Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,3,Mod(639,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.639");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.e (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: | \(34.8774738381\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 640) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 639.5 | ||
Character | \(\chi\) | \(=\) | 1280.639 |
Dual form | 1280.3.e.k.639.6 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 0.933412i | − | 0.311137i | −0.987825 | − | 0.155569i | \(-0.950279\pi\) | ||
0.987825 | − | 0.155569i | \(-0.0497210\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.723593 | + | 4.94736i | 0.144719 | + | 0.989473i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.91082 | 0.987260 | 0.493630 | − | 0.869672i | \(-0.335670\pi\) | ||||
0.493630 | + | 0.869672i | \(0.335670\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.12874 | 0.903194 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.8128 | −1.07389 | −0.536944 | − | 0.843618i | \(-0.680421\pi\) | ||||
−0.536944 | + | 0.843618i | \(0.680421\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.4577 | −1.03521 | −0.517605 | − | 0.855620i | \(-0.673176\pi\) | ||||
−0.517605 | + | 0.855620i | \(0.673176\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.61793 | − | 0.675411i | 0.307862 | − | 0.0450274i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 28.7701i | − | 1.69236i | −0.532899 | − | 0.846179i | \(-0.678898\pi\) | ||
0.532899 | − | 0.846179i | \(-0.321102\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −30.1635 | −1.58755 | −0.793777 | − | 0.608209i | \(-0.791888\pi\) | ||||
−0.793777 | + | 0.608209i | \(0.791888\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 6.45064i | − | 0.307174i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −39.5266 | −1.71855 | −0.859275 | − | 0.511514i | \(-0.829085\pi\) | ||||
−0.859275 | + | 0.511514i | \(0.829085\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.9528 | + | 7.15976i | −0.958113 | + | 0.286390i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 15.9882i | − | 0.592155i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 18.9999i | − | 0.655170i | −0.944822 | − | 0.327585i | \(-0.893765\pi\) | ||
0.944822 | − | 0.327585i | \(-0.106235\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.41602i | − | 0.206968i | −0.994631 | − | 0.103484i | \(-0.967001\pi\) | ||
0.994631 | − | 0.103484i | \(-0.0329991\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.0262i | 0.334127i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.00062 | + | 34.1903i | 0.142875 | + | 0.976867i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 51.5200 | 1.39243 | 0.696217 | − | 0.717832i | \(-0.254865\pi\) | ||||
0.696217 | + | 0.717832i | \(0.254865\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.5616i | 0.322092i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 17.0345 | 0.415477 | 0.207738 | − | 0.978184i | \(-0.433390\pi\) | ||||
0.207738 | + | 0.978184i | \(0.433390\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 58.0207i | − | 1.34932i | −0.738129 | − | 0.674660i | \(-0.764290\pi\) | ||
0.738129 | − | 0.674660i | \(-0.235710\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.88190 | + | 40.2158i | 0.130709 | + | 0.893685i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 48.1230 | 1.02389 | 0.511947 | − | 0.859017i | \(-0.328924\pi\) | ||||
0.511947 | + | 0.859017i | \(0.328924\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.24057 | −0.0253178 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −26.8543 | −0.526556 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.02173 | −0.0758817 | −0.0379409 | − | 0.999280i | \(-0.512080\pi\) | ||||
−0.0379409 | + | 0.999280i | \(0.512080\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.54765 | − | 58.4421i | −0.155412 | − | 1.06258i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 28.1550i | 0.493947i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −45.6972 | −0.774529 | −0.387264 | − | 0.921969i | \(-0.626580\pi\) | ||||
−0.387264 | + | 0.921969i | \(0.626580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 37.8458i | − | 0.620422i | −0.950668 | − | 0.310211i | \(-0.899600\pi\) | ||
0.950668 | − | 0.310211i | \(-0.100400\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 56.1763 | 0.891687 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.73792 | − | 66.5802i | −0.149814 | − | 1.02431i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.82746i | − | 0.0571263i | −0.999592 | − | 0.0285632i | \(-0.990907\pi\) | ||
0.999592 | − | 0.0285632i | \(-0.00909317\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 36.8947i | 0.534705i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 119.629i | − | 1.68492i | −0.538760 | − | 0.842459i | \(-0.681107\pi\) | ||
0.538760 | − | 0.842459i | \(-0.318893\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 82.9311i | 1.13604i | 0.823014 | + | 0.568021i | \(0.192291\pi\) | ||||
−0.823014 | + | 0.568021i | \(0.807709\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.68301 | + | 22.3579i | 0.0891068 | + | 0.298105i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −81.6360 | −1.06021 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 83.2914i | − | 1.05432i | −0.849766 | − | 0.527161i | \(-0.823257\pi\) | ||
0.849766 | − | 0.527161i | \(-0.176743\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 58.2351 | 0.718952 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 115.831i | 1.39555i | 0.716317 | + | 0.697775i | \(0.245826\pi\) | ||||
−0.716317 | + | 0.697775i | \(0.754174\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 142.336 | − | 20.8178i | 1.67454 | − | 0.244916i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −17.7348 | −0.203848 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −54.7938 | −0.615661 | −0.307830 | − | 0.951441i | \(-0.599603\pi\) | ||||
−0.307830 | + | 0.951441i | \(0.599603\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −93.0039 | −1.02202 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.98879 | −0.0643956 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.8261 | − | 149.230i | −0.229749 | − | 1.57084i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 51.8578i | − | 0.534617i | −0.963611 | − | 0.267308i | \(-0.913866\pi\) | ||
0.963611 | − | 0.267308i | \(-0.0861342\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −96.0230 | −0.969929 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.60567i | 0.0356997i | 0.999841 | + | 0.0178498i | \(0.00568208\pi\) | ||||
−0.999841 | + | 0.0178498i | \(0.994318\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.24447 | 0.0800434 | 0.0400217 | − | 0.999199i | \(-0.487257\pi\) | ||||
0.0400217 | + | 0.999199i | \(0.487257\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 31.9137 | − | 4.66764i | 0.303940 | − | 0.0444537i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 52.6034i | − | 0.491620i | −0.969318 | − | 0.245810i | \(-0.920946\pi\) | ||
0.969318 | − | 0.245810i | \(-0.0790540\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 110.432i | 1.01313i | 0.862201 | + | 0.506567i | \(0.169086\pi\) | ||||
−0.862201 | + | 0.506567i | \(0.830914\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 48.0894i | − | 0.433238i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 88.3827i | 0.782148i | 0.920359 | + | 0.391074i | \(0.127896\pi\) | ||||
−0.920359 | + | 0.391074i | \(0.872104\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −28.6012 | − | 195.553i | −0.248706 | − | 1.70046i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −109.394 | −0.934994 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 198.825i | − | 1.67080i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.5416 | 0.153237 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 15.9003i | − | 0.129270i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −52.7541 | − | 113.323i | −0.422032 | − | 0.906581i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −69.5834 | −0.547901 | −0.273950 | − | 0.961744i | \(-0.588330\pi\) | ||||
−0.273950 | + | 0.961744i | \(0.588330\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −54.1573 | −0.419824 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −154.902 | −1.18246 | −0.591230 | − | 0.806503i | \(-0.701357\pi\) | ||||
−0.591230 | + | 0.806503i | \(0.701357\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −208.455 | −1.56733 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 79.0993 | − | 11.5689i | 0.585921 | − | 0.0856959i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 72.4528i | − | 0.528852i | −0.964406 | − | 0.264426i | \(-0.914817\pi\) | ||
0.964406 | − | 0.264426i | \(-0.0851825\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −103.567 | −0.745087 | −0.372544 | − | 0.928015i | \(-0.621514\pi\) | ||||
−0.372544 | + | 0.928015i | \(0.621514\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 44.9186i | − | 0.318572i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 158.973 | 1.11170 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 93.9995 | − | 13.7482i | 0.648273 | − | 0.0948153i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.15797i | 0.00787731i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 115.086i | − | 0.772391i | −0.922417 | − | 0.386195i | \(-0.873789\pi\) | ||
0.922417 | − | 0.386195i | \(-0.126211\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 176.561i | 1.16928i | 0.811293 | + | 0.584640i | \(0.198764\pi\) | ||||
−0.811293 | + | 0.584640i | \(0.801236\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 233.864i | − | 1.52853i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 31.7424 | − | 4.64259i | 0.204790 | − | 0.0299522i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 79.1290 | 0.504006 | 0.252003 | − | 0.967726i | \(-0.418911\pi\) | ||||
0.252003 | + | 0.967726i | \(0.418911\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.75393i | 0.0236096i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −273.161 | −1.69666 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.6626i | 0.0654147i | 0.999465 | + | 0.0327074i | \(0.0104129\pi\) | ||||
−0.999465 | + | 0.0327074i | \(0.989587\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −54.5506 | + | 7.97848i | −0.330610 | + | 0.0483544i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.5606 | 0.117129 | 0.0585647 | − | 0.998284i | \(-0.481348\pi\) | ||||
0.0585647 | + | 0.998284i | \(0.481348\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1103 | 0.0716584 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −245.191 | −1.43387 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 202.219 | 1.16890 | 0.584448 | − | 0.811431i | \(-0.301311\pi\) | ||||
0.584448 | + | 0.811431i | \(0.301311\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −165.534 | + | 49.4798i | −0.945907 | + | 0.282742i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 42.6543i | 0.240985i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 66.7608 | 0.372965 | 0.186483 | − | 0.982458i | \(-0.440291\pi\) | ||||
0.186483 | + | 0.982458i | \(0.440291\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 138.580i | 0.765636i | 0.923824 | + | 0.382818i | \(0.125046\pi\) | ||||
−0.923824 | + | 0.382818i | \(0.874954\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −35.3257 | −0.193037 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 37.2796 | + | 254.888i | 0.201511 | + | 1.37778i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 339.854i | 1.81740i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 110.491i | − | 0.584611i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 61.3227i | 0.321061i | 0.987031 | + | 0.160531i | \(0.0513205\pi\) | ||||
−0.987031 | + | 0.160531i | \(0.948680\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 365.204i | 1.89225i | 0.323800 | + | 0.946126i | \(0.395040\pi\) | ||||
−0.323800 | + | 0.946126i | \(0.604960\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −62.1468 | + | 9.08949i | −0.318702 | + | 0.0466128i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 151.856 | 0.770844 | 0.385422 | − | 0.922740i | \(-0.374056\pi\) | ||||
0.385422 | + | 0.922740i | \(0.374056\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 29.1323i | − | 0.146393i | −0.997318 | − | 0.0731967i | \(-0.976680\pi\) | ||
0.997318 | − | 0.0731967i | \(-0.0233201\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.57260 | −0.0177741 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 131.305i | − | 0.646823i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.3261 | + | 84.2761i | 0.0601272 | + | 0.411103i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −321.302 | −1.55218 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 356.315 | 1.70486 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −227.463 | −1.07802 | −0.539012 | − | 0.842298i | \(-0.681202\pi\) | ||||
−0.539012 | + | 0.842298i | \(0.681202\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −111.663 | −0.524241 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 287.050 | − | 41.9834i | 1.33511 | − | 0.195272i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 44.3399i | − | 0.204332i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 77.4089 | 0.353465 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 387.180i | 1.75194i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.518789 | 0.00232641 | 0.00116320 | − | 0.999999i | \(-0.499630\pi\) | ||||
0.00116320 | + | 0.999999i | \(0.499630\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −194.706 | + | 58.1998i | −0.865361 | + | 0.258666i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 375.370i | − | 1.65361i | −0.562489 | − | 0.826805i | \(-0.690156\pi\) | ||
0.562489 | − | 0.826805i | \(-0.309844\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.43677i | − | 0.0193745i | −0.999953 | − | 0.00968727i | \(-0.996916\pi\) | ||
0.999953 | − | 0.00968727i | \(-0.00308360\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 76.2000i | 0.329870i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 259.393i | − | 1.11328i | −0.830755 | − | 0.556638i | \(-0.812091\pi\) | ||
0.830755 | − | 0.556638i | \(-0.187909\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 34.8215 | + | 238.082i | 0.148177 | + | 1.01312i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −77.7452 | −0.328039 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 389.947i | − | 1.63158i | −0.578351 | − | 0.815788i | \(-0.696304\pi\) | ||
0.578351 | − | 0.815788i | \(-0.303696\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 216.169 | 0.896967 | 0.448483 | − | 0.893791i | \(-0.351964\pi\) | ||||
0.448483 | + | 0.893791i | \(0.351964\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 198.251i | − | 0.815848i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.897670 | − | 6.13756i | −0.00366396 | − | 0.0250513i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 405.932 | 1.64345 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 108.118 | 0.434208 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −181.548 | −0.723300 | −0.361650 | − | 0.932314i | \(-0.617786\pi\) | ||||
−0.361650 | + | 0.932314i | \(0.617786\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 466.919 | 1.84553 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19.4316 | − | 132.858i | −0.0762024 | − | 0.521013i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 256.554i | − | 0.998266i | −0.866525 | − | 0.499133i | \(-0.833652\pi\) | ||
0.866525 | − | 0.499133i | \(-0.166348\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 356.046 | 1.37469 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 154.445i | − | 0.591745i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −379.271 | −1.44209 | −0.721047 | − | 0.692886i | \(-0.756339\pi\) | ||||
−0.721047 | + | 0.692886i | \(0.756339\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.91010 | − | 19.8970i | −0.0109815 | − | 0.0750829i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 51.1452i | 0.191555i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 203.365i | − | 0.756005i | −0.925804 | − | 0.378003i | \(-0.876611\pi\) | ||
0.925804 | − | 0.378003i | \(-0.123389\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 432.023i | 1.59418i | 0.603861 | + | 0.797090i | \(0.293628\pi\) | ||||
−0.603861 | + | 0.797090i | \(0.706372\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 86.8110i | 0.317989i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 282.949 | − | 84.5766i | 1.02891 | − | 0.307551i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −199.461 | −0.720077 | −0.360039 | − | 0.932937i | \(-0.617237\pi\) | ||||
−0.360039 | + | 0.932937i | \(0.617237\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 52.1541i | − | 0.186932i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −382.351 | −1.36068 | −0.680340 | − | 0.732897i | \(-0.738168\pi\) | ||||
−0.680340 | + | 0.732897i | \(0.738168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 300.383i | − | 1.06142i | −0.847552 | − | 0.530712i | \(-0.821925\pi\) | ||
0.847552 | − | 0.530712i | \(-0.178075\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −139.293 | + | 20.3728i | −0.488747 | + | 0.0714834i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 117.723 | 0.410183 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −538.717 | −1.86407 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −48.4047 | −0.166339 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.5540 | 0.0462594 | 0.0231297 | − | 0.999732i | \(-0.492637\pi\) | ||||
0.0231297 | + | 0.999732i | \(0.492637\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −33.0662 | − | 226.081i | −0.112089 | − | 0.766375i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 188.865i | 0.635908i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 531.939 | 1.77906 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 400.971i | − | 1.33213i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.36557 | 0.0111075 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 187.237 | − | 27.3849i | 0.613891 | − | 0.0897867i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 305.607i | 0.995463i | 0.867331 | + | 0.497732i | \(0.165834\pi\) | ||||
−0.867331 | + | 0.497732i | \(0.834166\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 7.69549i | − | 0.0249045i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 266.374i | 0.856509i | 0.903658 | + | 0.428254i | \(0.140871\pi\) | ||||
−0.903658 | + | 0.428254i | \(0.859129\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 507.453i | − | 1.62126i | −0.585561 | − | 0.810628i | \(-0.699126\pi\) | ||
0.585561 | − | 0.810628i | \(-0.300874\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 40.6488 | + | 277.924i | 0.129044 | + | 0.882300i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −425.070 | −1.34092 | −0.670458 | − | 0.741948i | \(-0.733902\pi\) | ||||
−0.670458 | + | 0.741948i | \(0.733902\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 224.442i | 0.703579i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −49.1006 | −0.152962 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 867.807i | 2.68671i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 322.350 | − | 96.3541i | 0.991848 | − | 0.296474i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 103.078 | 0.315224 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 332.570 | 1.01085 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 245.761 | 0.742479 | 0.371240 | − | 0.928537i | \(-0.378933\pi\) | ||||
0.371240 | + | 0.928537i | \(0.378933\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 418.793 | 1.25764 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.9359 | − | 2.76953i | 0.0565249 | − | 0.00826725i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 155.538i | 0.461538i | 0.973009 | + | 0.230769i | \(0.0741241\pi\) | ||||
−0.973009 | + | 0.230769i | \(0.925876\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 82.4975 | 0.243355 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 75.7910i | 0.222261i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −347.204 | −1.01226 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −182.531 | + | 26.6967i | −0.529076 | + | 0.0773818i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 143.795i | − | 0.414395i | −0.978299 | − | 0.207198i | \(-0.933566\pi\) | ||
0.978299 | − | 0.207198i | \(-0.0664343\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 384.926i | 1.10294i | 0.834195 | + | 0.551470i | \(0.185933\pi\) | ||||
−0.834195 | + | 0.551470i | \(0.814067\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 215.164i | 0.613004i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 463.015i | − | 1.31166i | −0.754910 | − | 0.655829i | \(-0.772319\pi\) | ||
0.754910 | − | 0.655829i | \(-0.227681\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 591.849 | − | 86.5629i | 1.66718 | − | 0.243839i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −185.585 | −0.519847 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.1612i | 0.0923711i | 0.998933 | + | 0.0461856i | \(0.0147066\pi\) | ||||
−0.998933 | + | 0.0461856i | \(0.985293\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 548.838 | 1.52033 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 17.3070i | − | 0.0476777i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −410.291 | + | 60.0084i | −1.12408 | + | 0.164407i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 288.141 | 0.785125 | 0.392562 | − | 0.919725i | \(-0.371589\pi\) | ||||
0.392562 | + | 0.919725i | \(0.371589\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 138.469 | 0.375256 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.7935 | −0.0749150 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −139.091 | −0.372898 | −0.186449 | − | 0.982465i | \(-0.559698\pi\) | ||||
−0.186449 | + | 0.982465i | \(0.559698\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −105.777 | + | 49.2413i | −0.282071 | + | 0.131310i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 255.696i | 0.678238i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 384.173 | 1.01365 | 0.506825 | − | 0.862049i | \(-0.330819\pi\) | ||||
0.506825 | + | 0.862049i | \(0.330819\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 64.9500i | 0.170472i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 357.786 | 0.934167 | 0.467084 | − | 0.884213i | \(-0.345305\pi\) | ||||
0.467084 | + | 0.884213i | \(0.345305\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −59.0712 | − | 403.883i | −0.153432 | − | 1.04905i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 471.636i | − | 1.21870i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 511.950i | 1.31607i | 0.752989 | + | 0.658033i | \(0.228611\pi\) | ||||
−0.752989 | + | 0.658033i | \(0.771389\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1137.18i | 2.90840i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 144.588i | 0.367908i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 412.073 | − | 60.2691i | 1.04322 | − | 0.152580i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.0817 | 0.0279137 | 0.0139568 | − | 0.999903i | \(-0.495557\pi\) | ||||
0.0139568 | + | 0.999903i | \(0.495557\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 194.574i | 0.487654i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 679.510 | 1.69454 | 0.847269 | − | 0.531164i | \(-0.178245\pi\) | ||||
0.847269 | + | 0.531164i | \(0.178245\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 86.3450i | 0.214256i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 42.1385 | + | 288.110i | 0.104046 | + | 0.711384i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −608.595 | −1.49532 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −773.907 | −1.89219 | −0.946097 | − | 0.323884i | \(-0.895011\pi\) | ||||
−0.946097 | + | 0.323884i | \(0.895011\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −67.6283 | −0.164546 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −315.805 | −0.764661 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −573.056 | + | 83.8142i | −1.38086 | + | 0.201962i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 96.6709i | 0.231825i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.5511 | −0.0848474 | −0.0424237 | − | 0.999100i | \(-0.513508\pi\) | ||||
−0.0424237 | + | 0.999100i | \(0.513508\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 549.424i | − | 1.30504i | −0.757770 | − | 0.652522i | \(-0.773711\pi\) | ||
0.757770 | − | 0.652522i | \(-0.226289\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 391.180 | 0.924775 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 205.987 | + | 689.125i | 0.484675 | + | 1.62147i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 261.545i | − | 0.612518i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 148.387i | − | 0.345891i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 707.347i | 1.64118i | 0.571520 | + | 0.820588i | \(0.306354\pi\) | ||||
−0.571520 | + | 0.820588i | \(0.693646\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 209.829i | 0.484594i | 0.970202 | + | 0.242297i | \(0.0779008\pi\) | ||||
−0.970202 | + | 0.242297i | \(0.922099\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.8328 | − | 87.7403i | −0.0295006 | − | 0.201702i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1192.26 | 2.72829 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 551.120i | 1.25540i | 0.778456 | + | 0.627699i | \(0.216003\pi\) | ||||
−0.778456 | + | 0.627699i | \(0.783997\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.0843 | −0.0228669 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 374.038i | − | 0.844330i | −0.906519 | − | 0.422165i | \(-0.861270\pi\) | ||
0.906519 | − | 0.422165i | \(-0.138730\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −39.6484 | − | 271.085i | −0.0890976 | − | 0.609180i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −107.423 | −0.240320 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −429.736 | −0.957096 | −0.478548 | − | 0.878061i | \(-0.658837\pi\) | ||||
−0.478548 | + | 0.878061i | \(0.658837\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −201.225 | −0.446176 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 164.804 | 0.363807 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −67.2970 | − | 460.124i | −0.147905 | − | 1.01126i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.8641i | 0.0565953i | 0.999600 | + | 0.0282977i | \(0.00900863\pi\) | ||||
−0.999600 | + | 0.0282977i | \(0.990991\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −459.981 | −1.00214 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 33.7766i | − | 0.0732680i | −0.999329 | − | 0.0366340i | \(-0.988336\pi\) | ||
0.999329 | − | 0.0366340i | \(-0.0116636\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 598.561 | 1.29279 | 0.646394 | − | 0.763004i | \(-0.276276\pi\) | ||||
0.646394 | + | 0.763004i | \(0.276276\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.33345 | − | 29.6287i | −0.00931924 | − | 0.0637177i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 620.732i | 1.32919i | 0.747204 | + | 0.664595i | \(0.231396\pi\) | ||||
−0.747204 | + | 0.664595i | \(0.768604\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 26.4509i | − | 0.0563985i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 73.8600i | − | 0.156815i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 685.386i | 1.44902i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 722.502 | − | 215.964i | 1.52106 | − | 0.454660i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32.6916 | −0.0685359 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 183.309i | 0.382690i | 0.981523 | + | 0.191345i | \(0.0612850\pi\) | ||||
−0.981523 | + | 0.191345i | \(0.938715\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −693.342 | −1.44146 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 254.972i | 0.527893i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 256.559 | − | 37.5240i | 0.528989 | − | 0.0773690i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −311.586 | −0.639807 | −0.319903 | − | 0.947450i | \(-0.603650\pi\) | ||||
−0.319903 | + | 0.947450i | \(0.603650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.95260 | 0.0203530 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −707.884 | −1.44172 | −0.720859 | − | 0.693081i | \(-0.756253\pi\) | ||||
−0.720859 | + | 0.693081i | \(0.756253\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −546.629 | −1.10878 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −69.4816 | − | 475.061i | −0.140367 | − | 0.959719i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 826.736i | − | 1.66345i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 583.958 | 1.17026 | 0.585128 | − | 0.810941i | \(-0.301044\pi\) | ||||
0.585128 | + | 0.810941i | \(0.301044\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 18.2581i | − | 0.0364433i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −767.659 | −1.52616 | −0.763080 | − | 0.646304i | \(-0.776314\pi\) | ||||
−0.763080 | + | 0.646304i | \(0.776314\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.8385 | + | 2.60904i | −0.0353238 | + | 0.00516641i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 11.3039i | − | 0.0222956i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 70.8826i | − | 0.139259i | −0.997573 | − | 0.0696293i | \(-0.977818\pi\) | ||
0.997573 | − | 0.0696293i | \(-0.0221816\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 573.122i | 1.12157i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 482.260i | 0.940077i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.96565 | + | 40.7884i | 0.0115838 | + | 0.0792008i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −568.467 | −1.09955 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 188.754i | − | 0.363688i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −167.378 | −0.321263 | −0.160632 | − | 0.987014i | \(-0.551353\pi\) | ||||
−0.160632 | + | 0.987014i | \(0.551353\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 342.892i | 0.655624i | 0.944743 | + | 0.327812i | \(0.106311\pi\) | ||||
−0.944743 | + | 0.327812i | \(0.893689\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 46.1851 | + | 154.511i | 0.0879716 | + | 0.294307i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −184.589 | −0.350264 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1033.36 | 1.95341 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −371.461 | −0.699549 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −229.246 | −0.430105 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 260.248 | − | 38.0635i | 0.486445 | − | 0.0711467i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 62.3154i | − | 0.116044i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.6546 | 0.0271885 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 176.843i | − | 0.326881i | −0.986553 | − | 0.163441i | \(-0.947741\pi\) | ||
0.986553 | − | 0.163441i | \(-0.0522592\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 129.352 | 0.238218 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −546.345 | + | 79.9075i | −1.00247 | + | 0.146619i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 278.331i | 0.508832i | 0.967095 | + | 0.254416i | \(0.0818832\pi\) | ||||
−0.967095 | + | 0.254416i | \(0.918117\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 307.638i | − | 0.560361i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 573.105i | 1.04012i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 575.612i | − | 1.04089i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 237.916 | − | 34.7972i | 0.428677 | − | 0.0626977i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 445.245 | 0.799363 | 0.399682 | − | 0.916654i | \(-0.369121\pi\) | ||||
0.399682 | + | 0.916654i | \(0.369121\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 780.827i | 1.39683i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 317.224 | 0.565462 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 191.846i | 0.340758i | 0.985379 | + | 0.170379i | \(0.0544991\pi\) | ||||
−0.985379 | + | 0.170379i | \(0.945501\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −437.261 | + | 63.9532i | −0.773914 | + | 0.113191i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 402.452 | 0.709793 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 198.465 | 0.348796 | 0.174398 | − | 0.984675i | \(-0.444202\pi\) | ||||
0.174398 | + | 0.984675i | \(0.444202\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 198.296 | 0.347279 | 0.173639 | − | 0.984809i | \(-0.444447\pi\) | ||||
0.173639 | + | 0.984809i | \(0.444447\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 57.2393 | 0.0998941 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 946.775 | − | 283.001i | 1.64656 | − | 0.492176i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 146.589i | 0.254054i | 0.991899 | + | 0.127027i | \(0.0405435\pi\) | ||||
−0.991899 | + | 0.127027i | \(0.959456\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 340.886 | 0.588750 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 800.484i | 1.37777i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 47.5078 | 0.0814885 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −79.1570 | − | 541.214i | −0.135311 | − | 0.925152i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 167.717i | 0.285718i | 0.989743 | + | 0.142859i | \(0.0456296\pi\) | ||||
−0.989743 | + | 0.142859i | \(0.954370\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 193.530i | 0.328573i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 141.745i | − | 0.239839i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 443.963i | 0.748674i | 0.927293 | + | 0.374337i | \(0.122130\pi\) | ||||
−0.927293 | + | 0.374337i | \(0.877870\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 983.659 | − | 143.868i | 1.65321 | − | 0.241795i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −27.1924 | −0.0455485 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 426.294i | − | 0.711676i | −0.934548 | − | 0.355838i | \(-0.884195\pi\) | ||
0.934548 | − | 0.355838i | \(-0.115805\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −54.1068 | −0.0900279 | −0.0450140 | − | 0.998986i | \(-0.514333\pi\) | ||||
−0.0450140 | + | 0.998986i | \(0.514333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 31.1125i | − | 0.0515961i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.4166 | + | 91.7323i | 0.0221762 | + | 0.151624i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −408.990 | −0.673790 | −0.336895 | − | 0.941542i | \(-0.609377\pi\) | ||||
−0.336895 | + | 0.941542i | \(0.609377\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −122.562 | −0.201251 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −647.626 | −1.05994 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −185.150 | −0.302039 | −0.151020 | − | 0.988531i | \(-0.548256\pi\) | ||||
−0.151020 | + | 0.988531i | \(0.548256\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 78.6643 | − | 11.5053i | 0.127909 | − | 0.0187078i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 415.587i | 0.673561i | 0.941583 | + | 0.336781i | \(0.109338\pi\) | ||||
−0.941583 | + | 0.336781i | \(0.890662\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 935.377 | 1.51111 | 0.755555 | − | 0.655086i | \(-0.227367\pi\) | ||||
0.755555 | + | 0.655086i | \(0.227367\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 631.959i | 1.01765i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −378.670 | −0.607817 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 522.476 | − | 342.993i | 0.835961 | − | 0.548789i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 332.589i | − | 0.530444i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1482.24i | − | 2.35649i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 366.911i | 0.581475i | 0.956803 | + | 0.290738i | \(0.0939007\pi\) | ||||
−0.956803 | + | 0.290738i | \(0.906099\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 212.317i | 0.335414i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −50.3501 | − | 344.254i | −0.0792915 | − | 0.542133i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.6953 | 0.0262092 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 972.435i | − | 1.52181i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −627.281 | −0.978597 | −0.489299 | − | 0.872116i | \(-0.662747\pi\) | ||||
−0.489299 | + | 0.872116i | \(0.662747\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1231.97i | − | 1.91598i | −0.286808 | − | 0.957988i | \(-0.592594\pi\) | ||
0.286808 | − | 0.957988i | \(-0.407406\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −39.1878 | − | 267.936i | −0.0607563 | − | 0.415404i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 341.377 | 0.527630 | 0.263815 | − | 0.964573i | \(-0.415019\pi\) | ||||
0.263815 | + | 0.964573i | \(0.415019\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 539.811 | 0.831758 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −41.3874 | −0.0635752 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −404.426 | −0.619336 | −0.309668 | − | 0.950845i | \(-0.600218\pi\) | ||||
−0.309668 | + | 0.950845i | \(0.600218\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −112.086 | − | 766.358i | −0.171124 | − | 1.17001i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 674.126i | 1.02607i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −161.287 | −0.244745 | −0.122373 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122373 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 630.605i | 0.954017i | 0.878899 | + | 0.477009i | \(0.158279\pi\) | ||||
−0.878899 | + | 0.477009i | \(0.841721\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 361.398 | 0.545095 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −150.836 | − | 1031.30i | −0.226822 | − | 1.55083i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 751.003i | 1.12594i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 0.484244i | − | 0.000723833i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 447.064i | 0.666265i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 799.682i | − | 1.18823i | −0.804378 | − | 0.594117i | \(-0.797501\pi\) | ||
0.804378 | − | 0.594117i | \(-0.202499\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 114.472 | + | 382.962i | 0.169587 | + | 0.567351i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 473.351 | 0.699189 | 0.349595 | − | 0.936901i | \(-0.386319\pi\) | ||||
0.349595 | + | 0.936901i | \(0.386319\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 358.380i | − | 0.527805i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −350.375 | −0.514500 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 421.137i | − | 0.616598i | −0.951289 | − | 0.308299i | \(-0.900240\pi\) | ||
0.951289 | − | 0.308299i | \(-0.0997597\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 358.450 | − | 52.4263i | 0.523285 | − | 0.0765348i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.14134 | −0.00602814 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 54.1233 | 0.0785535 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 103.427 | 0.149677 | 0.0748387 | − | 0.997196i | \(-0.476156\pi\) | ||||
0.0748387 | + | 0.997196i | \(0.476156\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −663.598 | −0.957572 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −74.9405 | − | 512.384i | −0.107828 | − | 0.737244i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 490.085i | − | 0.703135i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −242.121 | −0.346382 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1025.80i | − | 1.46333i | −0.681664 | − | 0.731666i | \(-0.738743\pi\) | ||
0.681664 | − | 0.731666i | \(-0.261257\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1554.03 | −2.21056 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 222.229 | − | 32.5028i | 0.315218 | − | 0.0461033i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.9181i | 0.0352448i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1216.11i | 1.71525i | 0.514279 | + | 0.857623i | \(0.328059\pi\) | ||||
−0.514279 | + | 0.857623i | \(0.671941\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 677.054i | − | 0.952257i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 253.604i | 0.355685i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 115.032 | + | 786.497i | 0.160884 | + | 1.10000i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −363.981 | −0.507644 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1009.14i | − | 1.40353i | −0.712407 | − | 0.701767i | \(-0.752395\pi\) | ||
0.712407 | − | 0.701767i | \(-0.247605\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 56.9761 | 0.0790237 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 201.775i | − | 0.279080i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 136.035 | + | 455.102i | 0.187634 | + | 0.627727i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 94.2492 | 0.129641 | 0.0648206 | − | 0.997897i | \(-0.479352\pi\) | ||||
0.0648206 | + | 0.997897i | \(0.479352\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 339.066 | 0.465111 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1669.26 | −2.28353 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 504.116 | 0.687743 | 0.343872 | − | 0.939017i | \(-0.388262\pi\) | ||||
0.343872 | + | 0.939017i | \(0.388262\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.72888 | + | 0.837896i | −0.00779439 | + | 0.00113999i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 45.2130i | 0.0613473i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −117.256 | −0.158669 | −0.0793343 | − | 0.996848i | \(-0.525279\pi\) | ||||
−0.0793343 | + | 0.996848i | \(0.525279\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 378.902i | − | 0.511339i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 790.636 | 1.06411 | 0.532056 | − | 0.846709i | \(-0.321419\pi\) | ||||
0.532056 | + | 0.846709i | \(0.321419\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 569.374 | − | 83.2757i | 0.764260 | − | 0.111779i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 941.557i | 1.26045i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 363.533i | − | 0.485357i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 310.766i | 0.413803i | 0.978362 | + | 0.206901i | \(0.0663380\pi\) | ||||
−0.978362 | + | 0.206901i | \(0.933662\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 169.459i | 0.225046i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −873.513 | + | 127.759i | −1.15697 | + | 0.169217i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −540.769 | −0.714358 | −0.357179 | − | 0.934036i | \(-0.616261\pi\) | ||||
−0.357179 | + | 0.934036i | \(0.616261\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 435.828i | − | 0.574214i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.6841 | 0.0376926 | 0.0188463 | − | 0.999822i | \(-0.494001\pi\) | ||||
0.0188463 | + | 0.999822i | \(0.494001\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 763.172i | 1.00023i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1157.01 | − | 169.223i | 1.51244 | − | 0.221206i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 614.980 | 0.801799 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −704.747 | −0.916447 | −0.458223 | − | 0.888837i | \(-0.651514\pi\) | ||||
−0.458223 | + | 0.888837i | \(0.651514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −239.471 | −0.310598 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −74.4042 | −0.0962538 | −0.0481269 | − | 0.998841i | \(-0.515325\pi\) | ||||
−0.0481269 | + | 0.998841i | \(0.515325\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45.9371 | + | 153.682i | 0.0592737 | + | 0.198299i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 332.337i | − | 0.427719i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −513.822 | −0.659592 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1413.15i | 1.80941i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −303.774 | −0.387962 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 57.2572 | + | 391.480i | 0.0729391 | + | 0.498700i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1039.46i | − | 1.32079i | −0.750918 | − | 0.660396i | \(-0.770388\pi\) | ||
0.750918 | − | 0.660396i | \(-0.229612\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 354.016i | 0.448689i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 610.797i | 0.772183i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 509.318i | 0.642267i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.5721 | + | 2.71632i | −0.0233611 | + | 0.00341676i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1215.20 | 1.52472 | 0.762360 | − | 0.647153i | \(-0.224040\pi\) | ||||
0.762360 | + | 0.647153i | \(0.224040\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1384.50i | − | 1.73280i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −445.405 | −0.556061 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 979.647i | − | 1.21998i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −197.658 | − | 1351.43i | −0.245538 | − | 1.67879i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −189.824 | −0.235222 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −888.501 | −1.09827 | −0.549135 | − | 0.835733i | \(-0.685043\pi\) | ||||
−0.549135 | + | 0.835733i | \(0.685043\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1255.39 | −1.54796 | −0.773978 | − | 0.633212i | \(-0.781736\pi\) | ||||
−0.773978 | + | 0.633212i | \(0.781736\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 403.255 | 0.496009 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −52.7517 | + | 7.71539i | −0.0647261 | + | 0.00946673i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1750.11i | 2.14212i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −756.005 | −0.923082 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 952.864i | − | 1.16061i | −0.814398 | − | 0.580307i | \(-0.802933\pi\) | ||
0.814398 | − | 0.580307i | \(-0.197067\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1353.86 | 1.64503 | 0.822514 | − | 0.568745i | \(-0.192571\pi\) | ||||
0.822514 | + | 0.568745i | \(0.192571\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −78.9449 | − | 264.108i | −0.0956908 | − | 0.320131i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1590.93i | − | 1.92373i | −0.273521 | − | 0.961866i | \(-0.588188\pi\) | ||
0.273521 | − | 0.961866i | \(-0.411812\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 266.156i | − | 0.321057i | −0.987031 | − | 0.160528i | \(-0.948680\pi\) | ||
0.987031 | − | 0.160528i | \(-0.0513198\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 186.180i | 0.224043i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.6914i | 0.0428468i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.1539 | + | 96.7734i | 0.0169508 | + | 0.115896i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −102.580 | −0.122557 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 531.574i | − | 0.633581i | −0.948496 | − | 0.316790i | \(-0.897395\pi\) | ||
0.948496 | − | 0.316790i | \(-0.102605\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 480.003 | 0.570753 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 356.891i | 0.423358i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.76291 | + | 59.9139i | 0.0103703 | + | 0.0709040i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 128.138 | 0.151284 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −280.381 | −0.330248 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2036.41 | −2.39297 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1363.88 | 1.59892 | 0.799459 | − | 0.600720i | \(-0.205119\pi\) | ||||
0.799459 | + | 0.600720i | \(0.205119\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −177.419 | − | 1213.05i | −0.207508 | − | 1.41877i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 649.944i | − | 0.758395i | −0.925316 | − | 0.379197i | \(-0.876200\pi\) | ||
0.925316 | − | 0.379197i | \(-0.123800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 551.416 | 0.641927 | 0.320964 | − | 0.947092i | \(-0.395993\pi\) | ||||
0.320964 | + | 0.947092i | \(0.395993\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 109.884i | − | 0.127623i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 443.453 | 0.513851 | 0.256926 | − | 0.966431i | \(-0.417290\pi\) | ||||
0.256926 | + | 0.966431i | \(0.417290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 146.324 | + | 1000.45i | 0.169161 | + | 1.15659i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 502.845i | 0.579983i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 983.903i | 1.13222i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 51.5089i | 0.0591377i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 421.539i | − | 0.482862i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −364.574 | − | 783.152i | −0.416656 | − | 0.895031i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1131.01 | 1.28964 | 0.644819 | − | 0.764336i | \(-0.276933\pi\) | ||||
0.644819 | + | 0.764336i | \(0.276933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 12.6515i | − | 0.0143930i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 180.319 | 0.204675 | 0.102338 | − | 0.994750i | \(-0.467368\pi\) | ||||
0.102338 | + | 0.994750i | \(0.467368\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 561.730i | 0.636161i | 0.948064 | + | 0.318080i | \(0.103038\pi\) | ||||
−0.948064 | + | 0.318080i | \(0.896962\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −211.026 | + | 30.8644i | −0.238448 | + | 0.0348750i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 602.367 | 0.679106 | 0.339553 | − | 0.940587i | \(-0.389724\pi\) | ||||
0.339553 | + | 0.940587i | \(0.389724\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −480.878 | −0.540921 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −687.918 | −0.772074 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1451.56 | −1.62549 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 48.3077 | + | 330.290i | 0.0539751 | + | 0.369039i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 496.518i | − | 0.553532i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −121.904 | −0.135599 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 115.706i | 0.128419i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −374.271 | −0.414475 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −685.606 | + | 100.276i | −0.757576 | + | 0.110802i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1581.18i | − | 1.74330i | −0.490127 | − | 0.871651i | \(-0.663049\pi\) | ||
0.490127 | − | 0.871651i | \(-0.336951\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.3095i | 0.0322437i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 407.039i | − | 0.446805i | −0.974726 | − | 0.223402i | \(-0.928284\pi\) | ||
0.974726 | − | 0.223402i | \(-0.0717164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1368.28i | − | 1.49866i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −25.5614 | − | 174.769i | −0.0279360 | − | 0.191004i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1070.50 | −1.16740 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 330.930i | 0.360098i | 0.983658 | + | 0.180049i | \(0.0576256\pi\) | ||||
−0.983658 | + | 0.180049i | \(0.942374\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 285.257 | 0.309726 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1609.94i | 1.74424i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1234.05 | + | 368.871i | −1.33411 | + | 0.398780i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 67.0172 | 0.0722947 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 713.506 | 0.768036 | 0.384018 | − | 0.923326i | \(-0.374540\pi\) | ||||
0.384018 | + | 0.923326i | \(0.374540\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.4200 | 0.0401934 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 248.637 | 0.266492 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1681.38 | + | 245.916i | −1.79827 | + | 0.263012i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 309.292i | − | 0.330087i | −0.986286 | − | 0.165044i | \(-0.947223\pi\) | ||
0.986286 | − | 0.165044i | \(-0.0527765\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −473.663 | −0.504434 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 439.051i | − | 0.466579i | −0.972407 | − | 0.233290i | \(-0.925051\pi\) | ||
0.972407 | − | 0.233290i | \(-0.0749490\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −673.318 | −0.714017 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 546.641 | − | 79.9509i | 0.578456 | − | 0.0846041i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 52.2559i | − | 0.0551804i | −0.999619 | − | 0.0275902i | \(-0.991217\pi\) | ||
0.999619 | − | 0.0275902i | \(-0.00878335\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1116.06i | − | 1.17604i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 396.766i | 0.417209i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 138.100i | 0.144911i | 0.997372 | + | 0.0724553i | \(0.0230835\pi\) | ||||
−0.997372 | + | 0.0724553i | \(0.976917\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −303.385 | + | 44.3727i | −0.317681 | + | 0.0464635i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 209.497 | 0.218910 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 500.708i | − | 0.522115i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 919.835 | 0.957164 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 427.599i | − | 0.444028i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1806.80 | + | 264.260i | −1.87233 | + | 0.273844i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1231.77 | −1.27380 | −0.636902 | − | 0.770945i | \(-0.719784\pi\) | ||||
−0.636902 | + | 0.770945i | \(0.719784\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 810.021 | 0.835935 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −198.353 | −0.204277 | −0.102138 | − | 0.994770i | \(-0.532568\pi\) | ||||
−0.102138 | + | 0.994770i | \(0.532568\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −715.734 | −0.735595 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −89.9381 | − | 300.886i | −0.0922442 | − | 0.308601i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1521.90i | − | 1.55773i | −0.627194 | − | 0.778863i | \(-0.715797\pi\) | ||
0.627194 | − | 0.778863i | \(-0.284203\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 647.267 | 0.661151 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 897.669i | 0.915055i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −313.432 | −0.318852 | −0.159426 | − | 0.987210i | \(-0.550964\pi\) | ||||
−0.159426 | + | 0.987210i | \(0.550964\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 109.882 | + | 751.289i | 0.111556 | + | 0.762730i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 310.425i | − | 0.314513i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2293.36i | 2.31887i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 751.646i | 0.758472i | 0.925300 | + | 0.379236i | \(0.123813\pi\) | ||||
−0.925300 | + | 0.379236i | \(0.876187\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 229.396i | − | 0.231013i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 144.128 | − | 21.0799i | 0.144852 | − | 0.0211859i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 589.360 | 0.591134 | 0.295567 | − | 0.955322i | \(-0.404491\pi\) | ||||
0.295567 | + | 0.955322i | \(0.404491\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 823.711i | − | 0.824536i |
(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 | 1280.3.e.k.639.5 | 24 | ||
4.3 | odd | 2 | 1280.3.e.l.639.20 | 24 | |||
5.4 | even | 2 | inner | 1280.3.e.k.639.20 | 24 | ||
8.3 | odd | 2 | inner | 1280.3.e.k.639.19 | 24 | ||
8.5 | even | 2 | 1280.3.e.l.639.6 | 24 | |||
16.3 | odd | 4 | 640.3.h.b.639.11 | yes | 24 | ||
16.5 | even | 4 | 640.3.h.a.639.11 | ✓ | 24 | ||
16.11 | odd | 4 | 640.3.h.a.639.14 | yes | 24 | ||
16.13 | even | 4 | 640.3.h.b.639.14 | yes | 24 | ||
20.19 | odd | 2 | 1280.3.e.l.639.5 | 24 | |||
40.19 | odd | 2 | inner | 1280.3.e.k.639.6 | 24 | ||
40.29 | even | 2 | 1280.3.e.l.639.19 | 24 | |||
80.19 | odd | 4 | 640.3.h.b.639.13 | yes | 24 | ||
80.29 | even | 4 | 640.3.h.b.639.12 | yes | 24 | ||
80.59 | odd | 4 | 640.3.h.a.639.12 | yes | 24 | ||
80.69 | even | 4 | 640.3.h.a.639.13 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.3.h.a.639.11 | ✓ | 24 | 16.5 | even | 4 | ||
640.3.h.a.639.12 | yes | 24 | 80.59 | odd | 4 | ||
640.3.h.a.639.13 | yes | 24 | 80.69 | even | 4 | ||
640.3.h.a.639.14 | yes | 24 | 16.11 | odd | 4 | ||
640.3.h.b.639.11 | yes | 24 | 16.3 | odd | 4 | ||
640.3.h.b.639.12 | yes | 24 | 80.29 | even | 4 | ||
640.3.h.b.639.13 | yes | 24 | 80.19 | odd | 4 | ||
640.3.h.b.639.14 | yes | 24 | 16.13 | even | 4 | ||
1280.3.e.k.639.5 | 24 | 1.1 | even | 1 | trivial | ||
1280.3.e.k.639.6 | 24 | 40.19 | odd | 2 | inner | ||
1280.3.e.k.639.19 | 24 | 8.3 | odd | 2 | inner | ||
1280.3.e.k.639.20 | 24 | 5.4 | even | 2 | inner | ||
1280.3.e.l.639.5 | 24 | 20.19 | odd | 2 | |||
1280.3.e.l.639.6 | 24 | 8.5 | even | 2 | |||
1280.3.e.l.639.19 | 24 | 40.29 | even | 2 | |||
1280.3.e.l.639.20 | 24 | 4.3 | odd | 2 |