Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6864,2,Mod(1,6864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6864.a (trivial) |
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: | yes |
Analytic conductor: | \(54.8093159474\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1716) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.51414\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6864.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.51414 | −0.677143 | −0.338571 | − | 0.940941i | \(-0.609944\pi\) | ||||
−0.338571 | + | 0.940941i | \(0.609944\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.32088 | 0.499247 | 0.249624 | − | 0.968343i | \(-0.419693\pi\) | ||||
0.249624 | + | 0.968343i | \(0.419693\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.51414 | 0.390948 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.83502 | −1.17266 | −0.586332 | − | 0.810071i | \(-0.699429\pi\) | ||||
−0.586332 | + | 0.810071i | \(0.699429\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.32088 | −1.22069 | −0.610347 | − | 0.792134i | \(-0.708970\pi\) | ||||
−0.610347 | + | 0.792134i | \(0.708970\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.32088 | −0.288241 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.73566 | −1.82151 | −0.910756 | − | 0.412945i | \(-0.864500\pi\) | ||||
−0.910756 | + | 0.412945i | \(0.864500\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.70739 | −0.541478 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.4485 | 1.94024 | 0.970120 | − | 0.242624i | \(-0.0780081\pi\) | ||||
0.970120 | + | 0.242624i | \(0.0780081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.485863 | −0.0872636 | −0.0436318 | − | 0.999048i | \(-0.513893\pi\) | ||||
−0.0436318 | + | 0.999048i | \(0.513893\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.64177 | 0.434304 | 0.217152 | − | 0.976138i | \(-0.430323\pi\) | ||||
0.217152 | + | 0.976138i | \(0.430323\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.7357 | 1.67663 | 0.838314 | − | 0.545187i | \(-0.183541\pi\) | ||||
0.838314 | + | 0.545187i | \(0.183541\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.193252 | 0.0294707 | 0.0147354 | − | 0.999891i | \(-0.495309\pi\) | ||||
0.0147354 | + | 0.999891i | \(0.495309\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.51414 | −0.225714 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.02827 | −0.733449 | −0.366725 | − | 0.930330i | \(-0.619521\pi\) | ||||
−0.366725 | + | 0.930330i | \(0.619521\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.25526 | −0.750752 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.83502 | 0.677038 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.67004 | −1.05356 | −0.526781 | − | 0.850001i | \(-0.676601\pi\) | ||||
−0.526781 | + | 0.850001i | \(0.676601\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.51414 | 0.204166 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.32088 | 0.704768 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.02827 | 0.915003 | 0.457502 | − | 0.889209i | \(-0.348744\pi\) | ||||
0.457502 | + | 0.889209i | \(0.348744\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.25526 | 0.800905 | 0.400452 | − | 0.916318i | \(-0.368853\pi\) | ||||
0.400452 | + | 0.916318i | \(0.368853\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.32088 | 0.166416 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.51414 | 0.187806 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.18418 | −1.12203 | −0.561013 | − | 0.827807i | \(-0.689588\pi\) | ||||
−0.561013 | + | 0.827807i | \(0.689588\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.73566 | 1.05165 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.6983 | −1.74437 | −0.872185 | − | 0.489177i | \(-0.837297\pi\) | ||||
−0.872185 | + | 0.489177i | \(0.837297\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.9909 | 1.28639 | 0.643195 | − | 0.765702i | \(-0.277608\pi\) | ||||
0.643195 | + | 0.765702i | \(0.277608\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.70739 | 0.312622 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.32088 | −0.150529 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.5051 | 1.85696 | 0.928482 | − | 0.371376i | \(-0.121114\pi\) | ||||
0.928482 | + | 0.371376i | \(0.121114\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.386505 | −0.0424244 | −0.0212122 | − | 0.999775i | \(-0.506753\pi\) | ||||
−0.0212122 | + | 0.999775i | \(0.506753\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.32088 | 0.794061 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.4485 | −1.12020 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.92892 | −0.310464 | −0.155232 | − | 0.987878i | \(-0.549613\pi\) | ||||
−0.155232 | + | 0.987878i | \(0.549613\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.32088 | −0.138466 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.485863 | 0.0503817 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.05655 | 0.826584 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.64177 | −0.674369 | −0.337185 | − | 0.941439i | \(-0.609475\pi\) | ||||
−0.337185 | + | 0.941439i | \(0.609475\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.4768 | 1.54000 | 0.769999 | − | 0.638045i | \(-0.220257\pi\) | ||||
0.769999 | + | 0.638045i | \(0.220257\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.22699 | 0.317965 | 0.158982 | − | 0.987281i | \(-0.449179\pi\) | ||||
0.158982 | + | 0.987281i | \(0.449179\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.25526 | 0.218025 | 0.109012 | − | 0.994040i | \(-0.465231\pi\) | ||||
0.109012 | + | 0.994040i | \(0.465231\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.1222 | 1.25688 | 0.628438 | − | 0.777860i | \(-0.283695\pi\) | ||||
0.628438 | + | 0.777860i | \(0.283695\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.64177 | −0.250746 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.25526 | −0.776590 | −0.388295 | − | 0.921535i | \(-0.626936\pi\) | ||||
−0.388295 | + | 0.921535i | \(0.626936\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.2270 | 1.23342 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.38650 | −0.585450 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.7357 | −0.968002 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.6700 | 1.04380 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.22153 | 0.818278 | 0.409139 | − | 0.912472i | \(-0.365829\pi\) | ||||
0.409139 | + | 0.912472i | \(0.365829\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.193252 | −0.0170149 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.9253 | −1.74088 | −0.870441 | − | 0.492273i | \(-0.836166\pi\) | ||||
−0.870441 | + | 0.492273i | \(0.836166\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.02827 | −0.609429 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.51414 | 0.130316 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.92892 | −0.250234 | −0.125117 | − | 0.992142i | \(-0.539931\pi\) | ||||
−0.125117 | + | 0.992142i | \(0.539931\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.80675 | 0.153246 | 0.0766232 | − | 0.997060i | \(-0.475586\pi\) | ||||
0.0766232 | + | 0.997060i | \(0.475586\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.02827 | 0.423457 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.8205 | −1.31382 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.25526 | 0.433447 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.1504 | −0.831557 | −0.415778 | − | 0.909466i | \(-0.636491\pi\) | ||||
−0.415778 | + | 0.909466i | \(0.636491\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.96265 | 0.647992 | 0.323996 | − | 0.946059i | \(-0.394974\pi\) | ||||
0.323996 | + | 0.946059i | \(0.394974\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.83502 | −0.390888 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.735663 | 0.0590899 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.3492 | −1.46442 | −0.732211 | − | 0.681078i | \(-0.761512\pi\) | ||||
−0.732211 | + | 0.681078i | \(0.761512\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.67004 | 0.608274 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.5388 | −0.909385 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.8259 | 1.70954 | 0.854770 | − | 0.519007i | \(-0.173698\pi\) | ||||
0.854770 | + | 0.519007i | \(0.173698\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.51414 | −0.117875 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.9819 | −1.70101 | −0.850503 | − | 0.525969i | \(-0.823703\pi\) | ||||
−0.850503 | + | 0.525969i | \(0.823703\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.32088 | −0.406898 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.50506 | −0.190457 | −0.0952283 | − | 0.995455i | \(-0.530358\pi\) | ||||
−0.0952283 | + | 0.995455i | \(0.530358\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.57615 | −0.270331 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.02827 | −0.528277 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.7074 | 1.02454 | 0.512269 | − | 0.858825i | \(-0.328805\pi\) | ||||
0.512269 | + | 0.858825i | \(0.328805\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.6892 | 1.90947 | 0.954733 | − | 0.297463i | \(-0.0961406\pi\) | ||||
0.954733 | + | 0.297463i | \(0.0961406\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.25526 | −0.462402 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.83502 | 0.353572 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.32088 | −0.0960802 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.9536 | −1.37143 | −0.685716 | − | 0.727869i | \(-0.740511\pi\) | ||||
−0.685716 | + | 0.727869i | \(0.740511\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.934380 | −0.0672581 | −0.0336291 | − | 0.999434i | \(-0.510706\pi\) | ||||
−0.0336291 | + | 0.999434i | \(0.510706\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.51414 | −0.108430 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.99093 | −0.355589 | −0.177794 | − | 0.984068i | \(-0.556896\pi\) | ||||
−0.177794 | + | 0.984068i | \(0.556896\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000 | 0.283552 | 0.141776 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141776 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.18418 | 0.647802 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.8013 | 0.968660 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.2553 | −1.13532 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.73566 | −0.607171 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.32088 | 0.368053 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.6363 | 1.00760 | 0.503802 | − | 0.863819i | \(-0.331934\pi\) | ||||
0.503802 | + | 0.863819i | \(0.331934\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.6983 | 1.00711 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.292611 | −0.0199559 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.641769 | −0.0435661 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.9909 | −0.742698 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.83502 | 0.325239 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.9108 | −1.66815 | −0.834074 | − | 0.551652i | \(-0.813998\pi\) | ||||
−0.834074 | + | 0.551652i | \(0.813998\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.70739 | −0.180493 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.60442 | 0.571096 | 0.285548 | − | 0.958364i | \(-0.407824\pi\) | ||||
0.285548 | + | 0.958364i | \(0.407824\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.3684 | −1.74247 | −0.871235 | − | 0.490866i | \(-0.836680\pi\) | ||||
−0.871235 | + | 0.490866i | \(0.836680\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.32088 | 0.0869078 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.75020 | −0.376708 | −0.188354 | − | 0.982101i | \(-0.560315\pi\) | ||||
−0.188354 | + | 0.982101i | \(0.560315\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.61350 | 0.496650 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.5051 | −1.07212 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.3209 | −0.991026 | −0.495513 | − | 0.868601i | \(-0.665020\pi\) | ||||
−0.495513 | + | 0.868601i | \(0.665020\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.3118 | 1.43723 | 0.718615 | − | 0.695408i | \(-0.244776\pi\) | ||||
0.718615 | + | 0.695408i | \(0.244776\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.95719 | 0.508366 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.32088 | 0.338560 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.386505 | 0.0244938 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.4431 | 1.16412 | 0.582058 | − | 0.813148i | \(-0.302248\pi\) | ||||
0.582058 | + | 0.813148i | \(0.302248\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.73566 | 0.549206 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.32088 | −0.458452 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.4713 | 0.715562 | 0.357781 | − | 0.933806i | \(-0.383533\pi\) | ||||
0.357781 | + | 0.933806i | \(0.383533\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.48947 | 0.216825 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.4485 | 0.646747 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.31181 | 0.512528 | 0.256264 | − | 0.966607i | \(-0.417508\pi\) | ||||
0.256264 | + | 0.966607i | \(0.417508\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.6135 | 0.713411 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.92892 | 0.179247 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.4431 | 1.24643 | 0.623217 | − | 0.782049i | \(-0.285825\pi\) | ||||
0.623217 | + | 0.782049i | \(0.285825\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.2926 | 1.11120 | 0.555598 | − | 0.831451i | \(-0.312489\pi\) | ||||
0.555598 | + | 0.831451i | \(0.312489\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.32088 | 0.0799436 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.70739 | 0.163262 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.5279 | 1.29348 | 0.646742 | − | 0.762709i | \(-0.276131\pi\) | ||||
0.646742 | + | 0.762709i | \(0.276131\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.485863 | −0.0290879 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.57615 | −0.571265 | −0.285633 | − | 0.958339i | \(-0.592204\pi\) | ||||
−0.285633 | + | 0.958339i | \(0.592204\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.38104 | 0.141538 | 0.0707691 | − | 0.997493i | \(-0.477455\pi\) | ||||
0.0707691 | + | 0.997493i | \(0.477455\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.05655 | −0.477229 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.1806 | 0.837053 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.37743 | 0.375143 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.64177 | 0.389347 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.8031 | 0.981650 | 0.490825 | − | 0.871258i | \(-0.336695\pi\) | ||||
0.490825 | + | 0.871258i | \(0.336695\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.6418 | −0.619588 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.73566 | 0.505196 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.255264 | 0.0147132 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.4768 | −0.889118 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.47133 | −0.542327 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.6044 | 1.74669 | 0.873343 | − | 0.487105i | \(-0.161947\pi\) | ||||
0.873343 | + | 0.487105i | \(0.161947\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.22699 | −0.183577 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34.0192 | 1.92905 | 0.964526 | − | 0.263988i | \(-0.0850379\pi\) | ||||
0.964526 | + | 0.263988i | \(0.0850379\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.0192 | 0.679365 | 0.339683 | − | 0.940540i | \(-0.389680\pi\) | ||||
0.339683 | + | 0.940540i | \(0.389680\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.00000 | −0.112687 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.6382 | 0.878327 | 0.439163 | − | 0.898407i | \(-0.355275\pi\) | ||||
0.439163 | + | 0.898407i | \(0.355275\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.4485 | −0.585005 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.25526 | −0.125877 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.7266 | 1.43147 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.70739 | 0.150179 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.1222 | −0.725658 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.64177 | −0.366173 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.1276 | 0.941420 | 0.470710 | − | 0.882288i | \(-0.343998\pi\) | ||||
0.470710 | + | 0.882288i | \(0.343998\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.64177 | 0.144768 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.9061 | 0.759772 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.8013 | −1.18759 | −0.593796 | − | 0.804616i | \(-0.702371\pi\) | ||||
−0.593796 | + | 0.804616i | \(0.702371\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.25526 | 0.448364 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.485863 | 0.0263110 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.1878 | −0.874058 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.2270 | −0.712117 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.6418 | 0.893377 | 0.446688 | − | 0.894690i | \(-0.352603\pi\) | ||||
0.446688 | + | 0.894690i | \(0.352603\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.1979 | 1.88410 | 0.942051 | − | 0.335471i | \(-0.108895\pi\) | ||||
0.942051 | + | 0.335471i | \(0.108895\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.7411 | 1.52974 | 0.764868 | − | 0.644187i | \(-0.222804\pi\) | ||||
0.764868 | + | 0.644187i | \(0.222804\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.2553 | 1.18119 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.38650 | 0.338010 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.26434 | 0.277841 | 0.138921 | − | 0.990304i | \(-0.455637\pi\) | ||||
0.138921 | + | 0.990304i | \(0.455637\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.31181 | 0.490095 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.6418 | −0.871070 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.7266 | 1.86491 | 0.932456 | − | 0.361282i | \(-0.117661\pi\) | ||||
0.932456 | + | 0.361282i | \(0.117661\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.7357 | 0.558876 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.1312 | −0.525988 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.3684 | −1.05463 | −0.527317 | − | 0.849669i | \(-0.676802\pi\) | ||||
−0.527317 | + | 0.849669i | \(0.676802\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.6700 | −0.602638 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.4485 | −0.538126 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.4576 | 0.794003 | 0.397002 | − | 0.917818i | \(-0.370051\pi\) | ||||
0.397002 | + | 0.917818i | \(0.370051\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.22153 | −0.472433 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.7266 | −1.00798 | −0.503991 | − | 0.863709i | \(-0.668135\pi\) | ||||
−0.503991 | + | 0.863709i | \(0.668135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | 0.101929 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.193252 | 0.00982357 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.3118 | −0.928446 | −0.464223 | − | 0.885718i | \(-0.653666\pi\) | ||||
−0.464223 | + | 0.885718i | \(0.653666\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.2371 | 2.13602 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.9253 | 1.00510 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −24.9909 | −1.25743 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.9819 | −1.10324 | −0.551619 | − | 0.834096i | \(-0.685990\pi\) | ||||
−0.551619 | + | 0.834096i | \(0.685990\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.02827 | 0.351854 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.9572 | −0.996614 | −0.498307 | − | 0.867001i | \(-0.666045\pi\) | ||||
−0.498307 | + | 0.867001i | \(0.666045\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.485863 | 0.0242026 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.51414 | −0.0752381 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.64177 | −0.130948 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.9909 | 0.939041 | 0.469520 | − | 0.882922i | \(-0.344427\pi\) | ||||
0.469520 | + | 0.882922i | \(0.344427\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.92892 | 0.144473 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.28354 | 0.456813 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.585221 | 0.0287274 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.80675 | −0.0884768 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.5188 | −1.49094 | −0.745471 | − | 0.666539i | \(-0.767775\pi\) | ||||
−0.745471 | + | 0.666539i | \(0.767775\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.9253 | −0.678678 | −0.339339 | − | 0.940664i | \(-0.610203\pi\) | ||||
−0.339339 | + | 0.940664i | \(0.610203\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.02827 | −0.244483 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.0903 | 0.634972 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.26248 | 0.399850 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.00000 | −0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.58522 | −0.220862 | −0.110431 | − | 0.993884i | \(-0.535223\pi\) | ||||
−0.110431 | + | 0.993884i | \(0.535223\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.9427 | −1.39090 | −0.695448 | − | 0.718577i | \(-0.744794\pi\) | ||||
−0.695448 | + | 0.718577i | \(0.744794\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.8205 | 0.758534 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 46.4815 | 2.22351 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.7494 | −1.08577 | −0.542885 | − | 0.839807i | \(-0.682668\pi\) | ||||
−0.542885 | + | 0.839807i | \(0.682668\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.25526 | −0.250251 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.77301 | 0.226773 | 0.113386 | − | 0.993551i | \(-0.463830\pi\) | ||||
0.113386 | + | 0.993551i | \(0.463830\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.43478 | 0.210229 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.1504 | 0.480099 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.95719 | 0.375523 | 0.187761 | − | 0.982215i | \(-0.439877\pi\) | ||||
0.187761 | + | 0.982215i | \(0.439877\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.7357 | −0.505523 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.96265 | −0.374118 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.00000 | 0.0937614 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.5279 | 0.819919 | 0.409960 | − | 0.912104i | \(-0.365543\pi\) | ||||
0.409960 | + | 0.912104i | \(0.365543\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.83502 | 0.225679 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.6610 | −0.496531 | −0.248265 | − | 0.968692i | \(-0.579861\pi\) | ||||
−0.248265 | + | 0.968692i | \(0.579861\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.9572 | 0.741593 | 0.370797 | − | 0.928714i | \(-0.379085\pi\) | ||||
0.370797 | + | 0.928714i | \(0.379085\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.735663 | −0.0341156 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.9053 | −1.43013 | −0.715064 | − | 0.699059i | \(-0.753602\pi\) | ||||
−0.715064 | + | 0.699059i | \(0.753602\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.1312 | −0.560169 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.3492 | 0.845485 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.193252 | −0.00888576 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.4057 | 0.660979 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.67004 | −0.351187 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.5479 | 0.664709 | 0.332355 | − | 0.943154i | \(-0.392157\pi\) | ||||
0.332355 | + | 0.943154i | \(0.392157\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.64177 | −0.120454 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.5388 | 0.525034 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0565 | 0.456644 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.3437 | 1.64689 | 0.823445 | − | 0.567396i | \(-0.192049\pi\) | ||||
0.823445 | + | 0.567396i | \(0.192049\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.8259 | −0.987004 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.3401 | 1.86565 | 0.932826 | − | 0.360327i | \(-0.117335\pi\) | ||||
0.932826 | + | 0.360327i | \(0.117335\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −50.5188 | −2.27525 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.51414 | 0.0680554 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.4148 | −0.870872 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.2234 | −0.547194 | −0.273597 | − | 0.961844i | \(-0.588213\pi\) | ||||
−0.273597 | + | 0.961844i | \(0.588213\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.9819 | 0.982077 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.1987 | −0.722265 | −0.361133 | − | 0.932515i | \(-0.617610\pi\) | ||||
−0.361133 | + | 0.932515i | \(0.617610\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.4340 | −1.04280 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.24073 | −0.320940 | −0.160470 | − | 0.987041i | \(-0.551301\pi\) | ||||
−0.160470 | + | 0.987041i | \(0.551301\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.5177 | 0.642227 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.32088 | 0.234923 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.88611 | −0.215308 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.02827 | 0.221143 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.50506 | 0.109960 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.65991 | −0.291776 | −0.145888 | − | 0.989301i | \(-0.546604\pi\) | ||||
−0.145888 | + | 0.989301i | \(0.546604\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.3063 | −0.713027 | −0.356513 | − | 0.934290i | \(-0.616035\pi\) | ||||
−0.356513 | + | 0.934290i | \(0.616035\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.57615 | 0.156076 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.34916 | 0.102331 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 53.3118 | 2.31790 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.02827 | 0.305001 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.7357 | −0.465013 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.41478 | −0.147634 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.7074 | −0.591518 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.25526 | 0.226360 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.2835 | 1.68893 | 0.844466 | − | 0.535610i | \(-0.179918\pi\) | ||||
0.844466 | + | 0.535610i | \(0.179918\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.6892 | −1.10243 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.8688 | −0.851084 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.03374 | −0.0441994 | −0.0220997 | − | 0.999756i | \(-0.507035\pi\) | ||||
−0.0220997 | + | 0.999756i | \(0.507035\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.25526 | 0.266968 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −55.5953 | −2.36844 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.8013 | 0.927085 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.00000 | 0.169791 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.8314 | −1.34874 | −0.674370 | − | 0.738393i | \(-0.735585\pi\) | ||||
−0.674370 | + | 0.738393i | \(0.735585\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.193252 | −0.00817371 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.83502 | −0.204135 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.2088 | 1.23101 | 0.615503 | − | 0.788135i | \(-0.288953\pi\) | ||||
0.615503 | + | 0.788135i | \(0.288953\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.4996 | 0.525862 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.32088 | 0.0554719 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.5616 | −1.36505 | −0.682527 | − | 0.730860i | \(-0.739119\pi\) | ||||
−0.682527 | + | 0.730860i | \(0.739119\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.16498 | 0.0487528 | 0.0243764 | − | 0.999703i | \(-0.492240\pi\) | ||||
0.0243764 | + | 0.999703i | \(0.492240\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.9536 | 0.791797 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.6508 | 0.986308 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.2654 | −1.38486 | −0.692428 | − | 0.721487i | \(-0.743459\pi\) | ||||
−0.692428 | + | 0.721487i | \(0.743459\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.934380 | 0.0388315 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.510528 | −0.0211803 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.67004 | 0.317661 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.51414 | 0.0626019 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.3118 | 0.838358 | 0.419179 | − | 0.907904i | \(-0.362318\pi\) | ||||
0.419179 | + | 0.907904i | \(0.362318\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.58522 | 0.106522 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.99093 | 0.205299 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.1998 | 1.73294 | 0.866468 | − | 0.499232i | \(-0.166384\pi\) | ||||
0.866468 | + | 0.499232i | \(0.166384\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.67004 | 0.396433 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.00000 | −0.163709 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.98907 | 0.326425 | 0.163212 | − | 0.986591i | \(-0.447814\pi\) | ||||
0.163212 | + | 0.986591i | \(0.447814\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.8861 | 0.607217 | 0.303608 | − | 0.952797i | \(-0.401809\pi\) | ||||
0.303608 | + | 0.952797i | \(0.401809\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.18418 | −0.374009 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.51414 | −0.0615584 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.4949 | −0.710098 | −0.355049 | − | 0.934848i | \(-0.615536\pi\) | ||||
−0.355049 | + | 0.934848i | \(0.615536\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.8013 | −0.559256 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.02827 | 0.203422 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.6508 | 0.793690 | 0.396845 | − | 0.917886i | \(-0.370105\pi\) | ||||
0.396845 | + | 0.917886i | \(0.370105\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.2553 | 0.655476 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.1276 | 0.850566 | 0.425283 | − | 0.905060i | \(-0.360174\pi\) | ||||
0.425283 | + | 0.905060i | \(0.360174\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.18418 | −0.288757 | −0.144378 | − | 0.989523i | \(-0.546118\pi\) | ||||
−0.144378 | + | 0.989523i | \(0.546118\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.73566 | 0.350550 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.86876 | −0.154999 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.13310 | −0.165324 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.32088 | −0.212496 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.7730 | −0.509293 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.9855 | −1.07427 | −0.537137 | − | 0.843495i | \(-0.680494\pi\) | ||||
−0.537137 | + | 0.843495i | \(0.680494\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.6363 | −0.581741 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.9627 | −0.554091 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.25526 | 0.208221 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.6983 | −0.581456 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46.5489 | 1.83857 | 0.919286 | − | 0.393590i | \(-0.128767\pi\) | ||||
0.919286 | + | 0.393590i | \(0.128767\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.9217 | 1.45605 | 0.728025 | − | 0.685551i | \(-0.240439\pi\) | ||||
0.728025 | + | 0.685551i | \(0.240439\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.292611 | 0.0115215 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.1595 | 0.674610 | 0.337305 | − | 0.941395i | \(-0.390485\pi\) | ||||
0.337305 | + | 0.941395i | \(0.390485\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.02827 | −0.275884 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.641769 | 0.0251529 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.5852 | −0.570764 | −0.285382 | − | 0.958414i | \(-0.592120\pi\) | ||||
−0.285382 | + | 0.958414i | \(0.592120\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.1696 | 1.17883 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.9909 | 0.428797 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.0848 | −1.67835 | −0.839173 | − | 0.543864i | \(-0.816961\pi\) | ||||
−0.839173 | + | 0.543864i | \(0.816961\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.8397 | −1.16063 | −0.580315 | − | 0.814392i | \(-0.697070\pi\) | ||||
−0.580315 | + | 0.814392i | \(0.697070\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.83502 | −0.187777 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.6418 | 0.412670 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −91.2747 | −3.53417 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.9108 | 0.963106 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.25526 | −0.241482 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 49.4713 | 1.90698 | 0.953490 | − | 0.301425i | \(-0.0974624\pi\) | ||||
0.953490 | + | 0.301425i | \(0.0974624\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.70739 | 0.104207 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.11856 | 0.312022 | 0.156011 | − | 0.987755i | \(-0.450137\pi\) | ||||
0.156011 | + | 0.987755i | \(0.450137\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.77301 | −0.336677 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.60442 | −0.329722 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 45.3785 | 1.73636 | 0.868180 | − | 0.496250i | \(-0.165290\pi\) | ||||
0.868180 | + | 0.496250i | \(0.165290\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.43478 | 0.169444 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.3684 | 1.00602 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.67004 | 0.292205 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.67365 | 0.253878 | 0.126939 | − | 0.991911i | \(-0.459485\pi\) | ||||
0.126939 | + | 0.991911i | \(0.459485\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.32088 | −0.0501763 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.73566 | −0.103770 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −51.9072 | −1.96612 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.75020 | 0.217493 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.0329 | −1.73864 | −0.869320 | − | 0.494250i | \(-0.835443\pi\) | ||||
−0.869320 | + | 0.494250i | \(0.835443\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0565 | −0.530153 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.61350 | −0.286741 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.4431 | 0.768840 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.9891 | 0.450259 | 0.225130 | − | 0.974329i | \(-0.427719\pi\) | ||||
0.225130 | + | 0.974329i | \(0.427719\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.5051 | 0.618988 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.24434 | 0.158952 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.51414 | −0.0566255 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.3209 | 0.572169 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.7375 | 0.736085 | 0.368043 | − | 0.929809i | \(-0.380028\pi\) | ||||
0.368043 | + | 0.929809i | \(0.380028\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.26248 | 0.158743 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.3118 | −0.829785 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.2882 | −1.05060 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.8405 | −0.550403 | −0.275202 | − | 0.961387i | \(-0.588745\pi\) | ||||
−0.275202 | + | 0.961387i | \(0.588745\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.934380 | −0.0345593 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.5935 | 1.42548 | 0.712742 | − | 0.701427i | \(-0.247453\pi\) | ||||
0.712742 | + | 0.701427i | \(0.247453\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.95719 | −0.293505 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.18418 | 0.338304 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.9053 | 1.13687 | 0.568435 | − | 0.822728i | \(-0.307549\pi\) | ||||
0.568435 | + | 0.822728i | \(0.307549\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.32088 | −0.195468 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.3118 | −1.77239 | −0.886194 | − | 0.463314i | \(-0.846660\pi\) | ||||
−0.886194 | + | 0.463314i | \(0.846660\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.3692 | 0.563082 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.386505 | −0.0141415 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.97894 | 0.108848 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.61350 | −0.277820 | −0.138910 | − | 0.990305i | \(-0.544360\pi\) | ||||
−0.138910 | + | 0.990305i | \(0.544360\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.4431 | −0.672102 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0565 | −0.438783 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.27447 | 0.0826668 | 0.0413334 | − | 0.999145i | \(-0.486839\pi\) | ||||
0.0413334 | + | 0.999145i | \(0.486839\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.73566 | −0.317084 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.00907 | −0.109079 | −0.0545394 | − | 0.998512i | \(-0.517369\pi\) | ||||
−0.0545394 | + | 0.998512i | \(0.517369\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.3329 | 0.627492 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.32088 | 0.264687 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.02827 | −0.253776 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.11310 | −0.220444 | −0.110222 | − | 0.993907i | \(-0.535156\pi\) | ||||
−0.110222 | + | 0.993907i | \(0.535156\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.4713 | −0.413130 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.32635 | −0.119640 | −0.0598202 | − | 0.998209i | \(-0.519053\pi\) | ||||
−0.0598202 | + | 0.998209i | \(0.519053\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.31542 | 0.0472513 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.48947 | −0.125184 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −57.1232 | −2.04665 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.6983 | 0.525947 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.4485 | −0.373400 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.7831 | 0.991623 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.43398 | −0.193700 | −0.0968502 | − | 0.995299i | \(-0.530877\pi\) | ||||
−0.0968502 | + | 0.995299i | \(0.530877\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.31181 | −0.295908 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9043 | −0.387711 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.25526 | −0.222131 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.6135 | −0.411888 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.4540 | 0.866204 | 0.433102 | − | 0.901345i | \(-0.357419\pi\) | ||||
0.433102 | + | 0.901345i | \(0.357419\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.3118 | 0.860090 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.92892 | −0.103488 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.9909 | −0.387861 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.4713 | 0.615783 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.4431 | −0.719630 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.175107 | 0.00615644 | 0.00307822 | − | 0.999995i | \(-0.499020\pi\) | ||||
0.00307822 | + | 0.999995i | \(0.499020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.0192 | −1.47549 | −0.737747 | − | 0.675077i | \(-0.764110\pi\) | ||||
−0.737747 | + | 0.675077i | \(0.764110\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.2926 | −0.641550 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.0475 | −1.15760 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.02827 | −0.0359747 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.32088 | −0.0461554 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.0293 | −0.873530 | −0.436765 | − | 0.899576i | \(-0.643876\pi\) | ||||
−0.436765 | + | 0.899576i | \(0.643876\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.2726 | −1.02038 | −0.510190 | − | 0.860062i | \(-0.670425\pi\) | ||||
−0.510190 | + | 0.860062i | \(0.670425\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.70739 | −0.0942592 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.6610 | 0.370718 | 0.185359 | − | 0.982671i | \(-0.440655\pi\) | ||||
0.185359 | + | 0.982671i | \(0.440655\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −52.2827 | −1.81585 | −0.907927 | − | 0.419128i | \(-0.862336\pi\) | ||||
−0.907927 | + | 0.419128i | \(0.862336\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.5279 | −0.746794 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.4093 | 0.880381 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.2835 | 1.15182 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.485863 | 0.0167939 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.8680 | 1.06568 | 0.532840 | − | 0.846216i | \(-0.321125\pi\) | ||||
0.532840 | + | 0.846216i | \(0.321125\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 80.1715 | 2.76453 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.57615 | 0.329820 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.51414 | −0.0520879 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.32088 | 0.0453861 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.38104 | −0.0817171 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.0776 | −0.791090 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.4924 | 1.52339 | 0.761695 | − | 0.647936i | \(-0.224367\pi\) | ||||
0.761695 | + | 0.647936i | \(0.224367\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.05655 | 0.275528 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.3346 | 0.387183 | 0.193592 | − | 0.981082i | \(-0.437986\pi\) | ||||
0.193592 | + | 0.981082i | \(0.437986\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.6700 | 0.466416 | 0.233208 | − | 0.972427i | \(-0.425078\pi\) | ||||
0.233208 | + | 0.972427i | \(0.425078\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.1806 | −0.483273 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.2734 | −0.553953 | −0.276977 | − | 0.960877i | \(-0.589332\pi\) | ||||
−0.276977 | + | 0.960877i | \(0.589332\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.79301 | 0.128966 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.37743 | −0.216589 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.5051 | −0.559896 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.18418 | 0.311194 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.64177 | −0.224790 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.4148 | 0.521115 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.42571 | 0.183213 | 0.0916065 | − | 0.995795i | \(-0.470800\pi\) | ||||
0.0916065 | + | 0.995795i | \(0.470800\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.8031 | −0.566756 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.60257 | −0.0539919 | −0.0269959 | − | 0.999636i | \(-0.508594\pi\) | ||||
−0.0269959 | + | 0.999636i | \(0.508594\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.2835 | 0.447027 | 0.223513 | − | 0.974701i | \(-0.428247\pi\) | ||||
0.223513 | + | 0.974701i | \(0.428247\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.6418 | 0.357719 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.8789 | 1.37258 | 0.686289 | − | 0.727329i | \(-0.259238\pi\) | ||||
0.686289 | + | 0.727329i | \(0.259238\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.1806 | 0.408523 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.7549 | 0.895317 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.7549 | −0.693759 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.73566 | −0.291675 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.07655 | −0.169312 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.0848 | 1.23547 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.255264 | −0.00849466 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −38.8970 | −1.29298 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.2937 | −0.873067 | −0.436533 | − | 0.899688i | \(-0.643794\pi\) | ||||
−0.436533 | + | 0.899688i | \(0.643794\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.4768 | 0.513333 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.5569 | −0.714214 | −0.357107 | − | 0.934064i | \(-0.616237\pi\) | ||||
−0.357107 | + | 0.934064i | \(0.616237\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.386505 | 0.0127914 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.47133 | 0.313112 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −26.3190 | −0.869131 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.7785 | −1.27918 | −0.639592 | − | 0.768715i | \(-0.720897\pi\) | ||||
−0.639592 | + | 0.768715i | \(0.720897\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.6044 | −1.00845 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.6983 | 0.483801 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.15230 | −0.235166 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.22699 | 0.105988 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.2023 | 0.761244 | 0.380622 | − | 0.924731i | \(-0.375710\pi\) | ||||
0.380622 | + | 0.924731i | \(0.375710\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.9627 | 0.916439 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −34.0192 | −1.11374 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.32088 | −0.239419 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.60257 | 0.117691 | 0.0588454 | − | 0.998267i | \(-0.481258\pi\) | ||||
0.0588454 | + | 0.998267i | \(0.481258\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.0192 | −0.392232 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.3382 | 0.858602 | 0.429301 | − | 0.903162i | \(-0.358760\pi\) | ||||
0.429301 | + | 0.903162i | \(0.358760\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −93.7831 | −3.05400 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.00000 | 0.0650600 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.8970 | −1.13400 | −0.567001 | − | 0.823717i | \(-0.691896\pi\) | ||||
−0.567001 | + | 0.823717i | \(0.691896\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.9909 | −0.356781 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.6382 | −0.507102 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.8532 | −0.545928 | −0.272964 | − | 0.962024i | \(-0.588004\pi\) | ||||
−0.272964 | + | 0.962024i | \(0.588004\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.6983 | 0.928656 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.4485 | 0.337753 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.86876 | −0.124929 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7639 | −0.992385 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.25526 | 0.0726749 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.41478 | 0.0455433 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.3492 | −1.04028 | −0.520139 | − | 0.854081i | \(-0.674120\pi\) | ||||
−0.520139 | + | 0.854081i | \(0.674120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −25.7266 | −0.826457 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.98000 | −0.0956327 | −0.0478164 | − | 0.998856i | \(-0.515226\pi\) | ||||
−0.0478164 | + | 0.998856i | \(0.515226\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.38650 | 0.0765078 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.70739 | −0.0867059 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.2407 | −0.487594 | −0.243797 | − | 0.969826i | \(-0.578393\pi\) | ||||
−0.243797 | + | 0.969826i | \(0.578393\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.92892 | 0.0936086 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.1222 | 0.418959 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.75566 | −0.311157 | −0.155579 | − | 0.987824i | \(-0.549724\pi\) | ||||
−0.155579 | + | 0.987824i | \(0.549724\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.55695 | 0.240784 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.64177 | 0.211410 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.68819 | −0.0536813 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.6519 | −1.00546 | −0.502728 | − | 0.864445i | \(-0.667670\pi\) | ||||
−0.502728 | + | 0.864445i | \(0.667670\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.1276 | −0.543529 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.05655 | −0.192005 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0848 | 0.351060 | 0.175530 | − | 0.984474i | \(-0.443836\pi\) | ||||
0.175530 | + | 0.984474i | \(0.443836\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.64177 | −0.0835819 |
(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 | 6864.2.a.br.1.1 | 3 | ||
4.3 | odd | 2 | 1716.2.a.g.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 5148.2.a.m.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1716.2.a.g.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
5148.2.a.m.1.3 | 3 | 12.11 | even | 2 | |||
6864.2.a.br.1.1 | 3 | 1.1 | even | 1 | trivial |