Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,3,Mod(19,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("99.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.k (of order \(10\), 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: | \(2.69755461717\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 28.1 | ||
Root | \(1.64608 - 1.06057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.28 |
Dual form | 99.3.k.c.46.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(e\left(\frac{9}{10}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.35440 | + | 0.764990i | −1.17720 | + | 0.382495i | −0.831325 | − | 0.555786i | \(-0.812417\pi\) |
−0.345873 | + | 0.938281i | \(0.612417\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.72190 | − | 1.25104i | 0.430476 | − | 0.312759i | ||||
\(5\) | 0.789076 | − | 2.42853i | 0.157815 | − | 0.485705i | −0.840620 | − | 0.541625i | \(-0.817809\pi\) |
0.998435 | + | 0.0559199i | \(0.0178092\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.100159 | − | 0.137856i | −0.0143084 | − | 0.0196938i | 0.801803 | − | 0.597589i | \(-0.203874\pi\) |
−0.816111 | + | 0.577895i | \(0.803874\pi\) | |||||||
\(8\) | 2.72337 | − | 3.74840i | 0.340422 | − | 0.468550i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.32135i | 0.632135i | ||||||||
\(11\) | 7.69573 | + | 7.85976i | 0.699612 | + | 0.714523i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.3310 | − | 5.95611i | 1.41008 | − | 0.458163i | 0.497643 | − | 0.867382i | \(-0.334199\pi\) |
0.912436 | + | 0.409219i | \(0.134199\pi\) | |||||||
\(14\) | 0.341272 | + | 0.247948i | 0.0243766 | + | 0.0177106i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.17525 | + | 19.0055i | −0.385953 | + | 1.18784i | ||||
\(17\) | 19.3014 | + | 6.27142i | 1.13538 | + | 0.368907i | 0.815618 | − | 0.578591i | \(-0.196397\pi\) |
0.319761 | + | 0.947498i | \(0.396397\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.57343 | − | 11.8003i | 0.451233 | − | 0.621069i | −0.521429 | − | 0.853295i | \(-0.674601\pi\) |
0.972662 | + | 0.232226i | \(0.0746008\pi\) | |||||||
\(20\) | −1.67946 | − | 5.16886i | −0.0839732 | − | 0.258443i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −24.1314 | − | 12.6178i | −1.09688 | − | 0.573538i | ||||
\(23\) | −7.74583 | −0.336775 | −0.168388 | − | 0.985721i | \(-0.553856\pi\) | ||||
−0.168388 | + | 0.985721i | \(0.553856\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.9503 | + | 10.8620i | 0.598013 | + | 0.434482i | ||||
\(26\) | −38.6022 | + | 28.0461i | −1.48470 | + | 1.07870i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.344927 | − | 0.112074i | −0.0123188 | − | 0.00400263i | ||||
\(29\) | −22.4904 | − | 30.9554i | −0.775532 | − | 1.06743i | −0.995761 | − | 0.0919801i | \(-0.970680\pi\) |
0.220229 | − | 0.975448i | \(-0.429320\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −13.0940 | − | 40.2993i | −0.422389 | − | 1.29998i | −0.905473 | − | 0.424405i | \(-0.860483\pi\) |
0.483084 | − | 0.875574i | \(-0.339517\pi\) | |||||||
\(32\) | − | 30.9373i | − | 0.966789i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −50.2408 | −1.47767 | ||||||||
\(35\) | −0.413821 | + | 0.134459i | −0.0118235 | + | 0.00384167i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −41.7807 | + | 30.3554i | −1.12921 | + | 0.820417i | −0.985579 | − | 0.169214i | \(-0.945877\pi\) |
−0.143628 | + | 0.989632i | \(0.545877\pi\) | |||||||
\(38\) | −11.1581 | + | 34.3412i | −0.293635 | + | 0.903716i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.95414 | − | 9.57156i | −0.173854 | − | 0.239289i | ||||
\(41\) | 27.1820 | − | 37.4128i | 0.662976 | − | 0.912508i | −0.336600 | − | 0.941648i | \(-0.609277\pi\) |
0.999575 | + | 0.0291401i | \(0.00927689\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 59.7836i | 1.39032i | 0.718857 | + | 0.695158i | \(0.244666\pi\) | ||||
−0.718857 | + | 0.695158i | \(0.755334\pi\) | |||||||
\(44\) | 23.0842 | + | 3.90611i | 0.524640 | + | 0.0887753i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.2367 | − | 5.92548i | 0.396451 | − | 0.128815i | ||||
\(47\) | 27.6137 | + | 20.0626i | 0.587526 | + | 0.426863i | 0.841430 | − | 0.540367i | \(-0.181714\pi\) |
−0.253903 | + | 0.967230i | \(0.581714\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.1329 | − | 46.5742i | 0.308834 | − | 0.950493i | ||||
\(50\) | −43.5083 | − | 14.1367i | −0.870167 | − | 0.282734i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 24.1130 | − | 33.1887i | 0.463711 | − | 0.638244i | ||||
\(53\) | 4.70489 | + | 14.4801i | 0.0887714 | + | 0.273210i | 0.985580 | − | 0.169208i | \(-0.0541208\pi\) |
−0.896809 | + | 0.442418i | \(0.854121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 25.1602 | − | 12.4873i | 0.457457 | − | 0.227042i | ||||
\(56\) | −0.789510 | −0.0140984 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 76.6320 | + | 55.6764i | 1.32124 | + | 0.959938i | ||||
\(59\) | −21.3110 | + | 15.4833i | −0.361203 | + | 0.262430i | −0.753554 | − | 0.657386i | \(-0.771662\pi\) |
0.392350 | + | 0.919816i | \(0.371662\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 60.2698 | + | 19.5828i | 0.988029 | + | 0.321030i | 0.758072 | − | 0.652171i | \(-0.226142\pi\) |
0.229957 | + | 0.973201i | \(0.426142\pi\) | |||||||
\(62\) | 61.6572 | + | 84.8638i | 0.994470 | + | 1.36877i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.03430 | − | 3.18325i | −0.0161609 | − | 0.0497382i | ||||
\(65\) | − | 49.2172i | − | 0.757188i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.91469 | −0.0435028 | −0.0217514 | − | 0.999763i | \(-0.506924\pi\) | ||||
−0.0217514 | + | 0.999763i | \(0.506924\pi\) | |||||||
\(68\) | 41.0810 | − | 13.3480i | 0.604133 | − | 0.196295i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.871439 | − | 0.633137i | 0.0124491 | − | 0.00904482i | ||||
\(71\) | −29.9080 | + | 92.0473i | −0.421239 | + | 1.29644i | 0.485311 | + | 0.874342i | \(0.338707\pi\) |
−0.906550 | + | 0.422099i | \(0.861293\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.1852 | − | 14.0187i | −0.139523 | − | 0.192037i | 0.733537 | − | 0.679649i | \(-0.237868\pi\) |
−0.873060 | + | 0.487612i | \(0.837868\pi\) | |||||||
\(74\) | 75.1467 | − | 103.431i | 1.01550 | − | 1.39771i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 31.0447i | − | 0.408483i | ||||||
\(77\) | 0.312725 | − | 1.84813i | 0.00406136 | − | 0.0240017i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −50.1945 | + | 16.3092i | −0.635374 | + | 0.206445i | −0.608954 | − | 0.793205i | \(-0.708411\pi\) |
−0.0264197 | + | 0.999651i | \(0.508411\pi\) | |||||||
\(80\) | 41.2825 | + | 29.9935i | 0.516031 | + | 0.374919i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −35.3768 | + | 108.879i | −0.431424 | + | 1.32779i | ||||
\(83\) | −22.3267 | − | 7.25438i | −0.268996 | − | 0.0874021i | 0.171413 | − | 0.985199i | \(-0.445167\pi\) |
−0.440409 | + | 0.897797i | \(0.645167\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 30.4606 | − | 41.9255i | 0.358360 | − | 0.493241i | ||||
\(86\) | −45.7338 | − | 140.754i | −0.531789 | − | 1.63668i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 50.4198 | − | 7.44162i | 0.572953 | − | 0.0845639i | ||||
\(89\) | −97.1861 | −1.09198 | −0.545989 | − | 0.837792i | \(-0.683846\pi\) | ||||
−0.545989 | + | 0.837792i | \(0.683846\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.65710 | − | 1.93050i | −0.0291989 | − | 0.0212142i | ||||
\(92\) | −13.3376 | + | 9.69032i | −0.144974 | + | 0.105330i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −80.3613 | − | 26.1110i | −0.854908 | − | 0.277776i | ||||
\(95\) | −21.8923 | − | 30.1321i | −0.230445 | − | 0.317180i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.6408 | − | 48.1375i | −0.161246 | − | 0.496263i | 0.837494 | − | 0.546446i | \(-0.184020\pi\) |
−0.998740 | + | 0.0501828i | \(0.984020\pi\) | |||||||
\(98\) | 121.230i | 1.23705i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 39.3318 | 0.393318 | ||||||||
\(101\) | −62.5858 | + | 20.3354i | −0.619662 | + | 0.201340i | −0.601990 | − | 0.798504i | \(-0.705625\pi\) |
−0.0176716 | + | 0.999844i | \(0.505625\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −112.599 | + | 81.8082i | −1.09320 | + | 0.794254i | −0.979936 | − | 0.199311i | \(-0.936130\pi\) |
−0.113261 | + | 0.993565i | \(0.536130\pi\) | |||||||
\(104\) | 27.5963 | − | 84.9328i | 0.265349 | − | 0.816661i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22.1543 | − | 30.4928i | −0.209003 | − | 0.287668i | ||||
\(107\) | 7.57953 | − | 10.4323i | 0.0708367 | − | 0.0974984i | −0.772129 | − | 0.635466i | \(-0.780808\pi\) |
0.842965 | + | 0.537968i | \(0.180808\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 117.681i | − | 1.07964i | −0.841780 | − | 0.539821i | \(-0.818492\pi\) | ||
0.841780 | − | 0.539821i | \(-0.181508\pi\) | |||||||
\(110\) | −49.6843 | + | 48.6474i | −0.451675 | + | 0.442249i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.23853 | − | 1.05226i | 0.0289154 | − | 0.00939519i | ||||
\(113\) | 142.095 | + | 103.238i | 1.25748 | + | 0.913614i | 0.998631 | − | 0.0523039i | \(-0.0166564\pi\) |
0.258850 | + | 0.965918i | \(0.416656\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.11205 | + | 18.8110i | −0.0531483 | + | 0.163574i | ||||
\(116\) | −77.4528 | − | 25.1659i | −0.667696 | − | 0.216948i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 38.3299 | − | 52.7566i | 0.324830 | − | 0.447090i | ||||
\(119\) | −1.06865 | − | 3.28896i | −0.00898025 | − | 0.0276384i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.55156 | + | 120.973i | −0.0210872 | + | 0.999778i | ||||
\(122\) | −156.880 | −1.28590 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −72.9627 | − | 53.0105i | −0.588408 | − | 0.427504i | ||||
\(125\) | 89.8214 | − | 65.2591i | 0.718571 | − | 0.522073i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −56.9179 | − | 18.4937i | −0.448172 | − | 0.145620i | 0.0762307 | − | 0.997090i | \(-0.475711\pi\) |
−0.524403 | + | 0.851470i | \(0.675711\pi\) | |||||||
\(128\) | 77.6082 | + | 106.818i | 0.606314 | + | 0.834519i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 37.6507 | + | 115.877i | 0.289621 | + | 0.891361i | ||||
\(131\) | − | 27.1623i | − | 0.207346i | −0.994611 | − | 0.103673i | \(-0.966940\pi\) | ||
0.994611 | − | 0.103673i | \(-0.0330595\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.48545 | −0.0186876 | ||||||||
\(134\) | 6.86233 | − | 2.22971i | 0.0512114 | − | 0.0166396i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 76.0728 | − | 55.2701i | 0.559359 | − | 0.406398i | ||||
\(137\) | 25.0824 | − | 77.1956i | 0.183083 | − | 0.563472i | −0.816827 | − | 0.576883i | \(-0.804269\pi\) |
0.999910 | + | 0.0134110i | \(0.00426898\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 114.273 | + | 157.283i | 0.822108 | + | 1.13153i | 0.989341 | + | 0.145617i | \(0.0465167\pi\) |
−0.167233 | + | 0.985917i | \(0.553483\pi\) | |||||||
\(140\) | −0.544347 | + | 0.749230i | −0.00388820 | + | 0.00535164i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 239.595i | − | 1.68729i | ||||||
\(143\) | 187.884 | + | 98.2408i | 1.31388 | + | 0.686999i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −92.9228 | + | 30.1924i | −0.640847 | + | 0.208224i | ||||
\(146\) | 34.7041 | + | 25.2140i | 0.237699 | + | 0.172699i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −33.9666 | + | 104.538i | −0.229504 | + | 0.706340i | ||||
\(149\) | −115.358 | − | 37.4820i | −0.774212 | − | 0.251557i | −0.104845 | − | 0.994489i | \(-0.533435\pi\) |
−0.669367 | + | 0.742932i | \(0.733435\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −60.2816 | + | 82.9704i | −0.399216 | + | 0.549473i | −0.960547 | − | 0.278118i | \(-0.910289\pi\) |
0.561331 | + | 0.827591i | \(0.310289\pi\) | |||||||
\(152\) | −20.8837 | − | 64.2733i | −0.137392 | − | 0.422850i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.677520 | + | 4.59046i | 0.00439948 | + | 0.0298082i | ||||
\(155\) | −108.200 | −0.698066 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −143.464 | − | 104.232i | −0.913781 | − | 0.663901i | 0.0281874 | − | 0.999603i | \(-0.491026\pi\) |
−0.941968 | + | 0.335702i | \(0.891026\pi\) | |||||||
\(158\) | 105.701 | − | 76.7966i | 0.668997 | − | 0.486054i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −75.1320 | − | 24.4119i | −0.469575 | − | 0.152574i | ||||
\(161\) | 0.775811 | + | 1.06781i | 0.00481870 | + | 0.00663237i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 32.5033 | + | 100.035i | 0.199407 | + | 0.613711i | 0.999897 | + | 0.0143648i | \(0.00457262\pi\) |
−0.800490 | + | 0.599346i | \(0.795427\pi\) | |||||||
\(164\) | − | 98.4270i | − | 0.600165i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 58.1154 | 0.350093 | ||||||||
\(167\) | 123.073 | − | 39.9889i | 0.736965 | − | 0.239454i | 0.0836021 | − | 0.996499i | \(-0.473358\pi\) |
0.653363 | + | 0.757045i | \(0.273358\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 163.828 | − | 119.028i | 0.969394 | − | 0.704306i | ||||
\(170\) | −39.6438 | + | 122.011i | −0.233199 | + | 0.717713i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 74.7915 | + | 102.942i | 0.434834 | + | 0.598498i | ||||
\(173\) | −26.3311 | + | 36.2416i | −0.152203 | + | 0.209489i | −0.878309 | − | 0.478093i | \(-0.841328\pi\) |
0.726106 | + | 0.687583i | \(0.241328\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.14892i | − | 0.0179939i | ||||||
\(176\) | −196.901 | + | 97.7249i | −1.11876 | + | 0.555255i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 228.815 | − | 74.3464i | 1.28548 | − | 0.417676i | ||||
\(179\) | −257.046 | − | 186.755i | −1.43601 | − | 1.04332i | −0.988857 | − | 0.148867i | \(-0.952437\pi\) |
−0.447155 | − | 0.894457i | \(-0.647563\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 102.216 | − | 314.588i | 0.564729 | − | 1.73806i | −0.104027 | − | 0.994574i | \(-0.533173\pi\) |
0.668756 | − | 0.743482i | \(-0.266827\pi\) | |||||||
\(182\) | 7.73267 | + | 2.51250i | 0.0424872 | + | 0.0138049i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −21.0948 | + | 29.0345i | −0.114646 | + | 0.157796i | ||||
\(185\) | 40.7509 | + | 125.418i | 0.220275 | + | 0.677937i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 99.2468 | + | 199.968i | 0.530732 | + | 1.06935i | ||||
\(188\) | 72.6472 | 0.386421 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 74.5939 | + | 54.1956i | 0.392599 | + | 0.285240i | ||||
\(191\) | −102.778 | + | 74.6723i | −0.538103 | + | 0.390955i | −0.823380 | − | 0.567490i | \(-0.807914\pi\) |
0.285277 | + | 0.958445i | \(0.407914\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 201.049 | + | 65.3248i | 1.04171 | + | 0.338471i | 0.779408 | − | 0.626517i | \(-0.215520\pi\) |
0.262297 | + | 0.964987i | \(0.415520\pi\) | |||||||
\(194\) | 73.6494 | + | 101.370i | 0.379636 | + | 0.522524i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −32.2086 | − | 99.1280i | −0.164330 | − | 0.505755i | ||||
\(197\) | 2.87439i | 0.0145908i | 0.999973 | + | 0.00729541i | \(0.00232222\pi\) | ||||
−0.999973 | + | 0.00729541i | \(0.997678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −158.546 | −0.796713 | −0.398357 | − | 0.917231i | \(-0.630419\pi\) | ||||
−0.398357 | + | 0.917231i | \(0.630419\pi\) | |||||||
\(200\) | 81.4306 | − | 26.4584i | 0.407153 | − | 0.132292i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 131.795 | − | 95.7550i | 0.652453 | − | 0.474035i | ||||
\(203\) | −2.01479 | + | 6.20090i | −0.00992510 | + | 0.0305463i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −69.4094 | − | 95.5338i | −0.338582 | − | 0.466019i | ||||
\(206\) | 202.521 | − | 278.746i | 0.983112 | − | 1.35314i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 385.170i | 1.85178i | ||||||||
\(209\) | 158.726 | − | 23.4269i | 0.759456 | − | 0.112091i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −338.566 | + | 110.007i | −1.60458 | + | 0.521359i | −0.968234 | − | 0.250045i | \(-0.919554\pi\) |
−0.636345 | + | 0.771405i | \(0.719554\pi\) | |||||||
\(212\) | 26.2166 | + | 19.0474i | 0.123663 | + | 0.0898465i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.86459 | + | 30.3601i | −0.0460962 | + | 0.141870i | ||||
\(215\) | 145.186 | + | 47.1738i | 0.675284 | + | 0.219413i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.24404 | + | 5.84142i | −0.0195578 | + | 0.0269190i | ||||
\(218\) | 90.0247 | + | 277.067i | 0.412957 | + | 1.27095i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 27.7013 | − | 52.9783i | 0.125915 | − | 0.240810i | ||||
\(221\) | 391.169 | 1.76999 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 172.623 | + | 125.418i | 0.774092 | + | 0.562411i | 0.903200 | − | 0.429219i | \(-0.141211\pi\) |
−0.129108 | + | 0.991631i | \(0.541211\pi\) | |||||||
\(224\) | −4.26490 | + | 3.09863i | −0.0190397 | + | 0.0138332i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −413.525 | − | 134.362i | −1.82976 | − | 0.594524i | ||||
\(227\) | −103.890 | − | 142.993i | −0.457666 | − | 0.629923i | 0.516357 | − | 0.856374i | \(-0.327288\pi\) |
−0.974023 | + | 0.226451i | \(0.927288\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.4570 | − | 59.8825i | −0.0849650 | − | 0.261495i | 0.899544 | − | 0.436831i | \(-0.143899\pi\) |
−0.984509 | + | 0.175335i | \(0.943899\pi\) | |||||||
\(230\) | − | 48.9641i | − | 0.212887i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −177.283 | −0.764151 | ||||||||
\(233\) | −292.304 | + | 94.9755i | −1.25453 | + | 0.407620i | −0.859541 | − | 0.511067i | \(-0.829250\pi\) |
−0.394985 | + | 0.918688i | \(0.629250\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 70.5118 | − | 51.2298i | 0.300050 | − | 0.217999i | ||||
\(236\) | −17.3253 | + | 53.3217i | −0.0734122 | + | 0.225939i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.03205 | + | 6.92602i | 0.0211431 | + | 0.0291009i | ||||
\(239\) | −219.365 | + | 301.930i | −0.917847 | + | 1.26331i | 0.0465686 | + | 0.998915i | \(0.485171\pi\) |
−0.964415 | + | 0.264392i | \(0.914829\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0743i | 0.0542501i | 0.999632 | + | 0.0271250i | \(0.00863523\pi\) | ||||
−0.999632 | + | 0.0271250i | \(0.991365\pi\) | |||||||
\(242\) | −86.5358 | − | 286.771i | −0.357586 | − | 1.18500i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 128.278 | − | 41.6799i | 0.525728 | − | 0.170819i | ||||
\(245\) | −101.166 | − | 73.5011i | −0.412921 | − | 0.300005i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 86.8758 | − | 267.376i | 0.351724 | − | 1.08249i | ||||
\(248\) | −186.718 | − | 60.6684i | −0.752895 | − | 0.244630i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −161.553 | + | 222.358i | −0.646211 | + | 0.889433i | ||||
\(251\) | −42.7719 | − | 131.638i | −0.170406 | − | 0.524456i | 0.828988 | − | 0.559267i | \(-0.188917\pi\) |
−0.999394 | + | 0.0348107i | \(0.988917\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −59.6098 | − | 60.8803i | −0.235612 | − | 0.240634i | ||||
\(254\) | 148.155 | 0.583286 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −253.604 | − | 184.254i | −0.990641 | − | 0.719743i | ||||
\(257\) | −232.910 | + | 169.219i | −0.906264 | + | 0.658439i | −0.940067 | − | 0.340989i | \(-0.889238\pi\) |
0.0338032 | + | 0.999429i | \(0.489238\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.36939 | + | 2.71938i | 0.0323142 | + | 0.0104995i | ||||
\(260\) | −61.5726 | − | 84.7474i | −0.236818 | − | 0.325952i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 20.7789 | + | 63.9508i | 0.0793087 | + | 0.244087i | ||||
\(263\) | − | 338.296i | − | 1.28629i | −0.765742 | − | 0.643147i | \(-0.777628\pi\) | ||
0.765742 | − | 0.643147i | \(-0.222372\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 38.8779 | 0.146709 | ||||||||
\(266\) | 5.85174 | − | 1.90134i | 0.0219990 | − | 0.00714791i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.01881 | + | 3.64638i | −0.0187269 | + | 0.0136059i | ||||
\(269\) | 19.5161 | − | 60.0645i | 0.0725507 | − | 0.223288i | −0.908206 | − | 0.418524i | \(-0.862547\pi\) |
0.980756 | + | 0.195236i | \(0.0625474\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −97.9877 | − | 134.868i | −0.361578 | − | 0.497670i | 0.589009 | − | 0.808126i | \(-0.299518\pi\) |
−0.950588 | + | 0.310457i | \(0.899518\pi\) | |||||||
\(272\) | −238.382 | + | 328.105i | −0.876406 | + | 1.20627i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 200.937i | 0.733346i | ||||||||
\(275\) | 29.6806 | + | 201.097i | 0.107929 | + | 0.731263i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 40.3083 | − | 13.0970i | 0.145517 | − | 0.0472815i | −0.235353 | − | 0.971910i | \(-0.575625\pi\) |
0.380870 | + | 0.924629i | \(0.375625\pi\) | |||||||
\(278\) | −389.364 | − | 282.889i | −1.40059 | − | 1.01759i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.622984 | + | 1.91735i | −0.00222494 | + | 0.00684767i | ||||
\(281\) | 135.807 | + | 44.1263i | 0.483298 | + | 0.157033i | 0.540525 | − | 0.841328i | \(-0.318226\pi\) |
−0.0572268 | + | 0.998361i | \(0.518226\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 152.286 | − | 209.604i | 0.538114 | − | 0.740650i | −0.450226 | − | 0.892915i | \(-0.648657\pi\) |
0.988340 | + | 0.152264i | \(0.0486565\pi\) | |||||||
\(284\) | 63.6559 | + | 195.913i | 0.224140 | + | 0.689833i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −517.507 | − | 87.5684i | −1.80947 | − | 0.306183i | ||||
\(287\) | −7.88011 | −0.0274568 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 99.4092 | + | 72.2250i | 0.343976 | + | 0.249914i | ||||
\(290\) | 195.680 | − | 142.170i | 0.674759 | − | 0.490241i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −35.0758 | − | 11.3968i | −0.120123 | − | 0.0390302i | ||||
\(293\) | −67.6072 | − | 93.0533i | −0.230741 | − | 0.317588i | 0.677909 | − | 0.735146i | \(-0.262886\pi\) |
−0.908651 | + | 0.417557i | \(0.862886\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.7857 | + | 63.9719i | 0.0704601 | + | 0.216854i | ||||
\(296\) | 239.280i | 0.808378i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 300.271 | 1.00762 | ||||||||
\(299\) | −141.989 | + | 46.1350i | −0.474880 | + | 0.154298i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.24155 | − | 5.98784i | 0.0273806 | − | 0.0198931i | ||||
\(302\) | 78.4551 | − | 241.460i | 0.259785 | − | 0.799537i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 171.327 | + | 235.812i | 0.563576 | + | 0.775696i | ||||
\(305\) | 95.1149 | − | 130.914i | 0.311852 | − | 0.429227i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.9819i | 0.0748596i | 0.999299 | + | 0.0374298i | \(0.0119171\pi\) | ||||
−0.999299 | + | 0.0374298i | \(0.988083\pi\) | |||||||
\(308\) | −1.77359 | − | 3.57353i | −0.00575842 | − | 0.0116024i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 254.746 | − | 82.7721i | 0.821762 | − | 0.267007i | ||||
\(311\) | 481.079 | + | 349.524i | 1.54688 | + | 1.12387i | 0.945831 | + | 0.324659i | \(0.105250\pi\) |
0.601047 | + | 0.799214i | \(0.294750\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −161.264 | + | 496.318i | −0.515219 | + | 1.58568i | 0.267664 | + | 0.963512i | \(0.413748\pi\) |
−0.782883 | + | 0.622169i | \(0.786252\pi\) | |||||||
\(314\) | 417.507 | + | 135.656i | 1.32964 | + | 0.432026i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −66.0268 | + | 90.8781i | −0.208946 | + | 0.287589i | ||||
\(317\) | −47.4779 | − | 146.122i | −0.149773 | − | 0.460953i | 0.847821 | − | 0.530282i | \(-0.177914\pi\) |
−0.997594 | + | 0.0693294i | \(0.977914\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 70.2219 | − | 414.994i | 0.220131 | − | 1.30092i | ||||
\(320\) | −8.54675 | −0.0267086 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.64343 | − | 1.92057i | −0.00820942 | − | 0.00596449i | ||||
\(323\) | 239.484 | − | 173.995i | 0.741437 | − | 0.538686i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 338.750 | + | 110.067i | 1.04231 | + | 0.338667i | ||||
\(326\) | −153.051 | − | 210.657i | −0.469482 | − | 0.646187i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −66.2115 | − | 203.778i | −0.201864 | − | 0.621275i | ||||
\(329\) | − | 5.81617i | − | 0.0176783i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 297.441 | 0.898613 | 0.449306 | − | 0.893378i | \(-0.351671\pi\) | ||||
0.449306 | + | 0.893378i | \(0.351671\pi\) | |||||||
\(332\) | −47.5199 | + | 15.4401i | −0.143132 | + | 0.0465065i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −259.172 | + | 188.299i | −0.775964 | + | 0.563771i | ||||
\(335\) | −2.29991 | + | 7.07840i | −0.00686540 | + | 0.0211295i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.45661 | + | 3.38123i | 0.00728964 | + | 0.0100333i | 0.812646 | − | 0.582757i | \(-0.198026\pi\) |
−0.805357 | + | 0.592791i | \(0.798026\pi\) | |||||||
\(338\) | −294.660 | + | 405.565i | −0.871776 | + | 1.19990i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 110.299i | − | 0.324409i | ||||||
\(341\) | 215.975 | − | 413.049i | 0.633357 | − | 1.21129i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.8772 | + | 5.15881i | −0.0462891 | + | 0.0150402i | ||||
\(344\) | 224.093 | + | 162.813i | 0.651433 | + | 0.473293i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 34.2693 | − | 105.470i | 0.0990443 | − | 0.304827i | ||||
\(347\) | 557.200 | + | 181.045i | 1.60576 | + | 0.521745i | 0.968524 | − | 0.248920i | \(-0.0800757\pi\) |
0.637241 | + | 0.770665i | \(0.280076\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −135.909 | + | 187.062i | −0.389424 | + | 0.535996i | −0.958050 | − | 0.286600i | \(-0.907475\pi\) |
0.568627 | + | 0.822596i | \(0.307475\pi\) | |||||||
\(350\) | 2.40890 | + | 7.41382i | 0.00688256 | + | 0.0211823i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 243.159 | − | 238.085i | 0.690794 | − | 0.676377i | ||||
\(353\) | 416.133 | 1.17885 | 0.589423 | − | 0.807824i | \(-0.299355\pi\) | ||||
0.589423 | + | 0.807824i | \(0.299355\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 199.940 | + | 145.265i | 0.563210 | + | 0.409196i | ||||
\(356\) | −167.345 | + | 121.583i | −0.470071 | + | 0.341526i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 748.054 | + | 243.058i | 2.08954 | + | 0.678932i | ||||
\(359\) | −22.2795 | − | 30.6650i | −0.0620598 | − | 0.0854179i | 0.776859 | − | 0.629675i | \(-0.216812\pi\) |
−0.838919 | + | 0.544257i | \(0.816812\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 45.8115 | + | 140.993i | 0.126902 | + | 0.390563i | ||||
\(362\) | 818.859i | 2.26204i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.99039 | −0.0192044 | ||||||||
\(365\) | −42.0817 | + | 13.6732i | −0.115292 | + | 0.0374607i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −177.269 | + | 128.793i | −0.483021 | + | 0.350935i | −0.802494 | − | 0.596660i | \(-0.796494\pi\) |
0.319473 | + | 0.947595i | \(0.396494\pi\) | |||||||
\(368\) | 47.8324 | − | 147.213i | 0.129979 | − | 0.400035i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −191.887 | − | 264.110i | −0.518615 | − | 0.713812i | ||||
\(371\) | 1.52495 | − | 2.09891i | 0.00411037 | − | 0.00565744i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.9491i | 0.0481209i | 0.999711 | + | 0.0240605i | \(0.00765942\pi\) | ||||
−0.999711 | + | 0.0240605i | \(0.992341\pi\) | |||||||
\(374\) | −386.640 | − | 394.881i | −1.03380 | − | 1.05583i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 150.405 | − | 48.8695i | 0.400013 | − | 0.129972i | ||||
\(377\) | −596.647 | − | 433.489i | −1.58262 | − | 1.14984i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.1040 | + | 43.4075i | −0.0372136 | + | 0.114532i | −0.967938 | − | 0.251190i | \(-0.919178\pi\) |
0.930724 | + | 0.365722i | \(0.119178\pi\) | |||||||
\(380\) | −75.3929 | − | 24.4966i | −0.198402 | − | 0.0644648i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 184.856 | − | 254.432i | 0.483916 | − | 0.666053i | ||||
\(383\) | 8.70857 | + | 26.8022i | 0.0227378 | + | 0.0699797i | 0.961782 | − | 0.273818i | \(-0.0882866\pi\) |
−0.939044 | + | 0.343798i | \(0.888287\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.24146 | − | 2.21778i | −0.0110168 | − | 0.00576045i | ||||
\(386\) | −523.322 | −1.35576 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −87.1538 | − | 63.3210i | −0.224623 | − | 0.163198i | ||||
\(389\) | −456.950 | + | 331.994i | −1.17468 | + | 0.853454i | −0.991562 | − | 0.129637i | \(-0.958619\pi\) |
−0.183118 | + | 0.983091i | \(0.558619\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −149.506 | − | 48.5773i | −0.382367 | − | 0.124239i | ||||
\(392\) | −133.366 | − | 183.563i | −0.340220 | − | 0.468272i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.19888 | − | 6.76745i | −0.00558091 | − | 0.0171763i | ||||
\(395\) | 134.768i | 0.341185i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.35093 | 0.0159973 | 0.00799866 | − | 0.999968i | \(-0.497454\pi\) | ||||
0.00799866 | + | 0.999968i | \(0.497454\pi\) | |||||||
\(398\) | 373.280 | − | 121.286i | 0.937889 | − | 0.304739i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −298.760 | + | 217.062i | −0.746900 | + | 0.542655i | ||||
\(401\) | 51.2418 | − | 157.706i | 0.127785 | − | 0.393282i | −0.866613 | − | 0.498981i | \(-0.833708\pi\) |
0.994398 | + | 0.105698i | \(0.0337078\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −480.055 | − | 660.739i | −1.19120 | − | 1.63955i | ||||
\(404\) | −82.3265 | + | 113.313i | −0.203779 | + | 0.280477i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 16.1407i | − | 0.0397554i | ||||||
\(407\) | −560.119 | − | 94.7788i | −1.37621 | − | 0.232872i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36.1697 | − | 11.7523i | 0.0884346 | − | 0.0287341i | −0.264466 | − | 0.964395i | \(-0.585196\pi\) |
0.352900 | + | 0.935661i | \(0.385196\pi\) | |||||||
\(410\) | 236.500 | + | 171.827i | 0.576828 | + | 0.419090i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −91.5402 | + | 281.732i | −0.222185 | + | 0.683815i | ||||
\(413\) | 4.26896 | + | 1.38707i | 0.0103365 | + | 0.00335852i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −35.2349 | + | 48.4967i | −0.0849034 | + | 0.116859i | ||||
\(416\) | −184.266 | − | 567.112i | −0.442947 | − | 1.36325i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −355.783 | + | 176.580i | −0.851156 | + | 0.422441i | ||||
\(419\) | 254.746 | 0.607985 | 0.303993 | − | 0.952674i | \(-0.401680\pi\) | ||||
0.303993 | + | 0.952674i | \(0.401680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −448.793 | − | 326.067i | −1.06602 | − | 0.774507i | −0.0908248 | − | 0.995867i | \(-0.528950\pi\) |
−0.975192 | + | 0.221360i | \(0.928950\pi\) | |||||||
\(422\) | 712.965 | − | 517.999i | 1.68949 | − | 1.22749i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 67.0905 | + | 21.7990i | 0.158232 | + | 0.0514128i | ||||
\(425\) | 220.442 | + | 303.413i | 0.518688 | + | 0.713913i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.33691 | − | 10.2700i | −0.00781478 | − | 0.0240514i | ||||
\(428\) | − | 27.4457i | − | 0.0641256i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −377.913 | −0.878867 | ||||||||
\(431\) | −29.9493 | + | 9.73111i | −0.0694879 | + | 0.0225780i | −0.343555 | − | 0.939133i | \(-0.611631\pi\) |
0.274067 | + | 0.961711i | \(0.411631\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −512.897 | + | 372.641i | −1.18452 | + | 0.860604i | −0.992674 | − | 0.120821i | \(-0.961447\pi\) |
−0.191845 | + | 0.981425i | \(0.561447\pi\) | |||||||
\(434\) | 5.52353 | − | 16.9997i | 0.0127270 | − | 0.0391697i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −147.223 | − | 202.635i | −0.337668 | − | 0.464760i | ||||
\(437\) | −66.4083 | + | 91.4032i | −0.151964 | + | 0.209161i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 336.283i | − | 0.766021i | −0.923744 | − | 0.383010i | \(-0.874887\pi\) | ||
0.923744 | − | 0.383010i | \(-0.125113\pi\) | |||||||
\(440\) | 21.7129 | − | 128.318i | 0.0493475 | − | 0.291632i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −920.966 | + | 299.240i | −2.08363 | + | 0.677014i | ||||
\(443\) | −394.592 | − | 286.688i | −0.890728 | − | 0.647152i | 0.0453398 | − | 0.998972i | \(-0.485563\pi\) |
−0.936068 | + | 0.351820i | \(0.885563\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −76.6873 | + | 236.019i | −0.172331 | + | 0.530380i | ||||
\(446\) | −502.365 | − | 163.228i | −1.12638 | − | 0.365983i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.335237 | + | 0.461414i | −0.000748297 | + | 0.00102994i | ||||
\(449\) | 206.541 | + | 635.666i | 0.460001 | + | 1.41574i | 0.865162 | + | 0.501493i | \(0.167216\pi\) |
−0.405161 | + | 0.914245i | \(0.632784\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 503.241 | − | 74.2749i | 1.11583 | − | 0.164689i | ||||
\(452\) | 373.830 | 0.827057 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 353.986 | + | 257.186i | 0.779706 | + | 0.566489i | ||||
\(455\) | −6.78491 | + | 4.92953i | −0.0149119 | + | 0.0108341i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 486.453 | + | 158.058i | 1.06445 | + | 0.345860i | 0.788323 | − | 0.615262i | \(-0.210950\pi\) |
0.276125 | + | 0.961122i | \(0.410950\pi\) | |||||||
\(458\) | 91.6189 | + | 126.103i | 0.200041 | + | 0.275333i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13.0088 | + | 40.0371i | 0.0282801 | + | 0.0870371i | ||||
\(461\) | − | 75.7082i | − | 0.164226i | −0.996623 | − | 0.0821131i | \(-0.973833\pi\) | ||
0.996623 | − | 0.0821131i | \(-0.0261669\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 292.607 | 0.631980 | 0.315990 | − | 0.948763i | \(-0.397663\pi\) | ||||
0.315990 | + | 0.948763i | \(0.397663\pi\) | |||||||
\(464\) | 727.206 | − | 236.283i | 1.56725 | − | 0.509232i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 615.545 | − | 447.220i | 1.32091 | − | 0.959699i | ||||
\(467\) | −239.339 | + | 736.611i | −0.512504 | + | 1.57733i | 0.275273 | + | 0.961366i | \(0.411232\pi\) |
−0.787778 | + | 0.615960i | \(0.788768\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.291931 | + | 0.401808i | 0.000622454 | + | 0.000856734i | ||||
\(470\) | −126.822 | + | 174.556i | −0.269835 | + | 0.371396i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 122.049i | 0.258579i | ||||||||
\(473\) | −469.884 | + | 460.078i | −0.993413 | + | 0.972681i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 256.351 | − | 83.2935i | 0.539686 | − | 0.175355i | ||||
\(476\) | −5.95473 | − | 4.32636i | −0.0125099 | − | 0.00908900i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 285.499 | − | 878.676i | 0.597279 | − | 1.83823i | ||||
\(479\) | −62.4240 | − | 20.2828i | −0.130322 | − | 0.0423440i | 0.243130 | − | 0.969994i | \(-0.421826\pi\) |
−0.373452 | + | 0.927650i | \(0.621826\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −585.083 | + | 805.297i | −1.21639 | + | 1.67421i | ||||
\(482\) | −10.0017 | − | 30.7820i | −0.0207504 | − | 0.0638631i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 146.948 | + | 211.496i | 0.303612 | + | 0.436976i | ||||
\(485\) | −129.245 | −0.266485 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.6563 | + | 10.6484i | 0.0300951 | + | 0.0218653i | 0.602731 | − | 0.797944i | \(-0.294079\pi\) |
−0.572636 | + | 0.819810i | \(0.694079\pi\) | |||||||
\(488\) | 237.541 | − | 172.584i | 0.486765 | − | 0.353655i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 294.412 | + | 95.6601i | 0.600840 | + | 0.195225i | ||||
\(491\) | −250.927 | − | 345.371i | −0.511053 | − | 0.703404i | 0.473043 | − | 0.881039i | \(-0.343155\pi\) |
−0.984096 | + | 0.177635i | \(0.943155\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −239.963 | − | 738.531i | −0.486741 | − | 1.49804i | ||||
\(494\) | 695.969i | 1.40884i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 846.766 | 1.70719 | ||||||||
\(497\) | 15.6849 | − | 5.09632i | 0.0315591 | − | 0.0102542i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −230.872 | + | 167.738i | −0.462669 | + | 0.336149i | −0.794577 | − | 0.607163i | \(-0.792307\pi\) |
0.331908 | + | 0.943312i | \(0.392307\pi\) | |||||||
\(500\) | 73.0224 | − | 224.740i | 0.146045 | − | 0.449480i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 201.404 | + | 277.209i | 0.401203 | + | 0.552209i | ||||
\(503\) | 319.511 | − | 439.769i | 0.635210 | − | 0.874292i | −0.363139 | − | 0.931735i | \(-0.618295\pi\) |
0.998349 | + | 0.0574435i | \(0.0182949\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 168.038i | 0.332748i | ||||||||
\(506\) | 186.918 | + | 97.7355i | 0.369403 | + | 0.193153i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −121.143 | + | 39.3619i | −0.238471 | + | 0.0774841i | ||||
\(509\) | 158.973 | + | 115.501i | 0.312324 | + | 0.226917i | 0.732893 | − | 0.680344i | \(-0.238170\pi\) |
−0.420569 | + | 0.907261i | \(0.638170\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.912435 | + | 2.80819i | −0.00178559 | + | 0.00549547i | ||||
\(512\) | 235.746 | + | 76.5987i | 0.460442 | + | 0.149607i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 418.911 | − | 576.582i | 0.815003 | − | 1.12175i | ||||
\(515\) | 109.824 | + | 338.003i | 0.213250 | + | 0.656317i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 54.8210 | + | 371.433i | 0.106037 | + | 0.718440i | ||||
\(518\) | −21.7851 | −0.0420563 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −184.486 | − | 134.037i | −0.354781 | − | 0.257763i | ||||
\(521\) | −463.782 | + | 336.958i | −0.890178 | + | 0.646752i | −0.935924 | − | 0.352201i | \(-0.885433\pi\) |
0.0457468 | + | 0.998953i | \(0.485433\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −945.004 | − | 307.050i | −1.80689 | − | 0.587094i | −0.806897 | − | 0.590693i | \(-0.798855\pi\) |
−0.999994 | + | 0.00359838i | \(0.998855\pi\) | |||||||
\(524\) | −33.9811 | − | 46.7709i | −0.0648493 | − | 0.0892575i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 258.793 | + | 796.482i | 0.492001 | + | 1.51422i | ||||
\(527\) | − | 859.954i | − | 1.63179i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −469.002 | −0.886583 | ||||||||
\(530\) | −91.5341 | + | 29.7412i | −0.172706 | + | 0.0561155i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.27971 | + | 3.10939i | −0.00804457 | + | 0.00584472i | ||||
\(533\) | 275.439 | − | 847.715i | 0.516772 | − | 1.59046i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.3544 | − | 26.6390i | −0.0361764 | − | 0.0497925i | ||||
\(536\) | −7.93778 | + | 10.9254i | −0.0148093 | + | 0.0203832i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 156.345i | 0.290604i | ||||||||
\(539\) | 482.520 | − | 239.481i | 0.895213 | − | 0.444307i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 215.044 | − | 69.8719i | 0.397493 | − | 0.129153i | −0.103448 | − | 0.994635i | \(-0.532987\pi\) |
0.500941 | + | 0.865482i | \(0.332987\pi\) | |||||||
\(542\) | 333.875 | + | 242.574i | 0.616005 | + | 0.447554i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 194.021 | − | 597.134i | 0.356655 | − | 1.09767i | ||||
\(545\) | −285.791 | − | 92.8592i | −0.524388 | − | 0.170384i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 268.871 | − | 370.069i | 0.491538 | − | 0.676543i | −0.489133 | − | 0.872209i | \(-0.662687\pi\) |
0.980671 | + | 0.195666i | \(0.0626868\pi\) | |||||||
\(548\) | −53.3851 | − | 164.302i | −0.0974181 | − | 0.299822i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −223.717 | − | 450.757i | −0.406758 | − | 0.819559i | ||||
\(551\) | −558.104 | −1.01289 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.27574 | + | 5.28613i | 0.0131569 | + | 0.00955901i | ||||
\(554\) | −84.8827 | + | 61.6709i | −0.153218 | + | 0.111319i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 393.534 | + | 127.867i | 0.707796 | + | 0.229977i | ||||
\(557\) | 165.248 | + | 227.445i | 0.296676 | + | 0.408339i | 0.931168 | − | 0.364590i | \(-0.118791\pi\) |
−0.634492 | + | 0.772929i | \(0.718791\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 356.078 | + | 1095.89i | 0.636991 | + | 1.96046i | ||||
\(560\) | − | 8.69517i | − | 0.0155271i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −353.499 | −0.629002 | ||||||||
\(563\) | −214.219 | + | 69.6039i | −0.380495 | + | 0.123630i | −0.493019 | − | 0.870019i | \(-0.664107\pi\) |
0.112524 | + | 0.993649i | \(0.464107\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 362.841 | − | 263.620i | 0.642197 | − | 0.466583i | ||||
\(566\) | −198.197 | + | 609.988i | −0.350172 | + | 1.07772i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 263.580 | + | 362.786i | 0.464049 | + | 0.638708i | ||||
\(569\) | 87.1966 | − | 120.016i | 0.153245 | − | 0.210924i | −0.725491 | − | 0.688232i | \(-0.758387\pi\) |
0.878736 | + | 0.477308i | \(0.158387\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 111.405i | − | 0.195106i | −0.995230 | − | 0.0975528i | \(-0.968899\pi\) | ||
0.995230 | − | 0.0975528i | \(-0.0311015\pi\) | |||||||
\(572\) | 446.422 | − | 65.8888i | 0.780458 | − | 0.115190i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.5529 | − | 6.02820i | 0.0323221 | − | 0.0105021i | ||||
\(575\) | −115.803 | − | 84.1355i | −0.201396 | − | 0.146323i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −167.056 | + | 514.146i | −0.289526 | + | 0.891068i | 0.695480 | + | 0.718545i | \(0.255192\pi\) |
−0.985006 | + | 0.172523i | \(0.944808\pi\) | |||||||
\(578\) | −289.300 | − | 93.9993i | −0.500519 | − | 0.162629i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −122.232 | + | 168.238i | −0.210745 | + | 0.290066i | ||||
\(581\) | 1.23615 | + | 3.80446i | 0.00212762 | + | 0.00654813i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −77.6029 | + | 148.415i | −0.133110 | + | 0.254570i | ||||
\(584\) | −80.2858 | −0.137476 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 230.359 | + | 167.366i | 0.393104 | + | 0.285607i | ||||
\(587\) | 278.485 | − | 202.331i | 0.474420 | − | 0.344687i | −0.324741 | − | 0.945803i | \(-0.605277\pi\) |
0.799162 | + | 0.601116i | \(0.205277\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −587.805 | − | 190.990i | −0.997972 | − | 0.324261i | ||||
\(590\) | −97.8757 | − | 134.714i | −0.165891 | − | 0.228329i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −318.913 | − | 981.513i | −0.538704 | − | 1.65796i | ||||
\(593\) | 723.311i | 1.21975i | 0.792498 | + | 0.609874i | \(0.208780\pi\) | ||||
−0.792498 | + | 0.609874i | \(0.791220\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.83059 | −0.0148413 | ||||||||
\(596\) | −245.526 | + | 79.7763i | −0.411956 | + | 0.133853i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 299.006 | − | 217.240i | 0.500009 | − | 0.363278i | ||||
\(599\) | 87.6892 | − | 269.880i | 0.146393 | − | 0.450550i | −0.850795 | − | 0.525498i | \(-0.823879\pi\) |
0.997187 | + | 0.0749478i | \(0.0238790\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 604.280 | + | 831.720i | 1.00546 | + | 1.38389i | 0.921916 | + | 0.387390i | \(0.126623\pi\) |
0.0835420 | + | 0.996504i | \(0.473377\pi\) | |||||||
\(602\) | −14.8232 | + | 20.4024i | −0.0246233 | + | 0.0338911i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 218.282i | 0.361393i | ||||||||
\(605\) | 291.773 | + | 101.654i | 0.482270 | + | 0.168022i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 599.620 | − | 194.828i | 0.987842 | − | 0.320969i | 0.229845 | − | 0.973227i | \(-0.426178\pi\) |
0.757997 | + | 0.652258i | \(0.226178\pi\) | |||||||
\(608\) | −365.069 | − | 265.238i | −0.600443 | − | 0.436247i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −123.790 | + | 380.986i | −0.202934 | + | 0.624568i | ||||
\(611\) | 625.683 | + | 203.297i | 1.02403 | + | 0.332728i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 330.524 | − | 454.927i | 0.539190 | − | 0.742132i | −0.449306 | − | 0.893378i | \(-0.648329\pi\) |
0.988496 | + | 0.151246i | \(0.0483286\pi\) | |||||||
\(614\) | −17.5809 | − | 54.1085i | −0.0286334 | − | 0.0881246i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.07586 | − | 6.20536i | −0.00986340 | − | 0.0100736i | ||||
\(617\) | 892.792 | 1.44699 | 0.723494 | − | 0.690331i | \(-0.242535\pi\) | ||||
0.723494 | + | 0.690331i | \(0.242535\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −524.551 | − | 381.109i | −0.847417 | − | 0.615684i | 0.0770159 | − | 0.997030i | \(-0.475461\pi\) |
−0.924433 | + | 0.381346i | \(0.875461\pi\) | |||||||
\(620\) | −186.310 | + | 135.362i | −0.300501 | + | 0.218327i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1400.03 | − | 454.898i | −2.25086 | − | 0.731348i | ||||
\(623\) | 9.73402 | + | 13.3977i | 0.0156244 | + | 0.0215052i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 55.1554 | + | 169.751i | 0.0882486 | + | 0.271601i | ||||
\(626\) | − | 1291.89i | − | 2.06373i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −377.429 | −0.601002 | ||||||||
\(629\) | −996.799 | + | 323.880i | −1.58474 | + | 0.514912i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 824.719 | − | 599.193i | 1.30700 | − | 0.949593i | 0.307005 | − | 0.951708i | \(-0.400673\pi\) |
0.999998 | + | 0.00211458i | \(0.000673092\pi\) | |||||||
\(632\) | −75.5650 | + | 232.565i | −0.119565 | + | 0.367983i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 223.564 | + | 307.709i | 0.352624 | + | 0.485346i | ||||
\(635\) | −89.8251 | + | 123.634i | −0.141457 | + | 0.194699i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 943.885i | − | 1.48177i | ||||||
\(638\) | 152.136 | + | 1030.78i | 0.238458 | + | 1.61564i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 320.650 | − | 104.186i | 0.501016 | − | 0.162790i | ||||
\(641\) | 353.056 | + | 256.510i | 0.550789 | + | 0.400172i | 0.828076 | − | 0.560615i | \(-0.189435\pi\) |
−0.277287 | + | 0.960787i | \(0.589435\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −159.050 | + | 489.507i | −0.247357 | + | 0.761285i | 0.747883 | + | 0.663830i | \(0.231070\pi\) |
−0.995240 | + | 0.0974552i | \(0.968930\pi\) | |||||||
\(644\) | 2.67175 | + | 0.868103i | 0.00414867 | + | 0.00134799i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −430.736 | + | 592.857i | −0.666774 | + | 0.917736i | ||||
\(647\) | −74.4847 | − | 229.240i | −0.115123 | − | 0.354313i | 0.876849 | − | 0.480765i | \(-0.159641\pi\) |
−0.991973 | + | 0.126452i | \(0.959641\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −285.699 | − | 48.3437i | −0.440214 | − | 0.0744895i | ||||
\(650\) | −881.753 | −1.35654 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 181.115 | + | 131.588i | 0.277784 | + | 0.201822i | ||||
\(653\) | −131.498 | + | 95.5386i | −0.201374 | + | 0.146307i | −0.683903 | − | 0.729573i | \(-0.739719\pi\) |
0.482528 | + | 0.875881i | \(0.339719\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −65.9644 | − | 21.4331i | −0.100709 | − | 0.0327223i | ||||
\(656\) | 543.192 | + | 747.640i | 0.828037 | + | 1.13969i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.44931 | + | 13.6936i | 0.00676187 | + | 0.0208109i | ||||
\(659\) | − | 1078.94i | − | 1.63724i | −0.574332 | − | 0.818622i | \(-0.694738\pi\) | ||
0.574332 | − | 0.818622i | \(-0.305262\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 428.584 | 0.648387 | 0.324193 | − | 0.945991i | \(-0.394907\pi\) | ||||
0.324193 | + | 0.945991i | \(0.394907\pi\) | |||||||
\(662\) | −700.293 | + | 227.539i | −1.05785 | + | 0.343715i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −87.9961 | + | 63.9329i | −0.132524 | + | 0.0962845i | ||||
\(665\) | −1.96121 | + | 6.03599i | −0.00294919 | + | 0.00907667i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 174.207 | + | 239.775i | 0.261180 | + | 0.359483i | ||||
\(668\) | 161.893 | − | 222.826i | 0.242354 | − | 0.333572i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 18.4248i | − | 0.0274996i | ||||||
\(671\) | 309.903 | + | 624.410i | 0.461853 | + | 0.930566i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −249.836 | + | 81.1765i | −0.371227 | + | 0.120619i | −0.488688 | − | 0.872459i | \(-0.662524\pi\) |
0.117461 | + | 0.993077i | \(0.462524\pi\) | |||||||
\(674\) | −8.37044 | − | 6.08148i | −0.0124191 | − | 0.00902297i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 133.187 | − | 409.909i | 0.197023 | − | 0.606374i | ||||
\(677\) | −142.544 | − | 46.3152i | −0.210552 | − | 0.0684125i | 0.201842 | − | 0.979418i | \(-0.435307\pi\) |
−0.412394 | + | 0.911006i | \(0.635307\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.06950 | + | 6.97757i | −0.00746613 | + | 0.0102762i | ||||
\(680\) | −74.1978 | − | 228.357i | −0.109114 | − | 0.335819i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −192.512 | + | 1137.70i | −0.282276 | + | 1.66818i | ||||
\(683\) | 52.4276 | 0.0767608 | 0.0383804 | − | 0.999263i | \(-0.487780\pi\) | ||||
0.0383804 | + | 0.999263i | \(0.487780\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −167.680 | − | 121.826i | −0.244788 | − | 0.177849i | ||||
\(686\) | 33.4347 | − | 24.2917i | 0.0487387 | − | 0.0354107i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1136.21 | − | 369.178i | −1.65147 | − | 0.536596i | ||||
\(689\) | 172.491 | + | 237.413i | 0.250350 | + | 0.344577i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −60.7905 | − | 187.094i | −0.0879747 | − | 0.270758i | 0.897385 | − | 0.441249i | \(-0.145465\pi\) |
−0.985359 | + | 0.170491i | \(0.945465\pi\) | |||||||
\(692\) | 95.3458i | 0.137783i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1450.37 | −2.08987 | ||||||||
\(695\) | 472.137 | − | 153.407i | 0.679334 | − | 0.220729i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 759.283 | − | 551.652i | 1.08936 | − | 0.791466i | ||||
\(698\) | 176.882 | − | 544.388i | 0.253413 | − | 0.779925i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.93942 | − | 5.42215i | −0.00562774 | − | 0.00774593i | ||||
\(701\) | 521.017 | − | 717.119i | 0.743248 | − | 1.02299i | −0.255177 | − | 0.966894i | \(-0.582134\pi\) |
0.998425 | − | 0.0560992i | \(-0.0178663\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 753.275i | 1.07152i | ||||||||
\(704\) | 17.0599 | − | 32.6268i | 0.0242328 | − | 0.0463448i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −979.741 | + | 318.337i | −1.38774 | + | 0.450903i | ||||
\(707\) | 9.07187 | + | 6.59110i | 0.0128315 | + | 0.00932263i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 95.8971 | − | 295.141i | 0.135257 | − | 0.416278i | −0.860373 | − | 0.509665i | \(-0.829769\pi\) |
0.995630 | + | 0.0933872i | \(0.0297694\pi\) | |||||||
\(710\) | −581.863 | − | 189.059i | −0.819526 | − | 0.266280i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −264.674 | + | 364.292i | −0.371733 | + | 0.511647i | ||||
\(713\) | 101.424 | + | 312.152i | 0.142250 | + | 0.437800i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 386.836 | − | 378.763i | 0.541029 | − | 0.529738i | ||||
\(716\) | −676.246 | −0.944478 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 75.9131 | + | 55.1541i | 0.105729 | + | 0.0768163i | ||||
\(719\) | 364.996 | − | 265.185i | 0.507644 | − | 0.368825i | −0.304285 | − | 0.952581i | \(-0.598418\pi\) |
0.811929 | + | 0.583756i | \(0.198418\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.5556 | + | 7.32875i | 0.0312837 | + | 0.0101647i | ||||
\(722\) | −215.717 | − | 296.909i | −0.298777 | − | 0.411231i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −217.555 | − | 669.567i | −0.300491 | − | 0.924816i | ||||
\(725\) | − | 707.086i | − | 0.975290i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −89.6851 | −0.123363 | −0.0616817 | − | 0.998096i | \(-0.519646\pi\) | ||||
−0.0616817 | + | 0.998096i | \(0.519646\pi\) | |||||||
\(728\) | −14.4725 | + | 4.70241i | −0.0198799 | + | 0.00645936i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 88.6171 | − | 64.3841i | 0.121393 | − | 0.0881974i | ||||
\(731\) | −374.928 | + | 1153.91i | −0.512897 | + | 1.57854i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −327.682 | − | 451.016i | −0.447042 | − | 0.615301i | 0.524716 | − | 0.851277i | \(-0.324171\pi\) |
−0.971759 | + | 0.235976i | \(0.924171\pi\) | |||||||
\(734\) | 318.835 | − | 438.839i | 0.434381 | − | 0.597874i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 239.635i | 0.325591i | ||||||||
\(737\) | −22.4306 | − | 22.9087i | −0.0304351 | − | 0.0310838i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 91.0451 | − | 29.5823i | 0.123200 | − | 0.0400302i | −0.246768 | − | 0.969075i | \(-0.579369\pi\) |
0.369968 | + | 0.929044i | \(0.379369\pi\) | |||||||
\(740\) | 227.072 | + | 164.977i | 0.306854 | + | 0.222943i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.98469 | + | 6.10823i | −0.00267478 | + | 0.00823212i | ||||
\(743\) | −1066.46 | − | 346.515i | −1.43535 | − | 0.466373i | −0.514904 | − | 0.857248i | \(-0.672172\pi\) |
−0.920444 | + | 0.390876i | \(0.872172\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −182.052 | + | 250.573i | −0.244365 | + | 0.336339i | ||||
\(746\) | −13.7309 | − | 42.2593i | −0.0184060 | − | 0.0566479i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 421.061 | + | 220.164i | 0.562915 | + | 0.294337i | ||||
\(749\) | −2.19732 | −0.00293367 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 206.616 | + | 150.115i | 0.275121 | + | 0.199887i | 0.716786 | − | 0.697293i | \(-0.245612\pi\) |
−0.441666 | + | 0.897180i | \(0.645612\pi\) | |||||||
\(752\) | −551.820 | + | 400.920i | −0.733803 | + | 0.533139i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1736.36 | + | 564.177i | 2.30286 | + | 0.748245i | ||||
\(755\) | 153.929 | + | 211.865i | 0.203880 | + | 0.280616i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.2727 | + | 117.791i | 0.0505584 | + | 0.155603i | 0.973148 | − | 0.230180i | \(-0.0739314\pi\) |
−0.922590 | + | 0.385783i | \(0.873931\pi\) | |||||||
\(758\) | − | 112.988i | − | 0.149061i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −172.568 | −0.227063 | ||||||||
\(761\) | 331.927 | − | 107.850i | 0.436172 | − | 0.141721i | −0.0826967 | − | 0.996575i | \(-0.526353\pi\) |
0.518869 | + | 0.854854i | \(0.326353\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.2231 | + | 11.7867i | −0.0212622 | + | 0.0154479i | ||||
\(764\) | −83.5555 | + | 257.157i | −0.109366 | + | 0.336593i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −41.0068 | − | 56.4411i | −0.0535337 | − | 0.0736829i | ||||
\(767\) | −298.432 | + | 410.757i | −0.389090 | + | 0.535537i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 867.000i | − | 1.12744i | −0.825966 | − | 0.563719i | \(-0.809370\pi\) | ||
0.825966 | − | 0.563719i | \(-0.190630\pi\) | |||||||
\(770\) | 11.6827 | + | 1.97684i | 0.0151723 | + | 0.00256733i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 427.911 | − | 139.037i | 0.554289 | − | 0.180099i | ||||
\(773\) | −140.552 | − | 102.117i | −0.181827 | − | 0.132105i | 0.493149 | − | 0.869945i | \(-0.335846\pi\) |
−0.674976 | + | 0.737840i | \(0.735846\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 241.973 | − | 744.716i | 0.312223 | − | 0.960924i | ||||
\(776\) | −223.034 | − | 72.4683i | −0.287416 | − | 0.0933870i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 821.870 | − | 1131.21i | 1.05639 | − | 1.45399i | ||||
\(779\) | −208.440 | − | 641.512i | −0.267574 | − | 0.823507i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −953.633 | + | 473.302i | −1.22104 | + | 0.606020i | ||||
\(782\) | 389.157 | 0.497643 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 791.714 | + | 575.214i | 1.00984 | + | 0.733691i | ||||
\(785\) | −366.335 | + | 266.158i | −0.466669 | + | 0.339055i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.0442 | + | 13.9859i | 0.0546940 | + | 0.0177712i | 0.336236 | − | 0.941778i | \(-0.390846\pi\) |
−0.281542 | + | 0.959549i | \(0.590846\pi\) | |||||||
\(788\) | 3.59597 | + | 4.94943i | 0.00456341 | + | 0.00628100i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −103.096 | − | 317.297i | −0.130501 | − | 0.401642i | ||||
\(791\) | − | 29.9290i | − | 0.0378369i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1221.44 | 1.54028 | ||||||||
\(794\) | −14.9526 | + | 4.85840i | −0.0188320 | + | 0.00611889i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −273.001 | + | 198.347i | −0.342966 | + | 0.249179i | ||||
\(797\) | −291.551 | + | 897.301i | −0.365810 | + | 1.12585i | 0.583662 | + | 0.811997i | \(0.301619\pi\) |
−0.949472 | + | 0.313852i | \(0.898381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 407.164 | + | 560.414i | 0.509593 | + | 0.701394i | ||||
\(800\) | 336.042 | − | 462.522i | 0.420052 | − | 0.578152i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 410.502i | 0.511848i | ||||||||
\(803\) | 31.8012 | − | 187.937i | 0.0396030 | − | 0.234044i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.20539 | − | 1.04149i | 0.00398185 | − | 0.00129378i | ||||
\(806\) | 1635.70 | + | 1188.40i | 2.02940 | + | 1.47445i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −94.2194 | + | 289.977i | −0.116608 | + | 0.358883i | ||||
\(809\) | −502.635 | − | 163.316i | −0.621304 | − | 0.201874i | −0.0185847 | − | 0.999827i | \(-0.505916\pi\) |
−0.602719 | + | 0.797953i | \(0.705916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 430.074 | − | 591.946i | 0.530301 | − | 0.729896i | −0.456876 | − | 0.889531i | \(-0.651032\pi\) |
0.987176 | + | 0.159634i | \(0.0510316\pi\) | |||||||
\(812\) | 4.28827 | + | 13.1979i | 0.00528112 | + | 0.0162536i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1391.25 | − | 205.339i | 1.70915 | − | 0.252259i | ||||
\(815\) | 268.585 | 0.329552 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 705.465 | + | 512.550i | 0.863482 | + | 0.627356i | ||||
\(818\) | −76.1675 | + | 55.3390i | −0.0931143 | + | 0.0676515i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −239.033 | − | 77.6664i | −0.291503 | − | 0.0947151i | ||||
\(821\) | 661.205 | + | 910.071i | 0.805366 | + | 1.10849i | 0.992022 | + | 0.126066i | \(0.0402350\pi\) |
−0.186656 | + | 0.982425i | \(0.559765\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 73.6727 | + | 226.741i | 0.0895172 | + | 0.275506i | 0.985786 | − | 0.168005i | \(-0.0537326\pi\) |
−0.896269 | + | 0.443511i | \(0.853733\pi\) | |||||||
\(824\) | 644.861i | 0.782599i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.1119 | −0.0134527 | ||||||||
\(827\) | 1461.01 | − | 474.709i | 1.76663 | − | 0.574014i | 0.768780 | − | 0.639513i | \(-0.220864\pi\) |
0.997853 | + | 0.0654992i | \(0.0208640\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1275.44 | + | 926.658i | −1.53852 | + | 1.11780i | −0.587269 | + | 0.809392i | \(0.699797\pi\) |
−0.951253 | + | 0.308410i | \(0.900203\pi\) | |||||||
\(830\) | 45.8575 | − | 141.135i | 0.0552499 | − | 0.170042i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −37.9196 | − | 52.1918i | −0.0455764 | − | 0.0627306i | ||||
\(833\) | 584.172 | − | 804.044i | 0.701287 | − | 0.965239i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 330.441i | − | 0.395738i | ||||||
\(836\) | 244.004 | − | 238.911i | 0.291870 | − | 0.285779i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −599.773 | + | 194.878i | −0.715719 | + | 0.232551i | ||||
\(839\) | −38.4075 | − | 27.9047i | −0.0457777 | − | 0.0332595i | 0.564661 | − | 0.825323i | \(-0.309007\pi\) |
−0.610439 | + | 0.792063i | \(0.709007\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −192.535 | + | 592.563i | −0.228936 | + | 0.704593i | ||||
\(842\) | 1306.07 | + | 424.369i | 1.55116 | + | 0.504002i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −445.356 | + | 612.980i | −0.527673 | + | 0.726280i | ||||
\(845\) | −159.790 | − | 491.782i | −0.189100 | − | 0.581990i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.9325 | − | 11.7647i | 0.0199911 | − | 0.0138899i | ||||
\(848\) | −304.256 | −0.358792 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −751.116 | − | 545.718i | −0.883666 | − | 0.642021i | ||||
\(851\) | 323.626 | − | 235.128i | 0.380289 | − | 0.276296i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 706.895 | + | 229.684i | 0.828716 | + | 0.269266i | 0.692505 | − | 0.721413i | \(-0.256507\pi\) |
0.136212 | + | 0.990680i | \(0.456507\pi\) | |||||||
\(854\) | 15.7128 | + | 21.6269i | 0.0183991 | + | 0.0253242i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.4627 | − | 56.8222i | −0.0215685 | − | 0.0663811i | ||||
\(857\) | 572.262i | 0.667750i | 0.942617 | + | 0.333875i | \(0.108356\pi\) | ||||
−0.942617 | + | 0.333875i | \(0.891644\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −792.198 | −0.922233 | −0.461117 | − | 0.887340i | \(-0.652551\pi\) | ||||
−0.461117 | + | 0.887340i | \(0.652551\pi\) | |||||||
\(860\) | 309.013 | − | 100.404i | 0.359317 | − | 0.116749i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 63.0682 | − | 45.8218i | 0.0731650 | − | 0.0531575i | ||||
\(863\) | −325.355 | + | 1001.34i | −0.377005 | + | 1.16030i | 0.565111 | + | 0.825015i | \(0.308833\pi\) |
−0.942116 | + | 0.335287i | \(0.891167\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 67.2365 | + | 92.5432i | 0.0777301 | + | 0.106986i | ||||
\(866\) | 922.496 | − | 1269.71i | 1.06524 | − | 1.46617i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.3678i | 0.0177049i | ||||||||
\(869\) | −514.470 | − | 269.006i | −0.592025 | − | 0.309558i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.4292 | + | 17.3602i | −0.0613424 | + | 0.0199314i | ||||
\(872\) | −441.115 | − | 320.489i | −0.505866 | − | 0.367533i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 86.4290 | − | 266.001i | 0.0988890 | − | 0.304349i | ||||
\(875\) | −17.9928 | − | 5.84621i | −0.0205632 | − | 0.00668138i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 834.571 | − | 1148.69i | 0.951621 | − | 1.30979i | 0.000816940 | − | 1.00000i | \(-0.499740\pi\) |
0.950804 | − | 0.309794i | \(-0.100260\pi\) | |||||||
\(878\) | 257.253 | + | 791.744i | 0.292999 | + | 0.901758i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 81.9574 | + | 555.292i | 0.0931334 | + | 0.631014i | ||||
\(881\) | −952.550 | −1.08121 | −0.540607 | − | 0.841275i | \(-0.681805\pi\) | ||||
−0.540607 | + | 0.841275i | \(0.681805\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −287.851 | − | 209.136i | −0.325992 | − | 0.236847i | 0.412736 | − | 0.910851i | \(-0.364573\pi\) |
−0.738728 | + | 0.674004i | \(0.764573\pi\) | |||||||
\(884\) | 673.555 | − | 489.367i | 0.761940 | − | 0.553582i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1148.34 | + | 373.118i | 1.29610 | + | 0.421127i | ||||
\(887\) | −606.794 | − | 835.180i | −0.684097 | − | 0.941578i | 0.315877 | − | 0.948800i | \(-0.397701\pi\) |
−0.999974 | + | 0.00722178i | \(0.997701\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.15133 | + | 9.69880i | 0.00354480 | + | 0.0109098i | ||||
\(890\) | − | 614.348i | − | 0.690278i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 454.142 | 0.509128 | ||||||||
\(893\) | 473.489 | − | 153.846i | 0.530223 | − | 0.172280i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −656.368 | + | 476.880i | −0.733373 | + | 0.532826i | ||||
\(896\) | 6.95249 | − | 21.3976i | 0.00775948 | − | 0.0238812i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −972.557 | − | 1338.61i | −1.08303 | − | 1.49066i | ||||
\(899\) | −952.992 | + | 1311.68i | −1.06006 | + | 1.45904i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 308.994i | 0.342946i | ||||||||
\(902\) | −1128.01 | + | 559.847i | −1.25056 | + | 0.620673i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 773.957 | − | 251.474i | 0.856147 | − | 0.278179i | ||||
\(905\) | −683.330 | − | 496.468i | −0.755061 | − | 0.548584i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −335.921 | + | 1033.86i | −0.370365 | + | 1.13987i | 0.576188 | + | 0.817317i | \(0.304540\pi\) |
−0.946553 | + | 0.322549i | \(0.895460\pi\) | |||||||
\(908\) | −357.778 | − | 116.249i | −0.394028 | − | 0.128028i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.2033 | − | 16.7965i | 0.0134103 | − | 0.0184576i | ||||
\(911\) | −123.647 | − | 380.547i | −0.135727 | − | 0.417724i | 0.859976 | − | 0.510335i | \(-0.170479\pi\) |
−0.995702 | + | 0.0926112i | \(0.970479\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −114.802 | − | 231.310i | −0.125742 | − | 0.253351i | ||||
\(914\) | −1266.21 | −1.38536 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −108.418 | − | 78.7705i | −0.118361 | − | 0.0859940i | ||||
\(917\) | −3.74450 | + | 2.72054i | −0.00408342 | + | 0.00296678i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1281.48 | − | 416.379i | −1.39443 | − | 0.453079i | −0.487047 | − | 0.873376i | \(-0.661926\pi\) |
−0.907387 | + | 0.420297i | \(0.861926\pi\) | |||||||
\(920\) | 53.8656 | + | 74.1396i | 0.0585496 | + | 0.0805866i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 57.9160 | + | 178.247i | 0.0628156 | + | 0.193327i | ||||
\(923\) | 1865.46i | 2.02108i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −954.357 | −1.03174 | ||||||||
\(926\) | −688.912 | + | 223.841i | −0.743966 | + | 0.241729i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −957.676 | + | 695.792i | −1.03198 | + | 0.749776i | ||||
\(929\) | 461.399 | − | 1420.04i | 0.496662 | − | 1.52857i | −0.317689 | − | 0.948195i | \(-0.602907\pi\) |
0.814351 | − | 0.580373i | \(-0.197093\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −419.849 | − | 577.873i | −0.450966 | − | 0.620701i | ||||
\(932\) | −384.503 | + | 529.222i | −0.412556 | + | 0.567835i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 1917.37i | − | 2.05286i | ||||||
\(935\) | 563.941 | − | 83.2338i | 0.603145 | − | 0.0890201i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −529.343 | + | 171.994i | −0.564934 | + | 0.183558i | −0.577540 | − | 0.816362i | \(-0.695987\pi\) |
0.0126060 | + | 0.999921i | \(0.495987\pi\) | |||||||
\(938\) | −0.994700 | − | 0.722692i | −0.00106045 | − | 0.000770461i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 57.3242 | − | 176.426i | 0.0609832 | − | 0.187687i | ||||
\(941\) | −801.454 | − | 260.408i | −0.851704 | − | 0.276735i | −0.149544 | − | 0.988755i | \(-0.547781\pi\) |
−0.702160 | + | 0.712020i | \(0.747781\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −210.547 | + | 289.793i | −0.223274 | + | 0.307310i | ||||
\(944\) | −162.667 | − | 500.639i | −0.172317 | − | 0.530338i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 754.339 | − | 1442.66i | 0.797399 | − | 1.52501i | ||||
\(947\) | −789.960 | −0.834171 | −0.417085 | − | 0.908867i | \(-0.636948\pi\) | ||||
−0.417085 | + | 0.908867i | \(0.636948\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −270.202 | − | 196.313i | −0.284723 | − | 0.206863i | ||||
\(950\) | −539.833 | + | 392.212i | −0.568245 | + | 0.412854i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.2387 | − | 4.95135i | −0.0160070 | − | 0.00520100i | ||||
\(953\) | −686.198 | − | 944.471i | −0.720040 | − | 0.991050i | −0.999522 | − | 0.0308995i | \(-0.990163\pi\) |
0.279482 | − | 0.960151i | \(-0.409837\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 100.244 | + | 308.520i | 0.104968 | + | 0.323058i | ||||
\(956\) | 794.330i | 0.830889i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 162.487 | 0.169611 | ||||||||
\(959\) | −13.1541 | + | 4.27404i | −0.0137165 | + | 0.00445676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −675.117 | + | 490.501i | −0.702515 | + | 0.510407i | ||||
\(962\) | 761.472 | − | 2343.57i | 0.791551 | − | 2.43614i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.3564 | + | 22.5127i | 0.0169672 | + | 0.0233534i | ||||
\(965\) | 317.286 | − | 436.707i | 0.328794 | − | 0.452546i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 840.359i | 0.869037i | 0.900663 | + | 0.434518i | \(0.143081\pi\) | ||||
−0.900663 | + | 0.434518i | \(0.856919\pi\) | |||||||
\(968\) | 446.507 | + | 339.019i | 0.461267 | + | 0.350226i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 304.294 | − | 98.8712i | 0.313705 | − | 0.101929i | ||||
\(971\) | 1011.70 | + | 735.040i | 1.04191 | + | 0.756993i | 0.970658 | − | 0.240465i | \(-0.0773001\pi\) |
0.0712535 | + | 0.997458i | \(0.477300\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.2371 | − | 31.5065i | 0.0105212 | − | 0.0323808i | ||||
\(974\) | −42.6527 | − | 13.8587i | −0.0437912 | − | 0.0142286i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −744.361 | + | 1024.53i | −0.762665 | + | 1.04972i | ||||
\(977\) | −35.4053 | − | 108.966i | −0.0362388 | − | 0.111532i | 0.931301 | − | 0.364251i | \(-0.118675\pi\) |
−0.967540 | + | 0.252720i | \(0.918675\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −747.918 | − | 763.859i | −0.763961 | − | 0.780244i | ||||
\(980\) | −266.150 | −0.271582 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 854.987 | + | 621.185i | 0.870659 | + | 0.632571i | ||||
\(983\) | −690.929 | + | 501.989i | −0.702878 | + | 0.510670i | −0.880868 | − | 0.473362i | \(-0.843040\pi\) |
0.177991 | + | 0.984032i | \(0.443040\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.98053 | + | 2.26811i | 0.00708684 | + | 0.00230265i | ||||
\(986\) | 1129.94 | + | 1555.23i | 1.14598 | + | 1.57731i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −184.906 | − | 569.081i | −0.187151 | − | 0.575993i | ||||
\(989\) | − | 463.073i | − | 0.468224i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1236.21 | 1.24743 | 0.623716 | − | 0.781651i | \(-0.285622\pi\) | ||||
0.623716 | + | 0.781651i | \(0.285622\pi\) | |||||||
\(992\) | −1246.75 | + | 405.094i | −1.25681 | + | 0.408361i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −33.0297 | + | 23.9975i | −0.0332291 | + | 0.0241424i | ||||
\(995\) | −125.105 | + | 385.033i | −0.125733 | + | 0.386968i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 414.382 | + | 570.347i | 0.415628 | + | 0.572063i | 0.964580 | − | 0.263791i | \(-0.0849729\pi\) |
−0.548952 | + | 0.835854i | \(0.684973\pi\) | |||||||
\(998\) | 415.246 | − | 571.537i | 0.416078 | − | 0.572682i | ||||
\(999\) | 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 | 99.3.k.c.28.1 | 16 | ||
3.2 | odd | 2 | 33.3.g.a.28.4 | yes | 16 | ||
11.2 | odd | 10 | inner | 99.3.k.c.46.1 | 16 | ||
11.3 | even | 5 | 1089.3.c.m.604.13 | 16 | |||
11.8 | odd | 10 | 1089.3.c.m.604.4 | 16 | |||
12.11 | even | 2 | 528.3.bf.b.193.3 | 16 | |||
33.2 | even | 10 | 33.3.g.a.13.4 | ✓ | 16 | ||
33.5 | odd | 10 | 363.3.g.g.40.1 | 16 | |||
33.8 | even | 10 | 363.3.c.e.241.13 | 16 | |||
33.14 | odd | 10 | 363.3.c.e.241.4 | 16 | |||
33.17 | even | 10 | 363.3.g.a.40.4 | 16 | |||
33.20 | odd | 10 | 363.3.g.f.112.1 | 16 | |||
33.26 | odd | 10 | 363.3.g.a.118.4 | 16 | |||
33.29 | even | 10 | 363.3.g.g.118.1 | 16 | |||
33.32 | even | 2 | 363.3.g.f.94.1 | 16 | |||
132.35 | odd | 10 | 528.3.bf.b.145.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.g.a.13.4 | ✓ | 16 | 33.2 | even | 10 | ||
33.3.g.a.28.4 | yes | 16 | 3.2 | odd | 2 | ||
99.3.k.c.28.1 | 16 | 1.1 | even | 1 | trivial | ||
99.3.k.c.46.1 | 16 | 11.2 | odd | 10 | inner | ||
363.3.c.e.241.4 | 16 | 33.14 | odd | 10 | |||
363.3.c.e.241.13 | 16 | 33.8 | even | 10 | |||
363.3.g.a.40.4 | 16 | 33.17 | even | 10 | |||
363.3.g.a.118.4 | 16 | 33.26 | odd | 10 | |||
363.3.g.f.94.1 | 16 | 33.32 | even | 2 | |||
363.3.g.f.112.1 | 16 | 33.20 | odd | 10 | |||
363.3.g.g.40.1 | 16 | 33.5 | odd | 10 | |||
363.3.g.g.118.1 | 16 | 33.29 | even | 10 | |||
528.3.bf.b.145.3 | 16 | 132.35 | odd | 10 | |||
528.3.bf.b.193.3 | 16 | 12.11 | even | 2 | |||
1089.3.c.m.604.4 | 16 | 11.8 | odd | 10 | |||
1089.3.c.m.604.13 | 16 | 11.3 | even | 5 |