Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(541,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("1080.541");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.k (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{18} + 5x^{16} + 28x^{12} - 28x^{10} + 112x^{8} + 320x^{4} - 256x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 541.6 | ||
Root | \(-1.17425 - 0.788128i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.541 |
Dual form | 1080.2.k.d.541.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).
\(n\) | \(217\) | \(271\) | \(541\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.17425 | + | 0.788128i | −0.830317 | + | 0.557291i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.757708 | − | 1.85091i | 0.378854 | − | 0.925456i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.12726 | 0.804027 | 0.402014 | − | 0.915634i | \(-0.368310\pi\) | ||||
0.402014 | + | 0.915634i | \(0.368310\pi\) | |||||||
\(8\) | 0.569020 | + | 2.77060i | 0.201179 | + | 0.979554i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.788128 | + | 1.17425i | 0.249228 | + | 0.371329i | ||||
\(11\) | 5.48036i | 1.65239i | 0.563384 | + | 0.826195i | \(0.309499\pi\) | ||||
−0.563384 | + | 0.826195i | \(0.690501\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.91228i | 1.36242i | 0.732088 | + | 0.681210i | \(0.238546\pi\) | ||||
−0.732088 | + | 0.681210i | \(0.761454\pi\) | |||||||
\(14\) | −2.49792 | + | 1.67655i | −0.667598 | + | 0.448077i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.85176 | − | 2.80490i | −0.712939 | − | 0.701226i | ||||
\(17\) | 0.235541 | 0.0571270 | 0.0285635 | − | 0.999592i | \(-0.490907\pi\) | ||||
0.0285635 | + | 0.999592i | \(0.490907\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.23139i | − | 1.20016i | −0.799939 | − | 0.600081i | \(-0.795135\pi\) | ||
0.799939 | − | 0.600081i | \(-0.204865\pi\) | |||||||
\(20\) | −1.85091 | − | 0.757708i | −0.413877 | − | 0.169429i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.31922 | − | 6.43529i | −0.920862 | − | 1.37201i | ||||
\(23\) | −7.42390 | −1.54799 | −0.773995 | − | 0.633192i | \(-0.781744\pi\) | ||||
−0.773995 | + | 0.633192i | \(0.781744\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −3.87150 | − | 5.76822i | −0.759264 | − | 1.13124i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.61184 | − | 3.93737i | 0.304609 | − | 0.744092i | ||||
\(29\) | 4.24894i | 0.789008i | 0.918894 | + | 0.394504i | \(0.129083\pi\) | ||||
−0.918894 | + | 0.394504i | \(0.870917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.05609 | 0.908100 | 0.454050 | − | 0.890976i | \(-0.349979\pi\) | ||||
0.454050 | + | 0.890976i | \(0.349979\pi\) | |||||||
\(32\) | 5.55929 | + | 1.04610i | 0.982752 | + | 0.184926i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.276583 | + | 0.185636i | −0.0474335 | + | 0.0318363i | ||||
\(35\) | − | 2.12726i | − | 0.359572i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.27608i | 0.374185i | 0.982342 | + | 0.187093i | \(0.0599065\pi\) | ||||
−0.982342 | + | 0.187093i | \(0.940094\pi\) | |||||||
\(38\) | 4.12300 | + | 6.14294i | 0.668839 | + | 0.996516i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.77060 | − | 0.569020i | 0.438070 | − | 0.0899700i | ||||
\(41\) | −3.26132 | −0.509332 | −0.254666 | − | 0.967029i | \(-0.581966\pi\) | ||||
−0.254666 | + | 0.967029i | \(0.581966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.90812i | 1.51097i | 0.655163 | + | 0.755487i | \(0.272600\pi\) | ||||
−0.655163 | + | 0.755487i | \(0.727400\pi\) | |||||||
\(44\) | 10.1437 | + | 4.15251i | 1.52921 | + | 0.626015i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.71749 | − | 5.85098i | 1.28532 | − | 0.862680i | ||||
\(47\) | 8.17359 | 1.19224 | 0.596121 | − | 0.802895i | \(-0.296708\pi\) | ||||
0.596121 | + | 0.802895i | \(0.296708\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.47478 | −0.353540 | ||||||||
\(50\) | 1.17425 | − | 0.788128i | 0.166063 | − | 0.111458i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.09220 | + | 3.72207i | 1.26086 | + | 0.516159i | ||||
\(53\) | 10.6637i | 1.46477i | 0.680890 | + | 0.732386i | \(0.261593\pi\) | ||||
−0.680890 | + | 0.732386i | \(0.738407\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.48036 | 0.738971 | ||||||||
\(56\) | 1.21045 | + | 5.89377i | 0.161753 | + | 0.787589i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.34871 | − | 4.98930i | −0.439707 | − | 0.655127i | ||||
\(59\) | − | 0.702988i | − | 0.0915212i | −0.998952 | − | 0.0457606i | \(-0.985429\pi\) | ||
0.998952 | − | 0.0457606i | \(-0.0145711\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.319109i | − | 0.0408577i | −0.999791 | − | 0.0204288i | \(-0.993497\pi\) | ||
0.999791 | − | 0.0204288i | \(-0.00650315\pi\) | |||||||
\(62\) | −5.93709 | + | 3.98485i | −0.754012 | + | 0.506076i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.35243 | + | 3.15305i | −0.919054 | + | 0.394132i | ||||
\(65\) | 4.91228 | 0.609293 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.70667i | 0.330672i | 0.986237 | + | 0.165336i | \(0.0528708\pi\) | ||||
−0.986237 | + | 0.165336i | \(0.947129\pi\) | |||||||
\(68\) | 0.178471 | − | 0.435965i | 0.0216428 | − | 0.0528685i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.67655 | + | 2.49792i | 0.200386 | + | 0.298559i | ||||
\(71\) | −7.18836 | −0.853101 | −0.426551 | − | 0.904464i | \(-0.640271\pi\) | ||||
−0.426551 | + | 0.904464i | \(0.640271\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.66370 | 1.13105 | 0.565525 | − | 0.824731i | \(-0.308673\pi\) | ||||
0.565525 | + | 0.824731i | \(0.308673\pi\) | |||||||
\(74\) | −1.79384 | − | 2.67268i | −0.208530 | − | 0.310693i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.68284 | − | 3.96386i | −1.11070 | − | 0.454686i | ||||
\(77\) | 11.6581i | 1.32857i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.8565 | −1.22146 | −0.610729 | − | 0.791840i | \(-0.709123\pi\) | ||||
−0.610729 | + | 0.791840i | \(0.709123\pi\) | |||||||
\(80\) | −2.80490 | + | 2.85176i | −0.313598 | + | 0.318836i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.82959 | − | 2.57033i | 0.422907 | − | 0.283846i | ||||
\(83\) | − | 8.53645i | − | 0.936997i | −0.883464 | − | 0.468498i | \(-0.844795\pi\) | ||
0.883464 | − | 0.468498i | \(-0.155205\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 0.235541i | − | 0.0255480i | ||||||
\(86\) | −7.80887 | − | 11.6346i | −0.842052 | − | 1.25459i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −15.1839 | + | 3.11843i | −1.61861 | + | 0.332426i | ||||
\(89\) | 9.90812 | 1.05026 | 0.525129 | − | 0.851022i | \(-0.324017\pi\) | ||||
0.525129 | + | 0.851022i | \(0.324017\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.4497i | 1.09542i | ||||||||
\(92\) | −5.62515 | + | 13.7410i | −0.586462 | + | 1.43260i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.59781 | + | 6.44184i | −0.989939 | + | 0.664425i | ||||
\(95\) | −5.23139 | −0.536729 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.8895 | 1.51180 | 0.755902 | − | 0.654685i | \(-0.227199\pi\) | ||||
0.755902 | + | 0.654685i | \(0.227199\pi\) | |||||||
\(98\) | 2.90600 | − | 1.95044i | 0.293550 | − | 0.197025i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.757708 | + | 1.85091i | −0.0757708 | + | 0.185091i | ||||
\(101\) | − | 6.13283i | − | 0.610240i | −0.952314 | − | 0.305120i | \(-0.901303\pi\) | ||
0.952314 | − | 0.305120i | \(-0.0986965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.82788 | −0.869837 | −0.434918 | − | 0.900470i | \(-0.643223\pi\) | ||||
−0.434918 | + | 0.900470i | \(0.643223\pi\) | |||||||
\(104\) | −13.6099 | + | 2.79519i | −1.33457 | + | 0.274090i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.40436 | − | 12.5218i | −0.816304 | − | 1.21623i | ||||
\(107\) | 7.48593i | 0.723693i | 0.932238 | + | 0.361846i | \(0.117853\pi\) | ||||
−0.932238 | + | 0.361846i | \(0.882147\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.8462i | 1.70935i | 0.519160 | + | 0.854677i | \(0.326245\pi\) | ||||
−0.519160 | + | 0.854677i | \(0.673755\pi\) | |||||||
\(110\) | −6.43529 | + | 4.31922i | −0.613581 | + | 0.411822i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.06642 | − | 5.96675i | −0.573223 | − | 0.563805i | ||||
\(113\) | 14.8609 | 1.39800 | 0.698998 | − | 0.715124i | \(-0.253630\pi\) | ||||
0.698998 | + | 0.715124i | \(0.253630\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.42390i | 0.692282i | ||||||||
\(116\) | 7.86441 | + | 3.21945i | 0.730192 | + | 0.298919i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.554045 | + | 0.825481i | 0.0510039 | + | 0.0759917i | ||||
\(119\) | 0.501055 | 0.0459316 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −19.0343 | −1.73039 | ||||||||
\(122\) | 0.251498 | + | 0.374712i | 0.0227696 | + | 0.0339248i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.83104 | − | 9.35838i | 0.344038 | − | 0.840407i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.82788 | 0.605876 | 0.302938 | − | 0.953010i | \(-0.402032\pi\) | ||||
0.302938 | + | 0.953010i | \(0.402032\pi\) | |||||||
\(128\) | 6.14856 | − | 9.49712i | 0.543461 | − | 0.839435i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.76822 | + | 3.87150i | −0.505907 | + | 0.339553i | ||||
\(131\) | − | 21.3874i | − | 1.86863i | −0.356452 | − | 0.934314i | \(-0.616014\pi\) | ||
0.356452 | − | 0.934314i | \(-0.383986\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 11.1285i | − | 0.964963i | ||||||
\(134\) | −2.13320 | − | 3.17829i | −0.184280 | − | 0.274563i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.134027 | + | 0.652588i | 0.0114927 | + | 0.0559590i | ||||
\(137\) | 19.6081 | 1.67523 | 0.837617 | − | 0.546259i | \(-0.183948\pi\) | ||||
0.837617 | + | 0.546259i | \(0.183948\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.901666i | 0.0764784i | 0.999269 | + | 0.0382392i | \(0.0121749\pi\) | ||||
−0.999269 | + | 0.0382392i | \(0.987825\pi\) | |||||||
\(140\) | −3.93737 | − | 1.61184i | −0.332768 | − | 0.136225i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.44090 | − | 5.66535i | 0.708345 | − | 0.475425i | ||||
\(143\) | −26.9210 | −2.25125 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.24894 | 0.352855 | ||||||||
\(146\) | −11.3476 | + | 7.61624i | −0.939131 | + | 0.630324i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.21283 | + | 1.72461i | 0.346292 | + | 0.141762i | ||||
\(149\) | − | 1.75106i | − | 0.143453i | −0.997424 | − | 0.0717264i | \(-0.977149\pi\) | ||
0.997424 | − | 0.0717264i | \(-0.0228508\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.90141 | 0.236114 | 0.118057 | − | 0.993007i | \(-0.462334\pi\) | ||||
0.118057 | + | 0.993007i | \(0.462334\pi\) | |||||||
\(152\) | 14.4941 | − | 2.97676i | 1.17562 | − | 0.241447i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.18810 | − | 13.6895i | −0.740398 | − | 1.10313i | ||||
\(155\) | − | 5.05609i | − | 0.406115i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.7601i | 1.57703i | 0.615018 | + | 0.788513i | \(0.289149\pi\) | ||||
−0.615018 | + | 0.788513i | \(0.710851\pi\) | |||||||
\(158\) | 12.7483 | − | 8.55635i | 1.01420 | − | 0.680707i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.04610 | − | 5.55929i | 0.0827014 | − | 0.439500i | ||||
\(161\) | −15.7925 | −1.24463 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.4946i | 1.68359i | 0.539799 | + | 0.841794i | \(0.318500\pi\) | ||||
−0.539799 | + | 0.841794i | \(0.681500\pi\) | |||||||
\(164\) | −2.47113 | + | 6.03641i | −0.192963 | + | 0.471364i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.72781 | + | 10.0239i | 0.522180 | + | 0.778005i | ||||
\(167\) | −19.0666 | −1.47541 | −0.737707 | − | 0.675121i | \(-0.764091\pi\) | ||||
−0.737707 | + | 0.675121i | \(0.764091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1305 | −0.856190 | ||||||||
\(170\) | 0.185636 | + | 0.276583i | 0.0142376 | + | 0.0212129i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 18.3391 | + | 7.50747i | 1.39834 | + | 0.572439i | ||||
\(173\) | 9.31060i | 0.707872i | 0.935270 | + | 0.353936i | \(0.115157\pi\) | ||||
−0.935270 | + | 0.353936i | \(0.884843\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.12726 | −0.160805 | ||||||||
\(176\) | 15.3719 | − | 15.6286i | 1.15870 | − | 1.17805i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.6346 | + | 7.80887i | −0.872048 | + | 0.585300i | ||||
\(179\) | − | 2.70620i | − | 0.202271i | −0.994873 | − | 0.101136i | \(-0.967752\pi\) | ||
0.994873 | − | 0.101136i | \(-0.0322476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.42390i | 0.551814i | 0.961184 | + | 0.275907i | \(0.0889782\pi\) | ||||
−0.961184 | + | 0.275907i | \(0.911022\pi\) | |||||||
\(182\) | −8.23568 | − | 12.2705i | −0.610469 | − | 0.909549i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.22435 | − | 20.5686i | −0.311423 | − | 1.51634i | ||||
\(185\) | 2.27608 | 0.167341 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.29085i | 0.0943960i | ||||||||
\(188\) | 6.19320 | − | 15.1286i | 0.451685 | − | 1.10337i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.14294 | − | 4.12300i | 0.445655 | − | 0.299114i | ||||
\(191\) | −13.2099 | −0.955837 | −0.477919 | − | 0.878404i | \(-0.658609\pi\) | ||||
−0.477919 | + | 0.878404i | \(0.658609\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.73487 | −0.268842 | −0.134421 | − | 0.990924i | \(-0.542917\pi\) | ||||
−0.134421 | + | 0.990924i | \(0.542917\pi\) | |||||||
\(194\) | −17.4840 | + | 11.7349i | −1.25528 | + | 0.842515i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.87516 | + | 4.58060i | −0.133940 | + | 0.327186i | ||||
\(197\) | − | 7.00321i | − | 0.498958i | −0.968380 | − | 0.249479i | \(-0.919741\pi\) | ||
0.968380 | − | 0.249479i | \(-0.0802594\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.2769 | 1.50828 | 0.754140 | − | 0.656714i | \(-0.228054\pi\) | ||||
0.754140 | + | 0.656714i | \(0.228054\pi\) | |||||||
\(200\) | −0.569020 | − | 2.77060i | −0.0402358 | − | 0.195911i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.83346 | + | 7.20146i | 0.340081 | + | 0.506693i | ||||
\(203\) | 9.03858i | 0.634384i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.26132i | 0.227780i | ||||||||
\(206\) | 10.3661 | − | 6.95750i | 0.722241 | − | 0.484752i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.7785 | − | 14.0086i | 0.955365 | − | 0.971323i | ||||
\(209\) | 28.6699 | 1.98314 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 24.4773i | − | 1.68509i | −0.538628 | − | 0.842544i | \(-0.681057\pi\) | ||
0.538628 | − | 0.842544i | \(-0.318943\pi\) | |||||||
\(212\) | 19.7376 | + | 8.07998i | 1.35558 | + | 0.554935i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.89988 | − | 8.79033i | −0.403307 | − | 0.600895i | ||||
\(215\) | 9.90812 | 0.675728 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.7556 | 0.730138 | ||||||||
\(218\) | −14.0651 | − | 20.9558i | −0.952607 | − | 1.41931i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.15251 | − | 10.1437i | 0.279962 | − | 0.683886i | ||||
\(221\) | 1.15704i | 0.0778310i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.9862 | −1.13748 | −0.568741 | − | 0.822516i | \(-0.692569\pi\) | ||||
−0.568741 | + | 0.822516i | \(0.692569\pi\) | |||||||
\(224\) | 11.8260 | + | 2.22532i | 0.790160 | + | 0.148685i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −17.4504 | + | 11.7123i | −1.16078 | + | 0.779090i | ||||
\(227\) | − | 20.5203i | − | 1.36198i | −0.732294 | − | 0.680988i | \(-0.761550\pi\) | ||
0.732294 | − | 0.680988i | \(-0.238450\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.01268i | − | 0.199083i | −0.995033 | − | 0.0995416i | \(-0.968262\pi\) | ||
0.995033 | − | 0.0995416i | \(-0.0317376\pi\) | |||||||
\(230\) | −5.85098 | − | 8.71749i | −0.385802 | − | 0.574814i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.7721 | + | 2.41773i | −0.772876 | + | 0.158732i | ||||
\(233\) | −15.2379 | −0.998267 | −0.499134 | − | 0.866525i | \(-0.666348\pi\) | ||||
−0.499134 | + | 0.866525i | \(0.666348\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 8.17359i | − | 0.533186i | ||||||
\(236\) | −1.30117 | − | 0.532660i | −0.0846989 | − | 0.0346732i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.588362 | + | 0.394896i | −0.0381379 | + | 0.0255973i | ||||
\(239\) | 15.8761 | 1.02694 | 0.513470 | − | 0.858108i | \(-0.328360\pi\) | ||||
0.513470 | + | 0.858108i | \(0.328360\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.9838 | 1.35169 | 0.675843 | − | 0.737046i | \(-0.263780\pi\) | ||||
0.675843 | + | 0.737046i | \(0.263780\pi\) | |||||||
\(242\) | 22.3510 | − | 15.0015i | 1.43678 | − | 0.964332i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.590642 | − | 0.241791i | −0.0378120 | − | 0.0154791i | ||||
\(245\) | 2.47478i | 0.158108i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 25.6980 | 1.63513 | ||||||||
\(248\) | 2.87702 | + | 14.0084i | 0.182691 | + | 0.889534i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.788128 | − | 1.17425i | −0.0498456 | − | 0.0742659i | ||||
\(251\) | − | 8.49787i | − | 0.536381i | −0.963366 | − | 0.268190i | \(-0.913574\pi\) | ||
0.963366 | − | 0.268190i | \(-0.0864256\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 40.6856i | − | 2.55788i | ||||||
\(254\) | −8.01761 | + | 5.38124i | −0.503070 | + | 0.337649i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.265028 | + | 15.9978i | 0.0165642 | + | 0.999863i | ||||
\(257\) | −0.222442 | −0.0138756 | −0.00693778 | − | 0.999976i | \(-0.502208\pi\) | ||||
−0.00693778 | + | 0.999976i | \(0.502208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.84181i | 0.300855i | ||||||||
\(260\) | 3.72207 | − | 9.09220i | 0.230833 | − | 0.563874i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.8560 | + | 25.1141i | 1.04137 | + | 1.55155i | ||||
\(263\) | 7.74301 | 0.477454 | 0.238727 | − | 0.971087i | \(-0.423270\pi\) | ||||
0.238727 | + | 0.971087i | \(0.423270\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.6637 | 0.655066 | ||||||||
\(266\) | 8.77068 | + | 13.0676i | 0.537765 | + | 0.801226i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.00980 | + | 2.05086i | 0.306022 | + | 0.125276i | ||||
\(269\) | − | 2.50903i | − | 0.152978i | −0.997070 | − | 0.0764890i | \(-0.975629\pi\) | ||
0.997070 | − | 0.0764890i | \(-0.0243710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.00558 | −0.425559 | −0.212779 | − | 0.977100i | \(-0.568252\pi\) | ||||
−0.212779 | + | 0.977100i | \(0.568252\pi\) | |||||||
\(272\) | −0.671704 | − | 0.660669i | −0.0407281 | − | 0.0400589i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −23.0247 | + | 15.4537i | −1.39098 | + | 0.933592i | ||||
\(275\) | − | 5.48036i | − | 0.330478i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 8.13052i | − | 0.488516i | −0.969710 | − | 0.244258i | \(-0.921456\pi\) | ||
0.969710 | − | 0.244258i | \(-0.0785443\pi\) | |||||||
\(278\) | −0.710629 | − | 1.05878i | −0.0426207 | − | 0.0635013i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.89377 | − | 1.21045i | 0.352220 | − | 0.0723383i | ||||
\(281\) | 20.2038 | 1.20526 | 0.602628 | − | 0.798023i | \(-0.294120\pi\) | ||||
0.602628 | + | 0.798023i | \(0.294120\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 27.4626i | − | 1.63248i | −0.577712 | − | 0.816241i | \(-0.696054\pi\) | ||
0.577712 | − | 0.816241i | \(-0.303946\pi\) | |||||||
\(284\) | −5.44668 | + | 13.3050i | −0.323201 | + | 0.789508i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 31.6119 | − | 21.2172i | 1.86925 | − | 1.25460i | ||||
\(287\) | −6.93765 | −0.409517 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9445 | −0.996737 | ||||||||
\(290\) | −4.98930 | + | 3.34871i | −0.292982 | + | 0.196643i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.32227 | − | 17.8867i | 0.428503 | − | 1.04674i | ||||
\(293\) | − | 5.00321i | − | 0.292291i | −0.989263 | − | 0.146145i | \(-0.953313\pi\) | ||
0.989263 | − | 0.146145i | \(-0.0466867\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.702988 | −0.0409295 | ||||||||
\(296\) | −6.30611 | + | 1.29514i | −0.366535 | + | 0.0752783i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.38006 | + | 2.05618i | 0.0799449 | + | 0.119111i | ||||
\(299\) | − | 36.4683i | − | 2.10901i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.0771i | 1.21486i | ||||||||
\(302\) | −3.40697 | + | 2.28668i | −0.196049 | + | 0.131584i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14.6735 | + | 14.9186i | −0.841585 | + | 0.855643i | ||||
\(305\) | −0.319109 | −0.0182721 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.18634i | − | 0.524292i | −0.965028 | − | 0.262146i | \(-0.915570\pi\) | ||
0.965028 | − | 0.262146i | \(-0.0844302\pi\) | |||||||
\(308\) | 21.5782 | + | 8.83346i | 1.22953 | + | 0.503333i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.98485 | + | 5.93709i | 0.226324 | + | 0.337204i | ||||
\(311\) | −1.99798 | −0.113295 | −0.0566475 | − | 0.998394i | \(-0.518041\pi\) | ||||
−0.0566475 | + | 0.998394i | \(0.518041\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.6052 | −0.599440 | −0.299720 | − | 0.954027i | \(-0.596893\pi\) | ||||
−0.299720 | + | 0.954027i | \(0.596893\pi\) | |||||||
\(314\) | −15.5735 | − | 23.2032i | −0.878862 | − | 1.30943i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.22610 | + | 20.0945i | −0.462754 | + | 1.13041i | ||||
\(317\) | − | 9.76229i | − | 0.548305i | −0.961686 | − | 0.274152i | \(-0.911603\pi\) | ||
0.961686 | − | 0.274152i | \(-0.0883973\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.2857 | −1.30375 | ||||||||
\(320\) | 3.15305 | + | 7.35243i | 0.176261 | + | 0.411013i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.5443 | − | 12.4465i | 1.03343 | − | 0.693619i | ||||
\(323\) | − | 1.23220i | − | 0.0685616i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.91228i | − | 0.272484i | ||||||
\(326\) | −16.9405 | − | 25.2400i | −0.938248 | − | 1.39791i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.85575 | − | 9.03580i | −0.102467 | − | 0.498918i | ||||
\(329\) | 17.3873 | 0.958594 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 5.62096i | − | 0.308956i | −0.987996 | − | 0.154478i | \(-0.950630\pi\) | ||
0.987996 | − | 0.154478i | \(-0.0493696\pi\) | |||||||
\(332\) | −15.8002 | − | 6.46814i | −0.867150 | − | 0.354985i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 22.3888 | − | 15.0269i | 1.22506 | − | 0.822235i | ||||
\(335\) | 2.70667 | 0.147881 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.804011 | −0.0437973 | −0.0218986 | − | 0.999760i | \(-0.506971\pi\) | ||||
−0.0218986 | + | 0.999760i | \(0.506971\pi\) | |||||||
\(338\) | 13.0699 | − | 8.77224i | 0.710910 | − | 0.477147i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.435965 | − | 0.178471i | −0.0236435 | − | 0.00967895i | ||||
\(341\) | 27.7092i | 1.50054i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1553 | −1.08828 | ||||||||
\(344\) | −27.4514 | + | 5.63792i | −1.48008 | + | 0.303976i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.33795 | − | 10.9329i | −0.394490 | − | 0.587758i | ||||
\(347\) | 10.7019i | 0.574507i | 0.957855 | + | 0.287253i | \(0.0927421\pi\) | ||||
−0.957855 | + | 0.287253i | \(0.907258\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 24.9915i | − | 1.33776i | −0.743369 | − | 0.668881i | \(-0.766774\pi\) | ||
0.743369 | − | 0.668881i | \(-0.233226\pi\) | |||||||
\(350\) | 2.49792 | − | 1.67655i | 0.133520 | − | 0.0896154i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.73299 | + | 30.4669i | −0.305570 | + | 1.62389i | ||||
\(353\) | −15.4860 | −0.824237 | −0.412119 | − | 0.911130i | \(-0.635211\pi\) | ||||
−0.412119 | + | 0.911130i | \(0.635211\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.18836i | 0.381518i | ||||||||
\(356\) | 7.50747 | − | 18.3391i | 0.397895 | − | 0.971969i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.13283 | + | 3.17775i | 0.112724 | + | 0.167949i | ||||
\(359\) | 11.9335 | 0.629826 | 0.314913 | − | 0.949121i | \(-0.398025\pi\) | ||||
0.314913 | + | 0.949121i | \(0.398025\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.36740 | −0.440390 | ||||||||
\(362\) | −5.85098 | − | 8.71749i | −0.307521 | − | 0.458181i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 19.3414 | + | 7.91780i | 1.01377 | + | 0.415006i | ||||
\(365\) | − | 9.66370i | − | 0.505821i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.95514 | 0.363055 | 0.181528 | − | 0.983386i | \(-0.441896\pi\) | ||||
0.181528 | + | 0.983386i | \(0.441896\pi\) | |||||||
\(368\) | 21.1712 | + | 20.8233i | 1.10362 | + | 1.08549i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.67268 | + | 1.79384i | −0.138946 | + | 0.0932575i | ||||
\(371\) | 22.6844i | 1.17772i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 11.6296i | − | 0.602156i | −0.953600 | − | 0.301078i | \(-0.902654\pi\) | ||
0.953600 | − | 0.301078i | \(-0.0973464\pi\) | |||||||
\(374\) | −1.01735 | − | 1.51577i | −0.0526060 | − | 0.0783787i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.65094 | + | 22.6457i | 0.239854 | + | 1.16787i | ||||
\(377\) | −20.8720 | −1.07496 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 0.235541i | − | 0.0120989i | −0.999982 | − | 0.00604945i | \(-0.998074\pi\) | ||
0.999982 | − | 0.00604945i | \(-0.00192561\pi\) | |||||||
\(380\) | −3.96386 | + | 9.68284i | −0.203342 | + | 0.496719i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.5117 | − | 10.4111i | 0.793648 | − | 0.532679i | ||||
\(383\) | −4.23305 | −0.216299 | −0.108149 | − | 0.994135i | \(-0.534493\pi\) | ||||
−0.108149 | + | 0.994135i | \(0.534493\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.6581 | 0.594153 | ||||||||
\(386\) | 4.38566 | − | 2.94356i | 0.223224 | − | 0.149823i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.2819 | − | 27.5593i | 0.572753 | − | 1.39911i | ||||
\(389\) | − | 27.0991i | − | 1.37398i | −0.726667 | − | 0.686990i | \(-0.758932\pi\) | ||
0.726667 | − | 0.686990i | \(-0.241068\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.74863 | −0.0884320 | ||||||||
\(392\) | −1.40820 | − | 6.85662i | −0.0711248 | − | 0.346312i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.51943 | + | 8.22350i | 0.278065 | + | 0.414294i | ||||
\(395\) | 10.8565i | 0.546252i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 21.9552i | − | 1.10190i | −0.834539 | − | 0.550949i | \(-0.814266\pi\) | ||
0.834539 | − | 0.550949i | \(-0.185734\pi\) | |||||||
\(398\) | −24.9843 | + | 16.7689i | −1.25235 | + | 0.840550i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.85176 | + | 2.80490i | 0.142588 | + | 0.140245i | ||||
\(401\) | 8.36813 | 0.417884 | 0.208942 | − | 0.977928i | \(-0.432998\pi\) | ||||
0.208942 | + | 0.977928i | \(0.432998\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.8369i | 1.23721i | ||||||||
\(404\) | −11.3513 | − | 4.64690i | −0.564750 | − | 0.231192i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.12355 | − | 10.6135i | −0.353536 | − | 0.526740i | ||||
\(407\) | −12.4737 | −0.618300 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.2474 | −1.39675 | −0.698373 | − | 0.715734i | \(-0.746092\pi\) | ||||
−0.698373 | + | 0.715734i | \(0.746092\pi\) | |||||||
\(410\) | −2.57033 | − | 3.82959i | −0.126940 | − | 0.189130i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.68896 | + | 16.3396i | −0.329541 | + | 0.804996i | ||||
\(413\) | − | 1.49544i | − | 0.0735856i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.53645 | −0.419038 | ||||||||
\(416\) | −5.13873 | + | 27.3088i | −0.251947 | + | 1.33892i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −33.6655 | + | 22.5955i | −1.64663 | + | 1.10518i | ||||
\(419\) | 8.68443i | 0.424262i | 0.977241 | + | 0.212131i | \(0.0680404\pi\) | ||||
−0.977241 | + | 0.212131i | \(0.931960\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.73033i | 0.230542i | 0.993334 | + | 0.115271i | \(0.0367737\pi\) | ||||
−0.993334 | + | 0.115271i | \(0.963226\pi\) | |||||||
\(422\) | 19.2913 | + | 28.7424i | 0.939084 | + | 1.39916i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −29.5448 | + | 6.06786i | −1.43482 | + | 0.294681i | ||||
\(425\) | −0.235541 | −0.0114254 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 0.678826i | − | 0.0328507i | ||||||
\(428\) | 13.8558 | + | 5.67215i | 0.669746 | + | 0.274174i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.6346 | + | 7.80887i | −0.561069 | + | 0.376577i | ||||
\(431\) | −39.1052 | −1.88363 | −0.941817 | − | 0.336127i | \(-0.890883\pi\) | ||||
−0.941817 | + | 0.336127i | \(0.890883\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.8221 | 1.62538 | 0.812692 | − | 0.582693i | \(-0.198001\pi\) | ||||
0.812692 | + | 0.582693i | \(0.198001\pi\) | |||||||
\(434\) | −12.6297 | + | 8.47679i | −0.606246 | + | 0.406899i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 33.0317 | + | 13.5222i | 1.58193 | + | 0.647596i | ||||
\(437\) | 38.8373i | 1.85784i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.59960 | 0.0763448 | 0.0381724 | − | 0.999271i | \(-0.487846\pi\) | ||||
0.0381724 | + | 0.999271i | \(0.487846\pi\) | |||||||
\(440\) | 3.11843 | + | 15.1839i | 0.148666 | + | 0.723863i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.911896 | − | 1.35865i | −0.0433745 | − | 0.0646244i | ||||
\(443\) | 8.64862i | 0.410909i | 0.978667 | + | 0.205454i | \(0.0658672\pi\) | ||||
−0.978667 | + | 0.205454i | \(0.934133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 9.90812i | − | 0.469690i | ||||||
\(446\) | 19.9460 | − | 13.3873i | 0.944472 | − | 0.633909i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −15.6405 | + | 6.70735i | −0.738945 | + | 0.316893i | ||||
\(449\) | 15.9597 | 0.753184 | 0.376592 | − | 0.926379i | \(-0.377096\pi\) | ||||
0.376592 | + | 0.926379i | \(0.377096\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 17.8732i | − | 0.841615i | ||||||
\(452\) | 11.2602 | − | 27.5062i | 0.529636 | − | 1.29378i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.1726 | + | 24.0958i | 0.759017 | + | 1.13087i | ||||
\(455\) | 10.4497 | 0.489888 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.6462 | −1.05934 | −0.529672 | − | 0.848203i | \(-0.677685\pi\) | ||||
−0.529672 | + | 0.848203i | \(0.677685\pi\) | |||||||
\(458\) | 2.37438 | + | 3.53762i | 0.110947 | + | 0.165302i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13.7410 | + | 5.62515i | 0.640677 | + | 0.262274i | ||||
\(461\) | 22.4400i | 1.04513i | 0.852599 | + | 0.522566i | \(0.175025\pi\) | ||||
−0.852599 | + | 0.522566i | \(0.824975\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.8710 | 1.43470 | 0.717348 | − | 0.696715i | \(-0.245356\pi\) | ||||
0.717348 | + | 0.696715i | \(0.245356\pi\) | |||||||
\(464\) | 11.9179 | − | 12.1169i | 0.553273 | − | 0.562514i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.8930 | − | 12.0094i | 0.828879 | − | 0.556325i | ||||
\(467\) | − | 3.05734i | − | 0.141477i | −0.997495 | − | 0.0707383i | \(-0.977464\pi\) | ||
0.997495 | − | 0.0707383i | \(-0.0225355\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.75777i | 0.265869i | ||||||||
\(470\) | 6.44184 | + | 9.59781i | 0.297140 | + | 0.442714i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.94770 | − | 0.400014i | 0.0896500 | − | 0.0184122i | ||||
\(473\) | −54.3001 | −2.49672 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.23139i | 0.240032i | ||||||||
\(476\) | 0.379654 | − | 0.927409i | 0.0174014 | − | 0.0425077i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.6425 | + | 12.5124i | −0.852686 | + | 0.572304i | ||||
\(479\) | 22.4262 | 1.02468 | 0.512341 | − | 0.858782i | \(-0.328779\pi\) | ||||
0.512341 | + | 0.858782i | \(0.328779\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.1807 | −0.509798 | ||||||||
\(482\) | −24.6402 | + | 16.5379i | −1.12233 | + | 0.753282i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.4225 | + | 35.2309i | −0.655566 | + | 1.60140i | ||||
\(485\) | − | 14.8895i | − | 0.676100i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.9961 | −0.543594 | −0.271797 | − | 0.962355i | \(-0.587618\pi\) | ||||
−0.271797 | + | 0.962355i | \(0.587618\pi\) | |||||||
\(488\) | 0.884122 | − | 0.181579i | 0.0400223 | − | 0.00821971i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.95044 | − | 2.90600i | −0.0881121 | − | 0.131280i | ||||
\(491\) | 0.261916i | 0.0118201i | 0.999983 | + | 0.00591005i | \(0.00188124\pi\) | ||||
−0.999983 | + | 0.00591005i | \(0.998119\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.00080i | 0.0450736i | ||||||||
\(494\) | −30.1758 | + | 20.2533i | −1.35767 | + | 0.911240i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.4187 | − | 14.1818i | −0.647420 | − | 0.636784i | ||||
\(497\) | −15.2915 | −0.685917 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 43.0171i | − | 1.92571i | −0.270018 | − | 0.962855i | \(-0.587030\pi\) | ||
0.270018 | − | 0.962855i | \(-0.412970\pi\) | |||||||
\(500\) | 1.85091 | + | 0.757708i | 0.0827753 | + | 0.0338857i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.69741 | + | 9.97859i | 0.298920 | + | 0.445366i | ||||
\(503\) | −21.3295 | −0.951037 | −0.475518 | − | 0.879706i | \(-0.657740\pi\) | ||||
−0.475518 | + | 0.879706i | \(0.657740\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.13283 | −0.272908 | ||||||||
\(506\) | 32.0655 | + | 47.7749i | 1.42548 | + | 2.12385i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.17354 | − | 12.6378i | 0.229539 | − | 0.560712i | ||||
\(509\) | 15.0919i | 0.668936i | 0.942407 | + | 0.334468i | \(0.108557\pi\) | ||||
−0.942407 | + | 0.334468i | \(0.891443\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.5572 | 0.909396 | ||||||||
\(512\) | −12.9195 | − | 18.5765i | −0.570968 | − | 0.820972i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.261202 | − | 0.175313i | 0.0115211 | − | 0.00773272i | ||||
\(515\) | 8.82788i | 0.389003i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.7942i | 1.97005i | ||||||||
\(518\) | −3.81596 | − | 5.68547i | −0.167664 | − | 0.249805i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.79519 | + | 13.6099i | 0.122577 | + | 0.596836i | ||||
\(521\) | 33.8443 | 1.48274 | 0.741372 | − | 0.671094i | \(-0.234175\pi\) | ||||
0.741372 | + | 0.671094i | \(0.234175\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.5034i | 0.459281i | 0.973276 | + | 0.229640i | \(0.0737550\pi\) | ||||
−0.973276 | + | 0.229640i | \(0.926245\pi\) | |||||||
\(524\) | −39.5862 | − | 16.2054i | −1.72933 | − | 0.707937i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.09220 | + | 6.10248i | −0.396439 | + | 0.266081i | ||||
\(527\) | 1.19091 | 0.0518770 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.1143 | 1.39627 | ||||||||
\(530\) | −12.5218 | + | 8.40436i | −0.543913 | + | 0.365062i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −20.5979 | − | 8.43216i | −0.893031 | − | 0.365580i | ||||
\(533\) | − | 16.0205i | − | 0.693924i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.48593 | 0.323645 | ||||||||
\(536\) | −7.49909 | + | 1.54015i | −0.323911 | + | 0.0665243i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.97743 | + | 2.94621i | 0.0852532 | + | 0.127020i | ||||
\(539\) | − | 13.5627i | − | 0.584186i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.2058i | 0.782728i | 0.920236 | + | 0.391364i | \(0.127997\pi\) | ||||
−0.920236 | + | 0.391364i | \(0.872003\pi\) | |||||||
\(542\) | 8.22627 | − | 5.52129i | 0.353349 | − | 0.237160i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.30944 | + | 0.246399i | 0.0561417 | + | 0.0105643i | ||||
\(545\) | 17.8462 | 0.764446 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.81348i | − | 0.334080i | −0.985950 | − | 0.167040i | \(-0.946579\pi\) | ||
0.985950 | − | 0.167040i | \(-0.0534209\pi\) | |||||||
\(548\) | 14.8572 | − | 36.2929i | 0.634669 | − | 1.55036i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.31922 | + | 6.43529i | 0.184172 | + | 0.274402i | ||||
\(551\) | 22.2278 | 0.946937 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.0947 | −0.982085 | ||||||||
\(554\) | 6.40789 | + | 9.54723i | 0.272245 | + | 0.405623i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.66891 | + | 0.683200i | 0.0707774 | + | 0.0289741i | ||||
\(557\) | 14.7679i | 0.625735i | 0.949797 | + | 0.312867i | \(0.101290\pi\) | ||||
−0.949797 | + | 0.312867i | \(0.898710\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.6715 | −2.05858 | ||||||||
\(560\) | −5.96675 | + | 6.06642i | −0.252141 | + | 0.256353i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.7242 | + | 15.9231i | −1.00074 | + | 0.671678i | ||||
\(563\) | 29.5041i | 1.24345i | 0.783236 | + | 0.621724i | \(0.213567\pi\) | ||||
−0.783236 | + | 0.621724i | \(0.786433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 14.8609i | − | 0.625203i | ||||||
\(566\) | 21.6440 | + | 32.2478i | 0.909767 | + | 1.35548i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.09032 | − | 19.9161i | −0.171626 | − | 0.835659i | ||||
\(569\) | 29.0862 | 1.21935 | 0.609677 | − | 0.792650i | \(-0.291299\pi\) | ||||
0.609677 | + | 0.792650i | \(0.291299\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 42.1417i | − | 1.76357i | −0.471649 | − | 0.881787i | \(-0.656341\pi\) | ||
0.471649 | − | 0.881787i | \(-0.343659\pi\) | |||||||
\(572\) | −20.3983 | + | 49.8285i | −0.852895 | + | 2.08343i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.14651 | − | 5.46776i | 0.340029 | − | 0.228220i | ||||
\(575\) | 7.42390 | 0.309598 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.8258 | −1.40819 | −0.704094 | − | 0.710107i | \(-0.748646\pi\) | ||||
−0.704094 | + | 0.710107i | \(0.748646\pi\) | |||||||
\(578\) | 19.8970 | − | 13.3545i | 0.827608 | − | 0.555472i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.21945 | − | 7.86441i | 0.133681 | − | 0.326552i | ||||
\(581\) | − | 18.1592i | − | 0.753371i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −58.4409 | −2.42037 | ||||||||
\(584\) | 5.49884 | + | 26.7742i | 0.227544 | + | 1.10793i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.94317 | + | 5.87501i | 0.162891 | + | 0.242694i | ||||
\(587\) | − | 2.36693i | − | 0.0976937i | −0.998806 | − | 0.0488469i | \(-0.984445\pi\) | ||
0.998806 | − | 0.0488469i | \(-0.0155546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 26.4504i | − | 1.08987i | ||||||
\(590\) | 0.825481 | − | 0.554045i | 0.0339845 | − | 0.0228097i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.38419 | − | 6.49083i | 0.262389 | − | 0.266771i | ||||
\(593\) | 14.0133 | 0.575459 | 0.287729 | − | 0.957712i | \(-0.407100\pi\) | ||||
0.287729 | + | 0.957712i | \(0.407100\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 0.501055i | − | 0.0205413i | ||||||
\(596\) | −3.24107 | − | 1.32680i | −0.132759 | − | 0.0543477i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 28.7417 | + | 42.8227i | 1.17533 | + | 1.75115i | ||||
\(599\) | 0.194646 | 0.00795304 | 0.00397652 | − | 0.999992i | \(-0.498734\pi\) | ||||
0.00397652 | + | 0.999992i | \(0.498734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.3962 | −1.64780 | −0.823898 | − | 0.566738i | \(-0.808205\pi\) | ||||
−0.823898 | + | 0.566738i | \(0.808205\pi\) | |||||||
\(602\) | −16.6115 | − | 24.7497i | −0.677033 | − | 1.00872i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.19842 | − | 5.37026i | 0.0894526 | − | 0.218513i | ||||
\(605\) | 19.0343i | 0.773855i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.9823 | 1.41989 | 0.709944 | − | 0.704258i | \(-0.248720\pi\) | ||||
0.709944 | + | 0.704258i | \(0.248720\pi\) | |||||||
\(608\) | 5.47255 | − | 29.0828i | 0.221941 | − | 1.17946i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.374712 | − | 0.251498i | 0.0151716 | − | 0.0101829i | ||||
\(611\) | 40.1510i | 1.62433i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.46784i | 0.261233i | 0.991433 | + | 0.130617i | \(0.0416957\pi\) | ||||
−0.991433 | + | 0.130617i | \(0.958304\pi\) | |||||||
\(614\) | 7.24001 | + | 10.7870i | 0.292183 | + | 0.435329i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −32.3000 | + | 6.63371i | −1.30140 | + | 0.267280i | ||||
\(617\) | 20.9261 | 0.842451 | 0.421226 | − | 0.906956i | \(-0.361600\pi\) | ||||
0.421226 | + | 0.906956i | \(0.361600\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 11.1568i | − | 0.448430i | −0.974540 | − | 0.224215i | \(-0.928018\pi\) | ||
0.974540 | − | 0.224215i | \(-0.0719818\pi\) | |||||||
\(620\) | −9.35838 | − | 3.83104i | −0.375842 | − | 0.153858i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.34612 | − | 1.57466i | 0.0940708 | − | 0.0631383i | ||||
\(623\) | 21.0771 | 0.844437 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 12.4531 | − | 8.35824i | 0.497726 | − | 0.334062i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 36.5742 | + | 14.9724i | 1.45947 | + | 0.597463i | ||||
\(629\) | 0.536109i | 0.0213761i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.79278 | 0.190798 | 0.0953989 | − | 0.995439i | \(-0.469587\pi\) | ||||
0.0953989 | + | 0.995439i | \(0.469587\pi\) | |||||||
\(632\) | −6.17760 | − | 30.0791i | −0.245732 | − | 1.19648i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.69394 | + | 11.4633i | 0.305565 | + | 0.455267i | ||||
\(635\) | − | 6.82788i | − | 0.270956i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 12.1568i | − | 0.481670i | ||||||
\(638\) | 27.3431 | − | 18.3521i | 1.08252 | − | 0.726567i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.49712 | − | 6.14856i | −0.375407 | − | 0.243043i | ||||
\(641\) | −42.9892 | −1.69797 | −0.848986 | − | 0.528416i | \(-0.822786\pi\) | ||||
−0.848986 | + | 0.528416i | \(0.822786\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.0578i | 1.10649i | 0.833017 | + | 0.553247i | \(0.186611\pi\) | ||||
−0.833017 | + | 0.553247i | \(0.813389\pi\) | |||||||
\(644\) | −11.9661 | + | 29.2306i | −0.471532 | + | 1.15185i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.971134 | + | 1.44691i | 0.0382088 | + | 0.0569279i | ||||
\(647\) | −5.30186 | −0.208437 | −0.104219 | − | 0.994554i | \(-0.533234\pi\) | ||||
−0.104219 | + | 0.994554i | \(0.533234\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.85263 | 0.151229 | ||||||||
\(650\) | 3.87150 | + | 5.76822i | 0.151853 | + | 0.226248i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 39.7846 | + | 16.2866i | 1.55809 | + | 0.637834i | ||||
\(653\) | 10.6725i | 0.417647i | 0.977953 | + | 0.208823i | \(0.0669634\pi\) | ||||
−0.977953 | + | 0.208823i | \(0.933037\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.3874 | −0.835676 | ||||||||
\(656\) | 9.30048 | + | 9.14768i | 0.363123 | + | 0.357157i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −20.4170 | + | 13.7034i | −0.795938 | + | 0.534216i | ||||
\(659\) | 15.6338i | 0.609008i | 0.952511 | + | 0.304504i | \(0.0984907\pi\) | ||||
−0.952511 | + | 0.304504i | \(0.901509\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.2867i | 1.37249i | 0.727369 | + | 0.686247i | \(0.240743\pi\) | ||||
−0.727369 | + | 0.686247i | \(0.759257\pi\) | |||||||
\(662\) | 4.43004 | + | 6.60040i | 0.172178 | + | 0.256532i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23.6511 | − | 4.85741i | 0.917839 | − | 0.188504i | ||||
\(665\) | −11.1285 | −0.431545 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 31.5437i | − | 1.22138i | ||||||
\(668\) | −14.4469 | + | 35.2905i | −0.558967 | + | 1.36543i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.17829 | + | 2.13320i | −0.122788 | + | 0.0824127i | ||||
\(671\) | 1.74883 | 0.0675128 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.2233 | 1.66614 | 0.833068 | − | 0.553170i | \(-0.186582\pi\) | ||||
0.833068 | + | 0.553170i | \(0.186582\pi\) | |||||||
\(674\) | 0.944107 | − | 0.633664i | 0.0363657 | − | 0.0244078i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.43365 | + | 20.6015i | −0.324371 | + | 0.792367i | ||||
\(677\) | − | 39.8297i | − | 1.53078i | −0.643566 | − | 0.765391i | \(-0.722546\pi\) | ||
0.643566 | − | 0.765391i | \(-0.277454\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.6739 | 1.21553 | ||||||||
\(680\) | 0.652588 | − | 0.134027i | 0.0250256 | − | 0.00513971i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −21.8384 | − | 32.5374i | −0.836235 | − | 1.24592i | ||||
\(683\) | − | 14.7286i | − | 0.563574i | −0.959477 | − | 0.281787i | \(-0.909073\pi\) | ||
0.959477 | − | 0.281787i | \(-0.0909271\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 19.6081i | − | 0.749187i | ||||||
\(686\) | 23.6673 | − | 15.8849i | 0.903621 | − | 0.606490i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 27.7913 | − | 28.2556i | 1.05953 | − | 1.07723i | ||||
\(689\) | −52.3831 | −1.99564 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 31.2491i | − | 1.18877i | −0.804180 | − | 0.594386i | \(-0.797395\pi\) | ||
0.804180 | − | 0.594386i | \(-0.202605\pi\) | |||||||
\(692\) | 17.2331 | + | 7.05472i | 0.655105 | + | 0.268180i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.43445 | − | 12.5666i | −0.320167 | − | 0.477023i | ||||
\(695\) | 0.901666 | 0.0342022 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.768172 | −0.0290966 | ||||||||
\(698\) | 19.6965 | + | 29.3461i | 0.745522 | + | 1.11077i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.61184 | + | 3.93737i | −0.0609218 | + | 0.148818i | ||||
\(701\) | − | 4.52968i | − | 0.171084i | −0.996335 | − | 0.0855419i | \(-0.972738\pi\) | ||
0.996335 | − | 0.0855419i | \(-0.0272621\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.9071 | 0.449083 | ||||||||
\(704\) | −17.2799 | − | 40.2940i | −0.651259 | − | 1.51864i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.1844 | − | 12.2050i | 0.684379 | − | 0.459340i | ||||
\(707\) | − | 13.0461i | − | 0.490649i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 15.1260i | − | 0.568069i | −0.958814 | − | 0.284035i | \(-0.908327\pi\) | ||
0.958814 | − | 0.284035i | \(-0.0916731\pi\) | |||||||
\(710\) | −5.66535 | − | 8.44090i | −0.212617 | − | 0.316781i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.63792 | + | 27.4514i | 0.211290 | + | 1.02879i | ||||
\(713\) | −37.5359 | −1.40573 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.9210i | 1.00679i | ||||||||
\(716\) | −5.00894 | − | 2.05051i | −0.187193 | − | 0.0766312i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.0129 | + | 9.40513i | −0.522956 | + | 0.350996i | ||||
\(719\) | 12.8773 | 0.480243 | 0.240122 | − | 0.970743i | \(-0.422813\pi\) | ||||
0.240122 | + | 0.970743i | \(0.422813\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.7792 | −0.699373 | ||||||||
\(722\) | 9.82539 | − | 6.59458i | 0.365663 | − | 0.245425i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.7410 | + | 5.62515i | 0.510680 | + | 0.209057i | ||||
\(725\) | − | 4.24894i | − | 0.157802i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.50213 | 0.278239 | 0.139119 | − | 0.990276i | \(-0.455573\pi\) | ||||
0.139119 | + | 0.990276i | \(0.455573\pi\) | |||||||
\(728\) | −28.9519 | + | 5.94608i | −1.07303 | + | 0.220376i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.61624 | + | 11.3476i | 0.281890 | + | 0.419992i | ||||
\(731\) | 2.33376i | 0.0863174i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 12.4046i | − | 0.458174i | −0.973406 | − | 0.229087i | \(-0.926426\pi\) | ||
0.973406 | − | 0.229087i | \(-0.0735740\pi\) | |||||||
\(734\) | −8.16704 | + | 5.48154i | −0.301451 | + | 0.202327i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −41.2716 | − | 7.76613i | −1.52129 | − | 0.286263i | ||||
\(737\) | −14.8335 | −0.546399 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.6664i | 1.82701i | 0.406830 | + | 0.913504i | \(0.366634\pi\) | ||||
−0.406830 | + | 0.913504i | \(0.633366\pi\) | |||||||
\(740\) | 1.72461 | − | 4.21283i | 0.0633978 | − | 0.154867i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.8782 | − | 26.6371i | −0.656331 | − | 0.977879i | ||||
\(743\) | −26.1312 | −0.958662 | −0.479331 | − | 0.877634i | \(-0.659121\pi\) | ||||
−0.479331 | + | 0.877634i | \(0.659121\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.75106 | −0.0641540 | ||||||||
\(746\) | 9.16558 | + | 13.6560i | 0.335576 | + | 0.499980i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.38924 | + | 0.978085i | 0.0873594 | + | 0.0357623i | ||||
\(749\) | 15.9245i | 0.581869i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.6818 | 1.55748 | 0.778741 | − | 0.627346i | \(-0.215859\pi\) | ||||
0.778741 | + | 0.627346i | \(0.215859\pi\) | |||||||
\(752\) | −23.3091 | − | 22.9261i | −0.849995 | − | 0.836030i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 24.5088 | − | 16.4498i | 0.892558 | − | 0.599065i | ||||
\(755\) | − | 2.90141i | − | 0.105593i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 37.3850i | − | 1.35878i | −0.733777 | − | 0.679391i | \(-0.762244\pi\) | ||
0.733777 | − | 0.679391i | \(-0.237756\pi\) | |||||||
\(758\) | 0.185636 | + | 0.276583i | 0.00674261 | + | 0.0100459i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.97676 | − | 14.4941i | −0.107979 | − | 0.525755i | ||||
\(761\) | −20.2038 | −0.732386 | −0.366193 | − | 0.930539i | \(-0.619339\pi\) | ||||
−0.366193 | + | 0.930539i | \(0.619339\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 37.9634i | 1.37437i | ||||||||
\(764\) | −10.0093 | + | 24.4504i | −0.362123 | + | 0.884586i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.97065 | − | 3.33619i | 0.179597 | − | 0.120541i | ||||
\(767\) | 3.45327 | 0.124690 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.9265 | 1.04312 | 0.521558 | − | 0.853216i | \(-0.325351\pi\) | ||||
0.521558 | + | 0.853216i | \(0.325351\pi\) | |||||||
\(770\) | −13.6895 | + | 9.18810i | −0.493336 | + | 0.331116i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.82994 | + | 6.91292i | −0.101852 | + | 0.248801i | ||||
\(773\) | 47.0349i | 1.69173i | 0.533400 | + | 0.845863i | \(0.320914\pi\) | ||||
−0.533400 | + | 0.845863i | \(0.679086\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.05609 | −0.181620 | ||||||||
\(776\) | 8.47245 | + | 41.2530i | 0.304143 | + | 1.48089i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.3576 | + | 31.8210i | 0.765706 | + | 1.14084i | ||||
\(779\) | 17.0612i | 0.611281i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 39.3948i | − | 1.40966i | ||||||
\(782\) | 2.05332 | − | 1.37814i | 0.0734266 | − | 0.0492823i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.05747 | + | 6.94152i | 0.252052 | + | 0.247911i | ||||
\(785\) | 19.7601 | 0.705267 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 27.5698i | − | 0.982756i | −0.870946 | − | 0.491378i | \(-0.836493\pi\) | ||
0.870946 | − | 0.491378i | \(-0.163507\pi\) | |||||||
\(788\) | −12.9623 | − | 5.30639i | −0.461764 | − | 0.189032i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.55635 | − | 12.7483i | −0.304421 | − | 0.453563i | ||||
\(791\) | 31.6129 | 1.12403 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.56755 | 0.0556653 | ||||||||
\(794\) | 17.3035 | + | 25.7808i | 0.614078 | + | 0.914925i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.1217 | − | 39.3817i | 0.571418 | − | 1.39585i | ||||
\(797\) | − | 46.4890i | − | 1.64672i | −0.567516 | − | 0.823362i | \(-0.692096\pi\) | ||
0.567516 | − | 0.823362i | \(-0.307904\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.92521 | 0.0681091 | ||||||||
\(800\) | −5.55929 | − | 1.04610i | −0.196550 | − | 0.0369852i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.82624 | + | 6.59516i | −0.346977 | + | 0.232883i | ||||
\(803\) | 52.9605i | 1.86894i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.7925i | 0.556614i | ||||||||
\(806\) | −19.5747 | − | 29.1647i | −0.689488 | − | 1.02728i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.9916 | − | 3.48971i | 0.597763 | − | 0.122767i | ||||
\(809\) | −47.2189 | −1.66013 | −0.830064 | − | 0.557668i | \(-0.811696\pi\) | ||||
−0.830064 | + | 0.557668i | \(0.811696\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 9.83765i | − | 0.345447i | −0.984970 | − | 0.172723i | \(-0.944743\pi\) | ||
0.984970 | − | 0.172723i | \(-0.0552567\pi\) | |||||||
\(812\) | 16.7296 | + | 6.84860i | 0.587094 | + | 0.240339i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.6472 | − | 9.83090i | 0.513385 | − | 0.344573i | ||||
\(815\) | 21.4946 | 0.752923 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.8332 | 1.81341 | ||||||||
\(818\) | 33.1695 | − | 22.2626i | 1.15974 | − | 0.778394i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.03641 | + | 2.47113i | 0.210801 | + | 0.0862955i | ||||
\(821\) | 35.6781i | 1.24517i | 0.782551 | + | 0.622587i | \(0.213918\pi\) | ||||
−0.782551 | + | 0.622587i | \(0.786082\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.7092 | −0.826450 | −0.413225 | − | 0.910629i | \(-0.635598\pi\) | ||||
−0.413225 | + | 0.910629i | \(0.635598\pi\) | |||||||
\(824\) | −5.02324 | − | 24.4585i | −0.174993 | − | 0.852053i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.17859 | + | 1.75601i | 0.0410086 | + | 0.0610994i | ||||
\(827\) | − | 9.64454i | − | 0.335373i | −0.985840 | − | 0.167687i | \(-0.946370\pi\) | ||
0.985840 | − | 0.167687i | \(-0.0536297\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.3639i | 1.05458i | 0.849685 | + | 0.527291i | \(0.176792\pi\) | ||||
−0.849685 | + | 0.527291i | \(0.823208\pi\) | |||||||
\(830\) | 10.0239 | − | 6.72781i | 0.347934 | − | 0.233526i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15.4887 | − | 36.1172i | −0.536973 | − | 1.25214i | ||||
\(833\) | −0.582911 | −0.0201967 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.0666i | 0.659825i | ||||||||
\(836\) | 21.7234 | − | 53.0654i | 0.751319 | − | 1.83531i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.84444 | − | 10.1977i | −0.236437 | − | 0.352272i | ||||
\(839\) | 5.58047 | 0.192659 | 0.0963296 | − | 0.995349i | \(-0.469290\pi\) | ||||
0.0963296 | + | 0.995349i | \(0.469290\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.9465 | 0.377467 | ||||||||
\(842\) | −3.72811 | − | 5.55457i | −0.128479 | − | 0.191423i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −45.3054 | − | 18.5467i | −1.55947 | − | 0.638402i | ||||
\(845\) | 11.1305i | 0.382900i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −40.4909 | −1.39128 | ||||||||
\(848\) | 29.9107 | − | 30.4103i | 1.02714 | − | 1.04429i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.276583 | − | 0.185636i | 0.00948670 | − | 0.00636727i | ||||
\(851\) | − | 16.8974i | − | 0.579235i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 50.6473i | − | 1.73413i | −0.498193 | − | 0.867066i | \(-0.666003\pi\) | ||
0.498193 | − | 0.867066i | \(-0.333997\pi\) | |||||||
\(854\) | 0.535002 | + | 0.797109i | 0.0183074 | + | 0.0272765i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.7405 | + | 4.25965i | −0.708896 | + | 0.145592i | ||||
\(857\) | −19.1906 | −0.655539 | −0.327769 | − | 0.944758i | \(-0.606297\pi\) | ||||
−0.327769 | + | 0.944758i | \(0.606297\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.31864i | − | 0.0449915i | −0.999747 | − | 0.0224957i | \(-0.992839\pi\) | ||
0.999747 | − | 0.0224957i | \(-0.00716122\pi\) | |||||||
\(860\) | 7.50747 | − | 18.3391i | 0.256003 | − | 0.625357i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 45.9192 | − | 30.8199i | 1.56401 | − | 1.04973i | ||||
\(863\) | 12.3923 | 0.421840 | 0.210920 | − | 0.977503i | \(-0.432354\pi\) | ||||
0.210920 | + | 0.977503i | \(0.432354\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.31060 | 0.316570 | ||||||||
\(866\) | −39.7154 | + | 26.6561i | −1.34959 | + | 0.905812i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.14961 | − | 19.9077i | 0.276616 | − | 0.675710i | ||||
\(869\) | − | 59.4978i | − | 2.01832i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.2959 | −0.450514 | ||||||||
\(872\) | −49.4446 | + | 10.1548i | −1.67440 | + | 0.343886i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −30.6088 | − | 45.6045i | −1.03536 | − | 1.54260i | ||||
\(875\) | 2.12726i | 0.0719144i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.8292i | 1.24363i | 0.783163 | + | 0.621816i | \(0.213605\pi\) | ||||
−0.783163 | + | 0.621816i | \(0.786395\pi\) | |||||||
\(878\) | −1.87833 | + | 1.26069i | −0.0633904 | + | 0.0425462i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15.6286 | − | 15.3719i | −0.526841 | − | 0.518186i | ||||
\(881\) | −21.4110 | −0.721356 | −0.360678 | − | 0.932690i | \(-0.617455\pi\) | ||||
−0.360678 | + | 0.932690i | \(0.617455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.59479i | 0.0536690i | 0.999640 | + | 0.0268345i | \(0.00854271\pi\) | ||||
−0.999640 | + | 0.0268345i | \(0.991457\pi\) | |||||||
\(884\) | 2.14158 | + | 0.876699i | 0.0720292 | + | 0.0294866i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.81622 | − | 10.1556i | −0.228996 | − | 0.341185i | ||||
\(887\) | 28.6129 | 0.960727 | 0.480363 | − | 0.877070i | \(-0.340505\pi\) | ||||
0.480363 | + | 0.877070i | \(0.340505\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.5247 | 0.487141 | ||||||||
\(890\) | 7.80887 | + | 11.6346i | 0.261754 | + | 0.389992i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.8706 | + | 31.4401i | −0.430940 | + | 1.05269i | ||||
\(893\) | − | 42.7592i | − | 1.43088i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.70620 | −0.0904584 | ||||||||
\(896\) | 13.0796 | − | 20.2028i | 0.436957 | − | 0.674928i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.7406 | + | 12.5783i | −0.625381 | + | 0.419742i | ||||
\(899\) | 21.4830i | 0.716498i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.51173i | 0.0836780i | ||||||||
\(902\) | 14.0864 | + | 20.9875i | 0.469024 | + | 0.698808i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.45615 | + | 41.1736i | 0.281247 | + | 1.36941i | ||||
\(905\) | 7.42390 | 0.246779 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.3412i | 1.30630i | 0.757228 | + | 0.653151i | \(0.226553\pi\) | ||||
−0.757228 | + | 0.653151i | \(0.773447\pi\) | |||||||
\(908\) | −37.9812 | − | 15.5484i | −1.26045 | − | 0.515991i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.2705 | + | 8.23568i | −0.406763 | + | 0.273010i | ||||
\(911\) | 33.6919 | 1.11626 | 0.558131 | − | 0.829753i | \(-0.311519\pi\) | ||||
0.558131 | + | 0.829753i | \(0.311519\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46.7828 | 1.54828 | ||||||||
\(914\) | 26.5922 | − | 17.8481i | 0.879592 | − | 0.590363i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.57620 | − | 2.28273i | −0.184243 | − | 0.0754235i | ||||
\(917\) | − | 45.4965i | − | 1.50243i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.2196 | 1.29373 | 0.646867 | − | 0.762603i | \(-0.276079\pi\) | ||||
0.646867 | + | 0.762603i | \(0.276079\pi\) | |||||||
\(920\) | −20.5686 | + | 4.22435i | −0.678128 | + | 0.139273i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.6856 | − | 26.3500i | −0.582443 | − | 0.867792i | ||||
\(923\) | − | 35.3112i | − | 1.16228i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.27608i | − | 0.0748371i | ||||||
\(926\) | −36.2501 | + | 24.3303i | −1.19125 | + | 0.799543i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.44481 | + | 23.6211i | −0.145908 | + | 0.775399i | ||||
\(929\) | 45.1242 | 1.48048 | 0.740239 | − | 0.672344i | \(-0.234712\pi\) | ||||
0.740239 | + | 0.672344i | \(0.234712\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.9465i | 0.424305i | ||||||||
\(932\) | −11.5459 | + | 28.2040i | −0.378198 | + | 0.923853i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.40957 | + | 3.59007i | 0.0788436 | + | 0.117471i | ||||
\(935\) | 1.29085 | 0.0422152 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.9008 | −1.85887 | −0.929435 | − | 0.368986i | \(-0.879705\pi\) | ||||
−0.929435 | + | 0.368986i | \(0.879705\pi\) | |||||||
\(938\) | −4.53786 | − | 6.76104i | −0.148166 | − | 0.220756i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.1286 | − | 6.19320i | −0.493441 | − | 0.202000i | ||||
\(941\) | − | 56.6437i | − | 1.84653i | −0.384163 | − | 0.923265i | \(-0.625510\pi\) | ||
0.384163 | − | 0.923265i | \(-0.374490\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.2117 | 0.788441 | ||||||||
\(944\) | −1.97181 | + | 2.00475i | −0.0641771 | + | 0.0652491i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 63.7616 | − | 42.7954i | 2.07307 | − | 1.39140i | ||||
\(947\) | 19.1789i | 0.623230i | 0.950208 | + | 0.311615i | \(0.100870\pi\) | ||||
−0.950208 | + | 0.311615i | \(0.899130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 47.4708i | 1.54097i | ||||||||
\(950\) | −4.12300 | − | 6.14294i | −0.133768 | − | 0.199303i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.285111 | + | 1.38822i | 0.00924048 | + | 0.0449926i | ||||
\(953\) | 29.3512 | 0.950777 | 0.475389 | − | 0.879776i | \(-0.342307\pi\) | ||||
0.475389 | + | 0.879776i | \(0.342307\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.2099i | 0.427463i | ||||||||
\(956\) | 12.0295 | − | 29.3853i | 0.389060 | − | 0.950388i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.3339 | + | 17.6748i | −0.850811 | + | 0.571045i | ||||
\(959\) | 41.7115 | 1.34693 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.43596 | −0.175354 | ||||||||
\(962\) | 13.1289 | − | 8.81186i | 0.423294 | − | 0.284106i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.8996 | − | 38.8392i | 0.512092 | − | 1.25093i | ||||
\(965\) | 3.73487i | 0.120230i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −57.6440 | −1.85371 | −0.926854 | − | 0.375423i | \(-0.877497\pi\) | ||||
−0.926854 | + | 0.375423i | \(0.877497\pi\) | |||||||
\(968\) | −10.8309 | − | 52.7365i | −0.348119 | − | 1.69501i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.7349 | + | 17.4840i | 0.376784 | + | 0.561377i | ||||
\(971\) | − | 6.42670i | − | 0.206243i | −0.994669 | − | 0.103121i | \(-0.967117\pi\) | ||
0.994669 | − | 0.103121i | \(-0.0328830\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.91808i | 0.0614907i | ||||||||
\(974\) | 14.0863 | − | 9.45444i | 0.451356 | − | 0.302940i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.895069 | + | 0.910020i | −0.0286505 | + | 0.0291290i | ||||
\(977\) | −29.6408 | −0.948293 | −0.474147 | − | 0.880446i | \(-0.657243\pi\) | ||||
−0.474147 | + | 0.880446i | \(0.657243\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.3001i | 1.73544i | ||||||||
\(980\) | 4.58060 | + | 1.87516i | 0.146322 | + | 0.0598998i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.206423 | − | 0.307554i | −0.00658723 | − | 0.00981443i | ||||
\(983\) | −20.4287 | −0.651573 | −0.325787 | − | 0.945443i | \(-0.605629\pi\) | ||||
−0.325787 | + | 0.945443i | \(0.605629\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.00321 | −0.223141 | ||||||||
\(986\) | −0.788756 | − | 1.17518i | −0.0251191 | − | 0.0374254i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 19.4716 | − | 47.5648i | 0.619474 | − | 1.51324i | ||||
\(989\) | − | 73.5569i | − | 2.33897i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.0135 | 1.36637 | 0.683184 | − | 0.730246i | \(-0.260595\pi\) | ||||
0.683184 | + | 0.730246i | \(0.260595\pi\) | |||||||
\(992\) | 28.1083 | + | 5.28917i | 0.892438 | + | 0.167931i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 17.9560 | − | 12.0516i | 0.569529 | − | 0.382255i | ||||
\(995\) | − | 21.2769i | − | 0.674523i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.4261i | 1.62868i | 0.580387 | + | 0.814341i | \(0.302901\pi\) | ||||
−0.580387 | + | 0.814341i | \(0.697099\pi\) | |||||||
\(998\) | 33.9030 | + | 50.5127i | 1.07318 | + | 1.59895i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1080.2.k.d.541.6 | yes | 20 | |
3.2 | odd | 2 | inner | 1080.2.k.d.541.15 | yes | 20 | |
4.3 | odd | 2 | 4320.2.k.d.2161.4 | 20 | |||
8.3 | odd | 2 | 4320.2.k.d.2161.13 | 20 | |||
8.5 | even | 2 | inner | 1080.2.k.d.541.5 | ✓ | 20 | |
12.11 | even | 2 | 4320.2.k.d.2161.14 | 20 | |||
24.5 | odd | 2 | inner | 1080.2.k.d.541.16 | yes | 20 | |
24.11 | even | 2 | 4320.2.k.d.2161.3 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.2.k.d.541.5 | ✓ | 20 | 8.5 | even | 2 | inner | |
1080.2.k.d.541.6 | yes | 20 | 1.1 | even | 1 | trivial | |
1080.2.k.d.541.15 | yes | 20 | 3.2 | odd | 2 | inner | |
1080.2.k.d.541.16 | yes | 20 | 24.5 | odd | 2 | inner | |
4320.2.k.d.2161.3 | 20 | 24.11 | even | 2 | |||
4320.2.k.d.2161.4 | 20 | 4.3 | odd | 2 | |||
4320.2.k.d.2161.13 | 20 | 8.3 | odd | 2 | |||
4320.2.k.d.2161.14 | 20 | 12.11 | even | 2 |