Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(55,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.55");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.g (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.90322347067\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 29x^{6} + 2x^{5} + 595x^{4} - 288x^{3} + 2526x^{2} + 1872x + 6084 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 55.2 | ||
Root | \(-0.733051 - 1.26968i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.55 |
Dual form | 117.4.g.e.100.2 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.733051 | − | 1.26968i | −0.259173 | − | 0.448900i | 0.706848 | − | 0.707366i | \(-0.250117\pi\) |
−0.966021 | + | 0.258465i | \(0.916783\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.92527 | − | 5.06672i | 0.365659 | − | 0.633340i | ||||
\(5\) | −9.85055 | −0.881060 | −0.440530 | − | 0.897738i | \(-0.645209\pi\) | ||||
−0.440530 | + | 0.897738i | \(0.645209\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −14.9698 | + | 25.9285i | −0.808293 | + | 1.40001i | 0.105752 | + | 0.994393i | \(0.466275\pi\) |
−0.914045 | + | 0.405613i | \(0.867058\pi\) | |||||||
\(8\) | −20.3063 | −0.897421 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.22095 | + | 12.5071i | 0.228347 | + | 0.395508i | ||||
\(11\) | 23.4629 | + | 40.6389i | 0.643120 | + | 1.11392i | 0.984732 | + | 0.174076i | \(0.0556938\pi\) |
−0.341612 | + | 0.939841i | \(0.610973\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.71050 | − | 46.7251i | 0.0791621 | − | 0.996862i | ||||
\(14\) | 43.8945 | 0.837950 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.51663 | − | 14.7512i | −0.133072 | − | 0.230488i | ||||
\(17\) | −24.1308 | + | 41.7958i | −0.344270 | + | 0.596292i | −0.985221 | − | 0.171289i | \(-0.945207\pi\) |
0.640951 | + | 0.767582i | \(0.278540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −60.1501 | + | 104.183i | −0.726283 | + | 1.25796i | 0.232161 | + | 0.972677i | \(0.425421\pi\) |
−0.958444 | + | 0.285282i | \(0.907913\pi\) | |||||||
\(20\) | −28.8155 | + | 49.9100i | −0.322167 | + | 0.558010i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 34.3990 | − | 59.5807i | 0.333358 | − | 0.577393i | ||||
\(23\) | 65.3485 | + | 113.187i | 0.592440 | + | 1.02614i | 0.993903 | + | 0.110260i | \(0.0351685\pi\) |
−0.401463 | + | 0.915875i | \(0.631498\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −27.9667 | −0.223734 | ||||||||
\(26\) | −62.0459 | + | 29.5407i | −0.468008 | + | 0.222823i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 87.5815 | + | 151.696i | 0.591120 | + | 1.02385i | ||||
\(29\) | −97.4729 | − | 168.828i | −0.624147 | − | 1.08105i | −0.988705 | − | 0.149874i | \(-0.952113\pi\) |
0.364558 | − | 0.931181i | \(-0.381220\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −32.0123 | −0.185470 | −0.0927351 | − | 0.995691i | \(-0.529561\pi\) | ||||
−0.0927351 | + | 0.995691i | \(0.529561\pi\) | |||||||
\(32\) | −93.7115 | + | 162.313i | −0.517688 | + | 0.896661i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 70.7565 | 0.356901 | ||||||||
\(35\) | 147.461 | − | 255.409i | 0.712155 | − | 1.23349i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16.2125 | + | 28.0808i | 0.0720355 | + | 0.124769i | 0.899793 | − | 0.436316i | \(-0.143717\pi\) |
−0.827758 | + | 0.561086i | \(0.810384\pi\) | |||||||
\(38\) | 176.372 | 0.752931 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 200.028 | 0.790681 | ||||||||
\(41\) | −120.913 | − | 209.427i | −0.460570 | − | 0.797731i | 0.538419 | − | 0.842677i | \(-0.319022\pi\) |
−0.998989 | + | 0.0449461i | \(0.985688\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −48.2044 | + | 83.4924i | −0.170956 | + | 0.296104i | −0.938754 | − | 0.344587i | \(-0.888019\pi\) |
0.767799 | + | 0.640691i | \(0.221352\pi\) | |||||||
\(44\) | 274.541 | 0.940651 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 95.8076 | − | 165.944i | 0.307088 | − | 0.531892i | ||||
\(47\) | −539.015 | −1.67284 | −0.836419 | − | 0.548090i | \(-0.815355\pi\) | ||||
−0.836419 | + | 0.548090i | \(0.815355\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −276.690 | − | 479.241i | −0.806676 | − | 1.39720i | ||||
\(50\) | 20.5010 | + | 35.5088i | 0.0579857 | + | 0.100434i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −225.889 | − | 155.484i | −0.602406 | − | 0.414648i | ||||
\(53\) | 152.277 | 0.394657 | 0.197328 | − | 0.980337i | \(-0.436774\pi\) | ||||
0.197328 | + | 0.980337i | \(0.436774\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −231.122 | − | 400.315i | −0.566627 | − | 0.981427i | ||||
\(56\) | 303.981 | − | 526.511i | 0.725379 | − | 1.25639i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −142.905 | + | 247.519i | −0.323524 | + | 0.560359i | ||||
\(59\) | 163.896 | − | 283.876i | 0.361652 | − | 0.626399i | −0.626581 | − | 0.779356i | \(-0.715546\pi\) |
0.988233 | + | 0.152957i | \(0.0488796\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 49.2090 | − | 85.2325i | 0.103288 | − | 0.178900i | −0.809749 | − | 0.586776i | \(-0.800397\pi\) |
0.913037 | + | 0.407876i | \(0.133730\pi\) | |||||||
\(62\) | 23.4666 | + | 40.6454i | 0.0480688 | + | 0.0832576i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 138.515 | 0.270537 | ||||||||
\(65\) | −36.5504 | + | 460.267i | −0.0697465 | + | 0.878295i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 220.575 | + | 382.048i | 0.402202 | + | 0.696635i | 0.993991 | − | 0.109458i | \(-0.0349115\pi\) |
−0.591789 | + | 0.806093i | \(0.701578\pi\) | |||||||
\(68\) | 141.178 | + | 244.528i | 0.251771 | + | 0.436080i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −432.385 | −0.738284 | ||||||||
\(71\) | 172.524 | − | 298.821i | 0.288379 | − | 0.499486i | −0.685044 | − | 0.728501i | \(-0.740217\pi\) |
0.973423 | + | 0.229015i | \(0.0735505\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 773.839 | 1.24070 | 0.620349 | − | 0.784326i | \(-0.286991\pi\) | ||||
0.620349 | + | 0.784326i | \(0.286991\pi\) | |||||||
\(74\) | 23.7691 | − | 41.1694i | 0.0373393 | − | 0.0646735i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 351.911 | + | 609.528i | 0.531144 | + | 0.919969i | ||||
\(77\) | −1404.94 | −2.07932 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −150.332 | −0.214097 | −0.107049 | − | 0.994254i | \(-0.534140\pi\) | ||||
−0.107049 | + | 0.994254i | \(0.534140\pi\) | |||||||
\(80\) | 83.8934 | + | 145.308i | 0.117245 | + | 0.203074i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −177.270 | + | 307.041i | −0.238734 | + | 0.413500i | ||||
\(83\) | −337.966 | −0.446947 | −0.223473 | − | 0.974710i | \(-0.571740\pi\) | ||||
−0.223473 | + | 0.974710i | \(0.571740\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 237.702 | − | 411.711i | 0.303322 | − | 0.525369i | ||||
\(86\) | 141.345 | 0.177228 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −476.444 | − | 825.226i | −0.577149 | − | 0.999652i | ||||
\(89\) | 84.9567 | + | 147.149i | 0.101184 | + | 0.175256i | 0.912173 | − | 0.409806i | \(-0.134404\pi\) |
−0.810989 | + | 0.585062i | \(0.801070\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1155.96 | + | 795.673i | 1.33163 | + | 0.916584i | ||||
\(92\) | 764.649 | 0.866524 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 395.125 | + | 684.377i | 0.433554 | + | 0.750937i | ||||
\(95\) | 592.511 | − | 1026.26i | 0.639899 | − | 1.10834i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −107.101 | + | 185.504i | −0.112107 | + | 0.194176i | −0.916620 | − | 0.399760i | \(-0.869093\pi\) |
0.804512 | + | 0.593936i | \(0.202427\pi\) | |||||||
\(98\) | −405.656 | + | 702.616i | −0.418137 | + | 0.724234i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −81.8104 | + | 141.700i | −0.0818104 | + | 0.141700i | ||||
\(101\) | 797.556 | + | 1381.41i | 0.785741 | + | 1.36094i | 0.928555 | + | 0.371194i | \(0.121051\pi\) |
−0.142815 | + | 0.989749i | \(0.545615\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1570.30 | −1.50219 | −0.751096 | − | 0.660193i | \(-0.770475\pi\) | ||||
−0.751096 | + | 0.660193i | \(0.770475\pi\) | |||||||
\(104\) | −75.3465 | + | 948.814i | −0.0710417 | + | 0.894604i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −111.626 | − | 193.343i | −0.102284 | − | 0.177161i | ||||
\(107\) | −3.36651 | − | 5.83096i | −0.00304161 | − | 0.00526823i | 0.864501 | − | 0.502632i | \(-0.167635\pi\) |
−0.867542 | + | 0.497364i | \(0.834302\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −542.422 | −0.476648 | −0.238324 | − | 0.971186i | \(-0.576598\pi\) | ||||
−0.238324 | + | 0.971186i | \(0.576598\pi\) | |||||||
\(110\) | −338.848 | + | 586.903i | −0.293708 | + | 0.508718i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 509.969 | 0.430246 | ||||||||
\(113\) | −721.411 | + | 1249.52i | −0.600572 | + | 1.04022i | 0.392162 | + | 0.919896i | \(0.371727\pi\) |
−0.992735 | + | 0.120325i | \(0.961606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −643.719 | − | 1114.95i | −0.521975 | − | 0.904087i | ||||
\(116\) | −1140.54 | −0.912900 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −480.577 | −0.374921 | ||||||||
\(119\) | −722.467 | − | 1251.35i | −0.556542 | − | 0.963958i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −435.513 | + | 754.330i | −0.327207 | + | 0.566739i | ||||
\(122\) | −144.291 | −0.107078 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −93.6446 | + | 162.197i | −0.0678188 | + | 0.117466i | ||||
\(125\) | 1506.81 | 1.07818 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1246.42 | + | 2158.86i | 0.870881 | + | 1.50841i | 0.861087 | + | 0.508458i | \(0.169784\pi\) |
0.00979442 | + | 0.999952i | \(0.496882\pi\) | |||||||
\(128\) | 648.153 | + | 1122.63i | 0.447572 | + | 0.775217i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 611.186 | − | 290.992i | 0.412343 | − | 0.196321i | ||||
\(131\) | −744.561 | −0.496585 | −0.248292 | − | 0.968685i | \(-0.579869\pi\) | ||||
−0.248292 | + | 0.968685i | \(0.579869\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1800.87 | − | 3119.20i | −1.17410 | − | 2.03360i | ||||
\(134\) | 323.386 | − | 560.121i | 0.208480 | − | 0.361097i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 490.008 | − | 848.718i | 0.308955 | − | 0.535125i | ||||
\(137\) | −111.083 | + | 192.402i | −0.0692736 | + | 0.119985i | −0.898582 | − | 0.438806i | \(-0.855401\pi\) |
0.829308 | + | 0.558792i | \(0.188735\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 388.573 | − | 673.028i | 0.237110 | − | 0.410687i | −0.722774 | − | 0.691085i | \(-0.757133\pi\) |
0.959884 | + | 0.280398i | \(0.0904665\pi\) | |||||||
\(140\) | −862.726 | − | 1494.28i | −0.520812 | − | 0.902072i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −505.876 | −0.298959 | ||||||||
\(143\) | 1985.91 | − | 945.514i | 1.16133 | − | 0.552922i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 960.161 | + | 1663.05i | 0.549911 | + | 0.952473i | ||||
\(146\) | −567.263 | − | 982.529i | −0.321555 | − | 0.556950i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 189.704 | 0.105362 | ||||||||
\(149\) | 889.147 | − | 1540.05i | 0.488871 | − | 0.846750i | −0.511047 | − | 0.859553i | \(-0.670742\pi\) |
0.999918 | + | 0.0128032i | \(0.00407549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1166.00 | 0.628394 | 0.314197 | − | 0.949358i | \(-0.398265\pi\) | ||||
0.314197 | + | 0.949358i | \(0.398265\pi\) | |||||||
\(152\) | 1221.43 | − | 2115.57i | 0.651781 | − | 1.12892i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1029.89 | + | 1783.82i | 0.538902 | + | 0.933407i | ||||
\(155\) | 315.338 | 0.163410 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 517.628 | 0.263129 | 0.131564 | − | 0.991308i | \(-0.458000\pi\) | ||||
0.131564 | + | 0.991308i | \(0.458000\pi\) | |||||||
\(158\) | 110.201 | + | 190.874i | 0.0554882 | + | 0.0961083i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 923.109 | − | 1598.87i | 0.456114 | − | 0.790012i | ||||
\(161\) | −3913.02 | −1.91546 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −305.094 | + | 528.438i | −0.146606 | + | 0.253929i | −0.929971 | − | 0.367633i | \(-0.880168\pi\) |
0.783365 | + | 0.621562i | \(0.213502\pi\) | |||||||
\(164\) | −1414.81 | −0.673647 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 247.746 | + | 429.109i | 0.115836 | + | 0.200635i | ||||
\(167\) | 1491.51 | + | 2583.36i | 0.691115 | + | 1.19705i | 0.971473 | + | 0.237150i | \(0.0762133\pi\) |
−0.280358 | + | 0.959895i | \(0.590453\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2169.46 | − | 346.747i | −0.987467 | − | 0.157827i | ||||
\(170\) | −696.990 | −0.314451 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 282.022 | + | 488.476i | 0.125023 | + | 0.216546i | ||||
\(173\) | 489.106 | − | 847.157i | 0.214948 | − | 0.372301i | −0.738308 | − | 0.674463i | \(-0.764375\pi\) |
0.953257 | + | 0.302162i | \(0.0977084\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 418.657 | − | 725.134i | 0.180843 | − | 0.313229i | ||||
\(176\) | 399.649 | − | 692.213i | 0.171163 | − | 0.296463i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 124.555 | − | 215.736i | 0.0524483 | − | 0.0908431i | ||||
\(179\) | 926.471 | + | 1604.69i | 0.386858 | + | 0.670058i | 0.992025 | − | 0.126040i | \(-0.0402269\pi\) |
−0.605167 | + | 0.796099i | \(0.706894\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 852.777 | 0.350201 | 0.175101 | − | 0.984551i | \(-0.443975\pi\) | ||||
0.175101 | + | 0.984551i | \(0.443975\pi\) | |||||||
\(182\) | 162.871 | − | 2050.97i | 0.0663339 | − | 0.835320i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1326.99 | − | 2298.41i | −0.531668 | − | 0.920875i | ||||
\(185\) | −159.702 | − | 276.612i | −0.0634676 | − | 0.109929i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2264.71 | −0.885627 | ||||||||
\(188\) | −1576.77 | + | 2731.04i | −0.611689 | + | 1.05948i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1737.36 | −0.663377 | ||||||||
\(191\) | 2220.65 | − | 3846.27i | 0.841258 | − | 1.45710i | −0.0475730 | − | 0.998868i | \(-0.515149\pi\) |
0.888831 | − | 0.458234i | \(-0.151518\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1241.21 | + | 2149.85i | 0.462925 | + | 0.801810i | 0.999105 | − | 0.0422935i | \(-0.0134665\pi\) |
−0.536180 | + | 0.844104i | \(0.680133\pi\) | |||||||
\(194\) | 314.041 | 0.116221 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3237.57 | −1.17987 | ||||||||
\(197\) | 630.115 | + | 1091.39i | 0.227888 | + | 0.394713i | 0.957182 | − | 0.289487i | \(-0.0934848\pi\) |
−0.729294 | + | 0.684200i | \(0.760151\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2760.48 | − | 4781.30i | 0.983344 | − | 1.70320i | 0.334266 | − | 0.942479i | \(-0.391511\pi\) |
0.649077 | − | 0.760722i | \(-0.275155\pi\) | |||||||
\(200\) | 567.901 | 0.200783 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1169.30 | − | 2025.28i | 0.407285 | − | 0.705438i | ||||
\(203\) | 5836.60 | 2.01798 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1191.06 | + | 2062.97i | 0.405790 | + | 0.702849i | ||||
\(206\) | 1151.11 | + | 1993.78i | 0.389327 | + | 0.674334i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −720.853 | + | 343.206i | −0.240299 | + | 0.114409i | ||||
\(209\) | −5645.18 | −1.86835 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2263.90 | + | 3921.18i | 0.738640 | + | 1.27936i | 0.953108 | + | 0.302631i | \(0.0978649\pi\) |
−0.214468 | + | 0.976731i | \(0.568802\pi\) | |||||||
\(212\) | 445.451 | − | 771.543i | 0.144310 | − | 0.249952i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.93564 | + | 8.54879i | −0.00157661 | + | 0.00273076i | ||||
\(215\) | 474.839 | − | 822.446i | 0.150622 | − | 0.260885i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 479.217 | − | 830.029i | 0.149914 | − | 0.259659i | ||||
\(218\) | 397.623 | + | 688.703i | 0.123534 | + | 0.213967i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2704.38 | −0.828770 | ||||||||
\(221\) | 1863.37 | + | 1282.60i | 0.567168 | + | 0.390393i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2240.59 | − | 3880.81i | −0.672829 | − | 1.16537i | −0.977099 | − | 0.212787i | \(-0.931746\pi\) |
0.304270 | − | 0.952586i | \(-0.401588\pi\) | |||||||
\(224\) | −2805.68 | − | 4859.59i | −0.836887 | − | 1.44953i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2115.32 | 0.622607 | ||||||||
\(227\) | −2879.88 | + | 4988.09i | −0.842044 | + | 1.45846i | 0.0461191 | + | 0.998936i | \(0.485315\pi\) |
−0.888163 | + | 0.459528i | \(0.848019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4635.08 | −1.33753 | −0.668766 | − | 0.743473i | \(-0.733177\pi\) | ||||
−0.668766 | + | 0.743473i | \(0.733177\pi\) | |||||||
\(230\) | −943.757 | + | 1634.64i | −0.270563 | + | 0.468629i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1979.31 | + | 3428.27i | 0.560122 | + | 0.970160i | ||||
\(233\) | −5886.33 | −1.65505 | −0.827524 | − | 0.561431i | \(-0.810251\pi\) | ||||
−0.827524 | + | 0.561431i | \(0.810251\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5309.59 | 1.47387 | ||||||||
\(236\) | −958.882 | − | 1660.83i | −0.264483 | − | 0.458097i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1059.21 | + | 1834.61i | −0.288481 | + | 0.499663i | ||||
\(239\) | −2135.84 | −0.578060 | −0.289030 | − | 0.957320i | \(-0.593333\pi\) | ||||
−0.289030 | + | 0.957320i | \(0.593333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2346.46 | + | 4064.19i | −0.627173 | + | 1.08630i | 0.360943 | + | 0.932588i | \(0.382455\pi\) |
−0.988116 | + | 0.153708i | \(0.950879\pi\) | |||||||
\(242\) | 1277.01 | 0.339212 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −287.899 | − | 498.656i | −0.0755364 | − | 0.130833i | ||||
\(245\) | 2725.55 | + | 4720.79i | 0.710730 | + | 1.23102i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4644.77 | + | 3197.09i | 1.19652 | + | 0.823587i | ||||
\(248\) | 650.051 | 0.166445 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1104.57 | − | 1913.16i | −0.279435 | − | 0.483996i | ||||
\(251\) | −1951.44 | + | 3379.99i | −0.490732 | + | 0.849973i | −0.999943 | − | 0.0106687i | \(-0.996604\pi\) |
0.509211 | + | 0.860642i | \(0.329937\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3066.53 | + | 5311.38i | −0.762020 | + | 1.31986i | ||||
\(254\) | 1827.38 | − | 3165.11i | 0.451417 | − | 0.781877i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1504.32 | − | 2605.56i | 0.367265 | − | 0.636122i | ||||
\(257\) | −2065.42 | − | 3577.40i | −0.501312 | − | 0.868297i | −0.999999 | − | 0.00151510i | \(-0.999518\pi\) |
0.498687 | − | 0.866782i | \(-0.333816\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −970.790 | −0.232903 | ||||||||
\(260\) | 2225.13 | + | 1531.60i | 0.530756 | + | 0.365330i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 545.801 | + | 945.356i | 0.128701 | + | 0.222917i | ||||
\(263\) | 3176.09 | + | 5501.14i | 0.744661 | + | 1.28979i | 0.950353 | + | 0.311174i | \(0.100722\pi\) |
−0.205692 | + | 0.978617i | \(0.565944\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1500.01 | −0.347716 | ||||||||
\(266\) | −2640.26 | + | 4573.06i | −0.608589 | + | 1.05411i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2580.97 | 0.588276 | ||||||||
\(269\) | 90.7619 | − | 157.204i | 0.0205719 | − | 0.0356316i | −0.855556 | − | 0.517710i | \(-0.826785\pi\) |
0.876128 | + | 0.482078i | \(0.160118\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1730.18 | − | 2996.75i | −0.387825 | − | 0.671733i | 0.604331 | − | 0.796733i | \(-0.293440\pi\) |
−0.992157 | + | 0.125000i | \(0.960107\pi\) | |||||||
\(272\) | 822.053 | 0.183251 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 325.719 | 0.0718153 | ||||||||
\(275\) | −656.180 | − | 1136.54i | −0.143888 | − | 0.249221i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3218.97 | − | 5575.42i | 0.698228 | − | 1.20937i | −0.270853 | − | 0.962621i | \(-0.587306\pi\) |
0.969080 | − | 0.246745i | \(-0.0793611\pi\) | |||||||
\(278\) | −1139.37 | −0.245810 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2994.38 | + | 5186.42i | −0.639102 | + | 1.10696i | ||||
\(281\) | 2974.26 | 0.631421 | 0.315711 | − | 0.948855i | \(-0.397757\pi\) | ||||
0.315711 | + | 0.948855i | \(0.397757\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1517.86 | − | 2629.01i | −0.318825 | − | 0.552221i | 0.661418 | − | 0.750017i | \(-0.269955\pi\) |
−0.980243 | + | 0.197797i | \(0.936621\pi\) | |||||||
\(284\) | −1009.36 | − | 1748.27i | −0.210896 | − | 0.365283i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2656.28 | − | 1828.37i | −0.549192 | − | 0.378020i | ||||
\(287\) | 7240.15 | 1.48910 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1291.91 | + | 2237.65i | 0.262957 | + | 0.455455i | ||||
\(290\) | 1407.69 | − | 2438.20i | 0.285044 | − | 0.493710i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2263.69 | − | 3920.83i | 0.453673 | − | 0.785784i | ||||
\(293\) | −977.872 | + | 1693.72i | −0.194976 | + | 0.337708i | −0.946893 | − | 0.321550i | \(-0.895796\pi\) |
0.751917 | + | 0.659258i | \(0.229129\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1614.47 | + | 2796.34i | −0.318637 | + | 0.551895i | ||||
\(296\) | −329.216 | − | 570.218i | −0.0646462 | − | 0.111970i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2607.16 | −0.506808 | ||||||||
\(299\) | 5531.15 | − | 2633.43i | 1.06981 | − | 0.509349i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1443.22 | − | 2499.73i | −0.276365 | − | 0.478678i | ||||
\(302\) | −854.736 | − | 1480.45i | −0.162863 | − | 0.282086i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2049.10 | 0.386593 | ||||||||
\(305\) | −484.735 | + | 839.586i | −0.0910029 | + | 0.157622i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1027.56 | −0.191029 | −0.0955147 | − | 0.995428i | \(-0.530450\pi\) | ||||
−0.0955147 | + | 0.995428i | \(0.530450\pi\) | |||||||
\(308\) | −4109.83 | + | 7118.43i | −0.760322 | + | 1.31692i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −231.159 | − | 400.379i | −0.0423515 | − | 0.0733549i | ||||
\(311\) | −3405.61 | −0.620947 | −0.310474 | − | 0.950582i | \(-0.600488\pi\) | ||||
−0.310474 | + | 0.950582i | \(0.600488\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4813.20 | 0.869196 | 0.434598 | − | 0.900625i | \(-0.356890\pi\) | ||||
0.434598 | + | 0.900625i | \(0.356890\pi\) | |||||||
\(314\) | −379.447 | − | 657.222i | −0.0681957 | − | 0.118118i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −439.763 | + | 761.691i | −0.0782866 | + | 0.135596i | ||||
\(317\) | −1141.33 | −0.202219 | −0.101110 | − | 0.994875i | \(-0.532239\pi\) | ||||
−0.101110 | + | 0.994875i | \(0.532239\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4573.99 | − | 7922.38i | 0.802803 | − | 1.39050i | ||||
\(320\) | −1364.45 | −0.238359 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2868.44 | + | 4968.29i | 0.496435 | + | 0.859850i | ||||
\(323\) | −2902.94 | − | 5028.04i | −0.500074 | − | 0.866154i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −103.771 | + | 1306.75i | −0.0177113 | + | 0.223032i | ||||
\(326\) | 894.597 | 0.151985 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2455.29 | + | 4252.69i | 0.413325 | + | 0.715900i | ||||
\(329\) | 8068.94 | − | 13975.8i | 1.35214 | − | 2.34198i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3826.28 | + | 6627.32i | −0.635382 | + | 1.10051i | 0.351052 | + | 0.936356i | \(0.385824\pi\) |
−0.986434 | + | 0.164158i | \(0.947509\pi\) | |||||||
\(332\) | −988.643 | + | 1712.38i | −0.163430 | + | 0.283069i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2186.70 | − | 3787.47i | 0.358236 | − | 0.620483i | ||||
\(335\) | −2172.79 | − | 3763.38i | −0.354364 | − | 0.613777i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2503.69 | −0.404702 | −0.202351 | − | 0.979313i | \(-0.564858\pi\) | ||||
−0.202351 | + | 0.979313i | \(0.564858\pi\) | |||||||
\(338\) | 1150.07 | + | 3008.71i | 0.185076 | + | 0.484178i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1390.68 | − | 2408.74i | −0.221825 | − | 0.384212i | ||||
\(341\) | −751.100 | − | 1300.94i | −0.119280 | − | 0.206598i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6298.69 | 0.991537 | ||||||||
\(344\) | 978.853 | − | 1695.42i | 0.153419 | − | 0.265730i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1434.16 | −0.222835 | ||||||||
\(347\) | 2248.06 | − | 3893.75i | 0.347787 | − | 0.602385i | −0.638069 | − | 0.769979i | \(-0.720267\pi\) |
0.985856 | + | 0.167594i | \(0.0535999\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1788.81 | − | 3098.31i | −0.274363 | − | 0.475211i | 0.695611 | − | 0.718418i | \(-0.255134\pi\) |
−0.969974 | + | 0.243208i | \(0.921800\pi\) | |||||||
\(350\) | −1227.59 | −0.187478 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8794.96 | −1.33174 | ||||||||
\(353\) | −4022.58 | − | 6967.32i | −0.606517 | − | 1.05052i | −0.991810 | − | 0.127724i | \(-0.959233\pi\) |
0.385293 | − | 0.922794i | \(-0.374100\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1699.46 | + | 2943.55i | −0.254079 | + | 0.440077i | ||||
\(356\) | 994.086 | 0.147996 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1358.30 | − | 2352.64i | 0.200526 | − | 0.347322i | ||||
\(359\) | 2172.90 | 0.319447 | 0.159724 | − | 0.987162i | \(-0.448940\pi\) | ||||
0.159724 | + | 0.987162i | \(0.448940\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3806.57 | − | 6593.17i | −0.554974 | − | 0.961244i | ||||
\(362\) | −625.129 | − | 1082.75i | −0.0907625 | − | 0.157205i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7412.96 | − | 3529.39i | 1.06743 | − | 0.508215i | ||||
\(365\) | −7622.74 | −1.09313 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3831.38 | − | 6636.15i | −0.544949 | − | 0.943880i | −0.998610 | − | 0.0527056i | \(-0.983216\pi\) |
0.453661 | − | 0.891175i | \(-0.350118\pi\) | |||||||
\(368\) | 1113.10 | − | 1927.94i | 0.157675 | − | 0.273100i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −234.139 | + | 405.541i | −0.0328981 | + | 0.0569812i | ||||
\(371\) | −2279.55 | + | 3948.30i | −0.318998 | + | 0.552521i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5271.27 | + | 9130.10i | −0.731732 | + | 1.26740i | 0.224411 | + | 0.974495i | \(0.427954\pi\) |
−0.956143 | + | 0.292902i | \(0.905379\pi\) | |||||||
\(374\) | 1660.15 | + | 2875.46i | 0.229530 | + | 0.397558i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10945.4 | 1.50124 | ||||||||
\(377\) | −8250.17 | + | 3927.99i | −1.12707 | + | 0.536610i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2737.77 | − | 4741.96i | −0.371055 | − | 0.642686i | 0.618673 | − | 0.785648i | \(-0.287671\pi\) |
−0.989728 | + | 0.142962i | \(0.954337\pi\) | |||||||
\(380\) | −3466.51 | − | 6004.18i | −0.467970 | − | 0.810547i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6511.39 | −0.872124 | ||||||||
\(383\) | 404.042 | − | 699.822i | 0.0539050 | − | 0.0933661i | −0.837814 | − | 0.545956i | \(-0.816167\pi\) |
0.891719 | + | 0.452590i | \(0.149500\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13839.4 | 1.83200 | ||||||||
\(386\) | 1819.75 | − | 3151.89i | 0.239955 | − | 0.415614i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 626.597 | + | 1085.30i | 0.0819862 | + | 0.142004i | ||||
\(389\) | 7060.26 | 0.920230 | 0.460115 | − | 0.887859i | \(-0.347808\pi\) | ||||
0.460115 | + | 0.887859i | \(0.347808\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6307.65 | −0.815836 | ||||||||
\(392\) | 5618.55 | + | 9731.62i | 0.723928 | + | 1.25388i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 923.813 | − | 1600.09i | 0.118124 | − | 0.204598i | ||||
\(395\) | 1480.85 | 0.188633 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 709.947 | − | 1229.66i | 0.0897511 | − | 0.155453i | −0.817655 | − | 0.575709i | \(-0.804726\pi\) |
0.907406 | + | 0.420255i | \(0.138060\pi\) | |||||||
\(398\) | −8094.29 | −1.01942 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 238.182 | + | 412.544i | 0.0297728 | + | 0.0515680i | ||||
\(401\) | 5335.37 | + | 9241.13i | 0.664428 | + | 1.15082i | 0.979440 | + | 0.201735i | \(0.0646580\pi\) |
−0.315012 | + | 0.949088i | \(0.602009\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −118.782 | + | 1495.78i | −0.0146822 | + | 0.184888i | ||||
\(404\) | 9332.28 | 1.14925 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4278.52 | − | 7410.62i | −0.523004 | − | 0.905869i | ||||
\(407\) | −760.782 | + | 1317.71i | −0.0926550 | + | 0.160483i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3175.78 | + | 5500.61i | −0.383942 | + | 0.665007i | −0.991622 | − | 0.129175i | \(-0.958767\pi\) |
0.607680 | + | 0.794182i | \(0.292100\pi\) | |||||||
\(410\) | 1746.21 | − | 3024.52i | 0.210339 | − | 0.364318i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4593.54 | + | 7956.25i | −0.549290 | + | 0.951399i | ||||
\(413\) | 4906.98 | + | 8499.15i | 0.584641 | + | 1.01263i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3329.15 | 0.393787 | ||||||||
\(416\) | 7236.37 | + | 4980.94i | 0.852866 | + | 0.587045i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4138.20 | + | 7167.57i | 0.484225 | + | 0.838702i | ||||
\(419\) | 2808.94 | + | 4865.22i | 0.327507 | + | 0.567259i | 0.982017 | − | 0.188795i | \(-0.0604581\pi\) |
−0.654509 | + | 0.756054i | \(0.727125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1518.29 | −0.175765 | −0.0878825 | − | 0.996131i | \(-0.528010\pi\) | ||||
−0.0878825 | + | 0.996131i | \(0.528010\pi\) | |||||||
\(422\) | 3319.10 | − | 5748.85i | 0.382870 | − | 0.663151i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3092.17 | −0.354173 | ||||||||
\(425\) | 674.860 | − | 1168.89i | 0.0770248 | − | 0.133411i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1473.30 | + | 2551.83i | 0.166974 | + | 0.289207i | ||||
\(428\) | −39.3918 | −0.00444878 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1392.33 | −0.156149 | ||||||||
\(431\) | −2485.07 | − | 4304.26i | −0.277730 | − | 0.481042i | 0.693091 | − | 0.720850i | \(-0.256249\pi\) |
−0.970820 | + | 0.239809i | \(0.922915\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1649.36 | − | 2856.77i | 0.183055 | − | 0.317061i | −0.759864 | − | 0.650082i | \(-0.774735\pi\) |
0.942919 | + | 0.333021i | \(0.108068\pi\) | |||||||
\(434\) | −1405.16 | −0.155415 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1586.73 | + | 2748.30i | −0.174291 | + | 0.301880i | ||||
\(437\) | −15722.9 | −1.72112 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3024.24 | + | 5238.13i | 0.328790 | + | 0.569481i | 0.982272 | − | 0.187461i | \(-0.0600257\pi\) |
−0.653482 | + | 0.756942i | \(0.726692\pi\) | |||||||
\(440\) | 4693.24 | + | 8128.92i | 0.508503 | + | 0.880753i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 262.542 | − | 3306.10i | 0.0282530 | − | 0.355781i | ||||
\(443\) | −6822.62 | −0.731722 | −0.365861 | − | 0.930670i | \(-0.619225\pi\) | ||||
−0.365861 | + | 0.930670i | \(0.619225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −836.869 | − | 1449.50i | −0.0891493 | − | 0.154411i | ||||
\(446\) | −3284.93 | + | 5689.66i | −0.348757 | + | 0.604066i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2073.54 | + | 3591.48i | −0.218673 | + | 0.378753i | ||||
\(449\) | 205.205 | − | 355.426i | 0.0215684 | − | 0.0373576i | −0.855040 | − | 0.518563i | \(-0.826467\pi\) |
0.876608 | + | 0.481205i | \(0.159801\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5673.91 | − | 9827.51i | 0.592404 | − | 1.02607i | ||||
\(452\) | 4220.65 | + | 7310.38i | 0.439209 | + | 0.760733i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8444.38 | 0.872939 | ||||||||
\(455\) | −11386.9 | − | 7837.81i | −1.17324 | − | 0.807565i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8321.41 | + | 14413.1i | 0.851771 | + | 1.47531i | 0.879609 | + | 0.475697i | \(0.157804\pi\) |
−0.0278385 | + | 0.999612i | \(0.508862\pi\) | |||||||
\(458\) | 3397.75 | + | 5885.07i | 0.346651 | + | 0.600418i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7532.21 | −0.763459 | ||||||||
\(461\) | −5864.85 | + | 10158.2i | −0.592523 | + | 1.02628i | 0.401368 | + | 0.915917i | \(0.368535\pi\) |
−0.993891 | + | 0.110364i | \(0.964798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3564.93 | −0.357832 | −0.178916 | − | 0.983864i | \(-0.557259\pi\) | ||||
−0.178916 | + | 0.983864i | \(0.557259\pi\) | |||||||
\(464\) | −1660.28 | + | 2875.69i | −0.166113 | + | 0.287717i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4314.98 | + | 7473.76i | 0.428943 | + | 0.742951i | ||||
\(467\) | −1134.81 | −0.112447 | −0.0562233 | − | 0.998418i | \(-0.517906\pi\) | ||||
−0.0562233 | + | 0.998418i | \(0.517906\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13207.9 | −1.30039 | ||||||||
\(470\) | −3892.20 | − | 6741.49i | −0.381987 | − | 0.661620i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3328.12 | + | 5764.48i | −0.324554 | + | 0.562144i | ||||
\(473\) | −4524.05 | −0.439780 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1682.20 | − | 2913.66i | 0.162494 | − | 0.281448i | ||||
\(476\) | −8453.65 | −0.814018 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1565.68 | + | 2711.84i | 0.149817 | + | 0.259491i | ||||
\(479\) | −9686.30 | − | 16777.2i | −0.923963 | − | 1.60035i | −0.793220 | − | 0.608935i | \(-0.791597\pi\) |
−0.130743 | − | 0.991416i | \(-0.541736\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1372.24 | − | 653.335i | 0.130080 | − | 0.0619325i | ||||
\(482\) | 6880.29 | 0.650184 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2547.99 | + | 4413.24i | 0.239293 | + | 0.414467i | ||||
\(485\) | 1055.00 | − | 1827.31i | 0.0987733 | − | 0.171080i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4522.98 | − | 7834.02i | 0.420853 | − | 0.728939i | −0.575170 | − | 0.818034i | \(-0.695064\pi\) |
0.996023 | + | 0.0890946i | \(0.0283973\pi\) | |||||||
\(488\) | −999.253 | + | 1730.76i | −0.0926927 | + | 0.160549i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3995.93 | − | 6921.15i | 0.368403 | − | 0.638093i | ||||
\(491\) | 7201.66 | + | 12473.6i | 0.661927 | + | 1.14649i | 0.980109 | + | 0.198462i | \(0.0635947\pi\) |
−0.318181 | + | 0.948030i | \(0.603072\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9408.40 | 0.859499 | ||||||||
\(494\) | 654.429 | − | 8241.01i | 0.0596036 | − | 0.750568i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 272.637 | + | 472.221i | 0.0246809 | + | 0.0427486i | ||||
\(497\) | 5165.31 | + | 8946.58i | 0.466189 | + | 0.807463i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9319.75 | −0.836091 | −0.418045 | − | 0.908426i | \(-0.637285\pi\) | ||||
−0.418045 | + | 0.908426i | \(0.637285\pi\) | |||||||
\(500\) | 4407.82 | − | 7634.57i | 0.394247 | − | 0.682856i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5722.02 | 0.508737 | ||||||||
\(503\) | 1372.99 | − | 2378.09i | 0.121707 | − | 0.210802i | −0.798734 | − | 0.601684i | \(-0.794497\pi\) |
0.920441 | + | 0.390882i | \(0.127830\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7856.37 | − | 13607.6i | −0.692285 | − | 1.19907i | ||||
\(506\) | 8991.69 | 0.789979 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14584.5 | 1.27378 | ||||||||
\(509\) | −591.055 | − | 1023.74i | −0.0514697 | − | 0.0891481i | 0.839143 | − | 0.543911i | \(-0.183057\pi\) |
−0.890612 | + | 0.454763i | \(0.849724\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11584.2 | + | 20064.5i | −1.00285 | + | 1.73698i | ||||
\(512\) | 5959.48 | 0.514403 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3028.11 | + | 5244.84i | −0.259852 | + | 0.450078i | ||||
\(515\) | 15468.3 | 1.32352 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12646.8 | − | 21905.0i | −1.07584 | − | 1.86340i | ||||
\(518\) | 711.639 | + | 1232.59i | 0.0603622 | + | 0.104550i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 742.205 | − | 9346.33i | 0.0625920 | − | 0.788200i | ||||
\(521\) | −10858.8 | −0.913115 | −0.456558 | − | 0.889694i | \(-0.650918\pi\) | ||||
−0.456558 | + | 0.889694i | \(0.650918\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5080.87 | + | 8800.33i | 0.424801 | + | 0.735777i | 0.996402 | − | 0.0847546i | \(-0.0270106\pi\) |
−0.571601 | + | 0.820532i | \(0.693677\pi\) | |||||||
\(524\) | −2178.05 | + | 3772.48i | −0.181581 | + | 0.314507i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4656.47 | − | 8065.23i | 0.385992 | − | 0.668557i | ||||
\(527\) | 772.482 | − | 1337.98i | 0.0638517 | − | 0.110594i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2457.36 | + | 4256.28i | −0.201970 | + | 0.349821i | ||||
\(530\) | 1099.58 | + | 1904.53i | 0.0901184 | + | 0.156090i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −21072.1 | −1.71728 | ||||||||
\(533\) | −10234.1 | + | 4872.57i | −0.831687 | + | 0.395975i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.1620 | + | 57.4382i | 0.00267984 | + | 0.00464162i | ||||
\(536\) | −4479.07 | − | 7757.98i | −0.360945 | − | 0.625175i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −266.132 | −0.0213267 | ||||||||
\(539\) | 12983.9 | − | 22488.7i | 1.03758 | − | 1.79714i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9573.04 | −0.760771 | −0.380386 | − | 0.924828i | \(-0.624209\pi\) | ||||
−0.380386 | + | 0.924828i | \(0.624209\pi\) | |||||||
\(542\) | −2536.61 | + | 4393.54i | −0.201027 | + | 0.348190i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4522.67 | − | 7833.49i | −0.356448 | − | 0.617386i | ||||
\(545\) | 5343.15 | 0.419955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15958.9 | 1.24745 | 0.623724 | − | 0.781645i | \(-0.285619\pi\) | ||||
0.623724 | + | 0.781645i | \(0.285619\pi\) | |||||||
\(548\) | 649.898 | + | 1125.66i | 0.0506611 | + | 0.0877475i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −962.027 | + | 1666.28i | −0.0745836 | + | 0.129183i | ||||
\(551\) | 23452.0 | 1.81323 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2250.44 | − | 3897.88i | 0.173053 | − | 0.299737i | ||||
\(554\) | −9438.67 | −0.723846 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2273.36 | − | 3937.58i | −0.173403 | − | 0.300343i | ||||
\(557\) | −1072.55 | − | 1857.70i | −0.0815892 | − | 0.141317i | 0.822344 | − | 0.568991i | \(-0.192666\pi\) |
−0.903933 | + | 0.427675i | \(0.859333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3722.33 | + | 2562.15i | 0.281642 | + | 0.193859i | ||||
\(560\) | −5023.47 | −0.379072 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2180.28 | − | 3776.36i | −0.163647 | − | 0.283445i | ||||
\(563\) | −11159.3 | + | 19328.5i | −0.835362 | + | 1.44689i | 0.0583740 | + | 0.998295i | \(0.481408\pi\) |
−0.893736 | + | 0.448594i | \(0.851925\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7106.29 | − | 12308.5i | 0.529140 | − | 0.916497i | ||||
\(566\) | −2225.34 | + | 3854.40i | −0.165261 | + | 0.286241i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3503.33 | + | 6067.95i | −0.258797 | + | 0.448249i | ||||
\(569\) | −9876.51 | − | 17106.6i | −0.727671 | − | 1.26036i | −0.957865 | − | 0.287218i | \(-0.907270\pi\) |
0.230194 | − | 0.973145i | \(-0.426064\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10640.6 | −0.779850 | −0.389925 | − | 0.920847i | \(-0.627499\pi\) | ||||
−0.389925 | + | 0.920847i | \(0.627499\pi\) | |||||||
\(572\) | 1018.69 | − | 12828.0i | 0.0744639 | − | 0.937699i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5307.40 | − | 9192.69i | −0.385935 | − | 0.668459i | ||||
\(575\) | −1827.59 | − | 3165.47i | −0.132549 | − | 0.229581i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6547.89 | 0.472430 | 0.236215 | − | 0.971701i | \(-0.424093\pi\) | ||||
0.236215 | + | 0.971701i | \(0.424093\pi\) | |||||||
\(578\) | 1894.07 | − | 3280.62i | 0.136302 | − | 0.236083i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11234.9 | 0.804319 | ||||||||
\(581\) | 5059.29 | − | 8762.94i | 0.361264 | − | 0.625728i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3572.85 | + | 6188.35i | 0.253812 | + | 0.439615i | ||||
\(584\) | −15713.8 | −1.11343 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2867.32 | 0.202130 | ||||||||
\(587\) | 2950.17 | + | 5109.84i | 0.207439 | + | 0.359294i | 0.950907 | − | 0.309477i | \(-0.100154\pi\) |
−0.743468 | + | 0.668771i | \(0.766821\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1925.54 | − | 3335.14i | 0.134704 | − | 0.233314i | ||||
\(590\) | 4733.94 | 0.330328 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 276.151 | − | 478.308i | 0.0191719 | − | 0.0332067i | ||||
\(593\) | 15261.5 | 1.05686 | 0.528428 | − | 0.848978i | \(-0.322782\pi\) | ||||
0.528428 | + | 0.848978i | \(0.322782\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7116.70 | + | 12326.5i | 0.490346 | + | 0.849305i | ||||
\(596\) | −5202.00 | − | 9010.13i | −0.357520 | − | 0.619243i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7398.23 | − | 5092.35i | −0.505913 | − | 0.348230i | ||||
\(599\) | 18900.6 | 1.28925 | 0.644623 | − | 0.764501i | \(-0.277014\pi\) | ||||
0.644623 | + | 0.764501i | \(0.277014\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9253.48 | + | 16027.5i | 0.628049 | + | 1.08781i | 0.987943 | + | 0.154819i | \(0.0494794\pi\) |
−0.359894 | + | 0.932993i | \(0.617187\pi\) | |||||||
\(602\) | −2115.91 | + | 3664.86i | −0.143252 | + | 0.248120i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3410.86 | − | 5907.79i | 0.229778 | − | 0.397987i | ||||
\(605\) | 4290.04 | − | 7430.56i | 0.288289 | − | 0.499331i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3204.25 | − | 5549.92i | 0.214261 | − | 0.371111i | −0.738783 | − | 0.673944i | \(-0.764599\pi\) |
0.953044 | + | 0.302833i | \(0.0979324\pi\) | |||||||
\(608\) | −11273.5 | − | 19526.3i | −0.751976 | − | 1.30246i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1421.34 | 0.0943418 | ||||||||
\(611\) | −2000.01 | + | 25185.5i | −0.132425 | + | 1.66759i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1753.63 | + | 3037.38i | 0.115544 | + | 0.200128i | 0.917997 | − | 0.396587i | \(-0.129806\pi\) |
−0.802453 | + | 0.596715i | \(0.796472\pi\) | |||||||
\(614\) | 753.255 | + | 1304.68i | 0.0495096 | + | 0.0857532i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28529.1 | 1.86602 | ||||||||
\(617\) | 7253.89 | − | 12564.1i | 0.473307 | − | 0.819792i | −0.526226 | − | 0.850345i | \(-0.676393\pi\) |
0.999533 | + | 0.0305526i | \(0.00972671\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4750.85 | 0.308486 | 0.154243 | − | 0.988033i | \(-0.450706\pi\) | ||||
0.154243 | + | 0.988033i | \(0.450706\pi\) | |||||||
\(620\) | 922.451 | − | 1597.73i | 0.0597525 | − | 0.103494i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2496.49 | + | 4324.04i | 0.160933 | + | 0.278743i | ||||
\(623\) | −5087.14 | −0.327146 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11347.0 | −0.726209 | ||||||||
\(626\) | −3528.32 | − | 6111.23i | −0.225272 | − | 0.390182i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1514.20 | − | 2622.68i | 0.0962154 | − | 0.166650i | ||||
\(629\) | −1564.88 | −0.0991986 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2412.60 | + | 4178.74i | −0.152209 | + | 0.263634i | −0.932039 | − | 0.362357i | \(-0.881972\pi\) |
0.779830 | + | 0.625991i | \(0.215305\pi\) | |||||||
\(632\) | 3052.69 | 0.192135 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 836.652 | + | 1449.12i | 0.0524096 | + | 0.0907762i | ||||
\(635\) | −12277.9 | − | 21266.0i | −0.767298 | − | 1.32900i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23419.2 | + | 11150.1i | −1.45668 | + | 0.693539i | ||||
\(638\) | −13411.9 | −0.832258 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6384.66 | − | 11058.6i | −0.394337 | − | 0.683013i | ||||
\(641\) | −2955.95 | + | 5119.85i | −0.182142 | + | 0.315479i | −0.942610 | − | 0.333897i | \(-0.891636\pi\) |
0.760468 | + | 0.649376i | \(0.224970\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11704.1 | + | 20272.2i | −0.717833 | + | 1.24332i | 0.244024 | + | 0.969769i | \(0.421532\pi\) |
−0.961857 | + | 0.273554i | \(0.911801\pi\) | |||||||
\(644\) | −11446.6 | + | 19826.2i | −0.700405 | + | 1.21314i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4256.01 | + | 7371.62i | −0.259211 | + | 0.448967i | ||||
\(647\) | −8199.33 | − | 14201.7i | −0.498221 | − | 0.862944i | 0.501777 | − | 0.864997i | \(-0.332680\pi\) |
−0.999998 | + | 0.00205298i | \(0.999347\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15381.9 | 0.930342 | ||||||||
\(650\) | 1735.22 | − | 826.157i | 0.104709 | − | 0.0498532i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1784.97 | + | 3091.65i | 0.107216 | + | 0.185703i | ||||
\(653\) | 13764.8 | + | 23841.3i | 0.824897 | + | 1.42876i | 0.901998 | + | 0.431741i | \(0.142100\pi\) |
−0.0771005 | + | 0.997023i | \(0.524566\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7334.34 | 0.437521 | ||||||||
\(656\) | −2059.54 | + | 3567.22i | −0.122578 | + | 0.212312i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −23659.8 | −1.40175 | ||||||||
\(659\) | −12089.9 | + | 20940.3i | −0.714650 | + | 1.23781i | 0.248444 | + | 0.968646i | \(0.420081\pi\) |
−0.963094 | + | 0.269164i | \(0.913253\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2262.52 | − | 3918.80i | −0.133134 | − | 0.230595i | 0.791749 | − | 0.610847i | \(-0.209171\pi\) |
−0.924883 | + | 0.380251i | \(0.875838\pi\) | |||||||
\(662\) | 11219.4 | 0.658695 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6862.84 | 0.401099 | ||||||||
\(665\) | 17739.6 | + | 30725.8i | 1.03445 | + | 1.79172i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12739.4 | − | 22065.3i | 0.739539 | − | 1.28092i | ||||
\(668\) | 17452.2 | 1.01085 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3185.53 | + | 5517.49i | −0.183683 | + | 0.318148i | ||||
\(671\) | 4618.34 | 0.265706 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1643.59 | − | 2846.78i | −0.0941393 | − | 0.163054i | 0.815110 | − | 0.579307i | \(-0.196677\pi\) |
−0.909249 | + | 0.416253i | \(0.863343\pi\) | |||||||
\(674\) | 1835.33 | + | 3178.89i | 0.104888 | + | 0.181671i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8103.14 | + | 9977.74i | −0.461035 | + | 0.567691i | ||||
\(677\) | 9724.21 | 0.552041 | 0.276020 | − | 0.961152i | \(-0.410984\pi\) | ||||
0.276020 | + | 0.961152i | \(0.410984\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3206.55 | − | 5553.91i | −0.181231 | − | 0.313902i | ||||
\(680\) | −4826.84 | + | 8360.34i | −0.272207 | + | 0.471477i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1101.19 | + | 1907.31i | −0.0618280 | + | 0.107089i | ||||
\(683\) | 7274.33 | − | 12599.5i | 0.407532 | − | 0.705867i | −0.587080 | − | 0.809529i | \(-0.699723\pi\) |
0.994613 | + | 0.103662i | \(0.0330560\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1094.23 | − | 1895.26i | 0.0610342 | − | 0.105714i | ||||
\(686\) | −4617.26 | − | 7997.33i | −0.256979 | − | 0.445101i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1642.15 | 0.0909979 | ||||||||
\(689\) | 565.022 | − | 7115.13i | 0.0312418 | − | 0.393418i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3364.48 | − | 5827.45i | −0.185226 | − | 0.320820i | 0.758427 | − | 0.651758i | \(-0.225968\pi\) |
−0.943653 | + | 0.330938i | \(0.892635\pi\) | |||||||
\(692\) | −2861.54 | − | 4956.33i | −0.157196 | − | 0.272271i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6591.76 | −0.360548 | ||||||||
\(695\) | −3827.65 | + | 6629.69i | −0.208908 | + | 0.361839i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11670.9 | 0.634241 | ||||||||
\(698\) | −2622.57 | + | 4542.43i | −0.142215 | + | 0.246323i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2449.37 | − | 4242.43i | −0.132254 | − | 0.229070i | ||||
\(701\) | 29159.8 | 1.57111 | 0.785557 | − | 0.618789i | \(-0.212376\pi\) | ||||
0.785557 | + | 0.618789i | \(0.212376\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3900.73 | −0.209273 | ||||||||
\(704\) | 3249.96 | + | 5629.10i | 0.173988 | + | 0.301356i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5897.52 | + | 10214.8i | −0.314385 | + | 0.544531i | ||||
\(707\) | −47757.0 | −2.54044 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10244.5 | − | 17744.0i | 0.542653 | − | 0.939903i | −0.456097 | − | 0.889930i | \(-0.650753\pi\) |
0.998751 | − | 0.0499730i | \(-0.0159135\pi\) | |||||||
\(710\) | 4983.16 | 0.263401 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1725.16 | − | 2988.06i | −0.0908047 | − | 0.157278i | ||||
\(713\) | −2091.96 | − | 3623.37i | −0.109880 | − | 0.190318i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19562.3 | + | 9313.83i | −1.02320 | + | 0.487157i | ||||
\(716\) | 10840.7 | 0.565833 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1592.85 | − | 2758.90i | −0.0827919 | − | 0.143400i | ||||
\(719\) | −8995.06 | + | 15579.9i | −0.466563 | + | 0.808111i | −0.999271 | − | 0.0381883i | \(-0.987841\pi\) |
0.532707 | + | 0.846300i | \(0.321175\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23507.0 | − | 40715.3i | 1.21421 | − | 2.10308i | ||||
\(722\) | −5580.82 | + | 9666.26i | −0.287668 | + | 0.498256i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2494.60 | − | 4320.78i | 0.128054 | − | 0.221796i | ||||
\(725\) | 2726.00 | + | 4721.57i | 0.139643 | + | 0.241869i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37652.7 | −1.92086 | −0.960428 | − | 0.278528i | \(-0.910153\pi\) | ||||
−0.960428 | + | 0.278528i | \(0.910153\pi\) | |||||||
\(728\) | −23473.4 | − | 16157.2i | −1.19503 | − | 0.822561i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5587.85 | + | 9678.45i | 0.283309 | + | 0.490706i | ||||
\(731\) | −2326.42 | − | 4029.48i | −0.117710 | − | 0.203879i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4524.26 | 0.227977 | 0.113989 | − | 0.993482i | \(-0.463637\pi\) | ||||
0.113989 | + | 0.993482i | \(0.463637\pi\) | |||||||
\(734\) | −5617.19 | + | 9729.26i | −0.282472 | + | 0.489256i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24495.6 | −1.22679 | ||||||||
\(737\) | −10350.7 | + | 17927.9i | −0.517329 | + | 0.896040i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −409.151 | − | 708.671i | −0.0203665 | − | 0.0352759i | 0.855663 | − | 0.517534i | \(-0.173150\pi\) |
−0.876029 | + | 0.482258i | \(0.839817\pi\) | |||||||
\(740\) | −1868.68 | −0.0928300 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6684.10 | 0.330702 | ||||||||
\(743\) | 19501.1 | + | 33776.9i | 0.962888 | + | 1.66777i | 0.715185 | + | 0.698935i | \(0.246342\pi\) |
0.247702 | + | 0.968836i | \(0.420324\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8758.59 | + | 15170.3i | −0.430725 | + | 0.746037i | ||||
\(746\) | 15456.4 | 0.758579 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6624.90 | + | 11474.7i | −0.323838 | + | 0.560903i | ||||
\(749\) | 201.584 | 0.00983407 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11188.8 | + | 19379.7i | 0.543658 | + | 0.941643i | 0.998690 | + | 0.0511678i | \(0.0162943\pi\) |
−0.455032 | + | 0.890475i | \(0.650372\pi\) | |||||||
\(752\) | 4590.59 | + | 7951.13i | 0.222608 | + | 0.385569i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11035.1 | + | 7595.67i | 0.532990 | + | 0.366868i | ||||
\(755\) | −11485.7 | −0.553653 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17256.3 | + | 29888.8i | 0.828521 | + | 1.43504i | 0.899198 | + | 0.437542i | \(0.144151\pi\) |
−0.0706770 | + | 0.997499i | \(0.522516\pi\) | |||||||
\(758\) | −4013.85 | + | 6952.19i | −0.192335 | + | 0.333133i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12031.7 | + | 20839.5i | −0.574258 | + | 0.994645i | ||||
\(761\) | 9987.78 | − | 17299.3i | 0.475764 | − | 0.824048i | −0.523850 | − | 0.851810i | \(-0.675505\pi\) |
0.999615 | + | 0.0277624i | \(0.00883820\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8119.95 | − | 14064.2i | 0.385271 | − | 0.667309i | ||||
\(764\) | −12992.0 | − | 22502.8i | −0.615228 | − | 1.06561i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1184.73 | −0.0558827 | ||||||||
\(767\) | −12656.0 | − | 8711.38i | −0.595804 | − | 0.410104i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16532.4 | + | 28635.0i | 0.775260 | + | 1.34279i | 0.934648 | + | 0.355574i | \(0.115715\pi\) |
−0.159388 | + | 0.987216i | \(0.550952\pi\) | |||||||
\(770\) | −10145.0 | − | 17571.6i | −0.474805 | − | 0.822387i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14523.6 | 0.677091 | ||||||||
\(773\) | −9282.01 | + | 16076.9i | −0.431890 | + | 0.748055i | −0.997036 | − | 0.0769359i | \(-0.975486\pi\) |
0.565146 | + | 0.824991i | \(0.308820\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 895.279 | 0.0414960 | ||||||||
\(776\) | 2174.82 | − | 3766.90i | 0.100608 | − | 0.174257i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5175.53 | − | 8964.28i | −0.238498 | − | 0.413091i | ||||
\(779\) | 29091.6 | 1.33802 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16191.7 | 0.741848 | ||||||||
\(782\) | 4623.83 | + | 8008.71i | 0.211442 | + | 0.366229i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4712.93 | + | 8163.04i | −0.214693 | + | 0.371858i | ||||
\(785\) | −5098.91 | −0.231832 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18218.4 | + | 31555.2i | −0.825179 | + | 1.42925i | 0.0766032 | + | 0.997062i | \(0.475593\pi\) |
−0.901782 | + | 0.432190i | \(0.857741\pi\) | |||||||
\(788\) | 7373.04 | 0.333317 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1085.54 | − | 1880.21i | −0.0488884 | − | 0.0846772i | ||||
\(791\) | −21598.8 | − | 37410.2i | −0.970877 | − | 1.68161i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3799.90 | − | 2615.55i | −0.170162 | − | 0.117126i | ||||
\(794\) | −2081.71 | −0.0930441 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16150.3 | − | 27973.2i | −0.719137 | − | 1.24558i | ||||
\(797\) | 6182.80 | − | 10708.9i | 0.274788 | − | 0.475947i | −0.695294 | − | 0.718726i | \(-0.744726\pi\) |
0.970082 | + | 0.242779i | \(0.0780590\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13006.9 | − | 22528.6i | 0.575907 | − | 0.997501i | ||||
\(800\) | 2620.80 | − | 4539.37i | 0.115824 | − | 0.200614i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7822.19 | − | 13548.4i | 0.344403 | − | 0.596523i | ||||
\(803\) | 18156.5 | + | 31448.0i | 0.797918 | + | 1.38204i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38545.4 | 1.68763 | ||||||||
\(806\) | 1986.23 | − | 945.665i | 0.0868015 | − | 0.0413271i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16195.4 | − | 28051.3i | −0.705140 | − | 1.22134i | ||||
\(809\) | −4046.87 | − | 7009.39i | −0.175872 | − | 0.304619i | 0.764591 | − | 0.644516i | \(-0.222941\pi\) |
−0.940463 | + | 0.339897i | \(0.889608\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15984.7 | 0.692105 | 0.346052 | − | 0.938215i | \(-0.387522\pi\) | ||||
0.346052 | + | 0.938215i | \(0.387522\pi\) | |||||||
\(812\) | 17073.6 | − | 29572.4i | 0.737891 | − | 1.27806i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2230.77 | 0.0960546 | ||||||||
\(815\) | 3005.34 | − | 5205.40i | 0.129169 | − | 0.223727i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5798.99 | − | 10044.2i | −0.248325 | − | 0.430111i | ||||
\(818\) | 9312.03 | 0.398029 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13936.6 | 0.593523 | ||||||||
\(821\) | −13430.9 | − | 23263.1i | −0.570942 | − | 0.988900i | −0.996470 | − | 0.0839550i | \(-0.973245\pi\) |
0.425528 | − | 0.904945i | \(-0.360089\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2602.97 | − | 4508.48i | 0.110248 | − | 0.190955i | −0.805622 | − | 0.592429i | \(-0.798169\pi\) |
0.915870 | + | 0.401475i | \(0.131502\pi\) | |||||||
\(824\) | 31886.9 | 1.34810 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7194.14 | − | 12460.6i | 0.303046 | − | 0.524891i | ||||
\(827\) | −46621.5 | −1.96032 | −0.980162 | − | 0.198200i | \(-0.936491\pi\) | ||||
−0.980162 | + | 0.198200i | \(0.936491\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20914.9 | + | 36225.6i | 0.876241 | + | 1.51769i | 0.855435 | + | 0.517910i | \(0.173290\pi\) |
0.0208053 | + | 0.999784i | \(0.493377\pi\) | |||||||
\(830\) | −2440.44 | − | 4226.96i | −0.102059 | − | 0.176771i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 513.960 | − | 6472.12i | 0.0214163 | − | 0.269688i | ||||
\(833\) | 26707.0 | 1.11086 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14692.1 | − | 25447.5i | −0.608913 | − | 1.05467i | ||||
\(836\) | −16513.7 | + | 28602.5i | −0.683179 | + | 1.18330i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4118.19 | − | 7132.91i | 0.169762 | − | 0.294036i | ||||
\(839\) | 6342.54 | − | 10985.6i | 0.260988 | − | 0.452044i | −0.705517 | − | 0.708693i | \(-0.749285\pi\) |
0.966505 | + | 0.256649i | \(0.0826185\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6807.43 | + | 11790.8i | −0.279119 | + | 0.483448i | ||||
\(842\) | 1112.99 | + | 1927.75i | 0.0455535 | + | 0.0789009i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 26490.1 | 1.08036 | ||||||||
\(845\) | 21370.4 | + | 3415.64i | 0.870017 | + | 0.139055i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13039.1 | − | 22584.3i | −0.528959 | − | 0.916183i | ||||
\(848\) | −1296.88 | − | 2246.27i | −0.0525179 | − | 0.0909636i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1978.83 | −0.0798509 | ||||||||
\(851\) | −2118.92 | + | 3670.08i | −0.0853534 | + | 0.147836i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37493.3 | −1.50498 | −0.752488 | − | 0.658606i | \(-0.771146\pi\) | ||||
−0.752488 | + | 0.658606i | \(0.771146\pi\) | |||||||
\(854\) | 2160.00 | − | 3741.24i | 0.0865501 | − | 0.149909i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 68.3614 | + | 118.405i | 0.00272961 | + | 0.00472782i | ||||
\(857\) | 11826.3 | 0.471386 | 0.235693 | − | 0.971828i | \(-0.424264\pi\) | ||||
0.235693 | + | 0.971828i | \(0.424264\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36498.7 | −1.44973 | −0.724866 | − | 0.688890i | \(-0.758099\pi\) | ||||
−0.724866 | + | 0.688890i | \(0.758099\pi\) | |||||||
\(860\) | −2778.07 | − | 4811.76i | −0.110153 | − | 0.190790i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3643.36 | + | 6310.48i | −0.143960 | + | 0.249346i | ||||
\(863\) | −2292.79 | −0.0904372 | −0.0452186 | − | 0.998977i | \(-0.514398\pi\) | ||||
−0.0452186 | + | 0.998977i | \(0.514398\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4817.96 | + | 8344.95i | −0.189382 | + | 0.328020i | ||||
\(866\) | −4836.24 | −0.189772 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2803.68 | − | 4856.12i | −0.109635 | − | 0.189893i | ||||
\(869\) | −3527.22 | − | 6109.33i | −0.137690 | − | 0.238487i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18669.6 | − | 8888.81i | 0.726288 | − | 0.345793i | ||||
\(872\) | 11014.6 | 0.427753 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11525.7 | + | 19963.1i | 0.446066 | + | 0.772609i | ||||
\(875\) | −22556.6 | + | 39069.2i | −0.871488 | + | 1.50946i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10400.1 | − | 18013.6i | 0.400442 | − | 0.693587i | −0.593337 | − | 0.804954i | \(-0.702190\pi\) |
0.993779 | + | 0.111368i | \(0.0355231\pi\) | |||||||
\(878\) | 4433.84 | − | 7679.63i | 0.170427 | − | 0.295188i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3936.76 | + | 6818.67i | −0.150805 | + | 0.261202i | ||||
\(881\) | −9627.95 | − | 16676.1i | −0.368188 | − | 0.637721i | 0.621094 | − | 0.783736i | \(-0.286689\pi\) |
−0.989282 | + | 0.146015i | \(0.953355\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1744.49 | 0.0664857 | 0.0332429 | − | 0.999447i | \(-0.489417\pi\) | ||||
0.0332429 | + | 0.999447i | \(0.489417\pi\) | |||||||
\(884\) | 11949.4 | − | 5689.25i | 0.454642 | − | 0.216460i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5001.33 | + | 8662.56i | 0.189642 | + | 0.328470i | ||||
\(887\) | 1485.35 | + | 2572.70i | 0.0562268 | + | 0.0973877i | 0.892769 | − | 0.450515i | \(-0.148760\pi\) |
−0.836542 | + | 0.547903i | \(0.815426\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −74634.6 | −2.81571 | ||||||||
\(890\) | −1226.94 | + | 2125.11i | −0.0462101 | + | 0.0800382i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −26217.3 | −0.984104 | ||||||||
\(893\) | 32421.8 | − | 56156.2i | 1.21495 | − | 2.10436i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9126.24 | − | 15807.1i | −0.340845 | − | 0.590361i | ||||
\(896\) | −38810.9 | −1.44708 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −601.703 | −0.0223598 | ||||||||
\(899\) | 3120.33 | + | 5404.57i | 0.115761 | + | 0.200503i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3674.56 | + | 6364.52i | −0.135868 | + | 0.235331i | ||||
\(902\) | −16637.1 | −0.614140 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14649.2 | − | 25373.2i | 0.538966 | − | 0.933516i | ||||
\(905\) | −8400.32 | −0.308548 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16501.7 | − | 28581.7i | −0.604111 | − | 1.04635i | −0.992191 | − | 0.124726i | \(-0.960195\pi\) |
0.388080 | − | 0.921626i | \(-0.373138\pi\) | |||||||
\(908\) | 16848.8 | + | 29183.1i | 0.615802 | + | 1.06660i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1604.36 | + | 20203.2i | −0.0584441 | + | 0.735967i | ||||
\(911\) | −14977.0 | −0.544686 | −0.272343 | − | 0.962200i | \(-0.587799\pi\) | ||||
−0.272343 | + | 0.962200i | \(0.587799\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7929.66 | − | 13734.6i | −0.287441 | − | 0.497862i | ||||
\(914\) | 12200.0 | − | 21131.1i | 0.441511 | − | 0.764720i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13558.9 | + | 23484.7i | −0.489080 | + | 0.847112i | ||||
\(917\) | 11145.9 | − | 19305.3i | 0.401386 | − | 0.695221i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5712.69 | + | 9894.67i | −0.205054 | + | 0.355163i | −0.950150 | − | 0.311794i | \(-0.899070\pi\) |
0.745096 | + | 0.666957i | \(0.232404\pi\) | |||||||
\(920\) | 13071.6 | + | 22640.6i | 0.468431 | + | 0.811346i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17196.9 | 0.614263 | ||||||||
\(923\) | −13322.3 | − | 9169.99i | −0.475090 | − | 0.327014i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −453.410 | − | 785.329i | −0.0161168 | − | 0.0279151i | ||||
\(926\) | 2613.27 | + | 4526.32i | 0.0927403 | + | 0.160631i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 36537.3 | 1.29245 | ||||||||
\(929\) | 5977.10 | − | 10352.6i | 0.211090 | − | 0.365618i | −0.740966 | − | 0.671542i | \(-0.765632\pi\) |
0.952056 | + | 0.305924i | \(0.0989655\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 66571.7 | 2.34350 | ||||||||
\(932\) | −17219.1 | + | 29824.4i | −0.605183 | + | 1.04821i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 831.870 | + | 1440.84i | 0.0291431 | + | 0.0504773i | ||||
\(935\) | 22308.7 | 0.780290 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42546.4 | 1.48338 | 0.741692 | − | 0.670740i | \(-0.234024\pi\) | ||||
0.741692 | + | 0.670740i | \(0.234024\pi\) | |||||||
\(938\) | 9682.04 | + | 16769.8i | 0.337025 | + | 0.583745i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15532.0 | − | 26902.2i | 0.538934 | − | 0.933461i | ||||
\(941\) | −20665.1 | −0.715903 | −0.357951 | − | 0.933740i | \(-0.616525\pi\) | ||||
−0.357951 | + | 0.933740i | \(0.616525\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15802.9 | − | 27371.5i | 0.545720 | − | 0.945215i | ||||
\(944\) | −5583.37 | −0.192503 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3316.36 | + | 5744.10i | 0.113979 | + | 0.197417i | ||||
\(947\) | −4746.87 | − | 8221.81i | −0.162885 | − | 0.282126i | 0.773017 | − | 0.634385i | \(-0.218747\pi\) |
−0.935902 | + | 0.352260i | \(0.885413\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2871.33 | − | 36157.7i | 0.0982163 | − | 1.23681i | ||||
\(950\) | −4932.56 | −0.168456 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 14670.6 | + | 25410.3i | 0.499452 | + | 0.865076i | ||||
\(953\) | 26667.1 | − | 46188.7i | 0.906433 | − | 1.56999i | 0.0874512 | − | 0.996169i | \(-0.472128\pi\) |
0.818982 | − | 0.573819i | \(-0.194539\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21874.6 | + | 37887.9i | −0.741199 | + | 1.28379i | ||||
\(956\) | −6247.93 | + | 10821.7i | −0.211373 | + | 0.366108i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14201.1 | + | 24597.0i | −0.478932 | + | 0.829534i | ||||
\(959\) | −3325.79 | − | 5760.44i | −0.111987 | − | 0.193967i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28766.2 | −0.965601 | ||||||||
\(962\) | −1835.45 | − | 1263.37i | −0.0615147 | − | 0.0423418i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13728.1 | + | 23777.7i | 0.458663 | + | 0.794428i | ||||
\(965\) | −12226.6 | − | 21177.2i | −0.407865 | − | 0.706443i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42110.1 | −1.40038 | −0.700191 | − | 0.713956i | \(-0.746902\pi\) | ||||
−0.700191 | + | 0.713956i | \(0.746902\pi\) | |||||||
\(968\) | 8843.65 | − | 15317.7i | 0.293642 | − | 0.508604i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3093.47 | −0.102397 | ||||||||
\(971\) | −6913.86 | + | 11975.2i | −0.228503 | + | 0.395779i | −0.957365 | − | 0.288882i | \(-0.906716\pi\) |
0.728862 | + | 0.684661i | \(0.240050\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11633.7 | + | 20150.2i | 0.383309 | + | 0.663911i | ||||
\(974\) | −13262.3 | −0.436295 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1676.38 | −0.0549791 | ||||||||
\(977\) | 566.943 | + | 981.973i | 0.0185651 | + | 0.0321557i | 0.875159 | − | 0.483836i | \(-0.160757\pi\) |
−0.856594 | + | 0.515992i | \(0.827424\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3986.65 | + | 6905.09i | −0.130147 | + | 0.225421i | ||||
\(980\) | 31891.9 | 1.03954 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10558.4 | − | 18287.6i | 0.343107 | − | 0.594279i | ||||
\(983\) | −26250.2 | −0.851729 | −0.425865 | − | 0.904787i | \(-0.640030\pi\) | ||||
−0.425865 | + | 0.904787i | \(0.640030\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6206.98 | − | 10750.8i | −0.200783 | − | 0.347766i | ||||
\(986\) | −6896.84 | − | 11945.7i | −0.222759 | − | 0.385829i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 29786.0 | − | 14181.4i | 0.959128 | − | 0.456651i | ||||
\(989\) | −12600.3 | −0.405124 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14680.2 | + | 25426.8i | 0.470566 | + | 0.815045i | 0.999433 | − | 0.0336599i | \(-0.0107163\pi\) |
−0.528867 | + | 0.848705i | \(0.677383\pi\) | |||||||
\(992\) | 2999.92 | − | 5196.01i | 0.0960156 | − | 0.166304i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7572.87 | − | 13116.6i | 0.241647 | − | 0.418544i | ||||
\(995\) | −27192.3 | + | 47098.4i | −0.866384 | + | 1.50062i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8417.95 | + | 14580.3i | −0.267401 | + | 0.463153i | −0.968190 | − | 0.250216i | \(-0.919498\pi\) |
0.700789 | + | 0.713369i | \(0.252832\pi\) | |||||||
\(998\) | 6831.85 | + | 11833.1i | 0.216692 | + | 0.375321i | ||||
\(999\) | 0 | 0 |
(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 | 117.4.g.e.55.2 | 8 | ||
3.2 | odd | 2 | 39.4.e.c.16.3 | ✓ | 8 | ||
12.11 | even | 2 | 624.4.q.i.289.4 | 8 | |||
13.3 | even | 3 | 1521.4.a.v.1.3 | 4 | |||
13.9 | even | 3 | inner | 117.4.g.e.100.2 | 8 | ||
13.10 | even | 6 | 1521.4.a.bb.1.2 | 4 | |||
39.2 | even | 12 | 507.4.b.h.337.5 | 8 | |||
39.11 | even | 12 | 507.4.b.h.337.4 | 8 | |||
39.23 | odd | 6 | 507.4.a.i.1.3 | 4 | |||
39.29 | odd | 6 | 507.4.a.m.1.2 | 4 | |||
39.35 | odd | 6 | 39.4.e.c.22.3 | yes | 8 | ||
156.35 | even | 6 | 624.4.q.i.529.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.c.16.3 | ✓ | 8 | 3.2 | odd | 2 | ||
39.4.e.c.22.3 | yes | 8 | 39.35 | odd | 6 | ||
117.4.g.e.55.2 | 8 | 1.1 | even | 1 | trivial | ||
117.4.g.e.100.2 | 8 | 13.9 | even | 3 | inner | ||
507.4.a.i.1.3 | 4 | 39.23 | odd | 6 | |||
507.4.a.m.1.2 | 4 | 39.29 | odd | 6 | |||
507.4.b.h.337.4 | 8 | 39.11 | even | 12 | |||
507.4.b.h.337.5 | 8 | 39.2 | even | 12 | |||
624.4.q.i.289.4 | 8 | 12.11 | even | 2 | |||
624.4.q.i.529.4 | 8 | 156.35 | even | 6 | |||
1521.4.a.v.1.3 | 4 | 13.3 | even | 3 | |||
1521.4.a.bb.1.2 | 4 | 13.10 | even | 6 |