Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7360,2,Mod(1,7360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7360 = 2^{6} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7360.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: | \(58.7698958877\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.86081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7360.1 |
$q$-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 | ||||||||
\(3\) | 1.46260 | 0.844432 | 0.422216 | − | 0.906495i | \(-0.361252\pi\) | ||||
0.422216 | + | 0.906495i | \(0.361252\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.53740 | −0.581083 | −0.290542 | − | 0.956862i | \(-0.593835\pi\) | ||||
−0.290542 | + | 0.956862i | \(0.593835\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.860806 | −0.286935 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.860806 | −0.259543 | −0.129771 | − | 0.991544i | \(-0.541424\pi\) | ||||
−0.129771 | + | 0.991544i | \(0.541424\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.139194 | −0.0386055 | −0.0193028 | − | 0.999814i | \(-0.506145\pi\) | ||||
−0.0193028 | + | 0.999814i | \(0.506145\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.46260 | −0.377641 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.50761 | 1.33579 | 0.667896 | − | 0.744254i | \(-0.267195\pi\) | ||||
0.667896 | + | 0.744254i | \(0.267195\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.25901 | 1.20650 | 0.603250 | − | 0.797552i | \(-0.293872\pi\) | ||||
0.603250 | + | 0.797552i | \(0.293872\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.24860 | −0.490685 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.64681 | −1.08673 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.76663 | −1.81362 | −0.906809 | − | 0.421543i | \(-0.861489\pi\) | ||||
−0.906809 | + | 0.421543i | \(0.861489\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.78600 | −1.21880 | −0.609401 | − | 0.792862i | \(-0.708590\pi\) | ||||
−0.609401 | + | 0.792862i | \(0.708590\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.25901 | −0.219166 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.53740 | 0.259868 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12.0900 | 1.98759 | 0.993795 | − | 0.111232i | \(-0.0354796\pi\) | ||||
0.993795 | + | 0.111232i | \(0.0354796\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.203585 | −0.0325997 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.98062 | −1.55871 | −0.779356 | − | 0.626582i | \(-0.784454\pi\) | ||||
−0.779356 | + | 0.626582i | \(0.784454\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.4432 | 1.74508 | 0.872538 | − | 0.488547i | \(-0.162473\pi\) | ||||
0.872538 | + | 0.488547i | \(0.162473\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.860806 | 0.128321 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.32340 | 0.338903 | 0.169452 | − | 0.985538i | \(-0.445800\pi\) | ||||
0.169452 | + | 0.985538i | \(0.445800\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.63640 | −0.662342 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.05543 | 1.12799 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.149606 | −0.0205500 | −0.0102750 | − | 0.999947i | \(-0.503271\pi\) | ||||
−0.0102750 | + | 0.999947i | \(0.503271\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.860806 | 0.116071 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.69182 | 1.01881 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.0152 | −1.43406 | −0.717030 | − | 0.697042i | \(-0.754499\pi\) | ||||
−0.717030 | + | 0.697042i | \(0.754499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.43281 | −0.567563 | −0.283782 | − | 0.958889i | \(-0.591589\pi\) | ||||
−0.283782 | + | 0.958889i | \(0.591589\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.32340 | 0.166733 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.139194 | 0.0172649 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.4972 | −1.28244 | −0.641219 | − | 0.767358i | \(-0.721571\pi\) | ||||
−0.641219 | + | 0.767358i | \(0.721571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.46260 | 0.176076 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.31299 | −0.867892 | −0.433946 | − | 0.900939i | \(-0.642879\pi\) | ||||
−0.433946 | + | 0.900939i | \(0.642879\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.11982 | 0.833312 | 0.416656 | − | 0.909064i | \(-0.363202\pi\) | ||||
0.416656 | + | 0.909064i | \(0.363202\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.46260 | 0.168886 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.32340 | 0.150816 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.79641 | −0.764656 | −0.382328 | − | 0.924027i | \(-0.624878\pi\) | ||||
−0.382328 | + | 0.924027i | \(0.624878\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.67660 | −0.630733 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.6468 | 1.16864 | 0.584320 | − | 0.811524i | \(-0.301361\pi\) | ||||
0.584320 | + | 0.811524i | \(0.301361\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.50761 | −0.597385 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.2847 | −1.53148 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.2936 | −1.83312 | −0.916560 | − | 0.399897i | \(-0.869046\pi\) | ||||
−0.916560 | + | 0.399897i | \(0.869046\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.213997 | 0.0224330 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.92520 | −1.02919 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.25901 | −0.539563 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.93561 | 0.196531 | 0.0982657 | − | 0.995160i | \(-0.468671\pi\) | ||||
0.0982657 | + | 0.995160i | \(0.468671\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.740987 | 0.0744720 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.4224 | 1.53459 | 0.767293 | − | 0.641297i | \(-0.221603\pi\) | ||||
0.767293 | + | 0.641297i | \(0.221603\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.91478 | −0.779867 | −0.389933 | − | 0.920843i | \(-0.627502\pi\) | ||||
−0.389933 | + | 0.920843i | \(0.627502\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.24860 | 0.219441 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.27839 | −0.413607 | −0.206804 | − | 0.978382i | \(-0.566306\pi\) | ||||
−0.206804 | + | 0.978382i | \(0.566306\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.7770 | 1.70273 | 0.851366 | − | 0.524572i | \(-0.175775\pi\) | ||||
0.851366 | + | 0.524572i | \(0.175775\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.6829 | 1.67838 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.20359 | −0.301368 | −0.150684 | − | 0.988582i | \(-0.548148\pi\) | ||||
−0.150684 | + | 0.988582i | \(0.548148\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.119819 | 0.0110773 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.46742 | −0.776207 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2590 | −0.932638 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.5976 | −1.31623 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.2099 | 1.34966 | 0.674828 | − | 0.737975i | \(-0.264218\pi\) | ||||
0.674828 | + | 0.737975i | \(0.264218\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.7368 | 1.47360 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.6918 | 1.10889 | 0.554445 | − | 0.832220i | \(-0.312931\pi\) | ||||
0.554445 | + | 0.832220i | \(0.312931\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.08522 | −0.701077 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.64681 | 0.486000 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.0346 | −1.19906 | −0.599529 | − | 0.800353i | \(-0.704645\pi\) | ||||
−0.599529 | + | 0.800353i | \(0.704645\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.2638 | 1.20984 | 0.604921 | − | 0.796285i | \(-0.293205\pi\) | ||||
0.604921 | + | 0.796285i | \(0.293205\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.39821 | 0.286181 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.119819 | 0.0100198 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.76663 | 0.811074 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.78119 | −0.559303 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.46260 | 0.365590 | 0.182795 | − | 0.983151i | \(-0.441485\pi\) | ||||
0.182795 | + | 0.983151i | \(0.441485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.7562 | −0.875328 | −0.437664 | − | 0.899139i | \(-0.644194\pi\) | ||||
−0.437664 | + | 0.899139i | \(0.644194\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.74099 | −0.383286 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.78600 | 0.545065 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.5180 | −1.15866 | −0.579332 | − | 0.815091i | \(-0.696687\pi\) | ||||
−0.579332 | + | 0.815091i | \(0.696687\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.218814 | −0.0173531 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.53740 | −0.121164 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.30403 | −0.102139 | −0.0510697 | − | 0.998695i | \(-0.516263\pi\) | ||||
−0.0510697 | + | 0.998695i | \(0.516263\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.25901 | 0.0980141 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.44322 | −0.266445 | −0.133222 | − | 0.991086i | \(-0.542532\pi\) | ||||
−0.133222 | + | 0.991086i | \(0.542532\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9806 | −0.998510 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.52699 | −0.346188 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.35801 | −0.711476 | −0.355738 | − | 0.934586i | \(-0.615770\pi\) | ||||
−0.355738 | + | 0.934586i | \(0.615770\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.53740 | −0.116217 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.1109 | −1.21097 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.4134 | −1.37628 | −0.688142 | − | 0.725576i | \(-0.741574\pi\) | ||||
−0.688142 | + | 0.725576i | \(0.741574\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.94457 | 0.144539 | 0.0722694 | − | 0.997385i | \(-0.476976\pi\) | ||||
0.0722694 | + | 0.997385i | \(0.476976\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.48342 | −0.479268 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.0900 | −0.888877 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.74099 | −0.346695 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.68141 | 0.631480 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.775591 | 0.0561198 | 0.0280599 | − | 0.999606i | \(-0.491067\pi\) | ||||
0.0280599 | + | 0.999606i | \(0.491067\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7666 | −0.846980 | −0.423490 | − | 0.905901i | \(-0.639195\pi\) | ||||
−0.423490 | + | 0.905901i | \(0.639195\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.203585 | 0.0145790 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.68141 | −0.689772 | −0.344886 | − | 0.938645i | \(-0.612082\pi\) | ||||
−0.344886 | + | 0.938645i | \(0.612082\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.29362 | 0.233478 | 0.116739 | − | 0.993163i | \(-0.462756\pi\) | ||||
0.116739 | + | 0.993163i | \(0.462756\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.3532 | −1.08293 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.0152 | 1.05386 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.98062 | 0.697077 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.860806 | −0.0598301 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.52699 | −0.313138 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.2396 | −1.11798 | −0.558991 | − | 0.829173i | \(-0.688812\pi\) | ||||
−0.558991 | + | 0.829173i | \(0.688812\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.6960 | −0.732876 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.4432 | −0.780421 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.4328 | 0.708225 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.4134 | 0.703675 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.766628 | −0.0515690 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.2936 | −1.42593 | −0.712963 | − | 0.701202i | \(-0.752647\pi\) | ||||
−0.712963 | + | 0.701202i | \(0.752647\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.860806 | −0.0573871 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −29.6620 | −1.96874 | −0.984369 | − | 0.176117i | \(-0.943646\pi\) | ||||
−0.984369 | + | 0.176117i | \(0.943646\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.6829 | −1.30068 | −0.650340 | − | 0.759643i | \(-0.725374\pi\) | ||||
−0.650340 | + | 0.759643i | \(0.725374\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.93561 | 0.127354 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.52699 | −0.362085 | −0.181043 | − | 0.983475i | \(-0.557947\pi\) | ||||
−0.181043 | + | 0.983475i | \(0.557947\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.32340 | −0.151562 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.94043 | −0.645700 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.3982 | 1.12540 | 0.562698 | − | 0.826662i | \(-0.309763\pi\) | ||||
0.562698 | + | 0.826662i | \(0.309763\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.0900 | −1.03645 | −0.518225 | − | 0.855244i | \(-0.673407\pi\) | ||||
−0.518225 | + | 0.855244i | \(0.673407\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.63785 | 0.554118 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.63640 | 0.296209 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.732024 | −0.0465776 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.5720 | 0.986836 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.0498 | −1.83361 | −0.916805 | − | 0.399336i | \(-0.869241\pi\) | ||||
−0.916805 | + | 0.399336i | \(0.869241\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.860806 | −0.0541184 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.05543 | −0.504450 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.56304 | −0.409391 | −0.204696 | − | 0.978826i | \(-0.565620\pi\) | ||||
−0.204696 | + | 0.978826i | \(0.565620\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.5872 | −1.15495 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.40717 | 0.520391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.561593 | 0.0346293 | 0.0173147 | − | 0.999850i | \(-0.494488\pi\) | ||||
0.0173147 | + | 0.999850i | \(0.494488\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.149606 | 0.00919024 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −25.2936 | −1.54794 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.26943 | 0.443225 | 0.221612 | − | 0.975135i | \(-0.428868\pi\) | ||||
0.221612 | + | 0.975135i | \(0.428868\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.184210 | −0.0111900 | −0.00559498 | − | 0.999984i | \(-0.501781\pi\) | ||||
−0.00559498 | + | 0.999984i | \(0.501781\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.312992 | 0.0189431 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.860806 | −0.0519085 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.8954 | −1.55590 | −0.777952 | − | 0.628323i | \(-0.783741\pi\) | ||||
−0.777952 | + | 0.628323i | \(0.783741\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.84143 | 0.349717 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.7756 | −1.59730 | −0.798649 | − | 0.601797i | \(-0.794452\pi\) | ||||
−0.798649 | + | 0.601797i | \(0.794452\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.70079 | 0.338877 | 0.169438 | − | 0.985541i | \(-0.445805\pi\) | ||||
0.169438 | + | 0.985541i | \(0.445805\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.69182 | −0.455624 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.3442 | 0.905741 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.3338 | 0.784342 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.83102 | 0.165957 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.05398 | −0.0615741 | −0.0307871 | − | 0.999526i | \(-0.509801\pi\) | ||||
−0.0307871 | + | 0.999526i | \(0.509801\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.0152 | 0.641331 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.86081 | 0.282053 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.139194 | −0.00804981 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.5928 | −1.01403 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.5568 | 1.29585 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.43281 | 0.253822 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.8760 | 1.02024 | 0.510120 | − | 0.860103i | \(-0.329601\pi\) | ||||
0.510120 | + | 0.860103i | \(0.329601\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.5762 | −0.658544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.9315 | −0.960095 | −0.480048 | − | 0.877242i | \(-0.659381\pi\) | ||||
−0.480048 | + | 0.877242i | \(0.659381\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.9959 | −1.13023 | −0.565116 | − | 0.825011i | \(-0.691169\pi\) | ||||
−0.565116 | + | 0.825011i | \(0.691169\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.32340 | −0.0745654 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.29776 | −0.185221 | −0.0926104 | − | 0.995702i | \(-0.529521\pi\) | ||||
−0.0926104 | + | 0.995702i | \(0.529521\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.40717 | 0.470711 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.25756 | −0.349263 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.9646 | 1.61163 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.139194 | −0.00772110 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.0007 | 1.43784 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.57201 | −0.196931 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8802 | −0.707959 | −0.353979 | − | 0.935253i | \(-0.615172\pi\) | ||||
−0.353979 | + | 0.935253i | \(0.615172\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.4072 | −0.570309 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.4972 | 0.573523 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.22026 | −0.502260 | −0.251130 | − | 0.967953i | \(-0.580802\pi\) | ||||
−0.251130 | + | 0.967953i | \(0.580802\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.68556 | −0.254485 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.84143 | 0.316331 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8898 | 0.965959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.46260 | −0.0787437 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.2984 | 1.68019 | 0.840094 | − | 0.542441i | \(-0.182500\pi\) | ||||
0.840094 | + | 0.542441i | \(0.182500\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.89541 | −0.529689 | −0.264845 | − | 0.964291i | \(-0.585321\pi\) | ||||
−0.264845 | + | 0.964291i | \(0.585321\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.786003 | 0.0419537 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.4287 | 1.03408 | 0.517042 | − | 0.855960i | \(-0.327033\pi\) | ||||
0.517042 | + | 0.855960i | \(0.327033\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.31299 | 0.388133 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.3844 | −0.655453 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.1440 | 0.693714 | 0.346857 | − | 0.937918i | \(-0.387249\pi\) | ||||
0.346857 | + | 0.937918i | \(0.387249\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.65722 | 0.455643 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.0048 | −0.787549 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.11982 | −0.372668 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.7424 | 0.821748 | 0.410874 | − | 0.911692i | \(-0.365224\pi\) | ||||
0.410874 | + | 0.911692i | \(0.365224\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.59138 | 0.447249 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.230005 | 0.0119413 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.6620 | −1.43229 | −0.716143 | − | 0.697954i | \(-0.754094\pi\) | ||||
−0.716143 | + | 0.697954i | \(0.754094\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.46260 | −0.0755283 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.35946 | 0.0700156 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.2140 | 1.44926 | 0.724628 | − | 0.689140i | \(-0.242012\pi\) | ||||
0.724628 | + | 0.689140i | \(0.242012\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.2459 | 1.13969 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.5928 | 1.10334 | 0.551671 | − | 0.834062i | \(-0.313990\pi\) | ||||
0.551671 | + | 0.834062i | \(0.313990\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.32340 | −0.0674469 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.85039 | −0.500724 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.2501 | −0.874612 | −0.437306 | − | 0.899313i | \(-0.644067\pi\) | ||||
−0.437306 | + | 0.899313i | \(0.644067\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.50761 | 0.278532 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.5630 | 0.936382 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.79641 | 0.341965 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.8850 | −1.75083 | −0.875414 | − | 0.483374i | \(-0.839411\pi\) | ||||
−0.875414 | + | 0.483374i | \(0.839411\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.8254 | −0.592012 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.21881 | 0.210678 | 0.105339 | − | 0.994436i | \(-0.466407\pi\) | ||||
0.105339 | + | 0.994436i | \(0.466407\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.944572 | 0.0470525 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.67660 | 0.282072 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.4072 | −0.515864 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.8165 | 1.91935 | 0.959675 | − | 0.281111i | \(-0.0907030\pi\) | ||||
0.959675 | + | 0.281111i | \(0.0907030\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.5270 | −1.01252 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.9348 | 0.833309 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.6468 | −0.522631 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.8623 | 1.02163 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.0305 | 1.07626 | 0.538129 | − | 0.842862i | \(-0.319131\pi\) | ||||
0.538129 | + | 0.842862i | \(0.319131\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.2203 | 0.839264 | 0.419632 | − | 0.907694i | \(-0.362159\pi\) | ||||
0.419632 | + | 0.907694i | \(0.362159\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.00000 | −0.0972433 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.50761 | 0.267159 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.81501 | 0.329801 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.175247 | 0.00846102 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.8116 | 0.568947 | 0.284473 | − | 0.958684i | \(-0.408181\pi\) | ||||
0.284473 | + | 0.958684i | \(0.408181\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.8642 | 0.954611 | 0.477306 | − | 0.878737i | \(-0.341613\pi\) | ||||
0.477306 | + | 0.878737i | \(0.341613\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.2847 | 0.684897 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.25901 | 0.251573 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.04647 | 0.240855 | 0.120427 | − | 0.992722i | \(-0.461574\pi\) | ||||
0.120427 | + | 0.992722i | \(0.461574\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.99104 | 0.190049 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.3193 | −0.680328 | −0.340164 | − | 0.940366i | \(-0.610483\pi\) | ||||
−0.340164 | + | 0.940366i | \(0.610483\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.2936 | 0.819796 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.52699 | 0.308716 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.3699 | −0.630963 | −0.315482 | − | 0.948932i | \(-0.602166\pi\) | ||||
−0.315482 | + | 0.948932i | \(0.602166\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.59138 | 0.404552 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.7320 | −0.739155 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.213997 | −0.0100323 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.38924 | 0.111764 | 0.0558821 | − | 0.998437i | \(-0.482203\pi\) | ||||
0.0558821 | + | 0.998437i | \(0.482203\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −31.1004 | −1.45164 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.2278 | −0.988676 | −0.494338 | − | 0.869270i | \(-0.664590\pi\) | ||||
−0.494338 | + | 0.869270i | \(0.664590\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.1261 | −1.63245 | −0.816224 | − | 0.577736i | \(-0.803936\pi\) | ||||
−0.816224 | + | 0.577736i | \(0.803936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.92520 | 0.460270 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.7756 | 0.776282 | 0.388141 | − | 0.921600i | \(-0.373117\pi\) | ||||
0.388141 | + | 0.921600i | \(0.373117\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.1384 | 0.745203 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.2340 | −0.978413 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.85039 | −0.452922 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.25901 | 0.241300 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.128782 | 0.00589652 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.61076 | 0.256362 | 0.128181 | − | 0.991751i | \(-0.459086\pi\) | ||||
0.128181 | + | 0.991751i | \(0.459086\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.68286 | −0.0767319 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.24860 | −0.102315 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.93561 | −0.0878915 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.2638 | −0.465099 | −0.232549 | − | 0.972585i | \(-0.574707\pi\) | ||||
−0.232549 | + | 0.972585i | \(0.574707\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.90727 | −0.0862498 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.28735 | 0.419132 | 0.209566 | − | 0.977794i | \(-0.432795\pi\) | ||||
0.209566 | + | 0.977794i | \(0.432795\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −53.7908 | −2.42262 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.740987 | −0.0333049 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.2430 | 0.504318 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.3082 | 0.595756 | 0.297878 | − | 0.954604i | \(-0.403721\pi\) | ||||
0.297878 | + | 0.954604i | \(0.403721\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.03605 | −0.224994 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.7383 | 1.68267 | 0.841334 | − | 0.540516i | \(-0.181771\pi\) | ||||
0.841334 | + | 0.540516i | \(0.181771\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.4224 | −0.686288 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.9854 | −0.843173 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.11982 | 0.0496351 | 0.0248176 | − | 0.999692i | \(-0.492100\pi\) | ||||
0.0248176 | + | 0.999692i | \(0.492100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.9460 | −0.484223 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −29.6966 | −1.31114 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.91478 | 0.348767 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.00000 | −0.0879599 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.6870 | −0.600793 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.9100 | −0.609407 | −0.304703 | − | 0.952447i | \(-0.598557\pi\) | ||||
−0.304703 | + | 0.952447i | \(0.598557\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.19799 | 0.358473 | 0.179237 | − | 0.983806i | \(-0.442637\pi\) | ||||
0.179237 | + | 0.983806i | \(0.442637\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.24860 | −0.0981370 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −37.3747 | −1.62807 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.48197 | 0.411483 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.38924 | 0.0601749 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.27839 | 0.184971 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.9315 | −1.16218 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.99104 | 0.171906 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.5478 | −1.01240 | −0.506200 | − | 0.862416i | \(-0.668950\pi\) | ||||
−0.506200 | + | 0.862416i | \(0.668950\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.84413 | 0.122053 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.7770 | −0.761485 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.77077 | 0.0757128 | 0.0378564 | − | 0.999283i | \(-0.487947\pi\) | ||||
0.0378564 | + | 0.999283i | \(0.487947\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.81579 | 0.162854 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −51.3628 | −2.18813 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.4488 | 0.444329 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17.6829 | −0.750596 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.5872 | 0.957052 | 0.478526 | − | 0.878073i | \(-0.341171\pi\) | ||||
0.478526 | + | 0.878073i | \(0.341171\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.59283 | −0.0673695 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.93416 | −0.292760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.8504 | 0.920884 | 0.460442 | − | 0.887690i | \(-0.347691\pi\) | ||||
0.460442 | + | 0.887690i | \(0.347691\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.20359 | 0.134776 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.72721 | 0.366508 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.4737 | 0.481002 | 0.240501 | − | 0.970649i | \(-0.422688\pi\) | ||||
0.240501 | + | 0.970649i | \(0.422688\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.7085 | 1.15956 | 0.579782 | − | 0.814771i | \(-0.303138\pi\) | ||||
0.579782 | + | 0.814771i | \(0.303138\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.13438 | 0.0473893 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.3442 | 0.846941 | 0.423471 | − | 0.905910i | \(-0.360812\pi\) | ||||
0.423471 | + | 0.905910i | \(0.360812\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.2099 | −0.715217 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.3684 | −0.679076 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.128782 | 0.00533360 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.119819 | −0.00495391 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.1690 | 0.502268 | 0.251134 | − | 0.967952i | \(-0.419197\pi\) | ||||
0.251134 | + | 0.967952i | \(0.419197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.6877 | −1.47049 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.1600 | −0.582465 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −40.5180 | −1.66388 | −0.831938 | − | 0.554869i | \(-0.812769\pi\) | ||||
−0.831938 | + | 0.554869i | \(0.812769\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.46742 | 0.347130 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.81724 | 0.197156 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.8913 | 1.18047 | 0.590233 | − | 0.807233i | \(-0.299036\pi\) | ||||
0.590233 | + | 0.807233i | \(0.299036\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.34278 | 0.217937 | 0.108968 | − | 0.994045i | \(-0.465245\pi\) | ||||
0.108968 | + | 0.994045i | \(0.465245\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.03605 | 0.367977 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.2590 | 0.417088 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.4376 | 1.64131 | 0.820656 | − | 0.571422i | \(-0.193608\pi\) | ||||
0.820656 | + | 0.571422i | \(0.193608\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.9612 | 0.889915 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.323404 | −0.0130835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.31154 | 0.214531 | 0.107266 | − | 0.994230i | \(-0.465790\pi\) | ||||
0.107266 | + | 0.994230i | \(0.465790\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.5976 | 0.588634 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.71680 | 0.391183 | 0.195592 | − | 0.980685i | \(-0.437337\pi\) | ||||
0.195592 | + | 0.980685i | \(0.437337\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.7562 | −0.954843 | −0.477421 | − | 0.878674i | \(-0.658428\pi\) | ||||
−0.477421 | + | 0.878674i | \(0.658428\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.64681 | −0.226599 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.5872 | 1.06520 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.62117 | −0.264424 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 66.5872 | 2.65501 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.24234 | −0.0494566 | −0.0247283 | − | 0.999694i | \(-0.507872\pi\) | ||||
−0.0247283 | + | 0.999694i | \(0.507872\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.7521 | −0.944060 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.2099 | −0.603585 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.645359 | 0.0255701 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.29507 | 0.249029 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.8864 | −1.37793 | −0.688966 | − | 0.724794i | \(-0.741935\pi\) | ||||
−0.688966 | + | 0.724794i | \(0.741935\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.1592 | 1.26824 | 0.634118 | − | 0.773236i | \(-0.281363\pi\) | ||||
0.634118 | + | 0.773236i | \(0.281363\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.7368 | −0.659012 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.9550 | −0.941768 | −0.470884 | − | 0.882195i | \(-0.656065\pi\) | ||||
−0.470884 | + | 0.882195i | \(0.656065\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.48197 | 0.372200 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.2590 | 0.598048 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.31926 | −0.169026 | −0.0845128 | − | 0.996422i | \(-0.526933\pi\) | ||||
−0.0845128 | + | 0.996422i | \(0.526933\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.6918 | −0.495911 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.12878 | −0.239107 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.14961 | −0.239555 | −0.119777 | − | 0.992801i | \(-0.538218\pi\) | ||||
−0.119777 | + | 0.992801i | \(0.538218\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.7473 | 0.612497 | 0.306249 | − | 0.951952i | \(-0.400926\pi\) | ||||
0.306249 | + | 0.951952i | \(0.400926\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.12127 | −0.0435465 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.08522 | 0.313531 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.76663 | −0.378165 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −31.1440 | −1.20410 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.81579 | 0.147307 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.5783 | 1.67982 | 0.839909 | − | 0.542727i | \(-0.182608\pi\) | ||||
0.839909 | + | 0.542727i | \(0.182608\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.64681 | −0.217346 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.1801 | −1.15991 | −0.579957 | − | 0.814647i | \(-0.696931\pi\) | ||||
−0.579957 | + | 0.814647i | \(0.696931\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.97581 | −0.114201 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −43.3836 | −1.66247 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.2832 | 1.12049 | 0.560245 | − | 0.828327i | \(-0.310707\pi\) | ||||
0.560245 | + | 0.828327i | \(0.310707\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.0346 | 0.536235 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.7881 | −1.09834 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0208243 | 0.000793344 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.9557 | −0.568940 | −0.284470 | − | 0.958685i | \(-0.591818\pi\) | ||||
−0.284470 | + | 0.958685i | \(0.591818\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.13919 | −0.0432744 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.2638 | −0.541058 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −54.9694 | −2.08212 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.08377 | −0.305756 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.9627 | −0.942828 | −0.471414 | − | 0.881912i | \(-0.656256\pi\) | ||||
−0.471414 | + | 0.881912i | \(0.656256\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 63.5816 | 2.39803 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.39821 | −0.127984 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.7104 | −0.891722 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.9717 | 1.46361 | 0.731806 | − | 0.681513i | \(-0.238678\pi\) | ||||
0.731806 | + | 0.681513i | \(0.238678\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.85039 | 0.219407 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.78600 | −0.254138 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.119819 | −0.00448098 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.4466 | 0.950320 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.2978 | 0.943447 | 0.471724 | − | 0.881746i | \(-0.343632\pi\) | ||||
0.471724 | + | 0.881746i | \(0.343632\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.1682 | 0.453168 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.5333 | −0.875211 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.76663 | −0.362723 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.7417 | −0.472562 | −0.236281 | − | 0.971685i | \(-0.575929\pi\) | ||||
−0.236281 | + | 0.971685i | \(0.575929\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.6635 | 1.09865 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 63.0249 | 2.33106 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.83247 | 0.363170 | 0.181585 | − | 0.983375i | \(-0.441877\pi\) | ||||
0.181585 | + | 0.983375i | \(0.441877\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.78119 | 0.250128 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.03605 | 0.332847 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.6918 | 0.834732 | 0.417366 | − | 0.908738i | \(-0.362953\pi\) | ||||
0.417366 | + | 0.908738i | \(0.362953\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.07066 | −0.0393316 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.08858 | −0.113309 | −0.0566546 | − | 0.998394i | \(-0.518043\pi\) | ||||
−0.0566546 | + | 0.998394i | \(0.518043\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.46260 | −0.163497 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.16484 | −0.335324 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.57760 | 0.240340 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.7577 | 0.392553 | 0.196276 | − | 0.980549i | \(-0.437115\pi\) | ||||
0.196276 | + | 0.980549i | \(0.437115\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −42.4882 | −1.54836 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.7562 | 0.391459 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.5333 | 0.709948 | 0.354974 | − | 0.934876i | \(-0.384490\pi\) | ||||
0.354974 | + | 0.934876i | \(0.384490\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.25901 | −0.0456993 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.6933 | −0.568881 | −0.284440 | − | 0.958694i | \(-0.591808\pi\) | ||||
−0.284440 | + | 0.958694i | \(0.591808\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.3304 | −0.989429 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.74099 | 0.171411 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.53326 | 0.0553626 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.4128 | 0.411555 | 0.205777 | − | 0.978599i | \(-0.434028\pi\) | ||||
0.205777 | + | 0.978599i | \(0.434028\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.59910 | −0.345703 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.5872 | 0.812406 | 0.406203 | − | 0.913783i | \(-0.366853\pi\) | ||||
0.406203 | + | 0.913783i | \(0.366853\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.78600 | −0.243760 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −27.1857 | −0.975280 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −52.4882 | −1.88059 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.29507 | 0.225255 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 55.1503 | 1.97091 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.5180 | 0.518171 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.42799 | −0.157841 | −0.0789205 | − | 0.996881i | \(-0.525147\pi\) | ||||
−0.0789205 | + | 0.996881i | \(0.525147\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.821385 | 0.0292421 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.92520 | 0.175120 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.617021 | 0.0219111 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.218814 | 0.00776053 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.5124 | −0.762009 | −0.381005 | − | 0.924573i | \(-0.624422\pi\) | ||||
−0.381005 | + | 0.924573i | \(0.624422\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.7964 | 0.452705 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.8864 | 0.525987 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.12878 | −0.216280 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.53740 | 0.0541863 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.6323 | 0.374273 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.37883 | 0.259426 | 0.129713 | − | 0.991552i | \(-0.458594\pi\) | ||||
0.129713 | + | 0.991552i | \(0.458594\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.0423 | 1.01981 | 0.509907 | − | 0.860230i | \(-0.329680\pi\) | ||||
0.509907 | + | 0.860230i | \(0.329680\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.269425 | −0.00944916 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.30403 | 0.0456782 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 60.1801 | 2.10543 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.184210 | −0.00643682 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.70079 | −0.198959 | −0.0994794 | − | 0.995040i | \(-0.531718\pi\) | ||||
−0.0994794 | + | 0.995040i | \(0.531718\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0034 | 0.557842 | 0.278921 | − | 0.960314i | \(-0.410023\pi\) | ||||
0.278921 | + | 0.960314i | \(0.410023\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.25901 | −0.0438332 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.7937 | 1.38376 | 0.691882 | − | 0.722011i | \(-0.256782\pi\) | ||||
0.691882 | + | 0.722011i | \(0.256782\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.3353 | 0.810467 | 0.405234 | − | 0.914213i | \(-0.367190\pi\) | ||||
0.405234 | + | 0.914213i | \(0.367190\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −37.8746 | −1.31385 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.5355 | −0.884752 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.44322 | 0.119158 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.3193 | 1.32451 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.1469 | −1.28245 | −0.641227 | − | 0.767351i | \(-0.721574\pi\) | ||||
−0.641227 | + | 0.767351i | \(0.721574\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 66.3870 | 2.28921 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −39.1619 | −1.34881 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.9806 | 0.446547 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.7722 | 0.541940 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.33796 | 0.286158 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0900 | 0.414441 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 53.7658 | 1.84091 | 0.920454 | − | 0.390851i | \(-0.127819\pi\) | ||||
0.920454 | + | 0.390851i | \(0.127819\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.52699 | 0.154820 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.9675 | −0.818715 | −0.409357 | − | 0.912374i | \(-0.634247\pi\) | ||||
−0.409357 | + | 0.912374i | \(0.634247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.70705 | 0.126483 | 0.0632415 | − | 0.997998i | \(-0.479856\pi\) | ||||
0.0632415 | + | 0.997998i | \(0.479856\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.4424 | 0.764836 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49.6296 | −1.68941 | −0.844705 | − | 0.535232i | \(-0.820224\pi\) | ||||
−0.844705 | + | 0.535232i | \(0.820224\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.35801 | 0.318182 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.5020 | 0.662323 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.85039 | 0.198461 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.46115 | 0.0495091 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.66618 | −0.0563918 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.53740 | 0.0519737 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.1004 | 0.442371 | 0.221185 | − | 0.975232i | \(-0.429007\pi\) | ||||
0.221185 | + | 0.975232i | \(0.429007\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.54155 | −0.0519951 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.88085 | 0.130749 | 0.0653746 | − | 0.997861i | \(-0.479176\pi\) | ||||
0.0653746 | + | 0.997861i | \(0.479176\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.8131 | −0.363890 | −0.181945 | − | 0.983309i | \(-0.558239\pi\) | ||||
−0.181945 | + | 0.983309i | \(0.558239\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.1109 | 0.541561 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.58387 | 0.288218 | 0.144109 | − | 0.989562i | \(-0.453968\pi\) | ||||
0.144109 | + | 0.989562i | \(0.453968\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.3836 | −0.784262 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.88645 | 0.163702 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.2188 | 0.408887 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.4134 | 0.615493 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.203585 | −0.00679751 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 66.2764 | 2.21044 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.823974 | −0.0274505 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.7312 | −0.856282 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.94457 | −0.0646398 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.2728 | −0.706351 | −0.353176 | − | 0.935557i | \(-0.614898\pi\) | ||||
−0.353176 | + | 0.935557i | \(0.614898\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.2757 | −0.440327 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.6441 | 0.915890 | 0.457945 | − | 0.888980i | \(-0.348586\pi\) | ||||
0.457945 | + | 0.888980i | \(0.348586\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.16484 | −0.303312 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.48342 | 0.214335 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.5124 | −0.644357 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.994404 | 0.0328024 | 0.0164012 | − | 0.999865i | \(-0.494779\pi\) | ||||
0.0164012 | + | 0.999865i | \(0.494779\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.1455 | 0.861522 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.01793 | 0.0335054 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.0900 | 0.397518 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.81309 | 0.223771 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.3747 | −0.602854 | −0.301427 | − | 0.953489i | \(-0.597463\pi\) | ||||
−0.301427 | + | 0.953489i | \(0.597463\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.3829 | −0.799116 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.7639 | −0.810735 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.74099 | 0.155047 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.0942 | −0.787122 | −0.393561 | − | 0.919298i | \(-0.628757\pi\) | ||||
−0.393561 | + | 0.919298i | \(0.628757\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.2459 | −0.954404 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51.9244 | −1.69269 | −0.846344 | − | 0.532637i | \(-0.821201\pi\) | ||||
−0.846344 | + | 0.532637i | \(0.821201\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.98062 | −0.325014 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.68141 | −0.282406 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.72643 | −0.153588 | −0.0767941 | − | 0.997047i | \(-0.524468\pi\) | ||||
−0.0767941 | + | 0.997047i | \(0.524468\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.991037 | −0.0321704 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.82330 | −0.156406 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.57682 | 0.115865 | 0.0579323 | − | 0.998321i | \(-0.481549\pi\) | ||||
0.0579323 | + | 0.998321i | \(0.481549\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.775591 | −0.0250975 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.2963 | 0.397483 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.5768 | 0.696752 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0498 | 0.485478 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.68286 | 0.118679 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.7666 | 0.378781 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.9646 | −1.09223 | −0.546114 | − | 0.837711i | \(-0.683894\pi\) | ||||
−0.546114 | + | 0.837711i | \(0.683894\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 42.3636 | 1.36092 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56.0561 | −1.79893 | −0.899463 | − | 0.436997i | \(-0.856042\pi\) | ||||
−0.899463 | + | 0.436997i | \(0.856042\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.9292 | −0.703019 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.203585 | −0.00651994 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −53.1219 | −1.69952 | −0.849761 | − | 0.527169i | \(-0.823254\pi\) | ||||
−0.849761 | + | 0.527169i | \(0.823254\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.8864 | 0.475773 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.3026 | −0.488574 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.7833 | −0.918045 | −0.459022 | − | 0.888425i | \(-0.651800\pi\) | ||||
−0.459022 | + | 0.888425i | \(0.651800\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.68141 | 0.308475 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.22441 | −0.166295 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.4432 | 0.363873 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.1641 | −1.52998 | −0.764991 | − | 0.644041i | \(-0.777257\pi\) | ||||
−0.764991 | + | 0.644041i | \(0.777257\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.8385 | −0.597823 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.29362 | −0.104415 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.5153 | −1.37814 | −0.689072 | − | 0.724693i | \(-0.741982\pi\) | ||||
−0.689072 | + | 0.724693i | \(0.741982\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −68.2701 | −2.15997 |
(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 | 7360.2.a.cf.1.2 | 3 | ||
4.3 | odd | 2 | 7360.2.a.bw.1.2 | 3 | |||
8.3 | odd | 2 | 920.2.a.i.1.2 | ✓ | 3 | ||
8.5 | even | 2 | 1840.2.a.q.1.2 | 3 | |||
24.11 | even | 2 | 8280.2.a.bl.1.2 | 3 | |||
40.3 | even | 4 | 4600.2.e.q.4049.4 | 6 | |||
40.19 | odd | 2 | 4600.2.a.v.1.2 | 3 | |||
40.27 | even | 4 | 4600.2.e.q.4049.3 | 6 | |||
40.29 | even | 2 | 9200.2.a.ci.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.i.1.2 | ✓ | 3 | 8.3 | odd | 2 | ||
1840.2.a.q.1.2 | 3 | 8.5 | even | 2 | |||
4600.2.a.v.1.2 | 3 | 40.19 | odd | 2 | |||
4600.2.e.q.4049.3 | 6 | 40.27 | even | 4 | |||
4600.2.e.q.4049.4 | 6 | 40.3 | even | 4 | |||
7360.2.a.bw.1.2 | 3 | 4.3 | odd | 2 | |||
7360.2.a.cf.1.2 | 3 | 1.1 | even | 1 | trivial | ||
8280.2.a.bl.1.2 | 3 | 24.11 | even | 2 | |||
9200.2.a.ci.1.2 | 3 | 40.29 | even | 2 |