Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(799,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("950.799");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.63107136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 13x^{4} + 42x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 799.3 | ||
Root | \(2.25342i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.799 |
Dual form | 950.2.b.h.799.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 3.25342i | 1.87836i | 0.343423 | + | 0.939181i | \(0.388414\pi\) | ||||
−0.343423 | + | 0.939181i | \(0.611586\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.25342 | 1.32820 | ||||||||
\(7\) | 0.0778929i | 0.0294407i | 0.999892 | + | 0.0147204i | \(0.00468581\pi\) | ||||
−0.999892 | + | 0.0147204i | \(0.995314\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −7.58473 | −2.52824 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.50684 | −1.35886 | −0.679431 | − | 0.733739i | \(-0.737773\pi\) | ||||
−0.679431 | + | 0.733739i | \(0.737773\pi\) | |||||||
\(12\) | − 3.25342i | − 0.939181i | ||||||||
\(13\) | − 5.33131i | − 1.47864i | −0.673354 | − | 0.739320i | \(-0.735147\pi\) | ||||
0.673354 | − | 0.739320i | \(-0.264853\pi\) | |||||||
\(14\) | 0.0778929 | 0.0208177 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 7.33131i | − 1.77810i | −0.457806 | − | 0.889052i | \(-0.651365\pi\) | ||||
0.457806 | − | 0.889052i | \(-0.348635\pi\) | |||||||
\(18\) | 7.58473i | 1.78774i | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.253418 | −0.0553003 | ||||||||
\(22\) | 4.50684i | 0.960861i | ||||||||
\(23\) | 3.40920i | 0.710868i | 0.934701 | + | 0.355434i | \(0.115667\pi\) | ||||
−0.934701 | + | 0.355434i | \(0.884333\pi\) | |||||||
\(24\) | −3.25342 | −0.664101 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.33131 | −1.04556 | ||||||||
\(27\) | − 14.9160i | − 2.87059i | ||||||||
\(28\) | − 0.0778929i | − 0.0147204i | ||||||||
\(29\) | 1.33131 | 0.247218 | 0.123609 | − | 0.992331i | \(-0.460553\pi\) | ||||
0.123609 | + | 0.992331i | \(0.460553\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50684 | −0.450241 | −0.225121 | − | 0.974331i | \(-0.572278\pi\) | ||||
−0.225121 | + | 0.974331i | \(0.572278\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 14.6626i | − 2.55243i | ||||||||
\(34\) | −7.33131 | −1.25731 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.58473 | 1.26412 | ||||||||
\(37\) | 5.50684i | 0.905318i | 0.891684 | + | 0.452659i | \(0.149525\pi\) | ||||
−0.891684 | + | 0.452659i | \(0.850475\pi\) | |||||||
\(38\) | 1.00000i | 0.162221i | ||||||||
\(39\) | 17.3450 | 2.77742 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0.253418i | 0.0391033i | ||||||||
\(43\) | 0.506836i | 0.0772918i | 0.999253 | + | 0.0386459i | \(0.0123044\pi\) | ||||
−0.999253 | + | 0.0386459i | \(0.987696\pi\) | |||||||
\(44\) | 4.50684 | 0.679431 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.40920 | 0.502660 | ||||||||
\(47\) | 5.66262i | 0.825978i | 0.910736 | + | 0.412989i | \(0.135515\pi\) | ||||
−0.910736 | + | 0.412989i | \(0.864485\pi\) | |||||||
\(48\) | 3.25342i | 0.469590i | ||||||||
\(49\) | 6.99393 | 0.999133 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 23.8518 | 3.33992 | ||||||||
\(52\) | 5.33131i | 0.739320i | ||||||||
\(53\) | − 12.9358i | − 1.77687i | −0.459006 | − | 0.888433i | \(-0.651794\pi\) | ||||
0.459006 | − | 0.888433i | \(-0.348206\pi\) | |||||||
\(54\) | −14.9160 | −2.02982 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.0778929 | −0.0104089 | ||||||||
\(57\) | − 3.25342i | − 0.430926i | ||||||||
\(58\) | − 1.33131i | − 0.174810i | ||||||||
\(59\) | −7.56499 | −0.984878 | −0.492439 | − | 0.870347i | \(-0.663894\pi\) | ||||
−0.492439 | + | 0.870347i | \(0.663894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.15579 | −0.276020 | −0.138010 | − | 0.990431i | \(-0.544071\pi\) | ||||
−0.138010 | + | 0.990431i | \(0.544071\pi\) | |||||||
\(62\) | 2.50684i | 0.318369i | ||||||||
\(63\) | − 0.590796i | − 0.0744333i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −14.6626 | −1.80484 | ||||||||
\(67\) | 4.58473i | 0.560114i | 0.959983 | + | 0.280057i | \(0.0903533\pi\) | ||||
−0.959983 | + | 0.280057i | \(0.909647\pi\) | |||||||
\(68\) | 7.33131i | 0.889052i | ||||||||
\(69\) | −11.0916 | −1.33527 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8579 | −1.28859 | −0.644297 | − | 0.764775i | \(-0.722850\pi\) | ||||
−0.644297 | + | 0.764775i | \(0.722850\pi\) | |||||||
\(72\) | − 7.58473i | − 0.893869i | ||||||||
\(73\) | − 5.09763i | − 0.596633i | −0.954467 | − | 0.298316i | \(-0.903575\pi\) | ||||
0.954467 | − | 0.298316i | \(-0.0964250\pi\) | |||||||
\(74\) | 5.50684 | 0.640157 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | − 0.351050i | − 0.0400059i | ||||||||
\(78\) | − 17.3450i | − 1.96393i | ||||||||
\(79\) | −17.0137 | −1.91419 | −0.957094 | − | 0.289778i | \(-0.906418\pi\) | ||||
−0.957094 | + | 0.289778i | \(0.906418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 25.7739 | 2.86377 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 13.1695i | − 1.44554i | −0.691091 | − | 0.722768i | \(-0.742870\pi\) | ||||
0.691091 | − | 0.722768i | \(-0.257130\pi\) | |||||||
\(84\) | 0.253418 | 0.0276502 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.506836 | 0.0546535 | ||||||||
\(87\) | 4.33131i | 0.464365i | ||||||||
\(88\) | − 4.50684i | − 0.480430i | ||||||||
\(89\) | −15.0137 | −1.59145 | −0.795723 | − | 0.605661i | \(-0.792909\pi\) | ||||
−0.795723 | + | 0.605661i | \(0.792909\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.415271 | 0.0435322 | ||||||||
\(92\) | − 3.40920i | − 0.355434i | ||||||||
\(93\) | − 8.15579i | − 0.845716i | ||||||||
\(94\) | 5.66262 | 0.584055 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.25342 | 0.332051 | ||||||||
\(97\) | − 7.67629i | − 0.779410i | −0.920940 | − | 0.389705i | \(-0.872577\pi\) | ||||
0.920940 | − | 0.389705i | \(-0.127423\pi\) | |||||||
\(98\) | − 6.99393i | − 0.706494i | ||||||||
\(99\) | 34.1831 | 3.43553 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.15579 | −0.413516 | −0.206758 | − | 0.978392i | \(-0.566291\pi\) | ||||
−0.206758 | + | 0.978392i | \(0.566291\pi\) | |||||||
\(102\) | − 23.8518i | − 2.36168i | ||||||||
\(103\) | 2.35105i | 0.231656i | 0.993269 | + | 0.115828i | \(0.0369521\pi\) | ||||
−0.993269 | + | 0.115828i | \(0.963048\pi\) | |||||||
\(104\) | 5.33131 | 0.522778 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.9358 | −1.25643 | ||||||||
\(107\) | 14.0334i | 1.35666i | 0.734757 | + | 0.678331i | \(0.237296\pi\) | ||||
−0.734757 | + | 0.678331i | \(0.762704\pi\) | |||||||
\(108\) | 14.9160i | 1.43530i | ||||||||
\(109\) | 0.0778929 | 0.00746078 | 0.00373039 | − | 0.999993i | \(-0.498813\pi\) | ||||
0.00373039 | + | 0.999993i | \(0.498813\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.9160 | −1.70052 | ||||||||
\(112\) | 0.0778929i | 0.00736018i | ||||||||
\(113\) | − 6.00000i | − 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | −3.25342 | −0.304711 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.33131 | −0.123609 | ||||||||
\(117\) | 40.4365i | 3.73836i | ||||||||
\(118\) | 7.56499i | 0.696414i | ||||||||
\(119\) | 0.571057 | 0.0523487 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.31157 | 0.846506 | ||||||||
\(122\) | 2.15579i | 0.195176i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.50684 | 0.225121 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.590796 | −0.0526323 | ||||||||
\(127\) | − 17.8321i | − 1.58234i | −0.611596 | − | 0.791171i | \(-0.709472\pi\) | ||||
0.611596 | − | 0.791171i | \(-0.290528\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −1.64895 | −0.145182 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.49316 | −0.130458 | −0.0652292 | − | 0.997870i | \(-0.520778\pi\) | ||||
−0.0652292 | + | 0.997870i | \(0.520778\pi\) | |||||||
\(132\) | 14.6626i | 1.27622i | ||||||||
\(133\) | − 0.0778929i | − 0.00675417i | ||||||||
\(134\) | 4.58473 | 0.396060 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.33131 | 0.628655 | ||||||||
\(137\) | 8.42894i | 0.720133i | 0.932927 | + | 0.360067i | \(0.117246\pi\) | ||||
−0.932927 | + | 0.360067i | \(0.882754\pi\) | |||||||
\(138\) | 11.0916i | 0.944177i | ||||||||
\(139\) | −8.81841 | −0.747968 | −0.373984 | − | 0.927435i | \(-0.622008\pi\) | ||||
−0.373984 | + | 0.927435i | \(0.622008\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.4229 | −1.55149 | ||||||||
\(142\) | 10.8579i | 0.911174i | ||||||||
\(143\) | 24.0273i | 2.00927i | ||||||||
\(144\) | −7.58473 | −0.632061 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.09763 | −0.421883 | ||||||||
\(147\) | 22.7542i | 1.87673i | ||||||||
\(148\) | − 5.50684i | − 0.452659i | ||||||||
\(149\) | −17.6763 | −1.44810 | −0.724049 | − | 0.689748i | \(-0.757721\pi\) | ||||
−0.724049 | + | 0.689748i | \(0.757721\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0000 | 1.62758 | 0.813788 | − | 0.581161i | \(-0.197401\pi\) | ||||
0.813788 | + | 0.581161i | \(0.197401\pi\) | |||||||
\(152\) | − 1.00000i | − 0.0811107i | ||||||||
\(153\) | 55.6060i | 4.49548i | ||||||||
\(154\) | −0.351050 | −0.0282884 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −17.3450 | −1.38871 | ||||||||
\(157\) | − 0.506836i | − 0.0404499i | −0.999795 | − | 0.0202250i | \(-0.993562\pi\) | ||||
0.999795 | − | 0.0202250i | \(-0.00643824\pi\) | |||||||
\(158\) | 17.0137i | 1.35354i | ||||||||
\(159\) | 42.0855 | 3.33760 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.265553 | −0.0209285 | ||||||||
\(162\) | − 25.7739i | − 2.02499i | ||||||||
\(163\) | 0.830542i | 0.0650531i | 0.999471 | + | 0.0325265i | \(0.0103553\pi\) | ||||
−0.999471 | + | 0.0325265i | \(0.989645\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.1695 | −1.02215 | ||||||||
\(167\) | − 16.5068i | − 1.27734i | −0.769482 | − | 0.638669i | \(-0.779485\pi\) | ||||
0.769482 | − | 0.638669i | \(-0.220515\pi\) | |||||||
\(168\) | − 0.253418i | − 0.0195516i | ||||||||
\(169\) | −15.4229 | −1.18638 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.58473 | 0.580019 | ||||||||
\(172\) | − 0.506836i | − 0.0386459i | ||||||||
\(173\) | 18.8321i | 1.43178i | 0.698215 | + | 0.715888i | \(0.253978\pi\) | ||||
−0.698215 | + | 0.715888i | \(0.746022\pi\) | |||||||
\(174\) | 4.33131 | 0.328356 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.50684 | −0.339716 | ||||||||
\(177\) | − 24.6121i | − 1.84996i | ||||||||
\(178\) | 15.0137i | 1.12532i | ||||||||
\(179\) | 7.15579 | 0.534849 | 0.267424 | − | 0.963579i | \(-0.413827\pi\) | ||||
0.267424 | + | 0.963579i | \(0.413827\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.5205 | 0.930642 | 0.465321 | − | 0.885142i | \(-0.345939\pi\) | ||||
0.465321 | + | 0.885142i | \(0.345939\pi\) | |||||||
\(182\) | − 0.415271i | − 0.0307819i | ||||||||
\(183\) | − 7.01367i | − 0.518466i | ||||||||
\(184\) | −3.40920 | −0.251330 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −8.15579 | −0.598011 | ||||||||
\(187\) | 33.0410i | 2.41620i | ||||||||
\(188\) | − 5.66262i | − 0.412989i | ||||||||
\(189\) | 1.16185 | 0.0845124 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.90237 | −0.354723 | −0.177361 | − | 0.984146i | \(-0.556756\pi\) | ||||
−0.177361 | + | 0.984146i | \(0.556756\pi\) | |||||||
\(192\) | − 3.25342i | − 0.234795i | ||||||||
\(193\) | 18.1558i | 1.30688i | 0.756977 | + | 0.653441i | \(0.226675\pi\) | ||||
−0.756977 | + | 0.653441i | \(0.773325\pi\) | |||||||
\(194\) | −7.67629 | −0.551126 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.99393 | −0.499567 | ||||||||
\(197\) | 2.98633i | 0.212767i | 0.994325 | + | 0.106384i | \(0.0339271\pi\) | ||||
−0.994325 | + | 0.106384i | \(0.966073\pi\) | |||||||
\(198\) | − 34.1831i | − 2.42929i | ||||||||
\(199\) | 3.06422 | 0.217217 | 0.108608 | − | 0.994085i | \(-0.465361\pi\) | ||||
0.108608 | + | 0.994085i | \(0.465361\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.9160 | −1.05210 | ||||||||
\(202\) | 4.15579i | 0.292400i | ||||||||
\(203\) | 0.103700i | 0.00727829i | ||||||||
\(204\) | −23.8518 | −1.66996 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.35105 | 0.163805 | ||||||||
\(207\) | − 25.8579i | − 1.79725i | ||||||||
\(208\) | − 5.33131i | − 0.369660i | ||||||||
\(209\) | 4.50684 | 0.311744 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.2534 | 1.32546 | 0.662730 | − | 0.748858i | \(-0.269398\pi\) | ||||
0.662730 | + | 0.748858i | \(0.269398\pi\) | |||||||
\(212\) | 12.9358i | 0.888433i | ||||||||
\(213\) | − 35.3252i | − 2.42045i | ||||||||
\(214\) | 14.0334 | 0.959304 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.9160 | 1.01491 | ||||||||
\(217\) | − 0.195265i | − 0.0132554i | ||||||||
\(218\) | − 0.0778929i | − 0.00527557i | ||||||||
\(219\) | 16.5847 | 1.12069 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −39.0855 | −2.62918 | ||||||||
\(222\) | 17.9160i | 1.20245i | ||||||||
\(223\) | − 14.5068i | − 0.971450i | −0.874112 | − | 0.485725i | \(-0.838556\pi\) | ||||
0.874112 | − | 0.485725i | \(-0.161444\pi\) | |||||||
\(224\) | 0.0778929 | 0.00520444 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 21.5984i | 1.43354i | 0.697312 | + | 0.716768i | \(0.254379\pi\) | ||||
−0.697312 | + | 0.716768i | \(0.745621\pi\) | |||||||
\(228\) | 3.25342i | 0.215463i | ||||||||
\(229\) | 19.0137 | 1.25646 | 0.628229 | − | 0.778028i | \(-0.283780\pi\) | ||||
0.628229 | + | 0.778028i | \(0.283780\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.14211 | 0.0751456 | ||||||||
\(232\) | 1.33131i | 0.0874048i | ||||||||
\(233\) | − 6.01367i | − 0.393969i | −0.980407 | − | 0.196984i | \(-0.936885\pi\) | ||||
0.980407 | − | 0.196984i | \(-0.0631148\pi\) | |||||||
\(234\) | 40.4365 | 2.64342 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.56499 | 0.492439 | ||||||||
\(237\) | − 55.3526i | − 3.59554i | ||||||||
\(238\) | − 0.571057i | − 0.0370161i | ||||||||
\(239\) | −15.4092 | −0.996739 | −0.498369 | − | 0.866965i | \(-0.666068\pi\) | ||||
−0.498369 | + | 0.866965i | \(0.666068\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.81841 | −0.310381 | −0.155190 | − | 0.987885i | \(-0.549599\pi\) | ||||
−0.155190 | + | 0.987885i | \(0.549599\pi\) | |||||||
\(242\) | − 9.31157i | − 0.598570i | ||||||||
\(243\) | 39.1052i | 2.50860i | ||||||||
\(244\) | 2.15579 | 0.138010 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.33131i | 0.339223i | ||||||||
\(248\) | − 2.50684i | − 0.159184i | ||||||||
\(249\) | 42.8458 | 2.71524 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.52051 | 0.0959736 | 0.0479868 | − | 0.998848i | \(-0.484719\pi\) | ||||
0.0479868 | + | 0.998848i | \(0.484719\pi\) | |||||||
\(252\) | 0.590796i | 0.0372167i | ||||||||
\(253\) | − 15.3647i | − 0.965972i | ||||||||
\(254\) | −17.8321 | −1.11888 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 16.5068i | − 1.02967i | −0.857290 | − | 0.514834i | \(-0.827854\pi\) | ||||
0.857290 | − | 0.514834i | \(-0.172146\pi\) | |||||||
\(258\) | 1.64895i | 0.102659i | ||||||||
\(259\) | −0.428943 | −0.0266532 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.0976 | −0.625028 | ||||||||
\(262\) | 1.49316i | 0.0922480i | ||||||||
\(263\) | − 18.0273i | − 1.11161i | −0.831311 | − | 0.555807i | \(-0.812409\pi\) | ||||
0.831311 | − | 0.555807i | \(-0.187591\pi\) | |||||||
\(264\) | 14.6626 | 0.902422 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.0778929 | −0.00477592 | ||||||||
\(267\) | − 48.8458i | − 2.98931i | ||||||||
\(268\) | − 4.58473i | − 0.280057i | ||||||||
\(269\) | −20.2089 | −1.23216 | −0.616080 | − | 0.787683i | \(-0.711280\pi\) | ||||
−0.616080 | + | 0.787683i | \(0.711280\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.08396 | 0.369574 | 0.184787 | − | 0.982779i | \(-0.440840\pi\) | ||||
0.184787 | + | 0.982779i | \(0.440840\pi\) | |||||||
\(272\) | − 7.33131i | − 0.444526i | ||||||||
\(273\) | 1.35105i | 0.0817693i | ||||||||
\(274\) | 8.42894 | 0.509211 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.0916 | 0.667634 | ||||||||
\(277\) | 31.3647i | 1.88452i | 0.334877 | + | 0.942262i | \(0.391305\pi\) | ||||
−0.334877 | + | 0.942262i | \(0.608695\pi\) | |||||||
\(278\) | 8.81841i | 0.528893i | ||||||||
\(279\) | 19.0137 | 1.13832 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.3252 | 0.675607 | 0.337804 | − | 0.941217i | \(-0.390316\pi\) | ||||
0.337804 | + | 0.941217i | \(0.390316\pi\) | |||||||
\(282\) | 18.4229i | 1.09707i | ||||||||
\(283\) | 26.1437i | 1.55408i | 0.629452 | + | 0.777039i | \(0.283279\pi\) | ||||
−0.629452 | + | 0.777039i | \(0.716721\pi\) | |||||||
\(284\) | 10.8579 | 0.644297 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.0273 | 1.42077 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 7.58473i | 0.446934i | ||||||||
\(289\) | −36.7481 | −2.16165 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.9742 | 1.46401 | ||||||||
\(292\) | 5.09763i | 0.298316i | ||||||||
\(293\) | 1.33131i | 0.0777760i | 0.999244 | + | 0.0388880i | \(0.0123816\pi\) | ||||
−0.999244 | + | 0.0388880i | \(0.987618\pi\) | |||||||
\(294\) | 22.7542 | 1.32705 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.50684 | −0.320078 | ||||||||
\(297\) | 67.2241i | 3.90074i | ||||||||
\(298\) | 17.6763i | 1.02396i | ||||||||
\(299\) | 18.1755 | 1.05112 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0394789 | −0.00227553 | ||||||||
\(302\) | − 20.0000i | − 1.15087i | ||||||||
\(303\) | − 13.5205i | − 0.776733i | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 55.6060 | 3.17878 | ||||||||
\(307\) | 2.84421i | 0.162328i | 0.996701 | + | 0.0811639i | \(0.0258637\pi\) | ||||
−0.996701 | + | 0.0811639i | \(0.974136\pi\) | |||||||
\(308\) | 0.351050i | 0.0200030i | ||||||||
\(309\) | −7.64895 | −0.435134 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.3895 | −0.929361 | −0.464681 | − | 0.885478i | \(-0.653831\pi\) | ||||
−0.464681 | + | 0.885478i | \(0.653831\pi\) | |||||||
\(312\) | 17.3450i | 0.981966i | ||||||||
\(313\) | − 21.0471i | − 1.18965i | −0.803855 | − | 0.594826i | \(-0.797221\pi\) | ||||
0.803855 | − | 0.594826i | \(-0.202779\pi\) | |||||||
\(314\) | −0.506836 | −0.0286024 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.0137 | 0.957094 | ||||||||
\(317\) | 30.8902i | 1.73497i | 0.497465 | + | 0.867484i | \(0.334264\pi\) | ||||
−0.497465 | + | 0.867484i | \(0.665736\pi\) | |||||||
\(318\) | − 42.0855i | − 2.36004i | ||||||||
\(319\) | −6.00000 | −0.335936 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −45.6566 | −2.54830 | ||||||||
\(322\) | 0.265553i | 0.0147987i | ||||||||
\(323\) | 7.33131i | 0.407925i | ||||||||
\(324\) | −25.7739 | −1.43188 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.830542 | 0.0459995 | ||||||||
\(327\) | 0.253418i | 0.0140140i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.441078 | −0.0243174 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.3845 | 1.56015 | 0.780076 | − | 0.625685i | \(-0.215181\pi\) | ||||
0.780076 | + | 0.625685i | \(0.215181\pi\) | |||||||
\(332\) | 13.1695i | 0.722768i | ||||||||
\(333\) | − 41.7679i | − 2.28886i | ||||||||
\(334\) | −16.5068 | −0.903214 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.253418 | −0.0138251 | ||||||||
\(337\) | 17.8716i | 0.973526i | 0.873534 | + | 0.486763i | \(0.161822\pi\) | ||||
−0.873534 | + | 0.486763i | \(0.838178\pi\) | |||||||
\(338\) | 15.4229i | 0.838894i | ||||||||
\(339\) | 19.5205 | 1.06021 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.2979 | 0.611816 | ||||||||
\(342\) | − 7.58473i | − 0.410135i | ||||||||
\(343\) | 1.09003i | 0.0588560i | ||||||||
\(344\) | −0.506836 | −0.0273268 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.8321 | 1.01242 | ||||||||
\(347\) | − 33.0410i | − 1.77373i | −0.462024 | − | 0.886867i | \(-0.652877\pi\) | ||||
0.462024 | − | 0.886867i | \(-0.347123\pi\) | |||||||
\(348\) | − 4.33131i | − 0.232183i | ||||||||
\(349\) | 19.7158 | 1.05536 | 0.527681 | − | 0.849443i | \(-0.323062\pi\) | ||||
0.527681 | + | 0.849443i | \(0.323062\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −79.5220 | −4.24457 | ||||||||
\(352\) | 4.50684i | 0.240215i | ||||||||
\(353\) | − 5.90997i | − 0.314556i | −0.987554 | − | 0.157278i | \(-0.949728\pi\) | ||||
0.987554 | − | 0.157278i | \(-0.0502719\pi\) | |||||||
\(354\) | −24.6121 | −1.30812 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 15.0137 | 0.795723 | ||||||||
\(357\) | 1.85789i | 0.0983298i | ||||||||
\(358\) | − 7.15579i | − 0.378195i | ||||||||
\(359\) | 7.00760 | 0.369847 | 0.184924 | − | 0.982753i | \(-0.440796\pi\) | ||||
0.184924 | + | 0.982753i | \(0.440796\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | − 12.5205i | − 0.658063i | ||||||||
\(363\) | 30.2944i | 1.59005i | ||||||||
\(364\) | −0.415271 | −0.0217661 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.01367 | −0.366611 | ||||||||
\(367\) | − 17.7158i | − 0.924756i | −0.886683 | − | 0.462378i | \(-0.846996\pi\) | ||||
0.886683 | − | 0.462378i | \(-0.153004\pi\) | |||||||
\(368\) | 3.40920i | 0.177717i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.00760 | 0.0523122 | ||||||||
\(372\) | 8.15579i | 0.422858i | ||||||||
\(373\) | 15.4487i | 0.799902i | 0.916536 | + | 0.399951i | \(0.130973\pi\) | ||||
−0.916536 | + | 0.399951i | \(0.869027\pi\) | |||||||
\(374\) | 33.0410 | 1.70851 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.66262 | −0.292027 | ||||||||
\(377\) | − 7.09763i | − 0.365547i | ||||||||
\(378\) | − 1.16185i | − 0.0597593i | ||||||||
\(379\) | −34.4563 | −1.76990 | −0.884950 | − | 0.465685i | \(-0.845808\pi\) | ||||
−0.884950 | + | 0.465685i | \(0.845808\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 58.0152 | 2.97221 | ||||||||
\(382\) | 4.90237i | 0.250827i | ||||||||
\(383\) | − 12.0273i | − 0.614569i | −0.951618 | − | 0.307284i | \(-0.900580\pi\) | ||||
0.951618 | − | 0.307284i | \(-0.0994203\pi\) | |||||||
\(384\) | −3.25342 | −0.166025 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.1558 | 0.924105 | ||||||||
\(387\) | − 3.84421i | − 0.195412i | ||||||||
\(388\) | 7.67629i | 0.389705i | ||||||||
\(389\) | 15.3647 | 0.779022 | 0.389511 | − | 0.921022i | \(-0.372644\pi\) | ||||
0.389511 | + | 0.921022i | \(0.372644\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.9939 | 1.26400 | ||||||||
\(392\) | 6.99393i | 0.353247i | ||||||||
\(393\) | − 4.85789i | − 0.245048i | ||||||||
\(394\) | 2.98633 | 0.150449 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −34.1831 | −1.71777 | ||||||||
\(397\) | − 1.32524i | − 0.0665121i | −0.999447 | − | 0.0332560i | \(-0.989412\pi\) | ||||
0.999447 | − | 0.0332560i | \(-0.0105877\pi\) | |||||||
\(398\) | − 3.06422i | − 0.153596i | ||||||||
\(399\) | 0.253418 | 0.0126868 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.46736 | −0.322964 | −0.161482 | − | 0.986876i | \(-0.551627\pi\) | ||||
−0.161482 | + | 0.986876i | \(0.551627\pi\) | |||||||
\(402\) | 14.9160i | 0.743944i | ||||||||
\(403\) | 13.3647i | 0.665744i | ||||||||
\(404\) | 4.15579 | 0.206758 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.103700 | 0.00514653 | ||||||||
\(407\) | − 24.8184i | − 1.23020i | ||||||||
\(408\) | 23.8518i | 1.18084i | ||||||||
\(409\) | 1.36472 | 0.0674812 | 0.0337406 | − | 0.999431i | \(-0.489258\pi\) | ||||
0.0337406 | + | 0.999431i | \(0.489258\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −27.4229 | −1.35267 | ||||||||
\(412\) | − 2.35105i | − 0.115828i | ||||||||
\(413\) | − 0.589259i | − 0.0289955i | ||||||||
\(414\) | −25.8579 | −1.27085 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.33131 | −0.261389 | ||||||||
\(417\) | − 28.6900i | − 1.40495i | ||||||||
\(418\) | − 4.50684i | − 0.220437i | ||||||||
\(419\) | −16.6231 | −0.812094 | −0.406047 | − | 0.913852i | \(-0.633093\pi\) | ||||
−0.406047 | + | 0.913852i | \(0.633093\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.1128 | −1.51635 | −0.758174 | − | 0.652053i | \(-0.773908\pi\) | ||||
−0.758174 | + | 0.652053i | \(0.773908\pi\) | |||||||
\(422\) | − 19.2534i | − 0.937242i | ||||||||
\(423\) | − 42.9495i | − 2.08827i | ||||||||
\(424\) | 12.9358 | 0.628217 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −35.3252 | −1.71151 | ||||||||
\(427\) | − 0.167920i | − 0.00812623i | ||||||||
\(428\) | − 14.0334i | − 0.678331i | ||||||||
\(429\) | −78.1710 | −3.77413 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.1831 | −0.490504 | −0.245252 | − | 0.969459i | \(-0.578871\pi\) | ||||
−0.245252 | + | 0.969459i | \(0.578871\pi\) | |||||||
\(432\) | − 14.9160i | − 0.717648i | ||||||||
\(433\) | 22.1953i | 1.06664i | 0.845915 | + | 0.533318i | \(0.179055\pi\) | ||||
−0.845915 | + | 0.533318i | \(0.820945\pi\) | |||||||
\(434\) | −0.195265 | −0.00937300 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0778929 | −0.00373039 | ||||||||
\(437\) | − 3.40920i | − 0.163084i | ||||||||
\(438\) | − 16.5847i | − 0.792449i | ||||||||
\(439\) | 9.32524 | 0.445070 | 0.222535 | − | 0.974925i | \(-0.428567\pi\) | ||||
0.222535 | + | 0.974925i | \(0.428567\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −53.0471 | −2.52605 | ||||||||
\(442\) | 39.0855i | 1.85911i | ||||||||
\(443\) | − 13.9879i | − 0.664584i | −0.943177 | − | 0.332292i | \(-0.892178\pi\) | ||||
0.943177 | − | 0.332292i | \(-0.107822\pi\) | |||||||
\(444\) | 17.9160 | 0.850258 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.5068 | −0.686919 | ||||||||
\(447\) | − 57.5084i | − 2.72005i | ||||||||
\(448\) | − 0.0778929i | − 0.00368009i | ||||||||
\(449\) | −13.4932 | −0.636782 | −0.318391 | − | 0.947960i | \(-0.603142\pi\) | ||||
−0.318391 | + | 0.947960i | \(0.603142\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000i | 0.282216i | ||||||||
\(453\) | 65.0684i | 3.05718i | ||||||||
\(454\) | 21.5984 | 1.01366 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.25342 | 0.152355 | ||||||||
\(457\) | − 9.68236i | − 0.452922i | −0.974020 | − | 0.226461i | \(-0.927284\pi\) | ||||
0.974020 | − | 0.226461i | \(-0.0727155\pi\) | |||||||
\(458\) | − 19.0137i | − 0.888451i | ||||||||
\(459\) | −109.354 | −5.10421 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.66262 | 0.403459 | 0.201729 | − | 0.979441i | \(-0.435344\pi\) | ||||
0.201729 | + | 0.979441i | \(0.435344\pi\) | |||||||
\(462\) | − 1.14211i | − 0.0531359i | ||||||||
\(463\) | 28.0015i | 1.30134i | 0.759360 | + | 0.650671i | \(0.225512\pi\) | ||||
−0.759360 | + | 0.650671i | \(0.774488\pi\) | |||||||
\(464\) | 1.33131 | 0.0618046 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.01367 | −0.278578 | ||||||||
\(467\) | − 16.9742i | − 0.785472i | −0.919651 | − | 0.392736i | \(-0.871529\pi\) | ||||
0.919651 | − | 0.392736i | \(-0.128471\pi\) | |||||||
\(468\) | − 40.4365i | − 1.86918i | ||||||||
\(469\) | −0.357118 | −0.0164902 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.64895 | 0.0759796 | ||||||||
\(472\) | − 7.56499i | − 0.348207i | ||||||||
\(473\) | − 2.28423i | − 0.105029i | ||||||||
\(474\) | −55.3526 | −2.54243 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.571057 | −0.0261743 | ||||||||
\(477\) | 98.1144i | 4.49235i | ||||||||
\(478\) | 15.4092i | 0.704801i | ||||||||
\(479\) | −10.0532 | −0.459340 | −0.229670 | − | 0.973269i | \(-0.573765\pi\) | ||||
−0.229670 | + | 0.973269i | \(0.573765\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.3587 | 1.33864 | ||||||||
\(482\) | 4.81841i | 0.219472i | ||||||||
\(483\) | − 0.863954i | − 0.0393113i | ||||||||
\(484\) | −9.31157 | −0.423253 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 39.1052 | 1.77385 | ||||||||
\(487\) | − 19.2089i | − 0.870440i | −0.900324 | − | 0.435220i | \(-0.856671\pi\) | ||||
0.900324 | − | 0.435220i | \(-0.143329\pi\) | |||||||
\(488\) | − 2.15579i | − 0.0975878i | ||||||||
\(489\) | −2.70210 | −0.122193 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.32524 | 0.240325 | 0.120162 | − | 0.992754i | \(-0.461658\pi\) | ||||
0.120162 | + | 0.992754i | \(0.461658\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 9.76025i | − 0.439580i | ||||||||
\(494\) | 5.33131 | 0.239867 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.50684 | −0.112560 | ||||||||
\(497\) | − 0.845752i | − 0.0379372i | ||||||||
\(498\) | − 42.8458i | − 1.91996i | ||||||||
\(499\) | 11.9605 | 0.535426 | 0.267713 | − | 0.963499i | \(-0.413732\pi\) | ||||
0.267713 | + | 0.963499i | \(0.413732\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 53.7036 | 2.39930 | ||||||||
\(502\) | − 1.52051i | − 0.0678636i | ||||||||
\(503\) | − 19.3313i | − 0.861941i | −0.902366 | − | 0.430970i | \(-0.858171\pi\) | ||||
0.902366 | − | 0.430970i | \(-0.141829\pi\) | |||||||
\(504\) | 0.590796 | 0.0263162 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.3647 | −0.683045 | ||||||||
\(507\) | − 50.1771i | − 2.22844i | ||||||||
\(508\) | 17.8321i | 0.791171i | ||||||||
\(509\) | 36.1573 | 1.60265 | 0.801323 | − | 0.598232i | \(-0.204130\pi\) | ||||
0.801323 | + | 0.598232i | \(0.204130\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.397069 | 0.0175653 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 14.9160i | 0.658559i | ||||||||
\(514\) | −16.5068 | −0.728085 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.64895 | 0.0725910 | ||||||||
\(517\) | − 25.5205i | − 1.12239i | ||||||||
\(518\) | 0.428943i | 0.0188467i | ||||||||
\(519\) | −61.2686 | −2.68939 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.5205 | −1.38094 | −0.690469 | − | 0.723362i | \(-0.742596\pi\) | ||||
−0.690469 | + | 0.723362i | \(0.742596\pi\) | |||||||
\(522\) | 10.0976i | 0.441961i | ||||||||
\(523\) | 5.59840i | 0.244801i | 0.992481 | + | 0.122400i | \(0.0390592\pi\) | ||||
−0.992481 | + | 0.122400i | \(0.960941\pi\) | |||||||
\(524\) | 1.49316 | 0.0652292 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.0273 | −0.786030 | ||||||||
\(527\) | 18.3784i | 0.800575i | ||||||||
\(528\) | − 14.6626i | − 0.638109i | ||||||||
\(529\) | 11.3773 | 0.494667 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 57.3784 | 2.49001 | ||||||||
\(532\) | 0.0778929i | 0.00337708i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −48.8458 | −2.11376 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.58473 | −0.198030 | ||||||||
\(537\) | 23.2808i | 1.00464i | ||||||||
\(538\) | 20.2089i | 0.871269i | ||||||||
\(539\) | −31.5205 | −1.35768 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.1968 | 0.653362 | 0.326681 | − | 0.945135i | \(-0.394070\pi\) | ||||
0.326681 | + | 0.945135i | \(0.394070\pi\) | |||||||
\(542\) | − 6.08396i | − 0.261328i | ||||||||
\(543\) | 40.7344i | 1.74808i | ||||||||
\(544\) | −7.33131 | −0.314327 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.35105 | 0.0578196 | ||||||||
\(547\) | 26.6505i | 1.13949i | 0.821821 | + | 0.569746i | \(0.192959\pi\) | ||||
−0.821821 | + | 0.569746i | \(0.807041\pi\) | |||||||
\(548\) | − 8.42894i | − 0.360067i | ||||||||
\(549\) | 16.3511 | 0.697846 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.33131 | −0.0567158 | ||||||||
\(552\) | − 11.0916i | − 0.472088i | ||||||||
\(553\) | − 1.32524i | − 0.0563551i | ||||||||
\(554\) | 31.3647 | 1.33256 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.81841 | 0.373984 | ||||||||
\(557\) | − 12.8458i | − 0.544292i | −0.962256 | − | 0.272146i | \(-0.912267\pi\) | ||||
0.962256 | − | 0.272146i | \(-0.0877334\pi\) | |||||||
\(558\) | − 19.0137i | − 0.804913i | ||||||||
\(559\) | 2.70210 | 0.114287 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −107.496 | −4.53849 | ||||||||
\(562\) | − 11.3252i | − 0.477727i | ||||||||
\(563\) | 10.1968i | 0.429744i | 0.976642 | + | 0.214872i | \(0.0689334\pi\) | ||||
−0.976642 | + | 0.214872i | \(0.931067\pi\) | |||||||
\(564\) | 18.4229 | 0.775743 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 26.1437 | 1.09890 | ||||||||
\(567\) | 2.00760i | 0.0843115i | ||||||||
\(568\) | − 10.8579i | − 0.455587i | ||||||||
\(569\) | 24.3784 | 1.02200 | 0.510998 | − | 0.859582i | \(-0.329276\pi\) | ||||
0.510998 | + | 0.859582i | \(0.329276\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.32371 | 0.348336 | 0.174168 | − | 0.984716i | \(-0.444276\pi\) | ||||
0.174168 | + | 0.984716i | \(0.444276\pi\) | |||||||
\(572\) | − 24.0273i | − 1.00463i | ||||||||
\(573\) | − 15.9495i | − 0.666298i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.58473 | 0.316030 | ||||||||
\(577\) | 7.29290i | 0.303607i | 0.988411 | + | 0.151804i | \(0.0485081\pi\) | ||||
−0.988411 | + | 0.151804i | \(0.951492\pi\) | |||||||
\(578\) | 36.7481i | 1.52852i | ||||||||
\(579\) | −59.0684 | −2.45480 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.02581 | 0.0425576 | ||||||||
\(582\) | − 24.9742i | − 1.03521i | ||||||||
\(583\) | 58.2994i | 2.41452i | ||||||||
\(584\) | 5.09763 | 0.210942 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.33131 | 0.0549959 | ||||||||
\(587\) | − 5.53264i | − 0.228357i | −0.993460 | − | 0.114178i | \(-0.963576\pi\) | ||||
0.993460 | − | 0.114178i | \(-0.0364235\pi\) | |||||||
\(588\) | − 22.7542i | − 0.938367i | ||||||||
\(589\) | 2.50684 | 0.103292 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.71577 | −0.399653 | ||||||||
\(592\) | 5.50684i | 0.226330i | ||||||||
\(593\) | − 26.3252i | − 1.08105i | −0.841329 | − | 0.540524i | \(-0.818226\pi\) | ||||
0.841329 | − | 0.540524i | \(-0.181774\pi\) | |||||||
\(594\) | 67.2241 | 2.75824 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.6763 | 0.724049 | ||||||||
\(597\) | 9.96919i | 0.408012i | ||||||||
\(598\) | − 18.1755i | − 0.743252i | ||||||||
\(599\) | −22.2994 | −0.911130 | −0.455565 | − | 0.890202i | \(-0.650563\pi\) | ||||
−0.455565 | + | 0.890202i | \(0.650563\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.4947 | 1.32549 | 0.662743 | − | 0.748847i | \(-0.269392\pi\) | ||||
0.662743 | + | 0.748847i | \(0.269392\pi\) | |||||||
\(602\) | 0.0394789i | 0.00160904i | ||||||||
\(603\) | − 34.7739i | − 1.41610i | ||||||||
\(604\) | −20.0000 | −0.813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −13.5205 | −0.549233 | ||||||||
\(607\) | − 8.35105i | − 0.338959i | −0.985534 | − | 0.169479i | \(-0.945791\pi\) | ||||
0.985534 | − | 0.169479i | \(-0.0542086\pi\) | |||||||
\(608\) | 1.00000i | 0.0405554i | ||||||||
\(609\) | −0.337378 | −0.0136713 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.1892 | 1.22132 | ||||||||
\(612\) | − 55.6060i | − 2.24774i | ||||||||
\(613\) | − 38.2994i | − 1.54690i | −0.633858 | − | 0.773450i | \(-0.718529\pi\) | ||||
0.633858 | − | 0.773450i | \(-0.281471\pi\) | |||||||
\(614\) | 2.84421 | 0.114783 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.351050 | 0.0141442 | ||||||||
\(617\) | 14.3526i | 0.577813i | 0.957357 | + | 0.288907i | \(0.0932917\pi\) | ||||
−0.957357 | + | 0.288907i | \(0.906708\pi\) | |||||||
\(618\) | 7.64895i | 0.307686i | ||||||||
\(619\) | 8.62314 | 0.346593 | 0.173297 | − | 0.984870i | \(-0.444558\pi\) | ||||
0.173297 | + | 0.984870i | \(0.444558\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 50.8518 | 2.04061 | ||||||||
\(622\) | 16.3895i | 0.657158i | ||||||||
\(623\) | − 1.16946i | − 0.0468533i | ||||||||
\(624\) | 17.3450 | 0.694355 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −21.0471 | −0.841211 | ||||||||
\(627\) | 14.6626i | 0.585569i | ||||||||
\(628\) | 0.506836i | 0.0202250i | ||||||||
\(629\) | 40.3723 | 1.60975 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.3374 | −0.411525 | −0.205762 | − | 0.978602i | \(-0.565967\pi\) | ||||
−0.205762 | + | 0.978602i | \(0.565967\pi\) | |||||||
\(632\) | − 17.0137i | − 0.676768i | ||||||||
\(633\) | 62.6394i | 2.48969i | ||||||||
\(634\) | 30.8902 | 1.22681 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −42.0855 | −1.66880 | ||||||||
\(637\) | − 37.2868i | − 1.47736i | ||||||||
\(638\) | 6.00000i | 0.237542i | ||||||||
\(639\) | 82.3541 | 3.25788 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.88369 | 0.232392 | 0.116196 | − | 0.993226i | \(-0.462930\pi\) | ||||
0.116196 | + | 0.993226i | \(0.462930\pi\) | |||||||
\(642\) | 45.6566i | 1.80192i | ||||||||
\(643\) | − 25.5084i | − 1.00595i | −0.864300 | − | 0.502976i | \(-0.832238\pi\) | ||||
0.864300 | − | 0.502976i | \(-0.167762\pi\) | |||||||
\(644\) | 0.265553 | 0.0104642 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.33131 | 0.288447 | ||||||||
\(647\) | 5.09157i | 0.200170i | 0.994979 | + | 0.100085i | \(0.0319115\pi\) | ||||
−0.994979 | + | 0.100085i | \(0.968089\pi\) | |||||||
\(648\) | 25.7739i | 1.01250i | ||||||||
\(649\) | 34.0942 | 1.33831 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.635277 | 0.0248985 | ||||||||
\(652\) | − 0.830542i | − 0.0325265i | ||||||||
\(653\) | − 11.1816i | − 0.437570i | −0.975773 | − | 0.218785i | \(-0.929791\pi\) | ||||
0.975773 | − | 0.218785i | \(-0.0702093\pi\) | |||||||
\(654\) | 0.253418 | 0.00990943 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 38.6642i | 1.50843i | ||||||||
\(658\) | 0.441078i | 0.0171950i | ||||||||
\(659\) | 13.7542 | 0.535787 | 0.267894 | − | 0.963449i | \(-0.413672\pi\) | ||||
0.267894 | + | 0.963449i | \(0.413672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.6171 | −0.490747 | −0.245374 | − | 0.969429i | \(-0.578911\pi\) | ||||
−0.245374 | + | 0.969429i | \(0.578911\pi\) | |||||||
\(662\) | − 28.3845i | − 1.10319i | ||||||||
\(663\) | − 127.161i | − 4.93854i | ||||||||
\(664\) | 13.1695 | 0.511074 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −41.7679 | −1.61847 | ||||||||
\(667\) | 4.53871i | 0.175740i | ||||||||
\(668\) | 16.5068i | 0.638669i | ||||||||
\(669\) | 47.1968 | 1.82473 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.71577 | 0.375073 | ||||||||
\(672\) | 0.253418i | 0.00977581i | ||||||||
\(673\) | 2.35105i | 0.0906263i | 0.998973 | + | 0.0453132i | \(0.0144286\pi\) | ||||
−0.998973 | + | 0.0453132i | \(0.985571\pi\) | |||||||
\(674\) | 17.8716 | 0.688387 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.4229 | 0.593188 | ||||||||
\(677\) | 23.7663i | 0.913414i | 0.889617 | + | 0.456707i | \(0.150971\pi\) | ||||
−0.889617 | + | 0.456707i | \(0.849029\pi\) | |||||||
\(678\) | − 19.5205i | − 0.749681i | ||||||||
\(679\) | 0.597928 | 0.0229464 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −70.2686 | −2.69270 | ||||||||
\(682\) | − 11.2979i | − 0.432619i | ||||||||
\(683\) | 28.1695i | 1.07787i | 0.842346 | + | 0.538937i | \(0.181174\pi\) | ||||
−0.842346 | + | 0.538937i | \(0.818826\pi\) | |||||||
\(684\) | −7.58473 | −0.290009 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.09003 | 0.0416174 | ||||||||
\(687\) | 61.8594i | 2.36008i | ||||||||
\(688\) | 0.506836i | 0.0193229i | ||||||||
\(689\) | −68.9647 | −2.62734 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.32371 | 0.0883979 | 0.0441990 | − | 0.999023i | \(-0.485926\pi\) | ||||
0.0441990 | + | 0.999023i | \(0.485926\pi\) | |||||||
\(692\) | − 18.8321i | − 0.715888i | ||||||||
\(693\) | 2.66262i | 0.101145i | ||||||||
\(694\) | −33.0410 | −1.25422 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.33131 | −0.164178 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | − 19.7158i | − 0.746253i | ||||||||
\(699\) | 19.5650 | 0.740016 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.7036 | 0.895274 | 0.447637 | − | 0.894215i | \(-0.352266\pi\) | ||||
0.447637 | + | 0.894215i | \(0.352266\pi\) | |||||||
\(702\) | 79.5220i | 3.00137i | ||||||||
\(703\) | − 5.50684i | − 0.207694i | ||||||||
\(704\) | 4.50684 | 0.169858 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.90997 | −0.222425 | ||||||||
\(707\) | − 0.323706i | − 0.0121742i | ||||||||
\(708\) | 24.6121i | 0.924978i | ||||||||
\(709\) | −9.05315 | −0.339998 | −0.169999 | − | 0.985444i | \(-0.554376\pi\) | ||||
−0.169999 | + | 0.985444i | \(0.554376\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 129.044 | 4.83953 | ||||||||
\(712\) | − 15.0137i | − 0.562661i | ||||||||
\(713\) | − 8.54631i | − 0.320062i | ||||||||
\(714\) | 1.85789 | 0.0695297 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.15579 | −0.267424 | ||||||||
\(717\) | − 50.1326i | − 1.87224i | ||||||||
\(718\) | − 7.00760i | − 0.261521i | ||||||||
\(719\) | −35.0734 | −1.30802 | −0.654008 | − | 0.756488i | \(-0.726914\pi\) | ||||
−0.654008 | + | 0.756488i | \(0.726914\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.183130 | −0.00682012 | ||||||||
\(722\) | − 1.00000i | − 0.0372161i | ||||||||
\(723\) | − 15.6763i | − 0.583008i | ||||||||
\(724\) | −12.5205 | −0.465321 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 30.2944 | 1.12433 | ||||||||
\(727\) | − 30.1386i | − 1.11778i | −0.829242 | − | 0.558890i | \(-0.811227\pi\) | ||||
0.829242 | − | 0.558890i | \(-0.188773\pi\) | |||||||
\(728\) | 0.415271i | 0.0153910i | ||||||||
\(729\) | −49.9039 | −1.84829 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.71577 | 0.137433 | ||||||||
\(732\) | 7.01367i | 0.259233i | ||||||||
\(733\) | 47.8321i | 1.76672i | 0.468697 | + | 0.883359i | \(0.344724\pi\) | ||||
−0.468697 | + | 0.883359i | \(0.655276\pi\) | |||||||
\(734\) | −17.7158 | −0.653901 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.40920 | 0.125665 | ||||||||
\(737\) | − 20.6626i | − 0.761117i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.4674 | 0.826475 | 0.413238 | − | 0.910623i | \(-0.364398\pi\) | ||||
0.413238 | + | 0.910623i | \(0.364398\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.3450 | −0.637184 | ||||||||
\(742\) | − 1.00760i | − 0.0369903i | ||||||||
\(743\) | − 11.7926i | − 0.432629i | −0.976324 | − | 0.216314i | \(-0.930596\pi\) | ||||
0.976324 | − | 0.216314i | \(-0.0694036\pi\) | |||||||
\(744\) | 8.15579 | 0.299006 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.4487 | 0.565616 | ||||||||
\(747\) | 99.8868i | 3.65467i | ||||||||
\(748\) | − 33.0410i | − 1.20810i | ||||||||
\(749\) | −1.09310 | −0.0399411 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.03948 | −0.0744216 | −0.0372108 | − | 0.999307i | \(-0.511847\pi\) | ||||
−0.0372108 | + | 0.999307i | \(0.511847\pi\) | |||||||
\(752\) | 5.66262i | 0.206495i | ||||||||
\(753\) | 4.94685i | 0.180273i | ||||||||
\(754\) | −7.09763 | −0.258481 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.16185 | −0.0422562 | ||||||||
\(757\) | − 43.3526i | − 1.57568i | −0.615882 | − | 0.787838i | \(-0.711200\pi\) | ||||
0.615882 | − | 0.787838i | \(-0.288800\pi\) | |||||||
\(758\) | 34.4563i | 1.25151i | ||||||||
\(759\) | 49.9879 | 1.81444 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.62921 | 0.240309 | 0.120154 | − | 0.992755i | \(-0.461661\pi\) | ||||
0.120154 | + | 0.992755i | \(0.461661\pi\) | |||||||
\(762\) | − 58.0152i | − 2.10167i | ||||||||
\(763\) | 0.00606730i | 0 0.000219651i | ||||||||
\(764\) | 4.90237 | 0.177361 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.0273 | −0.434566 | ||||||||
\(767\) | 40.3313i | 1.45628i | ||||||||
\(768\) | 3.25342i | 0.117398i | ||||||||
\(769\) | 19.6429 | 0.708340 | 0.354170 | − | 0.935181i | \(-0.384763\pi\) | ||||
0.354170 | + | 0.935181i | \(0.384763\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 53.7036 | 1.93409 | ||||||||
\(772\) | − 18.1558i | − 0.653441i | ||||||||
\(773\) | 14.4107i | 0.518318i | 0.965835 | + | 0.259159i | \(0.0834454\pi\) | ||||
−0.965835 | + | 0.259159i | \(0.916555\pi\) | |||||||
\(774\) | −3.84421 | −0.138177 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.67629 | 0.275563 | ||||||||
\(777\) | − 1.39553i | − 0.0500644i | ||||||||
\(778\) | − 15.3647i | − 0.550852i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48.9347 | 1.75102 | ||||||||
\(782\) | − 24.9939i | − 0.893781i | ||||||||
\(783\) | − 19.8579i | − 0.709663i | ||||||||
\(784\) | 6.99393 | 0.249783 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.85789 | −0.173275 | ||||||||
\(787\) | − 24.3176i | − 0.866830i | −0.901194 | − | 0.433415i | \(-0.857308\pi\) | ||||
0.901194 | − | 0.433415i | \(-0.142692\pi\) | |||||||
\(788\) | − 2.98633i | − 0.106384i | ||||||||
\(789\) | 58.6505 | 2.08801 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.467357 | 0.0166173 | ||||||||
\(792\) | 34.1831i | 1.21464i | ||||||||
\(793\) | 11.4932i | 0.408134i | ||||||||
\(794\) | −1.32524 | −0.0470311 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.06422 | −0.108608 | ||||||||
\(797\) | 7.30397i | 0.258720i | 0.991598 | + | 0.129360i | \(0.0412922\pi\) | ||||
−0.991598 | + | 0.129360i | \(0.958708\pi\) | |||||||
\(798\) | − 0.253418i | − 0.00897090i | ||||||||
\(799\) | 41.5144 | 1.46868 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 113.875 | 4.02356 | ||||||||
\(802\) | 6.46736i | 0.228370i | ||||||||
\(803\) | 22.9742i | 0.810742i | ||||||||
\(804\) | 14.9160 | 0.526048 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.3647 | 0.470752 | ||||||||
\(807\) | − 65.7481i | − 2.31444i | ||||||||
\(808\) | − 4.15579i | − 0.146200i | ||||||||
\(809\) | 0.584729 | 0.0205580 | 0.0102790 | − | 0.999947i | \(-0.496728\pi\) | ||||
0.0102790 | + | 0.999947i | \(0.496728\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.90997 | 0.0670682 | 0.0335341 | − | 0.999438i | \(-0.489324\pi\) | ||||
0.0335341 | + | 0.999438i | \(0.489324\pi\) | |||||||
\(812\) | − 0.103700i | − 0.00363914i | ||||||||
\(813\) | 19.7937i | 0.694194i | ||||||||
\(814\) | −24.8184 | −0.869885 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 23.8518 | 0.834981 | ||||||||
\(817\) | − 0.506836i | − 0.0177319i | ||||||||
\(818\) | − 1.36472i | − 0.0477164i | ||||||||
\(819\) | −3.14972 | −0.110060 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.2226 | −1.33398 | −0.666989 | − | 0.745067i | \(-0.732417\pi\) | ||||
−0.666989 | + | 0.745067i | \(0.732417\pi\) | |||||||
\(822\) | 27.4229i | 0.956483i | ||||||||
\(823\) | − 45.7481i | − 1.59468i | −0.603531 | − | 0.797340i | \(-0.706240\pi\) | ||||
0.603531 | − | 0.797340i | \(-0.293760\pi\) | |||||||
\(824\) | −2.35105 | −0.0819027 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.589259 | −0.0205029 | ||||||||
\(827\) | 22.6687i | 0.788268i | 0.919053 | + | 0.394134i | \(0.128955\pi\) | ||||
−0.919053 | + | 0.394134i | \(0.871045\pi\) | |||||||
\(828\) | 25.8579i | 0.898624i | ||||||||
\(829\) | 4.63028 | 0.160816 | 0.0804081 | − | 0.996762i | \(-0.474378\pi\) | ||||
0.0804081 | + | 0.996762i | \(0.474378\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −102.043 | −3.53982 | ||||||||
\(832\) | 5.33131i | 0.184830i | ||||||||
\(833\) | − 51.2747i | − 1.77656i | ||||||||
\(834\) | −28.6900 | −0.993452 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.50684 | −0.155872 | ||||||||
\(837\) | 37.3921i | 1.29246i | ||||||||
\(838\) | 16.6231i | 0.574237i | ||||||||
\(839\) | 50.4826 | 1.74285 | 0.871426 | − | 0.490527i | \(-0.163196\pi\) | ||||
0.871426 | + | 0.490527i | \(0.163196\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2276 | −0.938883 | ||||||||
\(842\) | 31.1128i | 1.07222i | ||||||||
\(843\) | 36.8458i | 1.26904i | ||||||||
\(844\) | −19.2534 | −0.662730 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −42.9495 | −1.47663 | ||||||||
\(847\) | 0.725305i | 0.0249218i | ||||||||
\(848\) | − 12.9358i | − 0.444216i | ||||||||
\(849\) | −85.0562 | −2.91912 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.7739 | −0.643562 | ||||||||
\(852\) | 35.3252i | 1.21022i | ||||||||
\(853\) | 36.2105i | 1.23982i | 0.784672 | + | 0.619912i | \(0.212832\pi\) | ||||
−0.784672 | + | 0.619912i | \(0.787168\pi\) | |||||||
\(854\) | −0.167920 | −0.00574611 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.0334 | −0.479652 | ||||||||
\(857\) | − 25.1968i | − 0.860706i | −0.902661 | − | 0.430353i | \(-0.858389\pi\) | ||||
0.902661 | − | 0.430353i | \(-0.141611\pi\) | |||||||
\(858\) | 78.1710i | 2.66871i | ||||||||
\(859\) | −18.8579 | −0.643423 | −0.321711 | − | 0.946838i | \(-0.604258\pi\) | ||||
−0.321711 | + | 0.946838i | \(0.604258\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.1831i | 0.346839i | ||||||||
\(863\) | 15.0137i | 0.511071i | 0.966800 | + | 0.255536i | \(0.0822518\pi\) | ||||
−0.966800 | + | 0.255536i | \(0.917748\pi\) | |||||||
\(864\) | −14.9160 | −0.507454 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 22.1953 | 0.754226 | ||||||||
\(867\) | − 119.557i | − 4.06037i | ||||||||
\(868\) | 0.195265i | 0.00662771i | ||||||||
\(869\) | 76.6778 | 2.60112 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.4426 | 0.828206 | ||||||||
\(872\) | 0.0778929i | 0.00263779i | ||||||||
\(873\) | 58.2226i | 1.97054i | ||||||||
\(874\) | −3.40920 | −0.115318 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.5847 | −0.560346 | ||||||||
\(877\) | − 35.1128i | − 1.18568i | −0.805322 | − | 0.592838i | \(-0.798007\pi\) | ||||
0.805322 | − | 0.592838i | \(-0.201993\pi\) | |||||||
\(878\) | − 9.32524i | − 0.314712i | ||||||||
\(879\) | −4.33131 | −0.146091 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.3389 | −1.39274 | −0.696372 | − | 0.717681i | \(-0.745203\pi\) | ||||
−0.696372 | + | 0.717681i | \(0.745203\pi\) | |||||||
\(882\) | 53.0471i | 1.78619i | ||||||||
\(883\) | − 12.6353i | − 0.425211i | −0.977138 | − | 0.212605i | \(-0.931805\pi\) | ||||
0.977138 | − | 0.212605i | \(-0.0681949\pi\) | |||||||
\(884\) | 39.0855 | 1.31459 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.9879 | −0.469932 | ||||||||
\(887\) | − 4.15579i | − 0.139538i | −0.997563 | − | 0.0697688i | \(-0.977774\pi\) | ||||
0.997563 | − | 0.0697688i | \(-0.0222262\pi\) | |||||||
\(888\) | − 17.9160i | − 0.601223i | ||||||||
\(889\) | 1.38899 | 0.0465853 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −116.159 | −3.89147 | ||||||||
\(892\) | 14.5068i | 0.485725i | ||||||||
\(893\) | − 5.66262i | − 0.189492i | ||||||||
\(894\) | −57.5084 | −1.92337 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.0778929 | −0.00260222 | ||||||||
\(897\) | 59.1326i | 1.97438i | ||||||||
\(898\) | 13.4932i | 0.450273i | ||||||||
\(899\) | −3.33738 | −0.111308 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −94.8362 | −3.15945 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 0.128441i | − 0.00427426i | ||||||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 65.0684 | 2.16175 | ||||||||
\(907\) | 41.7542i | 1.38643i | 0.720733 | + | 0.693213i | \(0.243805\pi\) | ||||
−0.720733 | + | 0.693213i | \(0.756195\pi\) | |||||||
\(908\) | − 21.5984i | − 0.716768i | ||||||||
\(909\) | 31.5205 | 1.04547 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.12998 | −0.302490 | −0.151245 | − | 0.988496i | \(-0.548328\pi\) | ||||
−0.151245 | + | 0.988496i | \(0.548328\pi\) | |||||||
\(912\) | − 3.25342i | − 0.107731i | ||||||||
\(913\) | 59.3526i | 1.96428i | ||||||||
\(914\) | −9.68236 | −0.320264 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.0137 | −0.628229 | ||||||||
\(917\) | − 0.116307i | − 0.00384079i | ||||||||
\(918\) | 109.354i | 3.60922i | ||||||||
\(919\) | −19.0197 | −0.627403 | −0.313702 | − | 0.949522i | \(-0.601569\pi\) | ||||
−0.313702 | + | 0.949522i | \(0.601569\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.25342 | −0.304910 | ||||||||
\(922\) | − 8.66262i | − 0.285288i | ||||||||
\(923\) | 57.8868i | 1.90537i | ||||||||
\(924\) | −1.14211 | −0.0375728 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 28.0015 | 0.920188 | ||||||||
\(927\) | − 17.8321i | − 0.585682i | ||||||||
\(928\) | − 1.33131i | − 0.0437024i | ||||||||
\(929\) | 7.77239 | 0.255004 | 0.127502 | − | 0.991838i | \(-0.459304\pi\) | ||||
0.127502 | + | 0.991838i | \(0.459304\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.99393 | −0.229217 | ||||||||
\(932\) | 6.01367i | 0.196984i | ||||||||
\(933\) | − 53.3218i | − 1.74568i | ||||||||
\(934\) | −16.9742 | −0.555413 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −40.4365 | −1.32171 | ||||||||
\(937\) | 45.9818i | 1.50216i | 0.660211 | + | 0.751080i | \(0.270467\pi\) | ||||
−0.660211 | + | 0.751080i | \(0.729533\pi\) | |||||||
\(938\) | 0.357118i | 0.0116603i | ||||||||
\(939\) | 68.4750 | 2.23460 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.6242 | −1.32431 | −0.662156 | − | 0.749366i | \(-0.730358\pi\) | ||||
−0.662156 | + | 0.749366i | \(0.730358\pi\) | |||||||
\(942\) | − 1.64895i | − 0.0537257i | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −7.56499 | −0.246219 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.28423 | −0.0742666 | ||||||||
\(947\) | 2.28423i | 0.0742274i | 0.999311 | + | 0.0371137i | \(0.0118164\pi\) | ||||
−0.999311 | + | 0.0371137i | \(0.988184\pi\) | |||||||
\(948\) | 55.3526i | 1.79777i | ||||||||
\(949\) | −27.1771 | −0.882205 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −100.499 | −3.25890 | ||||||||
\(952\) | 0.571057i | 0.0185081i | ||||||||
\(953\) | − 57.5084i | − 1.86288i | −0.363896 | − | 0.931439i | \(-0.618554\pi\) | ||||
0.363896 | − | 0.931439i | \(-0.381446\pi\) | |||||||
\(954\) | 98.1144 | 3.17657 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.4092 | 0.498369 | ||||||||
\(957\) | − 19.5205i | − 0.631008i | ||||||||
\(958\) | 10.0532i | 0.324803i | ||||||||
\(959\) | −0.656555 | −0.0212013 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.7158 | −0.797283 | ||||||||
\(962\) | − 29.3587i | − 0.946561i | ||||||||
\(963\) | − 106.440i | − 3.42997i | ||||||||
\(964\) | 4.81841 | 0.155190 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.863954 | −0.0277973 | ||||||||
\(967\) | 4.70210i | 0.151209i | 0.997138 | + | 0.0756047i | \(0.0240887\pi\) | ||||
−0.997138 | + | 0.0756047i | \(0.975911\pi\) | |||||||
\(968\) | 9.31157i | 0.299285i | ||||||||
\(969\) | −23.8518 | −0.766231 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.9863 | 0.480934 | 0.240467 | − | 0.970657i | \(-0.422699\pi\) | ||||
0.240467 | + | 0.970657i | \(0.422699\pi\) | |||||||
\(972\) | − 39.1052i | − 1.25430i | ||||||||
\(973\) | − 0.686891i | − 0.0220207i | ||||||||
\(974\) | −19.2089 | −0.615494 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.15579 | −0.0690050 | ||||||||
\(977\) | − 8.89737i | − 0.284652i | −0.989820 | − | 0.142326i | \(-0.954542\pi\) | ||||
0.989820 | − | 0.142326i | \(-0.0454581\pi\) | |||||||
\(978\) | 2.70210i | 0.0864037i | ||||||||
\(979\) | 67.6642 | 2.16256 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.590796 | −0.0188627 | ||||||||
\(982\) | − 5.32524i | − 0.169935i | ||||||||
\(983\) | − 1.60947i | − 0.0513341i | −0.999671 | − | 0.0256671i | \(-0.991829\pi\) | ||||
0.999671 | − | 0.0256671i | \(-0.00817098\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.76025 | −0.310830 | ||||||||
\(987\) | − 1.43501i | − 0.0456769i | ||||||||
\(988\) | − 5.33131i | − 0.169612i | ||||||||
\(989\) | −1.72791 | −0.0549443 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.8974 | 0.536763 | 0.268381 | − | 0.963313i | \(-0.413511\pi\) | ||||
0.268381 | + | 0.963313i | \(0.413511\pi\) | |||||||
\(992\) | 2.50684i | 0.0795921i | ||||||||
\(993\) | 92.3465i | 2.93053i | ||||||||
\(994\) | −0.845752 | −0.0268256 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −42.8458 | −1.35762 | ||||||||
\(997\) | − 24.1558i | − 0.765021i | −0.923951 | − | 0.382511i | \(-0.875060\pi\) | ||||
0.923951 | − | 0.382511i | \(-0.124940\pi\) | |||||||
\(998\) | − 11.9605i | − 0.378604i | ||||||||
\(999\) | 82.1402 | 2.59880 |
(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 | 950.2.b.h.799.3 | 6 | ||
5.2 | odd | 4 | 950.2.a.l.1.3 | yes | 3 | ||
5.3 | odd | 4 | 950.2.a.j.1.1 | ✓ | 3 | ||
5.4 | even | 2 | inner | 950.2.b.h.799.4 | 6 | ||
15.2 | even | 4 | 8550.2.a.ci.1.2 | 3 | |||
15.8 | even | 4 | 8550.2.a.cp.1.2 | 3 | |||
20.3 | even | 4 | 7600.2.a.bz.1.3 | 3 | |||
20.7 | even | 4 | 7600.2.a.bk.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.a.j.1.1 | ✓ | 3 | 5.3 | odd | 4 | ||
950.2.a.l.1.3 | yes | 3 | 5.2 | odd | 4 | ||
950.2.b.h.799.3 | 6 | 1.1 | even | 1 | trivial | ||
950.2.b.h.799.4 | 6 | 5.4 | even | 2 | inner | ||
7600.2.a.bk.1.1 | 3 | 20.7 | even | 4 | |||
7600.2.a.bz.1.3 | 3 | 20.3 | even | 4 | |||
8550.2.a.ci.1.2 | 3 | 15.2 | even | 4 | |||
8550.2.a.cp.1.2 | 3 | 15.8 | even | 4 |