Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(76,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (of order \(3\), 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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + 209529 x^{6} - 55412 x^{5} + 765088 x^{4} + 276096 x^{3} + 1572480 x^{2} + \cdots + 82944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 151.5 | ||
Root | \(-0.785104 - 1.35984i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.151 |
Dual form | 225.4.e.d.76.5 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.785104 | − | 1.35984i | 0.277576 | − | 0.480776i | −0.693206 | − | 0.720740i | \(-0.743802\pi\) |
0.970782 | + | 0.239964i | \(0.0771355\pi\) | |||||||
\(3\) | 3.89934 | + | 3.43441i | 0.750428 | + | 0.660952i | ||||
\(4\) | 2.76722 | + | 4.79297i | 0.345903 | + | 0.599121i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 7.73164 | − | 2.60611i | 0.526071 | − | 0.177324i | ||||
\(7\) | 17.1199 | − | 29.6525i | 0.924387 | − | 1.60109i | 0.131844 | − | 0.991271i | \(-0.457910\pi\) |
0.792544 | − | 0.609815i | \(-0.208756\pi\) | |||||||
\(8\) | 21.2519 | 0.939210 | ||||||||
\(9\) | 3.40971 | + | 26.7838i | 0.126285 | + | 0.991994i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.4480 | − | 23.2926i | 0.368611 | − | 0.638453i | −0.620737 | − | 0.784019i | \(-0.713167\pi\) |
0.989349 | + | 0.145565i | \(0.0465000\pi\) | |||||||
\(12\) | −5.67066 | + | 28.1932i | −0.136415 | + | 0.678223i | ||||
\(13\) | −9.74401 | − | 16.8771i | −0.207885 | − | 0.360067i | 0.743163 | − | 0.669110i | \(-0.233325\pi\) |
−0.951048 | + | 0.309043i | \(0.899991\pi\) | |||||||
\(14\) | −26.8818 | − | 46.5607i | −0.513176 | − | 0.888847i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.45281 | + | 9.44454i | −0.0852001 | + | 0.147571i | ||||
\(17\) | −29.1232 | −0.415495 | −0.207747 | − | 0.978182i | \(-0.566613\pi\) | ||||
−0.207747 | + | 0.978182i | \(0.566613\pi\) | |||||||
\(18\) | 39.0987 | + | 16.3915i | 0.511981 | + | 0.214639i | ||||
\(19\) | 47.1006 | 0.568717 | 0.284358 | − | 0.958718i | \(-0.408219\pi\) | ||||
0.284358 | + | 0.958718i | \(0.408219\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 168.595 | − | 56.8286i | 1.75193 | − | 0.590525i | ||||
\(22\) | −21.1162 | − | 36.5743i | −0.204636 | − | 0.354439i | ||||
\(23\) | 56.6083 | + | 98.0485i | 0.513202 | + | 0.888892i | 0.999883 | + | 0.0153124i | \(0.00487428\pi\) |
−0.486680 | + | 0.873580i | \(0.661792\pi\) | |||||||
\(24\) | 82.8684 | + | 72.9877i | 0.704810 | + | 0.620773i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −30.6003 | −0.230816 | ||||||||
\(27\) | −78.6910 | + | 116.150i | −0.560892 | + | 0.827889i | ||||
\(28\) | 189.498 | 1.27899 | ||||||||
\(29\) | −40.6219 | + | 70.3593i | −0.260114 | + | 0.450531i | −0.966272 | − | 0.257524i | \(-0.917093\pi\) |
0.706158 | + | 0.708054i | \(0.250427\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.41811 | + | 9.38445i | 0.0313910 | + | 0.0543708i | 0.881294 | − | 0.472568i | \(-0.156673\pi\) |
−0.849903 | + | 0.526939i | \(0.823340\pi\) | |||||||
\(32\) | 93.5697 | + | 162.067i | 0.516904 | + | 0.895304i | ||||
\(33\) | 132.435 | − | 44.6399i | 0.698603 | − | 0.235479i | ||||
\(34\) | −22.8648 | + | 39.6029i | −0.115332 | + | 0.199760i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −118.939 | + | 90.4594i | −0.550642 | + | 0.418794i | ||||
\(37\) | −410.002 | −1.82173 | −0.910864 | − | 0.412706i | \(-0.864584\pi\) | ||||
−0.910864 | + | 0.412706i | \(0.864584\pi\) | |||||||
\(38\) | 36.9789 | − | 64.0493i | 0.157862 | − | 0.273426i | ||||
\(39\) | 19.9677 | − | 99.2746i | 0.0819843 | − | 0.407606i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 221.755 | + | 384.091i | 0.844691 | + | 1.46305i | 0.885889 | + | 0.463897i | \(0.153549\pi\) |
−0.0411978 | + | 0.999151i | \(0.513117\pi\) | |||||||
\(42\) | 55.0869 | − | 273.879i | 0.202383 | − | 1.00620i | ||||
\(43\) | 169.748 | − | 294.012i | 0.602007 | − | 1.04271i | −0.390510 | − | 0.920599i | \(-0.627701\pi\) |
0.992517 | − | 0.122108i | \(-0.0389655\pi\) | |||||||
\(44\) | 148.854 | 0.510015 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 177.774 | 0.569811 | ||||||||
\(47\) | 118.121 | − | 204.591i | 0.366589 | − | 0.634950i | −0.622441 | − | 0.782667i | \(-0.713859\pi\) |
0.989030 | + | 0.147716i | \(0.0471923\pi\) | |||||||
\(48\) | −53.6988 | + | 18.1003i | −0.161474 | + | 0.0544283i | ||||
\(49\) | −414.681 | − | 718.249i | −1.20898 | − | 2.09402i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −113.561 | − | 100.021i | −0.311799 | − | 0.274622i | ||||
\(52\) | 53.9277 | − | 93.4055i | 0.143816 | − | 0.249096i | ||||
\(53\) | −609.634 | −1.57999 | −0.789997 | − | 0.613111i | \(-0.789918\pi\) | ||||
−0.789997 | + | 0.613111i | \(0.789918\pi\) | |||||||
\(54\) | 96.1643 | + | 198.197i | 0.242339 | + | 0.499466i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 363.830 | − | 630.173i | 0.868194 | − | 1.50376i | ||||
\(57\) | 183.661 | + | 161.763i | 0.426781 | + | 0.375894i | ||||
\(58\) | 63.7849 | + | 110.479i | 0.144403 | + | 0.250113i | ||||
\(59\) | −7.77272 | − | 13.4627i | −0.0171512 | − | 0.0297068i | 0.857322 | − | 0.514780i | \(-0.172126\pi\) |
−0.874474 | + | 0.485073i | \(0.838793\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −30.5255 | + | 52.8717i | −0.0640719 | + | 0.110976i | −0.896282 | − | 0.443485i | \(-0.853742\pi\) |
0.832210 | + | 0.554461i | \(0.187075\pi\) | |||||||
\(62\) | 17.0151 | 0.0348536 | ||||||||
\(63\) | 852.582 | + | 357.430i | 1.70500 | + | 0.714793i | ||||
\(64\) | 206.603 | 0.403521 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 43.2718 | − | 215.137i | 0.0807029 | − | 0.401235i | ||||
\(67\) | 108.445 | + | 187.832i | 0.197741 | + | 0.342497i | 0.947796 | − | 0.318879i | \(-0.103306\pi\) |
−0.750055 | + | 0.661376i | \(0.769973\pi\) | |||||||
\(68\) | −80.5903 | − | 139.587i | −0.143721 | − | 0.248932i | ||||
\(69\) | −116.003 | + | 576.740i | −0.202394 | + | 1.00625i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 65.4315 | 0.109370 | 0.0546852 | − | 0.998504i | \(-0.482584\pi\) | ||||
0.0546852 | + | 0.998504i | \(0.482584\pi\) | |||||||
\(72\) | 72.4627 | + | 569.208i | 0.118609 | + | 0.931691i | ||||
\(73\) | −711.811 | −1.14125 | −0.570624 | − | 0.821211i | \(-0.693299\pi\) | ||||
−0.570624 | + | 0.821211i | \(0.693299\pi\) | |||||||
\(74\) | −321.895 | + | 557.538i | −0.505669 | + | 0.875844i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 130.338 | + | 225.752i | 0.196721 | + | 0.340730i | ||||
\(77\) | −460.457 | − | 797.534i | −0.681479 | − | 1.18036i | ||||
\(78\) | −119.321 | − | 105.094i | −0.173211 | − | 0.152558i | ||||
\(79\) | 478.876 | − | 829.438i | 0.681997 | − | 1.18125i | −0.292373 | − | 0.956304i | \(-0.594445\pi\) |
0.974370 | − | 0.224949i | \(-0.0722217\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −705.748 | + | 182.650i | −0.968104 | + | 0.250549i | ||||
\(82\) | 696.404 | 0.937865 | ||||||||
\(83\) | −261.220 | + | 452.446i | −0.345453 | + | 0.598343i | −0.985436 | − | 0.170047i | \(-0.945608\pi\) |
0.639983 | + | 0.768389i | \(0.278942\pi\) | |||||||
\(84\) | 738.918 | + | 650.814i | 0.959792 | + | 0.845352i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −266.540 | − | 461.660i | −0.334206 | − | 0.578862i | ||||
\(87\) | −400.041 | + | 134.842i | −0.492976 | + | 0.166168i | ||||
\(88\) | 285.796 | − | 495.012i | 0.346204 | − | 0.599642i | ||||
\(89\) | −1602.24 | −1.90828 | −0.954141 | − | 0.299359i | \(-0.903227\pi\) | ||||
−0.954141 | + | 0.299359i | \(0.903227\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −667.266 | −0.768664 | ||||||||
\(92\) | −313.296 | + | 542.644i | −0.355036 | + | 0.614941i | ||||
\(93\) | −11.1029 | + | 55.2011i | −0.0123798 | + | 0.0615494i | ||||
\(94\) | −185.474 | − | 321.251i | −0.203513 | − | 0.352494i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −191.745 | + | 953.312i | −0.203854 | + | 1.01351i | ||||
\(97\) | 400.969 | − | 694.499i | 0.419714 | − | 0.726966i | −0.576197 | − | 0.817311i | \(-0.695464\pi\) |
0.995910 | + | 0.0903455i | \(0.0287971\pi\) | |||||||
\(98\) | −1302.27 | −1.34234 | ||||||||
\(99\) | 669.719 | + | 280.768i | 0.679892 | + | 0.285033i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −293.065 | + | 507.604i | −0.288724 | + | 0.500084i | −0.973505 | − | 0.228664i | \(-0.926564\pi\) |
0.684782 | + | 0.728748i | \(0.259898\pi\) | |||||||
\(102\) | −225.170 | + | 75.8984i | −0.218580 | + | 0.0736770i | ||||
\(103\) | −410.337 | − | 710.725i | −0.392541 | − | 0.679901i | 0.600243 | − | 0.799818i | \(-0.295071\pi\) |
−0.992784 | + | 0.119917i | \(0.961737\pi\) | |||||||
\(104\) | −207.079 | − | 358.671i | −0.195248 | − | 0.338179i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −478.626 | + | 829.005i | −0.438569 | + | 0.759623i | ||||
\(107\) | 1358.33 | 1.22724 | 0.613621 | − | 0.789600i | \(-0.289712\pi\) | ||||
0.613621 | + | 0.789600i | \(0.289712\pi\) | |||||||
\(108\) | −774.457 | − | 55.7517i | −0.690020 | − | 0.0496732i | ||||
\(109\) | 489.495 | 0.430139 | 0.215069 | − | 0.976599i | \(-0.431002\pi\) | ||||
0.215069 | + | 0.976599i | \(0.431002\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1598.74 | − | 1408.11i | −1.36708 | − | 1.20407i | ||||
\(112\) | 186.703 | + | 323.379i | 0.157516 | + | 0.272825i | ||||
\(113\) | 398.832 | + | 690.797i | 0.332026 | + | 0.575086i | 0.982909 | − | 0.184092i | \(-0.0589345\pi\) |
−0.650883 | + | 0.759178i | \(0.725601\pi\) | |||||||
\(114\) | 364.165 | − | 122.750i | 0.299185 | − | 0.100847i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −449.640 | −0.359897 | ||||||||
\(117\) | 418.810 | − | 318.528i | 0.330932 | − | 0.251692i | ||||
\(118\) | −24.4096 | −0.0190431 | ||||||||
\(119\) | −498.586 | + | 863.576i | −0.384078 | + | 0.665243i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 303.803 | + | 526.202i | 0.228251 | + | 0.395343i | ||||
\(122\) | 47.9314 | + | 83.0196i | 0.0355697 | + | 0.0616085i | ||||
\(123\) | −454.427 | + | 2259.30i | −0.333124 | + | 1.65621i | ||||
\(124\) | −29.9862 | + | 51.9377i | −0.0217165 | + | 0.0376141i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1155.41 | − | 878.756i | 0.816924 | − | 0.621316i | ||||
\(127\) | −1728.22 | −1.20752 | −0.603759 | − | 0.797167i | \(-0.706331\pi\) | ||||
−0.603759 | + | 0.797167i | \(0.706331\pi\) | |||||||
\(128\) | −586.352 | + | 1015.59i | −0.404896 | + | 0.701301i | ||||
\(129\) | 1671.66 | − | 563.469i | 1.14094 | − | 0.384579i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −319.551 | − | 553.478i | −0.213124 | − | 0.369142i | 0.739566 | − | 0.673084i | \(-0.235031\pi\) |
−0.952691 | + | 0.303942i | \(0.901697\pi\) | |||||||
\(132\) | 580.434 | + | 511.226i | 0.382729 | + | 0.337095i | ||||
\(133\) | 806.357 | − | 1396.65i | 0.525715 | − | 0.910564i | ||||
\(134\) | 340.562 | 0.219553 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −618.923 | −0.390237 | ||||||||
\(137\) | −1417.97 | + | 2456.00i | −0.884274 | + | 1.53161i | −0.0377300 | + | 0.999288i | \(0.512013\pi\) |
−0.846544 | + | 0.532319i | \(0.821321\pi\) | |||||||
\(138\) | 693.201 | + | 610.548i | 0.427603 | + | 0.376618i | ||||
\(139\) | −87.4981 | − | 151.551i | −0.0533920 | − | 0.0924777i | 0.838094 | − | 0.545526i | \(-0.183670\pi\) |
−0.891486 | + | 0.453048i | \(0.850337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1163.24 | − | 392.096i | 0.694770 | − | 0.234187i | ||||
\(142\) | 51.3706 | − | 88.9764i | 0.0303586 | − | 0.0525827i | ||||
\(143\) | −524.150 | −0.306515 | ||||||||
\(144\) | −271.554 | − | 113.844i | −0.157149 | − | 0.0658820i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −558.846 | + | 967.949i | −0.316784 | + | 0.548685i | ||||
\(147\) | 849.776 | − | 4224.88i | 0.476791 | − | 2.37049i | ||||
\(148\) | −1134.57 | − | 1965.13i | −0.630141 | − | 1.09144i | ||||
\(149\) | −511.766 | − | 886.405i | −0.281379 | − | 0.487363i | 0.690345 | − | 0.723480i | \(-0.257459\pi\) |
−0.971725 | + | 0.236117i | \(0.924125\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 436.998 | − | 756.902i | 0.235512 | − | 0.407920i | −0.723909 | − | 0.689895i | \(-0.757656\pi\) |
0.959421 | + | 0.281976i | \(0.0909898\pi\) | |||||||
\(152\) | 1000.98 | 0.534145 | ||||||||
\(153\) | −99.3015 | − | 780.031i | −0.0524709 | − | 0.412168i | ||||
\(154\) | −1446.03 | −0.756650 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 531.075 | − | 179.010i | 0.272564 | − | 0.0918736i | ||||
\(157\) | 61.7762 | + | 107.000i | 0.0314031 | + | 0.0543917i | 0.881300 | − | 0.472558i | \(-0.156669\pi\) |
−0.849897 | + | 0.526949i | \(0.823336\pi\) | |||||||
\(158\) | −751.936 | − | 1302.39i | −0.378613 | − | 0.655776i | ||||
\(159\) | −2377.17 | − | 2093.73i | −1.18567 | − | 1.04430i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3876.51 | 1.89759 | ||||||||
\(162\) | −305.711 | + | 1103.10i | −0.148265 | + | 0.534988i | ||||
\(163\) | 1410.89 | 0.677972 | 0.338986 | − | 0.940791i | \(-0.389916\pi\) | ||||
0.338986 | + | 0.940791i | \(0.389916\pi\) | |||||||
\(164\) | −1227.29 | + | 2125.73i | −0.584362 | + | 1.01214i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 410.170 | + | 710.435i | 0.191779 | + | 0.332172i | ||||
\(167\) | −1013.85 | − | 1756.04i | −0.469786 | − | 0.813692i | 0.529618 | − | 0.848236i | \(-0.322335\pi\) |
−0.999403 | + | 0.0345441i | \(0.989002\pi\) | |||||||
\(168\) | 3582.97 | − | 1207.72i | 1.64543 | − | 0.554627i | ||||
\(169\) | 908.608 | − | 1573.76i | 0.413568 | − | 0.716320i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 160.599 | + | 1261.53i | 0.0718206 | + | 0.564164i | ||||
\(172\) | 1878.92 | 0.832944 | ||||||||
\(173\) | 1351.99 | − | 2341.71i | 0.594160 | − | 1.02912i | −0.399505 | − | 0.916731i | \(-0.630818\pi\) |
0.993665 | − | 0.112384i | \(-0.0358488\pi\) | |||||||
\(174\) | −130.710 | + | 649.858i | −0.0569487 | + | 0.283135i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 146.659 | + | 254.020i | 0.0628115 | + | 0.108793i | ||||
\(177\) | 15.9281 | − | 79.1905i | 0.00676399 | − | 0.0336289i | ||||
\(178\) | −1257.93 | + | 2178.79i | −0.529694 | + | 0.917456i | ||||
\(179\) | −750.694 | −0.313461 | −0.156730 | − | 0.987641i | \(-0.550095\pi\) | ||||
−0.156730 | + | 0.987641i | \(0.550095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1134.08 | −0.465722 | −0.232861 | − | 0.972510i | \(-0.574809\pi\) | ||||
−0.232861 | + | 0.972510i | \(0.574809\pi\) | |||||||
\(182\) | −523.873 | + | 907.375i | −0.213363 | + | 0.369556i | ||||
\(183\) | −300.612 | + | 101.328i | −0.121431 | + | 0.0409309i | ||||
\(184\) | 1203.03 | + | 2083.72i | 0.482005 | + | 0.834857i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 66.3478 | + | 58.4369i | 0.0261551 | + | 0.0230366i | ||||
\(187\) | −391.649 | + | 678.355i | −0.153156 | + | 0.265274i | ||||
\(188\) | 1307.46 | 0.507216 | ||||||||
\(189\) | 2096.95 | + | 4321.85i | 0.807040 | + | 1.66333i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 267.627 | − | 463.544i | 0.101387 | − | 0.175607i | −0.810870 | − | 0.585227i | \(-0.801005\pi\) |
0.912256 | + | 0.409620i | \(0.134339\pi\) | |||||||
\(192\) | 805.615 | + | 709.558i | 0.302814 | + | 0.266708i | ||||
\(193\) | 1311.77 | + | 2272.06i | 0.489241 | + | 0.847391i | 0.999923 | − | 0.0123786i | \(-0.00394034\pi\) |
−0.510682 | + | 0.859770i | \(0.670607\pi\) | |||||||
\(194\) | −629.605 | − | 1090.51i | −0.233005 | − | 0.403577i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2295.03 | − | 3975.11i | 0.836382 | − | 1.44866i | ||||
\(197\) | −2954.08 | −1.06837 | −0.534186 | − | 0.845367i | \(-0.679382\pi\) | ||||
−0.534186 | + | 0.845367i | \(0.679382\pi\) | |||||||
\(198\) | 907.599 | − | 690.279i | 0.325759 | − | 0.247758i | ||||
\(199\) | 2639.35 | 0.940192 | 0.470096 | − | 0.882615i | \(-0.344219\pi\) | ||||
0.470096 | + | 0.882615i | \(0.344219\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −222.228 | + | 1104.86i | −0.0779838 | + | 0.387717i | ||||
\(202\) | 460.174 | + | 797.044i | 0.160286 | + | 0.277623i | ||||
\(203\) | 1390.89 | + | 2409.09i | 0.480892 | + | 0.832929i | ||||
\(204\) | 165.148 | − | 821.076i | 0.0566797 | − | 0.281798i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1288.63 | −0.435841 | ||||||||
\(207\) | −2433.10 | + | 1850.50i | −0.816966 | + | 0.621348i | ||||
\(208\) | 212.529 | 0.0708473 | ||||||||
\(209\) | 633.409 | − | 1097.10i | 0.209635 | − | 0.363099i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 995.327 | + | 1723.96i | 0.324745 | + | 0.562474i | 0.981461 | − | 0.191664i | \(-0.0613883\pi\) |
−0.656716 | + | 0.754138i | \(0.728055\pi\) | |||||||
\(212\) | −1686.99 | − | 2921.96i | −0.546524 | − | 0.946607i | ||||
\(213\) | 255.140 | + | 224.718i | 0.0820746 | + | 0.0722885i | ||||
\(214\) | 1066.43 | − | 1847.12i | 0.340654 | − | 0.590029i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1672.33 | + | 2468.40i | −0.526796 | + | 0.777562i | ||||
\(217\) | 371.030 | 0.116070 | ||||||||
\(218\) | 384.305 | − | 665.635i | 0.119396 | − | 0.206800i | ||||
\(219\) | −2775.59 | − | 2444.65i | −0.856425 | − | 0.754310i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 283.777 | + | 491.516i | 0.0863751 | + | 0.149606i | ||||
\(222\) | −3169.99 | + | 1068.51i | −0.958359 | + | 0.323035i | ||||
\(223\) | −337.450 | + | 584.481i | −0.101333 | + | 0.175515i | −0.912234 | − | 0.409669i | \(-0.865644\pi\) |
0.810901 | + | 0.585184i | \(0.198978\pi\) | |||||||
\(224\) | 6407.61 | 1.91128 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1252.50 | 0.368650 | ||||||||
\(227\) | 945.926 | − | 1638.39i | 0.276579 | − | 0.479048i | −0.693954 | − | 0.720020i | \(-0.744133\pi\) |
0.970532 | + | 0.240972i | \(0.0774661\pi\) | |||||||
\(228\) | −267.092 | + | 1327.92i | −0.0775815 | + | 0.385717i | ||||
\(229\) | −1704.26 | − | 2951.86i | −0.491792 | − | 0.851810i | 0.508163 | − | 0.861261i | \(-0.330325\pi\) |
−0.999955 | + | 0.00945146i | \(0.996991\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 943.580 | − | 4691.25i | 0.268758 | − | 1.33620i | ||||
\(232\) | −863.294 | + | 1495.27i | −0.244302 | + | 0.423143i | ||||
\(233\) | 2841.86 | 0.799041 | 0.399521 | − | 0.916724i | \(-0.369177\pi\) | ||||
0.399521 | + | 0.916724i | \(0.369177\pi\) | |||||||
\(234\) | −104.338 | − | 819.593i | −0.0291486 | − | 0.228968i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 43.0177 | − | 74.5088i | 0.0118653 | − | 0.0205513i | ||||
\(237\) | 4715.93 | − | 1589.60i | 1.29254 | − | 0.435679i | ||||
\(238\) | 782.884 | + | 1356.00i | 0.213222 | + | 0.369311i | ||||
\(239\) | −809.803 | − | 1402.62i | −0.219171 | − | 0.379615i | 0.735384 | − | 0.677651i | \(-0.237002\pi\) |
−0.954555 | + | 0.298036i | \(0.903668\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.3504 | + | 23.1235i | −0.00356835 | + | 0.00618057i | −0.867804 | − | 0.496907i | \(-0.834469\pi\) |
0.864236 | + | 0.503087i | \(0.167803\pi\) | |||||||
\(242\) | 954.068 | 0.253429 | ||||||||
\(243\) | −3379.24 | − | 1711.61i | −0.892093 | − | 0.451851i | ||||
\(244\) | −337.883 | −0.0886506 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2715.52 | + | 2391.73i | 0.703801 | + | 0.619884i | ||||
\(247\) | −458.949 | − | 794.923i | −0.118228 | − | 0.204776i | ||||
\(248\) | 115.145 | + | 199.437i | 0.0294828 | + | 0.0510657i | ||||
\(249\) | −2572.47 | + | 867.107i | −0.654714 | + | 0.220685i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −427.354 | −0.107467 | −0.0537337 | − | 0.998555i | \(-0.517112\pi\) | ||||
−0.0537337 | + | 0.998555i | \(0.517112\pi\) | |||||||
\(252\) | 646.133 | + | 5075.49i | 0.161518 | + | 1.26875i | ||||
\(253\) | 3045.07 | 0.756689 | ||||||||
\(254\) | −1356.83 | + | 2350.10i | −0.335178 | + | 0.580546i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1747.11 | + | 3026.08i | 0.426540 | + | 0.738789i | ||||
\(257\) | 1920.77 | + | 3326.88i | 0.466204 | + | 0.807490i | 0.999255 | − | 0.0385936i | \(-0.0122878\pi\) |
−0.533051 | + | 0.846083i | \(0.678954\pi\) | |||||||
\(258\) | 546.200 | − | 2715.58i | 0.131802 | − | 0.655288i | ||||
\(259\) | −7019.19 | + | 12157.6i | −1.68398 | + | 2.91674i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2023.00 | − | 848.107i | −0.479772 | − | 0.201136i | ||||
\(262\) | −1003.52 | −0.236633 | ||||||||
\(263\) | −399.437 | + | 691.845i | −0.0936514 | + | 0.162209i | −0.909045 | − | 0.416698i | \(-0.863187\pi\) |
0.815394 | + | 0.578907i | \(0.196521\pi\) | |||||||
\(264\) | 2814.49 | − | 948.684i | 0.656135 | − | 0.221165i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1266.15 | − | 2193.03i | −0.291852 | − | 0.505502i | ||||
\(267\) | −6247.68 | − | 5502.74i | −1.43203 | − | 1.26128i | ||||
\(268\) | −600.181 | + | 1039.54i | −0.136798 | + | 0.236941i | ||||
\(269\) | 7934.42 | 1.79840 | 0.899201 | − | 0.437536i | \(-0.144149\pi\) | ||||
0.899201 | + | 0.437536i | \(0.144149\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2309.09 | −0.517592 | −0.258796 | − | 0.965932i | \(-0.583326\pi\) | ||||
−0.258796 | + | 0.965932i | \(0.583326\pi\) | |||||||
\(272\) | 158.803 | − | 275.055i | 0.0354002 | − | 0.0613150i | ||||
\(273\) | −2601.90 | − | 2291.66i | −0.576828 | − | 0.508050i | ||||
\(274\) | 2226.51 | + | 3856.43i | 0.490907 | + | 0.850276i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3085.31 | + | 1039.97i | −0.672875 | + | 0.226807i | ||||
\(277\) | 380.651 | − | 659.307i | 0.0825672 | − | 0.143011i | −0.821785 | − | 0.569798i | \(-0.807021\pi\) |
0.904352 | + | 0.426787i | \(0.140355\pi\) | |||||||
\(278\) | −274.781 | −0.0592815 | ||||||||
\(279\) | −232.877 | + | 177.116i | −0.0499713 | + | 0.0380059i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 643.638 | − | 1114.81i | 0.136641 | − | 0.236670i | −0.789582 | − | 0.613645i | \(-0.789703\pi\) |
0.926223 | + | 0.376975i | \(0.123036\pi\) | |||||||
\(282\) | 380.079 | − | 1889.66i | 0.0802601 | − | 0.399034i | ||||
\(283\) | −1363.25 | − | 2361.22i | −0.286350 | − | 0.495972i | 0.686586 | − | 0.727049i | \(-0.259109\pi\) |
−0.972936 | + | 0.231076i | \(0.925775\pi\) | |||||||
\(284\) | 181.064 | + | 313.611i | 0.0378315 | + | 0.0655261i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −411.512 | + | 712.760i | −0.0850813 | + | 0.147365i | ||||
\(287\) | 15185.7 | 3.12329 | ||||||||
\(288\) | −4021.74 | + | 3058.76i | −0.822859 | + | 0.625830i | ||||
\(289\) | −4064.84 | −0.827364 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3948.71 | − | 1331.00i | 0.795454 | − | 0.268125i | ||||
\(292\) | −1969.74 | − | 3411.69i | −0.394761 | − | 0.683746i | ||||
\(293\) | −48.1869 | − | 83.4622i | −0.00960789 | − | 0.0166414i | 0.861181 | − | 0.508298i | \(-0.169725\pi\) |
−0.870789 | + | 0.491656i | \(0.836392\pi\) | |||||||
\(294\) | −5078.00 | − | 4472.53i | −1.00733 | − | 0.887223i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8713.33 | −1.71099 | ||||||||
\(297\) | 1647.19 | + | 3394.90i | 0.321817 | + | 0.663273i | ||||
\(298\) | −1607.16 | −0.312417 | ||||||||
\(299\) | 1103.18 | − | 1910.77i | 0.213374 | − | 0.369575i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5812.13 | − | 10066.9i | −1.11298 | − | 1.92773i | ||||
\(302\) | −686.178 | − | 1188.50i | −0.130745 | − | 0.226458i | ||||
\(303\) | −2886.08 | + | 972.815i | −0.547198 | + | 0.184445i | ||||
\(304\) | −256.831 | + | 444.844i | −0.0484547 | + | 0.0839261i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1138.68 | − | 477.372i | −0.212726 | − | 0.0891814i | ||||
\(307\) | −5258.02 | −0.977495 | −0.488747 | − | 0.872425i | \(-0.662546\pi\) | ||||
−0.488747 | + | 0.872425i | \(0.662546\pi\) | |||||||
\(308\) | 2548.37 | − | 4413.91i | 0.471451 | − | 0.816577i | ||||
\(309\) | 840.874 | − | 4180.62i | 0.154808 | − | 0.769668i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2615.66 | + | 4530.45i | 0.476914 | + | 0.826039i | 0.999650 | − | 0.0264555i | \(-0.00842202\pi\) |
−0.522736 | + | 0.852495i | \(0.675089\pi\) | |||||||
\(312\) | 424.351 | − | 2109.77i | 0.0770005 | − | 0.382828i | ||||
\(313\) | −1996.33 | + | 3457.74i | −0.360509 | + | 0.624419i | −0.988045 | − | 0.154168i | \(-0.950730\pi\) |
0.627536 | + | 0.778588i | \(0.284064\pi\) | |||||||
\(314\) | 194.003 | 0.0348670 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5300.63 | 0.943619 | ||||||||
\(317\) | −2366.79 | + | 4099.40i | −0.419344 | + | 0.726325i | −0.995874 | − | 0.0907509i | \(-0.971073\pi\) |
0.576529 | + | 0.817076i | \(0.304407\pi\) | |||||||
\(318\) | −4713.47 | + | 1588.78i | −0.831189 | + | 0.280170i | ||||
\(319\) | 1092.57 | + | 1892.38i | 0.191762 | + | 0.332141i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5296.60 | + | 4665.07i | 0.920958 | + | 0.811148i | ||||
\(322\) | 3043.47 | − | 5271.44i | 0.526726 | − | 0.912317i | ||||
\(323\) | −1371.72 | −0.236299 | ||||||||
\(324\) | −2828.40 | − | 2877.19i | −0.484979 | − | 0.493346i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1107.70 | − | 1918.59i | 0.188189 | − | 0.325953i | ||||
\(327\) | 1908.71 | + | 1681.12i | 0.322788 | + | 0.284301i | ||||
\(328\) | 4712.72 | + | 8162.67i | 0.793343 | + | 1.37411i | ||||
\(329\) | −4044.43 | − | 7005.15i | −0.677740 | − | 1.17388i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4684.92 | + | 8114.52i | −0.777965 | + | 1.34747i | 0.155148 | + | 0.987891i | \(0.450415\pi\) |
−0.933113 | + | 0.359583i | \(0.882919\pi\) | |||||||
\(332\) | −2891.42 | −0.477973 | ||||||||
\(333\) | −1397.99 | − | 10981.4i | −0.230058 | − | 1.80714i | ||||
\(334\) | −3183.92 | −0.521605 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −382.597 | + | 1902.18i | −0.0621201 | + | 0.308846i | ||||
\(337\) | 2724.41 | + | 4718.83i | 0.440381 | + | 0.762762i | 0.997718 | − | 0.0675246i | \(-0.0215101\pi\) |
−0.557337 | + | 0.830287i | \(0.688177\pi\) | |||||||
\(338\) | −1426.71 | − | 2471.13i | −0.229593 | − | 0.397667i | ||||
\(339\) | −817.296 | + | 4063.40i | −0.130942 | + | 0.651014i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 291.451 | 0.0462843 | ||||||||
\(342\) | 1841.57 | + | 772.047i | 0.291172 | + | 0.122069i | ||||
\(343\) | −16653.0 | −2.62150 | ||||||||
\(344\) | 3607.47 | − | 6248.31i | 0.565411 | − | 0.979321i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2122.90 | − | 3676.98i | −0.329850 | − | 0.571316i | ||||
\(347\) | −1948.77 | − | 3375.38i | −0.301486 | − | 0.522189i | 0.674987 | − | 0.737830i | \(-0.264149\pi\) |
−0.976473 | + | 0.215641i | \(0.930816\pi\) | |||||||
\(348\) | −1753.30 | − | 1544.25i | −0.270077 | − | 0.237874i | ||||
\(349\) | 3129.53 | − | 5420.51i | 0.480000 | − | 0.831384i | −0.519737 | − | 0.854326i | \(-0.673970\pi\) |
0.999737 | + | 0.0229422i | \(0.00730337\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2727.04 | + | 196.314i | 0.414697 | + | 0.0298532i | ||||
\(352\) | 5033.30 | 0.762147 | ||||||||
\(353\) | 171.433 | − | 296.931i | 0.0258483 | − | 0.0447706i | −0.852812 | − | 0.522218i | \(-0.825105\pi\) |
0.878660 | + | 0.477448i | \(0.158438\pi\) | |||||||
\(354\) | −95.1813 | − | 83.8324i | −0.0142905 | − | 0.0125866i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4433.75 | − | 7679.48i | −0.660080 | − | 1.14329i | ||||
\(357\) | −4910.03 | + | 1655.03i | −0.727917 | + | 0.245360i | ||||
\(358\) | −589.373 | + | 1020.82i | −0.0870093 | + | 0.150705i | ||||
\(359\) | 10448.9 | 1.53613 | 0.768066 | − | 0.640371i | \(-0.221219\pi\) | ||||
0.768066 | + | 0.640371i | \(0.221219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4640.53 | −0.676561 | ||||||||
\(362\) | −890.373 | + | 1542.17i | −0.129273 | + | 0.223908i | ||||
\(363\) | −622.561 | + | 3095.22i | −0.0900164 | + | 0.447540i | ||||
\(364\) | −1846.47 | − | 3198.18i | −0.265883 | − | 0.460523i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −98.2222 | + | 488.337i | −0.0140278 | + | 0.0697426i | ||||
\(367\) | −2586.87 | + | 4480.58i | −0.367938 | + | 0.637288i | −0.989243 | − | 0.146281i | \(-0.953270\pi\) |
0.621305 | + | 0.783569i | \(0.286603\pi\) | |||||||
\(368\) | −1234.70 | −0.174900 | ||||||||
\(369\) | −9531.32 | + | 7249.09i | −1.34466 | + | 1.02269i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10436.9 | + | 18077.2i | −1.46053 | + | 2.52970i | ||||
\(372\) | −295.302 | + | 99.5378i | −0.0411577 | + | 0.0138731i | ||||
\(373\) | 1050.53 | + | 1819.58i | 0.145830 | + | 0.252585i | 0.929682 | − | 0.368362i | \(-0.120081\pi\) |
−0.783852 | + | 0.620947i | \(0.786748\pi\) | |||||||
\(374\) | 614.970 | + | 1065.16i | 0.0850250 | + | 0.147268i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2510.29 | − | 4347.95i | 0.344304 | − | 0.596352i | ||||
\(377\) | 1583.28 | 0.216295 | ||||||||
\(378\) | 7523.36 | + | 541.593i | 1.02370 | + | 0.0736945i | ||||
\(379\) | 11242.6 | 1.52374 | 0.761868 | − | 0.647732i | \(-0.224282\pi\) | ||||
0.761868 | + | 0.647732i | \(0.224282\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6738.92 | − | 5935.41i | −0.906155 | − | 0.798111i | ||||
\(382\) | −420.231 | − | 727.862i | −0.0562851 | − | 0.0974886i | ||||
\(383\) | 3397.44 | + | 5884.53i | 0.453266 | + | 0.785080i | 0.998587 | − | 0.0531478i | \(-0.0169255\pi\) |
−0.545321 | + | 0.838227i | \(0.683592\pi\) | |||||||
\(384\) | −5774.34 | + | 1946.37i | −0.767372 | + | 0.258659i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4119.52 | 0.543207 | ||||||||
\(387\) | 8453.56 | + | 3544.01i | 1.11038 | + | 0.465509i | ||||
\(388\) | 4438.28 | 0.580721 | ||||||||
\(389\) | −3524.70 | + | 6104.96i | −0.459407 | + | 0.795717i | −0.998930 | − | 0.0462544i | \(-0.985272\pi\) |
0.539522 | + | 0.841971i | \(0.318605\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1648.62 | − | 2855.49i | −0.213233 | − | 0.369330i | ||||
\(392\) | −8812.77 | − | 15264.2i | −1.13549 | − | 1.96673i | ||||
\(393\) | 654.832 | − | 3255.67i | 0.0840506 | − | 0.417879i | ||||
\(394\) | −2319.26 | + | 4017.08i | −0.296555 | + | 0.513648i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 507.550 | + | 3986.89i | 0.0644074 | + | 0.505931i | ||||
\(397\) | −3011.36 | −0.380694 | −0.190347 | − | 0.981717i | \(-0.560961\pi\) | ||||
−0.190347 | + | 0.981717i | \(0.560961\pi\) | |||||||
\(398\) | 2072.16 | − | 3589.09i | 0.260975 | − | 0.452022i | ||||
\(399\) | 7940.93 | − | 2676.66i | 0.996350 | − | 0.335841i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2084.07 | + | 3609.72i | 0.259535 | + | 0.449528i | 0.966118 | − | 0.258103i | \(-0.0830973\pi\) |
−0.706582 | + | 0.707631i | \(0.749764\pi\) | |||||||
\(402\) | 1327.97 | + | 1169.63i | 0.164758 | + | 0.145114i | ||||
\(403\) | 105.588 | − | 182.884i | 0.0130514 | − | 0.0226058i | ||||
\(404\) | −3243.91 | −0.399481 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4367.96 | 0.533937 | ||||||||
\(407\) | −5513.71 | + | 9550.03i | −0.671510 | + | 1.16309i | ||||
\(408\) | −2413.39 | − | 2125.63i | −0.292845 | − | 0.257928i | ||||
\(409\) | 6302.68 | + | 10916.6i | 0.761974 | + | 1.31978i | 0.941832 | + | 0.336085i | \(0.109103\pi\) |
−0.179858 | + | 0.983693i | \(0.557564\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13964.1 | + | 4706.88i | −1.67590 | + | 0.564899i | ||||
\(412\) | 2270.99 | − | 3933.47i | 0.271562 | − | 0.470359i | ||||
\(413\) | −532.272 | −0.0634175 | ||||||||
\(414\) | 606.156 | + | 4761.46i | 0.0719588 | + | 0.565249i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1823.49 | − | 3158.37i | 0.214913 | − | 0.372240i | ||||
\(417\) | 179.303 | − | 891.454i | 0.0210564 | − | 0.104687i | ||||
\(418\) | −994.584 | − | 1722.67i | −0.116380 | − | 0.201575i | ||||
\(419\) | 2572.24 | + | 4455.24i | 0.299909 | + | 0.519458i | 0.976115 | − | 0.217255i | \(-0.0697102\pi\) |
−0.676206 | + | 0.736713i | \(0.736377\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1685.03 | − | 2918.56i | 0.195068 | − | 0.337867i | −0.751855 | − | 0.659329i | \(-0.770841\pi\) |
0.946923 | + | 0.321461i | \(0.104174\pi\) | |||||||
\(422\) | 3125.74 | 0.360566 | ||||||||
\(423\) | 5882.49 | + | 2466.13i | 0.676162 | + | 0.283469i | ||||
\(424\) | −12955.9 | −1.48395 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 505.893 | − | 170.522i | 0.0575366 | − | 0.0193939i | ||||
\(427\) | 1045.19 | + | 1810.31i | 0.118454 | + | 0.205169i | ||||
\(428\) | 3758.81 | + | 6510.45i | 0.424507 | + | 0.735267i | ||||
\(429\) | −2043.84 | − | 1800.14i | −0.230017 | − | 0.202592i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14948.3 | 1.67061 | 0.835306 | − | 0.549785i | \(-0.185290\pi\) | ||||
0.835306 | + | 0.549785i | \(0.185290\pi\) | |||||||
\(432\) | −667.893 | − | 1376.54i | −0.0743843 | − | 0.153308i | ||||
\(433\) | 14011.1 | 1.55504 | 0.777520 | − | 0.628858i | \(-0.216477\pi\) | ||||
0.777520 | + | 0.628858i | \(0.216477\pi\) | |||||||
\(434\) | 291.297 | − | 504.542i | 0.0322182 | − | 0.0558036i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1354.54 | + | 2346.13i | 0.148786 | + | 0.257705i | ||||
\(437\) | 2666.29 | + | 4618.14i | 0.291867 | + | 0.505528i | ||||
\(438\) | −5503.46 | + | 1855.06i | −0.600378 | + | 0.202370i | ||||
\(439\) | 2391.10 | − | 4141.50i | 0.259956 | − | 0.450257i | −0.706274 | − | 0.707939i | \(-0.749625\pi\) |
0.966230 | + | 0.257681i | \(0.0829585\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17823.5 | − | 13555.8i | 1.92458 | − | 1.46375i | ||||
\(442\) | 891.178 | 0.0959027 | ||||||||
\(443\) | 2387.01 | − | 4134.42i | 0.256005 | − | 0.443413i | −0.709163 | − | 0.705044i | \(-0.750927\pi\) |
0.965168 | + | 0.261631i | \(0.0842604\pi\) | |||||||
\(444\) | 2324.99 | − | 11559.3i | 0.248511 | − | 1.23554i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 529.867 | + | 917.757i | 0.0562555 | + | 0.0974374i | ||||
\(447\) | 1048.72 | − | 5214.01i | 0.110969 | − | 0.551709i | ||||
\(448\) | 3537.02 | − | 6126.30i | 0.373010 | − | 0.646072i | ||||
\(449\) | −855.812 | −0.0899516 | −0.0449758 | − | 0.998988i | \(-0.514321\pi\) | ||||
−0.0449758 | + | 0.998988i | \(0.514321\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11928.7 | 1.24545 | ||||||||
\(452\) | −2207.31 | + | 3823.18i | −0.229697 | + | 0.397848i | ||||
\(453\) | 4303.51 | − | 1450.59i | 0.446350 | − | 0.150452i | ||||
\(454\) | −1485.30 | − | 2572.62i | −0.153543 | − | 0.265945i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3903.15 | + | 3437.76i | 0.400837 | + | 0.353044i | ||||
\(457\) | −6708.99 | + | 11620.3i | −0.686725 | + | 1.18944i | 0.286166 | + | 0.958180i | \(0.407619\pi\) |
−0.972891 | + | 0.231263i | \(0.925714\pi\) | |||||||
\(458\) | −5352.08 | −0.546040 | ||||||||
\(459\) | 2291.73 | − | 3382.65i | 0.233048 | − | 0.343984i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7942.99 | − | 13757.7i | 0.802477 | − | 1.38993i | −0.115503 | − | 0.993307i | \(-0.536848\pi\) |
0.917981 | − | 0.396625i | \(-0.129819\pi\) | |||||||
\(462\) | −5638.55 | − | 4966.24i | −0.567812 | − | 0.500109i | ||||
\(463\) | 3280.69 | + | 5682.32i | 0.329302 | + | 0.570367i | 0.982373 | − | 0.186929i | \(-0.0598534\pi\) |
−0.653072 | + | 0.757296i | \(0.726520\pi\) | |||||||
\(464\) | −443.007 | − | 767.311i | −0.0443235 | − | 0.0767705i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2231.16 | − | 3864.48i | 0.221795 | − | 0.384160i | ||||
\(467\) | 6792.37 | 0.673048 | 0.336524 | − | 0.941675i | \(-0.390749\pi\) | ||||
0.336524 | + | 0.941675i | \(0.390749\pi\) | |||||||
\(468\) | 2685.64 | + | 1125.91i | 0.265264 | + | 0.111207i | ||||
\(469\) | 7426.25 | 0.731156 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −126.593 | + | 629.392i | −0.0123845 | + | 0.0615730i | ||||
\(472\) | −165.185 | − | 286.109i | −0.0161086 | − | 0.0279009i | ||||
\(473\) | −4565.54 | − | 7907.74i | −0.443813 | − | 0.768707i | ||||
\(474\) | 1540.89 | − | 7660.92i | 0.149315 | − | 0.742358i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5518.79 | −0.531415 | ||||||||
\(477\) | −2078.67 | − | 16328.3i | −0.199530 | − | 1.56734i | ||||
\(478\) | −2543.12 | −0.243346 | ||||||||
\(479\) | −8826.24 | + | 15287.5i | −0.841923 | + | 1.45825i | 0.0463438 | + | 0.998926i | \(0.485243\pi\) |
−0.888267 | + | 0.459328i | \(0.848090\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3995.07 | + | 6919.66i | 0.378710 | + | 0.655945i | ||||
\(482\) | 20.9629 | + | 36.3088i | 0.00198098 | + | 0.00343116i | ||||
\(483\) | 15115.8 | + | 13313.5i | 1.42401 | + | 1.25422i | ||||
\(484\) | −1681.38 | + | 2912.23i | −0.157906 | + | 0.273501i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4980.58 | + | 3251.44i | −0.464863 | + | 0.303474i | ||||
\(487\) | 5318.16 | 0.494844 | 0.247422 | − | 0.968908i | \(-0.420417\pi\) | ||||
0.247422 | + | 0.968908i | \(0.420417\pi\) | |||||||
\(488\) | −648.724 | + | 1123.62i | −0.0601770 | + | 0.104230i | ||||
\(489\) | 5501.54 | + | 4845.57i | 0.508769 | + | 0.448107i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5434.98 | − | 9413.66i | −0.499546 | − | 0.865239i | 0.500454 | − | 0.865763i | \(-0.333167\pi\) |
−1.00000 | 0.000523887i | \(0.999833\pi\) | ||||||||
\(492\) | −12086.3 | + | 4073.93i | −1.10750 | + | 0.373307i | ||||
\(493\) | 1183.04 | − | 2049.09i | 0.108076 | − | 0.187193i | ||||
\(494\) | −1441.29 | −0.131269 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −118.176 | −0.0106981 | ||||||||
\(497\) | 1120.18 | − | 1940.21i | 0.101101 | − | 0.175111i | ||||
\(498\) | −840.531 | + | 4178.92i | −0.0756328 | + | 0.376028i | ||||
\(499\) | −5185.25 | − | 8981.12i | −0.465178 | − | 0.805711i | 0.534032 | − | 0.845464i | \(-0.320676\pi\) |
−0.999210 | + | 0.0397529i | \(0.987343\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2077.61 | − | 10329.4i | 0.185271 | − | 0.921123i | ||||
\(502\) | −335.517 | + | 581.133i | −0.0298304 | + | 0.0516678i | ||||
\(503\) | 12396.4 | 1.09886 | 0.549432 | − | 0.835538i | \(-0.314844\pi\) | ||||
0.549432 | + | 0.835538i | \(0.314844\pi\) | |||||||
\(504\) | 18119.0 | + | 7596.07i | 1.60136 | + | 0.671341i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2390.70 | − | 4140.82i | 0.210039 | − | 0.363798i | ||||
\(507\) | 8947.89 | − | 3016.08i | 0.783806 | − | 0.264199i | ||||
\(508\) | −4782.37 | − | 8283.30i | −0.417684 | − | 0.723449i | ||||
\(509\) | −2780.52 | − | 4816.00i | −0.242130 | − | 0.419382i | 0.719190 | − | 0.694813i | \(-0.244513\pi\) |
−0.961321 | + | 0.275431i | \(0.911180\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12186.1 | + | 21107.0i | −1.05496 | + | 1.82724i | ||||
\(512\) | −3894.99 | −0.336203 | ||||||||
\(513\) | −3706.39 | + | 5470.72i | −0.318989 | + | 0.470834i | ||||
\(514\) | 6032.03 | 0.517629 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7326.55 | + | 6452.98i | 0.625065 | + | 0.550536i | ||||
\(517\) | −3176.97 | − | 5502.68i | −0.270258 | − | 0.468100i | ||||
\(518\) | 11021.6 | + | 19090.0i | 0.934868 | + | 1.61924i | ||||
\(519\) | 13314.2 | − | 4487.85i | 1.12607 | − | 0.379566i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2613.39 | −0.219760 | −0.109880 | − | 0.993945i | \(-0.535047\pi\) | ||||
−0.109880 | + | 0.993945i | \(0.535047\pi\) | |||||||
\(522\) | −2741.56 | + | 2085.11i | −0.229875 | + | 0.174833i | ||||
\(523\) | 2927.73 | 0.244781 | 0.122391 | − | 0.992482i | \(-0.460944\pi\) | ||||
0.122391 | + | 0.992482i | \(0.460944\pi\) | |||||||
\(524\) | 1768.53 | − | 3063.19i | 0.147440 | − | 0.255374i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 627.199 | + | 1086.34i | 0.0519908 | + | 0.0900508i | ||||
\(527\) | −157.793 | − | 273.305i | −0.0130428 | − | 0.0225908i | ||||
\(528\) | −300.537 | + | 1494.20i | −0.0247712 | + | 0.123156i | ||||
\(529\) | −325.506 | + | 563.793i | −0.0267532 | + | 0.0463379i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 334.081 | − | 254.087i | 0.0273030 | − | 0.0207654i | ||||
\(532\) | 8925.48 | 0.727384 | ||||||||
\(533\) | 4321.57 | − | 7485.18i | 0.351197 | − | 0.608291i | ||||
\(534\) | −12387.9 | + | 4175.62i | −1.00389 | + | 0.338383i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2304.66 | + | 3991.78i | 0.185720 | + | 0.321677i | ||||
\(537\) | −2927.21 | − | 2578.19i | −0.235230 | − | 0.207183i | ||||
\(538\) | 6229.35 | − | 10789.5i | 0.499194 | − | 0.864629i | ||||
\(539\) | −22306.5 | −1.78258 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4023.02 | −0.319710 | −0.159855 | − | 0.987140i | \(-0.551103\pi\) | ||||
−0.159855 | + | 0.987140i | \(0.551103\pi\) | |||||||
\(542\) | −1812.88 | + | 3140.00i | −0.143671 | + | 0.248846i | ||||
\(543\) | −4422.17 | − | 3894.90i | −0.349491 | − | 0.307820i | ||||
\(544\) | −2725.05 | − | 4719.92i | −0.214771 | − | 0.371994i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5159.06 | + | 1738.97i | −0.404372 | + | 0.136302i | ||||
\(547\) | 1652.77 | − | 2862.68i | 0.129191 | − | 0.223765i | −0.794172 | − | 0.607692i | \(-0.792095\pi\) |
0.923363 | + | 0.383927i | \(0.125429\pi\) | |||||||
\(548\) | −15695.4 | −1.22349 | ||||||||
\(549\) | −1520.19 | − | 637.312i | −0.118179 | − | 0.0495443i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1913.32 | + | 3313.96i | −0.147931 | + | 0.256224i | ||||
\(552\) | −2465.29 | + | 12256.8i | −0.190090 | + | 0.945082i | ||||
\(553\) | −16396.6 | − | 28399.8i | −1.26086 | − | 2.18387i | ||||
\(554\) | −597.702 | − | 1035.25i | −0.0458374 | − | 0.0793927i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 484.253 | − | 838.752i | 0.0369369 | − | 0.0639766i | ||||
\(557\) | −6472.87 | −0.492396 | −0.246198 | − | 0.969220i | \(-0.579181\pi\) | ||||
−0.246198 | + | 0.969220i | \(0.579181\pi\) | |||||||
\(558\) | 58.0166 | + | 455.731i | 0.00440150 | + | 0.0345746i | ||||
\(559\) | −6616.10 | −0.500593 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3856.92 | + | 1300.06i | −0.290266 | + | 0.0978404i | ||||
\(562\) | −1010.65 | − | 1750.49i | −0.0758569 | − | 0.131388i | ||||
\(563\) | −10277.6 | − | 17801.4i | −0.769362 | − | 1.33257i | −0.937909 | − | 0.346881i | \(-0.887241\pi\) |
0.168547 | − | 0.985694i | \(-0.446093\pi\) | |||||||
\(564\) | 5098.25 | + | 4490.37i | 0.380629 | + | 0.335246i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4281.18 | −0.317936 | ||||||||
\(567\) | −6666.29 | + | 24054.2i | −0.493753 | + | 1.78162i | ||||
\(568\) | 1390.54 | 0.102722 | ||||||||
\(569\) | −635.311 | + | 1100.39i | −0.0468078 | + | 0.0810735i | −0.888480 | − | 0.458915i | \(-0.848238\pi\) |
0.841672 | + | 0.539989i | \(0.181571\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8376.66 | + | 14508.8i | 0.613927 | + | 1.06335i | 0.990572 | + | 0.136995i | \(0.0437444\pi\) |
−0.376645 | + | 0.926358i | \(0.622922\pi\) | |||||||
\(572\) | −1450.44 | − | 2512.23i | −0.106024 | − | 0.183639i | ||||
\(573\) | 2635.57 | − | 888.376i | 0.192151 | − | 0.0647686i | ||||
\(574\) | 11922.4 | − | 20650.1i | 0.866951 | − | 1.50160i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 704.455 | + | 5533.62i | 0.0509588 | + | 0.400291i | ||||
\(577\) | 7800.01 | 0.562770 | 0.281385 | − | 0.959595i | \(-0.409206\pi\) | ||||
0.281385 | + | 0.959595i | \(0.409206\pi\) | |||||||
\(578\) | −3191.32 | + | 5527.53i | −0.229657 | + | 0.397777i | ||||
\(579\) | −2688.12 | + | 13364.7i | −0.192944 | + | 0.959271i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8944.12 | + | 15491.7i | 0.638665 | + | 1.10620i | ||||
\(582\) | 1290.20 | − | 6414.58i | 0.0918912 | − | 0.456861i | ||||
\(583\) | −8198.35 | + | 14200.0i | −0.582403 | + | 1.00875i | ||||
\(584\) | −15127.3 | −1.07187 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −151.327 | −0.0106677 | ||||||||
\(587\) | −1184.62 | + | 2051.83i | −0.0832958 | + | 0.144273i | −0.904664 | − | 0.426126i | \(-0.859878\pi\) |
0.821368 | + | 0.570399i | \(0.193211\pi\) | |||||||
\(588\) | 22601.2 | − | 7618.24i | 1.58514 | − | 0.534304i | ||||
\(589\) | 255.196 | + | 442.013i | 0.0178526 | + | 0.0309216i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11519.0 | − | 10145.5i | −0.801737 | − | 0.706143i | ||||
\(592\) | 2235.66 | − | 3872.28i | 0.155212 | − | 0.268834i | ||||
\(593\) | −11974.3 | −0.829218 | −0.414609 | − | 0.910000i | \(-0.636082\pi\) | ||||
−0.414609 | + | 0.910000i | \(0.636082\pi\) | |||||||
\(594\) | 5909.74 | + | 425.431i | 0.408215 | + | 0.0293866i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2832.34 | − | 4905.76i | 0.194660 | − | 0.337160i | ||||
\(597\) | 10291.7 | + | 9064.59i | 0.705547 | + | 0.621422i | ||||
\(598\) | −1732.23 | − | 3000.31i | −0.118455 | − | 0.205170i | ||||
\(599\) | −11099.7 | − | 19225.3i | −0.757134 | − | 1.31139i | −0.944307 | − | 0.329067i | \(-0.893266\pi\) |
0.187173 | − | 0.982327i | \(-0.440068\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5749.47 | − | 9958.38i | 0.390226 | − | 0.675891i | −0.602253 | − | 0.798305i | \(-0.705730\pi\) |
0.992479 | + | 0.122414i | \(0.0390635\pi\) | |||||||
\(602\) | −18252.5 | −1.23574 | ||||||||
\(603\) | −4661.09 | + | 3545.02i | −0.314783 | + | 0.239410i | ||||
\(604\) | 4837.08 | 0.325858 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −943.000 | + | 4688.37i | −0.0632125 | + | 0.314277i | ||||
\(607\) | −7636.51 | − | 13226.8i | −0.510636 | − | 0.884448i | −0.999924 | − | 0.0123257i | \(-0.996077\pi\) |
0.489288 | − | 0.872122i | \(-0.337257\pi\) | |||||||
\(608\) | 4407.19 | + | 7633.47i | 0.293972 | + | 0.509175i | ||||
\(609\) | −2850.24 | + | 14170.7i | −0.189651 | + | 0.942900i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4603.88 | −0.304833 | ||||||||
\(612\) | 3463.87 | − | 2634.47i | 0.228789 | − | 0.174007i | ||||
\(613\) | 16440.8 | 1.08326 | 0.541630 | − | 0.840617i | \(-0.317808\pi\) | ||||
0.541630 | + | 0.840617i | \(0.317808\pi\) | |||||||
\(614\) | −4128.09 | + | 7150.07i | −0.271329 | + | 0.469956i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9785.58 | − | 16949.1i | −0.640052 | − | 1.10860i | ||||
\(617\) | 4679.57 | + | 8105.25i | 0.305336 | + | 0.528857i | 0.977336 | − | 0.211694i | \(-0.0678979\pi\) |
−0.672000 | + | 0.740551i | \(0.734565\pi\) | |||||||
\(618\) | −5024.81 | − | 4425.68i | −0.327067 | − | 0.288070i | ||||
\(619\) | 12742.3 | − | 22070.3i | 0.827392 | − | 1.43308i | −0.0726861 | − | 0.997355i | \(-0.523157\pi\) |
0.900078 | − | 0.435729i | \(-0.143510\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15842.9 | − | 1140.50i | −1.02376 | − | 0.0736982i | ||||
\(622\) | 8214.25 | 0.529520 | ||||||||
\(623\) | −27430.2 | + | 47510.4i | −1.76399 | + | 3.05532i | ||||
\(624\) | 828.723 | + | 729.911i | 0.0531658 | + | 0.0468266i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3134.65 | + | 5429.38i | 0.200137 | + | 0.346648i | ||||
\(627\) | 6237.75 | − | 2102.57i | 0.397307 | − | 0.133921i | ||||
\(628\) | −341.897 | + | 592.183i | −0.0217248 | + | 0.0376285i | ||||
\(629\) | 11940.6 | 0.756919 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21733.8 | −1.37117 | −0.685585 | − | 0.727993i | \(-0.740454\pi\) | ||||
−0.685585 | + | 0.727993i | \(0.740454\pi\) | |||||||
\(632\) | 10177.0 | − | 17627.1i | 0.640539 | − | 1.10945i | ||||
\(633\) | −2039.65 | + | 10140.6i | −0.128071 | + | 0.636737i | ||||
\(634\) | 3716.35 | + | 6436.91i | 0.232800 | + | 0.403222i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3457.03 | − | 17187.5i | 0.215535 | − | 1.07159i | ||||
\(637\) | −8081.32 | + | 13997.3i | −0.502659 | + | 0.870631i | ||||
\(638\) | 3431.12 | 0.212914 | ||||||||
\(639\) | 223.102 | + | 1752.51i | 0.0138119 | + | 0.108495i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10162.4 | − | 17601.8i | 0.626195 | − | 1.08460i | −0.362113 | − | 0.932134i | \(-0.617945\pi\) |
0.988308 | − | 0.152468i | \(-0.0487220\pi\) | |||||||
\(642\) | 10502.1 | − | 3539.97i | 0.645617 | − | 0.217619i | ||||
\(643\) | 3363.72 | + | 5826.13i | 0.206302 | + | 0.357325i | 0.950547 | − | 0.310581i | \(-0.100524\pi\) |
−0.744245 | + | 0.667907i | \(0.767190\pi\) | |||||||
\(644\) | 10727.2 | + | 18580.0i | 0.656382 | + | 1.13689i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1076.94 | + | 1865.32i | −0.0655910 | + | 0.113607i | ||||
\(647\) | −6724.69 | −0.408616 | −0.204308 | − | 0.978907i | \(-0.565494\pi\) | ||||
−0.204308 | + | 0.978907i | \(0.565494\pi\) | |||||||
\(648\) | −14998.5 | + | 3881.66i | −0.909253 | + | 0.235318i | ||||
\(649\) | −418.110 | −0.0252885 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1446.77 | + | 1274.27i | 0.0871021 | + | 0.0767166i | ||||
\(652\) | 3904.25 | + | 6762.35i | 0.234512 | + | 0.406187i | ||||
\(653\) | −15398.2 | − | 26670.4i | −0.922782 | − | 1.59831i | −0.795089 | − | 0.606492i | \(-0.792576\pi\) |
−0.127693 | − | 0.991814i | \(-0.540757\pi\) | |||||||
\(654\) | 3784.60 | − | 1275.68i | 0.226283 | − | 0.0762737i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4836.75 | −0.287871 | ||||||||
\(657\) | −2427.07 | − | 19065.0i | −0.144123 | − | 1.13211i | ||||
\(658\) | −12701.2 | −0.752498 | ||||||||
\(659\) | −8267.16 | + | 14319.1i | −0.488684 | + | 0.846426i | −0.999915 | − | 0.0130174i | \(-0.995856\pi\) |
0.511231 | + | 0.859443i | \(0.329190\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −968.527 | − | 1677.54i | −0.0569914 | − | 0.0987121i | 0.836122 | − | 0.548543i | \(-0.184817\pi\) |
−0.893114 | + | 0.449831i | \(0.851484\pi\) | |||||||
\(662\) | 7356.30 | + | 12741.5i | 0.431889 | + | 0.748054i | ||||
\(663\) | −581.523 | + | 2891.19i | −0.0340641 | + | 0.169358i | ||||
\(664\) | −5551.42 | + | 9615.35i | −0.324453 | + | 0.561970i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16030.6 | − | 6720.53i | −0.932691 | − | 0.391014i | ||||
\(667\) | −9198.16 | −0.533964 | ||||||||
\(668\) | 5611.10 | − | 9718.72i | 0.325000 | − | 0.562917i | ||||
\(669\) | −3323.18 | + | 1120.15i | −0.192050 | + | 0.0647346i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 821.013 | + | 1422.04i | 0.0472352 | + | 0.0818138i | ||||
\(672\) | 24985.5 | + | 22006.3i | 1.43428 | + | 1.26326i | ||||
\(673\) | −230.294 | + | 398.881i | −0.0131905 | + | 0.0228465i | −0.872545 | − | 0.488533i | \(-0.837532\pi\) |
0.859355 | + | 0.511380i | \(0.170865\pi\) | |||||||
\(674\) | 8555.80 | 0.488957 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10057.3 | 0.572217 | ||||||||
\(677\) | 14529.8 | − | 25166.4i | 0.824854 | − | 1.42869i | −0.0771775 | − | 0.997017i | \(-0.524591\pi\) |
0.902031 | − | 0.431671i | \(-0.142076\pi\) | |||||||
\(678\) | 4883.92 | + | 4301.59i | 0.276646 | + | 0.243660i | ||||
\(679\) | −13729.1 | − | 23779.5i | −0.775956 | − | 1.34400i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9315.39 | − | 3139.95i | 0.524180 | − | 0.176686i | ||||
\(682\) | 228.820 | − | 396.327i | 0.0128474 | − | 0.0222524i | ||||
\(683\) | −14366.9 | −0.804881 | −0.402440 | − | 0.915446i | \(-0.631838\pi\) | ||||
−0.402440 | + | 0.915446i | \(0.631838\pi\) | |||||||
\(684\) | −5602.08 | + | 4260.69i | −0.313159 | + | 0.238175i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13074.3 | + | 22645.4i | −0.727667 | + | 1.26036i | ||||
\(687\) | 3492.41 | − | 17363.4i | 0.193950 | − | 0.964273i | ||||
\(688\) | 1851.21 | + | 3206.38i | 0.102582 | + | 0.177678i | ||||
\(689\) | 5940.28 | + | 10288.9i | 0.328457 | + | 0.568904i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6353.97 | − | 11005.4i | 0.349807 | − | 0.605883i | −0.636408 | − | 0.771352i | \(-0.719581\pi\) |
0.986215 | + | 0.165469i | \(0.0529139\pi\) | |||||||
\(692\) | 14965.0 | 0.822087 | ||||||||
\(693\) | 19791.0 | − | 15052.1i | 1.08485 | − | 0.825085i | ||||
\(694\) | −6119.97 | −0.334742 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8501.63 | + | 2865.66i | −0.463008 | + | 0.156067i | ||||
\(697\) | −6458.22 | − | 11186.0i | −0.350965 | − | 0.607889i | ||||
\(698\) | −4914.02 | − | 8511.33i | −0.266473 | − | 0.461545i | ||||
\(699\) | 11081.4 | + | 9760.11i | 0.599623 | + | 0.528128i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5959.06 | 0.321071 | 0.160535 | − | 0.987030i | \(-0.448678\pi\) | ||||
0.160535 | + | 0.987030i | \(0.448678\pi\) | |||||||
\(702\) | 2407.97 | − | 3554.21i | 0.129463 | − | 0.191090i | ||||
\(703\) | −19311.4 | −1.03605 | ||||||||
\(704\) | 2778.40 | − | 4812.32i | 0.148743 | − | 0.257630i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −269.186 | − | 466.243i | −0.0143498 | − | 0.0248545i | ||||
\(707\) | 10034.5 | + | 17380.2i | 0.533785 | + | 0.924542i | ||||
\(708\) | 423.634 | − | 142.795i | 0.0224875 | − | 0.00757989i | ||||
\(709\) | −225.912 | + | 391.292i | −0.0119666 | + | 0.0207268i | −0.871947 | − | 0.489601i | \(-0.837143\pi\) |
0.859980 | + | 0.510328i | \(0.170476\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23848.4 | + | 9998.00i | 1.25792 | + | 0.527362i | ||||
\(712\) | −34050.6 | −1.79228 | ||||||||
\(713\) | −613.421 | + | 1062.48i | −0.0322199 | + | 0.0558065i | ||||
\(714\) | −1604.31 | + | 7976.23i | −0.0840892 | + | 0.418071i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2077.34 | − | 3598.05i | −0.108427 | − | 0.187801i | ||||
\(717\) | 1659.47 | − | 8250.48i | 0.0864352 | − | 0.429735i | ||||
\(718\) | 8203.47 | − | 14208.8i | 0.426394 | − | 0.738536i | ||||
\(719\) | −13488.4 | −0.699627 | −0.349814 | − | 0.936819i | \(-0.613755\pi\) | ||||
−0.349814 | + | 0.936819i | \(0.613755\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28099.7 | −1.45144 | ||||||||
\(722\) | −3643.30 | + | 6310.39i | −0.187797 | + | 0.325275i | ||||
\(723\) | −131.473 | + | 44.3159i | −0.00676285 | + | 0.00227957i | ||||
\(724\) | −3138.26 | − | 5435.62i | −0.161094 | − | 0.279024i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3720.23 | + | 3276.66i | 0.190180 | + | 0.167504i | ||||
\(727\) | 14591.6 | − | 25273.3i | 0.744389 | − | 1.28932i | −0.206090 | − | 0.978533i | \(-0.566074\pi\) |
0.950480 | − | 0.310787i | \(-0.100593\pi\) | |||||||
\(728\) | −14180.7 | −0.721938 | ||||||||
\(729\) | −7298.46 | − | 18279.9i | −0.370800 | − | 0.928713i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4943.60 | + | 8562.57i | −0.250131 | + | 0.433239i | ||||
\(732\) | −1317.52 | − | 1160.43i | −0.0665259 | − | 0.0585938i | ||||
\(733\) | 6256.24 | + | 10836.1i | 0.315252 | + | 0.546032i | 0.979491 | − | 0.201488i | \(-0.0645777\pi\) |
−0.664239 | + | 0.747520i | \(0.731244\pi\) | |||||||
\(734\) | 4061.92 | + | 7035.45i | 0.204262 | + | 0.353792i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10593.6 | + | 18348.7i | −0.530553 | + | 0.918945i | ||||
\(737\) | 5833.46 | 0.291558 | ||||||||
\(738\) | 2374.53 | + | 18652.4i | 0.118439 | + | 0.930357i | ||||
\(739\) | −32248.2 | −1.60524 | −0.802619 | − | 0.596492i | \(-0.796561\pi\) | ||||
−0.802619 | + | 0.596492i | \(0.796561\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 940.490 | − | 4675.89i | 0.0466259 | − | 0.231813i | ||||
\(742\) | 16388.1 | + | 28384.9i | 0.810815 | + | 1.40437i | ||||
\(743\) | 9244.50 | + | 16011.9i | 0.456457 | + | 0.790607i | 0.998771 | − | 0.0495691i | \(-0.0157848\pi\) |
−0.542313 | + | 0.840176i | \(0.682451\pi\) | |||||||
\(744\) | −235.959 | + | 1173.13i | −0.0116272 | + | 0.0578078i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3299.12 | 0.161916 | ||||||||
\(747\) | −13008.9 | − | 5453.77i | −0.637178 | − | 0.267126i | ||||
\(748\) | −4335.12 | −0.211908 | ||||||||
\(749\) | 23254.5 | − | 40278.0i | 1.13445 | − | 1.96492i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1026.10 | + | 1777.26i | 0.0498575 | + | 0.0863558i | 0.889877 | − | 0.456200i | \(-0.150790\pi\) |
−0.840020 | + | 0.542556i | \(0.817457\pi\) | |||||||
\(752\) | 1288.18 | + | 2231.19i | 0.0624668 | + | 0.108196i | ||||
\(753\) | −1666.40 | − | 1467.71i | −0.0806466 | − | 0.0710308i | ||||
\(754\) | 1243.04 | − | 2153.01i | 0.0600384 | − | 0.103990i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −14911.8 | + | 22010.1i | −0.717377 | + | 1.05886i | ||||
\(757\) | −10118.9 | −0.485834 | −0.242917 | − | 0.970047i | \(-0.578104\pi\) | ||||
−0.242917 | + | 0.970047i | \(0.578104\pi\) | |||||||
\(758\) | 8826.65 | − | 15288.2i | 0.422953 | − | 0.732576i | ||||
\(759\) | 11873.8 | + | 10458.0i | 0.567841 | + | 0.500135i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13652.0 | − | 23646.0i | −0.650309 | − | 1.12637i | −0.983048 | − | 0.183349i | \(-0.941306\pi\) |
0.332739 | − | 0.943019i | \(-0.392027\pi\) | |||||||
\(762\) | −13362.0 | + | 4503.94i | −0.635240 | + | 0.214121i | ||||
\(763\) | 8380.10 | − | 14514.8i | 0.397615 | − | 0.688689i | ||||
\(764\) | 2962.34 | 0.140280 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10669.4 | 0.503264 | ||||||||
\(767\) | −151.475 | + | 262.362i | −0.00713096 | + | 0.0123512i | ||||
\(768\) | −3580.22 | + | 17800.0i | −0.168216 | + | 0.836330i | ||||
\(769\) | 11236.9 | + | 19462.9i | 0.526935 | + | 0.912679i | 0.999507 | + | 0.0313867i | \(0.00999234\pi\) |
−0.472572 | + | 0.881292i | \(0.656674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3936.10 | + | 19569.3i | −0.183859 | + | 0.914102i | ||||
\(772\) | −7259.94 | + | 12574.6i | −0.338460 | + | 0.586230i | ||||
\(773\) | 35405.6 | 1.64741 | 0.823707 | − | 0.567015i | \(-0.191902\pi\) | ||||
0.823707 | + | 0.567015i | \(0.191902\pi\) | |||||||
\(774\) | 11456.2 | − | 8713.08i | 0.532022 | − | 0.404632i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8521.35 | − | 14759.4i | 0.394200 | − | 0.682774i | ||||
\(777\) | −69124.4 | + | 23299.9i | −3.19154 | + | 1.07578i | ||||
\(778\) | 5534.52 | + | 9586.07i | 0.255041 | + | 0.441744i | ||||
\(779\) | 10444.8 | + | 18090.9i | 0.480390 | + | 0.832060i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 879.923 | − | 1524.07i | 0.0403151 | − | 0.0698278i | ||||
\(782\) | −5177.34 | −0.236754 | ||||||||
\(783\) | −4975.62 | − | 10254.9i | −0.227093 | − | 0.468044i | ||||
\(784\) | 9044.71 | 0.412022 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3913.08 | − | 3446.50i | −0.177576 | − | 0.156403i | ||||
\(787\) | −6090.02 | − | 10548.2i | −0.275840 | − | 0.477769i | 0.694507 | − | 0.719486i | \(-0.255623\pi\) |
−0.970347 | + | 0.241718i | \(0.922289\pi\) | |||||||
\(788\) | −8174.59 | − | 14158.8i | −0.369553 | − | 0.640085i | ||||
\(789\) | −3933.62 | + | 1325.91i | −0.177491 | + | 0.0598272i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27311.8 | 1.22768 | ||||||||
\(792\) | 14232.8 | + | 5966.86i | 0.638562 | + | 0.267706i | ||||
\(793\) | 1189.76 | 0.0532783 | ||||||||
\(794\) | −2364.23 | + | 4094.97i | −0.105672 | + | 0.183029i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7303.65 | + | 12650.3i | 0.325215 | + | 0.563289i | ||||
\(797\) | 1146.54 | + | 1985.86i | 0.0509567 | + | 0.0882596i | 0.890379 | − | 0.455221i | \(-0.150440\pi\) |
−0.839422 | + | 0.543480i | \(0.817106\pi\) | |||||||
\(798\) | 2594.63 | − | 12899.9i | 0.115099 | − | 0.572243i | ||||
\(799\) | −3440.05 | + | 5958.35i | −0.152316 | + | 0.263819i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5463.16 | − | 42914.1i | −0.240988 | − | 1.89300i | ||||
\(802\) | 6544.86 | 0.288164 | ||||||||
\(803\) | −9572.43 | + | 16579.9i | −0.420677 | + | 0.728634i | ||||
\(804\) | −5910.53 | + | 1992.27i | −0.259264 | + | 0.0873905i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −165.796 | − | 287.167i | −0.00724554 | − | 0.0125496i | ||||
\(807\) | 30939.0 | + | 27250.0i | 1.34957 | + | 1.18866i | ||||
\(808\) | −6228.19 | + | 10787.5i | −0.271172 | + | 0.469684i | ||||
\(809\) | −25264.0 | −1.09794 | −0.548972 | − | 0.835841i | \(-0.684981\pi\) | ||||
−0.548972 | + | 0.835841i | \(0.684981\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18781.2 | 0.813190 | 0.406595 | − | 0.913608i | \(-0.366716\pi\) | ||||
0.406595 | + | 0.913608i | \(0.366716\pi\) | |||||||
\(812\) | −7697.78 | + | 13333.0i | −0.332684 | + | 0.576225i | ||||
\(813\) | −9003.94 | − | 7930.37i | −0.388416 | − | 0.342103i | ||||
\(814\) | 8657.68 | + | 14995.5i | 0.372790 | + | 0.645692i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1563.88 | − | 527.139i | 0.0670916 | − | 0.0226147i | ||||
\(817\) | 7995.23 | − | 13848.1i | 0.342372 | − | 0.593005i | ||||
\(818\) | 19793.0 | 0.846023 | ||||||||
\(819\) | −2275.18 | − | 17871.9i | −0.0970711 | − | 0.762510i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15787.4 | + | 27344.6i | −0.671114 | + | 1.16240i | 0.306474 | + | 0.951879i | \(0.400851\pi\) |
−0.977588 | + | 0.210525i | \(0.932483\pi\) | |||||||
\(822\) | −4562.63 | + | 22684.3i | −0.193601 | + | 0.962537i | ||||
\(823\) | −473.129 | − | 819.484i | −0.0200392 | − | 0.0347089i | 0.855832 | − | 0.517254i | \(-0.173046\pi\) |
−0.875871 | + | 0.482545i | \(0.839712\pi\) | |||||||
\(824\) | −8720.45 | − | 15104.3i | −0.368679 | − | 0.638570i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −417.889 | + | 723.806i | −0.0176032 | + | 0.0304896i | ||||
\(827\) | −35044.7 | −1.47355 | −0.736774 | − | 0.676139i | \(-0.763652\pi\) | ||||
−0.736774 | + | 0.676139i | \(0.763652\pi\) | |||||||
\(828\) | −15602.3 | − | 6541.00i | −0.654853 | − | 0.274536i | ||||
\(829\) | 31029.2 | 1.29999 | 0.649993 | − | 0.759940i | \(-0.274772\pi\) | ||||
0.649993 | + | 0.759940i | \(0.274772\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3748.62 | − | 1263.55i | 0.156484 | − | 0.0527463i | ||||
\(832\) | −2013.14 | − | 3486.86i | −0.0838860 | − | 0.145295i | ||||
\(833\) | 12076.8 | + | 20917.7i | 0.502327 | + | 0.870055i | ||||
\(834\) | −1071.46 | − | 943.708i | −0.0444865 | − | 0.0391822i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7011.13 | 0.290054 | ||||||||
\(837\) | −1516.36 | − | 109.160i | −0.0626200 | − | 0.00450790i | ||||
\(838\) | 8077.90 | 0.332991 | ||||||||
\(839\) | 10599.9 | − | 18359.6i | 0.436175 | − | 0.755477i | −0.561216 | − | 0.827669i | \(-0.689666\pi\) |
0.997391 | + | 0.0721924i | \(0.0229996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8894.22 | + | 15405.2i | 0.364681 | + | 0.631647i | ||||
\(842\) | −2645.86 | − | 4582.76i | −0.108292 | − | 0.187568i | ||||
\(843\) | 6338.49 | − | 2136.52i | 0.258967 | − | 0.0872904i | ||||
\(844\) | −5508.58 | + | 9541.14i | −0.224660 | + | 0.389123i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7971.91 | − | 6063.08i | 0.323972 | − | 0.246398i | ||||
\(847\) | 20804.3 | 0.843971 | ||||||||
\(848\) | 3324.22 | − | 5757.71i | 0.134616 | − | 0.233161i | ||||
\(849\) | 2793.61 | − | 13889.2i | 0.112929 | − | 0.561455i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23209.5 | − | 40200.1i | −0.934915 | − | 1.61932i | ||||
\(852\) | −371.040 | + | 1844.72i | −0.0149197 | + | 0.0741774i | ||||
\(853\) | 5489.93 | − | 9508.84i | 0.220365 | − | 0.381684i | −0.734554 | − | 0.678551i | \(-0.762608\pi\) |
0.954919 | + | 0.296867i | \(0.0959417\pi\) | |||||||
\(854\) | 3282.32 | 0.131521 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 28867.2 | 1.15264 | ||||||||
\(857\) | 22407.2 | − | 38810.4i | 0.893133 | − | 1.54695i | 0.0570348 | − | 0.998372i | \(-0.481835\pi\) |
0.836098 | − | 0.548580i | \(-0.184831\pi\) | |||||||
\(858\) | −4052.54 | + | 1365.99i | −0.161249 | + | 0.0543523i | ||||
\(859\) | −18693.1 | − | 32377.4i | −0.742492 | − | 1.28603i | −0.951358 | − | 0.308089i | \(-0.900311\pi\) |
0.208866 | − | 0.977944i | \(-0.433023\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 59214.2 | + | 52153.9i | 2.34380 | + | 2.06434i | ||||
\(862\) | 11736.0 | − | 20327.3i | 0.463722 | − | 0.803191i | ||||
\(863\) | 30536.3 | 1.20448 | 0.602241 | − | 0.798314i | \(-0.294275\pi\) | ||||
0.602241 | + | 0.798314i | \(0.294275\pi\) | |||||||
\(864\) | −26187.2 | − | 1885.16i | −1.03114 | − | 0.0742299i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11000.2 | − | 19052.9i | 0.431643 | − | 0.747627i | ||||
\(867\) | −15850.2 | − | 13960.3i | −0.620877 | − | 0.546848i | ||||
\(868\) | 1026.72 | + | 1778.34i | 0.0401489 | + | 0.0695399i | ||||
\(869\) | −12879.8 | − | 22308.6i | −0.502784 | − | 0.870847i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2113.37 | − | 3660.47i | 0.0822146 | − | 0.142400i | ||||
\(872\) | 10402.7 | 0.403991 | ||||||||
\(873\) | 19968.5 | + | 8371.45i | 0.774149 | + | 0.324548i | ||||
\(874\) | 8373.25 | 0.324061 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4036.44 | − | 20068.2i | 0.155683 | − | 0.774021i | ||||
\(877\) | 17163.7 | + | 29728.4i | 0.660864 | + | 1.14465i | 0.980389 | + | 0.197072i | \(0.0631434\pi\) |
−0.319525 | + | 0.947578i | \(0.603523\pi\) | |||||||
\(878\) | −3754.52 | − | 6503.02i | −0.144315 | − | 0.249962i | ||||
\(879\) | 98.7460 | − | 490.941i | 0.00378910 | − | 0.0188385i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18009.6 | −0.688718 | −0.344359 | − | 0.938838i | \(-0.611904\pi\) | ||||
−0.344359 | + | 0.938838i | \(0.611904\pi\) | |||||||
\(882\) | −4440.37 | − | 34879.9i | −0.169518 | − | 1.33159i | ||||
\(883\) | 29074.4 | 1.10808 | 0.554039 | − | 0.832491i | \(-0.313086\pi\) | ||||
0.554039 | + | 0.832491i | \(0.313086\pi\) | |||||||
\(884\) | −1570.55 | + | 2720.27i | −0.0597548 | + | 0.103498i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3748.10 | − | 6491.90i | −0.142122 | − | 0.246162i | ||||
\(887\) | −16451.3 | − | 28494.5i | −0.622752 | − | 1.07864i | −0.988971 | − | 0.148109i | \(-0.952681\pi\) |
0.366220 | − | 0.930528i | \(-0.380652\pi\) | |||||||
\(888\) | −33976.2 | − | 29925.1i | −1.28397 | − | 1.13088i | ||||
\(889\) | −29586.9 | + | 51246.1i | −1.11621 | + | 1.93334i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5236.50 | + | 18895.0i | −0.196890 | + | 0.710444i | ||||
\(892\) | −3735.20 | −0.140206 | ||||||||
\(893\) | 5563.56 | − | 9636.36i | 0.208485 | − | 0.361107i | ||||
\(894\) | −6266.86 | − | 5519.64i | −0.234446 | − | 0.206493i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 20076.6 | + | 34773.7i | 0.748562 | + | 1.29655i | ||||
\(897\) | 10864.1 | − | 3661.96i | 0.404393 | − | 0.136309i | ||||
\(898\) | −671.902 | + | 1163.77i | −0.0249684 | + | 0.0432466i | ||||
\(899\) | −880.377 | −0.0326610 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17754.5 | 0.656479 | ||||||||
\(902\) | 9365.24 | − | 16221.1i | 0.345708 | − | 0.598783i | ||||
\(903\) | 11910.4 | − | 59215.5i | 0.438928 | − | 2.18225i | ||||
\(904\) | 8475.93 | + | 14680.7i | 0.311842 | + | 0.540127i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1406.13 | − | 6990.96i | 0.0515625 | − | 0.256357i | ||||
\(907\) | −407.908 | + | 706.517i | −0.0149331 | + | 0.0258649i | −0.873395 | − | 0.487012i | \(-0.838087\pi\) |
0.858462 | + | 0.512877i | \(0.171420\pi\) | |||||||
\(908\) | 10470.4 | 0.382677 | ||||||||
\(909\) | −14594.8 | − | 6118.63i | −0.532542 | − | 0.223259i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7921.41 | + | 13720.3i | −0.288088 | + | 0.498983i | −0.973353 | − | 0.229311i | \(-0.926353\pi\) |
0.685265 | + | 0.728293i | \(0.259686\pi\) | |||||||
\(912\) | −2529.24 | + | 852.536i | −0.0918329 | + | 0.0309543i | ||||
\(913\) | 7025.77 | + | 12169.0i | 0.254676 | + | 0.441112i | ||||
\(914\) | 10534.5 | + | 18246.3i | 0.381237 | + | 0.660322i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9432.11 | − | 16336.9i | 0.340225 | − | 0.589286i | ||||
\(917\) | −21882.7 | −0.788037 | ||||||||
\(918\) | −2800.61 | − | 5772.12i | −0.100691 | − | 0.207526i | ||||
\(919\) | 23848.4 | 0.856025 | 0.428013 | − | 0.903773i | \(-0.359214\pi\) | ||||
0.428013 | + | 0.903773i | \(0.359214\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20502.8 | − | 18058.2i | −0.733540 | − | 0.646077i | ||||
\(922\) | −12472.2 | − | 21602.4i | −0.445498 | − | 0.771624i | ||||
\(923\) | −637.566 | − | 1104.30i | −0.0227364 | − | 0.0393807i | ||||
\(924\) | 25096.1 | − | 8459.19i | 0.893508 | − | 0.301176i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 10302.7 | 0.365625 | ||||||||
\(927\) | 17636.8 | − | 13413.8i | 0.624886 | − | 0.475260i | ||||
\(928\) | −15203.9 | −0.537816 | ||||||||
\(929\) | 19796.0 | − | 34287.7i | 0.699123 | − | 1.21092i | −0.269647 | − | 0.962959i | \(-0.586907\pi\) |
0.968771 | − | 0.247958i | \(-0.0797595\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19531.7 | − | 33830.0i | −0.687569 | − | 1.19090i | ||||
\(932\) | 7864.07 | + | 13621.0i | 0.276391 | + | 0.478723i | ||||
\(933\) | −5360.07 | + | 26649.0i | −0.188082 | + | 0.935100i | ||||
\(934\) | 5332.72 | − | 9236.54i | 0.186822 | − | 0.323585i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8900.51 | − | 6769.33i | 0.310814 | − | 0.236391i | ||||
\(937\) | −10255.0 | −0.357540 | −0.178770 | − | 0.983891i | \(-0.557212\pi\) | ||||
−0.178770 | + | 0.983891i | \(0.557212\pi\) | |||||||
\(938\) | 5830.38 | − | 10098.5i | 0.202952 | − | 0.351523i | ||||
\(939\) | −19659.7 | + | 6626.71i | −0.683247 | + | 0.230303i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11947.2 | + | 20693.1i | 0.413886 | + | 0.716871i | 0.995311 | − | 0.0967289i | \(-0.0308380\pi\) |
−0.581425 | + | 0.813600i | \(0.697505\pi\) | |||||||
\(942\) | 756.484 | + | 666.286i | 0.0261652 | + | 0.0230454i | ||||
\(943\) | −25106.4 | + | 43485.5i | −0.866995 | + | 1.50168i | ||||
\(944\) | 169.533 | 0.00584514 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14337.7 | −0.492768 | ||||||||
\(947\) | −18128.6 | + | 31399.7i | −0.622072 | + | 1.07746i | 0.367028 | + | 0.930210i | \(0.380375\pi\) |
−0.989099 | + | 0.147250i | \(0.952958\pi\) | |||||||
\(948\) | 20668.9 | + | 18204.5i | 0.708118 | + | 0.623686i | ||||
\(949\) | 6935.89 | + | 12013.3i | 0.237248 | + | 0.410926i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23307.9 | + | 7856.43i | −0.794754 | + | 0.267889i | ||||
\(952\) | −10595.9 | + | 18352.6i | −0.360730 | + | 0.624803i | ||||
\(953\) | 46736.7 | 1.58861 | 0.794307 | − | 0.607516i | \(-0.207834\pi\) | ||||
0.794307 | + | 0.607516i | \(0.207834\pi\) | |||||||
\(954\) | −23835.9 | − | 9992.78i | −0.808927 | − | 0.339128i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4481.81 | − | 7762.72i | 0.151623 | − | 0.262620i | ||||
\(957\) | −2238.92 | + | 11131.4i | −0.0756259 | + | 0.375994i | ||||
\(958\) | 13859.0 | + | 24004.6i | 0.467396 | + | 0.809553i | ||||
\(959\) | 48551.0 | + | 84092.9i | 1.63482 | + | 2.83160i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14836.8 | − | 25698.1i | 0.498029 | − | 0.862612i | ||||
\(962\) | 12546.2 | 0.420484 | ||||||||
\(963\) | 4631.51 | + | 36381.4i | 0.154983 | + | 1.21742i | ||||
\(964\) | −147.774 | −0.00493721 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 29971.8 | − | 10102.6i | 0.998268 | − | 0.336488i | ||||
\(967\) | 22178.5 | + | 38414.3i | 0.737552 | + | 1.27748i | 0.953595 | + | 0.301094i | \(0.0973516\pi\) |
−0.216043 | + | 0.976384i | \(0.569315\pi\) | |||||||
\(968\) | 6456.39 | + | 11182.8i | 0.214376 | + | 0.371310i | ||||
\(969\) | −5348.80 | − | 4711.04i | −0.177325 | − | 0.156182i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −650.540 | −0.0215003 | −0.0107502 | − | 0.999942i | \(-0.503422\pi\) | ||||
−0.0107502 | + | 0.999942i | \(0.503422\pi\) | |||||||
\(972\) | −1147.42 | − | 20933.0i | −0.0378639 | − | 0.690769i | ||||
\(973\) | −5991.83 | −0.197420 | ||||||||
\(974\) | 4175.31 | − | 7231.85i | 0.137357 | − | 0.237909i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −332.899 | − | 576.598i | −0.0109179 | − | 0.0189103i | ||||
\(977\) | 25837.5 | + | 44751.9i | 0.846075 | + | 1.46544i | 0.884684 | + | 0.466190i | \(0.154374\pi\) |
−0.0386096 | + | 0.999254i | \(0.512293\pi\) | |||||||
\(978\) | 10908.5 | − | 3676.94i | 0.356662 | − | 0.120220i | ||||
\(979\) | −21546.9 | + | 37320.3i | −0.703414 | + | 1.21835i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1669.03 | + | 13110.5i | 0.0543202 | + | 0.426695i | ||||
\(982\) | −17068.1 | −0.554649 | ||||||||
\(983\) | 11759.5 | − | 20368.0i | 0.381556 | − | 0.660874i | −0.609729 | − | 0.792610i | \(-0.708722\pi\) |
0.991285 | + | 0.131736i | \(0.0420551\pi\) | |||||||
\(984\) | −9657.43 | + | 48014.4i | −0.312874 | + | 1.55553i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1857.62 | − | 3217.49i | −0.0599987 | − | 0.103921i | ||||
\(987\) | 8287.95 | − | 41205.7i | 0.267283 | − | 1.32887i | ||||
\(988\) | 2540.03 | − | 4399.46i | 0.0817905 | − | 0.141665i | ||||
\(989\) | 38436.6 | 1.23581 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27732.9 | −0.888966 | −0.444483 | − | 0.895787i | \(-0.646613\pi\) | ||||
−0.444483 | + | 0.895787i | \(0.646613\pi\) | |||||||
\(992\) | −1013.94 | + | 1756.20i | −0.0324523 | + | 0.0562090i | ||||
\(993\) | −46136.6 | + | 15551.3i | −1.47442 | + | 0.496986i | ||||
\(994\) | −1758.92 | − | 3046.53i | −0.0561262 | − | 0.0972135i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −11274.6 | − | 9930.30i | −0.358685 | − | 0.315917i | ||||
\(997\) | −17163.9 | + | 29728.7i | −0.545221 | + | 0.944351i | 0.453372 | + | 0.891322i | \(0.350221\pi\) |
−0.998593 | + | 0.0530293i | \(0.983112\pi\) | |||||||
\(998\) | −16283.9 | −0.516489 | ||||||||
\(999\) | 32263.5 | − | 47621.6i | 1.02179 | − | 1.50819i |
(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 | 225.4.e.d.151.5 | 14 | ||
5.2 | odd | 4 | 225.4.k.d.124.9 | 28 | |||
5.3 | odd | 4 | 225.4.k.d.124.6 | 28 | |||
5.4 | even | 2 | 45.4.e.c.16.3 | ✓ | 14 | ||
9.2 | odd | 6 | 2025.4.a.ba.1.5 | 7 | |||
9.4 | even | 3 | inner | 225.4.e.d.76.5 | 14 | ||
9.7 | even | 3 | 2025.4.a.bb.1.3 | 7 | |||
15.14 | odd | 2 | 135.4.e.c.46.5 | 14 | |||
45.4 | even | 6 | 45.4.e.c.31.3 | yes | 14 | ||
45.13 | odd | 12 | 225.4.k.d.49.9 | 28 | |||
45.14 | odd | 6 | 135.4.e.c.91.5 | 14 | |||
45.22 | odd | 12 | 225.4.k.d.49.6 | 28 | |||
45.29 | odd | 6 | 405.4.a.n.1.3 | 7 | |||
45.34 | even | 6 | 405.4.a.m.1.5 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.c.16.3 | ✓ | 14 | 5.4 | even | 2 | ||
45.4.e.c.31.3 | yes | 14 | 45.4 | even | 6 | ||
135.4.e.c.46.5 | 14 | 15.14 | odd | 2 | |||
135.4.e.c.91.5 | 14 | 45.14 | odd | 6 | |||
225.4.e.d.76.5 | 14 | 9.4 | even | 3 | inner | ||
225.4.e.d.151.5 | 14 | 1.1 | even | 1 | trivial | ||
225.4.k.d.49.6 | 28 | 45.22 | odd | 12 | |||
225.4.k.d.49.9 | 28 | 45.13 | odd | 12 | |||
225.4.k.d.124.6 | 28 | 5.3 | odd | 4 | |||
225.4.k.d.124.9 | 28 | 5.2 | odd | 4 | |||
405.4.a.m.1.5 | 7 | 45.34 | even | 6 | |||
405.4.a.n.1.3 | 7 | 45.29 | odd | 6 | |||
2025.4.a.ba.1.5 | 7 | 9.2 | odd | 6 | |||
2025.4.a.bb.1.3 | 7 | 9.7 | even | 3 |