Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(289,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 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("624.289");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.q (of order \(3\), 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: | \(36.8171918436\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.4 | ||
Root | \(-0.733051 - 1.26968i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.529 |
Dual form | 624.4.q.i.289.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −1.50000 | + | 2.59808i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.85055 | 0.881060 | 0.440530 | − | 0.897738i | \(-0.354791\pi\) | ||||
0.440530 | + | 0.897738i | \(0.354791\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.9698 | + | 25.9285i | 0.808293 | + | 1.40001i | 0.914045 | + | 0.405613i | \(0.132942\pi\) |
−0.105752 | + | 0.994393i | \(0.533725\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 23.4629 | − | 40.6389i | 0.643120 | − | 1.11392i | −0.341612 | − | 0.939841i | \(-0.610973\pi\) |
0.984732 | − | 0.174076i | \(-0.0556938\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.71050 | + | 46.7251i | 0.0791621 | + | 0.996862i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −14.7758 | + | 25.5925i | −0.254340 | + | 0.440530i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 24.1308 | + | 41.7958i | 0.344270 | + | 0.596292i | 0.985221 | − | 0.171289i | \(-0.0547932\pi\) |
−0.640951 | + | 0.767582i | \(0.721460\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 60.1501 | + | 104.183i | 0.726283 | + | 1.25796i | 0.958444 | + | 0.285282i | \(0.0920872\pi\) |
−0.232161 | + | 0.972677i | \(0.574579\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −89.8188 | −0.933337 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 65.3485 | − | 113.187i | 0.592440 | − | 1.02614i | −0.401463 | − | 0.915875i | \(-0.631498\pi\) |
0.993903 | − | 0.110260i | \(-0.0351685\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −27.9667 | −0.223734 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 97.4729 | − | 168.828i | 0.624147 | − | 1.08105i | −0.364558 | − | 0.931181i | \(-0.618780\pi\) |
0.988705 | − | 0.149874i | \(-0.0478867\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 32.0123 | 0.185470 | 0.0927351 | − | 0.995691i | \(-0.470439\pi\) | ||||
0.0927351 | + | 0.995691i | \(0.470439\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 70.3886 | + | 121.917i | 0.371306 | + | 0.643120i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 147.461 | + | 255.409i | 0.712155 | + | 1.23349i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16.2125 | − | 28.0808i | 0.0720355 | − | 0.124769i | −0.827758 | − | 0.561086i | \(-0.810384\pi\) |
0.899793 | + | 0.436316i | \(0.143717\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −126.961 | − | 60.4474i | −0.521283 | − | 0.248188i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 120.913 | − | 209.427i | 0.460570 | − | 0.797731i | −0.538419 | − | 0.842677i | \(-0.680978\pi\) |
0.998989 | + | 0.0449461i | \(0.0143116\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 48.2044 | + | 83.4924i | 0.170956 | + | 0.296104i | 0.938754 | − | 0.344587i | \(-0.111981\pi\) |
−0.767799 | + | 0.640691i | \(0.778648\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −44.3275 | − | 76.7774i | −0.146843 | − | 0.254340i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −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 | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −144.785 | −0.397528 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −152.277 | −0.394657 | −0.197328 | − | 0.980337i | \(-0.563226\pi\) | ||||
−0.197328 | + | 0.980337i | \(0.563226\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 231.122 | − | 400.315i | 0.566627 | − | 0.981427i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −360.901 | −0.838640 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 163.896 | + | 283.876i | 0.361652 | + | 0.626399i | 0.988233 | − | 0.152957i | \(-0.0488796\pi\) |
−0.626581 | + | 0.779356i | \(0.715546\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 49.2090 | + | 85.2325i | 0.103288 | + | 0.178900i | 0.913037 | − | 0.407876i | \(-0.133730\pi\) |
−0.809749 | + | 0.586776i | \(0.800397\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 134.728 | − | 233.356i | 0.269431 | − | 0.466668i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 36.5504 | + | 460.267i | 0.0697465 | + | 0.878295i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −220.575 | + | 382.048i | −0.402202 | + | 0.696635i | −0.993991 | − | 0.109458i | \(-0.965089\pi\) |
0.591789 | + | 0.806093i | \(0.298422\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 196.046 | + | 339.561i | 0.342045 | + | 0.592440i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 172.524 | + | 298.821i | 0.288379 | + | 0.499486i | 0.973423 | − | 0.229015i | \(-0.0735505\pi\) |
−0.685044 | + | 0.728501i | \(0.740217\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 773.839 | 1.24070 | 0.620349 | − | 0.784326i | \(-0.286991\pi\) | ||||
0.620349 | + | 0.784326i | \(0.286991\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 41.9501 | − | 72.6597i | 0.0645864 | − | 0.111867i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1404.94 | 2.07932 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 150.332 | 0.214097 | 0.107049 | − | 0.994254i | \(-0.465860\pi\) | ||||
0.107049 | + | 0.994254i | \(0.465860\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −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 | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 292.419 | + | 506.484i | 0.360351 | + | 0.624147i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −84.9567 | + | 147.149i | −0.101184 | + | 0.175256i | −0.912173 | − | 0.409806i | \(-0.865596\pi\) |
0.810989 | + | 0.585062i | \(0.198930\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1155.96 | + | 795.673i | −1.33163 | + | 0.916584i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −48.0184 | + | 83.1703i | −0.0535406 | + | 0.0927351i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 592.511 | + | 1026.26i | 0.639899 | + | 1.10834i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −107.101 | − | 185.504i | −0.112107 | − | 0.194176i | 0.804512 | − | 0.593936i | \(-0.202427\pi\) |
−0.916620 | + | 0.399760i | \(0.869093\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −422.332 | −0.428747 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −797.556 | + | 1381.41i | −0.785741 | + | 1.36094i | 0.142815 | + | 0.989749i | \(0.454385\pi\) |
−0.928555 | + | 0.371194i | \(0.878949\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1570.30 | 1.50219 | 0.751096 | − | 0.660193i | \(-0.229525\pi\) | ||||
0.751096 | + | 0.660193i | \(0.229525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −884.764 | −0.822325 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.36651 | + | 5.83096i | −0.00304161 | + | 0.00526823i | −0.867542 | − | 0.497364i | \(-0.834302\pi\) |
0.864501 | + | 0.502632i | \(0.167635\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −542.422 | −0.476648 | −0.238324 | − | 0.971186i | \(-0.576598\pi\) | ||||
−0.238324 | + | 0.971186i | \(0.576598\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 48.6374 | + | 84.2425i | 0.0415897 | + | 0.0720355i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 721.411 | + | 1249.52i | 0.600572 | + | 1.04022i | 0.992735 | + | 0.120325i | \(0.0383938\pi\) |
−0.392162 | + | 0.919896i | \(0.628273\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 643.719 | − | 1114.95i | 0.521975 | − | 0.904087i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 347.489 | − | 239.183i | 0.274576 | − | 0.188996i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −722.467 | + | 1251.35i | −0.556542 | + | 0.963958i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −435.513 | − | 754.330i | −0.327207 | − | 0.566739i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 362.738 | + | 628.280i | 0.265910 | + | 0.460570i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1506.81 | −1.07818 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1246.42 | + | 2158.86i | −0.870881 | + | 1.50841i | −0.00979442 | + | 0.999952i | \(0.503118\pi\) |
−0.861087 | + | 0.508458i | \(0.830216\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −289.226 | −0.197403 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −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 | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 265.965 | 0.169560 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 111.083 | + | 192.402i | 0.0692736 | + | 0.119985i | 0.898582 | − | 0.438806i | \(-0.144599\pi\) |
−0.829308 | + | 0.558792i | \(0.811265\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −388.573 | − | 673.028i | −0.237110 | − | 0.410687i | 0.722774 | − | 0.691085i | \(-0.242867\pi\) |
−0.959884 | + | 0.280398i | \(0.909534\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 808.522 | − | 1400.40i | 0.482907 | − | 0.836419i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1985.91 | + | 945.514i | 1.16133 | + | 0.552922i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 960.161 | − | 1663.05i | 0.549911 | − | 0.952473i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −830.070 | − | 1437.72i | −0.465735 | − | 0.806676i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −889.147 | − | 1540.05i | −0.488871 | − | 0.846750i | 0.511047 | − | 0.859553i | \(-0.329258\pi\) |
−0.999918 | + | 0.0128032i | \(0.995925\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1166.00 | −0.628394 | −0.314197 | − | 0.949358i | \(-0.601735\pi\) | ||||
−0.314197 | + | 0.949358i | \(0.601735\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 217.177 | − | 376.162i | 0.114757 | − | 0.198764i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 315.338 | 0.163410 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 517.628 | 0.263129 | 0.131564 | − | 0.991308i | \(-0.458000\pi\) | ||||
0.131564 | + | 0.991308i | \(0.458000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 228.415 | − | 395.626i | 0.113928 | − | 0.197328i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3913.02 | 1.91546 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 305.094 | + | 528.438i | 0.146606 | + | 0.253929i | 0.929971 | − | 0.367633i | \(-0.119832\pi\) |
−0.783365 | + | 0.621562i | \(0.786498\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 693.366 | + | 1200.95i | 0.327142 | + | 0.566627i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1491.51 | − | 2583.36i | 0.691115 | − | 1.19705i | −0.280358 | − | 0.959895i | \(-0.590453\pi\) |
0.971473 | − | 0.237150i | \(-0.0762133\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2169.46 | + | 346.747i | −0.987467 | + | 0.157827i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 541.351 | − | 937.647i | 0.242094 | − | 0.419320i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −489.106 | − | 847.157i | −0.214948 | − | 0.372301i | 0.738308 | − | 0.674463i | \(-0.235625\pi\) |
−0.953257 | + | 0.302162i | \(0.902292\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −418.657 | − | 725.134i | −0.180843 | − | 0.313229i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −983.377 | −0.417599 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 926.471 | − | 1604.69i | 0.386858 | − | 0.670058i | −0.605167 | − | 0.796099i | \(-0.706894\pi\) |
0.992025 | + | 0.126040i | \(0.0402269\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 852.777 | 0.350201 | 0.175101 | − | 0.984551i | \(-0.443975\pi\) | ||||
0.175101 | + | 0.984551i | \(0.443975\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −295.254 | −0.119267 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 159.702 | − | 276.612i | 0.0634676 | − | 0.109929i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2264.71 | 0.885627 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 404.185 | + | 700.068i | 0.155556 | + | 0.269431i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2220.65 | + | 3846.27i | 0.841258 | + | 1.45710i | 0.888831 | + | 0.458234i | \(0.151518\pi\) |
−0.0475730 | + | 0.998868i | \(0.515149\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1241.21 | − | 2149.85i | 0.462925 | − | 0.801810i | −0.536180 | − | 0.844104i | \(-0.680133\pi\) |
0.999105 | + | 0.0422935i | \(0.0134665\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1250.64 | − | 595.440i | −0.459281 | − | 0.218669i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −630.115 | + | 1091.39i | −0.227888 | + | 0.394713i | −0.957182 | − | 0.289487i | \(-0.906515\pi\) |
0.729294 | + | 0.684200i | \(0.239849\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2760.48 | − | 4781.30i | −0.983344 | − | 1.70320i | −0.649077 | − | 0.760722i | \(-0.724845\pi\) |
−0.334266 | − | 0.942479i | \(-0.608489\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −661.726 | − | 1146.14i | −0.232212 | − | 0.402202i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5836.60 | 2.01798 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1191.06 | − | 2062.97i | 0.405790 | − | 0.702849i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1176.27 | −0.394960 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5645.18 | 1.86835 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2263.90 | + | 3921.18i | −0.738640 | + | 1.27936i | 0.214468 | + | 0.976731i | \(0.431198\pi\) |
−0.953108 | + | 0.302631i | \(0.902135\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1035.15 | −0.332991 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 474.839 | + | 822.446i | 0.150622 | + | 0.260885i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 479.217 | + | 830.029i | 0.149914 | + | 0.259659i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1160.76 | + | 2010.49i | −0.358159 | + | 0.620349i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1863.37 | + | 1282.60i | −0.567168 | + | 0.390393i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2240.59 | − | 3880.81i | 0.672829 | − | 1.16537i | −0.304270 | − | 0.952586i | \(-0.598412\pi\) |
0.977099 | − | 0.212787i | \(-0.0682542\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 125.850 | + | 217.979i | 0.0372890 | + | 0.0645864i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2879.88 | − | 4988.09i | −0.842044 | − | 1.45846i | −0.888163 | − | 0.459528i | \(-0.848019\pi\) |
0.0461191 | − | 0.998936i | \(-0.485315\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4635.08 | −1.33753 | −0.668766 | − | 0.743473i | \(-0.733177\pi\) | ||||
−0.668766 | + | 0.743473i | \(0.733177\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2107.41 | + | 3650.14i | −0.600248 | + | 1.03966i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5886.33 | 1.65505 | 0.827524 | − | 0.561431i | \(-0.189749\pi\) | ||||
0.827524 | + | 0.561431i | \(0.189749\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5309.59 | −1.47387 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −225.498 | + | 390.574i | −0.0618046 | + | 0.107049i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −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 | −0.988116 | − | 0.153708i | \(-0.950879\pi\) |
0.360943 | − | 0.932588i | \(-0.382455\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −121.500 | − | 210.444i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2725.55 | + | 4720.79i | −0.710730 | + | 1.23102i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4644.77 | + | 3197.09i | −1.19652 | + | 0.823587i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 506.949 | − | 878.062i | 0.129022 | − | 0.223473i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1951.44 | − | 3379.99i | −0.490732 | − | 0.849973i | 0.509211 | − | 0.860642i | \(-0.329937\pi\) |
−0.999943 | + | 0.0106687i | \(0.996604\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3066.53 | − | 5311.38i | −0.762020 | − | 1.31986i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1426.21 | −0.350246 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2065.42 | − | 3577.40i | 0.501312 | − | 0.868297i | −0.498687 | − | 0.866782i | \(-0.666184\pi\) |
0.999999 | − | 0.00151510i | \(-0.000482272\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 970.790 | 0.232903 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1754.51 | −0.416098 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3176.09 | − | 5501.14i | 0.744661 | − | 1.28979i | −0.205692 | − | 0.978617i | \(-0.565944\pi\) |
0.950353 | − | 0.311174i | \(-0.100722\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1500.01 | −0.347716 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −254.870 | − | 441.448i | −0.0584187 | − | 0.101184i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −90.7619 | − | 157.204i | −0.0205719 | − | 0.0356316i | 0.855556 | − | 0.517710i | \(-0.173215\pi\) |
−0.876128 | + | 0.482078i | \(0.839882\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1730.18 | − | 2996.75i | 0.387825 | − | 0.671733i | −0.604331 | − | 0.796733i | \(-0.706560\pi\) |
0.992157 | + | 0.125000i | \(0.0398930\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −333.273 | − | 4196.79i | −0.0738849 | − | 0.930408i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −656.180 | + | 1136.54i | −0.143888 | + | 0.249221i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3218.97 | + | 5575.42i | 0.698228 | + | 1.20937i | 0.969080 | + | 0.246745i | \(0.0793611\pi\) |
−0.270853 | + | 0.962621i | \(0.587306\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −144.055 | − | 249.511i | −0.0309117 | − | 0.0535406i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2974.26 | −0.631421 | −0.315711 | − | 0.948855i | \(-0.602243\pi\) | ||||
−0.315711 | + | 0.948855i | \(0.602243\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1517.86 | − | 2629.01i | 0.318825 | − | 0.552221i | −0.661418 | − | 0.750017i | \(-0.730045\pi\) |
0.980243 | + | 0.197797i | \(0.0633785\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3555.07 | −0.738891 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7240.15 | 1.48910 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1291.91 | − | 2237.65i | 0.262957 | − | 0.455455i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 642.604 | 0.129451 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 977.872 | + | 1693.72i | 0.194976 | + | 0.337708i | 0.946893 | − | 0.321550i | \(-0.104204\pi\) |
−0.751917 | + | 0.659258i | \(0.770871\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1614.47 | + | 2796.34i | 0.318637 | + | 0.551895i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 633.498 | − | 1097.25i | 0.123769 | − | 0.214373i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5531.15 | + | 2633.43i | 1.06981 | + | 0.509349i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1443.22 | + | 2499.73i | −0.276365 | + | 0.478678i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2392.67 | − | 4144.22i | −0.453648 | − | 0.785741i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 484.735 | + | 839.586i | 0.0910029 | + | 0.157622i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1027.56 | 0.191029 | 0.0955147 | − | 0.995428i | \(-0.469550\pi\) | ||||
0.0955147 | + | 0.995428i | \(0.469550\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2355.44 | + | 4079.75i | −0.433646 | + | 0.751096i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −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 | \(0.356890\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1327.15 | − | 2298.69i | 0.237385 | − | 0.411163i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1141.33 | 0.202219 | 0.101110 | − | 0.994875i | \(-0.467761\pi\) | ||||
0.101110 | + | 0.994875i | \(0.467761\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4573.99 | − | 7922.38i | −0.802803 | − | 1.39050i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.0995 | − | 17.4929i | −0.00175608 | − | 0.00304161i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2902.94 | + | 5028.04i | −0.500074 | + | 0.866154i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −103.771 | − | 1306.75i | −0.0177113 | − | 0.223032i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 813.633 | − | 1409.25i | 0.137596 | − | 0.238324i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8068.94 | − | 13975.8i | −1.35214 | − | 2.34198i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3826.28 | + | 6627.32i | 0.635382 | + | 1.10051i | 0.986434 | + | 0.164158i | \(0.0524908\pi\) |
−0.351052 | + | 0.936356i | \(0.614176\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −291.825 | −0.0480237 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −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 | \(0.564858\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4328.47 | −0.693481 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 751.100 | − | 1300.94i | 0.119280 | − | 0.206598i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6298.69 | −0.991537 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1931.16 | + | 3344.86i | 0.301362 | + | 0.521975i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2248.06 | + | 3893.75i | 0.347787 | + | 0.602385i | 0.985856 | − | 0.167594i | \(-0.0535999\pi\) |
−0.638069 | + | 0.769979i | \(0.720267\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1788.81 | + | 3098.31i | −0.274363 | + | 0.475211i | −0.969974 | − | 0.243208i | \(-0.921800\pi\) |
0.695611 | + | 0.718418i | \(0.255134\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 100.183 | + | 1261.58i | 0.0152348 | + | 0.191846i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4022.58 | − | 6967.32i | 0.606517 | − | 1.05052i | −0.385293 | − | 0.922794i | \(-0.625900\pi\) |
0.991810 | − | 0.127724i | \(-0.0407672\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1699.46 | + | 2943.55i | 0.254079 | + | 0.440077i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2167.40 | − | 3754.05i | −0.321319 | − | 0.556542i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 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 | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2613.08 | 0.377826 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7622.74 | 1.09313 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3831.38 | − | 6636.15i | 0.544949 | − | 0.943880i | −0.453661 | − | 0.891175i | \(-0.649882\pi\) |
0.998610 | − | 0.0527056i | \(-0.0167845\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2176.43 | −0.307047 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2279.55 | − | 3948.30i | −0.318998 | − | 0.552521i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5271.27 | − | 9130.10i | −0.731732 | − | 1.26740i | −0.956143 | − | 0.292902i | \(-0.905379\pi\) |
0.224411 | − | 0.974495i | \(-0.427954\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2260.21 | − | 3914.80i | 0.311244 | − | 0.539091i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8250.17 | + | 3927.99i | 1.12707 | + | 0.536610i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2737.77 | − | 4741.96i | 0.371055 | − | 0.642686i | −0.618673 | − | 0.785648i | \(-0.712329\pi\) |
0.989728 | + | 0.142962i | \(0.0456628\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3739.26 | − | 6476.59i | −0.502803 | − | 0.870881i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 404.042 | + | 699.822i | 0.0539050 | + | 0.0933661i | 0.891719 | − | 0.452590i | \(-0.149500\pi\) |
−0.837814 | + | 0.545956i | \(0.816167\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13839.4 | 1.83200 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 433.839 | − | 751.432i | 0.0569852 | − | 0.0987013i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7060.26 | −0.920230 | −0.460115 | − | 0.887859i | \(-0.652192\pi\) | ||||
−0.460115 | + | 0.887859i | \(0.652192\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6307.65 | 0.815836 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1116.84 | − | 1934.43i | 0.143352 | − | 0.248292i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1480.85 | 0.188633 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 709.947 | + | 1229.66i | 0.0897511 | + | 0.155453i | 0.907406 | − | 0.420255i | \(-0.138060\pi\) |
−0.817655 | + | 0.575709i | \(0.804726\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5402.61 | − | 9357.60i | −0.677867 | − | 1.17410i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5335.37 | + | 9241.13i | −0.664428 | + | 1.15082i | 0.315012 | + | 0.949088i | \(0.397991\pi\) |
−0.979440 | + | 0.201735i | \(0.935342\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 118.782 | + | 1495.78i | 0.0146822 | + | 0.184888i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −398.947 | + | 690.997i | −0.0489478 | + | 0.0847800i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −760.782 | − | 1317.71i | −0.0926550 | − | 0.160483i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3175.78 | − | 5500.61i | −0.383942 | − | 0.665007i | 0.607680 | − | 0.794182i | \(-0.292100\pi\) |
−0.991622 | + | 0.129175i | \(0.958767\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −666.500 | −0.0799903 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4906.98 | + | 8499.15i | −0.584641 | + | 1.01263i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3329.15 | −0.393787 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2331.44 | 0.273791 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2808.94 | − | 4865.22i | 0.327507 | − | 0.567259i | −0.654509 | − | 0.756054i | \(-0.727125\pi\) |
0.982017 | + | 0.188795i | \(0.0604581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1518.29 | −0.175765 | −0.0878825 | − | 0.996131i | \(-0.528010\pi\) | ||||
−0.0878825 | + | 0.996131i | \(0.528010\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2425.57 | + | 4201.20i | 0.278806 | + | 0.482907i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −674.860 | − | 1168.89i | −0.0770248 | − | 0.133411i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1473.30 | + | 2551.83i | −0.166974 | + | 0.289207i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5435.39 | + | 3741.28i | −0.611709 | + | 0.421051i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2485.07 | + | 4304.26i | −0.277730 | + | 0.481042i | −0.970820 | − | 0.239809i | \(-0.922915\pi\) |
0.693091 | + | 0.720850i | \(0.256249\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1649.36 | + | 2856.77i | 0.183055 | + | 0.317061i | 0.942919 | − | 0.333021i | \(-0.108068\pi\) |
−0.759864 | + | 0.650082i | \(0.774735\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2880.48 | + | 4989.14i | 0.317491 | + | 0.549911i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15722.9 | 1.72112 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3024.24 | + | 5238.13i | −0.328790 | + | 0.569481i | −0.982272 | − | 0.187461i | \(-0.939974\pi\) |
0.653482 | + | 0.756942i | \(0.273308\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4980.42 | 0.537784 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −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 | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5334.88 | 0.564500 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −205.205 | − | 355.426i | −0.0215684 | − | 0.0373576i | 0.855040 | − | 0.518563i | \(-0.173533\pi\) |
−0.876608 | + | 0.481205i | \(0.840199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5673.91 | − | 9827.51i | −0.592404 | − | 1.02607i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1749.00 | − | 3029.35i | 0.181402 | − | 0.314197i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11386.9 | + | 7837.81i | −1.17324 | + | 0.807565i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8321.41 | − | 14413.1i | 0.851771 | − | 1.47531i | −0.0278385 | − | 0.999612i | \(-0.508862\pi\) |
0.879609 | − | 0.475697i | \(-0.157804\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 651.532 | + | 1128.49i | 0.0662547 | + | 0.114757i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5864.85 | + | 10158.2i | 0.592523 | + | 1.02628i | 0.993891 | + | 0.110364i | \(0.0352015\pi\) |
−0.401368 | + | 0.915917i | \(0.631465\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3564.93 | 0.357832 | 0.178916 | − | 0.983864i | \(-0.442741\pi\) | ||||
0.178916 | + | 0.983864i | \(0.442741\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −473.008 | + | 819.273i | −0.0471725 | + | 0.0817051i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −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 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −776.441 | + | 1344.84i | −0.0759587 | + | 0.131564i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4524.05 | 0.439780 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1682.20 | − | 2913.66i | −0.162494 | − | 0.281448i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 685.245 | + | 1186.88i | 0.0657761 | + | 0.113928i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9686.30 | + | 16777.2i | −0.923963 | + | 1.60035i | −0.130743 | + | 0.991416i | \(0.541736\pi\) |
−0.793220 | + | 0.608935i | \(0.791597\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1372.24 | + | 653.335i | 0.130080 | + | 0.0619325i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5869.53 | + | 10166.3i | −0.552946 | + | 0.957730i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1055.00 | − | 1827.31i | −0.0987733 | − | 0.171080i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4522.98 | − | 7834.02i | −0.420853 | − | 0.728939i | 0.575170 | − | 0.818034i | \(-0.304936\pi\) |
−0.996023 | + | 0.0890946i | \(0.971603\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1830.56 | −0.169286 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7201.66 | − | 12473.6i | 0.661927 | − | 1.14649i | −0.318181 | − | 0.948030i | \(-0.603072\pi\) |
0.980109 | − | 0.198462i | \(-0.0635947\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9408.40 | 0.859499 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4160.20 | −0.377751 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5165.31 | + | 8946.58i | −0.466189 | + | 0.807463i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9319.75 | 0.836091 | 0.418045 | − | 0.908426i | \(-0.362715\pi\) | ||||
0.418045 | + | 0.908426i | \(0.362715\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4474.52 | + | 7750.09i | 0.399015 | + | 0.691115i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1372.99 | + | 2378.09i | 0.121707 | + | 0.210802i | 0.920441 | − | 0.390882i | \(-0.127830\pi\) |
−0.798734 | + | 0.601684i | \(0.794497\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7856.37 | + | 13607.6i | −0.692285 | + | 1.19907i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2353.32 | − | 6156.55i | 0.206143 | − | 0.539294i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 591.055 | − | 1023.74i | 0.0514697 | − | 0.0891481i | −0.839143 | − | 0.543911i | \(-0.816943\pi\) |
0.890612 | + | 0.454763i | \(0.150276\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11584.2 | + | 20064.5i | 1.00285 | + | 1.73698i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1624.05 | + | 2812.94i | 0.139773 | + | 0.242094i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15468.3 | 1.32352 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12646.8 | + | 21905.0i | −1.07584 | + | 1.86340i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2934.64 | 0.248201 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10858.8 | 0.913115 | 0.456558 | − | 0.889694i | \(-0.349082\pi\) | ||||
0.456558 | + | 0.889694i | \(0.349082\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5080.87 | + | 8800.33i | −0.424801 | + | 0.735777i | −0.996402 | − | 0.0847546i | \(-0.972989\pi\) |
0.571601 | + | 0.820532i | \(0.306323\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2511.94 | 0.208819 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 772.482 | + | 1337.98i | 0.0638517 | + | 0.110594i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2457.36 | − | 4256.28i | −0.201970 | − | 0.349821i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1475.06 | − | 2554.89i | 0.120551 | − | 0.208800i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10234.1 | + | 4872.57i | 0.831687 | + | 0.395975i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33.1620 | + | 57.4382i | −0.00267984 | + | 0.00464162i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2779.41 | + | 4814.08i | 0.223353 | + | 0.386858i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 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 | \(0.624209\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1279.16 | + | 2215.58i | −0.101094 | + | 0.175101i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5343.15 | −0.419955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15958.9 | −1.24745 | −0.623724 | − | 0.781645i | \(-0.714381\pi\) | ||||
−0.623724 | + | 0.781645i | \(0.714381\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 442.881 | − | 767.092i | 0.0344293 | − | 0.0596333i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23452.0 | 1.81323 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2250.44 | + | 3897.88i | 0.173053 | + | 0.299737i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 479.105 | + | 829.835i | 0.0366430 | + | 0.0634676i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1072.55 | − | 1857.70i | 0.0815892 | − | 0.141317i | −0.822344 | − | 0.568991i | \(-0.807334\pi\) |
0.903933 | + | 0.427675i | \(0.140667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3722.33 | + | 2562.15i | −0.281642 | + | 0.193859i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3397.07 | + | 5883.90i | −0.255658 | + | 0.442813i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11159.3 | − | 19328.5i | −0.835362 | − | 1.44689i | −0.893736 | − | 0.448594i | \(-0.851925\pi\) |
0.0583740 | − | 0.998295i | \(-0.481408\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7106.29 | + | 12308.5i | 0.529140 | + | 0.916497i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2425.11 | −0.179621 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9876.51 | − | 17106.6i | 0.727671 | − | 1.26036i | −0.230194 | − | 0.973145i | \(-0.573936\pi\) |
0.957865 | − | 0.287218i | \(-0.0927304\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10640.6 | 0.779850 | 0.389925 | − | 0.920847i | \(-0.372501\pi\) | ||||
0.389925 | + | 0.920847i | \(0.372501\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13323.9 | −0.971401 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −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 | \(0.424093\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3723.64 | + | 6449.54i | 0.267270 | + | 0.462925i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5059.29 | − | 8762.94i | −0.361264 | − | 0.625728i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3572.85 | + | 6188.35i | −0.253812 | + | 0.439615i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3422.95 | − | 2356.09i | 0.241917 | − | 0.166517i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2950.17 | − | 5109.84i | 0.207439 | − | 0.359294i | −0.743468 | − | 0.668771i | \(-0.766821\pi\) |
0.950907 | + | 0.309477i | \(0.100154\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1925.54 | + | 3335.14i | 0.134704 | + | 0.233314i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1890.35 | − | 3274.18i | −0.131571 | − | 0.227888i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15261.5 | −1.05686 | −0.528428 | − | 0.848978i | \(-0.677218\pi\) | ||||
−0.528428 | + | 0.848978i | \(0.677218\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7116.70 | + | 12326.5i | −0.490346 | + | 0.849305i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16562.9 | 1.13547 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 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 | −0.359894 | − | 0.932993i | \(-0.617187\pi\) |
0.987943 | − | 0.154819i | \(-0.0494794\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3970.36 | 0.268135 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4290.04 | − | 7430.56i | −0.288289 | − | 0.499331i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3204.25 | − | 5549.92i | −0.214261 | − | 0.371111i | 0.738783 | − | 0.673944i | \(-0.235401\pi\) |
−0.953044 | + | 0.302833i | \(0.902068\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8754.90 | + | 15163.9i | −0.582539 | + | 1.00899i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2000.01 | − | 25185.5i | −0.132425 | − | 1.66759i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1753.63 | − | 3037.38i | 0.115544 | − | 0.200128i | −0.802453 | − | 0.596715i | \(-0.796472\pi\) |
0.917997 | + | 0.396587i | \(0.129806\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3573.17 | + | 6188.91i | 0.234283 | + | 0.405790i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7253.89 | − | 12564.1i | −0.473307 | − | 0.819792i | 0.526226 | − | 0.850345i | \(-0.323607\pi\) |
−0.999533 | + | 0.0305526i | \(0.990273\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4750.85 | −0.308486 | −0.154243 | − | 0.988033i | \(-0.549294\pi\) | ||||
−0.154243 | + | 0.988033i | \(0.549294\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1764.41 | − | 3056.05i | 0.114015 | − | 0.197480i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5087.14 | −0.327146 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11347.0 | −0.726209 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8467.76 | + | 14666.6i | −0.539346 | + | 0.934175i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1564.88 | 0.0991986 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2412.60 | + | 4178.74i | 0.152209 | + | 0.263634i | 0.932039 | − | 0.362357i | \(-0.118028\pi\) |
−0.779830 | + | 0.625991i | \(0.784695\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6791.69 | − | 11763.5i | −0.426454 | − | 0.738640i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12277.9 | + | 21266.0i | −0.767298 | + | 1.32900i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23419.2 | − | 11150.1i | −1.45668 | − | 0.693539i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1552.72 | − | 2689.39i | 0.0961262 | − | 0.166495i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2955.95 | + | 5119.85i | 0.182142 | + | 0.315479i | 0.942610 | − | 0.333897i | \(-0.108364\pi\) |
−0.760468 | + | 0.649376i | \(0.775030\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11704.1 | + | 20272.2i | 0.717833 | + | 1.24332i | 0.961857 | + | 0.273554i | \(0.0881991\pi\) |
−0.244024 | + | 0.969769i | \(0.578468\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2849.04 | −0.173924 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8199.33 | + | 14201.7i | −0.498221 | + | 0.862944i | −0.999998 | − | 0.00205298i | \(-0.999347\pi\) |
0.501777 | + | 0.864997i | \(0.332680\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15381.9 | 0.930342 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2875.30 | −0.173106 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13764.8 | + | 23841.3i | −0.824897 | + | 1.42876i | 0.0771005 | + | 0.997023i | \(0.475434\pi\) |
−0.901998 | + | 0.431741i | \(0.857900\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7334.34 | −0.437521 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3482.28 | − | 6031.48i | −0.206783 | − | 0.358159i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12089.9 | − | 20940.3i | −0.714650 | − | 1.23781i | −0.963094 | − | 0.269164i | \(-0.913253\pi\) |
0.248444 | − | 0.968646i | \(-0.420081\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2262.52 | + | 3918.80i | −0.133134 | + | 0.230595i | −0.924883 | − | 0.380251i | \(-0.875838\pi\) |
0.791749 | + | 0.610847i | \(0.209171\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −537.224 | − | 6765.08i | −0.0314692 | − | 0.396281i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17739.6 | + | 30725.8i | −1.03445 | + | 1.79172i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12739.4 | − | 22065.3i | −0.739539 | − | 1.28092i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6721.76 | + | 11642.4i | 0.388458 | + | 0.672829i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4618.34 | 0.265706 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1643.59 | + | 2846.78i | −0.0941393 | + | 0.163054i | −0.909249 | − | 0.416253i | \(-0.863343\pi\) |
0.815110 | + | 0.579307i | \(0.196677\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −755.102 | −0.0430576 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9724.21 | −0.552041 | −0.276020 | − | 0.961152i | \(-0.589016\pi\) | ||||
−0.276020 | + | 0.961152i | \(0.589016\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3206.55 | − | 5553.91i | 0.181231 | − | 0.313902i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17279.3 | 0.972309 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7274.33 | + | 12599.5i | 0.407532 | + | 0.705867i | 0.994613 | − | 0.103662i | \(-0.0330560\pi\) |
−0.587080 | + | 0.809529i | \(0.699723\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1094.23 | + | 1895.26i | 0.0610342 | + | 0.105714i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6952.62 | − | 12042.3i | 0.386112 | − | 0.668766i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −565.022 | − | 7115.13i | −0.0312418 | − | 0.393418i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3364.48 | − | 5827.45i | 0.185226 | − | 0.320820i | −0.758427 | − | 0.651758i | \(-0.774032\pi\) |
0.943653 | + | 0.330938i | \(0.107365\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6322.22 | − | 10950.4i | −0.346553 | − | 0.600248i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3827.65 | − | 6629.69i | −0.208908 | − | 0.361839i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11670.9 | 0.634241 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8829.49 | + | 15293.1i | −0.477771 | + | 0.827524i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29159.8 | −1.57111 | −0.785557 | − | 0.618789i | \(-0.787624\pi\) | ||||
−0.785557 | + | 0.618789i | \(0.787624\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3900.73 | 0.209273 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7964.39 | − | 13794.7i | 0.425470 | − | 0.736935i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −47757.0 | −2.54044 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10244.5 | + | 17744.0i | 0.542653 | + | 0.939903i | 0.998751 | + | 0.0499730i | \(0.0159135\pi\) |
−0.456097 | + | 0.889930i | \(0.650753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −676.495 | − | 1171.72i | −0.0356829 | − | 0.0618046i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2091.96 | − | 3623.37i | 0.109880 | − | 0.190318i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19562.3 | + | 9313.83i | 1.02320 | + | 0.487157i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3203.77 | − | 5549.09i | 0.166871 | − | 0.289030i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8995.06 | − | 15579.9i | −0.466563 | − | 0.808111i | 0.532707 | − | 0.846300i | \(-0.321175\pi\) |
−0.999271 | + | 0.0381883i | \(0.987841\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23507.0 | + | 40715.3i | 1.21421 | + | 2.10308i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14078.8 | 0.724197 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2726.00 | + | 4721.57i | −0.139643 | + | 0.241869i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37652.7 | 1.92086 | 0.960428 | − | 0.278528i | \(-0.0898465\pi\) | ||||
0.960428 | + | 0.278528i | \(0.0898465\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −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 | \(0.463637\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8176.64 | − | 14162.4i | −0.410340 | − | 0.710730i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10350.7 | + | 17927.9i | 0.517329 | + | 0.896040i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 409.151 | − | 708.671i | 0.0203665 | − | 0.0352759i | −0.855663 | − | 0.517534i | \(-0.826850\pi\) |
0.876029 | + | 0.482258i | \(0.160183\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1339.12 | − | 16863.1i | −0.0663885 | − | 0.836008i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19501.1 | − | 33776.9i | 0.962888 | − | 1.66777i | 0.247702 | − | 0.968836i | \(-0.420324\pi\) |
0.715185 | − | 0.698935i | \(-0.246342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8758.59 | − | 15170.3i | −0.430725 | − | 0.746037i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1520.85 | + | 2634.19i | 0.0744912 | + | 0.129022i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −201.584 | −0.00983407 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11188.8 | + | 19379.7i | −0.543658 | + | 0.941643i | 0.455032 | + | 0.890475i | \(0.349628\pi\) |
−0.998690 | + | 0.0511678i | \(0.983706\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11708.6 | 0.566649 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11485.7 | −0.553653 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17256.3 | − | 29888.8i | 0.828521 | − | 1.43504i | −0.0706770 | − | 0.997499i | \(-0.522516\pi\) |
0.899198 | − | 0.437542i | \(-0.144151\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18399.2 | 0.879905 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9987.78 | − | 17299.3i | −0.475764 | − | 0.824048i | 0.523850 | − | 0.851810i | \(-0.324495\pi\) |
−0.999615 | + | 0.0277624i | \(0.991162\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8119.95 | − | 14064.2i | −0.385271 | − | 0.667309i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2139.32 | − | 3705.40i | 0.101107 | − | 0.175123i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12656.0 | + | 8711.38i | −0.595804 | + | 0.410104i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16532.4 | − | 28635.0i | 0.775260 | − | 1.34279i | −0.159388 | − | 0.987216i | \(-0.550952\pi\) |
0.934648 | − | 0.355574i | \(-0.115715\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6196.25 | + | 10732.2i | 0.289432 | + | 0.501312i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9282.01 | + | 16076.9i | 0.431890 | + | 0.748055i | 0.997036 | − | 0.0769359i | \(-0.0245137\pi\) |
−0.565146 | + | 0.824991i | \(0.691180\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −895.279 | −0.0414960 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1456.19 | + | 2522.19i | −0.0672334 | + | 0.116452i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29091.6 | 1.33802 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16191.7 | 0.741848 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2631.77 | − | 4558.36i | 0.120117 | − | 0.208049i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5098.91 | 0.231832 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18218.4 | + | 31555.2i | 0.825179 | + | 1.42925i | 0.901782 | + | 0.432190i | \(0.142259\pi\) |
−0.0766032 | + | 0.997062i | \(0.524407\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9528.26 | + | 16503.4i | 0.429930 | + | 0.744661i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21598.8 | + | 37410.2i | −0.970877 | + | 1.68161i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3799.90 | + | 2615.55i | −0.170162 | + | 0.117126i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2250.01 | − | 3897.13i | 0.100377 | − | 0.173858i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6182.80 | − | 10708.9i | −0.274788 | − | 0.475947i | 0.695294 | − | 0.718726i | \(-0.255274\pi\) |
−0.970082 | + | 0.242779i | \(0.921941\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13006.9 | − | 22528.6i | −0.575907 | − | 0.997501i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1529.22 | 0.0674561 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18156.5 | − | 31448.0i | 0.797918 | − | 1.38204i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38545.4 | 1.68763 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 544.571 | 0.0237544 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4046.87 | − | 7009.39i | 0.175872 | − | 0.304619i | −0.764591 | − | 0.644516i | \(-0.777059\pi\) |
0.940463 | + | 0.339897i | \(0.110392\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15984.7 | −0.692105 | −0.346052 | − | 0.938215i | \(-0.612478\pi\) | ||||
−0.346052 | + | 0.938215i | \(0.612478\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5190.53 | + | 8990.26i | 0.223911 | + | 0.387825i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3005.34 | + | 5205.40i | 0.129169 | + | 0.223727i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5798.99 | + | 10044.2i | −0.248325 | + | 0.430111i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11403.5 | + | 5429.32i | 0.486533 | + | 0.231643i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13430.9 | − | 23263.1i | 0.570942 | − | 0.988900i | −0.425528 | − | 0.904945i | \(-0.639911\pi\) |
0.996470 | − | 0.0839550i | \(-0.0267552\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2602.97 | − | 4508.48i | −0.110248 | − | 0.190955i | 0.805622 | − | 0.592429i | \(-0.201831\pi\) |
−0.915870 | + | 0.401475i | \(0.868498\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1968.54 | − | 3409.61i | −0.0830737 | − | 0.143888i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −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 | 0.0208053 | − | 0.999784i | \(-0.493377\pi\) |
0.855435 | − | 0.517910i | \(-0.173290\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19313.8 | −0.806244 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26707.0 | −1.11086 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14692.1 | − | 25447.5i | 0.608913 | − | 1.05467i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 864.331 | 0.0356937 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6342.54 | + | 10985.6i | 0.260988 | + | 0.452044i | 0.966505 | − | 0.256649i | \(-0.0826185\pi\) |
−0.705517 | + | 0.708693i | \(0.749285\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6807.43 | − | 11790.8i | −0.279119 | − | 0.483448i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4461.39 | − | 7727.35i | 0.182276 | − | 0.315711i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21370.4 | + | 3415.64i | −0.870017 | + | 0.139055i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13039.1 | − | 22584.3i | 0.528959 | − | 0.916183i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4553.58 | + | 7887.03i | 0.184074 | + | 0.318825i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −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 | \(0.771146\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5332.60 | − | 9236.34i | 0.213300 | − | 0.369446i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11826.3 | −0.471386 | −0.235693 | − | 0.971828i | \(-0.575736\pi\) | ||||
−0.235693 | + | 0.971828i | \(0.575736\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36498.7 | 1.44973 | 0.724866 | − | 0.688890i | \(-0.241901\pi\) | ||||
0.724866 | + | 0.688890i | \(0.241901\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10860.2 | + | 18810.5i | −0.429867 | + | 0.744552i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −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 | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3875.72 | + | 6712.95i | 0.151818 | + | 0.262957i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3527.22 | − | 6109.33i | 0.137690 | − | 0.238487i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18669.6 | − | 8888.81i | −0.726288 | − | 0.345793i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −963.906 | + | 1669.53i | −0.0373691 | + | 0.0647253i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −22556.6 | − | 39069.2i | −0.871488 | − | 1.50946i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10400.1 | + | 18013.6i | 0.400442 | + | 0.693587i | 0.993779 | − | 0.111368i | \(-0.0355231\pi\) |
−0.593337 | + | 0.804954i | \(0.702190\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5867.23 | −0.225139 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9627.95 | − | 16676.1i | 0.368188 | − | 0.637721i | −0.621094 | − | 0.783736i | \(-0.713311\pi\) |
0.989282 | + | 0.146015i | \(0.0466448\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1744.49 | −0.0664857 | −0.0332429 | − | 0.999447i | \(-0.510583\pi\) | ||||
−0.0332429 | + | 0.999447i | \(0.510583\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9686.80 | −0.367930 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1485.35 | − | 2572.70i | 0.0562268 | − | 0.0973877i | −0.836542 | − | 0.547903i | \(-0.815426\pi\) |
0.892769 | + | 0.450515i | \(0.148760\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −74634.6 | −2.81571 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1900.49 | + | 3291.75i | 0.0714578 | + | 0.123769i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32421.8 | − | 56156.2i | −1.21495 | − | 2.10436i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9126.24 | − | 15807.1i | 0.340845 | − | 0.590361i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15138.6 | + | 10420.2i | −0.563503 | + | 0.387871i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3120.33 | − | 5404.57i | 0.115761 | − | 0.200503i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3674.56 | − | 6364.52i | −0.135868 | − | 0.235331i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4329.66 | − | 7499.19i | −0.159559 | − | 0.276365i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8400.32 | 0.308548 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16501.7 | − | 28581.7i | 0.604111 | − | 1.04635i | −0.388080 | − | 0.921626i | \(-0.626862\pi\) |
0.992191 | − | 0.124726i | \(-0.0398051\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14356.0 | 0.523827 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −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 | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2908.41 | −0.105081 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11145.9 | − | 19305.3i | −0.401386 | − | 0.695221i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5712.69 | + | 9894.67i | 0.205054 | + | 0.355163i | 0.950150 | − | 0.311794i | \(-0.100930\pi\) |
−0.745096 | + | 0.666957i | \(0.767596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1541.34 | + | 2669.68i | −0.0551455 | + | 0.0955147i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13322.3 | + | 9169.99i | −0.475090 | + | 0.327014i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −453.410 | + | 785.329i | −0.0161168 | + | 0.0279151i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7066.33 | − | 12239.2i | −0.250365 | − | 0.433646i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5977.10 | − | 10352.6i | −0.211090 | − | 0.365618i | 0.740966 | − | 0.671542i | \(-0.234368\pi\) |
−0.952056 | + | 0.305924i | \(0.901035\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −66571.7 | −2.34350 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5108.42 | − | 8848.04i | 0.179252 | − | 0.310474i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22308.7 | 0.780290 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42546.4 | 1.48338 | 0.741692 | − | 0.670740i | \(-0.234024\pi\) | ||||
0.741692 | + | 0.670740i | \(0.234024\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7219.81 | + | 12505.1i | −0.250915 | + | 0.434598i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20665.1 | 0.715903 | 0.357951 | − | 0.933740i | \(-0.383475\pi\) | ||||
0.357951 | + | 0.933740i | \(0.383475\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15802.9 | − | 27371.5i | −0.545720 | − | 0.945215i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3981.44 | + | 6896.06i | 0.137054 | + | 0.237385i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4746.87 | + | 8221.81i | −0.162885 | + | 0.282126i | −0.935902 | − | 0.352260i | \(-0.885413\pi\) |
0.773017 | + | 0.634385i | \(0.218747\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2871.33 | + | 36157.7i | 0.0982163 | + | 1.23681i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1711.99 | + | 2965.26i | −0.0583756 | + | 0.101110i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26667.1 | − | 46188.7i | −0.906433 | − | 1.56999i | −0.818982 | − | 0.573819i | \(-0.805461\pi\) |
−0.0874512 | − | 0.996169i | \(-0.527872\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21874.6 | + | 37887.9i | 0.741199 | + | 1.28379i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27443.9 | 0.926997 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3325.79 | + | 5760.44i | −0.111987 | + | 0.193967i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28766.2 | −0.965601 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 60.5972 | 0.00202774 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12226.6 | − | 21177.2i | 0.407865 | − | 0.706443i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42110.1 | 1.40038 | 0.700191 | − | 0.713956i | \(-0.253098\pi\) | ||||
0.700191 | + | 0.713956i | \(0.253098\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8708.83 | − | 15084.1i | −0.288718 | − | 0.500074i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6913.86 | − | 11975.2i | −0.228503 | − | 0.395779i | 0.728862 | − | 0.684661i | \(-0.240050\pi\) |
−0.957365 | + | 0.288882i | \(0.906716\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11633.7 | − | 20150.2i | 0.383309 | − | 0.663911i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3550.69 | + | 1690.52i | 0.116629 | + | 0.0555281i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −566.943 | + | 981.973i | −0.0185651 | + | 0.0321557i | −0.875159 | − | 0.483836i | \(-0.839243\pi\) |
0.856594 | + | 0.515992i | \(0.172576\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3986.65 | + | 6905.09i | 0.130147 | + | 0.225421i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2440.90 | + | 4227.76i | 0.0794413 | + | 0.137596i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −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 | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 48413.7 | 1.56132 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12600.3 | 0.405124 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14680.2 | + | 25426.8i | −0.470566 | + | 0.815045i | −0.999433 | − | 0.0336599i | \(-0.989284\pi\) |
0.528867 | + | 0.848705i | \(0.322617\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22957.7 | −0.733676 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27192.3 | − | 47098.4i | −0.866384 | − | 1.50062i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8417.95 | − | 14580.3i | −0.267401 | − | 0.463153i | 0.700789 | − | 0.713369i | \(-0.252832\pi\) |
−0.968190 | + | 0.250216i | \(0.919498\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 437.737 | − | 758.182i | 0.0138632 | − | 0.0240118i |
(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 | 624.4.q.i.529.4 | 8 | ||
4.3 | odd | 2 | 39.4.e.c.22.3 | yes | 8 | ||
12.11 | even | 2 | 117.4.g.e.100.2 | 8 | |||
13.3 | even | 3 | inner | 624.4.q.i.289.4 | 8 | ||
52.3 | odd | 6 | 39.4.e.c.16.3 | ✓ | 8 | ||
52.7 | even | 12 | 507.4.b.h.337.4 | 8 | |||
52.19 | even | 12 | 507.4.b.h.337.5 | 8 | |||
52.35 | odd | 6 | 507.4.a.m.1.2 | 4 | |||
52.43 | odd | 6 | 507.4.a.i.1.3 | 4 | |||
156.35 | even | 6 | 1521.4.a.v.1.3 | 4 | |||
156.95 | even | 6 | 1521.4.a.bb.1.2 | 4 | |||
156.107 | even | 6 | 117.4.g.e.55.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.c.16.3 | ✓ | 8 | 52.3 | odd | 6 | ||
39.4.e.c.22.3 | yes | 8 | 4.3 | odd | 2 | ||
117.4.g.e.55.2 | 8 | 156.107 | even | 6 | |||
117.4.g.e.100.2 | 8 | 12.11 | even | 2 | |||
507.4.a.i.1.3 | 4 | 52.43 | odd | 6 | |||
507.4.a.m.1.2 | 4 | 52.35 | odd | 6 | |||
507.4.b.h.337.4 | 8 | 52.7 | even | 12 | |||
507.4.b.h.337.5 | 8 | 52.19 | even | 12 | |||
624.4.q.i.289.4 | 8 | 13.3 | even | 3 | inner | ||
624.4.q.i.529.4 | 8 | 1.1 | even | 1 | trivial | ||
1521.4.a.v.1.3 | 4 | 156.35 | even | 6 | |||
1521.4.a.bb.1.2 | 4 | 156.95 | even | 6 |