Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(649,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.3 | ||
Root | \(1.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.649 |
Dual form | 675.2.b.i.649.2 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.30278i | 0.921201i | 0.887607 | + | 0.460601i | \(0.152366\pi\) | ||||
−0.887607 | + | 0.460601i | \(0.847634\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.302776 | 0.151388 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.60555i | 1.74073i | 0.492403 | + | 0.870367i | \(0.336119\pi\) | ||||
−0.492403 | + | 0.870367i | \(0.663881\pi\) | |||||||
\(8\) | 3.00000i | 1.06066i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.60555 | −0.785603 | −0.392802 | − | 0.919623i | \(-0.628494\pi\) | ||||
−0.392802 | + | 0.919623i | \(0.628494\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.605551i | 0.167950i | 0.996468 | + | 0.0839749i | \(0.0267615\pi\) | ||||
−0.996468 | + | 0.0839749i | \(0.973238\pi\) | |||||||
\(14\) | −6.00000 | −1.60357 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.30278 | −0.825694 | ||||||||
\(17\) | − 5.60555i | − 1.35955i | −0.733423 | − | 0.679773i | \(-0.762078\pi\) | ||||
0.733423 | − | 0.679773i | \(-0.237922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.60555 | 0.827170 | 0.413585 | − | 0.910465i | \(-0.364276\pi\) | ||||
0.413585 | + | 0.910465i | \(0.364276\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 3.39445i | − 0.723699i | ||||||||
\(23\) | 3.00000i | 0.625543i | 0.949828 | + | 0.312772i | \(0.101257\pi\) | ||||
−0.949828 | + | 0.312772i | \(0.898743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.788897 | −0.154716 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.39445i | 0.263526i | ||||||||
\(29\) | −8.60555 | −1.59801 | −0.799005 | − | 0.601324i | \(-0.794640\pi\) | ||||
−0.799005 | + | 0.601324i | \(0.794640\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.60555 | 0.288366 | 0.144183 | − | 0.989551i | \(-0.453945\pi\) | ||||
0.144183 | + | 0.989551i | \(0.453945\pi\) | |||||||
\(32\) | 1.69722i | 0.300030i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.30278 | 1.25242 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 4.69722i | 0.761990i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.60555 | 0.406919 | 0.203459 | − | 0.979083i | \(-0.434782\pi\) | ||||
0.203459 | + | 0.979083i | \(0.434782\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.60555i | 1.00734i | 0.863897 | + | 0.503669i | \(0.168017\pi\) | ||||
−0.863897 | + | 0.503669i | \(0.831983\pi\) | |||||||
\(44\) | −0.788897 | −0.118931 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.90833 | −0.576251 | ||||||||
\(47\) | 5.21110i | 0.760117i | 0.924962 | + | 0.380059i | \(0.124096\pi\) | ||||
−0.924962 | + | 0.380059i | \(0.875904\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.2111 | −2.03016 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.183346i | 0.0254255i | ||||||||
\(53\) | 5.60555i | 0.769982i | 0.922920 | + | 0.384991i | \(0.125795\pi\) | ||||
−0.922920 | + | 0.384991i | \(0.874205\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −13.8167 | −1.84633 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 11.2111i | − 1.47209i | ||||||||
\(59\) | 8.60555 | 1.12035 | 0.560174 | − | 0.828375i | \(-0.310734\pi\) | ||||
0.560174 | + | 0.828375i | \(0.310734\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2111 | 1.30740 | 0.653699 | − | 0.756755i | \(-0.273216\pi\) | ||||
0.653699 | + | 0.756755i | \(0.273216\pi\) | |||||||
\(62\) | 2.09167i | 0.265643i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.81665 | −1.10208 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 15.2111i | − 1.85833i | −0.369663 | − | 0.929166i | \(-0.620527\pi\) | ||||
0.369663 | − | 0.929166i | \(-0.379473\pi\) | |||||||
\(68\) | − 1.69722i | − 0.205819i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.6056 | 1.73336 | 0.866680 | − | 0.498864i | \(-0.166249\pi\) | ||||
0.866680 | + | 0.498864i | \(0.166249\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 5.39445i | − 0.631372i | −0.948864 | − | 0.315686i | \(-0.897765\pi\) | ||||
0.948864 | − | 0.315686i | \(-0.102235\pi\) | |||||||
\(74\) | −2.60555 | −0.302889 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.09167 | 0.125223 | ||||||||
\(77\) | − 12.0000i | − 1.36753i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.39445 | 0.494414 | 0.247207 | − | 0.968963i | \(-0.420487\pi\) | ||||
0.247207 | + | 0.968963i | \(0.420487\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.39445i | 0.374854i | ||||||||
\(83\) | − 3.00000i | − 0.329293i | −0.986353 | − | 0.164646i | \(-0.947352\pi\) | ||||
0.986353 | − | 0.164646i | \(-0.0526483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.60555 | −0.927960 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 7.81665i | − 0.833258i | ||||||||
\(89\) | −7.81665 | −0.828564 | −0.414282 | − | 0.910149i | \(-0.635967\pi\) | ||||
−0.414282 | + | 0.910149i | \(0.635967\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.78890 | −0.292356 | ||||||||
\(92\) | 0.908327i | 0.0946996i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.78890 | −0.700221 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00000i | 0.812277i | 0.913812 | + | 0.406138i | \(0.133125\pi\) | ||||
−0.913812 | + | 0.406138i | \(0.866875\pi\) | |||||||
\(98\) | − 18.5139i | − 1.87018i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0000 | 1.19404 | 0.597022 | − | 0.802225i | \(-0.296350\pi\) | ||||
0.597022 | + | 0.802225i | \(0.296350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000i | 0.394132i | 0.980390 | + | 0.197066i | \(0.0631413\pi\) | ||||
−0.980390 | + | 0.197066i | \(0.936859\pi\) | |||||||
\(104\) | −1.81665 | −0.178138 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.30278 | −0.709308 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | 0.670478 | 0.335239 | − | 0.942133i | \(-0.391183\pi\) | ||||
0.335239 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 15.2111i | − 1.43731i | ||||||||
\(113\) | 0.788897i | 0.0742132i | 0.999311 | + | 0.0371066i | \(0.0118141\pi\) | ||||
−0.999311 | + | 0.0371066i | \(0.988186\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.60555 | −0.241919 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.2111i | 1.03207i | ||||||||
\(119\) | 25.8167 | 2.36661 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.21110 | −0.382828 | ||||||||
\(122\) | 13.3028i | 1.20438i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.486122 | 0.0436550 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 4.78890i | − 0.424946i | −0.977167 | − | 0.212473i | \(-0.931848\pi\) | ||||
0.977167 | − | 0.212473i | \(-0.0681517\pi\) | |||||||
\(128\) | − 8.09167i | − 0.715210i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.6056i | 1.43988i | ||||||||
\(134\) | 19.8167 | 1.71190 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.8167 | 1.44202 | ||||||||
\(137\) | − 4.81665i | − 0.411515i | −0.978603 | − | 0.205757i | \(-0.934034\pi\) | ||||
0.978603 | − | 0.205757i | \(-0.0659657\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 19.0278i | 1.59677i | ||||||||
\(143\) | − 1.57779i | − 0.131942i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.02776 | 0.581621 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.605551i | 0.0497760i | ||||||||
\(149\) | 13.0278 | 1.06728 | 0.533638 | − | 0.845713i | \(-0.320825\pi\) | ||||
0.533638 | + | 0.845713i | \(0.320825\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4222 | −1.17366 | −0.586831 | − | 0.809709i | \(-0.699625\pi\) | ||||
−0.586831 | + | 0.809709i | \(0.699625\pi\) | |||||||
\(152\) | 10.8167i | 0.877346i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 15.6333 | 1.25977 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.81665i | 0.304602i | 0.988334 | + | 0.152301i | \(0.0486683\pi\) | ||||
−0.988334 | + | 0.152301i | \(0.951332\pi\) | |||||||
\(158\) | 5.72498i | 0.455455i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.8167 | −1.08890 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2.00000i | − 0.156652i | −0.996928 | − | 0.0783260i | \(-0.975042\pi\) | ||||
0.996928 | − | 0.0783260i | \(-0.0249575\pi\) | |||||||
\(164\) | 0.788897 | 0.0616025 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.90833 | 0.303345 | ||||||||
\(167\) | − 3.00000i | − 0.232147i | −0.993241 | − | 0.116073i | \(-0.962969\pi\) | ||||
0.993241 | − | 0.116073i | \(-0.0370308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6333 | 0.971793 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000i | 0.152499i | ||||||||
\(173\) | − 10.8167i | − 0.822375i | −0.911551 | − | 0.411187i | \(-0.865114\pi\) | ||||
0.911551 | − | 0.411187i | \(-0.134886\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.60555 | 0.648668 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 10.1833i | − 0.763274i | ||||||||
\(179\) | 6.78890 | 0.507426 | 0.253713 | − | 0.967280i | \(-0.418348\pi\) | ||||
0.253713 | + | 0.967280i | \(0.418348\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | − 3.63331i | − 0.269319i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.00000 | −0.663489 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.6056i | 1.06806i | ||||||||
\(188\) | 1.57779i | 0.115073i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.4222 | 1.18827 | 0.594135 | − | 0.804366i | \(-0.297495\pi\) | ||||
0.594135 | + | 0.804366i | \(0.297495\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 21.8167i | − 1.57040i | −0.619244 | − | 0.785199i | \(-0.712561\pi\) | ||||
0.619244 | − | 0.785199i | \(-0.287439\pi\) | |||||||
\(194\) | −10.4222 | −0.748271 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.30278 | −0.307341 | ||||||||
\(197\) | − 1.18335i | − 0.0843099i | −0.999111 | − | 0.0421550i | \(-0.986578\pi\) | ||||
0.999111 | − | 0.0421550i | \(-0.0134223\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.2111 | −0.936510 | −0.468255 | − | 0.883593i | \(-0.655117\pi\) | ||||
−0.468255 | + | 0.883593i | \(0.655117\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.6333i | 1.09996i | ||||||||
\(203\) | − 39.6333i | − 2.78171i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.21110 | −0.363075 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 2.00000i | − 0.138675i | ||||||||
\(209\) | −9.39445 | −0.649828 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.8167 | 0.882335 | 0.441167 | − | 0.897425i | \(-0.354564\pi\) | ||||
0.441167 | + | 0.897425i | \(0.354564\pi\) | |||||||
\(212\) | 1.69722i | 0.116566i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.39445i | 0.501968i | ||||||||
\(218\) | 9.11943i | 0.617646i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.39445 | 0.228335 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0000i | 0.669650i | 0.942280 | + | 0.334825i | \(0.108677\pi\) | ||||
−0.942280 | + | 0.334825i | \(0.891323\pi\) | |||||||
\(224\) | −7.81665 | −0.522272 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.02776 | −0.0683653 | ||||||||
\(227\) | − 26.2111i | − 1.73969i | −0.493323 | − | 0.869846i | \(-0.664218\pi\) | ||||
0.493323 | − | 0.869846i | \(-0.335782\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.21110 | 0.410441 | 0.205221 | − | 0.978716i | \(-0.434209\pi\) | ||||
0.205221 | + | 0.978716i | \(0.434209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 25.8167i | − 1.69495i | ||||||||
\(233\) | 18.0000i | 1.17922i | 0.807688 | + | 0.589610i | \(0.200718\pi\) | ||||
−0.807688 | + | 0.589610i | \(0.799282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.60555 | 0.169607 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 33.6333i | 2.18012i | ||||||||
\(239\) | 0.788897 | 0.0510295 | 0.0255148 | − | 0.999674i | \(-0.491878\pi\) | ||||
0.0255148 | + | 0.999674i | \(0.491878\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.2111 | 1.81724 | 0.908618 | − | 0.417627i | \(-0.137138\pi\) | ||||
0.908618 | + | 0.417627i | \(0.137138\pi\) | |||||||
\(242\) | − 5.48612i | − 0.352661i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.09167 | 0.197924 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.18335i | 0.138923i | ||||||||
\(248\) | 4.81665i | 0.305858i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.6333 | −0.986766 | −0.493383 | − | 0.869812i | \(-0.664240\pi\) | ||||
−0.493383 | + | 0.869812i | \(0.664240\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 7.81665i | − 0.491429i | ||||||||
\(254\) | 6.23886 | 0.391461 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.09167 | −0.443230 | ||||||||
\(257\) | 22.8167i | 1.42326i | 0.702553 | + | 0.711632i | \(0.252044\pi\) | ||||
−0.702553 | + | 0.711632i | \(0.747956\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.21110 | −0.572350 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.81665i | 0.482914i | ||||||||
\(263\) | 17.2111i | 1.06128i | 0.847597 | + | 0.530641i | \(0.178049\pi\) | ||||
−0.847597 | + | 0.530641i | \(0.821951\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −21.6333 | −1.32642 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 4.60555i | − 0.281329i | ||||||||
\(269\) | −11.2111 | −0.683553 | −0.341776 | − | 0.939781i | \(-0.611029\pi\) | ||||
−0.341776 | + | 0.939781i | \(0.611029\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.2389 | −1.16868 | −0.584339 | − | 0.811510i | \(-0.698646\pi\) | ||||
−0.584339 | + | 0.811510i | \(0.698646\pi\) | |||||||
\(272\) | 18.5139i | 1.12257i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.27502 | 0.379088 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 29.0278i | − 1.74411i | −0.489409 | − | 0.872054i | \(-0.662787\pi\) | ||||
0.489409 | − | 0.872054i | \(-0.337213\pi\) | |||||||
\(278\) | 5.21110i | 0.312541i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.81665 | 0.108372 | 0.0541862 | − | 0.998531i | \(-0.482744\pi\) | ||||
0.0541862 | + | 0.998531i | \(0.482744\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 10.6056i | − 0.630435i | −0.949020 | − | 0.315217i | \(-0.897923\pi\) | ||||
0.949020 | − | 0.315217i | \(-0.102077\pi\) | |||||||
\(284\) | 4.42221 | 0.262410 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.05551 | 0.121545 | ||||||||
\(287\) | 12.0000i | 0.708338i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.4222 | −0.848365 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 1.63331i | − 0.0955821i | ||||||||
\(293\) | 28.8167i | 1.68349i | 0.539878 | + | 0.841743i | \(0.318470\pi\) | ||||
−0.539878 | + | 0.841743i | \(0.681530\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.00000 | −0.348743 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.9722i | 0.983176i | ||||||||
\(299\) | −1.81665 | −0.105060 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.4222 | −1.75351 | ||||||||
\(302\) | − 18.7889i | − 1.08118i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.9083 | −0.682989 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 20.4222i | − 1.16556i | −0.812631 | − | 0.582778i | \(-0.801966\pi\) | ||||
0.812631 | − | 0.582778i | \(-0.198034\pi\) | |||||||
\(308\) | − 3.63331i | − 0.207027i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.8167 | 0.783471 | 0.391735 | − | 0.920078i | \(-0.371875\pi\) | ||||
0.391735 | + | 0.920078i | \(0.371875\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 23.6333i | − 1.33583i | −0.744236 | − | 0.667917i | \(-0.767186\pi\) | ||||
0.744236 | − | 0.667917i | \(-0.232814\pi\) | |||||||
\(314\) | −4.97224 | −0.280600 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.33053 | 0.0748483 | ||||||||
\(317\) | − 0.394449i | − 0.0221544i | −0.999939 | − | 0.0110772i | \(-0.996474\pi\) | ||||
0.999939 | − | 0.0110772i | \(-0.00352606\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.4222 | 1.25540 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 18.0000i | − 1.00310i | ||||||||
\(323\) | − 20.2111i | − 1.12458i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.60555 | 0.144308 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.81665i | 0.431603i | ||||||||
\(329\) | −24.0000 | −1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.7889 | 0.812871 | 0.406436 | − | 0.913679i | \(-0.366772\pi\) | ||||
0.406436 | + | 0.913679i | \(0.366772\pi\) | |||||||
\(332\) | − 0.908327i | − 0.0498509i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.90833 | 0.213854 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 0.605551i | − 0.0329865i | −0.999864 | − | 0.0164932i | \(-0.994750\pi\) | ||||
0.999864 | − | 0.0164932i | \(-0.00525020\pi\) | |||||||
\(338\) | 16.4584i | 0.895217i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.18335 | −0.226541 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 33.2111i | − 1.79323i | ||||||||
\(344\) | −19.8167 | −1.06844 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.0917 | 0.757573 | ||||||||
\(347\) | 1.57779i | 0.0847005i | 0.999103 | + | 0.0423502i | \(0.0134845\pi\) | ||||
−0.999103 | + | 0.0423502i | \(0.986515\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.8444 | −1.38342 | −0.691710 | − | 0.722176i | \(-0.743142\pi\) | ||||
−0.691710 | + | 0.722176i | \(0.743142\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 4.42221i | − 0.235704i | ||||||||
\(353\) | 21.6333i | 1.15142i | 0.817652 | + | 0.575712i | \(0.195275\pi\) | ||||
−0.817652 | + | 0.575712i | \(0.804725\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.36669 | −0.125434 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.84441i | 0.467442i | ||||||||
\(359\) | −33.6333 | −1.77510 | −0.887549 | − | 0.460713i | \(-0.847594\pi\) | ||||
−0.887549 | + | 0.460713i | \(0.847594\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.00000 | −0.315789 | ||||||||
\(362\) | − 9.11943i | − 0.479307i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.844410 | −0.0442591 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.60555i | 0.240408i | 0.992749 | + | 0.120204i | \(0.0383548\pi\) | ||||
−0.992749 | + | 0.120204i | \(0.961645\pi\) | |||||||
\(368\) | − 9.90833i | − 0.516507i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.8167 | −1.34033 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.7889i | 0.558628i | 0.960200 | + | 0.279314i | \(0.0901070\pi\) | ||||
−0.960200 | + | 0.279314i | \(0.909893\pi\) | |||||||
\(374\) | −19.0278 | −0.983902 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.6333 | −0.806226 | ||||||||
\(377\) | − 5.21110i | − 0.268385i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.3944 | −0.739393 | −0.369697 | − | 0.929153i | \(-0.620538\pi\) | ||||
−0.369697 | + | 0.929153i | \(0.620538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.3944i | 1.09464i | ||||||||
\(383\) | 18.6333i | 0.952118i | 0.879413 | + | 0.476059i | \(0.157935\pi\) | ||||
−0.879413 | + | 0.476059i | \(0.842065\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 28.4222 | 1.44665 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.42221i | 0.122969i | ||||||||
\(389\) | −4.18335 | −0.212104 | −0.106052 | − | 0.994361i | \(-0.533821\pi\) | ||||
−0.106052 | + | 0.994361i | \(0.533821\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.8167 | 0.850455 | ||||||||
\(392\) | − 42.6333i | − 2.15331i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.54163 | 0.0776664 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 12.6056i | − 0.632654i | −0.948650 | − | 0.316327i | \(-0.897550\pi\) | ||||
0.948650 | − | 0.316327i | \(-0.102450\pi\) | |||||||
\(398\) | − 17.2111i | − 0.862715i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.0000 | −1.49813 | −0.749064 | − | 0.662497i | \(-0.769497\pi\) | ||||
−0.749064 | + | 0.662497i | \(0.769497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.972244i | 0.0484309i | ||||||||
\(404\) | 3.63331 | 0.180764 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 51.6333 | 2.56252 | ||||||||
\(407\) | − 5.21110i | − 0.258305i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.00000 | −0.247234 | −0.123617 | − | 0.992330i | \(-0.539449\pi\) | ||||
−0.123617 | + | 0.992330i | \(0.539449\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.21110i | 0.0596667i | ||||||||
\(413\) | 39.6333i | 1.95023i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.02776 | −0.0503899 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 12.2389i | − 0.598622i | ||||||||
\(419\) | 13.0278 | 0.636448 | 0.318224 | − | 0.948016i | \(-0.396914\pi\) | ||||
0.318224 | + | 0.948016i | \(0.396914\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.4222 | −1.14153 | −0.570764 | − | 0.821114i | \(-0.693353\pi\) | ||||
−0.570764 | + | 0.821114i | \(0.693353\pi\) | |||||||
\(422\) | 16.6972i | 0.812808i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −16.8167 | −0.816689 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 47.0278i | 2.27583i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.8167 | 1.24354 | 0.621772 | − | 0.783198i | \(-0.286413\pi\) | ||||
0.621772 | + | 0.783198i | \(0.286413\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.2389i | 1.35707i | 0.734567 | + | 0.678536i | \(0.237385\pi\) | ||||
−0.734567 | + | 0.678536i | \(0.762615\pi\) | |||||||
\(434\) | −9.63331 | −0.462414 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.11943 | 0.101502 | ||||||||
\(437\) | 10.8167i | 0.517431i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.3944 | −0.973374 | −0.486687 | − | 0.873576i | \(-0.661795\pi\) | ||||
−0.486687 | + | 0.873576i | \(0.661795\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.42221i | 0.210343i | ||||||||
\(443\) | − 18.6333i | − 0.885295i | −0.896696 | − | 0.442648i | \(-0.854039\pi\) | ||||
0.896696 | − | 0.442648i | \(-0.145961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.0278 | −0.616882 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 40.6056i | − 1.91843i | ||||||||
\(449\) | 12.2389 | 0.577587 | 0.288794 | − | 0.957391i | \(-0.406746\pi\) | ||||
0.288794 | + | 0.957391i | \(0.406746\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.78890 | −0.319677 | ||||||||
\(452\) | 0.238859i | 0.0112350i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 34.1472 | 1.60261 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.21110i | 0.0566530i | 0.999599 | + | 0.0283265i | \(0.00901781\pi\) | ||||
−0.999599 | + | 0.0283265i | \(0.990982\pi\) | |||||||
\(458\) | 8.09167i | 0.378099i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.6333 | −1.00756 | −0.503782 | − | 0.863831i | \(-0.668058\pi\) | ||||
−0.503782 | + | 0.863831i | \(0.668058\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.2111i | 0.706920i | 0.935450 | + | 0.353460i | \(0.114995\pi\) | ||||
−0.935450 | + | 0.353460i | \(0.885005\pi\) | |||||||
\(464\) | 28.4222 | 1.31947 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.4500 | −1.08630 | ||||||||
\(467\) | − 2.21110i | − 0.102318i | −0.998691 | − | 0.0511588i | \(-0.983709\pi\) | ||||
0.998691 | − | 0.0511588i | \(-0.0162915\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 70.0555 | 3.23486 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 25.8167i | 1.18831i | ||||||||
\(473\) | − 17.2111i | − 0.791367i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.81665 | 0.358276 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.02776i | 0.0470085i | ||||||||
\(479\) | 16.1833 | 0.739436 | 0.369718 | − | 0.929144i | \(-0.379454\pi\) | ||||
0.369718 | + | 0.929144i | \(0.379454\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.21110 | −0.0552215 | ||||||||
\(482\) | 36.7527i | 1.67404i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.27502 | −0.0579554 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 8.18335i | − 0.370823i | −0.982661 | − | 0.185411i | \(-0.940638\pi\) | ||||
0.982661 | − | 0.185411i | \(-0.0593618\pi\) | |||||||
\(488\) | 30.6333i | 1.38670i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.7889 | 0.577155 | 0.288577 | − | 0.957457i | \(-0.406818\pi\) | ||||
0.288577 | + | 0.957457i | \(0.406818\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 48.2389i | 2.17257i | ||||||||
\(494\) | −2.84441 | −0.127976 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.30278 | −0.238102 | ||||||||
\(497\) | 67.2666i | 3.01732i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.6056 | 1.23579 | 0.617897 | − | 0.786259i | \(-0.287985\pi\) | ||||
0.617897 | + | 0.786259i | \(0.287985\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 20.3667i | − 0.909010i | ||||||||
\(503\) | − 31.4222i | − 1.40105i | −0.713629 | − | 0.700523i | \(-0.752950\pi\) | ||||
0.713629 | − | 0.700523i | \(-0.247050\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.1833 | 0.452705 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 1.44996i | − 0.0643316i | ||||||||
\(509\) | −32.8444 | −1.45580 | −0.727901 | − | 0.685682i | \(-0.759504\pi\) | ||||
−0.727901 | + | 0.685682i | \(0.759504\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.8444 | 1.09905 | ||||||||
\(512\) | − 25.4222i | − 1.12351i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −29.7250 | −1.31111 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 13.5778i | − 0.597151i | ||||||||
\(518\) | − 12.0000i | − 0.527250i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.3944 | −0.937308 | −0.468654 | − | 0.883382i | \(-0.655261\pi\) | ||||
−0.468654 | + | 0.883382i | \(0.655261\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 23.3944i | − 1.02297i | −0.859293 | − | 0.511484i | \(-0.829096\pi\) | ||||
0.859293 | − | 0.511484i | \(-0.170904\pi\) | |||||||
\(524\) | 1.81665 | 0.0793609 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.4222 | −0.977655 | ||||||||
\(527\) | − 9.00000i | − 0.392046i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0000 | 0.608696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.02776i | 0.217981i | ||||||||
\(533\) | 1.57779i | 0.0683419i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 45.6333 | 1.97106 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 14.6056i | − 0.629690i | ||||||||
\(539\) | 37.0278 | 1.59490 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.5778 | −0.497768 | −0.248884 | − | 0.968533i | \(-0.580064\pi\) | ||||
−0.248884 | + | 0.968533i | \(0.580064\pi\) | |||||||
\(542\) | − 25.0639i | − 1.07659i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.51388 | 0.407904 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 6.60555i | − 0.282433i | −0.989979 | − | 0.141216i | \(-0.954899\pi\) | ||||
0.989979 | − | 0.141216i | \(-0.0451014\pi\) | |||||||
\(548\) | − 1.45837i | − 0.0622983i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.0278 | −1.32183 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.2389i | 0.860644i | ||||||||
\(554\) | 37.8167 | 1.60668 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.21110 | 0.0513622 | ||||||||
\(557\) | − 33.6333i | − 1.42509i | −0.701627 | − | 0.712544i | \(-0.747543\pi\) | ||||
0.701627 | − | 0.712544i | \(-0.252457\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.36669i | 0.0998329i | ||||||||
\(563\) | − 24.0000i | − 1.01148i | −0.862686 | − | 0.505740i | \(-0.831220\pi\) | ||||
0.862686 | − | 0.505740i | \(-0.168780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 13.8167 | 0.580757 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 43.8167i | 1.83851i | ||||||||
\(569\) | −37.8167 | −1.58536 | −0.792678 | − | 0.609640i | \(-0.791314\pi\) | ||||
−0.792678 | + | 0.609640i | \(0.791314\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.4500 | −1.52538 | −0.762692 | − | 0.646762i | \(-0.776123\pi\) | ||||
−0.762692 | + | 0.646762i | \(0.776123\pi\) | |||||||
\(572\) | − 0.477718i | − 0.0199744i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15.6333 | −0.652522 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.8167i | 1.15802i | 0.815320 | + | 0.579011i | \(0.196561\pi\) | ||||
−0.815320 | + | 0.579011i | \(0.803439\pi\) | |||||||
\(578\) | − 18.7889i | − 0.781515i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.8167 | 0.573211 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 14.6056i | − 0.604900i | ||||||||
\(584\) | 16.1833 | 0.669672 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −37.5416 | −1.55083 | ||||||||
\(587\) | 21.0000i | 0.866763i | 0.901211 | + | 0.433381i | \(0.142680\pi\) | ||||
−0.901211 | + | 0.433381i | \(0.857320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.78890 | 0.238527 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 6.60555i | − 0.271486i | ||||||||
\(593\) | − 21.2389i | − 0.872175i | −0.899904 | − | 0.436088i | \(-0.856364\pi\) | ||||
0.899904 | − | 0.436088i | \(-0.143636\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.94449 | 0.161572 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 2.36669i | − 0.0967812i | ||||||||
\(599\) | 15.3944 | 0.629000 | 0.314500 | − | 0.949257i | \(-0.398163\pi\) | ||||
0.314500 | + | 0.949257i | \(0.398163\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.6333 | 1.33114 | 0.665570 | − | 0.746335i | \(-0.268188\pi\) | ||||
0.665570 | + | 0.746335i | \(0.268188\pi\) | |||||||
\(602\) | − 39.6333i | − 1.61533i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.36669 | −0.177678 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.3944i | 0.706019i | 0.935620 | + | 0.353009i | \(0.114842\pi\) | ||||
−0.935620 | + | 0.353009i | \(0.885158\pi\) | |||||||
\(608\) | 6.11943i | 0.248176i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.15559 | −0.127661 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 28.8444i | − 1.16501i | −0.812825 | − | 0.582507i | \(-0.802072\pi\) | ||||
0.812825 | − | 0.582507i | \(-0.197928\pi\) | |||||||
\(614\) | 26.6056 | 1.07371 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36.0000 | 1.45048 | ||||||||
\(617\) | − 26.4500i | − 1.06484i | −0.846482 | − | 0.532418i | \(-0.821284\pi\) | ||||
0.846482 | − | 0.532418i | \(-0.178716\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.63331 | 0.306809 | 0.153404 | − | 0.988164i | \(-0.450976\pi\) | ||||
0.153404 | + | 0.988164i | \(0.450976\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.0000i | 0.721734i | ||||||||
\(623\) | − 36.0000i | − 1.44231i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 30.7889 | 1.23057 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.15559i | 0.0461131i | ||||||||
\(629\) | 11.2111 | 0.447016 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.0278 | 1.19539 | 0.597693 | − | 0.801725i | \(-0.296084\pi\) | ||||
0.597693 | + | 0.801725i | \(0.296084\pi\) | |||||||
\(632\) | 13.1833i | 0.524405i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.513878 | 0.0204087 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 8.60555i | − 0.340964i | ||||||||
\(638\) | 29.2111i | 1.15648i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.0000 | −0.947943 | −0.473972 | − | 0.880540i | \(-0.657180\pi\) | ||||
−0.473972 | + | 0.880540i | \(0.657180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.0278i | 0.908126i | 0.890970 | + | 0.454063i | \(0.150026\pi\) | ||||
−0.890970 | + | 0.454063i | \(0.849974\pi\) | |||||||
\(644\) | −4.18335 | −0.164847 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.3305 | 1.03596 | ||||||||
\(647\) | 38.2111i | 1.50223i | 0.660169 | + | 0.751117i | \(0.270484\pi\) | ||||
−0.660169 | + | 0.751117i | \(0.729516\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.4222 | −0.880149 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 0.605551i | − 0.0237152i | ||||||||
\(653\) | − 27.2389i | − 1.06594i | −0.846134 | − | 0.532969i | \(-0.821076\pi\) | ||||
0.846134 | − | 0.532969i | \(-0.178924\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.60555 | −0.335990 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 31.2666i | − 1.21890i | ||||||||
\(659\) | 20.6056 | 0.802678 | 0.401339 | − | 0.915930i | \(-0.368545\pi\) | ||||
0.401339 | + | 0.915930i | \(0.368545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.8444 | 0.888545 | 0.444272 | − | 0.895892i | \(-0.353462\pi\) | ||||
0.444272 | + | 0.895892i | \(0.353462\pi\) | |||||||
\(662\) | 19.2666i | 0.748818i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.00000 | 0.349268 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 25.8167i | − 0.999625i | ||||||||
\(668\) | − 0.908327i | − 0.0351442i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.6056 | −1.02710 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.0278i | 0.425089i | 0.977151 | + | 0.212544i | \(0.0681750\pi\) | ||||
−0.977151 | + | 0.212544i | \(0.931825\pi\) | |||||||
\(674\) | 0.788897 | 0.0303872 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.82506 | 0.147118 | ||||||||
\(677\) | − 21.6333i | − 0.831436i | −0.909494 | − | 0.415718i | \(-0.863530\pi\) | ||||
0.909494 | − | 0.415718i | \(-0.136470\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.8444 | −1.41396 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 5.44996i | − 0.208690i | ||||||||
\(683\) | 9.00000i | 0.344375i | 0.985064 | + | 0.172188i | \(0.0550836\pi\) | ||||
−0.985064 | + | 0.172188i | \(0.944916\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 43.2666 | 1.65193 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 21.8167i | − 0.831752i | ||||||||
\(689\) | −3.39445 | −0.129318 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.39445 | 0.0910891 | 0.0455446 | − | 0.998962i | \(-0.485498\pi\) | ||||
0.0455446 | + | 0.998962i | \(0.485498\pi\) | |||||||
\(692\) | − 3.27502i | − 0.124498i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.05551 | −0.0780262 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 14.6056i | − 0.553225i | ||||||||
\(698\) | − 33.6695i | − 1.27441i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.4222 | 1.52673 | 0.763363 | − | 0.645970i | \(-0.223547\pi\) | ||||
0.763363 | + | 0.645970i | \(0.223547\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.21110i | 0.271972i | ||||||||
\(704\) | 22.9722 | 0.865799 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −28.1833 | −1.06069 | ||||||||
\(707\) | 55.2666i | 2.07851i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.8444 | −1.30861 | −0.654305 | − | 0.756231i | \(-0.727039\pi\) | ||||
−0.654305 | + | 0.756231i | \(0.727039\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 23.4500i | − 0.878824i | ||||||||
\(713\) | 4.81665i | 0.180385i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.05551 | 0.0768181 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 43.8167i | − 1.63522i | ||||||||
\(719\) | 49.2666 | 1.83733 | 0.918667 | − | 0.395032i | \(-0.129267\pi\) | ||||
0.918667 | + | 0.395032i | \(0.129267\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.4222 | −0.686079 | ||||||||
\(722\) | − 7.81665i | − 0.290906i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.11943 | −0.0787680 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 7.63331i | − 0.283104i | −0.989931 | − | 0.141552i | \(-0.954791\pi\) | ||||
0.989931 | − | 0.141552i | \(-0.0452092\pi\) | |||||||
\(728\) | − 8.36669i | − 0.310090i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.0278 | 1.36952 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 32.0000i | − 1.18195i | −0.806691 | − | 0.590973i | \(-0.798744\pi\) | ||||
0.806691 | − | 0.590973i | \(-0.201256\pi\) | |||||||
\(734\) | −6.00000 | −0.221464 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.09167 | −0.187682 | ||||||||
\(737\) | 39.6333i | 1.45991i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.0278 | −1.10459 | −0.552294 | − | 0.833649i | \(-0.686248\pi\) | ||||
−0.552294 | + | 0.833649i | \(0.686248\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 33.6333i | − 1.23472i | ||||||||
\(743\) | 34.4222i | 1.26283i | 0.775446 | + | 0.631414i | \(0.217525\pi\) | ||||
−0.775446 | + | 0.631414i | \(0.782475\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.0555 | −0.514609 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.42221i | 0.161692i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.02776 | 0.219956 | 0.109978 | − | 0.993934i | \(-0.464922\pi\) | ||||
0.109978 | + | 0.993934i | \(0.464922\pi\) | |||||||
\(752\) | − 17.2111i | − 0.627624i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.78890 | 0.247237 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.2111i | 1.13439i | 0.823585 | + | 0.567193i | \(0.191971\pi\) | ||||
−0.823585 | + | 0.567193i | \(0.808029\pi\) | |||||||
\(758\) | − 18.7527i | − 0.681130i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −53.4500 | −1.93756 | −0.968780 | − | 0.247923i | \(-0.920252\pi\) | ||||
−0.968780 | + | 0.247923i | \(0.920252\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.2389i | 1.16713i | ||||||||
\(764\) | 4.97224 | 0.179889 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.2750 | −0.877092 | ||||||||
\(767\) | 5.21110i | 0.188162i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.0000 | −1.47850 | −0.739249 | − | 0.673432i | \(-0.764819\pi\) | ||||
−0.739249 | + | 0.673432i | \(0.764819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 6.60555i | − 0.237739i | ||||||||
\(773\) | − 16.8167i | − 0.604853i | −0.953173 | − | 0.302426i | \(-0.902203\pi\) | ||||
0.953173 | − | 0.302426i | \(-0.0977967\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −24.0000 | −0.861550 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 5.44996i | − 0.195391i | ||||||||
\(779\) | 9.39445 | 0.336591 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.0555 | −1.36173 | ||||||||
\(782\) | 21.9083i | 0.783440i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 46.9361 | 1.67629 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2.97224i | − 0.105949i | −0.998596 | − | 0.0529745i | \(-0.983130\pi\) | ||||
0.998596 | − | 0.0529745i | \(-0.0168702\pi\) | |||||||
\(788\) | − 0.358288i | − 0.0127635i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.63331 | −0.129186 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.18335i | 0.219577i | ||||||||
\(794\) | 16.4222 | 0.582802 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.00000 | −0.141776 | ||||||||
\(797\) | − 37.6611i | − 1.33402i | −0.745047 | − | 0.667012i | \(-0.767573\pi\) | ||||
0.745047 | − | 0.667012i | \(-0.232427\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.2111 | 1.03341 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 39.0833i | − 1.38008i | ||||||||
\(803\) | 14.0555i | 0.496008i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.26662 | −0.0446146 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 36.0000i | 1.26648i | ||||||||
\(809\) | −50.6056 | −1.77920 | −0.889598 | − | 0.456744i | \(-0.849016\pi\) | ||||
−0.889598 | + | 0.456744i | \(0.849016\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.4222 | 1.48965 | 0.744823 | − | 0.667263i | \(-0.232534\pi\) | ||||
0.744823 | + | 0.667263i | \(0.232534\pi\) | |||||||
\(812\) | − 12.0000i | − 0.421117i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.78890 | 0.237951 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.8167i | 0.833239i | ||||||||
\(818\) | − 6.51388i | − 0.227752i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.0000 | 1.04701 | 0.523504 | − | 0.852023i | \(-0.324625\pi\) | ||||
0.523504 | + | 0.852023i | \(0.324625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 3.81665i | − 0.133040i | −0.997785 | − | 0.0665201i | \(-0.978810\pi\) | ||||
0.997785 | − | 0.0665201i | \(-0.0211897\pi\) | |||||||
\(824\) | −12.0000 | −0.418040 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −51.6333 | −1.79655 | ||||||||
\(827\) | − 33.7889i | − 1.17496i | −0.809240 | − | 0.587478i | \(-0.800121\pi\) | ||||
0.809240 | − | 0.587478i | \(-0.199879\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.2111 | 0.945081 | 0.472540 | − | 0.881309i | \(-0.343337\pi\) | ||||
0.472540 | + | 0.881309i | \(0.343337\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 5.33894i | − 0.185094i | ||||||||
\(833\) | 79.6611i | 2.76009i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.84441 | −0.0983760 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.9722i | 0.586296i | ||||||||
\(839\) | −18.7889 | −0.648665 | −0.324332 | − | 0.945943i | \(-0.605140\pi\) | ||||
−0.324332 | + | 0.945943i | \(0.605140\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45.0555 | 1.55364 | ||||||||
\(842\) | − 30.5139i | − 1.05158i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.88057 | 0.133575 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 19.3944i | − 0.666401i | ||||||||
\(848\) | − 18.5139i | − 0.635769i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | −0.205677 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 14.7889i | − 0.506362i | −0.967419 | − | 0.253181i | \(-0.918523\pi\) | ||||
0.967419 | − | 0.253181i | \(-0.0814769\pi\) | |||||||
\(854\) | −61.2666 | −2.09650 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 45.2389i | − 1.54533i | −0.634814 | − | 0.772665i | \(-0.718923\pi\) | ||||
0.634814 | − | 0.772665i | \(-0.281077\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.02776 | −0.205664 | −0.102832 | − | 0.994699i | \(-0.532790\pi\) | ||||
−0.102832 | + | 0.994699i | \(0.532790\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.6333i | 1.14556i | ||||||||
\(863\) | − 15.7889i | − 0.537460i | −0.963216 | − | 0.268730i | \(-0.913396\pi\) | ||||
0.963216 | − | 0.268730i | \(-0.0866040\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −36.7889 | −1.25014 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.23886i | 0.0759918i | ||||||||
\(869\) | −11.4500 | −0.388413 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.21110 | 0.312106 | ||||||||
\(872\) | 21.0000i | 0.711150i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.0917 | −0.476658 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 56.6611i | − 1.91331i | −0.291227 | − | 0.956654i | \(-0.594063\pi\) | ||||
0.291227 | − | 0.956654i | \(-0.405937\pi\) | |||||||
\(878\) | − 26.5694i | − 0.896674i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.6056 | −1.09851 | −0.549254 | − | 0.835655i | \(-0.685088\pi\) | ||||
−0.549254 | + | 0.835655i | \(0.685088\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.81665i | 0.195746i | 0.995199 | + | 0.0978730i | \(0.0312039\pi\) | ||||
−0.995199 | + | 0.0978730i | \(0.968796\pi\) | |||||||
\(884\) | 1.02776 | 0.0345672 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.2750 | 0.815535 | ||||||||
\(887\) | 12.6333i | 0.424185i | 0.977250 | + | 0.212092i | \(0.0680278\pi\) | ||||
−0.977250 | + | 0.212092i | \(0.931972\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.0555 | 0.739718 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.02776i | 0.101377i | ||||||||
\(893\) | 18.7889i | 0.628746i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 37.2666 | 1.24499 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.9445i | 0.532074i | ||||||||
\(899\) | −13.8167 | −0.460811 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.4222 | 1.04683 | ||||||||
\(902\) | − 8.84441i | − 0.294487i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.36669 | −0.0787150 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.4222i | 1.01015i | 0.863075 | + | 0.505076i | \(0.168536\pi\) | ||||
−0.863075 | + | 0.505076i | \(0.831464\pi\) | |||||||
\(908\) | − 7.93608i | − 0.263368i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.0278 | 1.02800 | 0.513998 | − | 0.857792i | \(-0.328164\pi\) | ||||
0.513998 | + | 0.857792i | \(0.328164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.81665i | 0.258693i | ||||||||
\(914\) | −1.57779 | −0.0521888 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.88057 | 0.0621358 | ||||||||
\(917\) | 27.6333i | 0.912532i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.42221 | 0.0799012 | 0.0399506 | − | 0.999202i | \(-0.487280\pi\) | ||||
0.0399506 | + | 0.999202i | \(0.487280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 28.1833i | − 0.928169i | ||||||||
\(923\) | 8.84441i | 0.291117i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −19.8167 | −0.651216 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 14.6056i | − 0.479451i | ||||||||
\(929\) | −26.6056 | −0.872900 | −0.436450 | − | 0.899729i | \(-0.643764\pi\) | ||||
−0.436450 | + | 0.899729i | \(0.643764\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −51.2389 | −1.67929 | ||||||||
\(932\) | 5.44996i | 0.178519i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.88057 | 0.0942551 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.7889i | 0.875155i | 0.899181 | + | 0.437578i | \(0.144163\pi\) | ||||
−0.899181 | + | 0.437578i | \(0.855837\pi\) | |||||||
\(938\) | 91.2666i | 2.97996i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.4222 | 0.926537 | 0.463269 | − | 0.886218i | \(-0.346676\pi\) | ||||
0.463269 | + | 0.886218i | \(0.346676\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.81665i | 0.254545i | ||||||||
\(944\) | −28.4222 | −0.925064 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.4222 | 0.729009 | ||||||||
\(947\) | 39.0000i | 1.26733i | 0.773608 | + | 0.633665i | \(0.218450\pi\) | ||||
−0.773608 | + | 0.633665i | \(0.781550\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.26662 | 0.106039 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 77.4500i | 2.51017i | ||||||||
\(953\) | − 26.8444i | − 0.869576i | −0.900533 | − | 0.434788i | \(-0.856823\pi\) | ||||
0.900533 | − | 0.434788i | \(-0.143177\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.238859 | 0.00772525 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.0833i | 0.681170i | ||||||||
\(959\) | 22.1833 | 0.716338 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.4222 | −0.916845 | ||||||||
\(962\) | − 1.57779i | − 0.0508701i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.54163 | 0.275108 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.0000i | 1.60789i | 0.594703 | + | 0.803946i | \(0.297270\pi\) | ||||
−0.594703 | + | 0.803946i | \(0.702730\pi\) | |||||||
\(968\) | − 12.6333i | − 0.406050i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0000 | −0.577647 | −0.288824 | − | 0.957382i | \(-0.593264\pi\) | ||||
−0.288824 | + | 0.957382i | \(0.593264\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.4222i | 0.590589i | ||||||||
\(974\) | 10.6611 | 0.341603 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −33.7250 | −1.07951 | ||||||||
\(977\) | − 0.788897i | − 0.0252391i | −0.999920 | − | 0.0126195i | \(-0.995983\pi\) | ||||
0.999920 | − | 0.0126195i | \(-0.00401703\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.3667 | 0.650922 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.6611i | 0.531676i | ||||||||
\(983\) | − 0.633308i | − 0.0201994i | −0.999949 | − | 0.0100997i | \(-0.996785\pi\) | ||||
0.999949 | − | 0.0100997i | \(-0.00321489\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −62.8444 | −2.00137 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.661064i | 0.0210312i | ||||||||
\(989\) | −19.8167 | −0.630133 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.8167 | −1.61424 | −0.807122 | − | 0.590385i | \(-0.798976\pi\) | ||||
−0.807122 | + | 0.590385i | \(0.798976\pi\) | |||||||
\(992\) | 2.72498i | 0.0865182i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −87.6333 | −2.77956 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.8722i | 1.70615i | 0.521789 | + | 0.853074i | \(0.325265\pi\) | ||||
−0.521789 | + | 0.853074i | \(0.674735\pi\) | |||||||
\(998\) | 35.9638i | 1.13842i | ||||||||
\(999\) | 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 | 675.2.b.i.649.3 | 4 | ||
3.2 | odd | 2 | 675.2.b.h.649.2 | 4 | |||
5.2 | odd | 4 | 675.2.a.p.1.1 | 2 | |||
5.3 | odd | 4 | 135.2.a.c.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 675.2.b.i.649.2 | 4 | ||
15.2 | even | 4 | 675.2.a.k.1.2 | 2 | |||
15.8 | even | 4 | 135.2.a.d.1.1 | yes | 2 | ||
15.14 | odd | 2 | 675.2.b.h.649.3 | 4 | |||
20.3 | even | 4 | 2160.2.a.ba.1.1 | 2 | |||
35.13 | even | 4 | 6615.2.a.p.1.2 | 2 | |||
40.3 | even | 4 | 8640.2.a.ck.1.1 | 2 | |||
40.13 | odd | 4 | 8640.2.a.cr.1.2 | 2 | |||
45.13 | odd | 12 | 405.2.e.k.136.1 | 4 | |||
45.23 | even | 12 | 405.2.e.j.136.2 | 4 | |||
45.38 | even | 12 | 405.2.e.j.271.2 | 4 | |||
45.43 | odd | 12 | 405.2.e.k.271.1 | 4 | |||
60.23 | odd | 4 | 2160.2.a.y.1.1 | 2 | |||
105.83 | odd | 4 | 6615.2.a.v.1.1 | 2 | |||
120.53 | even | 4 | 8640.2.a.df.1.2 | 2 | |||
120.83 | odd | 4 | 8640.2.a.cy.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.a.c.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
135.2.a.d.1.1 | yes | 2 | 15.8 | even | 4 | ||
405.2.e.j.136.2 | 4 | 45.23 | even | 12 | |||
405.2.e.j.271.2 | 4 | 45.38 | even | 12 | |||
405.2.e.k.136.1 | 4 | 45.13 | odd | 12 | |||
405.2.e.k.271.1 | 4 | 45.43 | odd | 12 | |||
675.2.a.k.1.2 | 2 | 15.2 | even | 4 | |||
675.2.a.p.1.1 | 2 | 5.2 | odd | 4 | |||
675.2.b.h.649.2 | 4 | 3.2 | odd | 2 | |||
675.2.b.h.649.3 | 4 | 15.14 | odd | 2 | |||
675.2.b.i.649.2 | 4 | 5.4 | even | 2 | inner | ||
675.2.b.i.649.3 | 4 | 1.1 | even | 1 | trivial | ||
2160.2.a.y.1.1 | 2 | 60.23 | odd | 4 | |||
2160.2.a.ba.1.1 | 2 | 20.3 | even | 4 | |||
6615.2.a.p.1.2 | 2 | 35.13 | even | 4 | |||
6615.2.a.v.1.1 | 2 | 105.83 | odd | 4 | |||
8640.2.a.ck.1.1 | 2 | 40.3 | even | 4 | |||
8640.2.a.cr.1.2 | 2 | 40.13 | odd | 4 | |||
8640.2.a.cy.1.1 | 2 | 120.83 | odd | 4 | |||
8640.2.a.df.1.2 | 2 | 120.53 | even | 4 |