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 | 49.3 | ||
Root | \(1.98116 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.49 |
Dual form | 225.4.k.c.124.3 |
$q$-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 | −0.526550 | − | 0.850144i | \(-0.676515\pi\) |
0.472972 | + | 0.881078i | \(0.343181\pi\) | |||||||
\(3\) | −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 | −0.288886 | − | 0.957363i | \(-0.593285\pi\) |
0.684658 | + | 0.728865i | \(0.259952\pi\) | |||||||
\(8\) | − | 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 | 0.727247 | − | 0.686376i | \(-0.240800\pi\) |
−0.230796 | + | 0.973002i | \(0.574133\pi\) | |||||||
\(14\) | −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 | \(-0.897583\pi\) | ||
0.948683 | − | 0.316229i | \(-0.102417\pi\) | |||||||
\(18\) | 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 | \(0.00949548\pi\) |
0.525608 | + | 0.850727i | \(0.323838\pi\) | |||||||
\(24\) | −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 | \(-0.955853\pi\) | ||
0.990397 | − | 0.138249i | \(-0.0441475\pi\) | |||||||
\(38\) | −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 | \(-0.281464\pi\) |
0.986752 | − | 0.162233i | \(-0.0518696\pi\) | |||||||
\(44\) | −251.101 | −0.860340 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −33.9920 | −0.108953 | ||||||||
\(47\) | 134.864 | − | 77.8637i | 0.418551 | − | 0.241651i | −0.275906 | − | 0.961185i | \(-0.588978\pi\) |
0.694457 | + | 0.719534i | \(0.255645\pi\) | |||||||
\(48\) | −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 | \(0.0587800\pi\) | ||||
−0.982998 | + | 0.183615i | \(0.941220\pi\) | |||||||
\(54\) | −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 | 0.863476 | − | 0.504389i | \(-0.168282\pi\) |
−0.00507574 | + | 0.999987i | \(0.501616\pi\) | |||||||
\(68\) | 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 | \(-0.837728\pi\) | ||
0.872845 | − | 0.487997i | \(-0.162272\pi\) | |||||||
\(74\) | 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 | −0.967350 | − | 0.253444i | \(-0.918437\pi\) |
−0.264186 | + | 0.964472i | \(0.585103\pi\) | |||||||
\(84\) | 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 | −0.643175 | − | 0.765719i | \(-0.722383\pi\) |
0.341544 | + | 0.939866i | \(0.389050\pi\) | |||||||
\(98\) | − | 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 | 0.215777 | − | 0.976443i | \(-0.430772\pi\) |
−0.737736 | + | 0.675090i | \(0.764105\pi\) | |||||||
\(104\) | 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 | \(-0.750869\pi\) | ||
0.709034 | − | 0.705175i | \(-0.249131\pi\) | |||||||
\(108\) | −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 | 0.901330 | − | 0.433134i | \(-0.142592\pi\) |
0.0755602 | + | 0.997141i | \(0.475925\pi\) | |||||||
\(114\) | 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 | \(-0.864459\pi\) | ||
0.910702 | − | 0.413063i | \(-0.135541\pi\) | |||||||
\(128\) | −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 | −0.366597 | − | 0.930380i | \(-0.619477\pi\) |
0.622434 | + | 0.782672i | \(0.286144\pi\) | |||||||
\(138\) | 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 | 0.172906 | − | 0.984938i | \(-0.444684\pi\) |
−0.766528 | + | 0.642211i | \(0.778017\pi\) | |||||||
\(158\) | −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 | \(-0.919623\pi\) | ||
0.968288 | − | 0.249838i | \(-0.0803774\pi\) | |||||||
\(164\) | 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 | 0.986077 | − | 0.166291i | \(-0.0531792\pi\) |
0.349026 | + | 0.937113i | \(0.386513\pi\) | |||||||
\(168\) | −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 | −0.255214 | − | 0.966885i | \(-0.582146\pi\) |
0.709740 | + | 0.704464i | \(0.248813\pi\) | |||||||
\(174\) | −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 | 0.947903 | − | 0.318559i | \(-0.103199\pi\) |
0.198072 | + | 0.980188i | \(0.436532\pi\) | |||||||
\(194\) | 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 | \(-0.928057\pi\) | ||
0.974567 | − | 0.224096i | \(-0.0719430\pi\) | |||||||
\(198\) | 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 | −0.623122 | − | 0.782125i | \(-0.714136\pi\) |
0.365779 | + | 0.930702i | \(0.380803\pi\) | |||||||
\(224\) | 282.906 | 0.0843860 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −237.101 | −0.0697863 | ||||||||
\(227\) | −2967.98 | + | 1713.57i | −0.867806 | + | 0.501028i | −0.866619 | − | 0.498971i | \(-0.833711\pi\) |
−0.00118754 | + | 0.999999i | \(0.500378\pi\) | |||||||
\(228\) | 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 | \(-0.784285\pi\) | ||
0.779025 | − | 0.626993i | \(-0.215715\pi\) | |||||||
\(234\) | 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 | 0.869676 | − | 0.493623i | \(-0.164328\pi\) |
0.00734758 | + | 0.999973i | \(0.497661\pi\) | |||||||
\(258\) | 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 | −0.185951 | − | 0.982559i | \(-0.559537\pi\) |
0.757945 | + | 0.652318i | \(0.226203\pi\) | |||||||
\(264\) | −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 | −0.439280 | − | 0.898350i | \(-0.644766\pi\) |
0.558354 | + | 0.829603i | \(0.311433\pi\) | |||||||
\(278\) | − | 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 | −0.370976 | − | 0.928642i | \(-0.620977\pi\) |
−0.989716 | + | 0.143047i | \(0.954310\pi\) | |||||||
\(284\) | 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 | 0.0204666 | − | 0.999791i | \(-0.493485\pi\) |
−0.855611 | + | 0.517620i | \(0.826818\pi\) | |||||||
\(294\) | −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 | \(-0.825321\pi\) | ||
0.853167 | − | 0.521638i | \(-0.174679\pi\) | |||||||
\(308\) | −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 | −0.836056 | − | 0.548643i | \(-0.815144\pi\) |
0.0571109 | + | 0.998368i | \(0.481811\pi\) | |||||||
\(314\) | 235.955 | 0.0424067 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4899.89 | −0.872280 | ||||||||
\(317\) | −3252.90 | + | 1878.06i | −0.576344 | + | 0.332752i | −0.759679 | − | 0.650298i | \(-0.774644\pi\) |
0.183335 | + | 0.983050i | \(0.441311\pi\) | |||||||
\(318\) | −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 | −0.390383 | − | 0.920653i | \(-0.627657\pi\) |
−0.992500 | + | 0.122245i | \(0.960991\pi\) | |||||||
\(338\) | 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 | 0.716335 | − | 0.697757i | \(-0.245818\pi\) |
−0.246107 | + | 0.969243i | \(0.579152\pi\) | |||||||
\(348\) | 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 | −0.924259 | − | 0.381765i | \(-0.875316\pi\) |
−0.131512 | + | 0.991315i | \(0.541983\pi\) | |||||||
\(354\) | −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 | −0.938295 | − | 0.345836i | \(-0.887595\pi\) |
−0.169645 | + | 0.985505i | \(0.554262\pi\) | |||||||
\(368\) | − | 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 | 0.443064 | − | 0.896490i | \(-0.353891\pi\) |
−0.554851 | + | 0.831950i | \(0.687225\pi\) | |||||||
\(374\) | −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 | 0.158278 | − | 0.987395i | \(-0.449406\pi\) |
−0.775970 | + | 0.630770i | \(0.782739\pi\) | |||||||
\(384\) | 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 | \(0.148709\pi\) | ||||
−0.892841 | + | 0.450372i | \(0.851291\pi\) | |||||||
\(398\) | 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 | \(0.0755715\pi\) | ||||
−0.971949 | + | 0.235191i | \(0.924428\pi\) | |||||||
\(434\) | 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 | −0.604535 | − | 0.796578i | \(-0.706641\pi\) |
0.387589 | + | 0.921832i | \(0.373308\pi\) | |||||||
\(444\) | 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 | −0.252794 | − | 0.967520i | \(-0.581350\pi\) |
0.711500 | + | 0.702686i | \(0.248016\pi\) | |||||||
\(458\) | 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 | 0.631916 | − | 0.775036i | \(-0.282269\pi\) |
−0.355243 | + | 0.934774i | \(0.615602\pi\) | |||||||
\(464\) | 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 | \(-0.860308\pi\) | ||
0.905238 | − | 0.424904i | \(-0.139692\pi\) | |||||||
\(468\) | 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 | \(-0.773017\pi\) | ||
0.756346 | − | 0.654172i | \(-0.226983\pi\) | |||||||
\(488\) | 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 | \(0.0457341\pi\) | ||||
−0.989696 | + | 0.143184i | \(0.954266\pi\) | |||||||
\(504\) | 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 | \(-0.717362\pi\) | ||
0.631015 | − | 0.775770i | \(-0.282638\pi\) | |||||||
\(524\) | −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 | −0.290745 | − | 0.956801i | \(-0.593903\pi\) |
0.683241 | + | 0.730193i | \(0.260570\pi\) | |||||||
\(548\) | 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 | \(0.204311\pi\) | ||||
−0.800982 | + | 0.598688i | \(0.795689\pi\) | |||||||
\(558\) | −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 | 0.618660 | − | 0.785659i | \(-0.287676\pi\) |
−0.371071 | + | 0.928605i | \(0.621009\pi\) | |||||||
\(564\) | 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 | \(0.209021\pi\) | ||||
−0.792037 | + | 0.610473i | \(0.790979\pi\) | |||||||
\(578\) | −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 | 0.0417777 | − | 0.999127i | \(-0.486698\pi\) |
0.886158 | + | 0.463383i | \(0.153365\pi\) | |||||||
\(588\) | −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 | \(0.199787\pi\) | ||||
−0.809409 | + | 0.587245i | \(0.800213\pi\) | |||||||
\(594\) | 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 | \(-0.952919\pi\) |
−0.622166 | − | 0.782885i | \(-0.713747\pi\) | |||||||
\(608\) | 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 | \(-0.770546\pi\) | ||
0.751244 | − | 0.660024i | \(-0.229454\pi\) | |||||||
\(614\) | 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 | 0.271155 | − | 0.962536i | \(-0.412595\pi\) |
−0.698003 | + | 0.716095i | \(0.745928\pi\) | |||||||
\(618\) | −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 | 0.641642 | − | 0.767004i | \(-0.278253\pi\) |
−0.343424 | + | 0.939180i | \(0.611587\pi\) | |||||||
\(644\) | −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 | \(-0.883768\pi\) | ||
0.934068 | − | 0.357094i | \(-0.116232\pi\) | |||||||
\(648\) | −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 | −0.354916 | − | 0.934898i | \(-0.615491\pi\) |
−0.987104 | + | 0.160082i | \(0.948824\pi\) | |||||||
\(654\) | 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 | −0.342343 | − | 0.939575i | \(-0.611220\pi\) |
0.642524 | + | 0.766265i | \(0.277887\pi\) | |||||||
\(674\) | 1728.62 | 0.0987892 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11755.0 | 0.668812 | ||||||||
\(677\) | 24334.1 | − | 14049.3i | 1.38144 | − | 0.797576i | 0.389112 | − | 0.921190i | \(-0.372782\pi\) |
0.992330 | + | 0.123614i | \(0.0394485\pi\) | |||||||
\(678\) | 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 | \(0.0750169\pi\) | ||||
−0.972358 | + | 0.233497i | \(0.924983\pi\) | |||||||
\(684\) | 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 | −0.371039 | − | 0.928617i | \(-0.620998\pi\) |
0.618687 | + | 0.785638i | \(0.287665\pi\) | |||||||
\(728\) | − | 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 | 0.788877 | − | 0.614552i | \(-0.210663\pi\) |
−0.137779 | + | 0.990463i | \(0.543996\pi\) | |||||||
\(734\) | 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 | −0.127014 | − | 0.991901i | \(-0.540539\pi\) |
−0.922518 | + | 0.385953i | \(0.873873\pi\) | |||||||
\(744\) | −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 | \(-0.857335\pi\) | ||
0.901230 | − | 0.433341i | \(-0.142665\pi\) | |||||||
\(758\) | 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 | \(0.217644\pi\) | ||||
−0.775211 | + | 0.631703i | \(0.782356\pi\) | |||||||
\(774\) | 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 | 0.904962 | − | 0.425492i | \(-0.139899\pi\) |
0.0839943 | + | 0.996466i | \(0.473232\pi\) | |||||||
\(788\) | 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 | \(-0.997072\pi\) |
−0.507945 | − | 0.861390i | \(-0.669595\pi\) | |||||||
\(798\) | 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 | 0.595312 | − | 0.803495i | \(-0.297029\pi\) |
−0.398191 | + | 0.917303i | \(0.630362\pi\) | |||||||
\(824\) | −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 | \(0.199233\pi\) | ||||
−0.810432 | + | 0.585833i | \(0.800767\pi\) | |||||||
\(828\) | 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 | −0.959991 | − | 0.280032i | \(-0.909655\pi\) |
−0.237480 | + | 0.971392i | \(0.576321\pi\) | |||||||
\(854\) | −1124.81 | −0.0450705 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4362.05 | −0.174173 | ||||||||
\(857\) | 17326.4 | − | 10003.4i | 0.690618 | − | 0.398729i | −0.113225 | − | 0.993569i | \(-0.536118\pi\) |
0.803844 | + | 0.594841i | \(0.202785\pi\) | |||||||
\(858\) | −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 | \(-0.922964\pi\) | ||
0.970857 | − | 0.239661i | \(-0.0770363\pi\) | |||||||
\(864\) | −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 | 0.780493 | − | 0.625165i | \(-0.214968\pi\) |
−0.151163 | + | 0.988509i | \(0.548302\pi\) | |||||||
\(878\) | −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 | \(0.190058\pi\) | ||||
−0.826978 | + | 0.562234i | \(0.809942\pi\) | |||||||
\(884\) | 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 | 0.458865 | − | 0.888506i | \(-0.348256\pi\) |
−0.540036 | + | 0.841642i | \(0.681590\pi\) | |||||||
\(888\) | 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 | −0.860018 | − | 0.510264i | \(-0.829548\pi\) |
0.0118922 | + | 0.999929i | \(0.496215\pi\) | |||||||
\(908\) | − | 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 | \(-0.963154\pi\) | ||
0.993308 | − | 0.115498i | \(-0.0368464\pi\) | |||||||
\(938\) | −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 | 0.0765835 | − | 0.997063i | \(-0.475599\pi\) |
0.901774 | + | 0.432208i | \(0.142265\pi\) | |||||||
\(948\) | 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 | \(-0.888145\pi\) | ||
0.938891 | − | 0.344215i | \(-0.111855\pi\) | |||||||
\(954\) | 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 | 0.452661 | − | 0.891683i | \(-0.350475\pi\) |
−0.545890 | + | 0.837857i | \(0.683808\pi\) | |||||||
\(968\) | −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 | −0.0775275 | − | 0.996990i | \(-0.524703\pi\) |
−0.902183 | + | 0.431354i | \(0.858036\pi\) | |||||||
\(978\) | 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 | −0.759035 | − | 0.651050i | \(-0.774329\pi\) |
0.184309 | + | 0.982868i | \(0.440995\pi\) | |||||||
\(984\) | −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 | −0.769415 | − | 0.638750i | \(-0.779452\pi\) |
0.168466 | + | 0.985707i | \(0.446119\pi\) | |||||||
\(998\) | − | 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.49.3 | 12 | ||
5.2 | odd | 4 | 225.4.e.c.76.2 | 6 | |||
5.3 | odd | 4 | 45.4.e.b.31.2 | yes | 6 | ||
5.4 | even | 2 | inner | 225.4.k.c.49.4 | 12 | ||
9.7 | even | 3 | inner | 225.4.k.c.124.4 | 12 | ||
15.8 | even | 4 | 135.4.e.b.91.2 | 6 | |||
45.7 | odd | 12 | 225.4.e.c.151.2 | 6 | |||
45.13 | odd | 12 | 405.4.a.h.1.2 | 3 | |||
45.22 | odd | 12 | 2025.4.a.s.1.2 | 3 | |||
45.23 | even | 12 | 405.4.a.j.1.2 | 3 | |||
45.32 | even | 12 | 2025.4.a.q.1.2 | 3 | |||
45.34 | even | 6 | inner | 225.4.k.c.124.3 | 12 | ||
45.38 | even | 12 | 135.4.e.b.46.2 | 6 | |||
45.43 | odd | 12 | 45.4.e.b.16.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.b.16.2 | ✓ | 6 | 45.43 | odd | 12 | ||
45.4.e.b.31.2 | yes | 6 | 5.3 | odd | 4 | ||
135.4.e.b.46.2 | 6 | 45.38 | even | 12 | |||
135.4.e.b.91.2 | 6 | 15.8 | even | 4 | |||
225.4.e.c.76.2 | 6 | 5.2 | odd | 4 | |||
225.4.e.c.151.2 | 6 | 45.7 | odd | 12 | |||
225.4.k.c.49.3 | 12 | 1.1 | even | 1 | trivial | ||
225.4.k.c.49.4 | 12 | 5.4 | even | 2 | inner | ||
225.4.k.c.124.3 | 12 | 45.34 | even | 6 | inner | ||
225.4.k.c.124.4 | 12 | 9.7 | even | 3 | inner | ||
405.4.a.h.1.2 | 3 | 45.13 | odd | 12 | |||
405.4.a.j.1.2 | 3 | 45.23 | even | 12 | |||
2025.4.a.q.1.2 | 3 | 45.32 | even | 12 | |||
2025.4.a.s.1.2 | 3 | 45.22 | odd | 12 |