Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,3,Mod(1599,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.1599");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.h (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: | \(43.5968422976\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{15})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1599.3 | ||
Root | \(1.93649 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1599 |
Dual form | 1600.3.h.i.1599.4 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.87298 | 1.29099 | 0.645497 | − | 0.763763i | \(-0.276650\pi\) | ||||
0.645497 | + | 0.763763i | \(0.276650\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.74597 | −1.10657 | −0.553283 | − | 0.832993i | \(-0.686625\pi\) | ||||
−0.553283 | + | 0.832993i | \(0.686625\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.00000 | 0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 19.3649i | − 1.76045i | −0.474559 | − | 0.880223i | \(-0.657393\pi\) | ||||
0.474559 | − | 0.880223i | \(-0.342607\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.0000i | 1.53846i | 0.638971 | + | 0.769231i | \(0.279360\pi\) | ||||
−0.638971 | + | 0.769231i | \(0.720640\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15.0000i | 0.882353i | 0.897420 | + | 0.441176i | \(0.145439\pi\) | ||||
−0.897420 | + | 0.441176i | \(0.854561\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.3649i | 1.01921i | 0.860410 | + | 0.509603i | \(0.170208\pi\) | ||||
−0.860410 | + | 0.509603i | \(0.829792\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −30.0000 | −1.42857 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.74597 | −0.336781 | −0.168391 | − | 0.985720i | \(-0.553857\pi\) | ||||
−0.168391 | + | 0.985720i | \(0.553857\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11.6190 | −0.430331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −48.0000 | −1.65517 | −0.827586 | − | 0.561339i | \(-0.810287\pi\) | ||||
−0.827586 | + | 0.561339i | \(0.810287\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 38.7298i | − 1.24935i | −0.780885 | − | 0.624675i | \(-0.785232\pi\) | ||||
0.780885 | − | 0.624675i | \(-0.214768\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 75.0000i | − 2.27273i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 10.0000i | − 0.270270i | −0.990827 | − | 0.135135i | \(-0.956853\pi\) | ||||
0.990827 | − | 0.135135i | \(-0.0431469\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 77.4597i | 1.98615i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 33.0000 | 0.804878 | 0.402439 | − | 0.915447i | \(-0.368163\pi\) | ||||
0.402439 | + | 0.915447i | \(0.368163\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −61.9677 | −1.44111 | −0.720555 | − | 0.693398i | \(-0.756113\pi\) | ||||
−0.720555 | + | 0.693398i | \(0.756113\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 15.4919 | 0.329616 | 0.164808 | − | 0.986326i | \(-0.447300\pi\) | ||||
0.164808 | + | 0.986326i | \(0.447300\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.0000 | 0.224490 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 58.0948i | 1.13911i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 30.0000i | 0.566038i | 0.959114 | + | 0.283019i | \(0.0913359\pi\) | ||||
−0.959114 | + | 0.283019i | \(0.908664\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 75.0000i | 1.31579i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 77.4597i | 1.31288i | 0.754380 | + | 0.656438i | \(0.227938\pi\) | ||||
−0.754380 | + | 0.656438i | \(0.772062\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −38.0000 | −0.622951 | −0.311475 | − | 0.950254i | \(-0.600823\pi\) | ||||
−0.311475 | + | 0.950254i | \(0.600823\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −46.4758 | −0.737711 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −58.0948 | −0.867086 | −0.433543 | − | 0.901133i | \(-0.642737\pi\) | ||||
−0.433543 | + | 0.901133i | \(0.642737\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −30.0000 | −0.434783 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 77.4597i | 1.09098i | 0.838117 | + | 0.545491i | \(0.183657\pi\) | ||||
−0.838117 | + | 0.545491i | \(0.816343\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 5.00000i | − 0.0684932i | −0.999413 | − | 0.0342466i | \(-0.989097\pi\) | ||||
0.999413 | − | 0.0342466i | \(-0.0109032\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 150.000i | 1.94805i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 38.7298i | − 0.490251i | −0.969491 | − | 0.245126i | \(-0.921171\pi\) | ||||
0.969491 | − | 0.245126i | \(-0.0788292\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −99.0000 | −1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.6190 | 0.139987 | 0.0699937 | − | 0.997547i | \(-0.477702\pi\) | ||||
0.0699937 | + | 0.997547i | \(0.477702\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −185.903 | −2.13682 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −87.0000 | −0.977528 | −0.488764 | − | 0.872416i | \(-0.662552\pi\) | ||||
−0.488764 | + | 0.872416i | \(0.662552\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 154.919i | − 1.70241i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 150.000i | − 1.61290i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 110.000i | 1.13402i | 0.823711 | + | 0.567010i | \(0.191900\pi\) | ||||
−0.823711 | + | 0.567010i | \(0.808100\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 116.190i | − 1.17363i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −42.0000 | −0.415842 | −0.207921 | − | 0.978146i | \(-0.566670\pi\) | ||||
−0.207921 | + | 0.978146i | \(0.566670\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −77.4597 | −0.752036 | −0.376018 | − | 0.926612i | \(-0.622707\pi\) | ||||
−0.376018 | + | 0.926612i | \(0.622707\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 42.6028 | 0.398157 | 0.199079 | − | 0.979984i | \(-0.436205\pi\) | ||||
0.199079 | + | 0.979984i | \(0.436205\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 58.0000 | 0.532110 | 0.266055 | − | 0.963958i | \(-0.414280\pi\) | ||||
0.266055 | + | 0.963958i | \(0.414280\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 38.7298i | − 0.348917i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 135.000i | 1.19469i | 0.801984 | + | 0.597345i | \(0.203778\pi\) | ||||
−0.801984 | + | 0.597345i | \(0.796222\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 120.000i | 1.02564i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 116.190i | − 0.976382i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −254.000 | −2.09917 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 127.808 | 1.03909 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 209.141 | 1.64678 | 0.823390 | − | 0.567476i | \(-0.192080\pi\) | ||||
0.823390 | + | 0.567476i | \(0.192080\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −240.000 | −1.86047 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 154.919i | 1.18259i | 0.806455 | + | 0.591295i | \(0.201383\pi\) | ||||
−0.806455 | + | 0.591295i | \(0.798617\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 150.000i | − 1.12782i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 105.000i | − 0.766423i | −0.923661 | − | 0.383212i | \(-0.874818\pi\) | ||||
0.923661 | − | 0.383212i | \(-0.125182\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.3649i | 0.139316i | 0.997571 | + | 0.0696580i | \(0.0221908\pi\) | ||||
−0.997571 | + | 0.0696580i | \(0.977809\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 60.0000 | 0.425532 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 387.298 | 2.70838 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 42.6028 | 0.289815 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −192.000 | −1.28859 | −0.644295 | − | 0.764777i | \(-0.722849\pi\) | ||||
−0.644295 | + | 0.764777i | \(0.722849\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 38.7298i | − 0.256489i | −0.991743 | − | 0.128244i | \(-0.959066\pi\) | ||||
0.991743 | − | 0.128244i | \(-0.0409342\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 90.0000i | 0.588235i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 110.000i | 0.700637i | 0.936631 | + | 0.350318i | \(0.113927\pi\) | ||||
−0.936631 | + | 0.350318i | \(0.886073\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 116.190i | 0.730752i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 60.0000 | 0.372671 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −127.808 | −0.784101 | −0.392050 | − | 0.919944i | \(-0.628234\pi\) | ||||
−0.392050 | + | 0.919944i | \(0.628234\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 294.347 | 1.76256 | 0.881278 | − | 0.472599i | \(-0.156684\pi\) | ||||
0.881278 | + | 0.472599i | \(0.156684\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −231.000 | −1.36686 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 116.190i | 0.679471i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 240.000i | − 1.38728i | −0.720320 | − | 0.693642i | \(-0.756005\pi\) | ||||
0.720320 | − | 0.693642i | \(-0.243995\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 300.000i | 1.69492i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 213.014i | − 1.19002i | −0.803717 | − | 0.595011i | \(-0.797148\pi\) | ||||
0.803717 | − | 0.595011i | \(-0.202852\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0000 | −0.121547 | −0.0607735 | − | 0.998152i | \(-0.519357\pi\) | ||||
−0.0607735 | + | 0.998152i | \(0.519357\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −147.173 | −0.804226 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 290.474 | 1.55334 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 90.0000 | 0.476190 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 116.190i | − 0.608322i | −0.952621 | − | 0.304161i | \(-0.901624\pi\) | ||||
0.952621 | − | 0.304161i | \(-0.0983761\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 295.000i | − 1.52850i | −0.644922 | − | 0.764249i | \(-0.723110\pi\) | ||||
0.644922 | − | 0.764249i | \(-0.276890\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 330.000i | 1.67513i | 0.546340 | + | 0.837563i | \(0.316021\pi\) | ||||
−0.546340 | + | 0.837563i | \(0.683979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 232.379i | − 1.16773i | −0.811849 | − | 0.583867i | \(-0.801539\pi\) | ||||
0.811849 | − | 0.583867i | \(-0.198461\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −225.000 | −1.11940 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 371.806 | 1.83156 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −46.4758 | −0.224521 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 375.000 | 1.79426 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 58.0948i | − 0.275331i | −0.990479 | − | 0.137665i | \(-0.956040\pi\) | ||||
0.990479 | − | 0.137665i | \(-0.0439598\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 300.000i | 1.40845i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 300.000i | 1.38249i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 19.3649i | − 0.0884243i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −300.000 | −1.35747 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.4919 | 0.0694706 | 0.0347353 | − | 0.999397i | \(-0.488941\pi\) | ||||
0.0347353 | + | 0.999397i | \(0.488941\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −30.9839 | −0.136493 | −0.0682464 | − | 0.997668i | \(-0.521740\pi\) | ||||
−0.0682464 | + | 0.997668i | \(0.521740\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −68.0000 | −0.296943 | −0.148472 | − | 0.988917i | \(-0.547435\pi\) | ||||
−0.148472 | + | 0.988917i | \(0.547435\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 580.948i | 2.51492i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 30.0000i | 0.128755i | 0.997926 | + | 0.0643777i | \(0.0205062\pi\) | ||||
−0.997926 | + | 0.0643777i | \(0.979494\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 150.000i | − 0.632911i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 154.919i | − 0.648198i | −0.946023 | − | 0.324099i | \(-0.894939\pi\) | ||||
0.946023 | − | 0.324099i | \(-0.105061\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 253.000 | 1.04979 | 0.524896 | − | 0.851166i | \(-0.324104\pi\) | ||||
0.524896 | + | 0.851166i | \(0.324104\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −278.855 | −1.14755 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −387.298 | −1.56801 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 45.0000 | 0.180723 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 367.933i | − 1.46587i | −0.680299 | − | 0.732935i | \(-0.738150\pi\) | ||||
0.680299 | − | 0.732935i | \(-0.261850\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 150.000i | 0.592885i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 270.000i | − 1.05058i | −0.850922 | − | 0.525292i | \(-0.823956\pi\) | ||||
0.850922 | − | 0.525292i | \(-0.176044\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 77.4597i | 0.299072i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −288.000 | −1.10345 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −100.698 | −0.382880 | −0.191440 | − | 0.981504i | \(-0.561316\pi\) | ||||
−0.191440 | + | 0.981504i | \(0.561316\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −336.950 | −1.26198 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −312.000 | −1.15985 | −0.579926 | − | 0.814669i | \(-0.696918\pi\) | ||||
−0.579926 | + | 0.814669i | \(0.696918\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 193.649i | − 0.714573i | −0.933995 | − | 0.357286i | \(-0.883702\pi\) | ||||
0.933995 | − | 0.357286i | \(-0.116298\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 600.000i | − 2.19780i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 440.000i | − 1.58845i | −0.607625 | − | 0.794224i | \(-0.707878\pi\) | ||||
0.607625 | − | 0.794224i | \(-0.292122\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 232.379i | − 0.832900i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 198.000 | 0.704626 | 0.352313 | − | 0.935882i | \(-0.385395\pi\) | ||||
0.352313 | + | 0.935882i | \(0.385395\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 213.014 | 0.752700 | 0.376350 | − | 0.926478i | \(-0.377179\pi\) | ||||
0.376350 | + | 0.926478i | \(0.377179\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −255.617 | −0.890651 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 64.0000 | 0.221453 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 426.028i | 1.46401i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 390.000i | 1.33106i | 0.746372 | + | 0.665529i | \(0.231794\pi\) | ||||
−0.746372 | + | 0.665529i | \(0.768206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 225.000i | 0.757576i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 154.919i | − 0.518125i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 480.000 | 1.59468 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −162.665 | −0.536849 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −375.679 | −1.22371 | −0.611856 | − | 0.790969i | \(-0.709577\pi\) | ||||
−0.611856 | + | 0.790969i | \(0.709577\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −300.000 | −0.970874 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 271.109i | − 0.871733i | −0.900011 | − | 0.435866i | \(-0.856442\pi\) | ||||
0.900011 | − | 0.435866i | \(-0.143558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 50.0000i | 0.159744i | 0.996805 | + | 0.0798722i | \(0.0254512\pi\) | ||||
−0.996805 | + | 0.0798722i | \(0.974549\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 300.000i | 0.946372i | 0.880962 | + | 0.473186i | \(0.156896\pi\) | ||||
−0.880962 | + | 0.473186i | \(0.843104\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 929.516i | 2.91384i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 165.000 | 0.514019 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −290.474 | −0.899300 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 224.633 | 0.686951 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −120.000 | −0.364742 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 213.014i | 0.643547i | 0.946817 | + | 0.321774i | \(0.104279\pi\) | ||||
−0.946817 | + | 0.321774i | \(0.895721\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 60.0000i | − 0.180180i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 125.000i | 0.370920i | 0.982652 | + | 0.185460i | \(0.0593775\pi\) | ||||
−0.982652 | + | 0.185460i | \(0.940623\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 522.853i | 1.54234i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −750.000 | −2.19941 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 294.347 | 0.858154 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 476.377 | 1.37284 | 0.686422 | − | 0.727203i | \(-0.259180\pi\) | ||||
0.686422 | + | 0.727203i | \(0.259180\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 242.000 | 0.693410 | 0.346705 | − | 0.937974i | \(-0.387301\pi\) | ||||
0.346705 | + | 0.937974i | \(0.387301\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 232.379i | − 0.662048i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 150.000i | 0.424929i | 0.977169 | + | 0.212465i | \(0.0681490\pi\) | ||||
−0.977169 | + | 0.212465i | \(0.931851\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 450.000i | − 1.26050i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 426.028i | 1.18671i | 0.804942 | + | 0.593354i | \(0.202197\pi\) | ||||
−0.804942 | + | 0.593354i | \(0.797803\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.0000 | −0.0387812 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −983.738 | −2.71002 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 511.234 | 1.39301 | 0.696504 | − | 0.717553i | \(-0.254738\pi\) | ||||
0.696504 | + | 0.717553i | \(0.254738\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 198.000 | 0.536585 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 232.379i | − 0.626358i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 250.000i | 0.670241i | 0.942175 | + | 0.335121i | \(0.108777\pi\) | ||||
−0.942175 | + | 0.335121i | \(0.891223\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 960.000i | − 2.54642i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 290.474i | 0.766422i | 0.923661 | + | 0.383211i | \(0.125182\pi\) | ||||
−0.923661 | + | 0.383211i | \(0.874818\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 810.000 | 2.12598 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −596.439 | −1.55728 | −0.778642 | − | 0.627469i | \(-0.784091\pi\) | ||||
−0.778642 | + | 0.627469i | \(0.784091\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −371.806 | −0.960740 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.0000 | 0.0462725 | 0.0231362 | − | 0.999732i | \(-0.492635\pi\) | ||||
0.0231362 | + | 0.999732i | \(0.492635\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 116.190i | − 0.297160i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 600.000i | 1.52672i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 100.000i | − 0.251889i | −0.992037 | − | 0.125945i | \(-0.959804\pi\) | ||||
0.992037 | − | 0.125945i | \(-0.0401962\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 580.948i | − 1.45601i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −183.000 | −0.456359 | −0.228180 | − | 0.973619i | \(-0.573277\pi\) | ||||
−0.228180 | + | 0.973619i | \(0.573277\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 774.597 | 1.92208 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −193.649 | −0.475796 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 47.0000 | 0.114914 | 0.0574572 | − | 0.998348i | \(-0.481701\pi\) | ||||
0.0574572 | + | 0.998348i | \(0.481701\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 406.663i | − 0.989448i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 600.000i | − 1.45278i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 75.0000i | 0.179856i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 406.663i | 0.970557i | 0.874360 | + | 0.485278i | \(0.161282\pi\) | ||||
−0.874360 | + | 0.485278i | \(0.838718\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 452.000 | 1.07363 | 0.536817 | − | 0.843699i | \(-0.319627\pi\) | ||||
0.536817 | + | 0.843699i | \(0.319627\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 92.9516 | 0.219744 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 294.347 | 0.689337 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1500.00 | 3.49650 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.7298i | 0.0898604i | 0.998990 | + | 0.0449302i | \(0.0143065\pi\) | ||||
−0.998990 | + | 0.0449302i | \(0.985693\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 55.0000i | − 0.127021i | −0.997981 | − | 0.0635104i | \(-0.979770\pi\) | ||||
0.997981 | − | 0.0635104i | \(-0.0202296\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 150.000i | − 0.343249i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 619.677i | 1.41157i | 0.708428 | + | 0.705783i | \(0.249405\pi\) | ||||
−0.708428 | + | 0.705783i | \(0.750595\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 66.0000 | 0.149660 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 321.458 | 0.725638 | 0.362819 | − | 0.931860i | \(-0.381814\pi\) | ||||
0.362819 | + | 0.931860i | \(0.381814\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −743.613 | −1.66356 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 627.000 | 1.39644 | 0.698218 | − | 0.715885i | \(-0.253977\pi\) | ||||
0.698218 | + | 0.715885i | \(0.253977\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 639.042i | − 1.41695i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 150.000i | − 0.331126i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 325.000i | − 0.711160i | −0.934646 | − | 0.355580i | \(-0.884283\pi\) | ||||
0.934646 | − | 0.355580i | \(-0.115717\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 174.284i | − 0.379704i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0000 | −0.0260304 | −0.0130152 | − | 0.999915i | \(-0.504143\pi\) | ||||
−0.0130152 | + | 0.999915i | \(0.504143\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 108.444 | 0.234219 | 0.117110 | − | 0.993119i | \(-0.462637\pi\) | ||||
0.117110 | + | 0.993119i | \(0.462637\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 340.823 | 0.729813 | 0.364906 | − | 0.931044i | \(-0.381101\pi\) | ||||
0.364906 | + | 0.931044i | \(0.381101\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 450.000 | 0.959488 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 426.028i | 0.904518i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1200.00i | 2.53700i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 180.000i | 0.377358i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 116.190i | 0.242567i | 0.992618 | + | 0.121283i | \(0.0387010\pi\) | ||||
−0.992618 | + | 0.121283i | \(0.961299\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 200.000 | 0.415800 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 232.379 | 0.481116 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −441.520 | −0.906612 | −0.453306 | − | 0.891355i | \(-0.649756\pi\) | ||||
−0.453306 | + | 0.891355i | \(0.649756\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −495.000 | −1.01227 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 720.000i | − 1.46045i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 600.000i | − 1.20724i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 309.839i | − 0.620919i | −0.950587 | − | 0.310460i | \(-0.899517\pi\) | ||||
0.950587 | − | 0.310460i | \(-0.100483\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1140.00 | 2.27545 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 46.4758 | 0.0923972 | 0.0461986 | − | 0.998932i | \(-0.485289\pi\) | ||||
0.0461986 | + | 0.998932i | \(0.485289\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −894.659 | −1.76461 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −618.000 | −1.21415 | −0.607073 | − | 0.794646i | \(-0.707656\pi\) | ||||
−0.607073 | + | 0.794646i | \(0.707656\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 38.7298i | 0.0757922i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 225.000i | − 0.438596i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 300.000i | − 0.580271i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 929.516i | − 1.79097i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −423.000 | −0.811900 | −0.405950 | − | 0.913895i | \(-0.633059\pi\) | ||||
−0.405950 | + | 0.913895i | \(0.633059\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −120.062 | −0.229565 | −0.114782 | − | 0.993391i | \(-0.536617\pi\) | ||||
−0.114782 | + | 0.993391i | \(0.536617\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 580.948 | 1.10237 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −469.000 | −0.886578 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 464.758i | 0.875250i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 660.000i | 1.23827i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 825.000i | − 1.53631i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 213.014i | − 0.395202i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | 0.0147874 | 0.00739372 | − | 0.999973i | \(-0.497646\pi\) | ||||
0.00739372 | + | 0.999973i | \(0.497646\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −85.2056 | −0.156916 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 398.917 | 0.729282 | 0.364641 | − | 0.931148i | \(-0.381192\pi\) | ||||
0.364641 | + | 0.931148i | \(0.381192\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −228.000 | −0.415301 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 929.516i | − 1.68696i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 300.000i | 0.542495i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 660.000i | − 1.18492i | −0.805600 | − | 0.592460i | \(-0.798157\pi\) | ||||
0.805600 | − | 0.592460i | \(-0.201843\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 1239.35i | − 2.21709i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1125.00 | 2.00535 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −542.218 | −0.963086 | −0.481543 | − | 0.876422i | \(-0.659924\pi\) | ||||
−0.481543 | + | 0.876422i | \(0.659924\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 766.851 | 1.35247 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −453.000 | −0.796134 | −0.398067 | − | 0.917356i | \(-0.630319\pi\) | ||||
−0.398067 | + | 0.917356i | \(0.630319\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1084.44i | 1.89919i | 0.313485 | + | 0.949593i | \(0.398503\pi\) | ||||
−0.313485 | + | 0.949593i | \(0.601497\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 450.000i | − 0.785340i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 325.000i | 0.563258i | 0.959523 | + | 0.281629i | \(0.0908748\pi\) | ||||
−0.959523 | + | 0.281629i | \(0.909125\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 1142.53i | − 1.97328i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −90.0000 | −0.154905 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 580.948 | 0.996479 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −755.232 | −1.28660 | −0.643298 | − | 0.765616i | \(-0.722434\pi\) | ||||
−0.643298 | + | 0.765616i | \(0.722434\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 750.000 | 1.27334 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1278.08i | 2.16258i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.0000i | 0.0252951i | 0.999920 | + | 0.0126476i | \(0.00402595\pi\) | ||||
−0.999920 | + | 0.0126476i | \(0.995974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 900.000i | − 1.50754i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1045.71i | 1.74575i | 0.487942 | + | 0.872876i | \(0.337748\pi\) | ||||
−0.487942 | + | 0.872876i | \(0.662252\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −637.000 | −1.05990 | −0.529950 | − | 0.848029i | \(-0.677789\pi\) | ||||
−0.529950 | + | 0.848029i | \(0.677789\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −348.569 | −0.578057 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −154.919 | −0.255221 | −0.127611 | − | 0.991824i | \(-0.540731\pi\) | ||||
−0.127611 | + | 0.991824i | \(0.540731\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1440.00 | 2.36453 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 309.839i | 0.507101i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 910.000i | 1.48450i | 0.670122 | + | 0.742251i | \(0.266242\pi\) | ||||
−0.670122 | + | 0.742251i | \(0.733758\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 630.000i | − 1.02107i | −0.859857 | − | 0.510535i | \(-0.829447\pi\) | ||||
0.859857 | − | 0.510535i | \(-0.170553\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 154.919i | − 0.250274i | −0.992139 | − | 0.125137i | \(-0.960063\pi\) | ||||
0.992139 | − | 0.125137i | \(-0.0399370\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 90.0000 | 0.144928 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 673.899 | 1.08170 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1452.37 | 2.31638 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 150.000 | 0.238474 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 348.569i | − 0.552406i | −0.961099 | − | 0.276203i | \(-0.910924\pi\) | ||||
0.961099 | − | 0.276203i | \(-0.0890763\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 225.000i | − 0.355450i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 220.000i | 0.345369i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 464.758i | 0.727321i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 858.000 | 1.33853 | 0.669267 | − | 0.743022i | \(-0.266608\pi\) | ||||
0.669267 | + | 0.743022i | \(0.266608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 650.661 | 1.01191 | 0.505957 | − | 0.862558i | \(-0.331139\pi\) | ||||
0.505957 | + | 0.862558i | \(0.331139\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 852.056 | 1.31693 | 0.658467 | − | 0.752610i | \(-0.271205\pi\) | ||||
0.658467 | + | 0.752610i | \(0.271205\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1500.00 | 2.31125 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1161.90i | 1.78478i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 990.000i | 1.51608i | 0.652208 | + | 0.758040i | \(0.273843\pi\) | ||||
−0.652208 | + | 0.758040i | \(0.726157\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 30.0000i | − 0.0456621i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 290.474i | 0.440780i | 0.975412 | + | 0.220390i | \(0.0707329\pi\) | ||||
−0.975412 | + | 0.220390i | \(0.929267\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −968.000 | −1.46445 | −0.732224 | − | 0.681064i | \(-0.761518\pi\) | ||||
−0.732224 | + | 0.681064i | \(0.761518\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1161.90 | −1.75248 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 371.806 | 0.557431 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 60.0000 | 0.0896861 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 735.867i | 1.09667i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 790.000i | − 1.17385i | −0.809642 | − | 0.586924i | \(-0.800339\pi\) | ||||
0.809642 | − | 0.586924i | \(-0.199661\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 852.056i | − 1.25487i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −120.000 | −0.176211 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 468.631 | 0.686136 | 0.343068 | − | 0.939311i | \(-0.388534\pi\) | ||||
0.343068 | + | 0.939311i | \(0.388534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −263.363 | −0.383352 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −600.000 | −0.870827 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1336.18i | − 1.93369i | −0.255365 | − | 0.966845i | \(-0.582196\pi\) | ||||
0.255365 | − | 0.966845i | \(-0.417804\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 900.000i | 1.29870i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 495.000i | 0.710187i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 116.190i | 0.166222i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 252.000 | 0.359486 | 0.179743 | − | 0.983714i | \(-0.442473\pi\) | ||||
0.179743 | + | 0.983714i | \(0.442473\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 193.649 | 0.275461 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 325.331 | 0.460156 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1028.00 | −1.44993 | −0.724965 | − | 0.688786i | \(-0.758144\pi\) | ||||
−0.724965 | + | 0.688786i | \(0.758144\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 232.379i | − 0.326834i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 300.000i | 0.420757i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 600.000i | − 0.836820i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1200.62i | − 1.66985i | −0.550361 | − | 0.834927i | \(-0.685510\pi\) | ||||
0.550361 | − | 0.834927i | \(-0.314490\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 600.000 | 0.832178 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 979.865 | 1.35528 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 681.645 | 0.937614 | 0.468807 | − | 0.883301i | \(-0.344684\pi\) | ||||
0.468807 | + | 0.883301i | \(0.344684\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −189.000 | −0.259259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 929.516i | − 1.27157i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 700.000i | − 0.954980i | −0.878637 | − | 0.477490i | \(-0.841547\pi\) | ||||
0.878637 | − | 0.477490i | \(-0.158453\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1125.00i | 1.52646i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1500.00 | −2.02429 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 735.867 | 0.990400 | 0.495200 | − | 0.868779i | \(-0.335095\pi\) | ||||
0.495200 | + | 0.868779i | \(0.335095\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 69.7137 | 0.0933249 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −330.000 | −0.440587 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1084.44i | 1.44399i | 0.691899 | + | 0.721994i | \(0.256774\pi\) | ||||
−0.691899 | + | 0.721994i | \(0.743226\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 1425.00i | − 1.89243i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 280.000i | 0.369881i | 0.982750 | + | 0.184941i | \(0.0592093\pi\) | ||||
−0.982750 | + | 0.184941i | \(0.940791\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 580.948i | 0.765412i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 537.000 | 0.705650 | 0.352825 | − | 0.935689i | \(-0.385221\pi\) | ||||
0.352825 | + | 0.935689i | \(0.385221\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −449.266 | −0.588815 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1549.19 | −2.01981 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 703.000 | 0.914174 | 0.457087 | − | 0.889422i | \(-0.348893\pi\) | ||||
0.457087 | + | 0.889422i | \(0.348893\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1045.71i | − 1.35630i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1320.00i | 1.70763i | 0.520574 | + | 0.853816i | \(0.325718\pi\) | ||||
−0.520574 | + | 0.853816i | \(0.674282\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 300.000i | 0.386100i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 639.042i | 0.820337i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1500.00 | 1.92061 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 557.710 | 0.712273 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −681.645 | −0.866131 | −0.433065 | − | 0.901362i | \(-0.642568\pi\) | ||||
−0.433065 | + | 0.901362i | \(0.642568\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −390.000 | −0.494297 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 1045.71i | − 1.32200i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 760.000i | − 0.958386i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 270.000i | 0.338770i | 0.985550 | + | 0.169385i | \(0.0541782\pi\) | ||||
−0.985550 | + | 0.169385i | \(0.945822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 232.379i | 0.290837i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −522.000 | −0.651685 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −96.8246 | −0.120579 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1208.37 | −1.49736 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −522.000 | −0.645241 | −0.322621 | − | 0.946528i | \(-0.604564\pi\) | ||||
−0.322621 | + | 0.946528i | \(0.604564\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 154.919i | − 0.191023i | −0.995428 | − | 0.0955113i | \(-0.969551\pi\) | ||||
0.995428 | − | 0.0955113i | \(-0.0304486\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 750.000i | − 0.922509i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 1200.00i | − 1.46879i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 929.516i | − 1.13494i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 282.000 | 0.343484 | 0.171742 | − | 0.985142i | \(-0.445061\pi\) | ||||
0.171742 | + | 0.985142i | \(0.445061\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −697.137 | −0.847068 | −0.423534 | − | 0.905880i | \(-0.639211\pi\) | ||||
−0.423534 | + | 0.905880i | \(0.639211\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −600.312 | −0.725892 | −0.362946 | − | 0.931810i | \(-0.618229\pi\) | ||||
−0.362946 | + | 0.931810i | \(0.618229\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 748.000 | 0.902292 | 0.451146 | − | 0.892450i | \(-0.351015\pi\) | ||||
0.451146 | + | 0.892450i | \(0.351015\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 1704.11i | − 2.05068i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 165.000i | 0.198079i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 450.000i | 0.537634i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 154.919i | − 0.184648i | −0.995729 | − | 0.0923238i | \(-0.970571\pi\) | ||||
0.995729 | − | 0.0923238i | \(-0.0294295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1463.00 | 1.73960 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 766.851 | 0.909669 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1967.48 | 2.32288 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 825.000 | 0.971731 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 77.4597i | 0.0910219i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1430.00i | − 1.67644i | −0.545335 | − | 0.838218i | \(-0.683598\pi\) | ||||
0.545335 | − | 0.838218i | \(-0.316402\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 975.000i | 1.13769i | 0.822445 | + | 0.568845i | \(0.192609\pi\) | ||||
−0.822445 | + | 0.568845i | \(0.807391\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 445.393i | − 0.518502i | −0.965810 | − | 0.259251i | \(-0.916524\pi\) | ||||
0.965810 | − | 0.259251i | \(-0.0834757\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −990.000 | −1.14983 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1673.13 | −1.93874 | −0.969368 | − | 0.245614i | \(-0.921011\pi\) | ||||
−0.969368 | + | 0.245614i | \(0.921011\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 247.871 | 0.285895 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −750.000 | −0.863061 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1161.90i | − 1.33398i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 660.000i | 0.756014i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 220.000i | − 0.250855i | −0.992103 | − | 0.125428i | \(-0.959970\pi\) | ||||
0.992103 | − | 0.125428i | \(-0.0400303\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1510.46i | 1.71839i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1602.00 | −1.81839 | −0.909194 | − | 0.416373i | \(-0.863301\pi\) | ||||
−0.909194 | + | 0.416373i | \(0.863301\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1576.30 | −1.78517 | −0.892584 | − | 0.450880i | \(-0.851110\pi\) | ||||
−0.892584 | + | 0.450880i | \(0.851110\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −108.444 | −0.122259 | −0.0611294 | − | 0.998130i | \(-0.519470\pi\) | ||||
−0.0611294 | + | 0.998130i | \(0.519470\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1620.00 | −1.82227 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1917.13i | 2.15166i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 300.000i | 0.335946i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 600.000i | − 0.668896i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1859.03i | 2.06789i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −450.000 | −0.499445 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1859.03 | 2.05873 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −340.823 | −0.375769 | −0.187885 | − | 0.982191i | \(-0.560163\pi\) | ||||
−0.187885 | + | 0.982191i | \(0.560163\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −252.000 | −0.277228 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 852.056i | 0.935298i | 0.883914 | + | 0.467649i | \(0.154899\pi\) | ||||
−0.883914 | + | 0.467649i | \(0.845101\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 225.000i | − 0.246440i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1200.00i | − 1.30862i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 890.786i | 0.969299i | 0.874708 | + | 0.484650i | \(0.161053\pi\) | ||||
−0.874708 | + | 0.484650i | \(0.838947\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1455.00 | −1.57980 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1549.19 | −1.67843 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −464.758 | −0.501357 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1518.00 | −1.63402 | −0.817008 | − | 0.576627i | \(-0.804369\pi\) | ||||
−0.817008 | + | 0.576627i | \(0.804369\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 213.014i | 0.228801i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1050.00i | − 1.12540i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 35.0000i | − 0.0373533i | −0.999826 | − | 0.0186766i | \(-0.994055\pi\) | ||||
0.999826 | − | 0.0186766i | \(-0.00594530\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 193.649i | 0.206229i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 468.000 | 0.497343 | 0.248672 | − | 0.968588i | \(-0.420006\pi\) | ||||
0.248672 | + | 0.968588i | \(0.420006\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −255.617 | −0.271068 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1533.70 | −1.61954 | −0.809768 | − | 0.586750i | \(-0.800407\pi\) | ||||
−0.809768 | + | 0.586750i | \(0.800407\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 100.000 | 0.105374 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1161.90i | 1.22176i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1485.00i | 1.55824i | 0.626877 | + | 0.779119i | \(0.284333\pi\) | ||||
−0.626877 | + | 0.779119i | \(0.715667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3600.00i | 3.76176i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 813.327i | 0.848099i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −539.000 | −0.560874 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 255.617 | 0.265438 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −402.790 | −0.416536 | −0.208268 | − | 0.978072i | \(-0.566783\pi\) | ||||
−0.208268 | + | 0.978072i | \(0.566783\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1125.00 | −1.16099 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 484.123i | − 0.498582i | −0.968429 | − | 0.249291i | \(-0.919802\pi\) | ||||
0.968429 | − | 0.249291i | \(-0.0801975\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 150.000i | − 0.154162i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1755.00i | 1.79632i | 0.439674 | + | 0.898158i | \(0.355094\pi\) | ||||
−0.439674 | + | 0.898158i | \(0.644906\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1684.75i | 1.72089i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 348.000 | 0.354740 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 426.028 | 0.433396 | 0.216698 | − | 0.976239i | \(-0.430471\pi\) | ||||
0.216698 | + | 0.976239i | \(0.430471\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −464.758 | −0.470879 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 480.000 | 0.485339 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 426.028i | − 0.429897i | −0.976625 | − | 0.214949i | \(-0.931042\pi\) | ||||
0.976625 | − | 0.214949i | \(-0.0689584\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 825.000i | 0.830816i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1700.00i | 1.70512i | 0.522633 | + | 0.852558i | \(0.324950\pi\) | ||||
−0.522633 | + | 0.852558i | \(0.675050\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 116.190i | 0.116306i |
(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 | 1600.3.h.i.1599.3 | 4 | ||
4.3 | odd | 2 | inner | 1600.3.h.i.1599.2 | 4 | ||
5.2 | odd | 4 | 1600.3.b.h.1151.1 | 2 | |||
5.3 | odd | 4 | 1600.3.b.g.1151.2 | 2 | |||
5.4 | even | 2 | inner | 1600.3.h.i.1599.1 | 4 | ||
8.3 | odd | 2 | 400.3.h.c.399.3 | 4 | |||
8.5 | even | 2 | 400.3.h.c.399.2 | 4 | |||
20.3 | even | 4 | 1600.3.b.g.1151.1 | 2 | |||
20.7 | even | 4 | 1600.3.b.h.1151.2 | 2 | |||
20.19 | odd | 2 | inner | 1600.3.h.i.1599.4 | 4 | ||
24.5 | odd | 2 | 3600.3.j.b.1999.1 | 4 | |||
24.11 | even | 2 | 3600.3.j.b.1999.4 | 4 | |||
40.3 | even | 4 | 400.3.b.d.351.2 | yes | 2 | ||
40.13 | odd | 4 | 400.3.b.d.351.1 | yes | 2 | ||
40.19 | odd | 2 | 400.3.h.c.399.1 | 4 | |||
40.27 | even | 4 | 400.3.b.c.351.1 | ✓ | 2 | ||
40.29 | even | 2 | 400.3.h.c.399.4 | 4 | |||
40.37 | odd | 4 | 400.3.b.c.351.2 | yes | 2 | ||
120.29 | odd | 2 | 3600.3.j.b.1999.3 | 4 | |||
120.53 | even | 4 | 3600.3.e.v.3151.2 | 2 | |||
120.59 | even | 2 | 3600.3.j.b.1999.2 | 4 | |||
120.77 | even | 4 | 3600.3.e.i.3151.1 | 2 | |||
120.83 | odd | 4 | 3600.3.e.v.3151.1 | 2 | |||
120.107 | odd | 4 | 3600.3.e.i.3151.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.3.b.c.351.1 | ✓ | 2 | 40.27 | even | 4 | ||
400.3.b.c.351.2 | yes | 2 | 40.37 | odd | 4 | ||
400.3.b.d.351.1 | yes | 2 | 40.13 | odd | 4 | ||
400.3.b.d.351.2 | yes | 2 | 40.3 | even | 4 | ||
400.3.h.c.399.1 | 4 | 40.19 | odd | 2 | |||
400.3.h.c.399.2 | 4 | 8.5 | even | 2 | |||
400.3.h.c.399.3 | 4 | 8.3 | odd | 2 | |||
400.3.h.c.399.4 | 4 | 40.29 | even | 2 | |||
1600.3.b.g.1151.1 | 2 | 20.3 | even | 4 | |||
1600.3.b.g.1151.2 | 2 | 5.3 | odd | 4 | |||
1600.3.b.h.1151.1 | 2 | 5.2 | odd | 4 | |||
1600.3.b.h.1151.2 | 2 | 20.7 | even | 4 | |||
1600.3.h.i.1599.1 | 4 | 5.4 | even | 2 | inner | ||
1600.3.h.i.1599.2 | 4 | 4.3 | odd | 2 | inner | ||
1600.3.h.i.1599.3 | 4 | 1.1 | even | 1 | trivial | ||
1600.3.h.i.1599.4 | 4 | 20.19 | odd | 2 | inner | ||
3600.3.e.i.3151.1 | 2 | 120.77 | even | 4 | |||
3600.3.e.i.3151.2 | 2 | 120.107 | odd | 4 | |||
3600.3.e.v.3151.1 | 2 | 120.83 | odd | 4 | |||
3600.3.e.v.3151.2 | 2 | 120.53 | even | 4 | |||
3600.3.j.b.1999.1 | 4 | 24.5 | odd | 2 | |||
3600.3.j.b.1999.2 | 4 | 120.59 | even | 2 | |||
3600.3.j.b.1999.3 | 4 | 120.29 | odd | 2 | |||
3600.3.j.b.1999.4 | 4 | 24.11 | even | 2 |