Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,4,Mod(7,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.54011460034\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.14 | ||
Character | \(\chi\) | \(=\) | 60.7 |
Dual form | 60.4.j.b.43.14 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.79539 | − | 0.431034i | 0.988320 | − | 0.152393i | ||||
\(3\) | 2.12132 | + | 2.12132i | 0.408248 | + | 0.408248i | ||||
\(4\) | 7.62842 | − | 2.40982i | 0.953552 | − | 0.301227i | ||||
\(5\) | 2.54602 | − | 10.8866i | 0.227723 | − | 0.973726i | ||||
\(6\) | 6.84428 | + | 5.01556i | 0.465694 | + | 0.341266i | ||||
\(7\) | −9.77420 | + | 9.77420i | −0.527757 | + | 0.527757i | −0.919903 | − | 0.392146i | \(-0.871733\pi\) |
0.392146 | + | 0.919903i | \(0.371733\pi\) | |||||||
\(8\) | 20.2857 | − | 10.0245i | 0.896510 | − | 0.443024i | ||||
\(9\) | 9.00000i | 0.333333i | ||||||||
\(10\) | 2.42464 | − | 31.5297i | 0.0766740 | − | 0.997056i | ||||
\(11\) | 32.5528i | 0.892276i | 0.894964 | + | 0.446138i | \(0.147201\pi\) | ||||
−0.894964 | + | 0.446138i | \(0.852799\pi\) | |||||||
\(12\) | 21.2943 | + | 11.0703i | 0.512262 | + | 0.266311i | ||||
\(13\) | −5.95358 | + | 5.95358i | −0.127017 | + | 0.127017i | −0.767758 | − | 0.640740i | \(-0.778628\pi\) |
0.640740 | + | 0.767758i | \(0.278628\pi\) | |||||||
\(14\) | −23.1097 | + | 31.5357i | −0.441166 | + | 0.602020i | ||||
\(15\) | 28.4949 | − | 17.6930i | 0.490490 | − | 0.304554i | ||||
\(16\) | 52.3856 | − | 36.7662i | 0.818525 | − | 0.574471i | ||||
\(17\) | −71.0654 | − | 71.0654i | −1.01388 | − | 1.01388i | −0.999902 | − | 0.0139739i | \(-0.995552\pi\) |
−0.0139739 | − | 0.999902i | \(-0.504448\pi\) | |||||||
\(18\) | 3.87930 | + | 25.1585i | 0.0507978 | + | 0.329440i | ||||
\(19\) | −104.985 | −1.26764 | −0.633822 | − | 0.773479i | \(-0.718515\pi\) | ||||
−0.633822 | + | 0.773479i | \(0.718515\pi\) | |||||||
\(20\) | −6.81253 | − | 89.1829i | −0.0761664 | − | 0.997095i | ||||
\(21\) | −41.4684 | −0.430912 | ||||||||
\(22\) | 14.0314 | + | 90.9978i | 0.135977 | + | 0.881855i | ||||
\(23\) | 83.3400 | + | 83.3400i | 0.755547 | + | 0.755547i | 0.975509 | − | 0.219962i | \(-0.0705932\pi\) |
−0.219962 | + | 0.975509i | \(0.570593\pi\) | |||||||
\(24\) | 64.2976 | + | 21.7673i | 0.546862 | + | 0.185135i | ||||
\(25\) | −112.036 | − | 55.4350i | −0.896284 | − | 0.443480i | ||||
\(26\) | −14.0764 | + | 19.2088i | −0.106177 | + | 0.144891i | ||||
\(27\) | −19.0919 | + | 19.0919i | −0.136083 | + | 0.136083i | ||||
\(28\) | −51.0077 | + | 98.1157i | −0.344270 | + | 0.662219i | ||||
\(29\) | 171.025i | 1.09512i | 0.836766 | + | 0.547561i | \(0.184443\pi\) | ||||
−0.836766 | + | 0.547561i | \(0.815557\pi\) | |||||||
\(30\) | 72.0280 | − | 61.7411i | 0.438349 | − | 0.375744i | ||||
\(31\) | − | 123.188i | − | 0.713716i | −0.934159 | − | 0.356858i | \(-0.883848\pi\) | ||
0.934159 | − | 0.356858i | \(-0.116152\pi\) | |||||||
\(32\) | 130.591 | − | 125.356i | 0.721419 | − | 0.692499i | ||||
\(33\) | −69.0549 | + | 69.0549i | −0.364270 | + | 0.364270i | ||||
\(34\) | −229.287 | − | 168.024i | −1.15654 | − | 0.847526i | ||||
\(35\) | 81.5224 | + | 131.293i | 0.393708 | + | 0.634074i | ||||
\(36\) | 21.6883 | + | 68.6558i | 0.100409 | + | 0.317851i | ||||
\(37\) | −52.1044 | − | 52.1044i | −0.231511 | − | 0.231511i | 0.581812 | − | 0.813323i | \(-0.302344\pi\) |
−0.813323 | + | 0.581812i | \(0.802344\pi\) | |||||||
\(38\) | −293.474 | + | 45.2521i | −1.25284 | + | 0.193181i | ||||
\(39\) | −25.2589 | −0.103709 | ||||||||
\(40\) | −57.4845 | − | 246.365i | −0.227228 | − | 0.973842i | ||||
\(41\) | 471.285 | 1.79518 | 0.897590 | − | 0.440831i | \(-0.145316\pi\) | ||||
0.897590 | + | 0.440831i | \(0.145316\pi\) | |||||||
\(42\) | −115.920 | + | 17.8743i | −0.425879 | + | 0.0656682i | ||||
\(43\) | −258.032 | − | 258.032i | −0.915106 | − | 0.915106i | 0.0815622 | − | 0.996668i | \(-0.474009\pi\) |
−0.996668 | + | 0.0815622i | \(0.974009\pi\) | |||||||
\(44\) | 78.4463 | + | 248.326i | 0.268778 | + | 0.850832i | ||||
\(45\) | 97.9793 | + | 22.9142i | 0.324575 | + | 0.0759078i | ||||
\(46\) | 268.890 | + | 197.045i | 0.861863 | + | 0.631582i | ||||
\(47\) | −54.3382 | + | 54.3382i | −0.168639 | + | 0.168639i | −0.786381 | − | 0.617742i | \(-0.788048\pi\) |
0.617742 | + | 0.786381i | \(0.288048\pi\) | |||||||
\(48\) | 189.119 | + | 33.1338i | 0.568688 | + | 0.0996343i | ||||
\(49\) | 151.930i | 0.442944i | ||||||||
\(50\) | −337.077 | − | 106.671i | −0.953399 | − | 0.301712i | ||||
\(51\) | − | 301.505i | − | 0.827827i | ||||||
\(52\) | −31.0694 | + | 59.7635i | −0.0828567 | + | 0.159379i | ||||
\(53\) | 331.639 | − | 331.639i | 0.859511 | − | 0.859511i | −0.131770 | − | 0.991280i | \(-0.542066\pi\) |
0.991280 | + | 0.131770i | \(0.0420660\pi\) | |||||||
\(54\) | −45.1400 | + | 61.5985i | −0.113755 | + | 0.155231i | ||||
\(55\) | 354.389 | + | 82.8802i | 0.868833 | + | 0.203192i | ||||
\(56\) | −100.295 | + | 296.258i | −0.239331 | + | 0.706949i | ||||
\(57\) | −222.707 | − | 222.707i | −0.517513 | − | 0.517513i | ||||
\(58\) | 73.7175 | + | 478.081i | 0.166889 | + | 1.08233i | ||||
\(59\) | 567.547 | 1.25234 | 0.626172 | − | 0.779685i | \(-0.284621\pi\) | ||||
0.626172 | + | 0.779685i | \(0.284621\pi\) | |||||||
\(60\) | 174.734 | − | 203.637i | 0.375968 | − | 0.438157i | ||||
\(61\) | 832.043 | 1.74643 | 0.873215 | − | 0.487336i | \(-0.162031\pi\) | ||||
0.873215 | + | 0.487336i | \(0.162031\pi\) | |||||||
\(62\) | −53.0982 | − | 344.358i | −0.108766 | − | 0.705380i | ||||
\(63\) | −87.9678 | − | 87.9678i | −0.175919 | − | 0.175919i | ||||
\(64\) | 311.019 | − | 406.707i | 0.607460 | − | 0.794350i | ||||
\(65\) | 49.6562 | + | 79.9722i | 0.0947554 | + | 0.152605i | ||||
\(66\) | −163.271 | + | 222.801i | −0.304503 | + | 0.415528i | ||||
\(67\) | 38.6168 | − | 38.6168i | 0.0704148 | − | 0.0704148i | −0.671022 | − | 0.741437i | \(-0.734145\pi\) |
0.741437 | + | 0.671022i | \(0.234145\pi\) | |||||||
\(68\) | −713.371 | − | 370.862i | −1.27219 | − | 0.661377i | ||||
\(69\) | 353.581i | 0.616902i | ||||||||
\(70\) | 284.479 | + | 331.877i | 0.485738 | + | 0.566669i | ||||
\(71\) | 534.459i | 0.893361i | 0.894694 | + | 0.446680i | \(0.147394\pi\) | ||||
−0.894694 | + | 0.446680i | \(0.852606\pi\) | |||||||
\(72\) | 90.2203 | + | 182.571i | 0.147675 | + | 0.298837i | ||||
\(73\) | −418.286 | + | 418.286i | −0.670640 | + | 0.670640i | −0.957864 | − | 0.287224i | \(-0.907268\pi\) |
0.287224 | + | 0.957864i | \(0.407268\pi\) | |||||||
\(74\) | −168.111 | − | 123.193i | −0.264088 | − | 0.193526i | ||||
\(75\) | −120.068 | − | 355.259i | −0.184857 | − | 0.546956i | ||||
\(76\) | −800.870 | + | 252.995i | −1.20876 | + | 0.381848i | ||||
\(77\) | −318.178 | − | 318.178i | −0.470905 | − | 0.470905i | ||||
\(78\) | −70.6085 | + | 10.8874i | −0.102498 | + | 0.0158046i | ||||
\(79\) | 76.6095 | 0.109104 | 0.0545522 | − | 0.998511i | \(-0.482627\pi\) | ||||
0.0545522 | + | 0.998511i | \(0.482627\pi\) | |||||||
\(80\) | −266.883 | − | 663.908i | −0.372981 | − | 0.927839i | ||||
\(81\) | −81.0000 | −0.111111 | ||||||||
\(82\) | 1317.43 | − | 203.140i | 1.77421 | − | 0.273574i | ||||
\(83\) | −908.404 | − | 908.404i | −1.20133 | − | 1.20133i | −0.973763 | − | 0.227565i | \(-0.926923\pi\) |
−0.227565 | − | 0.973763i | \(-0.573077\pi\) | |||||||
\(84\) | −316.339 | + | 99.9313i | −0.410897 | + | 0.129802i | ||||
\(85\) | −954.594 | + | 592.726i | −1.21812 | + | 0.756354i | ||||
\(86\) | −832.522 | − | 610.081i | −1.04387 | − | 0.764961i | ||||
\(87\) | −362.799 | + | 362.799i | −0.447081 | + | 0.447081i | ||||
\(88\) | 326.325 | + | 660.357i | 0.395300 | + | 0.799935i | ||||
\(89\) | − | 12.1097i | − | 0.0144227i | −0.999974 | − | 0.00721136i | \(-0.997705\pi\) | ||
0.999974 | − | 0.00721136i | \(-0.00229547\pi\) | |||||||
\(90\) | 283.767 | + | 21.8218i | 0.332352 | + | 0.0255580i | ||||
\(91\) | − | 116.383i | − | 0.134069i | ||||||
\(92\) | 836.586 | + | 434.918i | 0.948045 | + | 0.492863i | ||||
\(93\) | 261.321 | − | 261.321i | 0.291374 | − | 0.291374i | ||||
\(94\) | −128.475 | + | 175.318i | −0.140970 | + | 0.192369i | ||||
\(95\) | −267.294 | + | 1142.93i | −0.288672 | + | 1.23434i | ||||
\(96\) | 542.944 | + | 11.1050i | 0.577230 | + | 0.0118062i | ||||
\(97\) | −613.459 | − | 613.459i | −0.642138 | − | 0.642138i | 0.308943 | − | 0.951081i | \(-0.400025\pi\) |
−0.951081 | + | 0.308943i | \(0.900025\pi\) | |||||||
\(98\) | 65.4869 | + | 424.704i | 0.0675018 | + | 0.437771i | ||||
\(99\) | −292.975 | −0.297425 | ||||||||
\(100\) | −988.242 | − | 152.897i | −0.988242 | − | 0.152897i | ||||
\(101\) | −941.741 | −0.927789 | −0.463895 | − | 0.885890i | \(-0.653548\pi\) | ||||
−0.463895 | + | 0.885890i | \(0.653548\pi\) | |||||||
\(102\) | −129.959 | − | 842.824i | −0.126155 | − | 0.818157i | ||||
\(103\) | 779.115 | + | 779.115i | 0.745325 | + | 0.745325i | 0.973597 | − | 0.228272i | \(-0.0733076\pi\) |
−0.228272 | + | 0.973597i | \(0.573308\pi\) | |||||||
\(104\) | −61.0910 | + | 180.454i | −0.0576007 | + | 0.170144i | ||||
\(105\) | −105.580 | + | 451.450i | −0.0981287 | + | 0.419590i | ||||
\(106\) | 784.112 | − | 1070.01i | 0.718488 | − | 0.980455i | ||||
\(107\) | −541.238 | + | 541.238i | −0.489004 | + | 0.489004i | −0.907992 | − | 0.418988i | \(-0.862385\pi\) |
0.418988 | + | 0.907992i | \(0.362385\pi\) | |||||||
\(108\) | −99.6330 | + | 191.649i | −0.0887703 | + | 0.170754i | ||||
\(109\) | − | 697.524i | − | 0.612942i | −0.951880 | − | 0.306471i | \(-0.900852\pi\) | ||
0.951880 | − | 0.306471i | \(-0.0991482\pi\) | |||||||
\(110\) | 1026.38 | + | 78.9290i | 0.889650 | + | 0.0684144i | ||||
\(111\) | − | 221.060i | − | 0.189028i | ||||||
\(112\) | −152.667 | + | 871.387i | −0.128801 | + | 0.735164i | ||||
\(113\) | 715.431 | − | 715.431i | 0.595593 | − | 0.595593i | −0.343543 | − | 0.939137i | \(-0.611627\pi\) |
0.939137 | + | 0.343543i | \(0.111627\pi\) | |||||||
\(114\) | −718.547 | − | 526.559i | −0.590334 | − | 0.432603i | ||||
\(115\) | 1119.47 | − | 695.102i | 0.907751 | − | 0.563640i | ||||
\(116\) | 412.138 | + | 1304.65i | 0.329880 | + | 1.04426i | ||||
\(117\) | −53.5823 | − | 53.5823i | −0.0423392 | − | 0.0423392i | ||||
\(118\) | 1586.51 | − | 244.632i | 1.23772 | − | 0.190849i | ||||
\(119\) | 1389.22 | 1.07016 | ||||||||
\(120\) | 400.675 | − | 644.561i | 0.304804 | − | 0.490334i | ||||
\(121\) | 271.315 | 0.203843 | ||||||||
\(122\) | 2325.89 | − | 358.639i | 1.72603 | − | 0.266144i | ||||
\(123\) | 999.747 | + | 999.747i | 0.732879 | + | 0.732879i | ||||
\(124\) | −296.860 | − | 939.729i | −0.214991 | − | 0.680566i | ||||
\(125\) | −888.743 | + | 1078.55i | −0.635933 | + | 0.771744i | ||||
\(126\) | −283.822 | − | 207.987i | −0.200673 | − | 0.147055i | ||||
\(127\) | −1377.02 | + | 1377.02i | −0.962130 | + | 0.962130i | −0.999309 | − | 0.0371786i | \(-0.988163\pi\) |
0.0371786 | + | 0.999309i | \(0.488163\pi\) | |||||||
\(128\) | 694.116 | − | 1270.97i | 0.479311 | − | 0.877645i | ||||
\(129\) | − | 1094.74i | − | 0.747181i | ||||||
\(130\) | 173.279 | + | 202.150i | 0.116905 | + | 0.136382i | ||||
\(131\) | − | 2511.90i | − | 1.67531i | −0.546198 | − | 0.837656i | \(-0.683925\pi\) | ||
0.546198 | − | 0.837656i | \(-0.316075\pi\) | |||||||
\(132\) | −360.370 | + | 693.190i | −0.237623 | + | 0.457079i | ||||
\(133\) | 1026.15 | − | 1026.15i | 0.669008 | − | 0.669008i | ||||
\(134\) | 91.3038 | − | 124.594i | 0.0588616 | − | 0.0803231i | ||||
\(135\) | 159.237 | + | 256.454i | 0.101518 | + | 0.163497i | ||||
\(136\) | −2154.01 | − | 729.218i | −1.35812 | − | 0.459779i | ||||
\(137\) | 681.328 | + | 681.328i | 0.424889 | + | 0.424889i | 0.886883 | − | 0.461994i | \(-0.152866\pi\) |
−0.461994 | + | 0.886883i | \(0.652866\pi\) | |||||||
\(138\) | 152.406 | + | 988.398i | 0.0940118 | + | 0.609696i | ||||
\(139\) | −2059.15 | −1.25651 | −0.628254 | − | 0.778009i | \(-0.716230\pi\) | ||||
−0.628254 | + | 0.778009i | \(0.716230\pi\) | |||||||
\(140\) | 938.279 | + | 805.105i | 0.566422 | + | 0.486027i | ||||
\(141\) | −230.537 | −0.137693 | ||||||||
\(142\) | 230.370 | + | 1494.02i | 0.136142 | + | 0.882926i | ||||
\(143\) | −193.806 | − | 193.806i | −0.113335 | − | 0.113335i | ||||
\(144\) | 330.896 | + | 471.470i | 0.191490 | + | 0.272842i | ||||
\(145\) | 1861.88 | + | 435.433i | 1.06635 | + | 0.249385i | ||||
\(146\) | −988.978 | + | 1349.57i | −0.560606 | + | 0.765008i | ||||
\(147\) | −322.292 | + | 322.292i | −0.180831 | + | 0.180831i | ||||
\(148\) | −523.036 | − | 271.912i | −0.290495 | − | 0.151021i | ||||
\(149\) | 1201.46i | 0.660586i | 0.943878 | + | 0.330293i | \(0.107148\pi\) | ||||
−0.943878 | + | 0.330293i | \(0.892852\pi\) | |||||||
\(150\) | −488.765 | − | 941.333i | −0.266050 | − | 0.512397i | ||||
\(151\) | 1112.39i | 0.599505i | 0.954017 | + | 0.299752i | \(0.0969041\pi\) | ||||
−0.954017 | + | 0.299752i | \(0.903096\pi\) | |||||||
\(152\) | −2129.70 | + | 1052.42i | −1.13645 | + | 0.561596i | ||||
\(153\) | 639.589 | − | 639.589i | 0.337959 | − | 0.337959i | ||||
\(154\) | −1026.58 | − | 752.286i | −0.537168 | − | 0.393642i | ||||
\(155\) | −1341.10 | − | 313.639i | −0.694964 | − | 0.162530i | ||||
\(156\) | −192.686 | + | 60.8693i | −0.0988923 | + | 0.0312400i | ||||
\(157\) | −614.705 | − | 614.705i | −0.312476 | − | 0.312476i | 0.533392 | − | 0.845868i | \(-0.320917\pi\) |
−0.845868 | + | 0.533392i | \(0.820917\pi\) | |||||||
\(158\) | 214.153 | − | 33.0213i | 0.107830 | − | 0.0166268i | ||||
\(159\) | 1407.02 | 0.701787 | ||||||||
\(160\) | −1032.21 | − | 1740.85i | −0.510021 | − | 0.860162i | ||||
\(161\) | −1629.16 | −0.797491 | ||||||||
\(162\) | −226.427 | + | 34.9137i | −0.109813 | + | 0.0169326i | ||||
\(163\) | −1714.95 | − | 1714.95i | −0.824081 | − | 0.824081i | 0.162609 | − | 0.986691i | \(-0.448009\pi\) |
−0.986691 | + | 0.162609i | \(0.948009\pi\) | |||||||
\(164\) | 3595.16 | − | 1135.71i | 1.71180 | − | 0.540757i | ||||
\(165\) | 575.957 | + | 927.588i | 0.271747 | + | 0.437652i | ||||
\(166\) | −2930.90 | − | 2147.79i | −1.37037 | − | 1.00422i | ||||
\(167\) | 1908.98 | − | 1908.98i | 0.884559 | − | 0.884559i | −0.109435 | − | 0.993994i | \(-0.534904\pi\) |
0.993994 | + | 0.109435i | \(0.0349042\pi\) | |||||||
\(168\) | −841.216 | + | 415.700i | −0.386317 | + | 0.190904i | ||||
\(169\) | 2126.11i | 0.967733i | ||||||||
\(170\) | −2412.98 | + | 2068.36i | −1.08863 | + | 0.933154i | ||||
\(171\) | − | 944.866i | − | 0.422548i | ||||||
\(172\) | −2590.19 | − | 1346.57i | −1.14826 | − | 0.596947i | ||||
\(173\) | −55.3986 | + | 55.3986i | −0.0243461 | + | 0.0243461i | −0.719175 | − | 0.694829i | \(-0.755480\pi\) |
0.694829 | + | 0.719175i | \(0.255480\pi\) | |||||||
\(174\) | −857.785 | + | 1170.54i | −0.373727 | + | 0.509992i | ||||
\(175\) | 1636.89 | − | 553.225i | 0.707070 | − | 0.238971i | ||||
\(176\) | 1196.84 | + | 1705.30i | 0.512587 | + | 0.730350i | ||||
\(177\) | 1203.95 | + | 1203.95i | 0.511267 | + | 0.511267i | ||||
\(178\) | −5.21967 | − | 33.8512i | −0.00219793 | − | 0.0142543i | ||||
\(179\) | −75.7074 | −0.0316125 | −0.0158062 | − | 0.999875i | \(-0.505031\pi\) | ||||
−0.0158062 | + | 0.999875i | \(0.505031\pi\) | |||||||
\(180\) | 802.646 | − | 61.3128i | 0.332365 | − | 0.0253888i | ||||
\(181\) | 1328.71 | 0.545649 | 0.272824 | − | 0.962064i | \(-0.412042\pi\) | ||||
0.272824 | + | 0.962064i | \(0.412042\pi\) | |||||||
\(182\) | −50.1650 | − | 325.336i | −0.0204312 | − | 0.132503i | ||||
\(183\) | 1765.03 | + | 1765.03i | 0.712977 | + | 0.712977i | ||||
\(184\) | 2526.05 | + | 855.170i | 1.01208 | + | 0.342630i | ||||
\(185\) | −699.898 | + | 434.580i | −0.278149 | + | 0.172708i | ||||
\(186\) | 617.856 | − | 843.133i | 0.243567 | − | 0.332374i | ||||
\(187\) | 2313.38 | − | 2313.38i | 0.904658 | − | 0.904658i | ||||
\(188\) | −283.570 | + | 545.460i | −0.110008 | + | 0.211605i | ||||
\(189\) | − | 373.216i | − | 0.143637i | ||||||
\(190\) | −254.551 | + | 3310.15i | −0.0971953 | + | 1.26391i | ||||
\(191\) | − | 527.413i | − | 0.199803i | −0.994997 | − | 0.0999013i | \(-0.968147\pi\) | ||
0.994997 | − | 0.0999013i | \(-0.0318527\pi\) | |||||||
\(192\) | 1522.53 | − | 202.985i | 0.572287 | − | 0.0762977i | ||||
\(193\) | −1186.43 | + | 1186.43i | −0.442491 | + | 0.442491i | −0.892848 | − | 0.450357i | \(-0.851297\pi\) |
0.450357 | + | 0.892848i | \(0.351297\pi\) | |||||||
\(194\) | −1979.28 | − | 1450.44i | −0.732495 | − | 0.536780i | ||||
\(195\) | −64.3098 | + | 274.983i | −0.0236170 | + | 0.100984i | ||||
\(196\) | 366.123 | + | 1158.99i | 0.133427 | + | 0.422371i | ||||
\(197\) | −34.2184 | − | 34.2184i | −0.0123754 | − | 0.0123754i | 0.700892 | − | 0.713267i | \(-0.252785\pi\) |
−0.713267 | + | 0.700892i | \(0.752785\pi\) | |||||||
\(198\) | −818.980 | + | 126.282i | −0.293952 | + | 0.0453257i | ||||
\(199\) | −549.266 | −0.195660 | −0.0978302 | − | 0.995203i | \(-0.531190\pi\) | ||||
−0.0978302 | + | 0.995203i | \(0.531190\pi\) | |||||||
\(200\) | −2828.43 | − | 1.43981i | −1.00000 | − | 0.000509049i | ||||
\(201\) | 163.837 | 0.0574934 | ||||||||
\(202\) | −2632.53 | + | 405.922i | −0.916953 | + | 0.141389i | ||||
\(203\) | −1671.63 | − | 1671.63i | −0.577958 | − | 0.577958i | ||||
\(204\) | −726.572 | − | 2300.01i | −0.249364 | − | 0.789376i | ||||
\(205\) | 1199.90 | − | 5130.69i | 0.408804 | − | 1.74801i | ||||
\(206\) | 2513.76 | + | 1842.11i | 0.850202 | + | 0.623037i | ||||
\(207\) | −750.060 | + | 750.060i | −0.251849 | + | 0.251849i | ||||
\(208\) | −92.9915 | + | 530.772i | −0.0309990 | + | 0.176935i | ||||
\(209\) | − | 3417.56i | − | 1.13109i | ||||||
\(210\) | −100.546 | + | 1307.49i | −0.0330397 | + | 0.429644i | ||||
\(211\) | 3610.84i | 1.17811i | 0.808094 | + | 0.589054i | \(0.200499\pi\) | ||||
−0.808094 | + | 0.589054i | \(0.799501\pi\) | |||||||
\(212\) | 1730.69 | − | 3329.07i | 0.560681 | − | 1.07850i | ||||
\(213\) | −1133.76 | + | 1133.76i | −0.364713 | + | 0.364713i | ||||
\(214\) | −1279.68 | + | 1746.26i | −0.408772 | + | 0.557814i | ||||
\(215\) | −3466.05 | + | 2152.13i | −1.09945 | + | 0.682672i | ||||
\(216\) | −195.906 | + | 578.679i | −0.0617116 | + | 0.182287i | ||||
\(217\) | 1204.06 | + | 1204.06i | 0.376669 | + | 0.376669i | ||||
\(218\) | −300.656 | − | 1949.85i | −0.0934083 | − | 0.605783i | ||||
\(219\) | −1774.64 | −0.547575 | ||||||||
\(220\) | 2903.15 | − | 221.767i | 0.889684 | − | 0.0679615i | ||||
\(221\) | 846.188 | 0.257560 | ||||||||
\(222\) | −95.2844 | − | 617.950i | −0.0288066 | − | 0.186820i | ||||
\(223\) | 1003.49 | + | 1003.49i | 0.301339 | + | 0.301339i | 0.841538 | − | 0.540199i | \(-0.181651\pi\) |
−0.540199 | + | 0.841538i | \(0.681651\pi\) | |||||||
\(224\) | −51.1673 | + | 2501.67i | −0.0152623 | + | 0.746206i | ||||
\(225\) | 498.915 | − | 1008.32i | 0.147827 | − | 0.298761i | ||||
\(226\) | 1691.53 | − | 2308.28i | 0.497872 | − | 0.679401i | ||||
\(227\) | 1594.19 | − | 1594.19i | 0.466123 | − | 0.466123i | −0.434533 | − | 0.900656i | \(-0.643087\pi\) |
0.900656 | + | 0.434533i | \(0.143087\pi\) | |||||||
\(228\) | −2235.58 | − | 1162.22i | −0.649365 | − | 0.337587i | ||||
\(229\) | 1802.27i | 0.520074i | 0.965599 | + | 0.260037i | \(0.0837348\pi\) | ||||
−0.965599 | + | 0.260037i | \(0.916265\pi\) | |||||||
\(230\) | 2829.75 | − | 2425.61i | 0.811254 | − | 0.695392i | ||||
\(231\) | − | 1349.91i | − | 0.384493i | ||||||
\(232\) | 1714.44 | + | 3469.36i | 0.485165 | + | 0.981787i | ||||
\(233\) | −1616.15 | + | 1616.15i | −0.454410 | + | 0.454410i | −0.896815 | − | 0.442406i | \(-0.854125\pi\) |
0.442406 | + | 0.896815i | \(0.354125\pi\) | |||||||
\(234\) | −172.879 | − | 126.688i | −0.0482968 | − | 0.0353924i | ||||
\(235\) | 453.211 | + | 729.904i | 0.125805 | + | 0.202611i | ||||
\(236\) | 4329.48 | − | 1367.68i | 1.19418 | − | 0.377240i | ||||
\(237\) | 162.513 | + | 162.513i | 0.0445417 | + | 0.0445417i | ||||
\(238\) | 3883.40 | − | 598.799i | 1.05766 | − | 0.163086i | ||||
\(239\) | −321.450 | −0.0869995 | −0.0434998 | − | 0.999053i | \(-0.513851\pi\) | ||||
−0.0434998 | + | 0.999053i | \(0.513851\pi\) | |||||||
\(240\) | 842.216 | − | 1974.51i | 0.226520 | − | 0.531057i | ||||
\(241\) | −1712.86 | −0.457822 | −0.228911 | − | 0.973447i | \(-0.573517\pi\) | ||||
−0.228911 | + | 0.973447i | \(0.573517\pi\) | |||||||
\(242\) | 758.431 | − | 116.946i | 0.201462 | − | 0.0310643i | ||||
\(243\) | −171.827 | − | 171.827i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 6347.17 | − | 2005.07i | 1.66531 | − | 0.526072i | ||||
\(245\) | 1654.00 | + | 386.817i | 0.431306 | + | 0.100869i | ||||
\(246\) | 3225.61 | + | 2363.76i | 0.836005 | + | 0.612633i | ||||
\(247\) | 625.037 | − | 625.037i | 0.161013 | − | 0.161013i | ||||
\(248\) | −1234.90 | − | 2498.95i | −0.316193 | − | 0.639854i | ||||
\(249\) | − | 3854.03i | − | 0.980880i | ||||||
\(250\) | −2019.49 | + | 3398.03i | −0.510896 | + | 0.859642i | ||||
\(251\) | 5379.04i | 1.35268i | 0.736591 | + | 0.676339i | \(0.236434\pi\) | ||||
−0.736591 | + | 0.676339i | \(0.763566\pi\) | |||||||
\(252\) | −883.042 | − | 459.069i | −0.220740 | − | 0.114757i | ||||
\(253\) | −2712.95 | + | 2712.95i | −0.674157 | + | 0.674157i | ||||
\(254\) | −3255.76 | + | 4442.84i | −0.804270 | + | 1.09751i | ||||
\(255\) | −3282.36 | − | 767.639i | −0.806076 | − | 0.188515i | ||||
\(256\) | 1392.50 | − | 3852.03i | 0.339965 | − | 0.940438i | ||||
\(257\) | 1432.19 | + | 1432.19i | 0.347617 | + | 0.347617i | 0.859221 | − | 0.511604i | \(-0.170949\pi\) |
−0.511604 | + | 0.859221i | \(0.670949\pi\) | |||||||
\(258\) | −471.869 | − | 3060.22i | −0.113865 | − | 0.738454i | ||||
\(259\) | 1018.56 | 0.244363 | ||||||||
\(260\) | 571.517 | + | 490.399i | 0.136323 | + | 0.116974i | ||||
\(261\) | −1539.22 | −0.365040 | ||||||||
\(262\) | −1082.71 | − | 7021.75i | −0.255307 | − | 1.65574i | ||||
\(263\) | 3876.88 | + | 3876.88i | 0.908969 | + | 0.908969i | 0.996189 | − | 0.0872200i | \(-0.0277983\pi\) |
−0.0872200 | + | 0.996189i | \(0.527798\pi\) | |||||||
\(264\) | −708.588 | + | 2093.07i | −0.165192 | + | 0.487952i | ||||
\(265\) | −2766.05 | − | 4454.77i | −0.641197 | − | 1.03266i | ||||
\(266\) | 2426.17 | − | 3310.78i | 0.559242 | − | 0.763147i | ||||
\(267\) | 25.6885 | − | 25.6885i | 0.00588805 | − | 0.00588805i | ||||
\(268\) | 201.526 | − | 387.644i | 0.0459333 | − | 0.0883550i | ||||
\(269\) | − | 970.808i | − | 0.220042i | −0.993929 | − | 0.110021i | \(-0.964908\pi\) | ||
0.993929 | − | 0.110021i | \(-0.0350918\pi\) | |||||||
\(270\) | 555.670 | + | 648.252i | 0.125248 | + | 0.146116i | ||||
\(271\) | 6724.75i | 1.50738i | 0.657231 | + | 0.753689i | \(0.271727\pi\) | ||||
−0.657231 | + | 0.753689i | \(0.728273\pi\) | |||||||
\(272\) | −6335.61 | − | 1110.00i | −1.41233 | − | 0.247440i | ||||
\(273\) | 246.886 | − | 246.886i | 0.0547334 | − | 0.0547334i | ||||
\(274\) | 2198.25 | + | 1610.90i | 0.484677 | + | 0.355176i | ||||
\(275\) | 1804.57 | − | 3647.07i | 0.395707 | − | 0.799733i | ||||
\(276\) | 852.066 | + | 2697.27i | 0.185827 | + | 0.588248i | ||||
\(277\) | −3393.42 | − | 3393.42i | −0.736067 | − | 0.736067i | 0.235747 | − | 0.971814i | \(-0.424246\pi\) |
−0.971814 | + | 0.235747i | \(0.924246\pi\) | |||||||
\(278\) | −5756.12 | + | 887.562i | −1.24183 | + | 0.191483i | ||||
\(279\) | 1108.69 | 0.237905 | ||||||||
\(280\) | 2969.88 | + | 1846.15i | 0.633873 | + | 0.394031i | ||||
\(281\) | −3173.60 | −0.673740 | −0.336870 | − | 0.941551i | \(-0.609368\pi\) | ||||
−0.336870 | + | 0.941551i | \(0.609368\pi\) | |||||||
\(282\) | −644.442 | + | 99.3694i | −0.136085 | + | 0.0209836i | ||||
\(283\) | −2902.60 | − | 2902.60i | −0.609687 | − | 0.609687i | 0.333177 | − | 0.942864i | \(-0.391879\pi\) |
−0.942864 | + | 0.333177i | \(0.891879\pi\) | |||||||
\(284\) | 1287.95 | + | 4077.08i | 0.269104 | + | 0.851866i | ||||
\(285\) | −2991.54 | + | 1857.50i | −0.621766 | + | 0.386066i | ||||
\(286\) | −625.300 | − | 458.226i | −0.129282 | − | 0.0947395i | ||||
\(287\) | −4606.44 | + | 4606.44i | −0.947420 | + | 0.947420i | ||||
\(288\) | 1128.20 | + | 1175.32i | 0.230833 | + | 0.240473i | ||||
\(289\) | 5187.59i | 1.05589i | ||||||||
\(290\) | 5392.36 | + | 414.674i | 1.09190 | + | 0.0839673i | ||||
\(291\) | − | 2602.69i | − | 0.524303i | ||||||
\(292\) | −2182.87 | + | 4198.86i | −0.437476 | + | 0.841505i | ||||
\(293\) | −664.490 | + | 664.490i | −0.132491 | + | 0.132491i | −0.770242 | − | 0.637751i | \(-0.779865\pi\) |
0.637751 | + | 0.770242i | \(0.279865\pi\) | |||||||
\(294\) | −762.013 | + | 1039.85i | −0.151162 | + | 0.206277i | ||||
\(295\) | 1444.99 | − | 6178.65i | 0.285188 | − | 1.21944i | ||||
\(296\) | −1579.29 | − | 534.655i | −0.310117 | − | 0.104987i | ||||
\(297\) | −621.494 | − | 621.494i | −0.121423 | − | 0.121423i | ||||
\(298\) | 517.869 | + | 3358.54i | 0.100669 | + | 0.652870i | ||||
\(299\) | −992.343 | −0.191935 | ||||||||
\(300\) | −1772.04 | − | 2420.72i | −0.341028 | − | 0.465868i | ||||
\(301\) | 5044.12 | 0.965908 | ||||||||
\(302\) | 479.479 | + | 3109.57i | 0.0913606 | + | 0.592503i | ||||
\(303\) | −1997.73 | − | 1997.73i | −0.378768 | − | 0.378768i | ||||
\(304\) | −5499.70 | + | 3859.90i | −1.03760 | + | 0.728225i | ||||
\(305\) | 2118.40 | − | 9058.11i | 0.397703 | − | 1.70054i | ||||
\(306\) | 1512.22 | − | 2063.59i | 0.282509 | − | 0.385514i | ||||
\(307\) | 3273.06 | − | 3273.06i | 0.608480 | − | 0.608480i | −0.334069 | − | 0.942549i | \(-0.608422\pi\) |
0.942549 | + | 0.334069i | \(0.108422\pi\) | |||||||
\(308\) | −3193.94 | − | 1660.44i | −0.590882 | − | 0.307184i | ||||
\(309\) | 3305.51i | 0.608556i | ||||||||
\(310\) | −3884.08 | − | 298.687i | −0.711615 | − | 0.0547235i | ||||
\(311\) | − | 7895.36i | − | 1.43957i | −0.694199 | − | 0.719783i | \(-0.744241\pi\) | ||
0.694199 | − | 0.719783i | \(-0.255759\pi\) | |||||||
\(312\) | −512.395 | + | 253.208i | −0.0929764 | + | 0.0459457i | ||||
\(313\) | −6267.74 | + | 6267.74i | −1.13187 | + | 1.13187i | −0.141999 | + | 0.989867i | \(0.545353\pi\) |
−0.989867 | + | 0.141999i | \(0.954647\pi\) | |||||||
\(314\) | −1983.30 | − | 1453.38i | −0.356446 | − | 0.261207i | ||||
\(315\) | −1181.64 | + | 733.701i | −0.211358 | + | 0.131236i | ||||
\(316\) | 584.409 | − | 184.615i | 0.104037 | − | 0.0328652i | ||||
\(317\) | 5075.26 | + | 5075.26i | 0.899227 | + | 0.899227i | 0.995368 | − | 0.0961407i | \(-0.0306499\pi\) |
−0.0961407 | + | 0.995368i | \(0.530650\pi\) | |||||||
\(318\) | 3933.18 | − | 606.475i | 0.693590 | − | 0.106948i | ||||
\(319\) | −5567.34 | −0.977151 | ||||||||
\(320\) | −3635.79 | − | 4421.43i | −0.635147 | − | 0.772391i | ||||
\(321\) | −2296.28 | −0.399270 | ||||||||
\(322\) | −4554.15 | + | 702.224i | −0.788176 | + | 0.121532i | ||||
\(323\) | 7460.81 | + | 7460.81i | 1.28523 | + | 1.28523i | ||||
\(324\) | −617.902 | + | 195.195i | −0.105950 | + | 0.0334697i | ||||
\(325\) | 997.050 | − | 336.976i | 0.170173 | − | 0.0575140i | ||||
\(326\) | −5533.16 | − | 4054.75i | −0.940040 | − | 0.688871i | ||||
\(327\) | 1479.67 | − | 1479.67i | 0.250232 | − | 0.250232i | ||||
\(328\) | 9560.35 | − | 4724.39i | 1.60940 | − | 0.795307i | ||||
\(329\) | − | 1062.23i | − | 0.178001i | ||||||
\(330\) | 2009.85 | + | 2344.71i | 0.335268 | + | 0.391128i | ||||
\(331\) | 3395.92i | 0.563918i | 0.959426 | + | 0.281959i | \(0.0909842\pi\) | ||||
−0.959426 | + | 0.281959i | \(0.909016\pi\) | |||||||
\(332\) | −9118.77 | − | 4740.60i | −1.50740 | − | 0.783657i | ||||
\(333\) | 468.940 | − | 468.940i | 0.0771704 | − | 0.0771704i | ||||
\(334\) | 4513.51 | − | 6159.18i | 0.739426 | − | 1.00903i | ||||
\(335\) | −322.086 | − | 518.724i | −0.0525296 | − | 0.0845998i | ||||
\(336\) | −2172.35 | + | 1524.64i | −0.352712 | + | 0.247547i | ||||
\(337\) | 6558.61 | + | 6558.61i | 1.06015 | + | 1.06015i | 0.998071 | + | 0.0620770i | \(0.0197724\pi\) |
0.0620770 | + | 0.998071i | \(0.480228\pi\) | |||||||
\(338\) | 916.425 | + | 5943.31i | 0.147476 | + | 0.956430i | ||||
\(339\) | 3035.32 | 0.486300 | ||||||||
\(340\) | −5853.68 | + | 6821.96i | −0.933708 | + | 1.08815i | ||||
\(341\) | 4010.11 | 0.636832 | ||||||||
\(342\) | −407.269 | − | 2641.27i | −0.0643935 | − | 0.417612i | ||||
\(343\) | −4837.55 | − | 4837.55i | −0.761524 | − | 0.761524i | ||||
\(344\) | −7821.01 | − | 2647.73i | −1.22582 | − | 0.414988i | ||||
\(345\) | 3849.30 | + | 900.227i | 0.600693 | + | 0.140483i | ||||
\(346\) | −130.982 | + | 178.739i | −0.0203516 | + | 0.0277719i | ||||
\(347\) | −2120.84 | + | 2120.84i | −0.328106 | + | 0.328106i | −0.851866 | − | 0.523760i | \(-0.824529\pi\) |
0.523760 | + | 0.851866i | \(0.324529\pi\) | |||||||
\(348\) | −1893.30 | + | 3641.86i | −0.291643 | + | 0.560989i | ||||
\(349\) | − | 9509.41i | − | 1.45853i | −0.684231 | − | 0.729265i | \(-0.739862\pi\) | ||
0.684231 | − | 0.729265i | \(-0.260138\pi\) | |||||||
\(350\) | 4337.29 | − | 2252.04i | 0.662394 | − | 0.343932i | ||||
\(351\) | − | 227.330i | − | 0.0345698i | ||||||
\(352\) | 4080.68 | + | 4251.09i | 0.617901 | + | 0.643705i | ||||
\(353\) | 5502.52 | − | 5502.52i | 0.829659 | − | 0.829659i | −0.157811 | − | 0.987469i | \(-0.550444\pi\) |
0.987469 | + | 0.157811i | \(0.0504436\pi\) | |||||||
\(354\) | 3884.45 | + | 2846.56i | 0.583209 | + | 0.427382i | ||||
\(355\) | 5818.43 | + | 1360.75i | 0.869889 | + | 0.203439i | ||||
\(356\) | −29.1820 | − | 92.3776i | −0.00434451 | − | 0.0137528i | ||||
\(357\) | 2946.97 | + | 2946.97i | 0.436892 | + | 0.436892i | ||||
\(358\) | −211.632 | + | 32.6324i | −0.0312433 | + | 0.00481754i | ||||
\(359\) | 3705.16 | 0.544709 | 0.272355 | − | 0.962197i | \(-0.412198\pi\) | ||||
0.272355 | + | 0.962197i | \(0.412198\pi\) | |||||||
\(360\) | 2217.28 | − | 517.361i | 0.324614 | − | 0.0757425i | ||||
\(361\) | 4162.86 | 0.606920 | ||||||||
\(362\) | 3714.27 | − | 572.720i | 0.539275 | − | 0.0831533i | ||||
\(363\) | 575.546 | + | 575.546i | 0.0832185 | + | 0.0832185i | ||||
\(364\) | −280.462 | − | 887.819i | −0.0403851 | − | 0.127842i | ||||
\(365\) | 3488.74 | + | 5618.68i | 0.500299 | + | 0.805740i | ||||
\(366\) | 5694.74 | + | 4173.16i | 0.813302 | + | 0.595996i | ||||
\(367\) | 6714.02 | − | 6714.02i | 0.954956 | − | 0.954956i | −0.0440720 | − | 0.999028i | \(-0.514033\pi\) |
0.999028 | + | 0.0440720i | \(0.0140331\pi\) | |||||||
\(368\) | 7429.90 | + | 1301.72i | 1.05247 | + | 0.184394i | ||||
\(369\) | 4241.57i | 0.598393i | ||||||||
\(370\) | −1769.17 | + | 1516.50i | −0.248580 | + | 0.213079i | ||||
\(371\) | 6483.00i | 0.907226i | ||||||||
\(372\) | 1363.73 | − | 2623.20i | 0.190070 | − | 0.365610i | ||||
\(373\) | 6819.34 | − | 6819.34i | 0.946627 | − | 0.946627i | −0.0520187 | − | 0.998646i | \(-0.516566\pi\) |
0.998646 | + | 0.0520187i | \(0.0165655\pi\) | |||||||
\(374\) | 5469.65 | − | 7463.94i | 0.756227 | − | 1.03196i | ||||
\(375\) | −4173.25 | + | 402.632i | −0.574682 | + | 0.0554449i | ||||
\(376\) | −557.576 | + | 1647.00i | −0.0764755 | + | 0.225898i | ||||
\(377\) | −1018.21 | − | 1018.21i | −0.139100 | − | 0.139100i | ||||
\(378\) | −160.869 | − | 1043.28i | −0.0218894 | − | 0.141960i | ||||
\(379\) | −12484.6 | −1.69206 | −0.846030 | − | 0.533136i | \(-0.821014\pi\) | ||||
−0.846030 | + | 0.533136i | \(0.821014\pi\) | |||||||
\(380\) | 715.214 | + | 9362.87i | 0.0965519 | + | 1.26396i | ||||
\(381\) | −5842.19 | −0.785576 | ||||||||
\(382\) | −227.333 | − | 1474.33i | −0.0304486 | − | 0.197469i | ||||
\(383\) | 3159.41 | + | 3159.41i | 0.421510 | + | 0.421510i | 0.885723 | − | 0.464213i | \(-0.153663\pi\) |
−0.464213 | + | 0.885723i | \(0.653663\pi\) | |||||||
\(384\) | 4168.57 | − | 1223.68i | 0.553975 | − | 0.162619i | ||||
\(385\) | −4273.96 | + | 2653.78i | −0.565769 | + | 0.351297i | ||||
\(386\) | −2805.14 | + | 3827.91i | −0.369890 | + | 0.504756i | ||||
\(387\) | 2322.29 | − | 2322.29i | 0.305035 | − | 0.305035i | ||||
\(388\) | −6158.05 | − | 3201.40i | −0.805741 | − | 0.418883i | ||||
\(389\) | − | 2757.53i | − | 0.359414i | −0.983720 | − | 0.179707i | \(-0.942485\pi\) | ||
0.983720 | − | 0.179707i | \(-0.0575150\pi\) | |||||||
\(390\) | −61.2439 | + | 796.406i | −0.00795181 | + | 0.103404i | ||||
\(391\) | − | 11845.2i | − | 1.53206i | ||||||
\(392\) | 1523.02 | + | 3082.01i | 0.196235 | + | 0.397104i | ||||
\(393\) | 5328.55 | − | 5328.55i | 0.683943 | − | 0.683943i | ||||
\(394\) | −110.403 | − | 80.9045i | −0.0141168 | − | 0.0103449i | ||||
\(395\) | 195.050 | − | 834.016i | 0.0248456 | − | 0.106238i | ||||
\(396\) | −2234.94 | + | 706.016i | −0.283611 | + | 0.0895926i | ||||
\(397\) | −1824.49 | − | 1824.49i | −0.230651 | − | 0.230651i | 0.582314 | − | 0.812964i | \(-0.302148\pi\) |
−0.812964 | + | 0.582314i | \(0.802148\pi\) | |||||||
\(398\) | −1535.41 | + | 236.752i | −0.193375 | + | 0.0298174i | ||||
\(399\) | 4353.57 | 0.546243 | ||||||||
\(400\) | −7907.18 | + | 1215.12i | −0.988397 | + | 0.151890i | ||||
\(401\) | −2771.47 | −0.345139 | −0.172569 | − | 0.984997i | \(-0.555207\pi\) | ||||
−0.172569 | + | 0.984997i | \(0.555207\pi\) | |||||||
\(402\) | 457.989 | − | 70.6193i | 0.0568219 | − | 0.00876162i | ||||
\(403\) | 733.410 | + | 733.410i | 0.0906545 | + | 0.0906545i | ||||
\(404\) | −7184.00 | + | 2269.42i | −0.884696 | + | 0.279475i | ||||
\(405\) | −206.228 | + | 881.814i | −0.0253026 | + | 0.108192i | ||||
\(406\) | −5393.39 | − | 3952.33i | −0.659285 | − | 0.483131i | ||||
\(407\) | 1696.14 | − | 1696.14i | 0.206572 | − | 0.206572i | ||||
\(408\) | −3022.43 | − | 6116.24i | −0.366747 | − | 0.742155i | ||||
\(409\) | 6.56085i | 0.000793186i | 1.00000 | 0.000396593i | \(0.000126239\pi\) | |||||
−1.00000 | 0.000396593i | \(0.999874\pi\) | ||||||||
\(410\) | 1142.70 | − | 14859.5i | 0.137644 | − | 1.78990i | ||||
\(411\) | 2890.63i | 0.346920i | ||||||||
\(412\) | 7820.94 | + | 4065.89i | 0.935219 | + | 0.486195i | ||||
\(413\) | −5547.32 | + | 5547.32i | −0.660934 | + | 0.660934i | ||||
\(414\) | −1773.41 | + | 2420.01i | −0.210527 | + | 0.287288i | ||||
\(415\) | −12202.2 | + | 7576.60i | −1.44333 | + | 0.896194i | ||||
\(416\) | −31.1666 | + | 1523.80i | −0.00367324 | + | 0.179592i | ||||
\(417\) | −4368.11 | − | 4368.11i | −0.512967 | − | 0.512967i | ||||
\(418\) | −1473.08 | − | 9553.41i | −0.172370 | − | 1.11788i | ||||
\(419\) | 1900.10 | 0.221542 | 0.110771 | − | 0.993846i | \(-0.464668\pi\) | ||||
0.110771 | + | 0.993846i | \(0.464668\pi\) | |||||||
\(420\) | 282.505 | + | 3698.27i | 0.0328210 | + | 0.429660i | ||||
\(421\) | −6030.55 | −0.698125 | −0.349063 | − | 0.937099i | \(-0.613500\pi\) | ||||
−0.349063 | + | 0.937099i | \(0.613500\pi\) | |||||||
\(422\) | 1556.39 | + | 10093.7i | 0.179536 | + | 1.16435i | ||||
\(423\) | −489.044 | − | 489.044i | −0.0562131 | − | 0.0562131i | ||||
\(424\) | 3403.02 | − | 10052.0i | 0.389776 | − | 1.15134i | ||||
\(425\) | 4022.34 | + | 11901.4i | 0.459087 | + | 1.35836i | ||||
\(426\) | −2680.61 | + | 3657.99i | −0.304873 | + | 0.416033i | ||||
\(427\) | −8132.56 | + | 8132.56i | −0.921691 | + | 0.921691i | ||||
\(428\) | −2824.51 | + | 5433.08i | −0.318990 | + | 0.613593i | ||||
\(429\) | − | 822.249i | − | 0.0925374i | ||||||
\(430\) | −8761.31 | + | 7510.04i | −0.982577 | + | 0.842247i | ||||
\(431\) | − | 14432.2i | − | 1.61294i | −0.591278 | − | 0.806468i | \(-0.701376\pi\) | ||
0.591278 | − | 0.806468i | \(-0.298624\pi\) | |||||||
\(432\) | −298.204 | + | 1702.07i | −0.0332114 | + | 0.189563i | ||||
\(433\) | −6260.77 | + | 6260.77i | −0.694858 | + | 0.694858i | −0.963297 | − | 0.268439i | \(-0.913492\pi\) |
0.268439 | + | 0.963297i | \(0.413492\pi\) | |||||||
\(434\) | 3884.82 | + | 2846.84i | 0.429671 | + | 0.314868i | ||||
\(435\) | 3025.94 | + | 4873.33i | 0.333524 | + | 0.537146i | ||||
\(436\) | −1680.90 | − | 5321.00i | −0.184635 | − | 0.584472i | ||||
\(437\) | −8749.45 | − | 8749.45i | −0.957764 | − | 0.957764i | ||||
\(438\) | −4960.81 | + | 764.929i | −0.541179 | + | 0.0834469i | ||||
\(439\) | 15053.8 | 1.63663 | 0.818315 | − | 0.574770i | \(-0.194909\pi\) | ||||
0.818315 | + | 0.574770i | \(0.194909\pi\) | |||||||
\(440\) | 8019.86 | − | 1871.28i | 0.868936 | − | 0.202750i | ||||
\(441\) | −1367.37 | −0.147648 | ||||||||
\(442\) | 2365.43 | − | 364.736i | 0.254552 | − | 0.0392505i | ||||
\(443\) | −2684.03 | − | 2684.03i | −0.287860 | − | 0.287860i | 0.548374 | − | 0.836233i | \(-0.315247\pi\) |
−0.836233 | + | 0.548374i | \(0.815247\pi\) | |||||||
\(444\) | −532.714 | − | 1686.34i | −0.0569403 | − | 0.180248i | ||||
\(445\) | −131.833 | − | 30.8315i | −0.0140438 | − | 0.00328439i | ||||
\(446\) | 3237.68 | + | 2372.61i | 0.343741 | + | 0.251897i | ||||
\(447\) | −2548.68 | + | 2548.68i | −0.269683 | + | 0.269683i | ||||
\(448\) | 935.273 | + | 7015.21i | 0.0986328 | + | 0.739816i | ||||
\(449\) | 3435.64i | 0.361108i | 0.983565 | + | 0.180554i | \(0.0577891\pi\) | ||||
−0.983565 | + | 0.180554i | \(0.942211\pi\) | |||||||
\(450\) | 960.043 | − | 3033.70i | 0.100571 | − | 0.317800i | ||||
\(451\) | 15341.7i | 1.60180i | ||||||||
\(452\) | 3733.55 | − | 7181.66i | 0.388521 | − | 0.747338i | ||||
\(453\) | −2359.74 | + | 2359.74i | −0.244747 | + | 0.244747i | ||||
\(454\) | 3769.22 | − | 5143.52i | 0.389644 | − | 0.531712i | ||||
\(455\) | −1267.01 | − | 296.314i | −0.130546 | − | 0.0305306i | ||||
\(456\) | −6750.29 | − | 2285.25i | −0.693226 | − | 0.234685i | ||||
\(457\) | −3751.73 | − | 3751.73i | −0.384023 | − | 0.384023i | 0.488526 | − | 0.872549i | \(-0.337535\pi\) |
−0.872549 | + | 0.488526i | \(0.837535\pi\) | |||||||
\(458\) | 776.837 | + | 5038.04i | 0.0792559 | + | 0.514000i | ||||
\(459\) | 2713.55 | 0.275942 | ||||||||
\(460\) | 6864.74 | − | 8000.25i | 0.695805 | − | 0.810900i | ||||
\(461\) | −18065.6 | −1.82516 | −0.912579 | − | 0.408900i | \(-0.865913\pi\) | ||||
−0.912579 | + | 0.408900i | \(0.865913\pi\) | |||||||
\(462\) | −581.858 | − | 3773.54i | −0.0585942 | − | 0.380002i | ||||
\(463\) | −3971.95 | − | 3971.95i | −0.398687 | − | 0.398687i | 0.479083 | − | 0.877770i | \(-0.340969\pi\) |
−0.877770 | + | 0.479083i | \(0.840969\pi\) | |||||||
\(464\) | 6287.93 | + | 8959.24i | 0.629116 | + | 0.896384i | ||||
\(465\) | −2179.57 | − | 3510.22i | −0.217365 | − | 0.350070i | ||||
\(466\) | −3821.15 | + | 5214.38i | −0.379853 | + | 0.518351i | ||||
\(467\) | −2742.42 | + | 2742.42i | −0.271743 | + | 0.271743i | −0.829802 | − | 0.558058i | \(-0.811547\pi\) |
0.558058 | + | 0.829802i | \(0.311547\pi\) | |||||||
\(468\) | −537.871 | − | 279.625i | −0.0531263 | − | 0.0276189i | ||||
\(469\) | 754.896i | 0.0743238i | ||||||||
\(470\) | 1581.52 | + | 1845.02i | 0.155213 | + | 0.181073i | ||||
\(471\) | − | 2607.97i | − | 0.255136i | ||||||
\(472\) | 11513.1 | − | 5689.36i | 1.12274 | − | 0.554818i | ||||
\(473\) | 8399.68 | − | 8399.68i | 0.816528 | − | 0.816528i | ||||
\(474\) | 524.337 | + | 384.239i | 0.0508093 | + | 0.0372335i | ||||
\(475\) | 11762.1 | + | 5819.85i | 1.13617 | + | 0.562175i | ||||
\(476\) | 10597.5 | − | 3347.75i | 1.02045 | − | 0.322361i | ||||
\(477\) | 2984.75 | + | 2984.75i | 0.286504 | + | 0.286504i | ||||
\(478\) | −898.579 | + | 138.556i | −0.0859833 | + | 0.0132582i | ||||
\(479\) | −16289.2 | −1.55380 | −0.776901 | − | 0.629623i | \(-0.783209\pi\) | ||||
−0.776901 | + | 0.629623i | \(0.783209\pi\) | |||||||
\(480\) | 1503.24 | − | 5882.54i | 0.142945 | − | 0.559375i | ||||
\(481\) | 620.416 | 0.0588119 | ||||||||
\(482\) | −4788.12 | + | 738.302i | −0.452475 | + | 0.0697691i | ||||
\(483\) | −3455.98 | − | 3455.98i | −0.325574 | − | 0.325574i | ||||
\(484\) | 2069.70 | − | 653.819i | 0.194375 | − | 0.0614029i | ||||
\(485\) | −8240.36 | + | 5116.60i | −0.771496 | + | 0.479036i | ||||
\(486\) | −554.387 | − | 406.260i | −0.0517438 | − | 0.0379184i | ||||
\(487\) | −5831.62 | + | 5831.62i | −0.542620 | + | 0.542620i | −0.924296 | − | 0.381676i | \(-0.875347\pi\) |
0.381676 | + | 0.924296i | \(0.375347\pi\) | |||||||
\(488\) | 16878.6 | − | 8340.80i | 1.56569 | − | 0.773710i | ||||
\(489\) | − | 7275.92i | − | 0.672860i | ||||||
\(490\) | 4790.30 | + | 368.376i | 0.441640 | + | 0.0339623i | ||||
\(491\) | 2534.03i | 0.232911i | 0.993196 | + | 0.116455i | \(0.0371532\pi\) | ||||
−0.993196 | + | 0.116455i | \(0.962847\pi\) | |||||||
\(492\) | 10035.7 | + | 5217.28i | 0.919602 | + | 0.478076i | ||||
\(493\) | 12154.0 | − | 12154.0i | 1.11032 | − | 1.11032i | ||||
\(494\) | 1477.81 | − | 2016.64i | 0.134595 | − | 0.183670i | ||||
\(495\) | −745.922 | + | 3189.50i | −0.0677307 | + | 0.289611i | ||||
\(496\) | −4529.15 | − | 6453.27i | −0.410010 | − | 0.584195i | ||||
\(497\) | −5223.91 | − | 5223.91i | −0.471478 | − | 0.471478i | ||||
\(498\) | −1661.22 | − | 10773.5i | −0.149480 | − | 0.969424i | ||||
\(499\) | 12553.8 | 1.12623 | 0.563113 | − | 0.826380i | \(-0.309603\pi\) | ||||
0.563113 | + | 0.826380i | \(0.309603\pi\) | |||||||
\(500\) | −4180.61 | + | 10369.3i | −0.373925 | + | 0.927459i | ||||
\(501\) | 8099.12 | 0.722239 | ||||||||
\(502\) | 2318.55 | + | 15036.5i | 0.206139 | + | 1.33688i | ||||
\(503\) | −2754.13 | − | 2754.13i | −0.244137 | − | 0.244137i | 0.574422 | − | 0.818559i | \(-0.305227\pi\) |
−0.818559 | + | 0.574422i | \(0.805227\pi\) | |||||||
\(504\) | −2666.32 | − | 902.657i | −0.235650 | − | 0.0797769i | ||||
\(505\) | −2397.69 | + | 10252.3i | −0.211279 | + | 0.903413i | ||||
\(506\) | −6414.38 | + | 8753.13i | −0.563546 | + | 0.769020i | ||||
\(507\) | −4510.16 | + | 4510.16i | −0.395075 | + | 0.395075i | ||||
\(508\) | −7186.11 | + | 13822.8i | −0.627622 | + | 1.20726i | ||||
\(509\) | 6936.37i | 0.604026i | 0.953304 | + | 0.302013i | \(0.0976586\pi\) | ||||
−0.953304 | + | 0.302013i | \(0.902341\pi\) | |||||||
\(510\) | −9506.36 | − | 731.042i | −0.825390 | − | 0.0634728i | ||||
\(511\) | − | 8176.83i | − | 0.707870i | ||||||
\(512\) | 2232.22 | − | 11368.2i | 0.192678 | − | 0.981262i | ||||
\(513\) | 2004.36 | − | 2004.36i | 0.172504 | − | 0.172504i | ||||
\(514\) | 4620.85 | + | 3386.21i | 0.396531 | + | 0.290582i | ||||
\(515\) | 10465.6 | − | 6498.26i | 0.895470 | − | 0.556015i | ||||
\(516\) | −2638.12 | − | 8351.12i | −0.225071 | − | 0.712476i | ||||
\(517\) | −1768.86 | − | 1768.86i | −0.150473 | − | 0.150473i | ||||
\(518\) | 2847.27 | − | 439.033i | 0.241509 | − | 0.0372394i | ||||
\(519\) | −235.036 | −0.0198785 | ||||||||
\(520\) | 1808.99 | + | 1124.51i | 0.152557 | + | 0.0948330i | ||||
\(521\) | 16877.0 | 1.41918 | 0.709591 | − | 0.704613i | \(-0.248880\pi\) | ||||
0.709591 | + | 0.704613i | \(0.248880\pi\) | |||||||
\(522\) | −4302.73 | + | 663.457i | −0.360777 | + | 0.0556298i | ||||
\(523\) | 1435.21 | + | 1435.21i | 0.119995 | + | 0.119995i | 0.764554 | − | 0.644560i | \(-0.222959\pi\) |
−0.644560 | + | 0.764554i | \(0.722959\pi\) | |||||||
\(524\) | −6053.22 | − | 19161.8i | −0.504649 | − | 1.59750i | ||||
\(525\) | 4645.94 | + | 2298.80i | 0.386220 | + | 0.191101i | ||||
\(526\) | 12508.5 | + | 9166.34i | 1.03687 | + | 0.759831i | ||||
\(527\) | −8754.40 | + | 8754.40i | −0.723620 | + | 0.723620i | ||||
\(528\) | −1078.60 | + | 6156.37i | −0.0889013 | + | 0.507427i | ||||
\(529\) | 1724.10i | 0.141703i | ||||||||
\(530\) | −9652.35 | − | 11260.6i | −0.791078 | − | 0.922882i | ||||
\(531\) | 5107.92i | 0.417448i | ||||||||
\(532\) | 5355.05 | − | 10300.7i | 0.436411 | − | 0.839458i | ||||
\(533\) | −2805.84 | + | 2805.84i | −0.228019 | + | 0.228019i | ||||
\(534\) | 60.7367 | − | 82.8819i | 0.00492197 | − | 0.00671657i | ||||
\(535\) | 4514.23 | + | 7270.24i | 0.364799 | + | 0.587514i | ||||
\(536\) | 396.255 | − | 1170.48i | 0.0319321 | − | 0.0943229i | ||||
\(537\) | −160.600 | − | 160.600i | −0.0129057 | − | 0.0129057i | ||||
\(538\) | −418.451 | − | 2713.79i | −0.0335329 | − | 0.217472i | ||||
\(539\) | −4945.75 | −0.395229 | ||||||||
\(540\) | 1832.73 | + | 1572.61i | 0.146052 | + | 0.125323i | ||||
\(541\) | 16524.6 | 1.31321 | 0.656606 | − | 0.754234i | \(-0.271992\pi\) | ||||
0.656606 | + | 0.754234i | \(0.271992\pi\) | |||||||
\(542\) | 2898.59 | + | 18798.3i | 0.229714 | + | 1.48977i | ||||
\(543\) | 2818.62 | + | 2818.62i | 0.222760 | + | 0.222760i | ||||
\(544\) | −18188.9 | − | 372.023i | −1.43354 | − | 0.0293205i | ||||
\(545\) | −7593.65 | − | 1775.91i | −0.596837 | − | 0.139581i | ||||
\(546\) | 583.726 | − | 796.558i | 0.0457531 | − | 0.0624351i | ||||
\(547\) | 15728.1 | − | 15728.1i | 1.22940 | − | 1.22940i | 0.265215 | − | 0.964189i | \(-0.414557\pi\) |
0.964189 | − | 0.265215i | \(-0.0854428\pi\) | |||||||
\(548\) | 6839.33 | + | 3555.58i | 0.533142 | + | 0.277166i | ||||
\(549\) | 7488.39i | 0.582143i | ||||||||
\(550\) | 3472.45 | − | 10972.8i | 0.269211 | − | 0.850695i | ||||
\(551\) | − | 17955.1i | − | 1.38822i | ||||||
\(552\) | 3544.47 | + | 7172.65i | 0.273302 | + | 0.553058i | ||||
\(553\) | −748.797 | + | 748.797i | −0.0575806 | + | 0.0575806i | ||||
\(554\) | −10948.6 | − | 8023.25i | −0.839642 | − | 0.615298i | ||||
\(555\) | −2406.59 | − | 562.825i | −0.184061 | − | 0.0430461i | ||||
\(556\) | −15708.0 | + | 4962.16i | −1.19815 | + | 0.378494i | ||||
\(557\) | −3378.87 | − | 3378.87i | −0.257033 | − | 0.257033i | 0.566813 | − | 0.823846i | \(-0.308176\pi\) |
−0.823846 | + | 0.566813i | \(0.808176\pi\) | |||||||
\(558\) | 3099.23 | − | 477.884i | 0.235127 | − | 0.0362552i | ||||
\(559\) | 3072.43 | 0.232469 | ||||||||
\(560\) | 9097.74 | + | 3880.60i | 0.686517 | + | 0.292831i | ||||
\(561\) | 9814.84 | 0.738650 | ||||||||
\(562\) | −8871.45 | + | 1367.93i | −0.665871 | + | 0.102674i | ||||
\(563\) | −6575.77 | − | 6575.77i | −0.492248 | − | 0.492248i | 0.416766 | − | 0.909014i | \(-0.363163\pi\) |
−0.909014 | + | 0.416766i | \(0.863163\pi\) | |||||||
\(564\) | −1758.64 | + | 555.553i | −0.131298 | + | 0.0414769i | ||||
\(565\) | −5967.09 | − | 9610.10i | −0.444314 | − | 0.715575i | ||||
\(566\) | −9365.01 | − | 6862.77i | −0.695478 | − | 0.509653i | ||||
\(567\) | 791.710 | − | 791.710i | 0.0586397 | − | 0.0586397i | ||||
\(568\) | 5357.68 | + | 10841.9i | 0.395780 | + | 0.800907i | ||||
\(569\) | − | 5653.99i | − | 0.416569i | −0.978068 | − | 0.208284i | \(-0.933212\pi\) | ||
0.978068 | − | 0.208284i | \(-0.0667879\pi\) | |||||||
\(570\) | −7561.87 | + | 6481.90i | −0.555670 | + | 0.476310i | ||||
\(571\) | 4182.86i | 0.306562i | 0.988183 | + | 0.153281i | \(0.0489840\pi\) | ||||
−0.988183 | + | 0.153281i | \(0.951016\pi\) | |||||||
\(572\) | −1945.47 | − | 1011.40i | −0.142210 | − | 0.0739311i | ||||
\(573\) | 1118.81 | − | 1118.81i | 0.0815691 | − | 0.0815691i | ||||
\(574\) | −10891.3 | + | 14862.3i | −0.791973 | + | 1.08073i | ||||
\(575\) | −4717.09 | − | 13957.0i | −0.342115 | − | 1.01225i | ||||
\(576\) | 3660.37 | + | 2799.18i | 0.264783 | + | 0.202487i | ||||
\(577\) | 4154.43 | + | 4154.43i | 0.299742 | + | 0.299742i | 0.840913 | − | 0.541171i | \(-0.182019\pi\) |
−0.541171 | + | 0.840913i | \(0.682019\pi\) | |||||||
\(578\) | 2236.03 | + | 14501.3i | 0.160911 | + | 1.04356i | ||||
\(579\) | −5033.58 | −0.361293 | ||||||||
\(580\) | 15252.5 | − | 1165.11i | 1.09194 | − | 0.0834115i | ||||
\(581\) | 17757.8 | 1.26802 | ||||||||
\(582\) | −1121.85 | − | 7275.53i | −0.0799004 | − | 0.518179i | ||||
\(583\) | 10795.8 | + | 10795.8i | 0.766921 | + | 0.766921i | ||||
\(584\) | −4292.13 | + | 12678.3i | −0.304126 | + | 0.898345i | ||||
\(585\) | −719.750 | + | 446.906i | −0.0508683 | + | 0.0315851i | ||||
\(586\) | −1571.09 | + | 2143.93i | −0.110753 | + | 0.151135i | ||||
\(587\) | 867.446 | − | 867.446i | 0.0609938 | − | 0.0609938i | −0.675952 | − | 0.736946i | \(-0.736267\pi\) |
0.736946 | + | 0.675952i | \(0.236267\pi\) | |||||||
\(588\) | −1681.91 | + | 3235.24i | −0.117961 | + | 0.226903i | ||||
\(589\) | 12932.9i | 0.904738i | ||||||||
\(590\) | 1376.10 | − | 17894.6i | 0.0960222 | − | 1.24866i | ||||
\(591\) | − | 145.176i | − | 0.0101045i | ||||||
\(592\) | −4645.20 | − | 813.840i | −0.322494 | − | 0.0565010i | ||||
\(593\) | −6391.46 | + | 6391.46i | −0.442607 | + | 0.442607i | −0.892887 | − | 0.450280i | \(-0.851324\pi\) |
0.450280 | + | 0.892887i | \(0.351324\pi\) | |||||||
\(594\) | −2005.20 | − | 1469.43i | −0.138509 | − | 0.101501i | ||||
\(595\) | 3536.98 | − | 15123.8i | 0.243701 | − | 1.04204i | ||||
\(596\) | 2895.29 | + | 9165.23i | 0.198986 | + | 0.629903i | ||||
\(597\) | −1165.17 | − | 1165.17i | −0.0798780 | − | 0.0798780i | ||||
\(598\) | −2773.99 | + | 427.733i | −0.189694 | + | 0.0292497i | ||||
\(599\) | 9411.66 | 0.641986 | 0.320993 | − | 0.947081i | \(-0.395983\pi\) | ||||
0.320993 | + | 0.947081i | \(0.395983\pi\) | |||||||
\(600\) | −5996.94 | − | 6003.05i | −0.408040 | − | 0.408456i | ||||
\(601\) | −3491.06 | −0.236944 | −0.118472 | − | 0.992957i | \(-0.537800\pi\) | ||||
−0.118472 | + | 0.992957i | \(0.537800\pi\) | |||||||
\(602\) | 14100.3 | − | 2174.19i | 0.954626 | − | 0.147198i | ||||
\(603\) | 347.551 | + | 347.551i | 0.0234716 | + | 0.0234716i | ||||
\(604\) | 2680.66 | + | 8485.80i | 0.180587 | + | 0.571659i | ||||
\(605\) | 690.774 | − | 2953.69i | 0.0464197 | − | 0.198487i | ||||
\(606\) | −6445.54 | − | 4723.36i | −0.432066 | − | 0.316623i | ||||
\(607\) | −19182.5 | + | 19182.5i | −1.28269 | + | 1.28269i | −0.343559 | + | 0.939131i | \(0.611633\pi\) |
−0.939131 | + | 0.343559i | \(0.888367\pi\) | |||||||
\(608\) | −13710.1 | + | 13160.5i | −0.914501 | + | 0.877842i | ||||
\(609\) | − | 7092.13i | − | 0.471901i | ||||||
\(610\) | 2017.41 | − | 26234.1i | 0.133906 | − | 1.74129i | ||||
\(611\) | − | 647.014i | − | 0.0428402i | ||||||
\(612\) | 3337.76 | − | 6420.34i | 0.220459 | − | 0.424064i | ||||
\(613\) | 8775.20 | − | 8775.20i | 0.578184 | − | 0.578184i | −0.356219 | − | 0.934403i | \(-0.615934\pi\) |
0.934403 | + | 0.356219i | \(0.115934\pi\) | |||||||
\(614\) | 7738.68 | − | 10560.3i | 0.508645 | − | 0.694101i | ||||
\(615\) | 13429.2 | − | 8338.45i | 0.880517 | − | 0.546730i | ||||
\(616\) | −9644.03 | − | 3264.89i | −0.630794 | − | 0.213549i | ||||
\(617\) | 1130.84 | + | 1130.84i | 0.0737861 | + | 0.0737861i | 0.743037 | − | 0.669251i | \(-0.233385\pi\) |
−0.669251 | + | 0.743037i | \(0.733385\pi\) | |||||||
\(618\) | 1424.78 | + | 9240.18i | 0.0927399 | + | 0.601448i | ||||
\(619\) | −8002.68 | −0.519636 | −0.259818 | − | 0.965658i | \(-0.583663\pi\) | ||||
−0.259818 | + | 0.965658i | \(0.583663\pi\) | |||||||
\(620\) | −10986.3 | + | 839.222i | −0.711643 | + | 0.0543612i | ||||
\(621\) | −3182.23 | −0.205634 | ||||||||
\(622\) | −3403.17 | − | 22070.6i | −0.219380 | − | 1.42275i | ||||
\(623\) | 118.362 | + | 118.362i | 0.00761169 | + | 0.00761169i | ||||
\(624\) | −1323.20 | + | 928.674i | −0.0848886 | + | 0.0595780i | ||||
\(625\) | 9478.92 | + | 12421.4i | 0.606651 | + | 0.794968i | ||||
\(626\) | −14819.2 | + | 20222.4i | −0.946156 | + | 1.29113i | ||||
\(627\) | 7249.74 | − | 7249.74i | 0.461765 | − | 0.461765i | ||||
\(628\) | −6170.55 | − | 3207.90i | −0.392089 | − | 0.203836i | ||||
\(629\) | 7405.64i | 0.469447i | ||||||||
\(630\) | −2986.89 | + | 2560.31i | −0.188890 | + | 0.161913i | ||||
\(631\) | − | 15919.5i | − | 1.00435i | −0.864766 | − | 0.502175i | \(-0.832533\pi\) | ||
0.864766 | − | 0.502175i | \(-0.167467\pi\) | |||||||
\(632\) | 1554.08 | − | 767.971i | 0.0978131 | − | 0.0483358i | ||||
\(633\) | −7659.75 | + | 7659.75i | −0.480960 | + | 0.480960i | ||||
\(634\) | 16374.9 | + | 11999.7i | 1.02576 | + | 0.751688i | ||||
\(635\) | 11485.1 | + | 18496.9i | 0.717752 | + | 1.15595i | ||||
\(636\) | 10733.4 | − | 3390.67i | 0.669191 | − | 0.211397i | ||||
\(637\) | −904.528 | − | 904.528i | −0.0562617 | − | 0.0562617i | ||||
\(638\) | −15562.9 | + | 2399.71i | −0.965738 | + | 0.148911i | ||||
\(639\) | −4810.13 | −0.297787 | ||||||||
\(640\) | −12069.2 | − | 10792.5i | −0.745436 | − | 0.666578i | ||||
\(641\) | 2408.32 | 0.148398 | 0.0741989 | − | 0.997243i | \(-0.476360\pi\) | ||||
0.0741989 | + | 0.997243i | \(0.476360\pi\) | |||||||
\(642\) | −6419.00 | + | 989.774i | −0.394607 | + | 0.0608462i | ||||
\(643\) | −9551.66 | − | 9551.66i | −0.585818 | − | 0.585818i | 0.350678 | − | 0.936496i | \(-0.385951\pi\) |
−0.936496 | + | 0.350678i | \(0.885951\pi\) | |||||||
\(644\) | −12427.9 | + | 3925.98i | −0.760449 | + | 0.240226i | ||||
\(645\) | −11918.0 | − | 2787.23i | −0.727549 | − | 0.170150i | ||||
\(646\) | 24071.7 | + | 17640.0i | 1.46608 | + | 1.07436i | ||||
\(647\) | 8983.66 | − | 8983.66i | 0.545880 | − | 0.545880i | −0.379367 | − | 0.925246i | \(-0.623858\pi\) |
0.925246 | + | 0.379367i | \(0.123858\pi\) | |||||||
\(648\) | −1643.14 | + | 811.983i | −0.0996122 | + | 0.0492249i | ||||
\(649\) | 18475.2i | 1.11744i | ||||||||
\(650\) | 2641.90 | − | 1371.74i | 0.159421 | − | 0.0827756i | ||||
\(651\) | 5108.41i | 0.307549i | ||||||||
\(652\) | −17215.1 | − | 8949.64i | −1.03404 | − | 0.537569i | ||||
\(653\) | −14719.0 | + | 14719.0i | −0.882084 | + | 0.882084i | −0.993746 | − | 0.111662i | \(-0.964382\pi\) |
0.111662 | + | 0.993746i | \(0.464382\pi\) | |||||||
\(654\) | 3498.47 | − | 4774.05i | 0.209176 | − | 0.285443i | ||||
\(655\) | −27346.0 | − | 6395.36i | −1.63129 | − | 0.381508i | ||||
\(656\) | 24688.6 | − | 17327.4i | 1.46940 | − | 1.03128i | ||||
\(657\) | −3764.58 | − | 3764.58i | −0.223547 | − | 0.223547i | ||||
\(658\) | −457.855 | − | 2969.33i | −0.0271262 | − | 0.175922i | ||||
\(659\) | 6602.59 | 0.390289 | 0.195145 | − | 0.980774i | \(-0.437482\pi\) | ||||
0.195145 | + | 0.980774i | \(0.437482\pi\) | |||||||
\(660\) | 6628.96 | + | 5688.08i | 0.390957 | + | 0.335467i | ||||
\(661\) | −13404.0 | −0.788735 | −0.394367 | − | 0.918953i | \(-0.629036\pi\) | ||||
−0.394367 | + | 0.918953i | \(0.629036\pi\) | |||||||
\(662\) | 1463.76 | + | 9492.93i | 0.0859374 | + | 0.557331i | ||||
\(663\) | 1795.04 | + | 1795.04i | 0.105148 | + | 0.105148i | ||||
\(664\) | −27533.9 | − | 9321.33i | −1.60922 | − | 0.544786i | ||||
\(665\) | −8558.63 | − | 13783.8i | −0.499082 | − | 0.803779i | ||||
\(666\) | 1108.74 | − | 1513.00i | 0.0645088 | − | 0.0880293i | ||||
\(667\) | −14253.2 | + | 14253.2i | −0.827416 | + | 0.827416i | ||||
\(668\) | 9962.21 | − | 19162.8i | 0.577020 | − | 1.10993i | ||||
\(669\) | 4257.44i | 0.246042i | ||||||||
\(670\) | −1123.94 | − | 1311.21i | −0.0648085 | − | 0.0756065i | ||||
\(671\) | 27085.3i | 1.55830i | ||||||||
\(672\) | −5415.39 | + | 5198.31i | −0.310868 | + | 0.298406i | ||||
\(673\) | 5480.21 | − | 5480.21i | 0.313888 | − | 0.313888i | −0.532526 | − | 0.846414i | \(-0.678757\pi\) |
0.846414 | + | 0.532526i | \(0.178757\pi\) | |||||||
\(674\) | 21160.8 | + | 15506.9i | 1.20933 | + | 0.886206i | ||||
\(675\) | 3197.33 | − | 1080.61i | 0.182319 | − | 0.0616188i | ||||
\(676\) | 5123.53 | + | 16218.9i | 0.291507 | + | 0.922784i | ||||
\(677\) | 13646.9 | + | 13646.9i | 0.774733 | + | 0.774733i | 0.978930 | − | 0.204197i | \(-0.0654583\pi\) |
−0.204197 | + | 0.978930i | \(0.565458\pi\) | |||||||
\(678\) | 8484.89 | − | 1308.32i | 0.480620 | − | 0.0741089i | ||||
\(679\) | 11992.2 | 0.677786 | ||||||||
\(680\) | −13422.8 | + | 21593.2i | −0.756974 | + | 1.21774i | ||||
\(681\) | 6763.56 | 0.380588 | ||||||||
\(682\) | 11209.8 | − | 1728.49i | 0.629394 | − | 0.0970491i | ||||
\(683\) | −19003.1 | − | 19003.1i | −1.06462 | − | 1.06462i | −0.997763 | − | 0.0668566i | \(-0.978703\pi\) |
−0.0668566 | − | 0.997763i | \(-0.521297\pi\) | |||||||
\(684\) | −2276.95 | − | 7207.83i | −0.127283 | − | 0.402922i | ||||
\(685\) | 9152.01 | − | 5682.66i | 0.510482 | − | 0.316968i | ||||
\(686\) | −15608.0 | − | 11437.7i | −0.868681 | − | 0.636578i | ||||
\(687\) | −3823.18 | + | 3823.18i | −0.212319 | + | 0.212319i | ||||
\(688\) | −23004.0 | − | 4030.31i | −1.27474 | − | 0.223335i | ||||
\(689\) | 3948.88i | 0.218346i | ||||||||
\(690\) | 11148.3 | + | 857.309i | 0.615086 | + | 0.0473003i | ||||
\(691\) | − | 6492.09i | − | 0.357411i | −0.983903 | − | 0.178705i | \(-0.942809\pi\) | ||
0.983903 | − | 0.178705i | \(-0.0571909\pi\) | |||||||
\(692\) | −289.104 | + | 556.104i | −0.0158816 | + | 0.0305490i | ||||
\(693\) | 2863.60 | − | 2863.60i | 0.156968 | − | 0.156968i | ||||
\(694\) | −5014.43 | + | 6842.74i | −0.274273 | + | 0.374275i | ||||
\(695\) | −5242.64 | + | 22417.1i | −0.286136 | + | 1.22349i | ||||
\(696\) | −3722.76 | + | 10996.5i | −0.202745 | + | 0.598881i | ||||
\(697\) | −33492.1 | − | 33492.1i | −1.82009 | − | 1.82009i | ||||
\(698\) | −4098.88 | − | 26582.5i | −0.222271 | − | 1.44149i | ||||
\(699\) | −6856.74 | −0.371024 | ||||||||
\(700\) | 11153.7 | − | 8164.84i | 0.602244 | − | 0.440860i | ||||
\(701\) | 15538.8 | 0.837220 | 0.418610 | − | 0.908166i | \(-0.362517\pi\) | ||||
0.418610 | + | 0.908166i | \(0.362517\pi\) | |||||||
\(702\) | −97.9870 | − | 635.477i | −0.00526821 | − | 0.0341660i | ||||
\(703\) | 5470.18 | + | 5470.18i | 0.293474 | + | 0.293474i | ||||
\(704\) | 13239.5 | + | 10124.6i | 0.708780 | + | 0.542022i | ||||
\(705\) | −586.954 | + | 2509.77i | −0.0313560 | + | 0.134076i | ||||
\(706\) | 13009.9 | − | 17753.5i | 0.693534 | − | 0.946403i | ||||
\(707\) | 9204.77 | − | 9204.77i | 0.489648 | − | 0.489648i | ||||
\(708\) | 12085.5 | + | 6282.93i | 0.641528 | + | 0.333513i | ||||
\(709\) | − | 34906.4i | − | 1.84899i | −0.381189 | − | 0.924497i | \(-0.624485\pi\) | ||
0.381189 | − | 0.924497i | \(-0.375515\pi\) | |||||||
\(710\) | 16851.3 | + | 1295.87i | 0.890731 | + | 0.0684975i | ||||
\(711\) | 689.485i | 0.0363681i | ||||||||
\(712\) | −121.393 | − | 245.653i | −0.00638960 | − | 0.0129301i | ||||
\(713\) | 10266.5 | − | 10266.5i | 0.539246 | − | 0.539246i | ||||
\(714\) | 9508.18 | + | 6967.69i | 0.498368 | + | 0.365209i | ||||
\(715\) | −2603.32 | + | 1616.45i | −0.136166 | + | 0.0845480i | ||||
\(716\) | −577.528 | + | 182.441i | −0.0301442 | + | 0.00952253i | ||||
\(717\) | −681.899 | − | 681.899i | −0.0355174 | − | 0.0355174i | ||||
\(718\) | 10357.4 | − | 1597.05i | 0.538347 | − | 0.0830102i | ||||
\(719\) | 31209.2 | 1.61879 | 0.809394 | − | 0.587266i | \(-0.199796\pi\) | ||||
0.809394 | + | 0.587266i | \(0.199796\pi\) | |||||||
\(720\) | 5975.17 | − | 2401.95i | 0.309280 | − | 0.124327i | ||||
\(721\) | −15230.5 | −0.786702 | ||||||||
\(722\) | 11636.8 | − | 1794.33i | 0.599831 | − | 0.0924906i | ||||
\(723\) | −3633.53 | − | 3633.53i | −0.186905 | − | 0.186905i | ||||
\(724\) | 10136.0 | − | 3201.95i | 0.520304 | − | 0.164364i | ||||
\(725\) | 9480.77 | − | 19160.9i | 0.485665 | − | 0.981540i | ||||
\(726\) | 1856.95 | + | 1360.80i | 0.0949284 | + | 0.0695645i | ||||
\(727\) | 12172.2 | − | 12172.2i | 0.620965 | − | 0.620965i | −0.324813 | − | 0.945778i | \(-0.605301\pi\) |
0.945778 | + | 0.324813i | \(0.105301\pi\) | |||||||
\(728\) | −1166.68 | − | 2360.91i | −0.0593957 | − | 0.120194i | ||||
\(729\) | − | 729.000i | − | 0.0370370i | ||||||
\(730\) | 12174.2 | + | 14202.6i | 0.617245 | + | 0.720086i | ||||
\(731\) | 36674.4i | 1.85561i | ||||||||
\(732\) | 17717.8 | + | 9210.99i | 0.894629 | + | 0.465093i | ||||
\(733\) | −17574.9 | + | 17574.9i | −0.885598 | + | 0.885598i | −0.994097 | − | 0.108499i | \(-0.965396\pi\) |
0.108499 | + | 0.994097i | \(0.465396\pi\) | |||||||
\(734\) | 15874.3 | − | 21662.3i | 0.798273 | − | 1.08933i | ||||
\(735\) | 2688.10 | + | 4329.22i | 0.134901 | + | 0.217260i | ||||
\(736\) | 21330.6 | + | 436.279i | 1.06828 | + | 0.0218498i | ||||
\(737\) | 1257.08 | + | 1257.08i | 0.0628294 | + | 0.0628294i | ||||
\(738\) | 1828.26 | + | 11856.8i | 0.0911912 | + | 0.591404i | ||||
\(739\) | −22421.6 | −1.11609 | −0.558046 | − | 0.829810i | \(-0.688449\pi\) | ||||
−0.558046 | + | 0.829810i | \(0.688449\pi\) | |||||||
\(740\) | −4291.86 | + | 5001.78i | −0.213205 | + | 0.248472i | ||||
\(741\) | 2651.81 | 0.131466 | ||||||||
\(742\) | 2794.39 | + | 18122.5i | 0.138255 | + | 0.896630i | ||||
\(743\) | 21443.3 | + | 21443.3i | 1.05879 | + | 1.05879i | 0.998161 | + | 0.0606244i | \(0.0193092\pi\) |
0.0606244 | + | 0.998161i | \(0.480691\pi\) | |||||||
\(744\) | 2681.47 | − | 7920.69i | 0.132134 | − | 0.390305i | ||||
\(745\) | 13079.8 | + | 3058.94i | 0.643229 | + | 0.150431i | ||||
\(746\) | 16123.4 | − | 22002.1i | 0.791311 | − | 1.07983i | ||||
\(747\) | 8175.63 | − | 8175.63i | 0.400443 | − | 0.400443i | ||||
\(748\) | 12072.6 | − | 23222.2i | 0.590131 | − | 1.13515i | ||||
\(749\) | − | 10580.3i | − | 0.516151i | ||||||
\(750\) | −11492.3 | + | 2924.33i | −0.559520 | + | 0.142375i | ||||
\(751\) | − | 17054.5i | − | 0.828663i | −0.910126 | − | 0.414332i | \(-0.864015\pi\) | ||
0.910126 | − | 0.414332i | \(-0.135985\pi\) | |||||||
\(752\) | −848.730 | + | 4844.35i | −0.0411569 | + | 0.234914i | ||||
\(753\) | −11410.7 | + | 11410.7i | −0.552228 | + | 0.552228i | ||||
\(754\) | −3285.18 | − | 2407.41i | −0.158673 | − | 0.116277i | ||||
\(755\) | 12110.2 | + | 2832.18i | 0.583754 | + | 0.136521i | ||||
\(756\) | −899.381 | − | 2847.05i | −0.0432674 | − | 0.136966i | ||||
\(757\) | 17641.7 | + | 17641.7i | 0.847025 | + | 0.847025i | 0.989761 | − | 0.142735i | \(-0.0455898\pi\) |
−0.142735 | + | 0.989761i | \(0.545590\pi\) | |||||||
\(758\) | −34899.3 | + | 5381.28i | −1.67230 | + | 0.257859i | ||||
\(759\) | −11510.1 | −0.550447 | ||||||||
\(760\) | 6035.02 | + | 25864.6i | 0.288044 | + | 1.23448i | ||||
\(761\) | −20703.5 | −0.986206 | −0.493103 | − | 0.869971i | \(-0.664137\pi\) | ||||
−0.493103 | + | 0.869971i | \(0.664137\pi\) | |||||||
\(762\) | −16331.2 | + | 2518.18i | −0.776400 | + | 0.119717i | ||||
\(763\) | 6817.74 | + | 6817.74i | 0.323484 | + | 0.323484i | ||||
\(764\) | −1270.97 | − | 4023.33i | −0.0601859 | − | 0.190522i | ||||
\(765\) | −5334.53 | − | 8591.35i | −0.252118 | − | 0.406040i | ||||
\(766\) | 10193.6 | + | 7469.98i | 0.480822 | + | 0.352352i | ||||
\(767\) | −3378.94 | + | 3378.94i | −0.159070 | + | 0.159070i | ||||
\(768\) | 11125.3 | − | 5217.47i | 0.522722 | − | 0.245142i | ||||
\(769\) | 476.229i | 0.0223319i | 0.999938 | + | 0.0111660i | \(0.00355431\pi\) | ||||
−0.999938 | + | 0.0111660i | \(0.996446\pi\) | |||||||
\(770\) | −10803.5 | + | 9260.58i | −0.505625 | + | 0.433413i | ||||
\(771\) | 6076.26i | 0.283828i | ||||||||
\(772\) | −6191.49 | + | 11909.6i | −0.288648 | + | 0.555229i | ||||
\(773\) | 12209.8 | − | 12209.8i | 0.568118 | − | 0.568118i | −0.363483 | − | 0.931601i | \(-0.618413\pi\) |
0.931601 | + | 0.363483i | \(0.118413\pi\) | |||||||
\(774\) | 5490.72 | − | 7492.70i | 0.254987 | − | 0.347958i | ||||
\(775\) | −6828.93 | + | 13801.4i | −0.316519 | + | 0.639693i | ||||
\(776\) | −18594.1 | − | 6294.84i | −0.860165 | − | 0.291201i | ||||
\(777\) | 2160.69 | + | 2160.69i | 0.0997609 | + | 0.0997609i | ||||
\(778\) | −1188.59 | − | 7708.36i | −0.0547723 | − | 0.355216i | ||||
\(779\) | −49477.9 | −2.27565 | ||||||||
\(780\) | 172.077 | + | 2252.66i | 0.00789917 | + | 0.103408i | ||||
\(781\) | −17398.1 | −0.797125 | ||||||||
\(782\) | −5105.67 | − | 33111.9i | −0.233476 | − | 1.51417i | ||||
\(783\) | −3265.19 | − | 3265.19i | −0.149027 | − | 0.149027i | ||||
\(784\) | 5585.88 | + | 7958.94i | 0.254459 | + | 0.362561i | ||||
\(785\) | −8257.09 | + | 5126.98i | −0.375424 | + | 0.233108i | ||||
\(786\) | 12598.6 | − | 17192.2i | 0.571726 | − | 0.780183i | ||||
\(787\) | 623.561 | − | 623.561i | 0.0282434 | − | 0.0282434i | −0.692844 | − | 0.721087i | \(-0.743643\pi\) |
0.721087 | + | 0.692844i | \(0.243643\pi\) | |||||||
\(788\) | −343.492 | − | 178.572i | −0.0155284 | − | 0.00807280i | ||||
\(789\) | 16448.2i | 0.742170i | ||||||||
\(790\) | 185.751 | − | 2415.47i | 0.00836546 | − | 0.108783i | ||||
\(791\) | 13985.5i | 0.628658i | ||||||||
\(792\) | −5943.21 | + | 2936.93i | −0.266645 | + | 0.131767i | ||||
\(793\) | −4953.64 | + | 4953.64i | −0.221827 | + | 0.221827i | ||||
\(794\) | −5886.57 | − | 4313.74i | −0.263106 | − | 0.192807i | ||||
\(795\) | 3582.31 | − | 15317.7i | 0.159813 | − | 0.683349i | ||||
\(796\) | −4190.03 | + | 1323.63i | −0.186572 | + | 0.0589382i | ||||
\(797\) | −8360.92 | − | 8360.92i | −0.371592 | − | 0.371592i | 0.496465 | − | 0.868057i | \(-0.334631\pi\) |
−0.868057 | + | 0.496465i | \(0.834631\pi\) | |||||||
\(798\) | 12169.9 | − | 1876.53i | 0.539863 | − | 0.0832438i | ||||
\(799\) | 7723.13 | 0.341959 | ||||||||
\(800\) | −21579.9 | + | 6805.00i | −0.953706 | + | 0.300742i | ||||
\(801\) | 108.987 | 0.00480757 | ||||||||
\(802\) | −7747.34 | + | 1194.60i | −0.341107 | + | 0.0525969i | ||||
\(803\) | −13616.4 | − | 13616.4i | −0.598396 | − | 0.598396i | ||||
\(804\) | 1249.82 | − | 394.817i | 0.0548230 | − | 0.0173186i | ||||
\(805\) | −4147.89 | + | 17736.0i | −0.181607 | + | 0.776538i | ||||
\(806\) | 2366.29 | + | 1734.04i | 0.103411 | + | 0.0757805i | ||||
\(807\) | 2059.40 | − | 2059.40i | 0.0898317 | − | 0.0898317i | ||||
\(808\) | −19103.9 | + | 9440.47i | −0.831772 | + | 0.411033i | ||||
\(809\) | 954.713i | 0.0414906i | 0.999785 | + | 0.0207453i | \(0.00660391\pi\) | ||||
−0.999785 | + | 0.0207453i | \(0.993396\pi\) | |||||||
\(810\) | −196.396 | + | 2553.90i | −0.00851933 | + | 0.110784i | ||||
\(811\) | − | 22684.6i | − | 0.982200i | −0.871103 | − | 0.491100i | \(-0.836595\pi\) | ||
0.871103 | − | 0.491100i | \(-0.163405\pi\) | |||||||
\(812\) | −16780.2 | − | 8723.58i | −0.725210 | − | 0.377017i | ||||
\(813\) | −14265.3 | + | 14265.3i | −0.615384 | + | 0.615384i | ||||
\(814\) | 4010.29 | − | 5472.48i | 0.172679 | − | 0.235639i | ||||
\(815\) | −23036.3 | + | 14303.6i | −0.990092 | + | 0.614767i | ||||
\(816\) | −11085.2 | − | 15794.5i | −0.475563 | − | 0.677596i | ||||
\(817\) | 27089.5 | + | 27089.5i | 1.16003 | + | 1.16003i | ||||
\(818\) | 2.82795 | + | 18.3401i | 0.000120876 | + | 0.000783921i | ||||
\(819\) | 1047.45 | 0.0446896 | ||||||||
\(820\) | −3210.65 | − | 42030.6i | −0.136732 | − | 1.78997i | ||||
\(821\) | −19186.8 | −0.815621 | −0.407810 | − | 0.913067i | \(-0.633708\pi\) | ||||
−0.407810 | + | 0.913067i | \(0.633708\pi\) | |||||||
\(822\) | 1245.96 | + | 8080.44i | 0.0528684 | + | 0.342868i | ||||
\(823\) | 21296.2 | + | 21296.2i | 0.901990 | + | 0.901990i | 0.995608 | − | 0.0936185i | \(-0.0298434\pi\) |
−0.0936185 | + | 0.995608i | \(0.529843\pi\) | |||||||
\(824\) | 23615.1 | + | 7994.67i | 0.998388 | + | 0.337995i | ||||
\(825\) | 11564.7 | − | 3908.55i | 0.488036 | − | 0.164943i | ||||
\(826\) | −13115.8 | + | 17898.0i | −0.552492 | + | 0.753936i | ||||
\(827\) | 24547.4 | − | 24547.4i | 1.03216 | − | 1.03216i | 0.0326970 | − | 0.999465i | \(-0.489590\pi\) |
0.999465 | − | 0.0326970i | \(-0.0104096\pi\) | |||||||
\(828\) | −3914.26 | + | 7529.27i | −0.164288 | + | 0.316015i | ||||
\(829\) | − | 16962.8i | − | 0.710667i | −0.934740 | − | 0.355333i | \(-0.884367\pi\) | ||
0.934740 | − | 0.355333i | \(-0.115633\pi\) | |||||||
\(830\) | −30844.2 | + | 26439.1i | −1.28990 | + | 1.10568i | ||||
\(831\) | − | 14397.0i | − | 0.600996i | ||||||
\(832\) | 569.686 | + | 4273.05i | 0.0237383 | + | 0.178054i | ||||
\(833\) | 10797.0 | − | 10797.0i | 0.449091 | − | 0.449091i | ||||
\(834\) | −14093.4 | − | 10327.8i | −0.585148 | − | 0.428803i | ||||
\(835\) | −15922.0 | − | 25642.6i | −0.659883 | − | 1.06275i | ||||
\(836\) | −8235.69 | − | 26070.6i | −0.340714 | − | 1.07855i | ||||
\(837\) | 2351.89 | + | 2351.89i | 0.0971245 | + | 0.0971245i | ||||
\(838\) | 5311.52 | − | 819.007i | 0.218954 | − | 0.0337615i | ||||
\(839\) | 18232.5 | 0.750244 | 0.375122 | − | 0.926975i | \(-0.377601\pi\) | ||||
0.375122 | + | 0.926975i | \(0.377601\pi\) | |||||||
\(840\) | 2383.79 | + | 10216.4i | 0.0979151 | + | 0.419640i | ||||
\(841\) | −4860.51 | −0.199291 | ||||||||
\(842\) | −16857.7 | + | 2599.37i | −0.689971 | + | 0.106390i | ||||
\(843\) | −6732.22 | − | 6732.22i | −0.275053 | − | 0.275053i | ||||
\(844\) | 8701.46 | + | 27545.0i | 0.354878 | + | 1.12339i | ||||
\(845\) | 23146.1 | + | 5413.12i | 0.942307 | + | 0.220375i | ||||
\(846\) | −1577.86 | − | 1156.27i | −0.0641230 | − | 0.0469900i | ||||
\(847\) | −2651.89 | + | 2651.89i | −0.107580 | + | 0.107580i | ||||
\(848\) | 5180.00 | − | 29566.2i | 0.209766 | − | 1.19729i | ||||
\(849\) | − | 12314.7i | − | 0.497807i | ||||||
\(850\) | 16373.9 | + | 31535.2i | 0.660730 | + | 1.27253i | ||||
\(851\) | − | 8684.76i | − | 0.349835i | ||||||
\(852\) | −5916.64 | + | 11380.9i | −0.237912 | + | 0.457634i | ||||
\(853\) | −8029.34 | + | 8029.34i | −0.322297 | + | 0.322297i | −0.849648 | − | 0.527351i | \(-0.823185\pi\) |
0.527351 | + | 0.849648i | \(0.323185\pi\) | |||||||
\(854\) | −19228.3 | + | 26239.1i | −0.770466 | + | 1.05139i | ||||
\(855\) | −10286.4 | − | 2405.65i | −0.411446 | − | 0.0962240i | ||||
\(856\) | −5553.77 | + | 16405.0i | −0.221757 | + | 0.655038i | ||||
\(857\) | 10547.5 | + | 10547.5i | 0.420414 | + | 0.420414i | 0.885346 | − | 0.464932i | \(-0.153921\pi\) |
−0.464932 | + | 0.885346i | \(0.653921\pi\) | |||||||
\(858\) | −354.417 | − | 2298.51i | −0.0141021 | − | 0.0914565i | ||||
\(859\) | 6249.45 | 0.248229 | 0.124114 | − | 0.992268i | \(-0.460391\pi\) | ||||
0.124114 | + | 0.992268i | \(0.460391\pi\) | |||||||
\(860\) | −21254.2 | + | 24769.9i | −0.842747 | + | 0.982148i | ||||
\(861\) | −19543.5 | −0.773565 | ||||||||
\(862\) | −6220.77 | − | 40343.7i | −0.245801 | − | 1.59410i | ||||
\(863\) | −5052.25 | − | 5052.25i | −0.199282 | − | 0.199282i | 0.600410 | − | 0.799692i | \(-0.295004\pi\) |
−0.799692 | + | 0.600410i | \(0.795004\pi\) | |||||||
\(864\) | −99.9447 | + | 4886.50i | −0.00393540 | + | 0.192410i | ||||
\(865\) | 462.056 | + | 744.148i | 0.0181623 | + | 0.0292506i | ||||
\(866\) | −14802.7 | + | 20199.9i | −0.580850 | + | 0.792634i | ||||
\(867\) | −11004.5 | + | 11004.5i | −0.431065 | + | 0.431065i | ||||
\(868\) | 12086.7 | + | 6283.53i | 0.472637 | + | 0.245711i | ||||
\(869\) | 2493.85i | 0.0973512i | ||||||||
\(870\) | 10559.3 | + | 12318.6i | 0.411486 | + | 0.480045i | ||||
\(871\) | 459.816i | 0.0178878i | ||||||||
\(872\) | −6992.31 | − | 14149.8i | −0.271548 | − | 0.549508i | ||||
\(873\) | 5521.13 | − | 5521.13i | 0.214046 | − | 0.214046i | ||||
\(874\) | −28229.4 | − | 20686.8i | −1.09253 | − | 0.800620i | ||||
\(875\) | −1855.17 | − | 19228.7i | −0.0716756 | − | 0.742912i | ||||
\(876\) | −13537.7 | + | 4276.55i | −0.522142 | + | 0.164944i | ||||
\(877\) | 29012.5 | + | 29012.5i | 1.11709 | + | 1.11709i | 0.992167 | + | 0.124919i | \(0.0398669\pi\) |
0.124919 | + | 0.992167i | \(0.460133\pi\) | |||||||
\(878\) | 42081.4 | − | 6488.71i | 1.61751 | − | 0.249412i | ||||
\(879\) | −2819.19 | −0.108179 | ||||||||
\(880\) | 21612.1 | − | 8687.80i | 0.827889 | − | 0.332802i | ||||
\(881\) | 8105.88 | 0.309982 | 0.154991 | − | 0.987916i | \(-0.450465\pi\) | ||||
0.154991 | + | 0.987916i | \(0.450465\pi\) | |||||||
\(882\) | −3822.33 | + | 589.382i | −0.145924 | + | 0.0225006i | ||||
\(883\) | 19045.9 | + | 19045.9i | 0.725873 | + | 0.725873i | 0.969795 | − | 0.243922i | \(-0.0784341\pi\) |
−0.243922 | + | 0.969795i | \(0.578434\pi\) | |||||||
\(884\) | 6455.08 | − | 2039.16i | 0.245597 | − | 0.0775840i | ||||
\(885\) | 16172.2 | − | 10041.6i | 0.614262 | − | 0.381407i | ||||
\(886\) | −8659.81 | − | 6346.00i | −0.328366 | − | 0.240630i | ||||
\(887\) | 8078.84 | − | 8078.84i | 0.305818 | − | 0.305818i | −0.537467 | − | 0.843285i | \(-0.680619\pi\) |
0.843285 | + | 0.537467i | \(0.180619\pi\) | |||||||
\(888\) | −2216.01 | − | 4484.36i | −0.0837439 | − | 0.169465i | ||||
\(889\) | − | 26918.5i | − | 1.01554i | ||||||
\(890\) | −381.814 | − | 29.3616i | −0.0143803 | − | 0.00110585i | ||||
\(891\) | − | 2636.78i | − | 0.0991418i | ||||||
\(892\) | 10073.3 | + | 5236.81i | 0.378114 | + | 0.196571i | ||||
\(893\) | 5704.70 | − | 5704.70i | 0.213774 | − | 0.213774i | ||||
\(894\) | −6025.98 | + | 8223.12i | −0.225435 | + | 0.307631i | ||||
\(895\) | −192.753 | + | 824.195i | −0.00719890 | + | 0.0307819i | ||||
\(896\) | 5638.24 | + | 19207.1i | 0.210224 | + | 0.716144i | ||||
\(897\) | −2105.08 | − | 2105.08i | −0.0783573 | − | 0.0783573i | ||||
\(898\) | 1480.88 | + | 9603.95i | 0.0550306 | + | 0.356891i | ||||
\(899\) | 21068.2 | 0.781606 | ||||||||
\(900\) | 1376.07 | − | 8894.18i | 0.0509655 | − | 0.329414i | ||||
\(901\) | −47136.1 | −1.74287 | ||||||||
\(902\) | 6612.77 | + | 42885.9i | 0.244103 | + | 1.58309i | ||||
\(903\) | 10700.2 | + | 10700.2i | 0.394330 | + | 0.394330i | ||||
\(904\) | 7341.19 | − | 21684.8i | 0.270093 | − | 0.797817i | ||||
\(905\) | 3382.93 | − | 14465.1i | 0.124257 | − | 0.531312i | ||||
\(906\) | −5579.27 | + | 7613.53i | −0.204590 | + | 0.279186i | ||||
\(907\) | 11565.2 | − | 11565.2i | 0.423393 | − | 0.423393i | −0.462978 | − | 0.886370i | \(-0.653219\pi\) |
0.886370 | + | 0.462978i | \(0.153219\pi\) | |||||||
\(908\) | 8319.43 | − | 16002.8i | 0.304064 | − | 0.584881i | ||||
\(909\) | − | 8475.67i | − | 0.309263i | ||||||
\(910\) | −3669.52 | − | 282.188i | −0.133674 | − | 0.0102796i | ||||
\(911\) | 14979.7i | 0.544787i | 0.962186 | + | 0.272394i | \(0.0878153\pi\) | ||||
−0.962186 | + | 0.272394i | \(0.912185\pi\) | |||||||
\(912\) | −19854.7 | − | 3478.55i | −0.720894 | − | 0.126301i | ||||
\(913\) | 29571.1 | − | 29571.1i | 1.07192 | − | 1.07192i | ||||
\(914\) | −12104.7 | − | 8870.43i | −0.438060 | − | 0.321015i | ||||
\(915\) | 23709.0 | − | 14721.3i | 0.856605 | − | 0.531883i | ||||
\(916\) | 4343.13 | + | 13748.4i | 0.156660 | + | 0.495918i | ||||
\(917\) | 24551.8 | + | 24551.8i | 0.884158 | + | 0.884158i | ||||
\(918\) | 7585.42 | − | 1169.63i | 0.272719 | − | 0.0420518i | ||||
\(919\) | 14228.6 | 0.510727 | 0.255364 | − | 0.966845i | \(-0.417805\pi\) | ||||
0.255364 | + | 0.966845i | \(0.417805\pi\) | |||||||
\(920\) | 15741.3 | − | 25322.8i | 0.564102 | − | 0.907464i | ||||
\(921\) | 13886.4 | 0.496822 | ||||||||
\(922\) | −50500.4 | + | 7786.88i | −1.80384 | + | 0.278142i | ||||
\(923\) | −3181.95 | − | 3181.95i | −0.113472 | − | 0.113472i | ||||
\(924\) | −3253.04 | − | 10297.7i | −0.115820 | − | 0.366634i | ||||
\(925\) | 2949.14 | + | 8725.95i | 0.104829 | + | 0.310170i | ||||
\(926\) | −12815.2 | − | 9391.11i | −0.454788 | − | 0.333273i | ||||
\(927\) | −7012.04 | + | 7012.04i | −0.248442 | + | 0.248442i | ||||
\(928\) | 21439.0 | + | 22334.3i | 0.758371 | + | 0.790041i | ||||
\(929\) | 21373.3i | 0.754830i | 0.926044 | + | 0.377415i | \(0.123187\pi\) | ||||
−0.926044 | + | 0.377415i | \(0.876813\pi\) | |||||||
\(930\) | −7605.76 | − | 8872.98i | −0.268175 | − | 0.312857i | ||||
\(931\) | − | 15950.4i | − | 0.561496i | ||||||
\(932\) | −8434.04 | + | 16223.3i | −0.296423 | + | 0.570184i | ||||
\(933\) | 16748.6 | − | 16748.6i | 0.587700 | − | 0.587700i | ||||
\(934\) | −6484.06 | + | 8848.21i | −0.227157 | + | 0.309981i | ||||
\(935\) | −19294.9 | − | 31074.7i | −0.674877 | − | 1.08690i | ||||
\(936\) | −1624.09 | − | 549.819i | −0.0567147 | − | 0.0192002i | ||||
\(937\) | 18353.3 | + | 18353.3i | 0.639888 | + | 0.639888i | 0.950528 | − | 0.310639i | \(-0.100543\pi\) |
−0.310639 | + | 0.950528i | \(0.600543\pi\) | |||||||
\(938\) | 325.386 | + | 2110.23i | 0.0113265 | + | 0.0734557i | ||||
\(939\) | −26591.8 | −0.924164 | ||||||||
\(940\) | 5216.22 | + | 4475.86i | 0.180994 | + | 0.155305i | ||||
\(941\) | −3056.37 | −0.105882 | −0.0529409 | − | 0.998598i | \(-0.516859\pi\) | ||||
−0.0529409 | + | 0.998598i | \(0.516859\pi\) | |||||||
\(942\) | −1124.12 | − | 7290.30i | −0.0388810 | − | 0.252156i | ||||
\(943\) | 39276.9 | + | 39276.9i | 1.35634 | + | 1.35634i | ||||
\(944\) | 29731.3 | − | 20866.5i | 1.02507 | − | 0.719436i | ||||
\(945\) | −4063.05 | − | 950.216i | −0.139863 | − | 0.0327096i | ||||
\(946\) | 19859.8 | − | 27100.9i | 0.682557 | − | 0.931424i | ||||
\(947\) | 10860.0 | − | 10860.0i | 0.372652 | − | 0.372652i | −0.495791 | − | 0.868442i | \(-0.665122\pi\) |
0.868442 | + | 0.495791i | \(0.165122\pi\) | |||||||
\(948\) | 1631.35 | + | 848.092i | 0.0558900 | + | 0.0290557i | ||||
\(949\) | − | 4980.61i | − | 0.170366i | ||||||
\(950\) | 35388.1 | + | 11198.9i | 1.20857 | + | 0.382464i | ||||
\(951\) | 21532.5i | 0.734216i | ||||||||
\(952\) | 28181.2 | − | 13926.2i | 0.959410 | − | 0.474107i | ||||
\(953\) | −19966.0 | + | 19966.0i | −0.678659 | + | 0.678659i | −0.959697 | − | 0.281037i | \(-0.909322\pi\) |
0.281037 | + | 0.959697i | \(0.409322\pi\) | |||||||
\(954\) | 9630.06 | + | 7057.01i | 0.326818 | + | 0.239496i | ||||
\(955\) | −5741.73 | − | 1342.81i | −0.194553 | − | 0.0454997i | ||||
\(956\) | −2452.16 | + | 774.636i | −0.0829586 | + | 0.0262066i | ||||
\(957\) | −11810.1 | − | 11810.1i | −0.398920 | − | 0.398920i | ||||
\(958\) | −45534.6 | + | 7021.18i | −1.53565 | + | 0.236789i | ||||
\(959\) | −13318.9 | −0.448477 | ||||||||
\(960\) | 1666.58 | − | 17091.9i | 0.0560299 | − | 0.574625i | ||||
\(961\) | 14615.7 | 0.490609 | ||||||||
\(962\) | 1734.30 | − | 267.420i | 0.0581250 | − | 0.00896255i | ||||
\(963\) | −4871.14 | − | 4871.14i | −0.163001 | − | 0.163001i | ||||
\(964\) | −13066.4 | + | 4127.68i | −0.436558 | + | 0.137908i | ||||
\(965\) | 9895.46 | + | 15936.8i | 0.330100 | + | 0.531631i | ||||
\(966\) | −11150.4 | − | 8171.16i | −0.371387 | − | 0.272156i | ||||
\(967\) | −17217.7 | + | 17217.7i | −0.572580 | + | 0.572580i | −0.932849 | − | 0.360269i | \(-0.882685\pi\) |
0.360269 | + | 0.932849i | \(0.382685\pi\) | |||||||
\(968\) | 5503.81 | − | 2719.79i | 0.182747 | − | 0.0903072i | ||||
\(969\) | 31653.5i | 1.04939i | ||||||||
\(970\) | −20829.6 | + | 17854.8i | −0.689483 | + | 0.591012i | ||||
\(971\) | 10164.9i | 0.335950i | 0.985791 | + | 0.167975i | \(0.0537228\pi\) | ||||
−0.985791 | + | 0.167975i | \(0.946277\pi\) | |||||||
\(972\) | −1724.84 | − | 896.697i | −0.0569180 | − | 0.0295901i | ||||
\(973\) | 20126.5 | − | 20126.5i | 0.663131 | − | 0.663131i | ||||
\(974\) | −13788.0 | + | 18815.3i | −0.453590 | + | 0.618974i | ||||
\(975\) | 2829.90 | + | 1400.23i | 0.0929530 | + | 0.0459930i | ||||
\(976\) | 43587.1 | − | 30591.0i | 1.42950 | − | 1.00327i | ||||
\(977\) | 9513.40 | + | 9513.40i | 0.311526 | + | 0.311526i | 0.845500 | − | 0.533975i | \(-0.179302\pi\) |
−0.533975 | + | 0.845500i | \(0.679302\pi\) | |||||||
\(978\) | −3136.17 | − | 20339.0i | −0.102539 | − | 0.665000i | ||||
\(979\) | 394.203 | 0.0128690 | ||||||||
\(980\) | 13549.6 | − | 1035.03i | 0.441658 | − | 0.0337375i | ||||
\(981\) | 6277.71 | 0.204314 | ||||||||
\(982\) | 1092.25 | + | 7083.61i | 0.0354941 | + | 0.230191i | ||||
\(983\) | −6749.01 | − | 6749.01i | −0.218983 | − | 0.218983i | 0.589087 | − | 0.808070i | \(-0.299488\pi\) |
−0.808070 | + | 0.589087i | \(0.799488\pi\) | |||||||
\(984\) | 30302.5 | + | 10258.6i | 0.981716 | + | 0.332351i | ||||
\(985\) | −459.642 | + | 285.401i | −0.0148684 | + | 0.00923210i | ||||
\(986\) | 28736.3 | − | 39213.8i | 0.928144 | − | 1.26655i | ||||
\(987\) | 2253.32 | − | 2253.32i | 0.0726687 | − | 0.0726687i | ||||
\(988\) | 3261.82 | − | 6274.27i | 0.105033 | − | 0.202036i | ||||
\(989\) | − | 43008.8i | − | 1.38281i | ||||||
\(990\) | −710.361 | + | 9237.42i | −0.0228048 | + | 0.296550i | ||||
\(991\) | − | 7199.32i | − | 0.230771i | −0.993321 | − | 0.115385i | \(-0.963190\pi\) | ||
0.993321 | − | 0.115385i | \(-0.0368103\pi\) | |||||||
\(992\) | −15442.3 | − | 16087.2i | −0.494248 | − | 0.514888i | ||||
\(993\) | −7203.84 | + | 7203.84i | −0.230218 | + | 0.230218i | ||||
\(994\) | −16854.6 | − | 12351.2i | −0.537821 | − | 0.394121i | ||||
\(995\) | −1398.44 | + | 5979.63i | −0.0445564 | + | 0.190520i | ||||
\(996\) | −9287.50 | − | 29400.2i | −0.295468 | − | 0.935321i | ||||
\(997\) | −15867.5 | − | 15867.5i | −0.504041 | − | 0.504041i | 0.408650 | − | 0.912691i | \(-0.366000\pi\) |
−0.912691 | + | 0.408650i | \(0.866000\pi\) | |||||||
\(998\) | 35092.9 | − | 5411.13i | 1.11307 | − | 0.171630i | ||||
\(999\) | 1989.54 | 0.0630093 |
(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 | 60.4.j.b.7.14 | yes | 28 | |
3.2 | odd | 2 | 180.4.k.f.127.1 | 28 | |||
4.3 | odd | 2 | inner | 60.4.j.b.7.7 | ✓ | 28 | |
5.3 | odd | 4 | inner | 60.4.j.b.43.7 | yes | 28 | |
12.11 | even | 2 | 180.4.k.f.127.8 | 28 | |||
15.8 | even | 4 | 180.4.k.f.163.8 | 28 | |||
20.3 | even | 4 | inner | 60.4.j.b.43.14 | yes | 28 | |
60.23 | odd | 4 | 180.4.k.f.163.1 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.4.j.b.7.7 | ✓ | 28 | 4.3 | odd | 2 | inner | |
60.4.j.b.7.14 | yes | 28 | 1.1 | even | 1 | trivial | |
60.4.j.b.43.7 | yes | 28 | 5.3 | odd | 4 | inner | |
60.4.j.b.43.14 | yes | 28 | 20.3 | even | 4 | inner | |
180.4.k.f.127.1 | 28 | 3.2 | odd | 2 | |||
180.4.k.f.127.8 | 28 | 12.11 | even | 2 | |||
180.4.k.f.163.1 | 28 | 60.23 | odd | 4 | |||
180.4.k.f.163.8 | 28 | 15.8 | even | 4 |