Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,3,Mod(449,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.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: | \(85.8312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.9671731157401600000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 7x^{12} + 753x^{8} + 112x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.7 | ||
Root | \(0.359610 + 0.796626i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.449 |
Dual form | 3150.3.c.f.449.2 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.2717i | 1.02470i | 0.858776 | + | 0.512351i | \(0.171225\pi\) | ||||
−0.858776 | + | 0.512351i | \(0.828775\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 22.9496i | 1.76535i | 0.469980 | + | 0.882677i | \(0.344261\pi\) | ||||
−0.469980 | + | 0.882677i | \(0.655739\pi\) | |||||||
\(14\) | − 3.74166i | − 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 8.36199 | 0.491882 | 0.245941 | − | 0.969285i | \(-0.420903\pi\) | ||||
0.245941 | + | 0.969285i | \(0.420903\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.57092 | −0.187943 | −0.0939717 | − | 0.995575i | \(-0.529956\pi\) | ||||
−0.0939717 | + | 0.995575i | \(0.529956\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 15.9406i | − 0.724573i | ||||||||
\(23\) | −3.92441 | −0.170626 | −0.0853132 | − | 0.996354i | \(-0.527189\pi\) | ||||
−0.0853132 | + | 0.996354i | \(0.527189\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − 32.4556i | − 1.24829i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.29150i | 0.188982i | ||||||||
\(29\) | 43.5101i | 1.50035i | 0.661241 | + | 0.750173i | \(0.270030\pi\) | ||||
−0.661241 | + | 0.750173i | \(0.729970\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 46.3702 | 1.49581 | 0.747907 | − | 0.663804i | \(-0.231059\pi\) | ||||
0.747907 | + | 0.663804i | \(0.231059\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −11.8256 | −0.347813 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 27.9648i | 0.755805i | 0.925845 | + | 0.377902i | \(0.123355\pi\) | ||||
−0.925845 | + | 0.377902i | \(0.876645\pi\) | |||||||
\(38\) | 5.05005 | 0.132896 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 32.8306i | − 0.800748i | −0.916352 | − | 0.400374i | \(-0.868880\pi\) | ||||
0.916352 | − | 0.400374i | \(-0.131120\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 65.5572i | 1.52459i | 0.647232 | + | 0.762293i | \(0.275927\pi\) | ||||
−0.647232 | + | 0.762293i | \(0.724073\pi\) | |||||||
\(44\) | 22.5434i | 0.512351i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.54995 | 0.120651 | ||||||||
\(47\) | −5.65248 | −0.120266 | −0.0601328 | − | 0.998190i | \(-0.519152\pi\) | ||||
−0.0601328 | + | 0.998190i | \(0.519152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 45.8992i | 0.882677i | ||||||||
\(53\) | 24.7975 | 0.467878 | 0.233939 | − | 0.972251i | \(-0.424838\pi\) | ||||
0.233939 | + | 0.972251i | \(0.424838\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 7.48331i | − 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 61.5325i | − 1.06091i | ||||||||
\(59\) | − 58.6564i | − 0.994176i | −0.867700 | − | 0.497088i | \(-0.834403\pi\) | ||||
0.867700 | − | 0.497088i | \(-0.165597\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 28.2418 | 0.462980 | 0.231490 | − | 0.972837i | \(-0.425640\pi\) | ||||
0.231490 | + | 0.972837i | \(0.425640\pi\) | |||||||
\(62\) | −65.5774 | −1.05770 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 10.7504i | − 0.160454i | −0.996777 | − | 0.0802271i | \(-0.974435\pi\) | ||||
0.996777 | − | 0.0802271i | \(-0.0255646\pi\) | |||||||
\(68\) | 16.7240 | 0.245941 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 20.8535i | − 0.293711i | −0.989158 | − | 0.146856i | \(-0.953085\pi\) | ||||
0.989158 | − | 0.146856i | \(-0.0469153\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 113.896i | 1.56022i | 0.625642 | + | 0.780110i | \(0.284837\pi\) | ||||
−0.625642 | + | 0.780110i | \(0.715163\pi\) | |||||||
\(74\) | − 39.5482i | − 0.534435i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.14185 | −0.0939717 | ||||||||
\(77\) | −29.8222 | −0.387301 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −133.236 | −1.68654 | −0.843268 | − | 0.537494i | \(-0.819371\pi\) | ||||
−0.843268 | + | 0.537494i | \(0.819371\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 46.4295i | 0.566214i | ||||||||
\(83\) | 30.9830 | 0.373289 | 0.186644 | − | 0.982428i | \(-0.440239\pi\) | ||||
0.186644 | + | 0.982428i | \(0.440239\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − 92.7119i | − 1.07805i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 31.8812i | − 0.362287i | ||||||||
\(89\) | − 79.6261i | − 0.894675i | −0.894365 | − | 0.447337i | \(-0.852372\pi\) | ||||
0.894365 | − | 0.447337i | \(-0.147628\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −60.7189 | −0.667241 | ||||||||
\(92\) | −7.84882 | −0.0853132 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.99382 | 0.0850406 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 26.1819i | 0.269917i | 0.990851 | + | 0.134958i | \(0.0430901\pi\) | ||||
−0.990851 | + | 0.134958i | \(0.956910\pi\) | |||||||
\(98\) | 9.89949 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 170.729i | − 1.69038i | −0.534465 | − | 0.845191i | \(-0.679487\pi\) | ||||
0.534465 | − | 0.845191i | \(-0.320513\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 159.260i | − 1.54622i | −0.634274 | − | 0.773108i | \(-0.718701\pi\) | ||||
0.634274 | − | 0.773108i | \(-0.281299\pi\) | |||||||
\(104\) | − 64.9113i | − 0.624147i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −35.0690 | −0.330840 | ||||||||
\(107\) | −62.7625 | −0.586565 | −0.293283 | − | 0.956026i | \(-0.594748\pi\) | ||||
−0.293283 | + | 0.956026i | \(0.594748\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −44.5696 | −0.408895 | −0.204448 | − | 0.978878i | \(-0.565540\pi\) | ||||
−0.204448 | + | 0.978878i | \(0.565540\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.5830i | 0.0944911i | ||||||||
\(113\) | −128.003 | −1.13277 | −0.566385 | − | 0.824141i | \(-0.691659\pi\) | ||||
−0.566385 | + | 0.824141i | \(0.691659\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 87.0201i | 0.750173i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 82.9526i | 0.702988i | ||||||||
\(119\) | 22.1237i | 0.185914i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.05158 | −0.0500130 | ||||||||
\(122\) | −39.9399 | −0.327376 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 92.7405 | 0.747907 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 99.0952i | 0.780277i | 0.920756 | + | 0.390139i | \(0.127573\pi\) | ||||
−0.920756 | + | 0.390139i | \(0.872427\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 139.901i | 1.06795i | 0.845500 | + | 0.533975i | \(0.179302\pi\) | ||||
−0.845500 | + | 0.533975i | \(0.820698\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 9.44777i | − 0.0710359i | ||||||||
\(134\) | 15.2034i | 0.113458i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −23.6513 | −0.173906 | ||||||||
\(137\) | 200.351 | 1.46242 | 0.731208 | − | 0.682154i | \(-0.238957\pi\) | ||||
0.731208 | + | 0.682154i | \(0.238957\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 89.8593 | 0.646470 | 0.323235 | − | 0.946319i | \(-0.395230\pi\) | ||||
0.323235 | + | 0.946319i | \(0.395230\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 29.4913i | 0.207685i | ||||||||
\(143\) | −258.681 | −1.80896 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − 161.073i | − 1.10324i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 55.9296i | 0.377902i | ||||||||
\(149\) | 154.434i | 1.03647i | 0.855239 | + | 0.518234i | \(0.173411\pi\) | ||||
−0.855239 | + | 0.518234i | \(0.826589\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 293.829 | 1.94588 | 0.972942 | − | 0.231048i | \(-0.0742153\pi\) | ||||
0.972942 | + | 0.231048i | \(0.0742153\pi\) | |||||||
\(152\) | 10.1001 | 0.0664480 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 42.1749 | 0.273863 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 275.050i | 1.75191i | 0.482395 | + | 0.875954i | \(0.339767\pi\) | ||||
−0.482395 | + | 0.875954i | \(0.660233\pi\) | |||||||
\(158\) | 188.425 | 1.19256 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 10.3830i | − 0.0644907i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 121.606i | 0.746048i | 0.927822 | + | 0.373024i | \(0.121679\pi\) | ||||
−0.927822 | + | 0.373024i | \(0.878321\pi\) | |||||||
\(164\) | − 65.6613i | − 0.400374i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −43.8165 | −0.263955 | ||||||||
\(167\) | −155.389 | −0.930475 | −0.465238 | − | 0.885186i | \(-0.654031\pi\) | ||||
−0.465238 | + | 0.885186i | \(0.654031\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −357.684 | −2.11648 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 131.114i | 0.762293i | ||||||||
\(173\) | −191.015 | −1.10413 | −0.552067 | − | 0.833800i | \(-0.686161\pi\) | ||||
−0.552067 | + | 0.833800i | \(0.686161\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 45.0869i | 0.256175i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 112.608i | 0.632631i | ||||||||
\(179\) | − 321.028i | − 1.79345i | −0.442586 | − | 0.896726i | \(-0.645939\pi\) | ||||
0.442586 | − | 0.896726i | \(-0.354061\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.3100 | −0.117735 | −0.0588675 | − | 0.998266i | \(-0.518749\pi\) | ||||
−0.0588675 | + | 0.998266i | \(0.518749\pi\) | |||||||
\(182\) | 85.8696 | 0.471811 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 11.0999 | 0.0603256 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 94.2540i | 0.504032i | ||||||||
\(188\) | −11.3050 | −0.0601328 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 44.6968i | − 0.234015i | −0.993131 | − | 0.117007i | \(-0.962670\pi\) | ||||
0.993131 | − | 0.117007i | \(-0.0373301\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 237.337i | − 1.22973i | −0.788634 | − | 0.614863i | \(-0.789211\pi\) | ||||
0.788634 | − | 0.614863i | \(-0.210789\pi\) | |||||||
\(194\) | − 37.0268i | − 0.190860i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 199.475 | 1.01256 | 0.506282 | − | 0.862368i | \(-0.331020\pi\) | ||||
0.506282 | + | 0.862368i | \(0.331020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −75.1828 | −0.377803 | −0.188902 | − | 0.981996i | \(-0.560493\pi\) | ||||
−0.188902 | + | 0.981996i | \(0.560493\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 241.447i | 1.19528i | ||||||||
\(203\) | −115.117 | −0.567078 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 225.228i | 1.09334i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 91.7984i | 0.441339i | ||||||||
\(209\) | − 40.2504i | − 0.192586i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 177.079 | 0.839237 | 0.419619 | − | 0.907701i | \(-0.362164\pi\) | ||||
0.419619 | + | 0.907701i | \(0.362164\pi\) | |||||||
\(212\) | 49.5951 | 0.233939 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 88.7595 | 0.414764 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 122.684i | 0.565364i | ||||||||
\(218\) | 63.0309 | 0.289133 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 191.904i | 0.868346i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 257.329i | 1.15394i | 0.816765 | + | 0.576971i | \(0.195765\pi\) | ||||
−0.816765 | + | 0.576971i | \(0.804235\pi\) | |||||||
\(224\) | − 14.9666i | − 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 181.024 | 0.800990 | ||||||||
\(227\) | 111.108 | 0.489464 | 0.244732 | − | 0.969591i | \(-0.421300\pi\) | ||||
0.244732 | + | 0.969591i | \(0.421300\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −100.914 | −0.440671 | −0.220336 | − | 0.975424i | \(-0.570715\pi\) | ||||
−0.220336 | + | 0.975424i | \(0.570715\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 123.065i | − 0.530453i | ||||||||
\(233\) | 33.7780 | 0.144970 | 0.0724850 | − | 0.997370i | \(-0.476907\pi\) | ||||
0.0724850 | + | 0.997370i | \(0.476907\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − 117.313i | − 0.497088i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 31.2877i | − 0.131461i | ||||||||
\(239\) | − 440.484i | − 1.84303i | −0.388342 | − | 0.921515i | \(-0.626952\pi\) | ||||
0.388342 | − | 0.921515i | \(-0.373048\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −204.074 | −0.846780 | −0.423390 | − | 0.905947i | \(-0.639160\pi\) | ||||
−0.423390 | + | 0.905947i | \(0.639160\pi\) | |||||||
\(242\) | 8.55822 | 0.0353645 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 56.4835 | 0.231490 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 81.9513i | − 0.331787i | ||||||||
\(248\) | −131.155 | −0.528850 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.18183i | 0.0206447i | 0.999947 | + | 0.0103224i | \(0.00328577\pi\) | ||||
−0.999947 | + | 0.0103224i | \(0.996714\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 44.2348i | − 0.174841i | ||||||||
\(254\) | − 140.142i | − 0.551739i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −236.312 | −0.919501 | −0.459750 | − | 0.888048i | \(-0.652061\pi\) | ||||
−0.459750 | + | 0.888048i | \(0.652061\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −73.9878 | −0.285667 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 197.851i | − 0.755155i | ||||||||
\(263\) | −17.5835 | −0.0668572 | −0.0334286 | − | 0.999441i | \(-0.510643\pi\) | ||||
−0.0334286 | + | 0.999441i | \(0.510643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 13.3612i | 0.0502300i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 21.5009i | − 0.0802271i | ||||||||
\(269\) | − 19.9314i | − 0.0740944i | −0.999314 | − | 0.0370472i | \(-0.988205\pi\) | ||||
0.999314 | − | 0.0370472i | \(-0.0117952\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −87.0972 | −0.321392 | −0.160696 | − | 0.987004i | \(-0.551374\pi\) | ||||
−0.160696 | + | 0.987004i | \(0.551374\pi\) | |||||||
\(272\) | 33.4480 | 0.122970 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −283.339 | −1.03408 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 384.515i | 1.38814i | 0.719907 | + | 0.694071i | \(0.244185\pi\) | ||||
−0.719907 | + | 0.694071i | \(0.755815\pi\) | |||||||
\(278\) | −127.080 | −0.457123 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 246.478i | − 0.877147i | −0.898695 | − | 0.438573i | \(-0.855484\pi\) | ||||
0.898695 | − | 0.438573i | \(-0.144516\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 318.082i | − 1.12396i | −0.827150 | − | 0.561982i | \(-0.810039\pi\) | ||||
0.827150 | − | 0.561982i | \(-0.189961\pi\) | |||||||
\(284\) | − 41.7070i | − 0.146856i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 365.831 | 1.27913 | ||||||||
\(287\) | 86.8617 | 0.302654 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −219.077 | −0.758052 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 227.792i | 0.780110i | ||||||||
\(293\) | 397.217 | 1.35569 | 0.677845 | − | 0.735205i | \(-0.262914\pi\) | ||||
0.677845 | + | 0.735205i | \(0.262914\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − 79.0963i | − 0.267217i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 218.402i | − 0.732894i | ||||||||
\(299\) | − 90.0636i | − 0.301216i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −173.448 | −0.576239 | ||||||||
\(302\) | −415.536 | −1.37595 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14.2837 | −0.0469858 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 450.564i | 1.46764i | 0.679346 | + | 0.733818i | \(0.262263\pi\) | ||||
−0.679346 | + | 0.733818i | \(0.737737\pi\) | |||||||
\(308\) | −59.6443 | −0.193650 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 484.602i | 1.55821i | 0.626897 | + | 0.779103i | \(0.284325\pi\) | ||||
−0.626897 | + | 0.779103i | \(0.715675\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 364.372i | − 1.16413i | −0.813143 | − | 0.582064i | \(-0.802245\pi\) | ||||
0.813143 | − | 0.582064i | \(-0.197755\pi\) | |||||||
\(314\) | − 388.979i | − 1.23879i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −266.473 | −0.843268 | ||||||||
\(317\) | −510.623 | −1.61080 | −0.805399 | − | 0.592733i | \(-0.798049\pi\) | ||||
−0.805399 | + | 0.592733i | \(0.798049\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −490.433 | −1.53741 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 14.6838i | 0.0456018i | ||||||||
\(323\) | −29.8600 | −0.0924459 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − 171.977i | − 0.527536i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 92.8591i | 0.283107i | ||||||||
\(329\) | − 14.9551i | − 0.0454561i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 199.957 | 0.604101 | 0.302050 | − | 0.953292i | \(-0.402329\pi\) | ||||
0.302050 | + | 0.953292i | \(0.402329\pi\) | |||||||
\(332\) | 61.9660 | 0.186644 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 219.754 | 0.657945 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 197.218i | 0.585217i | 0.956232 | + | 0.292609i | \(0.0945233\pi\) | ||||
−0.956232 | + | 0.292609i | \(0.905477\pi\) | |||||||
\(338\) | 505.842 | 1.49657 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 522.672i | 1.53276i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 18.5203i | − 0.0539949i | ||||||||
\(344\) | − 185.424i | − 0.539023i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 270.136 | 0.780741 | ||||||||
\(347\) | −265.136 | −0.764080 | −0.382040 | − | 0.924146i | \(-0.624778\pi\) | ||||
−0.382040 | + | 0.924146i | \(0.624778\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −77.8495 | −0.223065 | −0.111532 | − | 0.993761i | \(-0.535576\pi\) | ||||
−0.111532 | + | 0.993761i | \(0.535576\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 63.7625i | − 0.181143i | ||||||||
\(353\) | −272.107 | −0.770842 | −0.385421 | − | 0.922741i | \(-0.625944\pi\) | ||||
−0.385421 | + | 0.922741i | \(0.625944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − 159.252i | − 0.447337i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 454.002i | 1.26816i | ||||||||
\(359\) | 695.157i | 1.93637i | 0.250236 | + | 0.968185i | \(0.419492\pi\) | ||||
−0.250236 | + | 0.968185i | \(0.580508\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −348.249 | −0.964677 | ||||||||
\(362\) | 30.1369 | 0.0832512 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −121.438 | −0.333621 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 161.491i | 0.440031i | 0.975496 | + | 0.220015i | \(0.0706108\pi\) | ||||
−0.975496 | + | 0.220015i | \(0.929389\pi\) | |||||||
\(368\) | −15.6976 | −0.0426566 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 65.6081i | 0.176841i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 459.127i | 1.23090i | 0.788175 | + | 0.615451i | \(0.211026\pi\) | ||||
−0.788175 | + | 0.615451i | \(0.788974\pi\) | |||||||
\(374\) | − 133.295i | − 0.356404i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.9876 | 0.0425203 | ||||||||
\(377\) | −998.539 | −2.64864 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 132.150 | 0.348680 | 0.174340 | − | 0.984685i | \(-0.444221\pi\) | ||||
0.174340 | + | 0.984685i | \(0.444221\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 63.2109i | 0.165474i | ||||||||
\(383\) | −178.047 | −0.464876 | −0.232438 | − | 0.972611i | \(-0.574670\pi\) | ||||
−0.232438 | + | 0.972611i | \(0.574670\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 335.646i | 0.869548i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 52.3639i | 0.134958i | ||||||||
\(389\) | 432.024i | 1.11060i | 0.831650 | + | 0.555301i | \(0.187397\pi\) | ||||
−0.831650 | + | 0.555301i | \(0.812603\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.8159 | −0.0839281 | ||||||||
\(392\) | 19.7990 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −282.100 | −0.715990 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 394.193i | − 0.992929i | −0.868057 | − | 0.496464i | \(-0.834631\pi\) | ||||
0.868057 | − | 0.496464i | \(-0.165369\pi\) | |||||||
\(398\) | 106.325 | 0.267147 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 711.381i | − 1.77402i | −0.461752 | − | 0.887009i | \(-0.652779\pi\) | ||||
0.461752 | − | 0.887009i | \(-0.347221\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1064.18i | 2.64064i | ||||||||
\(404\) | − 341.457i | − 0.845191i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 162.800 | 0.400985 | ||||||||
\(407\) | −315.211 | −0.774474 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 532.984 | 1.30314 | 0.651570 | − | 0.758588i | \(-0.274111\pi\) | ||||
0.651570 | + | 0.758588i | \(0.274111\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 318.521i | − 0.773108i | ||||||||
\(413\) | 155.190 | 0.375763 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − 129.823i | − 0.312073i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 56.9227i | 0.136179i | ||||||||
\(419\) | 537.395i | 1.28257i | 0.767305 | + | 0.641283i | \(0.221597\pi\) | ||||
−0.767305 | + | 0.641283i | \(0.778403\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 41.5394 | 0.0986685 | 0.0493342 | − | 0.998782i | \(-0.484290\pi\) | ||||
0.0493342 | + | 0.998782i | \(0.484290\pi\) | |||||||
\(422\) | −250.428 | −0.593430 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −70.1380 | −0.165420 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 74.7206i | 0.174990i | ||||||||
\(428\) | −125.525 | −0.293283 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.8004i | 0.0459406i | 0.999736 | + | 0.0229703i | \(0.00731232\pi\) | ||||
−0.999736 | + | 0.0229703i | \(0.992688\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 709.349i | − 1.63822i | −0.573637 | − | 0.819110i | \(-0.694468\pi\) | ||||
0.573637 | − | 0.819110i | \(-0.305532\pi\) | |||||||
\(434\) | − 173.502i | − 0.399773i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −89.1391 | −0.204448 | ||||||||
\(437\) | 14.0138 | 0.0320681 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −148.273 | −0.337751 | −0.168875 | − | 0.985637i | \(-0.554014\pi\) | ||||
−0.168875 | + | 0.985637i | \(0.554014\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 271.394i | − 0.614013i | ||||||||
\(443\) | −119.132 | −0.268921 | −0.134461 | − | 0.990919i | \(-0.542930\pi\) | ||||
−0.134461 | + | 0.990919i | \(0.542930\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − 363.918i | − 0.815960i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 21.1660i | 0.0472456i | ||||||||
\(449\) | 299.789i | 0.667682i | 0.942629 | + | 0.333841i | \(0.108345\pi\) | ||||
−0.942629 | + | 0.333841i | \(0.891655\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 370.058 | 0.820527 | ||||||||
\(452\) | −256.006 | −0.566385 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −157.131 | −0.346103 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 210.083i | − 0.459701i | −0.973226 | − | 0.229850i | \(-0.926176\pi\) | ||||
0.973226 | − | 0.229850i | \(-0.0738236\pi\) | |||||||
\(458\) | 142.713 | 0.311602 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 635.944i | 1.37949i | 0.724053 | + | 0.689744i | \(0.242277\pi\) | ||||
−0.724053 | + | 0.689744i | \(0.757723\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 630.339i | − 1.36142i | −0.732551 | − | 0.680712i | \(-0.761671\pi\) | ||||
0.732551 | − | 0.680712i | \(-0.238329\pi\) | |||||||
\(464\) | 174.040i | 0.375087i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −47.7693 | −0.102509 | ||||||||
\(467\) | 169.232 | 0.362381 | 0.181190 | − | 0.983448i | \(-0.442005\pi\) | ||||
0.181190 | + | 0.983448i | \(0.442005\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.4430 | 0.0606460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 165.905i | 0.351494i | ||||||||
\(473\) | −738.942 | −1.56225 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 44.2475i | 0.0929569i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 622.939i | 1.30322i | ||||||||
\(479\) | 572.103i | 1.19437i | 0.802103 | + | 0.597185i | \(0.203714\pi\) | ||||
−0.802103 | + | 0.597185i | \(0.796286\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −641.781 | −1.33426 | ||||||||
\(482\) | 288.604 | 0.598764 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.1032 | −0.0250065 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 468.392i | 0.961791i | 0.876778 | + | 0.480896i | \(0.159688\pi\) | ||||
−0.876778 | + | 0.480896i | \(0.840312\pi\) | |||||||
\(488\) | −79.8797 | −0.163688 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 294.928i | − 0.600668i | −0.953834 | − | 0.300334i | \(-0.902902\pi\) | ||||
0.953834 | − | 0.300334i | \(-0.0970981\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 363.831i | 0.737993i | ||||||||
\(494\) | 115.897i | 0.234609i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 185.481 | 0.373953 | ||||||||
\(497\) | 55.1732 | 0.111012 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −610.716 | −1.22388 | −0.611940 | − | 0.790904i | \(-0.709611\pi\) | ||||
−0.611940 | + | 0.790904i | \(0.709611\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 7.32821i | − 0.0145980i | ||||||||
\(503\) | −58.6435 | −0.116587 | −0.0582937 | − | 0.998299i | \(-0.518566\pi\) | ||||
−0.0582937 | + | 0.998299i | \(0.518566\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 62.5575i | 0.123631i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 198.190i | 0.390139i | ||||||||
\(509\) | − 225.419i | − 0.442866i | −0.975176 | − | 0.221433i | \(-0.928927\pi\) | ||||
0.975176 | − | 0.221433i | \(-0.0710734\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −301.341 | −0.589708 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 334.195 | 0.650185 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 63.7132i | − 0.123236i | ||||||||
\(518\) | 104.635 | 0.201997 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 6.65155i | − 0.0127669i | −0.999980 | − | 0.00638344i | \(-0.997968\pi\) | ||||
0.999980 | − | 0.00638344i | \(-0.00203193\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 516.493i | 0.987558i | 0.869587 | + | 0.493779i | \(0.164385\pi\) | ||||
−0.869587 | + | 0.493779i | \(0.835615\pi\) | |||||||
\(524\) | 279.803i | 0.533975i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.8668 | 0.0472752 | ||||||||
\(527\) | 387.747 | 0.735764 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −513.599 | −0.970887 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 18.8955i | − 0.0355179i | ||||||||
\(533\) | 753.450 | 1.41360 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 30.4068i | 0.0567292i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 28.1872i | 0.0523926i | ||||||||
\(539\) | − 78.9020i | − 0.146386i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −70.6311 | −0.130556 | −0.0652782 | − | 0.997867i | \(-0.520793\pi\) | ||||
−0.0652782 | + | 0.997867i | \(0.520793\pi\) | |||||||
\(542\) | 123.174 | 0.227259 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −47.3026 | −0.0869532 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 707.126i | − 1.29273i | −0.763026 | − | 0.646367i | \(-0.776287\pi\) | ||||
0.763026 | − | 0.646367i | \(-0.223713\pi\) | |||||||
\(548\) | 400.702 | 0.731208 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 155.371i | − 0.281980i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 352.510i | − 0.637451i | ||||||||
\(554\) | − 543.787i | − 0.981565i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 179.719 | 0.323235 | ||||||||
\(557\) | 420.729 | 0.755348 | 0.377674 | − | 0.925939i | \(-0.376724\pi\) | ||||
0.377674 | + | 0.925939i | \(0.376724\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1504.51 | −2.69143 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 348.573i | 0.620236i | ||||||||
\(563\) | −425.266 | −0.755357 | −0.377679 | − | 0.925937i | \(-0.623278\pi\) | ||||
−0.377679 | + | 0.925937i | \(0.623278\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 449.835i | 0.794762i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 58.9826i | 0.103843i | ||||||||
\(569\) | 565.501i | 0.993851i | 0.867793 | + | 0.496925i | \(0.165538\pi\) | ||||
−0.867793 | + | 0.496925i | \(0.834462\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −655.541 | −1.14806 | −0.574029 | − | 0.818835i | \(-0.694620\pi\) | ||||
−0.574029 | + | 0.818835i | \(0.694620\pi\) | |||||||
\(572\) | −517.363 | −0.904481 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −122.841 | −0.214009 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 866.848i | 1.50234i | 0.660111 | + | 0.751168i | \(0.270509\pi\) | ||||
−0.660111 | + | 0.751168i | \(0.729491\pi\) | |||||||
\(578\) | 309.822 | 0.536024 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 81.9733i | 0.141090i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 279.511i | 0.479435i | ||||||||
\(584\) | − 322.147i | − 0.551621i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −561.750 | −0.958617 | ||||||||
\(587\) | −72.2212 | −0.123034 | −0.0615172 | − | 0.998106i | \(-0.519594\pi\) | ||||
−0.0615172 | + | 0.998106i | \(0.519594\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −165.585 | −0.281128 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 111.859i | 0.188951i | ||||||||
\(593\) | −445.912 | −0.751959 | −0.375979 | − | 0.926628i | \(-0.622694\pi\) | ||||
−0.375979 | + | 0.926628i | \(0.622694\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 308.868i | 0.518234i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 127.369i | 0.212992i | ||||||||
\(599\) | − 624.774i | − 1.04303i | −0.853243 | − | 0.521514i | \(-0.825367\pi\) | ||||
0.853243 | − | 0.521514i | \(-0.174633\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 366.209 | 0.609333 | 0.304667 | − | 0.952459i | \(-0.401455\pi\) | ||||
0.304667 | + | 0.952459i | \(0.401455\pi\) | |||||||
\(602\) | 245.293 | 0.407463 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 587.657 | 0.972942 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 550.680i | − 0.907215i | −0.891201 | − | 0.453608i | \(-0.850137\pi\) | ||||
0.891201 | − | 0.453608i | \(-0.149863\pi\) | |||||||
\(608\) | 20.2002 | 0.0332240 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 129.722i | − 0.212311i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 380.620i | − 0.620914i | −0.950587 | − | 0.310457i | \(-0.899518\pi\) | ||||
0.950587 | − | 0.310457i | \(-0.100482\pi\) | |||||||
\(614\) | − 637.194i | − 1.03778i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 84.3498 | 0.136931 | ||||||||
\(617\) | −1097.16 | −1.77821 | −0.889106 | − | 0.457702i | \(-0.848673\pi\) | ||||
−0.889106 | + | 0.457702i | \(0.848673\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 223.332 | 0.360795 | 0.180398 | − | 0.983594i | \(-0.442262\pi\) | ||||
0.180398 | + | 0.983594i | \(0.442262\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 685.330i | − 1.10182i | ||||||||
\(623\) | 210.671 | 0.338155 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 515.300i | 0.823163i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 550.099i | 0.875954i | ||||||||
\(629\) | 233.841i | 0.371767i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −724.190 | −1.14769 | −0.573843 | − | 0.818965i | \(-0.694548\pi\) | ||||
−0.573843 | + | 0.818965i | \(0.694548\pi\) | |||||||
\(632\) | 376.849 | 0.596280 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 722.130 | 1.13901 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 160.647i | − 0.252193i | ||||||||
\(638\) | 693.577 | 1.08711 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 459.829i | 0.717362i | 0.933460 | + | 0.358681i | \(0.116773\pi\) | ||||
−0.933460 | + | 0.358681i | \(0.883227\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 816.842i | − 1.27036i | −0.772364 | − | 0.635180i | \(-0.780926\pi\) | ||||
0.772364 | − | 0.635180i | \(-0.219074\pi\) | |||||||
\(644\) | − 20.7660i | − 0.0322454i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 42.2284 | 0.0653691 | ||||||||
\(647\) | 726.332 | 1.12261 | 0.561307 | − | 0.827607i | \(-0.310299\pi\) | ||||
0.561307 | + | 0.827607i | \(0.310299\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 661.158 | 1.01873 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 243.212i | 0.373024i | ||||||||
\(653\) | −763.701 | −1.16953 | −0.584763 | − | 0.811204i | \(-0.698813\pi\) | ||||
−0.584763 | + | 0.811204i | \(0.698813\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − 131.323i | − 0.200187i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21.1497i | 0.0321423i | ||||||||
\(659\) | 343.226i | 0.520828i | 0.965497 | + | 0.260414i | \(0.0838591\pi\) | ||||
−0.965497 | + | 0.260414i | \(0.916141\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −541.334 | −0.818962 | −0.409481 | − | 0.912319i | \(-0.634290\pi\) | ||||
−0.409481 | + | 0.912319i | \(0.634290\pi\) | |||||||
\(662\) | −282.782 | −0.427164 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −87.6331 | −0.131978 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 170.751i | − 0.255999i | ||||||||
\(668\) | −310.779 | −0.465238 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 318.333i | 0.474416i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 984.277i | − 1.46252i | −0.682098 | − | 0.731261i | \(-0.738932\pi\) | ||||
0.682098 | − | 0.731261i | \(-0.261068\pi\) | |||||||
\(674\) | − 278.909i | − 0.413811i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −715.369 | −1.05824 | ||||||||
\(677\) | −1156.51 | −1.70829 | −0.854145 | − | 0.520034i | \(-0.825919\pi\) | ||||
−0.854145 | + | 0.520034i | \(0.825919\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −69.2709 | −0.102019 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 739.170i | − 1.08383i | ||||||||
\(683\) | −110.138 | −0.161256 | −0.0806281 | − | 0.996744i | \(-0.525693\pi\) | ||||
−0.0806281 | + | 0.996744i | \(0.525693\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 262.229i | 0.381147i | ||||||||
\(689\) | 569.094i | 0.825971i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 858.618 | 1.24257 | 0.621286 | − | 0.783584i | \(-0.286610\pi\) | ||||
0.621286 | + | 0.783584i | \(0.286610\pi\) | |||||||
\(692\) | −382.031 | −0.552067 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 374.958 | 0.540286 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 274.530i | − 0.393873i | ||||||||
\(698\) | 110.096 | 0.157730 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 54.6278i | − 0.0779285i | −0.999241 | − | 0.0389642i | \(-0.987594\pi\) | ||||
0.999241 | − | 0.0389642i | \(-0.0124058\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 99.8601i | − 0.142048i | ||||||||
\(704\) | 90.1737i | 0.128088i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 384.818 | 0.545067 | ||||||||
\(707\) | 451.705 | 0.638904 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −98.3377 | −0.138699 | −0.0693496 | − | 0.997592i | \(-0.522092\pi\) | ||||
−0.0693496 | + | 0.997592i | \(0.522092\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 225.216i | 0.316315i | ||||||||
\(713\) | −181.976 | −0.255225 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 642.056i | − 0.896726i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 983.100i | − 1.36922i | ||||||||
\(719\) | − 1302.52i | − 1.81157i | −0.423735 | − | 0.905786i | \(-0.639281\pi\) | ||||
0.423735 | − | 0.905786i | \(-0.360719\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 421.363 | 0.584415 | ||||||||
\(722\) | 492.498 | 0.682130 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −42.6201 | −0.0588675 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.4141i | 0.0404596i | 0.999795 | + | 0.0202298i | \(0.00643978\pi\) | ||||
−0.999795 | + | 0.0202298i | \(0.993560\pi\) | |||||||
\(728\) | 171.739 | 0.235905 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 548.189i | 0.749916i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 13.8012i | − 0.0188284i | −0.999956 | − | 0.00941421i | \(-0.997003\pi\) | ||||
0.999956 | − | 0.00941421i | \(-0.00299668\pi\) | |||||||
\(734\) | − 228.383i | − 0.311149i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.1998 | 0.0301628 | ||||||||
\(737\) | 121.176 | 0.164418 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.7420 | −0.0348335 | −0.0174168 | − | 0.999848i | \(-0.505544\pi\) | ||||
−0.0174168 | + | 0.999848i | \(0.505544\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 92.7839i | − 0.125046i | ||||||||
\(743\) | −567.032 | −0.763165 | −0.381583 | − | 0.924335i | \(-0.624621\pi\) | ||||
−0.381583 | + | 0.924335i | \(0.624621\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − 649.303i | − 0.870380i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 188.508i | 0.252016i | ||||||||
\(749\) | − 166.054i | − 0.221701i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −328.985 | −0.438062 | −0.219031 | − | 0.975718i | \(-0.570290\pi\) | ||||
−0.219031 | + | 0.975718i | \(0.570290\pi\) | |||||||
\(752\) | −22.6099 | −0.0300664 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1412.15 | 1.87287 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 323.996i | − 0.428000i | −0.976834 | − | 0.214000i | \(-0.931351\pi\) | ||||
0.976834 | − | 0.214000i | \(-0.0686493\pi\) | |||||||
\(758\) | −186.888 | −0.246554 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 725.410i | 0.953232i | 0.879112 | + | 0.476616i | \(0.158137\pi\) | ||||
−0.879112 | + | 0.476616i | \(0.841863\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 117.920i | − 0.154548i | ||||||||
\(764\) | − 89.3937i | − 0.117007i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 251.797 | 0.328717 | ||||||||
\(767\) | 1346.14 | 1.75507 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 942.014 | 1.22499 | 0.612493 | − | 0.790476i | \(-0.290167\pi\) | ||||
0.612493 | + | 0.790476i | \(0.290167\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 474.675i | − 0.614863i | ||||||||
\(773\) | 707.864 | 0.915737 | 0.457868 | − | 0.889020i | \(-0.348613\pi\) | ||||
0.457868 | + | 0.889020i | \(0.348613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − 74.0537i | − 0.0954300i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 610.974i | − 0.785314i | ||||||||
\(779\) | 117.236i | 0.150495i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 235.055 | 0.300966 | ||||||||
\(782\) | 46.4086 | 0.0593461 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 141.139i | 0.179338i | 0.995972 | + | 0.0896688i | \(0.0285808\pi\) | ||||
−0.995972 | + | 0.0896688i | \(0.971419\pi\) | |||||||
\(788\) | 398.950 | 0.506282 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 338.664i | − 0.428147i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 648.137i | 0.817323i | ||||||||
\(794\) | 557.473i | 0.702107i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −150.366 | −0.188902 | ||||||||
\(797\) | 1183.67 | 1.48515 | 0.742575 | − | 0.669763i | \(-0.233604\pi\) | ||||
0.742575 | + | 0.669763i | \(0.233604\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.2660 | −0.0591565 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1006.05i | 1.25442i | ||||||||
\(803\) | −1283.80 | −1.59876 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 1504.98i | − 1.86722i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 482.893i | 0.597640i | ||||||||
\(809\) | 1300.44i | 1.60747i | 0.594988 | + | 0.803735i | \(0.297157\pi\) | ||||
−0.594988 | + | 0.803735i | \(0.702843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 180.853 | 0.223000 | 0.111500 | − | 0.993764i | \(-0.464435\pi\) | ||||
0.111500 | + | 0.993764i | \(0.464435\pi\) | |||||||
\(812\) | −230.234 | −0.283539 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 445.776 | 0.547636 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 234.100i | − 0.286536i | ||||||||
\(818\) | −753.754 | −0.921459 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1312.33i | 1.59845i | 0.601029 | + | 0.799227i | \(0.294757\pi\) | ||||
−0.601029 | + | 0.799227i | \(0.705243\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 120.713i | − 0.146675i | −0.997307 | − | 0.0733373i | \(-0.976635\pi\) | ||||
0.997307 | − | 0.0733373i | \(-0.0233650\pi\) | |||||||
\(824\) | 450.456i | 0.546670i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −219.472 | −0.265705 | ||||||||
\(827\) | 573.888 | 0.693939 | 0.346970 | − | 0.937876i | \(-0.387211\pi\) | ||||
0.346970 | + | 0.937876i | \(0.387211\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1607.19 | 1.93871 | 0.969357 | − | 0.245657i | \(-0.0790038\pi\) | ||||
0.969357 | + | 0.245657i | \(0.0790038\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 183.597i | 0.220669i | ||||||||
\(833\) | −58.5339 | −0.0702688 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − 80.5009i | − 0.0962929i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 759.991i | − 0.906911i | ||||||||
\(839\) | 115.880i | 0.138116i | 0.997613 | + | 0.0690582i | \(0.0219994\pi\) | ||||
−0.997613 | + | 0.0690582i | \(0.978001\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1052.12 | −1.25104 | ||||||||
\(842\) | −58.7456 | −0.0697691 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 354.158 | 0.419619 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 16.0110i | − 0.0189031i | ||||||||
\(848\) | 99.1902 | 0.116970 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 109.745i | − 0.128960i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 93.1233i | 0.109171i | 0.998509 | + | 0.0545857i | \(0.0173838\pi\) | ||||
−0.998509 | + | 0.0545857i | \(0.982616\pi\) | |||||||
\(854\) | − 105.671i | − 0.123736i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 177.519 | 0.207382 | ||||||||
\(857\) | −347.355 | −0.405315 | −0.202658 | − | 0.979250i | \(-0.564958\pi\) | ||||
−0.202658 | + | 0.979250i | \(0.564958\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 705.651 | 0.821479 | 0.410740 | − | 0.911753i | \(-0.365271\pi\) | ||||
0.410740 | + | 0.911753i | \(0.365271\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 28.0020i | − 0.0324849i | ||||||||
\(863\) | 1504.37 | 1.74318 | 0.871591 | − | 0.490235i | \(-0.163089\pi\) | ||||
0.871591 | + | 0.490235i | \(0.163089\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1003.17i | 1.15840i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 245.368i | 0.282682i | ||||||||
\(869\) | − 1501.80i | − 1.72820i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 246.718 | 0.283259 | ||||||||
\(872\) | 126.062 | 0.144566 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −19.8185 | −0.0226756 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 552.772i | − 0.630298i | −0.949042 | − | 0.315149i | \(-0.897945\pi\) | ||||
0.949042 | − | 0.315149i | \(-0.102055\pi\) | |||||||
\(878\) | 209.689 | 0.238826 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 131.749i | − 0.149545i | −0.997201 | − | 0.0747726i | \(-0.976177\pi\) | ||||
0.997201 | − | 0.0747726i | \(-0.0238231\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 870.659i | − 0.986024i | −0.870022 | − | 0.493012i | \(-0.835896\pi\) | ||||
0.870022 | − | 0.493012i | \(-0.164104\pi\) | |||||||
\(884\) | 383.809i | 0.434173i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 168.478 | 0.190156 | ||||||||
\(887\) | 1488.49 | 1.67812 | 0.839060 | − | 0.544039i | \(-0.183106\pi\) | ||||
0.839060 | + | 0.544039i | \(0.183106\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −262.181 | −0.294917 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 514.658i | 0.576971i | ||||||||
\(893\) | 20.1846 | 0.0226031 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − 29.9333i | − 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 423.966i | − 0.472122i | ||||||||
\(899\) | 2017.57i | 2.24424i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 207.357 | 0.230141 | ||||||||
\(902\) | −523.341 | −0.580200 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 362.047 | 0.400495 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 217.860i | 0.240198i | 0.992762 | + | 0.120099i | \(0.0383213\pi\) | ||||
−0.992762 | + | 0.120099i | \(0.961679\pi\) | |||||||
\(908\) | 222.216 | 0.244732 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 752.667i | − 0.826198i | −0.910686 | − | 0.413099i | \(-0.864446\pi\) | ||||
0.910686 | − | 0.413099i | \(-0.135554\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 349.231i | 0.382510i | ||||||||
\(914\) | 297.102i | 0.325057i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −201.827 | −0.220336 | ||||||||
\(917\) | −370.144 | −0.403647 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1765.94 | 1.92159 | 0.960793 | − | 0.277266i | \(-0.0894282\pi\) | ||||
0.960793 | + | 0.277266i | \(0.0894282\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 899.361i | − 0.975446i | ||||||||
\(923\) | 478.580 | 0.518505 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 891.434i | 0.962672i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 246.130i | − 0.265226i | ||||||||
\(929\) | 1051.94i | 1.13234i | 0.824289 | + | 0.566169i | \(0.191575\pi\) | ||||
−0.824289 | + | 0.566169i | \(0.808425\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.9965 | 0.0268490 | ||||||||
\(932\) | 67.5560 | 0.0724850 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −239.330 | −0.256242 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 934.930i | − 0.997791i | −0.866662 | − | 0.498896i | \(-0.833739\pi\) | ||||
0.866662 | − | 0.498896i | \(-0.166261\pi\) | |||||||
\(938\) | −40.2245 | −0.0428832 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 962.012i | 1.02233i | 0.859483 | + | 0.511165i | \(0.170786\pi\) | ||||
−0.859483 | + | 0.511165i | \(0.829214\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 128.841i | 0.136629i | ||||||||
\(944\) | − 234.625i | − 0.248544i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1045.02 | 1.10467 | ||||||||
\(947\) | 1811.65 | 1.91304 | 0.956521 | − | 0.291665i | \(-0.0942091\pi\) | ||||
0.956521 | + | 0.291665i | \(0.0942091\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2613.87 | −2.75434 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 62.5754i | − 0.0657305i | ||||||||
\(953\) | 1140.52 | 1.19677 | 0.598385 | − | 0.801209i | \(-0.295809\pi\) | ||||
0.598385 | + | 0.801209i | \(0.295809\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − 880.969i | − 0.921515i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 809.076i | − 0.844547i | ||||||||
\(959\) | 530.079i | 0.552742i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1189.20 | 1.23746 | ||||||||
\(962\) | 907.615 | 0.943467 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −408.148 | −0.423390 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 535.438i | 0.553710i | 0.960912 | + | 0.276855i | \(0.0892922\pi\) | ||||
−0.960912 | + | 0.276855i | \(0.910708\pi\) | |||||||
\(968\) | 17.1164 | 0.0176823 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 182.412i | − 0.187860i | −0.995579 | − | 0.0939301i | \(-0.970057\pi\) | ||||
0.995579 | − | 0.0939301i | \(-0.0299430\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 237.745i | 0.244343i | ||||||||
\(974\) | − 662.407i | − 0.680089i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 112.967 | 0.115745 | ||||||||
\(977\) | 1146.82 | 1.17381 | 0.586906 | − | 0.809655i | \(-0.300346\pi\) | ||||
0.586906 | + | 0.809655i | \(0.300346\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 897.522 | 0.916775 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 417.091i | 0.424736i | ||||||||
\(983\) | −198.963 | −0.202403 | −0.101202 | − | 0.994866i | \(-0.532269\pi\) | ||||
−0.101202 | + | 0.994866i | \(0.532269\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − 514.534i | − 0.521840i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 163.903i | − 0.165893i | ||||||||
\(989\) | − 257.273i | − 0.260135i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1917.76 | 1.93517 | 0.967587 | − | 0.252539i | \(-0.0812658\pi\) | ||||
0.967587 | + | 0.252539i | \(0.0812658\pi\) | |||||||
\(992\) | −262.310 | −0.264425 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −78.0267 | −0.0784977 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1709.94i | − 1.71509i | −0.514410 | − | 0.857544i | \(-0.671989\pi\) | ||||
0.514410 | − | 0.857544i | \(-0.328011\pi\) | |||||||
\(998\) | 863.683 | 0.865414 | ||||||||
\(999\) | 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 | 3150.3.c.f.449.7 | 16 | ||
3.2 | odd | 2 | inner | 3150.3.c.f.449.14 | 16 | ||
5.2 | odd | 4 | 630.3.e.b.71.1 | ✓ | 8 | ||
5.3 | odd | 4 | 3150.3.e.f.701.8 | 8 | |||
5.4 | even | 2 | inner | 3150.3.c.f.449.11 | 16 | ||
15.2 | even | 4 | 630.3.e.b.71.7 | yes | 8 | ||
15.8 | even | 4 | 3150.3.e.f.701.3 | 8 | |||
15.14 | odd | 2 | inner | 3150.3.c.f.449.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.3.e.b.71.1 | ✓ | 8 | 5.2 | odd | 4 | ||
630.3.e.b.71.7 | yes | 8 | 15.2 | even | 4 | ||
3150.3.c.f.449.2 | 16 | 15.14 | odd | 2 | inner | ||
3150.3.c.f.449.7 | 16 | 1.1 | even | 1 | trivial | ||
3150.3.c.f.449.11 | 16 | 5.4 | even | 2 | inner | ||
3150.3.c.f.449.14 | 16 | 3.2 | odd | 2 | inner | ||
3150.3.e.f.701.3 | 8 | 15.8 | even | 4 | |||
3150.3.e.f.701.8 | 8 | 5.3 | odd | 4 |