i | ||||
\(283\) | 7.57162 | + | 13.1144i | 0.450086 | + | 0.779572i | 0.998391 | − | 0.0567067i | \(-0.0180600\pi\) |
−0.548305 | + | 0.836279i | \(0.684727\pi\) | |||||||
\(284\) | −6.53936 | + | 3.77550i | −0.388040 | + | 0.224035i | ||||
\(285\) | −14.0097 | −0.829865 | ||||||||
\(286\) | 5.97045 | + | 4.21483i | 0.353040 | + | 0.249228i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 30.6383 | − | 17.6890i | 1.80538 | − | 1.04234i | ||||
\(289\) | −10.4063 | − | 18.0242i | −0.612133 | − | 1.06025i | ||||
\(290\) | −2.60887 | + | 4.51869i | −0.153198 | + | 0.265347i | ||||
\(291\) | 32.7767i | 1.92141i | ||||||||
\(292\) | −13.6134 | − | 7.85969i | −0.796663 | − | 0.459954i | ||||
\(293\) | −21.5816 | − | 12.4601i | −1.26081 | − | 0.727929i | −0.287579 | − | 0.957757i | \(-0.592851\pi\) |
−0.973231 | + | 0.229827i | \(0.926184\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.22018 | + | 14.2378i | −0.478597 | + | 0.828955i | ||||
\(296\) | 12.1972 | + | 21.1262i | 0.708950 | + | 1.22794i | ||||
\(297\) | −34.1107 | + | 19.6939i | −1.97931 | + | 1.14275i | ||||
\(298\) | 1.24081 | 0.0718782 | ||||||||
\(299\) | −13.5259 | + | 6.24408i | −0.782223 | + | 0.361104i | ||||
\(300\) | −9.04467 | −0.522194 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.551066 | + | 0.954474i | 0.0317103 | + | 0.0549238i | ||||
\(303\) | −5.29365 | + | 9.16888i | −0.304112 | + | 0.526738i | ||||
\(304\) | 5.48221i | 0.314426i | ||||||||
\(305\) | −8.56438 | − | 4.94465i | −0.490395 | − | 0.283130i | ||||
\(306\) | −19.7404 | − | 11.3972i | −1.12849 | − | 0.651532i | ||||
\(307\) | 3.90158i | 0.222675i | 0.993783 | + | 0.111337i | \(0.0355134\pi\) | ||||
−0.993783 | + | 0.111337i | \(0.964487\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.0240 | + | 34.6825i | 1.13912 | + | 1.97302i | ||||
\(310\) | −4.02525 | + | 2.32398i | −0.228619 | + | 0.131993i | ||||
\(311\) | −19.7180 | −1.11810 | −0.559052 | − | 0.829132i | \(-0.688835\pi\) | ||||
−0.559052 | + | 0.829132i | \(0.688835\pi\) | |||||||
\(312\) | −9.72181 | − | 21.0594i | −0.550389 | − | 1.19225i | ||||
\(313\) | 2.89235 | 0.163485 | 0.0817427 | − | 0.996653i | \(-0.473951\pi\) | ||||
0.0817427 | + | 0.996653i | \(0.473951\pi\) | |||||||
\(314\) | −8.98714 | + | 5.18873i | −0.507173 | + | 0.292817i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.37668 | + | 7.58063i | −0.246207 | + | 0.426444i | ||||
\(317\) | 15.9537i | 0.896046i | 0.894022 | + | 0.448023i | \(0.147872\pi\) | ||||
−0.894022 | + | 0.448023i | \(0.852128\pi\) | |||||||
\(318\) | 3.07190 | + | 1.77356i | 0.172263 | + | 0.0994564i | ||||
\(319\) | −15.8662 | − | 9.16035i | −0.888336 | − | 0.512881i | ||||
\(320\) | − | 2.37354i | − | 0.132685i | ||||||
\(321\) | −28.0822 | + | 48.6398i | −1.56740 | + | 2.71481i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.3706 | − | 7.71955i | 0.743963 | − | 0.429527i | ||||
\(324\) | 24.0318 | 1.33510 | ||||||||
\(325\) | −0.571275 | + | 6.25291i | −0.0316886 | + | 0.346849i | ||||
\(326\) | −12.4750 | −0.690924 | ||||||||
\(327\) | 37.2888 | − | 21.5287i | 2.06208 | − | 1.19054i | ||||
\(328\) | 1.94216 | + | 3.36391i | 0.107238 | + | 0.185741i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 11.3102i | − | 0.622606i | ||||||
\(331\) | 3.31409 | + | 1.91339i | 0.182159 | + | 0.105169i | 0.588307 | − | 0.808638i | \(-0.299795\pi\) |
−0.406148 | + | 0.913807i | \(0.633128\pi\) | |||||||
\(332\) | 13.7142 | + | 7.91789i | 0.752664 | + | 0.434551i | ||||
\(333\) | 76.8342i | 4.21049i | ||||||||
\(334\) | −0.802674 | + | 1.39027i | −0.0439204 | + | 0.0760723i | ||||
\(335\) | −6.33654 | − | 10.9752i | −0.346202 | − | 0.599640i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.78172 | 0.532844 | 0.266422 | − | 0.963856i | \(-0.414158\pi\) | ||||
0.266422 | + | 0.963856i | \(0.414158\pi\) | |||||||
\(338\) | −6.92733 | + | 2.46123i | −0.376797 | + | 0.133873i | ||||
\(339\) | 31.3071 | 1.70037 | ||||||||
\(340\) | −16.1518 | + | 9.32525i | −0.875955 | + | 0.505733i | ||||
\(341\) | −8.16004 | − | 14.1336i | −0.441891 | − | 0.765378i | ||||
\(342\) | 4.65353 | − | 8.06015i | 0.251634 | − | 0.435843i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.56499 | − | 1.48090i | −0.138295 | − | 0.0798447i | ||||
\(345\) | 19.9665 | + | 11.5276i | 1.07496 | + | 0.620628i | ||||
\(346\) | − | 1.99523i | − | 0.107264i | ||||||
\(347\) | −2.66702 | + | 4.61941i | −0.143173 | + | 0.247983i | −0.928690 | − | 0.370857i | \(-0.879064\pi\) |
0.785517 | + | 0.618840i | \(0.212397\pi\) | |||||||
\(348\) | 13.2734 | + | 22.9902i | 0.711527 | + | 1.23240i | ||||
\(349\) | 12.7332 | − | 7.35149i | 0.681590 | − | 0.393516i | −0.118864 | − | 0.992911i | \(-0.537925\pi\) |
0.800454 | + | 0.599394i | \(0.204592\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.60481 | − | 39.4566i | 0.192411 | − | 2.10604i | ||||
\(352\) | −19.3451 | −1.03110 | ||||||||
\(353\) | 30.7588 | − | 17.7586i | 1.63713 | − | 0.945196i | 0.655313 | − | 0.755357i | \(-0.272537\pi\) |
0.981815 | − | 0.189839i | \(-0.0607966\pi\) | |||||||
\(354\) | −7.96016 | − | 13.7874i | −0.423078 | − | 0.732792i | ||||
\(355\) | 4.05624 | − | 7.02561i | 0.215283 | − | 0.372881i | ||||
\(356\) | 0.597560i | 0.0316706i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.27867 | − | 1.89294i | −0.173283 | − | 0.100045i | ||||
\(359\) | 15.9147i | 0.839945i | 0.907537 | + | 0.419972i | \(0.137960\pi\) | ||||
−0.907537 | + | 0.419972i | \(0.862040\pi\) | |||||||
\(360\) | −12.3129 | + | 21.3266i | −0.648948 | + | 1.12401i | ||||
\(361\) | −6.34806 | − | 10.9952i | −0.334108 | − | 0.578693i | ||||
\(362\) | 6.13731 | − | 3.54338i | 0.322570 | − | 0.186236i | ||||
\(363\) | 5.71051 | 0.299724 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.8882 | 0.883971 | ||||||||
\(366\) | 8.29348 | − | 4.78824i | 0.433507 | − | 0.250286i | ||||
\(367\) | 9.12231 | + | 15.8003i | 0.476181 | + | 0.824769i | 0.999628 | − | 0.0272893i | \(-0.00868752\pi\) |
−0.523447 | + | 0.852058i | \(0.675354\pi\) | |||||||
\(368\) | 4.51093 | − | 7.81316i | 0.235149 | − | 0.407289i | ||||
\(369\) | 12.2343i | 0.636890i | ||||||||
\(370\) | −10.3624 | − | 5.98274i | −0.538716 | − | 0.311028i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 23.6479i | 1.22608i | ||||||||
\(373\) | 6.78720 | − | 11.7558i | 0.351428 | − | 0.608691i | −0.635072 | − | 0.772453i | \(-0.719030\pi\) |
0.986500 | + | 0.163762i | \(0.0523629\pi\) | |||||||
\(374\) | 6.23207 | + | 10.7943i | 0.322252 | + | 0.558158i | ||||
\(375\) | 32.5770 | − | 18.8083i | 1.68227 | − | 0.971259i | ||||
\(376\) | −18.4516 | −0.951568 | ||||||||
\(377\) | 16.7323 | − | 7.72428i | 0.861758 | − | 0.397821i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.26632 | + | 3.61786i | −0.321879 | + | 0.185837i | −0.652230 | − | 0.758021i | \(-0.726166\pi\) |
0.330351 | + | 0.943858i | \(0.392833\pi\) | |||||||
\(380\) | −3.80756 | − | 6.59489i | −0.195324 | − | 0.338311i | ||||
\(381\) | −9.43128 | + | 16.3355i | −0.483179 | + | 0.836891i | ||||
\(382\) | 1.71711i | 0.0878549i | ||||||||
\(383\) | −17.6205 | − | 10.1732i | −0.900367 | − | 0.519827i | −0.0230476 | − | 0.999734i | \(-0.507337\pi\) |
−0.877319 | + | 0.479907i | \(0.840670\pi\) | |||||||
\(384\) | 30.8866 | + | 17.8324i | 1.57617 | + | 0.910004i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.61875 | + | 13.1961i | −0.387784 | + | 0.671662i | ||||
\(387\) | −4.66432 | − | 8.07884i | −0.237101 | − | 0.410671i | ||||
\(388\) | −15.4292 | + | 8.90804i | −0.783298 | + | 0.452237i | ||||
\(389\) | −2.48306 | −0.125896 | −0.0629481 | − | 0.998017i | \(-0.520050\pi\) | ||||
−0.0629481 | + | 0.998017i | \(0.520050\pi\) | |||||||
\(390\) | 9.29450 | + | 6.56144i | 0.470645 | + | 0.332251i | ||||
\(391\) | −25.4075 | −1.28491 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.23108 | − | 15.9887i | −0.465646 | − | 0.806523i | ||||
\(394\) | −2.62931 | + | 4.55410i | −0.132463 | + | 0.229432i | ||||
\(395\) | − | 9.40424i | − | 0.473179i | ||||||
\(396\) | −34.1879 | − | 19.7384i | −1.71800 | − | 0.991890i | ||||
\(397\) | −9.30034 | − | 5.36955i | −0.466771 | − | 0.269490i | 0.248116 | − | 0.968730i | \(-0.420188\pi\) |
−0.714887 | + | 0.699240i | \(0.753522\pi\) | |||||||
\(398\) | − | 9.83122i | − | 0.492795i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.90124 | − | 3.29305i | −0.0950621 | − | 0.164652i | ||||
\(401\) | 12.7773 | − | 7.37698i | 0.638068 | − | 0.368389i | −0.145802 | − | 0.989314i | \(-0.546576\pi\) |
0.783870 | + | 0.620925i | \(0.213243\pi\) | |||||||
\(402\) | 12.2722 | 0.612083 | ||||||||
\(403\) | 16.3486 | + | 1.49363i | 0.814383 | + | 0.0744032i | ||||
\(404\) | −5.75483 | −0.286313 | ||||||||
\(405\) | −22.3597 | + | 12.9094i | −1.11106 | + | 0.641472i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.0068 | − | 36.3849i | 1.04127 | − | 1.80353i | ||||
\(408\) | − | 39.5586i | − | 1.95844i | ||||||
\(409\) | 5.49448 | + | 3.17224i | 0.271685 | + | 0.156857i | 0.629653 | − | 0.776877i | \(-0.283197\pi\) |
−0.357968 | + | 0.933734i | \(0.616530\pi\) | |||||||
\(410\) | −1.65000 | − | 0.952628i | −0.0814877 | − | 0.0470469i | ||||
\(411\) | − | 11.1508i | − | 0.550028i | ||||||
\(412\) | −10.8842 | + | 18.8520i | −0.536227 | + | 0.928772i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −13.2643 | + | 7.65814i | −0.651904 | + | 0.376377i | ||||
\(415\) | −17.0133 | −0.835150 | ||||||||
\(416\) | 11.2227 | − | 15.8974i | 0.550240 | − | 0.779433i | ||||
\(417\) | 39.9269 | 1.95523 | ||||||||
\(418\) | −4.40736 | + | 2.54459i | −0.215571 | + | 0.124460i | ||||
\(419\) | −9.04253 | − | 15.6621i | −0.441756 | − | 0.765144i | 0.556064 | − | 0.831140i | \(-0.312311\pi\) |
−0.997820 | + | 0.0659953i | \(0.978978\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 19.7043i | − | 0.960327i | −0.877179 | − | 0.480164i | \(-0.840577\pi\) | ||
0.877179 | − | 0.480164i | \(-0.159423\pi\) | |||||||
\(422\) | −10.6879 | − | 6.17068i | −0.520281 | − | 0.300384i | ||||
\(423\) | −50.3301 | − | 29.0581i | −2.44713 | − | 1.41285i | ||||
\(424\) | 4.22312i | 0.205093i | ||||||||
\(425\) | −5.35431 | + | 9.27394i | −0.259722 | + | 0.449852i | ||||
\(426\) | 3.92794 | + | 6.80338i | 0.190309 | + | 0.329625i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −30.5287 | −1.47566 | ||||||||
\(429\) | −23.0387 | + | 32.6352i | −1.11232 | + | 1.57564i | ||||
\(430\) | 1.45276 | 0.0700584 | ||||||||
\(431\) | −9.09662 | + | 5.25193i | −0.438169 | + | 0.252977i | −0.702820 | − | 0.711367i | \(-0.748076\pi\) |
0.264652 | + | 0.964344i | \(0.414743\pi\) | |||||||
\(432\) | 11.9971 | + | 20.7795i | 0.577209 | + | 0.999755i | ||||
\(433\) | −4.55903 | + | 7.89646i | −0.219093 | + | 0.379480i | −0.954531 | − | 0.298112i | \(-0.903643\pi\) |
0.735438 | + | 0.677592i | \(0.236976\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −24.6997 | − | 14.2604i | −1.18426 | − | 0.683732i | ||||
\(436\) | 20.2687 | + | 11.7021i | 0.970694 | + | 0.560430i | ||||
\(437\) | − | 10.3741i | − | 0.496258i | ||||||
\(438\) | −8.17703 | + | 14.1630i | −0.390713 | + | 0.676735i | ||||
\(439\) | 14.6400 | + | 25.3573i | 0.698731 | + | 1.21024i | 0.968907 | + | 0.247427i | \(0.0795851\pi\) |
−0.270175 | + | 0.962811i | \(0.587082\pi\) | |||||||
\(440\) | 11.6616 | − | 6.73282i | 0.555944 | − | 0.320975i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.4859 | − | 1.14073i | −0.593896 | − | 0.0542591i | ||||
\(443\) | −26.7353 | −1.27023 | −0.635117 | − | 0.772416i | \(-0.719048\pi\) | ||||
−0.635117 | + | 0.772416i | \(0.719048\pi\) | |||||||
\(444\) | −52.7218 | + | 30.4389i | −2.50207 | + | 1.44457i | ||||
\(445\) | −0.320997 | − | 0.555983i | −0.0152167 | − | 0.0263561i | ||||
\(446\) | 0.540588 | − | 0.936325i | 0.0255976 | − | 0.0443363i | ||||
\(447\) | 6.78240i | 0.320797i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.3732 | − | 10.6077i | −0.867083 | − | 0.500611i | −0.000705260 | − | 1.00000i | \(-0.500224\pi\) |
−0.866378 | + | 0.499389i | \(0.833558\pi\) | |||||||
\(450\) | 6.45542i | 0.304311i | ||||||||
\(451\) | 3.34490 | − | 5.79354i | 0.157505 | − | 0.272807i | ||||
\(452\) | 8.50862 | + | 14.7374i | 0.400212 | + | 0.693187i | ||||
\(453\) | −5.21726 | + | 3.01219i | −0.245128 | + | 0.141525i | ||||
\(454\) | −5.84433 | −0.274288 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 16.1521 | 0.756389 | ||||||||
\(457\) | −12.6826 | + | 7.32231i | −0.593267 | + | 0.342523i | −0.766388 | − | 0.642377i | \(-0.777948\pi\) |
0.173121 | + | 0.984901i | \(0.444615\pi\) | |||||||
\(458\) | 1.72591 | + | 2.98936i | 0.0806463 | + | 0.139684i | ||||
\(459\) | 33.7863 | − | 58.5196i | 1.57701 | − | 2.73146i | ||||
\(460\) | 12.5319i | 0.584304i | ||||||||
\(461\) | −21.5594 | − | 12.4473i | −1.00412 | − | 0.579729i | −0.0946548 | − | 0.995510i | \(-0.530175\pi\) |
−0.909464 | + | 0.415782i | \(0.863508\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.1069i | 0.469706i | 0.972031 | + | 0.234853i | \(0.0754608\pi\) | ||||
−0.972031 | + | 0.234853i | \(0.924539\pi\) | |||||||
\(464\) | −5.58028 | + | 9.66533i | −0.259058 | + | 0.448701i | ||||
\(465\) | −12.7031 | − | 22.0025i | −0.589094 | − | 1.02034i | ||||
\(466\) | −3.49076 | + | 2.01539i | −0.161706 | + | 0.0933613i | ||||
\(467\) | −11.4825 | −0.531346 | −0.265673 | − | 0.964063i | \(-0.585594\pi\) | ||||
−0.265673 | + | 0.964063i | \(0.585594\pi\) | |||||||
\(468\) | 36.0542 | − | 16.6440i | 1.66660 | − | 0.769369i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.83797 | − | 4.52525i | 0.361539 | − | 0.208734i | ||||
\(471\) | −28.3621 | − | 49.1247i | −1.30686 | − | 2.26354i | ||||
\(472\) | 9.47717 | − | 16.4149i | 0.436222 | − | 0.755559i | ||||
\(473\) | 5.10099i | 0.234544i | ||||||||
\(474\) | 7.88670 | + | 4.55339i | 0.362248 | + | 0.209144i | ||||
\(475\) | −3.78661 | − | 2.18620i | −0.173741 | − | 0.100310i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.65068 | + | 11.5193i | −0.304514 | + | 0.527433i | ||||
\(478\) | −2.07074 | − | 3.58662i | −0.0947133 | − | 0.164048i | ||||
\(479\) | 0.936316 | − | 0.540582i | 0.0427814 | − | 0.0246998i | −0.478457 | − | 0.878111i | \(-0.658804\pi\) |
0.521238 | + | 0.853411i | \(0.325470\pi\) | |||||||
\(480\) | −30.1154 | −1.37457 | ||||||||
\(481\) | 17.7136 | + | 38.3711i | 0.807670 | + | 1.74957i | ||||
\(482\) | 0.148784 | 0.00677691 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.55200 | + | 2.68814i | 0.0705454 | + | 0.122188i | ||||
\(485\) | 9.57043 | − | 16.5765i | 0.434571 | − | 0.752699i | ||||
\(486\) | − | 6.35926i | − | 0.288462i | ||||||
\(487\) | 21.8824 | + | 12.6338i | 0.991588 | + | 0.572493i | 0.905748 | − | 0.423816i | \(-0.139310\pi\) |
0.0858391 | + | 0.996309i | \(0.472643\pi\) | |||||||
\(488\) | 9.87401 | + | 5.70076i | 0.446976 | + | 0.258061i | ||||
\(489\) | − | 68.1895i | − | 3.08364i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.8590 | + | 36.1289i | 0.941355 | + | 1.63047i | 0.762891 | + | 0.646527i | \(0.223779\pi\) |
0.178464 | + | 0.983946i | \(0.442887\pi\) | |||||||
\(492\) | −8.39485 | + | 4.84677i | −0.378469 | + | 0.218509i | ||||
\(493\) | 31.4306 | 1.41556 | ||||||||
\(494\) | 0.465769 | − | 5.09809i | 0.0209559 | − | 0.229374i | ||||
\(495\) | 42.4122 | 1.90628 | ||||||||
\(496\) | −8.60988 | + | 4.97091i | −0.386595 | + | 0.223201i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.23757 | − | 14.2679i | 0.369134 | − | 0.639360i | ||||
\(499\) | − | 10.4684i | − | 0.468628i | −0.972161 | − | 0.234314i | \(-0.924716\pi\) | ||
0.972161 | − | 0.234314i | \(-0.0752844\pi\) | |||||||
\(500\) | 17.7075 | + | 10.2234i | 0.791905 | + | 0.457206i | ||||
\(501\) | −7.59938 | − | 4.38750i | −0.339515 | − | 0.196019i | ||||
\(502\) | 7.51099i | 0.335232i | ||||||||
\(503\) | −1.28735 | + | 2.22976i | −0.0574001 | + | 0.0994199i | −0.893298 | − | 0.449466i | \(-0.851614\pi\) |
0.835897 | + | 0.548886i | \(0.184948\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.35441 | − | 3.09137i | 0.238268 | − | 0.137564i | ||||
\(506\) | 8.37508 | 0.372318 | ||||||||
\(507\) | −13.4533 | − | 37.8656i | −0.597484 | − | 1.68167i | ||||
\(508\) | −10.2529 | −0.454900 | ||||||||
\(509\) | 6.51841 | − | 3.76340i | 0.288923 | − | 0.166810i | −0.348533 | − | 0.937297i | \(-0.613320\pi\) |
0.637456 | + | 0.770487i | \(0.279987\pi\) | |||||||
\(510\) | 9.70176 | + | 16.8039i | 0.429601 | + | 0.744091i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.8730i | 0.922467i | ||||||||
\(513\) | 23.8939 | + | 13.7952i | 1.05494 | + | 0.609072i | ||||
\(514\) | −8.52855 | − | 4.92396i | −0.376178 | − | 0.217187i | ||||
\(515\) | − | 23.3871i | − | 1.03056i | ||||||
\(516\) | 3.69567 | − | 6.40109i | 0.162693 | − | 0.281792i | ||||
\(517\) | 15.8892 | + | 27.5210i | 0.698807 | + | 1.21037i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.9061 | 0.478726 | ||||||||
\(520\) | −1.23239 | + | 13.4892i | −0.0540440 | + | 0.591541i | ||||
\(521\) | 0.0156677 | 0.000686413 | 0.000343207 | − | 1.00000i | \(-0.499891\pi\) | ||||
0.000343207 | 1.00000i | \(0.499891\pi\) | ||||||||
\(522\) | 16.4087 | − | 9.47355i | 0.718188 | − | 0.414646i | ||||
\(523\) | −12.0357 | − | 20.8465i | −0.526286 | − | 0.911554i | −0.999531 | − | 0.0306229i | \(-0.990251\pi\) |
0.473245 | − | 0.880931i | \(-0.343082\pi\) | |||||||
\(524\) | 5.01764 | − | 8.69081i | 0.219197 | − | 0.379660i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.23326 | + | 3.59878i | 0.271783 | + | 0.156914i | ||||
\(527\) | 24.2473 | + | 13.9992i | 1.05623 | + | 0.609814i | ||||
\(528\) | − | 24.1921i | − | 1.05283i | ||||||
\(529\) | 2.96391 | − | 5.13363i | 0.128865 | − | 0.223202i | ||||
\(530\) | −1.03572 | − | 1.79392i | −0.0449888 | − | 0.0779228i | ||||
\(531\) | 51.7014 | − | 29.8498i | 2.24365 | − | 1.29537i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.82052 | + | 6.10980i | 0.122170 | + | 0.264645i | ||||
\(534\) | 0.621687 | 0.0269030 | ||||||||
\(535\) | 28.4045 | − | 16.3994i | 1.22804 | − | 0.709007i | ||||
\(536\) | 7.30550 | + | 12.6535i | 0.315550 | + | 0.546548i | ||||
\(537\) | 10.3470 | − | 17.9216i | 0.446508 | − | 0.773374i | ||||
\(538\) | − | 1.22241i | − | 0.0527020i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −28.8640 | − | 16.6646i | −1.24211 | − | 0.717132i | ||||
\(541\) | 37.7763i | 1.62413i | 0.583567 | + | 0.812065i | \(0.301656\pi\) | ||||
−0.583567 | + | 0.812065i | \(0.698344\pi\) | |||||||
\(542\) | −1.64835 | + | 2.85503i | −0.0708028 | + | 0.122634i | ||||
\(543\) | 19.3685 | + | 33.5472i | 0.831182 | + | 1.43965i | ||||
\(544\) | 28.7416 | − | 16.5940i | 1.23229 | − | 0.711461i | ||||
\(545\) | −25.1445 | −1.07707 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.4925 | 1.21825 | 0.609126 | − | 0.793074i | \(-0.291521\pi\) | ||||
0.609126 | + | 0.793074i | \(0.291521\pi\) | |||||||
\(548\) | 5.24908 | − | 3.03056i | 0.224229 | − | 0.129459i | ||||
\(549\) | 17.9554 | + | 31.0998i | 0.766320 | + | 1.32731i | ||||
\(550\) | 1.76494 | − | 3.05697i | 0.0752573 | − | 0.130349i | ||||
\(551\) | 12.8333i | 0.546717i | ||||||||
\(552\) | −23.0197 | − | 13.2904i | −0.979782 | − | 0.565677i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.58663i | 0.279839i | ||||||||
\(555\) | 32.7023 | − | 56.6421i | 1.38814 | − | 2.40432i | ||||
\(556\) | 10.8513 | + | 18.7950i | 0.460198 | + | 0.797087i | ||||
\(557\) | −17.2033 | + | 9.93232i | −0.728927 | + | 0.420846i | −0.818029 | − | 0.575177i | \(-0.804933\pi\) |
0.0891028 | + | 0.996022i | \(0.471600\pi\) | |||||||
\(558\) | 16.8781 | 0.714507 | ||||||||
\(559\) | −4.19189 | − | 2.95926i | −0.177298 | − | 0.125163i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −59.0026 | + | 34.0652i | −2.49109 | + | 1.43823i | ||||
\(562\) | −7.01056 | − | 12.1427i | −0.295723 | − | 0.512207i | ||||
\(563\) | −7.76983 | + | 13.4577i | −0.327459 | + | 0.567176i | −0.982007 | − | 0.188844i | \(-0.939526\pi\) |
0.654548 | + | 0.756021i | \(0.272859\pi\) | |||||||
\(564\) | − | 46.0471i | − | 1.93893i | ||||||
\(565\) | −15.8332 | − | 9.14131i | −0.666108 | − | 0.384578i | ||||
\(566\) | 7.41628 | + | 4.28179i | 0.311729 | + | 0.179977i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.67650 | + | 8.09994i | −0.196222 | + | 0.339866i | ||||
\(569\) | −15.5544 | − | 26.9410i | −0.652075 | − | 1.12943i | −0.982618 | − | 0.185637i | \(-0.940565\pi\) |
0.330543 | − | 0.943791i | \(-0.392768\pi\) | |||||||
\(570\) | −6.86116 | + | 3.96129i | −0.287382 | + | 0.165920i | ||||
\(571\) | 0.602653 | 0.0252202 | 0.0126101 | − | 0.999920i | \(-0.495986\pi\) | ||||
0.0126101 | + | 0.999920i | \(0.495986\pi\) | |||||||
\(572\) | −21.6240 | − | 1.97560i | −0.904145 | − | 0.0826040i | ||||
\(573\) | −9.38590 | −0.392102 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.59774 | + | 6.23148i | 0.150036 | + | 0.259871i | ||||
\(576\) | −4.30951 | + | 7.46429i | −0.179563 | + | 0.311012i | ||||
\(577\) | − | 5.21634i | − | 0.217159i | −0.994088 | − | 0.108580i | \(-0.965370\pi\) | ||
0.994088 | − | 0.108580i | \(-0.0346302\pi\) | |||||||
\(578\) | −10.1928 | − | 5.88479i | −0.423963 | − | 0.244775i | ||||
\(579\) | −72.1311 | − | 41.6449i | −2.99767 | − | 1.73070i | ||||
\(580\) | − | 15.5027i | − | 0.643714i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9.26771 | + | 16.0521i | 0.384159 | + | 0.665383i | ||||
\(583\) | 6.29887 | − | 3.63665i | 0.260872 | − | 0.150615i | ||||
\(584\) | −19.4707 | −0.805704 | ||||||||
\(585\) | −24.6048 | + | 34.8535i | −1.01728 | + | 1.44101i | ||||
\(586\) | −14.0926 | −0.582158 | ||||||||
\(587\) | 14.8865 | − | 8.59475i | 0.614433 | − | 0.354743i | −0.160265 | − | 0.987074i | \(-0.551235\pi\) |
0.774699 | + | 0.632331i | \(0.217902\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.71595 | + | 9.90032i | −0.235522 | + | 0.407936i | ||||
\(590\) | 9.29711i | 0.382756i | ||||||||
\(591\) | −24.8932 | − | 14.3721i | −1.02397 | − | 0.591189i | ||||
\(592\) | −22.1648 | − | 12.7969i | −0.910970 | − | 0.525949i | ||||
\(593\) | 10.6452i | 0.437147i | 0.975820 | + | 0.218574i | \(0.0701404\pi\) | ||||
−0.975820 | + | 0.218574i | \(0.929860\pi\) | |||||||
\(594\) | −11.1370 | + | 19.2898i | −0.456956 | + | 0.791471i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.19272 | + | 1.84332i | −0.130779 | + | 0.0755053i | ||||
\(597\) | 53.7385 | 2.19937 | ||||||||
\(598\) | −4.85867 | + | 6.88247i | −0.198686 | + | 0.281445i | ||||
\(599\) | 25.1472 | 1.02749 | 0.513744 | − | 0.857944i | \(-0.328258\pi\) | ||||
0.513744 | + | 0.857944i | \(0.328258\pi\) | |||||||
\(600\) | −9.70219 | + | 5.60156i | −0.396090 | + | 0.228683i | ||||
\(601\) | 1.62334 | + | 2.81170i | 0.0662172 | + | 0.114692i | 0.897233 | − | 0.441557i | \(-0.145574\pi\) |
−0.831016 | + | 0.556248i | \(0.812240\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 46.0196i | 1.87406i | ||||||||
\(604\) | −2.83589 | − | 1.63730i | −0.115391 | − | 0.0666208i | ||||
\(605\) | −2.88803 | − | 1.66740i | −0.117415 | − | 0.0677896i | ||||
\(606\) | 5.98718i | 0.243213i | ||||||||
\(607\) | −8.55622 | + | 14.8198i | −0.347286 | + | 0.601517i | −0.985766 | − | 0.168121i | \(-0.946230\pi\) |
0.638480 | + | 0.769638i | \(0.279563\pi\) | |||||||
\(608\) | 6.77543 | + | 11.7354i | 0.274780 | + | 0.475933i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.59245 | −0.226432 | ||||||||
\(611\) | −31.8341 | − | 2.90840i | −1.28787 | − | 0.117661i | ||||
\(612\) | 67.7254 | 2.73764 | ||||||||
\(613\) | 24.2857 | − | 14.0214i | 0.980891 | − | 0.566318i | 0.0783519 | − | 0.996926i | \(-0.475034\pi\) |
0.902539 | + | 0.430608i | \(0.141701\pi\) | |||||||
\(614\) | 1.10318 | + | 1.91077i | 0.0445208 | + | 0.0771122i | ||||
\(615\) | 5.20717 | − | 9.01908i | 0.209973 | − | 0.363684i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.4533 | − | 21.0463i | −1.46755 | − | 0.847293i | −0.468214 | − | 0.883615i | \(-0.655102\pi\) |
−0.999340 | + | 0.0363226i | \(0.988436\pi\) | |||||||
\(618\) | 19.6132 | + | 11.3237i | 0.788957 | + | 0.455504i | ||||
\(619\) | 27.1308i | 1.09048i | 0.838280 | + | 0.545239i | \(0.183561\pi\) | ||||
−0.838280 | + | 0.545239i | \(0.816439\pi\) | |||||||
\(620\) | 6.90490 | − | 11.9596i | 0.277308 | − | 0.480311i | ||||
\(621\) | −22.7022 | − | 39.3213i | −0.911007 | − | 1.57791i | ||||
\(622\) | −9.65673 | + | 5.57531i | −0.387200 | + | 0.223550i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 19.8806 | + | 14.0347i | 0.795861 | + | 0.561837i | ||||
\(625\) | −13.2599 | −0.530398 | ||||||||
\(626\) | 1.41651 | − | 0.817820i | 0.0566150 | − | 0.0326867i | ||||
\(627\) | −13.9090 | − | 24.0911i | −0.555473 | − | 0.962107i | ||||
\(628\) | 15.4165 | − | 26.7022i | 0.615185 | − | 1.06553i | ||||
\(629\) | 72.0776i | 2.87392i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.8647 | + | 8.00476i | 0.551943 | + | 0.318665i | 0.749905 | − | 0.661545i | \(-0.230099\pi\) |
−0.197962 | + | 0.980210i | \(0.563432\pi\) | |||||||
\(632\) | 10.8423i | 0.431284i | ||||||||
\(633\) | 33.7296 | − | 58.4214i | 1.34063 | − | 2.32204i | ||||
\(634\) | 4.51094 | + | 7.81317i | 0.179152 | + | 0.310301i | ||||
\(635\) | 9.53954 | − | 5.50765i | 0.378565 | − | 0.218565i | ||||
\(636\) | −10.5390 | −0.417900 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10.3604 | −0.410174 | ||||||||
\(639\) | −25.5120 | + | 14.7294i | −1.00924 | + | 0.582685i | ||||
\(640\) | −10.4137 | − | 18.0370i | −0.411637 | − | 0.712977i | ||||
\(641\) | −7.34069 | + | 12.7145i | −0.289940 | + | 0.502191i | −0.973795 | − | 0.227427i | \(-0.926969\pi\) |
0.683855 | + | 0.729618i | \(0.260302\pi\) | |||||||
\(642\) | 31.7613i | 1.25352i | ||||||||
\(643\) | 32.1673 | + | 18.5718i | 1.26855 | + | 0.732399i | 0.974714 | − | 0.223456i | \(-0.0717338\pi\) |
0.293839 | + | 0.955855i | \(0.405067\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.94095i | 0.312675i | ||||||||
\(646\) | 4.36545 | − | 7.56117i | 0.171756 | − | 0.297490i | ||||
\(647\) | 7.11422 | + | 12.3222i | 0.279689 | + | 0.484435i | 0.971307 | − | 0.237828i | \(-0.0764354\pi\) |
−0.691619 | + | 0.722263i | \(0.743102\pi\) | |||||||
\(648\) | 25.7788 | − | 14.8834i | 1.01269 | − | 0.584676i | ||||
\(649\) | −32.6443 | −1.28140 | ||||||||
\(650\) | 1.48825 | + | 3.22384i | 0.0583740 | + | 0.126450i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32.0993 | − | 18.5325i | 1.25710 | − | 0.725790i | ||||
\(653\) | 10.9227 | + | 18.9188i | 0.427440 | + | 0.740348i | 0.996645 | − | 0.0818478i | \(-0.0260821\pi\) |
−0.569205 | + | 0.822196i | \(0.692749\pi\) | |||||||
\(654\) | 12.1746 | − | 21.0870i | 0.476064 | − | 0.824568i | ||||
\(655\) | 10.7815i | 0.421267i | ||||||||
\(656\) | −3.52929 | − | 2.03764i | −0.137796 | − | 0.0795564i | ||||
\(657\) | −53.1100 | − | 30.6631i | −2.07202 | − | 1.19628i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.5525 | + | 28.6698i | −0.644796 | + | 1.11682i | 0.339553 | + | 0.940587i | \(0.389724\pi\) |
−0.984349 | + | 0.176232i | \(0.943609\pi\) | |||||||
\(660\) | 16.8022 | + | 29.1022i | 0.654024 | + | 1.13280i | ||||
\(661\) | 20.2155 | − | 11.6714i | 0.786290 | − | 0.453965i | −0.0523646 | − | 0.998628i | \(-0.516676\pi\) |
0.838655 | + | 0.544663i | \(0.183342\pi\) | |||||||
\(662\) | 2.16406 | 0.0841087 | ||||||||
\(663\) | 6.23537 | − | 68.2495i | 0.242162 | − | 2.65059i | ||||
\(664\) | 19.6149 | 0.761206 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 21.7251 | + | 37.6289i | 0.841829 | + | 1.45809i | ||||
\(667\) | 10.5596 | − | 18.2898i | 0.408871 | − | 0.708185i | ||||
\(668\) | − | 4.76974i | − | 0.184547i | ||||||
\(669\) | 5.11806 | + | 2.95491i | 0.197876 | + | 0.114243i | ||||
\(670\) | −6.20654 | − | 3.58335i | −0.239780 | − | 0.138437i | ||||
\(671\) | − | 19.6364i | − | 0.758055i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.2424 | − | 41.9890i | −0.934474 | − | 1.61856i | −0.775569 | − | 0.631263i | \(-0.782537\pi\) |
−0.158906 | − | 0.987294i | \(-0.550797\pi\) | |||||||
\(674\) | 4.79052 | − | 2.76581i | 0.184524 | − | 0.106535i | ||||
\(675\) | −19.1368 | −0.736575 | ||||||||
\(676\) | 14.1683 | − | 16.6241i | 0.544936 | − | 0.639387i | ||||
\(677\) | −43.8976 | −1.68712 | −0.843560 | − | 0.537034i | \(-0.819545\pi\) | ||||
−0.843560 | + | 0.537034i | \(0.819545\pi\) | |||||||
\(678\) | 15.3324 | − | 8.85216i | 0.588837 | − | 0.339965i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −11.5507 | + | 20.0064i | −0.442948 | + | 0.767209i | ||||
\(681\) | − | 31.9458i | − | 1.22416i | ||||||
\(682\) | −7.99263 | − | 4.61455i | −0.306054 | − | 0.176700i | ||||
\(683\) | −38.9086 | − | 22.4639i | −1.48880 | − | 0.859558i | −0.488879 | − | 0.872351i | \(-0.662594\pi\) |
−0.999918 | + | 0.0127938i | \(0.995927\pi\) | |||||||
\(684\) | 27.6527i | 1.05733i | ||||||||
\(685\) | −3.25590 | + | 5.63939i | −0.124402 | + | 0.215470i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.3402 | + | 9.43400i | −0.623416 | + | 0.359929i | ||||
\(688\) | 3.10741 | 0.118469 | ||||||||
\(689\) | −0.665662 | + | 7.28603i | −0.0253597 | + | 0.277576i | ||||
\(690\) | 13.0379 | 0.496344 | ||||||||
\(691\) | 39.3602 | − | 22.7246i | 1.49733 | − | 0.864486i | 0.497339 | − | 0.867556i | \(-0.334311\pi\) |
0.999995 | + | 0.00306990i | \(0.000977182\pi\) | |||||||
\(692\) | 2.96406 | + | 5.13391i | 0.112677 | + | 0.195162i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.01643i | 0.114502i | ||||||||
\(695\) | −20.1926 | − | 11.6582i | −0.765949 | − | 0.442221i | ||||
\(696\) | 28.4766 | + | 16.4410i | 1.07940 | + | 0.623194i | ||||
\(697\) | 11.4769i | 0.434717i | ||||||||
\(698\) | 4.15731 | − | 7.20067i | 0.157356 | − | 0.272549i | ||||
\(699\) | −11.0164 | − | 19.0809i | −0.416677 | − | 0.721706i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.7914 | 1.08744 | 0.543718 | − | 0.839268i | \(-0.317016\pi\) | ||||
0.543718 | + | 0.839268i | \(0.317016\pi\) | |||||||
\(702\) | −9.39104 | − | 20.3428i | −0.354442 | − | 0.767791i | ||||
\(703\) | −29.4298 | −1.10996 | ||||||||
\(704\) | 4.08154 | − | 2.35648i | 0.153829 | − | 0.0888131i | ||||
\(705\) | 24.7355 | + | 42.8432i | 0.931594 | + | 1.61357i | ||||
\(706\) | 10.0426 | − | 17.3943i | 0.377958 | − | 0.654643i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 40.9645 | + | 23.6509i | 1.53954 | + | 0.888854i | ||||
\(709\) | 15.0365 | + | 8.68132i | 0.564707 | + | 0.326034i | 0.755033 | − | 0.655687i | \(-0.227621\pi\) |
−0.190325 | + | 0.981721i | \(0.560954\pi\) | |||||||
\(710\) | − | 4.58765i | − | 0.172171i | ||||||
\(711\) | −17.0748 | + | 29.5744i | −0.640354 | + | 1.10913i | ||||
\(712\) | 0.370082 | + | 0.641002i | 0.0138694 | + | 0.0240226i | ||||
\(713\) | 16.2926 | − | 9.40653i | 0.610162 | − | 0.352277i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.1807 | − | 9.77782i | 0.792113 | − | 0.365670i | ||||
\(716\) | 11.2485 | 0.420374 | ||||||||
\(717\) | 19.6049 | − | 11.3189i | 0.732157 | − | 0.422711i | ||||
\(718\) | 4.49992 | + | 7.79409i | 0.167935 | + | 0.290873i | ||||
\(719\) | 4.99354 | − | 8.64906i | 0.186228 | − | 0.322556i | −0.757762 | − | 0.652531i | \(-0.773707\pi\) |
0.943989 | + | 0.329976i | \(0.107040\pi\) | |||||||
\(720\) | − | 25.8365i | − | 0.962871i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.21782 | − | 3.58986i | −0.231403 | − | 0.133601i | ||||
\(723\) | 0.813267i | 0.0302457i | ||||||||
\(724\) | −10.5279 | + | 18.2349i | −0.391267 | + | 0.677695i | ||||
\(725\) | −4.45061 | − | 7.70869i | −0.165292 | − | 0.286294i | ||||
\(726\) | 2.79668 | − | 1.61466i | 0.103794 | − | 0.0599257i | ||||
\(727\) | 8.00409 | 0.296855 | 0.148428 | − | 0.988923i | \(-0.452579\pi\) | ||||
0.148428 | + | 0.988923i | \(0.452579\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.14827 | −0.301788 | ||||||||
\(730\) | 8.27088 | − | 4.77520i | 0.306119 | − | 0.176738i | ||||
\(731\) | −4.37557 | − | 7.57871i | −0.161836 | − | 0.280309i | ||||
\(732\) | −14.2266 | + | 24.6412i | −0.525831 | + | 0.910765i | ||||
\(733\) | − | 44.8461i | − | 1.65643i | −0.560412 | − | 0.828214i | \(-0.689357\pi\) | ||
0.560412 | − | 0.828214i | \(-0.310643\pi\) | |||||||
\(734\) | 8.93516 | + | 5.15871i | 0.329803 | + | 0.190412i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 22.3001i | − | 0.821993i | ||||||
\(737\) | 12.5820 | − | 21.7926i | 0.463463 | − | 0.802742i | ||||
\(738\) | 3.45927 | + | 5.99163i | 0.127337 | + | 0.220555i | ||||
\(739\) | −21.7161 | + | 12.5378i | −0.798840 | + | 0.461210i | −0.843065 | − | 0.537811i | \(-0.819251\pi\) |
0.0442255 | + | 0.999022i | \(0.485918\pi\) | |||||||
\(740\) | 35.5513 | 1.30689 | ||||||||
\(741\) | 27.8667 | + | 2.54594i | 1.02371 | + | 0.0935275i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.9514 | − | 9.20957i | 0.585202 | − | 0.337866i | −0.177996 | − | 0.984031i | \(-0.556961\pi\) |
0.763198 | + | 0.646165i | \(0.223628\pi\) | |||||||
\(744\) | 14.6456 | + | 25.3670i | 0.536935 | + | 0.929999i | ||||
\(745\) | 1.98038 | − | 3.43013i | 0.0725556 | − | 0.125670i | ||||
\(746\) | − | 7.67639i | − | 0.281053i | ||||||
\(747\) | 53.5032 | + | 30.8901i | 1.95758 | + | 1.13021i | ||||
\(748\) | −32.0714 | − | 18.5164i | −1.17265 | − | 0.677028i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 10.6362 | − | 18.4225i | 0.388380 | − | 0.672694i | ||||
\(751\) | 5.84588 | + | 10.1254i | 0.213319 | + | 0.369480i | 0.952751 | − | 0.303752i | \(-0.0982393\pi\) |
−0.739432 | + | 0.673231i | \(0.764906\pi\) | |||||||
\(752\) | 16.7651 | − | 9.67936i | 0.611362 | − | 0.352970i | ||||
\(753\) | −41.0559 | −1.49616 | ||||||||
\(754\) | 6.01045 | − | 8.51401i | 0.218888 | − | 0.310062i | ||||
\(755\) | 3.51810 | 0.128037 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.77449 | − | 13.4658i | −0.282569 | − | 0.489423i | 0.689448 | − | 0.724335i | \(-0.257853\pi\) |
−0.972017 | + | 0.234912i | \(0.924520\pi\) | |||||||
\(758\) | −2.04592 | + | 3.54364i | −0.0743112 | + | 0.128711i | ||||
\(759\) | 45.7791i | 1.66168i | ||||||||
\(760\) | −8.16872 | − | 4.71621i | −0.296311 | − | 0.171075i | ||||
\(761\) | 27.6700 | + | 15.9753i | 1.00304 | + | 0.579103i | 0.909145 | − | 0.416479i | \(-0.136736\pi\) |
0.0938908 | + | 0.995582i | \(0.470070\pi\) | |||||||
\(762\) | 10.6669i | 0.386420i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.55090 | − | 4.41828i | −0.0922882 | − | 0.159848i | ||||
\(765\) | −63.0132 | + | 36.3807i | −2.27825 | + | 1.31535i | ||||
\(766\) | −11.5060 | −0.415729 | ||||||||
\(767\) | 18.9381 | − | 26.8265i | 0.683815 | − | 0.968647i | ||||
\(768\) | 12.0397 | 0.434446 | ||||||||
\(769\) | −12.5835 | + | 7.26510i | −0.453773 | + | 0.261986i | −0.709422 | − | 0.704783i | \(-0.751044\pi\) |
0.255649 | + | 0.966770i | \(0.417711\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.9149 | − | 46.6180i | 0.969316 | − | 1.67891i | ||||
\(772\) | − | 45.2730i | − | 1.62941i | ||||||
\(773\) | −36.4686 | − | 21.0551i | −1.31168 | − | 0.757301i | −0.329308 | − | 0.944222i | \(-0.606816\pi\) |
−0.982375 | + | 0.186922i | \(0.940149\pi\) | |||||||
\(774\) | −4.56863 | − | 2.63770i | −0.164216 | − | 0.0948101i | ||||
\(775\) | − | 7.92922i | − | 0.284826i | ||||||
\(776\) | −11.0339 | + | 19.1113i | −0.396094 | + | 0.686055i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.21606 | + | 0.702092i | −0.0435978 | + | 0.0251712i | ||||
\(779\) | −4.68608 | −0.167896 | ||||||||
\(780\) | −33.6631 | − | 3.07551i | −1.20533 | − | 0.110121i | ||||
\(781\) | 16.1083 | 0.576401 | ||||||||
\(782\) | −12.4431 | + | 7.18405i | −0.444966 | + | 0.256901i | ||||
\(783\) | 28.0839 | + | 48.6427i | 1.00364 | + | 1.73835i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33.1257i | 1.18231i | ||||||||
\(786\) | −9.04170 | − | 5.22023i | −0.322507 | − | 0.186199i | ||||
\(787\) | 5.27820 | + | 3.04737i | 0.188148 | + | 0.108627i | 0.591115 | − | 0.806587i | \(-0.298688\pi\) |
−0.402968 | + | 0.915214i | \(0.632021\pi\) | |||||||
\(788\) | − | 15.6242i | − | 0.556588i | ||||||
\(789\) | −19.6713 | + | 34.0717i | −0.700317 | + | 1.21298i | ||||
\(790\) | −2.65907 | − | 4.60565i | −0.0946056 | − | 0.163862i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −48.8976 | −1.73750 | ||||||||
\(793\) | 16.1368 | + | 11.3918i | 0.573035 | + | 0.404533i | ||||
\(794\) | −6.07302 | −0.215523 | ||||||||
\(795\) | 9.80575 | − | 5.66135i | 0.347774 | − | 0.200788i | ||||
\(796\) | 14.6050 | + | 25.2967i | 0.517662 | + | 0.896617i | ||||
\(797\) | 18.4019 | − | 31.8731i | 0.651830 | − | 1.12900i | −0.330849 | − | 0.943684i | \(-0.607335\pi\) |
0.982679 | − | 0.185318i | \(-0.0593316\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.2143 | − | 27.2592i | −1.67032 | − | 0.964361i | ||||
\(800\) | −8.13971 | − | 4.69946i | −0.287782 | − | 0.166151i | ||||
\(801\) | 2.33127i | 0.0823712i | ||||||||
\(802\) | 4.17172 | − | 7.22564i | 0.147309 | − | 0.255146i | ||||
\(803\) | 16.7668 | + | 29.0410i | 0.591689 | + | 1.02483i | ||||
\(804\) | −31.5776 | + | 18.2313i | −1.11366 | + | 0.642969i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.42894 | − | 3.89112i | 0.296897 | − | 0.137059i | ||||
\(807\) | 6.68185 | 0.235212 | ||||||||
\(808\) | −6.17319 | + | 3.56409i | −0.217172 | + | 0.125384i | ||||
\(809\) | 4.36667 | + | 7.56329i | 0.153524 | + | 0.265911i | 0.932521 | − | 0.361117i | \(-0.117604\pi\) |
−0.778997 | + | 0.627028i | \(0.784271\pi\) | |||||||
\(810\) | −7.30032 | + | 12.6445i | −0.256507 | + | 0.444283i | ||||
\(811\) | − | 37.1024i | − | 1.30284i | −0.758716 | − | 0.651421i | \(-0.774173\pi\) | ||
0.758716 | − | 0.651421i | \(-0.225827\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.6059 | − | 9.01008i | −0.547323 | − | 0.315997i | ||||
\(814\) | − | 23.7589i | − | 0.832750i | ||||||
\(815\) | −19.9106 | + | 34.4861i | −0.697437 | + | 1.20800i | ||||
\(816\) | 20.7517 | + | 35.9431i | 0.726456 | + | 1.25826i | ||||
\(817\) | 3.09443 | − | 1.78657i | 0.108261 | − | 0.0625043i | ||||
\(818\) | 3.58784 | 0.125446 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.66081 | 0.197684 | ||||||||
\(821\) | −36.5097 | + | 21.0789i | −1.27420 | + | 0.735658i | −0.975775 | − | 0.218776i | \(-0.929794\pi\) |
−0.298422 | + | 0.954434i | \(0.596460\pi\) | |||||||
\(822\) | −3.15291 | − | 5.46101i | −0.109971 | − | 0.190475i | ||||
\(823\) | −9.27261 | + | 16.0606i | −0.323223 | + | 0.559838i | −0.981151 | − | 0.193242i | \(-0.938100\pi\) |
0.657928 | + | 0.753081i | \(0.271433\pi\) | |||||||
\(824\) | 26.9633i | 0.939312i | ||||||||
\(825\) | 16.7097 | + | 9.64736i | 0.581757 | + | 0.335878i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.5050i | 0.434841i | 0.976078 | + | 0.217420i | \(0.0697642\pi\) | ||||
−0.976078 | + | 0.217420i | \(0.930236\pi\) | |||||||
\(828\) | 22.7535 | − | 39.4102i | 0.790739 | − | 1.36960i | ||||
\(829\) | −22.8833 | − | 39.6351i | −0.794770 | − | 1.37658i | −0.922985 | − | 0.384836i | \(-0.874258\pi\) |
0.128215 | − | 0.991746i | \(-0.459075\pi\) | |||||||
\(830\) | −8.33212 | + | 4.81055i | −0.289212 | + | 0.166977i | ||||
\(831\) | −36.0032 | −1.24894 | ||||||||
\(832\) | −0.431336 | + | 4.72120i | −0.0149539 | + | 0.163678i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 19.5539 | − | 11.2894i | 0.677095 | − | 0.390921i | ||||
\(835\) | 2.56220 | + | 4.43786i | 0.0886687 | + | 0.153579i | ||||
\(836\) | 7.56038 | − | 13.0950i | 0.261481 | − | 0.452899i | ||||
\(837\) | 50.0343i | 1.72944i | ||||||||
\(838\) | −8.85701 | − | 5.11360i | −0.305960 | − | 0.176646i | ||||
\(839\) | −11.1021 | − | 6.40978i | −0.383286 | − | 0.221290i | 0.295961 | − | 0.955200i | \(-0.404360\pi\) |
−0.679247 | + | 0.733910i | \(0.737693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.43713 | − | 2.48918i | 0.0495562 | − | 0.0858338i | ||||
\(842\) | −5.57144 | − | 9.65001i | −0.192004 | − | 0.332561i | ||||
\(843\) | 66.3731 | − | 38.3205i | 2.28601 | − | 1.31983i | ||||
\(844\) | 36.6681 | 1.26217 | ||||||||
\(845\) | −4.25243 | + | 23.0783i | −0.146288 | + | 0.793918i | ||||
\(846\) | −32.8650 | −1.12992 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.21537 | − | 3.83713i | −0.0760761 | − | 0.131768i | ||||
\(849\) | −23.4047 | + | 40.5382i | −0.803249 | + | 1.39127i | ||||
\(850\) | 6.05578i | 0.207712i | ||||||||
\(851\) | 41.9428 | + | 24.2157i | 1.43778 | + | 0.830104i | ||||
\(852\) | −20.2139 | − | 11.6705i | −0.692517 | − | 0.399825i | ||||
\(853\) | − | 4.51954i | − | 0.154746i | −0.997002 | − | 0.0773730i | \(-0.975347\pi\) | ||
0.997002 | − | 0.0773730i | \(-0.0246532\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.8545 | − | 25.7287i | −0.508012 | − | 0.879902i | ||||
\(856\) | −32.7481 | + | 18.9071i | −1.11931 | + | 0.646231i | ||||
\(857\) | −47.2746 | −1.61487 | −0.807435 | − | 0.589957i | \(-0.799145\pi\) | ||||
−0.807435 | + | 0.589957i | \(0.799145\pi\) | |||||||
\(858\) | −2.05536 | + | 22.4971i | −0.0701690 | + | 0.768037i | ||||
\(859\) | 48.0543 | 1.63959 | 0.819795 | − | 0.572657i | \(-0.194087\pi\) | ||||
0.819795 | + | 0.572657i | \(0.194087\pi\) | |||||||
\(860\) | −3.73809 | + | 2.15819i | −0.127468 | + | 0.0735936i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.97000 | + | 5.14419i | −0.101158 | + | 0.175212i | ||||
\(863\) | 27.5799i | 0.938831i | 0.882977 | + | 0.469415i | \(0.155535\pi\) | ||||
−0.882977 | + | 0.469415i | \(0.844465\pi\) | |||||||
\(864\) | 51.3625 | + | 29.6542i | 1.74739 | + | 1.00886i | ||||
\(865\) | −5.51566 | − | 3.18447i | −0.187538 | − | 0.108275i | ||||
\(866\) | 5.15631i | 0.175218i | ||||||||
\(867\) | 32.1669 | − | 55.7148i | 1.09245 | − | 1.89217i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.1715 | − | 9.33664i | 0.548581 | − | 0.316724i | ||||
\(870\) | −16.1286 | −0.546811 | ||||||||
\(871\) | 10.6095 | + | 22.9823i | 0.359489 | + | 0.778725i | ||||
\(872\) | 28.9895 | 0.981710 | ||||||||
\(873\) | −60.1940 | + | 34.7530i | −2.03726 | + | 1.17621i | ||||
\(874\) | −2.93329 | − | 5.08061i | −0.0992201 | − | 0.171854i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 48.5904i | − | 1.64172i | ||||||
\(877\) | 42.8238 | + | 24.7243i | 1.44606 | + | 0.834882i | 0.998243 | − | 0.0592452i | \(-0.0188694\pi\) |
0.447814 | + | 0.894127i | \(0.352203\pi\) | |||||||
\(878\) | 14.3397 | + | 8.27903i | 0.483941 | + | 0.279404i | ||||
\(879\) | − | 77.0315i | − | 2.59821i | ||||||
\(880\) | −7.06383 | + | 12.2349i | −0.238122 | + | 0.412439i | ||||
\(881\) | −0.618953 | − | 1.07206i | −0.0208530 | − | 0.0361185i | 0.855411 | − | 0.517951i | \(-0.173305\pi\) |
−0.876264 | + | 0.481832i | \(0.839972\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.4537 | −1.39503 | −0.697514 | − | 0.716571i | \(-0.745711\pi\) | ||||
−0.697514 | + | 0.716571i | \(0.745711\pi\) | |||||||
\(884\) | 33.8222 | − | 15.6136i | 1.13756 | − | 0.525143i | ||||
\(885\) | −50.8190 | −1.70826 | ||||||||
\(886\) | −13.0934 | + | 7.55948i | −0.439882 | + | 0.253966i | ||||
\(887\) | 0.585862 | + | 1.01474i | 0.0196713 | + | 0.0340717i | 0.875693 | − | 0.482867i | \(-0.160405\pi\) |
−0.856022 | + | 0.516939i | \(0.827071\pi\) | |||||||
\(888\) | −37.7030 | + | 65.3036i | −1.26523 | + | 2.19144i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.314411 | − | 0.181525i | −0.0105391 | − | 0.00608475i | ||||
\(891\) | −44.3979 | − | 25.6331i | −1.48738 | − | 0.858742i | ||||
\(892\) | 3.21234i | 0.107557i | ||||||||
\(893\) | 11.1301 | − | 19.2779i | 0.372455 | − | 0.645111i | ||||
\(894\) | 1.91774 | + | 3.32163i | 0.0641389 | + | 0.111092i | ||||
\(895\) | −10.4658 | + | 6.04243i | −0.349833 | + | 0.201976i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −37.6203 | − | 26.5580i | −1.25611 | − | 0.886747i | ||||
\(898\) | −11.9975 | −0.400361 | ||||||||
\(899\) | −20.1549 | + | 11.6364i | −0.672202 | + | 0.388096i | ||||
\(900\) | −9.59002 | − | 16.6104i | −0.319667 | − | 0.553680i | ||||
\(901\) | −6.23896 | + | 10.8062i | −0.207850 | + | 0.360007i | ||||
\(902\) | − | 3.78312i | − | 0.125964i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.2544 | + | 10.5392i | 0.607131 | + | 0.350527i | ||||
\(905\) | − | 22.6215i | − | 0.751965i | ||||||
\(906\) | −1.70341 | + | 2.95039i | −0.0565919 | + | 0.0980201i | ||||
\(907\) | −21.4768 | − | 37.1990i | −0.713127 | − | 1.23517i | −0.963677 | − | 0.267069i | \(-0.913945\pi\) |
0.250550 | − | 0.968104i | \(-0.419388\pi\) | |||||||
\(908\) | 15.0380 | − | 8.68221i | 0.499054 | − | 0.288129i | ||||
\(909\) | −22.4513 | −0.744664 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5412 | 0.813085 | 0.406543 | − | 0.913632i | \(-0.366734\pi\) | ||||
0.406543 | + | 0.913632i | \(0.366734\pi\) | |||||||
\(912\) | −14.6758 | + | 8.47307i | −0.485964 | + | 0.280571i | ||||
\(913\) | −16.8910 | − | 29.2560i | −0.559010 | − | 0.968234i | ||||
\(914\) | −4.14080 | + | 7.17208i | −0.136966 | + | 0.237231i | ||||
\(915\) | − | 30.5689i | − | 1.01058i | ||||||
\(916\) | −8.88184 | − | 5.12794i | −0.293464 | − | 0.169432i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 38.2127i | − | 1.26121i | ||||||
\(919\) | −18.3307 | + | 31.7498i | −0.604675 | + | 1.04733i | 0.387428 | + | 0.921900i | \(0.373364\pi\) |
−0.992103 | + | 0.125428i | \(0.959970\pi\) | |||||||
\(920\) | 7.76129 | + | 13.4430i | 0.255882 | + | 0.443201i | ||||
\(921\) | −10.4445 | + | 6.03011i | −0.344156 | + | 0.198699i | ||||
\(922\) | −14.0780 | −0.463635 | ||||||||
\(923\) | −9.34499 | + | 13.2375i | −0.307594 | + | 0.435717i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.6778 | − | 10.2063i | 0.581243 | − | 0.335581i | ||||
\(926\) | 2.85774 | + | 4.94976i | 0.0939113 | + | 0.162659i | ||||
\(927\) | −42.4626 | + | 73.5474i | −1.39466 | + | 2.41561i | ||||
\(928\) | 27.5865i | 0.905572i | ||||||||
\(929\) | 22.4866 | + | 12.9826i | 0.737762 | + | 0.425947i | 0.821255 | − | 0.570562i | \(-0.193274\pi\) |
−0.0834933 | + | 0.996508i | \(0.526608\pi\) | |||||||
\(930\) | −12.4425 | − | 7.18369i | −0.408006 | − | 0.235562i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.98804 | − | 10.3716i | 0.196145 | − | 0.339733i | ||||
\(933\) | −30.4753 | − | 52.7847i | −0.997716 | − | 1.72809i | ||||
\(934\) | −5.62345 | + | 3.24670i | −0.184005 | + | 0.106235i | ||||
\(935\) | 39.7865 | 1.30116 | ||||||||
\(936\) | 28.3672 | − | 40.1831i | 0.927211 | − | 1.31343i | ||||
\(937\) | 11.8632 | 0.387554 | 0.193777 | − | 0.981046i | \(-0.437926\pi\) | ||||
0.193777 | + | 0.981046i | \(0.437926\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.47029 | + | 7.74278i | 0.145883 | + | 0.252676i | ||||
\(940\) | −13.4452 | + | 23.2878i | −0.438535 | + | 0.759565i | ||||
\(941\) | 9.51954i | 0.310328i | 0.987889 | + | 0.155164i | \(0.0495906\pi\) | ||||
−0.987889 | + | 0.155164i | \(0.950409\pi\) | |||||||
\(942\) | −27.7803 | − | 16.0389i | −0.905130 | − | 0.522577i | ||||
\(943\) | 6.67853 | + | 3.85585i | 0.217483 | + | 0.125564i | ||||
\(944\) | 19.8862i | 0.647241i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.44232 | + | 2.49817i | 0.0468938 | + | 0.0812224i | ||||
\(947\) | 36.8812 | − | 21.2934i | 1.19848 | − | 0.691942i | 0.238263 | − | 0.971201i | \(-0.423422\pi\) |
0.960216 | + | 0.279258i | \(0.0900885\pi\) | |||||||
\(948\) | −27.0576 | −0.878791 | ||||||||
\(949\) | −33.5923 | − | 3.06904i | −1.09045 | − | 0.0996254i | ||||
\(950\) | −2.47261 | −0.0802222 | ||||||||
\(951\) | −42.7077 | + | 24.6573i | −1.38489 | + | 0.799567i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.7195 | − | 27.2270i | 0.509204 | − | 0.881968i | −0.490739 | − | 0.871307i | \(-0.663273\pi\) |
0.999943 | − | 0.0106611i | \(-0.00339359\pi\) | |||||||
\(954\) | 7.52199i | 0.243534i | ||||||||
\(955\) | 4.74682 | + | 2.74058i | 0.153603 | + | 0.0886830i | ||||
\(956\) | 10.6564 | + | 6.15248i | 0.344653 | + | 0.198985i | ||||
\(957\) | − | 56.6313i | − | 1.83063i | ||||||
\(958\) | 0.305702 | − | 0.529492i | 0.00987679 | − | 0.0171071i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6.35393 | − | 3.66844i | 0.205072 | − | 0.118398i | ||||
\(961\) | 10.2686 | 0.331244 | ||||||||
\(962\) | 19.5246 | + | 13.7834i | 0.629499 | + | 0.444394i | ||||
\(963\) | −119.102 | −3.83800 | ||||||||
\(964\) | −0.382834 | + | 0.221029i | −0.0123303 | + | 0.00711888i | ||||
\(965\) | 24.3197 | + | 42.1229i | 0.782879 | + | 1.35599i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.05894i | 0.194842i | 0.995243 | + | 0.0974212i | \(0.0310594\pi\) | ||||
−0.995243 | + | 0.0974212i | \(0.968941\pi\) | |||||||
\(968\) | 3.32965 | + | 1.92238i | 0.107019 | + | 0.0617875i | ||||
\(969\) | 41.3302 | + | 23.8620i | 1.32772 | + | 0.766558i | ||||
\(970\) | − | 10.8243i | − | 0.347546i | ||||||
\(971\) | 21.7346 | − | 37.6454i | 0.697497 | − | 1.20810i | −0.271835 | − | 0.962344i | \(-0.587631\pi\) |
0.969332 | − | 0.245756i | \(-0.0790361\pi\) | |||||||
\(972\) | 9.44717 | + | 16.3630i | 0.303018 | + | 0.524843i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 14.2890 | 0.457849 | ||||||||
\(975\) | −17.6219 | + | 8.13494i | −0.564352 | + | 0.260527i | ||||
\(976\) | −11.9621 | −0.382896 | ||||||||
\(977\) | −24.9570 | + | 14.4089i | −0.798445 | + | 0.460982i | −0.842927 | − | 0.538028i | \(-0.819169\pi\) |
0.0444824 | + | 0.999010i | \(0.485836\pi\) | |||||||
\(978\) | −19.2808 | − | 33.3953i | −0.616531 | − | 1.06786i | ||||
\(979\) | 0.637379 | − | 1.10397i | 0.0203707 | − | 0.0352831i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 79.0743 | + | 45.6536i | 2.52465 | + | 1.45761i | ||||
\(982\) | 20.4311 | + | 11.7959i | 0.651982 | + | 0.376422i | ||||
\(983\) | 31.1850i | 0.994647i | 0.867565 | + | 0.497323i | \(0.165684\pi\) | ||||
−0.867565 | + | 0.497323i | \(0.834316\pi\) | |||||||
\(984\) | −6.00343 | + | 10.3982i | −0.191382 | + | 0.331484i | ||||
\(985\) | 8.39298 | + | 14.5371i | 0.267423 | + | 0.463189i | ||||
\(986\) | 15.3929 | − | 8.88708i | 0.490209 | − | 0.283022i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.37514 | + | 13.8098i | 0.202820 | + | 0.439348i | ||||
\(989\) | −5.88019 | −0.186979 | ||||||||
\(990\) | 20.7710 | − | 11.9922i | 0.660146 | − | 0.381136i | ||||
\(991\) | 31.0698 | + | 53.8144i | 0.986963 | + | 1.70947i | 0.632865 | + | 0.774262i | \(0.281879\pi\) |
0.354099 | + | 0.935208i | \(0.384788\pi\) | |||||||
\(992\) | −12.2870 | + | 21.2818i | −0.390114 | + | 0.675697i | ||||
\(993\) | 11.8290i | 0.375382i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.1777 | − | 15.6910i | −0.861590 | − | 0.497440i | ||||
\(996\) | 48.9502i | 1.55105i | ||||||||
\(997\) | −8.65718 | + | 14.9947i | −0.274176 | + | 0.474886i | −0.969927 | − | 0.243397i | \(-0.921738\pi\) |
0.695751 | + | 0.718283i | \(0.255072\pi\) | |||||||
\(998\) | −2.95996 | − | 5.12679i | −0.0936958 | − | 0.162286i | ||||
\(999\) | −111.549 | + | 64.4029i | −3.52926 | + | 2.03762i |
(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 | 637.2.q.j.491.10 | yes | 32 | |
7.2 | even | 3 | 637.2.u.j.361.7 | 32 | |||
7.3 | odd | 6 | 637.2.k.j.569.9 | 32 | |||
7.4 | even | 3 | 637.2.k.j.569.10 | 32 | |||
7.5 | odd | 6 | 637.2.u.j.361.8 | 32 | |||
7.6 | odd | 2 | inner | 637.2.q.j.491.9 | ✓ | 32 | |
13.2 | odd | 12 | 8281.2.a.cx.1.19 | 32 | |||
13.4 | even | 6 | inner | 637.2.q.j.589.10 | yes | 32 | |
13.11 | odd | 12 | 8281.2.a.cx.1.13 | 32 | |||
91.4 | even | 6 | 637.2.u.j.30.7 | 32 | |||
91.17 | odd | 6 | 637.2.u.j.30.8 | 32 | |||
91.30 | even | 6 | 637.2.k.j.459.8 | 32 | |||
91.41 | even | 12 | 8281.2.a.cx.1.20 | 32 | |||
91.69 | odd | 6 | inner | 637.2.q.j.589.9 | yes | 32 | |
91.76 | even | 12 | 8281.2.a.cx.1.14 | 32 | |||
91.82 | odd | 6 | 637.2.k.j.459.7 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.k.j.459.7 | 32 | 91.82 | odd | 6 | |||
637.2.k.j.459.8 | 32 | 91.30 | even | 6 | |||
637.2.k.j.569.9 | 32 | 7.3 | odd | 6 | |||
637.2.k.j.569.10 | 32 | 7.4 | even | 3 | |||
637.2.q.j.491.9 | ✓ | 32 | 7.6 | odd | 2 | inner | |
637.2.q.j.491.10 | yes | 32 | 1.1 | even | 1 | trivial | |
637.2.q.j.589.9 | yes | 32 | 91.69 | odd | 6 | inner | |
637.2.q.j.589.10 | yes | 32 | 13.4 | even | 6 | inner | |
637.2.u.j.30.7 | 32 | 91.4 | even | 6 | |||
637.2.u.j.30.8 | 32 | 91.17 | odd | 6 | |||
637.2.u.j.361.7 | 32 | 7.2 | even | 3 | |||
637.2.u.j.361.8 | 32 | 7.5 | odd | 6 | |||
8281.2.a.cx.1.13 | 32 | 13.11 | odd | 12 | |||
8281.2.a.cx.1.14 | 32 | 91.76 | even | 12 | |||
8281.2.a.cx.1.19 | 32 | 13.2 | odd | 12 | |||
8281.2.a.cx.1.20 | 32 | 91.41 | even | 12 |