Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(91,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.h (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.1064390625.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 3x^{6} - 5x^{5} + 36x^{4} - 35x^{3} + 23x^{2} - 171x + 361 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 91.2 | ||
Root | \(2.36886 - 0.0809628i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.91 |
Dual form | 450.2.h.d.361.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | − | 0.587785i | −0.572061 | − | 0.415627i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | 2.05984 | − | 0.870094i | 0.921188 | − | 0.389118i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.92807 | 1.10671 | 0.553353 | − | 0.832947i | \(-0.313348\pi\) | ||||
0.553353 | + | 0.832947i | \(0.313348\pi\) | |||||||
\(8\) | 0.309017 | − | 0.951057i | 0.109254 | − | 0.336249i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.17787 | − | 0.506822i | −0.688704 | − | 0.160271i | ||||
\(11\) | 0.154000 | + | 0.111888i | 0.0464329 | + | 0.0337355i | 0.610760 | − | 0.791816i | \(-0.290864\pi\) |
−0.564327 | + | 0.825552i | \(0.690864\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.250822 | + | 0.182233i | −0.0695655 | + | 0.0505423i | −0.622025 | − | 0.782998i | \(-0.713690\pi\) |
0.552459 | + | 0.833540i | \(0.313690\pi\) | |||||||
\(14\) | −2.36886 | − | 1.72107i | −0.633103 | − | 0.459977i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | −1.86886 | + | 5.75175i | −0.453264 | + | 1.39500i | 0.419897 | + | 0.907572i | \(0.362066\pi\) |
−0.873161 | + | 0.487432i | \(0.837934\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | − | 3.07768i | 0.229416 | − | 0.706069i | −0.768398 | − | 0.639973i | \(-0.778946\pi\) |
0.997813 | − | 0.0660962i | \(-0.0210544\pi\) | |||||||
\(20\) | 1.46403 | + | 1.69015i | 0.327368 | + | 0.377929i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0588229 | − | 0.181038i | −0.0125411 | − | 0.0385975i | ||||
\(23\) | 3.61803 | + | 2.62866i | 0.754412 | + | 0.548113i | 0.897191 | − | 0.441642i | \(-0.145604\pi\) |
−0.142779 | + | 0.989755i | \(0.545604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.48587 | − | 3.58451i | 0.697175 | − | 0.716901i | ||||
\(26\) | 0.310033 | 0.0608025 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.904822 | + | 2.78476i | 0.170995 | + | 0.526270i | ||||
\(29\) | −2.10492 | − | 6.47829i | −0.390875 | − | 1.20299i | −0.932128 | − | 0.362129i | \(-0.882050\pi\) |
0.541253 | − | 0.840859i | \(-0.317950\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.522856 | + | 1.60919i | −0.0939078 | + | 0.289018i | −0.986968 | − | 0.160920i | \(-0.948554\pi\) |
0.893060 | + | 0.449938i | \(0.148554\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.89273 | − | 3.55478i | 0.839096 | − | 0.609639i | ||||
\(35\) | 6.03135 | − | 2.54769i | 1.01948 | − | 0.430639i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.89273 | − | 5.73440i | 1.29756 | − | 0.942730i | 0.297628 | − | 0.954682i | \(-0.403804\pi\) |
0.999929 | + | 0.0119519i | \(0.00380449\pi\) | |||||||
\(38\) | −2.61803 | + | 1.90211i | −0.424701 | + | 0.308563i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.190983 | − | 2.22790i | −0.0301971 | − | 0.352261i | ||||
\(41\) | 4.10492 | − | 2.98240i | 0.641081 | − | 0.465773i | −0.219140 | − | 0.975693i | \(-0.570325\pi\) |
0.860222 | + | 0.509920i | \(0.170325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.2394 | −1.56149 | −0.780744 | − | 0.624852i | \(-0.785159\pi\) | ||||
−0.780744 | + | 0.624852i | \(0.785159\pi\) | |||||||
\(44\) | −0.0588229 | + | 0.181038i | −0.00886789 | + | 0.0272926i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.38197 | − | 4.25325i | −0.203760 | − | 0.627108i | ||||
\(47\) | 3.31003 | + | 10.1872i | 0.482818 | + | 1.48596i | 0.835116 | + | 0.550073i | \(0.185400\pi\) |
−0.352299 | + | 0.935888i | \(0.614600\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.57358 | 0.224797 | ||||||||
\(50\) | −4.92705 | + | 0.850981i | −0.696790 | + | 0.120347i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.250822 | − | 0.182233i | −0.0347828 | − | 0.0252712i | ||||
\(53\) | −3.08144 | − | 9.48370i | −0.423268 | − | 1.30269i | −0.904643 | − | 0.426171i | \(-0.859862\pi\) |
0.481374 | − | 0.876515i | \(-0.340138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.414569 | + | 0.0964762i | 0.0559005 | + | 0.0130088i | ||||
\(56\) | 0.904822 | − | 2.78476i | 0.120912 | − | 0.372129i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.10492 | + | 6.47829i | −0.276390 | + | 0.850641i | ||||
\(59\) | 6.00810 | − | 4.36514i | 0.782188 | − | 0.568293i | −0.123447 | − | 0.992351i | \(-0.539395\pi\) |
0.905635 | + | 0.424058i | \(0.139395\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.48689 | + | 3.25992i | 0.574487 | + | 0.417390i | 0.836733 | − | 0.547612i | \(-0.184463\pi\) |
−0.262245 | + | 0.965001i | \(0.584463\pi\) | |||||||
\(62\) | 1.36886 | − | 0.994532i | 0.173845 | − | 0.126306i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | −0.358093 | + | 0.593609i | −0.0444160 | + | 0.0736282i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.66375 | + | 14.3535i | −0.569767 | + | 1.75356i | 0.0835754 | + | 0.996501i | \(0.473366\pi\) |
−0.653343 | + | 0.757062i | \(0.726634\pi\) | |||||||
\(68\) | −6.04775 | −0.733397 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.37696 | − | 1.48401i | −0.762192 | − | 0.177373i | ||||
\(71\) | −2.11842 | − | 6.51983i | −0.251410 | − | 0.773762i | −0.994516 | − | 0.104587i | \(-0.966648\pi\) |
0.743105 | − | 0.669175i | \(-0.233352\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.41496 | − | 6.84037i | −1.10194 | − | 0.800604i | −0.120562 | − | 0.992706i | \(-0.538470\pi\) |
−0.981375 | + | 0.192101i | \(0.938470\pi\) | |||||||
\(74\) | −9.75595 | −1.13411 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.23607 | 0.371202 | ||||||||
\(77\) | 0.450924 | + | 0.327615i | 0.0513875 | + | 0.0373352i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.485246 | + | 1.49343i | 0.0545944 | + | 0.168024i | 0.974636 | − | 0.223797i | \(-0.0718452\pi\) |
−0.920041 | + | 0.391821i | \(0.871845\pi\) | |||||||
\(80\) | −1.15502 | + | 1.91466i | −0.129135 | + | 0.214066i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.07397 | −0.560326 | ||||||||
\(83\) | −4.02324 | + | 12.3823i | −0.441608 | + | 1.35913i | 0.444552 | + | 0.895753i | \(0.353363\pi\) |
−0.886161 | + | 0.463378i | \(0.846637\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.15502 | + | 13.4738i | 0.125279 | + | 1.46143i | ||||
\(86\) | 8.28381 | + | 6.01854i | 0.893267 | + | 0.648996i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.154000 | − | 0.111888i | 0.0164165 | − | 0.0119273i | ||||
\(89\) | −7.51076 | − | 5.45689i | −0.796139 | − | 0.578429i | 0.113640 | − | 0.993522i | \(-0.463749\pi\) |
−0.909779 | + | 0.415093i | \(0.863749\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.734424 | + | 0.533590i | −0.0769885 | + | 0.0559354i | ||||
\(92\) | −1.38197 | + | 4.25325i | −0.144080 | + | 0.443432i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.31003 | − | 10.1872i | 0.341404 | − | 1.05073i | ||||
\(95\) | −0.618034 | − | 7.20963i | −0.0634089 | − | 0.739692i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.537611 | + | 1.65460i | 0.0545861 | + | 0.167999i | 0.974633 | − | 0.223810i | \(-0.0718495\pi\) |
−0.920047 | + | 0.391809i | \(0.871850\pi\) | |||||||
\(98\) | −1.27305 | − | 0.924925i | −0.128598 | − | 0.0934316i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.48626 | + | 2.20759i | 0.448626 | + | 0.220759i | ||||
\(101\) | 0.765188 | 0.0761391 | 0.0380695 | − | 0.999275i | \(-0.487879\pi\) | ||||
0.0380695 | + | 0.999275i | \(0.487879\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.74069 | + | 5.35728i | 0.171515 | + | 0.527869i | 0.999457 | − | 0.0329445i | \(-0.0104885\pi\) |
−0.827942 | + | 0.560814i | \(0.810488\pi\) | |||||||
\(104\) | 0.0958055 | + | 0.294859i | 0.00939450 | + | 0.0289133i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.08144 | + | 9.48370i | −0.299296 | + | 0.921138i | ||||
\(107\) | 8.81042 | 0.851736 | 0.425868 | − | 0.904785i | \(-0.359969\pi\) | ||||
0.425868 | + | 0.904785i | \(0.359969\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.8447 | + | 9.33220i | −1.23030 | + | 0.893862i | −0.996912 | − | 0.0785223i | \(-0.974980\pi\) |
−0.233384 | + | 0.972385i | \(0.574980\pi\) | |||||||
\(110\) | −0.278686 | − | 0.321728i | −0.0265717 | − | 0.0306756i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.36886 | + | 1.72107i | −0.223836 | + | 0.162626i | ||||
\(113\) | −15.4845 | + | 11.2502i | −1.45666 | + | 1.05833i | −0.472447 | + | 0.881359i | \(0.656629\pi\) |
−0.984217 | + | 0.176969i | \(0.943371\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.73974 | + | 2.26658i | 0.908236 | + | 0.211360i | ||||
\(116\) | 5.51076 | − | 4.00380i | 0.511661 | − | 0.371744i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.42642 | −0.683658 | ||||||||
\(119\) | −5.47214 | + | 16.8415i | −0.501630 | + | 1.54386i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.38799 | − | 10.4272i | −0.307999 | − | 0.947924i | ||||
\(122\) | −1.71384 | − | 5.27466i | −0.155164 | − | 0.477545i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.69200 | −0.151946 | ||||||||
\(125\) | 4.06148 | − | 10.4165i | 0.363270 | − | 0.931684i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.58371 | + | 4.78335i | 0.584210 | + | 0.424453i | 0.840239 | − | 0.542216i | \(-0.182414\pi\) |
−0.256029 | + | 0.966669i | \(0.582414\pi\) | |||||||
\(128\) | 0.309017 | + | 0.951057i | 0.0273135 | + | 0.0840623i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.638618 | − | 0.269758i | 0.0560105 | − | 0.0236593i | ||||
\(131\) | −5.13588 | + | 15.8066i | −0.448724 | + | 1.38103i | 0.429623 | + | 0.903008i | \(0.358646\pi\) |
−0.878347 | + | 0.478023i | \(0.841354\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.92807 | − | 9.01166i | 0.253896 | − | 0.781410i | ||||
\(134\) | 12.2098 | − | 8.87097i | 1.05477 | − | 0.766335i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.89273 | + | 3.55478i | 0.419548 | + | 0.304819i | ||||
\(137\) | −8.60657 | + | 6.25304i | −0.735309 | + | 0.534233i | −0.891238 | − | 0.453535i | \(-0.850163\pi\) |
0.155930 | + | 0.987768i | \(0.450163\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.5199 | − | 13.4555i | −1.57084 | − | 1.14128i | −0.926351 | − | 0.376662i | \(-0.877072\pi\) |
−0.644485 | − | 0.764617i | \(-0.722928\pi\) | |||||||
\(140\) | 4.28679 | + | 4.94887i | 0.362300 | + | 0.418256i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.11842 | + | 6.51983i | −0.177774 | + | 0.547132i | ||||
\(143\) | −0.0590164 | −0.00493520 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.97252 | − | 11.5128i | −0.828173 | − | 0.956082i | ||||
\(146\) | 3.59619 | + | 11.0679i | 0.297623 | + | 0.915990i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.89273 | + | 5.73440i | 0.648778 | + | 0.471365i | ||||
\(149\) | −1.40819 | −0.115363 | −0.0576815 | − | 0.998335i | \(-0.518371\pi\) | ||||
−0.0576815 | + | 0.998335i | \(0.518371\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.87234 | −0.640642 | −0.320321 | − | 0.947309i | \(-0.603791\pi\) | ||||
−0.320321 | + | 0.947309i | \(0.603791\pi\) | |||||||
\(152\) | −2.61803 | − | 1.90211i | −0.212351 | − | 0.154282i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.172237 | − | 0.530092i | −0.0138793 | − | 0.0427161i | ||||
\(155\) | 0.323143 | + | 3.76960i | 0.0259555 | + | 0.302782i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.95554 | −0.555113 | −0.277556 | − | 0.960709i | \(-0.589525\pi\) | ||||
−0.277556 | + | 0.960709i | \(0.589525\pi\) | |||||||
\(158\) | 0.485246 | − | 1.49343i | 0.0386041 | − | 0.118811i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.05984 | − | 0.870094i | 0.162845 | − | 0.0687869i | ||||
\(161\) | 10.5938 | + | 7.69688i | 0.834912 | + | 0.606599i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.3262 | − | 8.22899i | 0.887139 | − | 0.644545i | −0.0479912 | − | 0.998848i | \(-0.515282\pi\) |
0.935131 | + | 0.354303i | \(0.115282\pi\) | |||||||
\(164\) | 4.10492 | + | 2.98240i | 0.320541 | + | 0.232886i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.5330 | − | 7.65267i | 0.817519 | − | 0.593962i | ||||
\(167\) | −0.425647 | + | 1.31001i | −0.0329375 | + | 0.101371i | −0.966174 | − | 0.257892i | \(-0.916972\pi\) |
0.933236 | + | 0.359263i | \(0.116972\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.98752 | + | 12.2723i | −0.306732 | + | 0.944025i | ||||
\(170\) | 6.98525 | − | 11.5794i | 0.535744 | − | 0.888099i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.16414 | − | 9.73821i | −0.241263 | − | 0.742531i | ||||
\(173\) | −3.33555 | − | 2.42342i | −0.253597 | − | 0.184249i | 0.453722 | − | 0.891143i | \(-0.350096\pi\) |
−0.707320 | + | 0.706894i | \(0.750096\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.2069 | − | 10.4957i | 0.771567 | − | 0.793398i | ||||
\(176\) | −0.190355 | −0.0143485 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.86886 | + | 8.82943i | 0.215030 | + | 0.661794i | ||||
\(179\) | −1.33125 | − | 4.09715i | −0.0995020 | − | 0.306236i | 0.888899 | − | 0.458104i | \(-0.151471\pi\) |
−0.988401 | + | 0.151868i | \(0.951471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.01475 | − | 12.3561i | 0.298414 | − | 0.918425i | −0.683639 | − | 0.729820i | \(-0.739604\pi\) |
0.982053 | − | 0.188604i | \(-0.0603964\pi\) | |||||||
\(182\) | 0.907798 | 0.0672904 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.61803 | − | 2.62866i | 0.266725 | − | 0.193787i | ||||
\(185\) | 11.2683 | − | 18.6794i | 0.828461 | − | 1.37333i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.931355 | + | 0.676669i | −0.0681075 | + | 0.0494830i | ||||
\(188\) | −8.66578 | + | 6.29606i | −0.632017 | + | 0.459187i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.73771 | + | 6.19598i | −0.271162 | + | 0.449504i | ||||
\(191\) | −1.00000 | + | 0.726543i | −0.0723575 | + | 0.0525708i | −0.623376 | − | 0.781922i | \(-0.714239\pi\) |
0.551018 | + | 0.834493i | \(0.314239\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.4250 | 1.25428 | 0.627140 | − | 0.778906i | \(-0.284225\pi\) | ||||
0.627140 | + | 0.778906i | \(0.284225\pi\) | |||||||
\(194\) | 0.537611 | − | 1.65460i | 0.0385982 | − | 0.118793i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.486262 | + | 1.49656i | 0.0347330 | + | 0.106897i | ||||
\(197\) | −4.61741 | − | 14.2109i | −0.328977 | − | 1.01249i | −0.969614 | − | 0.244642i | \(-0.921330\pi\) |
0.640637 | − | 0.767844i | \(-0.278670\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.90436 | −0.347661 | −0.173830 | − | 0.984776i | \(-0.555614\pi\) | ||||
−0.173830 | + | 0.984776i | \(0.555614\pi\) | |||||||
\(200\) | −2.33187 | − | 4.42294i | −0.164888 | − | 0.312749i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.619050 | − | 0.449766i | −0.0435562 | − | 0.0316454i | ||||
\(203\) | −6.16336 | − | 18.9689i | −0.432583 | − | 1.33135i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.86051 | − | 9.71494i | 0.409316 | − | 0.678521i | ||||
\(206\) | 1.74069 | − | 5.35728i | 0.121279 | − | 0.373260i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.0958055 | − | 0.294859i | 0.00664292 | − | 0.0204448i | ||||
\(209\) | 0.498356 | − | 0.362077i | 0.0344720 | − | 0.0250454i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.996712 | + | 0.724153i | 0.0686165 | + | 0.0498528i | 0.621565 | − | 0.783363i | \(-0.286497\pi\) |
−0.552948 | + | 0.833216i | \(0.686497\pi\) | |||||||
\(212\) | 8.06731 | − | 5.86125i | 0.554065 | − | 0.402552i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.12778 | − | 5.17864i | −0.487245 | − | 0.354004i | ||||
\(215\) | −21.0914 | + | 8.90920i | −1.43842 | + | 0.607602i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.53096 | + | 4.71181i | −0.103928 | + | 0.319858i | ||||
\(218\) | 15.8769 | 1.07532 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.0363546 | + | 0.424091i | 0.00245102 | + | 0.0285922i | ||||
\(221\) | −0.579407 | − | 1.78323i | −0.0389752 | − | 0.119953i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.77203 | − | 2.74054i | −0.252594 | − | 0.183520i | 0.454282 | − | 0.890858i | \(-0.349896\pi\) |
−0.706876 | + | 0.707338i | \(0.749896\pi\) | |||||||
\(224\) | 2.92807 | 0.195640 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.1399 | 1.27317 | ||||||||
\(227\) | 0.464034 | + | 0.337140i | 0.0307990 | + | 0.0223768i | 0.603078 | − | 0.797682i | \(-0.293941\pi\) |
−0.572279 | + | 0.820059i | \(0.693941\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.18801 | + | 28.2778i | 0.607161 | + | 1.86865i | 0.481195 | + | 0.876614i | \(0.340203\pi\) |
0.125966 | + | 0.992035i | \(0.459797\pi\) | |||||||
\(230\) | −6.54736 | − | 7.55858i | −0.431720 | − | 0.498398i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.81168 | −0.447209 | ||||||||
\(233\) | 4.28819 | − | 13.1977i | 0.280929 | − | 0.864610i | −0.706661 | − | 0.707553i | \(-0.749799\pi\) |
0.987589 | − | 0.157057i | \(-0.0502008\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.6820 | + | 18.1040i | 1.02298 | + | 1.18098i | ||||
\(236\) | 6.00810 | + | 4.36514i | 0.391094 | + | 0.284147i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 14.3262 | − | 10.4086i | 0.928632 | − | 0.674691i | ||||
\(239\) | −1.73442 | − | 1.26013i | −0.112191 | − | 0.0815112i | 0.530275 | − | 0.847825i | \(-0.322089\pi\) |
−0.642466 | + | 0.766314i | \(0.722089\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.40748 | + | 1.02260i | −0.0906639 | + | 0.0658712i | −0.632194 | − | 0.774810i | \(-0.717845\pi\) |
0.541530 | + | 0.840682i | \(0.317845\pi\) | |||||||
\(242\) | −3.38799 | + | 10.4272i | −0.217788 | + | 0.670283i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.71384 | + | 5.27466i | −0.109717 | + | 0.337675i | ||||
\(245\) | 3.24132 | − | 1.36916i | 0.207080 | − | 0.0874724i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.310033 | + | 0.954184i | 0.0197269 | + | 0.0607133i | ||||
\(248\) | 1.36886 | + | 0.994532i | 0.0869224 | + | 0.0631529i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.40850 | + | 6.03988i | −0.595046 | + | 0.381996i | ||||
\(251\) | 6.39691 | 0.403770 | 0.201885 | − | 0.979409i | \(-0.435293\pi\) | ||||
0.201885 | + | 0.979409i | \(0.435293\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.263064 | + | 0.809628i | 0.0165387 | + | 0.0509009i | ||||
\(254\) | −2.51475 | − | 7.73962i | −0.157790 | − | 0.485627i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | 6.31003 | 0.393609 | 0.196805 | − | 0.980443i | \(-0.436944\pi\) | ||||
0.196805 | + | 0.980443i | \(0.436944\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.1104 | − | 16.7907i | 1.43601 | − | 1.04332i | ||||
\(260\) | −0.675213 | − | 0.157132i | −0.0418749 | − | 0.00974490i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.4459 | − | 9.76903i | 0.830691 | − | 0.603533i | ||||
\(263\) | 2.31332 | − | 1.68073i | 0.142646 | − | 0.103638i | −0.514174 | − | 0.857686i | \(-0.671901\pi\) |
0.656819 | + | 0.754048i | \(0.271901\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.5990 | − | 16.8537i | −0.896808 | − | 1.03532i | ||||
\(266\) | −7.66578 | + | 5.56951i | −0.470019 | + | 0.341489i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −15.0922 | −0.921903 | ||||||||
\(269\) | 2.99937 | − | 9.23112i | 0.182875 | − | 0.562831i | −0.817030 | − | 0.576595i | \(-0.804381\pi\) |
0.999905 | + | 0.0137635i | \(0.00438119\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.30503 | + | 16.3272i | 0.322257 | + | 0.991806i | 0.972663 | + | 0.232219i | \(0.0745988\pi\) |
−0.650406 | + | 0.759587i | \(0.725401\pi\) | |||||||
\(272\) | −1.86886 | − | 5.75175i | −0.113316 | − | 0.348751i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.6383 | 0.642683 | ||||||||
\(275\) | 0.937889 | − | 0.161988i | 0.0565568 | − | 0.00976827i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.65337 | + | 1.20125i | 0.0993415 | + | 0.0721758i | 0.636347 | − | 0.771403i | \(-0.280445\pi\) |
−0.537006 | + | 0.843579i | \(0.680445\pi\) | |||||||
\(278\) | 7.07397 | + | 21.7714i | 0.424268 | + | 1.30576i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.559211 | − | 6.52343i | −0.0334193 | − | 0.389850i | ||||
\(281\) | −1.59416 | + | 4.90632i | −0.0950997 | + | 0.292687i | −0.987280 | − | 0.158993i | \(-0.949175\pi\) |
0.892180 | + | 0.451680i | \(0.149175\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.90059 | + | 8.92710i | −0.172422 | + | 0.530661i | −0.999506 | − | 0.0314171i | \(-0.989998\pi\) |
0.827084 | + | 0.562078i | \(0.189998\pi\) | |||||||
\(284\) | 5.54610 | − | 4.02948i | 0.329101 | − | 0.239106i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0477452 | + | 0.0346889i | 0.00282323 | + | 0.00205120i | ||||
\(287\) | 12.0195 | − | 8.73267i | 0.709488 | − | 0.515473i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.8367 | − | 11.5060i | −0.931570 | − | 0.676825i | ||||
\(290\) | 1.30091 | + | 15.1757i | 0.0763923 | + | 0.891149i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.59619 | − | 11.0679i | 0.210451 | − | 0.647703i | ||||
\(293\) | 8.18160 | 0.477974 | 0.238987 | − | 0.971023i | \(-0.423185\pi\) | ||||
0.238987 | + | 0.971023i | \(0.423185\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.57764 | − | 14.2191i | 0.499410 | − | 0.827868i | ||||
\(296\) | −3.01475 | − | 9.27846i | −0.175229 | − | 0.539299i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.13925 | + | 0.827711i | 0.0659948 | + | 0.0479480i | ||||
\(299\) | −1.38651 | −0.0801840 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −29.9815 | −1.72811 | ||||||||
\(302\) | 6.36886 | + | 4.62724i | 0.366486 | + | 0.266268i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | + | 3.07768i | 0.0573539 | + | 0.176517i | ||||
\(305\) | 12.0787 | + | 2.81089i | 0.691625 | + | 0.160951i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.85865 | 0.334371 | 0.167185 | − | 0.985925i | \(-0.446532\pi\) | ||||
0.167185 | + | 0.985925i | \(0.446532\pi\) | |||||||
\(308\) | −0.172237 | + | 0.530092i | −0.00981414 | + | 0.0302048i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.95429 | − | 3.23961i | 0.110996 | − | 0.183997i | ||||
\(311\) | −15.4035 | − | 11.1913i | −0.873452 | − | 0.634600i | 0.0580591 | − | 0.998313i | \(-0.481509\pi\) |
−0.931511 | + | 0.363713i | \(0.881509\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.70542 | − | 7.05140i | 0.548583 | − | 0.398569i | −0.278680 | − | 0.960384i | \(-0.589897\pi\) |
0.827263 | + | 0.561815i | \(0.189897\pi\) | |||||||
\(314\) | 5.62715 | + | 4.08837i | 0.317559 | + | 0.230720i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.27039 | + | 0.922993i | −0.0714650 | + | 0.0519224i | ||||
\(317\) | −10.0778 | + | 31.0164i | −0.566028 | + | 1.74205i | 0.0988506 | + | 0.995102i | \(0.468483\pi\) |
−0.664878 | + | 0.746952i | \(0.731517\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.400683 | − | 1.23317i | 0.0224339 | − | 0.0690445i | ||||
\(320\) | −2.17787 | − | 0.506822i | −0.121747 | − | 0.0283322i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.04649 | − | 12.4538i | −0.225502 | − | 0.694024i | ||||
\(323\) | 15.8332 | + | 11.5035i | 0.880983 | + | 0.640072i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.221119 | + | 1.53431i | −0.0122655 | + | 0.0851084i | ||||
\(326\) | −14.0000 | −0.775388 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.56794 | − | 4.82563i | −0.0865751 | − | 0.266451i | ||||
\(329\) | 9.69200 | + | 29.8289i | 0.534337 | + | 1.64452i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.998744 | − | 3.07382i | 0.0548959 | − | 0.168952i | −0.919849 | − | 0.392272i | \(-0.871689\pi\) |
0.974745 | + | 0.223319i | \(0.0716893\pi\) | |||||||
\(332\) | −13.0195 | −0.714538 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.11436 | − | 0.809628i | 0.0609749 | − | 0.0443009i | ||||
\(335\) | 2.88235 | + | 33.6239i | 0.157480 | + | 1.83707i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.2445 | + | 12.5289i | −0.939367 | + | 0.682490i | −0.948268 | − | 0.317470i | \(-0.897167\pi\) |
0.00890132 | + | 0.999960i | \(0.497167\pi\) | |||||||
\(338\) | 10.4395 | − | 7.58471i | 0.567832 | − | 0.412554i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.4574 | + | 5.26211i | −0.675596 | + | 0.285378i | ||||
\(341\) | −0.260569 | + | 0.189314i | −0.0141106 | + | 0.0102519i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.8889 | −0.857922 | ||||||||
\(344\) | −3.16414 | + | 9.73821i | −0.170599 | + | 0.525049i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.27407 | + | 3.92117i | 0.0684942 | + | 0.210804i | ||||
\(347\) | −5.91496 | − | 18.2044i | −0.317532 | − | 0.977262i | −0.974700 | − | 0.223518i | \(-0.928246\pi\) |
0.657168 | − | 0.753744i | \(-0.271754\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.3745 | 0.769447 | 0.384724 | − | 0.923032i | \(-0.374297\pi\) | ||||
0.384724 | + | 0.923032i | \(0.374297\pi\) | |||||||
\(350\) | −14.4267 | + | 2.49173i | −0.771141 | + | 0.133189i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.154000 | + | 0.111888i | 0.00820825 | + | 0.00596364i | ||||
\(353\) | −7.53609 | − | 23.1937i | −0.401105 | − | 1.23448i | −0.924104 | − | 0.382142i | \(-0.875187\pi\) |
0.522998 | − | 0.852334i | \(-0.324813\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.0365 | − | 11.5866i | −0.532681 | − | 0.614952i | ||||
\(356\) | 2.86886 | − | 8.82943i | 0.152049 | − | 0.467959i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.33125 | + | 4.09715i | −0.0703585 | + | 0.216541i | ||||
\(359\) | −17.2576 | + | 12.5384i | −0.910821 | + | 0.661750i | −0.941222 | − | 0.337788i | \(-0.890321\pi\) |
0.0304014 | + | 0.999538i | \(0.490321\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.89919 | + | 5.01255i | 0.363115 | + | 0.263819i | ||||
\(362\) | −10.5108 | + | 7.63652i | −0.552433 | + | 0.401366i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.734424 | − | 0.533590i | −0.0384943 | − | 0.0279677i | ||||
\(365\) | −25.3451 | − | 5.89816i | −1.32662 | − | 0.308724i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.28553 | + | 10.1118i | −0.171503 | + | 0.527833i | −0.999457 | − | 0.0329641i | \(-0.989505\pi\) |
0.827953 | + | 0.560797i | \(0.189505\pi\) | |||||||
\(368\) | −4.47214 | −0.233126 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −20.0957 | + | 8.48859i | −1.04472 | + | 0.441301i | ||||
\(371\) | −9.02266 | − | 27.7689i | −0.468433 | − | 1.44169i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.997968 | − | 0.725066i | −0.0516728 | − | 0.0375425i | 0.561649 | − | 0.827376i | \(-0.310167\pi\) |
−0.613322 | + | 0.789833i | \(0.710167\pi\) | |||||||
\(374\) | 1.15122 | 0.0595281 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.7115 | 0.552403 | ||||||||
\(377\) | 1.70852 | + | 1.24131i | 0.0879932 | + | 0.0639308i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.82585 | + | 24.0855i | 0.401987 | + | 1.23719i | 0.923385 | + | 0.383875i | \(0.125411\pi\) |
−0.521398 | + | 0.853314i | \(0.674589\pi\) | |||||||
\(380\) | 6.66578 | − | 2.81568i | 0.341947 | − | 0.144441i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.23607 | 0.0632427 | ||||||||
\(383\) | −5.92681 | + | 18.2408i | −0.302846 | + | 0.932064i | 0.677626 | + | 0.735406i | \(0.263009\pi\) |
−0.980472 | + | 0.196657i | \(0.936991\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.21389 | + | 0.282489i | 0.0618654 | + | 0.0143970i | ||||
\(386\) | −14.0971 | − | 10.2422i | −0.717525 | − | 0.521313i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.40748 | + | 1.02260i | −0.0714541 | + | 0.0519145i | ||||
\(389\) | −6.71282 | − | 4.87715i | −0.340354 | − | 0.247281i | 0.404457 | − | 0.914557i | \(-0.367460\pi\) |
−0.744811 | + | 0.667275i | \(0.767460\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.8809 | + | 15.8974i | −1.10657 | + | 0.803968i | ||||
\(392\) | 0.486262 | − | 1.49656i | 0.0245599 | − | 0.0755877i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.61741 | + | 14.2109i | −0.232622 | + | 0.715936i | ||||
\(395\) | 2.29896 | + | 2.65402i | 0.115673 | + | 0.133538i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.73897 | − | 29.9735i | −0.488785 | − | 1.50432i | −0.826423 | − | 0.563049i | \(-0.809628\pi\) |
0.337639 | − | 0.941276i | \(-0.390372\pi\) | |||||||
\(398\) | 3.96771 | + | 2.88271i | 0.198883 | + | 0.144497i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.713211 | + | 4.94887i | −0.0356606 | + | 0.247444i | ||||
\(401\) | 13.6940 | 0.683847 | 0.341924 | − | 0.939728i | \(-0.388922\pi\) | ||||
0.341924 | + | 0.939728i | \(0.388922\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.162103 | − | 0.498901i | −0.00807492 | − | 0.0248520i | ||||
\(404\) | 0.236456 | + | 0.727737i | 0.0117641 | + | 0.0362063i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.16336 | + | 18.9689i | −0.305882 | + | 0.941409i | ||||
\(407\) | 1.85709 | 0.0920527 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.3488 | − | 17.6904i | 1.20397 | − | 0.874735i | 0.209300 | − | 0.977851i | \(-0.432881\pi\) |
0.994669 | + | 0.103116i | \(0.0328814\pi\) | |||||||
\(410\) | −10.4516 | + | 4.41483i | −0.516165 | + | 0.218033i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.55718 | + | 3.31098i | −0.224516 | + | 0.163120i | ||||
\(413\) | 17.5921 | − | 12.7814i | 0.865652 | − | 0.628933i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.48650 | + | 29.0061i | 0.122058 | + | 1.42385i | ||||
\(416\) | −0.250822 | + | 0.182233i | −0.0122976 | + | 0.00893470i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.616002 | −0.0301296 | ||||||||
\(419\) | −3.28756 | + | 10.1181i | −0.160608 | + | 0.494301i | −0.998686 | − | 0.0512500i | \(-0.983679\pi\) |
0.838078 | + | 0.545551i | \(0.183679\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.73916 | + | 11.5080i | 0.182236 | + | 0.560864i | 0.999890 | − | 0.0148461i | \(-0.00472583\pi\) |
−0.817654 | + | 0.575710i | \(0.804726\pi\) | |||||||
\(422\) | −0.380710 | − | 1.17170i | −0.0185327 | − | 0.0570377i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.97175 | −0.484271 | ||||||||
\(425\) | 14.1026 | + | 26.7488i | 0.684075 | + | 1.29751i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.1379 | + | 9.54525i | 0.635788 | + | 0.461927i | ||||
\(428\) | 2.72257 | + | 8.37921i | 0.131600 | + | 0.405024i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 22.3000 | + | 5.18954i | 1.07540 | + | 0.250262i | ||||
\(431\) | 0.337509 | − | 1.03875i | 0.0162572 | − | 0.0500346i | −0.942599 | − | 0.333927i | \(-0.891626\pi\) |
0.958856 | + | 0.283893i | \(0.0916260\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.74722 | − | 11.5328i | 0.180080 | − | 0.554229i | −0.819749 | − | 0.572723i | \(-0.805887\pi\) |
0.999829 | + | 0.0184940i | \(0.00588716\pi\) | |||||||
\(434\) | 4.00810 | − | 2.91206i | 0.192395 | − | 0.139783i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.8447 | − | 9.33220i | −0.615148 | − | 0.446931i | ||||
\(437\) | 11.7082 | − | 8.50651i | 0.560079 | − | 0.406921i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.2409 | − | 8.16698i | −0.536498 | − | 0.389789i | 0.286285 | − | 0.958145i | \(-0.407580\pi\) |
−0.822783 | + | 0.568356i | \(0.807580\pi\) | |||||||
\(440\) | 0.219863 | − | 0.364466i | 0.0104816 | − | 0.0173752i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.579407 | + | 1.78323i | −0.0275596 | + | 0.0848197i | ||||
\(443\) | 38.2047 | 1.81516 | 0.907579 | − | 0.419880i | \(-0.137928\pi\) | ||||
0.907579 | + | 0.419880i | \(0.137928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.2190 | − | 4.70524i | −0.958471 | − | 0.223050i | ||||
\(446\) | 1.44079 | + | 4.43429i | 0.0682233 | + | 0.209970i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.36886 | − | 1.72107i | −0.111918 | − | 0.0813131i | ||||
\(449\) | −14.8092 | −0.698888 | −0.349444 | − | 0.936957i | \(-0.613629\pi\) | ||||
−0.349444 | + | 0.936957i | \(0.613629\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.965855 | 0.0454803 | ||||||||
\(452\) | −15.4845 | − | 11.2502i | −0.728332 | − | 0.529164i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.177245 | − | 0.545504i | −0.00831852 | − | 0.0256018i | ||||
\(455\) | −1.04852 | + | 1.73813i | −0.0491554 | + | 0.0814847i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.86286 | 0.227475 | 0.113738 | − | 0.993511i | \(-0.463718\pi\) | ||||
0.113738 | + | 0.993511i | \(0.463718\pi\) | |||||||
\(458\) | 9.18801 | − | 28.2778i | 0.429327 | − | 1.32133i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.854102 | + | 9.96346i | 0.0398227 | + | 0.464549i | ||||
\(461\) | −16.4278 | − | 11.9355i | −0.765117 | − | 0.555890i | 0.135359 | − | 0.990797i | \(-0.456781\pi\) |
−0.900475 | + | 0.434907i | \(0.856781\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.3465 | + | 23.5011i | −1.50327 | + | 1.09219i | −0.534213 | + | 0.845350i | \(0.679392\pi\) |
−0.969056 | + | 0.246840i | \(0.920608\pi\) | |||||||
\(464\) | 5.51076 | + | 4.00380i | 0.255831 | + | 0.185872i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.2266 | + | 8.15663i | −0.520064 | + | 0.377848i | ||||
\(467\) | 4.92623 | − | 15.1614i | 0.227959 | − | 0.701585i | −0.770019 | − | 0.638021i | \(-0.779753\pi\) |
0.997978 | − | 0.0635638i | \(-0.0202466\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.6558 | + | 42.0281i | −0.630565 | + | 1.94068i | ||||
\(470\) | −2.04571 | − | 23.8641i | −0.0943617 | − | 1.10077i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.29489 | − | 7.06295i | −0.105631 | − | 0.325099i | ||||
\(473\) | −1.57687 | − | 1.14566i | −0.0725043 | − | 0.0526775i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.54610 | − | 14.3129i | −0.346239 | − | 0.656722i | ||||
\(476\) | −17.7082 | −0.811654 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.662491 | + | 2.03894i | 0.0303016 | + | 0.0932588i | ||||
\(479\) | 2.42768 | + | 7.47163i | 0.110923 | + | 0.341387i | 0.991075 | − | 0.133305i | \(-0.0425591\pi\) |
−0.880152 | + | 0.474693i | \(0.842559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.934674 | + | 2.87663i | −0.0426174 | + | 0.131163i | ||||
\(482\) | 1.73974 | 0.0792432 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.86987 | − | 6.44434i | 0.403176 | − | 0.292925i | ||||
\(485\) | 2.54704 | + | 2.94043i | 0.115655 | + | 0.133518i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.1264 | − | 24.0677i | 1.50110 | − | 1.09061i | 0.531158 | − | 0.847273i | \(-0.321757\pi\) |
0.969941 | − | 0.243340i | \(-0.0782430\pi\) | |||||||
\(488\) | 4.48689 | − | 3.25992i | 0.203112 | − | 0.147569i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.42705 | − | 0.797524i | −0.154818 | − | 0.0360285i | ||||
\(491\) | −6.08238 | + | 4.41911i | −0.274494 | + | 0.199432i | −0.716512 | − | 0.697574i | \(-0.754263\pi\) |
0.442018 | + | 0.897006i | \(0.354263\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.1953 | 1.85534 | ||||||||
\(494\) | 0.310033 | − | 0.954184i | 0.0139490 | − | 0.0429308i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.522856 | − | 1.60919i | −0.0234769 | − | 0.0722546i | ||||
\(497\) | −6.20288 | − | 19.0905i | −0.278237 | − | 0.856326i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.7513 | 0.705123 | 0.352561 | − | 0.935789i | \(-0.385311\pi\) | ||||
0.352561 | + | 0.935789i | \(0.385311\pi\) | |||||||
\(500\) | 11.1618 | + | 0.643811i | 0.499170 | + | 0.0287921i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.17521 | − | 3.76001i | −0.230981 | − | 0.167818i | ||||
\(503\) | −0.253049 | − | 0.778805i | −0.0112829 | − | 0.0347252i | 0.945257 | − | 0.326328i | \(-0.105811\pi\) |
−0.956539 | + | 0.291603i | \(0.905811\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.57616 | − | 0.665785i | 0.0701384 | − | 0.0296271i | ||||
\(506\) | 0.263064 | − | 0.809628i | 0.0116946 | − | 0.0359924i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.51475 | + | 7.73962i | −0.111574 | + | 0.343390i | ||||
\(509\) | 21.8047 | − | 15.8420i | 0.966477 | − | 0.702186i | 0.0118309 | − | 0.999930i | \(-0.496234\pi\) |
0.954646 | + | 0.297744i | \(0.0962340\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.5676 | − | 20.0291i | −1.21952 | − | 0.886033i | ||||
\(512\) | −0.809017 | + | 0.587785i | −0.0357538 | + | 0.0259767i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.10492 | − | 3.70894i | −0.225169 | − | 0.163595i | ||||
\(515\) | 8.24688 | + | 9.52058i | 0.363401 | + | 0.419527i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.630081 | + | 1.93919i | −0.0277109 | + | 0.0852855i | ||||
\(518\) | −28.5661 | −1.25512 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.453899 | + | 0.524002i | 0.0199048 | + | 0.0229790i | ||||
\(521\) | 4.77653 | + | 14.7007i | 0.209264 | + | 0.644048i | 0.999511 | + | 0.0312598i | \(0.00995193\pi\) |
−0.790248 | + | 0.612788i | \(0.790048\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.35778 | − | 6.07228i | −0.365460 | − | 0.265522i | 0.389866 | − | 0.920872i | \(-0.372521\pi\) |
−0.755326 | + | 0.655349i | \(0.772521\pi\) | |||||||
\(524\) | −16.6201 | −0.726051 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.85942 | −0.124677 | ||||||||
\(527\) | −8.27849 | − | 6.01468i | −0.360617 | − | 0.262003i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.927051 | − | 2.85317i | −0.0403066 | − | 0.124051i | ||||
\(530\) | 1.90443 | + | 22.2160i | 0.0827233 | + | 0.965003i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.47542 | 0.410812 | ||||||||
\(533\) | −0.486114 | + | 1.49610i | −0.0210559 | + | 0.0648035i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.1480 | − | 7.66589i | 0.784609 | − | 0.331425i | ||||
\(536\) | 12.2098 | + | 8.87097i | 0.527385 | + | 0.383168i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.85246 | + | 5.70514i | −0.338543 | + | 0.245966i | ||||
\(539\) | 0.242332 | + | 0.176064i | 0.0104380 | + | 0.00758362i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.9620 | − | 21.7687i | 1.28817 | − | 0.935908i | 0.288400 | − | 0.957510i | \(-0.406877\pi\) |
0.999767 | + | 0.0216018i | \(0.00687662\pi\) | |||||||
\(542\) | 5.30503 | − | 16.3272i | 0.227870 | − | 0.701313i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.86886 | + | 5.75175i | −0.0801265 | + | 0.246604i | ||||
\(545\) | −18.3381 | + | 30.3989i | −0.785516 | + | 1.30215i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.48341 | − | 23.0316i | −0.319967 | − | 0.984758i | −0.973661 | − | 0.227999i | \(-0.926782\pi\) |
0.653694 | − | 0.756759i | \(-0.273218\pi\) | |||||||
\(548\) | −8.60657 | − | 6.25304i | −0.367654 | − | 0.267117i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.853982 | − | 0.420226i | −0.0364139 | − | 0.0179185i | ||||
\(551\) | −22.0431 | −0.939066 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.42083 | + | 4.37287i | 0.0604199 | + | 0.185953i | ||||
\(554\) | −0.631532 | − | 1.94366i | −0.0268312 | − | 0.0825780i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.07397 | − | 21.7714i | 0.300003 | − | 0.923314i | ||||
\(557\) | −26.3623 | −1.11701 | −0.558504 | − | 0.829502i | \(-0.688624\pi\) | ||||
−0.558504 | + | 0.829502i | \(0.688624\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.56826 | − | 1.86595i | 0.108626 | − | 0.0789212i | ||||
\(560\) | −3.38197 | + | 5.60626i | −0.142914 | + | 0.236908i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.17357 | − | 3.03228i | 0.176051 | − | 0.127909i | ||||
\(563\) | 12.2197 | − | 8.87811i | 0.514998 | − | 0.374168i | −0.299718 | − | 0.954028i | \(-0.596893\pi\) |
0.814716 | + | 0.579860i | \(0.196893\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.1070 | + | 36.6466i | −0.930047 | + | 1.54173i | ||||
\(566\) | 7.59385 | − | 5.51725i | 0.319193 | − | 0.231907i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.85536 | −0.287644 | ||||||||
\(569\) | 3.55757 | − | 10.9491i | 0.149141 | − | 0.459009i | −0.848379 | − | 0.529389i | \(-0.822421\pi\) |
0.997520 | + | 0.0703802i | \(0.0224213\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.73974 | − | 29.9759i | −0.407596 | − | 1.25445i | −0.918708 | − | 0.394937i | \(-0.870767\pi\) |
0.511113 | − | 0.859514i | \(-0.329233\pi\) | |||||||
\(572\) | −0.0182371 | − | 0.0561279i | −0.000762530 | − | 0.00234682i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14.8569 | −0.620115 | ||||||||
\(575\) | 22.0344 | − | 3.80570i | 0.918900 | − | 0.158709i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.6769 | + | 7.75719i | 0.444483 | + | 0.322936i | 0.787414 | − | 0.616425i | \(-0.211420\pi\) |
−0.342930 | + | 0.939361i | \(0.611420\pi\) | |||||||
\(578\) | 6.04908 | + | 18.6171i | 0.251608 | + | 0.774371i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.86760 | − | 13.0421i | 0.326684 | − | 0.541543i | ||||
\(581\) | −11.7803 | + | 36.2561i | −0.488730 | + | 1.50416i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.586567 | − | 1.80527i | 0.0242931 | − | 0.0747666i | ||||
\(584\) | −9.41496 | + | 6.84037i | −0.389594 | + | 0.283056i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.61905 | − | 4.80902i | −0.273430 | − | 0.198659i | ||||
\(587\) | 24.9839 | − | 18.1519i | 1.03120 | − | 0.749208i | 0.0626487 | − | 0.998036i | \(-0.480045\pi\) |
0.968548 | + | 0.248828i | \(0.0800452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.42971 | + | 3.21837i | 0.182523 | + | 0.132611i | ||||
\(590\) | −15.2972 | + | 6.46168i | −0.629777 | + | 0.266023i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.01475 | + | 9.27846i | −0.123906 | + | 0.381342i | ||||
\(593\) | −5.13588 | −0.210905 | −0.105453 | − | 0.994424i | \(-0.533629\pi\) | ||||
−0.105453 | + | 0.994424i | \(0.533629\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.38197 | + | 39.4521i | 0.138647 | + | 1.61738i | ||||
\(596\) | −0.435153 | − | 1.33926i | −0.0178246 | − | 0.0548584i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.12171 | + | 0.814970i | 0.0458701 | + | 0.0333266i | ||||
\(599\) | 42.2558 | 1.72653 | 0.863263 | − | 0.504755i | \(-0.168417\pi\) | ||||
0.863263 | + | 0.504755i | \(0.168417\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.38893 | 0.179028 | 0.0895141 | − | 0.995986i | \(-0.471469\pi\) | ||||
0.0895141 | + | 0.995986i | \(0.471469\pi\) | |||||||
\(602\) | 24.2556 | + | 17.6227i | 0.988583 | + | 0.718247i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.43269 | − | 7.48704i | −0.0989846 | − | 0.304643i | ||||
\(605\) | −16.0513 | − | 18.5304i | −0.652579 | − | 0.753368i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.0265 | −1.21874 | −0.609368 | − | 0.792887i | \(-0.708577\pi\) | ||||
−0.609368 | + | 0.792887i | \(0.708577\pi\) | |||||||
\(608\) | 1.00000 | − | 3.07768i | 0.0405554 | − | 0.124817i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.11968 | − | 9.37374i | −0.328756 | − | 0.379532i | ||||
\(611\) | −2.68668 | − | 1.95199i | −0.108691 | − | 0.0789689i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.62512 | + | 2.63380i | −0.146417 | + | 0.106378i | −0.658582 | − | 0.752509i | \(-0.728844\pi\) |
0.512165 | + | 0.858887i | \(0.328844\pi\) | |||||||
\(614\) | −4.73974 | − | 3.44363i | −0.191281 | − | 0.138973i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.450924 | − | 0.327615i | 0.0181682 | − | 0.0132000i | ||||
\(617\) | 4.31692 | − | 13.2861i | 0.173793 | − | 0.534879i | −0.825783 | − | 0.563987i | \(-0.809267\pi\) |
0.999576 | + | 0.0291080i | \(0.00926666\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.54813 | − | 23.2308i | 0.303385 | − | 0.933723i | −0.676890 | − | 0.736084i | \(-0.736673\pi\) |
0.980275 | − | 0.197639i | \(-0.0633274\pi\) | |||||||
\(620\) | −3.48525 | + | 1.47220i | −0.139971 | + | 0.0591249i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.88361 | + | 18.1079i | 0.235911 | + | 0.726060i | ||||
\(623\) | −21.9920 | − | 15.9781i | −0.881092 | − | 0.640150i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.697366 | − | 24.9903i | −0.0278946 | − | 0.999611i | ||||
\(626\) | −11.9966 | −0.479479 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.14938 | − | 6.61511i | −0.0857696 | − | 0.263972i | ||||
\(629\) | 18.2325 | + | 56.1138i | 0.726976 | + | 2.23740i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.06269 | − | 9.42600i | 0.121924 | − | 0.375243i | −0.871404 | − | 0.490566i | \(-0.836790\pi\) |
0.993328 | + | 0.115322i | \(0.0367901\pi\) | |||||||
\(632\) | 1.57029 | 0.0624627 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26.3841 | − | 19.1692i | 1.04785 | − | 0.761306i | ||||
\(635\) | 17.7233 | + | 4.12448i | 0.703330 | + | 0.163675i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.394688 | + | 0.286758i | −0.0156381 | + | 0.0113617i | ||||
\(638\) | −1.04900 | + | 0.762144i | −0.0415304 | + | 0.0301736i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.46403 | + | 1.69015i | 0.0578710 | + | 0.0668090i | ||||
\(641\) | 31.9691 | − | 23.2269i | 1.26270 | − | 0.917407i | 0.263816 | − | 0.964573i | \(-0.415019\pi\) |
0.998887 | + | 0.0471657i | \(0.0150189\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.9508 | 0.905093 | 0.452547 | − | 0.891741i | \(-0.350516\pi\) | ||||
0.452547 | + | 0.891741i | \(0.350516\pi\) | |||||||
\(644\) | −4.04649 | + | 12.4538i | −0.159454 | + | 0.490749i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.04775 | − | 18.6130i | −0.237945 | − | 0.732320i | ||||
\(647\) | 0.761900 | + | 2.34489i | 0.0299534 | + | 0.0921870i | 0.964916 | − | 0.262560i | \(-0.0845669\pi\) |
−0.934962 | + | 0.354747i | \(0.884567\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.41366 | 0.0554909 | ||||||||
\(650\) | 1.08074 | − | 1.11132i | 0.0423900 | − | 0.0435894i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.3262 | + | 8.22899i | 0.443570 | + | 0.322272i | ||||
\(653\) | 8.27484 | + | 25.4673i | 0.323820 | + | 0.996614i | 0.971971 | + | 0.235102i | \(0.0755426\pi\) |
−0.648151 | + | 0.761512i | \(0.724457\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.17415 | + | 37.0278i | 0.124024 | + | 1.44680i | ||||
\(656\) | −1.56794 | + | 4.82563i | −0.0612178 | + | 0.188409i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.69200 | − | 29.8289i | 0.377833 | − | 1.16285i | ||||
\(659\) | 23.1334 | − | 16.8074i | 0.901150 | − | 0.654724i | −0.0376112 | − | 0.999292i | \(-0.511975\pi\) |
0.938761 | + | 0.344569i | \(0.111975\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.89981 | + | 1.38030i | 0.0738942 | + | 0.0536873i | 0.624119 | − | 0.781329i | \(-0.285458\pi\) |
−0.550225 | + | 0.835017i | \(0.685458\pi\) | |||||||
\(662\) | −2.61475 | + | 1.89972i | −0.101625 | + | 0.0738349i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.5330 | + | 7.65267i | 0.408759 | + | 0.296981i | ||||
\(665\) | −1.80964 | − | 21.1103i | −0.0701750 | − | 0.818621i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.41351 | − | 28.9718i | 0.364492 | − | 1.12179i | ||||
\(668\) | −1.37742 | −0.0532940 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17.4317 | − | 28.8965i | 0.673447 | − | 1.11637i | ||||
\(671\) | 0.326238 | + | 1.00406i | 0.0125943 | + | 0.0387612i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.3700 | + | 20.6120i | 1.09358 | + | 0.794534i | 0.980001 | − | 0.198994i | \(-0.0637675\pi\) |
0.113582 | + | 0.993529i | \(0.463767\pi\) | |||||||
\(674\) | 21.3154 | 0.821037 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.9039 | −0.496303 | ||||||||
\(677\) | 26.0549 | + | 18.9300i | 1.00137 | + | 0.727539i | 0.962382 | − | 0.271701i | \(-0.0875861\pi\) |
0.0389895 | + | 0.999240i | \(0.487586\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.57416 | + | 4.84477i | 0.0604107 | + | 0.185925i | ||||
\(680\) | 13.1712 | + | 3.06513i | 0.505093 | + | 0.117542i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.322080 | 0.0123331 | ||||||||
\(683\) | −4.26867 | + | 13.1376i | −0.163336 | + | 0.502697i | −0.998910 | − | 0.0466814i | \(-0.985135\pi\) |
0.835574 | + | 0.549378i | \(0.185135\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.2874 | + | 20.3688i | −0.469478 | + | 0.778251i | ||||
\(686\) | 12.8544 | + | 9.33928i | 0.490784 | + | 0.356575i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.28381 | − | 6.01854i | 0.315817 | − | 0.229455i | ||||
\(689\) | 2.50113 | + | 1.81718i | 0.0952856 | + | 0.0692291i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.9940 | − | 15.2531i | 0.798651 | − | 0.580254i | −0.111867 | − | 0.993723i | \(-0.535683\pi\) |
0.910518 | + | 0.413469i | \(0.135683\pi\) | |||||||
\(692\) | 1.27407 | − | 3.92117i | 0.0484327 | − | 0.149061i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.91496 | + | 18.2044i | −0.224529 | + | 0.691028i | ||||
\(695\) | −49.8555 | − | 11.6021i | −1.89113 | − | 0.440093i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.48251 | + | 29.1842i | 0.359176 | + | 1.10543i | ||||
\(698\) | −11.6292 | − | 8.44910i | −0.440171 | − | 0.319803i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 13.1361 | + | 6.46397i | 0.496497 | + | 0.244315i | ||||
\(701\) | −37.4437 | −1.41423 | −0.707115 | − | 0.707098i | \(-0.750004\pi\) | ||||
−0.707115 | + | 0.707098i | \(0.750004\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.75595 | − | 30.0257i | −0.367953 | − | 1.13244i | ||||
\(704\) | −0.0588229 | − | 0.181038i | −0.00221697 | − | 0.00682314i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.53609 | + | 23.1937i | −0.283624 | + | 0.872906i | ||||
\(707\) | 2.24052 | 0.0842635 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0996 | − | 10.2440i | 0.529522 | − | 0.384720i | −0.290657 | − | 0.956827i | \(-0.593874\pi\) |
0.820179 | + | 0.572107i | \(0.193874\pi\) | |||||||
\(710\) | 1.30926 | + | 15.2730i | 0.0491355 | + | 0.573187i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.51076 | + | 5.45689i | −0.281478 | + | 0.204506i | ||||
\(713\) | −6.12171 | + | 4.44768i | −0.229260 | + | 0.166567i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.121564 | + | 0.0513498i | −0.00454624 | + | 0.00192037i | ||||
\(716\) | 3.48525 | − | 2.53218i | 0.130250 | − | 0.0946320i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21.3316 | 0.796087 | ||||||||
\(719\) | 10.9650 | − | 33.7469i | 0.408926 | − | 1.25855i | −0.508646 | − | 0.860976i | \(-0.669854\pi\) |
0.917572 | − | 0.397570i | \(-0.130146\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.09685 | + | 15.6865i | 0.189817 | + | 0.584195i | ||||
\(722\) | −2.63525 | − | 8.11048i | −0.0980740 | − | 0.301841i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.9920 | 0.482845 | ||||||||
\(725\) | −30.5590 | − | 15.0374i | −1.13493 | − | 0.558475i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.4459 | + | 11.2221i | 0.572857 | + | 0.416205i | 0.836142 | − | 0.548513i | \(-0.184806\pi\) |
−0.263285 | + | 0.964718i | \(0.584806\pi\) | |||||||
\(728\) | 0.280525 | + | 0.863367i | 0.0103969 | + | 0.0319985i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 17.0377 | + | 19.6692i | 0.630595 | + | 0.727988i | ||||
\(731\) | 19.1359 | − | 58.8942i | 0.707766 | − | 2.17828i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.38352 | − | 10.4134i | 0.124973 | − | 0.384628i | −0.868923 | − | 0.494947i | \(-0.835187\pi\) |
0.993896 | + | 0.110319i | \(0.0351874\pi\) | |||||||
\(734\) | 8.60164 | − | 6.24945i | 0.317492 | − | 0.230672i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.61803 | + | 2.62866i | 0.133363 | + | 0.0968935i | ||||
\(737\) | −2.32421 | + | 1.68863i | −0.0856132 | + | 0.0622016i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.7566 | − | 28.1583i | −1.42568 | − | 1.03582i | −0.990800 | − | 0.135333i | \(-0.956790\pi\) |
−0.434884 | − | 0.900487i | \(-0.643210\pi\) | |||||||
\(740\) | 21.2472 | + | 4.94453i | 0.781063 | + | 0.181765i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.02266 | + | 27.7689i | −0.331232 | + | 1.01943i | ||||
\(743\) | −38.6016 | −1.41615 | −0.708077 | − | 0.706135i | \(-0.750437\pi\) | ||||
−0.708077 | + | 0.706135i | \(0.750437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.90064 | + | 1.22525i | −0.106271 | + | 0.0448898i | ||||
\(746\) | 0.381190 | + | 1.17318i | 0.0139563 | + | 0.0429532i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.931355 | − | 0.676669i | −0.0340537 | − | 0.0247415i | ||||
\(749\) | 25.7975 | 0.942620 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.2670 | −1.06797 | −0.533984 | − | 0.845495i | \(-0.679306\pi\) | ||||
−0.533984 | + | 0.845495i | \(0.679306\pi\) | |||||||
\(752\) | −8.66578 | − | 6.29606i | −0.316008 | − | 0.229594i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.652596 | − | 2.00848i | −0.0237662 | − | 0.0731447i | ||||
\(755\) | −16.2158 | + | 6.84967i | −0.590152 | + | 0.249285i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.0788 | −0.439012 | −0.219506 | − | 0.975611i | \(-0.570444\pi\) | ||||
−0.219506 | + | 0.975611i | \(0.570444\pi\) | |||||||
\(758\) | 7.82585 | − | 24.0855i | 0.284248 | − | 0.874824i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.04775 | − | 1.64011i | −0.255649 | − | 0.0594931i | ||||
\(761\) | −1.72093 | − | 1.25033i | −0.0623835 | − | 0.0453243i | 0.556156 | − | 0.831078i | \(-0.312276\pi\) |
−0.618540 | + | 0.785753i | \(0.712276\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −37.6101 | + | 27.3253i | −1.36158 | + | 0.989242i | ||||
\(764\) | −1.00000 | − | 0.726543i | −0.0361787 | − | 0.0262854i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.5166 | − | 11.2735i | 0.560637 | − | 0.407327i | ||||
\(767\) | −0.711492 | + | 2.18975i | −0.0256905 | + | 0.0790672i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.77310 | + | 8.53471i | −0.100000 | + | 0.307770i | −0.988525 | − | 0.151060i | \(-0.951731\pi\) |
0.888524 | + | 0.458830i | \(0.151731\pi\) | |||||||
\(770\) | −0.816012 | − | 0.942042i | −0.0294070 | − | 0.0339489i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.38463 | + | 16.5722i | 0.193797 | + | 0.596446i | ||||
\(773\) | 23.2575 | + | 16.8976i | 0.836515 | + | 0.607764i | 0.921395 | − | 0.388628i | \(-0.127051\pi\) |
−0.0848801 | + | 0.996391i | \(0.527051\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.94553 | + | 7.48360i | 0.141728 | + | 0.268819i | ||||
\(776\) | 1.73974 | 0.0624532 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.56407 | + | 7.89140i | 0.0919264 | + | 0.282920i | ||||
\(779\) | −5.07397 | − | 15.6161i | −0.181794 | − | 0.559503i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.403252 | − | 1.24108i | 0.0144295 | − | 0.0444094i | ||||
\(782\) | 27.0463 | 0.967175 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.27305 | + | 0.924925i | −0.0454661 | + | 0.0330330i | ||||
\(785\) | −14.3273 | + | 6.05197i | −0.511363 | + | 0.216004i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.9330 | − | 29.0130i | 1.42346 | − | 1.03420i | 0.432269 | − | 0.901745i | \(-0.357713\pi\) |
0.991189 | − | 0.132458i | \(-0.0422869\pi\) | |||||||
\(788\) | 12.0885 | − | 8.78283i | 0.430636 | − | 0.312875i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.299898 | − | 3.49844i | −0.0106699 | − | 0.124469i | ||||
\(791\) | −45.3398 | + | 32.9413i | −1.61210 | + | 1.17126i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.71948 | −0.0610603 | ||||||||
\(794\) | −9.73897 | + | 29.9735i | −0.345623 | + | 1.06372i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.51553 | − | 4.66432i | −0.0537165 | − | 0.165323i | ||||
\(797\) | −0.907289 | − | 2.79235i | −0.0321378 | − | 0.0989101i | 0.933701 | − | 0.358054i | \(-0.116560\pi\) |
−0.965839 | + | 0.259144i | \(0.916560\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −64.7804 | −2.29176 | ||||||||
\(800\) | 3.48587 | − | 3.58451i | 0.123244 | − | 0.126731i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.0787 | − | 8.04915i | −0.391203 | − | 0.284225i | ||||
\(803\) | −0.684553 | − | 2.10684i | −0.0241574 | − | 0.0743487i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.5186 | + | 6.63669i | 1.00515 | + | 0.233913i | ||||
\(806\) | −0.162103 | + | 0.498901i | −0.00570983 | + | 0.0175730i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.236456 | − | 0.727737i | 0.00831850 | − | 0.0256017i | ||||
\(809\) | −29.2720 | + | 21.2674i | −1.02915 | + | 0.747721i | −0.968138 | − | 0.250416i | \(-0.919433\pi\) |
−0.0610115 | + | 0.998137i | \(0.519433\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.5650 | + | 26.5660i | 1.28397 | + | 0.932858i | 0.999665 | − | 0.0258756i | \(-0.00823738\pi\) |
0.284304 | + | 0.958734i | \(0.408237\pi\) | |||||||
\(812\) | 16.1359 | − | 11.7234i | 0.566258 | − | 0.411411i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.50242 | − | 1.09157i | −0.0526598 | − | 0.0382596i | ||||
\(815\) | 16.1702 | − | 26.8053i | 0.566419 | − | 0.938948i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.2394 | + | 31.5135i | −0.358230 | + | 1.10252i | ||||
\(818\) | −30.0967 | −1.05231 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.0505 | + | 2.57160i | 0.385899 | + | 0.0898041i | ||||
\(821\) | 6.03945 | + | 18.5875i | 0.210778 | + | 0.648709i | 0.999426 | + | 0.0338640i | \(0.0107813\pi\) |
−0.788648 | + | 0.614845i | \(0.789219\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.1755 | + | 10.2991i | 0.494128 | + | 0.359005i | 0.806770 | − | 0.590866i | \(-0.201214\pi\) |
−0.312642 | + | 0.949871i | \(0.601214\pi\) | |||||||
\(824\) | 5.63298 | 0.196234 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.7451 | −0.756608 | ||||||||
\(827\) | −20.1268 | − | 14.6230i | −0.699879 | − | 0.508492i | 0.180014 | − | 0.983664i | \(-0.442386\pi\) |
−0.879893 | + | 0.475172i | \(0.842386\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.93738 | − | 15.1957i | −0.171482 | − | 0.527768i | 0.827973 | − | 0.560768i | \(-0.189494\pi\) |
−0.999455 | + | 0.0329996i | \(0.989494\pi\) | |||||||
\(830\) | 15.0377 | − | 24.9279i | 0.521967 | − | 0.865262i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.310033 | 0.0107485 | ||||||||
\(833\) | −2.94079 | + | 9.05082i | −0.101892 | + | 0.313592i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.263064 | + | 3.06875i | 0.00910371 | + | 0.106199i | ||||
\(836\) | 0.498356 | + | 0.362077i | 0.0172360 | + | 0.0125227i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.60696 | − | 6.25332i | 0.297322 | − | 0.216017i | ||||
\(839\) | −32.7244 | − | 23.7757i | −1.12977 | − | 0.820827i | −0.144110 | − | 0.989562i | \(-0.546032\pi\) |
−0.985662 | + | 0.168734i | \(0.946032\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0760 | + | 10.2268i | −0.485381 | + | 0.352650i | ||||
\(842\) | 3.73916 | − | 11.5080i | 0.128860 | − | 0.396590i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.380710 | + | 1.17170i | −0.0131046 | + | 0.0403317i | ||||
\(845\) | 2.46442 | + | 28.7485i | 0.0847787 | + | 0.988979i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.92026 | − | 30.5314i | −0.340864 | − | 1.04907i | ||||
\(848\) | 8.06731 | + | 5.86125i | 0.277033 | + | 0.201276i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.31332 | − | 29.9295i | 0.147946 | − | 1.02657i | ||||
\(851\) | 43.6299 | 1.49561 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.3509 | − | 41.0898i | −0.457126 | − | 1.40689i | −0.868621 | − | 0.495476i | \(-0.834993\pi\) |
0.411496 | − | 0.911412i | \(-0.365007\pi\) | |||||||
\(854\) | −5.01824 | − | 15.4445i | −0.171721 | − | 0.528501i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.72257 | − | 8.37921i | 0.0930555 | − | 0.286395i | ||||
\(857\) | −21.6193 | −0.738501 | −0.369250 | − | 0.929330i | \(-0.620386\pi\) | ||||
−0.369250 | + | 0.929330i | \(0.620386\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.5871 | − | 22.9494i | 1.07774 | − | 0.783023i | 0.100451 | − | 0.994942i | \(-0.467971\pi\) |
0.977287 | + | 0.211919i | \(0.0679713\pi\) | |||||||
\(860\) | −14.9908 | − | 17.3060i | −0.511181 | − | 0.590131i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.883610 | + | 0.641980i | −0.0300959 | + | 0.0218659i | ||||
\(863\) | −17.3283 | + | 12.5897i | −0.589861 | + | 0.428559i | −0.842266 | − | 0.539063i | \(-0.818779\pi\) |
0.252405 | + | 0.967622i | \(0.418779\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.97930 | − | 2.08961i | −0.305305 | − | 0.0710489i | ||||
\(866\) | −9.81035 | + | 7.12763i | −0.333369 | + | 0.242207i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.95429 | −0.168159 | ||||||||
\(869\) | −0.0923690 | + | 0.284283i | −0.00313340 | + | 0.00964362i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.44592 | − | 4.45007i | −0.0489930 | − | 0.150785i | ||||
\(872\) | 4.90623 | + | 15.0998i | 0.166146 | + | 0.511344i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.4721 | −0.489527 | ||||||||
\(875\) | 11.8923 | − | 30.5003i | 0.402033 | − | 1.03110i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.9859 | − | 27.5984i | −1.28269 | − | 0.931930i | −0.283061 | − | 0.959102i | \(-0.591350\pi\) |
−0.999631 | + | 0.0271718i | \(0.991350\pi\) | |||||||
\(878\) | 4.29363 | + | 13.2144i | 0.144903 | + | 0.445966i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.392101 | + | 0.165627i | −0.0132177 | + | 0.00558327i | ||||
\(881\) | −0.100961 | + | 0.310727i | −0.00340147 | + | 0.0104687i | −0.952743 | − | 0.303778i | \(-0.901752\pi\) |
0.949341 | + | 0.314247i | \(0.101752\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.29257 | + | 13.2112i | −0.144457 | + | 0.444592i | −0.996941 | − | 0.0781615i | \(-0.975095\pi\) |
0.852484 | + | 0.522753i | \(0.175095\pi\) | |||||||
\(884\) | 1.51691 | − | 1.10210i | 0.0510191 | − | 0.0370676i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30.9082 | − | 22.4561i | −1.03838 | − | 0.754429i | ||||
\(887\) | −4.39488 | + | 3.19307i | −0.147566 | + | 0.107213i | −0.659119 | − | 0.752039i | \(-0.729070\pi\) |
0.511553 | + | 0.859252i | \(0.329070\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.2775 | + | 14.0060i | 0.646548 | + | 0.469745i | ||||
\(890\) | 13.5918 | + | 15.6910i | 0.455599 | + | 0.525965i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.44079 | − | 4.43429i | 0.0482412 | − | 0.148471i | ||||
\(893\) | 34.6631 | 1.15996 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.30706 | − | 7.28117i | −0.210822 | − | 0.243383i | ||||
\(896\) | 0.904822 | + | 2.78476i | 0.0302280 | + | 0.0930322i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.9809 | + | 8.70461i | 0.399807 | + | 0.290477i | ||||
\(899\) | 11.5254 | 0.384392 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 60.3066 | 2.00910 | ||||||||
\(902\) | −0.781393 | − | 0.567715i | −0.0260175 | − | 0.0189028i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.91457 | + | 18.2032i | 0.196716 | + | 0.605428i | ||||
\(905\) | −2.48125 | − | 28.9449i | −0.0824797 | − | 0.962160i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.3381 | −1.60504 | −0.802521 | − | 0.596624i | \(-0.796508\pi\) | ||||
−0.802521 | + | 0.596624i | \(0.796508\pi\) | |||||||
\(908\) | −0.177245 | + | 0.545504i | −0.00588208 | + | 0.0181032i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.86992 | − | 0.789869i | 0.0619872 | − | 0.0261839i | ||||
\(911\) | 6.80839 | + | 4.94658i | 0.225572 | + | 0.163888i | 0.694831 | − | 0.719173i | \(-0.255479\pi\) |
−0.469259 | + | 0.883060i | \(0.655479\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.00501 | + | 1.45672i | −0.0663561 | + | 0.0482105i | ||||
\(914\) | −3.93414 | − | 2.85832i | −0.130130 | − | 0.0945448i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.0545 | + | 17.4766i | −0.794784 | + | 0.577444i | ||||
\(917\) | −15.0382 | + | 46.2829i | −0.496605 | + | 1.52839i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.87108 | − | 27.3024i | 0.292630 | − | 0.900623i | −0.691377 | − | 0.722494i | \(-0.742996\pi\) |
0.984007 | − | 0.178129i | \(-0.0570043\pi\) | |||||||
\(920\) | 5.16539 | − | 8.56264i | 0.170298 | − | 0.282302i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.27484 | + | 19.3120i | 0.206651 | + | 0.636006i | ||||
\(923\) | 1.71948 | + | 1.24927i | 0.0565972 | + | 0.0411203i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.95806 | − | 48.2809i | 0.228779 | − | 1.58747i | ||||
\(926\) | 39.9825 | 1.31391 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.10492 | − | 6.47829i | −0.0690975 | − | 0.212660i | ||||
\(929\) | 2.14735 | + | 6.60886i | 0.0704522 | + | 0.216830i | 0.980083 | − | 0.198588i | \(-0.0636355\pi\) |
−0.909631 | + | 0.415417i | \(0.863636\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.57358 | − | 4.84297i | 0.0515719 | − | 0.158722i | ||||
\(932\) | 13.8769 | 0.454552 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.8970 | + | 9.37024i | −0.422004 | + | 0.306604i | ||||
\(935\) | −1.32968 | + | 2.20420i | −0.0434851 | + | 0.0720849i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.1124 | + | 14.6125i | −0.657043 | + | 0.477370i | −0.865663 | − | 0.500627i | \(-0.833103\pi\) |
0.208620 | + | 0.977997i | \(0.433103\pi\) | |||||||
\(938\) | 35.7513 | − | 25.9748i | 1.16732 | − | 0.848108i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.3720 | + | 20.5089i | −0.403529 | + | 0.668927i | ||||
\(941\) | −0.380637 | + | 0.276549i | −0.0124084 | + | 0.00901524i | −0.593972 | − | 0.804486i | \(-0.702441\pi\) |
0.581564 | + | 0.813501i | \(0.302441\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.6915 | 0.738936 | ||||||||
\(944\) | −2.29489 | + | 7.06295i | −0.0746923 | + | 0.229879i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.602309 | + | 1.85372i | 0.0195828 | + | 0.0602695i | ||||
\(947\) | 10.1511 | + | 31.2420i | 0.329868 | + | 1.01523i | 0.969195 | + | 0.246294i | \(0.0792129\pi\) |
−0.639327 | + | 0.768935i | \(0.720787\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.60802 | 0.117121 | ||||||||
\(950\) | −2.30800 | + | 16.0149i | −0.0748814 | + | 0.519591i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 14.3262 | + | 10.4086i | 0.464316 | + | 0.337345i | ||||
\(953\) | 13.5051 | + | 41.5645i | 0.437474 | + | 1.34641i | 0.890530 | + | 0.454924i | \(0.150334\pi\) |
−0.453056 | + | 0.891482i | \(0.649666\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.42768 | + | 2.36665i | −0.0461986 | + | 0.0765831i | ||||
\(956\) | 0.662491 | − | 2.03894i | 0.0214265 | − | 0.0659440i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.42768 | − | 7.47163i | 0.0784347 | − | 0.241397i | ||||
\(959\) | −25.2006 | + | 18.3093i | −0.813770 | + | 0.591239i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.7634 | + | 16.5386i | 0.734304 | + | 0.533503i | ||||
\(962\) | 2.44701 | − | 1.77785i | 0.0788947 | − | 0.0573203i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.40748 | − | 1.02260i | −0.0453320 | − | 0.0329356i | ||||
\(965\) | 35.8927 | − | 15.1614i | 1.15543 | − | 0.488063i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.3952 | + | 41.2262i | −0.430760 | + | 1.32574i | 0.466609 | + | 0.884464i | \(0.345476\pi\) |
−0.897369 | + | 0.441281i | \(0.854524\pi\) | |||||||
\(968\) | −10.9638 | −0.352389 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.332262 | − | 3.87597i | −0.0106683 | − | 0.124450i | ||||
\(971\) | 9.30580 | + | 28.6403i | 0.298637 | + | 0.919111i | 0.981975 | + | 0.189009i | \(0.0605276\pi\) |
−0.683338 | + | 0.730102i | \(0.739472\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −54.2275 | − | 39.3986i | −1.73845 | − | 1.26306i | ||||
\(974\) | −40.9465 | −1.31201 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.54610 | −0.177526 | ||||||||
\(977\) | −1.14178 | − | 0.829555i | −0.0365289 | − | 0.0265398i | 0.569371 | − | 0.822081i | \(-0.307187\pi\) |
−0.605900 | + | 0.795541i | \(0.707187\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.546101 | − | 1.68073i | −0.0174535 | − | 0.0537162i | ||||
\(980\) | 2.30377 | + | 2.65958i | 0.0735912 | + | 0.0849572i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.51824 | 0.239917 | ||||||||
\(983\) | −3.00251 | + | 9.24078i | −0.0957653 | + | 0.294735i | −0.987452 | − | 0.157917i | \(-0.949522\pi\) |
0.891687 | + | 0.452652i | \(0.149522\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.8759 | − | 25.2546i | −0.697025 | − | 0.804679i | ||||
\(986\) | −33.3277 | − | 24.2140i | −1.06137 | − | 0.771130i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.811677 | + | 0.589718i | −0.0258229 | + | 0.0187614i | ||||
\(989\) | −37.0463 | − | 26.9157i | −1.17801 | − | 0.855871i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.3838 | + | 11.1770i | −0.488683 | + | 0.355049i | −0.804677 | − | 0.593712i | \(-0.797662\pi\) |
0.315995 | + | 0.948761i | \(0.397662\pi\) | |||||||
\(992\) | −0.522856 | + | 1.60919i | −0.0166007 | + | 0.0510917i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.20288 | + | 19.0905i | −0.196743 | + | 0.605514i | ||||
\(995\) | −10.1022 | + | 4.26725i | −0.320261 | + | 0.135281i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.41070 | − | 10.4970i | −0.108018 | − | 0.332445i | 0.882409 | − | 0.470483i | \(-0.155920\pi\) |
−0.990427 | + | 0.138038i | \(0.955920\pi\) | |||||||
\(998\) | −12.7430 | − | 9.25836i | −0.403374 | − | 0.293068i | ||||
\(999\) | 0 | 0 |
(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 | 450.2.h.d.91.2 | 8 | ||
3.2 | odd | 2 | 150.2.g.c.91.1 | yes | 8 | ||
15.2 | even | 4 | 750.2.h.e.49.2 | 16 | |||
15.8 | even | 4 | 750.2.h.e.49.3 | 16 | |||
15.14 | odd | 2 | 750.2.g.d.451.1 | 8 | |||
25.11 | even | 5 | inner | 450.2.h.d.361.2 | 8 | ||
75.2 | even | 20 | 750.2.h.e.199.4 | 16 | |||
75.8 | even | 20 | 3750.2.c.h.1249.5 | 8 | |||
75.11 | odd | 10 | 150.2.g.c.61.1 | ✓ | 8 | ||
75.14 | odd | 10 | 750.2.g.d.301.1 | 8 | |||
75.17 | even | 20 | 3750.2.c.h.1249.4 | 8 | |||
75.23 | even | 20 | 750.2.h.e.199.1 | 16 | |||
75.44 | odd | 10 | 3750.2.a.q.1.1 | 4 | |||
75.56 | odd | 10 | 3750.2.a.l.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.g.c.61.1 | ✓ | 8 | 75.11 | odd | 10 | ||
150.2.g.c.91.1 | yes | 8 | 3.2 | odd | 2 | ||
450.2.h.d.91.2 | 8 | 1.1 | even | 1 | trivial | ||
450.2.h.d.361.2 | 8 | 25.11 | even | 5 | inner | ||
750.2.g.d.301.1 | 8 | 75.14 | odd | 10 | |||
750.2.g.d.451.1 | 8 | 15.14 | odd | 2 | |||
750.2.h.e.49.2 | 16 | 15.2 | even | 4 | |||
750.2.h.e.49.3 | 16 | 15.8 | even | 4 | |||
750.2.h.e.199.1 | 16 | 75.23 | even | 20 | |||
750.2.h.e.199.4 | 16 | 75.2 | even | 20 | |||
3750.2.a.l.1.4 | 4 | 75.56 | odd | 10 | |||
3750.2.a.q.1.1 | 4 | 75.44 | odd | 10 | |||
3750.2.c.h.1249.4 | 8 | 75.17 | even | 20 | |||
3750.2.c.h.1249.5 | 8 | 75.8 | even | 20 |