Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,4,Mod(649,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.c (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: | \(79.6525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 270) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.649 |
Dual form | 1350.4.c.j.649.1 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.0000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | − 8.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.0822304 | −0.0411152 | − | 0.999154i | \(-0.513091\pi\) | ||||
−0.0411152 | + | 0.999154i | \(0.513091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 47.0000i | − 1.00273i | −0.865237 | − | 0.501364i | \(-0.832832\pi\) | ||||
0.865237 | − | 0.501364i | \(-0.167168\pi\) | |||||||
\(14\) | −28.0000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 39.0000i | 0.556405i | 0.960522 | + | 0.278203i | \(0.0897387\pi\) | ||||
−0.960522 | + | 0.278203i | \(0.910261\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −32.0000 | −0.386384 | −0.193192 | − | 0.981161i | \(-0.561884\pi\) | ||||
−0.193192 | + | 0.981161i | \(0.561884\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 6.00000i | − 0.0581456i | ||||||||
\(23\) | − 99.0000i | − 0.897519i | −0.893653 | − | 0.448759i | \(-0.851866\pi\) | ||||
0.893653 | − | 0.448759i | \(-0.148134\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 94.0000 | 0.709035 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 56.0000i | − 0.377964i | ||||||||
\(29\) | 51.0000 | 0.326568 | 0.163284 | − | 0.986579i | \(-0.447791\pi\) | ||||
0.163284 | + | 0.986579i | \(0.447791\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 83.0000 | 0.480879 | 0.240439 | − | 0.970664i | \(-0.422708\pi\) | ||||
0.240439 | + | 0.970664i | \(0.422708\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −78.0000 | −0.393438 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 314.000i | 1.39517i | 0.716502 | + | 0.697585i | \(0.245742\pi\) | ||||
−0.716502 | + | 0.697585i | \(0.754258\pi\) | |||||||
\(38\) | − 64.0000i | − 0.273215i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 108.000 | 0.411385 | 0.205692 | − | 0.978617i | \(-0.434055\pi\) | ||||
0.205692 | + | 0.978617i | \(0.434055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 299.000i | − 1.06040i | −0.847874 | − | 0.530199i | \(-0.822117\pi\) | ||||
0.847874 | − | 0.530199i | \(-0.177883\pi\) | |||||||
\(44\) | 12.0000 | 0.0411152 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 198.000 | 0.634641 | ||||||||
\(47\) | − 531.000i | − 1.64796i | −0.566616 | − | 0.823982i | \(-0.691748\pi\) | ||||
0.566616 | − | 0.823982i | \(-0.308252\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 147.000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 188.000i | 0.501364i | ||||||||
\(53\) | 564.000i | 1.46172i | 0.682525 | + | 0.730862i | \(0.260882\pi\) | ||||
−0.682525 | + | 0.730862i | \(0.739118\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 112.000 | 0.267261 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 102.000i | 0.230918i | ||||||||
\(59\) | 12.0000 | 0.0264791 | 0.0132396 | − | 0.999912i | \(-0.495786\pi\) | ||||
0.0132396 | + | 0.999912i | \(0.495786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 230.000 | 0.482762 | 0.241381 | − | 0.970430i | \(-0.422400\pi\) | ||||
0.241381 | + | 0.970430i | \(0.422400\pi\) | |||||||
\(62\) | 166.000i | 0.340033i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 268.000i | − 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | − 156.000i | − 0.278203i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −120.000 | −0.200583 | −0.100291 | − | 0.994958i | \(-0.531978\pi\) | ||||
−0.100291 | + | 0.994958i | \(0.531978\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 1106.00i | − 1.77325i | −0.462486 | − | 0.886627i | \(-0.653042\pi\) | ||||
0.462486 | − | 0.886627i | \(-0.346958\pi\) | |||||||
\(74\) | −628.000 | −0.986534 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 128.000 | 0.193192 | ||||||||
\(77\) | − 42.0000i | − 0.0621603i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 739.000 | 1.05246 | 0.526228 | − | 0.850344i | \(-0.323606\pi\) | ||||
0.526228 | + | 0.850344i | \(0.323606\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 216.000i | 0.290893i | ||||||||
\(83\) | 1086.00i | 1.43619i | 0.695944 | + | 0.718096i | \(0.254986\pi\) | ||||
−0.695944 | + | 0.718096i | \(0.745014\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 598.000 | 0.749814 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 24.0000i | 0.0290728i | ||||||||
\(89\) | −120.000 | −0.142921 | −0.0714605 | − | 0.997443i | \(-0.522766\pi\) | ||||
−0.0714605 | + | 0.997443i | \(0.522766\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 658.000 | 0.757991 | ||||||||
\(92\) | 396.000i | 0.448759i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1062.00 | 1.16529 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1642.00i | − 1.71876i | −0.511336 | − | 0.859381i | \(-0.670849\pi\) | ||||
0.511336 | − | 0.859381i | \(-0.329151\pi\) | |||||||
\(98\) | 294.000i | 0.303046i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −33.0000 | −0.0325111 | −0.0162556 | − | 0.999868i | \(-0.505175\pi\) | ||||
−0.0162556 | + | 0.999868i | \(0.505175\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1198.00i | 1.14604i | 0.819540 | + | 0.573022i | \(0.194229\pi\) | ||||
−0.819540 | + | 0.573022i | \(0.805771\pi\) | |||||||
\(104\) | −376.000 | −0.354518 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1128.00 | −1.03359 | ||||||||
\(107\) | 1542.00i | 1.39318i | 0.717467 | + | 0.696592i | \(0.245301\pi\) | ||||
−0.717467 | + | 0.696592i | \(0.754699\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 556.000 | 0.488579 | 0.244290 | − | 0.969702i | \(-0.421445\pi\) | ||||
0.244290 | + | 0.969702i | \(0.421445\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 224.000i | 0.188982i | ||||||||
\(113\) | 1605.00i | 1.33616i | 0.744091 | + | 0.668078i | \(0.232883\pi\) | ||||
−0.744091 | + | 0.668078i | \(0.767117\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −204.000 | −0.163284 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 24.0000i | 0.0187236i | ||||||||
\(119\) | −546.000 | −0.420603 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1322.00 | −0.993238 | ||||||||
\(122\) | 460.000i | 0.341364i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −332.000 | −0.240439 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1334.00i | 0.932074i | 0.884765 | + | 0.466037i | \(0.154319\pi\) | ||||
−0.884765 | + | 0.466037i | \(0.845681\pi\) | |||||||
\(128\) | − 128.000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2883.00 | 1.92282 | 0.961408 | − | 0.275127i | \(-0.0887199\pi\) | ||||
0.961408 | + | 0.275127i | \(0.0887199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 448.000i | − 0.292079i | ||||||||
\(134\) | 536.000 | 0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 312.000 | 0.196719 | ||||||||
\(137\) | − 282.000i | − 0.175860i | −0.996127 | − | 0.0879302i | \(-0.971975\pi\) | ||||
0.996127 | − | 0.0879302i | \(-0.0280253\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2494.00 | 1.52186 | 0.760929 | − | 0.648835i | \(-0.224743\pi\) | ||||
0.760929 | + | 0.648835i | \(0.224743\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 240.000i | − 0.141833i | ||||||||
\(143\) | 141.000i | 0.0824546i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2212.00 | 1.25388 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 1256.00i | − 0.697585i | ||||||||
\(149\) | 2595.00 | 1.42678 | 0.713392 | − | 0.700766i | \(-0.247158\pi\) | ||||
0.713392 | + | 0.700766i | \(0.247158\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1229.00 | 0.662348 | 0.331174 | − | 0.943570i | \(-0.392555\pi\) | ||||
0.331174 | + | 0.943570i | \(0.392555\pi\) | |||||||
\(152\) | 256.000i | 0.136608i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 84.0000 | 0.0439540 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1591.00i | − 0.808762i | −0.914591 | − | 0.404381i | \(-0.867487\pi\) | ||||
0.914591 | − | 0.404381i | \(-0.132513\pi\) | |||||||
\(158\) | 1478.00i | 0.744199i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1386.00 | 0.678460 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 457.000i | 0.219601i | 0.993954 | + | 0.109801i | \(0.0350212\pi\) | ||||
−0.993954 | + | 0.109801i | \(0.964979\pi\) | |||||||
\(164\) | −432.000 | −0.205692 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2172.00 | −1.01554 | ||||||||
\(167\) | 1164.00i | 0.539359i | 0.962950 | + | 0.269680i | \(0.0869178\pi\) | ||||
−0.962950 | + | 0.269680i | \(0.913082\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.00546199 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1196.00i | 0.530199i | ||||||||
\(173\) | 3942.00i | 1.73240i | 0.499700 | + | 0.866199i | \(0.333444\pi\) | ||||
−0.499700 | + | 0.866199i | \(0.666556\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −48.0000 | −0.0205576 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 240.000i | − 0.101060i | ||||||||
\(179\) | −1212.00 | −0.506085 | −0.253042 | − | 0.967455i | \(-0.581431\pi\) | ||||
−0.253042 | + | 0.967455i | \(0.581431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2288.00 | 0.939590 | 0.469795 | − | 0.882776i | \(-0.344328\pi\) | ||||
0.469795 | + | 0.882776i | \(0.344328\pi\) | |||||||
\(182\) | 1316.00i | 0.535980i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −792.000 | −0.317321 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 117.000i | − 0.0457534i | ||||||||
\(188\) | 2124.00i | 0.823982i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1938.00 | 0.734182 | 0.367091 | − | 0.930185i | \(-0.380354\pi\) | ||||
0.367091 | + | 0.930185i | \(0.380354\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1498.00i | 0.558696i | 0.960190 | + | 0.279348i | \(0.0901184\pi\) | ||||
−0.960190 | + | 0.279348i | \(0.909882\pi\) | |||||||
\(194\) | 3284.00 | 1.21535 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −588.000 | −0.214286 | ||||||||
\(197\) | 2124.00i | 0.768166i | 0.923299 | + | 0.384083i | \(0.125482\pi\) | ||||
−0.923299 | + | 0.384083i | \(0.874518\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 385.000 | 0.137145 | 0.0685727 | − | 0.997646i | \(-0.478155\pi\) | ||||
0.0685727 | + | 0.997646i | \(0.478155\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 66.0000i | − 0.0229888i | ||||||||
\(203\) | 714.000i | 0.246862i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2396.00 | −0.810375 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 752.000i | − 0.250682i | ||||||||
\(209\) | 96.0000 | 0.0317725 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3170.00 | 1.03427 | 0.517137 | − | 0.855903i | \(-0.326998\pi\) | ||||
0.517137 | + | 0.855903i | \(0.326998\pi\) | |||||||
\(212\) | − 2256.00i | − 0.730862i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3084.00 | −0.985130 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1162.00i | 0.363510i | ||||||||
\(218\) | 1112.00i | 0.345478i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1833.00 | 0.557923 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1388.00i | − 0.416804i | −0.978043 | − | 0.208402i | \(-0.933174\pi\) | ||||
0.978043 | − | 0.208402i | \(-0.0668263\pi\) | |||||||
\(224\) | −448.000 | −0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3210.00 | −0.944805 | ||||||||
\(227\) | 4644.00i | 1.35786i | 0.734205 | + | 0.678928i | \(0.237555\pi\) | ||||
−0.734205 | + | 0.678928i | \(0.762445\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4736.00 | −1.36665 | −0.683327 | − | 0.730113i | \(-0.739468\pi\) | ||||
−0.683327 | + | 0.730113i | \(0.739468\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 408.000i | − 0.115459i | ||||||||
\(233\) | 2814.00i | 0.791207i | 0.918421 | + | 0.395604i | \(0.129465\pi\) | ||||
−0.918421 | + | 0.395604i | \(0.870535\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −48.0000 | −0.0132396 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 1092.00i | − 0.297411i | ||||||||
\(239\) | −2202.00 | −0.595965 | −0.297982 | − | 0.954571i | \(-0.596314\pi\) | ||||
−0.297982 | + | 0.954571i | \(0.596314\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3485.00 | 0.931488 | 0.465744 | − | 0.884920i | \(-0.345787\pi\) | ||||
0.465744 | + | 0.884920i | \(0.345787\pi\) | |||||||
\(242\) | − 2644.00i | − 0.702325i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −920.000 | −0.241381 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1504.00i | 0.387438i | ||||||||
\(248\) | − 664.000i | − 0.170016i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6345.00 | 1.59559 | 0.797795 | − | 0.602929i | \(-0.206000\pi\) | ||||
0.797795 | + | 0.602929i | \(0.206000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 297.000i | 0.0738033i | ||||||||
\(254\) | −2668.00 | −0.659076 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − 525.000i | − 0.127426i | −0.997968 | − | 0.0637132i | \(-0.979706\pi\) | ||||
0.997968 | − | 0.0637132i | \(-0.0202943\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4396.00 | −1.05465 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5766.00i | 1.35964i | ||||||||
\(263\) | 5196.00i | 1.21825i | 0.793075 | + | 0.609124i | \(0.208479\pi\) | ||||
−0.793075 | + | 0.609124i | \(0.791521\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 896.000 | 0.206531 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1072.00i | 0.244339i | ||||||||
\(269\) | −7479.00 | −1.69518 | −0.847589 | − | 0.530654i | \(-0.821946\pi\) | ||||
−0.847589 | + | 0.530654i | \(0.821946\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −856.000 | −0.191876 | −0.0959378 | − | 0.995387i | \(-0.530585\pi\) | ||||
−0.0959378 | + | 0.995387i | \(0.530585\pi\) | |||||||
\(272\) | 624.000i | 0.139101i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 564.000 | 0.124352 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 7054.00i | − 1.53009i | −0.643979 | − | 0.765043i | \(-0.722718\pi\) | ||||
0.643979 | − | 0.765043i | \(-0.277282\pi\) | |||||||
\(278\) | 4988.00i | 1.07612i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1014.00 | −0.215268 | −0.107634 | − | 0.994191i | \(-0.534327\pi\) | ||||
−0.107634 | + | 0.994191i | \(0.534327\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 992.000i | − 0.208368i | −0.994558 | − | 0.104184i | \(-0.966777\pi\) | ||||
0.994558 | − | 0.104184i | \(-0.0332232\pi\) | |||||||
\(284\) | 480.000 | 0.100291 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −282.000 | −0.0583042 | ||||||||
\(287\) | 1512.00i | 0.310977i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3392.00 | 0.690413 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4424.00i | 0.886627i | ||||||||
\(293\) | − 4950.00i | − 0.986970i | −0.869754 | − | 0.493485i | \(-0.835723\pi\) | ||||
0.869754 | − | 0.493485i | \(-0.164277\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2512.00 | 0.493267 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5190.00i | 1.00889i | ||||||||
\(299\) | −4653.00 | −0.899966 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4186.00 | 0.801585 | ||||||||
\(302\) | 2458.00i | 0.468351i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −512.000 | −0.0965961 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 4777.00i | − 0.888071i | −0.896009 | − | 0.444035i | \(-0.853546\pi\) | ||||
0.896009 | − | 0.444035i | \(-0.146454\pi\) | |||||||
\(308\) | 168.000i | 0.0310802i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7692.00 | 1.40249 | 0.701243 | − | 0.712922i | \(-0.252629\pi\) | ||||
0.701243 | + | 0.712922i | \(0.252629\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2932.00i | 0.529477i | 0.964320 | + | 0.264739i | \(0.0852857\pi\) | ||||
−0.964320 | + | 0.264739i | \(0.914714\pi\) | |||||||
\(314\) | 3182.00 | 0.571881 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2956.00 | −0.526228 | ||||||||
\(317\) | − 8352.00i | − 1.47980i | −0.672720 | − | 0.739898i | \(-0.734874\pi\) | ||||
0.672720 | − | 0.739898i | \(-0.265126\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −153.000 | −0.0268538 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2772.00i | 0.479744i | ||||||||
\(323\) | − 1248.00i | − 0.214986i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −914.000 | −0.155282 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 864.000i | − 0.145446i | ||||||||
\(329\) | 7434.00 | 1.24574 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3070.00 | −0.509796 | −0.254898 | − | 0.966968i | \(-0.582042\pi\) | ||||
−0.254898 | + | 0.966968i | \(0.582042\pi\) | |||||||
\(332\) | − 4344.00i | − 0.718096i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2328.00 | −0.381385 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 1672.00i | − 0.270266i | −0.990827 | − | 0.135133i | \(-0.956854\pi\) | ||||
0.990827 | − | 0.135133i | \(-0.0431462\pi\) | |||||||
\(338\) | − 24.0000i | − 0.00386221i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −249.000 | −0.0395428 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6860.00i | 1.07990i | ||||||||
\(344\) | −2392.00 | −0.374907 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7884.00 | −1.22499 | ||||||||
\(347\) | 5076.00i | 0.785285i | 0.919691 | + | 0.392643i | \(0.128439\pi\) | ||||
−0.919691 | + | 0.392643i | \(0.871561\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8594.00 | −1.31813 | −0.659063 | − | 0.752087i | \(-0.729047\pi\) | ||||
−0.659063 | + | 0.752087i | \(0.729047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 96.0000i | − 0.0145364i | ||||||||
\(353\) | 12711.0i | 1.91654i | 0.285866 | + | 0.958269i | \(0.407719\pi\) | ||||
−0.285866 | + | 0.958269i | \(0.592281\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 480.000 | 0.0714605 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 2424.00i | − 0.357856i | ||||||||
\(359\) | −1464.00 | −0.215228 | −0.107614 | − | 0.994193i | \(-0.534321\pi\) | ||||
−0.107614 | + | 0.994193i | \(0.534321\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5835.00 | −0.850707 | ||||||||
\(362\) | 4576.00i | 0.664390i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2632.00 | −0.378995 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 7630.00i | − 1.08524i | −0.839979 | − | 0.542620i | \(-0.817433\pi\) | ||||
0.839979 | − | 0.542620i | \(-0.182567\pi\) | |||||||
\(368\) | − 1584.00i | − 0.224380i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7896.00 | −1.10496 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3883.00i | 0.539019i | 0.962998 | + | 0.269510i | \(0.0868616\pi\) | ||||
−0.962998 | + | 0.269510i | \(0.913138\pi\) | |||||||
\(374\) | 234.000 | 0.0323525 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4248.00 | −0.582643 | ||||||||
\(377\) | − 2397.00i | − 0.327458i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13768.0 | 1.86600 | 0.933001 | − | 0.359874i | \(-0.117180\pi\) | ||||
0.933001 | + | 0.359874i | \(0.117180\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3876.00i | 0.519145i | ||||||||
\(383\) | − 14139.0i | − 1.88634i | −0.332307 | − | 0.943171i | \(-0.607827\pi\) | ||||
0.332307 | − | 0.943171i | \(-0.392173\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2996.00 | −0.395058 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6568.00i | 0.859381i | ||||||||
\(389\) | 567.000 | 0.0739024 | 0.0369512 | − | 0.999317i | \(-0.488235\pi\) | ||||
0.0369512 | + | 0.999317i | \(0.488235\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3861.00 | 0.499384 | ||||||||
\(392\) | − 1176.00i | − 0.151523i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4248.00 | −0.543176 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 6685.00i | − 0.845115i | −0.906336 | − | 0.422557i | \(-0.861133\pi\) | ||||
0.906336 | − | 0.422557i | \(-0.138867\pi\) | |||||||
\(398\) | 770.000i | 0.0969764i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4572.00 | −0.569364 | −0.284682 | − | 0.958622i | \(-0.591888\pi\) | ||||
−0.284682 | + | 0.958622i | \(0.591888\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 3901.00i | − 0.482190i | ||||||||
\(404\) | 132.000 | 0.0162556 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1428.00 | −0.174558 | ||||||||
\(407\) | − 942.000i | − 0.114725i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.0000 | 0.00302242 | 0.00151121 | − | 0.999999i | \(-0.499519\pi\) | ||||
0.00151121 | + | 0.999999i | \(0.499519\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 4792.00i | − 0.573022i | ||||||||
\(413\) | 168.000i | 0.0200163i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1504.00 | 0.177259 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 192.000i | 0.0224666i | ||||||||
\(419\) | 12453.0 | 1.45195 | 0.725977 | − | 0.687719i | \(-0.241388\pi\) | ||||
0.725977 | + | 0.687719i | \(0.241388\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5048.00 | 0.584381 | 0.292191 | − | 0.956360i | \(-0.405616\pi\) | ||||
0.292191 | + | 0.956360i | \(0.405616\pi\) | |||||||
\(422\) | 6340.00i | 0.731342i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4512.00 | 0.516797 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3220.00i | 0.364934i | ||||||||
\(428\) | − 6168.00i | − 0.696592i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5400.00 | −0.603501 | −0.301750 | − | 0.953387i | \(-0.597571\pi\) | ||||
−0.301750 | + | 0.953387i | \(0.597571\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6298.00i | 0.698990i | 0.936938 | + | 0.349495i | \(0.113647\pi\) | ||||
−0.936938 | + | 0.349495i | \(0.886353\pi\) | |||||||
\(434\) | −2324.00 | −0.257040 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2224.00 | −0.244290 | ||||||||
\(437\) | 3168.00i | 0.346787i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6208.00 | 0.674924 | 0.337462 | − | 0.941339i | \(-0.390432\pi\) | ||||
0.337462 | + | 0.941339i | \(0.390432\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3666.00i | 0.394511i | ||||||||
\(443\) | − 3360.00i | − 0.360358i | −0.983634 | − | 0.180179i | \(-0.942332\pi\) | ||||
0.983634 | − | 0.180179i | \(-0.0576676\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2776.00 | 0.294725 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 896.000i | − 0.0944911i | ||||||||
\(449\) | 14394.0 | 1.51291 | 0.756453 | − | 0.654048i | \(-0.226931\pi\) | ||||
0.756453 | + | 0.654048i | \(0.226931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −324.000 | −0.0338283 | ||||||||
\(452\) | − 6420.00i | − 0.668078i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9288.00 | −0.960149 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 916.000i | − 0.0937608i | −0.998901 | − | 0.0468804i | \(-0.985072\pi\) | ||||
0.998901 | − | 0.0468804i | \(-0.0149280\pi\) | |||||||
\(458\) | − 9472.00i | − 0.966370i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8550.00 | −0.863803 | −0.431902 | − | 0.901921i | \(-0.642157\pi\) | ||||
−0.431902 | + | 0.901921i | \(0.642157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 3734.00i | − 0.374803i | −0.982283 | − | 0.187401i | \(-0.939993\pi\) | ||||
0.982283 | − | 0.187401i | \(-0.0600065\pi\) | |||||||
\(464\) | 816.000 | 0.0816419 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5628.00 | −0.559468 | ||||||||
\(467\) | − 9840.00i | − 0.975034i | −0.873113 | − | 0.487517i | \(-0.837903\pi\) | ||||
0.873113 | − | 0.487517i | \(-0.162097\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3752.00 | 0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 96.0000i | − 0.00936178i | ||||||||
\(473\) | 897.000i | 0.0871968i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2184.00 | 0.210301 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 4404.00i | − 0.421411i | ||||||||
\(479\) | −17280.0 | −1.64832 | −0.824158 | − | 0.566360i | \(-0.808351\pi\) | ||||
−0.824158 | + | 0.566360i | \(0.808351\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14758.0 | 1.39897 | ||||||||
\(482\) | 6970.00i | 0.658661i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5288.00 | 0.496619 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 4588.00i | − 0.426904i | −0.976954 | − | 0.213452i | \(-0.931529\pi\) | ||||
0.976954 | − | 0.213452i | \(-0.0684707\pi\) | |||||||
\(488\) | − 1840.00i | − 0.170682i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −636.000 | −0.0584568 | −0.0292284 | − | 0.999573i | \(-0.509305\pi\) | ||||
−0.0292284 | + | 0.999573i | \(0.509305\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1989.00i | 0.181704i | ||||||||
\(494\) | −3008.00 | −0.273960 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1328.00 | 0.120220 | ||||||||
\(497\) | − 1680.00i | − 0.151626i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11716.0 | 1.05106 | 0.525531 | − | 0.850774i | \(-0.323867\pi\) | ||||
0.525531 | + | 0.850774i | \(0.323867\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12690.0i | 1.12825i | ||||||||
\(503\) | 4653.00i | 0.412459i | 0.978504 | + | 0.206230i | \(0.0661194\pi\) | ||||
−0.978504 | + | 0.206230i | \(0.933881\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −594.000 | −0.0521868 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 5336.00i | − 0.466037i | ||||||||
\(509\) | 16479.0 | 1.43501 | 0.717504 | − | 0.696555i | \(-0.245285\pi\) | ||||
0.717504 | + | 0.696555i | \(0.245285\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15484.0 | 1.34045 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1050.00 | 0.0901041 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1593.00i | 0.135513i | ||||||||
\(518\) | − 8792.00i | − 0.745750i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3120.00 | −0.262360 | −0.131180 | − | 0.991359i | \(-0.541877\pi\) | ||||
−0.131180 | + | 0.991359i | \(0.541877\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 17645.0i | − 1.47526i | −0.675204 | − | 0.737631i | \(-0.735944\pi\) | ||||
0.675204 | − | 0.737631i | \(-0.264056\pi\) | |||||||
\(524\) | −11532.0 | −0.961408 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10392.0 | −0.861431 | ||||||||
\(527\) | 3237.00i | 0.267563i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2366.00 | 0.194460 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1792.00i | 0.146040i | ||||||||
\(533\) | − 5076.00i | − 0.412507i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2144.00 | −0.172774 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 14958.0i | − 1.19867i | ||||||||
\(539\) | −441.000 | −0.0352416 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2182.00 | −0.173404 | −0.0867019 | − | 0.996234i | \(-0.527633\pi\) | ||||
−0.0867019 | + | 0.996234i | \(0.527633\pi\) | |||||||
\(542\) | − 1712.00i | − 0.135677i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1248.00 | −0.0983595 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 4033.00i | − 0.315244i | −0.987499 | − | 0.157622i | \(-0.949617\pi\) | ||||
0.987499 | − | 0.157622i | \(-0.0503828\pi\) | |||||||
\(548\) | 1128.00i | 0.0879302i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1632.00 | −0.126181 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10346.0i | 0.795582i | ||||||||
\(554\) | 14108.0 | 1.08193 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9976.00 | −0.760929 | ||||||||
\(557\) | 960.000i | 0.0730278i | 0.999333 | + | 0.0365139i | \(0.0116253\pi\) | ||||
−0.999333 | + | 0.0365139i | \(0.988375\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14053.0 | −1.06329 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 2028.00i | − 0.152217i | ||||||||
\(563\) | − 23754.0i | − 1.77817i | −0.457739 | − | 0.889087i | \(-0.651340\pi\) | ||||
0.457739 | − | 0.889087i | \(-0.348660\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1984.00 | 0.147339 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 960.000i | 0.0709167i | ||||||||
\(569\) | −22536.0 | −1.66038 | −0.830192 | − | 0.557478i | \(-0.811769\pi\) | ||||
−0.830192 | + | 0.557478i | \(0.811769\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17726.0 | 1.29914 | 0.649571 | − | 0.760301i | \(-0.274949\pi\) | ||||
0.649571 | + | 0.760301i | \(0.274949\pi\) | |||||||
\(572\) | − 564.000i | − 0.0412273i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3024.00 | −0.219894 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17168.0i | 1.23867i | 0.785126 | + | 0.619336i | \(0.212598\pi\) | ||||
−0.785126 | + | 0.619336i | \(0.787402\pi\) | |||||||
\(578\) | 6784.00i | 0.488196i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15204.0 | −1.08566 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1692.00i | − 0.120198i | ||||||||
\(584\) | −8848.00 | −0.626940 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9900.00 | 0.697893 | ||||||||
\(587\) | − 7542.00i | − 0.530309i | −0.964206 | − | 0.265155i | \(-0.914577\pi\) | ||||
0.964206 | − | 0.265155i | \(-0.0854230\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2656.00 | −0.185804 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5024.00i | 0.348792i | ||||||||
\(593\) | − 15543.0i | − 1.07635i | −0.842834 | − | 0.538174i | \(-0.819114\pi\) | ||||
0.842834 | − | 0.538174i | \(-0.180886\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10380.0 | −0.713392 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 9306.00i | − 0.636372i | ||||||||
\(599\) | 16026.0 | 1.09316 | 0.546581 | − | 0.837406i | \(-0.315929\pi\) | ||||
0.546581 | + | 0.837406i | \(0.315929\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10469.0 | 0.710548 | 0.355274 | − | 0.934762i | \(-0.384388\pi\) | ||||
0.355274 | + | 0.934762i | \(0.384388\pi\) | |||||||
\(602\) | 8372.00i | 0.566806i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4916.00 | −0.331174 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 8074.00i | − 0.539891i | −0.962876 | − | 0.269945i | \(-0.912994\pi\) | ||||
0.962876 | − | 0.269945i | \(-0.0870056\pi\) | |||||||
\(608\) | − 1024.00i | − 0.0683038i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24957.0 | −1.65246 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 26855.0i | − 1.76943i | −0.466128 | − | 0.884717i | \(-0.654351\pi\) | ||||
0.466128 | − | 0.884717i | \(-0.345649\pi\) | |||||||
\(614\) | 9554.00 | 0.627961 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −336.000 | −0.0219770 | ||||||||
\(617\) | − 24447.0i | − 1.59514i | −0.603229 | − | 0.797568i | \(-0.706119\pi\) | ||||
0.603229 | − | 0.797568i | \(-0.293881\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1850.00 | −0.120126 | −0.0600628 | − | 0.998195i | \(-0.519130\pi\) | ||||
−0.0600628 | + | 0.998195i | \(0.519130\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15384.0i | 0.991708i | ||||||||
\(623\) | − 1680.00i | − 0.108038i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5864.00 | −0.374397 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6364.00i | 0.404381i | ||||||||
\(629\) | −12246.0 | −0.776280 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21728.0 | 1.37081 | 0.685403 | − | 0.728164i | \(-0.259626\pi\) | ||||
0.685403 | + | 0.728164i | \(0.259626\pi\) | |||||||
\(632\) | − 5912.00i | − 0.372099i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16704.0 | 1.04637 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6909.00i | − 0.429740i | ||||||||
\(638\) | − 306.000i | − 0.0189885i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23862.0 | −1.47035 | −0.735173 | − | 0.677879i | \(-0.762899\pi\) | ||||
−0.735173 | + | 0.677879i | \(0.762899\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 10523.0i | − 0.645391i | −0.946503 | − | 0.322696i | \(-0.895411\pi\) | ||||
0.946503 | − | 0.322696i | \(-0.104589\pi\) | |||||||
\(644\) | −5544.00 | −0.339230 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2496.00 | 0.152018 | ||||||||
\(647\) | − 5484.00i | − 0.333228i | −0.986022 | − | 0.166614i | \(-0.946717\pi\) | ||||
0.986022 | − | 0.166614i | \(-0.0532833\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.0000 | −0.00217739 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 1828.00i | − 0.109801i | ||||||||
\(653\) | − 26784.0i | − 1.60511i | −0.596576 | − | 0.802557i | \(-0.703473\pi\) | ||||
0.596576 | − | 0.802557i | \(-0.296527\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1728.00 | 0.102846 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14868.0i | 0.880874i | ||||||||
\(659\) | −12120.0 | −0.716431 | −0.358216 | − | 0.933639i | \(-0.616615\pi\) | ||||
−0.358216 | + | 0.933639i | \(0.616615\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18226.0 | −1.07248 | −0.536240 | − | 0.844066i | \(-0.680156\pi\) | ||||
−0.536240 | + | 0.844066i | \(0.680156\pi\) | |||||||
\(662\) | − 6140.00i | − 0.360480i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8688.00 | 0.507771 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 5049.00i | − 0.293101i | ||||||||
\(668\) | − 4656.00i | − 0.269680i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −690.000 | −0.0396977 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11062.0i | 0.633594i | 0.948493 | + | 0.316797i | \(0.102607\pi\) | ||||
−0.948493 | + | 0.316797i | \(0.897393\pi\) | |||||||
\(674\) | 3344.00 | 0.191107 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 48.0000 | 0.00273100 | ||||||||
\(677\) | 9348.00i | 0.530684i | 0.964154 | + | 0.265342i | \(0.0854848\pi\) | ||||
−0.964154 | + | 0.265342i | \(0.914515\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22988.0 | 1.29926 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 498.000i | − 0.0279610i | ||||||||
\(683\) | 19248.0i | 1.07834i | 0.842198 | + | 0.539169i | \(0.181261\pi\) | ||||
−0.842198 | + | 0.539169i | \(0.818739\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13720.0 | −0.763604 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 4784.00i | − 0.265099i | ||||||||
\(689\) | 26508.0 | 1.46571 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17710.0 | −0.974993 | −0.487496 | − | 0.873125i | \(-0.662090\pi\) | ||||
−0.487496 | + | 0.873125i | \(0.662090\pi\) | |||||||
\(692\) | − 15768.0i | − 0.866199i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10152.0 | −0.555280 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4212.00i | 0.228897i | ||||||||
\(698\) | − 17188.0i | − 0.932056i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19437.0 | 1.04725 | 0.523627 | − | 0.851947i | \(-0.324578\pi\) | ||||
0.523627 | + | 0.851947i | \(0.324578\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 10048.0i | − 0.539072i | ||||||||
\(704\) | 192.000 | 0.0102788 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −25422.0 | −1.35520 | ||||||||
\(707\) | − 462.000i | − 0.0245761i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19516.0 | 1.03376 | 0.516882 | − | 0.856057i | \(-0.327093\pi\) | ||||
0.516882 | + | 0.856057i | \(0.327093\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 960.000i | 0.0505302i | ||||||||
\(713\) | − 8217.00i | − 0.431598i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4848.00 | 0.253042 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 2928.00i | − 0.152189i | ||||||||
\(719\) | 17358.0 | 0.900340 | 0.450170 | − | 0.892943i | \(-0.351363\pi\) | ||||
0.450170 | + | 0.892943i | \(0.351363\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16772.0 | −0.866327 | ||||||||
\(722\) | − 11670.0i | − 0.601541i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9152.00 | −0.469795 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24428.0i | 1.24620i | 0.782144 | + | 0.623098i | \(0.214126\pi\) | ||||
−0.782144 | + | 0.623098i | \(0.785874\pi\) | |||||||
\(728\) | − 5264.00i | − 0.267990i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11661.0 | 0.590010 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21418.0i | 1.07925i | 0.841905 | + | 0.539626i | \(0.181434\pi\) | ||||
−0.841905 | + | 0.539626i | \(0.818566\pi\) | |||||||
\(734\) | 15260.0 | 0.767380 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3168.00 | 0.158660 | ||||||||
\(737\) | 804.000i | 0.0401842i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 664.000 | 0.0330523 | 0.0165261 | − | 0.999863i | \(-0.494739\pi\) | ||||
0.0165261 | + | 0.999863i | \(0.494739\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 15792.0i | − 0.781324i | ||||||||
\(743\) | − 34209.0i | − 1.68911i | −0.535471 | − | 0.844553i | \(-0.679866\pi\) | ||||
0.535471 | − | 0.844553i | \(-0.320134\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7766.00 | −0.381144 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 468.000i | 0.0228767i | ||||||||
\(749\) | −21588.0 | −1.05315 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6857.00 | 0.333176 | 0.166588 | − | 0.986027i | \(-0.446725\pi\) | ||||
0.166588 | + | 0.986027i | \(0.446725\pi\) | |||||||
\(752\) | − 8496.00i | − 0.411991i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4794.00 | 0.231548 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 23719.0i | − 1.13881i | −0.822056 | − | 0.569407i | \(-0.807173\pi\) | ||||
0.822056 | − | 0.569407i | \(-0.192827\pi\) | |||||||
\(758\) | 27536.0i | 1.31946i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14418.0 | 0.686796 | 0.343398 | − | 0.939190i | \(-0.388422\pi\) | ||||
0.343398 | + | 0.939190i | \(0.388422\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7784.00i | 0.369331i | ||||||||
\(764\) | −7752.00 | −0.367091 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28278.0 | 1.33385 | ||||||||
\(767\) | − 564.000i | − 0.0265513i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4849.00 | 0.227385 | 0.113693 | − | 0.993516i | \(-0.463732\pi\) | ||||
0.113693 | + | 0.993516i | \(0.463732\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 5992.00i | − 0.279348i | ||||||||
\(773\) | − 36258.0i | − 1.68708i | −0.537070 | − | 0.843538i | \(-0.680469\pi\) | ||||
0.537070 | − | 0.843538i | \(-0.319531\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13136.0 | −0.607674 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1134.00i | 0.0522569i | ||||||||
\(779\) | −3456.00 | −0.158953 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 360.000 | 0.0164940 | ||||||||
\(782\) | 7722.00i | 0.353118i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2352.00 | 0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 18877.0i | − 0.855009i | −0.904013 | − | 0.427505i | \(-0.859393\pi\) | ||||
0.904013 | − | 0.427505i | \(-0.140607\pi\) | |||||||
\(788\) | − 8496.00i | − 0.384083i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22470.0 | −1.01004 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 10810.0i | − 0.484079i | ||||||||
\(794\) | 13370.0 | 0.597586 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1540.00 | −0.0685727 | ||||||||
\(797\) | 16200.0i | 0.719992i | 0.932954 | + | 0.359996i | \(0.117222\pi\) | ||||
−0.932954 | + | 0.359996i | \(0.882778\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20709.0 | 0.916936 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 9144.00i | − 0.402601i | ||||||||
\(803\) | 3318.00i | 0.145815i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7802.00 | 0.340960 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 264.000i | 0.0114944i | ||||||||
\(809\) | −26760.0 | −1.16296 | −0.581478 | − | 0.813562i | \(-0.697525\pi\) | ||||
−0.581478 | + | 0.813562i | \(0.697525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10510.0 | −0.455063 | −0.227531 | − | 0.973771i | \(-0.573065\pi\) | ||||
−0.227531 | + | 0.973771i | \(0.573065\pi\) | |||||||
\(812\) | − 2856.00i | − 0.123431i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1884.00 | 0.0811231 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9568.00i | 0.409721i | ||||||||
\(818\) | 50.0000i | 0.00213717i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28230.0 | 1.20004 | 0.600021 | − | 0.799985i | \(-0.295159\pi\) | ||||
0.600021 | + | 0.799985i | \(0.295159\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39868.0i | 1.68859i | 0.535877 | + | 0.844296i | \(0.319981\pi\) | ||||
−0.535877 | + | 0.844296i | \(0.680019\pi\) | |||||||
\(824\) | 9584.00 | 0.405187 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −336.000 | −0.0141537 | ||||||||
\(827\) | − 32394.0i | − 1.36209i | −0.732241 | − | 0.681046i | \(-0.761525\pi\) | ||||
0.732241 | − | 0.681046i | \(-0.238475\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34820.0 | −1.45880 | −0.729402 | − | 0.684085i | \(-0.760202\pi\) | ||||
−0.729402 | + | 0.684085i | \(0.760202\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3008.00i | 0.125341i | ||||||||
\(833\) | 5733.00i | 0.238459i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −384.000 | −0.0158863 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24906.0i | 1.02669i | ||||||||
\(839\) | −1146.00 | −0.0471565 | −0.0235783 | − | 0.999722i | \(-0.507506\pi\) | ||||
−0.0235783 | + | 0.999722i | \(0.507506\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21788.0 | −0.893354 | ||||||||
\(842\) | 10096.0i | 0.413220i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12680.0 | −0.517137 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 18508.0i | − 0.750817i | ||||||||
\(848\) | 9024.00i | 0.365431i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31086.0 | 1.25219 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19393.0i | 0.778433i | 0.921146 | + | 0.389217i | \(0.127254\pi\) | ||||
−0.921146 | + | 0.389217i | \(0.872746\pi\) | |||||||
\(854\) | −6440.00 | −0.258047 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12336.0 | 0.492565 | ||||||||
\(857\) | 8430.00i | 0.336013i | 0.985786 | + | 0.168007i | \(0.0537330\pi\) | ||||
−0.985786 | + | 0.168007i | \(0.946267\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15470.0 | −0.614470 | −0.307235 | − | 0.951634i | \(-0.599404\pi\) | ||||
−0.307235 | + | 0.951634i | \(0.599404\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 10800.0i | − 0.426740i | ||||||||
\(863\) | 5871.00i | 0.231577i | 0.993274 | + | 0.115789i | \(0.0369395\pi\) | ||||
−0.993274 | + | 0.115789i | \(0.963060\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −12596.0 | −0.494260 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 4648.00i | − 0.181755i | ||||||||
\(869\) | −2217.00 | −0.0865438 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12596.0 | −0.490011 | ||||||||
\(872\) | − 4448.00i | − 0.172739i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6336.00 | −0.245216 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 11299.0i | − 0.435051i | −0.976055 | − | 0.217526i | \(-0.930201\pi\) | ||||
0.976055 | − | 0.217526i | \(-0.0697986\pi\) | |||||||
\(878\) | 12416.0i | 0.477243i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29682.0 | −1.13509 | −0.567544 | − | 0.823343i | \(-0.692106\pi\) | ||||
−0.567544 | + | 0.823343i | \(0.692106\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 40316.0i | − 1.53651i | −0.640142 | − | 0.768257i | \(-0.721124\pi\) | ||||
0.640142 | − | 0.768257i | \(-0.278876\pi\) | |||||||
\(884\) | −7332.00 | −0.278961 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6720.00 | 0.254811 | ||||||||
\(887\) | 21945.0i | 0.830711i | 0.909659 | + | 0.415356i | \(0.136343\pi\) | ||||
−0.909659 | + | 0.415356i | \(0.863657\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18676.0 | −0.704581 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5552.00i | 0.208402i | ||||||||
\(893\) | 16992.0i | 0.636748i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1792.00 | 0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 28788.0i | 1.06979i | ||||||||
\(899\) | 4233.00 | 0.157039 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21996.0 | −0.813311 | ||||||||
\(902\) | − 648.000i | − 0.0239202i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12840.0 | 0.472403 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24911.0i | 0.911969i | 0.889988 | + | 0.455985i | \(0.150713\pi\) | ||||
−0.889988 | + | 0.455985i | \(0.849287\pi\) | |||||||
\(908\) | − 18576.0i | − 0.678928i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33264.0 | −1.20975 | −0.604877 | − | 0.796319i | \(-0.706778\pi\) | ||||
−0.604877 | + | 0.796319i | \(0.706778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 3258.00i | − 0.118099i | ||||||||
\(914\) | 1832.00 | 0.0662989 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18944.0 | 0.683327 | ||||||||
\(917\) | 40362.0i | 1.45351i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23191.0 | 0.832427 | 0.416214 | − | 0.909267i | \(-0.363357\pi\) | ||||
0.416214 | + | 0.909267i | \(0.363357\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 17100.0i | − 0.610801i | ||||||||
\(923\) | 5640.00i | 0.201130i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7468.00 | 0.265026 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1632.00i | 0.0577296i | ||||||||
\(929\) | 2160.00 | 0.0762834 | 0.0381417 | − | 0.999272i | \(-0.487856\pi\) | ||||
0.0381417 | + | 0.999272i | \(0.487856\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4704.00 | −0.165593 | ||||||||
\(932\) | − 11256.0i | − 0.395604i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19680.0 | 0.689453 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2066.00i | 0.0720312i | 0.999351 | + | 0.0360156i | \(0.0114666\pi\) | ||||
−0.999351 | + | 0.0360156i | \(0.988533\pi\) | |||||||
\(938\) | 7504.00i | 0.261209i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22233.0 | 0.770218 | 0.385109 | − | 0.922871i | \(-0.374164\pi\) | ||||
0.385109 | + | 0.922871i | \(0.374164\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 10692.0i | − 0.369225i | ||||||||
\(944\) | 192.000 | 0.00661978 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1794.00 | −0.0616575 | ||||||||
\(947\) | 17754.0i | 0.609216i | 0.952478 | + | 0.304608i | \(0.0985254\pi\) | ||||
−0.952478 | + | 0.304608i | \(0.901475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −51982.0 | −1.77809 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4368.00i | 0.148706i | ||||||||
\(953\) | 33891.0i | 1.15198i | 0.817457 | + | 0.575990i | \(0.195383\pi\) | ||||
−0.817457 | + | 0.575990i | \(0.804617\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8808.00 | 0.297982 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 34560.0i | − 1.16554i | ||||||||
\(959\) | 3948.00 | 0.132938 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22902.0 | −0.768756 | ||||||||
\(962\) | 29516.0i | 0.989225i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13940.0 | −0.465744 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51074.0i | 1.69848i | 0.528008 | + | 0.849239i | \(0.322939\pi\) | ||||
−0.528008 | + | 0.849239i | \(0.677061\pi\) | |||||||
\(968\) | 10576.0i | 0.351163i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20967.0 | −0.692959 | −0.346479 | − | 0.938058i | \(-0.612623\pi\) | ||||
−0.346479 | + | 0.938058i | \(0.612623\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34916.0i | 1.15042i | ||||||||
\(974\) | 9176.00 | 0.301867 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3680.00 | 0.120691 | ||||||||
\(977\) | − 31749.0i | − 1.03965i | −0.854272 | − | 0.519826i | \(-0.825997\pi\) | ||||
0.854272 | − | 0.519826i | \(-0.174003\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 360.000 | 0.0117525 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 1272.00i | − 0.0413352i | ||||||||
\(983\) | 47325.0i | 1.53554i | 0.640727 | + | 0.767769i | \(0.278633\pi\) | ||||
−0.640727 | + | 0.767769i | \(0.721367\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3978.00 | −0.128484 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 6016.00i | − 0.193719i | ||||||||
\(989\) | −29601.0 | −0.951726 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2363.00 | 0.0757449 | 0.0378724 | − | 0.999283i | \(-0.487942\pi\) | ||||
0.0378724 | + | 0.999283i | \(0.487942\pi\) | |||||||
\(992\) | 2656.00i | 0.0850081i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3360.00 | 0.107216 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45569.0i | 1.44753i | 0.690048 | + | 0.723764i | \(0.257589\pi\) | ||||
−0.690048 | + | 0.723764i | \(0.742411\pi\) | |||||||
\(998\) | 23432.0i | 0.743213i | ||||||||
\(999\) | 0 | 0 |
(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 | 1350.4.c.j.649.2 | 2 | ||
3.2 | odd | 2 | 1350.4.c.k.649.1 | 2 | |||
5.2 | odd | 4 | 1350.4.a.e.1.1 | 1 | |||
5.3 | odd | 4 | 270.4.a.j.1.1 | yes | 1 | ||
5.4 | even | 2 | inner | 1350.4.c.j.649.1 | 2 | ||
15.2 | even | 4 | 1350.4.a.r.1.1 | 1 | |||
15.8 | even | 4 | 270.4.a.f.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 1350.4.c.k.649.2 | 2 | |||
20.3 | even | 4 | 2160.4.a.b.1.1 | 1 | |||
45.13 | odd | 12 | 810.4.e.f.541.1 | 2 | |||
45.23 | even | 12 | 810.4.e.n.541.1 | 2 | |||
45.38 | even | 12 | 810.4.e.n.271.1 | 2 | |||
45.43 | odd | 12 | 810.4.e.f.271.1 | 2 | |||
60.23 | odd | 4 | 2160.4.a.l.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.4.a.f.1.1 | ✓ | 1 | 15.8 | even | 4 | ||
270.4.a.j.1.1 | yes | 1 | 5.3 | odd | 4 | ||
810.4.e.f.271.1 | 2 | 45.43 | odd | 12 | |||
810.4.e.f.541.1 | 2 | 45.13 | odd | 12 | |||
810.4.e.n.271.1 | 2 | 45.38 | even | 12 | |||
810.4.e.n.541.1 | 2 | 45.23 | even | 12 | |||
1350.4.a.e.1.1 | 1 | 5.2 | odd | 4 | |||
1350.4.a.r.1.1 | 1 | 15.2 | even | 4 | |||
1350.4.c.j.649.1 | 2 | 5.4 | even | 2 | inner | ||
1350.4.c.j.649.2 | 2 | 1.1 | even | 1 | trivial | ||
1350.4.c.k.649.1 | 2 | 3.2 | odd | 2 | |||
1350.4.c.k.649.2 | 2 | 15.14 | odd | 2 | |||
2160.4.a.b.1.1 | 1 | 20.3 | even | 4 | |||
2160.4.a.l.1.1 | 1 | 60.23 | odd | 4 |