Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(673,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.673");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 722x^{3} + 11881x^{2} + 54936x + 127008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 673.6 | ||
Root | \(-4.87742 - 4.87742i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.673 |
Dual form | 1344.4.c.a.673.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 11.7548i | 1.05139i | 0.850674 | + | 0.525693i | \(0.176194\pi\) | ||||
−0.850674 | + | 0.525693i | \(0.823806\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 72.4604i | − 1.98615i | −0.117487 | − | 0.993074i | \(-0.537484\pi\) | ||||
0.117487 | − | 0.993074i | \(-0.462516\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 50.7056i | 1.08178i | 0.841092 | + | 0.540892i | \(0.181913\pi\) | ||||
−0.841092 | + | 0.540892i | \(0.818087\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −35.2645 | −0.607018 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 60.4604 | 0.862577 | 0.431288 | − | 0.902214i | \(-0.358059\pi\) | ||||
0.431288 | + | 0.902214i | \(0.358059\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 33.8235i | − 0.408403i | −0.978929 | − | 0.204201i | \(-0.934540\pi\) | ||||
0.978929 | − | 0.204201i | \(-0.0654597\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 21.0000i | − 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −116.852 | −1.05936 | −0.529682 | − | 0.848197i | \(-0.677689\pi\) | ||||
−0.529682 | + | 0.848197i | \(0.677689\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.1765 | −0.105412 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 13.1959i | 0.0844969i | 0.999107 | + | 0.0422485i | \(0.0134521\pi\) | ||||
−0.999107 | + | 0.0422485i | \(0.986548\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 250.117 | 1.44911 | 0.724553 | − | 0.689219i | \(-0.242046\pi\) | ||||
0.724553 | + | 0.689219i | \(0.242046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 217.381 | 1.14670 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 82.2839i | − 0.397386i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 92.7056i | − 0.411911i | −0.978561 | − | 0.205955i | \(-0.933970\pi\) | ||||
0.978561 | − | 0.205955i | \(-0.0660302\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −152.117 | −0.624568 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −69.1663 | −0.263462 | −0.131731 | − | 0.991285i | \(-0.542054\pi\) | ||||
−0.131731 | + | 0.991285i | \(0.542054\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 69.6471i | − 0.247002i | −0.992344 | − | 0.123501i | \(-0.960588\pi\) | ||||
0.992344 | − | 0.123501i | \(-0.0394122\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 105.794i | − 0.350462i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 346.039 | 1.07394 | 0.536968 | − | 0.843603i | \(-0.319570\pi\) | ||||
0.536968 | + | 0.843603i | \(0.319570\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 181.381i | 0.498009i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 585.232i | − 1.51675i | −0.651818 | − | 0.758376i | \(-0.725993\pi\) | ||||
0.651818 | − | 0.758376i | \(-0.274007\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 851.761 | 2.08821 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 101.471 | 0.235791 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 66.1946i | − 0.146064i | −0.997330 | − | 0.0730322i | \(-0.976732\pi\) | ||||
0.997330 | − | 0.0730322i | \(-0.0232676\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 492.057i | 1.03281i | 0.856344 | + | 0.516405i | \(0.172730\pi\) | ||||
−0.856344 | + | 0.516405i | \(0.827270\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −596.036 | −1.13737 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 543.704i | − 0.991403i | −0.868493 | − | 0.495701i | \(-0.834911\pi\) | ||||
0.868493 | − | 0.495701i | \(-0.165089\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 350.556i | − 0.611624i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 365.128 | 0.610319 | 0.305160 | − | 0.952301i | \(-0.401290\pi\) | ||||
0.305160 | + | 0.952301i | \(0.401290\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 374.174 | 0.599915 | 0.299957 | − | 0.953953i | \(-0.403028\pi\) | ||||
0.299957 | + | 0.953953i | \(0.403028\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 39.5294i | − 0.0608595i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 507.223i | 0.750694i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 670.176 | 0.954439 | 0.477220 | − | 0.878784i | \(-0.341645\pi\) | ||||
0.477220 | + | 0.878784i | \(0.341645\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 595.115i | 0.787017i | 0.919321 | + | 0.393508i | \(0.128739\pi\) | ||||
−0.919321 | + | 0.393508i | \(0.871261\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 710.703i | 0.906901i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −39.5876 | −0.0487843 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1036.53 | 1.23452 | 0.617260 | − | 0.786759i | \(-0.288243\pi\) | ||||
0.617260 | + | 0.786759i | \(0.288243\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 354.939i | − 0.408876i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 750.350i | 0.836642i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 397.590 | 0.429389 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −218.998 | −0.229236 | −0.114618 | − | 0.993410i | \(-0.536564\pi\) | ||||
−0.114618 | + | 0.993410i | \(0.536564\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 652.144i | 0.662050i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 446.361i | − 0.439748i | −0.975528 | − | 0.219874i | \(-0.929435\pi\) | ||||
0.975528 | − | 0.219874i | \(-0.0705647\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −335.995 | −0.321423 | −0.160712 | − | 0.987001i | \(-0.551379\pi\) | ||||
−0.160712 | + | 0.987001i | \(0.551379\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 246.852 | 0.229431 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1966.85i | 1.77703i | 0.458849 | + | 0.888514i | \(0.348262\pi\) | ||||
−0.458849 | + | 0.888514i | \(0.651738\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1161.76i | 1.02089i | 0.859911 | + | 0.510444i | \(0.170519\pi\) | ||||
−0.859911 | + | 0.510444i | \(0.829481\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 278.117 | 0.237817 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 252.726 | 0.210394 | 0.105197 | − | 0.994451i | \(-0.466453\pi\) | ||||
0.105197 | + | 0.994451i | \(0.466453\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1373.58i | − 1.11380i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 456.350i | − 0.360595i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −423.223 | −0.326023 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3919.51 | −2.94479 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 207.499i | − 0.152110i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1314.47i | 0.940557i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2119.46 | −1.48088 | −0.740438 | − | 0.672124i | \(-0.765382\pi\) | ||||
−0.740438 | + | 0.672124i | \(0.765382\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 208.941 | 0.142607 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1199.47i | − 0.799985i | −0.916518 | − | 0.399993i | \(-0.869013\pi\) | ||||
0.916518 | − | 0.399993i | \(-0.130987\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 236.765i | 0.154362i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 317.381 | 0.202339 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −466.885 | −0.291158 | −0.145579 | − | 0.989347i | \(-0.546504\pi\) | ||||
−0.145579 | + | 0.989347i | \(0.546504\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2256.57i | 1.37698i | 0.725246 | + | 0.688490i | \(0.241726\pi\) | ||||
−0.725246 | + | 0.688490i | \(0.758274\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1038.12i | 0.620037i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3674.15 | 2.14858 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −155.115 | −0.0888389 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1777.97i | 0.977566i | 0.872405 | + | 0.488783i | \(0.162559\pi\) | ||||
−0.872405 | + | 0.488783i | \(0.837441\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1853.75 | 0.999049 | 0.499525 | − | 0.866300i | \(-0.333508\pi\) | ||||
0.499525 | + | 0.866300i | \(0.333508\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −544.144 | −0.287526 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2940.08i | 1.52357i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 800.278i | − 0.406810i | −0.979095 | − | 0.203405i | \(-0.934799\pi\) | ||||
0.979095 | − | 0.203405i | \(-0.0652008\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1755.70 | 0.875697 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 817.965 | 0.400402 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 923.582i | 0.443807i | 0.975069 | + | 0.221903i | \(0.0712270\pi\) | ||||
−0.975069 | + | 0.221903i | \(0.928773\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2555.28i | 1.20563i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2439.11 | 1.13020 | 0.565102 | − | 0.825021i | \(-0.308837\pi\) | ||||
0.565102 | + | 0.825021i | \(0.308837\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −374.054 | −0.170257 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 304.412i | 0.136134i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 814.093i | 0.357771i | 0.983870 | + | 0.178885i | \(0.0572491\pi\) | ||||
−0.983870 | + | 0.178885i | \(0.942751\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 92.2353 | 0.0398419 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 198.584 | 0.0843304 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1490.42i | − 0.622340i | −0.950354 | − | 0.311170i | \(-0.899279\pi\) | ||||
0.950354 | − | 0.311170i | \(-0.100721\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 41.6575i | 0.0171071i | 0.999963 | + | 0.00855353i | \(0.00272271\pi\) | ||||
−0.999963 | + | 0.00855353i | \(0.997277\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1476.17 | −0.596293 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1089.74 | 0.433077 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 4380.99i | − 1.71321i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2597.64 | 0.984076 | 0.492038 | − | 0.870574i | \(-0.336252\pi\) | ||||
0.492038 | + | 0.870574i | \(0.336252\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1468.75 | 0.547788 | 0.273894 | − | 0.961760i | \(-0.411688\pi\) | ||||
0.273894 | + | 0.961760i | \(0.411688\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1788.11i | − 0.656662i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1366.23i | 0.494112i | 0.969001 | + | 0.247056i | \(0.0794632\pi\) | ||||
−0.969001 | + | 0.247056i | \(0.920537\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2876.46 | 1.02466 | 0.512329 | − | 0.858789i | \(-0.328783\pi\) | ||||
0.512329 | + | 0.858789i | \(0.328783\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1631.11 | 0.572387 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 92.3711i | − 0.0319368i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 813.039i | − 0.277001i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1051.67 | 0.353121 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2450.87 | −0.811148 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 5569.49i | − 1.81716i | −0.417716 | − | 0.908578i | \(-0.637169\pi\) | ||||
0.417716 | − | 0.908578i | \(-0.362831\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1095.38i | 0.352368i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 818.691 | 0.259694 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1750.82 | −0.547711 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1122.52i | 0.346361i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3065.68i | 0.933122i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5713.73 | −1.71578 | −0.857891 | − | 0.513831i | \(-0.828226\pi\) | ||||
−0.857891 | + | 0.513831i | \(0.828226\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 118.588 | 0.0351373 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1186.64i | − 0.346962i | −0.984837 | − | 0.173481i | \(-0.944498\pi\) | ||||
0.984837 | − | 0.173481i | \(-0.0555015\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5136.22i | 1.48214i | 0.671426 | + | 0.741072i | \(0.265682\pi\) | ||||
−0.671426 | + | 0.741072i | \(0.734318\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1521.67 | −0.433413 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3084.93 | 0.867383 | 0.433692 | − | 0.901061i | \(-0.357211\pi\) | ||||
0.433692 | + | 0.901061i | \(0.357211\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4067.63i | 1.12912i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2010.53i | 0.551046i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5795.47 | 1.56853 | 0.784263 | − | 0.620429i | \(-0.213041\pi\) | ||||
0.784263 | + | 0.620429i | \(0.213041\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4918.74 | 1.31471 | 0.657353 | − | 0.753583i | \(-0.271676\pi\) | ||||
0.657353 | + | 0.753583i | \(0.271676\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 575.988i | 0.150198i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1715.04 | 0.441803 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1785.35 | −0.454384 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 6190.85i | − 1.55682i | −0.627753 | − | 0.778412i | \(-0.716025\pi\) | ||||
0.627753 | − | 0.778412i | \(-0.283975\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8467.16i | 2.10405i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2132.11 | −0.523599 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1065.97 | 0.258730 | 0.129365 | − | 0.991597i | \(-0.458706\pi\) | ||||
0.129365 | + | 0.991597i | \(0.458706\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 648.939i | 0.155688i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 118.763i | − 0.0281656i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7817.25 | −1.83282 | −0.916411 | − | 0.400238i | \(-0.868927\pi\) | ||||
−0.916411 | + | 0.400238i | \(0.868927\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6879.32 | 1.59469 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3109.60i | 0.712750i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 3801.54i | − 0.861651i | −0.902435 | − | 0.430826i | \(-0.858222\pi\) | ||||
0.902435 | − | 0.430826i | \(-0.141778\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6241.27 | 1.39900 | 0.699502 | − | 0.714630i | \(-0.253405\pi\) | ||||
0.699502 | + | 0.714630i | \(0.253405\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1064.82 | 0.236065 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 954.773i | 0.209363i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5487.86i | 1.19037i | 0.803587 | + | 0.595187i | \(0.202922\pi\) | ||||
−0.803587 | + | 0.595187i | \(0.797078\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2251.05 | −0.483035 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3378.67 | 0.717276 | 0.358638 | − | 0.933477i | \(-0.383241\pi\) | ||||
0.358638 | + | 0.933477i | \(0.383241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8802.26i | 1.84891i | 0.381297 | + | 0.924453i | \(0.375478\pi\) | ||||
−0.381297 | + | 0.924453i | \(0.624522\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1192.77i | 0.247908i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 484.164 | 0.0995795 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1257.54 | −0.255961 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 656.993i | − 0.132349i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5034.83i | 1.00388i | 0.864901 | + | 0.501942i | \(0.167381\pi\) | ||||
−0.864901 | + | 0.501942i | \(0.832619\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 778.108 | 0.153570 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1956.43 | −0.382235 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 5925.05i | − 1.14600i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 487.529i | 0.0933579i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1339.08 | 0.253889 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5784.05 | −1.08588 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8342.24i | 1.55087i | 0.631428 | + | 0.775435i | \(0.282469\pi\) | ||||
−0.631428 | + | 0.775435i | \(0.717531\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1007.99i | − 0.185574i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8071.66 | 1.47171 | 0.735855 | − | 0.677139i | \(-0.236781\pi\) | ||||
0.735855 | + | 0.677139i | \(0.236781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6596.89 | −1.19130 | −0.595652 | − | 0.803242i | \(-0.703106\pi\) | ||||
−0.595652 | + | 0.803242i | \(0.703106\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 740.555i | 0.132462i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 10263.7i | − 1.81851i | −0.416242 | − | 0.909254i | \(-0.636653\pi\) | ||||
0.416242 | − | 0.909254i | \(-0.363347\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 956.178 | 0.167823 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5900.54 | −1.02597 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2044.98i | − 0.352279i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 668.120i | − 0.114033i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3485.29 | −0.589410 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2422.27 | −0.405909 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 11311.7i | − 1.87839i | −0.343383 | − | 0.939195i | \(-0.611573\pi\) | ||||
0.343383 | − | 0.939195i | \(-0.388427\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 834.350i | 0.137304i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6391.15 | 1.04235 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4700.58 | 0.759813 | 0.379907 | − | 0.925025i | \(-0.375956\pi\) | ||||
0.379907 | + | 0.925025i | \(0.375956\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 758.179i | 0.121471i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 18123.6i | − 2.87814i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4120.74 | 0.643052 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7390.19i | 1.14330i | 0.820496 | + | 0.571652i | \(0.193697\pi\) | ||||
−0.820496 | + | 0.571652i | \(0.806303\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10093.8i | 1.54816i | 0.633088 | + | 0.774080i | \(0.281787\pi\) | ||||
−0.633088 | + | 0.774080i | \(0.718213\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1369.05 | 0.208189 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10557.2 | −1.59180 | −0.795898 | − | 0.605431i | \(-0.793001\pi\) | ||||
−0.795898 | + | 0.605431i | \(0.793001\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4292.02i | 0.641681i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 1269.67i | − 0.188230i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8857.59 | 1.30219 | 0.651094 | − | 0.758997i | \(-0.274310\pi\) | ||||
0.651094 | + | 0.758997i | \(0.274310\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5714.97 | 0.833207 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 11758.5i | − 1.70017i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4398.36i | 0.630742i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10701.6 | 1.52212 | 0.761061 | − | 0.648680i | \(-0.224679\pi\) | ||||
0.761061 | + | 0.648680i | \(0.224679\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 622.497 | 0.0878208 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4096.62i | 0.573278i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 2451.52i | − 0.340308i | −0.985417 | − | 0.170154i | \(-0.945573\pi\) | ||||
0.985417 | − | 0.170154i | \(-0.0544265\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3943.41 | −0.543031 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −669.104 | −0.0914074 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 170.113i | 0.0230557i | 0.999934 | + | 0.0115279i | \(0.00366952\pi\) | ||||
−0.999934 | + | 0.0115279i | \(0.996330\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 6358.37i | − 0.854985i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4339.37 | 0.578933 | 0.289467 | − | 0.957188i | \(-0.406522\pi\) | ||||
0.289467 | + | 0.957188i | \(0.406522\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5962.33 | −0.789269 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 626.824i | 0.0823339i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 14598.8i | − 1.90280i | −0.307954 | − | 0.951401i | \(-0.599644\pi\) | ||||
0.307954 | − | 0.951401i | \(-0.400356\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7064.93 | −0.913782 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3598.41 | 0.461872 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7877.82i | 1.00348i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1185.22i | − 0.149835i | −0.997190 | − | 0.0749175i | \(-0.976131\pi\) | ||||
0.997190 | − | 0.0749175i | \(-0.0238693\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −710.294 | −0.0891208 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3672.99 | 0.457407 | 0.228704 | − | 0.973496i | \(-0.426551\pi\) | ||||
0.228704 | + | 0.973496i | \(0.426551\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12682.3i | 1.56762i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 952.143i | 0.116821i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6717.48 | −0.818116 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8842.03 | −1.06897 | −0.534487 | − | 0.845177i | \(-0.679495\pi\) | ||||
−0.534487 | + | 0.845177i | \(0.679495\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1400.65i | − 0.168100i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 463.362i | 0.0552072i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6995.49 | −0.827458 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6769.72 | −0.795000 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 10691.7i | − 1.24660i | −0.781984 | − | 0.623298i | \(-0.785792\pi\) | ||||
0.781984 | − | 0.623298i | \(-0.214208\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 15909.2i | − 1.84173i | −0.389881 | − | 0.920865i | \(-0.627484\pi\) | ||||
0.389881 | − | 0.920865i | \(-0.372516\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3114.35 | −0.357978 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −796.655 | −0.0909257 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3444.40i | − 0.390366i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11022.4i | 1.24049i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6689.77 | 0.747644 | 0.373822 | − | 0.927500i | \(-0.378047\pi\) | ||||
0.373822 | + | 0.927500i | \(0.378047\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13265.8 | 1.47232 | 0.736160 | − | 0.676808i | \(-0.236637\pi\) | ||||
0.736160 | + | 0.676808i | \(0.236637\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 465.346i | − 0.0512911i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3952.35i | 0.432647i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6722.13 | −0.730820 | −0.365410 | − | 0.930847i | \(-0.619071\pi\) | ||||
−0.365410 | + | 0.930847i | \(0.619071\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −441.000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 8937.62i | − 0.958554i | −0.877664 | − | 0.479277i | \(-0.840899\pi\) | ||||
0.877664 | − | 0.479277i | \(-0.159101\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12184.3i | 1.29796i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5333.92 | −0.564398 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12718.8 | 1.33683 | 0.668414 | − | 0.743790i | \(-0.266974\pi\) | ||||
0.668414 | + | 0.743790i | \(0.266974\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5011.82i | 0.523276i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5561.26i | 0.576801i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4172.25 | 0.429886 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6941.85 | −0.710560 | −0.355280 | − | 0.934760i | \(-0.615615\pi\) | ||||
−0.355280 | + | 0.934760i | \(0.615615\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 1632.43i | − 0.166003i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 10090.3i | − 1.01942i | −0.860347 | − | 0.509709i | \(-0.829753\pi\) | ||||
0.860347 | − | 0.509709i | \(-0.170247\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7973.79 | −0.800375 | −0.400187 | − | 0.916433i | \(-0.631055\pi\) | ||||
−0.400187 | + | 0.916433i | \(0.631055\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8820.25 | −0.879633 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9435.71i | 0.934973i | 0.884000 | + | 0.467486i | \(0.154840\pi\) | ||||
−0.884000 | + | 0.467486i | \(0.845160\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3805.93i | 0.374715i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2400.83 | 0.234872 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5046.65 | −0.490582 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 445.675i | 0.0430504i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5267.09i | 0.505584i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 444.695 | 0.0424189 | 0.0212094 | − | 0.999775i | \(-0.493248\pi\) | ||||
0.0212094 | + | 0.999775i | \(0.493248\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4700.69 | 0.445599 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2453.90i | 0.231172i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 2574.29i | − 0.241015i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12965.2 | −1.20638 | −0.603191 | − | 0.797597i | \(-0.706104\pi\) | ||||
−0.603191 | + | 0.797597i | \(0.706104\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2770.74 | −0.256232 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17323.6i | 1.59227i | 0.605120 | + | 0.796134i | \(0.293125\pi\) | ||||
−0.605120 | + | 0.796134i | \(0.706875\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 797.828i | 0.0728851i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7665.85 | −0.696069 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2555.89 | −0.230679 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 3053.26i | − 0.273913i | −0.990577 | − | 0.136957i | \(-0.956268\pi\) | ||||
0.990577 | − | 0.136957i | \(-0.0437321\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7317.33i | 0.652523i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4076.65 | −0.361369 | −0.180685 | − | 0.983541i | \(-0.557831\pi\) | ||||
−0.180685 | + | 0.983541i | \(0.557831\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5246.90 | 0.462345 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1122.16i | − 0.0982979i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 458.202i | 0.0399007i | 0.999801 | + | 0.0199503i | \(0.00635081\pi\) | ||||
−0.999801 | + | 0.0199503i | \(0.993649\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2619.22 | −0.226747 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −913.235 | −0.0785971 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 3949.57i | − 0.337940i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 25074.1i | − 2.13299i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2442.28 | −0.206559 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6244.54 | 0.525103 | 0.262551 | − | 0.964918i | \(-0.415436\pi\) | ||||
0.262551 | + | 0.964918i | \(0.415436\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 22863.4i | − 1.91156i | −0.294086 | − | 0.955779i | \(-0.595015\pi\) | ||||
0.294086 | − | 0.955779i | \(-0.404985\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 276.706i | 0.0230027i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15122.2 | 1.24997 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1487.42 | 0.122251 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 595.751i | 0.0486882i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3507.12i | − 0.285010i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23120.0 | −1.86834 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4471.25 | 0.359308 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 3550.56i | − 0.283736i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 20780.9i | − 1.65146i | −0.564066 | − | 0.825730i | \(-0.690764\pi\) | ||||
0.564066 | − | 0.825730i | \(-0.309236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −124.973 | −0.00987677 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13656.4 | −1.07335 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 9848.10i | − 0.769788i | −0.922961 | − | 0.384894i | \(-0.874238\pi\) | ||||
0.922961 | − | 0.384894i | \(-0.125762\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 4428.51i | − 0.344270i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 446.331 | 0.0345088 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4691.23 | −0.360744 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3269.22i | 0.250037i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 20834.5i | − 1.58489i | −0.609942 | − | 0.792446i | \(-0.708807\pi\) | ||||
0.609942 | − | 0.792446i | \(-0.291193\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3531.49 | 0.267203 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13143.0 | 0.989120 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2168.31i | − 0.162315i | −0.996701 | − | 0.0811575i | \(-0.974138\pi\) | ||||
0.996701 | − | 0.0811575i | \(-0.0258617\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2970.76i | 0.221205i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3909.14 | −0.288013 | −0.144007 | − | 0.989577i | \(-0.545999\pi\) | ||||
−0.144007 | + | 0.989577i | \(0.545999\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6744.18i | 0.494282i | 0.968979 | + | 0.247141i | \(0.0794912\pi\) | ||||
−0.968979 | + | 0.247141i | \(0.920509\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7792.92i | 0.568157i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1539.70 | 0.111669 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16895.9 | 1.21904 | 0.609521 | − | 0.792770i | \(-0.291362\pi\) | ||||
0.609521 | + | 0.792770i | \(0.291362\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4406.25i | 0.316265i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 4165.81i | − 0.297464i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −42406.2 | −3.01249 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5364.33 | 0.379124 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 14853.0i | − 1.04438i | −0.852831 | − | 0.522188i | \(-0.825116\pi\) | ||||
0.852831 | − | 0.522188i | \(-0.174884\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 8459.83i | − 0.591819i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4098.70 | −0.285276 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13967.4 | 0.967239 | 0.483620 | − | 0.875278i | \(-0.339322\pi\) | ||||
0.483620 | + | 0.875278i | \(0.339322\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 4974.92i | − 0.342776i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8629.39i | 0.591587i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1474.31 | 0.100565 | 0.0502826 | − | 0.998735i | \(-0.483988\pi\) | ||||
0.0502826 | + | 0.998735i | \(0.483988\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3720.31 | 0.252503 | 0.126252 | − | 0.991998i | \(-0.459705\pi\) | ||||
0.126252 | + | 0.991998i | \(0.459705\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4893.33i | 0.330468i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 46073.3i | − 3.09611i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10969.4 | 0.733501 | 0.366750 | − | 0.930319i | \(-0.380470\pi\) | ||||
0.366750 | + | 0.930319i | \(0.380470\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 277.113 | 0.0184387 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17546.1i | 1.16177i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 768.228i | 0.0506173i | 0.999680 | + | 0.0253087i | \(0.00805686\pi\) | ||||
−0.999680 | + | 0.0253087i | \(0.991943\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2439.12 | 0.159926 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9912.22 | 0.646760 | 0.323380 | − | 0.946269i | \(-0.395181\pi\) | ||||
0.323380 | + | 0.946269i | \(0.395181\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10821.1i | 0.702647i | 0.936254 | + | 0.351323i | \(0.114268\pi\) | ||||
−0.936254 | + | 0.351323i | \(0.885732\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3155.01i | 0.203875i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7255.73 | −0.466605 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17098.4 | −1.09430 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 7352.60i | − 0.468317i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 5605.02i | − 0.355305i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21838.3 | −1.37776 | −0.688881 | − | 0.724874i | \(-0.741898\pi\) | ||||
−0.688881 | + | 0.724874i | \(0.741898\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16708.5 | 1.04914 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 24913.9i | − 1.55697i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2484.57i | 0.154541i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3286.15 | −0.203440 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3288.45 | 0.202630 | 0.101315 | − | 0.994854i | \(-0.467695\pi\) | ||||
0.101315 | + | 0.994854i | \(0.467695\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 6563.13i | − 0.402527i | −0.979537 | − | 0.201263i | \(-0.935495\pi\) | ||||
0.979537 | − | 0.201263i | \(-0.0645047\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2456.07i | 0.149934i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13561.5 | −0.824043 | −0.412022 | − | 0.911174i | \(-0.635177\pi\) | ||||
−0.412022 | + | 0.911174i | \(0.635177\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4796.49 | −0.290106 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 5252.45i | − 0.316221i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9533.77i | 0.571340i | 0.958328 | + | 0.285670i | \(0.0922162\pi\) | ||||
−0.958328 | + | 0.285670i | \(0.907784\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14099.6 | 0.841093 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3367.57 | −0.199972 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 253.185i | 0.0149661i | 0.999972 | + | 0.00748307i | \(0.00238196\pi\) | ||||
−0.999972 | + | 0.00748307i | \(0.997618\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29105.5i | 1.71266i | 0.516425 | + | 0.856332i | \(0.327262\pi\) | ||||
−0.516425 | + | 0.856332i | \(0.672738\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9197.04 | −0.538738 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2783.13 | −0.162294 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1541.97i | − 0.0895130i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 17141.2i | − 0.990608i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35654.6 | 2.05132 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3546.16 | −0.203112 | −0.101556 | − | 0.994830i | \(-0.532382\pi\) | ||||
−0.101556 | + | 0.994830i | \(0.532382\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 355.765i | 0.0202865i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 3670.94i | − 0.208399i | −0.994556 | − | 0.104199i | \(-0.966772\pi\) | ||||
0.994556 | − | 0.104199i | \(-0.0332280\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1532.98 | 0.0866429 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3559.93 | 0.200319 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12118.2i | 0.678904i | 0.940623 | + | 0.339452i | \(0.110242\pi\) | ||||
−0.940623 | + | 0.339452i | \(0.889758\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 5488.16i | − 0.306119i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15408.6 | −0.855716 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29674.5 | 1.64080 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 27270.4i | − 1.50132i | −0.660686 | − | 0.750662i | \(-0.729735\pi\) | ||||
0.660686 | − | 0.750662i | \(-0.270265\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 4565.01i | − 0.250231i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26525.7 | −1.44774 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4181.82 | −0.227257 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9254.78i | 0.500784i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 28435.3i | − 1.53208i | −0.642796 | − | 0.766038i | \(-0.722226\pi\) | ||||
0.642796 | − | 0.766038i | \(-0.277774\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3135.63 | −0.168225 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12202.9 | −0.651898 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3124.53i | 0.166209i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24828.2i | 1.31515i | 0.753388 | + | 0.657577i | \(0.228418\pi\) | ||||
−0.753388 | + | 0.657577i | \(0.771582\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6031.59 | −0.318146 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29226.7 | −1.53513 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 43189.0i | 2.25899i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17386.4i | 0.905589i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20755.0 | −1.07654 | −0.538269 | − | 0.842773i | \(-0.680921\pi\) | ||||
−0.538269 | + | 0.842773i | \(0.680921\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2351.97 | 0.121487 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14756.2i | 0.759046i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 173.875i | − 0.00890697i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32260.1 | −1.64575 | −0.822875 | − | 0.568223i | \(-0.807631\pi\) | ||||
−0.822875 | + | 0.568223i | \(0.807631\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 4210.89i | − 0.213058i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26453.5i | 1.33299i | 0.745508 | + | 0.666497i | \(0.232207\pi\) | ||||
−0.745508 | + | 0.666497i | \(0.767793\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1727.96 | −0.0867168 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −39397.0 | −1.96907 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 3725.00i | − 0.185421i | −0.995693 | − | 0.0927107i | \(-0.970447\pi\) | ||||
0.995693 | − | 0.0927107i | \(-0.0295532\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5145.12i | 0.255075i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25781.9 | 1.27301 | 0.636505 | − | 0.771273i | \(-0.280379\pi\) | ||||
0.636505 | + | 0.771273i | \(0.280379\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20899.8 | −1.02780 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 5356.04i | − 0.262339i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 13767.9i | − 0.671654i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8267.60 | −0.401716 | −0.200858 | − | 0.979620i | \(-0.564373\pi\) | ||||
−0.200858 | + | 0.979620i | \(0.564373\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18572.5 | 0.898833 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21790.6i | 1.05039i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20675.7i | 0.992694i | 0.868124 | + | 0.496347i | \(0.165326\pi\) | ||||
−0.868124 | + | 0.496347i | \(0.834674\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25401.5 | −1.21478 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8607.01 | −0.409992 | −0.204996 | − | 0.978763i | \(-0.565718\pi\) | ||||
−0.204996 | + | 0.978763i | \(0.565718\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 8132.34i | − 0.385859i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 6396.33i | − 0.302300i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3356.43 | 0.158010 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35697.9 | −1.67399 | −0.836995 | − | 0.547210i | \(-0.815690\pi\) | ||||
−0.836995 | + | 0.547210i | \(0.815690\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3197.92i | 0.149378i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13279.0i | 0.617870i | 0.951083 | + | 0.308935i | \(0.0999726\pi\) | ||||
−0.951083 | + | 0.308935i | \(0.900027\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3295.66 | −0.152753 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1946.82 | −0.0898863 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2339.45i | 0.107599i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 26457.3i | − 1.21218i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 356.288 | 0.0162614 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9407.15 | 0.427714 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 14156.7i | − 0.641209i | −0.947213 | − | 0.320604i | \(-0.896114\pi\) | ||||
0.947213 | − | 0.320604i | \(-0.103886\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 23451.7i | − 1.05818i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1769.08 | −0.0795213 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24950.0 | −1.11728 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20637.9i | 0.920695i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 32003.6i | − 1.42236i | −0.703008 | − | 0.711182i | \(-0.748160\pi\) | ||||
0.703008 | − | 0.711182i | \(-0.251840\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20921.6 | 0.926351 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9328.80 | −0.411507 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 27112.8i | − 1.19152i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9615.06i | 0.420977i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11404.6 | 0.497475 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23023.1 | 1.00056 | 0.500278 | − | 0.865865i | \(-0.333231\pi\) | ||||
0.500278 | + | 0.865865i | \(0.333231\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 16578.4i | − 0.717812i | −0.933374 | − | 0.358906i | \(-0.883150\pi\) | ||||
0.933374 | − | 0.358906i | \(-0.116850\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18723.8i | 0.807716i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10856.6 | −0.466612 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2355.71 | −0.100876 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3194.45i | 0.136292i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5711.11i | 0.242776i | 0.992605 | + | 0.121388i | \(0.0387345\pi\) | ||||
−0.992605 | + | 0.121388i | \(0.961265\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6254.66 | −0.264913 | −0.132457 | − | 0.991189i | \(-0.542287\pi\) | ||||
−0.132457 | + | 0.991189i | \(0.542287\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2864.32 | −0.120876 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30670.6i | 1.28963i | 0.764339 | + | 0.644814i | \(0.223065\pi\) | ||||
−0.764339 | + | 0.644814i | \(0.776935\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34681.9i | 1.45302i | 0.687156 | + | 0.726510i | \(0.258859\pi\) | ||||
−0.687156 | + | 0.726510i | \(0.741141\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16463.6 | −0.687263 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2962.56 | 0.123225 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28671.4i | 1.18828i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 6753.15i | − 0.278881i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11537.3 | −0.474744 | −0.237372 | − | 0.971419i | \(-0.576286\pi\) | ||||
−0.237372 | + | 0.971419i | \(0.576286\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24214.9 | 0.992860 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10136.0i | 0.414119i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 4396.95i | − 0.179006i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27436.6 | 1.11302 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26406.8 | −1.06747 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10832.8i | 0.436363i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 13110.0i | − 0.526233i | −0.964764 | − | 0.263116i | \(-0.915250\pi\) | ||||
0.964764 | − | 0.263116i | \(-0.0847503\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3578.31 | −0.143130 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39493.4 | 1.57418 | 0.787088 | − | 0.616841i | \(-0.211588\pi\) | ||||
0.787088 | + | 0.616841i | \(0.211588\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 27189.9i | − 1.07999i | −0.841669 | − | 0.539994i | \(-0.818427\pi\) | ||||
0.841669 | − | 0.539994i | \(-0.181573\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1452.49i | 0.0574922i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44314.3 | 1.74794 | 0.873972 | − | 0.485976i | \(-0.161536\pi\) | ||||
0.873972 | + | 0.485976i | \(0.161536\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9569.53 | −0.376155 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 3772.61i | − 0.147779i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 48561.2i | − 1.89566i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27568.8 | 1.07248 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1970.98 | 0.0764119 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 9201.28i | − 0.355497i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 43050.0i | − 1.65758i | −0.559563 | − | 0.828788i | \(-0.689031\pi\) | ||||
0.559563 | − | 0.828788i | \(-0.310969\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15104.5 | −0.579593 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21065.2 | 0.805569 | 0.402784 | − | 0.915295i | \(-0.368042\pi\) | ||||
0.402784 | + | 0.915295i | \(0.368042\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38004.2i | 1.44841i | 0.689587 | + | 0.724203i | \(0.257792\pi\) | ||||
−0.689587 | + | 0.724203i | \(0.742208\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2334.32i | 0.0886637i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8568.20 | −0.324343 | −0.162171 | − | 0.986763i | \(-0.551850\pi\) | ||||
−0.162171 | + | 0.986763i | \(0.551850\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14836.2 | 0.559719 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 5869.29i | − 0.220683i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 11704.3i | − 0.438598i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17519.6 | 0.654319 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17775.2 | 0.661645 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3300.51i | 0.122445i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 35383.4i | − 1.30831i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1462.59 | −0.0539002 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −489.678 | −0.0179861 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 26976.9i | − 0.987600i | −0.869575 | − | 0.493800i | \(-0.835607\pi\) | ||||
0.869575 | − | 0.493800i | \(-0.164393\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4017.25i | 0.146583i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48524.9 | 1.76477 | 0.882384 | − | 0.470531i | \(-0.155937\pi\) | ||||
0.882384 | + | 0.470531i | \(0.155937\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43122.3 | 1.56313 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 17352.2i | − 0.626934i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8396.28i | 0.302366i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19675.1 | −0.706227 | −0.353114 | − | 0.935580i | \(-0.614877\pi\) | ||||
−0.353114 | + | 0.935580i | \(0.614877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25026.7 | −0.895395 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18514.0i | 0.660234i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1221.53i | 0.0434203i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3023.96 | 0.107141 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50122.0 | −1.77013 | −0.885065 | − | 0.465468i | \(-0.845886\pi\) | ||||
−0.885065 | + | 0.465468i | \(0.845886\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1657.35i | − 0.0583432i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24215.0i | 0.849692i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 51497.8 | 1.80124 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36136.2 | −1.25989 | −0.629945 | − | 0.776640i | \(-0.716923\pi\) | ||||
−0.629945 | + | 0.776640i | \(0.716923\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 19790.7i | − 0.687800i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14214.9i | 0.492445i | 0.969213 | + | 0.246223i | \(0.0791894\pi\) | ||||
−0.969213 | + | 0.246223i | \(0.920811\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8082.23 | 0.279103 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2221.67 | −0.0764771 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 40485.7i | − 1.38924i | −0.719377 | − | 0.694619i | \(-0.755573\pi\) | ||||
0.719377 | − | 0.694619i | \(-0.244427\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18972.7i | 0.648978i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30791.1 | 1.04992 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39737.8 | 1.35072 | 0.675359 | − | 0.737489i | \(-0.263989\pi\) | ||||
0.675359 | + | 0.737489i | \(0.263989\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30534.9i | 1.03464i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2868.53i | 0.0968929i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3268.19 | 0.110047 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32767.4 | 1.09991 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 17701.6i | − 0.592343i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17265.0i | 0.575936i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1577.22 | −0.0524508 | −0.0262254 | − | 0.999656i | \(-0.508349\pi\) | ||||
−0.0262254 | + | 0.999656i | \(0.508349\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6134.95 | 0.203388 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 3863.04i | − 0.127673i | −0.997960 | − | 0.0638367i | \(-0.979666\pi\) | ||||
0.997960 | − | 0.0638367i | \(-0.0203337\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 15796.0i | − 0.520449i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2004.36 | 0.0658369 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13916.9 | 0.455721 | 0.227861 | − | 0.973694i | \(-0.426827\pi\) | ||||
0.227861 | + | 0.973694i | \(0.426827\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 75107.6i | − 2.45194i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 10455.9i | − 0.340296i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4570.14 | −0.148286 | −0.0741428 | − | 0.997248i | \(-0.523622\pi\) | ||||
−0.0741428 | + | 0.997248i | \(0.523622\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16059.9 | −0.519503 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 7266.81i | − 0.234352i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8138.41i | 0.261665i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19916.6 | 0.638418 | 0.319209 | − | 0.947684i | \(-0.396583\pi\) | ||||
0.319209 | + | 0.947684i | \(0.396583\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33935.1 | 1.08449 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33812.4i | 1.07731i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8951.10i | 0.284337i | 0.989842 | + | 0.142169i | \(0.0454075\pi\) | ||||
−0.989842 | + | 0.142169i | \(0.954592\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2503.05 | −0.0792723 |
(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 | 1344.4.c.a.673.6 | yes | 6 | |
4.3 | odd | 2 | 1344.4.c.d.673.3 | yes | 6 | ||
8.3 | odd | 2 | 1344.4.c.d.673.4 | yes | 6 | ||
8.5 | even | 2 | inner | 1344.4.c.a.673.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.c.a.673.1 | ✓ | 6 | 8.5 | even | 2 | inner | |
1344.4.c.a.673.6 | yes | 6 | 1.1 | even | 1 | trivial | |
1344.4.c.d.673.3 | yes | 6 | 4.3 | odd | 2 | ||
1344.4.c.d.673.4 | yes | 6 | 8.3 | odd | 2 |