Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.7 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.26 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.847850 | + | 2.06909i | −0.379170 | + | 0.925327i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.67313i | 1.38831i | 0.719825 | + | 0.694156i | \(0.244222\pi\) | ||||
−0.719825 | + | 0.694156i | \(0.755778\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.98590 | −1.20179 | −0.600897 | − | 0.799327i | \(-0.705190\pi\) | ||||
−0.600897 | + | 0.799327i | \(0.705190\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.24921i | − | 0.346467i | −0.984881 | − | 0.173234i | \(-0.944578\pi\) | ||
0.984881 | − | 0.173234i | \(-0.0554216\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.06909 | + | 0.847850i | 0.534238 | + | 0.218914i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.354171i | − | 0.0858990i | −0.999077 | − | 0.0429495i | \(-0.986325\pi\) | ||
0.999077 | − | 0.0429495i | \(-0.0136755\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.69097 | −0.387936 | −0.193968 | − | 0.981008i | \(-0.562136\pi\) | ||||
−0.193968 | + | 0.981008i | \(0.562136\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.67313 | 0.801542 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.36335i | − | 0.284279i | −0.989847 | − | 0.142139i | \(-0.954602\pi\) | ||
0.989847 | − | 0.142139i | \(-0.0453981\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.56230 | − | 3.50856i | −0.712460 | − | 0.701713i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.677093 | 0.125733 | 0.0628665 | − | 0.998022i | \(-0.479976\pi\) | ||||
0.0628665 | + | 0.998022i | \(0.479976\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.344129 | 0.0618074 | 0.0309037 | − | 0.999522i | \(-0.490161\pi\) | ||||
0.0309037 | + | 0.999522i | \(0.490161\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.98590i | 0.693856i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.60004 | − | 3.11426i | −1.28464 | − | 0.526406i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.16175i | 1.34178i | 0.741555 | + | 0.670892i | \(0.234088\pi\) | ||||
−0.741555 | + | 0.670892i | \(0.765912\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.24921 | −0.200033 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.45089 | −0.851287 | −0.425643 | − | 0.904891i | \(-0.639952\pi\) | ||||
−0.425643 | + | 0.904891i | \(0.639952\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.6444i | − | 1.62325i | −0.584177 | − | 0.811626i | \(-0.698583\pi\) | ||
0.584177 | − | 0.811626i | \(-0.301417\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.847850 | − | 2.06909i | 0.126390 | − | 0.308442i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.1918i | 1.48663i | 0.668944 | + | 0.743313i | \(0.266747\pi\) | ||||
−0.668944 | + | 0.743313i | \(0.733253\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.49186 | −0.927408 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.354171 | −0.0495938 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.74012i | 0.651106i | 0.945524 | + | 0.325553i | \(0.105550\pi\) | ||||
−0.945524 | + | 0.325553i | \(0.894450\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.37945 | − | 8.24720i | 0.455684 | − | 1.11205i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.69097i | 0.223975i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.13578 | 0.668621 | 0.334311 | − | 0.942463i | \(-0.391497\pi\) | ||||
0.334311 | + | 0.942463i | \(0.391497\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.19082 | 0.664616 | 0.332308 | − | 0.943171i | \(-0.392173\pi\) | ||||
0.332308 | + | 0.943171i | \(0.392173\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 3.67313i | − | 0.462770i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.58472 | + | 1.05914i | 0.320595 | + | 0.131370i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.36335 | −0.164128 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.56237 | −0.422776 | −0.211388 | − | 0.977402i | \(-0.567798\pi\) | ||||
−0.211388 | + | 0.977402i | \(0.567798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.89398i | − | 0.572797i | −0.958111 | − | 0.286398i | \(-0.907542\pi\) | ||
0.958111 | − | 0.286398i | \(-0.0924581\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.50856 | + | 3.56230i | −0.405134 | + | 0.411339i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 14.6407i | − | 1.66846i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.19345 | 0.584308 | 0.292154 | − | 0.956371i | \(-0.405628\pi\) | ||||
0.292154 | + | 0.956371i | \(0.405628\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.49034i | − | 0.822171i | −0.911597 | − | 0.411086i | \(-0.865150\pi\) | ||
0.911597 | − | 0.411086i | \(-0.134850\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.732812 | + | 0.300284i | 0.0794847 | + | 0.0325704i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 0.677093i | − | 0.0725920i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.5662 | −1.22601 | −0.613007 | − | 0.790078i | \(-0.710040\pi\) | ||||
−0.613007 | + | 0.790078i | \(0.710040\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.58849 | 0.481004 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 0.344129i | − | 0.0356845i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.43369 | − | 3.49878i | 0.147094 | − | 0.358967i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 17.6632i | − | 1.79342i | −0.442617 | − | 0.896711i | \(-0.645950\pi\) | ||
0.442617 | − | 0.896711i | \(-0.354050\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.98590 | 0.400598 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.52695 | −0.549952 | −0.274976 | − | 0.961451i | \(-0.588670\pi\) | ||||
−0.274976 | + | 0.961451i | \(0.588670\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 18.0243i | − | 1.77599i | −0.459853 | − | 0.887995i | \(-0.652098\pi\) | ||
0.459853 | − | 0.887995i | \(-0.347902\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.11426 | + | 7.60004i | −0.303921 | + | 0.741688i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 18.2547i | − | 1.76474i | −0.470552 | − | 0.882372i | \(-0.655945\pi\) | ||
0.470552 | − | 0.882372i | \(-0.344055\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.4396 | 1.09572 | 0.547859 | − | 0.836571i | \(-0.315443\pi\) | ||||
0.547859 | + | 0.836571i | \(0.315443\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.16175 | 0.774679 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.1514i | − | 1.14311i | −0.820565 | − | 0.571553i | \(-0.806341\pi\) | ||
0.820565 | − | 0.571553i | \(-0.193659\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.82091 | + | 1.15592i | 0.263051 | + | 0.107790i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.24921i | 0.115489i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.30091 | 0.119255 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.88739 | 0.444308 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.45089i | 0.491491i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.2798 | − | 4.39599i | 0.919457 | − | 0.393190i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.07566i | − | 0.184185i | −0.995750 | − | 0.0920927i | \(-0.970644\pi\) | ||
0.995750 | − | 0.0920927i | \(-0.0293556\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.6444 | −0.937185 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.87477 | −0.688022 | −0.344011 | − | 0.938966i | \(-0.611786\pi\) | ||||
−0.344011 | + | 0.938966i | \(0.611786\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 6.21115i | − | 0.538575i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.06909 | − | 0.847850i | −0.178079 | − | 0.0729714i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 9.02338i | − | 0.770920i | −0.922725 | − | 0.385460i | \(-0.874043\pi\) | ||
0.922725 | − | 0.385460i | \(-0.125957\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.33603 | −0.282958 | −0.141479 | − | 0.989941i | \(-0.545186\pi\) | ||||
−0.141479 | + | 0.989941i | \(0.545186\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.1918 | 0.858304 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.97920i | 0.416382i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.574074 | + | 1.40097i | −0.0476742 | + | 0.116344i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.49186i | 0.535439i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.9548 | 0.897452 | 0.448726 | − | 0.893670i | \(-0.351878\pi\) | ||||
0.448726 | + | 0.893670i | \(0.351878\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.79175 | −0.471326 | −0.235663 | − | 0.971835i | \(-0.575726\pi\) | ||||
−0.235663 | + | 0.971835i | \(0.575726\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.354171i | 0.0286330i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.291770 | + | 0.712036i | −0.0234355 | + | 0.0571921i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.0431i | 1.59961i | 0.600258 | + | 0.799806i | \(0.295064\pi\) | ||||
−0.600258 | + | 0.799806i | \(0.704936\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.74012 | 0.375916 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.00777 | 0.394668 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 16.4495i | − | 1.28843i | −0.764846 | − | 0.644213i | \(-0.777185\pi\) | ||
0.764846 | − | 0.644213i | \(-0.222815\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.24720 | − | 3.37945i | −0.642043 | − | 0.263089i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.2670i | 0.794488i | 0.917713 | + | 0.397244i | \(0.130033\pi\) | ||||
−0.917713 | + | 0.397244i | \(0.869967\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.4395 | 0.879960 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.69097 | 0.129312 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 9.03279i | − | 0.686750i | −0.939198 | − | 0.343375i | \(-0.888430\pi\) | ||
0.939198 | − | 0.343375i | \(-0.111570\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.8874 | − | 13.0848i | 0.974196 | − | 0.989116i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.13578i | − | 0.386029i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.4474 | −1.22933 | −0.614666 | − | 0.788787i | \(-0.710709\pi\) | ||||
−0.614666 | + | 0.788787i | \(0.710709\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.0006 | 1.41230 | 0.706152 | − | 0.708060i | \(-0.250429\pi\) | ||||
0.706152 | + | 0.708060i | \(0.250429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 5.19082i | − | 0.383716i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.8874 | − | 6.91994i | −1.24159 | − | 0.508764i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.41169i | 0.103233i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.67313 | −0.267181 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.1050 | −1.67182 | −0.835910 | − | 0.548866i | \(-0.815060\pi\) | ||||
−0.835910 | + | 0.548866i | \(0.815060\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 2.97961i | − | 0.214477i | −0.994233 | − | 0.107239i | \(-0.965799\pi\) | ||
0.994233 | − | 0.107239i | \(-0.0342009\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.05914 | − | 2.58472i | 0.0758465 | − | 0.185096i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.15240i | 0.509587i | 0.966995 | + | 0.254794i | \(0.0820075\pi\) | ||||
−0.966995 | + | 0.254794i | \(0.917992\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.7887 | −0.977452 | −0.488726 | − | 0.872437i | \(-0.662538\pi\) | ||||
−0.488726 | + | 0.872437i | \(0.662538\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.48705i | 0.174557i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.62154 | − | 11.2784i | 0.322783 | − | 0.787718i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.36335i | 0.0947596i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.74004 | 0.466218 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.00933814 | −0.000642864 | −0.000321432 | − | 1.00000i | \(-0.500102\pi\) | ||||
−0.000321432 | 1.00000i | \(0.500102\pi\) | ||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.56237i | 0.244090i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.0242 | + | 9.02484i | 1.50204 | + | 0.615489i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.26403i | 0.0858080i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.89398 | −0.330704 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.442432 | −0.0297612 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.79157i | − | 0.588727i | −0.955694 | − | 0.294364i | \(-0.904892\pi\) | ||
0.955694 | − | 0.294364i | \(-0.0951077\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.56230 | + | 3.50856i | 0.237487 | + | 0.233904i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.8704i | 1.71708i | 0.512747 | + | 0.858540i | \(0.328628\pi\) | ||||
−0.512747 | + | 0.858540i | \(0.671372\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.38276 | 0.487867 | 0.243933 | − | 0.969792i | \(-0.421562\pi\) | ||||
0.243933 | + | 0.969792i | \(0.421562\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.6407 | −0.963288 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.02124i | − | 0.263440i | −0.991287 | − | 0.131720i | \(-0.957950\pi\) | ||
0.991287 | − | 0.131720i | \(-0.0420500\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.0878 | − | 8.64111i | −1.37561 | − | 0.563684i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 5.19345i | − | 0.337351i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.65242 | −0.300940 | −0.150470 | − | 0.988615i | \(-0.548079\pi\) | ||||
−0.150470 | + | 0.988615i | \(0.548079\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.31972 | 0.342674 | 0.171337 | − | 0.985213i | \(-0.445191\pi\) | ||||
0.171337 | + | 0.985213i | \(0.445191\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.50412 | − | 13.4323i | 0.351646 | − | 0.858156i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.11237i | 0.134407i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.49034 | −0.474681 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.4986 | 0.978261 | 0.489131 | − | 0.872211i | \(-0.337314\pi\) | ||||
0.489131 | + | 0.872211i | \(0.337314\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.43419i | 0.341645i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.300284 | − | 0.732812i | 0.0188045 | − | 0.0458905i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 11.0848i | − | 0.691448i | −0.938336 | − | 0.345724i | \(-0.887633\pi\) | ||
0.938336 | − | 0.345724i | \(-0.112367\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.9791 | −1.86281 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.677093 | −0.0419110 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 18.3141i | − | 1.12930i | −0.825331 | − | 0.564649i | \(-0.809011\pi\) | ||
0.825331 | − | 0.564649i | \(-0.190989\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.80775 | − | 4.01891i | −0.602486 | − | 0.246880i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.5662i | 0.707839i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.87552 | −0.236294 | −0.118147 | − | 0.992996i | \(-0.537695\pi\) | ||||
−0.118147 | + | 0.992996i | \(0.537695\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.86979 | −0.417310 | −0.208655 | − | 0.977989i | \(-0.566909\pi\) | ||||
−0.208655 | + | 0.977989i | \(0.566909\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 4.58849i | − | 0.277708i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.1990 | + | 13.9848i | 0.856230 | + | 0.843314i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.2508i | 1.75751i | 0.477274 | + | 0.878755i | \(0.341625\pi\) | ||||
−0.477274 | + | 0.878755i | \(0.658375\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.344129 | −0.0206025 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.06296 | −0.540651 | −0.270325 | − | 0.962769i | \(-0.587131\pi\) | ||||
−0.270325 | + | 0.962769i | \(0.587131\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.74959i | 0.163446i | 0.996655 | + | 0.0817232i | \(0.0260423\pi\) | ||||
−0.996655 | + | 0.0817232i | \(0.973958\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.49878 | − | 1.43369i | −0.207250 | − | 0.0849245i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 20.0218i | − | 1.18185i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8746 | 0.992621 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.6632 | −1.03543 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 5.28044i | − | 0.308487i | −0.988033 | − | 0.154243i | \(-0.950706\pi\) | ||
0.988033 | − | 0.154243i | \(-0.0492940\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.35437 | + | 10.6264i | −0.253521 | + | 0.618693i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.98590i | − | 0.231285i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.70311 | −0.0984933 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 39.0981 | 2.25358 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.52695i | 0.317515i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.40104 | + | 10.7403i | −0.252003 | + | 0.614987i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 31.1784i | − | 1.77944i | −0.456502 | − | 0.889722i | \(-0.650898\pi\) | ||
0.456502 | − | 0.889722i | \(-0.349102\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.0243 | −1.02537 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.4565 | −0.989869 | −0.494934 | − | 0.868930i | \(-0.664808\pi\) | ||||
−0.494934 | + | 0.868930i | \(0.664808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.3566i | 0.585388i | 0.956206 | + | 0.292694i | \(0.0945518\pi\) | ||||
−0.956206 | + | 0.292694i | \(0.905448\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.60004 | + | 3.11426i | 0.428214 | + | 0.175469i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.19437i | 0.123248i | 0.998099 | + | 0.0616240i | \(0.0196280\pi\) | ||||
−0.998099 | + | 0.0616240i | \(0.980372\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.69882 | −0.151105 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.2547 | −1.01888 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.598893i | 0.0333233i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.38292 | + | 4.45004i | −0.243120 | + | 0.246844i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 11.4396i | − | 0.632613i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −37.4357 | −2.06390 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.64862 | −0.530336 | −0.265168 | − | 0.964202i | \(-0.585427\pi\) | ||||
−0.265168 | + | 0.964202i | \(0.585427\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 8.16175i | − | 0.447261i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.06909 | + | 0.847850i | 0.113047 | + | 0.0463230i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.6003i | 1.44901i | 0.689269 | + | 0.724505i | \(0.257932\pi\) | ||||
−0.689269 | + | 0.724505i | \(0.742068\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.1514 | −0.659972 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.37166 | −0.0742798 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.86648i | 0.100780i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.15592 | − | 2.82091i | 0.0622326 | − | 0.151873i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 19.0663i | − | 1.02353i | −0.859125 | − | 0.511766i | \(-0.828992\pi\) | ||
0.859125 | − | 0.511766i | \(-0.171008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.9836 | −1.87263 | −0.936314 | − | 0.351164i | \(-0.885786\pi\) | ||||
−0.936314 | + | 0.351164i | \(0.885786\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.24921 | 0.0666776 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 14.8946i | − | 0.792758i | −0.918087 | − | 0.396379i | \(-0.870267\pi\) | ||
0.918087 | − | 0.396379i | \(-0.129733\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.02036 | − | 7.37089i | 0.160304 | − | 0.391206i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 1.30091i | − | 0.0688517i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.8058 | −1.09809 | −0.549043 | − | 0.835794i | \(-0.685008\pi\) | ||||
−0.549043 | + | 0.835794i | \(0.685008\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.1406 | −0.849506 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 4.88739i | − | 0.256521i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.1261 | + | 4.14936i | 0.530024 | + | 0.217187i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.13253i | 0.476714i | 0.971178 | + | 0.238357i | \(0.0766089\pi\) | ||||
−0.971178 | + | 0.238357i | \(0.923391\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.45089 | 0.283762 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.4111 | −0.903937 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.9166i | 0.979464i | 0.871873 | + | 0.489732i | \(0.162905\pi\) | ||||
−0.871873 | + | 0.489732i | \(0.837095\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.39599 | − | 10.2798i | −0.227008 | − | 0.530849i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.845828i | − | 0.0435624i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.68889 | 0.240852 | 0.120426 | − | 0.992722i | \(-0.461574\pi\) | ||||
0.120426 | + | 0.992722i | \(0.461574\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.07566 | −0.106339 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 11.1860i | − | 0.571575i | −0.958293 | − | 0.285788i | \(-0.907745\pi\) | ||
0.958293 | − | 0.285788i | \(-0.0922552\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 30.2930 | + | 12.4131i | 1.54387 | + | 0.632632i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.6444i | 0.541084i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.5925 | −1.65250 | −0.826252 | − | 0.563301i | \(-0.809531\pi\) | ||||
−0.826252 | + | 0.563301i | \(0.809531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.482860 | −0.0244193 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.87477i | 0.397230i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.40327 | + | 10.7457i | −0.221552 | + | 0.540676i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 16.4542i | − | 0.825811i | −0.910774 | − | 0.412906i | \(-0.864514\pi\) | ||
0.910774 | − | 0.412906i | \(-0.135486\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.21115 | −0.310947 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.9972 | 0.948674 | 0.474337 | − | 0.880343i | \(-0.342688\pi\) | ||||
0.474337 | + | 0.880343i | \(0.342688\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.429888i | − | 0.0214142i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.847850 | + | 2.06909i | −0.0421300 | + | 0.102814i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 32.5319i | − | 1.61255i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.04519 | 0.101128 | 0.0505641 | − | 0.998721i | \(-0.483898\pi\) | ||||
0.0505641 | + | 0.998721i | \(0.483898\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.02338 | −0.445091 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.8644i | 0.928254i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.4982 | + | 6.35069i | 0.760777 | + | 0.311743i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.33603i | 0.163366i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.8865 | 0.580695 | 0.290348 | − | 0.956921i | \(-0.406229\pi\) | ||||
0.290348 | + | 0.956921i | \(0.406229\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.8761 | 1.01744 | 0.508719 | − | 0.860933i | \(-0.330119\pi\) | ||||
0.508719 | + | 0.860933i | \(0.330119\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 10.1918i | − | 0.495542i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.24263 | + | 1.26166i | −0.0602764 | + | 0.0611996i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.0665i | 0.922694i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.97920 | 0.240398 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.98614 | 0.0956692 | 0.0478346 | − | 0.998855i | \(-0.484768\pi\) | ||||
0.0478346 | + | 0.998855i | \(0.484768\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.40462i | − | 0.403900i | −0.979396 | − | 0.201950i | \(-0.935272\pi\) | ||
0.979396 | − | 0.201950i | \(-0.0647279\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.40097 | + | 0.574074i | 0.0671713 | + | 0.0275247i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.30539i | 0.110282i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.1890 | −1.24993 | −0.624966 | − | 0.780652i | \(-0.714887\pi\) | ||||
−0.624966 | + | 0.780652i | \(0.714887\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.49186 | 0.309136 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.3510i | 1.48953i | 0.667327 | + | 0.744765i | \(0.267439\pi\) | ||||
−0.667327 | + | 0.744765i | \(0.732561\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.80640 | − | 23.9315i | 0.464868 | − | 1.13446i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 10.9548i | − | 0.518144i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.482287 | −0.0227605 | −0.0113803 | − | 0.999935i | \(-0.503623\pi\) | ||||
−0.0113803 | + | 0.999935i | \(0.503623\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.7267 | 1.02307 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.79175i | 0.272120i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.89035 | + | 9.49401i | −0.182383 | + | 0.445086i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 22.1593i | − | 1.03657i | −0.855208 | − | 0.518285i | \(-0.826571\pi\) | ||
0.855208 | − | 0.518285i | \(-0.173429\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.354171 | 0.0165313 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.56263 | −0.445376 | −0.222688 | − | 0.974890i | \(-0.571483\pi\) | ||||
−0.222688 | + | 0.974890i | \(0.571483\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.00166i | − | 0.278921i | −0.990228 | − | 0.139460i | \(-0.955463\pi\) | ||
0.990228 | − | 0.139460i | \(-0.0445368\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.712036 | + | 0.291770i | 0.0330199 | + | 0.0135305i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.2288i | 1.16745i | 0.811951 | + | 0.583726i | \(0.198406\pi\) | ||||
−0.811951 | + | 0.583726i | \(0.801594\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.67313 | 0.169609 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.0431 | 0.923537 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 42.4274i | 1.95081i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.02375 | + | 5.93288i | 0.276389 | + | 0.272219i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 4.74012i | − | 0.217035i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.5193 | −1.66861 | −0.834305 | − | 0.551303i | \(-0.814131\pi\) | ||||
−0.834305 | + | 0.551303i | \(0.814131\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.1957 | 0.464884 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 5.00777i | − | 0.227861i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 36.5467 | + | 14.9757i | 1.65950 | + | 0.680012i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 23.0782i | − | 1.04578i | −0.852402 | − | 0.522888i | \(-0.824855\pi\) | ||
0.852402 | − | 0.522888i | \(-0.175145\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.4495 | −0.743873 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.6298 | −1.02127 | −0.510635 | − | 0.859798i | \(-0.670590\pi\) | ||||
−0.510635 | + | 0.859798i | \(0.670590\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.239806i | − | 0.0108003i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.37945 | + | 8.24720i | −0.151895 | + | 0.370684i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 13.0851i | − | 0.586945i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.3444 | 0.865972 | 0.432986 | − | 0.901401i | \(-0.357460\pi\) | ||||
0.432986 | + | 0.901401i | \(0.357460\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.2670 | 0.458698 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 0.211980i | − | 0.00945172i | −0.999989 | − | 0.00472586i | \(-0.998496\pi\) | ||
0.999989 | − | 0.00472586i | \(-0.00150429\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.68603 | − | 11.4358i | 0.208525 | − | 0.508885i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 11.4395i | − | 0.508045i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.3733 | 0.548435 | 0.274218 | − | 0.961668i | \(-0.411581\pi\) | ||||
0.274218 | + | 0.961668i | \(0.411581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.9762 | 0.795220 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 1.69097i | − | 0.0746582i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 37.2940 | + | 15.2819i | 1.64337 | + | 0.673403i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 40.6234i | − | 1.78662i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.03279 | −0.396495 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.82228 | 0.167457 | 0.0837285 | − | 0.996489i | \(-0.473317\pi\) | ||||
0.0837285 | + | 0.996489i | \(0.473317\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 22.8462i | − | 0.998994i | −0.866316 | − | 0.499497i | \(-0.833518\pi\) | ||
0.866316 | − | 0.499497i | \(-0.166482\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.0848 | − | 12.8874i | −0.571066 | − | 0.562452i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 0.121880i | − | 0.00530920i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.1413 | 0.919186 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.13578 | −0.222874 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.80929i | 0.294943i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 37.7706 | + | 15.4772i | 1.63297 | + | 0.669139i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.4474i | 0.709756i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.8759 | 1.11455 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.2690 | 1.81729 | 0.908643 | − | 0.417573i | \(-0.137119\pi\) | ||||
0.908643 | + | 0.417573i | \(0.137119\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 19.0006i | − | 0.815394i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.69909 | + | 23.6697i | −0.415464 | + | 1.01390i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.6352i | 0.967811i | 0.875120 | + | 0.483906i | \(0.160782\pi\) | ||||
−0.875120 | + | 0.483906i | \(0.839218\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.19082 | −0.221539 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.14495 | −0.0487763 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.0762i | 0.811202i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.91994 | + | 16.8874i | −0.293735 | + | 0.716831i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.9334i | 1.01409i | 0.861920 | + | 0.507045i | \(0.169262\pi\) | ||||
−0.861920 | + | 0.507045i | \(0.830738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.2970 | −0.562404 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.41169 | 0.0596015 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.50398i | − | 0.0633850i | −0.999498 | − | 0.0316925i | \(-0.989910\pi\) | ||
0.999498 | − | 0.0316925i | \(-0.0100897\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.1423 | + | 10.3025i | 1.05775 | + | 0.433432i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.67313i | 0.154257i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −46.5849 | −1.95294 | −0.976469 | − | 0.215657i | \(-0.930811\pi\) | ||||
−0.976469 | + | 0.215657i | \(0.930811\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.19735 | 0.0919561 | 0.0459780 | − | 0.998942i | \(-0.485360\pi\) | ||||
0.0459780 | + | 0.998942i | \(0.485360\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.1050i | 0.965226i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.78341 | + | 4.85667i | −0.199482 | + | 0.202537i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.1751i | 1.29784i | 0.760857 | + | 0.648919i | \(0.224779\pi\) | ||||
−0.760857 | + | 0.648919i | \(0.775221\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.97961 | −0.123829 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.5130 | 1.14143 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 18.8936i | − | 0.782495i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.58472 | − | 1.05914i | −0.106865 | − | 0.0437900i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 19.7574i | − | 0.815477i | −0.913099 | − | 0.407738i | \(-0.866318\pi\) | ||
0.913099 | − | 0.407738i | \(-0.133682\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.581913 | −0.0239773 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.15240 | 0.294210 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.5399i | 1.82903i | 0.404547 | + | 0.914517i | \(0.367429\pi\) | ||||
−0.404547 | + | 0.914517i | \(0.632571\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.10298 | + | 2.69171i | −0.0452178 | + | 0.110349i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.7887i | 0.564332i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.4327 | 1.03915 | 0.519577 | − | 0.854424i | \(-0.326090\pi\) | ||||
0.519577 | + | 0.854424i | \(0.326090\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.66513 | −0.353458 | −0.176729 | − | 0.984260i | \(-0.556552\pi\) | ||||
−0.176729 | + | 0.984260i | \(0.556552\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000i | 0.0407231i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.14377 | + | 10.1125i | −0.168468 | + | 0.411130i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.3352i | 0.541258i | 0.962684 | + | 0.270629i | \(0.0872316\pi\) | ||||
−0.962684 | + | 0.270629i | \(0.912768\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.48705 | 0.100780 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.7316 | 0.515067 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 16.7704i | − | 0.677350i | −0.940903 | − | 0.338675i | \(-0.890021\pi\) | ||
0.940903 | − | 0.338675i | \(-0.109979\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.2784 | − | 4.62154i | −0.454789 | − | 0.186359i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 25.6884i | − | 1.03418i | −0.855932 | − | 0.517088i | \(-0.827016\pi\) | ||
0.855932 | − | 0.517088i | \(-0.172984\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.3538 | −1.66215 | −0.831075 | − | 0.556160i | \(-0.812274\pi\) | ||||
−0.831075 | + | 0.556160i | \(0.812274\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.36335 | 0.0547095 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 42.4841i | − | 1.70209i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.379950 | + | 24.9971i | 0.0151980 | + | 0.999885i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 6.74004i | − | 0.269171i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.89065 | 0.115258 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.06053 | 0.281075 | 0.140538 | − | 0.990075i | \(-0.455117\pi\) | ||||
0.140538 | + | 0.990075i | \(0.455117\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.00933814i | 0.000371158i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.29474 | + | 1.75985i | 0.170432 | + | 0.0698376i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.10966i | 0.321316i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.56237 | 0.140925 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.92465 | −0.194512 | −0.0972560 | − | 0.995259i | \(-0.531007\pi\) | ||||
−0.0972560 | + | 0.995259i | \(0.531007\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 17.0877i | − | 0.673871i | −0.941528 | − | 0.336936i | \(-0.890610\pi\) | ||
0.941528 | − | 0.336936i | \(-0.109390\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.02484 | − | 22.0242i | 0.355353 | − | 0.867202i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.7562i | 1.05190i | 0.850517 | + | 0.525948i | \(0.176289\pi\) | ||||
−0.850517 | + | 0.525948i | \(0.823711\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.4707 | −0.803545 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.26403 | 0.0495412 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.9516i | 0.859034i | 0.903059 | + | 0.429517i | \(0.141316\pi\) | ||||
−0.903059 | + | 0.429517i | \(0.858684\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.67663 | − | 16.2936i | 0.260877 | − | 0.636645i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.89398i | 0.190932i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.6068 | 0.724819 | 0.362409 | − | 0.932019i | \(-0.381954\pi\) | ||||
0.362409 | + | 0.932019i | \(0.381954\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.4378 | 0.989416 | 0.494708 | − | 0.869059i | \(-0.335275\pi\) | ||||
0.494708 | + | 0.869059i | \(0.335275\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.442432i | 0.0171826i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.8515 | + | 5.26613i | 0.498358 | + | 0.204212i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 0.923117i | − | 0.0357432i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.79157 | −0.339902 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.6901 | −0.798731 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.5740i | 0.484693i | 0.970190 | + | 0.242346i | \(0.0779170\pi\) | ||||
−0.970190 | + | 0.242346i | \(0.922083\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.50856 | − | 3.56230i | 0.135045 | − | 0.137113i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 21.8260i | − | 0.838843i | −0.907792 | − | 0.419422i | \(-0.862233\pi\) | ||
0.907792 | − | 0.419422i | \(-0.137767\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 64.8790 | 2.48983 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.8704 | 0.991356 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.52151i | 0.364331i | 0.983268 | + | 0.182165i | \(0.0583106\pi\) | ||||
−0.983268 | + | 0.182165i | \(0.941689\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.6702 | + | 7.65048i | 0.713353 | + | 0.292310i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.38276i | − | 0.281670i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.92138 | 0.225587 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.564108 | 0.0214597 | 0.0107298 | − | 0.999942i | \(-0.496585\pi\) | ||||
0.0107298 | + | 0.999942i | \(0.496585\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.6407i | 0.556154i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.82845 | − | 6.90256i | 0.107289 | − | 0.261829i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.93055i | 0.0731247i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.02124 | −0.152097 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.9780 | −1.05671 | −0.528356 | − | 0.849023i | \(-0.677192\pi\) | ||||
−0.528356 | + | 0.849023i | \(0.677192\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 13.8013i | − | 0.520526i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.64111 | + | 21.0878i | −0.325443 | + | 0.794211i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 20.3012i | − | 0.763504i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.8221 | 0.706881 | 0.353440 | − | 0.935457i | \(-0.385012\pi\) | ||||
0.353440 | + | 0.935457i | \(0.385012\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.19345 | −0.194769 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 0.469170i | − | 0.0175705i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.3024 | − | 4.22162i | −0.385290 | − | 0.157880i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.65242i | 0.173748i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.8755 | −0.853112 | −0.426556 | − | 0.904461i | \(-0.640273\pi\) | ||||
−0.426556 | + | 0.904461i | \(0.640273\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 66.2057 | 2.46563 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 5.31972i | − | 0.197843i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.41201 | − | 2.37562i | −0.0895797 | − | 0.0882285i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 37.5873i | − | 1.39404i | −0.717053 | − | 0.697018i | \(-0.754510\pi\) | ||
0.717053 | − | 0.697018i | \(-0.245490\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.76993 | −0.139436 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 23.6054i | − | 0.871886i | −0.899974 | − | 0.435943i | \(-0.856415\pi\) | ||
0.899974 | − | 0.435943i | \(-0.143585\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.4323 | − | 5.50412i | −0.495456 | − | 0.203023i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.98590i | 0.146822i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.12097 | −0.335520 | −0.167760 | − | 0.985828i | \(-0.553653\pi\) | ||||
−0.167760 | + | 0.985828i | \(0.553653\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.11237 | 0.0775999 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.75655i | − | 0.247874i | −0.992290 | − | 0.123937i | \(-0.960448\pi\) | ||
0.992290 | − | 0.123937i | \(-0.0395520\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.28803 | + | 22.6665i | −0.340287 | + | 0.830436i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.49034i | 0.274057i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 67.0517 | 2.45001 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.9238 | −1.34737 | −0.673683 | − | 0.739020i | \(-0.735289\pi\) | ||||
−0.673683 | + | 0.739020i | \(0.735289\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 15.4986i | − | 0.564799i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.91054 | − | 11.9837i | 0.178713 | − | 0.436131i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 17.3715i | − | 0.631378i | −0.948863 | − | 0.315689i | \(-0.897764\pi\) | ||
0.948863 | − | 0.315689i | \(-0.102236\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.43419 | 0.197249 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.6221 | 1.32755 | 0.663775 | − | 0.747933i | \(-0.268953\pi\) | ||||
0.663775 | + | 0.747933i | \(0.268953\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.0192i | 1.52120i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.732812 | − | 0.300284i | −0.0264949 | − | 0.0108568i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.41564i | − | 0.231655i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.7791 | −1.29023 | −0.645114 | − | 0.764086i | \(-0.723190\pi\) | ||||
−0.645114 | + | 0.764086i | \(0.723190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.0848 | −0.399208 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.5349i | 0.810524i | 0.914201 | + | 0.405262i | \(0.132820\pi\) | ||||
−0.914201 | + | 0.405262i | \(0.867180\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.22589 | − | 1.20740i | −0.0440353 | − | 0.0433711i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 29.9791i | 1.07550i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.21731 | 0.330244 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.1993 | 0.508090 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.677093i | 0.0241973i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −41.4710 | − | 16.9935i | −1.48016 | − | 0.606525i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 5.35297i | − | 0.190813i | −0.995438 | − | 0.0954064i | \(-0.969585\pi\) | ||
0.995438 | − | 0.0954064i | \(-0.0304151\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.3141 | −0.652001 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44.6335 | 1.58699 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.48440i | − | 0.230268i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.01891 | + | 9.80775i | −0.142536 | + | 0.347845i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.7721i | 1.44422i | 0.691777 | + | 0.722111i | \(0.256828\pi\) | ||||
−0.691777 | + | 0.722111i | \(0.743172\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.60963 | 0.127700 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.5662 | 0.408671 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.5069i | 0.688383i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.24584 | + | 10.3615i | −0.149646 | + | 0.365196i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.87552i | 0.136425i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.3161 | −0.679118 | −0.339559 | − | 0.940585i | \(-0.610278\pi\) | ||||
−0.339559 | + | 0.940585i | \(0.610278\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.7873 | −1.43224 | −0.716118 | − | 0.697979i | \(-0.754083\pi\) | ||||
−0.716118 | + | 0.697979i | \(0.754083\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.86979i | 0.240934i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 34.0356 | + | 13.9467i | 1.19222 | + | 0.488533i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.9993i | 0.629717i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.58849 | −0.160335 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.46470 | −0.120919 | −0.0604594 | − | 0.998171i | \(-0.519257\pi\) | ||||
−0.0604594 | + | 0.998171i | \(0.519257\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 5.13737i | − | 0.179077i | −0.995983 | − | 0.0895387i | \(-0.971461\pi\) | ||
0.995983 | − | 0.0895387i | \(-0.0285393\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.9848 | − | 14.1990i | 0.486888 | − | 0.494344i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.8139i | 0.549904i | 0.961458 | + | 0.274952i | \(0.0886619\pi\) | ||||
−0.961458 | + | 0.274952i | \(0.911338\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.764528 | −0.0265531 | −0.0132766 | − | 0.999912i | \(-0.504226\pi\) | ||||
−0.0132766 | + | 0.999912i | \(0.504226\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.2508 | 1.01470 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.29923i | 0.0796634i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.2435 | − | 8.70492i | −0.735161 | − | 0.301246i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.344129i | 0.0118948i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.2097 | −0.939383 | −0.469692 | − | 0.882831i | \(-0.655635\pi\) | ||||
−0.469692 | + | 0.882831i | \(0.655635\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5415 | −0.984191 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.06296i | 0.312145i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.69897 | + | 23.6694i | −0.333655 | + | 0.814251i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.9520i | 0.616837i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.74959 | 0.0943658 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.1274 | 0.381441 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.2637i | 0.454142i | 0.973878 | + | 0.227071i | \(0.0729149\pi\) | ||||
−0.973878 | + | 0.227071i | \(0.927085\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.43369 | + | 3.49878i | −0.0490312 | + | 0.119656i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 30.1619i | − | 1.03031i | −0.857096 | − | 0.515156i | \(-0.827734\pi\) | ||
0.857096 | − | 0.515156i | \(-0.172266\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.6052 | 0.907758 | 0.453879 | − | 0.891063i | \(-0.350040\pi\) | ||||
0.453879 | + | 0.891063i | \(0.350040\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.0218 | −0.682342 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 19.7440i | − | 0.672092i | −0.941846 | − | 0.336046i | \(-0.890910\pi\) | ||
0.941846 | − | 0.336046i | \(-0.109090\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.6897 | + | 7.65845i | 0.635468 | + | 0.260395i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 16.8746i | − | 0.573090i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.7005 | −0.702218 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.24921 | −0.0423277 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.6632i | 0.597807i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.1470 | + | 37.7592i | 0.545870 | + | 1.27649i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 25.9792i | − | 0.877254i | −0.898669 | − | 0.438627i | \(-0.855465\pi\) | ||
0.898669 | − | 0.438627i | \(-0.144535\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.28044 | −0.178105 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −55.9999 | −1.88669 | −0.943343 | − | 0.331820i | \(-0.892337\pi\) | ||||
−0.943343 | + | 0.331820i | \(0.892337\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.0916i | − | 0.339609i | −0.985478 | − | 0.169804i | \(-0.945686\pi\) | ||
0.985478 | − | 0.169804i | \(-0.0543136\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.6264 | + | 4.35437i | 0.357203 | + | 0.146371i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.754278i | 0.0253262i | 0.999920 | + | 0.0126631i | \(0.00403089\pi\) | ||||
−0.999920 | + | 0.0126631i | \(0.995969\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.62418 | 0.255707 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.98590 | −0.133533 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 17.2340i | − | 0.576715i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.9449 | − | 34.0311i | 0.466127 | − | 1.13753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.70311i | 0.0568651i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.233007 | 0.00777123 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.67881 | 0.0559293 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 39.0981i | − | 1.30110i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.1097 | + | 39.3140i | −0.535504 | + | 1.30684i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.545502i | 0.0181131i | 0.999959 | + | 0.00905655i | \(0.00288283\pi\) | ||||
−0.999959 | + | 0.00905655i | \(0.997117\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.52695 | 0.183317 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.04782 | −0.0678471 | −0.0339236 | − | 0.999424i | \(-0.510800\pi\) | ||||
−0.0339236 | + | 0.999424i | \(0.510800\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.8557i | 0.988080i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.7403 | + | 4.40104i | 0.355063 | + | 0.145494i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 28.9250i | − | 0.955189i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.4017 | −0.376107 | −0.188053 | − | 0.982159i | \(-0.560218\pi\) | ||||
−0.188053 | + | 0.982159i | \(0.560218\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.1784 | −1.02736 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.45014i | 0.146478i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.6360 | − | 29.0746i | 0.941547 | − | 0.955967i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.0243i | 0.591997i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.37804 | 0.0780211 | 0.0390105 | − | 0.999239i | \(-0.487579\pi\) | ||||
0.0390105 | + | 0.999239i | \(0.487579\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.9775 | 0.359775 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.4565i | 0.571501i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.92092 | − | 1.19690i | −0.0955242 | − | 0.0391428i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4.00582i | − | 0.130865i | −0.997857 | − | 0.0654323i | \(-0.979157\pi\) | ||
0.997857 | − | 0.0654323i | \(-0.0208426\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.3566 | 0.337974 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.21785 | −0.300493 | −0.150247 | − | 0.988649i | \(-0.548007\pi\) | ||||
−0.150247 | + | 0.988649i | \(0.548007\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.43150i | 0.242003i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.11426 | − | 7.60004i | 0.101307 | − | 0.247229i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 40.5049i | − | 1.31623i | −0.752916 | − | 0.658116i | \(-0.771353\pi\) | ||
0.752916 | − | 0.658116i | \(-0.228647\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.11358 | −0.198455 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.19437 | 0.0711573 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.4728i | 1.44061i | 0.693655 | + | 0.720307i | \(0.255999\pi\) | ||||
−0.693655 | + | 0.720307i | \(0.744001\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.5896 | − | 47.8064i | 0.633904 | − | 1.54698i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.69882i | 0.0872406i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 33.1440 | 1.07028 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8816 | −0.996180 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.2547i | 0.588248i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.16510 | + | 2.52627i | 0.198462 | + | 0.0813234i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.0992i | 0.324768i | 0.986728 | + | 0.162384i | \(0.0519184\pi\) | ||||
−0.986728 | + | 0.162384i | \(0.948082\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.598893 | 0.0192392 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.85147 | 0.123599 | 0.0617997 | − | 0.998089i | \(-0.480316\pi\) | ||||
0.0617997 | + | 0.998089i | \(0.480316\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 12.2537i | − | 0.392834i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.45004 | + | 4.38292i | 0.142515 | + | 0.140366i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.9997i | 1.34369i | 0.740692 | + | 0.671844i | \(0.234498\pi\) | ||||
−0.740692 | + | 0.671844i | \(0.765502\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46.1016 | 1.47341 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.4396 | −0.365239 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 17.9968i | − | 0.574010i | −0.957929 | − | 0.287005i | \(-0.907340\pi\) | ||
0.957929 | − | 0.287005i | \(-0.0926596\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.7990 | − | 6.06416i | −0.471535 | − | 0.193220i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 37.4357i | 1.19159i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.5120 | −0.461456 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.39621 | 0.171416 | 0.0857082 | − | 0.996320i | \(-0.472685\pi\) | ||||
0.0857082 | + | 0.996320i | \(0.472685\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.64862i | 0.306190i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.6907 | − | 28.5300i | 0.370621 | − | 0.904463i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.36110i | 0.138118i | 0.997613 | + | 0.0690588i | \(0.0219996\pi\) | ||||
−0.997613 | + | 0.0690588i | \(0.978000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.16175 | −0.258226 |
(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 | 4020.2.g.c.1609.7 | ✓ | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.26 | yes | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.7 | ✓ | 38 | 1.1 | even | 1 | trivial | |
4020.2.g.c.1609.26 | yes | 38 | 5.4 | even | 2 | inner |