Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,4,Mod(38,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.38");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.f (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: | \(11.8593839112\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Relative dimension: | \(66\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 38.20 | ||
Character | \(\chi\) | \(=\) | 201.38 |
Dual form | 201.4.f.a.164.20 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.38906 | + | 2.40592i | −0.491106 | + | 0.850621i | −0.999948 | − | 0.0102393i | \(-0.996741\pi\) |
0.508841 | + | 0.860860i | \(0.330074\pi\) | |||||||
\(3\) | −3.61547 | + | 3.73207i | −0.695798 | + | 0.718237i | ||||
\(4\) | 0.141034 | + | 0.244278i | 0.0176293 | + | 0.0305348i | ||||
\(5\) | 10.9301 | 0.977619 | 0.488810 | − | 0.872391i | \(-0.337431\pi\) | ||||
0.488810 | + | 0.872391i | \(0.337431\pi\) | |||||||
\(6\) | −3.95695 | − | 13.8826i | −0.269237 | − | 0.944592i | ||||
\(7\) | 2.00045 | − | 1.15496i | 0.108014 | − | 0.0623620i | −0.445020 | − | 0.895521i | \(-0.646803\pi\) |
0.553034 | + | 0.833159i | \(0.313470\pi\) | |||||||
\(8\) | −23.0086 | −1.01684 | ||||||||
\(9\) | −0.856687 | − | 26.9864i | −0.0317292 | − | 0.999497i | ||||
\(10\) | −15.1826 | + | 26.2970i | −0.480115 | + | 0.831583i | ||||
\(11\) | −18.3727 | − | 31.8225i | −0.503599 | − | 0.872259i | −0.999991 | − | 0.00416065i | \(-0.998676\pi\) |
0.496392 | − | 0.868098i | \(-0.334658\pi\) | |||||||
\(12\) | −1.42157 | − | 0.356832i | −0.0341976 | − | 0.00858405i | ||||
\(13\) | −16.5662 | − | 9.56448i | −0.353433 | − | 0.204055i | 0.312763 | − | 0.949831i | \(-0.398745\pi\) |
−0.666196 | + | 0.745777i | \(0.732079\pi\) | |||||||
\(14\) | 6.41723i | 0.122505i | ||||||||
\(15\) | −39.5175 | + | 40.7919i | −0.680226 | + | 0.702162i | ||||
\(16\) | 30.8319 | − | 53.4025i | 0.481749 | − | 0.834414i | ||||
\(17\) | −107.618 | − | 62.1332i | −1.53536 | − | 0.886442i | −0.999101 | − | 0.0423901i | \(-0.986503\pi\) |
−0.536261 | − | 0.844052i | \(-0.680164\pi\) | |||||||
\(18\) | 66.1171 | + | 35.4246i | 0.865775 | + | 0.463870i | ||||
\(19\) | −27.5352 | + | 47.6924i | −0.332474 | + | 0.575863i | −0.982996 | − | 0.183625i | \(-0.941217\pi\) |
0.650522 | + | 0.759487i | \(0.274550\pi\) | |||||||
\(20\) | 1.54152 | + | 2.66999i | 0.0172347 | + | 0.0298514i | ||||
\(21\) | −2.92218 | + | 11.6415i | −0.0303654 | + | 0.120971i | ||||
\(22\) | 102.083 | 0.989282 | ||||||||
\(23\) | −100.451 | − | 57.9956i | −0.910676 | − | 0.525779i | −0.0300276 | − | 0.999549i | \(-0.509560\pi\) |
−0.880649 | + | 0.473770i | \(0.842893\pi\) | |||||||
\(24\) | 83.1868 | − | 85.8695i | 0.707518 | − | 0.730335i | ||||
\(25\) | −5.53261 | −0.0442609 | ||||||||
\(26\) | 46.0227 | − | 26.5712i | 0.347146 | − | 0.200425i | ||||
\(27\) | 103.812 | + | 94.3714i | 0.739953 | + | 0.672659i | ||||
\(28\) | 0.564263 | + | 0.325777i | 0.00380842 | + | 0.00219879i | ||||
\(29\) | 152.435 | − | 88.0084i | 0.976086 | − | 0.563543i | 0.0749996 | − | 0.997184i | \(-0.476104\pi\) |
0.901086 | + | 0.433640i | \(0.142771\pi\) | |||||||
\(30\) | −43.2500 | − | 151.738i | −0.263211 | − | 0.923451i | ||||
\(31\) | −7.32049 | + | 4.22648i | −0.0424128 | + | 0.0244871i | −0.521056 | − | 0.853522i | \(-0.674462\pi\) |
0.478644 | + | 0.878009i | \(0.341129\pi\) | |||||||
\(32\) | −6.37946 | − | 11.0495i | −0.0352419 | − | 0.0610407i | ||||
\(33\) | 185.190 | + | 46.4851i | 0.976892 | + | 0.245213i | ||||
\(34\) | 298.975 | − | 172.613i | 1.50805 | − | 0.870674i | ||||
\(35\) | 21.8651 | − | 12.6238i | 0.105597 | − | 0.0609662i | ||||
\(36\) | 6.47137 | − | 4.01527i | 0.0299600 | − | 0.0185892i | ||||
\(37\) | 172.841 | − | 299.369i | 0.767968 | − | 1.33016i | −0.170695 | − | 0.985324i | \(-0.554601\pi\) |
0.938663 | − | 0.344836i | \(-0.112065\pi\) | |||||||
\(38\) | −76.4961 | − | 132.495i | −0.326561 | − | 0.565620i | ||||
\(39\) | 95.5899 | − | 27.2459i | 0.392478 | − | 0.111868i | ||||
\(40\) | −251.486 | −0.994086 | ||||||||
\(41\) | 200.399 | + | 347.102i | 0.763344 | + | 1.32215i | 0.941118 | + | 0.338080i | \(0.109777\pi\) |
−0.177773 | + | 0.984071i | \(0.556889\pi\) | |||||||
\(42\) | −23.9495 | − | 23.2013i | −0.0879879 | − | 0.0852391i | ||||
\(43\) | − | 97.5694i | − | 0.346028i | −0.984919 | − | 0.173014i | \(-0.944649\pi\) | ||
0.984919 | − | 0.173014i | \(-0.0553506\pi\) | |||||||
\(44\) | 5.18236 | − | 8.97611i | 0.0177561 | − | 0.0307545i | ||||
\(45\) | −9.36369 | − | 294.964i | −0.0310190 | − | 0.977127i | ||||
\(46\) | 279.066 | − | 161.119i | 0.894478 | − | 0.516427i | ||||
\(47\) | −316.170 | + | 182.541i | −0.981238 | + | 0.566518i | −0.902644 | − | 0.430389i | \(-0.858376\pi\) |
−0.0785941 | + | 0.996907i | \(0.525043\pi\) | |||||||
\(48\) | 87.8297 | + | 308.142i | 0.264107 | + | 0.926594i | ||||
\(49\) | −168.832 | + | 292.426i | −0.492222 | + | 0.852553i | ||||
\(50\) | 7.68512 | − | 13.3110i | 0.0217368 | − | 0.0376492i | ||||
\(51\) | 620.975 | − | 176.996i | 1.70498 | − | 0.485970i | ||||
\(52\) | − | 5.39567i | − | 0.0143893i | ||||||
\(53\) | −222.675 | −0.577109 | −0.288555 | − | 0.957463i | \(-0.593175\pi\) | ||||
−0.288555 | + | 0.957463i | \(0.593175\pi\) | |||||||
\(54\) | −371.252 | + | 118.677i | −0.935573 | + | 0.299072i | ||||
\(55\) | −200.816 | − | 347.824i | −0.492328 | − | 0.852737i | ||||
\(56\) | −46.0274 | + | 26.5739i | −0.109833 | + | 0.0634124i | ||||
\(57\) | −78.4385 | − | 275.194i | −0.182271 | − | 0.639480i | ||||
\(58\) | 488.995i | 1.10704i | ||||||||
\(59\) | 826.051i | 1.82276i | 0.411568 | + | 0.911379i | \(0.364981\pi\) | ||||
−0.411568 | + | 0.911379i | \(0.635019\pi\) | |||||||
\(60\) | −15.5379 | − | 3.90022i | −0.0334322 | − | 0.00839194i | ||||
\(61\) | −489.306 | − | 282.501i | −1.02704 | − | 0.592959i | −0.110901 | − | 0.993831i | \(-0.535374\pi\) |
−0.916134 | + | 0.400872i | \(0.868707\pi\) | |||||||
\(62\) | − | 23.4833i | − | 0.0481030i | ||||||
\(63\) | −32.8820 | − | 52.9955i | −0.0657578 | − | 0.105981i | ||||
\(64\) | 528.757 | 1.03273 | ||||||||
\(65\) | −181.070 | − | 104.541i | −0.345523 | − | 0.199488i | ||||
\(66\) | −369.079 | + | 380.982i | −0.688341 | + | 0.710539i | ||||
\(67\) | −308.545 | − | 453.391i | −0.562608 | − | 0.826724i | ||||
\(68\) | − | 35.0516i | − | 0.0625092i | ||||||
\(69\) | 579.623 | − | 165.210i | 1.01128 | − | 0.288245i | ||||
\(70\) | 70.1410i | 0.119764i | ||||||||
\(71\) | −561.555 | + | 324.214i | −0.938652 | + | 0.541931i | −0.889537 | − | 0.456862i | \(-0.848973\pi\) |
−0.0491143 | + | 0.998793i | \(0.515640\pi\) | |||||||
\(72\) | 19.7111 | + | 620.918i | 0.0322636 | + | 1.01633i | ||||
\(73\) | 33.9814 | − | 58.8576i | 0.0544826 | − | 0.0943666i | −0.837498 | − | 0.546441i | \(-0.815982\pi\) |
0.891980 | + | 0.452074i | \(0.149316\pi\) | |||||||
\(74\) | 480.171 | + | 831.681i | 0.754308 | + | 1.30650i | ||||
\(75\) | 20.0030 | − | 20.6481i | 0.0307966 | − | 0.0317898i | ||||
\(76\) | −15.5336 | −0.0234451 | ||||||||
\(77\) | −73.5074 | − | 42.4395i | −0.108792 | − | 0.0628108i | ||||
\(78\) | −67.2283 | + | 267.828i | −0.0975911 | + | 0.388789i | ||||
\(79\) | 432.403 | − | 249.648i | 0.615813 | − | 0.355540i | −0.159424 | − | 0.987210i | \(-0.550964\pi\) |
0.775237 | + | 0.631671i | \(0.217630\pi\) | |||||||
\(80\) | 336.997 | − | 583.695i | 0.470967 | − | 0.815739i | ||||
\(81\) | −727.532 | + | 46.2378i | −0.997987 | + | 0.0634264i | ||||
\(82\) | −1113.47 | −1.49953 | ||||||||
\(83\) | 266.538 | + | 153.886i | 0.352486 | + | 0.203508i | 0.665780 | − | 0.746148i | \(-0.268099\pi\) |
−0.313293 | + | 0.949656i | \(0.601432\pi\) | |||||||
\(84\) | −3.25590 | + | 0.928028i | −0.00422914 | + | 0.00120543i | ||||
\(85\) | −1176.28 | − | 679.123i | −1.50100 | − | 0.866603i | ||||
\(86\) | 234.744 | + | 135.530i | 0.294339 | + | 0.169936i | ||||
\(87\) | −222.672 | + | 887.091i | −0.274401 | + | 1.09317i | ||||
\(88\) | 422.730 | + | 732.190i | 0.512081 | + | 0.886951i | ||||
\(89\) | − | 1425.34i | − | 1.69759i | −0.528720 | − | 0.848796i | \(-0.677328\pi\) | ||
0.528720 | − | 0.848796i | \(-0.322672\pi\) | |||||||
\(90\) | 722.668 | + | 387.195i | 0.846398 | + | 0.453488i | ||||
\(91\) | −44.1864 | −0.0509010 | ||||||||
\(92\) | − | 32.7174i | − | 0.0370764i | ||||||
\(93\) | 10.6935 | − | 42.6013i | 0.0119233 | − | 0.0475005i | ||||
\(94\) | − | 1014.24i | − | 1.11288i | ||||||
\(95\) | −300.963 | + | 521.284i | −0.325033 | + | 0.562974i | ||||
\(96\) | 64.3025 | + | 16.1408i | 0.0683629 | + | 0.0171600i | ||||
\(97\) | −912.164 | − | 526.638i | −0.954806 | − | 0.551258i | −0.0602357 | − | 0.998184i | \(-0.519185\pi\) |
−0.894571 | + | 0.446926i | \(0.852519\pi\) | |||||||
\(98\) | −469.035 | − | 812.393i | −0.483467 | − | 0.837389i | ||||
\(99\) | −843.035 | + | 523.076i | −0.855841 | + | 0.531021i | ||||
\(100\) | −0.780286 | − | 1.35150i | −0.000780286 | − | 0.00135150i | ||||
\(101\) | 409.539 | + | 709.342i | 0.403471 | + | 0.698833i | 0.994142 | − | 0.108080i | \(-0.0344701\pi\) |
−0.590671 | + | 0.806913i | \(0.701137\pi\) | |||||||
\(102\) | −436.732 | + | 1739.87i | −0.423950 | + | 1.68895i | ||||
\(103\) | 585.028 | + | 1013.30i | 0.559656 | + | 0.969352i | 0.997525 | + | 0.0703137i | \(0.0224000\pi\) |
−0.437869 | + | 0.899039i | \(0.644267\pi\) | |||||||
\(104\) | 381.163 | + | 220.065i | 0.359386 | + | 0.207492i | ||||
\(105\) | −31.9398 | + | 127.243i | −0.0296857 | + | 0.118264i | ||||
\(106\) | 309.309 | − | 535.738i | 0.283422 | − | 0.490901i | ||||
\(107\) | − | 698.436i | − | 0.631031i | −0.948920 | − | 0.315515i | \(-0.897823\pi\) | ||
0.948920 | − | 0.315515i | \(-0.102177\pi\) | |||||||
\(108\) | −8.41179 | + | 38.6687i | −0.00749467 | + | 0.0344528i | ||||
\(109\) | 1283.25i | 1.12764i | 0.825896 | + | 0.563822i | \(0.190670\pi\) | ||||
−0.825896 | + | 0.563822i | \(0.809330\pi\) | |||||||
\(110\) | 1115.78 | 0.967141 | ||||||||
\(111\) | 492.364 | + | 1727.41i | 0.421019 | + | 1.47711i | ||||
\(112\) | − | 142.439i | − | 0.120171i | ||||||
\(113\) | −590.645 | − | 1023.03i | −0.491710 | − | 0.851666i | 0.508245 | − | 0.861213i | \(-0.330294\pi\) |
−0.999954 | + | 0.00954665i | \(0.996961\pi\) | |||||||
\(114\) | 771.051 | + | 193.544i | 0.633469 | + | 0.159009i | ||||
\(115\) | −1097.94 | − | 633.899i | −0.890294 | − | 0.514012i | ||||
\(116\) | 42.9971 | + | 24.8244i | 0.0344153 | + | 0.0198697i | ||||
\(117\) | −243.919 | + | 455.255i | −0.192738 | + | 0.359729i | ||||
\(118\) | −1987.41 | − | 1147.43i | −1.55048 | − | 0.895168i | ||||
\(119\) | −287.045 | −0.221121 | ||||||||
\(120\) | 909.242 | − | 938.564i | 0.691683 | − | 0.713989i | ||||
\(121\) | −9.61475 | + | 16.6532i | −0.00722370 | + | 0.0125118i | ||||
\(122\) | 1359.35 | − | 784.820i | 1.00877 | − | 0.582412i | ||||
\(123\) | −2019.95 | − | 507.034i | −1.48075 | − | 0.371688i | ||||
\(124\) | −2.06488 | − | 1.19216i | −0.00149541 | − | 0.000863377i | ||||
\(125\) | −1426.74 | −1.02089 | ||||||||
\(126\) | 173.178 | − | 5.49756i | 0.122444 | − | 0.00388699i | ||||
\(127\) | 566.100 | + | 980.514i | 0.395538 | + | 0.685091i | 0.993170 | − | 0.116679i | \(-0.0372250\pi\) |
−0.597632 | + | 0.801771i | \(0.703892\pi\) | |||||||
\(128\) | −683.439 | + | 1183.75i | −0.471937 | + | 0.817420i | ||||
\(129\) | 364.136 | + | 352.760i | 0.248530 | + | 0.240766i | ||||
\(130\) | 503.034 | − | 290.427i | 0.339377 | − | 0.195939i | ||||
\(131\) | 397.928i | 0.265398i | 0.991156 | + | 0.132699i | \(0.0423644\pi\) | ||||
−0.991156 | + | 0.132699i | \(0.957636\pi\) | |||||||
\(132\) | 14.7628 | + | 51.7938i | 0.00973436 | + | 0.0341521i | ||||
\(133\) | 127.208i | 0.0829350i | ||||||||
\(134\) | 1519.41 | − | 112.547i | 0.979529 | − | 0.0725569i | ||||
\(135\) | 1134.68 | + | 1031.49i | 0.723392 | + | 0.657604i | ||||
\(136\) | 2476.13 | + | 1429.59i | 1.56122 | + | 0.901373i | ||||
\(137\) | 883.595 | 0.551026 | 0.275513 | − | 0.961297i | \(-0.411152\pi\) | ||||
0.275513 | + | 0.961297i | \(0.411152\pi\) | |||||||
\(138\) | −407.649 | + | 1624.01i | −0.251459 | + | 1.00178i | ||||
\(139\) | − | 821.876i | − | 0.501515i | −0.968050 | − | 0.250758i | \(-0.919320\pi\) | ||
0.968050 | − | 0.250758i | \(-0.0806798\pi\) | |||||||
\(140\) | 6.16746 | + | 3.56078i | 0.00372318 | + | 0.00214958i | ||||
\(141\) | 461.850 | − | 1839.94i | 0.275849 | − | 1.09894i | ||||
\(142\) | − | 1801.41i | − | 1.06458i | ||||||
\(143\) | 702.903i | 0.411047i | ||||||||
\(144\) | −1467.55 | − | 786.294i | −0.849279 | − | 0.455031i | ||||
\(145\) | 1666.13 | − | 961.942i | 0.954240 | − | 0.550931i | ||||
\(146\) | 94.4044 | + | 163.513i | 0.0535135 | + | 0.0926880i | ||||
\(147\) | −480.945 | − | 1687.35i | −0.269848 | − | 0.946737i | ||||
\(148\) | 97.5056 | 0.0541548 | ||||||||
\(149\) | − | 122.637i | − | 0.0674283i | −0.999432 | − | 0.0337141i | \(-0.989266\pi\) | ||
0.999432 | − | 0.0337141i | \(-0.0107336\pi\) | |||||||
\(150\) | 21.8923 | + | 76.8070i | 0.0119166 | + | 0.0418084i | ||||
\(151\) | −210.923 | + | 365.330i | −0.113673 | + | 0.196888i | −0.917249 | − | 0.398315i | \(-0.869595\pi\) |
0.803575 | + | 0.595203i | \(0.202928\pi\) | |||||||
\(152\) | 633.546 | − | 1097.33i | 0.338075 | − | 0.585562i | ||||
\(153\) | −1584.56 | + | 2957.45i | −0.837280 | + | 1.56272i | ||||
\(154\) | 204.212 | − | 117.902i | 0.106856 | − | 0.0616936i | ||||
\(155\) | −80.0137 | + | 46.1960i | −0.0414636 | + | 0.0239390i | ||||
\(156\) | 20.1370 | + | 19.5079i | 0.0103349 | + | 0.0100121i | ||||
\(157\) | 1188.40 | − | 2058.37i | 0.604106 | − | 1.04634i | −0.388086 | − | 0.921623i | \(-0.626864\pi\) |
0.992192 | − | 0.124719i | \(-0.0398029\pi\) | |||||||
\(158\) | 1387.10i | 0.698431i | ||||||||
\(159\) | 805.076 | − | 831.039i | 0.401552 | − | 0.414501i | ||||
\(160\) | −69.7282 | − | 120.773i | −0.0344531 | − | 0.0596746i | ||||
\(161\) | −267.930 | −0.131154 | ||||||||
\(162\) | 899.340 | − | 1814.61i | 0.436166 | − | 0.880057i | ||||
\(163\) | −980.158 | − | 1697.68i | −0.470993 | − | 0.815785i | 0.528456 | − | 0.848961i | \(-0.322771\pi\) |
−0.999450 | + | 0.0331761i | \(0.989438\pi\) | |||||||
\(164\) | −56.5262 | + | 97.9063i | −0.0269144 | + | 0.0466171i | ||||
\(165\) | 2024.15 | + | 508.088i | 0.955028 | + | 0.239725i | ||||
\(166\) | −740.474 | + | 427.513i | −0.346216 | + | 0.199888i | ||||
\(167\) | −1350.43 | + | 779.669i | −0.625743 | + | 0.361273i | −0.779102 | − | 0.626898i | \(-0.784324\pi\) |
0.153358 | + | 0.988171i | \(0.450991\pi\) | |||||||
\(168\) | 67.2352 | − | 267.855i | 0.0308768 | − | 0.123009i | ||||
\(169\) | −915.541 | − | 1585.76i | −0.416723 | − | 0.721786i | ||||
\(170\) | 3267.83 | − | 1886.68i | 1.47430 | − | 0.851188i | ||||
\(171\) | 1310.64 | + | 702.219i | 0.586122 | + | 0.314035i | ||||
\(172\) | 23.8341 | − | 13.7606i | 0.0105659 | − | 0.00610021i | ||||
\(173\) | −3241.85 | − | 1871.68i | −1.42470 | − | 0.822551i | −0.428004 | − | 0.903777i | \(-0.640783\pi\) |
−0.996696 | + | 0.0812258i | \(0.974117\pi\) | |||||||
\(174\) | −1824.97 | − | 1767.95i | −0.795116 | − | 0.770276i | ||||
\(175\) | −11.0677 | + | 6.38994i | −0.00478080 | + | 0.00276019i | ||||
\(176\) | −2265.87 | −0.970433 | ||||||||
\(177\) | −3082.88 | − | 2986.57i | −1.30917 | − | 1.26827i | ||||
\(178\) | 3429.25 | + | 1979.88i | 1.44401 | + | 0.833698i | ||||
\(179\) | 1239.37 | 0.517514 | 0.258757 | − | 0.965942i | \(-0.416687\pi\) | ||||
0.258757 | + | 0.965942i | \(0.416687\pi\) | |||||||
\(180\) | 70.7328 | − | 43.8874i | 0.0292895 | − | 0.0181732i | ||||
\(181\) | −465.378 | − | 806.059i | −0.191112 | − | 0.331016i | 0.754507 | − | 0.656292i | \(-0.227876\pi\) |
−0.945619 | + | 0.325276i | \(0.894543\pi\) | |||||||
\(182\) | 61.3774 | − | 106.309i | 0.0249978 | − | 0.0432974i | ||||
\(183\) | 2823.38 | − | 804.748i | 1.14049 | − | 0.325075i | ||||
\(184\) | 2311.24 | + | 1334.39i | 0.926016 | + | 0.534635i | ||||
\(185\) | 1889.17 | − | 3272.13i | 0.750780 | − | 1.30039i | ||||
\(186\) | 87.6414 | + | 84.9034i | 0.0345494 | + | 0.0334700i | ||||
\(187\) | 4566.23i | 1.78564i | ||||||||
\(188\) | −89.1815 | − | 51.4890i | −0.0345970 | − | 0.0199746i | ||||
\(189\) | 316.667 | + | 68.8860i | 0.121874 | + | 0.0265118i | ||||
\(190\) | −836.111 | − | 1448.19i | −0.319252 | − | 0.552960i | ||||
\(191\) | −579.893 | + | 1004.40i | −0.219684 | + | 0.380503i | −0.954711 | − | 0.297534i | \(-0.903836\pi\) |
0.735027 | + | 0.678037i | \(0.237169\pi\) | |||||||
\(192\) | −1911.71 | + | 1973.36i | −0.718571 | + | 0.741744i | ||||
\(193\) | 1619.99 | 0.604193 | 0.302096 | − | 0.953277i | \(-0.402314\pi\) | ||||
0.302096 | + | 0.953277i | \(0.402314\pi\) | |||||||
\(194\) | 2534.10 | − | 1463.06i | 0.937823 | − | 0.541452i | ||||
\(195\) | 1044.81 | − | 297.801i | 0.383694 | − | 0.109364i | ||||
\(196\) | −95.2443 | −0.0347100 | ||||||||
\(197\) | 721.356 | + | 1249.42i | 0.260886 | + | 0.451867i | 0.966477 | − | 0.256751i | \(-0.0826521\pi\) |
−0.705592 | + | 0.708618i | \(0.749319\pi\) | |||||||
\(198\) | −87.4534 | − | 2754.86i | −0.0313891 | − | 0.988784i | ||||
\(199\) | −686.796 | + | 1189.57i | −0.244652 | + | 0.423749i | −0.962034 | − | 0.272931i | \(-0.912007\pi\) |
0.717382 | + | 0.696680i | \(0.245340\pi\) | |||||||
\(200\) | 127.297 | 0.0450064 | ||||||||
\(201\) | 2807.62 | + | 487.713i | 0.985245 | + | 0.171147i | ||||
\(202\) | −2275.49 | −0.792589 | ||||||||
\(203\) | 203.292 | − | 352.113i | 0.0702873 | − | 0.121741i | ||||
\(204\) | 130.815 | + | 126.728i | 0.0448965 | + | 0.0434938i | ||||
\(205\) | 2190.39 | + | 3793.86i | 0.746260 | + | 1.29256i | ||||
\(206\) | −3250.55 | −1.09940 | ||||||||
\(207\) | −1479.04 | + | 2760.50i | −0.496619 | + | 0.926900i | ||||
\(208\) | −1021.53 | + | 589.783i | −0.340532 | + | 0.196606i | ||||
\(209\) | 2023.59 | 0.669735 | ||||||||
\(210\) | −261.771 | − | 253.593i | −0.0860187 | − | 0.0833313i | ||||
\(211\) | 253.871 | − | 439.718i | 0.0828305 | − | 0.143467i | −0.821634 | − | 0.570015i | \(-0.806937\pi\) |
0.904465 | + | 0.426549i | \(0.140271\pi\) | |||||||
\(212\) | −31.4048 | − | 54.3947i | −0.0101740 | − | 0.0176219i | ||||
\(213\) | 820.298 | − | 3267.95i | 0.263878 | − | 1.05125i | ||||
\(214\) | 1680.38 | + | 970.168i | 0.536768 | + | 0.309903i | ||||
\(215\) | − | 1066.44i | − | 0.338283i | ||||||
\(216\) | −2388.57 | − | 2171.35i | −0.752416 | − | 0.683989i | ||||
\(217\) | −9.76284 | + | 16.9097i | −0.00305412 | + | 0.00528990i | ||||
\(218\) | −3087.40 | − | 1782.51i | −0.959197 | − | 0.553793i | ||||
\(219\) | 96.8016 | + | 339.619i | 0.0298687 | + | 0.104792i | ||||
\(220\) | 56.6438 | − | 98.1099i | 0.0173587 | − | 0.0300662i | ||||
\(221\) | 1188.54 | + | 2058.62i | 0.361765 | + | 0.626596i | ||||
\(222\) | −4839.94 | − | 1214.89i | −1.46322 | − | 0.367288i | ||||
\(223\) | 282.812 | 0.0849259 | 0.0424630 | − | 0.999098i | \(-0.486480\pi\) | ||||
0.0424630 | + | 0.999098i | \(0.486480\pi\) | |||||||
\(224\) | −25.5236 | − | 14.7360i | −0.00761324 | − | 0.00439550i | ||||
\(225\) | 4.73972 | + | 149.305i | 0.00140436 | + | 0.0442386i | ||||
\(226\) | 3281.76 | 0.965927 | ||||||||
\(227\) | −5078.39 | + | 2932.01i | −1.48486 | + | 0.857287i | −0.999852 | − | 0.0172198i | \(-0.994518\pi\) |
−0.485013 | + | 0.874507i | \(0.661185\pi\) | |||||||
\(228\) | 56.1614 | − | 57.9725i | 0.0163131 | − | 0.0168391i | ||||
\(229\) | −905.273 | − | 522.660i | −0.261232 | − | 0.150822i | 0.363664 | − | 0.931530i | \(-0.381525\pi\) |
−0.624896 | + | 0.780708i | \(0.714859\pi\) | |||||||
\(230\) | 3050.22 | − | 1761.04i | 0.874458 | − | 0.504869i | ||||
\(231\) | 424.152 | − | 120.896i | 0.120810 | − | 0.0344345i | ||||
\(232\) | −3507.31 | + | 2024.95i | −0.992527 | + | 0.573036i | ||||
\(233\) | −937.878 | − | 1624.45i | −0.263701 | − | 0.456744i | 0.703521 | − | 0.710674i | \(-0.251610\pi\) |
−0.967223 | + | 0.253930i | \(0.918277\pi\) | |||||||
\(234\) | −756.489 | − | 1219.23i | −0.211339 | − | 0.340612i | ||||
\(235\) | −3455.78 | + | 1995.19i | −0.959277 | + | 0.553839i | ||||
\(236\) | −201.786 | + | 116.501i | −0.0556575 | + | 0.0321339i | ||||
\(237\) | −631.639 | + | 2516.36i | −0.173120 | + | 0.689683i | ||||
\(238\) | 398.723 | − | 690.608i | 0.108594 | − | 0.188090i | ||||
\(239\) | −724.999 | − | 1255.73i | −0.196219 | − | 0.339861i | 0.751081 | − | 0.660210i | \(-0.229533\pi\) |
−0.947299 | + | 0.320350i | \(0.896200\pi\) | |||||||
\(240\) | 959.989 | + | 3368.03i | 0.258196 | + | 0.905856i | ||||
\(241\) | −6146.20 | −1.64279 | −0.821394 | − | 0.570361i | \(-0.806803\pi\) | ||||
−0.821394 | + | 0.570361i | \(0.806803\pi\) | |||||||
\(242\) | −26.7109 | − | 46.2646i | −0.00709521 | − | 0.0122893i | ||||
\(243\) | 2457.81 | − | 2882.37i | 0.648842 | − | 0.760923i | ||||
\(244\) | − | 159.369i | − | 0.0418137i | ||||||
\(245\) | −1845.35 | + | 3196.25i | −0.481206 | + | 0.833473i | ||||
\(246\) | 4025.71 | − | 4155.53i | 1.04337 | − | 1.07702i | ||||
\(247\) | 912.306 | − | 526.720i | 0.235015 | − | 0.135686i | ||||
\(248\) | 168.434 | − | 97.2453i | 0.0431272 | − | 0.0248995i | ||||
\(249\) | −1537.97 | + | 438.368i | −0.391426 | + | 0.111568i | ||||
\(250\) | 1981.82 | − | 3432.61i | 0.501365 | − | 0.868390i | ||||
\(251\) | 504.097 | − | 873.122i | 0.126766 | − | 0.219566i | −0.795656 | − | 0.605749i | \(-0.792874\pi\) |
0.922422 | + | 0.386184i | \(0.126207\pi\) | |||||||
\(252\) | 8.30816 | − | 15.5065i | 0.00207684 | − | 0.00387626i | ||||
\(253\) | 4262.15i | 1.05913i | ||||||||
\(254\) | −3145.39 | −0.777004 | ||||||||
\(255\) | 6787.33 | − | 1934.59i | 1.66682 | − | 0.475093i | ||||
\(256\) | 216.356 | + | 374.739i | 0.0528212 | + | 0.0914891i | ||||
\(257\) | 1395.74 | − | 805.832i | 0.338771 | − | 0.195589i | −0.320958 | − | 0.947094i | \(-0.604005\pi\) |
0.659728 | + | 0.751504i | \(0.270671\pi\) | |||||||
\(258\) | −1354.52 | + | 386.078i | −0.326855 | + | 0.0931634i | ||||
\(259\) | − | 798.496i | − | 0.191568i | ||||||
\(260\) | − | 58.9753i | − | 0.0140673i | ||||||
\(261\) | −2505.62 | − | 4038.28i | −0.594230 | − | 0.957714i | ||||
\(262\) | −957.383 | − | 552.745i | −0.225753 | − | 0.130339i | ||||
\(263\) | 6665.32i | 1.56274i | 0.624067 | + | 0.781371i | \(0.285479\pi\) | ||||
−0.624067 | + | 0.781371i | \(0.714521\pi\) | |||||||
\(264\) | −4260.95 | − | 1069.56i | −0.993347 | − | 0.249343i | ||||
\(265\) | −2433.86 | −0.564193 | ||||||||
\(266\) | −306.053 | − | 176.700i | −0.0705463 | − | 0.0407299i | ||||
\(267\) | 5319.47 | + | 5153.28i | 1.21927 | + | 1.18118i | ||||
\(268\) | 67.2381 | − | 139.314i | 0.0153255 | − | 0.0317536i | ||||
\(269\) | − | 2929.49i | − | 0.663994i | −0.943280 | − | 0.331997i | \(-0.892278\pi\) | ||
0.943280 | − | 0.331997i | \(-0.107722\pi\) | |||||||
\(270\) | −4057.82 | + | 1297.15i | −0.914634 | + | 0.292379i | ||||
\(271\) | − | 2223.95i | − | 0.498506i | −0.968438 | − | 0.249253i | \(-0.919815\pi\) | ||
0.968438 | − | 0.249253i | \(-0.0801850\pi\) | |||||||
\(272\) | −6636.14 | + | 3831.37i | −1.47932 | + | 0.854085i | ||||
\(273\) | 159.755 | − | 164.907i | 0.0354168 | − | 0.0365590i | ||||
\(274\) | −1227.37 | + | 2125.86i | −0.270613 | + | 0.468715i | ||||
\(275\) | 101.649 | + | 176.062i | 0.0222897 | + | 0.0386069i | ||||
\(276\) | 122.104 | + | 118.289i | 0.0266296 | + | 0.0257977i | ||||
\(277\) | 4490.48 | 0.974031 | 0.487016 | − | 0.873393i | \(-0.338085\pi\) | ||||
0.487016 | + | 0.873393i | \(0.338085\pi\) | |||||||
\(278\) | 1977.37 | + | 1141.63i | 0.426600 | + | 0.246297i | ||||
\(279\) | 120.329 | + | 193.933i | 0.0258205 | + | 0.0416145i | ||||
\(280\) | −503.085 | + | 290.456i | −0.107375 | + | 0.0619932i | ||||
\(281\) | 1642.13 | − | 2844.26i | 0.348617 | − | 0.603823i | −0.637387 | − | 0.770544i | \(-0.719985\pi\) |
0.986004 | + | 0.166721i | \(0.0533180\pi\) | |||||||
\(282\) | 3785.22 | + | 3666.96i | 0.799313 | + | 0.774341i | ||||
\(283\) | 3678.48 | 0.772660 | 0.386330 | − | 0.922361i | \(-0.373743\pi\) | ||||
0.386330 | + | 0.922361i | \(0.373743\pi\) | |||||||
\(284\) | −158.397 | − | 91.4503i | −0.0330955 | − | 0.0191077i | ||||
\(285\) | −857.342 | − | 3007.90i | −0.178191 | − | 0.625168i | ||||
\(286\) | −1691.13 | − | 976.373i | −0.349645 | − | 0.201868i | ||||
\(287\) | 801.777 | + | 462.906i | 0.164904 | + | 0.0952073i | ||||
\(288\) | −292.722 | + | 181.625i | −0.0598918 | + | 0.0371609i | ||||
\(289\) | 5264.57 | + | 9118.50i | 1.07156 | + | 1.85599i | ||||
\(290\) | 5344.78i | 1.08226i | ||||||||
\(291\) | 5263.36 | − | 1500.21i | 1.06029 | − | 0.302213i | ||||
\(292\) | 19.1702 | 0.00384195 | ||||||||
\(293\) | 9043.84i | 1.80323i | 0.432539 | + | 0.901615i | \(0.357618\pi\) | ||||
−0.432539 | + | 0.901615i | \(0.642382\pi\) | |||||||
\(294\) | 4727.69 | + | 1186.71i | 0.937839 | + | 0.235410i | ||||
\(295\) | 9028.84i | 1.78196i | ||||||||
\(296\) | −3976.81 | + | 6888.04i | −0.780904 | + | 1.35256i | ||||
\(297\) | 1095.82 | − | 5037.44i | 0.214093 | − | 0.984181i | ||||
\(298\) | 295.055 | + | 170.350i | 0.0573559 | + | 0.0331144i | ||||
\(299\) | 1109.40 | + | 1921.53i | 0.214575 | + | 0.371655i | ||||
\(300\) | 7.86498 | + | 1.97421i | 0.00151362 | + | 0.000379938i | ||||
\(301\) | −112.689 | − | 195.183i | −0.0215790 | − | 0.0373759i | ||||
\(302\) | −585.969 | − | 1014.93i | −0.111651 | − | 0.193386i | ||||
\(303\) | −4127.99 | − | 1036.18i | −0.782663 | − | 0.196459i | ||||
\(304\) | 1697.93 | + | 2940.90i | 0.320339 | + | 0.554843i | ||||
\(305\) | −5348.17 | − | 3087.76i | −1.00405 | − | 0.579688i | ||||
\(306\) | −4914.34 | − | 7920.38i | −0.918085 | − | 1.47967i | ||||
\(307\) | −4603.49 | + | 7973.47i | −0.855814 | + | 1.48231i | 0.0200738 | + | 0.999799i | \(0.493610\pi\) |
−0.875888 | + | 0.482515i | \(0.839723\pi\) | |||||||
\(308\) | − | 23.9417i | − | 0.00442923i | ||||||
\(309\) | −5896.86 | − | 1480.19i | −1.08563 | − | 0.272508i | ||||
\(310\) | − | 256.675i | − | 0.0470264i | ||||||
\(311\) | 4580.44 | 0.835154 | 0.417577 | − | 0.908641i | \(-0.362879\pi\) | ||||
0.417577 | + | 0.908641i | \(0.362879\pi\) | |||||||
\(312\) | −2199.38 | + | 626.890i | −0.399088 | + | 0.113752i | ||||
\(313\) | − | 9152.26i | − | 1.65277i | −0.563107 | − | 0.826384i | \(-0.690394\pi\) | ||
0.563107 | − | 0.826384i | \(-0.309606\pi\) | |||||||
\(314\) | 3301.51 | + | 5718.39i | 0.593360 | + | 1.02773i | ||||
\(315\) | −359.404 | − | 579.247i | −0.0642860 | − | 0.103609i | ||||
\(316\) | 121.967 | + | 70.4178i | 0.0217126 | + | 0.0125358i | ||||
\(317\) | 5243.50 | + | 3027.34i | 0.929036 | + | 0.536379i | 0.886507 | − | 0.462716i | \(-0.153125\pi\) |
0.0425295 | + | 0.999095i | \(0.486458\pi\) | |||||||
\(318\) | 881.115 | + | 3091.31i | 0.155379 | + | 0.545132i | ||||
\(319\) | −5601.30 | − | 3233.91i | −0.983111 | − | 0.567600i | ||||
\(320\) | 5779.37 | 1.00961 | ||||||||
\(321\) | 2606.61 | + | 2525.18i | 0.453230 | + | 0.439070i | ||||
\(322\) | 372.171 | − | 644.619i | 0.0644108 | − | 0.111563i | ||||
\(323\) | 5926.57 | − | 3421.70i | 1.02094 | − | 0.589439i | ||||
\(324\) | −113.902 | − | 171.199i | −0.0195305 | − | 0.0293551i | ||||
\(325\) | 91.6541 | + | 52.9165i | 0.0156432 | + | 0.00903163i | ||||
\(326\) | 5445.99 | 0.925231 | ||||||||
\(327\) | −4789.18 | − | 4639.56i | −0.809916 | − | 0.784613i | ||||
\(328\) | −4610.90 | − | 7986.31i | −0.776202 | − | 1.34442i | ||||
\(329\) | −421.655 | + | 730.328i | −0.0706583 | + | 0.122384i | ||||
\(330\) | −4034.08 | + | 4164.17i | −0.672935 | + | 0.694637i | ||||
\(331\) | 2773.13 | − | 1601.07i | 0.460499 | − | 0.265869i | −0.251755 | − | 0.967791i | \(-0.581008\pi\) |
0.712254 | + | 0.701922i | \(0.247674\pi\) | |||||||
\(332\) | 86.8126i | 0.0143508i | ||||||||
\(333\) | −8226.95 | − | 4407.88i | −1.35386 | − | 0.725376i | ||||
\(334\) | − | 4332.02i | − | 0.709694i | ||||||
\(335\) | −3372.43 | − | 4955.61i | −0.550016 | − | 0.808221i | ||||
\(336\) | 531.591 | + | 514.983i | 0.0863115 | + | 0.0836150i | ||||
\(337\) | −951.133 | − | 549.137i | −0.153743 | − | 0.0887638i | 0.421155 | − | 0.906989i | \(-0.361625\pi\) |
−0.574898 | + | 0.818225i | \(0.694958\pi\) | |||||||
\(338\) | 5086.96 | 0.818622 | ||||||||
\(339\) | 5953.47 | + | 1494.40i | 0.953829 | + | 0.239424i | ||||
\(340\) | − | 383.118i | − | 0.0611102i | ||||||
\(341\) | 268.995 | + | 155.304i | 0.0427181 | + | 0.0246633i | ||||
\(342\) | −3510.03 | + | 2177.86i | −0.554973 | + | 0.344343i | ||||
\(343\) | 1572.28i | 0.247508i | ||||||||
\(344\) | 2244.93i | 0.351856i | ||||||||
\(345\) | 6335.34 | − | 1805.76i | 0.988648 | − | 0.281794i | ||||
\(346\) | 9006.23 | − | 5199.75i | 1.39936 | − | 0.807920i | ||||
\(347\) | −4072.89 | − | 7054.44i | −0.630098 | − | 1.09136i | −0.987531 | − | 0.157423i | \(-0.949681\pi\) |
0.357433 | − | 0.933939i | \(-0.383652\pi\) | |||||||
\(348\) | −248.101 | + | 70.7162i | −0.0382173 | + | 0.0108931i | ||||
\(349\) | 1767.30 | 0.271064 | 0.135532 | − | 0.990773i | \(-0.456726\pi\) | ||||
0.135532 | + | 0.990773i | \(0.456726\pi\) | |||||||
\(350\) | − | 35.5040i | − | 0.00542220i | ||||||
\(351\) | −817.161 | − | 2556.29i | −0.124264 | − | 0.388731i | ||||
\(352\) | −234.416 | + | 406.021i | −0.0354955 | + | 0.0614801i | ||||
\(353\) | −302.770 | + | 524.412i | −0.0456510 | + | 0.0790698i | −0.887948 | − | 0.459944i | \(-0.847870\pi\) |
0.842297 | + | 0.539014i | \(0.181203\pi\) | |||||||
\(354\) | 11467.7 | − | 3268.65i | 1.72176 | − | 0.490753i | ||||
\(355\) | −6137.86 | + | 3543.69i | −0.917644 | + | 0.529802i | ||||
\(356\) | 348.179 | − | 201.021i | 0.0518356 | − | 0.0299273i | ||||
\(357\) | 1037.81 | − | 1071.27i | 0.153856 | − | 0.158817i | ||||
\(358\) | −1721.56 | + | 2981.83i | −0.254154 | + | 0.440208i | ||||
\(359\) | − | 4675.54i | − | 0.687370i | −0.939085 | − | 0.343685i | \(-0.888325\pi\) | ||
0.939085 | − | 0.343685i | \(-0.111675\pi\) | |||||||
\(360\) | 215.445 | + | 6786.71i | 0.0315415 | + | 0.993586i | ||||
\(361\) | 1913.12 | + | 3313.62i | 0.278921 | + | 0.483106i | ||||
\(362\) | 2585.75 | 0.375425 | ||||||||
\(363\) | −27.3891 | − | 96.0922i | −0.00396021 | − | 0.0138940i | ||||
\(364\) | −6.23178 | − | 10.7938i | −0.000897346 | − | 0.00155425i | ||||
\(365\) | 371.421 | − | 643.320i | 0.0532632 | − | 0.0922546i | ||||
\(366\) | −1985.69 | + | 7910.68i | −0.283589 | + | 1.12978i | ||||
\(367\) | −10843.5 | + | 6260.52i | −1.54231 | + | 0.890453i | −0.543618 | + | 0.839333i | \(0.682946\pi\) |
−0.998692 | + | 0.0511208i | \(0.983721\pi\) | |||||||
\(368\) | −6194.22 | + | 3576.24i | −0.877435 | + | 0.506587i | ||||
\(369\) | 9195.35 | − | 5705.42i | 1.29727 | − | 0.804911i | ||||
\(370\) | 5248.33 | + | 9090.37i | 0.737426 | + | 1.27726i | ||||
\(371\) | −445.450 | + | 257.181i | −0.0623359 | + | 0.0359897i | ||||
\(372\) | 11.9147 | − | 3.39605i | 0.00166062 | − | 0.000473325i | ||||
\(373\) | −1482.55 | + | 855.951i | −0.205800 | + | 0.118819i | −0.599358 | − | 0.800481i | \(-0.704577\pi\) |
0.393558 | + | 0.919300i | \(0.371244\pi\) | |||||||
\(374\) | −10986.0 | − | 6342.76i | −1.51891 | − | 0.876941i | ||||
\(375\) | 5158.33 | − | 5324.68i | 0.710333 | − | 0.733241i | ||||
\(376\) | 7274.62 | − | 4200.00i | 0.997766 | − | 0.576060i | ||||
\(377\) | −3367.02 | −0.459974 | ||||||||
\(378\) | −605.603 | + | 666.188i | −0.0824044 | + | 0.0906482i | ||||
\(379\) | −2697.83 | − | 1557.59i | −0.365641 | − | 0.211103i | 0.305911 | − | 0.952060i | \(-0.401039\pi\) |
−0.671553 | + | 0.740957i | \(0.734372\pi\) | |||||||
\(380\) | −169.784 | −0.0229204 | ||||||||
\(381\) | −5706.07 | − | 1432.30i | −0.767272 | − | 0.192596i | ||||
\(382\) | −1611.01 | − | 2790.35i | −0.215776 | − | 0.373735i | ||||
\(383\) | 7286.93 | − | 12621.3i | 0.972180 | − | 1.68387i | 0.283237 | − | 0.959050i | \(-0.408592\pi\) |
0.688943 | − | 0.724815i | \(-0.258075\pi\) | |||||||
\(384\) | −1946.88 | − | 6830.46i | −0.258728 | − | 0.907722i | ||||
\(385\) | −803.445 | − | 463.869i | −0.106357 | − | 0.0614051i | ||||
\(386\) | −2250.26 | + | 3897.56i | −0.296723 | + | 0.513939i | ||||
\(387\) | −2633.05 | + | 83.5865i | −0.345854 | + | 0.0109792i | ||||
\(388\) | − | 297.096i | − | 0.0388730i | ||||||
\(389\) | −3226.65 | − | 1862.91i | −0.420559 | − | 0.242810i | 0.274757 | − | 0.961514i | \(-0.411403\pi\) |
−0.695317 | + | 0.718704i | \(0.744736\pi\) | |||||||
\(390\) | −734.813 | + | 2927.39i | −0.0954070 | + | 0.380087i | ||||
\(391\) | 7206.91 | + | 12482.7i | 0.932145 | + | 1.61452i | ||||
\(392\) | 3884.58 | − | 6728.29i | 0.500513 | − | 0.866914i | ||||
\(393\) | −1485.10 | − | 1438.70i | −0.190619 | − | 0.184663i | ||||
\(394\) | −4008.02 | −0.512490 | ||||||||
\(395\) | 4726.22 | − | 2728.68i | 0.602030 | − | 0.347582i | ||||
\(396\) | −246.673 | − | 132.164i | −0.0313024 | − | 0.0167714i | ||||
\(397\) | −7680.12 | −0.970917 | −0.485458 | − | 0.874260i | \(-0.661347\pi\) | ||||
−0.485458 | + | 0.874260i | \(0.661347\pi\) | |||||||
\(398\) | −1908.00 | − | 3304.75i | −0.240300 | − | 0.416212i | ||||
\(399\) | −474.750 | − | 459.918i | −0.0595670 | − | 0.0577061i | ||||
\(400\) | −170.581 | + | 295.455i | −0.0213226 | + | 0.0369319i | ||||
\(401\) | −6014.43 | −0.748993 | −0.374496 | − | 0.927228i | \(-0.622184\pi\) | ||||
−0.374496 | + | 0.927228i | \(0.622184\pi\) | |||||||
\(402\) | −5073.35 | + | 6077.45i | −0.629442 | + | 0.754019i | ||||
\(403\) | 161.696 | 0.0199868 | ||||||||
\(404\) | −115.518 | + | 200.083i | −0.0142258 | + | 0.0246398i | ||||
\(405\) | −7952.01 | + | 505.385i | −0.975651 | + | 0.0620068i | ||||
\(406\) | 564.770 | + | 978.210i | 0.0690371 | + | 0.119576i | ||||
\(407\) | −12702.2 | −1.54699 | ||||||||
\(408\) | −14287.7 | + | 4072.43i | −1.73370 | + | 0.494155i | ||||
\(409\) | 7455.67 | − | 4304.54i | 0.901368 | − | 0.520405i | 0.0237240 | − | 0.999719i | \(-0.492448\pi\) |
0.877644 | + | 0.479314i | \(0.159114\pi\) | |||||||
\(410\) | −12170.3 | −1.46597 | ||||||||
\(411\) | −3194.62 | + | 3297.64i | −0.383403 | + | 0.395768i | ||||
\(412\) | −165.018 | + | 285.819i | −0.0197326 | + | 0.0341779i | ||||
\(413\) | 954.056 | + | 1652.47i | 0.113671 | + | 0.196884i | ||||
\(414\) | −4587.08 | − | 7392.95i | −0.544548 | − | 0.877641i | ||||
\(415\) | 2913.29 | + | 1681.99i | 0.344597 | + | 0.198953i | ||||
\(416\) | 244.065i | 0.0287651i | ||||||||
\(417\) | 3067.30 | + | 2971.47i | 0.360207 | + | 0.348954i | ||||
\(418\) | −2810.88 | + | 4868.59i | −0.328911 | + | 0.569691i | ||||
\(419\) | 569.415 | + | 328.752i | 0.0663907 | + | 0.0383307i | 0.532828 | − | 0.846224i | \(-0.321129\pi\) |
−0.466437 | + | 0.884554i | \(0.654463\pi\) | |||||||
\(420\) | −35.5874 | + | 10.1435i | −0.00413449 | + | 0.00117845i | ||||
\(421\) | 6462.55 | − | 11193.5i | 0.748137 | − | 1.29581i | −0.200578 | − | 0.979678i | \(-0.564282\pi\) |
0.948715 | − | 0.316133i | \(-0.102385\pi\) | |||||||
\(422\) | 705.284 | + | 1221.59i | 0.0813571 | + | 0.140915i | ||||
\(423\) | 5196.98 | + | 8375.92i | 0.597366 | + | 0.962768i | ||||
\(424\) | 5123.43 | 0.586830 | ||||||||
\(425\) | 595.408 | + | 343.759i | 0.0679565 | + | 0.0392347i | ||||
\(426\) | 6722.98 | + | 6512.94i | 0.764623 | + | 0.740735i | ||||
\(427\) | −1305.11 | −0.147912 | ||||||||
\(428\) | 170.613 | − | 98.5032i | 0.0192684 | − | 0.0111246i | ||||
\(429\) | −2623.28 | − | 2541.33i | −0.295229 | − | 0.286006i | ||||
\(430\) | 2565.78 | + | 1481.35i | 0.287751 | + | 0.166133i | ||||
\(431\) | 12741.0 | − | 7356.04i | 1.42393 | − | 0.822106i | 0.427298 | − | 0.904111i | \(-0.359465\pi\) |
0.996632 | + | 0.0820043i | \(0.0261321\pi\) | |||||||
\(432\) | 8240.41 | − | 2634.19i | 0.917748 | − | 0.293374i | ||||
\(433\) | 12252.8 | − | 7074.15i | 1.35989 | − | 0.785132i | 0.370280 | − | 0.928920i | \(-0.379262\pi\) |
0.989608 | + | 0.143789i | \(0.0459285\pi\) | |||||||
\(434\) | −27.1223 | − | 46.9772i | −0.00299980 | − | 0.00519580i | ||||
\(435\) | −2433.83 | + | 9696.00i | −0.268260 | + | 1.06871i | ||||
\(436\) | −313.470 | + | 180.982i | −0.0344323 | + | 0.0198795i | ||||
\(437\) | 5531.90 | − | 3193.85i | 0.605553 | − | 0.349616i | ||||
\(438\) | −951.560 | − | 238.854i | −0.103807 | − | 0.0260568i | ||||
\(439\) | −2915.82 | + | 5050.35i | −0.317003 | + | 0.549066i | −0.979861 | − | 0.199679i | \(-0.936010\pi\) |
0.662858 | + | 0.748745i | \(0.269343\pi\) | |||||||
\(440\) | 4620.49 | + | 8002.92i | 0.500621 | + | 0.867100i | ||||
\(441\) | 8036.16 | + | 4305.66i | 0.867742 | + | 0.464923i | ||||
\(442\) | −6603.82 | −0.710660 | ||||||||
\(443\) | −6824.66 | − | 11820.7i | −0.731940 | − | 1.26776i | −0.956053 | − | 0.293194i | \(-0.905282\pi\) |
0.224113 | − | 0.974563i | \(-0.428052\pi\) | |||||||
\(444\) | −352.529 | + | 363.898i | −0.0376808 | + | 0.0388960i | ||||
\(445\) | − | 15579.1i | − | 1.65960i | ||||||
\(446\) | −392.842 | + | 680.423i | −0.0417077 | + | 0.0722398i | ||||
\(447\) | 457.690 | + | 443.391i | 0.0484295 | + | 0.0469165i | ||||
\(448\) | 1057.75 | − | 610.693i | 0.111549 | − | 0.0644030i | ||||
\(449\) | 7412.97 | − | 4279.88i | 0.779153 | − | 0.449844i | −0.0569769 | − | 0.998375i | \(-0.518146\pi\) |
0.836130 | + | 0.548531i | \(0.184813\pi\) | |||||||
\(450\) | −365.800 | − | 195.990i | −0.0383200 | − | 0.0205313i | ||||
\(451\) | 7363.77 | − | 12754.4i | 0.768839 | − | 1.33167i | ||||
\(452\) | 166.602 | − | 288.563i | 0.0173369 | − | 0.0300285i | ||||
\(453\) | −600.849 | − | 2108.02i | −0.0623186 | − | 0.218639i | ||||
\(454\) | − | 16290.9i | − | 1.68408i | ||||||
\(455\) | −482.962 | −0.0497618 | ||||||||
\(456\) | 1804.76 | + | 6331.82i | 0.185341 | + | 0.650251i | ||||
\(457\) | 8285.86 | + | 14351.5i | 0.848132 | + | 1.46901i | 0.882873 | + | 0.469611i | \(0.155606\pi\) |
−0.0347414 | + | 0.999396i | \(0.511061\pi\) | |||||||
\(458\) | 2514.95 | − | 1452.01i | 0.256585 | − | 0.148140i | ||||
\(459\) | −5308.48 | − | 16606.3i | −0.539822 | − | 1.68870i | ||||
\(460\) | − | 357.605i | − | 0.0362466i | ||||||
\(461\) | 13991.0i | 1.41351i | 0.707460 | + | 0.706753i | \(0.249841\pi\) | ||||
−0.707460 | + | 0.706753i | \(0.750159\pi\) | |||||||
\(462\) | −298.306 | + | 1188.41i | −0.0300399 | + | 0.119675i | ||||
\(463\) | −3101.22 | − | 1790.49i | −0.311287 | − | 0.179721i | 0.336215 | − | 0.941785i | \(-0.390853\pi\) |
−0.647502 | + | 0.762064i | \(0.724186\pi\) | |||||||
\(464\) | − | 10853.9i | − | 1.08595i | ||||||
\(465\) | 116.881 | − | 465.637i | 0.0116564 | − | 0.0464374i | ||||
\(466\) | 5211.07 | 0.518022 | ||||||||
\(467\) | 15926.4 | + | 9195.13i | 1.57813 | + | 0.911134i | 0.995120 | + | 0.0986699i | \(0.0314588\pi\) |
0.583011 | + | 0.812464i | \(0.301875\pi\) | |||||||
\(468\) | −145.610 | + | 4.62240i | −0.0143821 | + | 0.000456561i | ||||
\(469\) | −1140.88 | − | 550.628i | −0.112326 | − | 0.0542125i | ||||
\(470\) | − | 11085.8i | − | 1.08797i | ||||||
\(471\) | 3385.35 | + | 11877.2i | 0.331186 | + | 1.16193i | ||||
\(472\) | − | 19006.2i | − | 1.85346i | ||||||
\(473\) | −3104.90 | + | 1792.62i | −0.301826 | + | 0.174259i | ||||
\(474\) | −5176.77 | − | 5015.04i | −0.501639 | − | 0.485967i | ||||
\(475\) | 152.342 | − | 263.864i | 0.0147156 | − | 0.0254882i | ||||
\(476\) | −40.4832 | − | 70.1189i | −0.00389820 | − | 0.00675188i | ||||
\(477\) | 190.763 | + | 6009.20i | 0.0183112 | + | 0.576818i | ||||
\(478\) | 4028.26 | 0.385457 | ||||||||
\(479\) | 12307.3 | + | 7105.65i | 1.17398 | + | 0.677798i | 0.954614 | − | 0.297844i | \(-0.0962676\pi\) |
0.219367 | + | 0.975643i | \(0.429601\pi\) | |||||||
\(480\) | 702.833 | + | 176.421i | 0.0668329 | + | 0.0167760i | ||||
\(481\) | −5726.61 | + | 3306.26i | −0.542850 | + | 0.313415i | ||||
\(482\) | 8537.44 | − | 14787.3i | 0.806783 | − | 1.39739i | ||||
\(483\) | 968.695 | − | 999.935i | 0.0912571 | − | 0.0942000i | ||||
\(484\) | −5.42403 | −0.000509394 | ||||||||
\(485\) | −9970.06 | − | 5756.21i | −0.933437 | − | 0.538920i | ||||
\(486\) | 3520.71 | + | 9917.08i | 0.328607 | + | 0.925613i | ||||
\(487\) | 1756.22 | + | 1013.95i | 0.163413 | + | 0.0943463i | 0.579476 | − | 0.814989i | \(-0.303257\pi\) |
−0.416063 | + | 0.909336i | \(0.636591\pi\) | |||||||
\(488\) | 11258.2 | + | 6499.93i | 1.04433 | + | 0.602947i | ||||
\(489\) | 9879.61 | + | 2479.91i | 0.913643 | + | 0.229337i | ||||
\(490\) | −5126.61 | − | 8879.55i | −0.472646 | − | 0.818647i | ||||
\(491\) | − | 854.119i | − | 0.0785048i | −0.999229 | − | 0.0392524i | \(-0.987502\pi\) | ||
0.999229 | − | 0.0392524i | \(-0.0124976\pi\) | |||||||
\(492\) | −161.024 | − | 564.938i | −0.0147551 | − | 0.0517670i | ||||
\(493\) | −21873.0 | −1.99819 | ||||||||
\(494\) | 2926.58i | 0.266545i | ||||||||
\(495\) | −9214.47 | + | 5717.28i | −0.836686 | + | 0.519137i | ||||
\(496\) | 521.243i | 0.0471865i | ||||||||
\(497\) | −748.907 | + | 1297.15i | −0.0675917 | + | 0.117072i | ||||
\(498\) | 1081.66 | − | 4309.16i | 0.0973298 | − | 0.387747i | ||||
\(499\) | −6829.44 | − | 3942.98i | −0.612681 | − | 0.353731i | 0.161333 | − | 0.986900i | \(-0.448421\pi\) |
−0.774014 | + | 0.633169i | \(0.781754\pi\) | |||||||
\(500\) | −201.218 | − | 348.520i | −0.0179975 | − | 0.0311726i | ||||
\(501\) | 1972.65 | − | 7858.76i | 0.175911 | − | 0.700805i | ||||
\(502\) | 1400.44 | + | 2425.63i | 0.124511 | + | 0.215660i | ||||
\(503\) | 4763.75 | + | 8251.06i | 0.422277 | + | 0.731405i | 0.996162 | − | 0.0875312i | \(-0.0278977\pi\) |
−0.573885 | + | 0.818936i | \(0.694564\pi\) | |||||||
\(504\) | 756.566 | + | 1219.35i | 0.0668654 | + | 0.107766i | ||||
\(505\) | 4476.30 | + | 7753.19i | 0.394441 | + | 0.683192i | ||||
\(506\) | −10254.4 | − | 5920.38i | −0.900916 | − | 0.520144i | ||||
\(507\) | 9228.30 | + | 2316.43i | 0.808369 | + | 0.202911i | ||||
\(508\) | −159.679 | + | 276.572i | −0.0139461 | + | 0.0241553i | ||||
\(509\) | − | 10901.0i | − | 0.949273i | −0.880182 | − | 0.474636i | \(-0.842580\pi\) | ||
0.880182 | − | 0.474636i | \(-0.157420\pi\) | |||||||
\(510\) | −4773.53 | + | 19017.0i | −0.414461 | + | 1.65115i | ||||
\(511\) | − | 156.989i | − | 0.0135906i | ||||||
\(512\) | −12137.1 | −1.04764 | ||||||||
\(513\) | −7359.30 | + | 2352.53i | −0.633375 | + | 0.202469i | ||||
\(514\) | 4477.39i | 0.384221i | ||||||||
\(515\) | 6394.43 | + | 11075.5i | 0.547130 | + | 0.947658i | ||||
\(516\) | −34.8159 | + | 138.702i | −0.00297032 | + | 0.0118333i | ||||
\(517\) | 11617.8 | + | 6707.55i | 0.988300 | + | 0.570596i | ||||
\(518\) | 1921.12 | + | 1109.16i | 0.162952 | + | 0.0940802i | ||||
\(519\) | 18706.1 | − | 5331.78i | 1.58209 | − | 0.450943i | ||||
\(520\) | 4166.16 | + | 2405.33i | 0.351343 | + | 0.202848i | ||||
\(521\) | −7177.17 | −0.603527 | −0.301763 | − | 0.953383i | \(-0.597575\pi\) | ||||
−0.301763 | + | 0.953383i | \(0.597575\pi\) | |||||||
\(522\) | 13196.2 | − | 418.916i | 1.10648 | − | 0.0351254i | ||||
\(523\) | 1116.42 | − | 1933.69i | 0.0933414 | − | 0.161672i | −0.815574 | − | 0.578653i | \(-0.803579\pi\) |
0.908915 | + | 0.416981i | \(0.136912\pi\) | |||||||
\(524\) | −97.2051 | + | 56.1214i | −0.00810386 | + | 0.00467877i | ||||
\(525\) | 16.1673 | − | 64.4081i | 0.00134400 | − | 0.00535429i | ||||
\(526\) | −16036.2 | − | 9258.52i | −1.32930 | − | 0.767472i | ||||
\(527\) | 1050.42 | 0.0868254 | ||||||||
\(528\) | 8192.19 | − | 8456.38i | 0.675226 | − | 0.697001i | ||||
\(529\) | 643.482 | + | 1114.54i | 0.0528875 | + | 0.0916038i | ||||
\(530\) | 3380.78 | − | 5855.68i | 0.277079 | − | 0.479914i | ||||
\(531\) | 22292.2 | − | 707.668i | 1.82184 | − | 0.0578346i | ||||
\(532\) | −31.0742 | + | 17.9407i | −0.00253240 | + | 0.00146208i | ||||
\(533\) | − | 7666.86i | − | 0.623056i | ||||||
\(534\) | −19787.4 | + | 5640.00i | −1.60353 | + | 0.457054i | ||||
\(535\) | − | 7633.98i | − | 0.616908i | ||||||
\(536\) | 7099.17 | + | 10431.9i | 0.572084 | + | 0.840649i | ||||
\(537\) | −4480.92 | + | 4625.42i | −0.360086 | + | 0.371698i | ||||
\(538\) | 7048.12 | + | 4069.24i | 0.564807 | + | 0.326091i | ||||
\(539\) | 12407.6 | 0.991530 | ||||||||
\(540\) | −91.9418 | + | 422.653i | −0.00732693 | + | 0.0336817i | ||||
\(541\) | − | 11178.6i | − | 0.888365i | −0.895936 | − | 0.444183i | \(-0.853494\pi\) | ||
0.895936 | − | 0.444183i | \(-0.146506\pi\) | |||||||
\(542\) | 5350.63 | + | 3089.19i | 0.424040 | + | 0.244819i | ||||
\(543\) | 4690.83 | + | 1177.46i | 0.370723 | + | 0.0930565i | ||||
\(544\) | 1585.51i | 0.124960i | ||||||||
\(545\) | 14026.1i | 1.10241i | ||||||||
\(546\) | 174.843 | + | 613.422i | 0.0137044 | + | 0.0480806i | ||||
\(547\) | −13770.5 | + | 7950.41i | −1.07639 | + | 0.621453i | −0.929920 | − | 0.367762i | \(-0.880124\pi\) |
−0.146468 | + | 0.989215i | \(0.546791\pi\) | |||||||
\(548\) | 124.617 | + | 215.843i | 0.00971418 | + | 0.0168255i | ||||
\(549\) | −7204.50 | + | 13446.6i | −0.560074 | + | 1.04533i | ||||
\(550\) | −564.786 | −0.0437865 | ||||||||
\(551\) | 9693.33i | 0.749455i | ||||||||
\(552\) | −13336.3 | + | 3801.24i | −1.02832 | + | 0.293100i | ||||
\(553\) | 576.667 | − | 998.817i | 0.0443443 | − | 0.0768066i | ||||
\(554\) | −6237.54 | + | 10803.7i | −0.478353 | + | 0.828532i | ||||
\(555\) | 5381.59 | + | 18880.8i | 0.411596 | + | 1.44405i | ||||
\(556\) | 200.766 | − | 115.913i | 0.0153137 | − | 0.00884134i | ||||
\(557\) | −21407.7 | + | 12359.8i | −1.62850 | + | 0.940214i | −0.643958 | + | 0.765061i | \(0.722709\pi\) |
−0.984541 | + | 0.175154i | \(0.943958\pi\) | |||||||
\(558\) | −633.731 | + | 20.1179i | −0.0480788 | + | 0.00152627i | ||||
\(559\) | −933.201 | + | 1616.35i | −0.0706086 | + | 0.122298i | ||||
\(560\) | − | 1556.87i | − | 0.117482i | ||||||
\(561\) | −17041.5 | − | 16509.1i | −1.28252 | − | 1.24245i | ||||
\(562\) | 4562.04 | + | 7901.68i | 0.342416 | + | 0.593082i | ||||
\(563\) | 5379.26 | 0.402680 | 0.201340 | − | 0.979521i | \(-0.435470\pi\) | ||||
0.201340 | + | 0.979521i | \(0.435470\pi\) | |||||||
\(564\) | 514.594 | − | 146.675i | 0.0384190 | − | 0.0109506i | ||||
\(565\) | −6455.81 | − | 11181.8i | −0.480705 | − | 0.832605i | ||||
\(566\) | −5109.62 | + | 8850.12i | −0.379458 | + | 0.657241i | ||||
\(567\) | −1401.99 | + | 932.767i | −0.103841 | + | 0.0690873i | ||||
\(568\) | 12920.6 | − | 7459.69i | 0.954462 | − | 0.551059i | ||||
\(569\) | 1654.32 | − | 955.122i | 0.121885 | − | 0.0703704i | −0.437818 | − | 0.899064i | \(-0.644249\pi\) |
0.559703 | + | 0.828693i | \(0.310915\pi\) | |||||||
\(570\) | 8427.67 | + | 2115.46i | 0.619292 | + | 0.155450i | ||||
\(571\) | 3347.28 | + | 5797.66i | 0.245323 | + | 0.424911i | 0.962222 | − | 0.272265i | \(-0.0877728\pi\) |
−0.716900 | + | 0.697176i | \(0.754439\pi\) | |||||||
\(572\) | −171.704 | + | 99.1332i | −0.0125512 | + | 0.00724645i | ||||
\(573\) | −1651.92 | − | 5795.60i | −0.120436 | − | 0.422539i | ||||
\(574\) | −2227.43 | + | 1286.01i | −0.161971 | + | 0.0935138i | ||||
\(575\) | 555.758 | + | 320.867i | 0.0403073 | + | 0.0232714i | ||||
\(576\) | −452.979 | − | 14269.2i | −0.0327676 | − | 1.03221i | ||||
\(577\) | −21932.4 | + | 12662.7i | −1.58243 | + | 0.913614i | −0.587921 | + | 0.808918i | \(0.700054\pi\) |
−0.994504 | + | 0.104696i | \(0.966613\pi\) | |||||||
\(578\) | −29251.2 | −2.10500 | ||||||||
\(579\) | −5857.02 | + | 6045.90i | −0.420396 | + | 0.433954i | ||||
\(580\) | 469.963 | + | 271.333i | 0.0336451 | + | 0.0194250i | ||||
\(581\) | 710.928 | 0.0507646 | ||||||||
\(582\) | −3701.72 | + | 14747.1i | −0.263645 | + | 1.05032i | ||||
\(583\) | 4091.15 | + | 7086.08i | 0.290631 | + | 0.503388i | ||||
\(584\) | −781.864 | + | 1354.23i | −0.0554003 | + | 0.0959561i | ||||
\(585\) | −2666.06 | + | 4975.99i | −0.188424 | + | 0.351678i | ||||
\(586\) | −21758.7 | − | 12562.4i | −1.53387 | − | 0.885578i | ||||
\(587\) | −8672.94 | + | 15022.0i | −0.609831 | + | 1.05626i | 0.381437 | + | 0.924395i | \(0.375429\pi\) |
−0.991268 | + | 0.131863i | \(0.957904\pi\) | |||||||
\(588\) | 344.353 | − | 355.458i | 0.0241512 | − | 0.0249300i | ||||
\(589\) | − | 465.509i | − | 0.0325653i | ||||||
\(590\) | −21722.7 | − | 12541.6i | −1.51578 | − | 0.875133i | ||||
\(591\) | −7270.98 | − | 1825.11i | −0.506071 | − | 0.127031i | ||||
\(592\) | −10658.0 | − | 18460.2i | −0.739936 | − | 1.28161i | ||||
\(593\) | 9864.02 | − | 17085.0i | 0.683080 | − | 1.18313i | −0.290956 | − | 0.956737i | \(-0.593973\pi\) |
0.974036 | − | 0.226393i | \(-0.0726934\pi\) | |||||||
\(594\) | 10597.5 | + | 9633.74i | 0.732022 | + | 0.665450i | ||||
\(595\) | −3137.44 | −0.216172 | ||||||||
\(596\) | 29.9575 | − | 17.2960i | 0.00205891 | − | 0.00118871i | ||||
\(597\) | −1956.45 | − | 6864.01i | −0.134124 | − | 0.470562i | ||||
\(598\) | −6164.06 | −0.421517 | ||||||||
\(599\) | 2467.54 | + | 4273.91i | 0.168316 | + | 0.291531i | 0.937828 | − | 0.347101i | \(-0.112834\pi\) |
−0.769512 | + | 0.638632i | \(0.779501\pi\) | |||||||
\(600\) | −460.240 | + | 475.082i | −0.0313154 | + | 0.0323253i | ||||
\(601\) | −2859.44 | + | 4952.69i | −0.194075 | + | 0.336147i | −0.946597 | − | 0.322420i | \(-0.895504\pi\) |
0.752522 | + | 0.658567i | \(0.228837\pi\) | |||||||
\(602\) | 626.125 | 0.0423903 | ||||||||
\(603\) | −11971.1 | + | 8714.93i | −0.808457 | + | 0.588556i | ||||
\(604\) | −118.989 | −0.00801591 | ||||||||
\(605\) | −105.090 | + | 182.022i | −0.00706203 | + | 0.0122318i | ||||
\(606\) | 8226.98 | − | 8492.29i | 0.551482 | − | 0.569267i | ||||
\(607\) | −8683.79 | − | 15040.8i | −0.580666 | − | 1.00574i | −0.995401 | − | 0.0958005i | \(-0.969459\pi\) |
0.414735 | − | 0.909942i | \(-0.363874\pi\) | |||||||
\(608\) | 702.640 | 0.0468681 | ||||||||
\(609\) | 579.111 | + | 2031.76i | 0.0385333 | + | 0.135190i | ||||
\(610\) | 14857.8 | − | 8578.17i | 0.986190 | − | 0.569377i | ||||
\(611\) | 6983.64 | 0.462402 | ||||||||
\(612\) | −945.916 | + | 30.0282i | −0.0624778 | + | 0.00198337i | ||||
\(613\) | −10020.8 | + | 17356.5i | −0.660255 | + | 1.14360i | 0.320293 | + | 0.947318i | \(0.396218\pi\) |
−0.980549 | + | 0.196277i | \(0.937115\pi\) | |||||||
\(614\) | −12789.0 | − | 22151.2i | −0.840591 | − | 1.45595i | ||||
\(615\) | −22078.2 | − | 5541.93i | −1.44761 | − | 0.363370i | ||||
\(616\) | 1691.30 | + | 976.472i | 0.110624 | + | 0.0638688i | ||||
\(617\) | 19429.1i | 1.26772i | 0.773446 | + | 0.633862i | \(0.218531\pi\) | ||||
−0.773446 | + | 0.633862i | \(0.781469\pi\) | |||||||
\(618\) | 11752.3 | − | 12131.3i | 0.764962 | − | 0.789631i | ||||
\(619\) | 12804.4 | − | 22177.9i | 0.831427 | − | 1.44007i | −0.0654796 | − | 0.997854i | \(-0.520858\pi\) |
0.896907 | − | 0.442220i | \(-0.145809\pi\) | |||||||
\(620\) | −22.5693 | − | 13.0304i | −0.00146194 | − | 0.000844054i | ||||
\(621\) | −4954.97 | − | 15500.4i | −0.320187 | − | 1.00163i | ||||
\(622\) | −6362.50 | + | 11020.2i | −0.410150 | + | 0.710400i | ||||
\(623\) | −1646.21 | − | 2851.32i | −0.105865 | − | 0.183364i | ||||
\(624\) | 1492.22 | − | 5944.78i | 0.0957317 | − | 0.381381i | ||||
\(625\) | −14902.8 | −0.953780 | ||||||||
\(626\) | 22019.6 | + | 12713.0i | 1.40588 | + | 0.811685i | ||||
\(627\) | −7316.24 | + | 7552.18i | −0.466001 | + | 0.481029i | ||||
\(628\) | 670.419 | 0.0425997 | ||||||||
\(629\) | −37201.5 | + | 21478.3i | −2.35822 | + | 1.36152i | ||||
\(630\) | 1892.85 | − | 60.0889i | 0.119703 | − | 0.00380000i | ||||
\(631\) | 8911.60 | + | 5145.11i | 0.562227 | + | 0.324602i | 0.754039 | − | 0.656830i | \(-0.228103\pi\) |
−0.191812 | + | 0.981432i | \(0.561436\pi\) | |||||||
\(632\) | −9948.98 | + | 5744.04i | −0.626185 | + | 0.361528i | ||||
\(633\) | 723.193 | + | 2537.26i | 0.0454097 | + | 0.159316i | ||||
\(634\) | −14567.1 | + | 8410.30i | −0.912511 | + | 0.526838i | ||||
\(635\) | 6187.54 | + | 10717.1i | 0.386685 | + | 0.669758i | ||||
\(636\) | 316.548 | + | 79.4577i | 0.0197357 | + | 0.00495394i | ||||
\(637\) | 5593.80 | − | 3229.58i | 0.347935 | − | 0.200880i | ||||
\(638\) | 15561.1 | − | 8984.18i | 0.965624 | − | 0.557503i | ||||
\(639\) | 9230.44 | + | 14876.6i | 0.571441 | + | 0.920984i | ||||
\(640\) | −7470.06 | + | 12938.5i | −0.461375 | + | 0.799125i | ||||
\(641\) | −7620.57 | − | 13199.2i | −0.469570 | − | 0.813319i | 0.529825 | − | 0.848107i | \(-0.322258\pi\) |
−0.999395 | + | 0.0347880i | \(0.988924\pi\) | |||||||
\(642\) | −9696.10 | + | 2763.68i | −0.596066 | + | 0.169897i | ||||
\(643\) | 1679.90 | 0.103031 | 0.0515153 | − | 0.998672i | \(-0.483595\pi\) | ||||
0.0515153 | + | 0.998672i | \(0.483595\pi\) | |||||||
\(644\) | −37.7873 | − | 65.4495i | −0.00231216 | − | 0.00400477i | ||||
\(645\) | 3980.05 | + | 3855.70i | 0.242968 | + | 0.235377i | ||||
\(646\) | 19011.8i | 1.15791i | ||||||||
\(647\) | −563.660 | + | 976.288i | −0.0342500 | + | 0.0593228i | −0.882642 | − | 0.470045i | \(-0.844238\pi\) |
0.848392 | + | 0.529368i | \(0.177571\pi\) | |||||||
\(648\) | 16739.5 | − | 1063.87i | 1.01480 | − | 0.0644947i | ||||
\(649\) | 26287.0 | − | 15176.8i | 1.58992 | − | 0.917939i | ||||
\(650\) | −254.626 | + | 147.008i | −0.0153650 | + | 0.00887098i | ||||
\(651\) | −27.8110 | − | 97.5723i | −0.00167435 | − | 0.00587429i | ||||
\(652\) | 276.471 | − | 478.862i | 0.0166065 | − | 0.0287633i | ||||
\(653\) | 4727.40 | − | 8188.10i | 0.283304 | − | 0.490697i | −0.688892 | − | 0.724864i | \(-0.741903\pi\) |
0.972196 | + | 0.234167i | \(0.0752361\pi\) | |||||||
\(654\) | 17814.9 | − | 5077.77i | 1.06516 | − | 0.303603i | ||||
\(655\) | 4349.40i | 0.259458i | ||||||||
\(656\) | 24714.8 | 1.47096 | ||||||||
\(657\) | −1617.47 | − | 866.615i | −0.0960478 | − | 0.0514610i | ||||
\(658\) | −1171.41 | − | 2028.94i | −0.0694015 | − | 0.120207i | ||||
\(659\) | −9779.57 | + | 5646.24i | −0.578085 | + | 0.333758i | −0.760372 | − | 0.649488i | \(-0.774983\pi\) |
0.182287 | + | 0.983245i | \(0.441650\pi\) | |||||||
\(660\) | 161.359 | + | 566.113i | 0.00951650 | + | 0.0333877i | ||||
\(661\) | − | 3774.15i | − | 0.222084i | −0.993816 | − | 0.111042i | \(-0.964581\pi\) | ||
0.993816 | − | 0.111042i | \(-0.0354188\pi\) | |||||||
\(662\) | 8895.90i | 0.522280i | ||||||||
\(663\) | −11980.1 | − | 3007.15i | −0.701760 | − | 0.176151i | ||||
\(664\) | −6132.66 | − | 3540.69i | −0.358424 | − | 0.206936i | ||||
\(665\) | 1390.40i | 0.0810789i | ||||||||
\(666\) | 22032.7 | − | 13670.6i | 1.28191 | − | 0.795382i | ||||
\(667\) | −20416.4 | −1.18520 | ||||||||
\(668\) | −380.912 | − | 219.920i | −0.0220628 | − | 0.0127380i | ||||
\(669\) | −1022.50 | + | 1055.47i | −0.0590913 | + | 0.0609970i | ||||
\(670\) | 16607.3 | − | 1230.16i | 0.957606 | − | 0.0709330i | ||||
\(671\) | 20761.2i | 1.19445i | ||||||||
\(672\) | 147.276 | − | 41.9780i | 0.00845429 | − | 0.00240972i | ||||
\(673\) | 1669.77i | 0.0956388i | 0.998856 | + | 0.0478194i | \(0.0152272\pi\) | ||||
−0.998856 | + | 0.0478194i | \(0.984773\pi\) | |||||||
\(674\) | 2642.36 | − | 1525.57i | 0.151009 | − | 0.0871849i | ||||
\(675\) | −574.354 | − | 522.120i | −0.0327509 | − | 0.0297725i | ||||
\(676\) | 258.245 | − | 447.293i | 0.0146930 | − | 0.0254491i | ||||
\(677\) | 15434.6 | + | 26733.6i | 0.876220 | + | 1.51766i | 0.855457 | + | 0.517873i | \(0.173276\pi\) |
0.0207628 | + | 0.999784i | \(0.493391\pi\) | |||||||
\(678\) | −11865.1 | + | 12247.8i | −0.672090 | + | 0.693764i | ||||
\(679\) | −2432.98 | −0.137510 | ||||||||
\(680\) | 27064.4 | + | 15625.6i | 1.52628 | + | 0.881200i | ||||
\(681\) | 7418.32 | − | 29553.5i | 0.417431 | − | 1.66298i | ||||
\(682\) | −747.299 | + | 431.453i | −0.0419583 | + | 0.0242246i | ||||
\(683\) | 15597.2 | − | 27015.1i | 0.873807 | − | 1.51348i | 0.0157791 | − | 0.999876i | \(-0.494977\pi\) |
0.858028 | − | 0.513603i | \(-0.171690\pi\) | |||||||
\(684\) | 13.3075 | + | 419.197i | 0.000743894 | + | 0.0234333i | ||||
\(685\) | 9657.79 | 0.538694 | ||||||||
\(686\) | −3782.78 | − | 2183.99i | −0.210535 | − | 0.121553i | ||||
\(687\) | 5223.60 | − | 1488.88i | 0.290091 | − | 0.0826846i | ||||
\(688\) | −5210.45 | − | 3008.26i | −0.288730 | − | 0.166699i | ||||
\(689\) | 3688.87 | + | 2129.77i | 0.203969 | + | 0.117762i | ||||
\(690\) | −4455.65 | + | 17750.6i | −0.245831 | + | 0.979355i | ||||
\(691\) | 8944.01 | + | 15491.5i | 0.492397 | + | 0.852856i | 0.999962 | − | 0.00875736i | \(-0.00278759\pi\) |
−0.507565 | + | 0.861614i | \(0.669454\pi\) | |||||||
\(692\) | − | 1055.88i | − | 0.0580038i | ||||||
\(693\) | −1082.32 | + | 2020.06i | −0.0593273 | + | 0.110730i | ||||
\(694\) | 22629.9 | 1.23778 | ||||||||
\(695\) | − | 8983.20i | − | 0.490291i | ||||||
\(696\) | 5123.35 | − | 20410.7i | 0.279023 | − | 1.11159i | ||||
\(697\) | − | 49805.8i | − | 2.70664i | ||||||
\(698\) | −2454.88 | + | 4251.98i | −0.133121 | + | 0.230573i | ||||
\(699\) | 9453.44 | + | 2372.94i | 0.511534 | + | 0.128402i | ||||
\(700\) | −3.12185 | − | 1.80240i | −0.000168564 | − | 9.73204e-5i | ||||
\(701\) | −10071.8 | − | 17444.8i | −0.542662 | − | 0.939918i | −0.998750 | − | 0.0499836i | \(-0.984083\pi\) |
0.456088 | − | 0.889935i | \(-0.349250\pi\) | |||||||
\(702\) | 7285.30 | + | 1584.81i | 0.391689 | + | 0.0852061i | ||||
\(703\) | 9518.41 | + | 16486.4i | 0.510660 | + | 0.884488i | ||||
\(704\) | −9714.71 | − | 16826.4i | −0.520081 | − | 0.900806i | ||||
\(705\) | 5048.07 | − | 20110.8i | 0.269676 | − | 1.07435i | ||||
\(706\) | −841.129 | − | 1456.88i | −0.0448390 | − | 0.0776634i | ||||
\(707\) | 1638.52 | + | 946.001i | 0.0871612 | + | 0.0503225i | ||||
\(708\) | 294.762 | − | 1174.29i | 0.0156467 | − | 0.0623340i | ||||
\(709\) | −3883.43 | + | 6726.29i | −0.205705 | + | 0.356292i | −0.950357 | − | 0.311161i | \(-0.899282\pi\) |
0.744652 | + | 0.667453i | \(0.232616\pi\) | |||||||
\(710\) | − | 19689.6i | − | 1.04076i | ||||||
\(711\) | −7107.54 | − | 11455.1i | −0.374900 | − | 0.604222i | ||||
\(712\) | 32795.0i | 1.72619i | ||||||||
\(713\) | 980.470 | 0.0514991 | ||||||||
\(714\) | 1135.83 | + | 3984.94i | 0.0595339 | + | 0.208869i | ||||
\(715\) | 7682.81i | 0.401847i | ||||||||
\(716\) | 174.794 | + | 302.752i | 0.00912339 | + | 0.0158022i | ||||
\(717\) | 7307.70 | + | 1834.33i | 0.380629 | + | 0.0955430i | ||||
\(718\) | 11249.0 | + | 6494.60i | 0.584691 | + | 0.337572i | ||||
\(719\) | −12808.2 | − | 7394.83i | −0.664348 | − | 0.383561i | 0.129584 | − | 0.991568i | \(-0.458636\pi\) |
−0.793932 | + | 0.608007i | \(0.791969\pi\) | |||||||
\(720\) | −16040.5 | − | 8594.28i | −0.830272 | − | 0.444847i | ||||
\(721\) | 2340.64 | + | 1351.37i | 0.120901 | + | 0.0698025i | ||||
\(722\) | −10629.8 | −0.547920 | ||||||||
\(723\) | 22221.4 | − | 22938.1i | 1.14305 | − | 1.17991i | ||||
\(724\) | 131.268 | − | 227.363i | 0.00673833 | − | 0.0116711i | ||||
\(725\) | −843.364 | + | 486.916i | −0.0432024 | + | 0.0249429i | ||||
\(726\) | 269.235 | + | 67.5816i | 0.0137634 | + | 0.00345481i | ||||
\(727\) | −17337.6 | − | 10009.8i | −0.884477 | − | 0.510653i | −0.0123450 | − | 0.999924i | \(-0.503930\pi\) |
−0.872132 | + | 0.489271i | \(0.837263\pi\) | |||||||
\(728\) | 1016.66 | 0.0517583 | ||||||||
\(729\) | 1871.06 | + | 19593.9i | 0.0950597 | + | 0.995472i | ||||
\(730\) | 1031.85 | + | 1787.22i | 0.0523158 | + | 0.0906136i | ||||
\(731\) | −6062.30 | + | 10500.2i | −0.306734 | + | 0.531278i | ||||
\(732\) | 594.776 | + | 576.194i | 0.0300322 | + | 0.0290939i | ||||
\(733\) | 27509.5 | − | 15882.6i | 1.38620 | − | 0.800325i | 0.393319 | − | 0.919402i | \(-0.371327\pi\) |
0.992885 | + | 0.119077i | \(0.0379936\pi\) | |||||||
\(734\) | − | 34784.9i | − | 1.74923i | ||||||
\(735\) | −5256.79 | − | 18442.9i | −0.263809 | − | 0.925549i | ||||
\(736\) | 1479.92i | 0.0741178i | ||||||||
\(737\) | −8759.22 | + | 18148.7i | −0.437788 | + | 0.907077i | ||||
\(738\) | 953.892 | + | 30048.4i | 0.0475789 | + | 1.49878i | ||||
\(739\) | −3012.45 | − | 1739.24i | −0.149952 | − | 0.0865750i | 0.423147 | − | 0.906061i | \(-0.360926\pi\) |
−0.573099 | + | 0.819486i | \(0.694259\pi\) | |||||||
\(740\) | 1065.75 | 0.0529428 | ||||||||
\(741\) | −1332.66 | + | 5309.13i | −0.0660683 | + | 0.263206i | ||||
\(742\) | − | 1428.96i | − | 0.0706990i | ||||||
\(743\) | −3572.25 | − | 2062.44i | −0.176384 | − | 0.101835i | 0.409209 | − | 0.912441i | \(-0.365805\pi\) |
−0.585593 | + | 0.810606i | \(0.699138\pi\) | |||||||
\(744\) | −246.042 | + | 980.194i | −0.0121241 | + | 0.0483006i | ||||
\(745\) | − | 1340.44i | − | 0.0659192i | ||||||
\(746\) | − | 4755.86i | − | 0.233411i | ||||||
\(747\) | 3924.49 | − | 7324.74i | 0.192222 | − | 0.358766i | ||||
\(748\) | −1115.43 | + | 643.993i | −0.0545242 | + | 0.0314796i | ||||
\(749\) | −806.665 | − | 1397.18i | −0.0393523 | − | 0.0681602i | ||||
\(750\) | 5645.53 | + | 19806.8i | 0.274861 | + | 0.964323i | ||||
\(751\) | −35785.7 | −1.73880 | −0.869399 | − | 0.494110i | \(-0.835494\pi\) | ||||
−0.869399 | + | 0.494110i | \(0.835494\pi\) | |||||||
\(752\) | 22512.4i | 1.09168i | ||||||||
\(753\) | 1436.00 | + | 5038.07i | 0.0694964 | + | 0.243822i | ||||
\(754\) | 4676.99 | − | 8100.78i | 0.225896 | − | 0.391264i | ||||
\(755\) | −2305.42 | + | 3993.10i | −0.111129 | + | 0.192482i | ||||
\(756\) | 27.8334 | + | 87.0700i | 0.00133901 | + | 0.00418877i | ||||
\(757\) | 8648.00 | − | 4992.93i | 0.415214 | − | 0.239724i | −0.277813 | − | 0.960635i | \(-0.589610\pi\) |
0.693028 | + | 0.720911i | \(0.256276\pi\) | |||||||
\(758\) | 7494.88 | − | 4327.17i | 0.359137 | − | 0.207348i | ||||
\(759\) | −15906.6 | − | 15409.7i | −0.760705 | − | 0.736939i | ||||
\(760\) | 6924.73 | − | 11994.0i | 0.330508 | − | 0.572457i | ||||
\(761\) | − | 26099.6i | − | 1.24325i | −0.783316 | − | 0.621623i | \(-0.786473\pi\) | ||
0.783316 | − | 0.621623i | \(-0.213527\pi\) | |||||||
\(762\) | 11372.1 | − | 11738.8i | 0.540638 | − | 0.558073i | ||||
\(763\) | 1482.10 | + | 2567.08i | 0.0703221 | + | 0.121801i | ||||
\(764\) | −327.139 | −0.0154914 | ||||||||
\(765\) | −17319.4 | + | 32325.2i | −0.818541 | + | 1.52774i | ||||
\(766\) | 20244.0 | + | 35063.6i | 0.954887 | + | 1.65391i | ||||
\(767\) | 7900.75 | − | 13684.5i | 0.371942 | − | 0.644223i | ||||
\(768\) | −2180.78 | − | 547.405i | −0.102464 | − | 0.0257198i | ||||
\(769\) | 20982.9 | − | 12114.5i | 0.983955 | − | 0.568087i | 0.0804932 | − | 0.996755i | \(-0.474350\pi\) |
0.903462 | + | 0.428668i | \(0.141017\pi\) | |||||||
\(770\) | 2232.06 | − | 1288.68i | 0.104465 | − | 0.0603128i | ||||
\(771\) | −2038.85 | + | 8122.48i | −0.0952365 | + | 0.379408i | ||||
\(772\) | 228.473 | + | 395.727i | 0.0106515 | + | 0.0184489i | ||||
\(773\) | −2242.05 | + | 1294.45i | −0.104322 | + | 0.0602303i | −0.551253 | − | 0.834338i | \(-0.685850\pi\) |
0.446931 | + | 0.894568i | \(0.352517\pi\) | |||||||
\(774\) | 3456.35 | − | 6451.01i | 0.160512 | − | 0.299582i | ||||
\(775\) | 40.5014 | − | 23.3835i | 0.00187723 | − | 0.00108382i | ||||
\(776\) | 20987.6 | + | 12117.2i | 0.970889 | + | 0.560543i | ||||
\(777\) | 2980.04 | + | 2886.94i | 0.137591 | + | 0.133293i | ||||
\(778\) | 8964.01 | − | 5175.37i | 0.413079 | − | 0.238491i | ||||
\(779\) | −22072.2 | −1.01517 | ||||||||
\(780\) | 220.100 | + | 213.224i | 0.0101036 | + | 0.00978799i | ||||
\(781\) | 20634.6 | + | 11913.4i | 0.945408 | + | 0.545831i | ||||
\(782\) | −40043.2 | −1.83113 | ||||||||
\(783\) | 24130.1 | + | 5249.15i | 1.10133 | + | 0.239577i | ||||
\(784\) | 10410.8 | + | 18032.1i | 0.474255 | + | 0.821434i | ||||
\(785\) | 12989.3 | − | 22498.2i | 0.590585 | − | 1.02292i | ||||
\(786\) | 5524.28 | − | 1574.58i | 0.250693 | − | 0.0714549i | ||||
\(787\) | −20050.3 | − | 11576.0i | −0.908152 | − | 0.524322i | −0.0283162 | − | 0.999599i | \(-0.509015\pi\) |
−0.879836 | + | 0.475277i | \(0.842348\pi\) | |||||||
\(788\) | −203.471 | + | 352.423i | −0.00919844 | + | 0.0159322i | ||||
\(789\) | −24875.4 | − | 24098.3i | −1.12242 | − | 1.08735i | ||||
\(790\) | 15161.2i | 0.682799i | ||||||||
\(791\) | −2363.11 | − | 1364.34i | −0.106223 | − | 0.0613279i | ||||
\(792\) | 19397.0 | − | 12035.2i | 0.870257 | − | 0.539966i | ||||
\(793\) | 5403.94 | + | 9359.91i | 0.241992 | + | 0.419143i | ||||
\(794\) | 10668.1 | − | 18477.7i | 0.476823 | − | 0.825882i | ||||
\(795\) | 8799.57 | − | 9083.35i | 0.392564 | − | 0.405224i | ||||
\(796\) | −387.446 | −0.0172521 | ||||||||
\(797\) | 19473.9 | − | 11243.3i | 0.865496 | − | 0.499695i | −0.000352611 | − | 1.00000i | \(-0.500112\pi\) |
0.865849 | + | 0.500305i | \(0.166779\pi\) | |||||||
\(798\) | 1765.98 | − | 503.358i | 0.0783397 | − | 0.0223292i | ||||
\(799\) | 45367.4 | 2.00874 | ||||||||
\(800\) | 35.2951 | + | 61.1328i | 0.00155984 | + | 0.00270172i | ||||
\(801\) | −38464.8 | + | 1221.07i | −1.69674 | + | 0.0538632i | ||||
\(802\) | 8354.39 | − | 14470.2i | 0.367835 | − | 0.637109i | ||||
\(803\) | −2497.33 | −0.109749 | ||||||||
\(804\) | 276.833 | + | 754.624i | 0.0121432 | + | 0.0331014i | ||||
\(805\) | −2928.51 | −0.128219 | ||||||||
\(806\) | −224.606 | + | 389.029i | −0.00981564 | + | 0.0170012i | ||||
\(807\) | 10933.1 | + | 10591.5i | 0.476905 | + | 0.462006i | ||||
\(808\) | −9422.89 | − | 16320.9i | −0.410267 | − | 0.710604i | ||||
\(809\) | 10634.0 | 0.462141 | 0.231070 | − | 0.972937i | \(-0.425777\pi\) | ||||
0.231070 | + | 0.972937i | \(0.425777\pi\) | |||||||
\(810\) | 9829.89 | − | 19833.9i | 0.426404 | − | 0.860361i | ||||
\(811\) | −26581.6 | + | 15346.9i | −1.15093 | + | 0.664492i | −0.949114 | − | 0.314931i | \(-0.898018\pi\) |
−0.201819 | + | 0.979423i | \(0.564685\pi\) | |||||||
\(812\) | 114.685 | 0.00495645 | ||||||||
\(813\) | 8299.92 | + | 8040.62i | 0.358045 | + | 0.346860i | ||||
\(814\) | 17644.1 | − | 30560.5i | 0.759737 | − | 1.31590i | ||||
\(815\) | −10713.2 | − | 18555.9i | −0.460452 | − | 0.797527i | ||||
\(816\) | 9693.82 | − | 38618.8i | 0.415872 | − | 1.65677i | ||||
\(817\) | 4653.32 | + | 2686.60i | 0.199265 | + | 0.115045i | ||||
\(818\) | 23917.0i | 1.02230i | ||||||||
\(819\) | 37.8539 | + | 1192.43i | 0.00161505 | + | 0.0508753i | ||||
\(820\) | −617.838 | + | 1070.13i | −0.0263120 | + | 0.0455737i | ||||
\(821\) | −13214.0 | − | 7629.13i | −0.561721 | − | 0.324310i | 0.192115 | − | 0.981372i | \(-0.438465\pi\) |
−0.753836 | + | 0.657062i | \(0.771799\pi\) | |||||||
\(822\) | −3496.35 | − | 12266.6i | −0.148357 | − | 0.520495i | ||||
\(823\) | 2212.65 | − | 3832.42i | 0.0937159 | − | 0.162321i | −0.815356 | − | 0.578960i | \(-0.803459\pi\) |
0.909072 | + | 0.416639i | \(0.136792\pi\) | |||||||
\(824\) | −13460.7 | − | 23314.5i | −0.569083 | − | 0.985680i | ||||
\(825\) | −1024.58 | − | 257.184i | −0.0432381 | − | 0.0108533i | ||||
\(826\) | −5300.96 | −0.223298 | ||||||||
\(827\) | −6737.03 | − | 3889.63i | −0.283276 | − | 0.163550i | 0.351629 | − | 0.936139i | \(-0.385628\pi\) |
−0.634906 | + | 0.772590i | \(0.718961\pi\) | |||||||
\(828\) | −882.926 | + | 28.0286i | −0.0370577 | + | 0.00117640i | ||||
\(829\) | −11747.1 | −0.492151 | −0.246076 | − | 0.969251i | \(-0.579141\pi\) | ||||
−0.246076 | + | 0.969251i | \(0.579141\pi\) | |||||||
\(830\) | −8093.47 | + | 4672.76i | −0.338468 | + | 0.195415i | ||||
\(831\) | −16235.2 | + | 16758.8i | −0.677729 | + | 0.699585i | ||||
\(832\) | −8759.47 | − | 5057.28i | −0.365000 | − | 0.210733i | ||||
\(833\) | 36338.7 | − | 20980.2i | 1.51148 | − | 0.872652i | ||||
\(834\) | −11409.8 | + | 3252.13i | −0.473727 | + | 0.135026i | ||||
\(835\) | −14760.3 | + | 8521.87i | −0.611739 | + | 0.353187i | ||||
\(836\) | 285.395 | + | 494.319i | 0.0118069 | + | 0.0204502i | ||||
\(837\) | −1158.82 | − | 252.083i | −0.0478549 | − | 0.0104101i | ||||
\(838\) | −1581.90 | + | 913.310i | −0.0652098 | + | 0.0376489i | ||||
\(839\) | −4739.10 | + | 2736.12i | −0.195008 | + | 0.112588i | −0.594325 | − | 0.804225i | \(-0.702581\pi\) |
0.399317 | + | 0.916813i | \(0.369247\pi\) | |||||||
\(840\) | 734.888 | − | 2927.69i | 0.0301858 | − | 0.120256i | ||||
\(841\) | 3296.47 | − | 5709.66i | 0.135162 | − | 0.234108i | ||||
\(842\) | 17953.7 | + | 31096.8i | 0.734829 | + | 1.27276i | ||||
\(843\) | 4677.88 | + | 16411.9i | 0.191121 | + | 0.670529i | ||||
\(844\) | 143.218 | 0.00584096 | ||||||||
\(845\) | −10007.0 | − | 17332.6i | −0.407397 | − | 0.705632i | ||||
\(846\) | −27370.7 | + | 868.887i | −1.11232 | + | 0.0353108i | ||||
\(847\) | 44.4186i | 0.00180194i | ||||||||
\(848\) | −6865.51 | + | 11891.4i | −0.278022 | + | 0.481548i | ||||
\(849\) | −13299.4 | + | 13728.3i | −0.537616 | + | 0.554953i | ||||
\(850\) | −1654.11 | + | 955.002i | −0.0667477 | + | 0.0385368i | ||||
\(851\) | −34724.1 | + | 20048.0i | −1.39874 | + | 0.807563i | ||||
\(852\) | 913.978 | − | 260.511i | 0.0367516 | − | 0.0104753i | ||||
\(853\) | −9511.17 | + | 16473.8i | −0.381778 | + | 0.661258i | −0.991316 | − | 0.131498i | \(-0.958021\pi\) |
0.609539 | + | 0.792756i | \(0.291355\pi\) | |||||||
\(854\) | 1812.87 | − | 3139.98i | 0.0726407 | − | 0.125817i | ||||
\(855\) | 14325.4 | + | 7675.34i | 0.573004 | + | 0.307007i | ||||
\(856\) | 16070.0i | 0.641660i | ||||||||
\(857\) | 42620.8 | 1.69883 | 0.849415 | − | 0.527725i | \(-0.176955\pi\) | ||||
0.849415 | + | 0.527725i | \(0.176955\pi\) | |||||||
\(858\) | 9758.12 | − | 2781.35i | 0.388271 | − | 0.110669i | ||||
\(859\) | 17196.6 | + | 29785.4i | 0.683050 | + | 1.18308i | 0.974045 | + | 0.226353i | \(0.0726802\pi\) |
−0.290995 | + | 0.956724i | \(0.593986\pi\) | |||||||
\(860\) | 260.509 | − | 150.405i | 0.0103294 | − | 0.00596368i | ||||
\(861\) | −4626.40 | + | 1318.66i | −0.183121 | + | 0.0521950i | ||||
\(862\) | 40871.9i | 1.61497i | ||||||||
\(863\) | − | 14740.9i | − | 0.581445i | −0.956807 | − | 0.290722i | \(-0.906104\pi\) | ||
0.956807 | − | 0.290722i | \(-0.0938956\pi\) | |||||||
\(864\) | 380.494 | − | 1749.12i | 0.0149823 | − | 0.0688730i | ||||
\(865\) | −35433.8 | − | 20457.7i | −1.39281 | − | 0.804142i | ||||
\(866\) | 39305.6i | 1.54233i | ||||||||
\(867\) | −53064.8 | − | 13320.0i | −2.07863 | − | 0.521765i | ||||
\(868\) | −5.50757 | −0.000215368 | ||||||||
\(869\) | −15888.9 | − | 9173.44i | −0.620245 | − | 0.358099i | ||||
\(870\) | −19947.1 | − | 19323.9i | −0.777321 | − | 0.753036i | ||||
\(871\) | 774.955 | + | 10462.0i | 0.0301474 | + | 0.406994i | ||||
\(872\) | − | 29525.8i | − | 1.14664i | ||||||
\(873\) | −13430.6 | + | 25067.2i | −0.520685 | + | 0.971817i | ||||
\(874\) | 17745.7i | 0.686795i | ||||||||
\(875\) | −2854.11 | + | 1647.82i | −0.110270 | + | 0.0636647i | ||||
\(876\) | −69.3092 | + | 71.5444i | −0.00267322 | + | 0.00275943i | ||||
\(877\) | 1649.50 | − | 2857.02i | 0.0635117 | − | 0.110006i | −0.832521 | − | 0.553993i | \(-0.813103\pi\) |
0.896033 | + | 0.443988i | \(0.146437\pi\) | |||||||
\(878\) | −8100.49 | − | 14030.5i | −0.311365 | − | 0.539300i | ||||
\(879\) | −33752.2 | − | 32697.8i | −1.29515 | − | 1.25469i | ||||
\(880\) | −24766.2 | −0.948714 | ||||||||
\(881\) | 21751.9 | + | 12558.5i | 0.831827 | + | 0.480256i | 0.854478 | − | 0.519488i | \(-0.173877\pi\) |
−0.0226507 | + | 0.999743i | \(0.507211\pi\) | |||||||
\(882\) | −21521.8 | + | 13353.5i | −0.821627 | + | 0.509793i | ||||
\(883\) | −15877.7 | + | 9166.97i | −0.605125 | + | 0.349369i | −0.771055 | − | 0.636768i | \(-0.780271\pi\) |
0.165930 | + | 0.986138i | \(0.446937\pi\) | |||||||
\(884\) | −335.250 | + | 580.670i | −0.0127553 | + | 0.0220928i | ||||
\(885\) | −33696.2 | − | 32643.5i | −1.27987 | − | 1.23989i | ||||
\(886\) | 37919.4 | 1.43784 | ||||||||
\(887\) | 28356.8 | + | 16371.8i | 1.07343 | + | 0.619743i | 0.929115 | − | 0.369790i | \(-0.120570\pi\) |
0.144310 | + | 0.989532i | \(0.453904\pi\) | |||||||
\(888\) | −11328.6 | − | 39745.3i | −0.428111 | − | 1.50199i | ||||
\(889\) | 2264.91 | + | 1307.65i | 0.0854473 | + | 0.0493330i | ||||
\(890\) | 37482.1 | + | 21640.3i | 1.41169 | + | 0.815039i | ||||
\(891\) | 14838.2 | + | 22302.4i | 0.557909 | + | 0.838561i | ||||
\(892\) | 39.8861 | + | 69.0847i | 0.00149718 | + | 0.00259319i | ||||
\(893\) | − | 20105.2i | − | 0.753411i | ||||||
\(894\) | −1702.52 | + | 485.269i | −0.0636922 | + | 0.0181542i | ||||
\(895\) | 13546.5 | 0.505932 | ||||||||
\(896\) | 3157.38i | 0.117724i | ||||||||
\(897\) | −11182.3 | − | 2806.90i | −0.416238 | − | 0.104481i | ||||
\(898\) | 23780.0i | 0.883685i | ||||||||
\(899\) | −743.933 | + | 1288.53i | −0.0275990 | + | 0.0478029i | ||||
\(900\) | −35.8035 | + | 22.2149i | −0.00132606 | + | 0.000822775i | ||||
\(901\) | 23963.8 | + | 13835.5i | 0.886072 | + | 0.511574i | ||||
\(902\) | 20457.4 | + | 35433.3i | 0.755163 | + | 1.30798i | ||||
\(903\) | 1135.86 | + | 285.116i | 0.0418594 | + | 0.0105073i | ||||
\(904\) | 13589.9 | + | 23538.4i | 0.499992 | + | 0.866011i | ||||
\(905\) | −5086.64 | − | 8810.32i | −0.186835 | − | 0.323608i | ||||
\(906\) | 5906.34 | + | 1482.57i | 0.216584 | + | 0.0543655i | ||||
\(907\) | −4612.61 | − | 7989.27i | −0.168863 | − | 0.292480i | 0.769157 | − | 0.639060i | \(-0.220676\pi\) |
−0.938021 | + | 0.346580i | \(0.887343\pi\) | |||||||
\(908\) | −1432.45 | − | 827.026i | −0.0523541 | − | 0.0302267i | ||||
\(909\) | 18791.7 | − | 11659.7i | 0.685679 | − | 0.425442i | ||||
\(910\) | 670.862 | − | 1161.97i | 0.0244383 | − | 0.0423284i | ||||
\(911\) | − | 45233.0i | − | 1.64504i | −0.568733 | − | 0.822522i | \(-0.692566\pi\) | ||
0.568733 | − | 0.822522i | \(-0.307434\pi\) | |||||||
\(912\) | −17114.5 | − | 4295.96i | −0.621400 | − | 0.155980i | ||||
\(913\) | − | 11309.2i | − | 0.409946i | ||||||
\(914\) | −46038.2 | −1.66609 | ||||||||
\(915\) | 30859.9 | − | 8795.99i | 1.11497 | − | 0.317799i | ||||
\(916\) | − | 294.851i | − | 0.0106355i | ||||||
\(917\) | 459.591 | + | 796.035i | 0.0165507 | + | 0.0286667i | ||||
\(918\) | 47327.1 | + | 10295.3i | 1.70155 | + | 0.370147i | ||||
\(919\) | 12662.9 | + | 7310.94i | 0.454528 | + | 0.262422i | 0.709741 | − | 0.704463i | \(-0.248812\pi\) |
−0.255213 | + | 0.966885i | \(0.582145\pi\) | |||||||
\(920\) | 25262.1 | + | 14585.1i | 0.905291 | + | 0.522670i | ||||
\(921\) | −13113.8 | − | 46008.4i | −0.469178 | − | 1.64607i | ||||
\(922\) | −33661.3 | − | 19434.3i | −1.20236 | − | 0.694182i | ||||
\(923\) | 12403.7 | 0.442334 | ||||||||
\(924\) | 89.3520 | + | 86.5605i | 0.00318124 | + | 0.00308185i | ||||
\(925\) | −956.259 | + | 1656.29i | −0.0339909 | + | 0.0588740i | ||||
\(926\) | 8615.54 | − | 4974.18i | 0.305750 | − | 0.176525i | ||||
\(927\) | 26844.1 | − | 16655.9i | 0.951107 | − | 0.590131i | ||||
\(928\) | −1944.91 | − | 1122.89i | −0.0687982 | − | 0.0397206i | ||||
\(929\) | −11466.9 | −0.404970 | −0.202485 | − | 0.979285i | \(-0.564902\pi\) | ||||
−0.202485 | + | 0.979285i | \(0.564902\pi\) | |||||||
\(930\) | 957.931 | + | 928.004i | 0.0337761 | + | 0.0327209i | ||||
\(931\) | −9297.66 | − | 16104.0i | −0.327302 | − | 0.566905i | ||||
\(932\) | 264.545 | − | 458.206i | 0.00929772 | − | 0.0161041i | ||||
\(933\) | −16560.5 | + | 17094.5i | −0.581099 | + | 0.599839i | ||||
\(934\) | −44245.5 | + | 25545.1i | −1.55006 | + | 0.894928i | ||||
\(935\) | 49909.4i | 1.74568i | ||||||||
\(936\) | 5612.22 | − | 10474.8i | 0.195984 | − | 0.365789i | ||||
\(937\) | 52258.1i | 1.82198i | 0.412424 | + | 0.910992i | \(0.364682\pi\) | ||||
−0.412424 | + | 0.910992i | \(0.635318\pi\) | |||||||
\(938\) | 2909.51 | − | 1980.00i | 0.101278 | − | 0.0689225i | ||||
\(939\) | 34156.9 | + | 33089.8i | 1.18708 | + | 1.14999i | ||||
\(940\) | −974.764 | − | 562.780i | −0.0338227 | − | 0.0195275i | ||||
\(941\) | −48460.8 | −1.67883 | −0.839413 | − | 0.543494i | \(-0.817101\pi\) | ||||
−0.839413 | + | 0.543494i | \(0.817101\pi\) | |||||||
\(942\) | −33278.0 | − | 8353.21i | −1.15101 | − | 0.288920i | ||||
\(943\) | − | 46489.1i | − | 1.60540i | ||||||
\(944\) | 44113.2 | + | 25468.8i | 1.52093 | + | 0.878112i | ||||
\(945\) | 3461.20 | + | 752.932i | 0.119146 | + | 0.0259184i | ||||
\(946\) | − | 9960.20i | − | 0.342319i | ||||||
\(947\) | 35357.9i | 1.21328i | 0.794976 | + | 0.606641i | \(0.207483\pi\) | ||||
−0.794976 | + | 0.606641i | \(0.792517\pi\) | |||||||
\(948\) | −703.773 | + | 200.596i | −0.0241113 | + | 0.00687243i | ||||
\(949\) | −1125.88 | + | 650.030i | −0.0385119 | + | 0.0222348i | ||||
\(950\) | 423.223 | + | 733.044i | 0.0144539 | + | 0.0250348i | ||||
\(951\) | −30256.0 | + | 8623.85i | −1.03167 | + | 0.294056i | ||||
\(952\) | 6604.50 | 0.224846 | ||||||||
\(953\) | 2417.80i | 0.0821829i | 0.999155 | + | 0.0410914i | \(0.0130835\pi\) | ||||
−0.999155 | + | 0.0410914i | \(0.986917\pi\) | |||||||
\(954\) | −14722.6 | − | 7888.17i | −0.499647 | − | 0.267703i | ||||
\(955\) | −6338.30 | + | 10978.3i | −0.214767 | + | 0.371987i | ||||
\(956\) | 204.499 | − | 354.203i | 0.00691838 | − | 0.0119830i | ||||
\(957\) | 32320.5 | − | 9212.31i | 1.09172 | − | 0.311172i | ||||
\(958\) | −34191.2 | + | 19740.3i | −1.15310 | + | 0.665742i | ||||
\(959\) | 1767.59 | − | 1020.52i | 0.0595186 | − | 0.0343631i | ||||
\(960\) | −20895.2 | + | 21569.0i | −0.702488 | + | 0.725143i | ||||
\(961\) | −14859.8 | + | 25737.9i | −0.498801 | + | 0.863948i | ||||
\(962\) | − | 18370.4i | − | 0.615680i | ||||||
\(963\) | −18848.3 | + | 598.341i | −0.630713 | + | 0.0200221i | ||||
\(964\) | −866.824 | − | 1501.38i | −0.0289611 | − | 0.0501621i | ||||
\(965\) | 17706.6 | 0.590670 | ||||||||
\(966\) | 1060.19 | + | 3719.57i | 0.0353116 | + | 0.123887i | ||||
\(967\) | −20455.9 | − | 35430.6i | −0.680265 | − | 1.17825i | −0.974900 | − | 0.222644i | \(-0.928531\pi\) |
0.294635 | − | 0.955610i | \(-0.404802\pi\) | |||||||
\(968\) | 221.221 | − | 383.167i | 0.00734538 | − | 0.0127226i | ||||
\(969\) | −8657.31 | + | 34489.4i | −0.287010 | + | 1.14341i | ||||
\(970\) | 27698.0 | − | 15991.4i | 0.916834 | − | 0.529334i | ||||
\(971\) | 10265.5 | − | 5926.79i | 0.339275 | − | 0.195880i | −0.320677 | − | 0.947189i | \(-0.603910\pi\) |
0.659951 | + | 0.751308i | \(0.270577\pi\) | |||||||
\(972\) | 1050.74 | + | 193.877i | 0.0346732 | + | 0.00639774i | ||||
\(973\) | −949.234 | − | 1644.12i | −0.0312755 | − | 0.0541707i | ||||
\(974\) | −4878.99 | + | 2816.88i | −0.160506 | + | 0.0926682i | ||||
\(975\) | −528.861 | + | 150.741i | −0.0173714 | + | 0.00495137i | ||||
\(976\) | −30172.5 | + | 17420.1i | −0.989547 | + | 0.571315i | ||||
\(977\) | −35942.2 | − | 20751.2i | −1.17696 | − | 0.679519i | −0.221652 | − | 0.975126i | \(-0.571145\pi\) |
−0.955310 | + | 0.295606i | \(0.904478\pi\) | |||||||
\(978\) | −19689.8 | + | 20324.8i | −0.643774 | + | 0.664536i | ||||
\(979\) | −45357.9 | + | 26187.4i | −1.48074 | + | 0.854906i | ||||
\(980\) | −1041.03 | −0.0339332 | ||||||||
\(981\) | 34630.3 | − | 1099.35i | 1.12708 | − | 0.0357792i | ||||
\(982\) | 2054.94 | + | 1186.42i | 0.0667778 | + | 0.0385542i | ||||
\(983\) | 34758.5 | 1.12780 | 0.563898 | − | 0.825844i | \(-0.309301\pi\) | ||||
0.563898 | + | 0.825844i | \(0.309301\pi\) | |||||||
\(984\) | 46476.0 | + | 11666.1i | 1.50569 | + | 0.377949i | ||||
\(985\) | 7884.50 | + | 13656.4i | 0.255047 | + | 0.441754i | ||||
\(986\) | 30382.9 | − | 52624.6i | 0.981326 | − | 1.69971i | ||||
\(987\) | −1201.15 | − | 4214.13i | −0.0387366 | − | 0.135904i | ||||
\(988\) | 257.332 | + | 148.571i | 0.00828627 | + | 0.00478408i | ||||
\(989\) | −5658.60 | + | 9800.98i | −0.181934 | + | 0.315119i | ||||
\(990\) | −955.875 | − | 30110.9i | −0.0306866 | − | 0.966654i | ||||
\(991\) | − | 26902.2i | − | 0.862338i | −0.902271 | − | 0.431169i | \(-0.858101\pi\) | ||
0.902271 | − | 0.431169i | \(-0.141899\pi\) | |||||||
\(992\) | 93.4015 | + | 53.9254i | 0.00298942 | + | 0.00172594i | ||||
\(993\) | −4050.89 | + | 16138.1i | −0.129457 | + | 0.515738i | ||||
\(994\) | −2080.55 | − | 3603.62i | −0.0663894 | − | 0.114990i | ||||
\(995\) | −7506.76 | + | 13002.1i | −0.239176 | + | 0.414265i | ||||
\(996\) | −323.991 | − | 313.869i | −0.0103073 | − | 0.00998525i | ||||
\(997\) | 37291.0 | 1.18457 | 0.592285 | − | 0.805728i | \(-0.298226\pi\) | ||||
0.592285 | + | 0.805728i | \(0.298226\pi\) | |||||||
\(998\) | 18973.0 | − | 10954.1i | 0.601783 | − | 0.347439i | ||||
\(999\) | 46194.9 | − | 14767.0i | 1.46300 | − | 0.467674i |
(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 | 201.4.f.a.38.20 | ✓ | 132 | |
3.2 | odd | 2 | inner | 201.4.f.a.38.47 | yes | 132 | |
67.30 | odd | 6 | inner | 201.4.f.a.164.47 | yes | 132 | |
201.164 | even | 6 | inner | 201.4.f.a.164.20 | yes | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.4.f.a.38.20 | ✓ | 132 | 1.1 | even | 1 | trivial | |
201.4.f.a.38.47 | yes | 132 | 3.2 | odd | 2 | inner | |
201.4.f.a.164.20 | yes | 132 | 201.164 | even | 6 | inner | |
201.4.f.a.164.47 | yes | 132 | 67.30 | odd | 6 | inner |