Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,5,Mod(151,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.151");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.c (of order \(2\), degree \(1\), 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: | \(31.0109889252\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + 234752 x^{8} - 632832 x^{7} + 1884160 x^{6} - 8847360 x^{5} + \cdots + 4294967296 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.6 | ||
Root | \(2.11879 - 3.39275i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.151 |
Dual form | 300.5.c.c.151.5 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.87881 | + | 3.53130i | −0.469702 | + | 0.882825i | ||||
\(3\) | − | 5.19615i | − | 0.577350i | ||||||
\(4\) | −8.94016 | − | 13.2693i | −0.558760 | − | 0.829329i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 18.3492 | + | 9.76257i | 0.509699 | + | 0.271183i | ||||
\(7\) | 7.86734i | 0.160558i | 0.996772 | + | 0.0802790i | \(0.0255811\pi\) | ||||
−0.996772 | + | 0.0802790i | \(0.974419\pi\) | |||||||
\(8\) | 63.6546 | − | 6.63999i | 0.994603 | − | 0.103750i | ||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 61.8527i | 0.511179i | 0.966785 | + | 0.255590i | \(0.0822696\pi\) | ||||
−0.966785 | + | 0.255590i | \(0.917730\pi\) | |||||||
\(12\) | −68.9491 | + | 46.4544i | −0.478813 | + | 0.322600i | ||||
\(13\) | 47.0192 | 0.278220 | 0.139110 | − | 0.990277i | \(-0.455576\pi\) | ||||
0.139110 | + | 0.990277i | \(0.455576\pi\) | |||||||
\(14\) | −27.7819 | − | 14.7812i | −0.141745 | − | 0.0754144i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −96.1470 | + | 237.259i | −0.375574 | + | 0.926792i | ||||
\(17\) | −239.844 | −0.829909 | −0.414955 | − | 0.909842i | \(-0.636203\pi\) | ||||
−0.414955 | + | 0.909842i | \(0.636203\pi\) | |||||||
\(18\) | 50.7278 | − | 95.3451i | 0.156567 | − | 0.294275i | ||||
\(19\) | 18.5518i | 0.0513901i | 0.999670 | + | 0.0256950i | \(0.00817988\pi\) | ||||
−0.999670 | + | 0.0256950i | \(0.991820\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 40.8799 | 0.0926982 | ||||||||
\(22\) | −218.420 | − | 116.209i | −0.451282 | − | 0.240102i | ||||
\(23\) | − | 580.792i | − | 1.09791i | −0.835853 | − | 0.548953i | \(-0.815027\pi\) | ||
0.835853 | − | 0.548953i | \(-0.184973\pi\) | |||||||
\(24\) | −34.5024 | − | 330.759i | −0.0599000 | − | 0.574235i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −88.3401 | + | 166.039i | −0.130681 | + | 0.245620i | ||||
\(27\) | 140.296i | 0.192450i | ||||||||
\(28\) | 104.394 | − | 70.3353i | 0.133155 | − | 0.0897134i | ||||
\(29\) | 254.128 | 0.302174 | 0.151087 | − | 0.988520i | \(-0.451723\pi\) | ||||
0.151087 | + | 0.988520i | \(0.451723\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1368.88i | 1.42443i | 0.701962 | + | 0.712214i | \(0.252308\pi\) | ||||
−0.701962 | + | 0.712214i | \(0.747692\pi\) | |||||||
\(32\) | −657.190 | − | 785.288i | −0.641788 | − | 0.766882i | ||||
\(33\) | 321.396 | 0.295129 | ||||||||
\(34\) | 450.620 | − | 846.960i | 0.389810 | − | 0.732665i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 241.384 | + | 358.270i | 0.186253 | + | 0.276443i | ||||
\(37\) | 1089.51 | 0.795840 | 0.397920 | − | 0.917420i | \(-0.369732\pi\) | ||||
0.397920 | + | 0.917420i | \(0.369732\pi\) | |||||||
\(38\) | −65.5120 | − | 34.8553i | −0.0453684 | − | 0.0241380i | ||||
\(39\) | − | 244.319i | − | 0.160631i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2011.08 | 1.19636 | 0.598178 | − | 0.801363i | \(-0.295891\pi\) | ||||
0.598178 | + | 0.801363i | \(0.295891\pi\) | |||||||
\(42\) | −76.8055 | + | 144.359i | −0.0435405 | + | 0.0818363i | ||||
\(43\) | − | 716.042i | − | 0.387259i | −0.981075 | − | 0.193629i | \(-0.937974\pi\) | ||
0.981075 | − | 0.193629i | \(-0.0620259\pi\) | |||||||
\(44\) | 820.740 | − | 552.973i | 0.423936 | − | 0.285626i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2050.95 | + | 1091.20i | 0.969258 | + | 0.515688i | ||||
\(47\) | − | 2546.81i | − | 1.15292i | −0.817124 | − | 0.576461i | \(-0.804433\pi\) | ||
0.817124 | − | 0.576461i | \(-0.195567\pi\) | |||||||
\(48\) | 1232.83 | + | 499.594i | 0.535084 | + | 0.216838i | ||||
\(49\) | 2339.10 | 0.974221 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1246.26i | 0.479148i | ||||||||
\(52\) | −420.359 | − | 623.911i | −0.155458 | − | 0.230736i | ||||
\(53\) | 1958.55 | 0.697242 | 0.348621 | − | 0.937264i | \(-0.386650\pi\) | ||||
0.348621 | + | 0.937264i | \(0.386650\pi\) | |||||||
\(54\) | −495.428 | − | 263.589i | −0.169900 | − | 0.0903942i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 52.2391 | + | 500.793i | 0.0166579 | + | 0.159692i | ||||
\(57\) | 96.3981 | 0.0296701 | ||||||||
\(58\) | −477.459 | + | 897.404i | −0.141932 | + | 0.266767i | ||||
\(59\) | 5125.74i | 1.47249i | 0.676715 | + | 0.736245i | \(0.263403\pi\) | ||||
−0.676715 | + | 0.736245i | \(0.736597\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7401.65 | 1.98915 | 0.994577 | − | 0.103998i | \(-0.0331637\pi\) | ||||
0.994577 | + | 0.103998i | \(0.0331637\pi\) | |||||||
\(62\) | −4833.91 | − | 2571.85i | −1.25752 | − | 0.669057i | ||||
\(63\) | − | 212.418i | − | 0.0535193i | ||||||
\(64\) | 4007.82 | − | 845.332i | 0.978472 | − | 0.206380i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −603.841 | + | 1134.95i | −0.138623 | + | 0.260548i | ||||
\(67\) | − | 2556.85i | − | 0.569582i | −0.958590 | − | 0.284791i | \(-0.908076\pi\) | ||
0.958590 | − | 0.284791i | \(-0.0919242\pi\) | |||||||
\(68\) | 2144.24 | + | 3182.55i | 0.463720 | + | 0.688268i | ||||
\(69\) | −3017.88 | −0.633876 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2346.78i | − | 0.465539i | −0.972532 | − | 0.232770i | \(-0.925221\pi\) | ||
0.972532 | − | 0.232770i | \(-0.0747788\pi\) | |||||||
\(72\) | −1718.67 | + | 179.280i | −0.331534 | + | 0.0345833i | ||||
\(73\) | 3540.66 | 0.664414 | 0.332207 | − | 0.943207i | \(-0.392207\pi\) | ||||
0.332207 | + | 0.943207i | \(0.392207\pi\) | |||||||
\(74\) | −2046.97 | + | 3847.37i | −0.373808 | + | 0.702588i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 246.169 | − | 165.856i | 0.0426193 | − | 0.0287147i | ||||
\(77\) | −486.616 | −0.0820739 | ||||||||
\(78\) | 862.764 | + | 459.028i | 0.141809 | + | 0.0754485i | ||||
\(79\) | 4948.38i | 0.792882i | 0.918060 | + | 0.396441i | \(0.129755\pi\) | ||||
−0.918060 | + | 0.396441i | \(0.870245\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | −3778.42 | + | 7101.71i | −0.561931 | + | 1.05617i | ||||
\(83\) | 8824.75i | 1.28099i | 0.767962 | + | 0.640496i | \(0.221271\pi\) | ||||
−0.767962 | + | 0.640496i | \(0.778729\pi\) | |||||||
\(84\) | −365.473 | − | 542.447i | −0.0517961 | − | 0.0768773i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2528.56 | + | 1345.30i | 0.341882 | + | 0.181896i | ||||
\(87\) | − | 1320.49i | − | 0.174460i | ||||||
\(88\) | 410.701 | + | 3937.21i | 0.0530348 | + | 0.508420i | ||||
\(89\) | −12929.7 | −1.63233 | −0.816166 | − | 0.577818i | \(-0.803904\pi\) | ||||
−0.816166 | + | 0.577818i | \(0.803904\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 369.916i | 0.0446705i | ||||||||
\(92\) | −7706.68 | + | 5192.37i | −0.910525 | + | 0.613466i | ||||
\(93\) | 7112.89 | 0.822394 | ||||||||
\(94\) | 8993.54 | + | 4784.96i | 1.01783 | + | 0.541530i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4080.47 | + | 3414.86i | −0.442760 | + | 0.370536i | ||||
\(97\) | 13176.9 | 1.40045 | 0.700227 | − | 0.713921i | \(-0.253082\pi\) | ||||
0.700227 | + | 0.713921i | \(0.253082\pi\) | |||||||
\(98\) | −4394.73 | + | 8260.08i | −0.457594 | + | 0.860067i | ||||
\(99\) | − | 1670.02i | − | 0.170393i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10201.8 | 1.00008 | 0.500040 | − | 0.866002i | \(-0.333319\pi\) | ||||
0.500040 | + | 0.866002i | \(0.333319\pi\) | |||||||
\(102\) | −4400.93 | − | 2341.49i | −0.423004 | − | 0.225057i | ||||
\(103\) | 4197.87i | 0.395689i | 0.980233 | + | 0.197845i | \(0.0633941\pi\) | ||||
−0.980233 | + | 0.197845i | \(0.936606\pi\) | |||||||
\(104\) | 2992.99 | − | 312.207i | 0.276719 | − | 0.0288653i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3679.74 | + | 6916.24i | −0.327496 | + | 0.615543i | ||||
\(107\) | 581.398i | 0.0507816i | 0.999678 | + | 0.0253908i | \(0.00808301\pi\) | ||||
−0.999678 | + | 0.0253908i | \(0.991917\pi\) | |||||||
\(108\) | 1861.63 | − | 1254.27i | 0.159604 | − | 0.107533i | ||||
\(109\) | 7223.44 | 0.607982 | 0.303991 | − | 0.952675i | \(-0.401681\pi\) | ||||
0.303991 | + | 0.952675i | \(0.401681\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 5661.23i | − | 0.459478i | ||||||
\(112\) | −1866.60 | − | 756.421i | −0.148804 | − | 0.0603014i | ||||
\(113\) | 2422.25 | 0.189698 | 0.0948488 | − | 0.995492i | \(-0.469763\pi\) | ||||
0.0948488 | + | 0.995492i | \(0.469763\pi\) | |||||||
\(114\) | −181.113 | + | 340.410i | −0.0139361 | + | 0.0261935i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2271.95 | − | 3372.10i | −0.168843 | − | 0.250602i | ||||
\(117\) | −1269.52 | −0.0927401 | ||||||||
\(118\) | −18100.5 | − | 9630.28i | −1.29995 | − | 0.691632i | ||||
\(119\) | − | 1886.93i | − | 0.133249i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10815.2 | 0.738696 | ||||||||
\(122\) | −13906.3 | + | 26137.4i | −0.934310 | + | 1.75608i | ||||
\(123\) | − | 10449.9i | − | 0.690717i | ||||||
\(124\) | 18164.0 | − | 12238.0i | 1.18132 | − | 0.795914i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 750.113 | + | 399.093i | 0.0472482 | + | 0.0251381i | ||||
\(127\) | − | 25636.4i | − | 1.58946i | −0.606964 | − | 0.794729i | \(-0.707613\pi\) | ||
0.606964 | − | 0.794729i | \(-0.292387\pi\) | |||||||
\(128\) | −4544.80 | + | 15741.0i | −0.277393 | + | 0.960757i | ||||
\(129\) | −3720.66 | −0.223584 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 19837.6i | − | 1.15597i | −0.816048 | − | 0.577984i | \(-0.803840\pi\) | ||
0.816048 | − | 0.577984i | \(-0.196160\pi\) | |||||||
\(132\) | −2873.33 | − | 4264.69i | −0.164907 | − | 0.244759i | ||||
\(133\) | −145.953 | −0.00825109 | ||||||||
\(134\) | 9029.02 | + | 4803.84i | 0.502841 | + | 0.267534i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15267.2 | + | 1592.56i | −0.825430 | + | 0.0861030i | ||||
\(137\) | 29095.2 | 1.55017 | 0.775086 | − | 0.631856i | \(-0.217707\pi\) | ||||
0.775086 | + | 0.631856i | \(0.217707\pi\) | |||||||
\(138\) | 5670.02 | − | 10657.1i | 0.297733 | − | 0.559602i | ||||
\(139\) | − | 3878.60i | − | 0.200745i | −0.994950 | − | 0.100373i | \(-0.967997\pi\) | ||
0.994950 | − | 0.100373i | \(-0.0320035\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13233.6 | −0.665640 | ||||||||
\(142\) | 8287.20 | + | 4409.15i | 0.410990 | + | 0.218665i | ||||
\(143\) | 2908.26i | 0.142220i | ||||||||
\(144\) | 2595.97 | − | 6405.99i | 0.125191 | − | 0.308931i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6652.22 | + | 12503.1i | −0.312076 | + | 0.586561i | ||||
\(147\) | − | 12154.3i | − | 0.562467i | ||||||
\(148\) | −9740.35 | − | 14456.9i | −0.444684 | − | 0.660014i | ||||
\(149\) | −35799.3 | −1.61251 | −0.806254 | − | 0.591570i | \(-0.798508\pi\) | ||||
−0.806254 | + | 0.591570i | \(0.798508\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8733.91i | 0.383049i | 0.981488 | + | 0.191525i | \(0.0613432\pi\) | ||||
−0.981488 | + | 0.191525i | \(0.938657\pi\) | |||||||
\(152\) | 123.184 | + | 1180.91i | 0.00533171 | + | 0.0511127i | ||||
\(153\) | 6475.78 | 0.276636 | ||||||||
\(154\) | 914.258 | − | 1718.39i | 0.0385503 | − | 0.0724569i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3241.93 | + | 2184.25i | −0.133216 | + | 0.0897539i | ||||
\(157\) | 34333.1 | 1.39288 | 0.696439 | − | 0.717616i | \(-0.254767\pi\) | ||||
0.696439 | + | 0.717616i | \(0.254767\pi\) | |||||||
\(158\) | −17474.2 | − | 9297.05i | −0.699976 | − | 0.372418i | ||||
\(159\) | − | 10176.9i | − | 0.402553i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4569.29 | 0.176278 | ||||||||
\(162\) | −1369.65 | + | 2574.32i | −0.0521891 | + | 0.0980917i | ||||
\(163\) | − | 41996.1i | − | 1.58064i | −0.612692 | − | 0.790322i | \(-0.709913\pi\) | ||
0.612692 | − | 0.790322i | \(-0.290087\pi\) | |||||||
\(164\) | −17979.3 | − | 26685.5i | −0.668477 | − | 0.992174i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −31162.8 | − | 16580.0i | −1.13089 | − | 0.601684i | ||||
\(167\) | 15039.8i | 0.539275i | 0.962962 | + | 0.269637i | \(0.0869039\pi\) | ||||
−0.962962 | + | 0.269637i | \(0.913096\pi\) | |||||||
\(168\) | 2602.20 | − | 271.442i | 0.0921980 | − | 0.00961743i | ||||
\(169\) | −26350.2 | −0.922594 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 500.899i | − | 0.0171300i | ||||||
\(172\) | −9501.35 | + | 6401.53i | −0.321165 | + | 0.216385i | ||||
\(173\) | −22917.0 | −0.765711 | −0.382855 | − | 0.923808i | \(-0.625059\pi\) | ||||
−0.382855 | + | 0.923808i | \(0.625059\pi\) | |||||||
\(174\) | 4663.05 | + | 2480.95i | 0.154018 | + | 0.0819444i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14675.1 | − | 5946.95i | −0.473757 | − | 0.191986i | ||||
\(177\) | 26634.1 | 0.850143 | ||||||||
\(178\) | 24292.4 | − | 45658.6i | 0.766709 | − | 1.44106i | ||||
\(179\) | 21591.7i | 0.673879i | 0.941526 | + | 0.336939i | \(0.109392\pi\) | ||||
−0.941526 | + | 0.336939i | \(0.890608\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7885.60 | −0.240701 | −0.120350 | − | 0.992731i | \(-0.538402\pi\) | ||||
−0.120350 | + | 0.992731i | \(0.538402\pi\) | |||||||
\(182\) | −1306.29 | − | 695.002i | −0.0394362 | − | 0.0209818i | ||||
\(183\) | − | 38460.1i | − | 1.14844i | ||||||
\(184\) | −3856.45 | − | 36970.1i | −0.113908 | − | 1.09198i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −13363.7 | + | 25117.7i | −0.386280 | + | 0.726030i | ||||
\(187\) | − | 14835.0i | − | 0.424232i | ||||||
\(188\) | −33794.3 | + | 22768.9i | −0.956153 | + | 0.644207i | ||||
\(189\) | −1103.76 | −0.0308994 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 53547.3i | − | 1.46781i | −0.679250 | − | 0.733907i | \(-0.737695\pi\) | ||
0.679250 | − | 0.733907i | \(-0.262305\pi\) | |||||||
\(192\) | −4392.48 | − | 20825.2i | −0.119154 | − | 0.564921i | ||||
\(193\) | 33661.0 | 0.903676 | 0.451838 | − | 0.892100i | \(-0.350769\pi\) | ||||
0.451838 | + | 0.892100i | \(0.350769\pi\) | |||||||
\(194\) | −24756.8 | + | 46531.5i | −0.657796 | + | 1.23636i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −20912.0 | − | 31038.2i | −0.544356 | − | 0.807950i | ||||
\(197\) | 9889.39 | 0.254822 | 0.127411 | − | 0.991850i | \(-0.459333\pi\) | ||||
0.127411 | + | 0.991850i | \(0.459333\pi\) | |||||||
\(198\) | 5897.35 | + | 3137.65i | 0.150427 | + | 0.0800339i | ||||
\(199\) | 10733.5i | 0.271042i | 0.990774 | + | 0.135521i | \(0.0432708\pi\) | ||||
−0.990774 | + | 0.135521i | \(0.956729\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13285.8 | −0.328848 | ||||||||
\(202\) | −19167.3 | + | 36025.7i | −0.469740 | + | 0.882896i | ||||
\(203\) | 1999.32i | 0.0485165i | ||||||||
\(204\) | 16537.0 | − | 11141.8i | 0.397372 | − | 0.267729i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14823.9 | − | 7886.98i | −0.349324 | − | 0.185856i | ||||
\(207\) | 15681.4i | 0.365968i | ||||||||
\(208\) | −4520.76 | + | 11155.7i | −0.104492 | + | 0.257852i | ||||
\(209\) | −1147.48 | −0.0262695 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 31245.2i | 0.701808i | 0.936411 | + | 0.350904i | \(0.114126\pi\) | ||||
−0.936411 | + | 0.350904i | \(0.885874\pi\) | |||||||
\(212\) | −17509.8 | − | 25988.6i | −0.389591 | − | 0.578243i | ||||
\(213\) | −12194.2 | −0.268779 | ||||||||
\(214\) | −2053.09 | − | 1092.34i | −0.0448312 | − | 0.0238522i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 931.565 | + | 8930.50i | 0.0199667 | + | 0.191412i | ||||
\(217\) | −10769.4 | −0.228703 | ||||||||
\(218\) | −13571.5 | + | 25508.1i | −0.285571 | + | 0.536742i | ||||
\(219\) | − | 18397.8i | − | 0.383599i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11277.3 | −0.230897 | ||||||||
\(222\) | 19991.5 | + | 10636.4i | 0.405639 | + | 0.215818i | ||||
\(223\) | 31962.3i | 0.642730i | 0.946955 | + | 0.321365i | \(0.104142\pi\) | ||||
−0.946955 | + | 0.321365i | \(0.895858\pi\) | |||||||
\(224\) | 6178.13 | − | 5170.34i | 0.123129 | − | 0.103044i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4550.94 | + | 8553.69i | −0.0891013 | + | 0.167470i | ||||
\(227\) | 31878.7i | 0.618656i | 0.950955 | + | 0.309328i | \(0.100104\pi\) | ||||
−0.950955 | + | 0.309328i | \(0.899896\pi\) | |||||||
\(228\) | −861.814 | − | 1279.13i | −0.0165785 | − | 0.0246063i | ||||
\(229\) | 21252.3 | 0.405260 | 0.202630 | − | 0.979255i | \(-0.435051\pi\) | ||||
0.202630 | + | 0.979255i | \(0.435051\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2528.53i | 0.0473854i | ||||||||
\(232\) | 16176.5 | − | 1687.41i | 0.300543 | − | 0.0313505i | ||||
\(233\) | −77716.9 | −1.43154 | −0.715770 | − | 0.698336i | \(-0.753924\pi\) | ||||
−0.715770 | + | 0.698336i | \(0.753924\pi\) | |||||||
\(234\) | 2385.18 | − | 4483.05i | 0.0435602 | − | 0.0818733i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 68014.8 | − | 45824.9i | 1.22118 | − | 0.822769i | ||||
\(237\) | 25712.5 | 0.457771 | ||||||||
\(238\) | 6663.33 | + | 3545.18i | 0.117635 | + | 0.0625871i | ||||
\(239\) | 56167.8i | 0.983313i | 0.870789 | + | 0.491657i | \(0.163608\pi\) | ||||
−0.870789 | + | 0.491657i | \(0.836392\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11285.3 | 0.194302 | 0.0971510 | − | 0.995270i | \(-0.469027\pi\) | ||||
0.0971510 | + | 0.995270i | \(0.469027\pi\) | |||||||
\(242\) | −20319.8 | + | 38191.9i | −0.346967 | + | 0.652139i | ||||
\(243\) | − | 3788.00i | − | 0.0641500i | ||||||
\(244\) | −66171.9 | − | 98214.4i | −1.11146 | − | 1.64966i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 36901.6 | + | 19633.3i | 0.609782 | + | 0.324431i | ||||
\(247\) | 872.292i | 0.0142978i | ||||||||
\(248\) | 9089.32 | + | 87135.3i | 0.147784 | + | 1.41674i | ||||
\(249\) | 45854.7 | 0.739581 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 74138.0i | − | 1.17677i | −0.808579 | − | 0.588387i | \(-0.799763\pi\) | ||
0.808579 | − | 0.588387i | \(-0.200237\pi\) | |||||||
\(252\) | −2818.63 | + | 1899.05i | −0.0443852 | + | 0.0299045i | ||||
\(253\) | 35923.5 | 0.561226 | ||||||||
\(254\) | 90529.7 | + | 48165.8i | 1.40321 | + | 0.746572i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −47047.5 | − | 45623.4i | −0.717888 | − | 0.696159i | ||||
\(257\) | −391.260 | −0.00592379 | −0.00296189 | − | 0.999996i | \(-0.500943\pi\) | ||||
−0.00296189 | + | 0.999996i | \(0.500943\pi\) | |||||||
\(258\) | 6990.41 | − | 13138.8i | 0.105018 | − | 0.197386i | ||||
\(259\) | 8571.51i | 0.127779i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6861.47 | −0.100725 | ||||||||
\(262\) | 70052.4 | + | 37271.0i | 1.02052 | + | 0.542960i | ||||
\(263\) | 62550.4i | 0.904313i | 0.891939 | + | 0.452157i | \(0.149345\pi\) | ||||
−0.891939 | + | 0.452157i | \(0.850655\pi\) | |||||||
\(264\) | 20458.3 | − | 2134.07i | 0.293537 | − | 0.0306196i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 274.219 | − | 515.406i | 0.00387555 | − | 0.00728427i | ||||
\(267\) | 67184.7i | 0.942427i | ||||||||
\(268\) | −33927.6 | + | 22858.7i | −0.472371 | + | 0.318260i | ||||
\(269\) | 47440.2 | 0.655604 | 0.327802 | − | 0.944746i | \(-0.393692\pi\) | ||||
0.327802 | + | 0.944746i | \(0.393692\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 139480.i | 1.89921i | 0.313453 | + | 0.949604i | \(0.398514\pi\) | ||||
−0.313453 | + | 0.949604i | \(0.601486\pi\) | |||||||
\(272\) | 23060.3 | − | 56905.0i | 0.311692 | − | 0.769153i | ||||
\(273\) | 1922.14 | 0.0257905 | ||||||||
\(274\) | −54664.2 | + | 102744.i | −0.728118 | + | 1.36853i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 26980.4 | + | 40045.1i | 0.354185 | + | 0.525692i | ||||
\(277\) | −147171. | −1.91806 | −0.959029 | − | 0.283307i | \(-0.908568\pi\) | ||||
−0.959029 | + | 0.283307i | \(0.908568\pi\) | |||||||
\(278\) | 13696.5 | + | 7287.13i | 0.177223 | + | 0.0942903i | ||||
\(279\) | − | 36959.6i | − | 0.474810i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31803.9 | 0.402780 | 0.201390 | − | 0.979511i | \(-0.435454\pi\) | ||||
0.201390 | + | 0.979511i | \(0.435454\pi\) | |||||||
\(282\) | 24863.4 | − | 46731.8i | 0.312653 | − | 0.587644i | ||||
\(283\) | 116313.i | 1.45229i | 0.687541 | + | 0.726146i | \(0.258690\pi\) | ||||
−0.687541 | + | 0.726146i | \(0.741310\pi\) | |||||||
\(284\) | −31140.1 | + | 20980.6i | −0.386085 | + | 0.260125i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10270.0 | − | 5464.07i | −0.125556 | − | 0.0668012i | ||||
\(287\) | 15821.8i | 0.192085i | ||||||||
\(288\) | 17744.1 | + | 21202.8i | 0.213929 | + | 0.255627i | ||||
\(289\) | −25996.0 | −0.311251 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 68469.0i | − | 0.808552i | ||||||
\(292\) | −31654.1 | − | 46982.0i | −0.371248 | − | 0.551018i | ||||
\(293\) | −50816.7 | −0.591931 | −0.295965 | − | 0.955199i | \(-0.595641\pi\) | ||||
−0.295965 | + | 0.955199i | \(0.595641\pi\) | |||||||
\(294\) | 42920.6 | + | 22835.7i | 0.496560 | + | 0.264192i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 69352.0 | − | 7234.30i | 0.791545 | − | 0.0825683i | ||||
\(297\) | −8677.69 | −0.0983765 | ||||||||
\(298\) | 67260.0 | − | 126418.i | 0.757398 | − | 1.42356i | ||||
\(299\) | − | 27308.4i | − | 0.305459i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5633.34 | 0.0621775 | ||||||||
\(302\) | −30842.1 | − | 16409.3i | −0.338166 | − | 0.179919i | ||||
\(303\) | − | 53010.2i | − | 0.577397i | ||||||
\(304\) | −4401.58 | − | 1783.70i | −0.0476279 | − | 0.0193008i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −12166.7 | + | 22867.9i | −0.129937 | + | 0.244222i | ||||
\(307\) | − | 104571.i | − | 1.10952i | −0.832011 | − | 0.554760i | \(-0.812810\pi\) | ||
0.832011 | − | 0.554760i | \(-0.187190\pi\) | |||||||
\(308\) | 4350.43 | + | 6457.04i | 0.0458596 | + | 0.0680663i | ||||
\(309\) | 21812.7 | 0.228451 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 42105.4i | 0.435329i | 0.976024 | + | 0.217664i | \(0.0698438\pi\) | ||||
−0.976024 | + | 0.217664i | \(0.930156\pi\) | |||||||
\(312\) | −1622.28 | − | 15552.0i | −0.0166654 | − | 0.159764i | ||||
\(313\) | 137890. | 1.40749 | 0.703745 | − | 0.710453i | \(-0.251510\pi\) | ||||
0.703745 | + | 0.710453i | \(0.251510\pi\) | |||||||
\(314\) | −64505.2 | + | 121240.i | −0.654238 | + | 1.22967i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 65661.4 | − | 44239.3i | 0.657561 | − | 0.443031i | ||||
\(317\) | −162907. | −1.62114 | −0.810569 | − | 0.585643i | \(-0.800842\pi\) | ||||
−0.810569 | + | 0.585643i | \(0.800842\pi\) | |||||||
\(318\) | 35937.8 | + | 19120.5i | 0.355384 | + | 0.189080i | ||||
\(319\) | 15718.5i | 0.154465i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3021.03 | 0.0293187 | ||||||||
\(322\) | −8584.82 | + | 16135.5i | −0.0827979 | + | 0.155622i | ||||
\(323\) | − | 4449.54i | − | 0.0426491i | ||||||
\(324\) | −6517.38 | − | 9673.30i | −0.0620845 | − | 0.0921477i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 148301. | + | 78902.6i | 1.39543 | + | 0.742431i | ||||
\(327\) | − | 37534.1i | − | 0.351019i | ||||||
\(328\) | 128014. | − | 13353.5i | 1.18990 | − | 0.124122i | ||||
\(329\) | 20036.6 | 0.185111 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 171369.i | 1.56414i | 0.623192 | + | 0.782069i | \(0.285836\pi\) | ||||
−0.623192 | + | 0.782069i | \(0.714164\pi\) | |||||||
\(332\) | 117098. | − | 78894.7i | 1.06236 | − | 0.715767i | ||||
\(333\) | −29416.6 | −0.265280 | ||||||||
\(334\) | −53110.2 | − | 28257.0i | −0.476085 | − | 0.253298i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3930.48 | + | 9699.12i | −0.0348151 | + | 0.0859120i | ||||
\(337\) | −150057. | −1.32129 | −0.660643 | − | 0.750700i | \(-0.729716\pi\) | ||||
−0.660643 | + | 0.750700i | \(0.729716\pi\) | |||||||
\(338\) | 49506.9 | − | 93050.4i | 0.433344 | − | 0.814489i | ||||
\(339\) | − | 12586.4i | − | 0.109522i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −84668.6 | −0.728138 | ||||||||
\(342\) | 1768.82 | + | 941.093i | 0.0151228 | + | 0.00804601i | ||||
\(343\) | 37292.0i | 0.316977i | ||||||||
\(344\) | −4754.51 | − | 45579.4i | −0.0401781 | − | 0.385169i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 43056.6 | − | 80926.7i | 0.359656 | − | 0.675989i | ||||
\(347\) | 105689.i | 0.877754i | 0.898547 | + | 0.438877i | \(0.144624\pi\) | ||||
−0.898547 | + | 0.438877i | \(0.855376\pi\) | |||||||
\(348\) | −17521.9 | + | 11805.4i | −0.144685 | + | 0.0974815i | ||||
\(349\) | 101691. | 0.834897 | 0.417448 | − | 0.908701i | \(-0.362924\pi\) | ||||
0.417448 | + | 0.908701i | \(0.362924\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6596.61i | 0.0535435i | ||||||||
\(352\) | 48572.1 | − | 40649.0i | 0.392014 | − | 0.328068i | ||||
\(353\) | 75384.5 | 0.604969 | 0.302484 | − | 0.953154i | \(-0.402184\pi\) | ||||
0.302484 | + | 0.953154i | \(0.402184\pi\) | |||||||
\(354\) | −50040.4 | + | 94053.1i | −0.399314 | + | 0.750527i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 115594. | + | 171568.i | 0.912082 | + | 1.35374i | ||||
\(357\) | −9804.79 | −0.0769311 | ||||||||
\(358\) | −76246.9 | − | 40566.7i | −0.594917 | − | 0.316522i | ||||
\(359\) | − | 157519.i | − | 1.22220i | −0.791553 | − | 0.611101i | \(-0.790727\pi\) | ||
0.791553 | − | 0.611101i | \(-0.209273\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 129977. | 0.997359 | ||||||||
\(362\) | 14815.5 | − | 27846.4i | 0.113058 | − | 0.212497i | ||||
\(363\) | − | 56197.7i | − | 0.426486i | ||||||
\(364\) | 4908.52 | − | 3307.11i | 0.0370465 | − | 0.0249601i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 135814. | + | 72259.1i | 1.01387 | + | 0.539424i | ||||
\(367\) | − | 105819.i | − | 0.785653i | −0.919613 | − | 0.392827i | \(-0.871497\pi\) | ||
0.919613 | − | 0.392827i | \(-0.128503\pi\) | |||||||
\(368\) | 137798. | + | 55841.4i | 1.01753 | + | 0.412345i | ||||
\(369\) | −54299.0 | −0.398786 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15408.6i | 0.111948i | ||||||||
\(372\) | −63590.4 | − | 94382.8i | −0.459521 | − | 0.682036i | ||||
\(373\) | −12801.2 | −0.0920098 | −0.0460049 | − | 0.998941i | \(-0.514649\pi\) | ||||
−0.0460049 | + | 0.998941i | \(0.514649\pi\) | |||||||
\(374\) | 52386.7 | + | 27872.1i | 0.374523 | + | 0.199263i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16910.8 | − | 162116.i | −0.119616 | − | 1.14670i | ||||
\(377\) | 11948.9 | 0.0840710 | ||||||||
\(378\) | 2073.75 | − | 3897.70i | 0.0145135 | − | 0.0272788i | ||||
\(379\) | − | 83667.5i | − | 0.582476i | −0.956651 | − | 0.291238i | \(-0.905933\pi\) | ||
0.956651 | − | 0.291238i | \(-0.0940672\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −133210. | −0.917674 | ||||||||
\(382\) | 189092. | + | 100605.i | 1.29582 | + | 0.689435i | ||||
\(383\) | − | 53274.8i | − | 0.363182i | −0.983374 | − | 0.181591i | \(-0.941875\pi\) | ||
0.983374 | − | 0.181591i | \(-0.0581247\pi\) | |||||||
\(384\) | 81792.8 | + | 23615.5i | 0.554693 | + | 0.160153i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −63242.6 | + | 118867.i | −0.424458 | + | 0.797788i | ||||
\(387\) | 19333.1i | 0.129086i | ||||||||
\(388\) | −117803. | − | 174847.i | −0.782518 | − | 1.16144i | ||||
\(389\) | 130363. | 0.861497 | 0.430749 | − | 0.902472i | \(-0.358250\pi\) | ||||
0.430749 | + | 0.902472i | \(0.358250\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 139299.i | 0.911162i | ||||||||
\(392\) | 148895. | − | 15531.6i | 0.968964 | − | 0.101075i | ||||
\(393\) | −103079. | −0.667398 | ||||||||
\(394\) | −18580.3 | + | 34922.4i | −0.119690 | + | 0.224963i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −22160.0 | + | 14930.3i | −0.141312 | + | 0.0952088i | ||||
\(397\) | −213615. | −1.35535 | −0.677674 | − | 0.735362i | \(-0.737012\pi\) | ||||
−0.677674 | + | 0.735362i | \(0.737012\pi\) | |||||||
\(398\) | −37903.3 | − | 20166.2i | −0.239283 | − | 0.127309i | ||||
\(399\) | 758.397i | 0.00476377i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −99636.7 | −0.619627 | −0.309814 | − | 0.950797i | \(-0.600267\pi\) | ||||
−0.309814 | + | 0.950797i | \(0.600267\pi\) | |||||||
\(402\) | 24961.5 | − | 46916.2i | 0.154461 | − | 0.290316i | ||||
\(403\) | 64363.5i | 0.396305i | ||||||||
\(404\) | −91205.9 | − | 135371.i | −0.558805 | − | 0.829396i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7060.18 | − | 3756.33i | −0.0428316 | − | 0.0227883i | ||||
\(407\) | 67388.8i | 0.406817i | ||||||||
\(408\) | 8275.19 | + | 79330.5i | 0.0497116 | + | 0.476563i | ||||
\(409\) | 235531. | 1.40800 | 0.703999 | − | 0.710201i | \(-0.251396\pi\) | ||||
0.703999 | + | 0.710201i | \(0.251396\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 151183.i | − | 0.894992i | ||||||
\(412\) | 55702.6 | − | 37529.6i | 0.328157 | − | 0.221095i | ||||
\(413\) | −40325.9 | −0.236420 | ||||||||
\(414\) | −55375.7 | − | 29462.3i | −0.323086 | − | 0.171896i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −30900.6 | − | 36923.6i | −0.178558 | − | 0.213362i | ||||
\(417\) | −20153.8 | −0.115900 | ||||||||
\(418\) | 2155.89 | − | 4052.09i | 0.0123388 | − | 0.0231914i | ||||
\(419\) | − | 201684.i | − | 1.14880i | −0.818575 | − | 0.574399i | \(-0.805236\pi\) | ||
0.818575 | − | 0.574399i | \(-0.194764\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12875.0 | −0.0726412 | −0.0363206 | − | 0.999340i | \(-0.511564\pi\) | ||||
−0.0363206 | + | 0.999340i | \(0.511564\pi\) | |||||||
\(422\) | −110336. | − | 58703.7i | −0.619574 | − | 0.329641i | ||||
\(423\) | 68763.8i | 0.384308i | ||||||||
\(424\) | 124671. | − | 13004.8i | 0.693479 | − | 0.0723388i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 22910.6 | − | 43061.5i | 0.126246 | − | 0.237285i | ||||
\(427\) | 58231.3i | 0.319375i | ||||||||
\(428\) | 7714.73 | − | 5197.79i | 0.0421146 | − | 0.0283747i | ||||
\(429\) | 15111.8 | 0.0821110 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 99240.2i | 0.534236i | 0.963664 | + | 0.267118i | \(0.0860713\pi\) | ||||
−0.963664 | + | 0.267118i | \(0.913929\pi\) | |||||||
\(432\) | −33286.5 | − | 13489.0i | −0.178361 | − | 0.0722793i | ||||
\(433\) | −269220. | −1.43592 | −0.717962 | − | 0.696082i | \(-0.754925\pi\) | ||||
−0.717962 | + | 0.696082i | \(0.754925\pi\) | |||||||
\(434\) | 20233.7 | − | 38030.0i | 0.107422 | − | 0.201905i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −64578.7 | − | 95849.8i | −0.339716 | − | 0.504218i | ||||
\(437\) | 10774.7 | 0.0564214 | ||||||||
\(438\) | 64968.2 | + | 34565.9i | 0.338651 | + | 0.180177i | ||||
\(439\) | 277426.i | 1.43952i | 0.694221 | + | 0.719762i | \(0.255749\pi\) | ||||
−0.694221 | + | 0.719762i | \(0.744251\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −63155.8 | −0.324740 | ||||||||
\(442\) | 21187.8 | − | 39823.4i | 0.108453 | − | 0.203842i | ||||
\(443\) | − | 241969.i | − | 1.23297i | −0.787366 | − | 0.616485i | \(-0.788556\pi\) | ||
0.787366 | − | 0.616485i | \(-0.211444\pi\) | |||||||
\(444\) | −75120.4 | + | 50612.4i | −0.381059 | + | 0.256738i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −112869. | − | 60051.1i | −0.567418 | − | 0.301892i | ||||
\(447\) | 186018.i | 0.930981i | ||||||||
\(448\) | 6650.52 | + | 31530.9i | 0.0331360 | + | 0.157102i | ||||
\(449\) | −150123. | −0.744653 | −0.372326 | − | 0.928102i | \(-0.621440\pi\) | ||||
−0.372326 | + | 0.928102i | \(0.621440\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 124390.i | 0.611553i | ||||||||
\(452\) | −21655.3 | − | 32141.5i | −0.105995 | − | 0.157322i | ||||
\(453\) | 45382.7 | 0.221154 | ||||||||
\(454\) | −112573. | − | 59894.0i | −0.546165 | − | 0.290584i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6136.18 | − | 640.082i | 0.0295100 | − | 0.00307827i | ||||
\(457\) | 199480. | 0.955141 | 0.477571 | − | 0.878593i | \(-0.341517\pi\) | ||||
0.477571 | + | 0.878593i | \(0.341517\pi\) | |||||||
\(458\) | −39928.9 | + | 75048.1i | −0.190352 | + | 0.357774i | ||||
\(459\) | − | 33649.1i | − | 0.159716i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −123874. | −0.582879 | −0.291440 | − | 0.956589i | \(-0.594134\pi\) | ||||
−0.291440 | + | 0.956589i | \(0.594134\pi\) | |||||||
\(462\) | −8929.00 | − | 4750.62i | −0.0418330 | − | 0.0222570i | ||||
\(463\) | 426435.i | 1.98926i | 0.103503 | + | 0.994629i | \(0.466995\pi\) | ||||
−0.103503 | + | 0.994629i | \(0.533005\pi\) | |||||||
\(464\) | −24433.7 | + | 60294.2i | −0.113489 | + | 0.280053i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 146015. | − | 274442.i | 0.672397 | − | 1.26380i | ||||
\(467\) | 229937.i | 1.05433i | 0.849763 | + | 0.527164i | \(0.176745\pi\) | ||||
−0.849763 | + | 0.527164i | \(0.823255\pi\) | |||||||
\(468\) | 11349.7 | + | 16845.6i | 0.0518195 | + | 0.0769121i | ||||
\(469\) | 20115.7 | 0.0914510 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 178400.i | − | 0.804179i | ||||||
\(472\) | 34034.9 | + | 326277.i | 0.152771 | + | 1.46454i | ||||
\(473\) | 44289.1 | 0.197959 | ||||||||
\(474\) | −48308.9 | + | 90798.7i | −0.215016 | + | 0.404132i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −25038.2 | + | 16869.5i | −0.110507 | + | 0.0744540i | ||||
\(477\) | −52880.9 | −0.232414 | ||||||||
\(478\) | −198345. | − | 105529.i | −0.868093 | − | 0.461864i | ||||
\(479\) | 27874.0i | 0.121486i | 0.998153 | + | 0.0607432i | \(0.0193471\pi\) | ||||
−0.998153 | + | 0.0607432i | \(0.980653\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 51227.7 | 0.221419 | ||||||||
\(482\) | −21202.8 | + | 39851.6i | −0.0912640 | + | 0.171535i | ||||
\(483\) | − | 23742.7i | − | 0.101774i | ||||||
\(484\) | −96690.1 | − | 143510.i | −0.412754 | − | 0.612622i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 13376.5 | + | 7116.91i | 0.0566333 | + | 0.0301314i | ||||
\(487\) | − | 20395.8i | − | 0.0859968i | −0.999075 | − | 0.0429984i | \(-0.986309\pi\) | ||
0.999075 | − | 0.0429984i | \(-0.0136910\pi\) | |||||||
\(488\) | 471149. | − | 49146.9i | 1.97842 | − | 0.206375i | ||||
\(489\) | −218218. | −0.912585 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 373834.i | − | 1.55066i | −0.631557 | − | 0.775330i | \(-0.717584\pi\) | ||
0.631557 | − | 0.775330i | \(-0.282416\pi\) | |||||||
\(492\) | −138662. | + | 93423.4i | −0.572832 | + | 0.385945i | ||||
\(493\) | −60951.1 | −0.250777 | ||||||||
\(494\) | −3080.32 | − | 1638.87i | −0.0126224 | − | 0.00671568i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −324778. | − | 131613.i | −1.32015 | − | 0.534979i | ||||
\(497\) | 18462.9 | 0.0747461 | ||||||||
\(498\) | −86152.2 | + | 161927.i | −0.347382 | + | 0.652920i | ||||
\(499\) | 277828.i | 1.11577i | 0.829919 | + | 0.557884i | \(0.188387\pi\) | ||||
−0.829919 | + | 0.557884i | \(0.811613\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 78149.3 | 0.311351 | ||||||||
\(502\) | 261803. | + | 139291.i | 1.03889 | + | 0.552733i | ||||
\(503\) | − | 250329.i | − | 0.989409i | −0.869061 | − | 0.494704i | \(-0.835276\pi\) | ||
0.869061 | − | 0.494704i | \(-0.164724\pi\) | |||||||
\(504\) | −1410.46 | − | 13521.4i | −0.00555262 | − | 0.0532305i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −67493.4 | + | 126857.i | −0.263609 | + | 0.495465i | ||||
\(507\) | 136920.i | 0.532660i | ||||||||
\(508\) | −340176. | + | 229193.i | −1.31818 | + | 0.888126i | ||||
\(509\) | −41577.1 | −0.160479 | −0.0802396 | − | 0.996776i | \(-0.525569\pi\) | ||||
−0.0802396 | + | 0.996776i | \(0.525569\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27855.6i | 0.106677i | ||||||||
\(512\) | 249503. | − | 80421.2i | 0.951780 | − | 0.306783i | ||||
\(513\) | −2602.75 | −0.00989002 | ||||||||
\(514\) | 735.103 | − | 1381.66i | 0.00278241 | − | 0.00522967i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 33263.3 | + | 49370.5i | 0.124930 | + | 0.185425i | ||||
\(517\) | 157527. | 0.589350 | ||||||||
\(518\) | −30268.6 | − | 16104.2i | −0.112806 | − | 0.0600178i | ||||
\(519\) | 119080.i | 0.442083i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −476195. | −1.75432 | −0.877161 | − | 0.480196i | \(-0.840565\pi\) | ||||
−0.877161 | + | 0.480196i | \(0.840565\pi\) | |||||||
\(522\) | 12891.4 | − | 24229.9i | 0.0473106 | − | 0.0889223i | ||||
\(523\) | − | 105663.i | − | 0.386294i | −0.981170 | − | 0.193147i | \(-0.938131\pi\) | ||
0.981170 | − | 0.193147i | \(-0.0618694\pi\) | |||||||
\(524\) | −263230. | + | 177351.i | −0.958678 | + | 0.645909i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −220884. | − | 117520.i | −0.798350 | − | 0.424758i | ||||
\(527\) | − | 328316.i | − | 1.18215i | ||||||
\(528\) | −30901.2 | + | 76254.0i | −0.110843 | + | 0.273524i | ||||
\(529\) | −57478.3 | −0.205396 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 138395.i | − | 0.490830i | ||||||
\(532\) | 1304.85 | + | 1936.70i | 0.00461038 | + | 0.00684287i | ||||
\(533\) | 94559.2 | 0.332851 | ||||||||
\(534\) | −237249. | − | 126227.i | −0.831998 | − | 0.442660i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −16977.5 | − | 162756.i | −0.0590941 | − | 0.566508i | ||||
\(537\) | 112194. | 0.389064 | ||||||||
\(538\) | −89131.0 | + | 167526.i | −0.307939 | + | 0.578784i | ||||
\(539\) | 144680.i | 0.498001i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 258293. | 0.882507 | 0.441254 | − | 0.897382i | \(-0.354534\pi\) | ||||
0.441254 | + | 0.897382i | \(0.354534\pi\) | |||||||
\(542\) | −492545. | − | 262055.i | −1.67667 | − | 0.892061i | ||||
\(543\) | 40974.8i | 0.138969i | ||||||||
\(544\) | 157623. | + | 188346.i | 0.532625 | + | 0.636443i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3611.33 | + | 6787.66i | −0.0121139 | + | 0.0227685i | ||||
\(547\) | 40859.8i | 0.136559i | 0.997666 | + | 0.0682796i | \(0.0217510\pi\) | ||||
−0.997666 | + | 0.0682796i | \(0.978249\pi\) | |||||||
\(548\) | −260115. | − | 386072.i | −0.866174 | − | 1.28560i | ||||
\(549\) | −199844. | −0.663052 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4714.54i | 0.0155288i | ||||||||
\(552\) | −192102. | + | 20038.7i | −0.630455 | + | 0.0657645i | ||||
\(553\) | −38930.6 | −0.127304 | ||||||||
\(554\) | 276505. | − | 519704.i | 0.900916 | − | 1.69331i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −51466.1 | + | 34675.3i | −0.166484 | + | 0.112168i | ||||
\(557\) | 445511. | 1.43598 | 0.717989 | − | 0.696055i | \(-0.245063\pi\) | ||||
0.717989 | + | 0.696055i | \(0.245063\pi\) | |||||||
\(558\) | 130516. | + | 69440.1i | 0.419174 | + | 0.223019i | ||||
\(559\) | − | 33667.7i | − | 0.107743i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −77084.8 | −0.244931 | ||||||||
\(562\) | −59753.5 | + | 112309.i | −0.189187 | + | 0.355585i | ||||
\(563\) | − | 320372.i | − | 1.01074i | −0.862904 | − | 0.505368i | \(-0.831357\pi\) | ||
0.862904 | − | 0.505368i | \(-0.168643\pi\) | |||||||
\(564\) | 118310. | + | 175600.i | 0.371933 | + | 0.552035i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −410735. | − | 218529.i | −1.28212 | − | 0.682144i | ||||
\(567\) | 5735.29i | 0.0178398i | ||||||||
\(568\) | −15582.6 | − | 149384.i | −0.0482996 | − | 0.463027i | ||||
\(569\) | 26018.1 | 0.0803619 | 0.0401810 | − | 0.999192i | \(-0.487207\pi\) | ||||
0.0401810 | + | 0.999192i | \(0.487207\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 321694.i | − | 0.986667i | −0.869840 | − | 0.493334i | \(-0.835778\pi\) | ||
0.869840 | − | 0.493334i | \(-0.164222\pi\) | |||||||
\(572\) | 38590.5 | − | 26000.3i | 0.117947 | − | 0.0794671i | ||||
\(573\) | −278240. | −0.847443 | ||||||||
\(574\) | −55871.6 | − | 29726.2i | −0.169577 | − | 0.0902225i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −108211. | + | 22824.0i | −0.326157 | + | 0.0687933i | ||||
\(577\) | 259440. | 0.779267 | 0.389633 | − | 0.920970i | \(-0.372602\pi\) | ||||
0.389633 | + | 0.920970i | \(0.372602\pi\) | |||||||
\(578\) | 48841.4 | − | 91799.6i | 0.146195 | − | 0.274780i | ||||
\(579\) | − | 174908.i | − | 0.521738i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −69427.3 | −0.205673 | ||||||||
\(582\) | 241785. | + | 128640.i | 0.713810 | + | 0.379779i | ||||
\(583\) | 121142.i | 0.356415i | ||||||||
\(584\) | 225379. | − | 23510.0i | 0.660828 | − | 0.0689328i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 95474.7 | − | 179449.i | 0.278031 | − | 0.522571i | ||||
\(587\) | − | 236459.i | − | 0.686247i | −0.939290 | − | 0.343123i | \(-0.888515\pi\) | ||
0.939290 | − | 0.343123i | \(-0.111485\pi\) | |||||||
\(588\) | −161279. | + | 108662.i | −0.466470 | + | 0.314284i | ||||
\(589\) | −25395.1 | −0.0732015 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 51386.8i | − | 0.147122i | ||||||
\(592\) | −104753. | + | 258495.i | −0.298897 | + | 0.737579i | ||||
\(593\) | 94856.8 | 0.269748 | 0.134874 | − | 0.990863i | \(-0.456937\pi\) | ||||
0.134874 | + | 0.990863i | \(0.456937\pi\) | |||||||
\(594\) | 16303.7 | − | 30643.5i | 0.0462076 | − | 0.0868492i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 320051. | + | 475030.i | 0.901005 | + | 1.33730i | ||||
\(597\) | 55773.0 | 0.156486 | ||||||||
\(598\) | 96434.1 | + | 51307.2i | 0.269667 | + | 0.143475i | ||||
\(599\) | − | 201635.i | − | 0.561969i | −0.959712 | − | 0.280985i | \(-0.909339\pi\) | ||
0.959712 | − | 0.280985i | \(-0.0906610\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 371285. | 1.02792 | 0.513959 | − | 0.857815i | \(-0.328178\pi\) | ||||
0.513959 | + | 0.857815i | \(0.328178\pi\) | |||||||
\(602\) | −10584.0 | + | 19893.0i | −0.0292049 | + | 0.0548919i | ||||
\(603\) | 69035.1i | 0.189861i | ||||||||
\(604\) | 115893. | − | 78082.6i | 0.317674 | − | 0.214033i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 187195. | + | 99596.0i | 0.509740 | + | 0.271204i | ||||
\(607\) | − | 258037.i | − | 0.700332i | −0.936688 | − | 0.350166i | \(-0.886125\pi\) | ||
0.936688 | − | 0.350166i | \(-0.113875\pi\) | |||||||
\(608\) | 14568.5 | − | 12192.1i | 0.0394101 | − | 0.0329815i | ||||
\(609\) | 10388.7 | 0.0280110 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 119749.i | − | 0.320766i | ||||||
\(612\) | −57894.5 | − | 85928.9i | −0.154573 | − | 0.229423i | ||||
\(613\) | 259378. | 0.690258 | 0.345129 | − | 0.938555i | \(-0.387835\pi\) | ||||
0.345129 | + | 0.938555i | \(0.387835\pi\) | |||||||
\(614\) | 369272. | + | 196469.i | 0.979511 | + | 0.521143i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −30975.4 | + | 3231.13i | −0.0816310 | + | 0.00851516i | ||||
\(617\) | 423059. | 1.11130 | 0.555650 | − | 0.831417i | \(-0.312470\pi\) | ||||
0.555650 | + | 0.831417i | \(0.312470\pi\) | |||||||
\(618\) | −40982.0 | + | 77027.4i | −0.107304 | + | 0.201682i | ||||
\(619\) | − | 178609.i | − | 0.466145i | −0.972459 | − | 0.233073i | \(-0.925122\pi\) | ||
0.972459 | − | 0.233073i | \(-0.0748780\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 81482.9 | 0.211292 | ||||||||
\(622\) | −148687. | − | 79108.0i | −0.384319 | − | 0.204475i | ||||
\(623\) | − | 101722.i | − | 0.262084i | ||||||
\(624\) | 57966.8 | + | 23490.5i | 0.148871 | + | 0.0603287i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −259069. | + | 486932.i | −0.661101 | + | 1.24257i | ||||
\(627\) | 5962.48i | 0.0151667i | ||||||||
\(628\) | −306943. | − | 455575.i | −0.778285 | − | 1.15515i | ||||
\(629\) | −261311. | −0.660475 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 637150.i | 1.60023i | 0.599846 | + | 0.800116i | \(0.295229\pi\) | ||||
−0.599846 | + | 0.800116i | \(0.704771\pi\) | |||||||
\(632\) | 32857.2 | + | 314987.i | 0.0822614 | + | 0.788603i | ||||
\(633\) | 162355. | 0.405189 | ||||||||
\(634\) | 306070. | − | 575272.i | 0.761452 | − | 1.43118i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −135041. | + | 90983.5i | −0.333849 | + | 0.224930i | ||||
\(637\) | 109983. | 0.271048 | ||||||||
\(638\) | −55506.8 | − | 29532.1i | −0.136366 | − | 0.0725526i | ||||
\(639\) | 63363.1i | 0.155180i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 744727. | 1.81251 | 0.906257 | − | 0.422727i | \(-0.138927\pi\) | ||||
0.906257 | + | 0.422727i | \(0.138927\pi\) | |||||||
\(642\) | −5675.94 | + | 10668.2i | −0.0137711 | + | 0.0258833i | ||||
\(643\) | − | 36186.6i | − | 0.0875237i | −0.999042 | − | 0.0437619i | \(-0.986066\pi\) | ||
0.999042 | − | 0.0437619i | \(-0.0139343\pi\) | |||||||
\(644\) | −40850.2 | − | 60631.1i | −0.0984968 | − | 0.146192i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15712.7 | + | 8359.82i | 0.0376517 | + | 0.0200324i | ||||
\(647\) | − | 362450.i | − | 0.865845i | −0.901431 | − | 0.432922i | \(-0.857482\pi\) | ||
0.901431 | − | 0.432922i | \(-0.142518\pi\) | |||||||
\(648\) | 46404.2 | − | 4840.55i | 0.110511 | − | 0.0115278i | ||||
\(649\) | −317041. | −0.752706 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 55959.5i | 0.132042i | ||||||||
\(652\) | −557258. | + | 375452.i | −1.31087 | + | 0.883200i | ||||
\(653\) | 190115. | 0.445850 | 0.222925 | − | 0.974836i | \(-0.428439\pi\) | ||||
0.222925 | + | 0.974836i | \(0.428439\pi\) | |||||||
\(654\) | 132544. | + | 70519.3i | 0.309888 | + | 0.164874i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −193359. | + | 477145.i | −0.449321 | + | 1.10877i | ||||
\(657\) | −95597.8 | −0.221471 | ||||||||
\(658\) | −37644.9 | + | 70755.2i | −0.0869470 | + | 0.163421i | ||||
\(659\) | − | 345083.i | − | 0.794608i | −0.917687 | − | 0.397304i | \(-0.869946\pi\) | ||
0.917687 | − | 0.397304i | \(-0.130054\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37084.2 | 0.0848761 | 0.0424381 | − | 0.999099i | \(-0.486487\pi\) | ||||
0.0424381 | + | 0.999099i | \(0.486487\pi\) | |||||||
\(662\) | −605154. | − | 321969.i | −1.38086 | − | 0.734679i | ||||
\(663\) | 58598.4i | 0.133309i | ||||||||
\(664\) | 58596.2 | + | 561736.i | 0.132903 | + | 1.27408i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 55268.2 | − | 103879.i | 0.124603 | − | 0.234196i | ||||
\(667\) | − | 147596.i | − | 0.331759i | ||||||
\(668\) | 199568. | − | 134459.i | 0.447236 | − | 0.301325i | ||||
\(669\) | 166081. | 0.371080 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 457812.i | 1.01681i | ||||||||
\(672\) | −26865.9 | − | 32102.5i | −0.0594926 | − | 0.0710886i | ||||
\(673\) | 239821. | 0.529490 | 0.264745 | − | 0.964319i | \(-0.414712\pi\) | ||||
0.264745 | + | 0.964319i | \(0.414712\pi\) | |||||||
\(674\) | 281929. | − | 529897.i | 0.620611 | − | 1.16646i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 235575. | + | 349648.i | 0.515508 | + | 0.765134i | ||||
\(677\) | −294470. | −0.642487 | −0.321244 | − | 0.946997i | \(-0.604101\pi\) | ||||
−0.321244 | + | 0.946997i | \(0.604101\pi\) | |||||||
\(678\) | 44446.3 | + | 23647.4i | 0.0966887 | + | 0.0514427i | ||||
\(679\) | 103667.i | 0.224854i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 165647. | 0.357181 | ||||||||
\(682\) | 159076. | − | 298990.i | 0.342008 | − | 0.642819i | ||||
\(683\) | − | 393749.i | − | 0.844070i | −0.906579 | − | 0.422035i | \(-0.861316\pi\) | ||
0.906579 | − | 0.422035i | \(-0.138684\pi\) | |||||||
\(684\) | −6646.56 | + | 4478.12i | −0.0142064 | + | 0.00957157i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −131689. | − | 70064.6i | −0.279835 | − | 0.148885i | ||||
\(687\) | − | 110430.i | − | 0.233977i | ||||||
\(688\) | 169887. | + | 68845.2i | 0.358909 | + | 0.145444i | ||||
\(689\) | 92089.6 | 0.193987 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 675096.i | − | 1.41387i | −0.707279 | − | 0.706935i | \(-0.750077\pi\) | ||
0.707279 | − | 0.706935i | \(-0.249923\pi\) | |||||||
\(692\) | 204881. | + | 304091.i | 0.427849 | + | 0.635027i | ||||
\(693\) | 13138.6 | 0.0273580 | ||||||||
\(694\) | −373221. | − | 198570.i | −0.774903 | − | 0.412283i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8768.04 | − | 84055.3i | −0.0181002 | − | 0.173519i | ||||
\(697\) | −482344. | −0.992867 | ||||||||
\(698\) | −191058. | + | 359102.i | −0.392153 | + | 0.737068i | ||||
\(699\) | 403829.i | 0.826500i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 110087. | 0.224027 | 0.112013 | − | 0.993707i | \(-0.464270\pi\) | ||||
0.112013 | + | 0.993707i | \(0.464270\pi\) | |||||||
\(702\) | −23294.6 | − | 12393.8i | −0.0472695 | − | 0.0251495i | ||||
\(703\) | 20212.3i | 0.0408983i | ||||||||
\(704\) | 52286.1 | + | 247894.i | 0.105497 | + | 0.500174i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −141633. | + | 266205.i | −0.284155 | + | 0.534081i | ||||
\(707\) | 80261.2i | 0.160571i | ||||||||
\(708\) | −238113. | − | 353415.i | −0.475026 | − | 0.705048i | ||||
\(709\) | −539972. | −1.07418 | −0.537092 | − | 0.843524i | \(-0.680477\pi\) | ||||
−0.537092 | + | 0.843524i | \(0.680477\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 133606.i | − | 0.264294i | ||||||
\(712\) | −823035. | + | 85853.1i | −1.62352 | + | 0.169354i | ||||
\(713\) | 795032. | 1.56389 | ||||||||
\(714\) | 18421.3 | − | 34623.7i | 0.0361347 | − | 0.0679167i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 286507. | − | 193034.i | 0.558867 | − | 0.376537i | ||||
\(717\) | 291857. | 0.567716 | ||||||||
\(718\) | 556245. | + | 295947.i | 1.07899 | + | 0.574070i | ||||
\(719\) | 206020.i | 0.398520i | 0.979947 | + | 0.199260i | \(0.0638539\pi\) | ||||
−0.979947 | + | 0.199260i | \(0.936146\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33026.0 | −0.0635310 | ||||||||
\(722\) | −244201. | + | 458987.i | −0.468461 | + | 0.880494i | ||||
\(723\) | − | 58639.9i | − | 0.112180i | ||||||
\(724\) | 70498.6 | + | 104636.i | 0.134494 | + | 0.199620i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 198451. | + | 105585.i | 0.376513 | + | 0.200321i | ||||
\(727\) | − | 961559.i | − | 1.81931i | −0.415363 | − | 0.909656i | \(-0.636345\pi\) | ||
0.415363 | − | 0.909656i | \(-0.363655\pi\) | |||||||
\(728\) | 2456.24 | + | 23546.9i | 0.00463456 | + | 0.0444294i | ||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 171738.i | 0.321390i | ||||||||
\(732\) | −510337. | + | 343839.i | −0.952434 | + | 0.641702i | ||||
\(733\) | 454366. | 0.845665 | 0.422832 | − | 0.906208i | \(-0.361036\pi\) | ||||
0.422832 | + | 0.906208i | \(0.361036\pi\) | |||||||
\(734\) | 373678. | + | 198813.i | 0.693595 | + | 0.369023i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −456089. | + | 381691.i | −0.841964 | + | 0.704622i | ||||
\(737\) | 158148. | 0.291158 | ||||||||
\(738\) | 102017. | − | 191746.i | 0.187310 | − | 0.352058i | ||||
\(739\) | 259643.i | 0.475432i | 0.971335 | + | 0.237716i | \(0.0763987\pi\) | ||||
−0.971335 | + | 0.237716i | \(0.923601\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4532.56 | 0.00825481 | ||||||||
\(742\) | −54412.4 | − | 28949.8i | −0.0988303 | − | 0.0525821i | ||||
\(743\) | 834340.i | 1.51135i | 0.654946 | + | 0.755676i | \(0.272691\pi\) | ||||
−0.654946 | + | 0.755676i | \(0.727309\pi\) | |||||||
\(744\) | 452768. | − | 47229.5i | 0.817956 | − | 0.0853233i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 24051.1 | − | 45205.0i | 0.0432172 | − | 0.0812285i | ||||
\(747\) | − | 238268.i | − | 0.426997i | ||||||
\(748\) | −196849. | + | 132627.i | −0.351828 | + | 0.237044i | ||||
\(749\) | −4574.06 | −0.00815339 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 597678.i | 1.05971i | 0.848088 | + | 0.529855i | \(0.177754\pi\) | ||||
−0.848088 | + | 0.529855i | \(0.822246\pi\) | |||||||
\(752\) | 604252. | + | 244868.i | 1.06852 | + | 0.433008i | ||||
\(753\) | −385232. | −0.679411 | ||||||||
\(754\) | −22449.7 | + | 42195.2i | −0.0394883 | + | 0.0742199i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 9867.77 | + | 14646.1i | 0.0172654 | + | 0.0256258i | ||||
\(757\) | 266595. | 0.465221 | 0.232611 | − | 0.972570i | \(-0.425273\pi\) | ||||
0.232611 | + | 0.972570i | \(0.425273\pi\) | |||||||
\(758\) | 295455. | + | 157195.i | 0.514225 | + | 0.273590i | ||||
\(759\) | − | 186664.i | − | 0.324024i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 441424. | 0.762230 | 0.381115 | − | 0.924528i | \(-0.375540\pi\) | ||||
0.381115 | + | 0.924528i | \(0.375540\pi\) | |||||||
\(762\) | 250277. | − | 470406.i | 0.431033 | − | 0.810146i | ||||
\(763\) | 56829.3i | 0.0976165i | ||||||||
\(764\) | −710534. | + | 478722.i | −1.21730 | + | 0.820156i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 188129. | + | 100093.i | 0.320626 | + | 0.170587i | ||||
\(767\) | 241008.i | 0.409677i | ||||||||
\(768\) | −237066. | + | 244466.i | −0.401927 | + | 0.414473i | ||||
\(769\) | −292264. | −0.494223 | −0.247112 | − | 0.968987i | \(-0.579481\pi\) | ||||
−0.247112 | + | 0.968987i | \(0.579481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2033.05i | 0.00342010i | ||||||||
\(772\) | −300935. | − | 446657.i | −0.504938 | − | 0.749445i | ||||
\(773\) | −617969. | −1.03421 | −0.517104 | − | 0.855923i | \(-0.672990\pi\) | ||||
−0.517104 | + | 0.855923i | \(0.672990\pi\) | |||||||
\(774\) | −68271.1 | − | 36323.2i | −0.113961 | − | 0.0606321i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 838768. | − | 87494.3i | 1.39290 | − | 0.145297i | ||||
\(777\) | 44538.9 | 0.0737730 | ||||||||
\(778\) | −244926. | + | 460350.i | −0.404647 | + | 0.760551i | ||||
\(779\) | 37309.1i | 0.0614809i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 145155. | 0.237974 | ||||||||
\(782\) | −491908. | − | 261717.i | −0.804396 | − | 0.427974i | ||||
\(783\) | 35653.2i | 0.0581534i | ||||||||
\(784\) | −224898. | + | 554973.i | −0.365892 | + | 0.902901i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 193666. | − | 364003.i | 0.313478 | − | 0.589196i | ||||
\(787\) | 829635.i | 1.33948i | 0.742594 | + | 0.669742i | \(0.233595\pi\) | ||||
−0.742594 | + | 0.669742i | \(0.766405\pi\) | |||||||
\(788\) | −88412.8 | − | 131225.i | −0.142384 | − | 0.211332i | ||||
\(789\) | 325022. | 0.522105 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19056.7i | 0.0304575i | ||||||||
\(792\) | −11088.9 | − | 106305.i | −0.0176783 | − | 0.169473i | ||||
\(793\) | 348020. | 0.553423 | ||||||||
\(794\) | 401342. | − | 754339.i | 0.636610 | − | 1.19654i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 142426. | − | 95959.5i | 0.224783 | − | 0.151447i | ||||
\(797\) | 406136. | 0.639373 | 0.319687 | − | 0.947523i | \(-0.396422\pi\) | ||||
0.319687 | + | 0.947523i | \(0.396422\pi\) | |||||||
\(798\) | −2678.13 | − | 1424.88i | −0.00420557 | − | 0.00223755i | ||||
\(799\) | 610836.i | 0.956821i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 349102. | 0.544110 | ||||||||
\(802\) | 187198. | − | 351847.i | 0.291040 | − | 0.547022i | ||||
\(803\) | 218999.i | 0.339634i | ||||||||
\(804\) | 118777. | + | 176293.i | 0.183747 | + | 0.272724i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −227287. | − | 120927.i | −0.349868 | − | 0.186145i | ||||
\(807\) | − | 246506.i | − | 0.378513i | ||||||
\(808\) | 649393. | − | 67740.0i | 0.994683 | − | 0.103758i | ||||
\(809\) | 559872. | 0.855445 | 0.427722 | − | 0.903910i | \(-0.359316\pi\) | ||||
0.427722 | + | 0.903910i | \(0.359316\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.17497e6i | − | 1.78642i | −0.449636 | − | 0.893212i | \(-0.648446\pi\) | ||
0.449636 | − | 0.893212i | \(-0.351554\pi\) | |||||||
\(812\) | 26529.5 | − | 17874.2i | 0.0402361 | − | 0.0271091i | ||||
\(813\) | 724758. | 1.09651 | ||||||||
\(814\) | −237970. | − | 126611.i | −0.359148 | − | 0.191083i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −295687. | − | 119825.i | −0.444071 | − | 0.179956i | ||||
\(817\) | 13283.9 | 0.0199013 | ||||||||
\(818\) | −442518. | + | 831731.i | −0.661339 | + | 1.24302i | ||||
\(819\) | − | 9987.74i | − | 0.0148902i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.26453e6 | 1.87604 | 0.938019 | − | 0.346584i | \(-0.112658\pi\) | ||||
0.938019 | + | 0.346584i | \(0.112658\pi\) | |||||||
\(822\) | 533872. | + | 284044.i | 0.790121 | + | 0.420379i | ||||
\(823\) | − | 30196.9i | − | 0.0445823i | −0.999752 | − | 0.0222911i | \(-0.992904\pi\) | ||
0.999752 | − | 0.0222911i | \(-0.00709607\pi\) | |||||||
\(824\) | 27873.8 | + | 267214.i | 0.0410527 | + | 0.393554i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 75764.7 | − | 142403.i | 0.111047 | − | 0.208718i | ||||
\(827\) | 414905.i | 0.606649i | 0.952887 | + | 0.303324i | \(0.0980965\pi\) | ||||
−0.952887 | + | 0.303324i | \(0.901903\pi\) | |||||||
\(828\) | 208080. | − | 140194.i | 0.303508 | − | 0.204489i | ||||
\(829\) | 184231. | 0.268074 | 0.134037 | − | 0.990976i | \(-0.457206\pi\) | ||||
0.134037 | + | 0.990976i | \(0.457206\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 764721.i | 1.10739i | ||||||||
\(832\) | 188445. | − | 39746.9i | 0.272231 | − | 0.0574191i | ||||
\(833\) | −561020. | −0.808515 | ||||||||
\(834\) | 37865.1 | − | 71169.0i | 0.0544386 | − | 0.102320i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10258.7 | + | 15226.2i | 0.0146784 | + | 0.0217861i | ||||
\(837\) | −192048. | −0.274131 | ||||||||
\(838\) | 712207. | + | 378926.i | 1.01419 | + | 0.539593i | ||||
\(839\) | 1.18916e6i | 1.68934i | 0.535290 | + | 0.844668i | \(0.320202\pi\) | ||||
−0.535290 | + | 0.844668i | \(0.679798\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −642700. | −0.908691 | ||||||||
\(842\) | 24189.7 | − | 45465.5i | 0.0341197 | − | 0.0641295i | ||||
\(843\) | − | 165258.i | − | 0.232545i | ||||||
\(844\) | 414601. | − | 279337.i | 0.582030 | − | 0.392142i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −242826. | − | 129194.i | −0.339276 | − | 0.180510i | ||||
\(847\) | 85087.3i | 0.118604i | ||||||||
\(848\) | −188309. | + | 464684.i | −0.261866 | + | 0.646198i | ||||
\(849\) | 604378. | 0.838481 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 632776.i | − | 0.873757i | ||||||
\(852\) | 109019. | + | 161809.i | 0.150183 | + | 0.222906i | ||||
\(853\) | −695023. | −0.955215 | −0.477608 | − | 0.878573i | \(-0.658496\pi\) | ||||
−0.477608 | + | 0.878573i | \(0.658496\pi\) | |||||||
\(854\) | −205632. | − | 109405.i | −0.281952 | − | 0.150011i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3860.48 | + | 37008.7i | 0.00526858 | + | 0.0505075i | ||||
\(857\) | −584255. | −0.795501 | −0.397751 | − | 0.917494i | \(-0.630209\pi\) | ||||
−0.397751 | + | 0.917494i | \(0.630209\pi\) | |||||||
\(858\) | −28392.1 | + | 53364.2i | −0.0385677 | + | 0.0724896i | ||||
\(859\) | − | 1.10752e6i | − | 1.50095i | −0.660901 | − | 0.750473i | \(-0.729826\pi\) | ||
0.660901 | − | 0.750473i | \(-0.270174\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 82212.6 | 0.110900 | ||||||||
\(862\) | −350447. | − | 186453.i | −0.471637 | − | 0.250932i | ||||
\(863\) | 1.13453e6i | 1.52332i | 0.647974 | + | 0.761662i | \(0.275616\pi\) | ||||
−0.647974 | + | 0.761662i | \(0.724384\pi\) | |||||||
\(864\) | 110173. | − | 92201.3i | 0.147587 | − | 0.123512i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 505813. | − | 950697.i | 0.674456 | − | 1.26767i | ||||
\(867\) | 135079.i | 0.179701i | ||||||||
\(868\) | 96280.3 | + | 142902.i | 0.127790 | + | 0.189670i | ||||
\(869\) | −306070. | −0.405305 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 120221.i | − | 0.158469i | ||||||
\(872\) | 459805. | − | 47963.6i | 0.604701 | − | 0.0630781i | ||||
\(873\) | −355775. | −0.466818 | ||||||||
\(874\) | −20243.7 | + | 38048.9i | −0.0265013 | + | 0.0498103i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −244125. | + | 164479.i | −0.318130 | + | 0.214340i | ||||
\(877\) | −337283. | −0.438526 | −0.219263 | − | 0.975666i | \(-0.570365\pi\) | ||||
−0.219263 | + | 0.975666i | \(0.570365\pi\) | |||||||
\(878\) | −979676. | − | 521231.i | −1.27085 | − | 0.676147i | ||||
\(879\) | 264051.i | 0.341751i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.31898e6 | −1.69936 | −0.849680 | − | 0.527298i | \(-0.823205\pi\) | ||||
−0.849680 | + | 0.527298i | \(0.823205\pi\) | |||||||
\(882\) | 118658. | − | 223022.i | 0.152531 | − | 0.286689i | ||||
\(883\) | − | 902766.i | − | 1.15785i | −0.815379 | − | 0.578927i | \(-0.803472\pi\) | ||
0.815379 | − | 0.578927i | \(-0.196528\pi\) | |||||||
\(884\) | 100821. | + | 149641.i | 0.129016 | + | 0.191490i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 854466. | + | 454614.i | 1.08850 | + | 0.579129i | ||||
\(887\) | − | 451995.i | − | 0.574495i | −0.957856 | − | 0.287247i | \(-0.907260\pi\) | ||
0.957856 | − | 0.287247i | \(-0.0927402\pi\) | |||||||
\(888\) | −37590.5 | − | 360364.i | −0.0476708 | − | 0.456999i | ||||
\(889\) | 201690. | 0.255200 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 45090.6i | 0.0567977i | ||||||||
\(892\) | 424117. | − | 285748.i | 0.533035 | − | 0.359132i | ||||
\(893\) | 47247.9 | 0.0592488 | ||||||||
\(894\) | −656887. | − | 349493.i | −0.821894 | − | 0.437284i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −123840. | − | 35755.5i | −0.154257 | − | 0.0445376i | ||||
\(897\) | −141899. | −0.176357 | ||||||||
\(898\) | 282052. | − | 530129.i | 0.349765 | − | 0.657398i | ||||
\(899\) | 347870.i | 0.430426i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −469747. | −0.578647 | ||||||||
\(902\) | −439260. | − | 233706.i | −0.539894 | − | 0.287247i | ||||
\(903\) | − | 29271.7i | − | 0.0358982i | ||||||
\(904\) | 154187. | − | 16083.7i | 0.188674 | − | 0.0196811i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −85265.4 | + | 160260.i | −0.103876 | + | 0.195240i | ||||
\(907\) | 1.02817e6i | 1.24982i | 0.780695 | + | 0.624912i | \(0.214865\pi\) | ||||
−0.780695 | + | 0.624912i | \(0.785135\pi\) | |||||||
\(908\) | 423007. | − | 285001.i | 0.513069 | − | 0.345680i | ||||
\(909\) | −275449. | −0.333360 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 825314.i | 0.994449i | 0.867622 | + | 0.497224i | \(0.165647\pi\) | ||||
−0.867622 | + | 0.497224i | \(0.834353\pi\) | |||||||
\(912\) | −9268.38 | + | 22871.3i | −0.0111433 | + | 0.0274980i | ||||
\(913\) | −545834. | −0.654816 | ||||||||
\(914\) | −374785. | + | 704425.i | −0.448632 | + | 0.843222i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −189999. | − | 282002.i | −0.226443 | − | 0.336094i | ||||
\(917\) | 156069. | 0.185600 | ||||||||
\(918\) | 118825. | + | 63220.3i | 0.141001 | + | 0.0750190i | ||||
\(919\) | − | 726978.i | − | 0.860776i | −0.902644 | − | 0.430388i | \(-0.858377\pi\) | ||
0.902644 | − | 0.430388i | \(-0.141623\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −543367. | −0.640581 | ||||||||
\(922\) | 232736. | − | 437437.i | 0.273779 | − | 0.514580i | ||||
\(923\) | − | 110344.i | − | 0.129522i | ||||||
\(924\) | 33551.8 | − | 22605.5i | 0.0392981 | − | 0.0264771i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.50587e6 | − | 801190.i | −1.75617 | − | 0.934359i | ||||
\(927\) | − | 113342.i | − | 0.131896i | ||||||
\(928\) | −167011. | − | 199564.i | −0.193932 | − | 0.231732i | ||||
\(929\) | 403513. | 0.467548 | 0.233774 | − | 0.972291i | \(-0.424892\pi\) | ||||
0.233774 | + | 0.972291i | \(0.424892\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 43394.6i | 0.0500653i | ||||||||
\(932\) | 694802. | + | 1.03125e6i | 0.799888 | + | 1.18722i | ||||
\(933\) | 218786. | 0.251337 | ||||||||
\(934\) | −811978. | − | 432008.i | −0.930788 | − | 0.495220i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −80810.7 | + | 8429.59i | −0.0922396 | + | 0.00962177i | ||||
\(937\) | −348791. | −0.397270 | −0.198635 | − | 0.980074i | \(-0.563651\pi\) | ||||
−0.198635 | + | 0.980074i | \(0.563651\pi\) | |||||||
\(938\) | −37793.4 | + | 71034.4i | −0.0429547 | + | 0.0807352i | ||||
\(939\) | − | 716499.i | − | 0.812615i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.02657e6 | −1.15934 | −0.579669 | − | 0.814852i | \(-0.696818\pi\) | ||||
−0.579669 | + | 0.814852i | \(0.696818\pi\) | |||||||
\(942\) | 629983. | + | 335179.i | 0.709949 | + | 0.377724i | ||||
\(943\) | − | 1.16802e6i | − | 1.31349i | ||||||
\(944\) | −1.21613e6 | − | 492824.i | −1.36469 | − | 0.553029i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −83210.7 | + | 156398.i | −0.0929815 | + | 0.174763i | ||||
\(947\) | 202208.i | 0.225475i | 0.993625 | + | 0.112737i | \(0.0359619\pi\) | ||||
−0.993625 | + | 0.112737i | \(0.964038\pi\) | |||||||
\(948\) | −229874. | − | 341186.i | −0.255784 | − | 0.379643i | ||||
\(949\) | 166479. | 0.184853 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 846488.i | 0.935965i | ||||||||
\(952\) | −12529.2 | − | 120112.i | −0.0138245 | − | 0.132529i | ||||
\(953\) | −1.22625e6 | −1.35018 | −0.675092 | − | 0.737734i | \(-0.735896\pi\) | ||||
−0.675092 | + | 0.737734i | \(0.735896\pi\) | |||||||
\(954\) | 99353.1 | − | 186738.i | 0.109165 | − | 0.205181i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 745306. | − | 502150.i | 0.815490 | − | 0.549436i | ||||
\(957\) | 81675.8 | 0.0891805 | ||||||||
\(958\) | −98431.4 | − | 52369.8i | −0.107251 | − | 0.0570624i | ||||
\(959\) | 228902.i | 0.248892i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −950300. | −1.02900 | ||||||||
\(962\) | −96247.0 | + | 180900.i | −0.104001 | + | 0.195474i | ||||
\(963\) | − | 15697.7i | − | 0.0169272i | ||||||
\(964\) | −100892. | − | 149747.i | −0.108568 | − | 0.161140i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 83842.7 | + | 44608.0i | 0.0898485 | + | 0.0478034i | ||||
\(967\) | 1.77133e6i | 1.89429i | 0.320811 | + | 0.947143i | \(0.396045\pi\) | ||||
−0.320811 | + | 0.947143i | \(0.603955\pi\) | |||||||
\(968\) | 688440. | − | 71813.2i | 0.734710 | − | 0.0766396i | ||||
\(969\) | −23120.5 | −0.0246235 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 491594.i | − | 0.521397i | −0.965420 | − | 0.260698i | \(-0.916047\pi\) | ||
0.965420 | − | 0.260698i | \(-0.0839528\pi\) | |||||||
\(972\) | −50263.9 | + | 33865.3i | −0.0532015 | + | 0.0358445i | ||||
\(973\) | 30514.2 | 0.0322312 | ||||||||
\(974\) | 72023.6 | + | 38319.7i | 0.0759201 | + | 0.0403928i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −711646. | + | 1.75611e6i | −0.747075 | + | 1.84353i | ||||
\(977\) | −1.81510e6 | −1.90156 | −0.950782 | − | 0.309859i | \(-0.899718\pi\) | ||||
−0.950782 | + | 0.309859i | \(0.899718\pi\) | |||||||
\(978\) | 409990. | − | 770594.i | 0.428643 | − | 0.805653i | ||||
\(979\) | − | 799736.i | − | 0.834414i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −195033. | −0.202661 | ||||||||
\(982\) | 1.32012e6 | + | 702363.i | 1.36896 | + | 0.728348i | ||||
\(983\) | 373738.i | 0.386777i | 0.981122 | + | 0.193388i | \(0.0619477\pi\) | ||||
−0.981122 | + | 0.193388i | \(0.938052\pi\) | |||||||
\(984\) | −69387.0 | − | 665182.i | −0.0716618 | − | 0.686989i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 114515. | − | 215237.i | 0.117790 | − | 0.221392i | ||||
\(987\) | − | 104113.i | − | 0.106874i | ||||||
\(988\) | 11574.7 | − | 7798.43i | 0.0118575 | − | 0.00798902i | ||||
\(989\) | −415871. | −0.425174 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 499462.i | − | 0.508575i | −0.967129 | − | 0.254287i | \(-0.918159\pi\) | ||
0.967129 | − | 0.254287i | \(-0.0818409\pi\) | |||||||
\(992\) | 1.07496e6 | − | 899612.i | 1.09237 | − | 0.914181i | ||||
\(993\) | 890457. | 0.903056 | ||||||||
\(994\) | −34688.3 | + | 65198.2i | −0.0351084 | + | 0.0659877i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −409949. | − | 608459.i | −0.413248 | − | 0.613356i | ||||
\(997\) | 1.27264e6 | 1.28031 | 0.640157 | − | 0.768244i | \(-0.278869\pi\) | ||||
0.640157 | + | 0.768244i | \(0.278869\pi\) | |||||||
\(998\) | −981093. | − | 521985.i | −0.985029 | − | 0.524079i | ||||
\(999\) | 152853.i | 0.153159i |
(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 | 300.5.c.c.151.6 | yes | 16 | |
4.3 | odd | 2 | inner | 300.5.c.c.151.5 | yes | 16 | |
5.2 | odd | 4 | 300.5.f.c.199.5 | 32 | |||
5.3 | odd | 4 | 300.5.f.c.199.28 | 32 | |||
5.4 | even | 2 | 300.5.c.b.151.11 | ✓ | 16 | ||
20.3 | even | 4 | 300.5.f.c.199.6 | 32 | |||
20.7 | even | 4 | 300.5.f.c.199.27 | 32 | |||
20.19 | odd | 2 | 300.5.c.b.151.12 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.5.c.b.151.11 | ✓ | 16 | 5.4 | even | 2 | ||
300.5.c.b.151.12 | yes | 16 | 20.19 | odd | 2 | ||
300.5.c.c.151.5 | yes | 16 | 4.3 | odd | 2 | inner | |
300.5.c.c.151.6 | yes | 16 | 1.1 | even | 1 | trivial | |
300.5.f.c.199.5 | 32 | 5.2 | odd | 4 | |||
300.5.f.c.199.6 | 32 | 20.3 | even | 4 | |||
300.5.f.c.199.27 | 32 | 20.7 | even | 4 | |||
300.5.f.c.199.28 | 32 | 5.3 | odd | 4 |