Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(49,225)]
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, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 23x^{10} + 198x^{8} - 719x^{6} + 886x^{4} + 585x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(-1.98116 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.49 |
Dual form | 225.4.k.c.124.4 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.151541 | − | 0.0874923i | 0.0535779 | − | 0.0309332i | −0.472972 | − | 0.881078i | \(-0.656819\pi\) |
0.526550 | + | 0.850144i | \(0.323485\pi\) | |||||||
\(3\) | 0.151541 | + | 5.19394i | 0.0291641 | + | 0.999575i | ||||
\(4\) | −3.98469 | + | 6.90169i | −0.498086 | + | 0.862711i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.477395 | + | 0.773837i | 0.0324826 | + | 0.0526529i | ||||
\(7\) | −7.32979 | + | 4.23186i | −0.395772 | + | 0.228499i | −0.684658 | − | 0.728865i | \(-0.740048\pi\) |
0.288886 | + | 0.957363i | \(0.406715\pi\) | |||||||
\(8\) | 2.79440i | 0.123496i | ||||||||
\(9\) | −26.9541 | + | 1.57419i | −0.998299 | + | 0.0583034i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.7541 | + | 27.2870i | 0.431823 | + | 0.747939i | 0.997030 | − | 0.0770098i | \(-0.0245373\pi\) |
−0.565208 | + | 0.824949i | \(0.691204\pi\) | |||||||
\(12\) | −36.4508 | − | 19.6504i | −0.876870 | − | 0.472714i | ||||
\(13\) | −23.2697 | − | 13.4348i | −0.496451 | − | 0.286626i | 0.230796 | − | 0.973002i | \(-0.425867\pi\) |
−0.727247 | + | 0.686376i | \(0.759200\pi\) | |||||||
\(14\) | −0.740510 | + | 1.28260i | −0.0141364 | + | 0.0244850i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −31.6330 | − | 54.7900i | −0.494266 | − | 0.856094i | ||||
\(17\) | 44.3307i | 0.632457i | 0.948683 | + | 0.316229i | \(0.102417\pi\) | ||||
−0.948683 | + | 0.316229i | \(0.897583\pi\) | |||||||
\(18\) | −3.94692 | + | 2.59683i | −0.0516832 | + | 0.0340044i | ||||
\(19\) | 90.2082 | 1.08922 | 0.544610 | − | 0.838689i | \(-0.316678\pi\) | ||||
0.544610 | + | 0.838689i | \(0.316678\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −23.0908 | − | 37.4292i | −0.239944 | − | 0.388939i | ||||
\(22\) | 4.77480 | + | 2.75673i | 0.0462723 | + | 0.0267153i | ||||
\(23\) | −168.232 | − | 97.1287i | −1.52516 | − | 0.880553i | −0.999555 | − | 0.0298265i | \(-0.990505\pi\) |
−0.525608 | − | 0.850727i | \(-0.676162\pi\) | |||||||
\(24\) | −14.5139 | + | 0.423466i | −0.123443 | + | 0.00360165i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.70176 | −0.0354650 | ||||||||
\(27\) | −12.2609 | − | 139.759i | −0.0873931 | − | 0.996174i | ||||
\(28\) | − | 67.4506i | − | 0.455248i | ||||||
\(29\) | 1.87186 | + | 3.24215i | 0.0119860 | + | 0.0207604i | 0.871956 | − | 0.489584i | \(-0.162851\pi\) |
−0.859970 | + | 0.510344i | \(0.829518\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 125.832 | − | 217.947i | 0.729035 | − | 1.26273i | −0.228257 | − | 0.973601i | \(-0.573303\pi\) |
0.957292 | − | 0.289124i | \(-0.0933641\pi\) | |||||||
\(32\) | −28.9476 | − | 16.7129i | −0.159914 | − | 0.0923265i | ||||
\(33\) | −139.339 | + | 85.9611i | −0.735027 | + | 0.453452i | ||||
\(34\) | 3.87859 | + | 6.71792i | 0.0195639 | + | 0.0338857i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 96.5390 | − | 192.301i | 0.446940 | − | 0.890283i | ||||
\(37\) | 62.2293i | 0.276498i | 0.990397 | + | 0.138249i | \(0.0441475\pi\) | ||||
−0.990397 | + | 0.138249i | \(0.955853\pi\) | |||||||
\(38\) | 13.6703 | − | 7.89252i | 0.0583581 | − | 0.0336931i | ||||
\(39\) | 66.2532 | − | 122.898i | 0.272026 | − | 0.504599i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 102.173 | − | 176.969i | 0.389188 | − | 0.674094i | −0.603152 | − | 0.797626i | \(-0.706089\pi\) |
0.992341 | + | 0.123532i | \(0.0394223\pi\) | |||||||
\(42\) | −6.77397 | − | 3.65180i | −0.0248868 | − | 0.0134163i | ||||
\(43\) | −456.968 | + | 263.831i | −1.62063 | + | 0.935669i | −0.633874 | + | 0.773436i | \(0.718536\pi\) |
−0.986752 | + | 0.162233i | \(0.948130\pi\) | |||||||
\(44\) | −251.101 | −0.860340 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −33.9920 | −0.108953 | ||||||||
\(47\) | −134.864 | + | 77.8637i | −0.418551 | + | 0.241651i | −0.694457 | − | 0.719534i | \(-0.744355\pi\) |
0.275906 | + | 0.961185i | \(0.411022\pi\) | |||||||
\(48\) | 279.782 | − | 172.603i | 0.841315 | − | 0.519023i | ||||
\(49\) | −135.683 | + | 235.009i | −0.395577 | + | 0.685159i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −230.251 | + | 6.71792i | −0.632188 | + | 0.0184450i | ||||
\(52\) | 185.445 | − | 107.067i | 0.494551 | − | 0.285529i | ||||
\(53\) | − | 141.694i | − | 0.367230i | −0.982998 | − | 0.183615i | \(-0.941220\pi\) | ||
0.982998 | − | 0.183615i | \(-0.0587800\pi\) | |||||||
\(54\) | −14.0859 | − | 20.1065i | −0.0354972 | − | 0.0506695i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −11.8255 | − | 20.4823i | −0.0282187 | − | 0.0488762i | ||||
\(57\) | 13.6703 | + | 468.536i | 0.0317661 | + | 1.08876i | ||||
\(58\) | 0.567326 | + | 0.327546i | 0.00128437 | + | 0.000741533i | ||||
\(59\) | −246.923 | + | 427.683i | −0.544857 | + | 0.943721i | 0.453758 | + | 0.891125i | \(0.350083\pi\) |
−0.998616 | + | 0.0525961i | \(0.983250\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 379.742 | + | 657.732i | 0.797065 | + | 1.38056i | 0.921520 | + | 0.388331i | \(0.126948\pi\) |
−0.124455 | + | 0.992225i | \(0.539718\pi\) | |||||||
\(62\) | − | 44.0373i | − | 0.0902055i | ||||||
\(63\) | 190.906 | − | 125.604i | 0.381776 | − | 0.251185i | ||||
\(64\) | 500.280 | 0.977108 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −13.5947 | + | 25.2178i | −0.0253545 | + | 0.0470317i | ||||
\(67\) | −470.763 | − | 271.795i | −0.858401 | − | 0.495598i | 0.00507574 | − | 0.999987i | \(-0.498384\pi\) |
−0.863476 | + | 0.504389i | \(0.831718\pi\) | |||||||
\(68\) | −305.956 | − | 176.644i | −0.545627 | − | 0.315018i | ||||
\(69\) | 478.987 | − | 888.505i | 0.835699 | − | 1.55019i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −928.207 | −1.55152 | −0.775760 | − | 0.631028i | \(-0.782633\pi\) | ||||
−0.775760 | + | 0.631028i | \(0.782633\pi\) | |||||||
\(72\) | −4.39891 | − | 75.3203i | −0.00720024 | − | 0.123286i | ||||
\(73\) | 608.739i | 0.975993i | 0.872845 | + | 0.487997i | \(0.162272\pi\) | ||||
−0.872845 | + | 0.487997i | \(0.837728\pi\) | |||||||
\(74\) | 5.44459 | + | 9.43030i | 0.00855298 | + | 0.0148142i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −359.452 | + | 622.589i | −0.542526 | + | 0.939682i | ||||
\(77\) | −230.949 | − | 133.338i | −0.341806 | − | 0.197342i | ||||
\(78\) | −0.712510 | − | 24.4207i | −0.00103431 | − | 0.0354500i | ||||
\(79\) | 307.420 | + | 532.467i | 0.437816 | + | 0.758319i | 0.997521 | − | 0.0703726i | \(-0.0224188\pi\) |
−0.559705 | + | 0.828692i | \(0.689085\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 724.044 | − | 84.8617i | 0.993201 | − | 0.116408i | ||||
\(82\) | − | 35.7573i | − | 0.0481553i | ||||||
\(83\) | 931.246 | − | 537.655i | 1.23154 | − | 0.711028i | 0.264186 | − | 0.964472i | \(-0.414897\pi\) |
0.967350 | + | 0.253444i | \(0.0815634\pi\) | |||||||
\(84\) | 350.334 | − | 10.2215i | 0.455055 | − | 0.0132769i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −46.1663 | + | 79.9623i | −0.0578865 | + | 0.100262i | ||||
\(87\) | −16.5559 | + | 10.2136i | −0.0204020 | + | 0.0125864i | ||||
\(88\) | −76.2506 | + | 44.0233i | −0.0923675 | + | 0.0533284i | ||||
\(89\) | −1505.15 | −1.79265 | −0.896324 | − | 0.443400i | \(-0.853772\pi\) | ||||
−0.896324 | + | 0.443400i | \(0.853772\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 227.416 | 0.261975 | ||||||||
\(92\) | 1340.70 | − | 774.055i | 1.51933 | − | 0.877183i | ||||
\(93\) | 1151.07 | + | 620.536i | 1.28345 | + | 0.691898i | ||||
\(94\) | −13.6249 | + | 23.5991i | −0.0149501 | + | 0.0258943i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 82.4190 | − | 152.885i | 0.0876234 | − | 0.162539i | ||||
\(97\) | 288.160 | − | 166.369i | 0.301631 | − | 0.174147i | −0.341544 | − | 0.939866i | \(-0.610950\pi\) |
0.643175 | + | 0.765719i | \(0.277617\pi\) | |||||||
\(98\) | 47.4848i | 0.0489458i | ||||||||
\(99\) | −467.593 | − | 710.695i | −0.474695 | − | 0.721490i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 247.493 | + | 428.670i | 0.243826 | + | 0.422319i | 0.961801 | − | 0.273750i | \(-0.0882640\pi\) |
−0.717975 | + | 0.696069i | \(0.754931\pi\) | |||||||
\(102\) | −34.3047 | + | 21.1632i | −0.0333007 | + | 0.0205438i | ||||
\(103\) | 545.622 | + | 315.015i | 0.521959 | + | 0.301353i | 0.737736 | − | 0.675090i | \(-0.235895\pi\) |
−0.215777 | + | 0.976443i | \(0.569228\pi\) | |||||||
\(104\) | 37.5421 | − | 65.0248i | 0.0353972 | − | 0.0613097i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.3971 | − | 21.4725i | −0.0113596 | − | 0.0196754i | ||||
\(107\) | 1561.00i | 1.41035i | 0.709034 | + | 0.705175i | \(0.249131\pi\) | ||||
−0.709034 | + | 0.705175i | \(0.750869\pi\) | |||||||
\(108\) | 1013.43 | + | 472.277i | 0.902939 | + | 0.420786i | ||||
\(109\) | 936.140 | 0.822623 | 0.411311 | − | 0.911495i | \(-0.365071\pi\) | ||||
0.411311 | + | 0.911495i | \(0.365071\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −323.215 | + | 9.43030i | −0.276381 | + | 0.00806382i | ||||
\(112\) | 463.727 | + | 267.733i | 0.391233 | + | 0.225878i | ||||
\(113\) | −1173.45 | − | 677.490i | −0.976890 | − | 0.564008i | −0.0755602 | − | 0.997141i | \(-0.524075\pi\) |
−0.901330 | + | 0.433134i | \(0.857408\pi\) | |||||||
\(114\) | 43.0649 | + | 69.8065i | 0.0353807 | + | 0.0573506i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −29.8351 | −0.0238803 | ||||||||
\(117\) | 648.363 | + | 325.491i | 0.512318 | + | 0.257194i | ||||
\(118\) | 86.4153i | 0.0674167i | ||||||||
\(119\) | −187.601 | − | 324.935i | −0.144516 | − | 0.250309i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 169.115 | − | 292.915i | 0.127058 | − | 0.220071i | ||||
\(122\) | 115.093 | + | 66.4490i | 0.0854101 | + | 0.0493115i | ||||
\(123\) | 934.648 | + | 503.862i | 0.685157 | + | 0.369363i | ||||
\(124\) | 1002.80 | + | 1736.90i | 0.726244 | + | 1.25789i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 17.9407 | − | 35.7370i | 0.0126848 | − | 0.0252675i | ||||
\(127\) | 1182.37i | 0.826126i | 0.910702 | + | 0.413063i | \(0.135541\pi\) | ||||
−0.910702 | + | 0.413063i | \(0.864459\pi\) | |||||||
\(128\) | 307.393 | − | 177.474i | 0.212266 | − | 0.122552i | ||||
\(129\) | −1439.57 | − | 2333.48i | −0.982535 | − | 1.59265i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1126.87 | + | 1951.80i | −0.751569 | + | 1.30176i | 0.195494 | + | 0.980705i | \(0.437369\pi\) |
−0.947062 | + | 0.321050i | \(0.895964\pi\) | |||||||
\(132\) | −38.0522 | − | 1304.21i | −0.0250910 | − | 0.859974i | ||||
\(133\) | −661.207 | + | 381.748i | −0.431082 | + | 0.248885i | ||||
\(134\) | −95.1199 | −0.0613217 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −123.877 | −0.0781059 | ||||||||
\(137\) | −410.246 | + | 236.856i | −0.255837 | + | 0.147708i | −0.622434 | − | 0.782672i | \(-0.713856\pi\) |
0.366597 | + | 0.930380i | \(0.380523\pi\) | |||||||
\(138\) | −5.15119 | − | 176.553i | −0.00317753 | − | 0.108907i | ||||
\(139\) | −68.5193 | + | 118.679i | −0.0418110 | + | 0.0724188i | −0.886174 | − | 0.463353i | \(-0.846646\pi\) |
0.844363 | + | 0.535772i | \(0.179979\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −424.857 | − | 688.675i | −0.253755 | − | 0.411326i | ||||
\(142\) | −140.662 | + | 81.2110i | −0.0831272 | + | 0.0479935i | ||||
\(143\) | − | 846.613i | − | 0.495086i | ||||||
\(144\) | 938.889 | + | 1427.02i | 0.543339 | + | 0.825820i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 53.2600 | + | 92.2490i | 0.0301906 | + | 0.0522917i | ||||
\(147\) | −1241.19 | − | 669.115i | −0.696404 | − | 0.375426i | ||||
\(148\) | −429.487 | − | 247.965i | −0.238538 | − | 0.137720i | ||||
\(149\) | −71.5553 | + | 123.937i | −0.0393426 | + | 0.0681433i | −0.885026 | − | 0.465541i | \(-0.845860\pi\) |
0.845684 | + | 0.533685i | \(0.179193\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −108.421 | − | 187.790i | −0.0584314 | − | 0.101206i | 0.835330 | − | 0.549749i | \(-0.185277\pi\) |
−0.893761 | + | 0.448543i | \(0.851943\pi\) | |||||||
\(152\) | 252.077i | 0.134514i | ||||||||
\(153\) | −69.7850 | − | 1194.89i | −0.0368744 | − | 0.631381i | ||||
\(154\) | −46.6644 | −0.0244177 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 584.202 | + | 946.967i | 0.299831 | + | 0.486013i | ||||
\(157\) | 1167.78 | + | 674.215i | 0.593622 | + | 0.342728i | 0.766528 | − | 0.642211i | \(-0.221983\pi\) |
−0.172906 | + | 0.984938i | \(0.555316\pi\) | |||||||
\(158\) | 93.1736 | + | 53.7938i | 0.0469145 | + | 0.0270861i | ||||
\(159\) | 735.951 | − | 21.4725i | 0.367074 | − | 0.0107099i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1644.14 | 0.804822 | ||||||||
\(162\) | 102.298 | − | 76.2083i | 0.0496127 | − | 0.0369598i | ||||
\(163\) | 1039.85i | 0.499676i | 0.968288 | + | 0.249838i | \(0.0803774\pi\) | ||||
−0.968288 | + | 0.249838i | \(0.919623\pi\) | |||||||
\(164\) | 814.254 | + | 1410.33i | 0.387699 | + | 0.671514i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 94.0813 | − | 162.954i | 0.0439887 | − | 0.0761907i | ||||
\(167\) | −2881.31 | − | 1663.52i | −1.33510 | − | 0.770822i | −0.349026 | − | 0.937113i | \(-0.613487\pi\) |
−0.986077 | + | 0.166291i | \(0.946821\pi\) | |||||||
\(168\) | 104.592 | − | 64.5248i | 0.0480324 | − | 0.0296321i | ||||
\(169\) | −737.513 | − | 1277.41i | −0.335691 | − | 0.581434i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2431.48 | + | 142.005i | −1.08737 | + | 0.0635052i | ||||
\(172\) | − | 4205.13i | − | 1.86418i | ||||||
\(173\) | −1034.25 | + | 597.127i | −0.454525 | + | 0.262420i | −0.709740 | − | 0.704464i | \(-0.751187\pi\) |
0.255214 | + | 0.966885i | \(0.417854\pi\) | |||||||
\(174\) | −1.61528 | + | 2.99630i | −0.000703760 | + | 0.00130545i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 996.702 | − | 1726.34i | 0.426871 | − | 0.739362i | ||||
\(177\) | −2258.78 | − | 1217.69i | −0.959210 | − | 0.517103i | ||||
\(178\) | −228.092 | + | 131.689i | −0.0960463 | + | 0.0554523i | ||||
\(179\) | −2323.70 | −0.970288 | −0.485144 | − | 0.874434i | \(-0.661233\pi\) | ||||
−0.485144 | + | 0.874434i | \(0.661233\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2527.12 | 1.03779 | 0.518893 | − | 0.854839i | \(-0.326344\pi\) | ||||
0.518893 | + | 0.854839i | \(0.326344\pi\) | |||||||
\(182\) | 34.4629 | − | 19.8972i | 0.0140361 | − | 0.00810372i | ||||
\(183\) | −3358.68 | + | 2072.03i | −1.35672 | + | 0.836988i | ||||
\(184\) | 271.416 | − | 470.106i | 0.108745 | − | 0.188352i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 228.727 | − | 6.67346i | 0.0901671 | − | 0.00263076i | ||||
\(187\) | −1209.65 | + | 698.391i | −0.473039 | + | 0.273109i | ||||
\(188\) | − | 1241.05i | − | 0.481452i | ||||||
\(189\) | 681.311 | + | 972.520i | 0.262212 | + | 0.374288i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1194.43 | − | 2068.82i | −0.452493 | − | 0.783741i | 0.546047 | − | 0.837754i | \(-0.316132\pi\) |
−0.998540 | + | 0.0540134i | \(0.982799\pi\) | |||||||
\(192\) | 75.8129 | + | 2598.42i | 0.0284965 | + | 0.976693i | ||||
\(193\) | −3072.64 | − | 1773.99i | −1.14597 | − | 0.661629i | −0.198072 | − | 0.980188i | \(-0.563468\pi\) |
−0.947903 | + | 0.318559i | \(0.896801\pi\) | |||||||
\(194\) | 29.1120 | − | 50.4235i | 0.0107738 | − | 0.0186608i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1081.31 | − | 1872.88i | −0.394063 | − | 0.682536i | ||||
\(197\) | 1239.26i | 0.448192i | 0.974567 | + | 0.224096i | \(0.0719430\pi\) | ||||
−0.974567 | + | 0.224096i | \(0.928057\pi\) | |||||||
\(198\) | −133.040 | − | 66.7887i | −0.0477512 | − | 0.0239720i | ||||
\(199\) | −516.657 | −0.184044 | −0.0920222 | − | 0.995757i | \(-0.529333\pi\) | ||||
−0.0920222 | + | 0.995757i | \(0.529333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1340.35 | − | 2486.30i | 0.470353 | − | 0.872489i | ||||
\(202\) | 75.0107 | + | 43.3074i | 0.0261274 | + | 0.0150847i | ||||
\(203\) | −27.4406 | − | 15.8429i | −0.00948746 | − | 0.00547759i | ||||
\(204\) | 871.114 | − | 1615.89i | 0.298971 | − | 0.554583i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 110.246 | 0.0372873 | ||||||||
\(207\) | 4687.43 | + | 2353.18i | 1.57391 | + | 0.790133i | ||||
\(208\) | 1699.93i | 0.566678i | ||||||||
\(209\) | 1421.15 | + | 2461.51i | 0.470350 | + | 0.814670i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.92159 | − | 15.4527i | 0.00291084 | − | 0.00504173i | −0.864566 | − | 0.502519i | \(-0.832407\pi\) |
0.867477 | + | 0.497477i | \(0.165740\pi\) | |||||||
\(212\) | 977.928 | + | 564.607i | 0.316813 | + | 0.182912i | ||||
\(213\) | −140.662 | − | 4821.05i | −0.0452487 | − | 1.55086i | ||||
\(214\) | 136.575 | + | 236.555i | 0.0436266 | + | 0.0755635i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 390.543 | − | 34.2618i | 0.123024 | − | 0.0107927i | ||||
\(217\) | 2130.01i | 0.666334i | ||||||||
\(218\) | 141.864 | − | 81.9050i | 0.0440744 | − | 0.0254464i | ||||
\(219\) | −3161.76 | + | 92.2490i | −0.975578 | + | 0.0284640i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 595.573 | − | 1031.56i | 0.181279 | − | 0.313984i | ||||
\(222\) | −48.1554 | + | 29.7079i | −0.0145584 | + | 0.00898138i | ||||
\(223\) | 856.978 | − | 494.777i | 0.257343 | − | 0.148577i | −0.365779 | − | 0.930702i | \(-0.619197\pi\) |
0.623122 | + | 0.782125i | \(0.285864\pi\) | |||||||
\(224\) | 282.906 | 0.0843860 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −237.101 | −0.0697863 | ||||||||
\(227\) | 2967.98 | − | 1713.57i | 0.867806 | − | 0.501028i | 0.00118754 | − | 0.999999i | \(-0.499622\pi\) |
0.866619 | + | 0.498971i | \(0.166289\pi\) | |||||||
\(228\) | −3288.16 | − | 1772.62i | −0.955104 | − | 0.514890i | ||||
\(229\) | 549.805 | − | 952.290i | 0.158656 | − | 0.274800i | −0.775728 | − | 0.631067i | \(-0.782617\pi\) |
0.934384 | + | 0.356267i | \(0.115951\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 657.554 | − | 1219.74i | 0.187290 | − | 0.347416i | ||||
\(232\) | −9.05985 | + | 5.23071i | −0.00256383 | + | 0.00148023i | ||||
\(233\) | 4459.91i | 1.25399i | 0.779025 | + | 0.626993i | \(0.215715\pi\) | ||||
−0.779025 | + | 0.626993i | \(0.784285\pi\) | |||||||
\(234\) | 126.732 | − | 7.40147i | 0.0354047 | − | 0.00206773i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1967.82 | − | 3408.37i | −0.542772 | − | 0.940109i | ||||
\(237\) | −2719.02 | + | 1677.41i | −0.745228 | + | 0.459745i | ||||
\(238\) | −56.8586 | − | 32.8273i | −0.0154857 | − | 0.00894067i | ||||
\(239\) | 3272.23 | − | 5667.66i | 0.885618 | − | 1.53394i | 0.0406148 | − | 0.999175i | \(-0.487068\pi\) |
0.845003 | − | 0.534761i | \(-0.179598\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 105.162 | + | 182.147i | 0.0281083 | + | 0.0486851i | 0.879737 | − | 0.475460i | \(-0.157718\pi\) |
−0.851629 | + | 0.524145i | \(0.824385\pi\) | |||||||
\(242\) | − | 59.1849i | − | 0.0157213i | ||||||
\(243\) | 550.489 | + | 3747.78i | 0.145325 | + | 0.989384i | ||||
\(244\) | −6052.61 | −1.58803 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 185.722 | − | 5.41871i | 0.0481349 | − | 0.00140441i | ||||
\(247\) | −2099.12 | − | 1211.93i | −0.540744 | − | 0.312199i | ||||
\(248\) | 609.031 | + | 351.624i | 0.155942 | + | 0.0900329i | ||||
\(249\) | 2933.67 | + | 4755.36i | 0.746642 | + | 1.21028i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 816.143 | 0.205237 | 0.102618 | − | 0.994721i | \(-0.467278\pi\) | ||||
0.102618 | + | 0.994721i | \(0.467278\pi\) | |||||||
\(252\) | 106.180 | + | 1818.07i | 0.0265425 | + | 0.454474i | ||||
\(253\) | − | 6120.71i | − | 1.52097i | ||||||
\(254\) | 103.448 | + | 179.177i | 0.0255547 | + | 0.0442621i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1970.06 | + | 3412.25i | −0.480972 | + | 0.833069i | ||||
\(257\) | −3613.36 | − | 2086.17i | −0.877023 | − | 0.506350i | −0.00734758 | − | 0.999973i | \(-0.502339\pi\) |
−0.869676 | + | 0.493623i | \(0.835672\pi\) | |||||||
\(258\) | −422.316 | − | 227.667i | −0.101908 | − | 0.0549378i | ||||
\(259\) | −263.346 | − | 456.128i | −0.0631795 | − | 0.109430i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −55.5579 | − | 84.4425i | −0.0131760 | − | 0.0200263i | ||||
\(262\) | 394.371i | 0.0929937i | ||||||||
\(263\) | −2439.64 | + | 1408.52i | −0.571994 | + | 0.330241i | −0.757945 | − | 0.652318i | \(-0.773797\pi\) |
0.185951 | + | 0.982559i | \(0.440463\pi\) | |||||||
\(264\) | −240.209 | − | 389.370i | −0.0559995 | − | 0.0907729i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −66.8001 | + | 115.701i | −0.0153976 | + | 0.0266695i | ||||
\(267\) | −228.092 | − | 7817.66i | −0.0522810 | − | 1.79189i | ||||
\(268\) | 3751.69 | − | 2166.04i | 0.855115 | − | 0.493701i | ||||
\(269\) | 102.610 | 0.0232573 | 0.0116287 | − | 0.999932i | \(-0.496298\pi\) | ||||
0.0116287 | + | 0.999932i | \(0.496298\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3337.27 | −0.748061 | −0.374031 | − | 0.927416i | \(-0.622025\pi\) | ||||
−0.374031 | + | 0.927416i | \(0.622025\pi\) | |||||||
\(272\) | 2428.88 | − | 1402.31i | 0.541443 | − | 0.312602i | ||||
\(273\) | 34.4629 | + | 1181.19i | 0.00764026 | + | 0.261863i | ||||
\(274\) | −41.4461 | + | 71.7867i | −0.00913814 | + | 0.0158277i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4223.57 | + | 6846.23i | 0.921120 | + | 1.49310i | ||||
\(277\) | −548.959 | + | 316.941i | −0.119075 | + | 0.0687479i | −0.558354 | − | 0.829603i | \(-0.688567\pi\) |
0.439280 | + | 0.898350i | \(0.355234\pi\) | |||||||
\(278\) | 23.9796i | 0.00517339i | ||||||||
\(279\) | −3048.59 | + | 6072.65i | −0.654173 | + | 1.30308i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3101.20 | + | 5371.44i | 0.658370 | + | 1.14033i | 0.981037 | + | 0.193818i | \(0.0620872\pi\) |
−0.322667 | + | 0.946513i | \(0.604579\pi\) | |||||||
\(282\) | −124.637 | − | 67.1909i | −0.0263193 | − | 0.0141885i | ||||
\(283\) | 6477.98 | + | 3740.06i | 1.36069 | + | 0.785596i | 0.989716 | − | 0.143047i | \(-0.0456899\pi\) |
0.370976 | + | 0.928642i | \(0.379023\pi\) | |||||||
\(284\) | 3698.62 | − | 6406.19i | 0.772791 | − | 1.33851i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −74.0722 | − | 128.297i | −0.0153146 | − | 0.0265257i | ||||
\(287\) | 1729.52i | 0.355716i | ||||||||
\(288\) | 806.564 | + | 404.911i | 0.165025 | + | 0.0828459i | ||||
\(289\) | 2947.79 | 0.599998 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 907.780 | + | 1471.47i | 0.182869 | + | 0.296424i | ||||
\(292\) | −4201.33 | − | 2425.64i | −0.842000 | − | 0.486129i | ||||
\(293\) | 4188.54 | + | 2418.26i | 0.835144 | + | 0.482171i | 0.855611 | − | 0.517620i | \(-0.173182\pi\) |
−0.0204666 | + | 0.999791i | \(0.506515\pi\) | |||||||
\(294\) | −246.633 | + | 7.19590i | −0.0489250 | + | 0.00142746i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −173.893 | −0.0341464 | ||||||||
\(297\) | 3620.45 | − | 2536.35i | 0.707339 | − | 0.495535i | ||||
\(298\) | 25.0422i | 0.00486796i | ||||||||
\(299\) | 2609.81 | + | 4520.31i | 0.504779 | + | 0.874303i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2232.99 | − | 3867.65i | 0.427599 | − | 0.740623i | ||||
\(302\) | −32.8604 | − | 18.9719i | −0.00626126 | − | 0.00361494i | ||||
\(303\) | −2188.98 | + | 1350.42i | −0.415029 | + | 0.256039i | ||||
\(304\) | −2853.56 | − | 4942.51i | −0.538365 | − | 0.932475i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −115.119 | − | 174.970i | −0.0215063 | − | 0.0326874i | ||||
\(307\) | 5611.86i | 1.04328i | 0.853167 | + | 0.521638i | \(0.174679\pi\) | ||||
−0.853167 | + | 0.521638i | \(0.825321\pi\) | |||||||
\(308\) | 1840.52 | − | 1062.63i | 0.340498 | − | 0.196587i | ||||
\(309\) | −1553.49 | + | 2881.67i | −0.286002 | + | 0.530525i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5460.70 | + | 9458.21i | −0.995653 | + | 1.72452i | −0.417163 | + | 0.908831i | \(0.636976\pi\) |
−0.578489 | + | 0.815690i | \(0.696358\pi\) | |||||||
\(312\) | 343.424 | + | 185.138i | 0.0623159 | + | 0.0335941i | ||||
\(313\) | 4313.44 | − | 2490.36i | 0.778946 | − | 0.449724i | −0.0571109 | − | 0.998368i | \(-0.518189\pi\) |
0.836056 | + | 0.548643i | \(0.184856\pi\) | |||||||
\(314\) | 235.955 | 0.0424067 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4899.89 | −0.872280 | ||||||||
\(317\) | 3252.90 | − | 1878.06i | 0.576344 | − | 0.332752i | −0.183335 | − | 0.983050i | \(-0.558689\pi\) |
0.759679 | + | 0.650298i | \(0.225356\pi\) | |||||||
\(318\) | 109.648 | − | 67.6440i | 0.0193357 | − | 0.0119286i | ||||
\(319\) | −58.9789 | + | 102.154i | −0.0103517 | + | 0.0179296i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8107.73 | + | 236.555i | −1.40975 | + | 0.0411316i | ||||
\(322\) | 249.155 | − | 143.849i | 0.0431206 | − | 0.0248957i | ||||
\(323\) | 3998.99i | 0.688885i | ||||||||
\(324\) | −2299.40 | + | 5335.27i | −0.394273 | + | 0.914827i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 90.9788 | + | 157.580i | 0.0154566 | + | 0.0267716i | ||||
\(327\) | 141.864 | + | 4862.25i | 0.0239911 | + | 0.822273i | ||||
\(328\) | 494.520 | + | 285.511i | 0.0832479 | + | 0.0480632i | ||||
\(329\) | 659.016 | − | 1141.45i | 0.110434 | − | 0.191277i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 453.477 | + | 785.445i | 0.0753031 | + | 0.130429i | 0.901218 | − | 0.433366i | \(-0.142674\pi\) |
−0.825915 | + | 0.563795i | \(0.809341\pi\) | |||||||
\(332\) | 8569.55i | 1.41661i | ||||||||
\(333\) | −97.9609 | − | 1677.33i | −0.0161208 | − | 0.276028i | ||||
\(334\) | −582.182 | −0.0953759 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1320.32 | + | 2449.14i | −0.214372 | + | 0.397654i | ||||
\(337\) | 8555.20 | + | 4939.35i | 1.38288 | + | 0.798408i | 0.992500 | − | 0.122245i | \(-0.0390093\pi\) |
0.390383 | + | 0.920653i | \(0.372343\pi\) | |||||||
\(338\) | −223.527 | − | 129.053i | −0.0359712 | − | 0.0207680i | ||||
\(339\) | 3341.02 | − | 6197.48i | 0.535278 | − | 0.992923i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7929.49 | 1.25925 | ||||||||
\(342\) | −356.045 | + | 234.255i | −0.0562944 | + | 0.0370382i | ||||
\(343\) | − | 5199.81i | − | 0.818553i | ||||||
\(344\) | −737.247 | − | 1276.95i | −0.115551 | − | 0.200141i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −104.488 | + | 180.979i | −0.0162350 | + | 0.0281199i | ||||
\(347\) | −3039.50 | − | 1754.86i | −0.470228 | − | 0.271486i | 0.246107 | − | 0.969243i | \(-0.420848\pi\) |
−0.716335 | + | 0.697757i | \(0.754182\pi\) | |||||||
\(348\) | −4.52124 | − | 154.962i | −0.000696448 | − | 0.0238702i | ||||
\(349\) | −5196.48 | − | 9000.57i | −0.797024 | − | 1.38049i | −0.921546 | − | 0.388269i | \(-0.873073\pi\) |
0.124522 | − | 0.992217i | \(-0.460260\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1592.33 | + | 3416.88i | −0.242143 | + | 0.519600i | ||||
\(352\) | − | 1053.19i | − | 0.159475i | ||||||
\(353\) | 7002.16 | − | 4042.70i | 1.05577 | − | 0.609550i | 0.131512 | − | 0.991315i | \(-0.458017\pi\) |
0.924259 | + | 0.381765i | \(0.124684\pi\) | |||||||
\(354\) | −448.836 | + | 13.0955i | −0.0673881 | + | 0.00196615i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5997.56 | − | 10388.1i | 0.892893 | − | 1.54654i | ||||
\(357\) | 1659.26 | − | 1023.63i | 0.245987 | − | 0.151754i | ||||
\(358\) | −352.136 | + | 203.306i | −0.0519860 | + | 0.0300141i | ||||
\(359\) | 8189.49 | 1.20397 | 0.601984 | − | 0.798508i | \(-0.294377\pi\) | ||||
0.601984 | + | 0.798508i | \(0.294377\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1278.52 | 0.186400 | ||||||||
\(362\) | 382.962 | − | 221.103i | 0.0556024 | − | 0.0321020i | ||||
\(363\) | 1547.01 | + | 833.983i | 0.223683 | + | 0.120586i | ||||
\(364\) | −906.184 | + | 1569.56i | −0.130486 | + | 0.226008i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −327.691 | + | 607.856i | −0.0467996 | + | 0.0868119i | ||||
\(367\) | 7789.60 | − | 4497.33i | 1.10794 | − | 0.639669i | 0.169645 | − | 0.985505i | \(-0.445738\pi\) |
0.938295 | + | 0.345836i | \(0.112405\pi\) | |||||||
\(368\) | 12289.9i | 1.74091i | ||||||||
\(369\) | −2475.39 | + | 4930.86i | −0.349224 | + | 0.695638i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 599.629 | + | 1038.59i | 0.0839116 | + | 0.145339i | ||||
\(372\) | −8869.42 | + | 5471.71i | −1.23618 | + | 0.762621i | ||||
\(373\) | 805.288 | + | 464.934i | 0.111786 | + | 0.0645398i | 0.554851 | − | 0.831950i | \(-0.312775\pi\) |
−0.443064 | + | 0.896490i | \(0.646109\pi\) | |||||||
\(374\) | −122.208 | + | 211.670i | −0.0168963 | + | 0.0292652i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −217.582 | − | 376.863i | −0.0298429 | − | 0.0516894i | ||||
\(377\) | − | 100.592i | − | 0.0137420i | ||||||
\(378\) | 188.335 | + | 87.7673i | 0.0256267 | + | 0.0119425i | ||||
\(379\) | −3449.71 | −0.467546 | −0.233773 | − | 0.972291i | \(-0.575107\pi\) | ||||
−0.233773 | + | 0.972291i | \(0.575107\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6141.14 | + | 179.177i | −0.825775 | + | 0.0240932i | ||||
\(382\) | −362.012 | − | 209.007i | −0.0484872 | − | 0.0279941i | ||||
\(383\) | 4629.89 | + | 2673.07i | 0.617692 | + | 0.356625i | 0.775970 | − | 0.630770i | \(-0.217261\pi\) |
−0.158278 | + | 0.987395i | \(0.550594\pi\) | |||||||
\(384\) | 968.370 | + | 1569.69i | 0.128690 | + | 0.208601i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −620.841 | −0.0818652 | ||||||||
\(387\) | 11901.8 | − | 7830.66i | 1.56332 | − | 1.02857i | ||||
\(388\) | 2651.72i | 0.346960i | ||||||||
\(389\) | 3861.72 | + | 6688.70i | 0.503334 | + | 0.871801i | 0.999993 | + | 0.00385448i | \(0.00122692\pi\) |
−0.496658 | + | 0.867946i | \(0.665440\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4305.78 | − | 7457.83i | 0.556912 | − | 0.964600i | ||||
\(392\) | −656.709 | − | 379.151i | −0.0846144 | − | 0.0488521i | ||||
\(393\) | −10308.3 | − | 5557.14i | −1.32312 | − | 0.713284i | ||||
\(394\) | 108.426 | + | 187.799i | 0.0138640 | + | 0.0240132i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6768.20 | − | 395.282i | 0.858876 | − | 0.0501607i | ||||
\(397\) | − | 7125.03i | − | 0.900744i | −0.892841 | − | 0.450372i | \(-0.851291\pi\) | ||
0.892841 | − | 0.450372i | \(-0.148709\pi\) | |||||||
\(398\) | −78.2948 | + | 45.2035i | −0.00986071 | + | 0.00569308i | ||||
\(399\) | −2082.98 | − | 3376.42i | −0.261352 | − | 0.423640i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 896.547 | − | 1552.86i | 0.111649 | − | 0.193382i | −0.804786 | − | 0.593565i | \(-0.797720\pi\) |
0.916435 | + | 0.400183i | \(0.131053\pi\) | |||||||
\(402\) | −14.4146 | − | 494.047i | −0.00178839 | − | 0.0612956i | ||||
\(403\) | −5856.15 | + | 3381.05i | −0.723860 | + | 0.417921i | ||||
\(404\) | −3944.73 | −0.485786 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.54451 | −0.000677757 | ||||||||
\(407\) | −1698.05 | + | 980.369i | −0.206804 | + | 0.119398i | ||||
\(408\) | −18.7725 | − | 643.412i | −0.00227789 | − | 0.0780727i | ||||
\(409\) | 1569.87 | − | 2719.09i | 0.189792 | − | 0.328729i | −0.755389 | − | 0.655277i | \(-0.772552\pi\) |
0.945181 | + | 0.326548i | \(0.105885\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1292.38 | − | 2094.90i | −0.155106 | − | 0.251420i | ||||
\(412\) | −4348.27 | + | 2510.48i | −0.519961 | + | 0.300200i | ||||
\(413\) | − | 4179.77i | − | 0.497997i | ||||||
\(414\) | 916.224 | − | 53.5100i | 0.108768 | − | 0.00635235i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 449.068 | + | 777.808i | 0.0529263 | + | 0.0916711i | ||||
\(417\) | −626.795 | − | 337.900i | −0.0736074 | − | 0.0396812i | ||||
\(418\) | 430.726 | + | 248.680i | 0.0504007 | + | 0.0290989i | ||||
\(419\) | 1228.70 | − | 2128.17i | 0.143260 | − | 0.248133i | −0.785463 | − | 0.618909i | \(-0.787575\pi\) |
0.928722 | + | 0.370776i | \(0.120908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1339.33 | + | 2319.80i | 0.155048 | + | 0.268551i | 0.933076 | − | 0.359678i | \(-0.117113\pi\) |
−0.778029 | + | 0.628229i | \(0.783780\pi\) | |||||||
\(422\) | − | 3.12228i | − | 0.000360167i | ||||||
\(423\) | 3512.56 | − | 2311.04i | 0.403750 | − | 0.265643i | ||||
\(424\) | 395.949 | 0.0453514 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −443.121 | − | 718.281i | −0.0503974 | − | 0.0816921i | ||||
\(427\) | −5566.86 | − | 3214.03i | −0.630911 | − | 0.364257i | ||||
\(428\) | −10773.5 | − | 6220.09i | −1.21672 | − | 0.702476i | ||||
\(429\) | 4397.26 | − | 128.297i | 0.494876 | − | 0.0144388i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9472.42 | −1.05863 | −0.529316 | − | 0.848425i | \(-0.677551\pi\) | ||||
−0.529316 | + | 0.848425i | \(0.677551\pi\) | |||||||
\(432\) | −7269.57 | + | 5092.79i | −0.809623 | + | 0.567192i | ||||
\(433\) | − | 4238.21i | − | 0.470382i | −0.971949 | − | 0.235191i | \(-0.924428\pi\) | ||
0.971949 | − | 0.235191i | \(-0.0755715\pi\) | |||||||
\(434\) | 186.360 | + | 322.784i | 0.0206119 | + | 0.0357008i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3730.23 | + | 6460.94i | −0.409737 | + | 0.709686i | ||||
\(437\) | −15175.9 | − | 8761.80i | −1.66124 | − | 0.959116i | ||||
\(438\) | −471.065 | + | 290.609i | −0.0513889 | + | 0.0317028i | ||||
\(439\) | 2429.47 | + | 4207.96i | 0.264128 | + | 0.457483i | 0.967335 | − | 0.253503i | \(-0.0815826\pi\) |
−0.703207 | + | 0.710985i | \(0.748249\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3287.25 | − | 6548.05i | 0.354957 | − | 0.707057i | ||||
\(442\) | − | 208.432i | − | 0.0224301i | ||||||
\(443\) | 2022.82 | − | 1167.88i | 0.216946 | − | 0.125254i | −0.387589 | − | 0.921832i | \(-0.626692\pi\) |
0.604535 | + | 0.796578i | \(0.293359\pi\) | |||||||
\(444\) | 1222.83 | − | 2268.31i | 0.130705 | − | 0.242453i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 86.5783 | − | 149.958i | 0.00919193 | − | 0.0159209i | ||||
\(447\) | −654.568 | − | 352.873i | −0.0692617 | − | 0.0373385i | ||||
\(448\) | −3666.94 | + | 2117.11i | −0.386712 | + | 0.223268i | ||||
\(449\) | −13290.5 | −1.39692 | −0.698460 | − | 0.715649i | \(-0.746131\pi\) | ||||
−0.698460 | + | 0.715649i | \(0.746131\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6438.58 | 0.672241 | ||||||||
\(452\) | 9351.64 | − | 5399.17i | 0.973151 | − | 0.561849i | ||||
\(453\) | 958.941 | − | 591.588i | 0.0994591 | − | 0.0613582i | ||||
\(454\) | 299.848 | − | 519.351i | 0.0309968 | − | 0.0536880i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1309.28 | + | 38.2001i | −0.134457 | + | 0.00392299i | ||||
\(457\) | −4481.35 | + | 2587.31i | −0.458706 | + | 0.264834i | −0.711500 | − | 0.702686i | \(-0.751984\pi\) |
0.252794 | + | 0.967520i | \(0.418650\pi\) | |||||||
\(458\) | − | 192.415i | − | 0.0196309i | ||||||
\(459\) | 6195.63 | − | 543.534i | 0.630037 | − | 0.0552724i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3170.44 | − | 5491.37i | −0.320309 | − | 0.554791i | 0.660243 | − | 0.751052i | \(-0.270453\pi\) |
−0.980552 | + | 0.196261i | \(0.937120\pi\) | |||||||
\(462\) | −7.07157 | − | 242.372i | −0.000712119 | − | 0.0244073i | ||||
\(463\) | −2756.38 | − | 1591.40i | −0.276673 | − | 0.159737i | 0.355243 | − | 0.934774i | \(-0.384398\pi\) |
−0.631916 | + | 0.775036i | \(0.717731\pi\) | |||||||
\(464\) | 118.425 | − | 205.118i | 0.0118486 | − | 0.0205223i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 390.208 | + | 675.860i | 0.0387898 | + | 0.0671859i | ||||
\(467\) | 8576.23i | 0.849808i | 0.905238 | + | 0.424904i | \(0.139692\pi\) | ||||
−0.905238 | + | 0.424904i | \(0.860308\pi\) | |||||||
\(468\) | −4829.96 | + | 3177.82i | −0.477062 | + | 0.313877i | ||||
\(469\) | 4600.79 | 0.452974 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3324.87 | + | 6167.53i | −0.325269 | + | 0.603365i | ||||
\(472\) | −1195.11 | − | 690.000i | −0.116546 | − | 0.0672877i | ||||
\(473\) | −14398.3 | − | 8312.84i | −1.39965 | − | 0.808086i | ||||
\(474\) | −265.282 | + | 492.090i | −0.0257064 | + | 0.0476845i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2990.13 | 0.287925 | ||||||||
\(477\) | 223.054 | + | 3819.23i | 0.0214107 | + | 0.366605i | ||||
\(478\) | − | 1145.18i | − | 0.109580i | ||||||
\(479\) | 1458.82 | + | 2526.76i | 0.139155 | + | 0.241024i | 0.927177 | − | 0.374623i | \(-0.122228\pi\) |
−0.788022 | + | 0.615647i | \(0.788895\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 836.037 | − | 1448.06i | 0.0792516 | − | 0.137268i | ||||
\(482\) | 31.8729 | + | 18.4018i | 0.00301197 | + | 0.00173896i | ||||
\(483\) | 249.155 | + | 8539.56i | 0.0234719 | + | 0.804479i | ||||
\(484\) | 1347.74 | + | 2334.35i | 0.126572 | + | 0.219229i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 411.324 | + | 519.779i | 0.0383910 | + | 0.0485137i | ||||
\(487\) | 14061.0i | 1.30834i | 0.756346 | + | 0.654172i | \(0.226983\pi\) | ||||
−0.756346 | + | 0.654172i | \(0.773017\pi\) | |||||||
\(488\) | −1837.96 | + | 1061.15i | −0.170493 | + | 0.0984343i | ||||
\(489\) | −5400.92 | + | 157.580i | −0.499464 | + | 0.0145726i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 466.331 | − | 807.709i | 0.0428620 | − | 0.0742391i | −0.843799 | − | 0.536660i | \(-0.819686\pi\) |
0.886661 | + | 0.462421i | \(0.153019\pi\) | |||||||
\(492\) | −7201.78 | + | 4442.91i | −0.659921 | + | 0.407118i | ||||
\(493\) | −143.727 | + | 82.9806i | −0.0131301 | + | 0.00758065i | ||||
\(494\) | −424.137 | −0.0386292 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15921.8 | −1.44135 | ||||||||
\(497\) | 6803.57 | − | 3928.04i | 0.614048 | − | 0.354521i | ||||
\(498\) | 860.629 | + | 463.959i | 0.0774412 | + | 0.0417480i | ||||
\(499\) | −7215.39 | + | 12497.4i | −0.647305 | + | 1.12117i | 0.336459 | + | 0.941698i | \(0.390771\pi\) |
−0.983764 | + | 0.179467i | \(0.942563\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8203.60 | − | 15217.4i | 0.731557 | − | 1.35701i | ||||
\(502\) | 123.679 | − | 71.4062i | 0.0109962 | − | 0.00634864i | ||||
\(503\) | − | 3230.55i | − | 0.286368i | −0.989696 | − | 0.143184i | \(-0.954266\pi\) | ||
0.989696 | − | 0.143184i | \(-0.0457341\pi\) | |||||||
\(504\) | 350.988 | + | 533.467i | 0.0310203 | + | 0.0471478i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −535.515 | − | 927.539i | −0.0470485 | − | 0.0814904i | ||||
\(507\) | 6523.03 | − | 4024.18i | 0.571397 | − | 0.352505i | ||||
\(508\) | −8160.32 | − | 4711.36i | −0.712708 | − | 0.411482i | ||||
\(509\) | −180.378 | + | 312.424i | −0.0157075 | + | 0.0272062i | −0.873772 | − | 0.486335i | \(-0.838333\pi\) |
0.858065 | + | 0.513541i | \(0.171667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2576.10 | − | 4461.93i | −0.223013 | − | 0.386270i | ||||
\(512\) | 3529.04i | 0.304615i | ||||||||
\(513\) | −1106.03 | − | 12607.4i | −0.0951903 | − | 1.08505i | ||||
\(514\) | −730.096 | −0.0626521 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 21841.2 | − | 637.250i | 1.86338 | − | 0.0543670i | ||||
\(517\) | −4249.33 | − | 2453.35i | −0.361480 | − | 0.208701i | ||||
\(518\) | −79.8154 | − | 46.0814i | −0.00677005 | − | 0.00390869i | ||||
\(519\) | −3258.18 | − | 5281.37i | −0.275565 | − | 0.446679i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11698.8 | −0.983747 | −0.491873 | − | 0.870667i | \(-0.663688\pi\) | ||||
−0.491873 | + | 0.870667i | \(0.663688\pi\) | |||||||
\(522\) | −15.8074 | − | 7.93562i | −0.00132542 | − | 0.000665388i | ||||
\(523\) | 18557.3i | 1.55154i | 0.631015 | + | 0.775770i | \(0.282638\pi\) | ||||
−0.631015 | + | 0.775770i | \(0.717362\pi\) | |||||||
\(524\) | −8980.49 | − | 15554.7i | −0.748692 | − | 1.29677i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −246.470 | + | 426.899i | −0.0204308 | + | 0.0353872i | ||||
\(527\) | 9661.75 | + | 5578.21i | 0.798619 | + | 0.461083i | ||||
\(528\) | 9117.54 | + | 4915.20i | 0.751496 | + | 0.405126i | ||||
\(529\) | 12784.5 | + | 22143.3i | 1.05075 | + | 1.81995i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5982.32 | − | 11916.5i | 0.488909 | − | 0.973883i | ||||
\(532\) | − | 6084.59i | − | 0.495866i | ||||||
\(533\) | −4755.07 | + | 2745.34i | −0.386426 | + | 0.223103i | ||||
\(534\) | −718.551 | − | 1164.74i | −0.0582298 | − | 0.0943882i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 759.503 | − | 1315.50i | 0.0612044 | − | 0.106009i | ||||
\(537\) | −352.136 | − | 12069.2i | −0.0282976 | − | 0.969875i | ||||
\(538\) | 15.5496 | − | 8.97756i | 0.00124608 | − | 0.000719424i | ||||
\(539\) | −8550.26 | −0.683276 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22755.3 | 1.80837 | 0.904185 | − | 0.427140i | \(-0.140479\pi\) | ||||
0.904185 | + | 0.427140i | \(0.140479\pi\) | |||||||
\(542\) | −505.733 | + | 291.985i | −0.0400795 | + | 0.0231399i | ||||
\(543\) | 382.962 | + | 13125.7i | 0.0302661 | + | 1.03734i | ||||
\(544\) | 740.893 | − | 1283.26i | 0.0583925 | − | 0.101139i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 108.567 | + | 175.983i | 0.00850962 | + | 0.0137937i | ||||
\(547\) | −5021.30 | + | 2899.05i | −0.392496 | + | 0.226608i | −0.683241 | − | 0.730193i | \(-0.739430\pi\) |
0.290745 | + | 0.956801i | \(0.406097\pi\) | |||||||
\(548\) | − | 3775.18i | − | 0.294284i | ||||||
\(549\) | −11271.0 | − | 17130.8i | −0.876200 | − | 1.33174i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 168.857 | + | 292.468i | 0.0130554 | + | 0.0226127i | ||||
\(552\) | 2482.84 | + | 1338.48i | 0.191443 | + | 0.103205i | ||||
\(553\) | −4506.65 | − | 2601.92i | −0.346550 | − | 0.200081i | ||||
\(554\) | −55.4599 | + | 96.0593i | −0.00425318 | + | 0.00736673i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −546.056 | − | 945.797i | −0.0416510 | − | 0.0721416i | ||||
\(557\) | − | 15740.3i | − | 1.19738i | −0.800982 | − | 0.598688i | \(-0.795689\pi\) | ||
0.800982 | − | 0.598688i | \(-0.204311\pi\) | |||||||
\(558\) | 69.3231 | + | 1186.98i | 0.00525929 | + | 0.0900521i | ||||
\(559\) | 14178.0 | 1.07275 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3810.72 | − | 6177.01i | −0.286789 | − | 0.464873i | ||||
\(562\) | 939.919 | + | 542.662i | 0.0705482 | + | 0.0407310i | ||||
\(563\) | −3307.45 | − | 1909.56i | −0.247589 | − | 0.142946i | 0.371071 | − | 0.928605i | \(-0.378991\pi\) |
−0.618660 | + | 0.785659i | \(0.712324\pi\) | |||||||
\(564\) | 6445.94 | − | 188.070i | 0.481247 | − | 0.0140411i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1308.91 | 0.0972040 | ||||||||
\(567\) | −4947.97 | + | 3686.07i | −0.366482 | + | 0.273016i | ||||
\(568\) | − | 2593.78i | − | 0.191607i | ||||||
\(569\) | 4445.56 | + | 7699.93i | 0.327535 | + | 0.567308i | 0.982022 | − | 0.188766i | \(-0.0604487\pi\) |
−0.654487 | + | 0.756073i | \(0.727115\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4193.31 | + | 7263.03i | −0.307329 | + | 0.532309i | −0.977777 | − | 0.209647i | \(-0.932768\pi\) |
0.670448 | + | 0.741956i | \(0.266102\pi\) | |||||||
\(572\) | 5843.06 | + | 3373.49i | 0.427116 | + | 0.246596i | ||||
\(573\) | 10564.3 | − | 6517.33i | 0.770211 | − | 0.475158i | ||||
\(574\) | 151.320 | + | 262.094i | 0.0110034 | + | 0.0190585i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −13484.6 | + | 787.536i | −0.975446 | + | 0.0569687i | ||||
\(577\) | − | 16922.3i | − | 1.22095i | −0.792037 | − | 0.610473i | \(-0.790979\pi\) | ||
0.792037 | − | 0.610473i | \(-0.209021\pi\) | |||||||
\(578\) | 446.711 | − | 257.909i | 0.0321466 | − | 0.0185599i | ||||
\(579\) | 8748.35 | − | 16227.9i | 0.627926 | − | 1.16478i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4550.56 | + | 7881.80i | −0.324938 | + | 0.562809i | ||||
\(582\) | 266.309 | + | 143.565i | 0.0189671 | + | 0.0102250i | ||||
\(583\) | 3866.40 | − | 2232.27i | 0.274666 | − | 0.158578i | ||||
\(584\) | −1701.06 | −0.120531 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 846.315 | 0.0596603 | ||||||||
\(587\) | −13197.0 | + | 7619.29i | −0.927936 | + | 0.535744i | −0.886158 | − | 0.463383i | \(-0.846635\pi\) |
−0.0417777 | + | 0.999127i | \(0.513302\pi\) | |||||||
\(588\) | 9563.77 | − | 5900.07i | 0.670754 | − | 0.413800i | ||||
\(589\) | 11351.1 | − | 19660.6i | 0.794079 | − | 1.37539i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6436.66 | + | 187.799i | −0.448002 | + | 0.0130711i | ||||
\(592\) | 3409.55 | − | 1968.50i | 0.236709 | − | 0.136664i | ||||
\(593\) | − | 16960.2i | − | 1.17449i | −0.809409 | − | 0.587245i | \(-0.800213\pi\) | ||
0.809409 | − | 0.587245i | \(-0.199787\pi\) | |||||||
\(594\) | 326.735 | − | 701.123i | 0.0225692 | − | 0.0484300i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −570.252 | − | 987.705i | −0.0391920 | − | 0.0678825i | ||||
\(597\) | −78.2948 | − | 2683.49i | −0.00536749 | − | 0.183966i | ||||
\(598\) | 790.986 | + | 456.676i | 0.0540900 | + | 0.0312289i | ||||
\(599\) | −12456.1 | + | 21574.5i | −0.849651 | + | 1.47164i | 0.0318690 | + | 0.999492i | \(0.489854\pi\) |
−0.881520 | + | 0.472147i | \(0.843479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2175.63 | + | 3768.31i | 0.147664 | + | 0.255761i | 0.930364 | − | 0.366638i | \(-0.119491\pi\) |
−0.782700 | + | 0.622399i | \(0.786158\pi\) | |||||||
\(602\) | − | 781.476i | − | 0.0529080i | ||||||
\(603\) | 13116.8 | + | 6584.91i | 0.885835 | + | 0.444707i | ||||
\(604\) | 1728.09 | 0.116416 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −213.569 | + | 396.164i | −0.0143163 | + | 0.0265562i | ||||
\(607\) | 24096.0 | + | 13911.8i | 1.61125 | + | 0.930254i | 0.989082 | + | 0.147369i | \(0.0470805\pi\) |
0.622166 | + | 0.782885i | \(0.286253\pi\) | |||||||
\(608\) | −2611.31 | − | 1507.64i | −0.174182 | − | 0.100564i | ||||
\(609\) | 78.1285 | − | 144.926i | 0.00519856 | − | 0.00964317i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4184.33 | 0.277054 | ||||||||
\(612\) | 8524.84 | + | 4279.64i | 0.563066 | + | 0.282670i | ||||
\(613\) | 20034.6i | 1.32005i | 0.751244 | + | 0.660024i | \(0.229454\pi\) | ||||
−0.751244 | + | 0.660024i | \(0.770546\pi\) | |||||||
\(614\) | 490.994 | + | 850.427i | 0.0322719 | + | 0.0558965i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 372.600 | − | 645.363i | 0.0243709 | − | 0.0422117i | ||||
\(617\) | 6541.86 | + | 3776.95i | 0.426848 | + | 0.246441i | 0.698003 | − | 0.716095i | \(-0.254072\pi\) |
−0.271155 | + | 0.962536i | \(0.587405\pi\) | |||||||
\(618\) | 16.7067 | + | 572.609i | 0.00108745 | + | 0.0372714i | ||||
\(619\) | 6192.54 | + | 10725.8i | 0.402099 | + | 0.696456i | 0.993979 | − | 0.109570i | \(-0.0349474\pi\) |
−0.591880 | + | 0.806026i | \(0.701614\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11512.0 | + | 24702.8i | −0.743896 | + | 1.59628i | ||||
\(622\) | 1911.08i | 0.123195i | ||||||||
\(623\) | 11032.4 | − | 6369.58i | 0.709479 | − | 0.409618i | ||||
\(624\) | −8829.35 | + | 257.610i | −0.566437 | + | 0.0165267i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 435.775 | − | 754.785i | 0.0278228 | − | 0.0481906i | ||||
\(627\) | −12569.6 | + | 7754.40i | −0.800606 | + | 0.493909i | ||||
\(628\) | −9306.45 | + | 5373.08i | −0.591350 | + | 0.341416i | ||||
\(629\) | −2758.67 | −0.174873 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1325.17 | −0.0836043 | −0.0418022 | − | 0.999126i | \(-0.513310\pi\) | ||||
−0.0418022 | + | 0.999126i | \(0.513310\pi\) | |||||||
\(632\) | −1487.92 | + | 859.053i | −0.0936494 | + | 0.0540685i | ||||
\(633\) | 81.6122 | + | 43.9965i | 0.00512447 | + | 0.00276257i | ||||
\(634\) | 328.632 | − | 569.207i | 0.0205862 | − | 0.0356563i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2784.34 | + | 5164.86i | −0.173595 | + | 0.322013i | ||||
\(637\) | 6314.60 | − | 3645.74i | 0.392769 | − | 0.226765i | ||||
\(638\) | 20.6408i | 0.00128084i | ||||||||
\(639\) | 25019.0 | − | 1461.18i | 1.54888 | − | 0.0904589i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11255.8 | + | 19495.6i | 0.693568 | + | 1.20129i | 0.970661 | + | 0.240451i | \(0.0772955\pi\) |
−0.277094 | + | 0.960843i | \(0.589371\pi\) | |||||||
\(642\) | −1207.96 | + | 745.212i | −0.0742590 | + | 0.0458118i | ||||
\(643\) | −4862.40 | − | 2807.31i | −0.298218 | − | 0.172176i | 0.343424 | − | 0.939180i | \(-0.388413\pi\) |
−0.641642 | + | 0.767004i | \(0.721747\pi\) | |||||||
\(644\) | −6551.38 | + | 11347.3i | −0.400871 | + | 0.694328i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 349.881 | + | 606.012i | 0.0213094 | + | 0.0369090i | ||||
\(647\) | 11753.6i | 0.714188i | 0.934068 | + | 0.357094i | \(0.116232\pi\) | ||||
−0.934068 | + | 0.357094i | \(0.883768\pi\) | |||||||
\(648\) | 237.137 | + | 2023.27i | 0.0143760 | + | 0.122656i | ||||
\(649\) | −15560.2 | −0.941127 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11063.2 | + | 322.784i | −0.666051 | + | 0.0194330i | ||||
\(652\) | −7176.71 | − | 4143.48i | −0.431076 | − | 0.248882i | ||||
\(653\) | 22393.9 | + | 12929.1i | 1.34202 | + | 0.774816i | 0.987104 | − | 0.160082i | \(-0.0511760\pi\) |
0.354916 | + | 0.934898i | \(0.384509\pi\) | |||||||
\(654\) | 446.908 | + | 724.420i | 0.0267209 | + | 0.0433135i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12928.1 | −0.769450 | ||||||||
\(657\) | −958.272 | − | 16408.0i | −0.0569037 | − | 0.974333i | ||||
\(658\) | − | 230.635i | − | 0.0136643i | ||||||
\(659\) | −8847.75 | − | 15324.8i | −0.523004 | − | 0.905869i | −0.999642 | − | 0.0267695i | \(-0.991478\pi\) |
0.476638 | − | 0.879100i | \(-0.341855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3115.05 | + | 5395.42i | −0.183300 | + | 0.317485i | −0.943002 | − | 0.332786i | \(-0.892011\pi\) |
0.759702 | + | 0.650271i | \(0.225345\pi\) | |||||||
\(662\) | 137.441 | + | 79.3515i | 0.00806916 | + | 0.00465873i | ||||
\(663\) | 5448.13 | + | 2937.05i | 0.319137 | + | 0.172044i | ||||
\(664\) | 1502.42 | + | 2602.27i | 0.0878091 | + | 0.152090i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −161.599 | − | 245.614i | −0.00940214 | − | 0.0142903i | ||||
\(667\) | − | 727.243i | − | 0.0422174i | ||||||
\(668\) | 22962.2 | − | 13257.2i | 1.32999 | − | 0.767872i | ||||
\(669\) | 2699.71 | + | 4376.12i | 0.156019 | + | 0.252901i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11965.0 | + | 20724.0i | −0.688381 | + | 1.19231i | ||||
\(672\) | 42.8719 | + | 1469.40i | 0.00246104 | + | 0.0843501i | ||||
\(673\) | −5240.91 | + | 3025.84i | −0.300182 | + | 0.173310i | −0.642524 | − | 0.766265i | \(-0.722113\pi\) |
0.342343 | + | 0.939575i | \(0.388780\pi\) | |||||||
\(674\) | 1728.62 | 0.0987892 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11755.0 | 0.668812 | ||||||||
\(677\) | −24334.1 | + | 14049.3i | −1.38144 | + | 0.797576i | −0.992330 | − | 0.123614i | \(-0.960551\pi\) |
−0.389112 | + | 0.921190i | \(0.627218\pi\) | |||||||
\(678\) | −35.9305 | − | 1231.49i | −0.00203525 | − | 0.0697566i | ||||
\(679\) | −1408.10 | + | 2438.90i | −0.0795846 | + | 0.137845i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9349.93 | + | 15155.9i | 0.526124 | + | 0.852825i | ||||
\(682\) | 1201.64 | − | 693.769i | 0.0674682 | − | 0.0389528i | ||||
\(683\) | − | 8335.71i | − | 0.466994i | −0.972358 | − | 0.233497i | \(-0.924983\pi\) | ||
0.972358 | − | 0.233497i | \(-0.0750169\pi\) | |||||||
\(684\) | 8708.61 | − | 17347.1i | 0.486816 | − | 0.969714i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −454.944 | − | 787.986i | −0.0253205 | − | 0.0438563i | ||||
\(687\) | 5029.46 | + | 2711.34i | 0.279310 | + | 0.150574i | ||||
\(688\) | 28910.6 | + | 16691.5i | 1.60204 | + | 0.924939i | ||||
\(689\) | −1903.63 | + | 3297.18i | −0.105258 | + | 0.182312i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8442.55 | + | 14622.9i | 0.464790 | + | 0.805039i | 0.999192 | − | 0.0401909i | \(-0.0127966\pi\) |
−0.534402 | + | 0.845230i | \(0.679463\pi\) | |||||||
\(692\) | − | 9517.46i | − | 0.522832i | ||||||
\(693\) | 6434.92 | + | 3230.46i | 0.352731 | + | 0.177078i | ||||
\(694\) | −614.146 | −0.0335917 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −28.5409 | − | 46.2637i | −0.00155437 | − | 0.00251957i | ||||
\(697\) | 7845.14 | + | 4529.39i | 0.426335 | + | 0.246145i | ||||
\(698\) | −1574.96 | − | 909.305i | −0.0854057 | − | 0.0493090i | ||||
\(699\) | −23164.5 | + | 675.860i | −1.25345 | + | 0.0365714i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16875.2 | 0.909226 | 0.454613 | − | 0.890689i | \(-0.349778\pi\) | ||||
0.454613 | + | 0.890689i | \(0.349778\pi\) | |||||||
\(702\) | 57.6479 | + | 657.115i | 0.00309940 | + | 0.0353293i | ||||
\(703\) | 5613.59i | 0.301167i | ||||||||
\(704\) | 7881.47 | + | 13651.1i | 0.421938 | + | 0.730817i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 707.410 | − | 1225.27i | 0.0377106 | − | 0.0653168i | ||||
\(707\) | −3628.14 | − | 2094.71i | −0.192999 | − | 0.111428i | ||||
\(708\) | 17404.6 | − | 10737.3i | 0.923879 | − | 0.569959i | ||||
\(709\) | −9503.71 | − | 16460.9i | −0.503412 | − | 0.871936i | −0.999992 | − | 0.00394482i | \(-0.998744\pi\) |
0.496580 | − | 0.867991i | \(-0.334589\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9124.43 | − | 13868.2i | −0.481284 | − | 0.731503i | ||||
\(712\) | − | 4205.99i | − | 0.221385i | ||||||
\(713\) | −42337.9 | + | 24443.8i | −2.22379 | + | 1.28391i | ||||
\(714\) | 161.887 | − | 300.295i | 0.00848524 | − | 0.0157398i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9259.23 | − | 16037.4i | 0.483287 | − | 0.837078i | ||||
\(717\) | 29933.4 | + | 16136.9i | 1.55911 | + | 0.840506i | ||||
\(718\) | 1241.04 | − | 716.517i | 0.0645061 | − | 0.0372426i | ||||
\(719\) | −17588.1 | −0.912275 | −0.456138 | − | 0.889909i | \(-0.650767\pi\) | ||||
−0.456138 | + | 0.889909i | \(0.650767\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5332.40 | −0.275435 | ||||||||
\(722\) | 193.748 | − | 111.861i | 0.00998693 | − | 0.00576596i | ||||
\(723\) | −930.123 | + | 573.810i | −0.0478446 | + | 0.0295162i | ||||
\(724\) | −10069.8 | + | 17441.4i | −0.516907 | + | 0.895309i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 307.403 | − | 8.96895i | 0.0157146 | − | 0.000458497i | ||||
\(727\) | −4854.40 | + | 2802.69i | −0.247648 | + | 0.142979i | −0.618687 | − | 0.785638i | \(-0.712335\pi\) |
0.371039 | + | 0.928617i | \(0.379002\pi\) | |||||||
\(728\) | 635.491i | 0.0323528i | ||||||||
\(729\) | −19382.3 | + | 3427.15i | −0.984725 | + | 0.174117i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11695.8 | − | 20257.7i | −0.591771 | − | 1.02498i | ||||
\(732\) | −917.220 | − | 31436.9i | −0.0463134 | − | 1.58735i | ||||
\(733\) | −12921.2 | − | 7460.04i | −0.651097 | − | 0.375911i | 0.137779 | − | 0.990463i | \(-0.456004\pi\) |
−0.788877 | + | 0.614552i | \(0.789337\pi\) | |||||||
\(734\) | 786.963 | − | 1363.06i | 0.0395740 | − | 0.0685443i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3246.60 | + | 5623.27i | 0.162597 | + | 0.281626i | ||||
\(737\) | − | 17127.6i | − | 0.856042i | ||||||
\(738\) | 56.2889 | + | 963.806i | 0.00280762 | + | 0.0480734i | ||||
\(739\) | 27418.8 | 1.36484 | 0.682421 | − | 0.730959i | \(-0.260927\pi\) | ||||
0.682421 | + | 0.730959i | \(0.260927\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5976.58 | − | 11086.4i | 0.296296 | − | 0.549619i | ||||
\(742\) | 181.737 | + | 104.926i | 0.00899161 | + | 0.00519131i | ||||
\(743\) | 21255.9 | + | 12272.1i | 1.04953 | + | 0.605948i | 0.922518 | − | 0.385953i | \(-0.126127\pi\) |
0.127014 | + | 0.991901i | \(0.459461\pi\) | |||||||
\(744\) | −1734.02 | + | 3216.56i | −0.0854467 | + | 0.158501i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 162.712 | 0.00798569 | ||||||||
\(747\) | −24254.5 | + | 15957.9i | −1.18799 | + | 0.781621i | ||||
\(748\) | − | 11131.5i | − | 0.544128i | ||||||
\(749\) | −6605.92 | − | 11441.8i | −0.322263 | − | 0.558176i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −767.283 | + | 1328.97i | −0.0372817 | + | 0.0645738i | −0.884064 | − | 0.467365i | \(-0.845203\pi\) |
0.846782 | + | 0.531939i | \(0.178537\pi\) | |||||||
\(752\) | 8532.30 | + | 4926.13i | 0.413752 | + | 0.238880i | ||||
\(753\) | 123.679 | + | 4239.00i | 0.00598555 | + | 0.205150i | ||||
\(754\) | −8.80102 | − | 15.2438i | −0.000425085 | − | 0.000736269i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9426.85 | + | 827.005i | −0.453507 | + | 0.0397856i | ||||
\(757\) | 18051.1i | 0.866681i | 0.901230 | + | 0.433341i | \(0.142665\pi\) | ||||
−0.901230 | + | 0.433341i | \(0.857335\pi\) | |||||||
\(758\) | −522.773 | + | 301.823i | −0.0250501 | + | 0.0144627i | ||||
\(759\) | 31790.6 | − | 927.539i | 1.52032 | − | 0.0443578i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6462.29 | + | 11193.0i | −0.307829 | + | 0.533176i | −0.977887 | − | 0.209133i | \(-0.932936\pi\) |
0.670058 | + | 0.742309i | \(0.266269\pi\) | |||||||
\(762\) | −914.958 | + | 564.455i | −0.0434980 | + | 0.0268347i | ||||
\(763\) | −6861.71 | + | 3961.61i | −0.325571 | + | 0.187968i | ||||
\(764\) | 19037.8 | 0.901522 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 935.491 | 0.0441262 | ||||||||
\(767\) | 11491.6 | − | 6634.70i | 0.540990 | − | 0.312341i | ||||
\(768\) | −18021.6 | − | 9715.30i | −0.846741 | − | 0.456472i | ||||
\(769\) | −1686.16 | + | 2920.51i | −0.0790695 | + | 0.136952i | −0.902849 | − | 0.429958i | \(-0.858528\pi\) |
0.823779 | + | 0.566911i | \(0.191862\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10287.9 | − | 19083.7i | 0.480557 | − | 0.891418i | ||||
\(772\) | 24487.0 | − | 14137.6i | 1.14159 | − | 0.659097i | ||||
\(773\) | − | 27152.6i | − | 1.26341i | −0.775211 | − | 0.631703i | \(-0.782356\pi\) | ||
0.775211 | − | 0.631703i | \(-0.217644\pi\) | |||||||
\(774\) | 1118.49 | − | 2227.99i | 0.0519424 | − | 0.103467i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 464.901 | + | 805.232i | 0.0215064 | + | 0.0372502i | ||||
\(777\) | 2329.19 | − | 1436.92i | 0.107541 | − | 0.0663441i | ||||
\(778\) | 1170.42 | + | 675.742i | 0.0539352 | + | 0.0311395i | ||||
\(779\) | 9216.83 | − | 15964.0i | 0.423912 | − | 0.734236i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14623.1 | − | 25327.9i | −0.669982 | − | 1.16044i | ||||
\(782\) | − | 1506.89i | − | 0.0689083i | ||||||
\(783\) | 430.170 | − | 301.361i | 0.0196335 | − | 0.0137545i | ||||
\(784\) | 17168.2 | 0.782080 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2048.34 | + | 59.7635i | −0.0929541 | + | 0.00271208i | ||||
\(787\) | −21834.3 | − | 12606.0i | −0.988957 | − | 0.570974i | −0.0839943 | − | 0.996466i | \(-0.526768\pi\) |
−0.904962 | + | 0.425492i | \(0.860101\pi\) | |||||||
\(788\) | −8553.01 | − | 4938.08i | −0.386660 | − | 0.223238i | ||||
\(789\) | −7685.50 | − | 12457.9i | −0.346782 | − | 0.562120i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11468.2 | 0.515500 | ||||||||
\(792\) | 1985.96 | − | 1306.64i | 0.0891011 | − | 0.0586230i | ||||
\(793\) | − | 20407.0i | − | 0.913838i | ||||||
\(794\) | −623.386 | − | 1079.74i | −0.0278629 | − | 0.0482599i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2058.72 | − | 3565.80i | 0.0916700 | − | 0.158777i | ||||
\(797\) | 33928.2 | + | 19588.5i | 1.50790 | + | 0.870588i | 0.999958 | + | 0.00919851i | \(0.00292802\pi\) |
0.507945 | + | 0.861390i | \(0.330405\pi\) | |||||||
\(798\) | −611.068 | − | 329.422i | −0.0271072 | − | 0.0146133i | ||||
\(799\) | −3451.75 | − | 5978.61i | −0.152834 | − | 0.264716i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40569.9 | − | 2369.40i | 1.78960 | − | 0.104517i | ||||
\(802\) | − | 313.764i | − | 0.0138147i | ||||||
\(803\) | −16610.6 | + | 9590.16i | −0.729983 | + | 0.421456i | ||||
\(804\) | 11818.8 | + | 19157.8i | 0.518430 | + | 0.840353i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −591.631 | + | 1024.74i | −0.0258552 | + | 0.0447826i | ||||
\(807\) | 15.5496 | + | 532.949i | 0.000678279 | + | 0.0232474i | ||||
\(808\) | −1197.87 | + | 691.593i | −0.0521548 | + | 0.0301116i | ||||
\(809\) | 36739.0 | 1.59663 | 0.798316 | − | 0.602239i | \(-0.205725\pi\) | ||||
0.798316 | + | 0.602239i | \(0.205725\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29660.0 | −1.28422 | −0.642111 | − | 0.766611i | \(-0.721941\pi\) | ||||
−0.642111 | + | 0.766611i | \(0.721941\pi\) | |||||||
\(812\) | 218.685 | − | 126.258i | 0.00945115 | − | 0.00545662i | ||||
\(813\) | −505.733 | − | 17333.6i | −0.0218165 | − | 0.747743i | ||||
\(814\) | −171.549 | + | 297.132i | −0.00738674 | + | 0.0127942i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7651.61 | + | 12402.9i | 0.328260 | + | 0.532096i | ||||
\(817\) | −41222.2 | + | 23799.7i | −1.76522 | + | 1.01915i | ||||
\(818\) | − | 549.405i | − | 0.0234835i | ||||||
\(819\) | −6129.80 | + | 357.997i | −0.261529 | + | 0.0152740i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10056.6 | − | 17418.6i | −0.427501 | − | 0.740453i | 0.569149 | − | 0.822234i | \(-0.307273\pi\) |
−0.996650 | + | 0.0817808i | \(0.973939\pi\) | |||||||
\(822\) | −379.137 | − | 204.390i | −0.0160875 | − | 0.00867265i | ||||
\(823\) | −4654.06 | − | 2687.02i | −0.197121 | − | 0.113808i | 0.398191 | − | 0.917303i | \(-0.369638\pi\) |
−0.595312 | + | 0.803495i | \(0.702971\pi\) | |||||||
\(824\) | −880.277 | + | 1524.68i | −0.0372159 | + | 0.0644598i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −365.697 | − | 633.406i | −0.0154046 | − | 0.0266816i | ||||
\(827\) | − | 27865.2i | − | 1.17167i | −0.810432 | − | 0.585833i | \(-0.800767\pi\) | ||
0.810432 | − | 0.585833i | \(-0.199233\pi\) | |||||||
\(828\) | −34918.9 | + | 22974.5i | −1.46560 | + | 0.964273i | ||||
\(829\) | −24363.1 | −1.02070 | −0.510352 | − | 0.859965i | \(-0.670485\pi\) | ||||
−0.510352 | + | 0.859965i | \(0.670485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1729.36 | − | 2803.23i | −0.0721913 | − | 0.117019i | ||||
\(832\) | −11641.4 | − | 6721.15i | −0.485086 | − | 0.280065i | ||||
\(833\) | −10418.1 | − | 6014.91i | −0.433333 | − | 0.250185i | ||||
\(834\) | −124.549 | + | 3.63390i | −0.00517119 | + | 0.000150877i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −22651.4 | −0.937099 | ||||||||
\(837\) | −32003.0 | − | 14914.0i | −1.32161 | − | 0.615892i | ||||
\(838\) | − | 430.007i | − | 0.0177259i | ||||||
\(839\) | −17765.3 | − | 30770.4i | −0.731020 | − | 1.26616i | −0.956448 | − | 0.291903i | \(-0.905711\pi\) |
0.225428 | − | 0.974260i | \(-0.427622\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12187.5 | − | 21109.4i | 0.499713 | − | 0.865528i | ||||
\(842\) | 405.928 | + | 234.363i | 0.0166143 | + | 0.00959226i | ||||
\(843\) | −27429.0 | + | 16921.4i | −1.12065 | + | 0.691347i | ||||
\(844\) | 71.0996 | + | 123.148i | 0.00289970 | + | 0.00502243i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 330.098 | − | 657.540i | 0.0134149 | − | 0.0267219i | ||||
\(847\) | 2862.68i | 0.116131i | ||||||||
\(848\) | −7763.42 | + | 4482.22i | −0.314383 | + | 0.181509i | ||||
\(849\) | −18444.0 | + | 34213.0i | −0.745578 | + | 1.38302i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6044.25 | − | 10468.9i | 0.243471 | − | 0.421705i | ||||
\(852\) | 33833.9 | + | 18239.6i | 1.36048 | + | 0.733426i | ||||
\(853\) | 29832.4 | − | 17223.8i | 1.19747 | − | 0.691360i | 0.237480 | − | 0.971392i | \(-0.423679\pi\) |
0.959991 | + | 0.280032i | \(0.0903452\pi\) | |||||||
\(854\) | −1124.81 | −0.0450705 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4362.05 | −0.174173 | ||||||||
\(857\) | −17326.4 | + | 10003.4i | −0.690618 | + | 0.398729i | −0.803844 | − | 0.594841i | \(-0.797215\pi\) |
0.113225 | + | 0.993569i | \(0.463882\pi\) | |||||||
\(858\) | 655.141 | − | 404.169i | 0.0260678 | − | 0.0160817i | ||||
\(859\) | 893.190 | − | 1547.05i | 0.0354776 | − | 0.0614490i | −0.847741 | − | 0.530410i | \(-0.822038\pi\) |
0.883219 | + | 0.468961i | \(0.155371\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8983.04 | + | 262.094i | −0.355565 | + | 0.0103741i | ||||
\(862\) | −1435.46 | + | 828.764i | −0.0567192 | + | 0.0327469i | ||||
\(863\) | 12151.9i | 0.479322i | 0.970857 | + | 0.239661i | \(0.0770363\pi\) | ||||
−0.970857 | + | 0.239661i | \(0.922964\pi\) | |||||||
\(864\) | −1980.86 | + | 4250.61i | −0.0779978 | + | 0.167371i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −370.811 | − | 642.263i | −0.0145504 | − | 0.0252021i | ||||
\(867\) | 446.711 | + | 15310.7i | 0.0174984 | + | 0.599743i | ||||
\(868\) | −14700.7 | − | 8487.43i | −0.574854 | − | 0.331892i | ||||
\(869\) | −9686.27 | + | 16777.1i | −0.378118 | + | 0.654919i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7303.02 | + | 12649.2i | 0.284102 | + | 0.492080i | ||||
\(872\) | 2615.94i | 0.101591i | ||||||||
\(873\) | −7505.18 | + | 4937.94i | −0.290964 | + | 0.191436i | ||||
\(874\) | −3066.36 | −0.118674 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11961.9 | − | 22189.0i | 0.461366 | − | 0.855819i | ||||
\(877\) | −16344.7 | − | 9436.64i | −0.629330 | − | 0.363344i | 0.151163 | − | 0.988509i | \(-0.451698\pi\) |
−0.780493 | + | 0.625165i | \(0.785032\pi\) | |||||||
\(878\) | 736.328 | + | 425.119i | 0.0283028 | + | 0.0163406i | ||||
\(879\) | −11925.5 | + | 22121.5i | −0.457609 | + | 0.848851i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23587.2 | 0.902014 | 0.451007 | − | 0.892520i | \(-0.351065\pi\) | ||||
0.451007 | + | 0.892520i | \(0.351065\pi\) | |||||||
\(882\) | −74.7502 | − | 1279.91i | −0.00285371 | − | 0.0488625i | ||||
\(883\) | − | 29504.5i | − | 1.12447i | −0.826978 | − | 0.562234i | \(-0.809942\pi\) | ||
0.826978 | − | 0.562234i | \(-0.190058\pi\) | |||||||
\(884\) | 4746.35 | + | 8220.92i | 0.180585 | + | 0.312782i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 204.360 | − | 353.963i | 0.00774901 | − | 0.0134217i | ||||
\(887\) | 2144.31 | + | 1238.02i | 0.0811714 | + | 0.0468643i | 0.540036 | − | 0.841642i | \(-0.318410\pi\) |
−0.458865 | + | 0.888506i | \(0.651744\pi\) | |||||||
\(888\) | −26.3520 | − | 903.192i | −0.000995850 | − | 0.0341319i | ||||
\(889\) | −5003.60 | − | 8666.49i | −0.188769 | − | 0.326957i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13722.3 | + | 18420.0i | 0.515953 | + | 0.692586i | ||||
\(892\) | 7886.13i | 0.296017i | ||||||||
\(893\) | −12165.8 | + | 7023.94i | −0.455894 | + | 0.263211i | ||||
\(894\) | −130.068 | + | 3.79492i | −0.00486589 | + | 0.000141970i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1502.09 | + | 2601.69i | −0.0560058 | + | 0.0970048i | ||||
\(897\) | −23082.8 | + | 14240.2i | −0.859210 | + | 0.530063i | ||||
\(898\) | −2014.06 | + | 1162.82i | −0.0748440 | + | 0.0432112i | ||||
\(899\) | 942.157 | 0.0349529 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6281.40 | 0.232257 | ||||||||
\(902\) | 975.709 | − | 563.326i | 0.0360173 | − | 0.0207946i | ||||
\(903\) | 20426.7 | + | 11011.9i | 0.752778 | + | 0.405817i | ||||
\(904\) | 1893.17 | − | 3279.07i | 0.0696527 | − | 0.120642i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 93.5595 | − | 173.550i | 0.00343080 | − | 0.00636403i | ||||
\(907\) | 23167.1 | − | 13375.5i | 0.848126 | − | 0.489666i | −0.0118922 | − | 0.999929i | \(-0.503785\pi\) |
0.860018 | + | 0.510264i | \(0.170452\pi\) | |||||||
\(908\) | 27312.1i | 0.998221i | ||||||||
\(909\) | −7345.75 | − | 11164.8i | −0.268034 | − | 0.407385i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6334.11 | − | 10971.0i | −0.230360 | − | 0.398996i | 0.727554 | − | 0.686051i | \(-0.240657\pi\) |
−0.957914 | + | 0.287055i | \(0.907324\pi\) | |||||||
\(912\) | 25238.7 | − | 15570.2i | 0.916377 | − | 0.565330i | ||||
\(913\) | 29341.9 | + | 16940.6i | 1.06361 | + | 0.614076i | ||||
\(914\) | −452.739 | + | 784.167i | −0.0163843 | + | 0.0283785i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4381.61 | + | 7589.16i | 0.158048 | + | 0.273748i | ||||
\(917\) | − | 19075.1i | − | 0.686930i | ||||||
\(918\) | 891.337 | − | 624.437i | 0.0320463 | − | 0.0224504i | ||||
\(919\) | −46565.5 | −1.67144 | −0.835721 | − | 0.549155i | \(-0.814950\pi\) | ||||
−0.835721 | + | 0.549155i | \(0.814950\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29147.7 | + | 850.427i | −1.04283 | + | 0.0304262i | ||||
\(922\) | −960.905 | − | 554.779i | −0.0343229 | − | 0.0198163i | ||||
\(923\) | 21599.1 | + | 12470.3i | 0.770253 | + | 0.444706i | ||||
\(924\) | 5798.13 | + | 9398.53i | 0.206433 | + | 0.334620i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −556.940 | −0.0197648 | ||||||||
\(927\) | −15202.6 | − | 7632.03i | −0.538641 | − | 0.270408i | ||||
\(928\) | − | 125.136i | − | 0.00442651i | ||||||
\(929\) | 2305.46 | + | 3993.17i | 0.0814205 | + | 0.141024i | 0.903860 | − | 0.427828i | \(-0.140721\pi\) |
−0.822440 | + | 0.568852i | \(0.807388\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12239.7 | + | 21199.8i | −0.430870 | + | 0.746289i | ||||
\(932\) | −30780.9 | − | 17771.4i | −1.08183 | − | 0.624593i | ||||
\(933\) | −49952.9 | − | 26929.3i | −1.75283 | − | 0.944935i | ||||
\(934\) | 750.354 | + | 1299.65i | 0.0262873 | + | 0.0455309i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −909.551 | + | 1811.78i | −0.0317624 | + | 0.0632692i | ||||
\(937\) | 6625.43i | 0.230996i | 0.993308 | + | 0.115498i | \(0.0368464\pi\) | ||||
−0.993308 | + | 0.115498i | \(0.963154\pi\) | |||||||
\(938\) | 697.209 | − | 402.534i | 0.0242694 | − | 0.0140119i | ||||
\(939\) | 13588.5 | + | 22026.4i | 0.472250 | + | 0.765498i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21721.3 | − | 37622.4i | 0.752491 | − | 1.30335i | −0.194121 | − | 0.980978i | \(-0.562185\pi\) |
0.946612 | − | 0.322375i | \(-0.104481\pi\) | |||||||
\(942\) | 35.7568 | + | 1225.53i | 0.00123675 | + | 0.0423886i | ||||
\(943\) | −34377.4 | + | 19847.8i | −1.18715 | + | 0.685402i | ||||
\(944\) | 31243.7 | 1.07722 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2909.24 | −0.0999868 | ||||||||
\(947\) | −28511.7 | + | 16461.2i | −0.978357 | + | 0.564855i | −0.901774 | − | 0.432208i | \(-0.857735\pi\) |
−0.0765835 | + | 0.997063i | \(0.524401\pi\) | |||||||
\(948\) | −742.536 | − | 25449.8i | −0.0254393 | − | 0.871909i | ||||
\(949\) | 8178.28 | − | 14165.2i | 0.279745 | − | 0.484533i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10247.5 | + | 16610.8i | 0.349419 | + | 0.566394i | ||||
\(952\) | 907.996 | − | 524.232i | 0.0309121 | − | 0.0178471i | ||||
\(953\) | 20253.5i | 0.688430i | 0.938891 | + | 0.344215i | \(0.111855\pi\) | ||||
−0.938891 | + | 0.344215i | \(0.888145\pi\) | |||||||
\(954\) | 367.955 | + | 559.255i | 0.0124874 | + | 0.0189796i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 26077.6 | + | 45167.8i | 0.882229 | + | 1.52806i | ||||
\(957\) | −539.522 | − | 290.853i | −0.0182239 | − | 0.00982437i | ||||
\(958\) | 442.144 | + | 255.272i | 0.0149113 | + | 0.00860904i | ||||
\(959\) | 2004.68 | − | 3472.20i | 0.0675020 | − | 0.116917i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16771.8 | − | 29049.7i | −0.562983 | − | 0.975116i | ||||
\(962\) | − | 292.587i | − | 0.00980602i | ||||||
\(963\) | −2457.31 | − | 42075.3i | −0.0822282 | − | 1.40795i | ||||
\(964\) | −1676.16 | −0.0560015 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 784.903 | + | 1272.30i | 0.0261427 | + | 0.0423762i | ||||
\(967\) | 2803.43 | + | 1618.56i | 0.0932289 | + | 0.0538257i | 0.545890 | − | 0.837857i | \(-0.316192\pi\) |
−0.452661 | + | 0.891683i | \(0.649525\pi\) | |||||||
\(968\) | 818.521 | + | 472.573i | 0.0271780 | + | 0.0156912i | ||||
\(969\) | −20770.5 | + | 606.012i | −0.688592 | + | 0.0200907i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1731.06 | −0.0572114 | −0.0286057 | − | 0.999591i | \(-0.509107\pi\) | ||||
−0.0286057 | + | 0.999591i | \(0.509107\pi\) | |||||||
\(972\) | −28059.5 | − | 11134.4i | −0.925936 | − | 0.367425i | ||||
\(973\) | − | 1159.86i | − | 0.0382151i | ||||||
\(974\) | 1230.23 | + | 2130.81i | 0.0404712 | + | 0.0700982i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24024.8 | − | 41612.1i | 0.787924 | − | 1.36472i | ||||
\(977\) | 29918.5 | + | 17273.4i | 0.979710 | + | 0.565636i | 0.902183 | − | 0.431354i | \(-0.141964\pi\) |
0.0775275 | + | 0.996990i | \(0.475297\pi\) | |||||||
\(978\) | −804.674 | + | 496.418i | −0.0263094 | + | 0.0162308i | ||||
\(979\) | −23712.3 | − | 41071.0i | −0.774106 | − | 1.34079i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25232.8 | + | 1473.66i | −0.821224 | + | 0.0479617i | ||||
\(982\) | − | 163.201i | − | 0.00530343i | ||||||
\(983\) | 17713.0 | − | 10226.6i | 0.574726 | − | 0.331818i | −0.184309 | − | 0.982868i | \(-0.559005\pi\) |
0.759035 | + | 0.651050i | \(0.225671\pi\) | |||||||
\(984\) | −1407.99 | + | 2611.78i | −0.0456149 | + | 0.0846142i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −14.5203 | + | 25.1500i | −0.000468987 | + | 0.000812310i | ||||
\(987\) | 6028.49 | + | 3249.91i | 0.194416 | + | 0.104808i | ||||
\(988\) | 16728.7 | − | 9658.31i | 0.538675 | − | 0.311004i | ||||
\(989\) | 102502. | 3.29563 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5387.77 | −0.172703 | −0.0863513 | − | 0.996265i | \(-0.527521\pi\) | ||||
−0.0863513 | + | 0.996265i | \(0.527521\pi\) | |||||||
\(992\) | −7285.05 | + | 4206.03i | −0.233166 | + | 0.134618i | ||||
\(993\) | −4010.84 | + | 2474.36i | −0.128177 | + | 0.0790750i | ||||
\(994\) | 687.347 | − | 1190.52i | 0.0219329 | − | 0.0379889i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −44509.8 | + | 1298.64i | −1.41601 | + | 0.0413142i | ||||
\(997\) | 18918.2 | − | 10922.4i | 0.600949 | − | 0.346958i | −0.168466 | − | 0.985707i | \(-0.553881\pi\) |
0.769415 | + | 0.638750i | \(0.220548\pi\) | |||||||
\(998\) | 2525.16i | 0.0800929i | ||||||||
\(999\) | 8697.13 | − | 762.988i | 0.275440 | − | 0.0241640i |
(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.k.c.49.4 | 12 | ||
5.2 | odd | 4 | 45.4.e.b.31.2 | yes | 6 | ||
5.3 | odd | 4 | 225.4.e.c.76.2 | 6 | |||
5.4 | even | 2 | inner | 225.4.k.c.49.3 | 12 | ||
9.7 | even | 3 | inner | 225.4.k.c.124.3 | 12 | ||
15.2 | even | 4 | 135.4.e.b.91.2 | 6 | |||
45.2 | even | 12 | 135.4.e.b.46.2 | 6 | |||
45.7 | odd | 12 | 45.4.e.b.16.2 | ✓ | 6 | ||
45.13 | odd | 12 | 2025.4.a.s.1.2 | 3 | |||
45.22 | odd | 12 | 405.4.a.h.1.2 | 3 | |||
45.23 | even | 12 | 2025.4.a.q.1.2 | 3 | |||
45.32 | even | 12 | 405.4.a.j.1.2 | 3 | |||
45.34 | even | 6 | inner | 225.4.k.c.124.4 | 12 | ||
45.43 | odd | 12 | 225.4.e.c.151.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.b.16.2 | ✓ | 6 | 45.7 | odd | 12 | ||
45.4.e.b.31.2 | yes | 6 | 5.2 | odd | 4 | ||
135.4.e.b.46.2 | 6 | 45.2 | even | 12 | |||
135.4.e.b.91.2 | 6 | 15.2 | even | 4 | |||
225.4.e.c.76.2 | 6 | 5.3 | odd | 4 | |||
225.4.e.c.151.2 | 6 | 45.43 | odd | 12 | |||
225.4.k.c.49.3 | 12 | 5.4 | even | 2 | inner | ||
225.4.k.c.49.4 | 12 | 1.1 | even | 1 | trivial | ||
225.4.k.c.124.3 | 12 | 9.7 | even | 3 | inner | ||
225.4.k.c.124.4 | 12 | 45.34 | even | 6 | inner | ||
405.4.a.h.1.2 | 3 | 45.22 | odd | 12 | |||
405.4.a.j.1.2 | 3 | 45.32 | even | 12 | |||
2025.4.a.q.1.2 | 3 | 45.23 | even | 12 | |||
2025.4.a.s.1.2 | 3 | 45.13 | odd | 12 |