Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(68,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.68");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.g (of order \(6\), degree \(2\), not 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: | \(8.67328077084\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 80.5 | ||
Root | \(-2.59957 + 1.49740i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.80 |
Dual form | 147.4.g.d.68.5 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.24076 | − | 1.29370i | 0.792229 | − | 0.457393i | −0.0485179 | − | 0.998822i | \(-0.515450\pi\) |
0.840747 | + | 0.541429i | \(0.182116\pi\) | |||||||
\(3\) | −2.59358 | − | 4.50260i | −0.499134 | − | 0.866525i | ||||
\(4\) | −0.652660 | + | 1.13044i | −0.0815825 | + | 0.141305i | ||||
\(5\) | 8.05907 | + | 13.9587i | 0.720825 | + | 1.24851i | 0.960670 | + | 0.277694i | \(0.0895701\pi\) |
−0.239845 | + | 0.970811i | \(0.577097\pi\) | |||||||
\(6\) | −11.6366 | − | 6.73392i | −0.791771 | − | 0.458185i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 24.0767i | 1.06405i | ||||||||
\(9\) | −13.5467 | + | 23.3556i | −0.501731 | + | 0.865024i | ||||
\(10\) | 36.1169 | + | 20.8521i | 1.14212 | + | 0.659401i | ||||
\(11\) | 30.8296 | + | 17.7995i | 0.845043 | + | 0.487886i | 0.858975 | − | 0.512017i | \(-0.171102\pi\) |
−0.0139322 | + | 0.999903i | \(0.504435\pi\) | |||||||
\(12\) | 6.78264 | + | 0.00678109i | 0.163165 | + | 0.000163128i | ||||
\(13\) | 7.40831i | 0.158054i | 0.996872 | + | 0.0790268i | \(0.0251813\pi\) | ||||
−0.996872 | + | 0.0790268i | \(0.974819\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 41.9486 | − | 72.4897i | 0.722073 | − | 1.24778i | ||||
\(16\) | 25.9268 | + | 44.9065i | 0.405106 | + | 0.701664i | ||||
\(17\) | 14.4601 | − | 25.0457i | 0.206300 | − | 0.357322i | −0.744246 | − | 0.667905i | \(-0.767191\pi\) |
0.950546 | + | 0.310584i | \(0.100524\pi\) | |||||||
\(18\) | −0.139688 | + | 69.8599i | −0.00182915 | + | 0.914785i | ||||
\(19\) | −30.4580 | + | 17.5849i | −0.367765 | + | 0.212329i | −0.672482 | − | 0.740114i | \(-0.734772\pi\) |
0.304716 | + | 0.952443i | \(0.401438\pi\) | |||||||
\(20\) | −21.0393 | −0.235227 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 92.1090 | 0.892623 | ||||||||
\(23\) | 48.0017 | − | 27.7138i | 0.435175 | − | 0.251249i | −0.266374 | − | 0.963870i | \(-0.585825\pi\) |
0.701549 | + | 0.712621i | \(0.252492\pi\) | |||||||
\(24\) | 108.407 | − | 62.4446i | 0.922024 | − | 0.531102i | ||||
\(25\) | −67.3971 | + | 116.735i | −0.539177 | + | 0.933881i | ||||
\(26\) | 9.58416 | + | 16.6003i | 0.0722927 | + | 0.125215i | ||||
\(27\) | 140.295 | + | 0.420792i | 0.999996 | + | 0.00299931i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 68.1510i | − | 0.436390i | −0.975905 | − | 0.218195i | \(-0.929983\pi\) | ||
0.975905 | − | 0.218195i | \(-0.0700169\pi\) | |||||||
\(30\) | 0.216652 | − | 216.701i | 0.00131850 | − | 1.31880i | ||||
\(31\) | 154.734 | + | 89.3356i | 0.896484 | + | 0.517585i | 0.876058 | − | 0.482206i | \(-0.160164\pi\) |
0.0204262 | + | 0.999791i | \(0.493498\pi\) | |||||||
\(32\) | −50.6165 | − | 29.2234i | −0.279619 | − | 0.161438i | ||||
\(33\) | 0.184935 | − | 184.977i | 0.000975549 | − | 0.975771i | ||||
\(34\) | − | 74.8285i | − | 0.377440i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −17.5608 | − | 30.5571i | −0.0812998 | − | 0.141468i | ||||
\(37\) | 116.838 | + | 202.370i | 0.519137 | + | 0.899172i | 0.999753 | + | 0.0222405i | \(0.00707996\pi\) |
−0.480615 | + | 0.876931i | \(0.659587\pi\) | |||||||
\(38\) | −45.4994 | + | 78.8072i | −0.194236 | + | 0.336427i | ||||
\(39\) | 33.3566 | − | 19.2140i | 0.136957 | − | 0.0788899i | ||||
\(40\) | −336.079 | + | 194.035i | −1.32847 | + | 0.766992i | ||||
\(41\) | −370.068 | −1.40963 | −0.704816 | − | 0.709390i | \(-0.748970\pi\) | ||||
−0.704816 | + | 0.709390i | \(0.748970\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −187.068 | −0.663432 | −0.331716 | − | 0.943379i | \(-0.607628\pi\) | ||||
−0.331716 | + | 0.943379i | \(0.607628\pi\) | |||||||
\(44\) | −40.2425 | + | 23.2340i | −0.137881 | + | 0.0796059i | ||||
\(45\) | −435.189 | − | 0.870180i | −1.44165 | − | 0.00288264i | ||||
\(46\) | 71.7068 | − | 124.200i | 0.229839 | − | 0.398093i | ||||
\(47\) | 87.3726 | + | 151.334i | 0.271162 | + | 0.469666i | 0.969160 | − | 0.246434i | \(-0.0792588\pi\) |
−0.697998 | + | 0.716100i | \(0.745925\pi\) | |||||||
\(48\) | 134.953 | − | 233.206i | 0.405807 | − | 0.701259i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 348.768i | 0.986464i | ||||||||
\(51\) | −150.274 | − | 0.150240i | −0.412599 | − | 0.000412505i | ||||
\(52\) | −8.37465 | − | 4.83511i | −0.0223338 | − | 0.0128944i | ||||
\(53\) | −235.715 | − | 136.090i | −0.610905 | − | 0.352706i | 0.162415 | − | 0.986723i | \(-0.448072\pi\) |
−0.773319 | + | 0.634017i | \(0.781405\pi\) | |||||||
\(54\) | 314.913 | − | 180.558i | 0.793597 | − | 0.455015i | ||||
\(55\) | 573.789i | 1.40672i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 158.173 | + | 91.5321i | 0.367553 | + | 0.212697i | ||||
\(58\) | −88.1672 | − | 152.710i | −0.199602 | − | 0.345721i | ||||
\(59\) | 48.4354 | − | 83.8926i | 0.106877 | − | 0.185117i | −0.807626 | − | 0.589695i | \(-0.799248\pi\) |
0.914504 | + | 0.404578i | \(0.132581\pi\) | |||||||
\(60\) | 54.5671 | + | 94.7315i | 0.117410 | + | 0.203830i | ||||
\(61\) | 333.882 | − | 192.767i | 0.700807 | − | 0.404611i | −0.106841 | − | 0.994276i | \(-0.534073\pi\) |
0.807648 | + | 0.589665i | \(0.200740\pi\) | |||||||
\(62\) | 462.295 | 0.946960 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −566.055 | −1.10558 | ||||||||
\(65\) | −103.411 | + | 59.7041i | −0.197331 | + | 0.113929i | ||||
\(66\) | −238.892 | − | 414.730i | −0.445538 | − | 0.773480i | ||||
\(67\) | 509.009 | − | 881.630i | 0.928140 | − | 1.60759i | 0.141708 | − | 0.989908i | \(-0.454741\pi\) |
0.786432 | − | 0.617677i | \(-0.211926\pi\) | |||||||
\(68\) | 18.8751 | + | 32.6926i | 0.0336609 | + | 0.0583023i | ||||
\(69\) | −249.280 | − | 144.254i | −0.434924 | − | 0.251684i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 125.333i | − | 0.209497i | −0.994499 | − | 0.104749i | \(-0.966596\pi\) | ||
0.994499 | − | 0.104749i | \(-0.0334038\pi\) | |||||||
\(72\) | −562.326 | − | 326.160i | −0.920427 | − | 0.533866i | ||||
\(73\) | −195.346 | − | 112.783i | −0.313199 | − | 0.180825i | 0.335158 | − | 0.942162i | \(-0.391210\pi\) |
−0.648357 | + | 0.761337i | \(0.724544\pi\) | |||||||
\(74\) | 523.613 | + | 302.308i | 0.822551 | + | 0.474900i | ||||
\(75\) | 700.411 | + | 0.700251i | 1.07835 | + | 0.00107811i | ||||
\(76\) | − | 45.9079i | − | 0.0692894i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 49.8870 | − | 86.2076i | 0.0724178 | − | 0.125142i | ||||
\(79\) | 532.154 | + | 921.718i | 0.757874 | + | 1.31268i | 0.943933 | + | 0.330138i | \(0.107095\pi\) |
−0.186059 | + | 0.982539i | \(0.559572\pi\) | |||||||
\(80\) | −417.891 | + | 723.809i | −0.584021 | + | 1.01155i | ||||
\(81\) | −361.972 | − | 632.785i | −0.496533 | − | 0.868018i | ||||
\(82\) | −829.234 | + | 478.758i | −1.11675 | + | 0.644756i | ||||
\(83\) | 601.040 | 0.794852 | 0.397426 | − | 0.917634i | \(-0.369904\pi\) | ||||
0.397426 | + | 0.917634i | \(0.369904\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 466.140 | 0.594824 | ||||||||
\(86\) | −419.175 | + | 242.011i | −0.525590 | + | 0.303450i | ||||
\(87\) | −306.856 | + | 176.755i | −0.378143 | + | 0.217817i | ||||
\(88\) | −428.552 | + | 742.274i | −0.519134 | + | 0.899166i | ||||
\(89\) | −752.606 | − | 1303.55i | −0.896360 | − | 1.55254i | −0.832112 | − | 0.554607i | \(-0.812869\pi\) |
−0.0642474 | − | 0.997934i | \(-0.520465\pi\) | |||||||
\(90\) | −976.280 | + | 561.055i | −1.14343 | + | 0.657116i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 72.3506i | 0.0819900i | ||||||||
\(93\) | 0.928190 | − | 928.402i | 0.00103493 | − | 1.03517i | ||||
\(94\) | 391.562 | + | 226.069i | 0.429645 | + | 0.248055i | ||||
\(95\) | −490.926 | − | 283.436i | −0.530189 | − | 0.306105i | ||||
\(96\) | −0.303630 | + | 303.699i | −0.000322803 | + | 0.322876i | ||||
\(97\) | − | 327.463i | − | 0.342771i | −0.985204 | − | 0.171386i | \(-0.945176\pi\) | ||
0.985204 | − | 0.171386i | \(-0.0548244\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −833.358 | + | 478.920i | −0.846017 | + | 0.486195i | ||||
\(100\) | −87.9747 | − | 152.377i | −0.0879747 | − | 0.152377i | ||||
\(101\) | 547.845 | − | 948.895i | 0.539729 | − | 0.934837i | −0.459190 | − | 0.888338i | \(-0.651860\pi\) |
0.998918 | − | 0.0464990i | \(-0.0148064\pi\) | |||||||
\(102\) | −336.922 | + | 194.073i | −0.327062 | + | 0.188393i | ||||
\(103\) | −179.848 | + | 103.835i | −0.172048 | + | 0.0993318i | −0.583551 | − | 0.812076i | \(-0.698337\pi\) |
0.411503 | + | 0.911408i | \(0.365004\pi\) | |||||||
\(104\) | −178.367 | −0.168177 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −704.242 | −0.645302 | ||||||||
\(107\) | 1561.25 | − | 901.391i | 1.41058 | − | 0.814399i | 0.415138 | − | 0.909759i | \(-0.363733\pi\) |
0.995443 | + | 0.0953593i | \(0.0304000\pi\) | |||||||
\(108\) | −92.0409 | + | 158.321i | −0.0820059 | + | 0.141060i | ||||
\(109\) | −141.825 | + | 245.647i | −0.124627 | + | 0.215860i | −0.921587 | − | 0.388172i | \(-0.873107\pi\) |
0.796960 | + | 0.604032i | \(0.206440\pi\) | |||||||
\(110\) | 742.313 | + | 1285.72i | 0.643425 | + | 1.11444i | ||||
\(111\) | 608.160 | − | 1050.94i | 0.520036 | − | 0.898652i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1037.39i | − | 0.863627i | −0.901963 | − | 0.431814i | \(-0.857874\pi\) | ||
0.901963 | − | 0.431814i | \(-0.142126\pi\) | |||||||
\(114\) | 472.843 | + | 0.472735i | 0.388472 | + | 0.000388383i | ||||
\(115\) | 773.697 | + | 446.694i | 0.627371 | + | 0.362213i | ||||
\(116\) | 77.0406 | + | 44.4794i | 0.0616641 | + | 0.0356018i | ||||
\(117\) | −173.026 | − | 100.358i | −0.136720 | − | 0.0793003i | ||||
\(118\) | − | 250.644i | − | 0.195540i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1745.31 | + | 1009.98i | 1.32770 | + | 0.768320i | ||||
\(121\) | −31.8573 | − | 55.1785i | −0.0239349 | − | 0.0414564i | ||||
\(122\) | 498.767 | − | 863.890i | 0.370133 | − | 0.641090i | ||||
\(123\) | 959.799 | + | 1666.27i | 0.703595 | + | 1.22148i | ||||
\(124\) | −201.977 | + | 116.611i | −0.146275 | + | 0.0844518i | ||||
\(125\) | −157.864 | −0.112958 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1645.81 | 1.14994 | 0.574968 | − | 0.818176i | \(-0.305015\pi\) | ||||
0.574968 | + | 0.818176i | \(0.305015\pi\) | |||||||
\(128\) | −863.461 | + | 498.520i | −0.596249 | + | 0.344245i | ||||
\(129\) | 485.175 | + | 842.291i | 0.331142 | + | 0.574881i | ||||
\(130\) | −154.479 | + | 267.565i | −0.104221 | + | 0.180516i | ||||
\(131\) | −314.185 | − | 544.184i | −0.209545 | − | 0.362943i | 0.742026 | − | 0.670371i | \(-0.233865\pi\) |
−0.951571 | + | 0.307428i | \(0.900532\pi\) | |||||||
\(132\) | 208.985 | + | 120.936i | 0.137802 | + | 0.0797437i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 2634.03i | − | 1.69810i | ||||||
\(135\) | 1124.78 | + | 1961.74i | 0.717077 | + | 1.25066i | ||||
\(136\) | 603.016 | + | 348.151i | 0.380207 | + | 0.219513i | ||||
\(137\) | 432.079 | + | 249.461i | 0.269453 | + | 0.155569i | 0.628639 | − | 0.777697i | \(-0.283612\pi\) |
−0.359186 | + | 0.933266i | \(0.616946\pi\) | |||||||
\(138\) | −745.199 | − | 0.745029i | −0.459678 | − | 0.000459573i | ||||
\(139\) | 1216.65i | 0.742410i | 0.928551 | + | 0.371205i | \(0.121055\pi\) | ||||
−0.928551 | + | 0.371205i | \(0.878945\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 454.788 | − | 785.900i | 0.271631 | − | 0.469395i | ||||
\(142\) | −162.144 | − | 280.841i | −0.0958226 | − | 0.165970i | ||||
\(143\) | −131.864 | + | 228.395i | −0.0771121 | + | 0.133562i | ||||
\(144\) | −1400.04 | − | 2.79945i | −0.810211 | − | 0.00162005i | ||||
\(145\) | 951.300 | − | 549.233i | 0.544835 | − | 0.314561i | ||||
\(146\) | −583.631 | −0.330833 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −305.022 | −0.169410 | ||||||||
\(149\) | −2010.18 | + | 1160.58i | −1.10524 | + | 0.638111i | −0.937592 | − | 0.347736i | \(-0.886950\pi\) |
−0.167648 | + | 0.985847i | \(0.553617\pi\) | |||||||
\(150\) | 1570.36 | − | 904.555i | 0.854795 | − | 0.492377i | ||||
\(151\) | −488.726 | + | 846.497i | −0.263390 | + | 0.456205i | −0.967141 | − | 0.254242i | \(-0.918174\pi\) |
0.703750 | + | 0.710447i | \(0.251507\pi\) | |||||||
\(152\) | −423.386 | − | 733.326i | −0.225929 | − | 0.391320i | ||||
\(153\) | 389.070 | + | 677.012i | 0.205585 | + | 0.357733i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2879.85i | 1.49235i | ||||||||
\(156\) | −0.0502364 | + | 50.2479i | −2.57829e−5 | + | 0.0257888i | ||||
\(157\) | 143.752 | + | 82.9950i | 0.0730740 | + | 0.0421893i | 0.536092 | − | 0.844160i | \(-0.319900\pi\) |
−0.463018 | + | 0.886349i | \(0.653233\pi\) | |||||||
\(158\) | 2384.86 | + | 1376.90i | 1.20082 | + | 0.693293i | ||||
\(159\) | −1.41397 | + | 1414.29i | −0.000705251 | + | 0.705412i | ||||
\(160\) | − | 942.055i | − | 0.465475i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1629.73 | − | 949.635i | −0.790393 | − | 0.460558i | ||||
\(163\) | −488.511 | − | 846.127i | −0.234743 | − | 0.406587i | 0.724455 | − | 0.689322i | \(-0.242092\pi\) |
−0.959198 | + | 0.282735i | \(0.908758\pi\) | |||||||
\(164\) | 241.528 | − | 418.340i | 0.115001 | − | 0.199188i | ||||
\(165\) | 2583.54 | − | 1488.16i | 1.21896 | − | 0.702142i | ||||
\(166\) | 1346.79 | − | 777.568i | 0.629704 | − | 0.363560i | ||||
\(167\) | −1.00709 | −0.000466651 | −0.000233326 | − | 1.00000i | \(-0.500074\pi\) | ||||
−0.000233326 | 1.00000i | \(0.500074\pi\) | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2142.12 | 0.975019 | ||||||||
\(170\) | 1044.51 | − | 603.048i | 0.471236 | − | 0.272068i | ||||
\(171\) | 1.89874 | − | 949.584i | 0.000849123 | − | 0.424658i | ||||
\(172\) | 122.092 | − | 211.469i | 0.0541245 | − | 0.0937463i | ||||
\(173\) | 1978.27 | + | 3426.47i | 0.869395 | + | 1.50584i | 0.862616 | + | 0.505860i | \(0.168825\pi\) |
0.00677983 | + | 0.999977i | \(0.497842\pi\) | |||||||
\(174\) | −458.923 | + | 793.046i | −0.199948 | + | 0.345521i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1845.93i | 0.790582i | ||||||||
\(177\) | −503.356 | − | 0.503241i | −0.213754 | − | 0.000213706i | ||||
\(178\) | −3372.82 | − | 1947.30i | −1.42024 | − | 0.819978i | ||||
\(179\) | −2423.54 | − | 1399.23i | −1.01198 | − | 0.584266i | −0.100208 | − | 0.994967i | \(-0.531951\pi\) |
−0.911770 | + | 0.410701i | \(0.865284\pi\) | |||||||
\(180\) | 285.014 | − | 491.387i | 0.118020 | − | 0.203477i | ||||
\(181\) | − | 1506.74i | − | 0.618758i | −0.950939 | − | 0.309379i | \(-0.899879\pi\) | ||
0.950939 | − | 0.309379i | \(-0.100121\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1733.90 | − | 1003.38i | −0.700403 | − | 0.405312i | ||||
\(184\) | 667.255 | + | 1155.72i | 0.267341 | + | 0.463048i | ||||
\(185\) | −1883.21 | + | 3261.82i | −0.748414 | + | 1.29629i | ||||
\(186\) | −1199.00 | − | 2081.53i | −0.472660 | − | 0.820565i | ||||
\(187\) | 891.599 | − | 514.765i | 0.348664 | − | 0.201301i | ||||
\(188\) | −228.098 | −0.0884882 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1466.73 | −0.560041 | ||||||||
\(191\) | 3184.51 | − | 1838.58i | 1.20640 | − | 0.696518i | 0.244433 | − | 0.969666i | \(-0.421398\pi\) |
0.961972 | + | 0.273148i | \(0.0880650\pi\) | |||||||
\(192\) | 1468.11 | + | 2548.71i | 0.551830 | + | 0.958009i | ||||
\(193\) | 64.7335 | − | 112.122i | 0.0241431 | − | 0.0418171i | −0.853701 | − | 0.520763i | \(-0.825648\pi\) |
0.877845 | + | 0.478946i | \(0.158981\pi\) | |||||||
\(194\) | −423.640 | − | 733.766i | −0.156781 | − | 0.271553i | ||||
\(195\) | 537.026 | + | 310.769i | 0.197217 | + | 0.114126i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3044.81i | 1.10119i | 0.834774 | + | 0.550593i | \(0.185598\pi\) | ||||
−0.834774 | + | 0.550593i | \(0.814402\pi\) | |||||||
\(198\) | −1247.78 | + | 2151.27i | −0.447856 | + | 0.772140i | ||||
\(199\) | −3458.29 | − | 1996.64i | −1.23192 | − | 0.711248i | −0.264488 | − | 0.964389i | \(-0.585203\pi\) |
−0.967429 | + | 0.253141i | \(0.918536\pi\) | |||||||
\(200\) | −2810.59 | − | 1622.70i | −0.993695 | − | 0.573710i | ||||
\(201\) | −5289.78 | − | 5.28857i | −1.85628 | − | 0.00185586i | ||||
\(202\) | − | 2835.00i | − | 0.987473i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 98.2476 | − | 169.778i | 0.0337191 | − | 0.0582687i | ||||
\(205\) | −2982.40 | − | 5165.67i | −1.01610 | − | 1.75993i | ||||
\(206\) | −268.664 | + | 465.339i | −0.0908674 | + | 0.157387i | ||||
\(207\) | −2.99240 | + | 1496.54i | −0.00100476 | + | 0.502496i | ||||
\(208\) | −332.682 | + | 192.074i | −0.110901 | + | 0.0640285i | ||||
\(209\) | −1252.01 | −0.414370 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4383.67 | −1.43026 | −0.715129 | − | 0.698992i | \(-0.753632\pi\) | ||||
−0.715129 | + | 0.698992i | \(0.753632\pi\) | |||||||
\(212\) | 307.683 | − | 177.641i | 0.0996783 | − | 0.0575493i | ||||
\(213\) | −564.324 | + | 325.061i | −0.181534 | + | 0.104567i | ||||
\(214\) | 2332.27 | − | 4039.60i | 0.745002 | − | 1.29038i | ||||
\(215\) | −1507.59 | − | 2611.23i | −0.478219 | − | 0.828299i | ||||
\(216\) | −10.1313 | + | 3377.85i | −0.00319141 | + | 1.06404i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 733.916i | 0.228014i | ||||||||
\(219\) | −1.17181 | + | 1172.07i | −0.000361568 | + | 0.361650i | ||||
\(220\) | −648.634 | − | 374.489i | −0.198777 | − | 0.114764i | ||||
\(221\) | 185.546 | + | 107.125i | 0.0564759 | + | 0.0326064i | ||||
\(222\) | 3.14096 | − | 3141.68i | 0.000949583 | − | 0.949799i | ||||
\(223\) | 4851.53i | 1.45687i | 0.685114 | + | 0.728436i | \(0.259753\pi\) | ||||
−0.685114 | + | 0.728436i | \(0.740247\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1813.42 | − | 3155.48i | −0.537308 | − | 0.934958i | ||||
\(226\) | −1342.08 | − | 2324.55i | −0.395017 | − | 0.684190i | ||||
\(227\) | 1184.05 | − | 2050.83i | 0.346203 | − | 0.599642i | −0.639368 | − | 0.768901i | \(-0.720804\pi\) |
0.985572 | + | 0.169259i | \(0.0541374\pi\) | |||||||
\(228\) | −206.705 | + | 119.066i | −0.0600410 | + | 0.0345847i | ||||
\(229\) | 3737.27 | − | 2157.72i | 1.07845 | − | 0.622646i | 0.147975 | − | 0.988991i | \(-0.452724\pi\) |
0.930479 | + | 0.366345i | \(0.119391\pi\) | |||||||
\(230\) | 2311.56 | 0.662695 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1640.85 | 0.464340 | ||||||||
\(233\) | −4826.98 | + | 2786.86i | −1.35719 | + | 0.783576i | −0.989245 | − | 0.146270i | \(-0.953273\pi\) |
−0.367949 | + | 0.929846i | \(0.619940\pi\) | |||||||
\(234\) | −517.544 | − | 1.03485i | −0.144585 | − | 0.000289104i | ||||
\(235\) | −1408.28 | + | 2439.22i | −0.390920 | + | 0.677094i | ||||
\(236\) | 63.2237 | + | 109.507i | 0.0174386 | + | 0.0302046i | ||||
\(237\) | 2769.94 | − | 4786.62i | 0.759186 | − | 1.31192i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4683.70i | − | 1.26763i | −0.773485 | − | 0.633814i | \(-0.781488\pi\) | ||
0.773485 | − | 0.633814i | \(-0.218512\pi\) | |||||||
\(240\) | 4342.85 | + | 4.34186i | 1.16804 | + | 0.00116778i | ||||
\(241\) | 1896.77 | + | 1095.10i | 0.506977 | + | 0.292703i | 0.731590 | − | 0.681745i | \(-0.238778\pi\) |
−0.224613 | + | 0.974448i | \(0.572112\pi\) | |||||||
\(242\) | −142.769 | − | 82.4279i | −0.0379238 | − | 0.0218953i | ||||
\(243\) | −1910.37 | + | 3270.99i | −0.504323 | + | 0.863515i | ||||
\(244\) | 503.245i | 0.132037i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4306.34 | + | 2492.01i | 1.11611 | + | 0.645872i | ||||
\(247\) | −130.275 | − | 225.642i | −0.0335594 | − | 0.0581266i | ||||
\(248\) | −2150.90 | + | 3725.47i | −0.550736 | + | 0.953902i | ||||
\(249\) | −1558.84 | − | 2706.24i | −0.396738 | − | 0.688759i | ||||
\(250\) | −353.735 | + | 204.229i | −0.0894887 | + | 0.0516663i | ||||
\(251\) | −2240.70 | −0.563473 | −0.281736 | − | 0.959492i | \(-0.590910\pi\) | ||||
−0.281736 | + | 0.959492i | \(0.590910\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1973.16 | 0.490323 | ||||||||
\(254\) | 3687.86 | − | 2129.19i | 0.911012 | − | 0.525973i | ||||
\(255\) | −1208.97 | − | 2098.84i | −0.296897 | − | 0.515429i | ||||
\(256\) | 974.345 | − | 1687.61i | 0.237877 | − | 0.412015i | ||||
\(257\) | 555.785 | + | 962.648i | 0.134898 | + | 0.233651i | 0.925559 | − | 0.378604i | \(-0.123596\pi\) |
−0.790660 | + | 0.612255i | \(0.790263\pi\) | |||||||
\(258\) | 2176.84 | + | 1259.70i | 0.525287 | + | 0.303975i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 155.866i | − | 0.0371784i | ||||||
\(261\) | 1591.71 | + | 923.223i | 0.377488 | + | 0.218950i | ||||
\(262\) | −1408.03 | − | 812.924i | −0.332016 | − | 0.191689i | ||||
\(263\) | 1782.86 | + | 1029.34i | 0.418007 | + | 0.241337i | 0.694224 | − | 0.719759i | \(-0.255748\pi\) |
−0.276217 | + | 0.961095i | \(0.589081\pi\) | |||||||
\(264\) | 4453.64 | + | 4.45262i | 1.03827 | + | 0.00103803i | ||||
\(265\) | − | 4387.04i | − | 1.01696i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3917.42 | + | 6769.54i | −0.897912 | + | 1.55164i | ||||
\(268\) | 664.420 | + | 1150.81i | 0.151440 | + | 0.262302i | ||||
\(269\) | 2414.62 | − | 4182.24i | 0.547294 | − | 0.947940i | −0.451165 | − | 0.892441i | \(-0.648991\pi\) |
0.998459 | − | 0.0554999i | \(-0.0176752\pi\) | |||||||
\(270\) | 5058.26 | + | 2940.65i | 1.14013 | + | 0.662824i | ||||
\(271\) | 191.772 | − | 110.720i | 0.0429865 | − | 0.0248183i | −0.478353 | − | 0.878168i | \(-0.658766\pi\) |
0.521339 | + | 0.853350i | \(0.325433\pi\) | |||||||
\(272\) | 1499.62 | 0.334293 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1290.91 | 0.284624 | ||||||||
\(275\) | −4155.65 | + | 2399.27i | −0.911255 | + | 0.526113i | ||||
\(276\) | 325.766 | − | 187.647i | 0.0710463 | − | 0.0409240i | ||||
\(277\) | −1233.58 | + | 2136.62i | −0.267576 | + | 0.463455i | −0.968235 | − | 0.250041i | \(-0.919556\pi\) |
0.700660 | + | 0.713496i | \(0.252889\pi\) | |||||||
\(278\) | 1573.99 | + | 2726.22i | 0.339573 | + | 0.588158i | ||||
\(279\) | −4182.63 | + | 2403.70i | −0.897517 | + | 0.515792i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4174.76i | − | 0.886282i | −0.896452 | − | 0.443141i | \(-0.853864\pi\) | ||
0.896452 | − | 0.443141i | \(-0.146136\pi\) | |||||||
\(282\) | 2.34884 | − | 2349.37i | 0.000495997 | − | 0.496111i | ||||
\(283\) | 5628.39 | + | 3249.55i | 1.18224 | + | 0.682565i | 0.956531 | − | 0.291630i | \(-0.0941977\pi\) |
0.225706 | + | 0.974195i | \(0.427531\pi\) | |||||||
\(284\) | 141.681 | + | 81.7998i | 0.0296030 | + | 0.0170913i | ||||
\(285\) | −2.94488 | + | 2945.55i | −0.000612069 | + | 0.612209i | ||||
\(286\) | 682.372i | 0.141082i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1368.22 | − | 786.299i | 0.279942 | − | 0.160879i | ||||
\(289\) | 2038.31 | + | 3530.46i | 0.414881 | + | 0.718595i | ||||
\(290\) | 1421.09 | − | 2461.40i | 0.287756 | − | 0.498408i | ||||
\(291\) | −1474.43 | + | 849.300i | −0.297020 | + | 0.171089i | ||||
\(292\) | 254.989 | − | 147.218i | 0.0511030 | − | 0.0295043i | ||||
\(293\) | −5637.32 | −1.12401 | −0.562007 | − | 0.827133i | \(-0.689970\pi\) | ||||
−0.562007 | + | 0.827133i | \(0.689970\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1561.38 | 0.308159 | ||||||||
\(296\) | −4872.38 | + | 2813.07i | −0.956762 | + | 0.552387i | ||||
\(297\) | 4317.76 | + | 2510.16i | 0.843576 | + | 0.490418i | ||||
\(298\) | −3002.90 | + | 5201.17i | −0.583735 | + | 1.01106i | ||||
\(299\) | 205.312 | + | 355.611i | 0.0397108 | + | 0.0687810i | ||||
\(300\) | −457.922 | + | 791.315i | −0.0881270 | + | 0.152289i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2529.06i | 0.481892i | ||||||||
\(303\) | −5693.37 | − | 5.69207i | −1.07946 | − | 0.00107921i | ||||
\(304\) | −1579.36 | − | 911.841i | −0.297968 | − | 0.172032i | ||||
\(305\) | 5381.56 | + | 3107.05i | 1.01032 | + | 0.583308i | ||||
\(306\) | 1747.67 | + | 1013.68i | 0.326495 | + | 0.189373i | ||||
\(307\) | 3442.95i | 0.640064i | 0.947407 | + | 0.320032i | \(0.103694\pi\) | ||||
−0.947407 | + | 0.320032i | \(0.896306\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 933.976 | + | 540.477i | 0.171948 | + | 0.0995037i | ||||
\(310\) | 3725.67 | + | 6453.05i | 0.682593 | + | 1.18228i | ||||
\(311\) | 75.7324 | − | 131.172i | 0.0138083 | − | 0.0239167i | −0.859039 | − | 0.511911i | \(-0.828938\pi\) |
0.872847 | + | 0.487994i | \(0.162271\pi\) | |||||||
\(312\) | 462.609 | + | 803.116i | 0.0839426 | + | 0.145729i | ||||
\(313\) | −8335.31 | + | 4812.40i | −1.50524 | + | 0.869050i | −0.505257 | + | 0.862969i | \(0.668602\pi\) |
−0.999982 | + | 0.00608123i | \(0.998064\pi\) | |||||||
\(314\) | 429.484 | 0.0771885 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1389.26 | −0.247317 | ||||||||
\(317\) | 7866.93 | − | 4541.98i | 1.39385 | − | 0.804741i | 0.400112 | − | 0.916466i | \(-0.368971\pi\) |
0.993739 | + | 0.111726i | \(0.0356377\pi\) | |||||||
\(318\) | 1826.50 | + | 3170.91i | 0.322092 | + | 0.559170i | ||||
\(319\) | 1213.05 | − | 2101.07i | 0.212909 | − | 0.368768i | ||||
\(320\) | −4561.87 | − | 7901.39i | −0.796926 | − | 1.38032i | ||||
\(321\) | −8107.83 | − | 4691.87i | −1.40977 | − | 0.815809i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1017.12i | 0.175214i | ||||||||
\(324\) | 951.570 | + | 3.80543i | 0.163164 | + | 0.000652509i | ||||
\(325\) | −864.811 | − | 499.299i | −0.147603 | − | 0.0852188i | ||||
\(326\) | −2189.27 | − | 1263.98i | −0.371941 | − | 0.214740i | ||||
\(327\) | 1473.88 | + | 1.47355i | 0.249254 | + | 0.000249197i | ||||
\(328\) | − | 8910.00i | − | 1.49992i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3863.85 | − | 6676.95i | 0.644539 | − | 1.11380i | ||||
\(331\) | 702.788 | + | 1217.26i | 0.116703 | + | 0.202136i | 0.918459 | − | 0.395516i | \(-0.129434\pi\) |
−0.801756 | + | 0.597651i | \(0.796101\pi\) | |||||||
\(332\) | −392.275 | + | 679.440i | −0.0648460 | + | 0.112317i | ||||
\(333\) | −6309.25 | − | 12.6156i | −1.03827 | − | 0.00207607i | ||||
\(334\) | −2.25664 | + | 1.30287i | −0.000369695 | + | 0.000213443i | ||||
\(335\) | 16408.6 | 2.67611 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7983.35 | 1.29045 | 0.645223 | − | 0.763994i | \(-0.276764\pi\) | ||||
0.645223 | + | 0.763994i | \(0.276764\pi\) | |||||||
\(338\) | 4799.97 | − | 2771.27i | 0.772438 | − | 0.445967i | ||||
\(339\) | −4670.97 | + | 2690.56i | −0.748354 | + | 0.431066i | ||||
\(340\) | −304.231 | + | 526.944i | −0.0485272 | + | 0.0840516i | ||||
\(341\) | 3180.25 | + | 5508.36i | 0.505045 | + | 0.874764i | ||||
\(342\) | −1224.23 | − | 2130.25i | −0.193563 | − | 0.336815i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 4503.97i | − | 0.705924i | ||||||
\(345\) | 4.64112 | − | 4642.18i | 0.000724260 | − | 0.724425i | ||||
\(346\) | 8865.68 | + | 5118.60i | 1.37752 | + | 0.795312i | ||||
\(347\) | 2268.41 | + | 1309.67i | 0.350935 | + | 0.202612i | 0.665097 | − | 0.746757i | \(-0.268390\pi\) |
−0.314162 | + | 0.949369i | \(0.601724\pi\) | |||||||
\(348\) | 0.462138 | − | 462.243i | 7.11873e−5 | − | 0.0712036i | ||||
\(349\) | 6032.33i | 0.925224i | 0.886561 | + | 0.462612i | \(0.153088\pi\) | ||||
−0.886561 | + | 0.462612i | \(0.846912\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.11736 | + | 1039.35i | −0.000474052 | + | 0.158053i | ||||
\(352\) | −1040.32 | − | 1801.89i | −0.157527 | − | 0.272845i | ||||
\(353\) | 2658.15 | − | 4604.06i | 0.400791 | − | 0.694190i | −0.593031 | − | 0.805180i | \(-0.702069\pi\) |
0.993822 | + | 0.110990i | \(0.0354020\pi\) | |||||||
\(354\) | −1128.55 | + | 650.066i | −0.169440 | + | 0.0976005i | ||||
\(355\) | 1749.49 | − | 1010.07i | 0.261558 | − | 0.151011i | ||||
\(356\) | 1964.78 | 0.292509 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7240.77 | −1.06896 | ||||||||
\(359\) | 1612.51 | − | 930.982i | 0.237061 | − | 0.136867i | −0.376764 | − | 0.926309i | \(-0.622963\pi\) |
0.613825 | + | 0.789442i | \(0.289630\pi\) | |||||||
\(360\) | 20.9510 | − | 10477.9i | 0.00306727 | − | 1.53398i | ||||
\(361\) | −2811.04 | + | 4868.87i | −0.409832 | + | 0.709851i | ||||
\(362\) | −1949.28 | − | 3376.25i | −0.283016 | − | 0.490198i | ||||
\(363\) | −165.822 | + | 286.550i | −0.0239763 | + | 0.0414325i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3635.70i | − | 0.521373i | ||||||
\(366\) | −5183.34 | − | 5.18215i | −0.740266 | − | 0.000740097i | ||||
\(367\) | 1675.89 | + | 967.574i | 0.238367 | + | 0.137621i | 0.614426 | − | 0.788975i | \(-0.289388\pi\) |
−0.376059 | + | 0.926596i | \(0.622721\pi\) | |||||||
\(368\) | 2489.06 | + | 1437.06i | 0.352585 | + | 0.203565i | ||||
\(369\) | 5013.21 | − | 8643.18i | 0.707255 | − | 1.21937i | ||||
\(370\) | 9745.28i | 1.36928i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1048.90 | + | 606.980i | 0.146190 | + | 0.0845980i | ||||
\(373\) | −3871.04 | − | 6704.83i | −0.537359 | − | 0.930732i | −0.999045 | − | 0.0436892i | \(-0.986089\pi\) |
0.461687 | − | 0.887043i | \(-0.347244\pi\) | |||||||
\(374\) | 1331.91 | − | 2306.93i | 0.184148 | − | 0.318953i | ||||
\(375\) | 409.432 | + | 710.797i | 0.0563812 | + | 0.0978810i | ||||
\(376\) | −3643.61 | + | 2103.64i | −0.499747 | + | 0.288529i | ||||
\(377\) | 504.884 | 0.0689730 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3722.15 | −0.504470 | −0.252235 | − | 0.967666i | \(-0.581166\pi\) | ||||
−0.252235 | + | 0.967666i | \(0.581166\pi\) | |||||||
\(380\) | 640.815 | − | 369.975i | 0.0865082 | − | 0.0499455i | ||||
\(381\) | −4268.53 | − | 7410.41i | −0.573972 | − | 0.996448i | ||||
\(382\) | 4757.15 | − | 8239.63i | 0.637165 | − | 1.10360i | ||||
\(383\) | −3546.73 | − | 6143.12i | −0.473184 | − | 0.819578i | 0.526345 | − | 0.850271i | \(-0.323562\pi\) |
−0.999529 | + | 0.0306926i | \(0.990229\pi\) | |||||||
\(384\) | 4484.08 | + | 2594.87i | 0.595905 | + | 0.344841i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 334.984i | − | 0.0441716i | ||||||
\(387\) | 2534.16 | − | 4369.09i | 0.332864 | − | 0.573885i | ||||
\(388\) | 370.177 | + | 213.722i | 0.0484353 | + | 0.0279641i | ||||
\(389\) | −6173.12 | − | 3564.05i | −0.804601 | − | 0.464537i | 0.0404765 | − | 0.999180i | \(-0.487112\pi\) |
−0.845077 | + | 0.534644i | \(0.820446\pi\) | |||||||
\(390\) | 1605.39 | + | 1.60502i | 0.208441 | + | 0.000208394i | ||||
\(391\) | − | 1602.98i | − | 0.207330i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1635.38 | + | 2826.03i | −0.209908 | + | 0.362733i | ||||
\(394\) | 3939.08 | + | 6822.69i | 0.503675 | + | 0.872391i | ||||
\(395\) | −8577.33 | + | 14856.4i | −1.09259 | + | 1.89242i | ||||
\(396\) | 2.50870 | − | 1254.63i | 0.000318351 | − | 0.159211i | ||||
\(397\) | −7738.99 | + | 4468.11i | −0.978360 | + | 0.564857i | −0.901775 | − | 0.432206i | \(-0.857735\pi\) |
−0.0765855 | + | 0.997063i | \(0.524402\pi\) | |||||||
\(398\) | −10332.3 | −1.30128 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6989.56 | −0.873695 | ||||||||
\(401\) | −7719.60 | + | 4456.91i | −0.961343 | + | 0.555032i | −0.896586 | − | 0.442869i | \(-0.853961\pi\) |
−0.0647568 | + | 0.997901i | \(0.520627\pi\) | |||||||
\(402\) | −11860.0 | + | 6831.56i | −1.47145 | + | 0.847580i | ||||
\(403\) | −661.826 | + | 1146.32i | −0.0818062 | + | 0.141692i | ||||
\(404\) | 715.112 | + | 1238.61i | 0.0880648 | + | 0.152533i | ||||
\(405\) | 5915.71 | − | 10152.3i | 0.725812 | − | 1.24561i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8318.63i | 1.01312i | ||||||||
\(408\) | 3.61727 | − | 3618.09i | 0.000438925 | − | 0.439025i | ||||
\(409\) | 2680.13 | + | 1547.37i | 0.324019 | + | 0.187073i | 0.653183 | − | 0.757200i | \(-0.273433\pi\) |
−0.329163 | + | 0.944273i | \(0.606767\pi\) | |||||||
\(410\) | −13365.7 | − | 7716.69i | −1.60996 | − | 0.929513i | ||||
\(411\) | 2.59188 | − | 2592.47i | 0.000311066 | − | 0.311137i | ||||
\(412\) | − | 271.076i | − | 0.0324149i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1929.38 | + | 3357.26i | 0.229043 | + | 0.398552i | ||||
\(415\) | 4843.82 | + | 8389.74i | 0.572949 | + | 0.992377i | ||||
\(416\) | 216.496 | − | 374.983i | 0.0255159 | − | 0.0441948i | ||||
\(417\) | 5478.09 | − | 3155.48i | 0.643317 | − | 0.370562i | ||||
\(418\) | −2805.45 | + | 1619.73i | −0.328276 | + | 0.189530i | ||||
\(419\) | −7234.25 | −0.843476 | −0.421738 | − | 0.906718i | \(-0.638580\pi\) | ||||
−0.421738 | + | 0.906718i | \(0.638580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 406.124 | 0.0470148 | 0.0235074 | − | 0.999724i | \(-0.492517\pi\) | ||||
0.0235074 | + | 0.999724i | \(0.492517\pi\) | |||||||
\(422\) | −9822.77 | + | 5671.18i | −1.13309 | + | 0.654191i | ||||
\(423\) | −4718.11 | − | 9.43408i | −0.542323 | − | 0.00108440i | ||||
\(424\) | 3276.60 | − | 5675.23i | 0.375296 | − | 0.650032i | ||||
\(425\) | 1949.14 | + | 3376.01i | 0.222464 | + | 0.385319i | ||||
\(426\) | −843.982 | + | 1458.45i | −0.0959885 | + | 0.165874i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2353.21i | 0.265763i | ||||||||
\(429\) | 1370.37 | + | 1.37006i | 0.154224 | + | 0.000154189i | ||||
\(430\) | −6756.31 | − | 3900.76i | −0.757717 | − | 0.437468i | ||||
\(431\) | 10590.4 | + | 6114.37i | 1.18358 | + | 0.683338i | 0.956839 | − | 0.290618i | \(-0.0938609\pi\) |
0.226737 | + | 0.973956i | \(0.427194\pi\) | |||||||
\(432\) | 3618.52 | + | 6311.09i | 0.403000 | + | 0.702876i | ||||
\(433\) | 3252.79i | 0.361014i | 0.983574 | + | 0.180507i | \(0.0577738\pi\) | ||||
−0.983574 | + | 0.180507i | \(0.942226\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4940.24 | − | 2858.84i | −0.544521 | − | 0.315105i | ||||
\(436\) | −185.126 | − | 320.648i | −0.0203348 | − | 0.0352208i | ||||
\(437\) | −974.689 | + | 1688.21i | −0.106695 | + | 0.184801i | ||||
\(438\) | 1513.69 | + | 2627.85i | 0.165130 | + | 0.286675i | ||||
\(439\) | 13036.8 | − | 7526.81i | 1.41734 | − | 0.818303i | 0.421278 | − | 0.906932i | \(-0.361582\pi\) |
0.996065 | + | 0.0886287i | \(0.0282485\pi\) | |||||||
\(440\) | −13814.9 | −1.49682 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 554.353 | 0.0596558 | ||||||||
\(443\) | 204.373 | − | 117.995i | 0.0219189 | − | 0.0126549i | −0.489001 | − | 0.872283i | \(-0.662638\pi\) |
0.510919 | + | 0.859629i | \(0.329305\pi\) | |||||||
\(444\) | 791.098 | + | 1373.39i | 0.0845583 | + | 0.146798i | ||||
\(445\) | 12130.6 | − | 21010.8i | 1.29224 | − | 2.23822i | ||||
\(446\) | 6276.44 | + | 10871.1i | 0.666364 | + | 1.15418i | ||||
\(447\) | 10439.2 | + | 6040.99i | 1.10460 | + | 0.639215i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5874.66i | 0.617466i | 0.951149 | + | 0.308733i | \(0.0999049\pi\) | ||||
−0.951149 | + | 0.308733i | \(0.900095\pi\) | |||||||
\(450\) | −8145.69 | − | 4724.66i | −0.853315 | − | 0.494939i | ||||
\(451\) | −11409.0 | − | 6587.02i | −1.19120 | − | 0.687739i | ||||
\(452\) | 1172.71 | + | 677.066i | 0.122035 | + | 0.0704568i | ||||
\(453\) | 5078.98 | + | 5.07782i | 0.526780 | + | 0.000526660i | ||||
\(454\) | − | 6127.24i | − | 0.633405i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2203.79 | + | 3808.27i | −0.226320 | + | 0.391094i | ||||
\(457\) | −153.883 | − | 266.533i | −0.0157513 | − | 0.0272821i | 0.858042 | − | 0.513579i | \(-0.171681\pi\) |
−0.873794 | + | 0.486297i | \(0.838347\pi\) | |||||||
\(458\) | 5582.89 | − | 9669.85i | 0.569588 | − | 0.986556i | ||||
\(459\) | 2039.23 | − | 3507.71i | 0.207370 | − | 0.356701i | ||||
\(460\) | −1009.92 | + | 583.079i | −0.102365 | + | 0.0591004i | ||||
\(461\) | 4752.26 | 0.480119 | 0.240060 | − | 0.970758i | \(-0.422833\pi\) | ||||
0.240060 | + | 0.970758i | \(0.422833\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9529.43 | −0.956523 | −0.478261 | − | 0.878218i | \(-0.658733\pi\) | ||||
−0.478261 | + | 0.878218i | \(0.658733\pi\) | |||||||
\(464\) | 3060.42 | − | 1766.94i | 0.306199 | − | 0.176784i | ||||
\(465\) | 12966.8 | − | 7469.10i | 1.29316 | − | 0.744884i | ||||
\(466\) | −7210.74 | + | 12489.4i | −0.716805 | + | 1.24154i | ||||
\(467\) | 3269.28 | + | 5662.56i | 0.323949 | + | 0.561097i | 0.981299 | − | 0.192489i | \(-0.0616559\pi\) |
−0.657350 | + | 0.753586i | \(0.728323\pi\) | |||||||
\(468\) | 226.376 | − | 130.096i | 0.0223595 | − | 0.0128497i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7287.61i | 0.715218i | ||||||||
\(471\) | 0.862312 | − | 862.509i | 8.43593e−5 | − | 0.0843786i | ||||
\(472\) | 2019.85 | + | 1166.16i | 0.196973 | + | 0.113723i | ||||
\(473\) | −5767.23 | − | 3329.71i | −0.560629 | − | 0.323679i | ||||
\(474\) | 14.3059 | − | 14309.2i | 0.00138627 | − | 1.38659i | ||||
\(475\) | − | 4740.69i | − | 0.457932i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6371.64 | − | 3661.70i | 0.611609 | − | 0.351484i | ||||
\(478\) | −6059.32 | − | 10495.0i | −0.579805 | − | 1.00425i | ||||
\(479\) | −3671.28 | + | 6358.85i | −0.350199 | + | 0.606562i | −0.986284 | − | 0.165057i | \(-0.947219\pi\) |
0.636085 | + | 0.771619i | \(0.280553\pi\) | |||||||
\(480\) | −4241.69 | + | 2443.29i | −0.403345 | + | 0.232334i | ||||
\(481\) | −1499.22 | + | 865.574i | −0.142117 | + | 0.0820515i | ||||
\(482\) | 5666.94 | 0.535523 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 83.1680 | 0.00781066 | ||||||||
\(485\) | 4570.96 | − | 2639.05i | 0.427952 | − | 0.247078i | ||||
\(486\) | −48.9940 | + | 9800.97i | −0.00457287 | + | 0.914775i | ||||
\(487\) | −3508.78 | + | 6077.39i | −0.326485 | + | 0.565489i | −0.981812 | − | 0.189857i | \(-0.939198\pi\) |
0.655327 | + | 0.755345i | \(0.272531\pi\) | |||||||
\(488\) | 4641.19 | + | 8038.77i | 0.430526 | + | 0.745693i | ||||
\(489\) | −2542.77 | + | 4394.06i | −0.235150 | + | 0.406352i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 224.222i | 0.0206089i | 0.999947 | + | 0.0103045i | \(0.00328007\pi\) | ||||
−0.999947 | + | 0.0103045i | \(0.996720\pi\) | |||||||
\(492\) | −2510.04 | − | 2.50946i | −0.230002 | − | 0.000229950i | ||||
\(493\) | −1706.89 | − | 985.471i | −0.155932 | − | 0.0900272i | ||||
\(494\) | −583.829 | − | 337.074i | −0.0531735 | − | 0.0306997i | ||||
\(495\) | −13401.2 | − | 7772.96i | −1.21685 | − | 0.705795i | ||||
\(496\) | 9264.74i | 0.838708i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6994.07 | − | 4047.36i | −0.629341 | − | 0.364189i | ||||
\(499\) | 10396.1 | + | 18006.6i | 0.932651 | + | 1.61540i | 0.778770 | + | 0.627309i | \(0.215844\pi\) |
0.153881 | + | 0.988089i | \(0.450823\pi\) | |||||||
\(500\) | 103.031 | − | 178.456i | 0.00921540 | − | 0.0159615i | ||||
\(501\) | 2.61196 | + | 4.53451i | 0.000232922 | + | 0.000404365i | ||||
\(502\) | −5020.87 | + | 2898.80i | −0.446399 | + | 0.257729i | ||||
\(503\) | 7341.52 | 0.650780 | 0.325390 | − | 0.945580i | \(-0.394504\pi\) | ||||
0.325390 | + | 0.945580i | \(0.394504\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17660.5 | 1.55620 | ||||||||
\(506\) | 4421.38 | − | 2552.69i | 0.388448 | − | 0.224270i | ||||
\(507\) | −5555.74 | − | 9645.09i | −0.486665 | − | 0.844878i | ||||
\(508\) | −1074.15 | + | 1860.49i | −0.0938146 | + | 0.162492i | ||||
\(509\) | −9956.11 | − | 17244.5i | −0.866988 | − | 1.50167i | −0.865060 | − | 0.501669i | \(-0.832720\pi\) |
−0.00192778 | − | 0.999998i | \(-0.500614\pi\) | |||||||
\(510\) | −5424.29 | − | 3138.95i | −0.470964 | − | 0.272539i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 13018.4i | − | 1.12370i | ||||||
\(513\) | −4280.52 | + | 2454.27i | −0.368400 | + | 0.211225i | ||||
\(514\) | 2490.76 | + | 1438.04i | 0.213741 | + | 0.123403i | ||||
\(515\) | −2898.81 | − | 1673.63i | −0.248032 | − | 0.143202i | ||||
\(516\) | −1268.81 | − | 1.26852i | −0.108249 | − | 0.000108224i | ||||
\(517\) | 6220.75i | 0.529184i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10297.2 | − | 17794.2i | 0.870900 | − | 1.50497i | ||||
\(520\) | −1437.47 | − | 2489.78i | −0.121226 | − | 0.209969i | ||||
\(521\) | −3745.90 | + | 6488.08i | −0.314992 | + | 0.545582i | −0.979436 | − | 0.201756i | \(-0.935335\pi\) |
0.664444 | + | 0.747338i | \(0.268668\pi\) | |||||||
\(522\) | 4761.02 | + | 9.51987i | 0.399203 | + | 0.000798225i | ||||
\(523\) | −249.515 | + | 144.058i | −0.0208614 | + | 0.0120444i | −0.510394 | − | 0.859940i | \(-0.670501\pi\) |
0.489533 | + | 0.871985i | \(0.337167\pi\) | |||||||
\(524\) | 820.223 | 0.0683809 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5326.62 | 0.441543 | ||||||||
\(527\) | 4474.94 | − | 2583.61i | 0.369889 | − | 0.213555i | ||||
\(528\) | 8311.49 | − | 4787.57i | 0.685059 | − | 0.394606i | ||||
\(529\) | −4547.39 | + | 7876.32i | −0.373748 | + | 0.647351i | ||||
\(530\) | −5675.53 | − | 9830.30i | −0.465149 | − | 0.805662i | ||||
\(531\) | 1303.23 | + | 2267.71i | 0.106507 | + | 0.185330i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2741.58i | − | 0.222797i | ||||||
\(534\) | −20.2323 | + | 20236.9i | −0.00163958 | + | 1.63996i | ||||
\(535\) | 25164.5 | + | 14528.7i | 2.03356 | + | 1.17408i | ||||
\(536\) | 21226.7 | + | 12255.2i | 1.71055 | + | 0.987586i | ||||
\(537\) | −14.5379 | + | 14541.2i | −0.00116826 | + | 1.16853i | ||||
\(538\) | − | 12495.2i | − | 1.00131i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2951.72 | − | 8.85317i | −0.235226 | − | 0.000705518i | ||||
\(541\) | −7400.87 | − | 12818.7i | −0.588149 | − | 1.01870i | −0.994475 | − | 0.104975i | \(-0.966524\pi\) |
0.406326 | − | 0.913728i | \(-0.366810\pi\) | |||||||
\(542\) | 286.478 | − | 496.194i | 0.0227034 | − | 0.0393235i | ||||
\(543\) | −6784.24 | + | 3907.85i | −0.536169 | + | 0.308843i | ||||
\(544\) | −1463.84 | + | 845.149i | −0.115371 | + | 0.0666093i | ||||
\(545\) | −4571.90 | −0.359337 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4036.80 | −0.315541 | −0.157771 | − | 0.987476i | \(-0.550431\pi\) | ||||
−0.157771 | + | 0.987476i | \(0.550431\pi\) | |||||||
\(548\) | −564.001 | + | 325.626i | −0.0439652 | + | 0.0253833i | ||||
\(549\) | −20.8141 | + | 10409.4i | −0.00161807 | + | 0.809221i | ||||
\(550\) | −6207.88 | + | 10752.4i | −0.481282 | + | 0.833604i | ||||
\(551\) | 1198.43 | + | 2075.74i | 0.0926585 | + | 0.160489i | ||||
\(552\) | 3473.16 | − | 6001.82i | 0.267803 | − | 0.462780i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6383.53i | 0.489549i | ||||||||
\(555\) | 19570.9 | + | 19.5664i | 1.49683 | + | 0.00149649i | ||||
\(556\) | −1375.35 | − | 794.059i | −0.104906 | − | 0.0605676i | ||||
\(557\) | −14891.1 | − | 8597.36i | −1.13277 | − | 0.654007i | −0.188142 | − | 0.982142i | \(-0.560246\pi\) |
−0.944631 | + | 0.328135i | \(0.893580\pi\) | |||||||
\(558\) | −6262.59 | + | 10797.2i | −0.475119 | + | 0.819143i | ||||
\(559\) | − | 1385.86i | − | 0.104858i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4630.21 | − | 2679.43i | −0.348463 | − | 0.201650i | ||||
\(562\) | −5400.90 | − | 9354.64i | −0.405380 | − | 0.702138i | ||||
\(563\) | 9453.63 | − | 16374.2i | 0.707678 | − | 1.22573i | −0.258038 | − | 0.966135i | \(-0.583076\pi\) |
0.965716 | − | 0.259600i | \(-0.0835907\pi\) | |||||||
\(564\) | 591.591 | + | 1027.04i | 0.0441675 | + | 0.0766773i | ||||
\(565\) | 14480.7 | − | 8360.43i | 1.07824 | − | 0.622524i | ||||
\(566\) | 16815.8 | 1.24880 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3017.60 | 0.222915 | ||||||||
\(569\) | 6255.57 | − | 3611.66i | 0.460891 | − | 0.266096i | −0.251528 | − | 0.967850i | \(-0.580933\pi\) |
0.712419 | + | 0.701754i | \(0.247600\pi\) | |||||||
\(570\) | 3804.07 | + | 6604.09i | 0.279535 | + | 0.485289i | ||||
\(571\) | 4965.17 | − | 8599.93i | 0.363898 | − | 0.630290i | −0.624700 | − | 0.780865i | \(-0.714779\pi\) |
0.988599 | + | 0.150574i | \(0.0481122\pi\) | |||||||
\(572\) | −172.125 | − | 298.129i | −0.0125820 | − | 0.0217926i | ||||
\(573\) | −16537.7 | − | 9570.08i | −1.20571 | − | 0.697724i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7471.31i | 0.541870i | ||||||||
\(576\) | 7668.19 | − | 13220.6i | 0.554701 | − | 0.956349i | ||||
\(577\) | −7254.16 | − | 4188.19i | −0.523388 | − | 0.302178i | 0.214932 | − | 0.976629i | \(-0.431047\pi\) |
−0.738320 | + | 0.674451i | \(0.764380\pi\) | |||||||
\(578\) | 9134.73 | + | 5273.94i | 0.657361 | + | 0.379528i | ||||
\(579\) | −672.730 | − | 0.672576i | −0.0482862 | − | 4.82752e-5i | ||||
\(580\) | 1433.85i | 0.102651i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2205.11 | + | 3810.56i | −0.157053 | + | 0.271397i | ||||
\(583\) | −4844.67 | − | 8391.21i | −0.344161 | − | 0.596104i | ||||
\(584\) | 2715.44 | − | 4703.27i | 0.192407 | − | 0.333258i | ||||
\(585\) | 6.44656 | − | 3224.01i | 0.000455611 | − | 0.227857i | ||||
\(586\) | −12631.9 | + | 7293.03i | −0.890476 | + | 0.514116i | ||||
\(587\) | −21277.2 | −1.49609 | −0.748043 | − | 0.663650i | \(-0.769006\pi\) | ||||
−0.748043 | + | 0.663650i | \(0.769006\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6283.84 | −0.439594 | ||||||||
\(590\) | 3498.67 | − | 2019.96i | 0.244132 | − | 0.140950i | ||||
\(591\) | 13709.5 | − | 7896.94i | 0.954204 | − | 0.549639i | ||||
\(592\) | −6058.48 | + | 10493.6i | −0.420611 | + | 0.728520i | ||||
\(593\) | −1424.49 | − | 2467.29i | −0.0986454 | − | 0.170859i | 0.812479 | − | 0.582991i | \(-0.198118\pi\) |
−0.911124 | + | 0.412132i | \(0.864784\pi\) | |||||||
\(594\) | 12922.5 | + | 38.7587i | 0.892619 | + | 0.00267725i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 3029.86i | − | 0.208235i | ||||||
\(597\) | −20.7450 | + | 20749.7i | −0.00142217 | + | 1.42249i | ||||
\(598\) | 920.111 | + | 531.227i | 0.0629200 | + | 0.0363269i | ||||
\(599\) | −3844.40 | − | 2219.57i | −0.262234 | − | 0.151401i | 0.363119 | − | 0.931743i | \(-0.381712\pi\) |
−0.625353 | + | 0.780342i | \(0.715045\pi\) | |||||||
\(600\) | −16.8597 | + | 16863.5i | −0.00114716 | + | 1.14742i | ||||
\(601\) | − | 7868.29i | − | 0.534033i | −0.963692 | − | 0.267017i | \(-0.913962\pi\) | ||
0.963692 | − | 0.267017i | \(-0.0860379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13695.6 | + | 23831.4i | 0.924924 | + | 1.60944i | ||||
\(604\) | −637.943 | − | 1104.95i | −0.0429761 | − | 0.0744367i | ||||
\(605\) | 513.480 | − | 889.374i | 0.0345057 | − | 0.0597656i | ||||
\(606\) | −12764.8 | + | 7352.78i | −0.855670 | + | 0.492881i | ||||
\(607\) | 15144.9 | − | 8743.92i | 1.01271 | − | 0.584686i | 0.100724 | − | 0.994914i | \(-0.467884\pi\) |
0.911983 | + | 0.410228i | \(0.134551\pi\) | |||||||
\(608\) | 2055.57 | 0.137112 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16078.4 | 1.06720 | ||||||||
\(611\) | −1121.13 | + | 647.284i | −0.0742324 | + | 0.0428581i | ||||
\(612\) | −1019.25 | − | 2.03804i | −0.0673216 | − | 0.000134613i | ||||
\(613\) | −6422.07 | + | 11123.3i | −0.423140 | + | 0.732900i | −0.996245 | − | 0.0865820i | \(-0.972406\pi\) |
0.573105 | + | 0.819482i | \(0.305739\pi\) | |||||||
\(614\) | 4454.16 | + | 7714.83i | 0.292761 | + | 0.507077i | ||||
\(615\) | −15523.8 | + | 26826.1i | −1.01786 | + | 1.75892i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 23625.5i | − | 1.54153i | −0.637117 | − | 0.770767i | \(-0.719873\pi\) | ||
0.637117 | − | 0.770767i | \(-0.280127\pi\) | |||||||
\(618\) | 2792.03 | + | 2.79140i | 0.181735 | + | 0.000181693i | ||||
\(619\) | −16529.1 | − | 9543.05i | −1.07328 | − | 0.619657i | −0.144202 | − | 0.989548i | \(-0.546062\pi\) |
−0.929075 | + | 0.369891i | \(0.879395\pi\) | |||||||
\(620\) | −3255.49 | − | 1879.56i | −0.210877 | − | 0.121750i | ||||
\(621\) | 6746.08 | − | 3867.92i | 0.435927 | − | 0.249942i | ||||
\(622\) | − | 391.901i | − | 0.0252633i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1727.67 | + | 999.772i | 0.110836 | + | 0.0641393i | ||||
\(625\) | 7152.40 | + | 12388.3i | 0.457754 | + | 0.792853i | ||||
\(626\) | −12451.6 | + | 21566.9i | −0.794996 | + | 1.37697i | ||||
\(627\) | 3247.18 | + | 5637.29i | 0.206826 | + | 0.359062i | ||||
\(628\) | −187.642 | + | 108.335i | −0.0119231 | + | 0.00688382i | ||||
\(629\) | 6757.98 | 0.428391 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.3893 | 0.00204342 | 0.00102171 | − | 0.999999i | \(-0.499675\pi\) | ||||
0.00102171 | + | 0.999999i | \(0.499675\pi\) | |||||||
\(632\) | −22191.9 | + | 12812.5i | −1.39675 | + | 0.806414i | ||||
\(633\) | 11369.4 | + | 19737.9i | 0.713891 | + | 1.23935i | ||||
\(634\) | 11751.9 | − | 20355.0i | 0.736166 | − | 1.27508i | ||||
\(635\) | 13263.7 | + | 22973.4i | 0.828902 | + | 1.43570i | ||||
\(636\) | −1597.85 | − | 924.648i | −0.0996207 | − | 0.0576489i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 6277.32i | − | 0.389532i | ||||||
\(639\) | 2927.23 | + | 1697.85i | 0.181220 | + | 0.105111i | ||||
\(640\) | −13917.4 | − | 8035.20i | −0.859583 | − | 0.496280i | ||||
\(641\) | 18742.7 | + | 10821.1i | 1.15490 | + | 0.666784i | 0.950078 | − | 0.312014i | \(-0.101004\pi\) |
0.204827 | + | 0.978798i | \(0.434337\pi\) | |||||||
\(642\) | −24237.6 | − | 24.2321i | −1.49000 | − | 0.00148966i | ||||
\(643\) | − | 19867.3i | − | 1.21849i | −0.792982 | − | 0.609246i | \(-0.791472\pi\) | ||
0.792982 | − | 0.609246i | \(-0.208528\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7847.24 | + | 13560.5i | −0.479046 | + | 0.827820i | ||||
\(646\) | 1315.85 | + | 2279.12i | 0.0801417 | + | 0.138809i | ||||
\(647\) | 11212.2 | − | 19420.1i | 0.681294 | − | 1.18004i | −0.293293 | − | 0.956023i | \(-0.594751\pi\) |
0.974586 | − | 0.224012i | \(-0.0719156\pi\) | |||||||
\(648\) | 15235.4 | − | 8715.08i | 0.923613 | − | 0.528335i | ||||
\(649\) | 2986.49 | − | 1724.25i | 0.180632 | − | 0.104288i | ||||
\(650\) | −2583.78 | −0.155914 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1275.33 | 0.0766038 | ||||||||
\(653\) | −17358.5 | + | 10021.9i | −1.04026 | + | 0.600594i | −0.919907 | − | 0.392137i | \(-0.871736\pi\) |
−0.120353 | + | 0.992731i | \(0.538403\pi\) | |||||||
\(654\) | 3304.53 | − | 1903.47i | 0.197580 | − | 0.113810i | ||||
\(655\) | 5064.07 | − | 8771.22i | 0.302091 | − | 0.523237i | ||||
\(656\) | −9594.67 | − | 16618.5i | −0.571050 | − | 0.989088i | ||||
\(657\) | 5280.41 | − | 3034.59i | 0.313559 | − | 0.180199i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 13217.9i | − | 0.781327i | −0.920533 | − | 0.390664i | \(-0.872246\pi\) | ||
0.920533 | − | 0.390664i | \(-0.127754\pi\) | |||||||
\(660\) | −3.89091 | + | 3891.80i | −0.000229475 | + | 0.229527i | ||||
\(661\) | −8470.90 | − | 4890.68i | −0.498457 | − | 0.287784i | 0.229619 | − | 0.973281i | \(-0.426252\pi\) |
−0.728076 | + | 0.685496i | \(0.759585\pi\) | |||||||
\(662\) | 3149.56 | + | 1818.40i | 0.184911 | + | 0.106758i | ||||
\(663\) | 1.11302 | − | 1113.28i | 6.51979e−5 | − | 0.0652128i | ||||
\(664\) | 14471.0i | 0.845761i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14153.8 | + | 8134.03i | −0.823499 | + | 0.473254i | ||||
\(667\) | −1888.72 | − | 3271.36i | −0.109642 | − | 0.189906i | ||||
\(668\) | 0.657286 | − | 1.13845i | 3.80706e−5 | − | 6.59402e-5i | ||||
\(669\) | 21844.5 | − | 12582.8i | 1.26242 | − | 0.727174i | ||||
\(670\) | 36767.7 | − | 21227.8i | 2.12009 | − | 1.22403i | ||||
\(671\) | 13724.6 | 0.789617 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4670.73 | −0.267524 | −0.133762 | − | 0.991014i | \(-0.542706\pi\) | ||||
−0.133762 | + | 0.991014i | \(0.542706\pi\) | |||||||
\(674\) | 17888.8 | − | 10328.1i | 1.02233 | − | 0.590242i | ||||
\(675\) | −9504.63 | + | 16349.1i | −0.541975 | + | 0.932260i | ||||
\(676\) | −1398.07 | + | 2421.53i | −0.0795445 | + | 0.137775i | ||||
\(677\) | −13521.0 | − | 23419.1i | −0.767584 | − | 1.32949i | −0.938870 | − | 0.344273i | \(-0.888125\pi\) |
0.171286 | − | 0.985221i | \(-0.445208\pi\) | |||||||
\(678\) | −6985.73 | + | 12071.8i | −0.395701 | + | 0.683795i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 11223.1i | 0.632921i | ||||||||
\(681\) | −12305.0 | − | 12.3022i | −0.692406 | − | 0.000692248i | ||||
\(682\) | 14252.4 | + | 8228.61i | 0.800222 | + | 0.462009i | ||||
\(683\) | −11596.9 | − | 6695.45i | −0.649694 | − | 0.375101i | 0.138645 | − | 0.990342i | \(-0.455725\pi\) |
−0.788339 | + | 0.615241i | \(0.789059\pi\) | |||||||
\(684\) | 1072.21 | + | 621.902i | 0.0599370 | + | 0.0347646i | ||||
\(685\) | 8041.69i | 0.448551i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19408.2 | − | 11231.2i | −1.07783 | − | 0.623724i | ||||
\(688\) | −4850.07 | − | 8400.57i | −0.268761 | − | 0.465507i | ||||
\(689\) | 1008.20 | − | 1746.25i | 0.0557464 | − | 0.0965557i | ||||
\(690\) | −5995.21 | − | 10408.0i | −0.330773 | − | 0.574241i | ||||
\(691\) | −26837.3 | + | 15494.6i | −1.47748 | + | 0.853025i | −0.999676 | − | 0.0254396i | \(-0.991901\pi\) |
−0.477807 | + | 0.878465i | \(0.658568\pi\) | |||||||
\(692\) | −5164.56 | −0.283710 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6777.28 | 0.370694 | ||||||||
\(695\) | −16982.9 | + | 9805.07i | −0.926903 | + | 0.535147i | ||||
\(696\) | −4255.66 | − | 7388.07i | −0.231768 | − | 0.402362i | ||||
\(697\) | −5351.23 | + | 9268.60i | −0.290807 | + | 0.503692i | ||||
\(698\) | 7804.05 | + | 13517.0i | 0.423191 | + | 0.732989i | ||||
\(699\) | 25067.3 | + | 14506.0i | 1.35641 | + | 0.784933i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2892.67i | − | 0.155855i | −0.996959 | − | 0.0779277i | \(-0.975170\pi\) | ||
0.996959 | − | 0.0779277i | \(-0.0248303\pi\) | |||||||
\(702\) | 1337.63 | + | 2332.97i | 0.0719168 | + | 0.125431i | ||||
\(703\) | −7117.31 | − | 4109.18i | −0.381841 | − | 0.220456i | ||||
\(704\) | −17451.2 | − | 10075.5i | −0.934259 | − | 0.539395i | ||||
\(705\) | 14635.3 | + | 14.6320i | 0.781841 | + | 0.000781662i | ||||
\(706\) | − | 13755.5i | − | 0.733277i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 329.089 | − | 568.685i | 0.0174688 | − | 0.0301871i | ||||
\(709\) | −7965.19 | − | 13796.1i | −0.421917 | − | 0.730781i | 0.574210 | − | 0.818708i | \(-0.305309\pi\) |
−0.996127 | + | 0.0879267i | \(0.971976\pi\) | |||||||
\(710\) | 2613.46 | − | 4526.64i | 0.138143 | − | 0.239270i | ||||
\(711\) | −28736.3 | − | 57.4595i | −1.51574 | − | 0.00303080i | ||||
\(712\) | 31385.2 | − | 18120.2i | 1.65198 | − | 0.953770i | ||||
\(713\) | 9903.30 | 0.520171 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4250.81 | −0.222337 | ||||||||
\(716\) | 3163.50 | − | 1826.45i | 0.165119 | − | 0.0953317i | ||||
\(717\) | −21088.8 | + | 12147.5i | −1.09843 | + | 0.632716i | ||||
\(718\) | 2408.83 | − | 4172.22i | 0.125204 | − | 0.216860i | ||||
\(719\) | −5938.87 | − | 10286.4i | −0.308042 | − | 0.533545i | 0.669892 | − | 0.742459i | \(-0.266341\pi\) |
−0.977934 | + | 0.208914i | \(0.933007\pi\) | |||||||
\(720\) | −11244.0 | − | 19565.4i | −0.581997 | − | 1.01272i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 14546.6i | 0.749819i | ||||||||
\(723\) | 11.3780 | − | 11380.6i | 0.000585273 | − | 0.585407i | ||||
\(724\) | 1703.28 | + | 983.389i | 0.0874336 | + | 0.0504798i | ||||
\(725\) | 7955.61 | + | 4593.18i | 0.407537 | + | 0.235291i | ||||
\(726\) | −0.856420 | + | 856.615i | −4.37806e−5 | + | 0.0437906i | ||||
\(727\) | 16795.8i | 0.856839i | 0.903580 | + | 0.428419i | \(0.140929\pi\) | ||||
−0.903580 | + | 0.428419i | \(0.859071\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19682.6 | + | 118.070i | 0.999982 | + | 0.00599859i | ||||
\(730\) | −4703.52 | − | 8146.74i | −0.238473 | − | 0.413047i | ||||
\(731\) | −2705.03 | + | 4685.24i | −0.136866 | + | 0.237059i | ||||
\(732\) | 2265.91 | − | 1305.20i | 0.114413 | − | 0.0659040i | ||||
\(733\) | −22048.4 | + | 12729.7i | −1.11102 | + | 0.641447i | −0.939093 | − | 0.343663i | \(-0.888332\pi\) |
−0.171926 | + | 0.985110i | \(0.554999\pi\) | |||||||
\(734\) | 5007.02 | 0.251788 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3239.57 | −0.162245 | ||||||||
\(737\) | 31385.1 | − | 18120.2i | 1.56864 | − | 0.905653i | ||||
\(738\) | 51.6941 | − | 25852.9i | 0.00257843 | − | 1.28951i | ||||
\(739\) | 9319.48 | − | 16141.8i | 0.463901 | − | 0.803499i | −0.535251 | − | 0.844693i | \(-0.679783\pi\) |
0.999151 | + | 0.0411940i | \(0.0131162\pi\) | |||||||
\(740\) | −2458.19 | − | 4257.72i | −0.122115 | − | 0.211509i | ||||
\(741\) | −678.099 | + | 1171.79i | −0.0336175 | + | 0.0580930i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14043.3i | 0.693401i | 0.937976 | + | 0.346700i | \(0.112698\pi\) | ||||
−0.937976 | + | 0.346700i | \(0.887302\pi\) | |||||||
\(744\) | 22352.8 | + | 22.3477i | 1.10147 | + | 0.00110122i | ||||
\(745\) | −32400.4 | − | 18706.4i | −1.59337 | − | 0.919932i | ||||
\(746\) | −17348.1 | − | 10016.0i | −0.851422 | − | 0.491569i | ||||
\(747\) | −8142.12 | + | 14037.7i | −0.398802 | + | 0.687566i | ||||
\(748\) | 1343.87i | 0.0656907i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1837.00 | + | 1063.04i | 0.0894370 | + | 0.0517557i | ||||
\(751\) | −8115.13 | − | 14055.8i | −0.394308 | − | 0.682961i | 0.598705 | − | 0.800970i | \(-0.295682\pi\) |
−0.993013 | + | 0.118009i | \(0.962349\pi\) | |||||||
\(752\) | −4530.58 | + | 7847.20i | −0.219699 | + | 0.380529i | ||||
\(753\) | 5811.43 | + | 10089.0i | 0.281248 | + | 0.488263i | ||||
\(754\) | 1131.32 | − | 653.170i | 0.0546424 | − | 0.0315478i | ||||
\(755\) | −15754.7 | −0.759433 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33345.7 | −1.60102 | −0.800508 | − | 0.599322i | \(-0.795437\pi\) | ||||
−0.800508 | + | 0.599322i | \(0.795437\pi\) | |||||||
\(758\) | −8340.45 | + | 4815.36i | −0.399655 | + | 0.230741i | ||||
\(759\) | −5117.55 | − | 8884.35i | −0.244737 | − | 0.424877i | ||||
\(760\) | 6824.19 | − | 11819.9i | 0.325710 | − | 0.564146i | ||||
\(761\) | 5394.02 | + | 9342.71i | 0.256942 | + | 0.445037i | 0.965421 | − | 0.260695i | \(-0.0839517\pi\) |
−0.708479 | + | 0.705732i | \(0.750618\pi\) | |||||||
\(762\) | −19151.6 | − | 11082.7i | −0.910486 | − | 0.526884i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4799.87i | 0.227295i | ||||||||
\(765\) | −6314.68 | + | 10887.0i | −0.298441 | + | 0.514537i | ||||
\(766\) | −15894.7 | − | 9176.84i | −0.749740 | − | 0.432862i | ||||
\(767\) | 621.503 | + | 358.825i | 0.0292584 | + | 0.0168923i | ||||
\(768\) | −10125.7 | − | 10.1234i | −0.475754 | − | 0.000475646i | ||||
\(769\) | − | 35799.6i | − | 1.67876i | −0.543543 | − | 0.839381i | \(-0.682918\pi\) | ||
0.543543 | − | 0.839381i | \(-0.317082\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2892.94 | − | 4999.17i | 0.135132 | − | 0.233516i | ||||
\(772\) | 84.4979 | + | 146.355i | 0.00393931 | + | 0.00682308i | ||||
\(773\) | −18306.3 | + | 31707.5i | −0.851788 | + | 1.47534i | 0.0278053 | + | 0.999613i | \(0.491148\pi\) |
−0.879593 | + | 0.475727i | \(0.842185\pi\) | |||||||
\(774\) | 26.1312 | − | 13068.5i | 0.00121352 | − | 0.606898i | ||||
\(775\) | −20857.2 | + | 12041.9i | −0.966727 | + | 0.558140i | ||||
\(776\) | 7884.22 | 0.364725 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18443.3 | −0.849904 | ||||||||
\(779\) | 11271.5 | − | 6507.62i | 0.518414 | − | 0.299306i | ||||
\(780\) | −701.801 | + | 404.250i | −0.0322160 | + | 0.0185570i | ||||
\(781\) | 2230.86 | − | 3863.97i | 0.102211 | − | 0.177034i | ||||
\(782\) | −2073.78 | − | 3591.89i | −0.0948314 | − | 0.164253i | ||||
\(783\) | 28.6773 | − | 9561.27i | 0.00130887 | − | 0.436388i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2675.45i | 0.121644i | ||||||||
\(786\) | −8.44622 | + | 8448.15i | −0.000383291 | + | 0.383378i | ||||
\(787\) | 34874.9 | + | 20135.0i | 1.57961 | + | 0.911990i | 0.994913 | + | 0.100742i | \(0.0321216\pi\) |
0.584701 | + | 0.811249i | \(0.301212\pi\) | |||||||
\(788\) | −3441.97 | − | 1987.22i | −0.155603 | − | 0.0898374i | ||||
\(789\) | 10.6947 | − | 10697.2i | 0.000482563 | − | 0.482673i | ||||
\(790\) | 44386.1i | 1.99897i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −11530.8 | − | 20064.5i | −0.517335 | − | 0.900203i | ||||
\(793\) | 1428.08 | + | 2473.51i | 0.0639503 | + | 0.110765i | ||||
\(794\) | −11560.8 | + | 20023.9i | −0.516723 | + | 0.894991i | ||||
\(795\) | −19753.1 | + | 11378.1i | −0.881219 | + | 0.507598i | ||||
\(796\) | 4514.17 | − | 2606.26i | 0.201006 | − | 0.116051i | ||||
\(797\) | −11444.6 | −0.508645 | −0.254323 | − | 0.967119i | \(-0.581852\pi\) | ||||
−0.254323 | + | 0.967119i | \(0.581852\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5053.68 | 0.223762 | ||||||||
\(800\) | 6822.81 | − | 3939.15i | 0.301528 | − | 0.174087i | ||||
\(801\) | 40640.6 | + | 81.2628i | 1.79272 | + | 0.00358462i | ||||
\(802\) | −11531.9 | + | 19973.8i | −0.507736 | + | 0.879424i | ||||
\(803\) | −4014.95 | − | 6954.10i | −0.176444 | − | 0.305610i | ||||
\(804\) | 3458.40 | − | 5976.32i | 0.151702 | − | 0.262150i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3424.83i | 0.149670i | ||||||||
\(807\) | −25093.5 | − | 25.0877i | −1.09459 | − | 0.00109434i | ||||
\(808\) | 22846.2 | + | 13190.3i | 0.994712 | + | 0.574297i | ||||
\(809\) | 2702.86 | + | 1560.50i | 0.117463 | + | 0.0678172i | 0.557580 | − | 0.830123i | \(-0.311730\pi\) |
−0.440117 | + | 0.897940i | \(0.645063\pi\) | |||||||
\(810\) | 121.581 | − | 30402.1i | 0.00527399 | − | 1.31879i | ||||
\(811\) | − | 3571.23i | − | 0.154628i | −0.997007 | − | 0.0773138i | \(-0.975366\pi\) | ||
0.997007 | − | 0.0773138i | \(-0.0246343\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −995.903 | − | 576.313i | −0.0429617 | − | 0.0248612i | ||||
\(814\) | 10761.8 | + | 18640.1i | 0.463394 | + | 0.802622i | ||||
\(815\) | 7873.89 | − | 13638.0i | 0.338418 | − | 0.586157i | ||||
\(816\) | −3889.37 | − | 6752.17i | −0.166857 | − | 0.289673i | ||||
\(817\) | 5697.71 | − | 3289.58i | 0.243987 | − | 0.140866i | ||||
\(818\) | 8007.37 | 0.342263 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7785.98 | 0.331583 | ||||||||
\(821\) | −24420.3 | + | 14099.1i | −1.03809 | + | 0.599344i | −0.919293 | − | 0.393574i | \(-0.871238\pi\) |
−0.118801 | + | 0.992918i | \(0.537905\pi\) | |||||||
\(822\) | −3348.08 | − | 5812.47i | −0.142066 | − | 0.246634i | ||||
\(823\) | 5700.86 | − | 9874.18i | 0.241457 | − | 0.418217i | −0.719672 | − | 0.694314i | \(-0.755708\pi\) |
0.961130 | + | 0.276097i | \(0.0890412\pi\) | |||||||
\(824\) | −2500.00 | − | 4330.13i | −0.105694 | − | 0.183067i | ||||
\(825\) | 21580.9 | + | 12488.5i | 0.910729 | + | 0.527024i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18948.2i | 0.796726i | 0.917228 | + | 0.398363i | \(0.130422\pi\) | ||||
−0.917228 | + | 0.398363i | \(0.869578\pi\) | |||||||
\(828\) | −1689.80 | − | 980.115i | −0.0709233 | − | 0.0411369i | ||||
\(829\) | −663.246 | − | 382.925i | −0.0277871 | − | 0.0160429i | 0.486042 | − | 0.873935i | \(-0.338440\pi\) |
−0.513829 | + | 0.857893i | \(0.671773\pi\) | |||||||
\(830\) | 21707.7 | + | 12532.9i | 0.907813 | + | 0.524126i | ||||
\(831\) | 12819.7 | + | 12.8168i | 0.535151 | + | 0.000535029i | ||||
\(832\) | − | 4193.51i | − | 0.174740i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8192.83 | − | 14157.7i | 0.340161 | − | 0.587819i | ||||
\(835\) | −8.11618 | − | 14.0576i | −0.000336374 | − | 0.000582617i | ||||
\(836\) | 817.136 | − | 1415.32i | 0.0338053 | − | 0.0585525i | ||||
\(837\) | 21670.9 | + | 12598.5i | 0.894928 | + | 0.520272i | ||||
\(838\) | −16210.2 | + | 9358.98i | −0.668225 | + | 0.385800i | ||||
\(839\) | −5355.68 | −0.220380 | −0.110190 | − | 0.993911i | \(-0.535146\pi\) | ||||
−0.110190 | + | 0.993911i | \(0.535146\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19744.4 | 0.809564 | ||||||||
\(842\) | 910.026 | − | 525.404i | 0.0372465 | − | 0.0215043i | ||||
\(843\) | −18797.3 | + | 10827.6i | −0.767986 | + | 0.442374i | ||||
\(844\) | 2861.05 | − | 4955.48i | 0.116684 | − | 0.202103i | ||||
\(845\) | 17263.5 | + | 29901.2i | 0.702818 | + | 1.21732i | ||||
\(846\) | −10584.4 | + | 6082.70i | −0.430140 | + | 0.247196i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 14113.5i | − | 0.571533i | ||||||
\(849\) | 33.7626 | − | 33770.3i | 0.00136482 | − | 1.36513i | ||||
\(850\) | 8735.11 | + | 5043.22i | 0.352485 | + | 0.203507i | ||||
\(851\) | 11216.8 | + | 6476.05i | 0.451832 | + | 0.260865i | ||||
\(852\) | 0.849894 | − | 850.088i | 3.41748e−5 | − | 0.0341826i | ||||
\(853\) | 8591.74i | 0.344872i | 0.985021 | + | 0.172436i | \(0.0551638\pi\) | ||||
−0.985021 | + | 0.172436i | \(0.944836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13270.3 | − | 7626.26i | 0.530800 | − | 0.305044i | ||||
\(856\) | 21702.5 | + | 37589.8i | 0.866560 | + | 1.50093i | ||||
\(857\) | 20273.3 | − | 35114.5i | 0.808080 | − | 1.39964i | −0.106112 | − | 0.994354i | \(-0.533840\pi\) |
0.914192 | − | 0.405281i | \(-0.132826\pi\) | |||||||
\(858\) | 3072.45 | − | 1769.78i | 0.122251 | − | 0.0704189i | ||||
\(859\) | 8352.92 | − | 4822.56i | 0.331779 | − | 0.191553i | −0.324852 | − | 0.945765i | \(-0.605314\pi\) |
0.656631 | + | 0.754212i | \(0.271981\pi\) | |||||||
\(860\) | 3935.78 | 0.156057 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 31640.7 | 1.25022 | ||||||||
\(863\) | 9951.19 | − | 5745.32i | 0.392517 | − | 0.226620i | −0.290733 | − | 0.956804i | \(-0.593899\pi\) |
0.683250 | + | 0.730184i | \(0.260566\pi\) | |||||||
\(864\) | −7088.97 | − | 4121.22i | −0.279134 | − | 0.162276i | ||||
\(865\) | −31886.1 | + | 55228.3i | −1.25336 | + | 2.17089i | ||||
\(866\) | 4208.14 | + | 7288.72i | 0.165125 | + | 0.286006i | ||||
\(867\) | 10609.7 | − | 18334.2i | 0.415599 | − | 0.718180i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37888.3i | 1.47902i | ||||||||
\(870\) | −14768.4 | − | 14.7650i | −0.575512 | − | 0.000575381i | ||||
\(871\) | 6531.39 | + | 3770.90i | 0.254085 | + | 0.146696i | ||||
\(872\) | −5914.37 | − | 3414.66i | −0.229686 | − | 0.132609i | ||||
\(873\) | 7648.11 | + | 4436.05i | 0.296506 | + | 0.171979i | ||||
\(874\) | 5043.84i | 0.195206i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1324.19 | − | 766.290i | −0.0510735 | − | 0.0295554i | ||||
\(877\) | 14714.7 | + | 25486.6i | 0.566568 | + | 0.981324i | 0.996902 | + | 0.0786543i | \(0.0250623\pi\) |
−0.430334 | + | 0.902670i | \(0.641604\pi\) | |||||||
\(878\) | 19474.9 | − | 33731.6i | 0.748573 | − | 1.29657i | ||||
\(879\) | 14620.8 | + | 25382.6i | 0.561033 | + | 0.973986i | ||||
\(880\) | −25766.8 | + | 14876.5i | −0.987046 | + | 0.569871i | ||||
\(881\) | −22330.5 | −0.853956 | −0.426978 | − | 0.904262i | \(-0.640422\pi\) | ||||
−0.426978 | + | 0.904262i | \(0.640422\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15519.2 | 0.591463 | 0.295732 | − | 0.955271i | \(-0.404437\pi\) | ||||
0.295732 | + | 0.955271i | \(0.404437\pi\) | |||||||
\(884\) | −242.197 | + | 139.832i | −0.00921489 | + | 0.00532022i | ||||
\(885\) | −4049.55 | − | 7030.25i | −0.153813 | − | 0.267027i | ||||
\(886\) | 305.301 | − | 528.797i | 0.0115765 | − | 0.0200511i | ||||
\(887\) | 19107.9 | + | 33095.9i | 0.723316 | + | 1.25282i | 0.959663 | + | 0.281152i | \(0.0907165\pi\) |
−0.236347 | + | 0.971669i | \(0.575950\pi\) | |||||||
\(888\) | 25303.0 | + | 14642.5i | 0.956209 | + | 0.553343i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 62773.6i | − | 2.36424i | ||||||
\(891\) | 103.783 | − | 25951.4i | 0.00390218 | − | 0.975764i | ||||
\(892\) | −5484.36 | − | 3166.40i | −0.205863 | − | 0.118855i | ||||
\(893\) | −5322.39 | − | 3072.88i | −0.199448 | − | 0.115151i | ||||
\(894\) | 31207.0 | + | 31.1999i | 1.16747 | + | 0.00116720i | ||||
\(895\) | − | 45106.0i | − | 1.68461i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1068.68 | − | 1846.74i | 0.0397795 | − | 0.0687413i | ||||
\(898\) | 7600.07 | + | 13163.7i | 0.282425 | + | 0.489174i | ||||
\(899\) | 6088.31 | − | 10545.3i | 0.225869 | − | 0.391217i | ||||
\(900\) | 4750.63 | + | 9.49910i | 0.175949 | + | 0.000351818i | ||||
\(901\) | −6816.94 | + | 3935.76i | −0.252059 | + | 0.145526i | ||||
\(902\) | −34086.6 | −1.25827 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24977.0 | 0.918941 | ||||||||
\(905\) | 21032.2 | − | 12142.9i | 0.772522 | − | 0.446016i | ||||
\(906\) | 11387.4 | − | 6559.32i | 0.417571 | − | 0.240529i | ||||
\(907\) | 4432.30 | − | 7676.97i | 0.162262 | − | 0.281047i | −0.773417 | − | 0.633897i | \(-0.781454\pi\) |
0.935680 | + | 0.352850i | \(0.114788\pi\) | |||||||
\(908\) | 1545.56 | + | 2677.00i | 0.0564883 | + | 0.0978405i | ||||
\(909\) | 14740.5 | + | 25649.7i | 0.537858 | + | 0.935915i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 15145.0i | − | 0.550798i | −0.961330 | − | 0.275399i | \(-0.911190\pi\) | ||
0.961330 | − | 0.275399i | \(-0.0888100\pi\) | |||||||
\(912\) | −9.47397 | + | 9476.13i | −0.000343985 | + | 0.344064i | ||||
\(913\) | 18529.8 | + | 10698.2i | 0.671684 | + | 0.387797i | ||||
\(914\) | −689.630 | − | 398.158i | −0.0249573 | − | 0.0144091i | ||||
\(915\) | 32.2820 | − | 32289.3i | 0.00116635 | − | 1.16662i | ||||
\(916\) | 5633.02i | 0.203188i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 31.4872 | − | 10498.1i | 0.00113206 | − | 0.377439i | ||||
\(919\) | 2244.07 | + | 3886.84i | 0.0805495 | + | 0.139516i | 0.903486 | − | 0.428617i | \(-0.140999\pi\) |
−0.822937 | + | 0.568133i | \(0.807666\pi\) | |||||||
\(920\) | −10754.9 | + | 18628.0i | −0.385412 | + | 0.667552i | ||||
\(921\) | 15502.2 | − | 8929.55i | 0.554631 | − | 0.319477i | ||||
\(922\) | 10648.7 | − | 6148.02i | 0.380364 | − | 0.219603i | ||||
\(923\) | 928.506 | 0.0331118 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31498.2 | −1.11963 | ||||||||
\(926\) | −21353.2 | + | 12328.3i | −0.757785 | + | 0.437507i | ||||
\(927\) | 11.2116 | − | 5607.08i | 0.000397236 | − | 0.198663i | ||||
\(928\) | −1991.61 | + | 3449.56i | −0.0704501 | + | 0.122023i | ||||
\(929\) | −8911.93 | − | 15435.9i | −0.314737 | − | 0.545141i | 0.664644 | − | 0.747160i | \(-0.268583\pi\) |
−0.979382 | + | 0.202019i | \(0.935250\pi\) | |||||||
\(930\) | 19392.6 | − | 33511.6i | 0.683774 | − | 1.18160i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 7275.49i | − | 0.255704i | ||||||
\(933\) | −787.033 | − | 0.786854i | −0.0276166 | − | 2.76103e-5i | ||||
\(934\) | 14651.4 | + | 8458.97i | 0.513284 | + | 0.296345i | ||||
\(935\) | 14370.9 | + | 8297.05i | 0.502652 | + | 0.290206i | ||||
\(936\) | 2416.29 | − | 4165.89i | 0.0843793 | − | 0.145477i | ||||
\(937\) | 51270.5i | 1.78755i | 0.448516 | + | 0.893775i | \(0.351953\pi\) | ||||
−0.448516 | + | 0.893775i | \(0.648047\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 43286.5 | + | 25049.2i | 1.50437 | + | 0.870554i | ||||
\(940\) | −1838.26 | − | 3183.96i | −0.0637845 | − | 0.110478i | ||||
\(941\) | −5422.48 | + | 9392.01i | −0.187851 | + | 0.325367i | −0.944533 | − | 0.328415i | \(-0.893486\pi\) |
0.756683 | + | 0.653782i | \(0.226819\pi\) | |||||||
\(942\) | −1113.90 | − | 1933.79i | −0.0385274 | − | 0.0668857i | ||||
\(943\) | −17763.9 | + | 10256.0i | −0.613437 | + | 0.354168i | ||||
\(944\) | 5023.10 | 0.173186 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17230.6 | −0.592195 | ||||||||
\(947\) | −36916.8 | + | 21313.9i | −1.26677 | + | 0.731372i | −0.974376 | − | 0.224926i | \(-0.927786\pi\) |
−0.292397 | + | 0.956297i | \(0.594453\pi\) | |||||||
\(948\) | 3603.16 | + | 6255.29i | 0.123444 | + | 0.214306i | ||||
\(949\) | 835.531 | − | 1447.18i | 0.0285801 | − | 0.0495021i | ||||
\(950\) | −6133.05 | − | 10622.8i | −0.209455 | − | 0.362787i | ||||
\(951\) | −40854.2 | − | 23641.7i | −1.39305 | − | 0.806134i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33229.0i | 1.12948i | 0.825269 | + | 0.564739i | \(0.191023\pi\) | ||||
−0.825269 | + | 0.564739i | \(0.808977\pi\) | |||||||
\(954\) | 9540.17 | − | 16448.0i | 0.323768 | − | 0.558201i | ||||
\(955\) | 51328.4 | + | 29634.5i | 1.73921 | + | 1.00413i | ||||
\(956\) | 5294.64 | + | 3056.86i | 0.179122 | + | 0.103416i | ||||
\(957\) | −12606.4 | − | 12.6035i | −0.425817 | − | 0.000425720i | ||||
\(958\) | 18998.2i | 0.640715i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −23745.2 | + | 41033.1i | −0.798306 | + | 1.37952i | ||||
\(961\) | 1066.19 | + | 1846.70i | 0.0357891 | + | 0.0619885i | ||||
\(962\) | −2239.59 | + | 3879.09i | −0.0750596 | + | 0.130007i | ||||
\(963\) | −97.3279 | + | 48675.0i | −0.00325685 | + | 1.62880i | ||||
\(964\) | −2475.89 | + | 1429.45i | −0.0827209 | + | 0.0477589i | ||||
\(965\) | 2086.77 | 0.0696118 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16853.4 | −0.560464 | −0.280232 | − | 0.959932i | \(-0.590411\pi\) | ||||
−0.280232 | + | 0.959932i | \(0.590411\pi\) | |||||||
\(968\) | 1328.51 | − | 767.018i | 0.0441116 | − | 0.0254679i | ||||
\(969\) | 4579.68 | − | 2637.98i | 0.151827 | − | 0.0874552i | ||||
\(970\) | 6828.29 | − | 11826.9i | 0.226024 | − | 0.391485i | ||||
\(971\) | 634.824 | + | 1099.55i | 0.0209809 | + | 0.0363400i | 0.876325 | − | 0.481720i | \(-0.159988\pi\) |
−0.855344 | + | 0.518060i | \(0.826654\pi\) | |||||||
\(972\) | −2450.84 | − | 4294.41i | −0.0808751 | − | 0.141711i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 18157.3i | 0.597328i | ||||||||
\(975\) | −5.18768 | + | 5188.86i | −0.000170399 | + | 0.170438i | ||||
\(976\) | 17313.0 | + | 9995.66i | 0.567803 | + | 0.327821i | ||||
\(977\) | −49580.5 | − | 28625.3i | −1.62356 | − | 0.937364i | −0.985957 | − | 0.167001i | \(-0.946592\pi\) |
−0.637605 | − | 0.770363i | \(-0.720075\pi\) | |||||||
\(978\) | −13.1326 | + | 13135.6i | −0.000429382 | + | 0.429480i | ||||
\(979\) | − | 53583.9i | − | 1.74929i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3816.00 | − | 6640.13i | −0.124195 | − | 0.216109i | ||||
\(982\) | 290.077 | + | 502.428i | 0.00942640 | + | 0.0163270i | ||||
\(983\) | −30733.8 | + | 53232.4i | −0.997207 | + | 1.72721i | −0.433924 | + | 0.900950i | \(0.642871\pi\) |
−0.563283 | + | 0.826264i | \(0.690462\pi\) | |||||||
\(984\) | −40118.1 | + | 23108.8i | −1.29971 | + | 0.748659i | ||||
\(985\) | −42501.6 | + | 24538.3i | −1.37484 | + | 0.793762i | ||||
\(986\) | −5099.63 | −0.164711 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 340.100 | 0.0109514 | ||||||||
\(989\) | −8979.57 | + | 5184.36i | −0.288710 | + | 0.166687i | ||||
\(990\) | −40084.8 | − | 80.1514i | −1.28685 | − | 0.00257311i | ||||
\(991\) | 25996.6 | − | 45027.4i | 0.833308 | − | 1.44333i | −0.0620930 | − | 0.998070i | \(-0.519778\pi\) |
0.895401 | − | 0.445261i | \(-0.146889\pi\) | |||||||
\(992\) | −5221.39 | − | 9043.71i | −0.167116 | − | 0.289454i | ||||
\(993\) | 3658.12 | − | 6321.44i | 0.116905 | − | 0.202019i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 64364.3i | − | 2.05074i | ||||||
\(996\) | 4076.64 | + | 4.07571i | 0.129692 | + | 0.000129662i | ||||
\(997\) | −29417.3 | − | 16984.1i | −0.934460 | − | 0.539510i | −0.0462403 | − | 0.998930i | \(-0.514724\pi\) |
−0.888219 | + | 0.459420i | \(0.848057\pi\) | |||||||
\(998\) | 46590.3 | + | 26898.9i | 1.47775 | + | 0.853177i | ||||
\(999\) | 16306.7 | + | 28440.7i | 0.516438 | + | 0.900725i |
(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 | 147.4.g.d.80.5 | 12 | ||
3.2 | odd | 2 | inner | 147.4.g.d.80.2 | 12 | ||
7.2 | even | 3 | 21.4.g.a.5.2 | ✓ | 12 | ||
7.3 | odd | 6 | 147.4.c.a.146.10 | 12 | |||
7.4 | even | 3 | 147.4.c.a.146.9 | 12 | |||
7.5 | odd | 6 | inner | 147.4.g.d.68.2 | 12 | ||
7.6 | odd | 2 | 21.4.g.a.17.5 | yes | 12 | ||
21.2 | odd | 6 | 21.4.g.a.5.5 | yes | 12 | ||
21.5 | even | 6 | inner | 147.4.g.d.68.5 | 12 | ||
21.11 | odd | 6 | 147.4.c.a.146.4 | 12 | |||
21.17 | even | 6 | 147.4.c.a.146.3 | 12 | |||
21.20 | even | 2 | 21.4.g.a.17.2 | yes | 12 | ||
28.23 | odd | 6 | 336.4.bc.d.257.1 | 12 | |||
28.27 | even | 2 | 336.4.bc.d.17.2 | 12 | |||
84.23 | even | 6 | 336.4.bc.d.257.2 | 12 | |||
84.83 | odd | 2 | 336.4.bc.d.17.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.g.a.5.2 | ✓ | 12 | 7.2 | even | 3 | ||
21.4.g.a.5.5 | yes | 12 | 21.2 | odd | 6 | ||
21.4.g.a.17.2 | yes | 12 | 21.20 | even | 2 | ||
21.4.g.a.17.5 | yes | 12 | 7.6 | odd | 2 | ||
147.4.c.a.146.3 | 12 | 21.17 | even | 6 | |||
147.4.c.a.146.4 | 12 | 21.11 | odd | 6 | |||
147.4.c.a.146.9 | 12 | 7.4 | even | 3 | |||
147.4.c.a.146.10 | 12 | 7.3 | odd | 6 | |||
147.4.g.d.68.2 | 12 | 7.5 | odd | 6 | inner | ||
147.4.g.d.68.5 | 12 | 21.5 | even | 6 | inner | ||
147.4.g.d.80.2 | 12 | 3.2 | odd | 2 | inner | ||
147.4.g.d.80.5 | 12 | 1.1 | even | 1 | trivial | ||
336.4.bc.d.17.1 | 12 | 84.83 | odd | 2 | |||
336.4.bc.d.17.2 | 12 | 28.27 | even | 2 | |||
336.4.bc.d.257.1 | 12 | 28.23 | odd | 6 | |||
336.4.bc.d.257.2 | 12 | 84.23 | even | 6 |