Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,3,Mod(5,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.k (of order \(18\), degree \(6\), 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: | \(2.94278685509\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 41.2 | ||
Character | \(\chi\) | \(=\) | 108.41 |
Dual form | 108.3.k.a.29.2 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{17}{18}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −2.59609 | + | 1.50344i | −0.865362 | + | 0.501147i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.298552 | + | 0.355800i | −0.0597103 | + | 0.0711600i | −0.795073 | − | 0.606514i | \(-0.792567\pi\) |
0.735363 | + | 0.677674i | \(0.237012\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.1488 | − | 3.69384i | −1.44982 | − | 0.527692i | −0.507281 | − | 0.861781i | \(-0.669349\pi\) |
−0.942542 | + | 0.334089i | \(0.891571\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.47934 | − | 7.80612i | 0.497704 | − | 0.867347i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10.2314 | − | 12.1933i | −0.930125 | − | 1.10848i | −0.993875 | − | 0.110514i | \(-0.964750\pi\) |
0.0637495 | − | 0.997966i | \(-0.479694\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.11819 | + | 17.6841i | −0.239861 | + | 1.36032i | 0.592271 | + | 0.805739i | \(0.298232\pi\) |
−0.832131 | + | 0.554579i | \(0.812879\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.240142 | − | 1.37254i | 0.0160095 | − | 0.0915028i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −22.6442 | − | 13.0736i | −1.33201 | − | 0.769038i | −0.346405 | − | 0.938085i | \(-0.612598\pi\) |
−0.985608 | + | 0.169047i | \(0.945931\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.77864 | + | 3.08069i | 0.0936126 | + | 0.162142i | 0.909029 | − | 0.416733i | \(-0.136825\pi\) |
−0.815416 | + | 0.578875i | \(0.803492\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 31.9005 | − | 5.66850i | 1.51907 | − | 0.269928i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.41115 | + | 3.87710i | 0.0613543 | + | 0.168570i | 0.966582 | − | 0.256357i | \(-0.0825222\pi\) |
−0.905228 | + | 0.424926i | \(0.860300\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.30374 | + | 24.4077i | 0.172150 | + | 0.976310i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.107276 | + | 26.9998i | 0.00397319 | + | 0.999992i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 41.0456 | − | 7.23745i | 1.41537 | − | 0.249567i | 0.586924 | − | 0.809642i | \(-0.300339\pi\) |
0.828442 | + | 0.560075i | \(0.189228\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.62361 | + | 2.41080i | −0.213665 | + | 0.0777677i | −0.446635 | − | 0.894716i | \(-0.647378\pi\) |
0.232970 | + | 0.972484i | \(0.425156\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 44.8934 | + | 16.2726i | 1.36041 | + | 0.493108i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.34420 | − | 2.50812i | 0.124120 | − | 0.0716606i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.92909 | − | 8.53743i | 0.133219 | − | 0.230741i | −0.791697 | − | 0.610914i | \(-0.790802\pi\) |
0.924916 | + | 0.380173i | \(0.124135\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −18.4919 | − | 50.5976i | −0.474152 | − | 1.29737i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −42.8820 | − | 7.56125i | −1.04590 | − | 0.184421i | −0.375808 | − | 0.926697i | \(-0.622635\pi\) |
−0.670094 | + | 0.742277i | \(0.733746\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −27.2523 | + | 22.8674i | −0.633773 | + | 0.531799i | −0.902099 | − | 0.431529i | \(-0.857974\pi\) |
0.268326 | + | 0.963328i | \(0.413530\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.44010 | + | 3.92428i | 0.0320023 | + | 0.0872062i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.51742 | + | 15.1590i | −0.117392 | + | 0.322531i | −0.984447 | − | 0.175680i | \(-0.943788\pi\) |
0.867055 | + | 0.498212i | \(0.166010\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 51.8166 | + | 43.4793i | 1.05748 | + | 0.887332i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 78.4418 | − | 0.103888i | 1.53807 | − | 0.00203703i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 75.6950i | − | 1.42821i | −0.700040 | − | 0.714104i | \(-0.746834\pi\) | ||
0.700040 | − | 0.714104i | \(-0.253166\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.39296 | 0.134417 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.24914 | − | 5.32367i | −0.162266 | − | 0.0933977i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −18.4421 | + | 21.9784i | −0.312578 | + | 0.372516i | −0.899345 | − | 0.437240i | \(-0.855956\pi\) |
0.586767 | + | 0.809756i | \(0.300400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −55.9422 | − | 20.3613i | −0.917085 | − | 0.333792i | −0.160007 | − | 0.987116i | \(-0.551152\pi\) |
−0.757078 | + | 0.653324i | \(0.773374\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −74.2943 | + | 62.6764i | −1.17927 | + | 0.994864i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.36107 | − | 6.38908i | −0.0824780 | − | 0.0982935i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.03483 | + | 22.8827i | −0.0602214 | + | 0.341532i | −1.00000 | 0.000251397i | \(-0.999920\pi\) | |
0.939779 | + | 0.341784i | \(0.111031\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.49246 | − | 7.94372i | −0.137572 | − | 0.115126i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −32.2368 | − | 18.6119i | −0.454039 | − | 0.262139i | 0.255496 | − | 0.966810i | \(-0.417761\pi\) |
−0.709534 | + | 0.704671i | \(0.751095\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −26.0280 | − | 45.0817i | −0.356547 | − | 0.617558i | 0.630834 | − | 0.775918i | \(-0.282713\pi\) |
−0.987382 | + | 0.158360i | \(0.949380\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −47.8685 | − | 56.8942i | −0.638246 | − | 0.758590i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 58.7957 | + | 161.540i | 0.763580 | + | 2.09792i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −20.9619 | − | 118.881i | −0.265341 | − | 1.50482i | −0.768063 | − | 0.640374i | \(-0.778779\pi\) |
0.502722 | − | 0.864448i | \(-0.332332\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.8710 | − | 69.9325i | −0.504581 | − | 0.863364i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 115.091 | − | 20.2937i | 1.38664 | − | 0.244502i | 0.569997 | − | 0.821647i | \(-0.306944\pi\) |
0.816642 | + | 0.577145i | \(0.195833\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.4121 | − | 4.15365i | 0.134260 | − | 0.0488665i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −95.6769 | + | 80.4987i | −1.09974 | + | 0.925272i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −117.767 | + | 67.9930i | −1.32323 | + | 0.763966i | −0.984242 | − | 0.176826i | \(-0.943417\pi\) |
−0.338985 | + | 0.940792i | \(0.610084\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 96.9682 | − | 167.954i | 1.06558 | − | 1.84565i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.5710 | − | 16.2168i | 0.145925 | − | 0.174375i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.62713 | − | 0.286906i | −0.0171276 | − | 0.00302006i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −72.3238 | + | 60.6869i | −0.745606 | + | 0.625638i | −0.934337 | − | 0.356391i | \(-0.884007\pi\) |
0.188731 | + | 0.982029i | \(0.439563\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −141.012 | + | 25.2495i | −1.42436 | + | 0.255046i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 52.1346 | − | 143.239i | 0.516184 | − | 1.41820i | −0.358509 | − | 0.933526i | \(-0.616715\pi\) |
0.874693 | − | 0.484678i | \(-0.161063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.6643 | + | 13.9830i | 0.161790 | + | 0.135758i | 0.720088 | − | 0.693882i | \(-0.244101\pi\) |
−0.558299 | + | 0.829640i | \(0.688546\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.50710 | + | 13.0425i | −0.0714962 | + | 0.124215i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 49.8431i | 0.465823i | 0.972498 | + | 0.232912i | \(0.0748253\pi\) | ||||
−0.972498 | + | 0.232912i | \(0.925175\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 171.063 | 1.56939 | 0.784695 | − | 0.619882i | \(-0.212820\pi\) | ||||
0.784695 | + | 0.619882i | \(0.212820\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0391685 | + | 29.5745i | 0.000352869 | + | 0.266437i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 26.1647 | − | 31.1819i | 0.231546 | − | 0.275946i | −0.637744 | − | 0.770249i | \(-0.720132\pi\) |
0.869290 | + | 0.494303i | \(0.164577\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.80077 | − | 0.655428i | −0.0156589 | − | 0.00569937i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 124.077 | + | 103.554i | 1.06049 | + | 0.885078i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 181.519 | + | 216.325i | 1.52537 | + | 1.81786i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −22.9836 | + | 130.346i | −0.189947 | + | 1.07724i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 122.693 | − | 44.8408i | 0.997506 | − | 0.364559i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −20.0251 | − | 11.5615i | −0.160201 | − | 0.0924920i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −30.8908 | − | 53.5044i | −0.243235 | − | 0.421295i | 0.718399 | − | 0.695631i | \(-0.244875\pi\) |
−0.961634 | + | 0.274336i | \(0.911542\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 36.3695 | − | 100.338i | 0.281934 | − | 0.777812i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 77.3505 | + | 212.519i | 0.590462 | + | 1.62228i | 0.769651 | + | 0.638465i | \(0.220430\pi\) |
−0.179189 | + | 0.983815i | \(0.557347\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.67137 | − | 37.8352i | −0.0501607 | − | 0.284475i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.63855 | − | 8.02266i | −0.0713967 | − | 0.0594271i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −149.613 | + | 26.3808i | −1.09206 | + | 0.192560i | −0.690544 | − | 0.723290i | \(-0.742629\pi\) |
−0.401519 | + | 0.915851i | \(0.631518\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 159.710 | − | 58.1298i | 1.14899 | − | 0.418200i | 0.303841 | − | 0.952723i | \(-0.401731\pi\) |
0.845154 | + | 0.534523i | \(0.179509\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.46691 | − | 47.6491i | −0.0600490 | − | 0.337937i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 247.531 | − | 142.912i | 1.73099 | − | 0.999385i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.67915 | + | 16.7648i | −0.0667528 | + | 0.115619i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −199.889 | − | 34.9729i | −1.35979 | − | 0.237911i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −176.331 | − | 31.0919i | −1.18343 | − | 0.208671i | −0.452907 | − | 0.891558i | \(-0.649613\pi\) |
−0.730524 | + | 0.682887i | \(0.760724\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 92.0549 | − | 77.2432i | 0.609635 | − | 0.511544i | −0.284891 | − | 0.958560i | \(-0.591958\pi\) |
0.894526 | + | 0.447015i | \(0.147513\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −203.486 | + | 118.202i | −1.32997 | + | 0.772563i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.11973 | − | 3.07643i | 0.00722405 | − | 0.0198479i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.9795 | + | 20.9603i | 0.159105 | + | 0.133505i | 0.718865 | − | 0.695150i | \(-0.244662\pi\) |
−0.559760 | + | 0.828655i | \(0.689107\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 113.803 | + | 196.511i | 0.715741 | + | 1.23592i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 44.5603i | − | 0.276772i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −219.827 | −1.34863 | −0.674316 | − | 0.738443i | \(-0.735561\pi\) | ||||
−0.674316 | + | 0.738443i | \(0.735561\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −19.1928 | + | 11.1149i | −0.116320 | + | 0.0673628i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 78.0508 | − | 93.0173i | 0.467370 | − | 0.556990i | −0.479943 | − | 0.877300i | \(-0.659343\pi\) |
0.947313 | + | 0.320310i | \(0.103787\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −144.197 | − | 52.4835i | −0.853239 | − | 0.310553i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 32.0154 | − | 0.0848025i | 0.187224 | − | 0.000495921i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −49.6240 | − | 59.1396i | −0.286844 | − | 0.341847i | 0.603310 | − | 0.797506i | \(-0.293848\pi\) |
−0.890154 | + | 0.455659i | \(0.849404\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 46.4808 | − | 263.606i | 0.265604 | − | 1.50632i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.8340 | − | 84.7845i | 0.0838082 | − | 0.479009i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −128.588 | − | 74.2402i | −0.718367 | − | 0.414750i | 0.0957841 | − | 0.995402i | \(-0.469464\pi\) |
−0.814151 | + | 0.580653i | \(0.802797\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 42.2135 | + | 73.1159i | 0.233224 | + | 0.403955i | 0.958755 | − | 0.284234i | \(-0.0917393\pi\) |
−0.725531 | + | 0.688189i | \(0.758406\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 175.843 | − | 31.2460i | 0.960890 | − | 0.170743i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.56603 | + | 4.30263i | 0.00846503 | + | 0.0232575i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 72.2709 | + | 409.869i | 0.386475 | + | 2.19181i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 98.6443 | − | 274.410i | 0.521928 | − | 1.45191i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.92568 | + | 0.339550i | −0.0100821 | + | 0.00177775i | −0.178687 | − | 0.983906i | \(-0.557185\pi\) |
0.168605 | + | 0.985684i | \(0.446074\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −311.970 | + | 113.548i | −1.61643 | + | 0.588331i | −0.982697 | − | 0.185223i | \(-0.940699\pi\) |
−0.633731 | + | 0.773554i | \(0.718477\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23.5234 | + | 8.52655i | 0.120633 | + | 0.0437259i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −213.145 | + | 123.059i | −1.08195 | + | 0.624666i | −0.931423 | − | 0.363939i | \(-0.881432\pi\) |
−0.150531 | + | 0.988605i | \(0.548098\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −138.226 | + | 239.415i | −0.694604 | + | 1.20309i | 0.275710 | + | 0.961241i | \(0.411087\pi\) |
−0.970314 | + | 0.241849i | \(0.922246\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.9279 | − | 65.4716i | −0.119044 | − | 0.325729i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −443.296 | − | 78.1650i | −2.18372 | − | 0.385049i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.4928 | − | 13.0000i | 0.0755745 | − | 0.0634145i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 36.5861 | + | 6.35125i | 0.176745 | + | 0.0306824i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.3658 | − | 53.2072i | 0.0926594 | − | 0.254580i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −40.7896 | − | 34.2265i | −0.193316 | − | 0.162211i | 0.540992 | − | 0.841027i | \(-0.318049\pi\) |
−0.734308 | + | 0.678816i | \(0.762493\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 111.671 | − | 0.147898i | 0.524279 | − | 0.000694355i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 16.5234i | − | 0.0768532i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 76.1265 | 0.350813 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 135.349 | + | 77.9047i | 0.618030 | + | 0.355729i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 301.805 | − | 359.677i | 1.36563 | − | 1.62750i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 101.950 | + | 37.1068i | 0.457175 | + | 0.166398i | 0.560334 | − | 0.828267i | \(-0.310673\pi\) |
−0.103159 | + | 0.994665i | \(0.532895\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 209.808 | + | 75.7350i | 0.932479 | + | 0.336600i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −232.991 | − | 277.668i | −1.02639 | − | 1.22321i | −0.974462 | − | 0.224554i | \(-0.927907\pi\) |
−0.0519295 | − | 0.998651i | \(-0.516537\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −50.2795 | + | 285.149i | −0.219561 | + | 1.24519i | 0.653252 | + | 0.757140i | \(0.273404\pi\) |
−0.872814 | + | 0.488054i | \(0.837707\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −395.504 | − | 330.976i | −1.71214 | − | 1.43279i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 127.663 | + | 73.7062i | 0.547910 | + | 0.316336i | 0.748279 | − | 0.663385i | \(-0.230881\pi\) |
−0.200369 | + | 0.979721i | \(0.564214\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.74633 | − | 6.48883i | −0.0159418 | − | 0.0276120i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 233.149 | + | 277.110i | 0.983753 | + | 1.16924i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.66249 | − | 12.8101i | −0.0195083 | − | 0.0535987i | 0.929556 | − | 0.368680i | \(-0.120190\pi\) |
−0.949065 | + | 0.315082i | \(0.897968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −51.5844 | − | 292.550i | −0.214043 | − | 1.21390i | −0.882559 | − | 0.470201i | \(-0.844181\pi\) |
0.668516 | − | 0.743698i | \(-0.266930\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 211.244 | + | 120.104i | 0.869317 | + | 0.494254i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −30.9398 | + | 5.45553i | −0.126285 | + | 0.0222675i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −60.0255 | + | 21.8475i | −0.243018 | + | 0.0884514i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −268.276 | + | 225.717i | −1.07741 | + | 0.906492i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.182848 | + | 0.105567i | −0.000728476 | + | 0.000420586i | −0.500364 | − | 0.865815i | \(-0.666801\pi\) |
0.499636 | + | 0.866236i | \(0.333467\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.8366 | − | 56.8746i | 0.129789 | − | 0.224801i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −23.3820 | + | 27.9406i | −0.0916939 | + | 0.109571i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 190.970 | + | 33.6731i | 0.743073 | + | 0.131024i | 0.532353 | − | 0.846523i | \(-0.321308\pi\) |
0.210720 | + | 0.977546i | \(0.432419\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −81.5601 | + | 68.4370i | −0.314904 | + | 0.264236i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 127.361 | − | 352.826i | 0.487973 | − | 1.35182i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −139.835 | + | 384.194i | −0.531692 | + | 1.46081i | 0.325363 | + | 0.945589i | \(0.394513\pi\) |
−0.857056 | + | 0.515224i | \(0.827709\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.9323 | + | 22.5989i | 0.101631 | + | 0.0852787i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 203.511 | − | 353.572i | 0.762213 | − | 1.32424i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 120.090i | 0.446433i | 0.974769 | + | 0.223216i | \(0.0716557\pi\) | ||||
−0.974769 | + | 0.223216i | \(0.928344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.0289 | 0.0702175 | 0.0351088 | − | 0.999383i | \(-0.488822\pi\) | ||||
0.0351088 | + | 0.999383i | \(0.488822\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.770547 | + | 581.809i | 0.00282252 | + | 2.13117i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 253.577 | − | 302.202i | 0.922099 | − | 1.09891i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 299.169 | + | 108.889i | 1.08003 | + | 0.393099i | 0.819919 | − | 0.572479i | \(-0.194018\pi\) |
0.260112 | + | 0.965578i | \(0.416240\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.8504 | + | 62.5035i | −0.0388904 | + | 0.224027i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −154.692 | − | 184.354i | −0.550504 | − | 0.656065i | 0.417004 | − | 0.908905i | \(-0.363080\pi\) |
−0.967508 | + | 0.252839i | \(0.918636\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5135 | − | 87.9813i | 0.0548179 | − | 0.310888i | −0.945054 | − | 0.326915i | \(-0.893991\pi\) |
0.999872 | + | 0.0160274i | \(0.00510189\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.65551 | − | 1.70145i | 0.0163351 | − | 0.00597000i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 407.269 | + | 235.137i | 1.41905 | + | 0.819292i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 197.340 | + | 341.803i | 0.682838 | + | 1.18271i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 96.5199 | − | 266.283i | 0.331683 | − | 0.915062i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 106.539 | + | 292.713i | 0.363614 | + | 0.999022i | 0.977741 | + | 0.209814i | \(0.0672860\pi\) |
−0.614127 | + | 0.789207i | \(0.710492\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.31401 | − | 13.1234i | −0.00784410 | − | 0.0444861i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 328.118 | − | 277.553i | 1.10478 | − | 0.934522i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −72.9634 | + | 12.8654i | −0.244025 | + | 0.0430282i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 361.045 | − | 131.410i | 1.19948 | − | 0.436577i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 80.0047 | + | 450.241i | 0.264042 | + | 1.48594i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 23.9462 | − | 13.8253i | 0.0785120 | − | 0.0453289i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −296.790 | + | 514.055i | −0.966743 | + | 1.67445i | −0.261885 | + | 0.965099i | \(0.584344\pi\) |
−0.704858 | + | 0.709348i | \(0.748989\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −64.2847 | − | 11.2474i | −0.208041 | − | 0.0363992i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −538.372 | − | 94.9296i | −1.73110 | − | 0.305240i | −0.782720 | − | 0.622374i | \(-0.786168\pi\) |
−0.948381 | + | 0.317134i | \(0.897280\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 119.991 | − | 100.684i | 0.383357 | − | 0.321675i | −0.430662 | − | 0.902513i | \(-0.641720\pi\) |
0.814019 | + | 0.580839i | \(0.197275\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.119583 | − | 45.1461i | −0.000379629 | − | 0.143321i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.4734 | + | 39.7653i | −0.0456574 | + | 0.125443i | −0.960426 | − | 0.278536i | \(-0.910151\pi\) |
0.914768 | + | 0.403979i | \(0.132373\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −508.201 | − | 426.432i | −1.59311 | − | 1.33678i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −74.9361 | − | 129.397i | −0.233446 | − | 0.403106i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 93.0132i | − | 0.287966i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −445.050 | −1.36938 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −444.096 | + | 257.184i | −1.35809 | + | 0.786494i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 111.990 | − | 133.464i | 0.340395 | − | 0.405666i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 462.396 | + | 168.298i | 1.39697 | + | 0.508455i | 0.927277 | − | 0.374376i | \(-0.122143\pi\) |
0.469691 | + | 0.882831i | \(0.344365\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −44.5652 | − | 76.7191i | −0.133829 | − | 0.230388i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.93705 | − | 8.26725i | −0.0207076 | − | 0.0246784i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 113.729 | − | 644.988i | 0.337474 | − | 1.91391i | −0.0638222 | − | 0.997961i | \(-0.520329\pi\) |
0.401296 | − | 0.915948i | \(-0.368560\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.0458 | + | 120.288i | −0.0620820 | + | 0.354832i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 97.1642 | + | 56.0978i | 0.284939 | + | 0.164510i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −100.666 | − | 174.359i | −0.293487 | − | 0.508335i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.66036 | − | 1.00581i | 0.0164068 | − | 0.00291538i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −44.4825 | − | 122.215i | −0.128192 | − | 0.352204i | 0.858948 | − | 0.512062i | \(-0.171118\pi\) |
−0.987140 | + | 0.159859i | \(0.948896\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.3449 | + | 81.3537i | 0.0411027 | + | 0.233105i | 0.998438 | − | 0.0558751i | \(-0.0177949\pi\) |
−0.957335 | + | 0.288980i | \(0.906684\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −477.802 | − | 82.2934i | −1.36126 | − | 0.234454i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −65.5878 | + | 11.5649i | −0.185801 | + | 0.0327618i | −0.265774 | − | 0.964035i | \(-0.585628\pi\) |
0.0799732 | + | 0.996797i | \(0.474517\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.2464 | − | 5.91322i | 0.0457646 | − | 0.0166570i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −796.470 | − | 288.697i | −2.23101 | − | 0.808676i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 289.619 | − | 167.211i | 0.806737 | − | 0.465770i | −0.0390844 | − | 0.999236i | \(-0.512444\pi\) |
0.845821 | + | 0.533466i | \(0.179111\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 174.173 | − | 301.676i | 0.482473 | − | 0.835668i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −136.300 | − | 372.945i | −0.375483 | − | 1.02740i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.8108 | + | 4.19848i | 0.0652350 | + | 0.0115027i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 312.913 | − | 262.565i | 0.852624 | − | 0.715437i | −0.107742 | − | 0.994179i | \(-0.534362\pi\) |
0.960366 | + | 0.278742i | \(0.0899175\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −251.107 | + | 300.873i | −0.680507 | + | 0.815373i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −279.606 | + | 768.210i | −0.753654 | + | 2.07065i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −234.819 | − | 197.037i | −0.629543 | − | 0.528249i | 0.271244 | − | 0.962511i | \(-0.412565\pi\) |
−0.900787 | + | 0.434262i | \(0.857009\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 69.3689 | − | 0.0918722i | 0.184984 | − | 0.000244993i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 748.424i | 1.98521i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −98.9004 | −0.260951 | −0.130475 | − | 0.991452i | \(-0.541650\pi\) | ||||
−0.130475 | + | 0.991452i | \(0.541650\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 160.636 | + | 92.4597i | 0.421616 | + | 0.242676i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 319.309 | − | 380.537i | 0.833704 | − | 0.993570i | −0.166268 | − | 0.986081i | \(-0.553172\pi\) |
0.999972 | − | 0.00748907i | \(-0.00238387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −75.0293 | − | 27.3084i | −0.194881 | − | 0.0709310i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 56.4333 | + | 315.165i | 0.145822 | + | 0.814380i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 305.584 | + | 364.181i | 0.785563 | + | 0.936197i | 0.999171 | − | 0.0407223i | \(-0.0129659\pi\) |
−0.213608 | + | 0.976920i | \(0.568521\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.7335 | − | 106.243i | 0.0479117 | − | 0.271721i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −520.317 | − | 435.425i | −1.32396 | − | 1.10795i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 48.5561 | + | 28.0339i | 0.122927 | + | 0.0709718i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −217.038 | − | 375.920i | −0.546694 | − | 0.946902i | −0.998498 | − | 0.0547849i | \(-0.982553\pi\) |
0.451804 | − | 0.892117i | \(-0.350781\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 74.2024 | + | 88.1935i | 0.185971 | + | 0.221036i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 84.0625 | + | 230.960i | 0.209632 | + | 0.575960i | 0.999294 | − | 0.0375831i | \(-0.0119659\pi\) |
−0.789661 | + | 0.613543i | \(0.789744\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.9792 | − | 124.650i | −0.0545389 | − | 0.309306i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 37.0841 | + | 6.33655i | 0.0915657 | + | 0.0156458i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −154.531 | + | 27.2479i | −0.379682 | + | 0.0669482i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −328.561 | + | 119.587i | −0.803328 | + | 0.292388i | −0.710865 | − | 0.703329i | \(-0.751696\pi\) |
−0.0924633 | + | 0.995716i | \(0.529474\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 348.746 | − | 293.420i | 0.848530 | − | 0.713918i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 268.349 | − | 154.932i | 0.649756 | − | 0.375137i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.1401 | + | 47.0081i | −0.0653979 | + | 0.113272i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −327.227 | + | 391.025i | −0.784718 | + | 0.937709i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −271.509 | − | 47.8743i | −0.647993 | − | 0.114259i | −0.160015 | − | 0.987115i | \(-0.551154\pi\) |
−0.487978 | + | 0.872856i | \(0.662265\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 50.0550 | − | 42.0012i | 0.118896 | − | 0.0997652i | −0.581401 | − | 0.813617i | \(-0.697495\pi\) |
0.700297 | + | 0.713852i | \(0.253051\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 93.6184 | + | 110.972i | 0.221320 | + | 0.262345i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 221.643 | − | 608.960i | 0.521514 | − | 1.43285i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 492.532 | + | 413.284i | 1.15347 | + | 0.967877i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −427.752 | + | 743.160i | −0.997091 | + | 1.73231i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 105.508i | 0.244799i | 0.992481 | + | 0.122399i | \(0.0390589\pi\) | ||||
−0.992481 | + | 0.122399i | \(0.960941\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 599.181 | 1.38379 | 0.691895 | − | 0.721998i | \(-0.256776\pi\) | ||||
0.691895 | + | 0.721998i | \(0.256776\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0769143 | − | 58.0748i | −0.000176815 | − | 0.133505i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.43423 | + | 11.2433i | −0.0215886 | + | 0.0257283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 59.8973 | + | 21.8008i | 0.136440 | + | 0.0496602i | 0.409338 | − | 0.912383i | \(-0.365760\pi\) |
−0.272897 | + | 0.962043i | \(0.587982\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 571.508 | − | 209.728i | 1.29594 | − | 0.475574i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −85.6046 | − | 102.020i | −0.193238 | − | 0.230292i | 0.660722 | − | 0.750631i | \(-0.270250\pi\) |
−0.853960 | + | 0.520338i | \(0.825806\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.9677 | − | 62.2010i | 0.0246465 | − | 0.139777i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 504.516 | − | 184.386i | 1.12867 | − | 0.412496i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −120.484 | − | 69.5615i | −0.268339 | − | 0.154925i | 0.359794 | − | 0.933032i | \(-0.382847\pi\) |
−0.628132 | + | 0.778106i | \(0.716180\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 346.545 | + | 600.234i | 0.768393 | + | 1.33090i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −122.852 | + | 338.929i | −0.271196 | + | 0.748188i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 30.8079 | + | 84.6441i | 0.0677098 | + | 0.186031i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.0125 | − | 119.168i | −0.0459792 | − | 0.260761i | 0.953149 | − | 0.302500i | \(-0.0978212\pi\) |
−0.999129 | + | 0.0417393i | \(0.986710\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 350.556 | − | 612.791i | 0.763739 | − | 1.33506i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −266.202 | + | 46.9386i | −0.577445 | + | 0.101819i | −0.454740 | − | 0.890624i | \(-0.650268\pi\) |
−0.122705 | + | 0.992443i | \(0.539157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.9878 | − | 6.18304i | 0.0366906 | − | 0.0133543i | −0.323610 | − | 0.946191i | \(-0.604896\pi\) |
0.360300 | + | 0.932836i | \(0.382674\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.71831 | + | 9.67012i | 0.00369529 | + | 0.0207960i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −439.219 | + | 253.583i | −0.940511 | + | 0.543004i | −0.890120 | − | 0.455725i | \(-0.849380\pi\) |
−0.0503903 | + | 0.998730i | \(0.516047\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 125.474 | − | 217.327i | 0.267534 | − | 0.463383i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −96.3614 | − | 16.8596i | −0.204589 | − | 0.0357952i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 557.656 | + | 98.3298i | 1.17898 | + | 0.207885i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −67.5380 | + | 56.6711i | −0.142185 | + | 0.119308i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −590.884 | − | 339.064i | −1.23875 | − | 0.710825i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 210.140 | − | 577.355i | 0.438705 | − | 1.20533i | −0.501629 | − | 0.865083i | \(-0.667266\pi\) |
0.940335 | − | 0.340251i | \(-0.110512\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 135.607 | + | 113.788i | 0.281928 | + | 0.236565i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 66.9938 | + | 115.683i | 0.138703 | + | 0.239508i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 43.8510i | − | 0.0904144i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −218.562 | −0.448793 | −0.224396 | − | 0.974498i | \(-0.572041\pi\) | ||||
−0.224396 | + | 0.974498i | \(0.572041\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 570.690 | − | 330.496i | 1.16705 | − | 0.675862i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −128.585 | + | 153.242i | −0.261885 | + | 0.312102i | −0.880924 | − | 0.473258i | \(-0.843078\pi\) |
0.619039 | + | 0.785360i | \(0.287522\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1024.07 | − | 372.729i | −2.07721 | − | 0.756043i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 33.1156 | − | 57.7103i | 0.0669001 | − | 0.116587i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 258.414 | + | 307.965i | 0.519947 | + | 0.619648i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.1673 | + | 131.388i | −0.0464274 | + | 0.263303i | −0.999182 | − | 0.0404381i | \(-0.987125\pi\) |
0.952755 | + | 0.303741i | \(0.0982358\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −62.7808 | + | 358.826i | −0.125311 | + | 0.716219i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 156.930 | + | 90.6037i | 0.311989 | + | 0.180127i | 0.647816 | − | 0.761797i | \(-0.275683\pi\) |
−0.335827 | + | 0.941924i | \(0.609016\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 35.3994 | + | 61.3136i | 0.0700979 | + | 0.121413i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 453.255 | − | 80.5401i | 0.893993 | − | 0.158856i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 268.953 | + | 738.941i | 0.528394 | + | 1.45175i | 0.860961 | + | 0.508671i | \(0.169863\pi\) |
−0.332567 | + | 0.943080i | \(0.607915\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 97.6264 | + | 553.667i | 0.191050 | + | 1.08350i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −82.9872 | + | 48.3534i | −0.161769 | + | 0.0942560i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.95032 | + | 1.75451i | −0.0193210 | + | 0.00340682i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 241.288 | − | 87.8218i | 0.466709 | − | 0.169868i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 217.741 | + | 78.9248i | 0.419539 | + | 0.152071i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −169.525 | + | 97.8752i | −0.325384 | + | 0.187860i | −0.653790 | − | 0.756676i | \(-0.726822\pi\) |
0.328406 | + | 0.944537i | \(0.393489\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −79.9831 | + | 138.535i | −0.152931 | + | 0.264885i | −0.932304 | − | 0.361676i | \(-0.882205\pi\) |
0.779373 | + | 0.626561i | \(0.215538\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 275.647 | + | 754.224i | 0.525042 | + | 1.43662i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 181.504 | + | 32.0041i | 0.344411 | + | 0.0607289i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 392.197 | − | 329.092i | 0.741393 | − | 0.622103i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 88.9579 | + | 242.410i | 0.167529 | + | 0.456516i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 267.428 | − | 734.753i | 0.501742 | − | 1.37852i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.7342 | − | 14.8807i | −0.0331480 | − | 0.0278145i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 445.441 | − | 0.589942i | 0.829499 | − | 0.00109859i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1076.67i | − | 1.99753i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.2145 | −0.0632430 | −0.0316215 | − | 0.999500i | \(-0.510067\pi\) | ||||
−0.0316215 | + | 0.999500i | \(0.510067\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −219.515 | − | 126.350i | −0.404264 | − | 0.232688i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −51.0713 | + | 60.8644i | −0.0937087 | + | 0.111678i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 281.372 | + | 102.411i | 0.514391 | + | 0.187223i | 0.586155 | − | 0.810199i | \(-0.300641\pi\) |
−0.0717647 | + | 0.997422i | \(0.522863\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −409.527 | + | 345.486i | −0.745950 | + | 0.629301i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 95.3017 | + | 113.576i | 0.172961 | + | 0.206127i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −226.390 | + | 1283.92i | −0.409386 | + | 2.32174i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.5343 | − | 8.81558i | −0.0189807 | − | 0.0158839i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −686.079 | − | 396.108i | −1.23174 | − | 0.711146i | −0.264348 | − | 0.964427i | \(-0.585157\pi\) |
−0.967393 | + | 0.253282i | \(0.918490\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −319.412 | − | 553.237i | −0.571398 | − | 0.989691i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −803.834 | − | 955.400i | −1.43286 | − | 1.70303i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −334.881 | − | 920.079i | −0.594816 | − | 1.63424i | −0.761450 | − | 0.648224i | \(-0.775512\pi\) |
0.166634 | − | 0.986019i | \(-0.446710\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.28300 | + | 18.6188i | 0.00581061 | + | 0.0329536i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 156.470 | + | 860.699i | 0.275962 | + | 1.51799i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −552.043 | + | 97.3401i | −0.970199 | + | 0.171072i | −0.636219 | − | 0.771508i | \(-0.719503\pi\) |
−0.333979 | + | 0.942580i | \(0.608392\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.2223 | + | 10.6361i | −0.0511775 | + | 0.0186271i | −0.367482 | − | 0.930031i | \(-0.619780\pi\) |
0.316305 | + | 0.948658i | \(0.397558\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.48875 | − | 3.77665i | 0.00783377 | − | 0.00659102i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −88.5581 | + | 51.1290i | −0.154014 | + | 0.0889201i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −95.1751 | + | 164.848i | −0.164948 | + | 0.285699i | −0.936637 | − | 0.350302i | \(-0.886079\pi\) |
0.771689 | + | 0.636000i | \(0.219412\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 639.190 | − | 763.809i | 1.10396 | − | 1.31919i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1242.99 | − | 219.173i | −2.13940 | − | 0.377234i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −922.970 | + | 774.464i | −1.58314 | + | 1.32841i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −73.8879 | + | 13.2303i | −0.126304 | + | 0.0226160i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −150.974 | + | 414.798i | −0.257196 | + | 0.706641i | 0.742141 | + | 0.670244i | \(0.233810\pi\) |
−0.999337 | + | 0.0363972i | \(0.988412\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.2079 | − | 16.1174i | −0.0326111 | − | 0.0273640i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 368.331 | − | 639.923i | 0.623233 | − | 1.08278i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 435.642i | − | 0.734640i | −0.930095 | − | 0.367320i | \(-0.880275\pi\) | ||
0.930095 | − | 0.367320i | \(-0.119725\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −131.161 | −0.220439 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.09840 | − | 829.357i | −0.00183987 | − | 1.38921i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −615.387 | + | 733.389i | −1.02736 | + | 1.22436i | −0.0531765 | + | 0.998585i | \(0.516935\pi\) |
−0.974180 | + | 0.225771i | \(0.927510\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −214.739 | − | 78.1585i | −0.357302 | − | 0.130047i | 0.157131 | − | 0.987578i | \(-0.449775\pi\) |
−0.514433 | + | 0.857530i | \(0.671998\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 160.552 | + | 133.996i | 0.266255 | + | 0.222215i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −39.5154 | − | 47.0926i | −0.0653147 | − | 0.0778391i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.6802 | − | 134.297i | 0.0390118 | − | 0.221247i | −0.959069 | − | 0.283173i | \(-0.908613\pi\) |
0.998081 | + | 0.0619256i | \(0.0197241\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1268.35 | − | 463.545i | 2.08268 | − | 0.761158i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −250.869 | − | 144.839i | −0.410587 | − | 0.237053i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.5694 | − | 61.6081i | −0.0580252 | − | 0.100503i | 0.835554 | − | 0.549409i | \(-0.185147\pi\) |
−0.893579 | + | 0.448906i | \(0.851814\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20.6759 | + | 57.0415i | −0.0336194 | + | 0.0927505i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −348.112 | − | 956.431i | −0.564201 | − | 1.55013i | −0.813416 | − | 0.581682i | \(-0.802395\pi\) |
0.249215 | − | 0.968448i | \(-0.419828\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 63.4363 | + | 359.765i | 0.102482 | + | 0.581204i | 0.992196 | + | 0.124686i | \(0.0397924\pi\) |
−0.889714 | + | 0.456518i | \(0.849097\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −104.530 | + | 38.5167i | −0.168325 | + | 0.0620236i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1446.35 | − | 255.030i | 2.32158 | − | 0.409358i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −572.148 | + | 208.245i | −0.915437 | + | 0.333192i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 29.7184 | + | 167.246i | 0.0473977 | + | 0.266740i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −223.231 | + | 128.882i | −0.354898 | + | 0.204900i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 390.214 | − | 675.871i | 0.618406 | − | 1.07111i | −0.371371 | − | 0.928485i | \(-0.621112\pi\) |
0.989777 | − | 0.142626i | \(-0.0455546\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 157.351 | + | 27.5304i | 0.248580 | + | 0.0434919i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.2594 | + | 4.98289i | 0.0445029 | + | 0.00784707i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −930.467 | + | 780.754i | −1.46070 | + | 1.22567i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −289.686 | + | 168.275i | −0.453343 | + | 0.263341i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −96.5071 | + | 265.151i | −0.150557 | + | 0.413652i | −0.991927 | − | 0.126807i | \(-0.959527\pi\) |
0.841370 | + | 0.540459i | \(0.181749\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.0195 | − | 26.8675i | −0.0497970 | − | 0.0417846i | 0.617549 | − | 0.786532i | \(-0.288126\pi\) |
−0.667346 | + | 0.744747i | \(0.732570\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.8420 | + | 42.8963i | 0.0385147 | + | 0.0665059i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 383.618i | − | 0.592918i | −0.955046 | − | 0.296459i | \(-0.904194\pi\) | ||
0.955046 | − | 0.296459i | \(-0.0958058\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 456.677 | 0.703663 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −197.631 | + | 114.452i | −0.303581 | + | 0.175809i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.3773 | − | 46.9281i | 0.0603022 | − | 0.0718653i | −0.735050 | − | 0.678013i | \(-0.762841\pi\) |
0.795352 | + | 0.606147i | \(0.207286\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −98.7072 | − | 35.9265i | −0.150698 | − | 0.0548496i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −468.502 | + | 1.24097i | −0.713092 | + | 0.00188884i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −329.590 | − | 392.790i | −0.500137 | − | 0.596040i | 0.455629 | − | 0.890170i | \(-0.349415\pi\) |
−0.955765 | + | 0.294130i | \(0.904970\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.1600 | + | 188.060i | −0.0501664 | + | 0.284508i | −0.999563 | − | 0.0295731i | \(-0.990585\pi\) |
0.949396 | + | 0.314081i | \(0.101696\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −242.759 | + | 1387.50i | −0.366153 | + | 2.09276i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.4535 | + | 8.92209i | 0.0232384 | + | 0.0134167i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 85.9819 | + | 148.925i | 0.128908 | + | 0.223276i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −320.459 | + | 56.9432i | −0.479012 | + | 0.0851170i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 324.095 | + | 890.443i | 0.483003 | + | 1.32704i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −180.046 | − | 1021.09i | −0.267527 | − | 1.51722i | −0.761741 | − | 0.647882i | \(-0.775655\pi\) |
0.494214 | − | 0.869340i | \(-0.335456\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −658.542 | + | 118.819i | −0.975618 | + | 0.176027i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 482.182 | − | 85.0218i | 0.712234 | − | 0.125586i | 0.194220 | − | 0.980958i | \(-0.437782\pi\) |
0.518014 | + | 0.855372i | \(0.326671\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 958.165 | − | 348.743i | 1.41114 | − | 0.513613i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1022.32 | + | 370.562i | 1.50121 | + | 0.544144i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 251.274 | − | 145.073i | 0.367897 | − | 0.212406i | −0.304642 | − | 0.952467i | \(-0.598537\pi\) |
0.672540 | + | 0.740061i | \(0.265204\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.2808 | − | 61.1082i | 0.0515049 | − | 0.0892090i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −298.175 | − | 815.865i | −0.434024 | − | 1.18758i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1338.60 | + | 236.031i | 1.94282 | + | 0.342571i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 148.698 | − | 124.773i | 0.215193 | − | 0.180568i | −0.528819 | − | 0.848735i | \(-0.677365\pi\) |
0.744012 | + | 0.668166i | \(0.232921\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1524.36 | + | 264.625i | 2.19966 | + | 0.381855i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.9992 | + | 74.1796i | −0.0388477 | + | 0.106733i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 872.176 | + | 731.842i | 1.25133 | + | 1.04999i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −442.237 | + | 0.585699i | −0.632671 | + | 0.000837910i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 294.780i | 0.420513i | 0.977646 | + | 0.210257i | \(0.0674299\pi\) | ||||
−0.977646 | + | 0.210257i | \(0.932570\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.0683 | 0.0498837 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.4814 | + | 11.2132i | 0.0276331 | + | 0.0159052i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1058.20 | + | 1261.12i | −1.49675 | + | 1.78376i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 916.038 | + | 333.410i | 1.29201 | + | 0.470255i | 0.894387 | − | 0.447293i | \(-0.147612\pi\) |
0.397626 | + | 0.917548i | \(0.369834\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1021.89 | − | 368.877i | −1.43726 | − | 0.518814i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.6938 | − | 22.2784i | −0.0262185 | − | 0.0312460i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.0526 | + | 130.738i | −0.0322415 | + | 0.182850i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 31.3634 | + | 26.2463i | 0.0437426 | + | 0.0366058i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −574.371 | − | 331.613i | −0.798848 | − | 0.461215i | 0.0442205 | − | 0.999022i | \(-0.485920\pi\) |
−0.843068 | + | 0.537807i | \(0.819253\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −117.471 | − | 203.466i | −0.162928 | − | 0.282200i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 573.748 | + | 681.930i | 0.793566 | + | 0.943196i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 353.300 | + | 970.683i | 0.487310 | + | 1.33887i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −178.695 | − | 1013.43i | −0.245797 | − | 1.39399i | −0.818633 | − | 0.574316i | \(-0.805268\pi\) |
0.572836 | − | 0.819670i | \(-0.305843\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −728.977 | + | 5.79286i | −0.999968 | + | 0.00794631i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 916.066 | − | 161.527i | 1.25317 | − | 0.220967i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −93.4865 | + | 34.0263i | −0.127540 | + | 0.0464206i | −0.405001 | − | 0.914316i | \(-0.632729\pi\) |
0.277462 | + | 0.960737i | \(0.410507\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 72.1205 | − | 60.6792i | 0.0981231 | − | 0.0825567i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 320.297 | − | 184.923i | 0.434595 | − | 0.250914i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.7996 | − | 49.8824i | 0.0389710 | − | 0.0674998i | −0.845882 | − | 0.533370i | \(-0.820925\pi\) |
0.884853 | + | 0.465870i | \(0.154259\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 122.985 | − | 146.963i | 0.165972 | − | 0.198330i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1203.21 | + | 212.158i | 1.61939 | + | 0.285543i | 0.908540 | − | 0.417798i | \(-0.137198\pi\) |
0.710853 | + | 0.703340i | \(0.248309\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 63.7064 | − | 53.4560i | 0.0855120 | − | 0.0717531i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 357.117 | − | 989.317i | 0.478068 | − | 1.32439i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 184.113 | − | 505.845i | 0.245811 | − | 0.675361i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 623.699 | + | 523.346i | 0.830492 | + | 0.696865i | 0.955404 | − | 0.295302i | \(-0.0954204\pi\) |
−0.124912 | + | 0.992168i | \(0.539865\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.315974 | − | 0.548962i | 0.000419621 | − | 0.000729033i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 55.8142i | 0.0739261i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 646.428 | 0.853933 | 0.426967 | − | 0.904267i | \(-0.359582\pi\) | ||||
0.426967 | + | 0.904267i | \(0.359582\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.260932 | + | 197.019i | 0.000343785 | + | 0.259578i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −132.824 | + | 158.293i | −0.174539 | + | 0.208007i | −0.846221 | − | 0.532832i | \(-0.821128\pi\) |
0.671682 | + | 0.740840i | \(0.265572\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1736.08 | − | 631.882i | −2.27534 | − | 0.828154i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.6946 | − | 107.690i | 0.0244374 | − | 0.140771i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −331.164 | − | 394.665i | −0.431765 | − | 0.514557i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.9808 | − | 158.687i | 0.0363860 | − | 0.206355i | −0.961195 | − | 0.275870i | \(-0.911034\pi\) |
0.997581 | + | 0.0695149i | \(0.0221451\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −546.400 | + | 199.693i | −0.708689 | + | 0.259005i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −769.088 | − | 444.033i | −0.994940 | − | 0.574429i | −0.0881925 | − | 0.996103i | \(-0.528109\pi\) |
−0.906747 | + | 0.421675i | \(0.861442\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −87.3485 | − | 151.292i | −0.112708 | − | 0.195215i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 108.846 | − | 300.289i | 0.140085 | − | 0.386472i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −52.9777 | − | 145.555i | −0.0680073 | − | 0.186848i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 102.886 | + | 583.497i | 0.131737 | + | 0.747116i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 199.813 | + | 1107.45i | 0.255189 | + | 1.41436i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.9153 | + | 2.62997i | −0.0190004 | + | 0.00335028i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1121.88 | + | 408.332i | −1.42552 | + | 0.518847i | −0.935644 | − | 0.352945i | \(-0.885180\pi\) |
−0.489876 | + | 0.871792i | \(0.662958\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −214.588 | − | 1207.63i | −0.271975 | − | 1.53059i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −380.720 | + | 219.809i | −0.481315 | + | 0.277887i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 534.510 | − | 925.799i | 0.674035 | − | 1.16746i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −103.895 | − | 18.1776i | −0.130685 | − | 0.0228649i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 477.592 | + | 84.2124i | 0.599237 | + | 0.105662i | 0.465035 | − | 0.885292i | \(-0.346042\pi\) |
0.134202 | + | 0.990954i | \(0.457153\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 323.121 | − | 271.130i | 0.404406 | − | 0.339337i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.24179 | + | 1223.87i | 0.00404718 | + | 1.52793i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −283.393 | + | 778.615i | −0.352917 | + | 0.969632i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.8546 | + | 13.3036i | 0.0196951 | + | 0.0165262i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −180.549 | − | 311.765i | −0.223728 | − | 0.386326i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1260.59i | 1.55821i | 0.626893 | + | 0.779105i | \(0.284326\pi\) | ||||
−0.626893 | + | 0.779105i | \(0.715674\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 740.450 | 0.913009 | 0.456504 | − | 0.889721i | \(-0.349101\pi\) | ||||
0.456504 | + | 0.889721i | \(0.349101\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −49.4008 | + | 28.6089i | −0.0607636 | + | 0.0351893i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 65.6297 | − | 78.2144i | 0.0805272 | − | 0.0959686i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −118.919 | − | 43.2831i | −0.145556 | − | 0.0529780i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −876.714 | − | 1509.27i | −1.07047 | − | 1.84282i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 600.280 | + | 715.385i | 0.731157 | + | 0.871359i | 0.995664 | − | 0.0930252i | \(-0.0296537\pi\) |
−0.264507 | + | 0.964384i | \(0.585209\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.57884 | + | 42.9817i | −0.00920880 | + | 0.0522257i | −0.989066 | − | 0.147474i | \(-0.952886\pi\) |
0.979857 | + | 0.199700i | \(0.0639967\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −203.967 | + | 1165.78i | −0.247233 | + | 1.41307i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 620.289 | + | 358.124i | 0.750047 | + | 0.433040i | 0.825711 | − | 0.564093i | \(-0.190774\pi\) |
−0.0756636 | + | 0.997133i | \(0.524108\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −151.869 | − | 263.044i | −0.183195 | − | 0.317303i | 0.759772 | − | 0.650190i | \(-0.225311\pi\) |
−0.942967 | + | 0.332887i | \(0.891977\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −940.376 | + | 167.098i | −1.13162 | + | 0.201081i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −604.913 | − | 1661.99i | −0.726186 | − | 1.99518i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.79336 | + | 55.5409i | 0.0117286 | + | 0.0665161i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −65.8016 | − | 178.577i | −0.0786160 | − | 0.213354i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 546.700 | − | 96.3979i | 0.651609 | − | 0.114896i | 0.161934 | − | 0.986802i | \(-0.448227\pi\) |
0.489674 | + | 0.871905i | \(0.337116\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 842.081 | − | 306.492i | 1.00129 | − | 0.364438i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 678.759 | + | 246.030i | 0.805170 | + | 0.291851i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 61.7240 | − | 35.6363i | 0.0730461 | − | 0.0421732i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 714.734 | − | 1237.96i | 0.843841 | − | 1.46158i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 92.0002 | + | 251.731i | 0.108363 | + | 0.296503i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.0562 | + | 7.06298i | 0.0470695 | + | 0.00829963i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 199.807 | − | 167.658i | 0.234241 | − | 0.196551i | −0.518110 | − | 0.855314i | \(-0.673364\pi\) |
0.752351 | + | 0.658763i | \(0.228920\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.52807 | + | 11.4164i | −0.0111439 | + | 0.0133525i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 123.417 | − | 339.084i | 0.144010 | − | 0.395664i | −0.846627 | − | 0.532187i | \(-0.821370\pi\) |
0.990637 | + | 0.136523i | \(0.0435926\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −439.289 | − | 368.607i | −0.511396 | − | 0.429112i | 0.350224 | − | 0.936666i | \(-0.386105\pi\) |
−0.861620 | + | 0.507554i | \(0.830550\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1410.82 | + | 1.86849i | −1.63858 | + | 0.00217014i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 654.390i | 0.758273i | 0.925341 | + | 0.379137i | \(0.123779\pi\) | ||||
−0.925341 | + | 0.379137i | \(0.876221\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.8572 | 0.0414534 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1026.19 | − | 590.662i | −1.18361 | − | 0.681271i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1235.08 | + | 1471.91i | −1.42127 | + | 1.69380i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −392.079 | − | 142.705i | −0.450148 | − | 0.163840i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 149.766 | + | 836.406i | 0.171554 | + | 0.958082i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 160.523 | + | 191.304i | 0.183455 | + | 0.218634i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 139.814 | − | 792.923i | 0.159423 | − | 0.904131i | −0.795208 | − | 0.606337i | \(-0.792638\pi\) |
0.954630 | − | 0.297794i | \(-0.0962508\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −716.661 | − | 599.735i | −0.815314 | − | 0.682292i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1043.53 | + | 602.480i | 1.18448 | + | 0.683860i | 0.957047 | − | 0.289934i | \(-0.0936334\pi\) |
0.227433 | + | 0.973794i | \(0.426967\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −378.383 | − | 655.379i | −0.428520 | − | 0.742219i | 0.568222 | − | 0.822876i | \(-0.307632\pi\) |
−0.996742 | + | 0.0806566i | \(0.974298\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25.7376 | + | 30.5905i | 0.0290820 | + | 0.0345655i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −209.428 | − | 575.399i | −0.236108 | − | 0.648703i | −0.999994 | − | 0.00335135i | \(-0.998933\pi\) |
0.763886 | − | 0.645351i | \(-0.223289\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 115.866 | + | 657.109i | 0.130333 | + | 0.739155i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −434.540 | + | 1213.86i | −0.487699 | + | 1.36235i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −56.5136 | + | 9.96488i | −0.0632851 | + | 0.0111589i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 64.8047 | − | 23.5870i | 0.0724075 | − | 0.0263542i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 170.077 | − | 143.096i | 0.189606 | − | 0.159527i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −254.422 | + | 146.891i | −0.283006 | + | 0.163393i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −989.610 | + | 1714.05i | −1.09835 | + | 1.90239i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −739.738 | + | 883.960i | −0.819200 | + | 0.978915i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −38.6175 | − | 6.80931i | −0.0426713 | − | 0.00752410i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1232.60 | − | 1034.27i | 1.35898 | − | 1.14032i | 0.382688 | − | 0.923878i | \(-0.374998\pi\) |
0.976295 | − | 0.216445i | \(-0.0694460\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −884.610 | − | 1048.58i | −0.973168 | − | 1.15356i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −471.470 | + | 1295.35i | −0.517530 | + | 1.42190i | 0.355703 | + | 0.934599i | \(0.384241\pi\) |
−0.873233 | + | 0.487303i | \(0.837981\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1424.99 | − | 1195.71i | −1.56077 | − | 1.30964i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −41.3808 | + | 71.8934i | −0.0452249 | + | 0.0785720i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2442.52i | − | 2.66360i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1619.94 | −1.76272 | −0.881358 | − | 0.472449i | \(-0.843370\pi\) | ||||
−0.881358 | + | 0.472449i | \(0.843370\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.35841 | − | 1780.74i | −0.00256071 | − | 1.93348i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 429.656 | − | 512.044i | 0.465499 | − | 0.554760i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 229.593 | + | 83.5650i | 0.248209 | + | 0.0903406i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 183.798 | − | 67.4490i | 0.198272 | − | 0.0727606i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 63.3425 | + | 75.4887i | 0.0681836 | + | 0.0812580i | 0.799058 | − | 0.601254i | \(-0.205332\pi\) |
−0.730874 | + | 0.682512i | \(0.760888\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.7833 | + | 236.965i | −0.0448800 | + | 0.254527i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1540.38 | − | 562.965i | 1.65100 | − | 0.603392i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −167.408 | − | 96.6529i | −0.179046 | − | 0.103372i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 280.625 | + | 486.056i | 0.299493 | + | 0.518736i | 0.976020 | − | 0.217681i | \(-0.0698493\pi\) |
−0.676527 | + | 0.736417i | \(0.736516\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −160.134 | + | 441.784i | −0.170537 | + | 0.470483i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −253.931 | − | 697.670i | −0.269852 | − | 0.741414i | −0.998407 | − | 0.0564255i | \(-0.982030\pi\) |
0.728554 | − | 0.684988i | \(-0.240193\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.1972 | − | 176.928i | −0.0330829 | − | 0.187622i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 68.1848 | + | 117.023i | 0.0721532 | + | 0.123834i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −411.072 | + | 72.4830i | −0.434078 | + | 0.0765396i | −0.386417 | − | 0.922324i | \(-0.626288\pi\) |
−0.0476602 | + | 0.998864i | \(0.515176\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 878.392 | − | 319.708i | 0.925597 | − | 0.336890i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.2106 | − | 124.994i | −0.0233550 | − | 0.131434i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 474.227 | − | 273.795i | 0.497615 | − | 0.287298i | −0.230113 | − | 0.973164i | \(-0.573910\pi\) |
0.727728 | + | 0.685866i | \(0.240576\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.454104 | − | 0.786531i | 0.000475502 | − | 0.000823593i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1960.45 | + | 343.004i | 2.04854 | + | 0.358415i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1615.83 | + | 284.914i | 1.68491 | + | 0.297095i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −698.108 | + | 585.783i | −0.726440 | + | 0.609555i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 389.081 | + | 223.264i | 0.404030 | + | 0.231842i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 52.7389 | − | 144.899i | 0.0546517 | − | 0.150154i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −275.438 | − | 231.120i | −0.284838 | − | 0.239007i | 0.489162 | − | 0.872193i | \(-0.337303\pi\) |
−0.774000 | + | 0.633186i | \(0.781747\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 139.840 | + | 241.470i | 0.144313 | + | 0.249195i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 842.963i | 0.868139i | 0.900879 | + | 0.434069i | \(0.142923\pi\) | ||||
−0.900879 | + | 0.434069i | \(0.857077\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1835.58 | −1.88652 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1155.39 | − | 669.105i | 1.18501 | − | 0.686262i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −731.252 | + | 871.472i | −0.748467 | + | 0.891988i | −0.997060 | − | 0.0766199i | \(-0.975587\pi\) |
0.248594 | + | 0.968608i | \(0.420032\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2033.98 | + | 740.308i | 2.07761 | + | 0.756187i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 766.251 | − | 1335.34i | 0.781092 | − | 1.36120i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −614.192 | − | 731.965i | −0.624813 | − | 0.744624i | 0.357077 | − | 0.934075i | \(-0.383773\pi\) |
−0.981890 | + | 0.189451i | \(0.939329\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.8503 | − | 112.576i | 0.0201526 | − | 0.114291i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −90.0799 | + | 514.855i | −0.0912663 | + | 0.521636i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −127.116 | − | 73.3905i | −0.128530 | − | 0.0742068i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 734.903 | + | 1272.89i | 0.741577 | + | 1.28445i | 0.951777 | + | 0.306791i | \(0.0992551\pi\) |
−0.210200 | + | 0.977658i | \(0.567412\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1453.45 | + | 258.267i | −1.46369 | + | 0.260088i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −43.9161 | − | 120.659i | −0.0441368 | − | 0.121265i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 213.101 | + | 1208.56i | 0.213742 | + | 1.21219i | 0.883076 | + | 0.469230i | \(0.155468\pi\) |
−0.669334 | + | 0.742962i | \(0.733420\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 231.038 | + | 132.168i | 0.231269 | + | 0.132301i |
(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 | 108.3.k.a.41.2 | yes | 36 | |
3.2 | odd | 2 | 324.3.k.a.233.4 | 36 | |||
4.3 | odd | 2 | 432.3.bc.b.257.5 | 36 | |||
27.2 | odd | 18 | inner | 108.3.k.a.29.2 | ✓ | 36 | |
27.5 | odd | 18 | 2916.3.c.b.1457.17 | 36 | |||
27.22 | even | 9 | 2916.3.c.b.1457.20 | 36 | |||
27.25 | even | 9 | 324.3.k.a.89.4 | 36 | |||
108.83 | even | 18 | 432.3.bc.b.353.5 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.k.a.29.2 | ✓ | 36 | 27.2 | odd | 18 | inner | |
108.3.k.a.41.2 | yes | 36 | 1.1 | even | 1 | trivial | |
324.3.k.a.89.4 | 36 | 27.25 | even | 9 | |||
324.3.k.a.233.4 | 36 | 3.2 | odd | 2 | |||
432.3.bc.b.257.5 | 36 | 4.3 | odd | 2 | |||
432.3.bc.b.353.5 | 36 | 108.83 | even | 18 | |||
2916.3.c.b.1457.17 | 36 | 27.5 | odd | 18 | |||
2916.3.c.b.1457.20 | 36 | 27.22 | even | 9 |