Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(159,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.159");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.m (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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 37x^{14} + 559x^{12} + 4431x^{10} + 19684x^{8} + 48248x^{6} + 58656x^{4} + 25392x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 249.6 | ||
Root | \(-1.76701i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.249 |
Dual form | 370.2.m.c.159.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 1.53027 | − | 0.883503i | 0.883503 | − | 0.510091i | 0.0116912 | − | 0.999932i | \(-0.496278\pi\) |
0.871812 | + | 0.489841i | \(0.162945\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.03272 | + | 0.931689i | 0.909061 | + | 0.416664i | ||||
\(6\) | 1.76701i | 0.721377i | ||||||||
\(7\) | 3.45647 | − | 1.99560i | 1.30642 | − | 0.754264i | 0.324926 | − | 0.945739i | \(-0.394660\pi\) |
0.981497 | + | 0.191475i | \(0.0613271\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.0611550 | − | 0.105924i | 0.0203850 | − | 0.0353079i | ||||
\(10\) | −1.82323 | + | 1.29454i | −0.576555 | + | 0.409371i | ||||
\(11\) | −1.12438 | −0.339012 | −0.169506 | − | 0.985529i | \(-0.554217\pi\) | ||||
−0.169506 | + | 0.985529i | \(0.554217\pi\) | |||||||
\(12\) | −1.53027 | − | 0.883503i | −0.441751 | − | 0.255045i | ||||
\(13\) | −2.88034 | − | 4.98889i | −0.798862 | − | 1.38367i | −0.920358 | − | 0.391078i | \(-0.872102\pi\) |
0.121495 | − | 0.992592i | \(-0.461231\pi\) | |||||||
\(14\) | 3.99119i | 1.06669i | ||||||||
\(15\) | 3.93377 | − | 0.370178i | 1.01569 | − | 0.0955797i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.376657 | + | 0.652389i | −0.0913527 | + | 0.158228i | −0.908081 | − | 0.418796i | \(-0.862452\pi\) |
0.816728 | + | 0.577023i | \(0.195786\pi\) | |||||||
\(18\) | 0.0611550 | + | 0.105924i | 0.0144144 | + | 0.0249664i | ||||
\(19\) | −6.09832 | + | 3.52087i | −1.39905 | + | 0.807742i | −0.994293 | − | 0.106682i | \(-0.965977\pi\) |
−0.404757 | + | 0.914424i | \(0.632644\pi\) | |||||||
\(20\) | −0.209495 | − | 2.22623i | −0.0468444 | − | 0.497801i | ||||
\(21\) | 3.52623 | − | 6.10761i | 0.769486 | − | 1.33279i | ||||
\(22\) | 0.562188 | − | 0.973738i | 0.119859 | − | 0.207602i | ||||
\(23\) | 5.65184 | 1.17849 | 0.589245 | − | 0.807955i | \(-0.299425\pi\) | ||||
0.589245 | + | 0.807955i | \(0.299425\pi\) | |||||||
\(24\) | 1.53027 | − | 0.883503i | 0.312365 | − | 0.180344i | ||||
\(25\) | 3.26391 | + | 3.78773i | 0.652783 | + | 0.757545i | ||||
\(26\) | 5.76068 | 1.12976 | ||||||||
\(27\) | 5.08490i | 0.978589i | ||||||||
\(28\) | −3.45647 | − | 1.99560i | −0.653212 | − | 0.377132i | ||||
\(29\) | − | 2.65900i | − | 0.493764i | −0.969046 | − | 0.246882i | \(-0.920594\pi\) | ||
0.969046 | − | 0.246882i | \(-0.0794059\pi\) | |||||||
\(30\) | −1.64630 | + | 3.59183i | −0.300572 | + | 0.655776i | ||||
\(31\) | 2.29410i | 0.412032i | 0.978549 | + | 0.206016i | \(0.0660498\pi\) | ||||
−0.978549 | + | 0.206016i | \(0.933950\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −1.72060 | + | 0.993390i | −0.299518 | + | 0.172927i | ||||
\(34\) | −0.376657 | − | 0.652389i | −0.0645961 | − | 0.111884i | ||||
\(35\) | 8.88532 | − | 0.836134i | 1.50189 | − | 0.141332i | ||||
\(36\) | −0.122310 | −0.0203850 | ||||||||
\(37\) | 3.94471 | − | 4.63026i | 0.648506 | − | 0.761210i | ||||
\(38\) | − | 7.04173i | − | 1.14232i | ||||||
\(39\) | −8.81540 | − | 5.08958i | −1.41159 | − | 0.814984i | ||||
\(40\) | 2.03272 | + | 0.931689i | 0.321401 | + | 0.147313i | ||||
\(41\) | 2.08716 | + | 3.61506i | 0.325959 | + | 0.564578i | 0.981706 | − | 0.190403i | \(-0.0609795\pi\) |
−0.655747 | + | 0.754981i | \(0.727646\pi\) | |||||||
\(42\) | 3.52623 | + | 6.10761i | 0.544109 | + | 0.942424i | ||||
\(43\) | −8.57454 | −1.30760 | −0.653802 | − | 0.756665i | \(-0.726827\pi\) | ||||
−0.653802 | + | 0.756665i | \(0.726827\pi\) | |||||||
\(44\) | 0.562188 | + | 0.973738i | 0.0847531 | + | 0.146797i | ||||
\(45\) | 0.222999 | − | 0.158336i | 0.0332427 | − | 0.0236033i | ||||
\(46\) | −2.82592 | + | 4.89463i | −0.416659 | + | 0.721674i | ||||
\(47\) | 11.1824i | 1.63112i | 0.578672 | + | 0.815560i | \(0.303571\pi\) | ||||
−0.578672 | + | 0.815560i | \(0.696429\pi\) | |||||||
\(48\) | 1.76701i | 0.255045i | ||||||||
\(49\) | 4.46480 | − | 7.73327i | 0.637829 | − | 1.10475i | ||||
\(50\) | −4.91222 | + | 0.932768i | −0.694693 | + | 0.131913i | ||||
\(51\) | 1.33111i | 0.186393i | ||||||||
\(52\) | −2.88034 | + | 4.98889i | −0.399431 | + | 0.691835i | ||||
\(53\) | 0.361962 | + | 0.208979i | 0.0497194 | + | 0.0287055i | 0.524654 | − | 0.851316i | \(-0.324195\pi\) |
−0.474934 | + | 0.880021i | \(0.657528\pi\) | |||||||
\(54\) | −4.40365 | − | 2.54245i | −0.599261 | − | 0.345983i | ||||
\(55\) | −2.28554 | − | 1.04757i | −0.308183 | − | 0.141254i | ||||
\(56\) | 3.45647 | − | 1.99560i | 0.461891 | − | 0.266673i | ||||
\(57\) | −6.22139 | + | 10.7758i | −0.824044 | + | 1.42729i | ||||
\(58\) | 2.30276 | + | 1.32950i | 0.302367 | + | 0.174572i | ||||
\(59\) | −8.60234 | − | 4.96656i | −1.11993 | − | 0.646591i | −0.178546 | − | 0.983932i | \(-0.557139\pi\) |
−0.941383 | + | 0.337340i | \(0.890473\pi\) | |||||||
\(60\) | −2.28747 | − | 3.22165i | −0.295311 | − | 0.415914i | ||||
\(61\) | −5.28723 | + | 3.05258i | −0.676960 | + | 0.390843i | −0.798709 | − | 0.601718i | \(-0.794483\pi\) |
0.121749 | + | 0.992561i | \(0.461150\pi\) | |||||||
\(62\) | −1.98675 | − | 1.14705i | −0.252317 | − | 0.145675i | ||||
\(63\) | − | 0.488163i | − | 0.0615027i | ||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.20683 | − | 12.8246i | −0.149689 | − | 1.59070i | ||||
\(66\) | − | 1.98678i | − | 0.244556i | ||||||
\(67\) | 4.92123 | − | 2.84128i | 0.601224 | − | 0.347117i | −0.168299 | − | 0.985736i | \(-0.553827\pi\) |
0.769523 | + | 0.638619i | \(0.220494\pi\) | |||||||
\(68\) | 0.753314 | 0.0913527 | ||||||||
\(69\) | 8.64885 | − | 4.99341i | 1.04120 | − | 0.601136i | ||||
\(70\) | −3.71855 | + | 8.11298i | −0.444451 | + | 0.969687i | ||||
\(71\) | −0.469529 | − | 0.813247i | −0.0557228 | − | 0.0965147i | 0.836818 | − | 0.547480i | \(-0.184413\pi\) |
−0.892541 | + | 0.450966i | \(0.851080\pi\) | |||||||
\(72\) | 0.0611550 | − | 0.105924i | 0.00720719 | − | 0.0124832i | ||||
\(73\) | 8.97127i | 1.05001i | 0.851100 | + | 0.525004i | \(0.175936\pi\) | ||||
−0.851100 | + | 0.525004i | \(0.824064\pi\) | |||||||
\(74\) | 2.03757 | + | 5.73134i | 0.236863 | + | 0.666255i | ||||
\(75\) | 8.34114 | + | 2.91258i | 0.963152 | + | 0.336315i | ||||
\(76\) | 6.09832 | + | 3.52087i | 0.699525 | + | 0.403871i | ||||
\(77\) | −3.88638 | + | 2.24380i | −0.442894 | + | 0.255705i | ||||
\(78\) | 8.81540 | − | 5.08958i | 0.998148 | − | 0.576281i | ||||
\(79\) | 2.97626 | − | 1.71834i | 0.334855 | − | 0.193329i | −0.323139 | − | 0.946351i | \(-0.604738\pi\) |
0.657995 | + | 0.753023i | \(0.271405\pi\) | |||||||
\(80\) | −1.82323 | + | 1.29454i | −0.203843 | + | 0.144734i | ||||
\(81\) | 4.67599 | + | 8.09904i | 0.519554 | + | 0.899894i | ||||
\(82\) | −4.17431 | −0.460976 | ||||||||
\(83\) | −8.58455 | − | 4.95629i | −0.942276 | − | 0.544023i | −0.0516032 | − | 0.998668i | \(-0.516433\pi\) |
−0.890673 | + | 0.454644i | \(0.849766\pi\) | |||||||
\(84\) | −7.05246 | −0.769486 | ||||||||
\(85\) | −1.37346 | + | 0.975198i | −0.148973 | + | 0.105775i | ||||
\(86\) | 4.28727 | − | 7.42577i | 0.462308 | − | 0.800741i | ||||
\(87\) | −2.34923 | − | 4.06899i | −0.251864 | − | 0.436242i | ||||
\(88\) | −1.12438 | −0.119859 | ||||||||
\(89\) | 0.639228 | + | 0.369058i | 0.0677580 | + | 0.0391201i | 0.533496 | − | 0.845802i | \(-0.320878\pi\) |
−0.465738 | + | 0.884923i | \(0.654211\pi\) | |||||||
\(90\) | 0.0256233 | + | 0.272291i | 0.00270093 | + | 0.0287020i | ||||
\(91\) | −19.9116 | − | 11.4960i | −2.08731 | − | 1.20511i | ||||
\(92\) | −2.82592 | − | 4.89463i | −0.294622 | − | 0.510301i | ||||
\(93\) | 2.02684 | + | 3.51059i | 0.210174 | + | 0.364031i | ||||
\(94\) | −9.68424 | − | 5.59120i | −0.998854 | − | 0.576688i | ||||
\(95\) | −15.6765 | + | 1.47521i | −1.60838 | + | 0.151353i | ||||
\(96\) | −1.53027 | − | 0.883503i | −0.156183 | − | 0.0901721i | ||||
\(97\) | 1.90949 | 0.193879 | 0.0969395 | − | 0.995290i | \(-0.469095\pi\) | ||||
0.0969395 | + | 0.995290i | \(0.469095\pi\) | |||||||
\(98\) | 4.46480 | + | 7.73327i | 0.451013 | + | 0.781178i | ||||
\(99\) | −0.0687613 | + | 0.119098i | −0.00691077 | + | 0.0119698i | ||||
\(100\) | 1.64831 | − | 4.72049i | 0.164831 | − | 0.472049i | ||||
\(101\) | −3.66042 | −0.364226 | −0.182113 | − | 0.983278i | \(-0.558294\pi\) | ||||
−0.182113 | + | 0.983278i | \(0.558294\pi\) | |||||||
\(102\) | −1.15277 | − | 0.665555i | −0.114142 | − | 0.0658997i | ||||
\(103\) | −15.5340 | −1.53061 | −0.765304 | − | 0.643669i | \(-0.777411\pi\) | ||||
−0.765304 | + | 0.643669i | \(0.777411\pi\) | |||||||
\(104\) | −2.88034 | − | 4.98889i | −0.282440 | − | 0.489201i | ||||
\(105\) | 12.8582 | − | 9.12972i | 1.25483 | − | 0.890969i | ||||
\(106\) | −0.361962 | + | 0.208979i | −0.0351569 | + | 0.0202978i | ||||
\(107\) | 11.2563 | − | 6.49882i | 1.08819 | − | 0.628264i | 0.155093 | − | 0.987900i | \(-0.450432\pi\) |
0.933093 | + | 0.359635i | \(0.117099\pi\) | |||||||
\(108\) | 4.40365 | − | 2.54245i | 0.423741 | − | 0.244647i | ||||
\(109\) | −13.2003 | − | 7.62117i | −1.26435 | − | 0.729976i | −0.290441 | − | 0.956893i | \(-0.593802\pi\) |
−0.973914 | + | 0.226917i | \(0.927135\pi\) | |||||||
\(110\) | 2.04999 | − | 1.45555i | 0.195459 | − | 0.138782i | ||||
\(111\) | 1.94562 | − | 10.5707i | 0.184670 | − | 1.00333i | ||||
\(112\) | 3.99119i | 0.377132i | ||||||||
\(113\) | 3.12438 | − | 5.41158i | 0.293917 | − | 0.509078i | −0.680816 | − | 0.732455i | \(-0.738375\pi\) |
0.974732 | + | 0.223376i | \(0.0717079\pi\) | |||||||
\(114\) | −6.22139 | − | 10.7758i | −0.582687 | − | 1.00924i | ||||
\(115\) | 11.4886 | + | 5.26575i | 1.07132 | + | 0.491034i | ||||
\(116\) | −2.30276 | + | 1.32950i | −0.213806 | + | 0.123441i | ||||
\(117\) | −0.704589 | −0.0651393 | ||||||||
\(118\) | 8.60234 | − | 4.96656i | 0.791909 | − | 0.457209i | ||||
\(119\) | 3.00662i | 0.275616i | ||||||||
\(120\) | 3.93377 | − | 0.370178i | 0.359102 | − | 0.0337925i | ||||
\(121\) | −9.73578 | −0.885071 | ||||||||
\(122\) | − | 6.10516i | − | 0.552735i | ||||||
\(123\) | 6.38783 | + | 3.68802i | 0.575972 | + | 0.332537i | ||||
\(124\) | 1.98675 | − | 1.14705i | 0.178415 | − | 0.103008i | ||||
\(125\) | 3.10564 | + | 10.7403i | 0.277777 | + | 0.960646i | ||||
\(126\) | 0.422761 | + | 0.244081i | 0.0376626 | + | 0.0217445i | ||||
\(127\) | −14.9059 | − | 8.60590i | −1.32268 | − | 0.763650i | −0.338525 | − | 0.940957i | \(-0.609928\pi\) |
−0.984155 | + | 0.177308i | \(0.943261\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −13.1214 | + | 7.57563i | −1.15527 | + | 0.666997i | ||||
\(130\) | 11.7099 | + | 5.36716i | 1.02702 | + | 0.470731i | ||||
\(131\) | 9.49301 | + | 5.48079i | 0.829408 | + | 0.478859i | 0.853650 | − | 0.520847i | \(-0.174384\pi\) |
−0.0242418 | + | 0.999706i | \(0.507717\pi\) | |||||||
\(132\) | 1.72060 | + | 0.993390i | 0.149759 | + | 0.0864635i | ||||
\(133\) | −14.0525 | + | 24.3396i | −1.21850 | + | 2.11051i | ||||
\(134\) | 5.68255i | 0.490898i | ||||||||
\(135\) | −4.73754 | + | 10.3362i | −0.407742 | + | 0.889596i | ||||
\(136\) | −0.376657 | + | 0.652389i | −0.0322981 | + | 0.0559419i | ||||
\(137\) | − | 23.1827i | − | 1.98063i | −0.138833 | − | 0.990316i | \(-0.544335\pi\) | ||
0.138833 | − | 0.990316i | \(-0.455665\pi\) | |||||||
\(138\) | 9.98683i | 0.850135i | ||||||||
\(139\) | −0.122224 | + | 0.211698i | −0.0103669 | + | 0.0179560i | −0.871162 | − | 0.490995i | \(-0.836633\pi\) |
0.860795 | + | 0.508951i | \(0.169967\pi\) | |||||||
\(140\) | −5.16677 | − | 7.27685i | −0.436672 | − | 0.615006i | ||||
\(141\) | 9.87969 | + | 17.1121i | 0.832020 | + | 1.44110i | ||||
\(142\) | 0.939057 | 0.0788039 | ||||||||
\(143\) | 3.23859 | + | 5.60939i | 0.270824 | + | 0.469081i | ||||
\(144\) | 0.0611550 | + | 0.105924i | 0.00509625 | + | 0.00882697i | ||||
\(145\) | 2.47736 | − | 5.40500i | 0.205733 | − | 0.448861i | ||||
\(146\) | −7.76935 | − | 4.48564i | −0.642996 | − | 0.371234i | ||||
\(147\) | − | 15.7787i | − | 1.30140i | ||||||
\(148\) | −5.98227 | − | 1.10109i | −0.491740 | − | 0.0905087i | ||||
\(149\) | 16.5549 | 1.35623 | 0.678117 | − | 0.734954i | \(-0.262796\pi\) | ||||
0.678117 | + | 0.734954i | \(0.262796\pi\) | |||||||
\(150\) | −6.69294 | + | 5.76735i | −0.546476 | + | 0.470902i | ||||
\(151\) | 10.0750 | + | 17.4504i | 0.819891 | + | 1.42009i | 0.905762 | + | 0.423786i | \(0.139299\pi\) |
−0.0858716 | + | 0.996306i | \(0.527367\pi\) | |||||||
\(152\) | −6.09832 | + | 3.52087i | −0.494639 | + | 0.285580i | ||||
\(153\) | 0.0460689 | + | 0.0797937i | 0.00372445 | + | 0.00645094i | ||||
\(154\) | − | 4.48760i | − | 0.361621i | ||||||
\(155\) | −2.13738 | + | 4.66326i | −0.171679 | + | 0.374562i | ||||
\(156\) | 10.1792i | 0.814984i | ||||||||
\(157\) | 18.3795 | + | 10.6114i | 1.46685 | + | 0.846884i | 0.999312 | − | 0.0370902i | \(-0.0118089\pi\) |
0.467535 | + | 0.883975i | \(0.345142\pi\) | |||||||
\(158\) | 3.43669i | 0.273408i | ||||||||
\(159\) | 0.738534 | 0.0585696 | ||||||||
\(160\) | −0.209495 | − | 2.22623i | −0.0165620 | − | 0.175999i | ||||
\(161\) | 19.5354 | − | 11.2788i | 1.53961 | − | 0.888892i | ||||
\(162\) | −9.35197 | −0.734760 | ||||||||
\(163\) | 0.295353 | − | 0.511567i | 0.0231339 | − | 0.0400690i | −0.854227 | − | 0.519901i | \(-0.825969\pi\) |
0.877361 | + | 0.479832i | \(0.159302\pi\) | |||||||
\(164\) | 2.08716 | − | 3.61506i | 0.162980 | − | 0.282289i | ||||
\(165\) | −4.42303 | + | 0.416220i | −0.344333 | + | 0.0324027i | ||||
\(166\) | 8.58455 | − | 4.95629i | 0.666290 | − | 0.384683i | ||||
\(167\) | −1.67520 | − | 2.90153i | −0.129631 | − | 0.224527i | 0.793903 | − | 0.608045i | \(-0.208046\pi\) |
−0.923534 | + | 0.383518i | \(0.874713\pi\) | |||||||
\(168\) | 3.52623 | − | 6.10761i | 0.272054 | − | 0.471212i | ||||
\(169\) | −10.0927 | + | 17.4811i | −0.776362 | + | 1.34470i | ||||
\(170\) | −0.157815 | − | 1.67705i | −0.0121039 | − | 0.128624i | ||||
\(171\) | 0.861275i | 0.0658633i | ||||||||
\(172\) | 4.28727 | + | 7.42577i | 0.326901 | + | 0.566209i | ||||
\(173\) | 15.1720 | + | 8.75957i | 1.15351 | + | 0.665978i | 0.949740 | − | 0.313041i | \(-0.101348\pi\) |
0.203768 | + | 0.979019i | \(0.434681\pi\) | |||||||
\(174\) | 4.69847 | 0.356190 | ||||||||
\(175\) | 18.8404 | + | 6.57872i | 1.42420 | + | 0.497305i | ||||
\(176\) | 0.562188 | − | 0.973738i | 0.0423765 | − | 0.0733983i | ||||
\(177\) | −17.5519 | −1.31928 | ||||||||
\(178\) | −0.639228 | + | 0.369058i | −0.0479121 | + | 0.0276621i | ||||
\(179\) | 10.5351i | 0.787432i | 0.919232 | + | 0.393716i | \(0.128811\pi\) | ||||
−0.919232 | + | 0.393716i | \(0.871189\pi\) | |||||||
\(180\) | −0.248622 | − | 0.113955i | −0.0185312 | − | 0.00849370i | ||||
\(181\) | −1.36123 | − | 2.35772i | −0.101179 | − | 0.175248i | 0.810991 | − | 0.585058i | \(-0.198928\pi\) |
−0.912171 | + | 0.409810i | \(0.865595\pi\) | |||||||
\(182\) | 19.9116 | − | 11.4960i | 1.47595 | − | 0.852139i | ||||
\(183\) | −5.39393 | + | 9.34256i | −0.398731 | + | 0.690622i | ||||
\(184\) | 5.65184 | 0.416659 | ||||||||
\(185\) | 12.3324 | − | 5.73679i | 0.906700 | − | 0.421777i | ||||
\(186\) | −4.05368 | −0.297230 | ||||||||
\(187\) | 0.423504 | − | 0.733530i | 0.0309697 | − | 0.0536411i | ||||
\(188\) | 9.68424 | − | 5.59120i | 0.706296 | − | 0.407780i | ||||
\(189\) | 10.1474 | + | 17.5758i | 0.738114 | + | 1.27845i | ||||
\(190\) | 6.56070 | − | 14.3139i | 0.475963 | − | 1.03844i | ||||
\(191\) | 6.53981i | 0.473204i | 0.971607 | + | 0.236602i | \(0.0760337\pi\) | ||||
−0.971607 | + | 0.236602i | \(0.923966\pi\) | |||||||
\(192\) | 1.53027 | − | 0.883503i | 0.110438 | − | 0.0637613i | ||||
\(193\) | 16.1690 | 1.16387 | 0.581936 | − | 0.813235i | \(-0.302296\pi\) | ||||
0.581936 | + | 0.813235i | \(0.302296\pi\) | |||||||
\(194\) | −0.954744 | + | 1.65366i | −0.0685466 | + | 0.118726i | ||||
\(195\) | −13.1774 | − | 18.5589i | −0.943650 | − | 1.32903i | ||||
\(196\) | −8.92961 | −0.637829 | ||||||||
\(197\) | −10.6879 | − | 6.17064i | −0.761479 | − | 0.439640i | 0.0683477 | − | 0.997662i | \(-0.478227\pi\) |
−0.829826 | + | 0.558022i | \(0.811561\pi\) | |||||||
\(198\) | −0.0687613 | − | 0.119098i | −0.00488665 | − | 0.00846393i | ||||
\(199\) | − | 9.41652i | − | 0.667520i | −0.942658 | − | 0.333760i | \(-0.891683\pi\) | ||
0.942658 | − | 0.333760i | \(-0.108317\pi\) | |||||||
\(200\) | 3.26391 | + | 3.78773i | 0.230793 | + | 0.267833i | ||||
\(201\) | 5.02055 | − | 8.69585i | 0.354122 | − | 0.613358i | ||||
\(202\) | 1.83021 | − | 3.17002i | 0.128773 | − | 0.223042i | ||||
\(203\) | −5.30629 | − | 9.19076i | −0.372428 | − | 0.645065i | ||||
\(204\) | 1.15277 | − | 0.665555i | 0.0807104 | − | 0.0465982i | ||||
\(205\) | 0.874496 | + | 9.29299i | 0.0610775 | + | 0.649051i | ||||
\(206\) | 7.76698 | − | 13.4528i | 0.541151 | − | 0.937302i | ||||
\(207\) | 0.345638 | − | 0.598663i | 0.0240235 | − | 0.0416100i | ||||
\(208\) | 5.76068 | 0.399431 | ||||||||
\(209\) | 6.85681 | − | 3.95878i | 0.474295 | − | 0.273835i | ||||
\(210\) | 1.47745 | + | 15.7004i | 0.101954 | + | 1.08343i | ||||
\(211\) | −17.9571 | −1.23622 | −0.618110 | − | 0.786092i | \(-0.712101\pi\) | ||||
−0.618110 | + | 0.786092i | \(0.712101\pi\) | |||||||
\(212\) | − | 0.417958i | − | 0.0287055i | ||||||
\(213\) | −1.43701 | − | 0.829660i | −0.0984625 | − | 0.0568474i | ||||
\(214\) | 12.9976i | 0.888500i | ||||||||
\(215\) | −17.4296 | − | 7.98880i | −1.18869 | − | 0.544831i | ||||
\(216\) | 5.08490i | 0.345983i | ||||||||
\(217\) | 4.57809 | + | 7.92948i | 0.310781 | + | 0.538288i | ||||
\(218\) | 13.2003 | − | 7.62117i | 0.894034 | − | 0.516171i | ||||
\(219\) | 7.92615 | + | 13.7285i | 0.535599 | + | 0.927685i | ||||
\(220\) | 0.235551 | + | 2.50312i | 0.0158808 | + | 0.168761i | ||||
\(221\) | 4.33960 | 0.291913 | ||||||||
\(222\) | 8.18170 | + | 6.97032i | 0.549119 | + | 0.467817i | ||||
\(223\) | − | 18.1664i | − | 1.21651i | −0.793741 | − | 0.608255i | \(-0.791870\pi\) | ||
0.793741 | − | 0.608255i | \(-0.208130\pi\) | |||||||
\(224\) | −3.45647 | − | 1.99560i | −0.230945 | − | 0.133336i | ||||
\(225\) | 0.600814 | − | 0.114087i | 0.0400543 | − | 0.00760579i | ||||
\(226\) | 3.12438 | + | 5.41158i | 0.207830 | + | 0.359973i | ||||
\(227\) | 3.14423 | + | 5.44597i | 0.208690 | + | 0.361462i | 0.951302 | − | 0.308260i | \(-0.0997467\pi\) |
−0.742612 | + | 0.669722i | \(0.766413\pi\) | |||||||
\(228\) | 12.4428 | 0.824044 | ||||||||
\(229\) | −4.26079 | − | 7.37991i | −0.281561 | − | 0.487678i | 0.690208 | − | 0.723611i | \(-0.257519\pi\) |
−0.971769 | + | 0.235933i | \(0.924186\pi\) | |||||||
\(230\) | −10.3046 | + | 7.31655i | −0.679464 | + | 0.482439i | ||||
\(231\) | −3.96481 | + | 6.86725i | −0.260865 | + | 0.451832i | ||||
\(232\) | − | 2.65900i | − | 0.174572i | ||||||
\(233\) | − | 0.321449i | − | 0.0210588i | −0.999945 | − | 0.0105294i | \(-0.996648\pi\) | ||
0.999945 | − | 0.0105294i | \(-0.00335168\pi\) | |||||||
\(234\) | 0.352294 | − | 0.610192i | 0.0230302 | − | 0.0398895i | ||||
\(235\) | −10.4185 | + | 22.7307i | −0.679629 | + | 1.48279i | ||||
\(236\) | 9.93312i | 0.646591i | ||||||||
\(237\) | 3.03632 | − | 5.25907i | 0.197230 | − | 0.341613i | ||||
\(238\) | −2.60381 | − | 1.50331i | −0.168780 | − | 0.0974451i | ||||
\(239\) | −20.1752 | − | 11.6482i | −1.30503 | − | 0.753457i | −0.323764 | − | 0.946138i | \(-0.604948\pi\) |
−0.981261 | + | 0.192681i | \(0.938282\pi\) | |||||||
\(240\) | −1.64630 | + | 3.59183i | −0.106268 | + | 0.231852i | ||||
\(241\) | 19.9282 | − | 11.5055i | 1.28369 | − | 0.741136i | 0.306166 | − | 0.951978i | \(-0.400954\pi\) |
0.977520 | + | 0.210842i | \(0.0676205\pi\) | |||||||
\(242\) | 4.86789 | − | 8.43143i | 0.312920 | − | 0.541993i | ||||
\(243\) | 1.10011 | + | 0.635151i | 0.0705723 | + | 0.0407449i | ||||
\(244\) | 5.28723 | + | 3.05258i | 0.338480 | + | 0.195421i | ||||
\(245\) | 16.2807 | − | 11.5598i | 1.04014 | − | 0.738527i | ||||
\(246\) | −6.38783 | + | 3.68802i | −0.407273 | + | 0.235139i | ||||
\(247\) | 35.1305 | + | 20.2826i | 2.23530 | + | 1.29055i | ||||
\(248\) | 2.29410i | 0.145675i | ||||||||
\(249\) | −17.5156 | −1.11001 | ||||||||
\(250\) | −10.8542 | − | 2.68061i | −0.686482 | − | 0.169536i | ||||
\(251\) | 7.45541i | 0.470581i | 0.971925 | + | 0.235291i | \(0.0756042\pi\) | ||||
−0.971925 | + | 0.235291i | \(0.924396\pi\) | |||||||
\(252\) | −0.422761 | + | 0.244081i | −0.0266315 | + | 0.0153757i | ||||
\(253\) | −6.35479 | −0.399522 | ||||||||
\(254\) | 14.9059 | − | 8.60590i | 0.935276 | − | 0.539982i | ||||
\(255\) | −1.24018 | + | 2.70577i | −0.0776631 | + | 0.169442i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2.60820 | − | 4.51754i | 0.162695 | − | 0.281796i | −0.773139 | − | 0.634236i | \(-0.781315\pi\) |
0.935834 | + | 0.352440i | \(0.114648\pi\) | |||||||
\(258\) | − | 15.1513i | − | 0.943276i | ||||||
\(259\) | 4.39464 | − | 23.8764i | 0.273070 | − | 1.48361i | ||||
\(260\) | −10.5030 | + | 7.45745i | −0.651370 | + | 0.462492i | ||||
\(261\) | −0.281651 | − | 0.162611i | −0.0174337 | − | 0.0100654i | ||||
\(262\) | −9.49301 | + | 5.48079i | −0.586480 | + | 0.338605i | ||||
\(263\) | −20.2665 | + | 11.7008i | −1.24968 | + | 0.721505i | −0.971046 | − | 0.238892i | \(-0.923216\pi\) |
−0.278637 | + | 0.960396i | \(0.589883\pi\) | |||||||
\(264\) | −1.72060 | + | 0.993390i | −0.105896 | + | 0.0611389i | ||||
\(265\) | 0.541065 | + | 0.762032i | 0.0332374 | + | 0.0468113i | ||||
\(266\) | −14.0525 | − | 24.3396i | −0.861611 | − | 1.49235i | ||||
\(267\) | 1.30426 | 0.0798192 | ||||||||
\(268\) | −4.92123 | − | 2.84128i | −0.300612 | − | 0.173559i | ||||
\(269\) | 15.2189 | 0.927915 | 0.463958 | − | 0.885857i | \(-0.346429\pi\) | ||||
0.463958 | + | 0.885857i | \(0.346429\pi\) | |||||||
\(270\) | −6.58262 | − | 9.27092i | −0.400606 | − | 0.564210i | ||||
\(271\) | 1.48941 | − | 2.57974i | 0.0904755 | − | 0.156708i | −0.817236 | − | 0.576303i | \(-0.804495\pi\) |
0.907711 | + | 0.419595i | \(0.137828\pi\) | |||||||
\(272\) | −0.376657 | − | 0.652389i | −0.0228382 | − | 0.0395569i | ||||
\(273\) | −40.6269 | −2.45885 | ||||||||
\(274\) | 20.0768 | + | 11.5913i | 1.21288 | + | 0.700259i | ||||
\(275\) | −3.66987 | − | 4.25883i | −0.221301 | − | 0.256817i | ||||
\(276\) | −8.64885 | − | 4.99341i | −0.520599 | − | 0.300568i | ||||
\(277\) | −7.70564 | − | 13.3466i | −0.462987 | − | 0.801917i | 0.536121 | − | 0.844141i | \(-0.319889\pi\) |
−0.999108 | + | 0.0422243i | \(0.986556\pi\) | |||||||
\(278\) | −0.122224 | − | 0.211698i | −0.00733051 | − | 0.0126968i | ||||
\(279\) | 0.242999 | + | 0.140295i | 0.0145480 | + | 0.00839927i | ||||
\(280\) | 8.88532 | − | 0.836134i | 0.530999 | − | 0.0499685i | ||||
\(281\) | −10.1817 | − | 5.87838i | −0.607387 | − | 0.350675i | 0.164555 | − | 0.986368i | \(-0.447381\pi\) |
−0.771942 | + | 0.635693i | \(0.780714\pi\) | |||||||
\(282\) | −19.7594 | −1.17665 | ||||||||
\(283\) | −6.86014 | − | 11.8821i | −0.407793 | − | 0.706318i | 0.586849 | − | 0.809696i | \(-0.300368\pi\) |
−0.994642 | + | 0.103378i | \(0.967035\pi\) | |||||||
\(284\) | −0.469529 | + | 0.813247i | −0.0278614 | + | 0.0482574i | ||||
\(285\) | −22.6860 | + | 16.1077i | −1.34380 | + | 0.954140i | ||||
\(286\) | −6.47717 | −0.383003 | ||||||||
\(287\) | 14.4284 | + | 8.33024i | 0.851681 | + | 0.491718i | ||||
\(288\) | −0.122310 | −0.00720719 | ||||||||
\(289\) | 8.21626 | + | 14.2310i | 0.483309 | + | 0.837116i | ||||
\(290\) | 3.44219 | + | 4.84796i | 0.202132 | + | 0.284682i | ||||
\(291\) | 2.92204 | − | 1.68704i | 0.171293 | − | 0.0988959i | ||||
\(292\) | 7.76935 | − | 4.48564i | 0.454667 | − | 0.262502i | ||||
\(293\) | 16.2133 | − | 9.36075i | 0.947190 | − | 0.546861i | 0.0549833 | − | 0.998487i | \(-0.482489\pi\) |
0.892207 | + | 0.451627i | \(0.149156\pi\) | |||||||
\(294\) | 13.6647 | + | 7.88933i | 0.796943 | + | 0.460115i | ||||
\(295\) | −12.8589 | − | 18.1103i | −0.748672 | − | 1.05442i | ||||
\(296\) | 3.94471 | − | 4.63026i | 0.229281 | − | 0.269128i | ||||
\(297\) | − | 5.71734i | − | 0.331753i | ||||||
\(298\) | −8.27747 | + | 14.3370i | −0.479501 | + | 0.830520i | ||||
\(299\) | −16.2792 | − | 28.1964i | −0.941451 | − | 1.63064i | ||||
\(300\) | −1.64821 | − | 8.67993i | −0.0951593 | − | 0.501136i | ||||
\(301\) | −29.6377 | + | 17.1113i | −1.70829 | + | 0.986279i | ||||
\(302\) | −20.1500 | −1.15950 | ||||||||
\(303\) | −5.60144 | + | 3.23399i | −0.321794 | + | 0.185788i | ||||
\(304\) | − | 7.04173i | − | 0.403871i | ||||||
\(305\) | −13.5915 | + | 1.27900i | −0.778248 | + | 0.0732353i | ||||
\(306\) | −0.0921378 | −0.00526717 | ||||||||
\(307\) | 4.40733i | 0.251540i | 0.992059 | + | 0.125770i | \(0.0401401\pi\) | ||||
−0.992059 | + | 0.125770i | \(0.959860\pi\) | |||||||
\(308\) | 3.88638 | + | 2.24380i | 0.221447 | + | 0.127852i | ||||
\(309\) | −23.7712 | + | 13.7243i | −1.35230 | + | 0.780749i | ||||
\(310\) | −2.96981 | − | 4.18266i | −0.168674 | − | 0.237559i | ||||
\(311\) | 23.3952 | + | 13.5073i | 1.32662 | + | 0.765926i | 0.984776 | − | 0.173830i | \(-0.0556142\pi\) |
0.341847 | + | 0.939756i | \(0.388948\pi\) | |||||||
\(312\) | −8.81540 | − | 5.08958i | −0.499074 | − | 0.288141i | ||||
\(313\) | 3.20475 | − | 5.55078i | 0.181143 | − | 0.313749i | −0.761127 | − | 0.648603i | \(-0.775354\pi\) |
0.942270 | + | 0.334854i | \(0.108687\pi\) | |||||||
\(314\) | −18.3795 | + | 10.6114i | −1.03722 | + | 0.598838i | ||||
\(315\) | 0.454816 | − | 0.992299i | 0.0256260 | − | 0.0559097i | ||||
\(316\) | −2.97626 | − | 1.71834i | −0.167428 | − | 0.0966644i | ||||
\(317\) | 8.12713 | + | 4.69220i | 0.456465 | + | 0.263540i | 0.710557 | − | 0.703640i | \(-0.248443\pi\) |
−0.254092 | + | 0.967180i | \(0.581776\pi\) | |||||||
\(318\) | −0.369267 | + | 0.639590i | −0.0207075 | + | 0.0358664i | ||||
\(319\) | 2.98972i | 0.167392i | ||||||||
\(320\) | 2.03272 | + | 0.931689i | 0.113633 | + | 0.0520830i | ||||
\(321\) | 11.4835 | − | 19.8899i | 0.640944 | − | 1.11015i | ||||
\(322\) | 22.5576i | 1.25708i | ||||||||
\(323\) | − | 5.30463i | − | 0.295158i | ||||||
\(324\) | 4.67599 | − | 8.09904i | 0.259777 | − | 0.449947i | ||||
\(325\) | 9.49539 | − | 27.1932i | 0.526709 | − | 1.50841i | ||||
\(326\) | 0.295353 | + | 0.511567i | 0.0163581 | + | 0.0283331i | ||||
\(327\) | −26.9333 | −1.48941 | ||||||||
\(328\) | 2.08716 | + | 3.61506i | 0.115244 | + | 0.199608i | ||||
\(329\) | 22.3156 | + | 38.6517i | 1.23030 | + | 2.13094i | ||||
\(330\) | 1.85106 | − | 4.03857i | 0.101897 | − | 0.222316i | ||||
\(331\) | −13.3301 | − | 7.69616i | −0.732691 | − | 0.423019i | 0.0867151 | − | 0.996233i | \(-0.472363\pi\) |
−0.819406 | + | 0.573214i | \(0.805696\pi\) | |||||||
\(332\) | 9.91258i | 0.544023i | ||||||||
\(333\) | −0.249215 | − | 0.701001i | −0.0136569 | − | 0.0384146i | ||||
\(334\) | 3.35040 | 0.183326 | ||||||||
\(335\) | 12.6507 | − | 1.19046i | 0.691180 | − | 0.0650420i | ||||
\(336\) | 3.52623 | + | 6.10761i | 0.192372 | + | 0.333197i | ||||
\(337\) | 5.02764 | − | 2.90271i | 0.273873 | − | 0.158121i | −0.356773 | − | 0.934191i | \(-0.616123\pi\) |
0.630647 | + | 0.776070i | \(0.282790\pi\) | |||||||
\(338\) | −10.0927 | − | 17.4811i | −0.548971 | − | 0.950845i | ||||
\(339\) | − | 11.0416i | − | 0.599696i | ||||||
\(340\) | 1.53128 | + | 0.701854i | 0.0830451 | + | 0.0380634i | ||||
\(341\) | − | 2.57943i | − | 0.139684i | ||||||
\(342\) | −0.745886 | − | 0.430637i | −0.0403329 | − | 0.0232862i | ||||
\(343\) | − | 7.70143i | − | 0.415838i | ||||||
\(344\) | −8.57454 | −0.462308 | ||||||||
\(345\) | 22.2330 | − | 2.09219i | 1.19698 | − | 0.112640i | ||||
\(346\) | −15.1720 | + | 8.75957i | −0.815653 | + | 0.470917i | ||||
\(347\) | 2.99524 | 0.160793 | 0.0803966 | − | 0.996763i | \(-0.474381\pi\) | ||||
0.0803966 | + | 0.996763i | \(0.474381\pi\) | |||||||
\(348\) | −2.34923 | + | 4.06899i | −0.125932 | + | 0.218121i | ||||
\(349\) | 16.1132 | − | 27.9089i | 0.862520 | − | 1.49393i | −0.00696887 | − | 0.999976i | \(-0.502218\pi\) |
0.869489 | − | 0.493953i | \(-0.164448\pi\) | |||||||
\(350\) | −15.1175 | + | 13.0269i | −0.808067 | + | 0.696317i | ||||
\(351\) | 25.3680 | − | 14.6462i | 1.35404 | − | 0.781757i | ||||
\(352\) | 0.562188 | + | 0.973738i | 0.0299647 | + | 0.0519004i | ||||
\(353\) | −4.35239 | + | 7.53855i | −0.231654 | + | 0.401237i | −0.958295 | − | 0.285781i | \(-0.907747\pi\) |
0.726641 | + | 0.687017i | \(0.241080\pi\) | |||||||
\(354\) | 8.77594 | − | 15.2004i | 0.466436 | − | 0.807891i | ||||
\(355\) | −0.196728 | − | 2.09056i | −0.0104412 | − | 0.110955i | ||||
\(356\) | − | 0.738116i | − | 0.0391201i | ||||||
\(357\) | 2.65636 | + | 4.60094i | 0.140589 | + | 0.243508i | ||||
\(358\) | −9.12369 | − | 5.26756i | −0.482202 | − | 0.278399i | ||||
\(359\) | 25.8462 | 1.36411 | 0.682056 | − | 0.731300i | \(-0.261086\pi\) | ||||
0.682056 | + | 0.731300i | \(0.261086\pi\) | |||||||
\(360\) | 0.222999 | − | 0.158336i | 0.0117531 | − | 0.00834503i | ||||
\(361\) | 15.2930 | − | 26.4883i | 0.804895 | − | 1.39412i | ||||
\(362\) | 2.72246 | 0.143089 | ||||||||
\(363\) | −14.8984 | + | 8.60159i | −0.781963 | + | 0.451466i | ||||
\(364\) | 22.9920i | 1.20511i | ||||||||
\(365\) | −8.35843 | + | 18.2361i | −0.437500 | + | 0.954521i | ||||
\(366\) | −5.39393 | − | 9.34256i | −0.281945 | − | 0.488343i | ||||
\(367\) | −12.8318 | + | 7.40844i | −0.669814 | + | 0.386718i | −0.796006 | − | 0.605288i | \(-0.793058\pi\) |
0.126192 | + | 0.992006i | \(0.459724\pi\) | |||||||
\(368\) | −2.82592 | + | 4.89463i | −0.147311 | + | 0.255150i | ||||
\(369\) | 0.510560 | 0.0265787 | ||||||||
\(370\) | −1.19802 | + | 13.5486i | −0.0622819 | + | 0.704359i | ||||
\(371\) | 1.66815 | 0.0866061 | ||||||||
\(372\) | 2.02684 | − | 3.51059i | 0.105087 | − | 0.182016i | ||||
\(373\) | 18.1268 | − | 10.4655i | 0.938571 | − | 0.541884i | 0.0490590 | − | 0.998796i | \(-0.484378\pi\) |
0.889512 | + | 0.456912i | \(0.151044\pi\) | |||||||
\(374\) | 0.423504 | + | 0.733530i | 0.0218989 | + | 0.0379300i | ||||
\(375\) | 14.2416 | + | 13.6918i | 0.735433 | + | 0.707042i | ||||
\(376\) | 11.1824i | 0.576688i | ||||||||
\(377\) | −13.2655 | + | 7.65882i | −0.683206 | + | 0.394449i | ||||
\(378\) | −20.2948 | −1.04385 | ||||||||
\(379\) | 3.24827 | − | 5.62616i | 0.166852 | − | 0.288997i | −0.770459 | − | 0.637489i | \(-0.779973\pi\) |
0.937311 | + | 0.348493i | \(0.113306\pi\) | |||||||
\(380\) | 9.11584 | + | 12.8387i | 0.467632 | + | 0.658610i | ||||
\(381\) | −30.4133 | −1.55812 | ||||||||
\(382\) | −5.66364 | − | 3.26990i | −0.289777 | − | 0.167303i | ||||
\(383\) | 13.9034 | + | 24.0813i | 0.710428 | + | 1.23050i | 0.964697 | + | 0.263364i | \(0.0848320\pi\) |
−0.254269 | + | 0.967134i | \(0.581835\pi\) | |||||||
\(384\) | 1.76701i | 0.0901721i | ||||||||
\(385\) | −9.99044 | + | 0.940129i | −0.509160 | + | 0.0479134i | ||||
\(386\) | −8.08451 | + | 14.0028i | −0.411491 | + | 0.712723i | ||||
\(387\) | −0.524376 | + | 0.908246i | −0.0266555 | + | 0.0461687i | ||||
\(388\) | −0.954744 | − | 1.65366i | −0.0484698 | − | 0.0839521i | ||||
\(389\) | 15.8121 | − | 9.12913i | 0.801706 | − | 0.462865i | −0.0423611 | − | 0.999102i | \(-0.513488\pi\) |
0.844067 | + | 0.536237i | \(0.180155\pi\) | |||||||
\(390\) | 22.6612 | − | 2.13248i | 1.14749 | − | 0.107982i | ||||
\(391\) | −2.12880 | + | 3.68719i | −0.107658 | + | 0.186469i | ||||
\(392\) | 4.46480 | − | 7.73327i | 0.225507 | − | 0.390589i | ||||
\(393\) | 19.3692 | 0.977046 | ||||||||
\(394\) | 10.6879 | − | 6.17064i | 0.538447 | − | 0.310872i | ||||
\(395\) | 7.65086 | − | 0.719968i | 0.384957 | − | 0.0362255i | ||||
\(396\) | 0.137523 | 0.00691077 | ||||||||
\(397\) | − | 12.3519i | − | 0.619923i | −0.950749 | − | 0.309961i | \(-0.899684\pi\) | ||
0.950749 | − | 0.309961i | \(-0.100316\pi\) | |||||||
\(398\) | 8.15495 | + | 4.70826i | 0.408771 | + | 0.236004i | ||||
\(399\) | 49.6615i | 2.48619i | ||||||||
\(400\) | −4.91222 | + | 0.932768i | −0.245611 | + | 0.0466384i | ||||
\(401\) | 8.52882i | 0.425909i | 0.977062 | + | 0.212954i | \(0.0683086\pi\) | ||||
−0.977062 | + | 0.212954i | \(0.931691\pi\) | |||||||
\(402\) | 5.02055 | + | 8.69585i | 0.250402 | + | 0.433709i | ||||
\(403\) | 11.4450 | − | 6.60777i | 0.570116 | − | 0.329157i | ||||
\(404\) | 1.83021 | + | 3.17002i | 0.0910564 | + | 0.157714i | ||||
\(405\) | 1.95919 | + | 20.8197i | 0.0973529 | + | 1.03454i | ||||
\(406\) | 10.6126 | 0.526693 | ||||||||
\(407\) | −4.43533 | + | 5.20615i | −0.219851 | + | 0.258059i | ||||
\(408\) | 1.33111i | 0.0658997i | ||||||||
\(409\) | 15.7176 | + | 9.07457i | 0.777186 | + | 0.448708i | 0.835432 | − | 0.549594i | \(-0.185218\pi\) |
−0.0582462 | + | 0.998302i | \(0.518551\pi\) | |||||||
\(410\) | −8.48521 | − | 3.88916i | −0.419055 | − | 0.192072i | ||||
\(411\) | −20.4820 | − | 35.4758i | −1.01030 | − | 1.74989i | ||||
\(412\) | 7.76698 | + | 13.4528i | 0.382652 | + | 0.662772i | ||||
\(413\) | −39.6450 | −1.95080 | ||||||||
\(414\) | 0.345638 | + | 0.598663i | 0.0169872 | + | 0.0294227i | ||||
\(415\) | −12.8323 | − | 18.0729i | −0.629911 | − | 0.887163i | ||||
\(416\) | −2.88034 | + | 4.98889i | −0.141220 | + | 0.244601i | ||||
\(417\) | 0.431941i | 0.0211523i | ||||||||
\(418\) | 7.91756i | 0.387260i | ||||||||
\(419\) | −0.982935 | + | 1.70249i | −0.0480195 | + | 0.0831723i | −0.889036 | − | 0.457837i | \(-0.848624\pi\) |
0.841017 | + | 0.541009i | \(0.181958\pi\) | |||||||
\(420\) | −14.3357 | − | 6.57070i | −0.699510 | − | 0.320617i | ||||
\(421\) | 5.71401i | 0.278484i | 0.990258 | + | 0.139242i | \(0.0444666\pi\) | ||||
−0.990258 | + | 0.139242i | \(0.955533\pi\) | |||||||
\(422\) | 8.97857 | − | 15.5513i | 0.437070 | − | 0.757027i | ||||
\(423\) | 1.18448 | + | 0.683860i | 0.0575914 | + | 0.0332504i | ||||
\(424\) | 0.361962 | + | 0.208979i | 0.0175784 | + | 0.0101489i | ||||
\(425\) | −3.70045 | + | 0.702667i | −0.179498 | + | 0.0340843i | ||||
\(426\) | 1.43701 | − | 0.829660i | 0.0696235 | − | 0.0401972i | ||||
\(427\) | −12.1834 | + | 21.1023i | −0.589598 | + | 1.02121i | ||||
\(428\) | −11.2563 | − | 6.49882i | −0.544093 | − | 0.314132i | ||||
\(429\) | 9.91183 | + | 5.72260i | 0.478548 | + | 0.276290i | ||||
\(430\) | 15.6333 | − | 11.1001i | 0.753906 | − | 0.535295i | ||||
\(431\) | −25.7488 | + | 14.8661i | −1.24028 | + | 0.716074i | −0.969150 | − | 0.246470i | \(-0.920729\pi\) |
−0.271126 | + | 0.962544i | \(0.587396\pi\) | |||||||
\(432\) | −4.40365 | − | 2.54245i | −0.211871 | − | 0.122324i | ||||
\(433\) | − | 8.82129i | − | 0.423924i | −0.977278 | − | 0.211962i | \(-0.932015\pi\) | ||
0.977278 | − | 0.211962i | \(-0.0679853\pi\) | |||||||
\(434\) | −9.15617 | −0.439510 | ||||||||
\(435\) | −0.984304 | − | 10.4599i | −0.0471938 | − | 0.501513i | ||||
\(436\) | 15.2423i | 0.729976i | ||||||||
\(437\) | −34.4667 | + | 19.8994i | −1.64877 | + | 0.951916i | ||||
\(438\) | −15.8523 | −0.757452 | ||||||||
\(439\) | 27.7357 | − | 16.0132i | 1.32375 | − | 0.764270i | 0.339429 | − | 0.940632i | \(-0.389766\pi\) |
0.984325 | + | 0.176362i | \(0.0564328\pi\) | |||||||
\(440\) | −2.28554 | − | 1.04757i | −0.108959 | − | 0.0499409i | ||||
\(441\) | −0.546090 | − | 0.945856i | −0.0260043 | − | 0.0450408i | ||||
\(442\) | −2.16980 | + | 3.75820i | −0.103207 | + | 0.178759i | ||||
\(443\) | − | 19.6970i | − | 0.935831i | −0.883773 | − | 0.467916i | \(-0.845005\pi\) | ||
0.883773 | − | 0.467916i | \(-0.154995\pi\) | |||||||
\(444\) | −10.1273 | + | 3.60040i | −0.480621 | + | 0.170867i | ||||
\(445\) | 0.955524 | + | 1.34575i | 0.0452962 | + | 0.0637948i | ||||
\(446\) | 15.7325 | + | 9.08319i | 0.744958 | + | 0.430101i | ||||
\(447\) | 25.3336 | − | 14.6263i | 1.19824 | − | 0.691802i | ||||
\(448\) | 3.45647 | − | 1.99560i | 0.163303 | − | 0.0942830i | ||||
\(449\) | −9.02589 | + | 5.21110i | −0.425958 | + | 0.245927i | −0.697623 | − | 0.716465i | \(-0.745759\pi\) |
0.271665 | + | 0.962392i | \(0.412426\pi\) | |||||||
\(450\) | −0.201605 | + | 0.577364i | −0.00950375 | + | 0.0272172i | ||||
\(451\) | −2.34675 | − | 4.06469i | −0.110504 | − | 0.191399i | ||||
\(452\) | −6.24875 | −0.293917 | ||||||||
\(453\) | 30.8349 | + | 17.8026i | 1.44875 | + | 0.836437i | ||||
\(454\) | −6.28846 | −0.295132 | ||||||||
\(455\) | −29.7641 | − | 41.9196i | −1.39536 | − | 1.96522i | ||||
\(456\) | −6.22139 | + | 10.7758i | −0.291343 | + | 0.504622i | ||||
\(457\) | −20.2592 | − | 35.0899i | −0.947685 | − | 1.64144i | −0.750285 | − | 0.661115i | \(-0.770084\pi\) |
−0.197400 | − | 0.980323i | \(-0.563250\pi\) | |||||||
\(458\) | 8.52158 | 0.398187 | ||||||||
\(459\) | −3.31733 | − | 1.91526i | −0.154840 | − | 0.0893967i | ||||
\(460\) | −1.18403 | − | 12.5823i | −0.0552057 | − | 0.586653i | ||||
\(461\) | 0.172837 | + | 0.0997876i | 0.00804983 | + | 0.00464757i | 0.504020 | − | 0.863692i | \(-0.331854\pi\) |
−0.495970 | + | 0.868340i | \(0.665187\pi\) | |||||||
\(462\) | −3.96481 | − | 6.86725i | −0.184460 | − | 0.319493i | ||||
\(463\) | 10.5797 | + | 18.3246i | 0.491680 | + | 0.851615i | 0.999954 | − | 0.00958066i | \(-0.00304966\pi\) |
−0.508274 | + | 0.861195i | \(0.669716\pi\) | |||||||
\(464\) | 2.30276 | + | 1.32950i | 0.106903 | + | 0.0617205i | ||||
\(465\) | 0.849225 | + | 9.02444i | 0.0393819 | + | 0.418498i | ||||
\(466\) | 0.278383 | + | 0.160724i | 0.0128958 | + | 0.00744541i | ||||
\(467\) | 38.6513 | 1.78857 | 0.894283 | − | 0.447501i | \(-0.147686\pi\) | ||||
0.894283 | + | 0.447501i | \(0.147686\pi\) | |||||||
\(468\) | 0.352294 | + | 0.610192i | 0.0162848 | + | 0.0282061i | ||||
\(469\) | 11.3401 | − | 19.6416i | 0.523636 | − | 0.906964i | ||||
\(470\) | −14.4761 | − | 20.3881i | −0.667733 | − | 0.940431i | ||||
\(471\) | 37.5009 | 1.72795 | ||||||||
\(472\) | −8.60234 | − | 4.96656i | −0.395955 | − | 0.228605i | ||||
\(473\) | 9.64101 | 0.443294 | ||||||||
\(474\) | 3.03632 | + | 5.25907i | 0.139463 | + | 0.241557i | ||||
\(475\) | −33.2405 | − | 11.6070i | −1.52518 | − | 0.532564i | ||||
\(476\) | 2.60381 | − | 1.50331i | 0.119345 | − | 0.0689041i | ||||
\(477\) | 0.0442716 | − | 0.0255602i | 0.00202706 | − | 0.00117032i | ||||
\(478\) | 20.1752 | − | 11.6482i | 0.922792 | − | 0.532774i | ||||
\(479\) | −9.67769 | − | 5.58742i | −0.442185 | − | 0.255296i | 0.262339 | − | 0.964976i | \(-0.415506\pi\) |
−0.704524 | + | 0.709680i | \(0.748839\pi\) | |||||||
\(480\) | −2.28747 | − | 3.22165i | −0.104408 | − | 0.147048i | ||||
\(481\) | −34.4620 | − | 6.34300i | −1.57133 | − | 0.289216i | ||||
\(482\) | 23.0111i | 1.04813i | ||||||||
\(483\) | 19.9297 | − | 34.5192i | 0.906831 | − | 1.57068i | ||||
\(484\) | 4.86789 | + | 8.43143i | 0.221268 | + | 0.383247i | ||||
\(485\) | 3.88146 | + | 1.77905i | 0.176248 | + | 0.0807824i | ||||
\(486\) | −1.10011 | + | 0.635151i | −0.0499022 | + | 0.0288110i | ||||
\(487\) | 11.6266 | 0.526851 | 0.263425 | − | 0.964680i | \(-0.415148\pi\) | ||||
0.263425 | + | 0.964680i | \(0.415148\pi\) | |||||||
\(488\) | −5.28723 | + | 3.05258i | −0.239341 | + | 0.138184i | ||||
\(489\) | − | 1.04378i | − | 0.0472015i | ||||||
\(490\) | 1.87071 | + | 19.8794i | 0.0845099 | + | 0.898059i | ||||
\(491\) | −13.0950 | −0.590970 | −0.295485 | − | 0.955347i | \(-0.595481\pi\) | ||||
−0.295485 | + | 0.955347i | \(0.595481\pi\) | |||||||
\(492\) | − | 7.37603i | − | 0.332537i | ||||||
\(493\) | 1.73470 | + | 1.00153i | 0.0781270 | + | 0.0451066i | ||||
\(494\) | −35.1305 | + | 20.2826i | −1.58059 | + | 0.912556i | ||||
\(495\) | −0.250735 | + | 0.178029i | −0.0112697 | + | 0.00800181i | ||||
\(496\) | −1.98675 | − | 1.14705i | −0.0892075 | − | 0.0515040i | ||||
\(497\) | −3.24583 | − | 1.87398i | −0.145595 | − | 0.0840594i | ||||
\(498\) | 8.75779 | − | 15.1689i | 0.392446 | − | 0.679737i | ||||
\(499\) | −12.3985 | + | 7.15828i | −0.555033 | + | 0.320448i | −0.751149 | − | 0.660132i | \(-0.770500\pi\) |
0.196117 | + | 0.980581i | \(0.437167\pi\) | |||||||
\(500\) | 7.74859 | − | 8.05974i | 0.346527 | − | 0.360442i | ||||
\(501\) | −5.12702 | − | 2.96009i | −0.229059 | − | 0.132247i | ||||
\(502\) | −6.45658 | − | 3.72771i | −0.288171 | − | 0.166376i | ||||
\(503\) | −15.0547 | + | 26.0755i | −0.671255 | + | 1.16265i | 0.306293 | + | 0.951937i | \(0.400911\pi\) |
−0.977548 | + | 0.210711i | \(0.932422\pi\) | |||||||
\(504\) | − | 0.488163i | − | 0.0217445i | ||||||
\(505\) | −7.44062 | − | 3.41037i | −0.331103 | − | 0.151760i | ||||
\(506\) | 3.17740 | − | 5.50341i | 0.141252 | − | 0.244656i | ||||
\(507\) | 35.6677i | 1.58406i | ||||||||
\(508\) | 17.2118i | 0.763650i | ||||||||
\(509\) | −18.1189 | + | 31.3829i | −0.803107 | + | 1.39102i | 0.114455 | + | 0.993428i | \(0.463488\pi\) |
−0.917562 | + | 0.397593i | \(0.869846\pi\) | |||||||
\(510\) | −1.72318 | − | 2.42691i | −0.0763037 | − | 0.107466i | ||||
\(511\) | 17.9030 | + | 31.0090i | 0.791984 | + | 1.37176i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −17.9032 | − | 31.0093i | −0.790447 | − | 1.36909i | ||||
\(514\) | 2.60820 | + | 4.51754i | 0.115043 | + | 0.199260i | ||||
\(515\) | −31.5762 | − | 14.4728i | −1.39142 | − | 0.637749i | ||||
\(516\) | 13.1214 | + | 7.57563i | 0.577636 | + | 0.333498i | ||||
\(517\) | − | 12.5732i | − | 0.552970i | ||||||
\(518\) | 18.4802 | + | 15.7441i | 0.811976 | + | 0.691755i | ||||
\(519\) | 30.9564 | 1.35884 | ||||||||
\(520\) | −1.20683 | − | 12.8246i | −0.0529231 | − | 0.562396i | ||||
\(521\) | −20.5166 | − | 35.5358i | −0.898849 | − | 1.55685i | −0.828967 | − | 0.559297i | \(-0.811071\pi\) |
−0.0698821 | − | 0.997555i | \(-0.522262\pi\) | |||||||
\(522\) | 0.281651 | − | 0.162611i | 0.0123275 | − | 0.00711730i | ||||
\(523\) | 7.21437 | + | 12.4957i | 0.315462 | + | 0.546397i | 0.979536 | − | 0.201271i | \(-0.0645071\pi\) |
−0.664073 | + | 0.747667i | \(0.731174\pi\) | |||||||
\(524\) | − | 10.9616i | − | 0.478859i | ||||||
\(525\) | 34.6433 | − | 6.57831i | 1.51196 | − | 0.287101i | ||||
\(526\) | − | 23.4017i | − | 1.02036i | ||||||
\(527\) | −1.49664 | − | 0.864087i | −0.0651947 | − | 0.0376402i | ||||
\(528\) | − | 1.98678i | − | 0.0864635i | ||||||
\(529\) | 8.94326 | 0.388837 | ||||||||
\(530\) | −0.930472 | + | 0.0875600i | −0.0404171 | + | 0.00380336i | ||||
\(531\) | −1.05215 | + | 0.607461i | −0.0456595 | + | 0.0263615i | ||||
\(532\) | 28.1049 | 1.21850 | ||||||||
\(533\) | 12.0234 | − | 20.8252i | 0.520793 | − | 0.902040i | ||||
\(534\) | −0.652128 | + | 1.12952i | −0.0282203 | + | 0.0488791i | ||||
\(535\) | 28.9358 | − | 2.72294i | 1.25100 | − | 0.117723i | ||||
\(536\) | 4.92123 | − | 2.84128i | 0.212565 | − | 0.122724i | ||||
\(537\) | 9.30782 | + | 16.1216i | 0.401662 | + | 0.695699i | ||||
\(538\) | −7.60947 | + | 13.1800i | −0.328068 | + | 0.568230i | ||||
\(539\) | −5.02012 | + | 8.69510i | −0.216232 | + | 0.374525i | ||||
\(540\) | 11.3202 | − | 1.06526i | 0.487142 | − | 0.0458414i | ||||
\(541\) | 11.5162i | 0.495119i | 0.968873 | + | 0.247559i | \(0.0796286\pi\) | ||||
−0.968873 | + | 0.247559i | \(0.920371\pi\) | |||||||
\(542\) | 1.48941 | + | 2.57974i | 0.0639758 | + | 0.110809i | ||||
\(543\) | −4.16610 | − | 2.40530i | −0.178785 | − | 0.103221i | ||||
\(544\) | 0.753314 | 0.0322981 | ||||||||
\(545\) | −19.7319 | − | 27.7902i | −0.845221 | − | 1.19040i | ||||
\(546\) | 20.3135 | − | 35.1840i | 0.869336 | − | 1.50573i | ||||
\(547\) | 18.5360 | 0.792543 | 0.396271 | − | 0.918133i | \(-0.370304\pi\) | ||||
0.396271 | + | 0.918133i | \(0.370304\pi\) | |||||||
\(548\) | −20.0768 | + | 11.5913i | −0.857639 | + | 0.495158i | ||||
\(549\) | 0.746723i | 0.0318694i | ||||||||
\(550\) | 5.52319 | − | 1.04878i | 0.235510 | − | 0.0447202i | ||||
\(551\) | 9.36198 | + | 16.2154i | 0.398834 | + | 0.690800i | ||||
\(552\) | 8.64885 | − | 4.99341i | 0.368119 | − | 0.212534i | ||||
\(553\) | 6.85824 | − | 11.8788i | 0.291642 | − | 0.505139i | ||||
\(554\) | 15.4113 | 0.654762 | ||||||||
\(555\) | 13.8035 | − | 19.6746i | 0.585927 | − | 0.835140i | ||||
\(556\) | 0.244448 | 0.0103669 | ||||||||
\(557\) | −4.50635 | + | 7.80523i | −0.190940 | + | 0.330718i | −0.945562 | − | 0.325442i | \(-0.894487\pi\) |
0.754622 | + | 0.656160i | \(0.227820\pi\) | |||||||
\(558\) | −0.242999 | + | 0.140295i | −0.0102870 | + | 0.00593918i | ||||
\(559\) | 24.6976 | + | 42.7774i | 1.04460 | + | 1.80929i | ||||
\(560\) | −3.71855 | + | 8.11298i | −0.157137 | + | 0.342836i | ||||
\(561\) | − | 1.49667i | − | 0.0631894i | ||||||
\(562\) | 10.1817 | − | 5.87838i | 0.429487 | − | 0.247965i | ||||
\(563\) | 38.7581 | 1.63346 | 0.816730 | − | 0.577021i | \(-0.195785\pi\) | ||||
0.816730 | + | 0.577021i | \(0.195785\pi\) | |||||||
\(564\) | 9.87969 | − | 17.1121i | 0.416010 | − | 0.720550i | ||||
\(565\) | 11.3929 | − | 8.08929i | 0.479303 | − | 0.340319i | ||||
\(566\) | 13.7203 | 0.576706 | ||||||||
\(567\) | 32.3248 | + | 18.6628i | 1.35752 | + | 0.783762i | ||||
\(568\) | −0.469529 | − | 0.813247i | −0.0197010 | − | 0.0341231i | ||||
\(569\) | 8.08920i | 0.339117i | 0.985520 | + | 0.169559i | \(0.0542342\pi\) | ||||
−0.985520 | + | 0.169559i | \(0.945766\pi\) | |||||||
\(570\) | −2.60670 | − | 27.7005i | −0.109183 | − | 1.16025i | ||||
\(571\) | −15.6120 | + | 27.0408i | −0.653343 | + | 1.13162i | 0.328963 | + | 0.944343i | \(0.393301\pi\) |
−0.982306 | + | 0.187281i | \(0.940033\pi\) | |||||||
\(572\) | 3.23859 | − | 5.60939i | 0.135412 | − | 0.234541i | ||||
\(573\) | 5.77794 | + | 10.0077i | 0.241377 | + | 0.418077i | ||||
\(574\) | −14.4284 | + | 8.33024i | −0.602230 | + | 0.347697i | ||||
\(575\) | 18.4471 | + | 21.4076i | 0.769297 | + | 0.892759i | ||||
\(576\) | 0.0611550 | − | 0.105924i | 0.00254813 | − | 0.00441348i | ||||
\(577\) | −2.36064 | + | 4.08875i | −0.0982748 | + | 0.170217i | −0.910971 | − | 0.412471i | \(-0.864666\pi\) |
0.812696 | + | 0.582688i | \(0.197999\pi\) | |||||||
\(578\) | −16.4325 | −0.683503 | ||||||||
\(579\) | 24.7430 | − | 14.2854i | 1.02828 | − | 0.593680i | ||||
\(580\) | −5.91955 | + | 0.557046i | −0.245796 | + | 0.0231301i | ||||
\(581\) | −39.5630 | −1.64135 | ||||||||
\(582\) | 3.37408i | 0.139860i | ||||||||
\(583\) | −0.406982 | − | 0.234971i | −0.0168555 | − | 0.00973151i | ||||
\(584\) | 8.97127i | 0.371234i | ||||||||
\(585\) | −1.43223 | − | 0.656457i | −0.0592155 | − | 0.0271412i | ||||
\(586\) | 18.7215i | 0.773378i | ||||||||
\(587\) | 10.4048 | + | 18.0217i | 0.429453 | + | 0.743834i | 0.996825 | − | 0.0796274i | \(-0.0253730\pi\) |
−0.567372 | + | 0.823462i | \(0.692040\pi\) | |||||||
\(588\) | −13.6647 | + | 7.88933i | −0.563524 | + | 0.325351i | ||||
\(589\) | −8.07721 | − | 13.9901i | −0.332815 | − | 0.576453i | ||||
\(590\) | 22.1134 | − | 2.08094i | 0.910396 | − | 0.0856708i | ||||
\(591\) | −21.8071 | −0.897025 | ||||||||
\(592\) | 2.03757 | + | 5.73134i | 0.0837436 | + | 0.235557i | ||||
\(593\) | 45.0711i | 1.85085i | 0.378931 | + | 0.925425i | \(0.376292\pi\) | ||||
−0.378931 | + | 0.925425i | \(0.623708\pi\) | |||||||
\(594\) | 4.95136 | + | 2.85867i | 0.203157 | + | 0.117293i | ||||
\(595\) | −2.80123 | + | 6.11162i | −0.114839 | + | 0.250552i | ||||
\(596\) | −8.27747 | − | 14.3370i | −0.339058 | − | 0.587266i | ||||
\(597\) | −8.31952 | − | 14.4098i | −0.340495 | − | 0.589755i | ||||
\(598\) | 32.5584 | 1.33141 | ||||||||
\(599\) | 1.68917 | + | 2.92573i | 0.0690176 | + | 0.119542i | 0.898469 | − | 0.439037i | \(-0.144680\pi\) |
−0.829452 | + | 0.558579i | \(0.811347\pi\) | |||||||
\(600\) | 8.34114 | + | 2.91258i | 0.340526 | + | 0.118905i | ||||
\(601\) | 10.8586 | − | 18.8076i | 0.442931 | − | 0.767179i | −0.554974 | − | 0.831867i | \(-0.687272\pi\) |
0.997906 | + | 0.0646882i | \(0.0206053\pi\) | |||||||
\(602\) | − | 34.2226i | − | 1.39481i | ||||||
\(603\) | − | 0.695033i | − | 0.0283039i | ||||||
\(604\) | 10.0750 | − | 17.4504i | 0.409945 | − | 0.710046i | ||||
\(605\) | −19.7901 | − | 9.07071i | −0.804583 | − | 0.368777i | ||||
\(606\) | − | 6.46799i | − | 0.262744i | ||||||
\(607\) | 0.992390 | − | 1.71887i | 0.0402799 | − | 0.0697668i | −0.845183 | − | 0.534478i | \(-0.820508\pi\) |
0.885463 | + | 0.464711i | \(0.153842\pi\) | |||||||
\(608\) | 6.09832 | + | 3.52087i | 0.247320 | + | 0.142790i | ||||
\(609\) | −16.2401 | − | 9.37624i | −0.658083 | − | 0.379944i | ||||
\(610\) | 5.68811 | − | 12.4101i | 0.230305 | − | 0.502470i | ||||
\(611\) | 55.7878 | − | 32.2091i | 2.25693 | − | 1.30304i | ||||
\(612\) | 0.0460689 | − | 0.0797937i | 0.00186223 | − | 0.00322547i | ||||
\(613\) | −25.1987 | − | 14.5485i | −1.01777 | − | 0.587608i | −0.104310 | − | 0.994545i | \(-0.533263\pi\) |
−0.913456 | + | 0.406937i | \(0.866597\pi\) | |||||||
\(614\) | −3.81686 | − | 2.20367i | −0.154036 | − | 0.0889327i | ||||
\(615\) | 9.54860 | + | 13.4482i | 0.385037 | + | 0.542283i | ||||
\(616\) | −3.88638 | + | 2.24380i | −0.156587 | + | 0.0904053i | ||||
\(617\) | −7.57750 | − | 4.37487i | −0.305059 | − | 0.176126i | 0.339654 | − | 0.940550i | \(-0.389690\pi\) |
−0.644713 | + | 0.764425i | \(0.723023\pi\) | |||||||
\(618\) | − | 27.4486i | − | 1.10415i | ||||||
\(619\) | −1.50546 | −0.0605094 | −0.0302547 | − | 0.999542i | \(-0.509632\pi\) | ||||
−0.0302547 | + | 0.999542i | \(0.509632\pi\) | |||||||
\(620\) | 5.10719 | − | 0.480601i | 0.205110 | − | 0.0193014i | ||||
\(621\) | 28.7390i | 1.15326i | ||||||||
\(622\) | −23.3952 | + | 13.5073i | −0.938064 | + | 0.541591i | ||||
\(623\) | 2.94596 | 0.118028 | ||||||||
\(624\) | 8.81540 | − | 5.08958i | 0.352899 | − | 0.203746i | ||||
\(625\) | −3.69375 | + | 24.7256i | −0.147750 | + | 0.989025i | ||||
\(626\) | 3.20475 | + | 5.55078i | 0.128087 | + | 0.221854i | ||||
\(627\) | 6.99519 | − | 12.1160i | 0.279361 | − | 0.483867i | ||||
\(628\) | − | 21.2229i | − | 0.846884i | ||||||
\(629\) | 1.53493 | + | 4.31750i | 0.0612016 | + | 0.172150i | ||||
\(630\) | 0.631948 | + | 0.890032i | 0.0251774 | + | 0.0354597i | ||||
\(631\) | 7.86491 | + | 4.54081i | 0.313097 | + | 0.180767i | 0.648312 | − | 0.761375i | \(-0.275475\pi\) |
−0.335214 | + | 0.942142i | \(0.608809\pi\) | |||||||
\(632\) | 2.97626 | − | 1.71834i | 0.118389 | − | 0.0683520i | ||||
\(633\) | −27.4793 | + | 15.8652i | −1.09220 | + | 0.630584i | ||||
\(634\) | −8.12713 | + | 4.69220i | −0.322770 | + | 0.186351i | ||||
\(635\) | −22.2814 | − | 31.3810i | −0.884211 | − | 1.24532i | ||||
\(636\) | −0.369267 | − | 0.639590i | −0.0146424 | − | 0.0253614i | ||||
\(637\) | −51.4406 | −2.03815 | ||||||||
\(638\) | −2.58917 | − | 1.49486i | −0.102506 | − | 0.0591820i | ||||
\(639\) | −0.114856 | −0.00454364 | ||||||||
\(640\) | −1.82323 | + | 1.29454i | −0.0720694 | + | 0.0511713i | ||||
\(641\) | −3.26546 | + | 5.65594i | −0.128978 | + | 0.223396i | −0.923281 | − | 0.384126i | \(-0.874503\pi\) |
0.794303 | + | 0.607522i | \(0.207836\pi\) | |||||||
\(642\) | 11.4835 | + | 19.8899i | 0.453216 | + | 0.784992i | ||||
\(643\) | 6.69746 | 0.264122 | 0.132061 | − | 0.991242i | \(-0.457840\pi\) | ||||
0.132061 | + | 0.991242i | \(0.457840\pi\) | |||||||
\(644\) | −19.5354 | − | 11.2788i | −0.769803 | − | 0.444446i | ||||
\(645\) | −33.7302 | + | 3.17411i | −1.32813 | + | 0.124980i | ||||
\(646\) | 4.59395 | + | 2.65232i | 0.180746 | + | 0.104354i | ||||
\(647\) | 6.84571 | + | 11.8571i | 0.269132 | + | 0.466151i | 0.968638 | − | 0.248476i | \(-0.0799297\pi\) |
−0.699506 | + | 0.714627i | \(0.746596\pi\) | |||||||
\(648\) | 4.67599 | + | 8.09904i | 0.183690 | + | 0.318160i | ||||
\(649\) | 9.67226 | + | 5.58428i | 0.379670 | + | 0.219202i | ||||
\(650\) | 18.8024 | + | 21.8199i | 0.737489 | + | 0.855846i | ||||
\(651\) | 14.0114 | + | 8.08951i | 0.549152 | + | 0.317053i | ||||
\(652\) | −0.590707 | −0.0231339 | ||||||||
\(653\) | 5.32021 | + | 9.21488i | 0.208196 | + | 0.360606i | 0.951146 | − | 0.308741i | \(-0.0999075\pi\) |
−0.742950 | + | 0.669347i | \(0.766574\pi\) | |||||||
\(654\) | 13.4667 | − | 23.3249i | 0.526588 | − | 0.912077i | ||||
\(655\) | 14.1903 | + | 19.9855i | 0.554459 | + | 0.780896i | ||||
\(656\) | −4.17431 | −0.162980 | ||||||||
\(657\) | 0.950270 | + | 0.548638i | 0.0370736 | + | 0.0214044i | ||||
\(658\) | −44.6311 | −1.73990 | ||||||||
\(659\) | 6.31258 | + | 10.9337i | 0.245903 | + | 0.425917i | 0.962385 | − | 0.271689i | \(-0.0875822\pi\) |
−0.716482 | + | 0.697606i | \(0.754249\pi\) | |||||||
\(660\) | 2.57197 | + | 3.62235i | 0.100114 | + | 0.141000i | ||||
\(661\) | −38.4672 | + | 22.2090i | −1.49620 | + | 0.863831i | −0.999990 | − | 0.00437267i | \(-0.998608\pi\) |
−0.496208 | + | 0.868203i | \(0.665275\pi\) | |||||||
\(662\) | 13.3301 | − | 7.69616i | 0.518090 | − | 0.299120i | ||||
\(663\) | 6.64076 | − | 3.83405i | 0.257906 | − | 0.148902i | ||||
\(664\) | −8.58455 | − | 4.95629i | −0.333145 | − | 0.192341i | ||||
\(665\) | −51.2416 | + | 36.3830i | −1.98706 | + | 1.41087i | ||||
\(666\) | 0.731692 | + | 0.134674i | 0.0283525 | + | 0.00521850i | ||||
\(667\) | − | 15.0282i | − | 0.581895i | ||||||
\(668\) | −1.67520 | + | 2.90153i | −0.0648154 | + | 0.112264i | ||||
\(669\) | −16.0500 | − | 27.7995i | −0.620531 | − | 1.07479i | ||||
\(670\) | −5.29437 | + | 11.5510i | −0.204539 | + | 0.446256i | ||||
\(671\) | 5.94483 | − | 3.43225i | 0.229498 | − | 0.132501i | ||||
\(672\) | −7.05246 | −0.272054 | ||||||||
\(673\) | 33.3043 | − | 19.2282i | 1.28379 | − | 0.741194i | 0.306248 | − | 0.951952i | \(-0.400926\pi\) |
0.977538 | + | 0.210757i | \(0.0675930\pi\) | |||||||
\(674\) | 5.80542i | 0.223617i | ||||||||
\(675\) | −19.2602 | + | 16.5967i | −0.741325 | + | 0.638806i | ||||
\(676\) | 20.1854 | 0.776362 | ||||||||
\(677\) | − | 8.06447i | − | 0.309943i | −0.987919 | − | 0.154971i | \(-0.950471\pi\) | ||
0.987919 | − | 0.154971i | \(-0.0495285\pi\) | |||||||
\(678\) | 9.56229 | + | 5.52079i | 0.367238 | + | 0.212025i | ||||
\(679\) | 6.60009 | − | 3.81056i | 0.253288 | − | 0.146236i | ||||
\(680\) | −1.37346 | + | 0.975198i | −0.0526698 | + | 0.0373971i | ||||
\(681\) | 9.62306 | + | 5.55588i | 0.368756 | + | 0.212902i | ||||
\(682\) | 2.23385 | + | 1.28971i | 0.0855385 | + | 0.0493857i | ||||
\(683\) | 13.4194 | − | 23.2430i | 0.513478 | − | 0.889370i | −0.486400 | − | 0.873736i | \(-0.661690\pi\) |
0.999878 | − | 0.0156333i | \(-0.00497643\pi\) | |||||||
\(684\) | 0.745886 | − | 0.430637i | 0.0285197 | − | 0.0164658i | ||||
\(685\) | 21.5991 | − | 47.1240i | 0.825257 | − | 1.80051i | ||||
\(686\) | 6.66963 | + | 3.85072i | 0.254648 | + | 0.147021i | ||||
\(687\) | −13.0403 | − | 7.52884i | −0.497520 | − | 0.287243i | ||||
\(688\) | 4.28727 | − | 7.42577i | 0.163451 | − | 0.283105i | ||||
\(689\) | − | 2.40772i | − | 0.0917269i | ||||||
\(690\) | −9.30461 | + | 20.3004i | −0.354221 | + | 0.772825i | ||||
\(691\) | −4.51646 | + | 7.82274i | −0.171814 | + | 0.297591i | −0.939054 | − | 0.343769i | \(-0.888296\pi\) |
0.767240 | + | 0.641360i | \(0.221630\pi\) | |||||||
\(692\) | − | 17.5191i | − | 0.665978i | ||||||
\(693\) | 0.548879i | 0.0208502i | ||||||||
\(694\) | −1.49762 | + | 2.59396i | −0.0568489 | + | 0.0984653i | ||||
\(695\) | −0.445684 | + | 0.316449i | −0.0169058 | + | 0.0120036i | ||||
\(696\) | −2.34923 | − | 4.06899i | −0.0890475 | − | 0.154235i | ||||
\(697\) | −3.14457 | −0.119109 | ||||||||
\(698\) | 16.1132 | + | 27.9089i | 0.609894 | + | 1.05637i | ||||
\(699\) | −0.284001 | − | 0.491904i | −0.0107419 | − | 0.0186055i | ||||
\(700\) | −3.72286 | − | 19.6056i | −0.140711 | − | 0.741023i | ||||
\(701\) | 32.6055 | + | 18.8248i | 1.23149 | + | 0.711004i | 0.967341 | − | 0.253477i | \(-0.0815743\pi\) |
0.264153 | + | 0.964481i | \(0.414908\pi\) | |||||||
\(702\) | 29.2924i | 1.10557i | ||||||||
\(703\) | −7.75355 | + | 42.1256i | −0.292431 | + | 1.58880i | ||||
\(704\) | −1.12438 | −0.0423765 | ||||||||
\(705\) | 4.13948 | + | 43.9890i | 0.155902 | + | 1.65672i | ||||
\(706\) | −4.35239 | − | 7.53855i | −0.163804 | − | 0.283717i | ||||
\(707\) | −12.6522 | + | 7.30472i | −0.475833 | + | 0.274722i | ||||
\(708\) | 8.77594 | + | 15.2004i | 0.329820 | + | 0.571265i | ||||
\(709\) | − | 29.4137i | − | 1.10465i | −0.833628 | − | 0.552327i | \(-0.813740\pi\) | ||
0.833628 | − | 0.552327i | \(-0.186260\pi\) | |||||||
\(710\) | 1.90884 | + | 0.874909i | 0.0716376 | + | 0.0328347i | ||||
\(711\) | − | 0.420341i | − | 0.0157640i | ||||||
\(712\) | 0.639228 | + | 0.369058i | 0.0239561 | + | 0.0138310i | ||||
\(713\) | 12.9659i | 0.485575i | ||||||||
\(714\) | −5.31271 | −0.198823 | ||||||||
\(715\) | 1.35693 | + | 14.4197i | 0.0507464 | + | 0.539266i | ||||
\(716\) | 9.12369 | − | 5.26756i | 0.340968 | − | 0.196858i | ||||
\(717\) | −41.1647 | −1.53732 | ||||||||
\(718\) | −12.9231 | + | 22.3835i | −0.482287 | + | 0.835345i | ||||
\(719\) | 1.36520 | − | 2.36459i | 0.0509133 | − | 0.0881844i | −0.839446 | − | 0.543444i | \(-0.817120\pi\) |
0.890359 | + | 0.455259i | \(0.150453\pi\) | |||||||
\(720\) | 0.0256233 | + | 0.272291i | 0.000954925 | + | 0.0101477i | ||||
\(721\) | −53.6927 | + | 30.9995i | −1.99962 | + | 1.15448i | ||||
\(722\) | 15.2930 | + | 26.4883i | 0.569147 | + | 0.985791i | ||||
\(723\) | 20.3303 | − | 35.2132i | 0.756094 | − | 1.30959i | ||||
\(724\) | −1.36123 | + | 2.35772i | −0.0505897 | + | 0.0876239i | ||||
\(725\) | 10.0716 | − | 8.67874i | 0.374048 | − | 0.322320i | ||||
\(726\) | − | 17.2032i | − | 0.638470i | ||||||
\(727\) | −18.7699 | − | 32.5104i | −0.696136 | − | 1.20574i | −0.969796 | − | 0.243917i | \(-0.921568\pi\) |
0.273660 | − | 0.961826i | \(-0.411766\pi\) | |||||||
\(728\) | −19.9116 | − | 11.4960i | −0.737974 | − | 0.426069i | ||||
\(729\) | −25.8113 | −0.955973 | ||||||||
\(730\) | −11.6137 | − | 16.3567i | −0.429843 | − | 0.605387i | ||||
\(731\) | 3.22966 | − | 5.59393i | 0.119453 | − | 0.206899i | ||||
\(732\) | 10.7879 | 0.398731 | ||||||||
\(733\) | 25.6263 | − | 14.7953i | 0.946528 | − | 0.546478i | 0.0545272 | − | 0.998512i | \(-0.482635\pi\) |
0.892001 | + | 0.452034i | \(0.149302\pi\) | |||||||
\(734\) | − | 14.8169i | − | 0.546901i | ||||||
\(735\) | 14.7008 | − | 32.0736i | 0.542247 | − | 1.18305i | ||||
\(736\) | −2.82592 | − | 4.89463i | −0.104165 | − | 0.180419i | ||||
\(737\) | −5.53332 | + | 3.19466i | −0.203822 | + | 0.117677i | ||||
\(738\) | −0.255280 | + | 0.442158i | −0.00939699 | + | 0.0162761i | ||||
\(739\) | −53.4401 | −1.96582 | −0.982912 | − | 0.184074i | \(-0.941071\pi\) | ||||
−0.982912 | + | 0.184074i | \(0.941071\pi\) | |||||||
\(740\) | −11.1344 | − | 7.81182i | −0.409310 | − | 0.287168i | ||||
\(741\) | 71.6789 | 2.63319 | ||||||||
\(742\) | −0.834075 | + | 1.44466i | −0.0306199 | + | 0.0530352i | ||||
\(743\) | 1.25633 | − | 0.725343i | 0.0460903 | − | 0.0266102i | −0.476778 | − | 0.879024i | \(-0.658195\pi\) |
0.522868 | + | 0.852414i | \(0.324862\pi\) | |||||||
\(744\) | 2.02684 | + | 3.51059i | 0.0743076 | + | 0.128704i | ||||
\(745\) | 33.6516 | + | 15.4240i | 1.23290 | + | 0.565093i | ||||
\(746\) | 20.9310i | 0.766340i | ||||||||
\(747\) | −1.04998 | + | 0.606204i | −0.0384166 | + | 0.0221799i | ||||
\(748\) | −0.847008 | −0.0309697 | ||||||||
\(749\) | 25.9380 | − | 44.9260i | 0.947755 | − | 1.64156i | ||||
\(750\) | −18.9783 | + | 5.48769i | −0.692988 | + | 0.200382i | ||||
\(751\) | −15.9125 | −0.580654 | −0.290327 | − | 0.956928i | \(-0.593764\pi\) | ||||
−0.290327 | + | 0.956928i | \(0.593764\pi\) | |||||||
\(752\) | −9.68424 | − | 5.59120i | −0.353148 | − | 0.203890i | ||||
\(753\) | 6.58688 | + | 11.4088i | 0.240039 | + | 0.415760i | ||||
\(754\) | − | 15.3176i | − | 0.557835i | ||||||
\(755\) | 4.22131 | + | 44.8585i | 0.153629 | + | 1.63257i | ||||
\(756\) | 10.1474 | − | 17.5758i | 0.369057 | − | 0.639226i | ||||
\(757\) | 2.39331 | − | 4.14533i | 0.0869863 | − | 0.150665i | −0.819250 | − | 0.573437i | \(-0.805610\pi\) |
0.906236 | + | 0.422772i | \(0.138943\pi\) | |||||||
\(758\) | 3.24827 | + | 5.62616i | 0.117982 | + | 0.204351i | ||||
\(759\) | −9.72456 | + | 5.61448i | −0.352979 | + | 0.203793i | ||||
\(760\) | −15.6765 | + | 1.47521i | −0.568648 | + | 0.0535114i | ||||
\(761\) | 4.63171 | − | 8.02237i | 0.167900 | − | 0.290811i | −0.769782 | − | 0.638307i | \(-0.779635\pi\) |
0.937681 | + | 0.347497i | \(0.112968\pi\) | |||||||
\(762\) | 15.2067 | − | 26.3387i | 0.550880 | − | 0.954151i | ||||
\(763\) | −60.8351 | −2.20238 | ||||||||
\(764\) | 5.66364 | − | 3.26990i | 0.204903 | − | 0.118301i | ||||
\(765\) | 0.0193024 | + | 0.205120i | 0.000697879 | + | 0.00741614i | ||||
\(766\) | −27.8067 | −1.00470 | ||||||||
\(767\) | 57.2215i | 2.06615i | ||||||||
\(768\) | −1.53027 | − | 0.883503i | −0.0552189 | − | 0.0318807i | ||||
\(769\) | 35.9197i | 1.29530i | 0.761940 | + | 0.647648i | \(0.224247\pi\) | ||||
−0.761940 | + | 0.647648i | \(0.775753\pi\) | |||||||
\(770\) | 4.18105 | − | 9.12204i | 0.150674 | − | 0.328736i | ||||
\(771\) | − | 9.21742i | − | 0.331957i | ||||||
\(772\) | −8.08451 | − | 14.0028i | −0.290968 | − | 0.503971i | ||||
\(773\) | −9.41162 | + | 5.43380i | −0.338512 | + | 0.195440i | −0.659614 | − | 0.751605i | \(-0.729280\pi\) |
0.321102 | + | 0.947045i | \(0.395947\pi\) | |||||||
\(774\) | −0.524376 | − | 0.908246i | −0.0188483 | − | 0.0326462i | ||||
\(775\) | −8.68941 | + | 7.48773i | −0.312133 | + | 0.268967i | ||||
\(776\) | 1.90949 | 0.0685466 | ||||||||
\(777\) | −14.3699 | − | 40.4201i | −0.515516 | − | 1.45006i | ||||
\(778\) | 18.2583i | 0.654591i | ||||||||
\(779\) | −25.4563 | − | 14.6972i | −0.912066 | − | 0.526582i | ||||
\(780\) | −9.48380 | + | 20.6914i | −0.339575 | + | 0.740870i | ||||
\(781\) | 0.527927 | + | 0.914396i | 0.0188907 | + | 0.0327197i | ||||
\(782\) | −2.12880 | − | 3.68719i | −0.0761258 | − | 0.131854i | ||||
\(783\) | 13.5207 | 0.483191 | ||||||||
\(784\) | 4.46480 | + | 7.73327i | 0.159457 | + | 0.276188i | ||||
\(785\) | 27.4739 | + | 38.6941i | 0.980587 | + | 1.38105i | ||||
\(786\) | −9.68459 | + | 16.7742i | −0.345438 | + | 0.598316i | ||||
\(787\) | − | 26.5706i | − | 0.947140i | −0.880756 | − | 0.473570i | \(-0.842965\pi\) | ||
0.880756 | − | 0.473570i | \(-0.157035\pi\) | |||||||
\(788\) | 12.3413i | 0.439640i | ||||||||
\(789\) | −20.6755 | + | 35.8110i | −0.736066 | + | 1.27490i | ||||
\(790\) | −3.20192 | + | 6.98583i | −0.113919 | + | 0.248545i | ||||
\(791\) | − | 24.9400i | − | 0.886763i | ||||||
\(792\) | −0.0687613 | + | 0.119098i | −0.00244333 | + | 0.00423196i | ||||
\(793\) | 30.4580 | + | 17.5849i | 1.08160 | + | 0.624459i | ||||
\(794\) | 10.6970 | + | 6.17594i | 0.379624 | + | 0.219176i | ||||
\(795\) | 1.50123 | + | 0.688084i | 0.0532433 | + | 0.0244038i | ||||
\(796\) | −8.15495 | + | 4.70826i | −0.289044 | + | 0.166880i | ||||
\(797\) | −6.97209 | + | 12.0760i | −0.246964 | + | 0.427755i | −0.962682 | − | 0.270635i | \(-0.912766\pi\) |
0.715718 | + | 0.698390i | \(0.246100\pi\) | |||||||
\(798\) | −43.0082 | − | 24.8308i | −1.52247 | − | 0.879000i | ||||
\(799\) | −7.29527 | − | 4.21193i | −0.258088 | − | 0.149007i | ||||
\(800\) | 1.64831 | − | 4.72049i | 0.0582766 | − | 0.166895i | ||||
\(801\) | 0.0781840 | − | 0.0451395i | 0.00276249 | − | 0.00159493i | ||||
\(802\) | −7.38617 | − | 4.26441i | −0.260815 | − | 0.150582i | ||||
\(803\) | − | 10.0871i | − | 0.355966i | ||||||
\(804\) | −10.0411 | −0.354122 | ||||||||
\(805\) | 50.2184 | − | 4.72569i | 1.76997 | − | 0.166559i | ||||
\(806\) | 13.2155i | 0.465498i | ||||||||
\(807\) | 23.2891 | − | 13.4460i | 0.819816 | − | 0.473321i | ||||
\(808\) | −3.66042 | −0.128773 | ||||||||
\(809\) | −14.3319 | + | 8.27453i | −0.503883 | + | 0.290917i | −0.730316 | − | 0.683110i | \(-0.760627\pi\) |
0.226433 | + | 0.974027i | \(0.427294\pi\) | |||||||
\(810\) | −19.0100 | − | 8.71312i | −0.667942 | − | 0.306148i | ||||
\(811\) | 1.32946 | + | 2.30269i | 0.0466837 | + | 0.0808585i | 0.888423 | − | 0.459026i | \(-0.151801\pi\) |
−0.841739 | + | 0.539884i | \(0.818468\pi\) | |||||||
\(812\) | −5.30629 | + | 9.19076i | −0.186214 | + | 0.322532i | ||||
\(813\) | − | 5.26361i | − | 0.184603i | ||||||
\(814\) | −2.29099 | − | 6.44419i | −0.0802993 | − | 0.225869i | ||||
\(815\) | 1.07699 | − | 0.764696i | 0.0377254 | − | 0.0267861i | ||||
\(816\) | −1.15277 | − | 0.665555i | −0.0403552 | − | 0.0232991i | ||||
\(817\) | 52.2903 | − | 30.1898i | 1.82940 | − | 1.05621i | ||||
\(818\) | −15.7176 | + | 9.07457i | −0.549553 | + | 0.317285i | ||||
\(819\) | −2.43539 | + | 1.40607i | −0.0850995 | + | 0.0491322i | ||||
\(820\) | 7.61072 | − | 5.40383i | 0.265778 | − | 0.188710i | ||||
\(821\) | −24.4954 | − | 42.4272i | −0.854894 | − | 1.48072i | −0.876743 | − | 0.480959i | \(-0.840289\pi\) |
0.0218486 | − | 0.999761i | \(-0.493045\pi\) | |||||||
\(822\) | 40.9640 | 1.42878 | ||||||||
\(823\) | −26.2415 | − | 15.1505i | −0.914721 | − | 0.528115i | −0.0327742 | − | 0.999463i | \(-0.510434\pi\) |
−0.881947 | + | 0.471348i | \(0.843768\pi\) | |||||||
\(824\) | −15.5340 | −0.541151 | ||||||||
\(825\) | −9.37858 | − | 3.27483i | −0.326520 | − | 0.114015i | ||||
\(826\) | 19.8225 | − | 34.3336i | 0.689713 | − | 1.19462i | ||||
\(827\) | −23.4746 | − | 40.6592i | −0.816291 | − | 1.41386i | −0.908397 | − | 0.418108i | \(-0.862693\pi\) |
0.0921062 | − | 0.995749i | \(-0.470640\pi\) | |||||||
\(828\) | −0.691277 | −0.0240235 | ||||||||
\(829\) | 7.99309 | + | 4.61481i | 0.277611 | + | 0.160279i | 0.632342 | − | 0.774690i | \(-0.282094\pi\) |
−0.354730 | + | 0.934969i | \(0.615427\pi\) | |||||||
\(830\) | 22.0677 | − | 2.07663i | 0.765981 | − | 0.0720810i | ||||
\(831\) | −23.5834 | − | 13.6159i | −0.818100 | − | 0.472330i | ||||
\(832\) | −2.88034 | − | 4.98889i | −0.0998578 | − | 0.172959i | ||||
\(833\) | 3.36340 | + | 5.82557i | 0.116535 | + | 0.201844i | ||||
\(834\) | −0.374072 | − | 0.215971i | −0.0129531 | − | 0.00747845i | ||||
\(835\) | −0.701891 | − | 7.45877i | −0.0242899 | − | 0.258121i | ||||
\(836\) | −6.85681 | − | 3.95878i | −0.237148 | − | 0.136917i | ||||
\(837\) | −11.6652 | −0.403210 | ||||||||
\(838\) | −0.982935 | − | 1.70249i | −0.0339549 | − | 0.0588117i | ||||
\(839\) | 0.776431 | − | 1.34482i | 0.0268054 | − | 0.0464283i | −0.852312 | − | 0.523034i | \(-0.824800\pi\) |
0.879117 | + | 0.476606i | \(0.158133\pi\) | |||||||
\(840\) | 12.8582 | − | 9.12972i | 0.443651 | − | 0.315005i | ||||
\(841\) | 21.9297 | 0.756197 | ||||||||
\(842\) | −4.94848 | − | 2.85700i | −0.170536 | − | 0.0984589i | ||||
\(843\) | −20.7743 | −0.715504 | ||||||||
\(844\) | 8.97857 | + | 15.5513i | 0.309055 | + | 0.535299i | ||||
\(845\) | −36.8026 | + | 26.1309i | −1.26605 | + | 0.898930i | ||||
\(846\) | −1.18448 | + | 0.683860i | −0.0407233 | + | 0.0235116i | ||||
\(847\) | −33.6515 | + | 19.4287i | −1.15628 | + | 0.667577i | ||||
\(848\) | −0.361962 | + | 0.208979i | −0.0124298 | + | 0.00717637i | ||||
\(849\) | −20.9957 | − | 12.1219i | −0.720572 | − | 0.416023i | ||||
\(850\) | 1.24170 | − | 3.55601i | 0.0425898 | − | 0.121970i | ||||
\(851\) | 22.2948 | − | 26.1695i | 0.764257 | − | 0.897078i | ||||
\(852\) | 1.65932i | 0.0568474i | ||||||||
\(853\) | 8.67374 | − | 15.0234i | 0.296983 | − | 0.514390i | −0.678461 | − | 0.734636i | \(-0.737353\pi\) |
0.975444 | + | 0.220246i | \(0.0706862\pi\) | |||||||
\(854\) | −12.1834 | − | 21.1023i | −0.416909 | − | 0.722107i | ||||
\(855\) | −0.802440 | + | 1.75073i | −0.0274429 | + | 0.0598738i | ||||
\(856\) | 11.2563 | − | 6.49882i | 0.384732 | − | 0.222125i | ||||
\(857\) | −14.7315 | −0.503218 | −0.251609 | − | 0.967829i | \(-0.580960\pi\) | ||||
−0.251609 | + | 0.967829i | \(0.580960\pi\) | |||||||
\(858\) | −9.91183 | + | 5.72260i | −0.338384 | + | 0.195366i | ||||
\(859\) | 1.90770i | 0.0650899i | 0.999470 | + | 0.0325449i | \(0.0103612\pi\) | ||||
−0.999470 | + | 0.0325449i | \(0.989639\pi\) | |||||||
\(860\) | 1.79632 | + | 19.0889i | 0.0612540 | + | 0.650926i | ||||
\(861\) | 29.4392 | 1.00328 | ||||||||
\(862\) | − | 29.7322i | − | 1.01268i | ||||||
\(863\) | −47.6480 | − | 27.5096i | −1.62196 | − | 0.936437i | −0.986396 | − | 0.164385i | \(-0.947436\pi\) |
−0.635560 | − | 0.772052i | \(-0.719231\pi\) | |||||||
\(864\) | 4.40365 | − | 2.54245i | 0.149815 | − | 0.0864958i | ||||
\(865\) | 22.6793 | + | 31.9414i | 0.771119 | + | 1.08604i | ||||
\(866\) | 7.63946 | + | 4.41064i | 0.259599 | + | 0.149880i | ||||
\(867\) | 25.1462 | + | 14.5182i | 0.854011 | + | 0.493063i | ||||
\(868\) | 4.57809 | − | 7.92948i | 0.155390 | − | 0.269144i | ||||
\(869\) | −3.34643 | + | 1.93206i | −0.113520 | + | 0.0655408i | ||||
\(870\) | 9.55067 | + | 4.37751i | 0.323798 | + | 0.148411i | ||||
\(871\) | −28.3496 | − | 16.3677i | −0.960591 | − | 0.554597i | ||||
\(872\) | −13.2003 | − | 7.62117i | −0.447017 | − | 0.258085i | ||||
\(873\) | 0.116775 | − | 0.202260i | 0.00395223 | − | 0.00684546i | ||||
\(874\) | − | 39.7987i | − | 1.34621i | ||||||
\(875\) | 32.1680 | + | 30.9261i | 1.08748 | + | 1.04549i | ||||
\(876\) | 7.92615 | − | 13.7285i | 0.267800 | − | 0.463843i | ||||
\(877\) | − | 27.2837i | − | 0.921306i | −0.887580 | − | 0.460653i | \(-0.847615\pi\) | ||
0.887580 | − | 0.460653i | \(-0.152385\pi\) | |||||||
\(878\) | 32.0265i | 1.08084i | ||||||||
\(879\) | 16.5405 | − | 28.6490i | 0.557897 | − | 0.966306i | ||||
\(880\) | 2.04999 | − | 1.45555i | 0.0691052 | − | 0.0490667i | ||||
\(881\) | 6.66001 | + | 11.5355i | 0.224381 | + | 0.388640i | 0.956134 | − | 0.292931i | \(-0.0946305\pi\) |
−0.731752 | + | 0.681571i | \(0.761297\pi\) | |||||||
\(882\) | 1.09218 | 0.0367756 | ||||||||
\(883\) | −1.02963 | − | 1.78337i | −0.0346499 | − | 0.0600153i | 0.848180 | − | 0.529707i | \(-0.177698\pi\) |
−0.882830 | + | 0.469692i | \(0.844365\pi\) | |||||||
\(884\) | −2.16980 | − | 3.75820i | −0.0729782 | − | 0.126402i | ||||
\(885\) | −35.6781 | − | 16.3529i | −1.19931 | − | 0.549697i | ||||
\(886\) | 17.0581 | + | 9.84848i | 0.573077 | + | 0.330866i | ||||
\(887\) | 50.7096i | 1.70266i | 0.524630 | + | 0.851330i | \(0.324204\pi\) | ||||
−0.524630 | + | 0.851330i | \(0.675796\pi\) | |||||||
\(888\) | 1.94562 | − | 10.5707i | 0.0652909 | − | 0.354730i | ||||
\(889\) | −68.6956 | −2.30398 | ||||||||
\(890\) | −1.64322 | + | 0.154631i | −0.0550808 | + | 0.00518326i | ||||
\(891\) | −5.25757 | − | 9.10637i | −0.176135 | − | 0.305075i | ||||
\(892\) | −15.7325 | + | 9.08319i | −0.526765 | + | 0.304128i | ||||
\(893\) | −39.3718 | − | 68.1939i | −1.31753 | − | 2.28202i | ||||
\(894\) | 29.2527i | 0.978356i | ||||||||
\(895\) | −9.81546 | + | 21.4150i | −0.328095 | + | 0.715824i | ||||
\(896\) | 3.99119i | 0.133336i | ||||||||
\(897\) | −49.8232 | − | 28.7655i | −1.66355 | − | 0.960451i | ||||
\(898\) | − | 10.4222i | − | 0.347793i | ||||||
\(899\) | 6.10000 | 0.203446 | ||||||||
\(900\) | −0.399209 | − | 0.463277i | −0.0133070 | − | 0.0154426i | ||||
\(901\) | −0.272671 | + | 0.157427i | −0.00908399 | + | 0.00524465i | ||||
\(902\) | 4.69350 | 0.156276 | ||||||||
\(903\) | −30.2358 | + | 52.3699i | −1.00618 | + | 1.74276i | ||||
\(904\) | 3.12438 | − | 5.41158i | 0.103915 | − | 0.179986i | ||||
\(905\) | −0.570341 | − | 6.06082i | −0.0189588 | − | 0.201469i | ||||
\(906\) | −30.8349 | + | 17.8026i | −1.02442 | + | 0.591450i | ||||
\(907\) | 11.5434 | + | 19.9938i | 0.383293 | + | 0.663883i | 0.991531 | − | 0.129872i | \(-0.0414566\pi\) |
−0.608238 | + | 0.793755i | \(0.708123\pi\) | |||||||
\(908\) | 3.14423 | − | 5.44597i | 0.104345 | − | 0.180731i | ||||
\(909\) | −0.223853 | + | 0.387725i | −0.00742474 | + | 0.0128600i | ||||
\(910\) | 51.1855 | − | 4.81670i | 1.69678 | − | 0.159672i | ||||
\(911\) | − | 37.6751i | − | 1.24823i | −0.781331 | − | 0.624116i | \(-0.785459\pi\) | ||
0.781331 | − | 0.624116i | \(-0.214541\pi\) | |||||||
\(912\) | −6.22139 | − | 10.7758i | −0.206011 | − | 0.356821i | ||||
\(913\) | 9.65226 | + | 5.57274i | 0.319443 | + | 0.184431i | ||||
\(914\) | 40.5184 | 1.34023 | ||||||||
\(915\) | −19.6687 | + | 13.9654i | −0.650227 | + | 0.461680i | ||||
\(916\) | −4.26079 | + | 7.37991i | −0.140781 | + | 0.243839i | ||||
\(917\) | 43.7498 | 1.44475 | ||||||||
\(918\) | 3.31733 | − | 1.91526i | 0.109488 | − | 0.0632130i | ||||
\(919\) | 36.4837i | 1.20349i | 0.798690 | + | 0.601743i | \(0.205527\pi\) | ||||
−0.798690 | + | 0.601743i | \(0.794473\pi\) | |||||||
\(920\) | 11.4886 | + | 5.26575i | 0.378768 | + | 0.173607i | ||||
\(921\) | 3.89389 | + | 6.74441i | 0.128308 | + | 0.222236i | ||||
\(922\) | −0.172837 | + | 0.0997876i | −0.00569209 | + | 0.00328633i | ||||
\(923\) | −2.70480 | + | 4.68486i | −0.0890297 | + | 0.154204i | ||||
\(924\) | 7.92962 | 0.260865 | ||||||||
\(925\) | 30.4133 | − | 0.171297i | 0.999984 | − | 0.00563220i | ||||
\(926\) | −21.1594 | −0.695340 | ||||||||
\(927\) | −0.949980 | + | 1.64541i | −0.0312015 | + | 0.0540425i | ||||
\(928\) | −2.30276 | + | 1.32950i | −0.0755918 | + | 0.0436430i | ||||
\(929\) | −9.07242 | − | 15.7139i | −0.297656 | − | 0.515556i | 0.677943 | − | 0.735115i | \(-0.262872\pi\) |
−0.975599 | + | 0.219558i | \(0.929538\pi\) | |||||||
\(930\) | −8.24000 | − | 3.77677i | −0.270200 | − | 0.123845i | ||||
\(931\) | 62.8799i | 2.06081i | ||||||||
\(932\) | −0.278383 | + | 0.160724i | −0.00911873 | + | 0.00526470i | ||||
\(933\) | 47.7348 | 1.56277 | ||||||||
\(934\) | −19.3256 | + | 33.4730i | −0.632354 | + | 1.09527i | ||||
\(935\) | 1.54429 | − | 1.09649i | 0.0505036 | − | 0.0358590i | ||||
\(936\) | −0.704589 | −0.0230302 | ||||||||
\(937\) | 3.73106 | + | 2.15413i | 0.121888 | + | 0.0703723i | 0.559705 | − | 0.828692i | \(-0.310915\pi\) |
−0.437816 | + | 0.899064i | \(0.644248\pi\) | |||||||
\(938\) | 11.3401 | + | 19.6416i | 0.370266 | + | 0.641320i | ||||
\(939\) | − | 11.3256i | − | 0.369597i | ||||||
\(940\) | 24.8946 | − | 2.34265i | 0.811973 | − | 0.0764090i | ||||
\(941\) | −28.6354 | + | 49.5980i | −0.933488 | + | 1.61685i | −0.156179 | + | 0.987729i | \(0.549918\pi\) |
−0.777309 | + | 0.629119i | \(0.783416\pi\) | |||||||
\(942\) | −18.7505 | + | 32.4768i | −0.610923 | + | 1.05815i | ||||
\(943\) | 11.7963 | + | 20.4317i | 0.384139 | + | 0.665349i | ||||
\(944\) | 8.60234 | − | 4.96656i | 0.279982 | − | 0.161648i | ||||
\(945\) | 4.25165 | + | 45.1809i | 0.138306 | + | 1.46974i | ||||
\(946\) | −4.82050 | + | 8.34936i | −0.156728 | + | 0.271461i | ||||
\(947\) | −11.5548 | + | 20.0135i | −0.375480 | + | 0.650351i | −0.990399 | − | 0.138240i | \(-0.955856\pi\) |
0.614918 | + | 0.788591i | \(0.289189\pi\) | |||||||
\(948\) | −6.07265 | −0.197230 | ||||||||
\(949\) | 44.7567 | − | 25.8403i | 1.45286 | − | 0.838812i | ||||
\(950\) | 26.6722 | − | 22.9836i | 0.865359 | − | 0.745687i | ||||
\(951\) | 16.5823 | 0.537718 | ||||||||
\(952\) | 3.00662i | 0.0974451i | ||||||||
\(953\) | 52.4700 | + | 30.2936i | 1.69967 | + | 0.981305i | 0.946064 | + | 0.323980i | \(0.105021\pi\) |
0.753607 | + | 0.657325i | \(0.228312\pi\) | |||||||
\(954\) | 0.0511205i | 0.00165509i | ||||||||
\(955\) | −6.09306 | + | 13.2936i | −0.197167 | + | 0.430171i | ||||
\(956\) | 23.2963i | 0.753457i | ||||||||
\(957\) | 2.64142 | + | 4.57508i | 0.0853851 | + | 0.147891i | ||||
\(958\) | 9.67769 | − | 5.58742i | 0.312672 | − | 0.180521i | ||||
\(959\) | −46.2633 | − | 80.1304i | −1.49392 | − | 2.58754i | ||||
\(960\) | 3.93377 | − | 0.370178i | 0.126962 | − | 0.0119475i | ||||
\(961\) | 25.7371 | 0.830230 | ||||||||
\(962\) | 22.7242 | − | 26.6734i | 0.732657 | − | 0.859986i | ||||
\(963\) | − | 1.58974i | − | 0.0512287i | ||||||
\(964\) | −19.9282 | − | 11.5055i | −0.641843 | − | 0.370568i | ||||
\(965\) | 32.8671 | + | 15.0645i | 1.05803 | + | 0.484943i | ||||
\(966\) | 19.9297 | + | 34.5192i | 0.641227 | + | 1.11064i | ||||
\(967\) | 2.42170 | + | 4.19451i | 0.0778768 | + | 0.134886i | 0.902334 | − | 0.431038i | \(-0.141853\pi\) |
−0.824457 | + | 0.565925i | \(0.808519\pi\) | |||||||
\(968\) | −9.73578 | −0.312920 | ||||||||
\(969\) | −4.68666 | − | 8.11753i | −0.150557 | − | 0.260773i | ||||
\(970\) | −3.48143 | + | 2.47192i | −0.111782 | + | 0.0793684i | ||||
\(971\) | −19.2489 | + | 33.3400i | −0.617726 | + | 1.06993i | 0.372174 | + | 0.928163i | \(0.378613\pi\) |
−0.989900 | + | 0.141770i | \(0.954721\pi\) | |||||||
\(972\) | − | 1.27030i | − | 0.0407449i | ||||||
\(973\) | 0.975639i | 0.0312776i | ||||||||
\(974\) | −5.81329 | + | 10.0689i | −0.186270 | + | 0.322629i | ||||
\(975\) | −9.49479 | − | 50.0023i | −0.304077 | − | 1.60135i | ||||
\(976\) | − | 6.10516i | − | 0.195421i | ||||||
\(977\) | −15.2341 | + | 26.3861i | −0.487380 | + | 0.844168i | −0.999895 | − | 0.0145110i | \(-0.995381\pi\) |
0.512514 | + | 0.858679i | \(0.328714\pi\) | |||||||
\(978\) | 0.903942 | + | 0.521891i | 0.0289049 | + | 0.0166882i | ||||
\(979\) | −0.718732 | − | 0.414960i | −0.0229708 | − | 0.0132622i | ||||
\(980\) | −18.1514 | − | 8.31961i | −0.579825 | − | 0.265760i | ||||
\(981\) | −1.61452 | + | 0.932146i | −0.0515478 | + | 0.0297611i | ||||
\(982\) | 6.54751 | − | 11.3406i | 0.208939 | − | 0.361894i | ||||
\(983\) | 39.4371 | + | 22.7690i | 1.25785 | + | 0.726218i | 0.972656 | − | 0.232252i | \(-0.0746096\pi\) |
0.285191 | + | 0.958471i | \(0.407943\pi\) | |||||||
\(984\) | 6.38783 | + | 3.68802i | 0.203637 | + | 0.117570i | ||||
\(985\) | −15.9763 | − | 22.5010i | −0.509048 | − | 0.716940i | ||||
\(986\) | −1.73470 | + | 1.00153i | −0.0552441 | + | 0.0318952i | ||||
\(987\) | 68.2977 | + | 39.4317i | 2.17394 | + | 1.25513i | ||||
\(988\) | − | 40.5652i | − | 1.29055i | ||||||
\(989\) | −48.4619 | −1.54100 | ||||||||
\(990\) | −0.0288102 | − | 0.306157i | −0.000915650 | − | 0.00973031i | ||||
\(991\) | − | 45.1994i | − | 1.43581i | −0.696143 | − | 0.717903i | \(-0.745102\pi\) | ||
0.696143 | − | 0.717903i | \(-0.254898\pi\) | |||||||
\(992\) | 1.98675 | − | 1.14705i | 0.0630792 | − | 0.0364188i | ||||
\(993\) | −27.1983 | −0.863112 | ||||||||
\(994\) | 3.24583 | − | 1.87398i | 0.102951 | − | 0.0594390i | ||||
\(995\) | 8.77327 | − | 19.1412i | 0.278131 | − | 0.606816i | ||||
\(996\) | 8.75779 | + | 15.1689i | 0.277501 | + | 0.480646i | ||||
\(997\) | 1.77135 | − | 3.06806i | 0.0560991 | − | 0.0971666i | −0.836612 | − | 0.547796i | \(-0.815467\pi\) |
0.892711 | + | 0.450629i | \(0.148800\pi\) | |||||||
\(998\) | − | 14.3166i | − | 0.453182i | ||||||
\(999\) | 23.5444 | + | 20.0584i | 0.744911 | + | 0.634620i |
(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 | 370.2.m.c.249.6 | yes | 16 | |
5.4 | even | 2 | 370.2.m.d.249.3 | yes | 16 | ||
37.11 | even | 6 | 370.2.m.d.159.3 | yes | 16 | ||
185.159 | even | 6 | inner | 370.2.m.c.159.6 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.m.c.159.6 | ✓ | 16 | 185.159 | even | 6 | inner | |
370.2.m.c.249.6 | yes | 16 | 1.1 | even | 1 | trivial | |
370.2.m.d.159.3 | yes | 16 | 37.11 | even | 6 | ||
370.2.m.d.249.3 | yes | 16 | 5.4 | even | 2 |