Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(76,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("105.76");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.h (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: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.5 | ||
Root | \(-1.01714 + 1.76174i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.76 |
Dual form | 105.3.h.a.76.6 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.71214 | −0.856071 | −0.428035 | − | 0.903762i | \(-0.640794\pi\) | ||||
−0.428035 | + | 0.903762i | \(0.640794\pi\) | |||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | −1.06857 | −0.267143 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 2.96552i | 0.494253i | ||||||||
\(7\) | −3.33344 | + | 6.15534i | −0.476206 | + | 0.879334i | ||||
\(8\) | 8.67811 | 1.08476 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | − | 3.82847i | − | 0.382847i | ||||||
\(11\) | 17.0001 | 1.54546 | 0.772732 | − | 0.634732i | \(-0.218890\pi\) | ||||
0.772732 | + | 0.634732i | \(0.218890\pi\) | |||||||
\(12\) | 1.85082i | 0.154235i | ||||||||
\(13\) | 16.3319i | 1.25630i | 0.778091 | + | 0.628152i | \(0.216188\pi\) | ||||
−0.778091 | + | 0.628152i | \(0.783812\pi\) | |||||||
\(14\) | 5.70733 | − | 10.5388i | 0.407666 | − | 0.752772i | ||||
\(15\) | 3.87298 | 0.258199 | ||||||||
\(16\) | −10.5839 | −0.661492 | ||||||||
\(17\) | 13.4266i | 0.789801i | 0.918724 | + | 0.394900i | \(0.129221\pi\) | ||||
−0.918724 | + | 0.394900i | \(0.870779\pi\) | |||||||
\(18\) | 5.13643 | 0.285357 | ||||||||
\(19\) | 13.7499i | 0.723679i | 0.932240 | + | 0.361839i | \(0.117851\pi\) | ||||
−0.932240 | + | 0.361839i | \(0.882149\pi\) | |||||||
\(20\) | − | 2.38940i | − | 0.119470i | ||||||
\(21\) | 10.6614 | + | 5.77369i | 0.507684 | + | 0.274938i | ||||
\(22\) | −29.1066 | −1.32303 | ||||||||
\(23\) | −16.6179 | −0.722518 | −0.361259 | − | 0.932466i | \(-0.617653\pi\) | ||||
−0.361259 | + | 0.932466i | \(0.617653\pi\) | |||||||
\(24\) | − | 15.0309i | − | 0.626289i | ||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | − | 27.9626i | − | 1.07548i | ||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 3.56202 | − | 6.57741i | 0.127215 | − | 0.234907i | ||||
\(29\) | 32.1793 | 1.10963 | 0.554816 | − | 0.831973i | \(-0.312789\pi\) | ||||
0.554816 | + | 0.831973i | \(0.312789\pi\) | |||||||
\(30\) | −6.63110 | −0.221037 | ||||||||
\(31\) | − | 6.74366i | − | 0.217538i | −0.994067 | − | 0.108769i | \(-0.965309\pi\) | ||
0.994067 | − | 0.108769i | \(-0.0346908\pi\) | |||||||
\(32\) | −16.5913 | −0.518480 | ||||||||
\(33\) | − | 29.4450i | − | 0.892274i | ||||||
\(34\) | − | 22.9883i | − | 0.676125i | ||||||
\(35\) | −13.7637 | − | 7.45380i | −0.393250 | − | 0.212966i | ||||
\(36\) | 3.20571 | 0.0890475 | ||||||||
\(37\) | −69.2141 | −1.87065 | −0.935325 | − | 0.353789i | \(-0.884893\pi\) | ||||
−0.935325 | + | 0.353789i | \(0.884893\pi\) | |||||||
\(38\) | − | 23.5418i | − | 0.619520i | ||||||
\(39\) | 28.2878 | 0.725327 | ||||||||
\(40\) | 19.4048i | 0.485121i | ||||||||
\(41\) | − | 39.7391i | − | 0.969246i | −0.874723 | − | 0.484623i | \(-0.838957\pi\) | ||
0.874723 | − | 0.484623i | \(-0.161043\pi\) | |||||||
\(42\) | −18.2538 | − | 9.88538i | −0.434613 | − | 0.235366i | ||||
\(43\) | 43.2210 | 1.00514 | 0.502570 | − | 0.864537i | \(-0.332388\pi\) | ||||
0.502570 | + | 0.864537i | \(0.332388\pi\) | |||||||
\(44\) | −18.1658 | −0.412859 | ||||||||
\(45\) | − | 6.70820i | − | 0.149071i | ||||||
\(46\) | 28.4522 | 0.618526 | ||||||||
\(47\) | 40.1384i | 0.854009i | 0.904249 | + | 0.427005i | \(0.140431\pi\) | ||||
−0.904249 | + | 0.427005i | \(0.859569\pi\) | |||||||
\(48\) | 18.3318i | 0.381913i | ||||||||
\(49\) | −26.7763 | − | 41.0369i | −0.546456 | − | 0.837488i | ||||
\(50\) | 8.56071 | 0.171214 | ||||||||
\(51\) | 23.2556 | 0.455992 | ||||||||
\(52\) | − | 17.4518i | − | 0.335612i | ||||||
\(53\) | 22.5002 | 0.424533 | 0.212266 | − | 0.977212i | \(-0.431916\pi\) | ||||
0.212266 | + | 0.977212i | \(0.431916\pi\) | |||||||
\(54\) | − | 8.89655i | − | 0.164751i | ||||||
\(55\) | 38.0134i | 0.691153i | ||||||||
\(56\) | −28.9280 | + | 53.4167i | −0.516571 | + | 0.953869i | ||||
\(57\) | 23.8155 | 0.417816 | ||||||||
\(58\) | −55.0956 | −0.949924 | ||||||||
\(59\) | 81.6005i | 1.38306i | 0.722348 | + | 0.691529i | \(0.243063\pi\) | ||||
−0.722348 | + | 0.691529i | \(0.756937\pi\) | |||||||
\(60\) | −4.13855 | −0.0689759 | ||||||||
\(61\) | 14.9859i | 0.245671i | 0.992427 | + | 0.122836i | \(0.0391988\pi\) | ||||
−0.992427 | + | 0.122836i | \(0.960801\pi\) | |||||||
\(62\) | 11.5461i | 0.186228i | ||||||||
\(63\) | 10.0003 | − | 18.4660i | 0.158735 | − | 0.293111i | ||||
\(64\) | 70.7422 | 1.10535 | ||||||||
\(65\) | −36.5193 | −0.561836 | ||||||||
\(66\) | 50.4141i | 0.763850i | ||||||||
\(67\) | 72.0872 | 1.07593 | 0.537964 | − | 0.842968i | \(-0.319194\pi\) | ||||
0.537964 | + | 0.842968i | \(0.319194\pi\) | |||||||
\(68\) | − | 14.3473i | − | 0.210989i | ||||||
\(69\) | 28.7831i | 0.417146i | ||||||||
\(70\) | 23.5655 | + | 12.7620i | 0.336650 | + | 0.182314i | ||||
\(71\) | −25.7338 | −0.362448 | −0.181224 | − | 0.983442i | \(-0.558006\pi\) | ||||
−0.181224 | + | 0.983442i | \(0.558006\pi\) | |||||||
\(72\) | −26.0343 | −0.361588 | ||||||||
\(73\) | 75.0647i | 1.02828i | 0.857705 | + | 0.514142i | \(0.171890\pi\) | ||||
−0.857705 | + | 0.514142i | \(0.828110\pi\) | |||||||
\(74\) | 118.504 | 1.60141 | ||||||||
\(75\) | 8.66025i | 0.115470i | ||||||||
\(76\) | − | 14.6927i | − | 0.193325i | ||||||
\(77\) | −56.6689 | + | 104.641i | −0.735959 | + | 1.35898i | ||||
\(78\) | −48.4327 | −0.620931 | ||||||||
\(79\) | 80.0480 | 1.01327 | 0.506633 | − | 0.862162i | \(-0.330890\pi\) | ||||
0.506633 | + | 0.862162i | \(0.330890\pi\) | |||||||
\(80\) | − | 23.6663i | − | 0.295828i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 68.0389i | 0.829743i | ||||||||
\(83\) | − | 102.112i | − | 1.23027i | −0.788421 | − | 0.615135i | \(-0.789101\pi\) | ||
0.788421 | − | 0.615135i | \(-0.210899\pi\) | |||||||
\(84\) | −11.3924 | − | 6.16959i | −0.135624 | − | 0.0734476i | ||||
\(85\) | −30.0228 | −0.353210 | ||||||||
\(86\) | −74.0005 | −0.860471 | ||||||||
\(87\) | − | 55.7362i | − | 0.640646i | ||||||
\(88\) | 147.529 | 1.67646 | ||||||||
\(89\) | − | 128.381i | − | 1.44248i | −0.692683 | − | 0.721242i | \(-0.743571\pi\) | ||
0.692683 | − | 0.721242i | \(-0.256429\pi\) | |||||||
\(90\) | 11.4854i | 0.127616i | ||||||||
\(91\) | −100.529 | − | 54.4416i | −1.10471 | − | 0.598259i | ||||
\(92\) | 17.7574 | 0.193015 | ||||||||
\(93\) | −11.6804 | −0.125595 | ||||||||
\(94\) | − | 68.7227i | − | 0.731092i | ||||||
\(95\) | −30.7457 | −0.323639 | ||||||||
\(96\) | 28.7371i | 0.299344i | ||||||||
\(97\) | − | 159.448i | − | 1.64379i | −0.569636 | − | 0.821897i | \(-0.692916\pi\) | ||
0.569636 | − | 0.821897i | \(-0.307084\pi\) | |||||||
\(98\) | 45.8449 | + | 70.2610i | 0.467805 | + | 0.716949i | ||||
\(99\) | −51.0003 | −0.515155 | ||||||||
\(100\) | 5.34285 | 0.0534285 | ||||||||
\(101\) | − | 24.1380i | − | 0.238990i | −0.992835 | − | 0.119495i | \(-0.961872\pi\) | ||
0.992835 | − | 0.119495i | \(-0.0381276\pi\) | |||||||
\(102\) | −39.8168 | −0.390361 | ||||||||
\(103\) | 87.3469i | 0.848028i | 0.905656 | + | 0.424014i | \(0.139379\pi\) | ||||
−0.905656 | + | 0.424014i | \(0.860621\pi\) | |||||||
\(104\) | 141.730i | 1.36279i | ||||||||
\(105\) | −12.9104 | + | 23.8395i | −0.122956 | + | 0.227043i | ||||
\(106\) | −38.5236 | −0.363430 | ||||||||
\(107\) | 168.359 | 1.57344 | 0.786722 | − | 0.617307i | \(-0.211776\pi\) | ||||
0.786722 | + | 0.617307i | \(0.211776\pi\) | |||||||
\(108\) | − | 5.55245i | − | 0.0514116i | ||||||
\(109\) | −155.570 | −1.42725 | −0.713624 | − | 0.700529i | \(-0.752947\pi\) | ||||
−0.713624 | + | 0.700529i | \(0.752947\pi\) | |||||||
\(110\) | − | 65.0843i | − | 0.591676i | ||||||
\(111\) | 119.882i | 1.08002i | ||||||||
\(112\) | 35.2807 | − | 65.1473i | 0.315007 | − | 0.581672i | ||||
\(113\) | −20.9965 | −0.185810 | −0.0929050 | − | 0.995675i | \(-0.529615\pi\) | ||||
−0.0929050 | + | 0.995675i | \(0.529615\pi\) | |||||||
\(114\) | −40.7756 | −0.357680 | ||||||||
\(115\) | − | 37.1588i | − | 0.323120i | ||||||
\(116\) | −34.3859 | −0.296430 | ||||||||
\(117\) | − | 48.9958i | − | 0.418768i | ||||||
\(118\) | − | 139.712i | − | 1.18400i | ||||||
\(119\) | −82.6453 | − | 44.7568i | −0.694498 | − | 0.376108i | ||||
\(120\) | 33.6102 | 0.280085 | ||||||||
\(121\) | 168.004 | 1.38846 | ||||||||
\(122\) | − | 25.6581i | − | 0.210312i | ||||||
\(123\) | −68.8301 | −0.559594 | ||||||||
\(124\) | 7.20608i | 0.0581135i | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | −17.1220 | + | 31.6164i | −0.135889 | + | 0.250924i | ||||
\(127\) | −59.8712 | −0.471427 | −0.235713 | − | 0.971823i | \(-0.575743\pi\) | ||||
−0.235713 | + | 0.971823i | \(0.575743\pi\) | |||||||
\(128\) | −54.7554 | −0.427776 | ||||||||
\(129\) | − | 74.8609i | − | 0.580317i | ||||||
\(130\) | 62.5263 | 0.480971 | ||||||||
\(131\) | − | 166.868i | − | 1.27380i | −0.770947 | − | 0.636899i | \(-0.780217\pi\) | ||
0.770947 | − | 0.636899i | \(-0.219783\pi\) | |||||||
\(132\) | 31.4641i | 0.238364i | ||||||||
\(133\) | −84.6352 | − | 45.8345i | −0.636355 | − | 0.344620i | ||||
\(134\) | −123.423 | −0.921071 | ||||||||
\(135\) | −11.6190 | −0.0860663 | ||||||||
\(136\) | 116.518i | 0.856747i | ||||||||
\(137\) | 126.139 | 0.920726 | 0.460363 | − | 0.887731i | \(-0.347719\pi\) | ||||
0.460363 | + | 0.887731i | \(0.347719\pi\) | |||||||
\(138\) | − | 49.2807i | − | 0.357106i | ||||||
\(139\) | 211.650i | 1.52266i | 0.648365 | + | 0.761330i | \(0.275453\pi\) | ||||
−0.648365 | + | 0.761330i | \(0.724547\pi\) | |||||||
\(140\) | 14.7075 | + | 7.96491i | 0.105054 | + | 0.0568922i | ||||
\(141\) | 69.5218 | 0.493062 | ||||||||
\(142\) | 44.0599 | 0.310281 | ||||||||
\(143\) | 277.645i | 1.94157i | ||||||||
\(144\) | 31.7516 | 0.220497 | ||||||||
\(145\) | 71.9552i | 0.496243i | ||||||||
\(146\) | − | 128.521i | − | 0.880284i | ||||||
\(147\) | −71.0780 | + | 46.3780i | −0.483524 | + | 0.315496i | ||||
\(148\) | 73.9601 | 0.499730 | ||||||||
\(149\) | −64.1825 | −0.430755 | −0.215377 | − | 0.976531i | \(-0.569098\pi\) | ||||
−0.215377 | + | 0.976531i | \(0.569098\pi\) | |||||||
\(150\) | − | 14.8276i | − | 0.0988506i | ||||||
\(151\) | 110.915 | 0.734538 | 0.367269 | − | 0.930115i | \(-0.380293\pi\) | ||||
0.367269 | + | 0.930115i | \(0.380293\pi\) | |||||||
\(152\) | 119.323i | 0.785021i | ||||||||
\(153\) | − | 40.2798i | − | 0.263267i | ||||||
\(154\) | 97.0252 | − | 179.161i | 0.630033 | − | 1.16338i | ||||
\(155\) | 15.0793 | 0.0972858 | ||||||||
\(156\) | −30.2275 | −0.193766 | ||||||||
\(157\) | − | 290.451i | − | 1.85001i | −0.379956 | − | 0.925004i | \(-0.624061\pi\) | ||
0.379956 | − | 0.925004i | \(-0.375939\pi\) | |||||||
\(158\) | −137.053 | −0.867427 | ||||||||
\(159\) | − | 38.9716i | − | 0.245104i | ||||||
\(160\) | − | 37.0994i | − | 0.231871i | ||||||
\(161\) | 55.3948 | − | 102.289i | 0.344067 | − | 0.635334i | ||||
\(162\) | −15.4093 | −0.0951190 | ||||||||
\(163\) | −53.8559 | −0.330404 | −0.165202 | − | 0.986260i | \(-0.552828\pi\) | ||||
−0.165202 | + | 0.986260i | \(0.552828\pi\) | |||||||
\(164\) | 42.4640i | 0.258927i | ||||||||
\(165\) | 65.8411 | 0.399037 | ||||||||
\(166\) | 174.831i | 1.05320i | ||||||||
\(167\) | 41.7927i | 0.250255i | 0.992141 | + | 0.125128i | \(0.0399341\pi\) | ||||
−0.992141 | + | 0.125128i | \(0.960066\pi\) | |||||||
\(168\) | 92.5204 | + | 50.1047i | 0.550717 | + | 0.298242i | ||||
\(169\) | −97.7324 | −0.578298 | ||||||||
\(170\) | 51.4033 | 0.302372 | ||||||||
\(171\) | − | 41.2497i | − | 0.241226i | ||||||
\(172\) | −46.1847 | −0.268515 | ||||||||
\(173\) | − | 130.344i | − | 0.753434i | −0.926328 | − | 0.376717i | \(-0.877053\pi\) | ||
0.926328 | − | 0.376717i | \(-0.122947\pi\) | |||||||
\(174\) | 95.4283i | 0.548439i | ||||||||
\(175\) | 16.6672 | − | 30.7767i | 0.0952412 | − | 0.175867i | ||||
\(176\) | −179.927 | −1.02231 | ||||||||
\(177\) | 141.336 | 0.798509 | ||||||||
\(178\) | 219.807i | 1.23487i | ||||||||
\(179\) | 44.9934 | 0.251360 | 0.125680 | − | 0.992071i | \(-0.459889\pi\) | ||||
0.125680 | + | 0.992071i | \(0.459889\pi\) | |||||||
\(180\) | 7.16819i | 0.0398233i | ||||||||
\(181\) | 17.8944i | 0.0988640i | 0.998777 | + | 0.0494320i | \(0.0157411\pi\) | ||||
−0.998777 | + | 0.0494320i | \(0.984259\pi\) | |||||||
\(182\) | 172.119 | + | 93.2117i | 0.945710 | + | 0.512152i | ||||
\(183\) | 25.9564 | 0.141838 | ||||||||
\(184\) | −144.212 | −0.783761 | ||||||||
\(185\) | − | 154.767i | − | 0.836581i | ||||||
\(186\) | 19.9985 | 0.107519 | ||||||||
\(187\) | 228.254i | 1.22061i | ||||||||
\(188\) | − | 42.8907i | − | 0.228142i | ||||||
\(189\) | −31.9841 | − | 17.3211i | −0.169228 | − | 0.0916459i | ||||
\(190\) | 52.6410 | 0.277058 | ||||||||
\(191\) | 178.314 | 0.933583 | 0.466791 | − | 0.884367i | \(-0.345410\pi\) | ||||
0.466791 | + | 0.884367i | \(0.345410\pi\) | |||||||
\(192\) | − | 122.529i | − | 0.638173i | ||||||
\(193\) | −336.283 | −1.74240 | −0.871200 | − | 0.490928i | \(-0.836658\pi\) | ||||
−0.871200 | + | 0.490928i | \(0.836658\pi\) | |||||||
\(194\) | 272.998i | 1.40720i | ||||||||
\(195\) | 63.2534i | 0.324376i | ||||||||
\(196\) | 28.6124 | + | 43.8508i | 0.145982 | + | 0.223729i | ||||
\(197\) | 49.2082 | 0.249788 | 0.124894 | − | 0.992170i | \(-0.460141\pi\) | ||||
0.124894 | + | 0.992170i | \(0.460141\pi\) | |||||||
\(198\) | 87.3198 | 0.441009 | ||||||||
\(199\) | 171.789i | 0.863262i | 0.902050 | + | 0.431631i | \(0.142062\pi\) | ||||
−0.902050 | + | 0.431631i | \(0.857938\pi\) | |||||||
\(200\) | −43.3906 | −0.216953 | ||||||||
\(201\) | − | 124.859i | − | 0.621187i | ||||||
\(202\) | 41.3277i | 0.204592i | ||||||||
\(203\) | −107.268 | + | 198.075i | −0.528414 | + | 0.975737i | ||||
\(204\) | −24.8502 | −0.121815 | ||||||||
\(205\) | 88.8593 | 0.433460 | ||||||||
\(206\) | − | 149.550i | − | 0.725972i | ||||||
\(207\) | 49.8537 | 0.240839 | ||||||||
\(208\) | − | 172.855i | − | 0.831035i | ||||||
\(209\) | 233.750i | 1.11842i | ||||||||
\(210\) | 22.1044 | − | 40.8166i | 0.105259 | − | 0.194365i | ||||
\(211\) | −5.09458 | −0.0241449 | −0.0120725 | − | 0.999927i | \(-0.503843\pi\) | ||||
−0.0120725 | + | 0.999927i | \(0.503843\pi\) | |||||||
\(212\) | −24.0431 | −0.113411 | ||||||||
\(213\) | 44.5722i | 0.209259i | ||||||||
\(214\) | −288.254 | −1.34698 | ||||||||
\(215\) | 96.6451i | 0.449512i | ||||||||
\(216\) | 45.0928i | 0.208763i | ||||||||
\(217\) | 41.5095 | + | 22.4796i | 0.191288 | + | 0.103593i | ||||
\(218\) | 266.358 | 1.22183 | ||||||||
\(219\) | 130.016 | 0.593680 | ||||||||
\(220\) | − | 40.6200i | − | 0.184636i | ||||||
\(221\) | −219.283 | −0.992229 | ||||||||
\(222\) | − | 205.256i | − | 0.924574i | ||||||
\(223\) | − | 310.066i | − | 1.39043i | −0.718802 | − | 0.695215i | \(-0.755309\pi\) | ||
0.718802 | − | 0.695215i | \(-0.244691\pi\) | |||||||
\(224\) | 55.3063 | − | 102.125i | 0.246903 | − | 0.455917i | ||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | 35.9490 | 0.159067 | ||||||||
\(227\) | − | 108.558i | − | 0.478228i | −0.970991 | − | 0.239114i | \(-0.923143\pi\) | ||
0.970991 | − | 0.239114i | \(-0.0768570\pi\) | |||||||
\(228\) | −25.4486 | −0.111616 | ||||||||
\(229\) | 236.483i | 1.03268i | 0.856384 | + | 0.516339i | \(0.172706\pi\) | ||||
−0.856384 | + | 0.516339i | \(0.827294\pi\) | |||||||
\(230\) | 63.6211i | 0.276613i | ||||||||
\(231\) | 181.244 | + | 98.1534i | 0.784607 | + | 0.424906i | ||||
\(232\) | 279.256 | 1.20369 | ||||||||
\(233\) | 151.290 | 0.649312 | 0.324656 | − | 0.945832i | \(-0.394751\pi\) | ||||
0.324656 | + | 0.945832i | \(0.394751\pi\) | |||||||
\(234\) | 83.8878i | 0.358495i | ||||||||
\(235\) | −89.7523 | −0.381925 | ||||||||
\(236\) | − | 87.1958i | − | 0.369474i | ||||||
\(237\) | − | 138.647i | − | 0.585009i | ||||||
\(238\) | 141.500 | + | 76.6300i | 0.594540 | + | 0.321975i | ||||
\(239\) | 48.2956 | 0.202074 | 0.101037 | − | 0.994883i | \(-0.467784\pi\) | ||||
0.101037 | + | 0.994883i | \(0.467784\pi\) | |||||||
\(240\) | −40.9912 | −0.170797 | ||||||||
\(241\) | 230.735i | 0.957406i | 0.877977 | + | 0.478703i | \(0.158893\pi\) | ||||
−0.877977 | + | 0.478703i | \(0.841107\pi\) | |||||||
\(242\) | −287.646 | −1.18862 | ||||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | − | 16.0135i | − | 0.0656292i | ||||||
\(245\) | 91.7613 | − | 59.8737i | 0.374536 | − | 0.244382i | ||||
\(246\) | 117.847 | 0.479053 | ||||||||
\(247\) | −224.563 | −0.909160 | ||||||||
\(248\) | − | 58.5223i | − | 0.235977i | ||||||
\(249\) | −176.864 | −0.710297 | ||||||||
\(250\) | 19.1423i | 0.0765693i | ||||||||
\(251\) | − | 86.6812i | − | 0.345343i | −0.984979 | − | 0.172672i | \(-0.944760\pi\) | ||
0.984979 | − | 0.172672i | \(-0.0552399\pi\) | |||||||
\(252\) | −10.6861 | + | 19.7322i | −0.0424050 | + | 0.0783025i | ||||
\(253\) | −282.506 | −1.11663 | ||||||||
\(254\) | 102.508 | 0.403575 | ||||||||
\(255\) | 52.0010i | 0.203926i | ||||||||
\(256\) | −189.220 | −0.739141 | ||||||||
\(257\) | − | 141.110i | − | 0.549065i | −0.961578 | − | 0.274532i | \(-0.911477\pi\) | ||
0.961578 | − | 0.274532i | \(-0.0885231\pi\) | |||||||
\(258\) | 128.173i | 0.496793i | ||||||||
\(259\) | 230.721 | − | 426.036i | 0.890815 | − | 1.64493i | ||||
\(260\) | 39.0235 | 0.150090 | ||||||||
\(261\) | −96.5380 | −0.369877 | ||||||||
\(262\) | 285.701i | 1.09046i | ||||||||
\(263\) | 38.0901 | 0.144829 | 0.0724147 | − | 0.997375i | \(-0.476930\pi\) | ||||
0.0724147 | + | 0.997375i | \(0.476930\pi\) | |||||||
\(264\) | − | 255.527i | − | 0.967907i | ||||||
\(265\) | 50.3121i | 0.189857i | ||||||||
\(266\) | 144.908 | + | 78.4752i | 0.544765 | + | 0.295019i | ||||
\(267\) | −222.363 | −0.832819 | ||||||||
\(268\) | −77.0302 | −0.287426 | ||||||||
\(269\) | − | 454.220i | − | 1.68855i | −0.535909 | − | 0.844275i | \(-0.680031\pi\) | ||
0.535909 | − | 0.844275i | \(-0.319969\pi\) | |||||||
\(270\) | 19.8933 | 0.0736789 | ||||||||
\(271\) | 78.7098i | 0.290442i | 0.989399 | + | 0.145221i | \(0.0463893\pi\) | ||||
−0.989399 | + | 0.145221i | \(0.953611\pi\) | |||||||
\(272\) | − | 142.106i | − | 0.522447i | ||||||
\(273\) | −94.2956 | + | 174.121i | −0.345405 | + | 0.637805i | ||||
\(274\) | −215.969 | −0.788207 | ||||||||
\(275\) | −85.0005 | −0.309093 | ||||||||
\(276\) | − | 30.7567i | − | 0.111437i | ||||||
\(277\) | −85.3396 | −0.308085 | −0.154043 | − | 0.988064i | \(-0.549229\pi\) | ||||
−0.154043 | + | 0.988064i | \(0.549229\pi\) | |||||||
\(278\) | − | 362.374i | − | 1.30350i | ||||||
\(279\) | 20.2310i | 0.0725125i | ||||||||
\(280\) | −119.443 | − | 64.6849i | −0.426583 | − | 0.231018i | ||||
\(281\) | 167.376 | 0.595643 | 0.297821 | − | 0.954622i | \(-0.403740\pi\) | ||||
0.297821 | + | 0.954622i | \(0.403740\pi\) | |||||||
\(282\) | −119.031 | −0.422096 | ||||||||
\(283\) | − | 149.591i | − | 0.528588i | −0.964442 | − | 0.264294i | \(-0.914861\pi\) | ||
0.964442 | − | 0.264294i | \(-0.0851390\pi\) | |||||||
\(284\) | 27.4984 | 0.0968252 | ||||||||
\(285\) | 53.2531i | 0.186853i | ||||||||
\(286\) | − | 475.367i | − | 1.66212i | ||||||
\(287\) | 244.607 | + | 132.468i | 0.852291 | + | 0.461561i | ||||
\(288\) | 49.7740 | 0.172827 | ||||||||
\(289\) | 108.726 | 0.376215 | ||||||||
\(290\) | − | 123.197i | − | 0.424819i | ||||||
\(291\) | −276.172 | −0.949045 | ||||||||
\(292\) | − | 80.2119i | − | 0.274698i | ||||||
\(293\) | 145.805i | 0.497627i | 0.968551 | + | 0.248813i | \(0.0800406\pi\) | ||||
−0.968551 | + | 0.248813i | \(0.919959\pi\) | |||||||
\(294\) | 121.696 | − | 79.4056i | 0.413931 | − | 0.270087i | ||||
\(295\) | −182.464 | −0.618523 | ||||||||
\(296\) | −600.648 | −2.02921 | ||||||||
\(297\) | 88.3351i | 0.297425i | ||||||||
\(298\) | 109.889 | 0.368757 | ||||||||
\(299\) | − | 271.403i | − | 0.907701i | ||||||
\(300\) | − | 9.25409i | − | 0.0308470i | ||||||
\(301\) | −144.075 | + | 266.040i | −0.478653 | + | 0.883853i | ||||
\(302\) | −189.903 | −0.628817 | ||||||||
\(303\) | −41.8082 | −0.137981 | ||||||||
\(304\) | − | 145.527i | − | 0.478708i | ||||||
\(305\) | −33.5096 | −0.109868 | ||||||||
\(306\) | 68.9648i | 0.225375i | ||||||||
\(307\) | − | 205.594i | − | 0.669686i | −0.942274 | − | 0.334843i | \(-0.891317\pi\) | ||
0.942274 | − | 0.334843i | \(-0.108683\pi\) | |||||||
\(308\) | 60.5547 | − | 111.817i | 0.196606 | − | 0.363041i | ||||
\(309\) | 151.289 | 0.489609 | ||||||||
\(310\) | −25.8179 | −0.0832835 | ||||||||
\(311\) | 424.383i | 1.36458i | 0.731084 | + | 0.682288i | \(0.239015\pi\) | ||||
−0.731084 | + | 0.682288i | \(0.760985\pi\) | |||||||
\(312\) | 245.484 | 0.786809 | ||||||||
\(313\) | 363.503i | 1.16135i | 0.814135 | + | 0.580676i | \(0.197212\pi\) | ||||
−0.814135 | + | 0.580676i | \(0.802788\pi\) | |||||||
\(314\) | 497.294i | 1.58374i | ||||||||
\(315\) | 41.2912 | + | 22.3614i | 0.131083 | + | 0.0709886i | ||||
\(316\) | −85.5369 | −0.270686 | ||||||||
\(317\) | 441.407 | 1.39245 | 0.696226 | − | 0.717822i | \(-0.254861\pi\) | ||||
0.696226 | + | 0.717822i | \(0.254861\pi\) | |||||||
\(318\) | 66.7248i | 0.209827i | ||||||||
\(319\) | 547.052 | 1.71490 | ||||||||
\(320\) | 158.184i | 0.494326i | ||||||||
\(321\) | − | 291.606i | − | 0.908429i | ||||||
\(322\) | −94.8438 | + | 175.133i | −0.294546 | + | 0.543891i | ||||
\(323\) | −184.615 | −0.571562 | ||||||||
\(324\) | −9.61713 | −0.0296825 | ||||||||
\(325\) | − | 81.6597i | − | 0.251261i | ||||||
\(326\) | 92.2089 | 0.282849 | ||||||||
\(327\) | 269.455i | 0.824022i | ||||||||
\(328\) | − | 344.860i | − | 1.05140i | ||||||
\(329\) | −247.066 | − | 133.799i | −0.750959 | − | 0.406684i | ||||
\(330\) | −112.729 | −0.341604 | ||||||||
\(331\) | 509.327 | 1.53875 | 0.769376 | − | 0.638796i | \(-0.220567\pi\) | ||||
0.769376 | + | 0.638796i | \(0.220567\pi\) | |||||||
\(332\) | 109.114i | 0.328658i | ||||||||
\(333\) | 207.642 | 0.623550 | ||||||||
\(334\) | − | 71.5550i | − | 0.214236i | ||||||
\(335\) | 161.192i | 0.481170i | ||||||||
\(336\) | −112.838 | − | 61.1080i | −0.335829 | − | 0.181869i | ||||
\(337\) | 442.557 | 1.31323 | 0.656613 | − | 0.754228i | \(-0.271988\pi\) | ||||
0.656613 | + | 0.754228i | \(0.271988\pi\) | |||||||
\(338\) | 167.332 | 0.495064 | ||||||||
\(339\) | 36.3671i | 0.107277i | ||||||||
\(340\) | 32.0815 | 0.0943573 | ||||||||
\(341\) | − | 114.643i | − | 0.336197i | ||||||
\(342\) | 70.6253i | 0.206507i | ||||||||
\(343\) | 341.853 | − | 28.0231i | 0.996657 | − | 0.0816999i | ||||
\(344\) | 375.077 | 1.09034 | ||||||||
\(345\) | −64.3609 | −0.186553 | ||||||||
\(346\) | 223.167i | 0.644993i | ||||||||
\(347\) | −493.763 | −1.42295 | −0.711475 | − | 0.702712i | \(-0.751972\pi\) | ||||
−0.711475 | + | 0.702712i | \(0.751972\pi\) | |||||||
\(348\) | 59.5581i | 0.171144i | ||||||||
\(349\) | 324.460i | 0.929686i | 0.885393 | + | 0.464843i | \(0.153889\pi\) | ||||
−0.885393 | + | 0.464843i | \(0.846111\pi\) | |||||||
\(350\) | −28.5366 | + | 52.6940i | −0.0815332 | + | 0.150554i | ||||
\(351\) | −84.8633 | −0.241776 | ||||||||
\(352\) | −282.055 | −0.801292 | ||||||||
\(353\) | 529.424i | 1.49979i | 0.661559 | + | 0.749893i | \(0.269895\pi\) | ||||
−0.661559 | + | 0.749893i | \(0.730105\pi\) | |||||||
\(354\) | −241.988 | −0.683581 | ||||||||
\(355\) | − | 57.5425i | − | 0.162092i | ||||||
\(356\) | 137.184i | 0.385349i | ||||||||
\(357\) | −77.5211 | + | 143.146i | −0.217146 | + | 0.400969i | ||||
\(358\) | −77.0351 | −0.215182 | ||||||||
\(359\) | 64.2261 | 0.178903 | 0.0894514 | − | 0.995991i | \(-0.471489\pi\) | ||||
0.0894514 | + | 0.995991i | \(0.471489\pi\) | |||||||
\(360\) | − | 58.2145i | − | 0.161707i | ||||||
\(361\) | 171.940 | 0.476289 | ||||||||
\(362\) | − | 30.6377i | − | 0.0846346i | ||||||
\(363\) | − | 290.991i | − | 0.801627i | ||||||
\(364\) | 107.422 | + | 58.1747i | 0.295115 | + | 0.159821i | ||||
\(365\) | −167.850 | −0.459863 | ||||||||
\(366\) | −44.4411 | −0.121424 | ||||||||
\(367\) | − | 10.8172i | − | 0.0294747i | −0.999891 | − | 0.0147373i | \(-0.995309\pi\) | ||
0.999891 | − | 0.0147373i | \(-0.00469121\pi\) | |||||||
\(368\) | 175.882 | 0.477940 | ||||||||
\(369\) | 119.217i | 0.323082i | ||||||||
\(370\) | 264.984i | 0.716172i | ||||||||
\(371\) | −75.0033 | + | 138.497i | −0.202165 | + | 0.373306i | ||||
\(372\) | 12.4813 | 0.0335519 | ||||||||
\(373\) | 532.850 | 1.42855 | 0.714276 | − | 0.699864i | \(-0.246756\pi\) | ||||
0.714276 | + | 0.699864i | \(0.246756\pi\) | |||||||
\(374\) | − | 390.803i | − | 1.04493i | ||||||
\(375\) | −19.3649 | −0.0516398 | ||||||||
\(376\) | 348.326i | 0.926398i | ||||||||
\(377\) | 525.551i | 1.39403i | ||||||||
\(378\) | 54.7613 | + | 29.6561i | 0.144871 | + | 0.0784554i | ||||
\(379\) | 516.003 | 1.36149 | 0.680743 | − | 0.732523i | \(-0.261657\pi\) | ||||
0.680743 | + | 0.732523i | \(0.261657\pi\) | |||||||
\(380\) | 32.8539 | 0.0864578 | ||||||||
\(381\) | 103.700i | 0.272178i | ||||||||
\(382\) | −305.299 | −0.799213 | ||||||||
\(383\) | 415.069i | 1.08373i | 0.840465 | + | 0.541866i | \(0.182282\pi\) | ||||
−0.840465 | + | 0.541866i | \(0.817718\pi\) | |||||||
\(384\) | 94.8391i | 0.246977i | ||||||||
\(385\) | −233.985 | − | 126.715i | −0.607754 | − | 0.329131i | ||||
\(386\) | 575.765 | 1.49162 | ||||||||
\(387\) | −129.663 | −0.335046 | ||||||||
\(388\) | 170.381i | 0.439127i | ||||||||
\(389\) | 54.8032 | 0.140882 | 0.0704411 | − | 0.997516i | \(-0.477559\pi\) | ||||
0.0704411 | + | 0.997516i | \(0.477559\pi\) | |||||||
\(390\) | − | 108.299i | − | 0.277689i | ||||||
\(391\) | − | 223.122i | − | 0.570645i | ||||||
\(392\) | −232.368 | − | 356.123i | −0.592775 | − | 0.908477i | ||||
\(393\) | −289.023 | −0.735428 | ||||||||
\(394\) | −84.2514 | −0.213836 | ||||||||
\(395\) | 178.993i | 0.453146i | ||||||||
\(396\) | 54.4974 | 0.137620 | ||||||||
\(397\) | 19.9434i | 0.0502352i | 0.999685 | + | 0.0251176i | \(0.00799602\pi\) | ||||
−0.999685 | + | 0.0251176i | \(0.992004\pi\) | |||||||
\(398\) | − | 294.127i | − | 0.739013i | ||||||
\(399\) | −79.3877 | + | 146.593i | −0.198967 | + | 0.367400i | ||||
\(400\) | 52.9194 | 0.132298 | ||||||||
\(401\) | −239.505 | −0.597269 | −0.298634 | − | 0.954368i | \(-0.596531\pi\) | ||||
−0.298634 | + | 0.954368i | \(0.596531\pi\) | |||||||
\(402\) | 213.776i | 0.531781i | ||||||||
\(403\) | 110.137 | 0.273293 | ||||||||
\(404\) | 25.7931i | 0.0638444i | ||||||||
\(405\) | 20.1246i | 0.0496904i | ||||||||
\(406\) | 183.658 | − | 339.132i | 0.452359 | − | 0.835300i | ||||
\(407\) | −1176.65 | −2.89102 | ||||||||
\(408\) | 201.814 | 0.494643 | ||||||||
\(409\) | − | 663.541i | − | 1.62235i | −0.584804 | − | 0.811175i | \(-0.698829\pi\) | ||
0.584804 | − | 0.811175i | \(-0.301171\pi\) | |||||||
\(410\) | −152.140 | −0.371072 | ||||||||
\(411\) | − | 218.480i | − | 0.531581i | ||||||
\(412\) | − | 93.3363i | − | 0.226544i | ||||||
\(413\) | −502.278 | − | 272.010i | −1.21617 | − | 0.658621i | ||||
\(414\) | −85.3566 | −0.206175 | ||||||||
\(415\) | 228.330 | 0.550194 | ||||||||
\(416\) | − | 270.969i | − | 0.651368i | ||||||
\(417\) | 366.588 | 0.879108 | ||||||||
\(418\) | − | 400.213i | − | 0.957447i | ||||||
\(419\) | 110.648i | 0.264077i | 0.991245 | + | 0.132039i | \(0.0421523\pi\) | ||||
−0.991245 | + | 0.132039i | \(0.957848\pi\) | |||||||
\(420\) | 13.7956 | − | 25.4742i | 0.0328467 | − | 0.0606528i | ||||
\(421\) | −521.325 | −1.23830 | −0.619151 | − | 0.785272i | \(-0.712523\pi\) | ||||
−0.619151 | + | 0.785272i | \(0.712523\pi\) | |||||||
\(422\) | 8.72264 | 0.0206698 | ||||||||
\(423\) | − | 120.415i | − | 0.284670i | ||||||
\(424\) | 195.260 | 0.460518 | ||||||||
\(425\) | − | 67.1330i | − | 0.157960i | ||||||
\(426\) | − | 76.3140i | − | 0.179141i | ||||||
\(427\) | −92.2435 | − | 49.9548i | −0.216027 | − | 0.116990i | ||||
\(428\) | −179.903 | −0.420334 | ||||||||
\(429\) | 480.895 | 1.12097 | ||||||||
\(430\) | − | 165.470i | − | 0.384814i | ||||||
\(431\) | 573.019 | 1.32951 | 0.664755 | − | 0.747062i | \(-0.268536\pi\) | ||||
0.664755 | + | 0.747062i | \(0.268536\pi\) | |||||||
\(432\) | − | 54.9954i | − | 0.127304i | ||||||
\(433\) | − | 429.740i | − | 0.992472i | −0.868188 | − | 0.496236i | \(-0.834715\pi\) | ||
0.868188 | − | 0.496236i | \(-0.165285\pi\) | |||||||
\(434\) | −71.0702 | − | 38.4883i | −0.163756 | − | 0.0886827i | ||||
\(435\) | 124.630 | 0.286506 | ||||||||
\(436\) | 166.237 | 0.381279 | ||||||||
\(437\) | − | 228.495i | − | 0.522871i | ||||||
\(438\) | −222.606 | −0.508232 | ||||||||
\(439\) | 83.0494i | 0.189179i | 0.995516 | + | 0.0945893i | \(0.0301538\pi\) | ||||
−0.995516 | + | 0.0945893i | \(0.969846\pi\) | |||||||
\(440\) | 329.884i | 0.749737i | ||||||||
\(441\) | 80.3290 | + | 123.111i | 0.182152 | + | 0.279163i | ||||
\(442\) | 375.443 | 0.849419 | ||||||||
\(443\) | −410.010 | −0.925530 | −0.462765 | − | 0.886481i | \(-0.653143\pi\) | ||||
−0.462765 | + | 0.886481i | \(0.653143\pi\) | |||||||
\(444\) | − | 128.103i | − | 0.288520i | ||||||
\(445\) | 287.069 | 0.645099 | ||||||||
\(446\) | 530.876i | 1.19031i | ||||||||
\(447\) | 111.167i | 0.248696i | ||||||||
\(448\) | −235.815 | + | 435.442i | −0.526373 | + | 0.971969i | ||||
\(449\) | −205.948 | −0.458682 | −0.229341 | − | 0.973346i | \(-0.573657\pi\) | ||||
−0.229341 | + | 0.973346i | \(0.573657\pi\) | |||||||
\(450\) | −25.6821 | −0.0570714 | ||||||||
\(451\) | − | 675.569i | − | 1.49793i | ||||||
\(452\) | 22.4363 | 0.0496378 | ||||||||
\(453\) | − | 192.111i | − | 0.424086i | ||||||
\(454\) | 185.866i | 0.409397i | ||||||||
\(455\) | 121.735 | − | 224.789i | 0.267550 | − | 0.494041i | ||||
\(456\) | 206.674 | 0.453232 | ||||||||
\(457\) | −640.868 | −1.40234 | −0.701169 | − | 0.712995i | \(-0.747338\pi\) | ||||
−0.701169 | + | 0.712995i | \(0.747338\pi\) | |||||||
\(458\) | − | 404.893i | − | 0.884046i | ||||||
\(459\) | −69.7667 | −0.151997 | ||||||||
\(460\) | 39.7068i | 0.0863190i | ||||||||
\(461\) | 166.085i | 0.360272i | 0.983642 | + | 0.180136i | \(0.0576538\pi\) | ||||
−0.983642 | + | 0.180136i | \(0.942346\pi\) | |||||||
\(462\) | −310.316 | − | 168.052i | −0.671679 | − | 0.363750i | ||||
\(463\) | −10.4409 | −0.0225505 | −0.0112753 | − | 0.999936i | \(-0.503589\pi\) | ||||
−0.0112753 | + | 0.999936i | \(0.503589\pi\) | |||||||
\(464\) | −340.582 | −0.734013 | ||||||||
\(465\) | − | 26.1181i | − | 0.0561680i | ||||||
\(466\) | −259.029 | −0.555857 | ||||||||
\(467\) | − | 269.736i | − | 0.577592i | −0.957391 | − | 0.288796i | \(-0.906745\pi\) | ||
0.957391 | − | 0.288796i | \(-0.0932550\pi\) | |||||||
\(468\) | 52.3555i | 0.111871i | ||||||||
\(469\) | −240.298 | + | 443.721i | −0.512364 | + | 0.946100i | ||||
\(470\) | 153.669 | 0.326954 | ||||||||
\(471\) | −503.077 | −1.06810 | ||||||||
\(472\) | 708.138i | 1.50029i | ||||||||
\(473\) | 734.761 | 1.55341 | ||||||||
\(474\) | 237.384i | 0.500809i | ||||||||
\(475\) | − | 68.7495i | − | 0.144736i | ||||||
\(476\) | 88.3123 | + | 47.8258i | 0.185530 | + | 0.100474i | ||||
\(477\) | −67.5007 | −0.141511 | ||||||||
\(478\) | −82.6889 | −0.172989 | ||||||||
\(479\) | − | 649.820i | − | 1.35662i | −0.734777 | − | 0.678309i | \(-0.762713\pi\) | ||
0.734777 | − | 0.678309i | \(-0.237287\pi\) | |||||||
\(480\) | −64.2580 | −0.133871 | ||||||||
\(481\) | − | 1130.40i | − | 2.35011i | ||||||
\(482\) | − | 395.051i | − | 0.819608i | ||||||
\(483\) | −177.169 | − | 95.9467i | −0.366810 | − | 0.198647i | ||||
\(484\) | −179.524 | −0.370917 | ||||||||
\(485\) | 356.537 | 0.735127 | ||||||||
\(486\) | 26.6897i | 0.0549170i | ||||||||
\(487\) | 597.640 | 1.22719 | 0.613593 | − | 0.789622i | \(-0.289723\pi\) | ||||
0.613593 | + | 0.789622i | \(0.289723\pi\) | |||||||
\(488\) | 130.050i | 0.266495i | ||||||||
\(489\) | 93.2811i | 0.190759i | ||||||||
\(490\) | −157.108 | + | 102.512i | −0.320629 | + | 0.209209i | ||||
\(491\) | −107.625 | −0.219195 | −0.109598 | − | 0.993976i | \(-0.534956\pi\) | ||||
−0.109598 | + | 0.993976i | \(0.534956\pi\) | |||||||
\(492\) | 73.5498 | 0.149491 | ||||||||
\(493\) | 432.059i | 0.876388i | ||||||||
\(494\) | 384.483 | 0.778306 | ||||||||
\(495\) | − | 114.040i | − | 0.230384i | ||||||
\(496\) | 71.3741i | 0.143899i | ||||||||
\(497\) | 85.7821 | − | 158.400i | 0.172600 | − | 0.318713i | ||||
\(498\) | 302.816 | 0.608065 | ||||||||
\(499\) | −420.611 | −0.842908 | −0.421454 | − | 0.906850i | \(-0.638480\pi\) | ||||
−0.421454 | + | 0.906850i | \(0.638480\pi\) | |||||||
\(500\) | 11.9470i | 0.0238940i | ||||||||
\(501\) | 72.3870 | 0.144485 | ||||||||
\(502\) | 148.410i | 0.295638i | ||||||||
\(503\) | − | 837.716i | − | 1.66544i | −0.553694 | − | 0.832720i | \(-0.686782\pi\) | ||
0.553694 | − | 0.832720i | \(-0.313218\pi\) | |||||||
\(504\) | 86.7840 | − | 160.250i | 0.172190 | − | 0.317956i | ||||
\(505\) | 53.9742 | 0.106880 | ||||||||
\(506\) | 483.691 | 0.955910 | ||||||||
\(507\) | 169.278i | 0.333881i | ||||||||
\(508\) | 63.9766 | 0.125938 | ||||||||
\(509\) | 511.304i | 1.00453i | 0.864715 | + | 0.502264i | \(0.167499\pi\) | ||||
−0.864715 | + | 0.502264i | \(0.832501\pi\) | |||||||
\(510\) | − | 89.0331i | − | 0.174575i | ||||||
\(511\) | −462.049 | − | 250.224i | −0.904205 | − | 0.489675i | ||||
\(512\) | 542.993 | 1.06053 | ||||||||
\(513\) | −71.4466 | −0.139272 | ||||||||
\(514\) | 241.600i | 0.470038i | ||||||||
\(515\) | −195.314 | −0.379250 | ||||||||
\(516\) | 79.9942i | 0.155027i | ||||||||
\(517\) | 682.358i | 1.31984i | ||||||||
\(518\) | −395.027 | + | 729.434i | −0.762601 | + | 1.40817i | ||||
\(519\) | −225.762 | −0.434995 | ||||||||
\(520\) | −316.919 | −0.609459 | ||||||||
\(521\) | 958.401i | 1.83954i | 0.392455 | + | 0.919771i | \(0.371626\pi\) | ||||
−0.392455 | + | 0.919771i | \(0.628374\pi\) | |||||||
\(522\) | 165.287 | 0.316641 | ||||||||
\(523\) | − | 152.860i | − | 0.292275i | −0.989264 | − | 0.146138i | \(-0.953316\pi\) | ||
0.989264 | − | 0.146138i | \(-0.0466843\pi\) | |||||||
\(524\) | 178.310i | 0.340286i | ||||||||
\(525\) | −53.3068 | − | 28.8685i | −0.101537 | − | 0.0549875i | ||||
\(526\) | −65.2157 | −0.123984 | ||||||||
\(527\) | 90.5445 | 0.171811 | ||||||||
\(528\) | 311.643i | 0.590232i | ||||||||
\(529\) | −252.845 | −0.477968 | ||||||||
\(530\) | − | 86.1414i | − | 0.162531i | ||||||
\(531\) | − | 244.801i | − | 0.461020i | ||||||
\(532\) | 90.4387 | + | 48.9774i | 0.169998 | + | 0.0920627i | ||||
\(533\) | 649.017 | 1.21767 | ||||||||
\(534\) | 380.716 | 0.712952 | ||||||||
\(535\) | 376.461i | 0.703666i | ||||||||
\(536\) | 625.581 | 1.16713 | ||||||||
\(537\) | − | 77.9309i | − | 0.145123i | ||||||
\(538\) | 777.689i | 1.44552i | ||||||||
\(539\) | −455.200 | − | 697.632i | −0.844527 | − | 1.29431i | ||||
\(540\) | 12.4157 | 0.0229920 | ||||||||
\(541\) | −285.016 | −0.526832 | −0.263416 | − | 0.964682i | \(-0.584849\pi\) | ||||
−0.263416 | + | 0.964682i | \(0.584849\pi\) | |||||||
\(542\) | − | 134.762i | − | 0.248639i | ||||||
\(543\) | 30.9940 | 0.0570791 | ||||||||
\(544\) | − | 222.766i | − | 0.409495i | ||||||
\(545\) | − | 347.865i | − | 0.638285i | ||||||
\(546\) | 161.447 | − | 298.119i | 0.295691 | − | 0.546006i | ||||
\(547\) | −195.330 | −0.357092 | −0.178546 | − | 0.983932i | \(-0.557139\pi\) | ||||
−0.178546 | + | 0.983932i | \(0.557139\pi\) | |||||||
\(548\) | −134.789 | −0.245965 | ||||||||
\(549\) | − | 44.9578i | − | 0.0818904i | ||||||
\(550\) | 145.533 | 0.264605 | ||||||||
\(551\) | 442.463i | 0.803017i | ||||||||
\(552\) | 249.783i | 0.452505i | ||||||||
\(553\) | −266.835 | + | 492.722i | −0.482523 | + | 0.890999i | ||||
\(554\) | 146.113 | 0.263743 | ||||||||
\(555\) | −268.065 | −0.483000 | ||||||||
\(556\) | − | 226.163i | − | 0.406767i | ||||||
\(557\) | −27.9390 | −0.0501598 | −0.0250799 | − | 0.999685i | \(-0.507984\pi\) | ||||
−0.0250799 | + | 0.999685i | \(0.507984\pi\) | |||||||
\(558\) | − | 34.6383i | − | 0.0620759i | ||||||
\(559\) | 705.883i | 1.26276i | ||||||||
\(560\) | 145.674 | + | 78.8901i | 0.260132 | + | 0.140875i | ||||
\(561\) | 395.347 | 0.704719 | ||||||||
\(562\) | −286.571 | −0.509912 | ||||||||
\(563\) | − | 459.585i | − | 0.816314i | −0.912912 | − | 0.408157i | \(-0.866172\pi\) | ||
0.912912 | − | 0.408157i | \(-0.133828\pi\) | |||||||
\(564\) | −74.2889 | −0.131718 | ||||||||
\(565\) | − | 46.9497i | − | 0.0830968i | ||||||
\(566\) | 256.120i | 0.452509i | ||||||||
\(567\) | −30.0010 | + | 55.3980i | −0.0529118 | + | 0.0977037i | ||||
\(568\) | −223.321 | −0.393170 | ||||||||
\(569\) | −635.353 | −1.11661 | −0.558306 | − | 0.829635i | \(-0.688549\pi\) | ||||
−0.558306 | + | 0.829635i | \(0.688549\pi\) | |||||||
\(570\) | − | 91.1769i | − | 0.159959i | ||||||
\(571\) | 205.282 | 0.359513 | 0.179757 | − | 0.983711i | \(-0.442469\pi\) | ||||
0.179757 | + | 0.983711i | \(0.442469\pi\) | |||||||
\(572\) | − | 296.683i | − | 0.518676i | ||||||
\(573\) | − | 308.849i | − | 0.539004i | ||||||
\(574\) | −418.803 | − | 226.804i | −0.729621 | − | 0.395129i | ||||
\(575\) | 83.0895 | 0.144504 | ||||||||
\(576\) | −212.227 | −0.368449 | ||||||||
\(577\) | − | 185.464i | − | 0.321429i | −0.987001 | − | 0.160714i | \(-0.948620\pi\) | ||
0.987001 | − | 0.160714i | \(-0.0513798\pi\) | |||||||
\(578\) | −186.155 | −0.322067 | ||||||||
\(579\) | 582.460i | 1.00598i | ||||||||
\(580\) | − | 76.8892i | − | 0.132568i | ||||||
\(581\) | 628.537 | + | 340.386i | 1.08182 | + | 0.585862i | ||||
\(582\) | 472.846 | 0.812450 | ||||||||
\(583\) | 382.506 | 0.656100 | ||||||||
\(584\) | 651.420i | 1.11545i | ||||||||
\(585\) | 109.558 | 0.187279 | ||||||||
\(586\) | − | 249.638i | − | 0.426004i | ||||||
\(587\) | − | 673.958i | − | 1.14814i | −0.818806 | − | 0.574070i | \(-0.805364\pi\) | ||
0.818806 | − | 0.574070i | \(-0.194636\pi\) | |||||||
\(588\) | 75.9519 | − | 49.5581i | 0.129170 | − | 0.0842825i | ||||
\(589\) | 92.7247 | 0.157427 | ||||||||
\(590\) | 312.405 | 0.529499 | ||||||||
\(591\) | − | 85.2311i | − | 0.144215i | ||||||
\(592\) | 732.553 | 1.23742 | ||||||||
\(593\) | − | 0.486694i | − | 0.000820731i | −1.00000 | 0.000410366i | \(-0.999869\pi\) | |||
1.00000 | 0.000410366i | \(-0.000130623\pi\) | ||||||||
\(594\) | − | 151.242i | − | 0.254617i | ||||||
\(595\) | 100.079 | − | 184.800i | 0.168201 | − | 0.310589i | ||||
\(596\) | 68.5835 | 0.115073 | ||||||||
\(597\) | 297.547 | 0.498404 | ||||||||
\(598\) | 464.680i | 0.777057i | ||||||||
\(599\) | 580.285 | 0.968756 | 0.484378 | − | 0.874859i | \(-0.339046\pi\) | ||||
0.484378 | + | 0.874859i | \(0.339046\pi\) | |||||||
\(600\) | 75.1546i | 0.125258i | ||||||||
\(601\) | 781.851i | 1.30092i | 0.759542 | + | 0.650459i | \(0.225423\pi\) | ||||
−0.759542 | + | 0.650459i | \(0.774577\pi\) | |||||||
\(602\) | 246.676 | − | 455.498i | 0.409761 | − | 0.756641i | ||||
\(603\) | −216.262 | −0.358643 | ||||||||
\(604\) | −118.521 | −0.196226 | ||||||||
\(605\) | 375.667i | 0.620938i | ||||||||
\(606\) | 71.5816 | 0.118121 | ||||||||
\(607\) | − | 907.211i | − | 1.49458i | −0.664498 | − | 0.747290i | \(-0.731354\pi\) | ||
0.664498 | − | 0.747290i | \(-0.268646\pi\) | |||||||
\(608\) | − | 228.129i | − | 0.375213i | ||||||
\(609\) | 343.075 | + | 185.794i | 0.563342 | + | 0.305080i | ||||
\(610\) | 57.3732 | 0.0940544 | ||||||||
\(611\) | −655.539 | −1.07289 | ||||||||
\(612\) | 43.0418i | 0.0703298i | ||||||||
\(613\) | −911.642 | −1.48718 | −0.743590 | − | 0.668636i | \(-0.766879\pi\) | ||||
−0.743590 | + | 0.668636i | \(0.766879\pi\) | |||||||
\(614\) | 352.006i | 0.573299i | ||||||||
\(615\) | − | 153.909i | − | 0.250258i | ||||||
\(616\) | −491.779 | + | 908.089i | −0.798342 | + | 1.47417i | ||||
\(617\) | 637.918 | 1.03390 | 0.516951 | − | 0.856015i | \(-0.327067\pi\) | ||||
0.516951 | + | 0.856015i | \(0.327067\pi\) | |||||||
\(618\) | −259.029 | −0.419140 | ||||||||
\(619\) | − | 862.604i | − | 1.39354i | −0.717292 | − | 0.696772i | \(-0.754619\pi\) | ||
0.717292 | − | 0.696772i | \(-0.245381\pi\) | |||||||
\(620\) | −16.1133 | −0.0259892 | ||||||||
\(621\) | − | 86.3492i | − | 0.139049i | ||||||
\(622\) | − | 726.604i | − | 1.16817i | ||||||
\(623\) | 790.229 | + | 427.951i | 1.26843 | + | 0.686920i | ||||
\(624\) | −299.394 | −0.479798 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 622.369i | − | 0.994200i | ||||||
\(627\) | 404.866 | 0.645720 | ||||||||
\(628\) | 310.368i | 0.494216i | ||||||||
\(629\) | − | 929.310i | − | 1.47744i | ||||||
\(630\) | −70.6965 | − | 38.2859i | −0.112217 | − | 0.0607713i | ||||
\(631\) | −601.057 | −0.952547 | −0.476273 | − | 0.879297i | \(-0.658013\pi\) | ||||
−0.476273 | + | 0.879297i | \(0.658013\pi\) | |||||||
\(632\) | 694.665 | 1.09915 | ||||||||
\(633\) | 8.82406i | 0.0139401i | ||||||||
\(634\) | −755.752 | −1.19204 | ||||||||
\(635\) | − | 133.876i | − | 0.210828i | ||||||
\(636\) | 41.6438i | 0.0654777i | ||||||||
\(637\) | 670.213 | − | 437.309i | 1.05214 | − | 0.686514i | ||||
\(638\) | −936.631 | −1.46807 | ||||||||
\(639\) | 77.2014 | 0.120816 | ||||||||
\(640\) | − | 122.437i | − | 0.191307i | ||||||
\(641\) | −884.432 | −1.37977 | −0.689885 | − | 0.723919i | \(-0.742339\pi\) | ||||
−0.689885 | + | 0.723919i | \(0.742339\pi\) | |||||||
\(642\) | 499.270i | 0.777680i | ||||||||
\(643\) | 385.448i | 0.599453i | 0.954025 | + | 0.299726i | \(0.0968954\pi\) | ||||
−0.954025 | + | 0.299726i | \(0.903105\pi\) | |||||||
\(644\) | −59.1933 | + | 109.303i | −0.0919150 | + | 0.169725i | ||||
\(645\) | 167.394 | 0.259526 | ||||||||
\(646\) | 316.086 | 0.489298 | ||||||||
\(647\) | 1096.93i | 1.69540i | 0.530473 | + | 0.847702i | \(0.322014\pi\) | ||||
−0.530473 | + | 0.847702i | \(0.677986\pi\) | |||||||
\(648\) | 78.1030 | 0.120529 | ||||||||
\(649\) | 1387.22i | 2.13747i | ||||||||
\(650\) | 139.813i | 0.215097i | ||||||||
\(651\) | 38.9358 | − | 71.8966i | 0.0598093 | − | 0.110440i | ||||
\(652\) | 57.5488 | 0.0882650 | ||||||||
\(653\) | −556.888 | −0.852814 | −0.426407 | − | 0.904531i | \(-0.640221\pi\) | ||||
−0.426407 | + | 0.904531i | \(0.640221\pi\) | |||||||
\(654\) | − | 461.345i | − | 0.705421i | ||||||
\(655\) | 373.127 | 0.569660 | ||||||||
\(656\) | 420.594i | 0.641149i | ||||||||
\(657\) | − | 225.194i | − | 0.342761i | ||||||
\(658\) | 423.011 | + | 229.083i | 0.642874 | + | 0.348151i | ||||
\(659\) | −715.578 | −1.08585 | −0.542927 | − | 0.839780i | \(-0.682684\pi\) | ||||
−0.542927 | + | 0.839780i | \(0.682684\pi\) | |||||||
\(660\) | −70.3559 | −0.106600 | ||||||||
\(661\) | 280.365i | 0.424152i | 0.977253 | + | 0.212076i | \(0.0680225\pi\) | ||||
−0.977253 | + | 0.212076i | \(0.931978\pi\) | |||||||
\(662\) | −872.040 | −1.31728 | ||||||||
\(663\) | 379.809i | 0.572864i | ||||||||
\(664\) | − | 886.143i | − | 1.33455i | ||||||
\(665\) | 102.489 | − | 189.250i | 0.154119 | − | 0.284587i | ||||
\(666\) | −355.513 | −0.533803 | ||||||||
\(667\) | −534.753 | −0.801729 | ||||||||
\(668\) | − | 44.6584i | − | 0.0668539i | ||||||
\(669\) | −537.050 | −0.802765 | ||||||||
\(670\) | − | 275.983i | − | 0.411915i | ||||||
\(671\) | 254.763i | 0.379676i | ||||||||
\(672\) | −176.886 | − | 95.7933i | −0.263224 | − | 0.142550i | ||||
\(673\) | 1067.08 | 1.58556 | 0.792781 | − | 0.609506i | \(-0.208632\pi\) | ||||
0.792781 | + | 0.609506i | \(0.208632\pi\) | |||||||
\(674\) | −757.721 | −1.12421 | ||||||||
\(675\) | − | 25.9808i | − | 0.0384900i | ||||||
\(676\) | 104.434 | 0.154488 | ||||||||
\(677\) | − | 313.071i | − | 0.462439i | −0.972902 | − | 0.231219i | \(-0.925728\pi\) | ||
0.972902 | − | 0.231219i | \(-0.0742715\pi\) | |||||||
\(678\) | − | 62.2656i | − | 0.0918371i | ||||||
\(679\) | 981.456 | + | 531.511i | 1.44544 | + | 0.782785i | ||||
\(680\) | −260.541 | −0.383149 | ||||||||
\(681\) | −188.028 | −0.276105 | ||||||||
\(682\) | 196.285i | 0.287808i | ||||||||
\(683\) | 505.514 | 0.740138 | 0.370069 | − | 0.929004i | \(-0.379334\pi\) | ||||
0.370069 | + | 0.929004i | \(0.379334\pi\) | |||||||
\(684\) | 44.0782i | 0.0644418i | ||||||||
\(685\) | 282.056i | 0.411761i | ||||||||
\(686\) | −585.301 | + | 47.9795i | −0.853209 | + | 0.0699409i | ||||
\(687\) | 409.601 | 0.596217 | ||||||||
\(688\) | −457.446 | −0.664892 | ||||||||
\(689\) | 367.473i | 0.533342i | ||||||||
\(690\) | 110.195 | 0.159703 | ||||||||
\(691\) | − | 276.726i | − | 0.400472i | −0.979748 | − | 0.200236i | \(-0.935829\pi\) | ||
0.979748 | − | 0.200236i | \(-0.0641709\pi\) | |||||||
\(692\) | 139.282i | 0.201274i | ||||||||
\(693\) | 170.007 | − | 313.924i | 0.245320 | − | 0.452993i | ||||
\(694\) | 845.393 | 1.21815 | ||||||||
\(695\) | −473.263 | −0.680954 | ||||||||
\(696\) | − | 483.685i | − | 0.694950i | ||||||
\(697\) | 533.561 | 0.765511 | ||||||||
\(698\) | − | 555.522i | − | 0.795877i | ||||||
\(699\) | − | 262.041i | − | 0.374880i | ||||||
\(700\) | −17.8101 | + | 32.8870i | −0.0254430 | + | 0.0469815i | ||||
\(701\) | 854.178 | 1.21851 | 0.609256 | − | 0.792973i | \(-0.291468\pi\) | ||||
0.609256 | + | 0.792973i | \(0.291468\pi\) | |||||||
\(702\) | 145.298 | 0.206977 | ||||||||
\(703\) | − | 951.687i | − | 1.35375i | ||||||
\(704\) | 1202.63 | 1.70828 | ||||||||
\(705\) | 155.455i | 0.220504i | ||||||||
\(706\) | − | 906.450i | − | 1.28392i | ||||||
\(707\) | 148.577 | + | 80.4626i | 0.210152 | + | 0.113809i | ||||
\(708\) | −151.028 | −0.213316 | ||||||||
\(709\) | −452.996 | −0.638922 | −0.319461 | − | 0.947599i | \(-0.603502\pi\) | ||||
−0.319461 | + | 0.947599i | \(0.603502\pi\) | |||||||
\(710\) | 98.5210i | 0.138762i | ||||||||
\(711\) | −240.144 | −0.337755 | ||||||||
\(712\) | − | 1114.11i | − | 1.56476i | ||||||
\(713\) | 112.066i | 0.157175i | ||||||||
\(714\) | 132.727 | − | 245.086i | 0.185892 | − | 0.343258i | ||||
\(715\) | −620.833 | −0.868297 | ||||||||
\(716\) | −48.0786 | −0.0671489 | ||||||||
\(717\) | − | 83.6504i | − | 0.116667i | ||||||
\(718\) | −109.964 | −0.153153 | ||||||||
\(719\) | − | 840.685i | − | 1.16924i | −0.811306 | − | 0.584621i | \(-0.801243\pi\) | ||
0.811306 | − | 0.584621i | \(-0.198757\pi\) | |||||||
\(720\) | 70.9988i | 0.0986095i | ||||||||
\(721\) | −537.650 | − | 291.166i | −0.745700 | − | 0.403836i | ||||
\(722\) | −294.386 | −0.407737 | ||||||||
\(723\) | 399.645 | 0.552759 | ||||||||
\(724\) | − | 19.1214i | − | 0.0264108i | ||||||
\(725\) | −160.897 | −0.221926 | ||||||||
\(726\) | 498.217i | 0.686250i | ||||||||
\(727\) | 1339.58i | 1.84262i | 0.388829 | + | 0.921310i | \(0.372880\pi\) | ||||
−0.388829 | + | 0.921310i | \(0.627120\pi\) | |||||||
\(728\) | −872.398 | − | 472.450i | −1.19835 | − | 0.648970i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 287.383 | 0.393675 | ||||||||
\(731\) | 580.311i | 0.793860i | ||||||||
\(732\) | −27.7363 | −0.0378911 | ||||||||
\(733\) | − | 536.275i | − | 0.731616i | −0.930690 | − | 0.365808i | \(-0.880793\pi\) | ||
0.930690 | − | 0.365808i | \(-0.119207\pi\) | |||||||
\(734\) | 18.5206i | 0.0252324i | ||||||||
\(735\) | −103.704 | − | 158.935i | −0.141094 | − | 0.216238i | ||||
\(736\) | 275.713 | 0.374611 | ||||||||
\(737\) | 1225.49 | 1.66281 | ||||||||
\(738\) | − | 204.117i | − | 0.276581i | ||||||
\(739\) | −898.552 | −1.21590 | −0.607951 | − | 0.793974i | \(-0.708008\pi\) | ||||
−0.607951 | + | 0.793974i | \(0.708008\pi\) | |||||||
\(740\) | 165.380i | 0.223486i | ||||||||
\(741\) | 388.954i | 0.524904i | ||||||||
\(742\) | 128.416 | − | 237.126i | 0.173068 | − | 0.319576i | ||||
\(743\) | 532.720 | 0.716985 | 0.358493 | − | 0.933533i | \(-0.383291\pi\) | ||||
0.358493 | + | 0.933533i | \(0.383291\pi\) | |||||||
\(744\) | −101.364 | −0.136241 | ||||||||
\(745\) | − | 143.516i | − | 0.192639i | ||||||
\(746\) | −912.314 | −1.22294 | ||||||||
\(747\) | 306.337i | 0.410090i | ||||||||
\(748\) | − | 243.905i | − | 0.326076i | ||||||
\(749\) | −561.214 | + | 1036.30i | −0.749284 | + | 1.38358i | ||||
\(750\) | 33.1555 | 0.0442073 | ||||||||
\(751\) | 342.085 | 0.455506 | 0.227753 | − | 0.973719i | \(-0.426862\pi\) | ||||
0.227753 | + | 0.973719i | \(0.426862\pi\) | |||||||
\(752\) | − | 424.820i | − | 0.564921i | ||||||
\(753\) | −150.136 | −0.199384 | ||||||||
\(754\) | − | 899.818i | − | 1.19339i | ||||||
\(755\) | 248.014i | 0.328495i | ||||||||
\(756\) | 34.1772 | + | 18.5088i | 0.0452080 | + | 0.0244825i | ||||
\(757\) | 405.961 | 0.536276 | 0.268138 | − | 0.963381i | \(-0.413592\pi\) | ||||
0.268138 | + | 0.963381i | \(0.413592\pi\) | |||||||
\(758\) | −883.470 | −1.16553 | ||||||||
\(759\) | 489.315i | 0.644684i | ||||||||
\(760\) | −266.815 | −0.351072 | ||||||||
\(761\) | − | 577.340i | − | 0.758660i | −0.925261 | − | 0.379330i | \(-0.876155\pi\) | ||
0.925261 | − | 0.379330i | \(-0.123845\pi\) | |||||||
\(762\) | − | 177.549i | − | 0.233004i | ||||||
\(763\) | 518.584 | − | 957.586i | 0.679664 | − | 1.25503i | ||||
\(764\) | −190.541 | −0.249400 | ||||||||
\(765\) | 90.0684 | 0.117737 | ||||||||
\(766\) | − | 710.657i | − | 0.927751i | ||||||
\(767\) | −1332.69 | −1.73754 | ||||||||
\(768\) | 327.739i | 0.426743i | ||||||||
\(769\) | 828.522i | 1.07740i | 0.842497 | + | 0.538701i | \(0.181085\pi\) | ||||
−0.842497 | + | 0.538701i | \(0.818915\pi\) | |||||||
\(770\) | 400.616 | + | 216.955i | 0.520280 | + | 0.281760i | ||||
\(771\) | −244.409 | −0.317003 | ||||||||
\(772\) | 359.342 | 0.465469 | ||||||||
\(773\) | 438.991i | 0.567906i | 0.958838 | + | 0.283953i | \(0.0916460\pi\) | ||||
−0.958838 | + | 0.283953i | \(0.908354\pi\) | |||||||
\(774\) | 222.001 | 0.286824 | ||||||||
\(775\) | 33.7183i | 0.0435075i | ||||||||
\(776\) | − | 1383.71i | − | 1.78313i | ||||||
\(777\) | −737.916 | − | 399.621i | −0.949699 | − | 0.514312i | ||||
\(778\) | −93.8308 | −0.120605 | ||||||||
\(779\) | 546.408 | 0.701423 | ||||||||
\(780\) | − | 67.5906i | − | 0.0866547i | ||||||
\(781\) | −437.477 | −0.560150 | ||||||||
\(782\) | 382.017i | 0.488512i | ||||||||
\(783\) | 167.209i | 0.213549i | ||||||||
\(784\) | 283.397 | + | 434.330i | 0.361476 | + | 0.553992i | ||||
\(785\) | 649.469 | 0.827349 | ||||||||
\(786\) | 494.849 | 0.629579 | ||||||||
\(787\) | − | 285.209i | − | 0.362400i | −0.983446 | − | 0.181200i | \(-0.942002\pi\) | ||
0.983446 | − | 0.181200i | \(-0.0579982\pi\) | |||||||
\(788\) | −52.5824 | −0.0667289 | ||||||||
\(789\) | − | 65.9740i | − | 0.0836172i | ||||||
\(790\) | − | 306.461i | − | 0.387925i | ||||||
\(791\) | 69.9907 | − | 129.241i | 0.0884838 | − | 0.163389i | ||||
\(792\) | −442.586 | −0.558821 | ||||||||
\(793\) | −244.750 | −0.308638 | ||||||||
\(794\) | − | 34.1459i | − | 0.0430049i | ||||||
\(795\) | 87.1431 | 0.109614 | ||||||||
\(796\) | − | 183.569i | − | 0.230614i | ||||||
\(797\) | − | 1243.03i | − | 1.55964i | −0.626006 | − | 0.779818i | \(-0.715311\pi\) | ||
0.626006 | − | 0.779818i | \(-0.284689\pi\) | |||||||
\(798\) | 135.923 | − | 250.987i | 0.170330 | − | 0.314520i | ||||
\(799\) | −538.923 | −0.674497 | ||||||||
\(800\) | 82.9567 | 0.103696 | ||||||||
\(801\) | 385.143i | 0.480828i | ||||||||
\(802\) | 410.066 | 0.511304 | ||||||||
\(803\) | 1276.11i | 1.58918i | ||||||||
\(804\) | 133.420i | 0.165946i | ||||||||
\(805\) | 228.725 | + | 123.867i | 0.284130 | + | 0.153872i | ||||
\(806\) | −188.570 | −0.233958 | ||||||||
\(807\) | −786.732 | −0.974885 | ||||||||
\(808\) | − | 209.472i | − | 0.259248i | ||||||
\(809\) | −630.338 | −0.779157 | −0.389578 | − | 0.920993i | \(-0.627379\pi\) | ||||
−0.389578 | + | 0.920993i | \(0.627379\pi\) | |||||||
\(810\) | − | 34.4562i | − | 0.0425385i | ||||||
\(811\) | 1121.08i | 1.38234i | 0.722692 | + | 0.691170i | \(0.242905\pi\) | ||||
−0.722692 | + | 0.691170i | \(0.757095\pi\) | |||||||
\(812\) | 114.623 | − | 211.657i | 0.141162 | − | 0.260661i | ||||
\(813\) | 136.329 | 0.167687 | ||||||||
\(814\) | 2014.59 | 2.47492 | ||||||||
\(815\) | − | 120.425i | − | 0.147761i | ||||||
\(816\) | −246.134 | −0.301635 | ||||||||
\(817\) | 594.284i | 0.727398i | ||||||||
\(818\) | 1136.08i | 1.38885i | ||||||||
\(819\) | 301.586 | + | 163.325i | 0.368237 | + | 0.199420i | ||||
\(820\) | −94.9524 | −0.115796 | ||||||||
\(821\) | 544.285 | 0.662954 | 0.331477 | − | 0.943463i | \(-0.392453\pi\) | ||||
0.331477 | + | 0.943463i | \(0.392453\pi\) | |||||||
\(822\) | 374.069i | 0.455071i | ||||||||
\(823\) | 83.7611 | 0.101775 | 0.0508877 | − | 0.998704i | \(-0.483795\pi\) | ||||
0.0508877 | + | 0.998704i | \(0.483795\pi\) | |||||||
\(824\) | 758.006i | 0.919911i | ||||||||
\(825\) | 147.225i | 0.178455i | ||||||||
\(826\) | 859.972 | + | 465.721i | 1.04113 | + | 0.563826i | ||||
\(827\) | −957.378 | −1.15765 | −0.578826 | − | 0.815451i | \(-0.696489\pi\) | ||||
−0.578826 | + | 0.815451i | \(0.696489\pi\) | |||||||
\(828\) | −53.2722 | −0.0643384 | ||||||||
\(829\) | − | 9.08184i | − | 0.0109552i | −0.999985 | − | 0.00547759i | \(-0.998256\pi\) | ||
0.999985 | − | 0.00547759i | \(-0.00174358\pi\) | |||||||
\(830\) | −390.934 | −0.471005 | ||||||||
\(831\) | 147.812i | 0.177873i | ||||||||
\(832\) | 1155.36i | 1.38865i | ||||||||
\(833\) | 550.987 | − | 359.515i | 0.661449 | − | 0.431591i | ||||
\(834\) | −627.651 | −0.752579 | ||||||||
\(835\) | −93.4512 | −0.111918 | ||||||||
\(836\) | − | 249.778i | − | 0.298778i | ||||||
\(837\) | 35.0411 | 0.0418651 | ||||||||
\(838\) | − | 189.446i | − | 0.226069i | ||||||
\(839\) | − | 492.860i | − | 0.587437i | −0.955892 | − | 0.293719i | \(-0.905107\pi\) | ||
0.955892 | − | 0.293719i | \(-0.0948929\pi\) | |||||||
\(840\) | −112.038 | + | 206.882i | −0.133378 | + | 0.246288i | ||||
\(841\) | 194.509 | 0.231283 | ||||||||
\(842\) | 892.583 | 1.06007 | ||||||||
\(843\) | − | 289.903i | − | 0.343894i | ||||||
\(844\) | 5.44391 | 0.00645013 | ||||||||
\(845\) | − | 218.536i | − | 0.258623i | ||||||
\(846\) | 206.168i | 0.243697i | ||||||||
\(847\) | −560.030 | + | 1034.12i | −0.661193 | + | 1.22092i | ||||
\(848\) | −238.140 | −0.280825 | ||||||||
\(849\) | −259.098 | −0.305181 | ||||||||
\(850\) | 114.941i | 0.135225i | ||||||||
\(851\) | 1150.19 | 1.35158 | ||||||||
\(852\) | − | 47.6286i | − | 0.0559021i | ||||||
\(853\) | 519.198i | 0.608672i | 0.952565 | + | 0.304336i | \(0.0984346\pi\) | ||||
−0.952565 | + | 0.304336i | \(0.901565\pi\) | |||||||
\(854\) | 157.934 | + | 85.5297i | 0.184934 | + | 0.100152i | ||||
\(855\) | 92.2371 | 0.107880 | ||||||||
\(856\) | 1461.03 | 1.70682 | ||||||||
\(857\) | 479.468i | 0.559473i | 0.960077 | + | 0.279736i | \(0.0902470\pi\) | ||||
−0.960077 | + | 0.279736i | \(0.909753\pi\) | |||||||
\(858\) | −823.360 | −0.959627 | ||||||||
\(859\) | − | 1667.63i | − | 1.94136i | −0.240378 | − | 0.970679i | \(-0.577271\pi\) | ||
0.240378 | − | 0.970679i | \(-0.422729\pi\) | |||||||
\(860\) | − | 103.272i | − | 0.120084i | ||||||
\(861\) | 229.441 | − | 423.672i | 0.266482 | − | 0.492070i | ||||
\(862\) | −981.089 | −1.13815 | ||||||||
\(863\) | 1217.16 | 1.41039 | 0.705193 | − | 0.709016i | \(-0.250861\pi\) | ||||
0.705193 | + | 0.709016i | \(0.250861\pi\) | |||||||
\(864\) | − | 86.2112i | − | 0.0997814i | ||||||
\(865\) | 291.458 | 0.336946 | ||||||||
\(866\) | 735.776i | 0.849626i | ||||||||
\(867\) | − | 188.319i | − | 0.217208i | ||||||
\(868\) | −44.3558 | − | 24.0211i | −0.0511012 | − | 0.0276740i | ||||
\(869\) | 1360.82 | 1.56597 | ||||||||
\(870\) | −213.384 | −0.245269 | ||||||||
\(871\) | 1177.32i | 1.35169i | ||||||||
\(872\) | −1350.05 | −1.54823 | ||||||||
\(873\) | 478.344i | 0.547931i | ||||||||
\(874\) | 391.215i | 0.447615i | ||||||||
\(875\) | 68.8187 | + | 37.2690i | 0.0786500 | + | 0.0425932i | ||||
\(876\) | −138.931 | −0.158597 | ||||||||
\(877\) | −1027.18 | −1.17125 | −0.585623 | − | 0.810583i | \(-0.699150\pi\) | ||||
−0.585623 | + | 0.810583i | \(0.699150\pi\) | |||||||
\(878\) | − | 142.192i | − | 0.161950i | ||||||
\(879\) | 252.541 | 0.287305 | ||||||||
\(880\) | − | 402.329i | − | 0.457192i | ||||||
\(881\) | − | 149.054i | − | 0.169187i | −0.996416 | − | 0.0845937i | \(-0.973041\pi\) | ||
0.996416 | − | 0.0845937i | \(-0.0269592\pi\) | |||||||
\(882\) | −137.535 | − | 210.783i | −0.155935 | − | 0.238983i | ||||
\(883\) | 201.243 | 0.227908 | 0.113954 | − | 0.993486i | \(-0.463648\pi\) | ||||
0.113954 | + | 0.993486i | \(0.463648\pi\) | |||||||
\(884\) | 234.319 | 0.265067 | ||||||||
\(885\) | 316.037i | 0.357104i | ||||||||
\(886\) | 701.995 | 0.792319 | ||||||||
\(887\) | 951.252i | 1.07244i | 0.844079 | + | 0.536219i | \(0.180148\pi\) | ||||
−0.844079 | + | 0.536219i | \(0.819852\pi\) | |||||||
\(888\) | 1040.35i | 1.17157i | ||||||||
\(889\) | 199.577 | − | 368.527i | 0.224496 | − | 0.414542i | ||||
\(890\) | −491.503 | −0.552250 | ||||||||
\(891\) | 153.001 | 0.171718 | ||||||||
\(892\) | 331.327i | 0.371443i | ||||||||
\(893\) | −551.899 | −0.618028 | ||||||||
\(894\) | − | 190.334i | − | 0.212902i | ||||||
\(895\) | 100.608i | 0.112412i | ||||||||
\(896\) | 182.524 | − | 337.038i | 0.203710 | − | 0.376158i | ||||
\(897\) | −470.083 | −0.524062 | ||||||||
\(898\) | 352.613 | 0.392664 | ||||||||
\(899\) | − | 217.007i | − | 0.241387i | ||||||
\(900\) | −16.0286 | −0.0178095 | ||||||||
\(901\) | 302.102i | 0.335296i | ||||||||
\(902\) | 1156.67i | 1.28234i | ||||||||
\(903\) | 460.794 | + | 249.545i | 0.510293 | + | 0.276351i | ||||
\(904\) | −182.210 | −0.201560 | ||||||||
\(905\) | −40.0130 | −0.0442133 | ||||||||
\(906\) | 328.921i | 0.363047i | ||||||||
\(907\) | −559.990 | −0.617409 | −0.308705 | − | 0.951158i | \(-0.599895\pi\) | ||||
−0.308705 | + | 0.951158i | \(0.599895\pi\) | |||||||
\(908\) | 116.002i | 0.127755i | ||||||||
\(909\) | 72.4140i | 0.0796633i | ||||||||
\(910\) | −208.428 | + | 384.870i | −0.229042 | + | 0.422934i | ||||
\(911\) | −674.618 | −0.740525 | −0.370262 | − | 0.928927i | \(-0.620732\pi\) | ||||
−0.370262 | + | 0.928927i | \(0.620732\pi\) | |||||||
\(912\) | −252.061 | −0.276382 | ||||||||
\(913\) | − | 1735.92i | − | 1.90134i | ||||||
\(914\) | 1097.26 | 1.20050 | ||||||||
\(915\) | 58.0403i | 0.0634320i | ||||||||
\(916\) | − | 252.699i | − | 0.275872i | ||||||
\(917\) | 1027.13 | + | 556.244i | 1.12009 | + | 0.606591i | ||||
\(918\) | 119.450 | 0.130120 | ||||||||
\(919\) | 982.395 | 1.06898 | 0.534491 | − | 0.845174i | \(-0.320503\pi\) | ||||
0.534491 | + | 0.845174i | \(0.320503\pi\) | |||||||
\(920\) | − | 322.468i | − | 0.350509i | ||||||
\(921\) | −356.099 | −0.386644 | ||||||||
\(922\) | − | 284.362i | − | 0.308419i | ||||||
\(923\) | − | 420.283i | − | 0.455345i | ||||||
\(924\) | −193.672 | − | 104.884i | −0.209602 | − | 0.113511i | ||||
\(925\) | 346.070 | 0.374130 | ||||||||
\(926\) | 17.8763 | 0.0193049 | ||||||||
\(927\) | − | 262.041i | − | 0.282676i | ||||||
\(928\) | −533.898 | −0.575322 | ||||||||
\(929\) | 344.774i | 0.371124i | 0.982633 | + | 0.185562i | \(0.0594105\pi\) | ||||
−0.982633 | + | 0.185562i | \(0.940589\pi\) | |||||||
\(930\) | 44.7179i | 0.0480838i | ||||||||
\(931\) | 564.253 | − | 368.172i | 0.606072 | − | 0.395458i | ||||
\(932\) | −161.664 | −0.173459 | ||||||||
\(933\) | 735.053 | 0.787838 | ||||||||
\(934\) | 461.826i | 0.494460i | ||||||||
\(935\) | −510.391 | −0.545873 | ||||||||
\(936\) | − | 425.191i | − | 0.454264i | ||||||
\(937\) | − | 635.256i | − | 0.677967i | −0.940792 | − | 0.338984i | \(-0.889917\pi\) | ||
0.940792 | − | 0.338984i | \(-0.110083\pi\) | |||||||
\(938\) | 411.425 | − | 759.713i | 0.438620 | − | 0.809929i | ||||
\(939\) | 629.606 | 0.670507 | ||||||||
\(940\) | 95.9066 | 0.102028 | ||||||||
\(941\) | − | 1207.78i | − | 1.28351i | −0.766909 | − | 0.641756i | \(-0.778206\pi\) | ||
0.766909 | − | 0.641756i | \(-0.221794\pi\) | |||||||
\(942\) | 861.338 | 0.914372 | ||||||||
\(943\) | 660.380i | 0.700297i | ||||||||
\(944\) | − | 863.649i | − | 0.914883i | ||||||
\(945\) | 38.7311 | − | 71.5185i | 0.0409853 | − | 0.0756810i | ||||
\(946\) | −1258.02 | −1.32983 | ||||||||
\(947\) | −254.133 | −0.268356 | −0.134178 | − | 0.990957i | \(-0.542839\pi\) | ||||
−0.134178 | + | 0.990957i | \(0.542839\pi\) | |||||||
\(948\) | 148.154i | 0.156281i | ||||||||
\(949\) | −1225.95 | −1.29184 | ||||||||
\(950\) | 117.709i | 0.123904i | ||||||||
\(951\) | − | 764.540i | − | 0.803933i | ||||||
\(952\) | −717.205 | − | 388.405i | −0.753367 | − | 0.407988i | ||||
\(953\) | 424.523 | 0.445460 | 0.222730 | − | 0.974880i | \(-0.428503\pi\) | ||||
0.222730 | + | 0.974880i | \(0.428503\pi\) | |||||||
\(954\) | 115.571 | 0.121143 | ||||||||
\(955\) | 398.723i | 0.417511i | ||||||||
\(956\) | −51.6072 | −0.0539824 | ||||||||
\(957\) | − | 947.522i | − | 0.990096i | ||||||
\(958\) | 1112.58i | 1.16136i | ||||||||
\(959\) | −420.479 | + | 776.431i | −0.438455 | + | 0.809625i | ||||
\(960\) | 273.984 | 0.285400 | ||||||||
\(961\) | 915.523 | 0.952677 | ||||||||
\(962\) | 1935.41i | 2.01186i | ||||||||
\(963\) | −505.076 | −0.524482 | ||||||||
\(964\) | − | 246.557i | − | 0.255764i | ||||||
\(965\) | − | 751.952i | − | 0.779225i | ||||||
\(966\) | 303.339 | + | 164.274i | 0.314016 | + | 0.170056i | ||||
\(967\) | −46.7338 | −0.0483286 | −0.0241643 | − | 0.999708i | \(-0.507692\pi\) | ||||
−0.0241643 | + | 0.999708i | \(0.507692\pi\) | |||||||
\(968\) | 1457.95 | 1.50615 | ||||||||
\(969\) | 319.762i | 0.329991i | ||||||||
\(970\) | −610.441 | −0.629321 | ||||||||
\(971\) | − | 1724.03i | − | 1.77552i | −0.460303 | − | 0.887762i | \(-0.652259\pi\) | ||
0.460303 | − | 0.887762i | \(-0.347741\pi\) | |||||||
\(972\) | 16.6574i | 0.0171372i | ||||||||
\(973\) | −1302.77 | − | 705.522i | −1.33893 | − | 0.725100i | ||||
\(974\) | −1023.24 | −1.05056 | ||||||||
\(975\) | −141.439 | −0.145065 | ||||||||
\(976\) | − | 158.609i | − | 0.162510i | ||||||
\(977\) | −1613.20 | −1.65118 | −0.825589 | − | 0.564271i | \(-0.809157\pi\) | ||||
−0.825589 | + | 0.564271i | \(0.809157\pi\) | |||||||
\(978\) | − | 159.711i | − | 0.163303i | ||||||
\(979\) | − | 2182.49i | − | 2.22931i | ||||||
\(980\) | −98.0534 | + | 63.9792i | −0.100055 | + | 0.0652849i | ||||
\(981\) | 466.710 | 0.475749 | ||||||||
\(982\) | 184.269 | 0.187647 | ||||||||
\(983\) | − | 31.6909i | − | 0.0322389i | −0.999870 | − | 0.0161195i | \(-0.994869\pi\) | ||
0.999870 | − | 0.0161195i | \(-0.00513121\pi\) | |||||||
\(984\) | −597.315 | −0.607028 | ||||||||
\(985\) | 110.033i | 0.111708i | ||||||||
\(986\) | − | 739.747i | − | 0.750250i | ||||||
\(987\) | −231.747 | + | 427.930i | −0.234799 | + | 0.433566i | ||||
\(988\) | 239.961 | 0.242875 | ||||||||
\(989\) | −718.242 | −0.726231 | ||||||||
\(990\) | 195.253i | 0.197225i | ||||||||
\(991\) | −236.475 | −0.238623 | −0.119311 | − | 0.992857i | \(-0.538069\pi\) | ||||
−0.119311 | + | 0.992857i | \(0.538069\pi\) | |||||||
\(992\) | 111.886i | 0.112789i | ||||||||
\(993\) | − | 882.180i | − | 0.888399i | ||||||
\(994\) | −146.871 | + | 271.204i | −0.147758 | + | 0.272841i | ||||
\(995\) | −384.132 | −0.386062 | ||||||||
\(996\) | 188.992 | 0.189751 | ||||||||
\(997\) | − | 948.441i | − | 0.951295i | −0.879636 | − | 0.475648i | \(-0.842214\pi\) | ||
0.879636 | − | 0.475648i | \(-0.157786\pi\) | |||||||
\(998\) | 720.146 | 0.721589 | ||||||||
\(999\) | − | 359.647i | − | 0.360007i |
(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 | 105.3.h.a.76.5 | ✓ | 12 | |
3.2 | odd | 2 | 315.3.h.d.181.7 | 12 | |||
4.3 | odd | 2 | 1680.3.s.c.1441.11 | 12 | |||
5.2 | odd | 4 | 525.3.e.c.349.1 | 24 | |||
5.3 | odd | 4 | 525.3.e.c.349.16 | 24 | |||
5.4 | even | 2 | 525.3.h.d.76.8 | 12 | |||
7.6 | odd | 2 | inner | 105.3.h.a.76.6 | yes | 12 | |
21.20 | even | 2 | 315.3.h.d.181.8 | 12 | |||
28.27 | even | 2 | 1680.3.s.c.1441.2 | 12 | |||
35.13 | even | 4 | 525.3.e.c.349.2 | 24 | |||
35.27 | even | 4 | 525.3.e.c.349.15 | 24 | |||
35.34 | odd | 2 | 525.3.h.d.76.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.h.a.76.5 | ✓ | 12 | 1.1 | even | 1 | trivial | |
105.3.h.a.76.6 | yes | 12 | 7.6 | odd | 2 | inner | |
315.3.h.d.181.7 | 12 | 3.2 | odd | 2 | |||
315.3.h.d.181.8 | 12 | 21.20 | even | 2 | |||
525.3.e.c.349.1 | 24 | 5.2 | odd | 4 | |||
525.3.e.c.349.2 | 24 | 35.13 | even | 4 | |||
525.3.e.c.349.15 | 24 | 35.27 | even | 4 | |||
525.3.e.c.349.16 | 24 | 5.3 | odd | 4 | |||
525.3.h.d.76.7 | 12 | 35.34 | odd | 2 | |||
525.3.h.d.76.8 | 12 | 5.4 | even | 2 | |||
1680.3.s.c.1441.2 | 12 | 28.27 | even | 2 | |||
1680.3.s.c.1441.11 | 12 | 4.3 | odd | 2 |