Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,3,Mod(133,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.133");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.b (of order \(2\), degree \(1\), 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: | \(5.47685331364\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 133.8 | ||
Character | \(\chi\) | \(=\) | 201.133 |
Dual form | 201.3.b.a.133.15 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.30530i | − | 0.652652i | −0.945257 | − | 0.326326i | \(-0.894189\pi\) | ||
0.945257 | − | 0.326326i | \(-0.105811\pi\) | |||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 2.29618 | 0.574046 | ||||||||
\(5\) | 2.19844i | 0.439689i | 0.975535 | + | 0.219844i | \(0.0705549\pi\) | ||||
−0.975535 | + | 0.219844i | \(0.929445\pi\) | |||||||
\(6\) | 2.26085 | 0.376809 | ||||||||
\(7\) | 9.13473i | 1.30496i | 0.757805 | + | 0.652481i | \(0.226272\pi\) | ||||
−0.757805 | + | 0.652481i | \(0.773728\pi\) | |||||||
\(8\) | − | 8.21843i | − | 1.02730i | ||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 2.86963 | 0.286963 | ||||||||
\(11\) | 4.26648i | 0.387862i | 0.981015 | + | 0.193931i | \(0.0621237\pi\) | ||||
−0.981015 | + | 0.193931i | \(0.937876\pi\) | |||||||
\(12\) | 3.97711i | 0.331426i | ||||||||
\(13\) | 14.1682i | 1.08986i | 0.838480 | + | 0.544932i | \(0.183444\pi\) | ||||
−0.838480 | + | 0.544932i | \(0.816556\pi\) | |||||||
\(14\) | 11.9236 | 0.851685 | ||||||||
\(15\) | −3.80781 | −0.253854 | ||||||||
\(16\) | −1.54281 | −0.0964255 | ||||||||
\(17\) | −2.27802 | −0.134001 | −0.0670006 | − | 0.997753i | \(-0.521343\pi\) | ||||
−0.0670006 | + | 0.997753i | \(0.521343\pi\) | |||||||
\(18\) | 3.91591i | 0.217551i | ||||||||
\(19\) | −8.04803 | −0.423581 | −0.211790 | − | 0.977315i | \(-0.567929\pi\) | ||||
−0.211790 | + | 0.977315i | \(0.567929\pi\) | |||||||
\(20\) | 5.04803i | 0.252401i | ||||||||
\(21\) | −15.8218 | −0.753420 | ||||||||
\(22\) | 5.56905 | 0.253138 | ||||||||
\(23\) | 19.0132 | 0.826660 | 0.413330 | − | 0.910581i | \(-0.364366\pi\) | ||||
0.413330 | + | 0.910581i | \(0.364366\pi\) | |||||||
\(24\) | 14.2347 | 0.593114 | ||||||||
\(25\) | 20.1669 | 0.806674 | ||||||||
\(26\) | 18.4938 | 0.711301 | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 20.9750i | 0.749108i | ||||||||
\(29\) | 25.2117 | 0.869367 | 0.434684 | − | 0.900583i | \(-0.356860\pi\) | ||||
0.434684 | + | 0.900583i | \(0.356860\pi\) | |||||||
\(30\) | 4.97035i | 0.165678i | ||||||||
\(31\) | − | 9.14609i | − | 0.295035i | −0.989059 | − | 0.147518i | \(-0.952872\pi\) | ||
0.989059 | − | 0.147518i | \(-0.0471283\pi\) | |||||||
\(32\) | − | 30.8599i | − | 0.964371i | ||||||
\(33\) | −7.38975 | −0.223932 | ||||||||
\(34\) | 2.97351i | 0.0874561i | ||||||||
\(35\) | −20.0822 | −0.573777 | ||||||||
\(36\) | −6.88855 | −0.191349 | ||||||||
\(37\) | 3.39792 | 0.0918357 | 0.0459178 | − | 0.998945i | \(-0.485379\pi\) | ||||
0.0459178 | + | 0.998945i | \(0.485379\pi\) | |||||||
\(38\) | 10.5051i | 0.276451i | ||||||||
\(39\) | −24.5401 | −0.629233 | ||||||||
\(40\) | 18.0677 | 0.451694 | ||||||||
\(41\) | − | 43.7208i | − | 1.06636i | −0.846002 | − | 0.533180i | \(-0.820997\pi\) | ||
0.846002 | − | 0.533180i | \(-0.179003\pi\) | |||||||
\(42\) | 20.6523i | 0.491721i | ||||||||
\(43\) | 34.0526i | 0.791921i | 0.918267 | + | 0.395961i | \(0.129588\pi\) | ||||
−0.918267 | + | 0.395961i | \(0.870412\pi\) | |||||||
\(44\) | 9.79661i | 0.222650i | ||||||||
\(45\) | − | 6.59533i | − | 0.146563i | ||||||
\(46\) | − | 24.8180i | − | 0.539521i | ||||||
\(47\) | −6.95616 | −0.148004 | −0.0740018 | − | 0.997258i | \(-0.523577\pi\) | ||||
−0.0740018 | + | 0.997258i | \(0.523577\pi\) | |||||||
\(48\) | − | 2.67222i | − | 0.0556713i | ||||||
\(49\) | −34.4434 | −0.702926 | ||||||||
\(50\) | − | 26.3239i | − | 0.526477i | ||||||
\(51\) | − | 3.94565i | − | 0.0773656i | ||||||
\(52\) | 32.5328i | 0.625631i | ||||||||
\(53\) | − | 87.9202i | − | 1.65887i | −0.558602 | − | 0.829436i | \(-0.688662\pi\) | ||
0.558602 | − | 0.829436i | \(-0.311338\pi\) | |||||||
\(54\) | −6.78255 | −0.125603 | ||||||||
\(55\) | −9.37960 | −0.170538 | ||||||||
\(56\) | 75.0732 | 1.34059 | ||||||||
\(57\) | − | 13.9396i | − | 0.244554i | ||||||
\(58\) | − | 32.9089i | − | 0.567394i | ||||||
\(59\) | −84.3301 | −1.42932 | −0.714662 | − | 0.699470i | \(-0.753420\pi\) | ||||
−0.714662 | + | 0.699470i | \(0.753420\pi\) | |||||||
\(60\) | −8.74344 | −0.145724 | ||||||||
\(61\) | − | 23.7647i | − | 0.389584i | −0.980845 | − | 0.194792i | \(-0.937597\pi\) | ||
0.980845 | − | 0.194792i | \(-0.0624033\pi\) | |||||||
\(62\) | −11.9384 | −0.192555 | ||||||||
\(63\) | − | 27.4042i | − | 0.434987i | ||||||
\(64\) | −46.4527 | −0.725824 | ||||||||
\(65\) | −31.1480 | −0.479200 | ||||||||
\(66\) | 9.64587i | 0.146150i | ||||||||
\(67\) | 43.1590 | + | 51.2475i | 0.644164 | + | 0.764888i | ||||
\(68\) | −5.23075 | −0.0769228 | ||||||||
\(69\) | 32.9318i | 0.477273i | ||||||||
\(70\) | 26.2133i | 0.374476i | ||||||||
\(71\) | −36.5444 | −0.514710 | −0.257355 | − | 0.966317i | \(-0.582851\pi\) | ||||
−0.257355 | + | 0.966317i | \(0.582851\pi\) | |||||||
\(72\) | 24.6553i | 0.342435i | ||||||||
\(73\) | −121.058 | −1.65832 | −0.829162 | − | 0.559008i | \(-0.811182\pi\) | ||||
−0.829162 | + | 0.559008i | \(0.811182\pi\) | |||||||
\(74\) | − | 4.43532i | − | 0.0599367i | ||||||
\(75\) | 34.9300i | 0.465733i | ||||||||
\(76\) | −18.4798 | −0.243155 | ||||||||
\(77\) | −38.9731 | −0.506145 | ||||||||
\(78\) | 32.0322i | 0.410670i | ||||||||
\(79\) | − | 93.7490i | − | 1.18670i | −0.804946 | − | 0.593348i | \(-0.797806\pi\) | ||
0.804946 | − | 0.593348i | \(-0.202194\pi\) | |||||||
\(80\) | − | 3.39177i | − | 0.0423972i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −57.0689 | −0.695962 | ||||||||
\(83\) | 50.1032 | 0.603653 | 0.301826 | − | 0.953363i | \(-0.402404\pi\) | ||||
0.301826 | + | 0.953363i | \(0.402404\pi\) | |||||||
\(84\) | −36.3298 | −0.432498 | ||||||||
\(85\) | − | 5.00810i | − | 0.0589188i | ||||||
\(86\) | 44.4490 | 0.516849 | ||||||||
\(87\) | 43.6679i | 0.501930i | ||||||||
\(88\) | 35.0637 | 0.398452 | ||||||||
\(89\) | 52.8616 | 0.593951 | 0.296975 | − | 0.954885i | \(-0.404022\pi\) | ||||
0.296975 | + | 0.954885i | \(0.404022\pi\) | |||||||
\(90\) | −8.60890 | −0.0956545 | ||||||||
\(91\) | −129.423 | −1.42223 | ||||||||
\(92\) | 43.6578 | 0.474541 | ||||||||
\(93\) | 15.8415 | 0.170339 | ||||||||
\(94\) | 9.07990i | 0.0965947i | ||||||||
\(95\) | − | 17.6931i | − | 0.186244i | ||||||
\(96\) | 53.4509 | 0.556780 | ||||||||
\(97\) | − | 36.3620i | − | 0.374866i | −0.982277 | − | 0.187433i | \(-0.939983\pi\) | ||
0.982277 | − | 0.187433i | \(-0.0600168\pi\) | |||||||
\(98\) | 44.9590i | 0.458765i | ||||||||
\(99\) | − | 12.7994i | − | 0.129287i | ||||||
\(100\) | 46.3068 | 0.463068 | ||||||||
\(101\) | − | 4.47109i | − | 0.0442683i | −0.999755 | − | 0.0221341i | \(-0.992954\pi\) | ||
0.999755 | − | 0.0221341i | \(-0.00704609\pi\) | |||||||
\(102\) | −5.15027 | −0.0504928 | ||||||||
\(103\) | 48.0708 | 0.466707 | 0.233353 | − | 0.972392i | \(-0.425030\pi\) | ||||
0.233353 | + | 0.972392i | \(0.425030\pi\) | |||||||
\(104\) | 116.441 | 1.11962 | ||||||||
\(105\) | − | 34.7834i | − | 0.331270i | ||||||
\(106\) | −114.763 | −1.08267 | ||||||||
\(107\) | 127.742 | 1.19385 | 0.596924 | − | 0.802298i | \(-0.296389\pi\) | ||||
0.596924 | + | 0.802298i | \(0.296389\pi\) | |||||||
\(108\) | − | 11.9313i | − | 0.110475i | ||||||
\(109\) | − | 115.564i | − | 1.06022i | −0.847928 | − | 0.530112i | \(-0.822150\pi\) | ||
0.847928 | − | 0.530112i | \(-0.177850\pi\) | |||||||
\(110\) | 12.2432i | 0.111302i | ||||||||
\(111\) | 5.88537i | 0.0530214i | ||||||||
\(112\) | − | 14.0931i | − | 0.125832i | ||||||
\(113\) | 29.4439i | 0.260566i | 0.991477 | + | 0.130283i | \(0.0415885\pi\) | ||||
−0.991477 | + | 0.130283i | \(0.958411\pi\) | |||||||
\(114\) | −18.1954 | −0.159609 | ||||||||
\(115\) | 41.7994i | 0.363473i | ||||||||
\(116\) | 57.8906 | 0.499057 | ||||||||
\(117\) | − | 42.5047i | − | 0.363288i | ||||||
\(118\) | 110.076i | 0.932851i | ||||||||
\(119\) | − | 20.8091i | − | 0.174866i | ||||||
\(120\) | 31.2942i | 0.260785i | ||||||||
\(121\) | 102.797 | 0.849563 | ||||||||
\(122\) | −31.0201 | −0.254263 | ||||||||
\(123\) | 75.7266 | 0.615663 | ||||||||
\(124\) | − | 21.0011i | − | 0.169364i | ||||||
\(125\) | 99.2967i | 0.794374i | ||||||||
\(126\) | −35.7708 | −0.283895 | ||||||||
\(127\) | 214.525 | 1.68917 | 0.844585 | − | 0.535422i | \(-0.179847\pi\) | ||||
0.844585 | + | 0.535422i | \(0.179847\pi\) | |||||||
\(128\) | − | 62.8046i | − | 0.490661i | ||||||
\(129\) | −58.9809 | −0.457216 | ||||||||
\(130\) | 40.6576i | 0.312751i | ||||||||
\(131\) | −126.306 | −0.964167 | −0.482084 | − | 0.876125i | \(-0.660120\pi\) | ||||
−0.482084 | + | 0.876125i | \(0.660120\pi\) | |||||||
\(132\) | −16.9682 | −0.128547 | ||||||||
\(133\) | − | 73.5166i | − | 0.552757i | ||||||
\(134\) | 66.8935 | − | 56.3356i | 0.499205 | − | 0.420415i | ||||
\(135\) | 11.4234 | 0.0846181 | ||||||||
\(136\) | 18.7217i | 0.137660i | ||||||||
\(137\) | − | 37.0683i | − | 0.270572i | −0.990807 | − | 0.135286i | \(-0.956805\pi\) | ||
0.990807 | − | 0.135286i | \(-0.0431953\pi\) | |||||||
\(138\) | 42.9860 | 0.311493 | ||||||||
\(139\) | 17.3661i | 0.124936i | 0.998047 | + | 0.0624679i | \(0.0198971\pi\) | ||||
−0.998047 | + | 0.0624679i | \(0.980103\pi\) | |||||||
\(140\) | −46.1124 | −0.329374 | ||||||||
\(141\) | − | 12.0484i | − | 0.0854499i | ||||||
\(142\) | 47.7015i | 0.335926i | ||||||||
\(143\) | −60.4484 | −0.422716 | ||||||||
\(144\) | 4.62842 | 0.0321418 | ||||||||
\(145\) | 55.4264i | 0.382251i | ||||||||
\(146\) | 158.017i | 1.08231i | ||||||||
\(147\) | − | 59.6576i | − | 0.405834i | ||||||
\(148\) | 7.80225 | 0.0527179 | ||||||||
\(149\) | −95.2384 | −0.639184 | −0.319592 | − | 0.947555i | \(-0.603546\pi\) | ||||
−0.319592 | + | 0.947555i | \(0.603546\pi\) | |||||||
\(150\) | 45.5943 | 0.303962 | ||||||||
\(151\) | 72.3267 | 0.478985 | 0.239493 | − | 0.970898i | \(-0.423019\pi\) | ||||
0.239493 | + | 0.970898i | \(0.423019\pi\) | |||||||
\(152\) | 66.1422i | 0.435146i | ||||||||
\(153\) | 6.83406 | 0.0446671 | ||||||||
\(154\) | 50.8717i | 0.330336i | ||||||||
\(155\) | 20.1071 | 0.129723 | ||||||||
\(156\) | −56.3485 | −0.361208 | ||||||||
\(157\) | 226.414 | 1.44213 | 0.721065 | − | 0.692868i | \(-0.243653\pi\) | ||||
0.721065 | + | 0.692868i | \(0.243653\pi\) | |||||||
\(158\) | −122.371 | −0.774499 | ||||||||
\(159\) | 152.282 | 0.957750 | ||||||||
\(160\) | 67.8437 | 0.424023 | ||||||||
\(161\) | 173.680i | 1.07876i | ||||||||
\(162\) | − | 11.7477i | − | 0.0725168i | ||||||
\(163\) | 225.801 | 1.38528 | 0.692642 | − | 0.721281i | \(-0.256446\pi\) | ||||
0.692642 | + | 0.721281i | \(0.256446\pi\) | |||||||
\(164\) | − | 100.391i | − | 0.612140i | ||||||
\(165\) | − | 16.2460i | − | 0.0984603i | ||||||
\(166\) | − | 65.3998i | − | 0.393975i | ||||||
\(167\) | −70.9723 | −0.424984 | −0.212492 | − | 0.977163i | \(-0.568158\pi\) | ||||
−0.212492 | + | 0.977163i | \(0.568158\pi\) | |||||||
\(168\) | 130.031i | 0.773991i | ||||||||
\(169\) | −31.7385 | −0.187802 | ||||||||
\(170\) | −6.53708 | −0.0384534 | ||||||||
\(171\) | 24.1441 | 0.141194 | ||||||||
\(172\) | 78.1911i | 0.454599i | ||||||||
\(173\) | −194.180 | −1.12243 | −0.561213 | − | 0.827672i | \(-0.689665\pi\) | ||||
−0.561213 | + | 0.827672i | \(0.689665\pi\) | |||||||
\(174\) | 56.9998 | 0.327585 | ||||||||
\(175\) | 184.219i | 1.05268i | ||||||||
\(176\) | − | 6.58235i | − | 0.0373997i | ||||||
\(177\) | − | 146.064i | − | 0.825221i | ||||||
\(178\) | − | 69.0004i | − | 0.387643i | ||||||
\(179\) | 167.435i | 0.935392i | 0.883889 | + | 0.467696i | \(0.154916\pi\) | ||||
−0.883889 | + | 0.467696i | \(0.845084\pi\) | |||||||
\(180\) | − | 15.1441i | − | 0.0841338i | ||||||
\(181\) | −350.378 | −1.93579 | −0.967896 | − | 0.251350i | \(-0.919126\pi\) | ||||
−0.967896 | + | 0.251350i | \(0.919126\pi\) | |||||||
\(182\) | 168.936i | 0.928221i | ||||||||
\(183\) | 41.1616 | 0.224927 | ||||||||
\(184\) | − | 156.259i | − | 0.849231i | ||||||
\(185\) | 7.47013i | 0.0403791i | ||||||||
\(186\) | − | 20.6779i | − | 0.111172i | ||||||
\(187\) | − | 9.71912i | − | 0.0519739i | ||||||
\(188\) | −15.9726 | −0.0849608 | ||||||||
\(189\) | 47.4655 | 0.251140 | ||||||||
\(190\) | −23.0949 | −0.121552 | ||||||||
\(191\) | 193.984i | 1.01562i | 0.861469 | + | 0.507810i | \(0.169545\pi\) | ||||
−0.861469 | + | 0.507810i | \(0.830455\pi\) | |||||||
\(192\) | − | 80.4585i | − | 0.419055i | ||||||
\(193\) | −268.978 | −1.39367 | −0.696834 | − | 0.717233i | \(-0.745408\pi\) | ||||
−0.696834 | + | 0.717233i | \(0.745408\pi\) | |||||||
\(194\) | −47.4634 | −0.244657 | ||||||||
\(195\) | − | 53.9500i | − | 0.276666i | ||||||
\(196\) | −79.0883 | −0.403511 | ||||||||
\(197\) | 190.688i | 0.967957i | 0.875080 | + | 0.483978i | \(0.160809\pi\) | ||||
−0.875080 | + | 0.483978i | \(0.839191\pi\) | |||||||
\(198\) | −16.7071 | −0.0843795 | ||||||||
\(199\) | 50.1303 | 0.251911 | 0.125956 | − | 0.992036i | \(-0.459800\pi\) | ||||
0.125956 | + | 0.992036i | \(0.459800\pi\) | |||||||
\(200\) | − | 165.740i | − | 0.828699i | ||||||
\(201\) | −88.7632 | + | 74.7535i | −0.441608 | + | 0.371908i | ||||
\(202\) | −5.83613 | −0.0288918 | ||||||||
\(203\) | 230.302i | 1.13449i | ||||||||
\(204\) | − | 9.05993i | − | 0.0444114i | ||||||
\(205\) | 96.1176 | 0.468866 | ||||||||
\(206\) | − | 62.7470i | − | 0.304597i | ||||||
\(207\) | −57.0396 | −0.275553 | ||||||||
\(208\) | − | 21.8588i | − | 0.105091i | ||||||
\(209\) | − | 34.3367i | − | 0.164291i | ||||||
\(210\) | −45.4028 | −0.216204 | ||||||||
\(211\) | −45.4496 | −0.215401 | −0.107700 | − | 0.994183i | \(-0.534349\pi\) | ||||
−0.107700 | + | 0.994183i | \(0.534349\pi\) | |||||||
\(212\) | − | 201.881i | − | 0.952268i | ||||||
\(213\) | − | 63.2968i | − | 0.297168i | ||||||
\(214\) | − | 166.742i | − | 0.779167i | ||||||
\(215\) | −74.8627 | −0.348199 | ||||||||
\(216\) | −42.7042 | −0.197705 | ||||||||
\(217\) | 83.5470 | 0.385009 | ||||||||
\(218\) | −150.847 | −0.691957 | ||||||||
\(219\) | − | 209.678i | − | 0.957434i | ||||||
\(220\) | −21.5373 | −0.0978968 | ||||||||
\(221\) | − | 32.2755i | − | 0.146043i | ||||||
\(222\) | 7.68219 | 0.0346045 | ||||||||
\(223\) | 192.524 | 0.863335 | 0.431668 | − | 0.902033i | \(-0.357925\pi\) | ||||
0.431668 | + | 0.902033i | \(0.357925\pi\) | |||||||
\(224\) | 281.897 | 1.25847 | ||||||||
\(225\) | −60.5006 | −0.268891 | ||||||||
\(226\) | 38.4332 | 0.170059 | ||||||||
\(227\) | −126.627 | −0.557827 | −0.278913 | − | 0.960316i | \(-0.589974\pi\) | ||||
−0.278913 | + | 0.960316i | \(0.589974\pi\) | |||||||
\(228\) | − | 32.0079i | − | 0.140385i | ||||||
\(229\) | − | 449.069i | − | 1.96100i | −0.196516 | − | 0.980501i | \(-0.562963\pi\) | ||
0.196516 | − | 0.980501i | \(-0.437037\pi\) | |||||||
\(230\) | 54.5609 | 0.237221 | ||||||||
\(231\) | − | 67.5034i | − | 0.292223i | ||||||
\(232\) | − | 207.200i | − | 0.893104i | ||||||
\(233\) | 22.2708i | 0.0955828i | 0.998857 | + | 0.0477914i | \(0.0152183\pi\) | ||||
−0.998857 | + | 0.0477914i | \(0.984782\pi\) | |||||||
\(234\) | −55.4815 | −0.237100 | ||||||||
\(235\) | − | 15.2927i | − | 0.0650754i | ||||||
\(236\) | −193.637 | −0.820498 | ||||||||
\(237\) | 162.378 | 0.685139 | ||||||||
\(238\) | −27.1622 | −0.114127 | ||||||||
\(239\) | − | 351.927i | − | 1.47250i | −0.676710 | − | 0.736250i | \(-0.736595\pi\) | ||
0.676710 | − | 0.736250i | \(-0.263405\pi\) | |||||||
\(240\) | 5.87473 | 0.0244780 | ||||||||
\(241\) | 67.0523 | 0.278225 | 0.139113 | − | 0.990277i | \(-0.455575\pi\) | ||||
0.139113 | + | 0.990277i | \(0.455575\pi\) | |||||||
\(242\) | − | 134.181i | − | 0.554469i | ||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | − | 54.5680i | − | 0.223639i | ||||||
\(245\) | − | 75.7217i | − | 0.309068i | ||||||
\(246\) | − | 98.8462i | − | 0.401814i | ||||||
\(247\) | − | 114.026i | − | 0.461645i | ||||||
\(248\) | −75.1664 | −0.303091 | ||||||||
\(249\) | 86.7812i | 0.348519i | ||||||||
\(250\) | 129.612 | 0.518449 | ||||||||
\(251\) | 286.257i | 1.14047i | 0.821482 | + | 0.570234i | \(0.193147\pi\) | ||||
−0.821482 | + | 0.570234i | \(0.806853\pi\) | |||||||
\(252\) | − | 62.9251i | − | 0.249703i | ||||||
\(253\) | 81.1193i | 0.320630i | ||||||||
\(254\) | − | 280.020i | − | 1.10244i | ||||||
\(255\) | 8.67428 | 0.0340168 | ||||||||
\(256\) | −267.790 | −1.04605 | ||||||||
\(257\) | 220.859 | 0.859375 | 0.429688 | − | 0.902978i | \(-0.358624\pi\) | ||||
0.429688 | + | 0.902978i | \(0.358624\pi\) | |||||||
\(258\) | 76.9879i | 0.298403i | ||||||||
\(259\) | 31.0391i | 0.119842i | ||||||||
\(260\) | −71.5216 | −0.275083 | ||||||||
\(261\) | −75.6350 | −0.289789 | ||||||||
\(262\) | 164.868i | 0.629265i | ||||||||
\(263\) | −438.527 | −1.66740 | −0.833701 | − | 0.552217i | \(-0.813782\pi\) | ||||
−0.833701 | + | 0.552217i | \(0.813782\pi\) | |||||||
\(264\) | 60.7322i | 0.230046i | ||||||||
\(265\) | 193.287 | 0.729387 | ||||||||
\(266\) | −95.9615 | −0.360757 | ||||||||
\(267\) | 91.5590i | 0.342918i | ||||||||
\(268\) | 99.1009 | + | 117.674i | 0.369780 | + | 0.439081i | ||||
\(269\) | −173.853 | −0.646294 | −0.323147 | − | 0.946349i | \(-0.604741\pi\) | ||||
−0.323147 | + | 0.946349i | \(0.604741\pi\) | |||||||
\(270\) | − | 14.9111i | − | 0.0552261i | ||||||
\(271\) | 497.804i | 1.83692i | 0.395520 | + | 0.918458i | \(0.370565\pi\) | ||||
−0.395520 | + | 0.918458i | \(0.629435\pi\) | |||||||
\(272\) | 3.51455 | 0.0129211 | ||||||||
\(273\) | − | 224.167i | − | 0.821125i | ||||||
\(274\) | −48.3854 | −0.176589 | ||||||||
\(275\) | 86.0414i | 0.312878i | ||||||||
\(276\) | 75.6175i | 0.273976i | ||||||||
\(277\) | 99.6645 | 0.359800 | 0.179900 | − | 0.983685i | \(-0.442423\pi\) | ||||
0.179900 | + | 0.983685i | \(0.442423\pi\) | |||||||
\(278\) | 22.6680 | 0.0815396 | ||||||||
\(279\) | 27.4383i | 0.0983450i | ||||||||
\(280\) | 165.044i | 0.589443i | ||||||||
\(281\) | − | 86.7978i | − | 0.308889i | −0.988001 | − | 0.154445i | \(-0.950641\pi\) | ||
0.988001 | − | 0.154445i | \(-0.0493588\pi\) | |||||||
\(282\) | −15.7269 | −0.0557690 | ||||||||
\(283\) | 247.359 | 0.874061 | 0.437031 | − | 0.899447i | \(-0.356030\pi\) | ||||
0.437031 | + | 0.899447i | \(0.356030\pi\) | |||||||
\(284\) | −83.9127 | −0.295467 | ||||||||
\(285\) | 30.6454 | 0.107528 | ||||||||
\(286\) | 78.9035i | 0.275886i | ||||||||
\(287\) | 399.378 | 1.39156 | ||||||||
\(288\) | 92.5796i | 0.321457i | ||||||||
\(289\) | −283.811 | −0.982044 | ||||||||
\(290\) | 72.3482 | 0.249477 | ||||||||
\(291\) | 62.9808 | 0.216429 | ||||||||
\(292\) | −277.971 | −0.951954 | ||||||||
\(293\) | 32.6690 | 0.111498 | 0.0557491 | − | 0.998445i | \(-0.482245\pi\) | ||||
0.0557491 | + | 0.998445i | \(0.482245\pi\) | |||||||
\(294\) | −77.8713 | −0.264868 | ||||||||
\(295\) | − | 185.395i | − | 0.628458i | ||||||
\(296\) | − | 27.9256i | − | 0.0943431i | ||||||
\(297\) | 22.1693 | 0.0746440 | ||||||||
\(298\) | 124.315i | 0.417165i | ||||||||
\(299\) | 269.383i | 0.900947i | ||||||||
\(300\) | 80.2057i | 0.267352i | ||||||||
\(301\) | −311.062 | −1.03343 | ||||||||
\(302\) | − | 94.4083i | − | 0.312610i | ||||||
\(303\) | 7.74416 | 0.0255583 | ||||||||
\(304\) | 12.4166 | 0.0408440 | ||||||||
\(305\) | 52.2452 | 0.171296 | ||||||||
\(306\) | − | 8.92052i | − | 0.0291520i | ||||||
\(307\) | 151.568 | 0.493707 | 0.246853 | − | 0.969053i | \(-0.420603\pi\) | ||||
0.246853 | + | 0.969053i | \(0.420603\pi\) | |||||||
\(308\) | −89.4894 | −0.290550 | ||||||||
\(309\) | 83.2611i | 0.269453i | ||||||||
\(310\) | − | 26.2459i | − | 0.0846643i | ||||||
\(311\) | 326.893i | 1.05110i | 0.850762 | + | 0.525552i | \(0.176141\pi\) | ||||
−0.850762 | + | 0.525552i | \(0.823859\pi\) | |||||||
\(312\) | 201.681i | 0.646413i | ||||||||
\(313\) | − | 420.587i | − | 1.34373i | −0.740675 | − | 0.671864i | \(-0.765494\pi\) | ||
0.740675 | − | 0.671864i | \(-0.234506\pi\) | |||||||
\(314\) | − | 295.539i | − | 0.941208i | ||||||
\(315\) | 60.2466 | 0.191259 | ||||||||
\(316\) | − | 215.265i | − | 0.681218i | ||||||
\(317\) | 387.365 | 1.22197 | 0.610985 | − | 0.791642i | \(-0.290773\pi\) | ||||
0.610985 | + | 0.791642i | \(0.290773\pi\) | |||||||
\(318\) | − | 198.774i | − | 0.625077i | ||||||
\(319\) | 107.565i | 0.337194i | ||||||||
\(320\) | − | 102.124i | − | 0.319136i | ||||||
\(321\) | 221.255i | 0.689269i | ||||||||
\(322\) | 226.706 | 0.704055 | ||||||||
\(323\) | 18.3336 | 0.0567603 | ||||||||
\(324\) | 20.6657 | 0.0637829 | ||||||||
\(325\) | 285.728i | 0.879164i | ||||||||
\(326\) | − | 294.739i | − | 0.904108i | ||||||
\(327\) | 200.163 | 0.612120 | ||||||||
\(328\) | −359.316 | −1.09548 | ||||||||
\(329\) | − | 63.5427i | − | 0.193139i | ||||||
\(330\) | −21.2059 | −0.0642603 | ||||||||
\(331\) | − | 402.032i | − | 1.21460i | −0.794474 | − | 0.607299i | \(-0.792253\pi\) | ||
0.794474 | − | 0.607299i | \(-0.207747\pi\) | |||||||
\(332\) | 115.046 | 0.346524 | ||||||||
\(333\) | −10.1938 | −0.0306119 | ||||||||
\(334\) | 92.6403i | 0.277366i | ||||||||
\(335\) | −112.665 | + | 94.8825i | −0.336312 | + | 0.283231i | ||||
\(336\) | 24.4100 | 0.0726489 | ||||||||
\(337\) | 110.892i | 0.329057i | 0.986372 | + | 0.164529i | \(0.0526103\pi\) | ||||
−0.986372 | + | 0.164529i | \(0.947390\pi\) | |||||||
\(338\) | 41.4284i | 0.122569i | ||||||||
\(339\) | −50.9984 | −0.150438 | ||||||||
\(340\) | − | 11.4995i | − | 0.0338221i | ||||||
\(341\) | 39.0216 | 0.114433 | ||||||||
\(342\) | − | 31.5154i | − | 0.0921502i | ||||||
\(343\) | 132.971i | 0.387671i | ||||||||
\(344\) | 279.859 | 0.813544 | ||||||||
\(345\) | −72.3987 | −0.209851 | ||||||||
\(346\) | 253.463i | 0.732553i | ||||||||
\(347\) | 529.552i | 1.52609i | 0.646347 | + | 0.763044i | \(0.276296\pi\) | ||||
−0.646347 | + | 0.763044i | \(0.723704\pi\) | |||||||
\(348\) | 100.269i | 0.288131i | ||||||||
\(349\) | −7.71435 | −0.0221042 | −0.0110521 | − | 0.999939i | \(-0.503518\pi\) | ||||
−0.0110521 | + | 0.999939i | \(0.503518\pi\) | |||||||
\(350\) | 240.461 | 0.687033 | ||||||||
\(351\) | 73.6202 | 0.209744 | ||||||||
\(352\) | 131.663 | 0.374043 | ||||||||
\(353\) | − | 184.044i | − | 0.521370i | −0.965424 | − | 0.260685i | \(-0.916052\pi\) | ||
0.965424 | − | 0.260685i | \(-0.0839484\pi\) | |||||||
\(354\) | −190.658 | −0.538582 | ||||||||
\(355\) | − | 80.3408i | − | 0.226312i | ||||||
\(356\) | 121.380 | 0.340955 | ||||||||
\(357\) | 36.0424 | 0.100959 | ||||||||
\(358\) | 218.554 | 0.610485 | ||||||||
\(359\) | −177.535 | −0.494527 | −0.247264 | − | 0.968948i | \(-0.579531\pi\) | ||||
−0.247264 | + | 0.968948i | \(0.579531\pi\) | |||||||
\(360\) | −54.2032 | −0.150565 | ||||||||
\(361\) | −296.229 | −0.820579 | ||||||||
\(362\) | 457.350i | 1.26340i | ||||||||
\(363\) | 178.050i | 0.490496i | ||||||||
\(364\) | −297.179 | −0.816425 | ||||||||
\(365\) | − | 266.138i | − | 0.729146i | ||||||
\(366\) | − | 53.7284i | − | 0.146799i | ||||||
\(367\) | − | 431.616i | − | 1.17607i | −0.808837 | − | 0.588033i | \(-0.799903\pi\) | ||
0.808837 | − | 0.588033i | \(-0.200097\pi\) | |||||||
\(368\) | −29.3337 | −0.0797111 | ||||||||
\(369\) | 131.162i | 0.355453i | ||||||||
\(370\) | 9.75079 | 0.0263535 | ||||||||
\(371\) | 803.127 | 2.16476 | ||||||||
\(372\) | 36.3750 | 0.0977821 | ||||||||
\(373\) | 518.092i | 1.38899i | 0.719499 | + | 0.694493i | \(0.244371\pi\) | ||||
−0.719499 | + | 0.694493i | \(0.755629\pi\) | |||||||
\(374\) | −12.6864 | −0.0339209 | ||||||||
\(375\) | −171.987 | −0.458632 | ||||||||
\(376\) | 57.1687i | 0.152045i | ||||||||
\(377\) | 357.204i | 0.947492i | ||||||||
\(378\) | − | 61.9568i | − | 0.163907i | ||||||
\(379\) | 308.941i | 0.815147i | 0.913172 | + | 0.407573i | \(0.133625\pi\) | ||||
−0.913172 | + | 0.407573i | \(0.866375\pi\) | |||||||
\(380\) | − | 40.6267i | − | 0.106912i | ||||||
\(381\) | 371.567i | 0.975243i | ||||||||
\(382\) | 253.207 | 0.662847 | ||||||||
\(383\) | − | 18.3045i | − | 0.0477924i | −0.999714 | − | 0.0238962i | \(-0.992393\pi\) | ||
0.999714 | − | 0.0238962i | \(-0.00760712\pi\) | |||||||
\(384\) | 108.781 | 0.283283 | ||||||||
\(385\) | − | 85.6802i | − | 0.222546i | ||||||
\(386\) | 351.098i | 0.909579i | ||||||||
\(387\) | − | 102.158i | − | 0.263974i | ||||||
\(388\) | − | 83.4938i | − | 0.215190i | ||||||
\(389\) | −406.794 | −1.04574 | −0.522872 | − | 0.852411i | \(-0.675139\pi\) | ||||
−0.522872 | + | 0.852411i | \(0.675139\pi\) | |||||||
\(390\) | −70.4211 | −0.180567 | ||||||||
\(391\) | −43.3124 | −0.110773 | ||||||||
\(392\) | 283.070i | 0.722118i | ||||||||
\(393\) | − | 218.768i | − | 0.556662i | ||||||
\(394\) | 248.905 | 0.631739 | ||||||||
\(395\) | 206.102 | 0.521777 | ||||||||
\(396\) | − | 29.3898i | − | 0.0742168i | ||||||
\(397\) | −512.886 | −1.29190 | −0.645952 | − | 0.763378i | \(-0.723539\pi\) | ||||
−0.645952 | + | 0.763378i | \(0.723539\pi\) | |||||||
\(398\) | − | 65.4353i | − | 0.164410i | ||||||
\(399\) | 127.335 | 0.319134 | ||||||||
\(400\) | −31.1136 | −0.0777839 | ||||||||
\(401\) | − | 531.314i | − | 1.32497i | −0.749074 | − | 0.662487i | \(-0.769501\pi\) | ||
0.749074 | − | 0.662487i | \(-0.230499\pi\) | |||||||
\(402\) | 97.5760 | + | 115.863i | 0.242726 | + | 0.288216i | ||||
\(403\) | 129.584 | 0.321548 | ||||||||
\(404\) | − | 10.2665i | − | 0.0254120i | ||||||
\(405\) | 19.7860i | 0.0488543i | ||||||||
\(406\) | 300.614 | 0.740428 | ||||||||
\(407\) | 14.4971i | 0.0356195i | ||||||||
\(408\) | −32.4270 | −0.0794780 | ||||||||
\(409\) | 405.478i | 0.991390i | 0.868497 | + | 0.495695i | \(0.165087\pi\) | ||||
−0.868497 | + | 0.495695i | \(0.834913\pi\) | |||||||
\(410\) | − | 125.463i | − | 0.306006i | ||||||
\(411\) | 64.2042 | 0.156215 | ||||||||
\(412\) | 110.379 | 0.267911 | ||||||||
\(413\) | − | 770.333i | − | 1.86521i | ||||||
\(414\) | 74.4539i | 0.179840i | ||||||||
\(415\) | 110.149i | 0.265419i | ||||||||
\(416\) | 437.230 | 1.05103 | ||||||||
\(417\) | −30.0789 | −0.0721317 | ||||||||
\(418\) | −44.8199 | −0.107225 | ||||||||
\(419\) | 752.468 | 1.79587 | 0.897933 | − | 0.440131i | \(-0.145068\pi\) | ||||
0.897933 | + | 0.440131i | \(0.145068\pi\) | |||||||
\(420\) | − | 79.8690i | − | 0.190164i | ||||||
\(421\) | 477.671 | 1.13461 | 0.567305 | − | 0.823508i | \(-0.307986\pi\) | ||||
0.567305 | + | 0.823508i | \(0.307986\pi\) | |||||||
\(422\) | 59.3255i | 0.140582i | ||||||||
\(423\) | 20.8685 | 0.0493345 | ||||||||
\(424\) | −722.566 | −1.70416 | ||||||||
\(425\) | −45.9405 | −0.108095 | ||||||||
\(426\) | −82.6215 | −0.193947 | ||||||||
\(427\) | 217.084 | 0.508393 | ||||||||
\(428\) | 293.318 | 0.685324 | ||||||||
\(429\) | − | 104.700i | − | 0.244055i | ||||||
\(430\) | 97.7186i | 0.227252i | ||||||||
\(431\) | −151.453 | −0.351398 | −0.175699 | − | 0.984444i | \(-0.556219\pi\) | ||||
−0.175699 | + | 0.984444i | \(0.556219\pi\) | |||||||
\(432\) | 8.01667i | 0.0185571i | ||||||||
\(433\) | − | 622.368i | − | 1.43734i | −0.695352 | − | 0.718669i | \(-0.744752\pi\) | ||
0.695352 | − | 0.718669i | \(-0.255248\pi\) | |||||||
\(434\) | − | 109.054i | − | 0.251277i | ||||||
\(435\) | −96.0013 | −0.220693 | ||||||||
\(436\) | − | 265.357i | − | 0.608617i | ||||||
\(437\) | −153.019 | −0.350157 | ||||||||
\(438\) | −273.693 | −0.624871 | ||||||||
\(439\) | −235.751 | −0.537018 | −0.268509 | − | 0.963277i | \(-0.586531\pi\) | ||||
−0.268509 | + | 0.963277i | \(0.586531\pi\) | |||||||
\(440\) | 77.0856i | 0.175195i | ||||||||
\(441\) | 103.330 | 0.234309 | ||||||||
\(442\) | −42.1293 | −0.0953152 | ||||||||
\(443\) | − | 519.899i | − | 1.17359i | −0.809736 | − | 0.586794i | \(-0.800390\pi\) | ||
0.809736 | − | 0.586794i | \(-0.199610\pi\) | |||||||
\(444\) | 13.5139i | 0.0304367i | ||||||||
\(445\) | 116.213i | 0.261153i | ||||||||
\(446\) | − | 251.302i | − | 0.563457i | ||||||
\(447\) | − | 164.958i | − | 0.369033i | ||||||
\(448\) | − | 424.333i | − | 0.947173i | ||||||
\(449\) | −381.092 | −0.848756 | −0.424378 | − | 0.905485i | \(-0.639507\pi\) | ||||
−0.424378 | + | 0.905485i | \(0.639507\pi\) | |||||||
\(450\) | 78.9716i | 0.175492i | ||||||||
\(451\) | 186.534 | 0.413600 | ||||||||
\(452\) | 67.6086i | 0.149577i | ||||||||
\(453\) | 125.274i | 0.276542i | ||||||||
\(454\) | 165.286i | 0.364066i | ||||||||
\(455\) | − | 284.529i | − | 0.625338i | ||||||
\(456\) | −114.562 | −0.251232 | ||||||||
\(457\) | −202.700 | −0.443544 | −0.221772 | − | 0.975099i | \(-0.571184\pi\) | ||||
−0.221772 | + | 0.975099i | \(0.571184\pi\) | |||||||
\(458\) | −586.172 | −1.27985 | ||||||||
\(459\) | 11.8369i | 0.0257885i | ||||||||
\(460\) | 95.9791i | 0.208650i | ||||||||
\(461\) | 361.109 | 0.783316 | 0.391658 | − | 0.920111i | \(-0.371902\pi\) | ||||
0.391658 | + | 0.920111i | \(0.371902\pi\) | |||||||
\(462\) | −88.1125 | −0.190720 | ||||||||
\(463\) | − | 488.310i | − | 1.05466i | −0.849659 | − | 0.527332i | \(-0.823192\pi\) | ||
0.849659 | − | 0.527332i | \(-0.176808\pi\) | |||||||
\(464\) | −38.8967 | −0.0838292 | ||||||||
\(465\) | 34.8266i | 0.0748959i | ||||||||
\(466\) | 29.0702 | 0.0623823 | ||||||||
\(467\) | 697.376 | 1.49331 | 0.746655 | − | 0.665211i | \(-0.231658\pi\) | ||||
0.746655 | + | 0.665211i | \(0.231658\pi\) | |||||||
\(468\) | − | 97.5985i | − | 0.208544i | ||||||
\(469\) | −468.132 | + | 394.246i | −0.998149 | + | 0.840609i | ||||
\(470\) | −19.9616 | −0.0424716 | ||||||||
\(471\) | 392.161i | 0.832614i | ||||||||
\(472\) | 693.061i | 1.46835i | ||||||||
\(473\) | −145.285 | −0.307156 | ||||||||
\(474\) | − | 211.953i | − | 0.447157i | ||||||
\(475\) | −162.303 | −0.341691 | ||||||||
\(476\) | − | 47.7815i | − | 0.100381i | ||||||
\(477\) | 263.761i | 0.552957i | ||||||||
\(478\) | −459.372 | −0.961029 | ||||||||
\(479\) | −612.073 | −1.27781 | −0.638907 | − | 0.769284i | \(-0.720613\pi\) | ||||
−0.638907 | + | 0.769284i | \(0.720613\pi\) | |||||||
\(480\) | 117.509i | 0.244810i | ||||||||
\(481\) | 48.1425i | 0.100088i | ||||||||
\(482\) | − | 87.5236i | − | 0.181584i | ||||||
\(483\) | −300.823 | −0.622823 | ||||||||
\(484\) | 236.041 | 0.487688 | ||||||||
\(485\) | 79.9398 | 0.164824 | ||||||||
\(486\) | 20.3477 | 0.0418676 | ||||||||
\(487\) | 347.453i | 0.713456i | 0.934208 | + | 0.356728i | \(0.116108\pi\) | ||||
−0.934208 | + | 0.356728i | \(0.883892\pi\) | |||||||
\(488\) | −195.308 | −0.400222 | ||||||||
\(489\) | 391.100i | 0.799795i | ||||||||
\(490\) | −98.8398 | −0.201714 | ||||||||
\(491\) | −437.982 | −0.892020 | −0.446010 | − | 0.895028i | \(-0.647155\pi\) | ||||
−0.446010 | + | 0.895028i | \(0.647155\pi\) | |||||||
\(492\) | 173.882 | 0.353419 | ||||||||
\(493\) | −57.4327 | −0.116496 | ||||||||
\(494\) | −148.839 | −0.301293 | ||||||||
\(495\) | 28.1388 | 0.0568461 | ||||||||
\(496\) | 14.1107i | 0.0284489i | ||||||||
\(497\) | − | 333.823i | − | 0.671677i | ||||||
\(498\) | 113.276 | 0.227461 | ||||||||
\(499\) | 56.5316i | 0.113290i | 0.998394 | + | 0.0566449i | \(0.0180403\pi\) | ||||
−0.998394 | + | 0.0566449i | \(0.981960\pi\) | |||||||
\(500\) | 228.003i | 0.456007i | ||||||||
\(501\) | − | 122.928i | − | 0.245364i | ||||||
\(502\) | 373.653 | 0.744328 | ||||||||
\(503\) | − | 593.739i | − | 1.18040i | −0.807259 | − | 0.590198i | \(-0.799050\pi\) | ||
0.807259 | − | 0.590198i | \(-0.200950\pi\) | |||||||
\(504\) | −225.219 | −0.446864 | ||||||||
\(505\) | 9.82944 | 0.0194642 | ||||||||
\(506\) | 105.885 | 0.209260 | ||||||||
\(507\) | − | 54.9727i | − | 0.108427i | ||||||
\(508\) | 492.588 | 0.969661 | ||||||||
\(509\) | −964.817 | −1.89551 | −0.947757 | − | 0.318992i | \(-0.896656\pi\) | ||||
−0.947757 | + | 0.318992i | \(0.896656\pi\) | |||||||
\(510\) | − | 11.3226i | − | 0.0222011i | ||||||
\(511\) | − | 1105.83i | − | 2.16405i | ||||||
\(512\) | 98.3287i | 0.192048i | ||||||||
\(513\) | 41.8188i | 0.0815181i | ||||||||
\(514\) | − | 288.288i | − | 0.560873i | ||||||
\(515\) | 105.681i | 0.205206i | ||||||||
\(516\) | −135.431 | −0.262463 | ||||||||
\(517\) | − | 29.6783i | − | 0.0574049i | ||||||
\(518\) | 40.5154 | 0.0782151 | ||||||||
\(519\) | − | 336.329i | − | 0.648033i | ||||||
\(520\) | 255.988i | 0.492284i | ||||||||
\(521\) | − | 860.145i | − | 1.65095i | −0.564439 | − | 0.825475i | \(-0.690907\pi\) | ||
0.564439 | − | 0.825475i | \(-0.309093\pi\) | |||||||
\(522\) | 98.7266i | 0.189131i | ||||||||
\(523\) | −534.293 | −1.02159 | −0.510796 | − | 0.859702i | \(-0.670649\pi\) | ||||
−0.510796 | + | 0.859702i | \(0.670649\pi\) | |||||||
\(524\) | −290.022 | −0.553476 | ||||||||
\(525\) | −319.076 | −0.607764 | ||||||||
\(526\) | 572.410i | 1.08823i | ||||||||
\(527\) | 20.8350i | 0.0395350i | ||||||||
\(528\) | 11.4010 | 0.0215928 | ||||||||
\(529\) | −167.499 | −0.316633 | ||||||||
\(530\) | − | 252.299i | − | 0.476035i | ||||||
\(531\) | 252.990 | 0.476441 | ||||||||
\(532\) | − | 168.808i | − | 0.317308i | ||||||
\(533\) | 619.446 | 1.16219 | ||||||||
\(534\) | 119.512 | 0.223806 | ||||||||
\(535\) | 280.833i | 0.524921i | ||||||||
\(536\) | 421.174 | − | 354.699i | 0.785772 | − | 0.661752i | ||||
\(537\) | −290.006 | −0.540049 | ||||||||
\(538\) | 226.931i | 0.421805i | ||||||||
\(539\) | − | 146.952i | − | 0.272638i | ||||||
\(540\) | 26.2303 | 0.0485747 | ||||||||
\(541\) | 18.7475i | 0.0346534i | 0.999850 | + | 0.0173267i | \(0.00551553\pi\) | ||||
−0.999850 | + | 0.0173267i | \(0.994484\pi\) | |||||||
\(542\) | 649.785 | 1.19887 | ||||||||
\(543\) | − | 606.873i | − | 1.11763i | ||||||
\(544\) | 70.2994i | 0.129227i | ||||||||
\(545\) | 254.062 | 0.466168 | ||||||||
\(546\) | −292.606 | −0.535908 | ||||||||
\(547\) | − | 244.601i | − | 0.447168i | −0.974685 | − | 0.223584i | \(-0.928224\pi\) | ||
0.974685 | − | 0.223584i | \(-0.0717758\pi\) | |||||||
\(548\) | − | 85.1156i | − | 0.155321i | ||||||
\(549\) | 71.2940i | 0.129861i | ||||||||
\(550\) | 112.310 | 0.204200 | ||||||||
\(551\) | −202.904 | −0.368247 | ||||||||
\(552\) | 270.648 | 0.490304 | ||||||||
\(553\) | 856.372 | 1.54859 | ||||||||
\(554\) | − | 130.092i | − | 0.234824i | ||||||
\(555\) | −12.9386 | −0.0233129 | ||||||||
\(556\) | 39.8757i | 0.0717189i | ||||||||
\(557\) | −798.593 | −1.43374 | −0.716870 | − | 0.697207i | \(-0.754426\pi\) | ||||
−0.716870 | + | 0.697207i | \(0.754426\pi\) | |||||||
\(558\) | 35.8152 | 0.0641850 | ||||||||
\(559\) | −482.465 | −0.863086 | ||||||||
\(560\) | 30.9830 | 0.0553267 | ||||||||
\(561\) | 16.8340 | 0.0300071 | ||||||||
\(562\) | −113.297 | −0.201597 | ||||||||
\(563\) | 910.796i | 1.61775i | 0.587978 | + | 0.808877i | \(0.299924\pi\) | ||||
−0.587978 | + | 0.808877i | \(0.700076\pi\) | |||||||
\(564\) | − | 27.6654i | − | 0.0490521i | ||||||
\(565\) | −64.7307 | −0.114568 | ||||||||
\(566\) | − | 322.879i | − | 0.570457i | ||||||
\(567\) | 82.2126i | 0.144996i | ||||||||
\(568\) | 300.338i | 0.528763i | ||||||||
\(569\) | −88.1892 | −0.154990 | −0.0774949 | − | 0.996993i | \(-0.524692\pi\) | ||||
−0.0774949 | + | 0.996993i | \(0.524692\pi\) | |||||||
\(570\) | − | 40.0016i | − | 0.0701782i | ||||||
\(571\) | −520.918 | −0.912291 | −0.456146 | − | 0.889905i | \(-0.650770\pi\) | ||||
−0.456146 | + | 0.889905i | \(0.650770\pi\) | |||||||
\(572\) | −138.801 | −0.242658 | ||||||||
\(573\) | −335.989 | −0.586369 | ||||||||
\(574\) | − | 521.309i | − | 0.908204i | ||||||
\(575\) | 383.436 | 0.666846 | ||||||||
\(576\) | 139.358 | 0.241941 | ||||||||
\(577\) | 317.606i | 0.550443i | 0.961381 | + | 0.275222i | \(0.0887513\pi\) | ||||
−0.961381 | + | 0.275222i | \(0.911249\pi\) | |||||||
\(578\) | 370.459i | 0.640932i | ||||||||
\(579\) | − | 465.883i | − | 0.804634i | ||||||
\(580\) | 127.269i | 0.219430i | ||||||||
\(581\) | 457.679i | 0.787744i | ||||||||
\(582\) | − | 82.2091i | − | 0.141253i | ||||||
\(583\) | 375.109 | 0.643412 | ||||||||
\(584\) | 994.904i | 1.70360i | ||||||||
\(585\) | 93.4441 | 0.159733 | ||||||||
\(586\) | − | 42.6429i | − | 0.0727694i | ||||||
\(587\) | 1082.75i | 1.84455i | 0.386532 | + | 0.922276i | \(0.373673\pi\) | ||||
−0.386532 | + | 0.922276i | \(0.626327\pi\) | |||||||
\(588\) | − | 136.985i | − | 0.232967i | ||||||
\(589\) | 73.6080i | 0.124971i | ||||||||
\(590\) | −241.997 | −0.410164 | ||||||||
\(591\) | −330.280 | −0.558850 | ||||||||
\(592\) | −5.24234 | −0.00885530 | ||||||||
\(593\) | − | 17.7957i | − | 0.0300096i | −0.999887 | − | 0.0150048i | \(-0.995224\pi\) | ||
0.999887 | − | 0.0150048i | \(-0.00477636\pi\) | |||||||
\(594\) | − | 28.9376i | − | 0.0487165i | ||||||
\(595\) | 45.7476 | 0.0768868 | ||||||||
\(596\) | −218.685 | −0.366921 | ||||||||
\(597\) | 86.8283i | 0.145441i | ||||||||
\(598\) | 351.627 | 0.588004 | ||||||||
\(599\) | − | 945.801i | − | 1.57897i | −0.613773 | − | 0.789483i | \(-0.710349\pi\) | ||
0.613773 | − | 0.789483i | \(-0.289651\pi\) | |||||||
\(600\) | 287.070 | 0.478450 | ||||||||
\(601\) | 674.073 | 1.12158 | 0.560792 | − | 0.827956i | \(-0.310497\pi\) | ||||
0.560792 | + | 0.827956i | \(0.310497\pi\) | |||||||
\(602\) | 406.030i | 0.674468i | ||||||||
\(603\) | −129.477 | − | 153.742i | −0.214721 | − | 0.254963i | ||||
\(604\) | 166.075 | 0.274959 | ||||||||
\(605\) | 225.994i | 0.373543i | ||||||||
\(606\) | − | 10.1085i | − | 0.0166807i | ||||||
\(607\) | −500.176 | −0.824013 | −0.412007 | − | 0.911181i | \(-0.635172\pi\) | ||||
−0.412007 | + | 0.911181i | \(0.635172\pi\) | |||||||
\(608\) | 248.361i | 0.408489i | ||||||||
\(609\) | −398.894 | −0.654999 | ||||||||
\(610\) | − | 68.1959i | − | 0.111796i | ||||||
\(611\) | − | 98.5565i | − | 0.161304i | ||||||
\(612\) | 15.6923 | 0.0256409 | ||||||||
\(613\) | −1068.83 | −1.74360 | −0.871800 | − | 0.489861i | \(-0.837047\pi\) | ||||
−0.871800 | + | 0.489861i | \(0.837047\pi\) | |||||||
\(614\) | − | 197.842i | − | 0.322218i | ||||||
\(615\) | 166.481i | 0.270700i | ||||||||
\(616\) | 320.298i | 0.519964i | ||||||||
\(617\) | 525.779 | 0.852153 | 0.426077 | − | 0.904687i | \(-0.359895\pi\) | ||||
0.426077 | + | 0.904687i | \(0.359895\pi\) | |||||||
\(618\) | 108.681 | 0.175859 | ||||||||
\(619\) | 494.969 | 0.799626 | 0.399813 | − | 0.916597i | \(-0.369075\pi\) | ||||
0.399813 | + | 0.916597i | \(0.369075\pi\) | |||||||
\(620\) | 46.1697 | 0.0744672 | ||||||||
\(621\) | − | 98.7954i | − | 0.159091i | ||||||
\(622\) | 426.695 | 0.686004 | ||||||||
\(623\) | 482.877i | 0.775083i | ||||||||
\(624\) | 37.8606 | 0.0606741 | ||||||||
\(625\) | 285.873 | 0.457397 | ||||||||
\(626\) | −548.993 | −0.876986 | ||||||||
\(627\) | 59.4730 | 0.0948532 | ||||||||
\(628\) | 519.889 | 0.827848 | ||||||||
\(629\) | −7.74053 | −0.0123061 | ||||||||
\(630\) | − | 78.6400i | − | 0.124825i | ||||||
\(631\) | 196.595i | 0.311561i | 0.987792 | + | 0.155781i | \(0.0497893\pi\) | ||||
−0.987792 | + | 0.155781i | \(0.950211\pi\) | |||||||
\(632\) | −770.469 | −1.21910 | ||||||||
\(633\) | − | 78.7210i | − | 0.124362i | ||||||
\(634\) | − | 505.628i | − | 0.797521i | ||||||
\(635\) | 471.620i | 0.742708i | ||||||||
\(636\) | 349.668 | 0.549792 | ||||||||
\(637\) | − | 488.001i | − | 0.766093i | ||||||
\(638\) | 140.405 | 0.220070 | ||||||||
\(639\) | 109.633 | 0.171570 | ||||||||
\(640\) | 138.072 | 0.215738 | ||||||||
\(641\) | − | 1180.92i | − | 1.84231i | −0.389193 | − | 0.921156i | \(-0.627246\pi\) | ||
0.389193 | − | 0.921156i | \(-0.372754\pi\) | |||||||
\(642\) | 288.805 | 0.449852 | ||||||||
\(643\) | −246.496 | −0.383353 | −0.191677 | − | 0.981458i | \(-0.561392\pi\) | ||||
−0.191677 | + | 0.981458i | \(0.561392\pi\) | |||||||
\(644\) | 398.802i | 0.619258i | ||||||||
\(645\) | − | 129.666i | − | 0.201033i | ||||||
\(646\) | − | 23.9309i | − | 0.0370447i | ||||||
\(647\) | 1138.40i | 1.75951i | 0.475429 | + | 0.879754i | \(0.342293\pi\) | ||||
−0.475429 | + | 0.879754i | \(0.657707\pi\) | |||||||
\(648\) | − | 73.9659i | − | 0.114145i | ||||||
\(649\) | − | 359.793i | − | 0.554380i | ||||||
\(650\) | 372.962 | 0.573788 | ||||||||
\(651\) | 144.708i | 0.222285i | ||||||||
\(652\) | 518.481 | 0.795217 | ||||||||
\(653\) | − | 316.692i | − | 0.484980i | −0.970154 | − | 0.242490i | \(-0.922036\pi\) | ||
0.970154 | − | 0.242490i | \(-0.0779642\pi\) | |||||||
\(654\) | − | 261.274i | − | 0.399501i | ||||||
\(655\) | − | 277.676i | − | 0.423933i | ||||||
\(656\) | 67.4528i | 0.102824i | ||||||||
\(657\) | 363.173 | 0.552775 | ||||||||
\(658\) | −82.9425 | −0.126052 | ||||||||
\(659\) | −373.268 | −0.566416 | −0.283208 | − | 0.959059i | \(-0.591399\pi\) | ||||
−0.283208 | + | 0.959059i | \(0.591399\pi\) | |||||||
\(660\) | − | 37.3037i | − | 0.0565207i | ||||||
\(661\) | − | 180.368i | − | 0.272872i | −0.990649 | − | 0.136436i | \(-0.956435\pi\) | ||
0.990649 | − | 0.136436i | \(-0.0435648\pi\) | |||||||
\(662\) | −524.773 | −0.792709 | ||||||||
\(663\) | 55.9028 | 0.0843179 | ||||||||
\(664\) | − | 411.769i | − | 0.620134i | ||||||
\(665\) | 161.622 | 0.243041 | ||||||||
\(666\) | 13.3059i | 0.0199789i | ||||||||
\(667\) | 479.354 | 0.718672 | ||||||||
\(668\) | −162.965 | −0.243960 | ||||||||
\(669\) | 333.461i | 0.498447i | ||||||||
\(670\) | 123.850 | + | 147.061i | 0.184851 | + | 0.219495i | ||||
\(671\) | 101.391 | 0.151105 | ||||||||
\(672\) | 488.260i | 0.726577i | ||||||||
\(673\) | 882.215i | 1.31087i | 0.755252 | + | 0.655434i | \(0.227514\pi\) | ||||
−0.755252 | + | 0.655434i | \(0.772486\pi\) | |||||||
\(674\) | 144.748 | 0.214760 | ||||||||
\(675\) | − | 104.790i | − | 0.155244i | ||||||
\(676\) | −72.8774 | −0.107807 | ||||||||
\(677\) | 552.316i | 0.815829i | 0.913020 | + | 0.407914i | \(0.133744\pi\) | ||||
−0.913020 | + | 0.407914i | \(0.866256\pi\) | |||||||
\(678\) | 66.5683i | 0.0981834i | ||||||||
\(679\) | 332.157 | 0.489186 | ||||||||
\(680\) | −41.1587 | −0.0605275 | ||||||||
\(681\) | − | 219.324i | − | 0.322061i | ||||||
\(682\) | − | 50.9350i | − | 0.0746847i | ||||||
\(683\) | 251.021i | 0.367526i | 0.982971 | + | 0.183763i | \(0.0588280\pi\) | ||||
−0.982971 | + | 0.183763i | \(0.941172\pi\) | |||||||
\(684\) | 55.4393 | 0.0810516 | ||||||||
\(685\) | 81.4925 | 0.118967 | ||||||||
\(686\) | 173.568 | 0.253014 | ||||||||
\(687\) | 777.811 | 1.13218 | ||||||||
\(688\) | − | 52.5367i | − | 0.0763614i | ||||||
\(689\) | 1245.67 | 1.80794 | ||||||||
\(690\) | 94.5023i | 0.136960i | ||||||||
\(691\) | −608.855 | −0.881122 | −0.440561 | − | 0.897723i | \(-0.645220\pi\) | ||||
−0.440561 | + | 0.897723i | \(0.645220\pi\) | |||||||
\(692\) | −445.872 | −0.644324 | ||||||||
\(693\) | 116.919 | 0.168715 | ||||||||
\(694\) | 691.226 | 0.996003 | ||||||||
\(695\) | −38.1783 | −0.0549328 | ||||||||
\(696\) | 358.881 | 0.515634 | ||||||||
\(697\) | 99.5968i | 0.142894i | ||||||||
\(698\) | 10.0696i | 0.0144263i | ||||||||
\(699\) | −38.5742 | −0.0551848 | ||||||||
\(700\) | 423.000i | 0.604286i | ||||||||
\(701\) | − | 762.979i | − | 1.08841i | −0.838951 | − | 0.544207i | \(-0.816830\pi\) | ||
0.838951 | − | 0.544207i | \(-0.183170\pi\) | |||||||
\(702\) | − | 96.0967i | − | 0.136890i | ||||||
\(703\) | −27.3466 | −0.0388998 | ||||||||
\(704\) | − | 198.190i | − | 0.281519i | ||||||
\(705\) | 26.4878 | 0.0375713 | ||||||||
\(706\) | −240.233 | −0.340273 | ||||||||
\(707\) | 40.8423 | 0.0577684 | ||||||||
\(708\) | − | 335.390i | − | 0.473715i | ||||||
\(709\) | 618.375 | 0.872179 | 0.436090 | − | 0.899903i | \(-0.356363\pi\) | ||||
0.436090 | + | 0.899903i | \(0.356363\pi\) | |||||||
\(710\) | −104.869 | −0.147703 | ||||||||
\(711\) | 281.247i | 0.395565i | ||||||||
\(712\) | − | 434.439i | − | 0.610168i | ||||||
\(713\) | − | 173.896i | − | 0.243894i | ||||||
\(714\) | − | 47.0463i | − | 0.0658912i | ||||||
\(715\) | − | 132.892i | − | 0.185863i | ||||||
\(716\) | 384.462i | 0.536958i | ||||||||
\(717\) | 609.556 | 0.850148 | ||||||||
\(718\) | 231.737i | 0.322754i | ||||||||
\(719\) | −949.789 | −1.32099 | −0.660493 | − | 0.750832i | \(-0.729653\pi\) | ||||
−0.660493 | + | 0.750832i | \(0.729653\pi\) | |||||||
\(720\) | 10.1753i | 0.0141324i | ||||||||
\(721\) | 439.114i | 0.609035i | ||||||||
\(722\) | 386.669i | 0.535553i | ||||||||
\(723\) | 116.138i | 0.160633i | ||||||||
\(724\) | −804.533 | −1.11123 | ||||||||
\(725\) | 508.440 | 0.701296 | ||||||||
\(726\) | 232.409 | 0.320123 | ||||||||
\(727\) | − | 259.467i | − | 0.356901i | −0.983949 | − | 0.178451i | \(-0.942892\pi\) | ||
0.983949 | − | 0.178451i | \(-0.0571085\pi\) | |||||||
\(728\) | 1063.65i | 1.46106i | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −347.391 | −0.475878 | ||||||||
\(731\) | − | 77.5726i | − | 0.106118i | ||||||
\(732\) | 94.5145 | 0.129118 | ||||||||
\(733\) | − | 212.263i | − | 0.289581i | −0.989462 | − | 0.144790i | \(-0.953749\pi\) | ||
0.989462 | − | 0.144790i | \(-0.0462508\pi\) | |||||||
\(734\) | −563.390 | −0.767561 | ||||||||
\(735\) | 131.154 | 0.178441 | ||||||||
\(736\) | − | 586.745i | − | 0.797208i | ||||||
\(737\) | −218.646 | + | 184.137i | −0.296670 | + | 0.249846i | ||||
\(738\) | 171.207 | 0.231987 | ||||||||
\(739\) | − | 322.025i | − | 0.435758i | −0.975976 | − | 0.217879i | \(-0.930086\pi\) | ||
0.975976 | − | 0.217879i | \(-0.0699137\pi\) | |||||||
\(740\) | 17.1528i | 0.0231794i | ||||||||
\(741\) | 197.499 | 0.266531 | ||||||||
\(742\) | − | 1048.32i | − | 1.41284i | ||||||
\(743\) | −779.375 | −1.04896 | −0.524478 | − | 0.851424i | \(-0.675740\pi\) | ||||
−0.524478 | + | 0.851424i | \(0.675740\pi\) | |||||||
\(744\) | − | 130.192i | − | 0.174989i | ||||||
\(745\) | − | 209.376i | − | 0.281042i | ||||||
\(746\) | 676.267 | 0.906525 | ||||||||
\(747\) | −150.309 | −0.201218 | ||||||||
\(748\) | − | 22.3169i | − | 0.0298354i | ||||||
\(749\) | 1166.89i | 1.55793i | ||||||||
\(750\) | 224.495i | 0.299327i | ||||||||
\(751\) | −39.6346 | −0.0527758 | −0.0263879 | − | 0.999652i | \(-0.508401\pi\) | ||||
−0.0263879 | + | 0.999652i | \(0.508401\pi\) | |||||||
\(752\) | 10.7320 | 0.0142713 | ||||||||
\(753\) | −495.812 | −0.658449 | ||||||||
\(754\) | 466.260 | 0.618382 | ||||||||
\(755\) | 159.006i | 0.210604i | ||||||||
\(756\) | 108.989 | 0.144166 | ||||||||
\(757\) | 1401.87i | 1.85188i | 0.377668 | + | 0.925941i | \(0.376726\pi\) | ||||
−0.377668 | + | 0.925941i | \(0.623274\pi\) | |||||||
\(758\) | 403.261 | 0.532007 | ||||||||
\(759\) | −140.503 | −0.185116 | ||||||||
\(760\) | −145.410 | −0.191329 | ||||||||
\(761\) | 151.310 | 0.198831 | 0.0994153 | − | 0.995046i | \(-0.468303\pi\) | ||||
0.0994153 | + | 0.995046i | \(0.468303\pi\) | |||||||
\(762\) | 485.008 | 0.636494 | ||||||||
\(763\) | 1055.65 | 1.38355 | ||||||||
\(764\) | 445.422i | 0.583013i | ||||||||
\(765\) | 15.0243i | 0.0196396i | ||||||||
\(766\) | −23.8929 | −0.0311918 | ||||||||
\(767\) | − | 1194.81i | − | 1.55777i | ||||||
\(768\) | − | 463.826i | − | 0.603940i | ||||||
\(769\) | − | 461.300i | − | 0.599870i | −0.953960 | − | 0.299935i | \(-0.903035\pi\) | ||
0.953960 | − | 0.299935i | \(-0.0969650\pi\) | |||||||
\(770\) | −111.839 | −0.145245 | ||||||||
\(771\) | 382.540i | 0.496160i | ||||||||
\(772\) | −617.622 | −0.800029 | ||||||||
\(773\) | 679.969 | 0.879649 | 0.439824 | − | 0.898084i | \(-0.355041\pi\) | ||||
0.439824 | + | 0.898084i | \(0.355041\pi\) | |||||||
\(774\) | −133.347 | −0.172283 | ||||||||
\(775\) | − | 184.448i | − | 0.237997i | ||||||
\(776\) | −298.839 | −0.385101 | ||||||||
\(777\) | −53.7613 | −0.0691908 | ||||||||
\(778\) | 530.990i | 0.682507i | ||||||||
\(779\) | 351.866i | 0.451690i | ||||||||
\(780\) | − | 123.879i | − | 0.158819i | ||||||
\(781\) | − | 155.916i | − | 0.199636i | ||||||
\(782\) | 56.5359i | 0.0722965i | ||||||||
\(783\) | − | 131.004i | − | 0.167310i | ||||||
\(784\) | 53.1395 | 0.0677799 | ||||||||
\(785\) | 497.759i | 0.634088i | ||||||||
\(786\) | −285.559 | −0.363307 | ||||||||
\(787\) | − | 790.065i | − | 1.00389i | −0.864898 | − | 0.501947i | \(-0.832617\pi\) | ||
0.864898 | − | 0.501947i | \(-0.167383\pi\) | |||||||
\(788\) | 437.854i | 0.555652i | ||||||||
\(789\) | − | 759.550i | − | 0.962675i | ||||||
\(790\) | − | 269.025i | − | 0.340538i | ||||||
\(791\) | −268.962 | −0.340028 | ||||||||
\(792\) | −105.191 | −0.132817 | ||||||||
\(793\) | 336.703 | 0.424594 | ||||||||
\(794\) | 669.472i | 0.843163i | ||||||||
\(795\) | 334.784i | 0.421112i | ||||||||
\(796\) | 115.108 | 0.144609 | ||||||||
\(797\) | 888.931 | 1.11535 | 0.557673 | − | 0.830061i | \(-0.311694\pi\) | ||||
0.557673 | + | 0.830061i | \(0.311694\pi\) | |||||||
\(798\) | − | 166.210i | − | 0.208283i | ||||||
\(799\) | 15.8463 | 0.0198326 | ||||||||
\(800\) | − | 622.347i | − | 0.777933i | ||||||
\(801\) | −158.585 | −0.197984 | ||||||||
\(802\) | −693.526 | −0.864746 | ||||||||
\(803\) | − | 516.490i | − | 0.643200i | ||||||
\(804\) | −203.817 | + | 171.648i | −0.253503 | + | 0.213492i | ||||
\(805\) | −381.826 | −0.474319 | ||||||||
\(806\) | − | 169.146i | − | 0.209859i | ||||||
\(807\) | − | 301.122i | − | 0.373138i | ||||||
\(808\) | −36.7454 | −0.0454769 | ||||||||
\(809\) | − | 752.068i | − | 0.929626i | −0.885409 | − | 0.464813i | \(-0.846121\pi\) | ||
0.885409 | − | 0.464813i | \(-0.153879\pi\) | |||||||
\(810\) | 25.8267 | 0.0318848 | ||||||||
\(811\) | 1099.10i | 1.35524i | 0.735411 | + | 0.677621i | \(0.236989\pi\) | ||||
−0.735411 | + | 0.677621i | \(0.763011\pi\) | |||||||
\(812\) | 528.815i | 0.651250i | ||||||||
\(813\) | −862.222 | −1.06054 | ||||||||
\(814\) | 18.9232 | 0.0232471 | ||||||||
\(815\) | 496.411i | 0.609094i | ||||||||
\(816\) | 6.08738i | 0.00746002i | ||||||||
\(817\) | − | 274.057i | − | 0.335443i | ||||||
\(818\) | 529.272 | 0.647032 | ||||||||
\(819\) | 388.269 | 0.474077 | ||||||||
\(820\) | 220.704 | 0.269151 | ||||||||
\(821\) | 570.245 | 0.694573 | 0.347287 | − | 0.937759i | \(-0.387103\pi\) | ||||
0.347287 | + | 0.937759i | \(0.387103\pi\) | |||||||
\(822\) | − | 83.8059i | − | 0.101954i | ||||||
\(823\) | −967.829 | −1.17598 | −0.587988 | − | 0.808870i | \(-0.700080\pi\) | ||||
−0.587988 | + | 0.808870i | \(0.700080\pi\) | |||||||
\(824\) | − | 395.066i | − | 0.479450i | ||||||
\(825\) | −149.028 | −0.180640 | ||||||||
\(826\) | −1005.52 | −1.21733 | ||||||||
\(827\) | −1005.58 | −1.21594 | −0.607969 | − | 0.793961i | \(-0.708015\pi\) | ||||
−0.607969 | + | 0.793961i | \(0.708015\pi\) | |||||||
\(828\) | −130.973 | −0.158180 | ||||||||
\(829\) | −63.3910 | −0.0764668 | −0.0382334 | − | 0.999269i | \(-0.512173\pi\) | ||||
−0.0382334 | + | 0.999269i | \(0.512173\pi\) | |||||||
\(830\) | 143.778 | 0.173226 | ||||||||
\(831\) | 172.624i | 0.207730i | ||||||||
\(832\) | − | 658.153i | − | 0.791049i | ||||||
\(833\) | 78.4626 | 0.0941929 | ||||||||
\(834\) | 39.2621i | 0.0470769i | ||||||||
\(835\) | − | 156.028i | − | 0.186860i | ||||||
\(836\) | − | 78.8435i | − | 0.0943104i | ||||||
\(837\) | −47.5245 | −0.0567795 | ||||||||
\(838\) | − | 982.199i | − | 1.17208i | ||||||
\(839\) | −1014.89 | −1.20964 | −0.604818 | − | 0.796363i | \(-0.706754\pi\) | ||||
−0.604818 | + | 0.796363i | \(0.706754\pi\) | |||||||
\(840\) | −285.865 | −0.340315 | ||||||||
\(841\) | −205.372 | −0.244200 | ||||||||
\(842\) | − | 623.505i | − | 0.740505i | ||||||
\(843\) | 150.338 | 0.178337 | ||||||||
\(844\) | −104.361 | −0.123650 | ||||||||
\(845\) | − | 69.7753i | − | 0.0825743i | ||||||
\(846\) | − | 27.2397i | − | 0.0321982i | ||||||
\(847\) | 939.025i | 1.10865i | ||||||||
\(848\) | 135.644i | 0.159958i | ||||||||
\(849\) | 428.439i | 0.504639i | ||||||||
\(850\) | 59.9663i | 0.0705486i | ||||||||
\(851\) | 64.6053 | 0.0759169 | ||||||||
\(852\) | − | 145.341i | − | 0.170588i | ||||||
\(853\) | 30.4715 | 0.0357228 | 0.0178614 | − | 0.999840i | \(-0.494314\pi\) | ||||
0.0178614 | + | 0.999840i | \(0.494314\pi\) | |||||||
\(854\) | − | 283.360i | − | 0.331803i | ||||||
\(855\) | 53.0794i | 0.0620812i | ||||||||
\(856\) | − | 1049.84i | − | 1.22644i | ||||||
\(857\) | − | 116.993i | − | 0.136515i | −0.997668 | − | 0.0682574i | \(-0.978256\pi\) | ||
0.997668 | − | 0.0682574i | \(-0.0217439\pi\) | |||||||
\(858\) | −136.665 | −0.159283 | ||||||||
\(859\) | 571.567 | 0.665387 | 0.332694 | − | 0.943035i | \(-0.392043\pi\) | ||||
0.332694 | + | 0.943035i | \(0.392043\pi\) | |||||||
\(860\) | −171.899 | −0.199882 | ||||||||
\(861\) | 691.742i | 0.803417i | ||||||||
\(862\) | 197.691i | 0.229340i | ||||||||
\(863\) | −1438.95 | −1.66739 | −0.833693 | − | 0.552229i | \(-0.813778\pi\) | ||||
−0.833693 | + | 0.552229i | \(0.813778\pi\) | |||||||
\(864\) | −160.353 | −0.185593 | ||||||||
\(865\) | − | 426.893i | − | 0.493518i | ||||||
\(866\) | −812.378 | −0.938081 | ||||||||
\(867\) | − | 491.574i | − | 0.566983i | ||||||
\(868\) | 191.839 | 0.221013 | ||||||||
\(869\) | 399.978 | 0.460274 | ||||||||
\(870\) | 125.311i | 0.144035i | ||||||||
\(871\) | −726.085 | + | 611.486i | −0.833623 | + | 0.702050i | ||||
\(872\) | −949.758 | −1.08917 | ||||||||
\(873\) | 109.086i | 0.124955i | ||||||||
\(874\) | 199.736i | 0.228531i | ||||||||
\(875\) | −907.049 | −1.03663 | ||||||||
\(876\) | − | 481.459i | − | 0.549611i | ||||||
\(877\) | −473.773 | −0.540220 | −0.270110 | − | 0.962829i | \(-0.587060\pi\) | ||||
−0.270110 | + | 0.962829i | \(0.587060\pi\) | |||||||
\(878\) | 307.727i | 0.350486i | ||||||||
\(879\) | 56.5843i | 0.0643735i | ||||||||
\(880\) | 14.4709 | 0.0164442 | ||||||||
\(881\) | 775.606 | 0.880370 | 0.440185 | − | 0.897907i | \(-0.354913\pi\) | ||||
0.440185 | + | 0.897907i | \(0.354913\pi\) | |||||||
\(882\) | − | 134.877i | − | 0.152922i | ||||||
\(883\) | 926.204i | 1.04893i | 0.851432 | + | 0.524464i | \(0.175734\pi\) | ||||
−0.851432 | + | 0.524464i | \(0.824266\pi\) | |||||||
\(884\) | − | 74.1105i | − | 0.0838354i | ||||||
\(885\) | 321.113 | 0.362840 | ||||||||
\(886\) | −678.626 | −0.765944 | ||||||||
\(887\) | −469.230 | −0.529008 | −0.264504 | − | 0.964385i | \(-0.585208\pi\) | ||||
−0.264504 | + | 0.964385i | \(0.585208\pi\) | |||||||
\(888\) | 48.3685 | 0.0544690 | ||||||||
\(889\) | 1959.62i | 2.20430i | ||||||||
\(890\) | 151.693 | 0.170442 | ||||||||
\(891\) | 38.3983i | 0.0430957i | ||||||||
\(892\) | 442.070 | 0.495594 | ||||||||
\(893\) | 55.9834 | 0.0626914 | ||||||||
\(894\) | −215.320 | −0.240850 | ||||||||
\(895\) | −368.097 | −0.411281 | ||||||||
\(896\) | 573.703 | 0.640294 | ||||||||
\(897\) | −466.585 | −0.520162 | ||||||||
\(898\) | 497.440i | 0.553942i | ||||||||
\(899\) | − | 230.588i | − | 0.256494i | ||||||
\(900\) | −138.920 | −0.154356 | ||||||||
\(901\) | 200.284i | 0.222291i | ||||||||
\(902\) | − | 243.483i | − | 0.269937i | ||||||
\(903\) | − | 538.775i | − | 0.596650i | ||||||
\(904\) | 241.983 | 0.267680 | ||||||||
\(905\) | − | 770.287i | − | 0.851146i | ||||||
\(906\) | 163.520 | 0.180486 | ||||||||
\(907\) | 254.129 | 0.280186 | 0.140093 | − | 0.990138i | \(-0.455260\pi\) | ||||
0.140093 | + | 0.990138i | \(0.455260\pi\) | |||||||
\(908\) | −290.758 | −0.320218 | ||||||||
\(909\) | 13.4133i | 0.0147561i | ||||||||
\(910\) | −371.396 | −0.408128 | ||||||||
\(911\) | 288.361 | 0.316533 | 0.158266 | − | 0.987396i | \(-0.449410\pi\) | ||||
0.158266 | + | 0.987396i | \(0.449410\pi\) | |||||||
\(912\) | 21.5061i | 0.0235813i | ||||||||
\(913\) | 213.764i | 0.234134i | ||||||||
\(914\) | 264.584i | 0.289480i | ||||||||
\(915\) | 90.4914i | 0.0988977i | ||||||||
\(916\) | − | 1031.15i | − | 1.12570i | ||||||
\(917\) | − | 1153.77i | − | 1.25820i | ||||||
\(918\) | 15.4508 | 0.0168309 | ||||||||
\(919\) | − | 517.961i | − | 0.563614i | −0.959471 | − | 0.281807i | \(-0.909066\pi\) | ||
0.959471 | − | 0.281807i | \(-0.0909337\pi\) | |||||||
\(920\) | 343.525 | 0.373397 | ||||||||
\(921\) | 262.523i | 0.285042i | ||||||||
\(922\) | − | 471.356i | − | 0.511232i | ||||||
\(923\) | − | 517.769i | − | 0.560963i | ||||||
\(924\) | − | 155.000i | − | 0.167749i | ||||||
\(925\) | 68.5253 | 0.0740815 | ||||||||
\(926\) | −637.392 | −0.688329 | ||||||||
\(927\) | −144.212 | −0.155569 | ||||||||
\(928\) | − | 778.029i | − | 0.838393i | ||||||
\(929\) | − | 648.006i | − | 0.697531i | −0.937210 | − | 0.348766i | \(-0.886601\pi\) | ||
0.937210 | − | 0.348766i | \(-0.113399\pi\) | |||||||
\(930\) | 45.4593 | 0.0488809 | ||||||||
\(931\) | 277.201 | 0.297746 | ||||||||
\(932\) | 51.1378i | 0.0548689i | ||||||||
\(933\) | −566.196 | −0.606855 | ||||||||
\(934\) | − | 910.287i | − | 0.974612i | ||||||
\(935\) | 21.3669 | 0.0228523 | ||||||||
\(936\) | −349.322 | −0.373207 | ||||||||
\(937\) | 1311.04i | 1.39918i | 0.714542 | + | 0.699592i | \(0.246635\pi\) | ||||
−0.714542 | + | 0.699592i | \(0.753365\pi\) | |||||||
\(938\) | 514.610 | + | 611.054i | 0.548625 | + | 0.651444i | ||||
\(939\) | 728.478 | 0.775802 | ||||||||
\(940\) | − | 35.1149i | − | 0.0373563i | ||||||
\(941\) | 311.971i | 0.331531i | 0.986165 | + | 0.165765i | \(0.0530095\pi\) | ||||
−0.986165 | + | 0.165765i | \(0.946991\pi\) | |||||||
\(942\) | 511.889 | 0.543407 | ||||||||
\(943\) | − | 831.271i | − | 0.881518i | ||||||
\(944\) | 130.105 | 0.137823 | ||||||||
\(945\) | 104.350i | 0.110423i | ||||||||
\(946\) | 189.641i | 0.200466i | ||||||||
\(947\) | 393.116 | 0.415117 | 0.207559 | − | 0.978223i | \(-0.433448\pi\) | ||||
0.207559 | + | 0.978223i | \(0.433448\pi\) | |||||||
\(948\) | 372.850 | 0.393301 | ||||||||
\(949\) | − | 1715.17i | − | 1.80735i | ||||||
\(950\) | 211.855i | 0.223006i | ||||||||
\(951\) | 670.935i | 0.705505i | ||||||||
\(952\) | −171.018 | −0.179641 | ||||||||
\(953\) | 534.730 | 0.561102 | 0.280551 | − | 0.959839i | \(-0.409483\pi\) | ||||
0.280551 | + | 0.959839i | \(0.409483\pi\) | |||||||
\(954\) | 344.288 | 0.360888 | ||||||||
\(955\) | −426.462 | −0.446557 | ||||||||
\(956\) | − | 808.090i | − | 0.845282i | ||||||
\(957\) | −186.308 | −0.194679 | ||||||||
\(958\) | 798.941i | 0.833967i | ||||||||
\(959\) | 338.609 | 0.353086 | ||||||||
\(960\) | 176.883 | 0.184254 | ||||||||
\(961\) | 877.349 | 0.912954 | ||||||||
\(962\) | 62.8405 | 0.0653228 | ||||||||
\(963\) | −383.225 | −0.397949 | ||||||||
\(964\) | 153.964 | 0.159714 | ||||||||
\(965\) | − | 591.332i | − | 0.612780i | ||||||
\(966\) | 392.666i | 0.406486i | ||||||||
\(967\) | 1743.86 | 1.80338 | 0.901688 | − | 0.432387i | \(-0.142329\pi\) | ||||
0.901688 | + | 0.432387i | \(0.142329\pi\) | |||||||
\(968\) | − | 844.831i | − | 0.872760i | ||||||
\(969\) | 31.7547i | 0.0327706i | ||||||||
\(970\) | − | 104.346i | − | 0.107573i | ||||||
\(971\) | 933.434 | 0.961312 | 0.480656 | − | 0.876909i | \(-0.340399\pi\) | ||||
0.480656 | + | 0.876909i | \(0.340399\pi\) | |||||||
\(972\) | 35.7940i | 0.0368251i | ||||||||
\(973\) | −158.635 | −0.163036 | ||||||||
\(974\) | 453.531 | 0.465638 | ||||||||
\(975\) | −494.896 | −0.507586 | ||||||||
\(976\) | 36.6643i | 0.0375659i | ||||||||
\(977\) | 1076.60 | 1.10195 | 0.550974 | − | 0.834522i | \(-0.314256\pi\) | ||||
0.550974 | + | 0.834522i | \(0.314256\pi\) | |||||||
\(978\) | 510.503 | 0.521987 | ||||||||
\(979\) | 225.533i | 0.230371i | ||||||||
\(980\) | − | 173.871i | − | 0.177419i | ||||||
\(981\) | 346.693i | 0.353408i | ||||||||
\(982\) | 571.699i | 0.582178i | ||||||||
\(983\) | − | 1507.23i | − | 1.53330i | −0.642068 | − | 0.766648i | \(-0.721923\pi\) | ||
0.642068 | − | 0.766648i | \(-0.278077\pi\) | |||||||
\(984\) | − | 622.354i | − | 0.632473i | ||||||
\(985\) | −419.216 | −0.425600 | ||||||||
\(986\) | 74.9670i | 0.0760315i | ||||||||
\(987\) | 110.059 | 0.111509 | ||||||||
\(988\) | − | 261.825i | − | 0.265005i | ||||||
\(989\) | 647.449i | 0.654650i | ||||||||
\(990\) | − | 36.7297i | − | 0.0371007i | ||||||
\(991\) | − | 42.8503i | − | 0.0432394i | −0.999766 | − | 0.0216197i | \(-0.993118\pi\) | ||
0.999766 | − | 0.0216197i | \(-0.00688230\pi\) | |||||||
\(992\) | −282.247 | −0.284523 | ||||||||
\(993\) | 696.339 | 0.701248 | ||||||||
\(994\) | −435.741 | −0.438371 | ||||||||
\(995\) | 110.209i | 0.110762i | ||||||||
\(996\) | 199.266i | 0.200066i | ||||||||
\(997\) | 618.244 | 0.620104 | 0.310052 | − | 0.950720i | \(-0.399654\pi\) | ||||
0.310052 | + | 0.950720i | \(0.399654\pi\) | |||||||
\(998\) | 73.7909 | 0.0739388 | ||||||||
\(999\) | − | 17.6561i | − | 0.0176738i |
(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 | 201.3.b.a.133.8 | ✓ | 22 | |
3.2 | odd | 2 | 603.3.b.e.334.15 | 22 | |||
67.66 | odd | 2 | inner | 201.3.b.a.133.15 | yes | 22 | |
201.200 | even | 2 | 603.3.b.e.334.8 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.3.b.a.133.8 | ✓ | 22 | 1.1 | even | 1 | trivial | |
201.3.b.a.133.15 | yes | 22 | 67.66 | odd | 2 | inner | |
603.3.b.e.334.8 | 22 | 201.200 | even | 2 | |||
603.3.b.e.334.15 | 22 | 3.2 | odd | 2 |