Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(694,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, 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("1155.694");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 694.6 | ||
Root | \(1.45161 - 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.694 |
Dual form | 1155.2.c.c.694.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.21432i | 1.56576i | 0.622172 | + | 0.782880i | \(0.286250\pi\) | ||||
−0.622172 | + | 0.782880i | \(0.713750\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −2.90321 | −1.45161 | ||||||||
\(5\) | 0.311108 | + | 2.21432i | 0.139132 | + | 0.990274i | ||||
\(6\) | −2.21432 | −0.903992 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − | 2.00000i | − | 0.707107i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −4.90321 | + | 0.688892i | −1.55053 | + | 0.217847i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | − | 2.90321i | − | 0.838085i | ||||||
\(13\) | 1.31111i | 0.363636i | 0.983332 | + | 0.181818i | \(0.0581982\pi\) | ||||
−0.983332 | + | 0.181818i | \(0.941802\pi\) | |||||||
\(14\) | −2.21432 | −0.591802 | ||||||||
\(15\) | −2.21432 | + | 0.311108i | −0.571735 | + | 0.0803277i | ||||
\(16\) | −1.37778 | −0.344446 | ||||||||
\(17\) | − | 1.90321i | − | 0.461597i | −0.973002 | − | 0.230798i | \(-0.925866\pi\) | ||
0.973002 | − | 0.230798i | \(-0.0741338\pi\) | |||||||
\(18\) | − | 2.21432i | − | 0.521920i | ||||||
\(19\) | −0.377784 | −0.0866697 | −0.0433348 | − | 0.999061i | \(-0.513798\pi\) | ||||
−0.0433348 | + | 0.999061i | \(0.513798\pi\) | |||||||
\(20\) | −0.903212 | − | 6.42864i | −0.201964 | − | 1.43749i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | − | 2.21432i | − | 0.472095i | ||||||
\(23\) | 2.52543i | 0.526588i | 0.964716 | + | 0.263294i | \(0.0848089\pi\) | ||||
−0.964716 | + | 0.263294i | \(0.915191\pi\) | |||||||
\(24\) | 2.00000 | 0.408248 | ||||||||
\(25\) | −4.80642 | + | 1.37778i | −0.961285 | + | 0.275557i | ||||
\(26\) | −2.90321 | −0.569367 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | − | 2.90321i | − | 0.548655i | ||||||
\(29\) | 6.11753 | 1.13600 | 0.567999 | − | 0.823030i | \(-0.307718\pi\) | ||||
0.567999 | + | 0.823030i | \(0.307718\pi\) | |||||||
\(30\) | −0.688892 | − | 4.90321i | −0.125774 | − | 0.895200i | ||||
\(31\) | −4.96989 | −0.892618 | −0.446309 | − | 0.894879i | \(-0.647262\pi\) | ||||
−0.446309 | + | 0.894879i | \(0.647262\pi\) | |||||||
\(32\) | − | 7.05086i | − | 1.24643i | ||||||
\(33\) | − | 1.00000i | − | 0.174078i | ||||||
\(34\) | 4.21432 | 0.722750 | ||||||||
\(35\) | −2.21432 | + | 0.311108i | −0.374288 | + | 0.0525868i | ||||
\(36\) | 2.90321 | 0.483869 | ||||||||
\(37\) | 1.31111i | 0.215545i | 0.994176 | + | 0.107772i | \(0.0343718\pi\) | ||||
−0.994176 | + | 0.107772i | \(0.965628\pi\) | |||||||
\(38\) | − | 0.836535i | − | 0.135704i | ||||||
\(39\) | −1.31111 | −0.209945 | ||||||||
\(40\) | 4.42864 | − | 0.622216i | 0.700229 | − | 0.0983809i | ||||
\(41\) | −2.68889 | −0.419934 | −0.209967 | − | 0.977708i | \(-0.567336\pi\) | ||||
−0.209967 | + | 0.977708i | \(0.567336\pi\) | |||||||
\(42\) | − | 2.21432i | − | 0.341677i | ||||||
\(43\) | 6.11753i | 0.932915i | 0.884544 | + | 0.466457i | \(0.154470\pi\) | ||||
−0.884544 | + | 0.466457i | \(0.845530\pi\) | |||||||
\(44\) | 2.90321 | 0.437676 | ||||||||
\(45\) | −0.311108 | − | 2.21432i | −0.0463772 | − | 0.330091i | ||||
\(46\) | −5.59210 | −0.824511 | ||||||||
\(47\) | 1.59210i | 0.232232i | 0.993236 | + | 0.116116i | \(0.0370445\pi\) | ||||
−0.993236 | + | 0.116116i | \(0.962956\pi\) | |||||||
\(48\) | − | 1.37778i | − | 0.198866i | ||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −3.05086 | − | 10.6430i | −0.431456 | − | 1.50514i | ||||
\(51\) | 1.90321 | 0.266503 | ||||||||
\(52\) | − | 3.80642i | − | 0.527856i | ||||||
\(53\) | − | 11.4286i | − | 1.56984i | −0.619594 | − | 0.784922i | \(-0.712703\pi\) | ||
0.619594 | − | 0.784922i | \(-0.287297\pi\) | |||||||
\(54\) | 2.21432 | 0.301331 | ||||||||
\(55\) | −0.311108 | − | 2.21432i | −0.0419498 | − | 0.298579i | ||||
\(56\) | 2.00000 | 0.267261 | ||||||||
\(57\) | − | 0.377784i | − | 0.0500388i | ||||||
\(58\) | 13.5462i | 1.77870i | ||||||||
\(59\) | 7.21432 | 0.939224 | 0.469612 | − | 0.882873i | \(-0.344394\pi\) | ||||
0.469612 | + | 0.882873i | \(0.344394\pi\) | |||||||
\(60\) | 6.42864 | − | 0.903212i | 0.829934 | − | 0.116604i | ||||
\(61\) | −1.04593 | −0.133918 | −0.0669590 | − | 0.997756i | \(-0.521330\pi\) | ||||
−0.0669590 | + | 0.997756i | \(0.521330\pi\) | |||||||
\(62\) | − | 11.0049i | − | 1.39763i | ||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | 12.8573 | 1.60716 | ||||||||
\(65\) | −2.90321 | + | 0.407896i | −0.360099 | + | 0.0505933i | ||||
\(66\) | 2.21432 | 0.272564 | ||||||||
\(67\) | 2.00000i | 0.244339i | 0.992509 | + | 0.122169i | \(0.0389851\pi\) | ||||
−0.992509 | + | 0.122169i | \(0.961015\pi\) | |||||||
\(68\) | 5.52543i | 0.670057i | ||||||||
\(69\) | −2.52543 | −0.304026 | ||||||||
\(70\) | −0.688892 | − | 4.90321i | −0.0823384 | − | 0.586046i | ||||
\(71\) | 4.92396 | 0.584366 | 0.292183 | − | 0.956362i | \(-0.405618\pi\) | ||||
0.292183 | + | 0.956362i | \(0.405618\pi\) | |||||||
\(72\) | 2.00000i | 0.235702i | ||||||||
\(73\) | 12.4286i | 1.45466i | 0.686287 | + | 0.727331i | \(0.259240\pi\) | ||||
−0.686287 | + | 0.727331i | \(0.740760\pi\) | |||||||
\(74\) | −2.90321 | −0.337492 | ||||||||
\(75\) | −1.37778 | − | 4.80642i | −0.159093 | − | 0.554998i | ||||
\(76\) | 1.09679 | 0.125810 | ||||||||
\(77\) | − | 1.00000i | − | 0.113961i | ||||||
\(78\) | − | 2.90321i | − | 0.328724i | ||||||
\(79\) | 0.969888 | 0.109121 | 0.0545605 | − | 0.998510i | \(-0.482624\pi\) | ||||
0.0545605 | + | 0.998510i | \(0.482624\pi\) | |||||||
\(80\) | −0.428639 | − | 3.05086i | −0.0479234 | − | 0.341096i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 5.95407i | − | 0.657517i | ||||||
\(83\) | − | 6.71900i | − | 0.737506i | −0.929527 | − | 0.368753i | \(-0.879785\pi\) | ||
0.929527 | − | 0.368753i | \(-0.120215\pi\) | |||||||
\(84\) | 2.90321 | 0.316766 | ||||||||
\(85\) | 4.21432 | − | 0.592104i | 0.457107 | − | 0.0642227i | ||||
\(86\) | −13.5462 | −1.46072 | ||||||||
\(87\) | 6.11753i | 0.655868i | ||||||||
\(88\) | 2.00000i | 0.213201i | ||||||||
\(89\) | 11.3620 | 1.20437 | 0.602183 | − | 0.798358i | \(-0.294298\pi\) | ||||
0.602183 | + | 0.798358i | \(0.294298\pi\) | |||||||
\(90\) | 4.90321 | − | 0.688892i | 0.516844 | − | 0.0726156i | ||||
\(91\) | −1.31111 | −0.137441 | ||||||||
\(92\) | − | 7.33185i | − | 0.764398i | ||||||
\(93\) | − | 4.96989i | − | 0.515353i | ||||||
\(94\) | −3.52543 | −0.363620 | ||||||||
\(95\) | −0.117532 | − | 0.836535i | −0.0120585 | − | 0.0858267i | ||||
\(96\) | 7.05086 | 0.719625 | ||||||||
\(97\) | − | 8.54617i | − | 0.867732i | −0.900977 | − | 0.433866i | \(-0.857149\pi\) | ||
0.900977 | − | 0.433866i | \(-0.142851\pi\) | |||||||
\(98\) | − | 2.21432i | − | 0.223680i | ||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 13.9541 | − | 4.00000i | 1.39541 | − | 0.400000i | ||||
\(101\) | −4.75557 | −0.473197 | −0.236598 | − | 0.971608i | \(-0.576033\pi\) | ||||
−0.236598 | + | 0.971608i | \(0.576033\pi\) | |||||||
\(102\) | 4.21432i | 0.417280i | ||||||||
\(103\) | 11.3017i | 1.11359i | 0.830649 | + | 0.556797i | \(0.187970\pi\) | ||||
−0.830649 | + | 0.556797i | \(0.812030\pi\) | |||||||
\(104\) | 2.62222 | 0.257129 | ||||||||
\(105\) | −0.311108 | − | 2.21432i | −0.0303610 | − | 0.216095i | ||||
\(106\) | 25.3067 | 2.45800 | ||||||||
\(107\) | 8.83654i | 0.854260i | 0.904190 | + | 0.427130i | \(0.140475\pi\) | ||||
−0.904190 | + | 0.427130i | \(0.859525\pi\) | |||||||
\(108\) | 2.90321i | 0.279362i | ||||||||
\(109\) | −3.39853 | −0.325520 | −0.162760 | − | 0.986666i | \(-0.552040\pi\) | ||||
−0.162760 | + | 0.986666i | \(0.552040\pi\) | |||||||
\(110\) | 4.90321 | − | 0.688892i | 0.467503 | − | 0.0656833i | ||||
\(111\) | −1.31111 | −0.124445 | ||||||||
\(112\) | − | 1.37778i | − | 0.130188i | ||||||
\(113\) | 2.76049i | 0.259685i | 0.991535 | + | 0.129843i | \(0.0414472\pi\) | ||||
−0.991535 | + | 0.129843i | \(0.958553\pi\) | |||||||
\(114\) | 0.836535 | 0.0783487 | ||||||||
\(115\) | −5.59210 | + | 0.785680i | −0.521466 | + | 0.0732651i | ||||
\(116\) | −17.7605 | −1.64902 | ||||||||
\(117\) | − | 1.31111i | − | 0.121212i | ||||||
\(118\) | 15.9748i | 1.47060i | ||||||||
\(119\) | 1.90321 | 0.174467 | ||||||||
\(120\) | 0.622216 | + | 4.42864i | 0.0568003 | + | 0.404278i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − | 2.31603i | − | 0.209684i | ||||||
\(123\) | − | 2.68889i | − | 0.242449i | ||||||
\(124\) | 14.4286 | 1.29573 | ||||||||
\(125\) | −4.54617 | − | 10.2143i | −0.406622 | − | 0.913597i | ||||
\(126\) | 2.21432 | 0.197267 | ||||||||
\(127\) | 2.45875i | 0.218179i | 0.994032 | + | 0.109089i | \(0.0347935\pi\) | ||||
−0.994032 | + | 0.109089i | \(0.965207\pi\) | |||||||
\(128\) | 14.3684i | 1.27000i | ||||||||
\(129\) | −6.11753 | −0.538619 | ||||||||
\(130\) | −0.903212 | − | 6.42864i | −0.0792169 | − | 0.563829i | ||||
\(131\) | −5.73975 | −0.501484 | −0.250742 | − | 0.968054i | \(-0.580675\pi\) | ||||
−0.250742 | + | 0.968054i | \(0.580675\pi\) | |||||||
\(132\) | 2.90321i | 0.252692i | ||||||||
\(133\) | − | 0.377784i | − | 0.0327581i | ||||||
\(134\) | −4.42864 | −0.382576 | ||||||||
\(135\) | 2.21432 | − | 0.311108i | 0.190578 | − | 0.0267759i | ||||
\(136\) | −3.80642 | −0.326398 | ||||||||
\(137\) | 13.5669i | 1.15910i | 0.814937 | + | 0.579550i | \(0.196772\pi\) | ||||
−0.814937 | + | 0.579550i | \(0.803228\pi\) | |||||||
\(138\) | − | 5.59210i | − | 0.476032i | ||||||
\(139\) | −6.01429 | −0.510125 | −0.255063 | − | 0.966925i | \(-0.582096\pi\) | ||||
−0.255063 | + | 0.966925i | \(0.582096\pi\) | |||||||
\(140\) | 6.42864 | − | 0.903212i | 0.543319 | − | 0.0763353i | ||||
\(141\) | −1.59210 | −0.134079 | ||||||||
\(142\) | 10.9032i | 0.914977i | ||||||||
\(143\) | − | 1.31111i | − | 0.109640i | ||||||
\(144\) | 1.37778 | 0.114815 | ||||||||
\(145\) | 1.90321 | + | 13.5462i | 0.158053 | + | 1.12495i | ||||
\(146\) | −27.5210 | −2.27765 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | − | 3.80642i | − | 0.312886i | ||||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | 10.6430 | − | 3.05086i | 0.868994 | − | 0.249101i | ||||
\(151\) | −5.05086 | −0.411033 | −0.205516 | − | 0.978654i | \(-0.565887\pi\) | ||||
−0.205516 | + | 0.978654i | \(0.565887\pi\) | |||||||
\(152\) | 0.755569i | 0.0612847i | ||||||||
\(153\) | 1.90321i | 0.153866i | ||||||||
\(154\) | 2.21432 | 0.178435 | ||||||||
\(155\) | −1.54617 | − | 11.0049i | −0.124191 | − | 0.883937i | ||||
\(156\) | 3.80642 | 0.304758 | ||||||||
\(157\) | 8.88739i | 0.709291i | 0.935001 | + | 0.354645i | \(0.115398\pi\) | ||||
−0.935001 | + | 0.354645i | \(0.884602\pi\) | |||||||
\(158\) | 2.14764i | 0.170857i | ||||||||
\(159\) | 11.4286 | 0.906350 | ||||||||
\(160\) | 15.6128 | − | 2.19358i | 1.23430 | − | 0.173417i | ||||
\(161\) | −2.52543 | −0.199032 | ||||||||
\(162\) | 2.21432i | 0.173973i | ||||||||
\(163\) | 1.31111i | 0.102694i | 0.998681 | + | 0.0513469i | \(0.0163514\pi\) | ||||
−0.998681 | + | 0.0513469i | \(0.983649\pi\) | |||||||
\(164\) | 7.80642 | 0.609579 | ||||||||
\(165\) | 2.21432 | − | 0.311108i | 0.172385 | − | 0.0242197i | ||||
\(166\) | 14.8780 | 1.15476 | ||||||||
\(167\) | 15.1383i | 1.17143i | 0.810515 | + | 0.585717i | \(0.199187\pi\) | ||||
−0.810515 | + | 0.585717i | \(0.800813\pi\) | |||||||
\(168\) | 2.00000i | 0.154303i | ||||||||
\(169\) | 11.2810 | 0.867769 | ||||||||
\(170\) | 1.31111 | + | 9.33185i | 0.100557 | + | 0.715720i | ||||
\(171\) | 0.377784 | 0.0288899 | ||||||||
\(172\) | − | 17.7605i | − | 1.35422i | ||||||
\(173\) | 21.8622i | 1.66215i | 0.556159 | + | 0.831076i | \(0.312275\pi\) | ||||
−0.556159 | + | 0.831076i | \(0.687725\pi\) | |||||||
\(174\) | −13.5462 | −1.02693 | ||||||||
\(175\) | −1.37778 | − | 4.80642i | −0.104151 | − | 0.363331i | ||||
\(176\) | 1.37778 | 0.103854 | ||||||||
\(177\) | 7.21432i | 0.542261i | ||||||||
\(178\) | 25.1590i | 1.88575i | ||||||||
\(179\) | 15.8129 | 1.18191 | 0.590955 | − | 0.806705i | \(-0.298751\pi\) | ||||
0.590955 | + | 0.806705i | \(0.298751\pi\) | |||||||
\(180\) | 0.903212 | + | 6.42864i | 0.0673214 | + | 0.479162i | ||||
\(181\) | −21.5812 | −1.60412 | −0.802059 | − | 0.597245i | \(-0.796262\pi\) | ||||
−0.802059 | + | 0.597245i | \(0.796262\pi\) | |||||||
\(182\) | − | 2.90321i | − | 0.215200i | ||||||
\(183\) | − | 1.04593i | − | 0.0773176i | ||||||
\(184\) | 5.05086 | 0.372354 | ||||||||
\(185\) | −2.90321 | + | 0.407896i | −0.213448 | + | 0.0299891i | ||||
\(186\) | 11.0049 | 0.806920 | ||||||||
\(187\) | 1.90321i | 0.139177i | ||||||||
\(188\) | − | 4.62222i | − | 0.337110i | ||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 1.85236 | − | 0.260253i | 0.134384 | − | 0.0188807i | ||||
\(191\) | −5.53972 | −0.400840 | −0.200420 | − | 0.979710i | \(-0.564231\pi\) | ||||
−0.200420 | + | 0.979710i | \(0.564231\pi\) | |||||||
\(192\) | 12.8573i | 0.927894i | ||||||||
\(193\) | − | 9.31756i | − | 0.670693i | −0.942095 | − | 0.335346i | \(-0.891147\pi\) | ||
0.942095 | − | 0.335346i | \(-0.108853\pi\) | |||||||
\(194\) | 18.9240 | 1.35866 | ||||||||
\(195\) | −0.407896 | − | 2.90321i | −0.0292100 | − | 0.207903i | ||||
\(196\) | 2.90321 | 0.207372 | ||||||||
\(197\) | − | 27.0321i | − | 1.92596i | −0.269575 | − | 0.962979i | \(-0.586883\pi\) | ||
0.269575 | − | 0.962979i | \(-0.413117\pi\) | |||||||
\(198\) | 2.21432i | 0.157365i | ||||||||
\(199\) | 4.06022 | 0.287822 | 0.143911 | − | 0.989591i | \(-0.454032\pi\) | ||||
0.143911 | + | 0.989591i | \(0.454032\pi\) | |||||||
\(200\) | 2.75557 | + | 9.61285i | 0.194848 | + | 0.679731i | ||||
\(201\) | −2.00000 | −0.141069 | ||||||||
\(202\) | − | 10.5303i | − | 0.740913i | ||||||
\(203\) | 6.11753i | 0.429367i | ||||||||
\(204\) | −5.52543 | −0.386857 | ||||||||
\(205\) | −0.836535 | − | 5.95407i | −0.0584262 | − | 0.415850i | ||||
\(206\) | −25.0257 | −1.74362 | ||||||||
\(207\) | − | 2.52543i | − | 0.175529i | ||||||
\(208\) | − | 1.80642i | − | 0.125253i | ||||||
\(209\) | 0.377784 | 0.0261319 | ||||||||
\(210\) | 4.90321 | − | 0.688892i | 0.338354 | − | 0.0475381i | ||||
\(211\) | 5.41927 | 0.373078 | 0.186539 | − | 0.982448i | \(-0.440273\pi\) | ||||
0.186539 | + | 0.982448i | \(0.440273\pi\) | |||||||
\(212\) | 33.1798i | 2.27880i | ||||||||
\(213\) | 4.92396i | 0.337384i | ||||||||
\(214\) | −19.5669 | −1.33757 | ||||||||
\(215\) | −13.5462 | + | 1.90321i | −0.923841 | + | 0.129798i | ||||
\(216\) | −2.00000 | −0.136083 | ||||||||
\(217\) | − | 4.96989i | − | 0.337378i | ||||||
\(218\) | − | 7.52543i | − | 0.509686i | ||||||
\(219\) | −12.4286 | −0.839850 | ||||||||
\(220\) | 0.903212 | + | 6.42864i | 0.0608945 | + | 0.433419i | ||||
\(221\) | 2.49532 | 0.167853 | ||||||||
\(222\) | − | 2.90321i | − | 0.194851i | ||||||
\(223\) | 18.2924i | 1.22495i | 0.790491 | + | 0.612474i | \(0.209826\pi\) | ||||
−0.790491 | + | 0.612474i | \(0.790174\pi\) | |||||||
\(224\) | 7.05086 | 0.471105 | ||||||||
\(225\) | 4.80642 | − | 1.37778i | 0.320428 | − | 0.0918523i | ||||
\(226\) | −6.11261 | −0.406605 | ||||||||
\(227\) | 9.17484i | 0.608956i | 0.952519 | + | 0.304478i | \(0.0984819\pi\) | ||||
−0.952519 | + | 0.304478i | \(0.901518\pi\) | |||||||
\(228\) | 1.09679i | 0.0726366i | ||||||||
\(229\) | −0.112610 | −0.00744145 | −0.00372072 | − | 0.999993i | \(-0.501184\pi\) | ||||
−0.00372072 | + | 0.999993i | \(0.501184\pi\) | |||||||
\(230\) | −1.73975 | − | 12.3827i | −0.114716 | − | 0.816491i | ||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | − | 12.2351i | − | 0.803271i | ||||||
\(233\) | − | 20.3892i | − | 1.33574i | −0.744279 | − | 0.667869i | \(-0.767207\pi\) | ||
0.744279 | − | 0.667869i | \(-0.232793\pi\) | |||||||
\(234\) | 2.90321 | 0.189789 | ||||||||
\(235\) | −3.52543 | + | 0.495316i | −0.229974 | + | 0.0323109i | ||||
\(236\) | −20.9447 | −1.36338 | ||||||||
\(237\) | 0.969888i | 0.0630010i | ||||||||
\(238\) | 4.21432i | 0.273174i | ||||||||
\(239\) | −25.0207 | −1.61846 | −0.809229 | − | 0.587494i | \(-0.800115\pi\) | ||||
−0.809229 | + | 0.587494i | \(0.800115\pi\) | |||||||
\(240\) | 3.05086 | − | 0.428639i | 0.196932 | − | 0.0276686i | ||||
\(241\) | −1.18865 | −0.0765679 | −0.0382840 | − | 0.999267i | \(-0.512189\pi\) | ||||
−0.0382840 | + | 0.999267i | \(0.512189\pi\) | |||||||
\(242\) | 2.21432i | 0.142342i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 3.03657 | 0.194396 | ||||||||
\(245\) | −0.311108 | − | 2.21432i | −0.0198759 | − | 0.141468i | ||||
\(246\) | 5.95407 | 0.379617 | ||||||||
\(247\) | − | 0.495316i | − | 0.0315162i | ||||||
\(248\) | 9.93978i | 0.631176i | ||||||||
\(249\) | 6.71900 | 0.425800 | ||||||||
\(250\) | 22.6178 | − | 10.0667i | 1.43047 | − | 0.636673i | ||||
\(251\) | −27.8163 | −1.75575 | −0.877874 | − | 0.478892i | \(-0.841038\pi\) | ||||
−0.877874 | + | 0.478892i | \(0.841038\pi\) | |||||||
\(252\) | 2.90321i | 0.182885i | ||||||||
\(253\) | − | 2.52543i | − | 0.158772i | ||||||
\(254\) | −5.44446 | −0.341616 | ||||||||
\(255\) | 0.592104 | + | 4.21432i | 0.0370790 | + | 0.263911i | ||||
\(256\) | −6.10171 | −0.381357 | ||||||||
\(257\) | 31.6336i | 1.97325i | 0.163009 | + | 0.986625i | \(0.447880\pi\) | ||||
−0.163009 | + | 0.986625i | \(0.552120\pi\) | |||||||
\(258\) | − | 13.5462i | − | 0.843348i | ||||||
\(259\) | −1.31111 | −0.0814683 | ||||||||
\(260\) | 8.42864 | − | 1.18421i | 0.522722 | − | 0.0734415i | ||||
\(261\) | −6.11753 | −0.378666 | ||||||||
\(262\) | − | 12.7096i | − | 0.785204i | ||||||
\(263\) | − | 22.8573i | − | 1.40944i | −0.709485 | − | 0.704720i | \(-0.751073\pi\) | ||
0.709485 | − | 0.704720i | \(-0.248927\pi\) | |||||||
\(264\) | −2.00000 | −0.123091 | ||||||||
\(265\) | 25.3067 | − | 3.55554i | 1.55458 | − | 0.218415i | ||||
\(266\) | 0.836535 | 0.0512913 | ||||||||
\(267\) | 11.3620i | 0.695341i | ||||||||
\(268\) | − | 5.80642i | − | 0.354684i | ||||||
\(269\) | −1.48103 | −0.0902997 | −0.0451499 | − | 0.998980i | \(-0.514377\pi\) | ||||
−0.0451499 | + | 0.998980i | \(0.514377\pi\) | |||||||
\(270\) | 0.688892 | + | 4.90321i | 0.0419246 | + | 0.298400i | ||||
\(271\) | −25.4844 | −1.54807 | −0.774034 | − | 0.633144i | \(-0.781764\pi\) | ||||
−0.774034 | + | 0.633144i | \(0.781764\pi\) | |||||||
\(272\) | 2.62222i | 0.158995i | ||||||||
\(273\) | − | 1.31111i | − | 0.0793519i | ||||||
\(274\) | −30.0415 | −1.81487 | ||||||||
\(275\) | 4.80642 | − | 1.37778i | 0.289838 | − | 0.0830835i | ||||
\(276\) | 7.33185 | 0.441326 | ||||||||
\(277\) | − | 14.2395i | − | 0.855569i | −0.903881 | − | 0.427785i | \(-0.859294\pi\) | ||
0.903881 | − | 0.427785i | \(-0.140706\pi\) | |||||||
\(278\) | − | 13.3176i | − | 0.798734i | ||||||
\(279\) | 4.96989 | 0.297539 | ||||||||
\(280\) | 0.622216 | + | 4.42864i | 0.0371845 | + | 0.264662i | ||||
\(281\) | −2.23951 | −0.133598 | −0.0667990 | − | 0.997766i | \(-0.521279\pi\) | ||||
−0.0667990 | + | 0.997766i | \(0.521279\pi\) | |||||||
\(282\) | − | 3.52543i | − | 0.209936i | ||||||
\(283\) | 24.8321i | 1.47611i | 0.674738 | + | 0.738057i | \(0.264257\pi\) | ||||
−0.674738 | + | 0.738057i | \(0.735743\pi\) | |||||||
\(284\) | −14.2953 | −0.848269 | ||||||||
\(285\) | 0.836535 | − | 0.117532i | 0.0495521 | − | 0.00696198i | ||||
\(286\) | 2.90321 | 0.171671 | ||||||||
\(287\) | − | 2.68889i | − | 0.158720i | ||||||
\(288\) | 7.05086i | 0.415476i | ||||||||
\(289\) | 13.3778 | 0.786928 | ||||||||
\(290\) | −29.9956 | + | 4.21432i | −1.76140 | + | 0.247473i | ||||
\(291\) | 8.54617 | 0.500985 | ||||||||
\(292\) | − | 36.0830i | − | 2.11160i | ||||||
\(293\) | 25.6035i | 1.49577i | 0.663828 | + | 0.747886i | \(0.268931\pi\) | ||||
−0.663828 | + | 0.747886i | \(0.731069\pi\) | |||||||
\(294\) | 2.21432 | 0.129142 | ||||||||
\(295\) | 2.24443 | + | 15.9748i | 0.130676 | + | 0.930089i | ||||
\(296\) | 2.62222 | 0.152413 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | − | 22.1432i | − | 1.28272i | ||||||
\(299\) | −3.31111 | −0.191486 | ||||||||
\(300\) | 4.00000 | + | 13.9541i | 0.230940 | + | 0.805638i | ||||
\(301\) | −6.11753 | −0.352609 | ||||||||
\(302\) | − | 11.1842i | − | 0.643579i | ||||||
\(303\) | − | 4.75557i | − | 0.273200i | ||||||
\(304\) | 0.520505 | 0.0298530 | ||||||||
\(305\) | −0.325398 | − | 2.31603i | −0.0186322 | − | 0.132615i | ||||
\(306\) | −4.21432 | −0.240917 | ||||||||
\(307\) | 5.09234i | 0.290635i | 0.989385 | + | 0.145318i | \(0.0464204\pi\) | ||||
−0.989385 | + | 0.145318i | \(0.953580\pi\) | |||||||
\(308\) | 2.90321i | 0.165426i | ||||||||
\(309\) | −11.3017 | −0.642934 | ||||||||
\(310\) | 24.3684 | − | 3.42372i | 1.38403 | − | 0.194454i | ||||
\(311\) | 17.3274 | 0.982547 | 0.491274 | − | 0.871005i | \(-0.336532\pi\) | ||||
0.491274 | + | 0.871005i | \(0.336532\pi\) | |||||||
\(312\) | 2.62222i | 0.148454i | ||||||||
\(313\) | − | 15.4909i | − | 0.875596i | −0.899073 | − | 0.437798i | \(-0.855759\pi\) | ||
0.899073 | − | 0.437798i | \(-0.144241\pi\) | |||||||
\(314\) | −19.6795 | −1.11058 | ||||||||
\(315\) | 2.21432 | − | 0.311108i | 0.124763 | − | 0.0175289i | ||||
\(316\) | −2.81579 | −0.158401 | ||||||||
\(317\) | − | 12.4143i | − | 0.697259i | −0.937261 | − | 0.348630i | \(-0.886647\pi\) | ||
0.937261 | − | 0.348630i | \(-0.113353\pi\) | |||||||
\(318\) | 25.3067i | 1.41913i | ||||||||
\(319\) | −6.11753 | −0.342516 | ||||||||
\(320\) | 4.00000 | + | 28.4701i | 0.223607 | + | 1.59153i | ||||
\(321\) | −8.83654 | −0.493207 | ||||||||
\(322\) | − | 5.59210i | − | 0.311636i | ||||||
\(323\) | 0.719004i | 0.0400064i | ||||||||
\(324\) | −2.90321 | −0.161290 | ||||||||
\(325\) | −1.80642 | − | 6.30174i | −0.100202 | − | 0.349558i | ||||
\(326\) | −2.90321 | −0.160794 | ||||||||
\(327\) | − | 3.39853i | − | 0.187939i | ||||||
\(328\) | 5.37778i | 0.296938i | ||||||||
\(329\) | −1.59210 | −0.0877755 | ||||||||
\(330\) | 0.688892 | + | 4.90321i | 0.0379223 | + | 0.269913i | ||||
\(331\) | 32.5210 | 1.78751 | 0.893757 | − | 0.448551i | \(-0.148060\pi\) | ||||
0.893757 | + | 0.448551i | \(0.148060\pi\) | |||||||
\(332\) | 19.5067i | 1.07057i | ||||||||
\(333\) | − | 1.31111i | − | 0.0718483i | ||||||
\(334\) | −33.5210 | −1.83419 | ||||||||
\(335\) | −4.42864 | + | 0.622216i | −0.241962 | + | 0.0339953i | ||||
\(336\) | 1.37778 | 0.0751643 | ||||||||
\(337\) | − | 3.06668i | − | 0.167053i | −0.996506 | − | 0.0835263i | \(-0.973382\pi\) | ||
0.996506 | − | 0.0835263i | \(-0.0266182\pi\) | |||||||
\(338\) | 24.9797i | 1.35872i | ||||||||
\(339\) | −2.76049 | −0.149929 | ||||||||
\(340\) | −12.2351 | + | 1.71900i | −0.663539 | + | 0.0932261i | ||||
\(341\) | 4.96989 | 0.269135 | ||||||||
\(342\) | 0.836535i | 0.0452347i | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 12.2351 | 0.659670 | ||||||||
\(345\) | −0.785680 | − | 5.59210i | −0.0422996 | − | 0.301069i | ||||
\(346\) | −48.4099 | −2.60253 | ||||||||
\(347\) | 23.7146i | 1.27306i | 0.771250 | + | 0.636532i | \(0.219632\pi\) | ||||
−0.771250 | + | 0.636532i | \(0.780368\pi\) | |||||||
\(348\) | − | 17.7605i | − | 0.952062i | ||||||
\(349\) | −21.8385 | −1.16899 | −0.584495 | − | 0.811397i | \(-0.698707\pi\) | ||||
−0.584495 | + | 0.811397i | \(0.698707\pi\) | |||||||
\(350\) | 10.6430 | − | 3.05086i | 0.568890 | − | 0.163075i | ||||
\(351\) | 1.31111 | 0.0699818 | ||||||||
\(352\) | 7.05086i | 0.375812i | ||||||||
\(353\) | − | 31.1941i | − | 1.66029i | −0.557546 | − | 0.830146i | \(-0.688257\pi\) | ||
0.557546 | − | 0.830146i | \(-0.311743\pi\) | |||||||
\(354\) | −15.9748 | −0.849052 | ||||||||
\(355\) | 1.53188 | + | 10.9032i | 0.0813038 | + | 0.578682i | ||||
\(356\) | −32.9862 | −1.74826 | ||||||||
\(357\) | 1.90321i | 0.100729i | ||||||||
\(358\) | 35.0148i | 1.85059i | ||||||||
\(359\) | 7.16839 | 0.378333 | 0.189166 | − | 0.981945i | \(-0.439421\pi\) | ||||
0.189166 | + | 0.981945i | \(0.439421\pi\) | |||||||
\(360\) | −4.42864 | + | 0.622216i | −0.233410 | + | 0.0327936i | ||||
\(361\) | −18.8573 | −0.992488 | ||||||||
\(362\) | − | 47.7877i | − | 2.51167i | ||||||
\(363\) | 1.00000i | 0.0524864i | ||||||||
\(364\) | 3.80642 | 0.199511 | ||||||||
\(365\) | −27.5210 | + | 3.86665i | −1.44051 | + | 0.202390i | ||||
\(366\) | 2.31603 | 0.121061 | ||||||||
\(367\) | 17.9195i | 0.935391i | 0.883890 | + | 0.467695i | \(0.154916\pi\) | ||||
−0.883890 | + | 0.467695i | \(0.845084\pi\) | |||||||
\(368\) | − | 3.47949i | − | 0.181381i | ||||||
\(369\) | 2.68889 | 0.139978 | ||||||||
\(370\) | −0.903212 | − | 6.42864i | −0.0469558 | − | 0.334209i | ||||
\(371\) | 11.4286 | 0.593345 | ||||||||
\(372\) | 14.4286i | 0.748090i | ||||||||
\(373\) | 2.22369i | 0.115138i | 0.998342 | + | 0.0575691i | \(0.0183349\pi\) | ||||
−0.998342 | + | 0.0575691i | \(0.981665\pi\) | |||||||
\(374\) | −4.21432 | −0.217917 | ||||||||
\(375\) | 10.2143 | − | 4.54617i | 0.527465 | − | 0.234763i | ||||
\(376\) | 3.18421 | 0.164213 | ||||||||
\(377\) | 8.02074i | 0.413089i | ||||||||
\(378\) | 2.21432i | 0.113892i | ||||||||
\(379\) | −17.6780 | −0.908058 | −0.454029 | − | 0.890987i | \(-0.650014\pi\) | ||||
−0.454029 | + | 0.890987i | \(0.650014\pi\) | |||||||
\(380\) | 0.341219 | + | 2.42864i | 0.0175042 | + | 0.124587i | ||||
\(381\) | −2.45875 | −0.125966 | ||||||||
\(382\) | − | 12.2667i | − | 0.627619i | ||||||
\(383\) | 16.8365i | 0.860307i | 0.902756 | + | 0.430153i | \(0.141541\pi\) | ||||
−0.902756 | + | 0.430153i | \(0.858459\pi\) | |||||||
\(384\) | −14.3684 | −0.733235 | ||||||||
\(385\) | 2.21432 | − | 0.311108i | 0.112852 | − | 0.0158555i | ||||
\(386\) | 20.6321 | 1.05014 | ||||||||
\(387\) | − | 6.11753i | − | 0.310972i | ||||||
\(388\) | 24.8113i | 1.25961i | ||||||||
\(389\) | 15.4859 | 0.785169 | 0.392584 | − | 0.919716i | \(-0.371581\pi\) | ||||
0.392584 | + | 0.919716i | \(0.371581\pi\) | |||||||
\(390\) | 6.42864 | − | 0.903212i | 0.325527 | − | 0.0457359i | ||||
\(391\) | 4.80642 | 0.243071 | ||||||||
\(392\) | 2.00000i | 0.101015i | ||||||||
\(393\) | − | 5.73975i | − | 0.289532i | ||||||
\(394\) | 59.8578 | 3.01559 | ||||||||
\(395\) | 0.301740 | + | 2.14764i | 0.0151822 | + | 0.108060i | ||||
\(396\) | −2.90321 | −0.145892 | ||||||||
\(397\) | 16.9032i | 0.848348i | 0.905581 | + | 0.424174i | \(0.139435\pi\) | ||||
−0.905581 | + | 0.424174i | \(0.860565\pi\) | |||||||
\(398\) | 8.99063i | 0.450660i | ||||||||
\(399\) | 0.377784 | 0.0189129 | ||||||||
\(400\) | 6.62222 | − | 1.89829i | 0.331111 | − | 0.0949145i | ||||
\(401\) | 23.3210 | 1.16459 | 0.582296 | − | 0.812977i | \(-0.302154\pi\) | ||||
0.582296 | + | 0.812977i | \(0.302154\pi\) | |||||||
\(402\) | − | 4.42864i | − | 0.220880i | ||||||
\(403\) | − | 6.51606i | − | 0.324588i | ||||||
\(404\) | 13.8064 | 0.686895 | ||||||||
\(405\) | 0.311108 | + | 2.21432i | 0.0154591 | + | 0.110030i | ||||
\(406\) | −13.5462 | −0.672285 | ||||||||
\(407\) | − | 1.31111i | − | 0.0649892i | ||||||
\(408\) | − | 3.80642i | − | 0.188446i | ||||||
\(409\) | 2.60793 | 0.128954 | 0.0644768 | − | 0.997919i | \(-0.479462\pi\) | ||||
0.0644768 | + | 0.997919i | \(0.479462\pi\) | |||||||
\(410\) | 13.1842 | − | 1.85236i | 0.651122 | − | 0.0914814i | ||||
\(411\) | −13.5669 | −0.669207 | ||||||||
\(412\) | − | 32.8113i | − | 1.61650i | ||||||
\(413\) | 7.21432i | 0.354993i | ||||||||
\(414\) | 5.59210 | 0.274837 | ||||||||
\(415\) | 14.8780 | − | 2.09033i | 0.730333 | − | 0.102610i | ||||
\(416\) | 9.24443 | 0.453246 | ||||||||
\(417\) | − | 6.01429i | − | 0.294521i | ||||||
\(418\) | 0.836535i | 0.0409163i | ||||||||
\(419\) | 15.4222 | 0.753423 | 0.376712 | − | 0.926331i | \(-0.377055\pi\) | ||||
0.376712 | + | 0.926331i | \(0.377055\pi\) | |||||||
\(420\) | 0.903212 | + | 6.42864i | 0.0440722 | + | 0.313685i | ||||
\(421\) | 6.28592 | 0.306357 | 0.153178 | − | 0.988199i | \(-0.451049\pi\) | ||||
0.153178 | + | 0.988199i | \(0.451049\pi\) | |||||||
\(422\) | 12.0000i | 0.584151i | ||||||||
\(423\) | − | 1.59210i | − | 0.0774108i | ||||||
\(424\) | −22.8573 | −1.11005 | ||||||||
\(425\) | 2.62222 | + | 9.14764i | 0.127196 | + | 0.443726i | ||||
\(426\) | −10.9032 | −0.528262 | ||||||||
\(427\) | − | 1.04593i | − | 0.0506162i | ||||||
\(428\) | − | 25.6543i | − | 1.24005i | ||||||
\(429\) | 1.31111 | 0.0633009 | ||||||||
\(430\) | −4.21432 | − | 29.9956i | −0.203233 | − | 1.44651i | ||||
\(431\) | 16.3082 | 0.785538 | 0.392769 | − | 0.919637i | \(-0.371517\pi\) | ||||
0.392769 | + | 0.919637i | \(0.371517\pi\) | |||||||
\(432\) | 1.37778i | 0.0662887i | ||||||||
\(433\) | − | 14.8859i | − | 0.715369i | −0.933843 | − | 0.357684i | \(-0.883566\pi\) | ||
0.933843 | − | 0.357684i | \(-0.116434\pi\) | |||||||
\(434\) | 11.0049 | 0.528253 | ||||||||
\(435\) | −13.5462 | + | 1.90321i | −0.649489 | + | 0.0912520i | ||||
\(436\) | 9.86665 | 0.472527 | ||||||||
\(437\) | − | 0.954067i | − | 0.0456392i | ||||||
\(438\) | − | 27.5210i | − | 1.31500i | ||||||
\(439\) | −10.3176 | −0.492430 | −0.246215 | − | 0.969215i | \(-0.579187\pi\) | ||||
−0.246215 | + | 0.969215i | \(0.579187\pi\) | |||||||
\(440\) | −4.42864 | + | 0.622216i | −0.211127 | + | 0.0296630i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 5.52543i | 0.262818i | ||||||||
\(443\) | − | 4.17929i | − | 0.198564i | −0.995059 | − | 0.0992819i | \(-0.968345\pi\) | ||
0.995059 | − | 0.0992819i | \(-0.0316546\pi\) | |||||||
\(444\) | 3.80642 | 0.180645 | ||||||||
\(445\) | 3.53480 | + | 25.1590i | 0.167565 | + | 1.19265i | ||||
\(446\) | −40.5052 | −1.91797 | ||||||||
\(447\) | − | 10.0000i | − | 0.472984i | ||||||
\(448\) | 12.8573i | 0.607449i | ||||||||
\(449\) | 25.2192 | 1.19017 | 0.595085 | − | 0.803663i | \(-0.297118\pi\) | ||||
0.595085 | + | 0.803663i | \(0.297118\pi\) | |||||||
\(450\) | 3.05086 | + | 10.6430i | 0.143819 | + | 0.501714i | ||||
\(451\) | 2.68889 | 0.126615 | ||||||||
\(452\) | − | 8.01429i | − | 0.376960i | ||||||
\(453\) | − | 5.05086i | − | 0.237310i | ||||||
\(454\) | −20.3160 | −0.953479 | ||||||||
\(455\) | −0.407896 | − | 2.90321i | −0.0191225 | − | 0.136105i | ||||
\(456\) | −0.755569 | −0.0353827 | ||||||||
\(457\) | 27.5970i | 1.29093i | 0.763788 | + | 0.645467i | \(0.223337\pi\) | ||||
−0.763788 | + | 0.645467i | \(0.776663\pi\) | |||||||
\(458\) | − | 0.249353i | − | 0.0116515i | ||||||
\(459\) | −1.90321 | −0.0888343 | ||||||||
\(460\) | 16.2351 | − | 2.28100i | 0.756964 | − | 0.106352i | ||||
\(461\) | 33.5812 | 1.56403 | 0.782016 | − | 0.623258i | \(-0.214191\pi\) | ||||
0.782016 | + | 0.623258i | \(0.214191\pi\) | |||||||
\(462\) | 2.21432i | 0.103019i | ||||||||
\(463\) | 22.8889i | 1.06374i | 0.846827 | + | 0.531869i | \(0.178510\pi\) | ||||
−0.846827 | + | 0.531869i | \(0.821490\pi\) | |||||||
\(464\) | −8.42864 | −0.391290 | ||||||||
\(465\) | 11.0049 | − | 1.54617i | 0.510341 | − | 0.0717020i | ||||
\(466\) | 45.1481 | 2.09145 | ||||||||
\(467\) | − | 6.38715i | − | 0.295562i | −0.989020 | − | 0.147781i | \(-0.952787\pi\) | ||
0.989020 | − | 0.147781i | \(-0.0472131\pi\) | |||||||
\(468\) | 3.80642i | 0.175952i | ||||||||
\(469\) | −2.00000 | −0.0923514 | ||||||||
\(470\) | −1.09679 | − | 7.80642i | −0.0505911 | − | 0.360083i | ||||
\(471\) | −8.88739 | −0.409509 | ||||||||
\(472\) | − | 14.4286i | − | 0.664132i | ||||||
\(473\) | − | 6.11753i | − | 0.281284i | ||||||
\(474\) | −2.14764 | −0.0986445 | ||||||||
\(475\) | 1.81579 | − | 0.520505i | 0.0833142 | − | 0.0238824i | ||||
\(476\) | −5.52543 | −0.253258 | ||||||||
\(477\) | 11.4286i | 0.523281i | ||||||||
\(478\) | − | 55.4039i | − | 2.53412i | ||||||
\(479\) | 34.5970 | 1.58078 | 0.790389 | − | 0.612605i | \(-0.209878\pi\) | ||||
0.790389 | + | 0.612605i | \(0.209878\pi\) | |||||||
\(480\) | 2.19358 | + | 15.6128i | 0.100123 | + | 0.712626i | ||||
\(481\) | −1.71900 | −0.0783798 | ||||||||
\(482\) | − | 2.63206i | − | 0.119887i | ||||||
\(483\) | − | 2.52543i | − | 0.114911i | ||||||
\(484\) | −2.90321 | −0.131964 | ||||||||
\(485\) | 18.9240 | − | 2.65878i | 0.859293 | − | 0.120729i | ||||
\(486\) | −2.21432 | −0.100444 | ||||||||
\(487\) | − | 12.4572i | − | 0.564491i | −0.959342 | − | 0.282245i | \(-0.908921\pi\) | ||
0.959342 | − | 0.282245i | \(-0.0910792\pi\) | |||||||
\(488\) | 2.09187i | 0.0946943i | ||||||||
\(489\) | −1.31111 | −0.0592903 | ||||||||
\(490\) | 4.90321 | − | 0.688892i | 0.221505 | − | 0.0311210i | ||||
\(491\) | 16.4271 | 0.741345 | 0.370673 | − | 0.928764i | \(-0.379127\pi\) | ||||
0.370673 | + | 0.928764i | \(0.379127\pi\) | |||||||
\(492\) | 7.80642i | 0.351941i | ||||||||
\(493\) | − | 11.6430i | − | 0.524373i | ||||||
\(494\) | 1.09679 | 0.0493468 | ||||||||
\(495\) | 0.311108 | + | 2.21432i | 0.0139833 | + | 0.0995263i | ||||
\(496\) | 6.84743 | 0.307459 | ||||||||
\(497\) | 4.92396i | 0.220870i | ||||||||
\(498\) | 14.8780i | 0.666700i | ||||||||
\(499\) | 37.2623 | 1.66809 | 0.834044 | − | 0.551698i | \(-0.186020\pi\) | ||||
0.834044 | + | 0.551698i | \(0.186020\pi\) | |||||||
\(500\) | 13.1985 | + | 29.6543i | 0.590255 | + | 1.32618i | ||||
\(501\) | −15.1383 | −0.676328 | ||||||||
\(502\) | − | 61.5941i | − | 2.74908i | ||||||
\(503\) | − | 9.23506i | − | 0.411771i | −0.978576 | − | 0.205886i | \(-0.933993\pi\) | ||
0.978576 | − | 0.205886i | \(-0.0660075\pi\) | |||||||
\(504\) | −2.00000 | −0.0890871 | ||||||||
\(505\) | −1.47949 | − | 10.5303i | −0.0658366 | − | 0.468594i | ||||
\(506\) | 5.59210 | 0.248599 | ||||||||
\(507\) | 11.2810i | 0.501007i | ||||||||
\(508\) | − | 7.13828i | − | 0.316710i | ||||||
\(509\) | 43.3847 | 1.92299 | 0.961497 | − | 0.274816i | \(-0.0886170\pi\) | ||||
0.961497 | + | 0.274816i | \(0.0886170\pi\) | |||||||
\(510\) | −9.33185 | + | 1.31111i | −0.413221 | + | 0.0580568i | ||||
\(511\) | −12.4286 | −0.549811 | ||||||||
\(512\) | 15.2257i | 0.672887i | ||||||||
\(513\) | 0.377784i | 0.0166796i | ||||||||
\(514\) | −70.0469 | −3.08964 | ||||||||
\(515\) | −25.0257 | + | 3.51606i | −1.10276 | + | 0.154936i | ||||
\(516\) | 17.7605 | 0.781862 | ||||||||
\(517\) | − | 1.59210i | − | 0.0700207i | ||||||
\(518\) | − | 2.90321i | − | 0.127560i | ||||||
\(519\) | −21.8622 | −0.959644 | ||||||||
\(520\) | 0.815792 | + | 5.80642i | 0.0357748 | + | 0.254629i | ||||
\(521\) | 33.9195 | 1.48604 | 0.743020 | − | 0.669269i | \(-0.233393\pi\) | ||||
0.743020 | + | 0.669269i | \(0.233393\pi\) | |||||||
\(522\) | − | 13.5462i | − | 0.592900i | ||||||
\(523\) | 19.6731i | 0.860243i | 0.902771 | + | 0.430122i | \(0.141529\pi\) | ||||
−0.902771 | + | 0.430122i | \(0.858471\pi\) | |||||||
\(524\) | 16.6637 | 0.727957 | ||||||||
\(525\) | 4.80642 | − | 1.37778i | 0.209770 | − | 0.0601314i | ||||
\(526\) | 50.6133 | 2.20685 | ||||||||
\(527\) | 9.45875i | 0.412030i | ||||||||
\(528\) | 1.37778i | 0.0599604i | ||||||||
\(529\) | 16.6222 | 0.722705 | ||||||||
\(530\) | 7.87310 | + | 56.0370i | 0.341986 | + | 2.43409i | ||||
\(531\) | −7.21432 | −0.313075 | ||||||||
\(532\) | 1.09679i | 0.0475518i | ||||||||
\(533\) | − | 3.52543i | − | 0.152703i | ||||||
\(534\) | −25.1590 | −1.08874 | ||||||||
\(535\) | −19.5669 | + | 2.74912i | −0.845951 | + | 0.118855i | ||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | 15.8129i | 0.682376i | ||||||||
\(538\) | − | 3.27946i | − | 0.141388i | ||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | −6.42864 | + | 0.903212i | −0.276645 | + | 0.0388681i | ||||
\(541\) | −26.2844 | −1.13005 | −0.565027 | − | 0.825072i | \(-0.691134\pi\) | ||||
−0.565027 | + | 0.825072i | \(0.691134\pi\) | |||||||
\(542\) | − | 56.4306i | − | 2.42390i | ||||||
\(543\) | − | 21.5812i | − | 0.926138i | ||||||
\(544\) | −13.4193 | −0.575347 | ||||||||
\(545\) | −1.05731 | − | 7.52543i | −0.0452901 | − | 0.322354i | ||||
\(546\) | 2.90321 | 0.124246 | ||||||||
\(547\) | − | 3.43648i | − | 0.146933i | −0.997298 | − | 0.0734666i | \(-0.976594\pi\) | ||
0.997298 | − | 0.0734666i | \(-0.0234062\pi\) | |||||||
\(548\) | − | 39.3876i | − | 1.68256i | ||||||
\(549\) | 1.04593 | 0.0446393 | ||||||||
\(550\) | 3.05086 | + | 10.6430i | 0.130089 | + | 0.453817i | ||||
\(551\) | −2.31111 | −0.0984565 | ||||||||
\(552\) | 5.05086i | 0.214979i | ||||||||
\(553\) | 0.969888i | 0.0412439i | ||||||||
\(554\) | 31.5308 | 1.33962 | ||||||||
\(555\) | −0.407896 | − | 2.90321i | −0.0173142 | − | 0.123234i | ||||
\(556\) | 17.4608 | 0.740501 | ||||||||
\(557\) | 35.1941i | 1.49122i | 0.666383 | + | 0.745610i | \(0.267842\pi\) | ||||
−0.666383 | + | 0.745610i | \(0.732158\pi\) | |||||||
\(558\) | 11.0049i | 0.465876i | ||||||||
\(559\) | −8.02074 | −0.339241 | ||||||||
\(560\) | 3.05086 | − | 0.428639i | 0.128922 | − | 0.0181133i | ||||
\(561\) | −1.90321 | −0.0803537 | ||||||||
\(562\) | − | 4.95899i | − | 0.209182i | ||||||
\(563\) | − | 16.6780i | − | 0.702894i | −0.936208 | − | 0.351447i | \(-0.885690\pi\) | ||
0.936208 | − | 0.351447i | \(-0.114310\pi\) | |||||||
\(564\) | 4.62222 | 0.194630 | ||||||||
\(565\) | −6.11261 | + | 0.858810i | −0.257159 | + | 0.0361304i | ||||
\(566\) | −54.9862 | −2.31124 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | − | 9.84791i | − | 0.413209i | ||||||
\(569\) | 41.9481 | 1.75856 | 0.879278 | − | 0.476309i | \(-0.158026\pi\) | ||||
0.879278 | + | 0.476309i | \(0.158026\pi\) | |||||||
\(570\) | 0.260253 | + | 1.85236i | 0.0109008 | + | 0.0775867i | ||||
\(571\) | −3.76694 | −0.157642 | −0.0788209 | − | 0.996889i | \(-0.525116\pi\) | ||||
−0.0788209 | + | 0.996889i | \(0.525116\pi\) | |||||||
\(572\) | 3.80642i | 0.159155i | ||||||||
\(573\) | − | 5.53972i | − | 0.231425i | ||||||
\(574\) | 5.95407 | 0.248518 | ||||||||
\(575\) | −3.47949 | − | 12.1383i | −0.145105 | − | 0.506201i | ||||
\(576\) | −12.8573 | −0.535720 | ||||||||
\(577\) | − | 43.5812i | − | 1.81431i | −0.420797 | − | 0.907155i | \(-0.638250\pi\) | ||
0.420797 | − | 0.907155i | \(-0.361750\pi\) | |||||||
\(578\) | 29.6227i | 1.23214i | ||||||||
\(579\) | 9.31756 | 0.387225 | ||||||||
\(580\) | −5.52543 | − | 39.3274i | −0.229431 | − | 1.63298i | ||||
\(581\) | 6.71900 | 0.278751 | ||||||||
\(582\) | 18.9240i | 0.784423i | ||||||||
\(583\) | 11.4286i | 0.473326i | ||||||||
\(584\) | 24.8573 | 1.02860 | ||||||||
\(585\) | 2.90321 | − | 0.407896i | 0.120033 | − | 0.0168644i | ||||
\(586\) | −56.6943 | −2.34202 | ||||||||
\(587\) | 20.6015i | 0.850314i | 0.905120 | + | 0.425157i | \(0.139781\pi\) | ||||
−0.905120 | + | 0.425157i | \(0.860219\pi\) | |||||||
\(588\) | 2.90321i | 0.119726i | ||||||||
\(589\) | 1.87755 | 0.0773629 | ||||||||
\(590\) | −35.3733 | + | 4.96989i | −1.45630 | + | 0.204607i | ||||
\(591\) | 27.0321 | 1.11195 | ||||||||
\(592\) | − | 1.80642i | − | 0.0742436i | ||||||
\(593\) | − | 7.33185i | − | 0.301083i | −0.988604 | − | 0.150542i | \(-0.951898\pi\) | ||
0.988604 | − | 0.150542i | \(-0.0481017\pi\) | |||||||
\(594\) | −2.21432 | −0.0908546 | ||||||||
\(595\) | 0.592104 | + | 4.21432i | 0.0242739 | + | 0.172770i | ||||
\(596\) | 29.0321 | 1.18920 | ||||||||
\(597\) | 4.06022i | 0.166174i | ||||||||
\(598\) | − | 7.33185i | − | 0.299822i | ||||||
\(599\) | 2.16193 | 0.0883342 | 0.0441671 | − | 0.999024i | \(-0.485937\pi\) | ||||
0.0441671 | + | 0.999024i | \(0.485937\pi\) | |||||||
\(600\) | −9.61285 | + | 2.75557i | −0.392443 | + | 0.112496i | ||||
\(601\) | −3.51606 | −0.143423 | −0.0717115 | − | 0.997425i | \(-0.522846\pi\) | ||||
−0.0717115 | + | 0.997425i | \(0.522846\pi\) | |||||||
\(602\) | − | 13.5462i | − | 0.552101i | ||||||
\(603\) | − | 2.00000i | − | 0.0814463i | ||||||
\(604\) | 14.6637 | 0.596658 | ||||||||
\(605\) | 0.311108 | + | 2.21432i | 0.0126483 | + | 0.0900249i | ||||
\(606\) | 10.5303 | 0.427766 | ||||||||
\(607\) | 43.2958i | 1.75732i | 0.477447 | + | 0.878660i | \(0.341562\pi\) | ||||
−0.477447 | + | 0.878660i | \(0.658438\pi\) | |||||||
\(608\) | 2.66370i | 0.108027i | ||||||||
\(609\) | −6.11753 | −0.247895 | ||||||||
\(610\) | 5.12843 | − | 0.720535i | 0.207644 | − | 0.0291736i | ||||
\(611\) | −2.08742 | −0.0844480 | ||||||||
\(612\) | − | 5.52543i | − | 0.223352i | ||||||
\(613\) | − | 36.3466i | − | 1.46803i | −0.679135 | − | 0.734013i | \(-0.737645\pi\) | ||
0.679135 | − | 0.734013i | \(-0.262355\pi\) | |||||||
\(614\) | −11.2761 | −0.455065 | ||||||||
\(615\) | 5.95407 | − | 0.836535i | 0.240091 | − | 0.0337324i | ||||
\(616\) | −2.00000 | −0.0805823 | ||||||||
\(617\) | − | 31.1896i | − | 1.25565i | −0.778356 | − | 0.627823i | \(-0.783946\pi\) | ||
0.778356 | − | 0.627823i | \(-0.216054\pi\) | |||||||
\(618\) | − | 25.0257i | − | 1.00668i | ||||||
\(619\) | −14.5906 | −0.586445 | −0.293222 | − | 0.956044i | \(-0.594728\pi\) | ||||
−0.293222 | + | 0.956044i | \(0.594728\pi\) | |||||||
\(620\) | 4.48886 | + | 31.9496i | 0.180277 | + | 1.28313i | ||||
\(621\) | 2.52543 | 0.101342 | ||||||||
\(622\) | 38.3684i | 1.53843i | ||||||||
\(623\) | 11.3620i | 0.455207i | ||||||||
\(624\) | 1.80642 | 0.0723148 | ||||||||
\(625\) | 21.2034 | − | 13.2444i | 0.848137 | − | 0.529777i | ||||
\(626\) | 34.3017 | 1.37097 | ||||||||
\(627\) | 0.377784i | 0.0150873i | ||||||||
\(628\) | − | 25.8020i | − | 1.02961i | ||||||
\(629\) | 2.49532 | 0.0994948 | ||||||||
\(630\) | 0.688892 | + | 4.90321i | 0.0274461 | + | 0.195349i | ||||
\(631\) | 21.6365 | 0.861336 | 0.430668 | − | 0.902511i | \(-0.358278\pi\) | ||||
0.430668 | + | 0.902511i | \(0.358278\pi\) | |||||||
\(632\) | − | 1.93978i | − | 0.0771602i | ||||||
\(633\) | 5.41927i | 0.215397i | ||||||||
\(634\) | 27.4893 | 1.09174 | ||||||||
\(635\) | −5.44446 | + | 0.764937i | −0.216057 | + | 0.0303556i | ||||
\(636\) | −33.1798 | −1.31566 | ||||||||
\(637\) | − | 1.31111i | − | 0.0519480i | ||||||
\(638\) | − | 13.5462i | − | 0.536298i | ||||||
\(639\) | −4.92396 | −0.194789 | ||||||||
\(640\) | −31.8163 | + | 4.47013i | −1.25765 | + | 0.176697i | ||||
\(641\) | −4.78415 | −0.188963 | −0.0944813 | − | 0.995527i | \(-0.530119\pi\) | ||||
−0.0944813 | + | 0.995527i | \(0.530119\pi\) | |||||||
\(642\) | − | 19.5669i | − | 0.772245i | ||||||
\(643\) | − | 24.5832i | − | 0.969467i | −0.874662 | − | 0.484734i | \(-0.838917\pi\) | ||
0.874662 | − | 0.484734i | \(-0.161083\pi\) | |||||||
\(644\) | 7.33185 | 0.288915 | ||||||||
\(645\) | −1.90321 | − | 13.5462i | −0.0749389 | − | 0.533380i | ||||
\(646\) | −1.59210 | −0.0626405 | ||||||||
\(647\) | − | 19.0638i | − | 0.749474i | −0.927131 | − | 0.374737i | \(-0.877733\pi\) | ||
0.927131 | − | 0.374737i | \(-0.122267\pi\) | |||||||
\(648\) | − | 2.00000i | − | 0.0785674i | ||||||
\(649\) | −7.21432 | −0.283187 | ||||||||
\(650\) | 13.9541 | − | 4.00000i | 0.547324 | − | 0.156893i | ||||
\(651\) | 4.96989 | 0.194785 | ||||||||
\(652\) | − | 3.80642i | − | 0.149071i | ||||||
\(653\) | − | 25.7654i | − | 1.00828i | −0.863622 | − | 0.504139i | \(-0.831810\pi\) | ||
0.863622 | − | 0.504139i | \(-0.168190\pi\) | |||||||
\(654\) | 7.52543 | 0.294268 | ||||||||
\(655\) | −1.78568 | − | 12.7096i | −0.0697723 | − | 0.496607i | ||||
\(656\) | 3.70471 | 0.144645 | ||||||||
\(657\) | − | 12.4286i | − | 0.484887i | ||||||
\(658\) | − | 3.52543i | − | 0.137435i | ||||||
\(659\) | −50.0212 | −1.94855 | −0.974275 | − | 0.225362i | \(-0.927643\pi\) | ||||
−0.974275 | + | 0.225362i | \(0.927643\pi\) | |||||||
\(660\) | −6.42864 | + | 0.903212i | −0.250234 | + | 0.0351575i | ||||
\(661\) | 36.5195 | 1.42044 | 0.710221 | − | 0.703979i | \(-0.248595\pi\) | ||||
0.710221 | + | 0.703979i | \(0.248595\pi\) | |||||||
\(662\) | 72.0119i | 2.79882i | ||||||||
\(663\) | 2.49532i | 0.0969100i | ||||||||
\(664\) | −13.4380 | −0.521496 | ||||||||
\(665\) | 0.836535 | − | 0.117532i | 0.0324395 | − | 0.00455768i | ||||
\(666\) | 2.90321 | 0.112497 | ||||||||
\(667\) | 15.4494i | 0.598203i | ||||||||
\(668\) | − | 43.9496i | − | 1.70046i | ||||||
\(669\) | −18.2924 | −0.707224 | ||||||||
\(670\) | −1.37778 | − | 9.80642i | −0.0532285 | − | 0.378855i | ||||
\(671\) | 1.04593 | 0.0403778 | ||||||||
\(672\) | 7.05086i | 0.271993i | ||||||||
\(673\) | − | 27.5926i | − | 1.06362i | −0.846865 | − | 0.531808i | \(-0.821513\pi\) | ||
0.846865 | − | 0.531808i | \(-0.178487\pi\) | |||||||
\(674\) | 6.79060 | 0.261564 | ||||||||
\(675\) | 1.37778 | + | 4.80642i | 0.0530309 | + | 0.184999i | ||||
\(676\) | −32.7511 | −1.25966 | ||||||||
\(677\) | 17.3511i | 0.666856i | 0.942776 | + | 0.333428i | \(0.108205\pi\) | ||||
−0.942776 | + | 0.333428i | \(0.891795\pi\) | |||||||
\(678\) | − | 6.11261i | − | 0.234753i | ||||||
\(679\) | 8.54617 | 0.327972 | ||||||||
\(680\) | −1.18421 | − | 8.42864i | −0.0454123 | − | 0.323224i | ||||
\(681\) | −9.17484 | −0.351581 | ||||||||
\(682\) | 11.0049i | 0.421400i | ||||||||
\(683\) | − | 21.8983i | − | 0.837915i | −0.908006 | − | 0.418957i | \(-0.862396\pi\) | ||
0.908006 | − | 0.418957i | \(-0.137604\pi\) | |||||||
\(684\) | −1.09679 | −0.0419367 | ||||||||
\(685\) | −30.0415 | + | 4.22077i | −1.14783 | + | 0.161267i | ||||
\(686\) | 2.21432 | 0.0845431 | ||||||||
\(687\) | − | 0.112610i | − | 0.00429632i | ||||||
\(688\) | − | 8.42864i | − | 0.321339i | ||||||
\(689\) | 14.9842 | 0.570852 | ||||||||
\(690\) | 12.3827 | − | 1.73975i | 0.471402 | − | 0.0662310i | ||||
\(691\) | −0.726989 | −0.0276559 | −0.0138280 | − | 0.999904i | \(-0.504402\pi\) | ||||
−0.0138280 | + | 0.999904i | \(0.504402\pi\) | |||||||
\(692\) | − | 63.4706i | − | 2.41279i | ||||||
\(693\) | 1.00000i | 0.0379869i | ||||||||
\(694\) | −52.5116 | −1.99331 | ||||||||
\(695\) | −1.87109 | − | 13.3176i | −0.0709746 | − | 0.505164i | ||||
\(696\) | 12.2351 | 0.463769 | ||||||||
\(697\) | 5.11753i | 0.193840i | ||||||||
\(698\) | − | 48.3575i | − | 1.83036i | ||||||
\(699\) | 20.3892 | 0.771189 | ||||||||
\(700\) | 4.00000 | + | 13.9541i | 0.151186 | + | 0.527414i | ||||
\(701\) | 27.9940 | 1.05732 | 0.528660 | − | 0.848834i | \(-0.322695\pi\) | ||||
0.528660 | + | 0.848834i | \(0.322695\pi\) | |||||||
\(702\) | 2.90321i | 0.109575i | ||||||||
\(703\) | − | 0.495316i | − | 0.0186812i | ||||||
\(704\) | −12.8573 | −0.484577 | ||||||||
\(705\) | −0.495316 | − | 3.52543i | −0.0186547 | − | 0.132775i | ||||
\(706\) | 69.0736 | 2.59962 | ||||||||
\(707\) | − | 4.75557i | − | 0.178852i | ||||||
\(708\) | − | 20.9447i | − | 0.787150i | ||||||
\(709\) | 40.3319 | 1.51469 | 0.757347 | − | 0.653012i | \(-0.226495\pi\) | ||||
0.757347 | + | 0.653012i | \(0.226495\pi\) | |||||||
\(710\) | −24.1432 | + | 3.39207i | −0.906078 | + | 0.127302i | ||||
\(711\) | −0.969888 | −0.0363737 | ||||||||
\(712\) | − | 22.7239i | − | 0.851615i | ||||||
\(713\) | − | 12.5511i | − | 0.470042i | ||||||
\(714\) | −4.21432 | −0.157717 | ||||||||
\(715\) | 2.90321 | − | 0.407896i | 0.108574 | − | 0.0152544i | ||||
\(716\) | −45.9081 | −1.71567 | ||||||||
\(717\) | − | 25.0207i | − | 0.934417i | ||||||
\(718\) | 15.8731i | 0.592379i | ||||||||
\(719\) | 40.9418 | 1.52687 | 0.763435 | − | 0.645884i | \(-0.223511\pi\) | ||||
0.763435 | + | 0.645884i | \(0.223511\pi\) | |||||||
\(720\) | 0.428639 | + | 3.05086i | 0.0159745 | + | 0.113699i | ||||
\(721\) | −11.3017 | −0.420899 | ||||||||
\(722\) | − | 41.7560i | − | 1.55400i | ||||||
\(723\) | − | 1.18865i | − | 0.0442065i | ||||||
\(724\) | 62.6548 | 2.32855 | ||||||||
\(725\) | −29.4035 | + | 8.42864i | −1.09202 | + | 0.313032i | ||||
\(726\) | −2.21432 | −0.0821811 | ||||||||
\(727\) | 26.2464i | 0.973427i | 0.873562 | + | 0.486713i | \(0.161804\pi\) | ||||
−0.873562 | + | 0.486713i | \(0.838196\pi\) | |||||||
\(728\) | 2.62222i | 0.0971858i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −8.56199 | − | 60.9403i | −0.316894 | − | 2.25550i | ||||
\(731\) | 11.6430 | 0.430630 | ||||||||
\(732\) | 3.03657i | 0.112235i | ||||||||
\(733\) | − | 24.0129i | − | 0.886937i | −0.896290 | − | 0.443468i | \(-0.853748\pi\) | ||
0.896290 | − | 0.443468i | \(-0.146252\pi\) | |||||||
\(734\) | −39.6795 | −1.46460 | ||||||||
\(735\) | 2.21432 | − | 0.311108i | 0.0816764 | − | 0.0114754i | ||||
\(736\) | 17.8064 | 0.656353 | ||||||||
\(737\) | − | 2.00000i | − | 0.0736709i | ||||||
\(738\) | 5.95407i | 0.219172i | ||||||||
\(739\) | 29.2958 | 1.07766 | 0.538831 | − | 0.842414i | \(-0.318866\pi\) | ||||
0.538831 | + | 0.842414i | \(0.318866\pi\) | |||||||
\(740\) | 8.42864 | − | 1.18421i | 0.309843 | − | 0.0435324i | ||||
\(741\) | 0.495316 | 0.0181959 | ||||||||
\(742\) | 25.3067i | 0.929037i | ||||||||
\(743\) | 40.0830i | 1.47050i | 0.677795 | + | 0.735251i | \(0.262936\pi\) | ||||
−0.677795 | + | 0.735251i | \(0.737064\pi\) | |||||||
\(744\) | −9.93978 | −0.364410 | ||||||||
\(745\) | −3.11108 | − | 22.1432i | −0.113981 | − | 0.811264i | ||||
\(746\) | −4.92396 | −0.180279 | ||||||||
\(747\) | 6.71900i | 0.245835i | ||||||||
\(748\) | − | 5.52543i | − | 0.202030i | ||||||
\(749\) | −8.83654 | −0.322880 | ||||||||
\(750\) | 10.0667 | + | 22.6178i | 0.367583 | + | 0.825884i | ||||
\(751\) | −12.2444 | −0.446806 | −0.223403 | − | 0.974726i | \(-0.571717\pi\) | ||||
−0.223403 | + | 0.974726i | \(0.571717\pi\) | |||||||
\(752\) | − | 2.19358i | − | 0.0799915i | ||||||
\(753\) | − | 27.8163i | − | 1.01368i | ||||||
\(754\) | −17.7605 | −0.646799 | ||||||||
\(755\) | −1.57136 | − | 11.1842i | −0.0571877 | − | 0.407035i | ||||
\(756\) | −2.90321 | −0.105589 | ||||||||
\(757\) | 49.1655i | 1.78695i | 0.449113 | + | 0.893475i | \(0.351740\pi\) | ||||
−0.449113 | + | 0.893475i | \(0.648260\pi\) | |||||||
\(758\) | − | 39.1447i | − | 1.42180i | ||||||
\(759\) | 2.52543 | 0.0916672 | ||||||||
\(760\) | −1.67307 | + | 0.235063i | −0.0606887 | + | 0.00852664i | ||||
\(761\) | −37.6860 | −1.36612 | −0.683058 | − | 0.730364i | \(-0.739350\pi\) | ||||
−0.683058 | + | 0.730364i | \(0.739350\pi\) | |||||||
\(762\) | − | 5.44446i | − | 0.197232i | ||||||
\(763\) | − | 3.39853i | − | 0.123035i | ||||||
\(764\) | 16.0830 | 0.581862 | ||||||||
\(765\) | −4.21432 | + | 0.592104i | −0.152369 | + | 0.0214076i | ||||
\(766\) | −37.2815 | −1.34703 | ||||||||
\(767\) | 9.45875i | 0.341536i | ||||||||
\(768\) | − | 6.10171i | − | 0.220177i | ||||||
\(769\) | 7.78415 | 0.280704 | 0.140352 | − | 0.990102i | \(-0.455177\pi\) | ||||
0.140352 | + | 0.990102i | \(0.455177\pi\) | |||||||
\(770\) | 0.688892 | + | 4.90321i | 0.0248260 | + | 0.176699i | ||||
\(771\) | −31.6336 | −1.13926 | ||||||||
\(772\) | 27.0509i | 0.973582i | ||||||||
\(773\) | − | 43.0450i | − | 1.54822i | −0.633050 | − | 0.774111i | \(-0.718197\pi\) | ||
0.633050 | − | 0.774111i | \(-0.281803\pi\) | |||||||
\(774\) | 13.5462 | 0.486907 | ||||||||
\(775\) | 23.8874 | − | 6.84743i | 0.858060 | − | 0.245967i | ||||
\(776\) | −17.0923 | −0.613579 | ||||||||
\(777\) | − | 1.31111i | − | 0.0470357i | ||||||
\(778\) | 34.2908i | 1.22939i | ||||||||
\(779\) | 1.01582 | 0.0363956 | ||||||||
\(780\) | 1.18421 | + | 8.42864i | 0.0424015 | + | 0.301794i | ||||
\(781\) | −4.92396 | −0.176193 | ||||||||
\(782\) | 10.6430i | 0.380591i | ||||||||
\(783\) | − | 6.11753i | − | 0.218623i | ||||||
\(784\) | 1.37778 | 0.0492066 | ||||||||
\(785\) | −19.6795 | + | 2.76494i | −0.702392 | + | 0.0986848i | ||||
\(786\) | 12.7096 | 0.453338 | ||||||||
\(787\) | − | 9.21585i | − | 0.328510i | −0.986418 | − | 0.164255i | \(-0.947478\pi\) | ||
0.986418 | − | 0.164255i | \(-0.0525219\pi\) | |||||||
\(788\) | 78.4800i | 2.79573i | ||||||||
\(789\) | 22.8573 | 0.813741 | ||||||||
\(790\) | −4.75557 | + | 0.668149i | −0.169196 | + | 0.0237717i | ||||
\(791\) | −2.76049 | −0.0981518 | ||||||||
\(792\) | − | 2.00000i | − | 0.0710669i | ||||||
\(793\) | − | 1.37133i | − | 0.0486974i | ||||||
\(794\) | −37.4291 | −1.32831 | ||||||||
\(795\) | 3.55554 | + | 25.3067i | 0.126102 | + | 0.897535i | ||||
\(796\) | −11.7877 | −0.417804 | ||||||||
\(797\) | 15.4982i | 0.548975i | 0.961591 | + | 0.274488i | \(0.0885083\pi\) | ||||
−0.961591 | + | 0.274488i | \(0.911492\pi\) | |||||||
\(798\) | 0.836535i | 0.0296130i | ||||||||
\(799\) | 3.03011 | 0.107198 | ||||||||
\(800\) | 9.71456 | + | 33.8894i | 0.343461 | + | 1.19817i | ||||
\(801\) | −11.3620 | −0.401455 | ||||||||
\(802\) | 51.6400i | 1.82347i | ||||||||
\(803\) | − | 12.4286i | − | 0.438597i | ||||||
\(804\) | 5.80642 | 0.204777 | ||||||||
\(805\) | −0.785680 | − | 5.59210i | −0.0276916 | − | 0.197096i | ||||
\(806\) | 14.4286 | 0.508227 | ||||||||
\(807\) | − | 1.48103i | − | 0.0521346i | ||||||
\(808\) | 9.51114i | 0.334601i | ||||||||
\(809\) | 20.9304 | 0.735874 | 0.367937 | − | 0.929851i | \(-0.380064\pi\) | ||||
0.367937 | + | 0.929851i | \(0.380064\pi\) | |||||||
\(810\) | −4.90321 | + | 0.688892i | −0.172281 | + | 0.0242052i | ||||
\(811\) | −49.2770 | −1.73035 | −0.865175 | − | 0.501470i | \(-0.832793\pi\) | ||||
−0.865175 | + | 0.501470i | \(0.832793\pi\) | |||||||
\(812\) | − | 17.7605i | − | 0.623271i | ||||||
\(813\) | − | 25.4844i | − | 0.893778i | ||||||
\(814\) | 2.90321 | 0.101758 | ||||||||
\(815\) | −2.90321 | + | 0.407896i | −0.101695 | + | 0.0142880i | ||||
\(816\) | −2.62222 | −0.0917959 | ||||||||
\(817\) | − | 2.31111i | − | 0.0808554i | ||||||
\(818\) | 5.77478i | 0.201910i | ||||||||
\(819\) | 1.31111 | 0.0458138 | ||||||||
\(820\) | 2.42864 | + | 17.2859i | 0.0848118 | + | 0.603650i | ||||
\(821\) | −44.1862 | −1.54211 | −0.771055 | − | 0.636769i | \(-0.780271\pi\) | ||||
−0.771055 | + | 0.636769i | \(0.780271\pi\) | |||||||
\(822\) | − | 30.0415i | − | 1.04782i | ||||||
\(823\) | 7.10462i | 0.247652i | 0.992304 | + | 0.123826i | \(0.0395164\pi\) | ||||
−0.992304 | + | 0.123826i | \(0.960484\pi\) | |||||||
\(824\) | 22.6035 | 0.787430 | ||||||||
\(825\) | 1.37778 | + | 4.80642i | 0.0479683 | + | 0.167338i | ||||
\(826\) | −15.9748 | −0.555835 | ||||||||
\(827\) | 41.3461i | 1.43775i | 0.695141 | + | 0.718873i | \(0.255342\pi\) | ||||
−0.695141 | + | 0.718873i | \(0.744658\pi\) | |||||||
\(828\) | 7.33185i | 0.254799i | ||||||||
\(829\) | 3.40943 | 0.118414 | 0.0592072 | − | 0.998246i | \(-0.481143\pi\) | ||||
0.0592072 | + | 0.998246i | \(0.481143\pi\) | |||||||
\(830\) | 4.62867 | + | 32.9447i | 0.160663 | + | 1.14353i | ||||
\(831\) | 14.2395 | 0.493963 | ||||||||
\(832\) | 16.8573i | 0.584421i | ||||||||
\(833\) | 1.90321i | 0.0659424i | ||||||||
\(834\) | 13.3176 | 0.461149 | ||||||||
\(835\) | −33.5210 | + | 4.70964i | −1.16004 | + | 0.162984i | ||||
\(836\) | −1.09679 | −0.0379332 | ||||||||
\(837\) | 4.96989i | 0.171784i | ||||||||
\(838\) | 34.1497i | 1.17968i | ||||||||
\(839\) | −5.09526 | −0.175908 | −0.0879539 | − | 0.996125i | \(-0.528033\pi\) | ||||
−0.0879539 | + | 0.996125i | \(0.528033\pi\) | |||||||
\(840\) | −4.42864 | + | 0.622216i | −0.152803 | + | 0.0214685i | ||||
\(841\) | 8.42419 | 0.290489 | ||||||||
\(842\) | 13.9190i | 0.479682i | ||||||||
\(843\) | − | 2.23951i | − | 0.0771328i | ||||||
\(844\) | −15.7333 | −0.541562 | ||||||||
\(845\) | 3.50961 | + | 24.9797i | 0.120734 | + | 0.859329i | ||||
\(846\) | 3.52543 | 0.121207 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 15.7462i | 0.540727i | ||||||||
\(849\) | −24.8321 | −0.852235 | ||||||||
\(850\) | −20.2558 | + | 5.80642i | −0.694768 | + | 0.199159i | ||||
\(851\) | −3.31111 | −0.113503 | ||||||||
\(852\) | − | 14.2953i | − | 0.489748i | ||||||
\(853\) | 23.0257i | 0.788384i | 0.919028 | + | 0.394192i | \(0.128975\pi\) | ||||
−0.919028 | + | 0.394192i | \(0.871025\pi\) | |||||||
\(854\) | 2.31603 | 0.0792529 | ||||||||
\(855\) | 0.117532 | + | 0.836535i | 0.00401950 | + | 0.0286089i | ||||
\(856\) | 17.6731 | 0.604053 | ||||||||
\(857\) | 12.6923i | 0.433560i | 0.976220 | + | 0.216780i | \(0.0695554\pi\) | ||||
−0.976220 | + | 0.216780i | \(0.930445\pi\) | |||||||
\(858\) | 2.90321i | 0.0991140i | ||||||||
\(859\) | −41.9418 | −1.43104 | −0.715518 | − | 0.698595i | \(-0.753809\pi\) | ||||
−0.715518 | + | 0.698595i | \(0.753809\pi\) | |||||||
\(860\) | 39.3274 | − | 5.52543i | 1.34105 | − | 0.188416i | ||||
\(861\) | 2.68889 | 0.0916372 | ||||||||
\(862\) | 36.1116i | 1.22996i | ||||||||
\(863\) | − | 45.1659i | − | 1.53747i | −0.639569 | − | 0.768733i | \(-0.720887\pi\) | ||
0.639569 | − | 0.768733i | \(-0.279113\pi\) | |||||||
\(864\) | −7.05086 | −0.239875 | ||||||||
\(865\) | −48.4099 | + | 6.80150i | −1.64599 | + | 0.231258i | ||||
\(866\) | 32.9621 | 1.12010 | ||||||||
\(867\) | 13.3778i | 0.454333i | ||||||||
\(868\) | 14.4286i | 0.489740i | ||||||||
\(869\) | −0.969888 | −0.0329012 | ||||||||
\(870\) | −4.21432 | − | 29.9956i | −0.142879 | − | 1.01694i | ||||
\(871\) | −2.62222 | −0.0888504 | ||||||||
\(872\) | 6.79706i | 0.230177i | ||||||||
\(873\) | 8.54617i | 0.289244i | ||||||||
\(874\) | 2.11261 | 0.0714601 | ||||||||
\(875\) | 10.2143 | − | 4.54617i | 0.345307 | − | 0.153689i | ||||
\(876\) | 36.0830 | 1.21913 | ||||||||
\(877\) | − | 47.6671i | − | 1.60960i | −0.593544 | − | 0.804802i | \(-0.702272\pi\) | ||
0.593544 | − | 0.804802i | \(-0.297728\pi\) | |||||||
\(878\) | − | 22.8464i | − | 0.771028i | ||||||
\(879\) | −25.6035 | −0.863584 | ||||||||
\(880\) | 0.428639 | + | 3.05086i | 0.0144494 | + | 0.102844i | ||||
\(881\) | −8.53633 | −0.287596 | −0.143798 | − | 0.989607i | \(-0.545932\pi\) | ||||
−0.143798 | + | 0.989607i | \(0.545932\pi\) | |||||||
\(882\) | 2.21432i | 0.0745600i | ||||||||
\(883\) | 17.6258i | 0.593154i | 0.955009 | + | 0.296577i | \(0.0958451\pi\) | ||||
−0.955009 | + | 0.296577i | \(0.904155\pi\) | |||||||
\(884\) | −7.24443 | −0.243657 | ||||||||
\(885\) | −15.9748 | + | 2.24443i | −0.536987 | + | 0.0754457i | ||||
\(886\) | 9.25428 | 0.310903 | ||||||||
\(887\) | − | 14.2761i | − | 0.479344i | −0.970854 | − | 0.239672i | \(-0.922960\pi\) | ||
0.970854 | − | 0.239672i | \(-0.0770398\pi\) | |||||||
\(888\) | 2.62222i | 0.0879958i | ||||||||
\(889\) | −2.45875 | −0.0824639 | ||||||||
\(890\) | −55.7101 | + | 7.82717i | −1.86741 | + | 0.262367i | ||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | − | 53.1066i | − | 1.77814i | ||||||
\(893\) | − | 0.601472i | − | 0.0201275i | ||||||
\(894\) | 22.1432 | 0.740579 | ||||||||
\(895\) | 4.91951 | + | 35.0148i | 0.164441 | + | 1.17041i | ||||
\(896\) | −14.3684 | −0.480015 | ||||||||
\(897\) | − | 3.31111i | − | 0.110555i | ||||||
\(898\) | 55.8435i | 1.86352i | ||||||||
\(899\) | −30.4035 | −1.01401 | ||||||||
\(900\) | −13.9541 | + | 4.00000i | −0.465136 | + | 0.133333i | ||||
\(901\) | −21.7511 | −0.724635 | ||||||||
\(902\) | 5.95407i | 0.198249i | ||||||||
\(903\) | − | 6.11753i | − | 0.203579i | ||||||
\(904\) | 5.52098 | 0.183625 | ||||||||
\(905\) | −6.71408 | − | 47.7877i | −0.223184 | − | 1.58852i | ||||
\(906\) | 11.1842 | 0.371570 | ||||||||
\(907\) | 46.8736i | 1.55641i | 0.628009 | + | 0.778206i | \(0.283870\pi\) | ||||
−0.628009 | + | 0.778206i | \(0.716130\pi\) | |||||||
\(908\) | − | 26.6365i | − | 0.883963i | ||||||
\(909\) | 4.75557 | 0.157732 | ||||||||
\(910\) | 6.42864 | − | 0.903212i | 0.213107 | − | 0.0299412i | ||||
\(911\) | −14.5018 | −0.480465 | −0.240233 | − | 0.970715i | \(-0.577224\pi\) | ||||
−0.240233 | + | 0.970715i | \(0.577224\pi\) | |||||||
\(912\) | 0.520505i | 0.0172357i | ||||||||
\(913\) | 6.71900i | 0.222367i | ||||||||
\(914\) | −61.1086 | −2.02129 | ||||||||
\(915\) | 2.31603 | − | 0.325398i | 0.0765656 | − | 0.0107573i | ||||
\(916\) | 0.326929 | 0.0108020 | ||||||||
\(917\) | − | 5.73975i | − | 0.189543i | ||||||
\(918\) | − | 4.21432i | − | 0.139093i | ||||||
\(919\) | −0.990632 | −0.0326779 | −0.0163390 | − | 0.999867i | \(-0.505201\pi\) | ||||
−0.0163390 | + | 0.999867i | \(0.505201\pi\) | |||||||
\(920\) | 1.57136 | + | 11.1842i | 0.0518062 | + | 0.368732i | ||||
\(921\) | −5.09234 | −0.167798 | ||||||||
\(922\) | 74.3595i | 2.44890i | ||||||||
\(923\) | 6.45584i | 0.212496i | ||||||||
\(924\) | −2.90321 | −0.0955087 | ||||||||
\(925\) | −1.80642 | − | 6.30174i | −0.0593949 | − | 0.207200i | ||||
\(926\) | −50.6834 | −1.66556 | ||||||||
\(927\) | − | 11.3017i | − | 0.371198i | ||||||
\(928\) | − | 43.1338i | − | 1.41594i | ||||||
\(929\) | 40.8943 | 1.34170 | 0.670850 | − | 0.741593i | \(-0.265930\pi\) | ||||
0.670850 | + | 0.741593i | \(0.265930\pi\) | |||||||
\(930\) | 3.42372 | + | 24.3684i | 0.112268 | + | 0.799072i | ||||
\(931\) | 0.377784 | 0.0123814 | ||||||||
\(932\) | 59.1941i | 1.93897i | ||||||||
\(933\) | 17.3274i | 0.567274i | ||||||||
\(934\) | 14.1432 | 0.462780 | ||||||||
\(935\) | −4.21432 | + | 0.592104i | −0.137823 | + | 0.0193639i | ||||
\(936\) | −2.62222 | −0.0857098 | ||||||||
\(937\) | − | 16.5872i | − | 0.541880i | −0.962596 | − | 0.270940i | \(-0.912666\pi\) | ||
0.962596 | − | 0.270940i | \(-0.0873344\pi\) | |||||||
\(938\) | − | 4.42864i | − | 0.144600i | ||||||
\(939\) | 15.4909 | 0.505525 | ||||||||
\(940\) | 10.2351 | − | 1.43801i | 0.333831 | − | 0.0469026i | ||||
\(941\) | 35.9561 | 1.17213 | 0.586067 | − | 0.810262i | \(-0.300675\pi\) | ||||
0.586067 | + | 0.810262i | \(0.300675\pi\) | |||||||
\(942\) | − | 19.6795i | − | 0.641194i | ||||||
\(943\) | − | 6.79060i | − | 0.221132i | ||||||
\(944\) | −9.93978 | −0.323512 | ||||||||
\(945\) | 0.311108 | + | 2.21432i | 0.0101203 | + | 0.0720318i | ||||
\(946\) | 13.5462 | 0.440424 | ||||||||
\(947\) | − | 41.9675i | − | 1.36376i | −0.731465 | − | 0.681879i | \(-0.761163\pi\) | ||
0.731465 | − | 0.681879i | \(-0.238837\pi\) | |||||||
\(948\) | − | 2.81579i | − | 0.0914527i | ||||||
\(949\) | −16.2953 | −0.528967 | ||||||||
\(950\) | 1.15257 | + | 4.02074i | 0.0373942 | + | 0.130450i | ||||
\(951\) | 12.4143 | 0.402563 | ||||||||
\(952\) | − | 3.80642i | − | 0.123367i | ||||||
\(953\) | 7.83500i | 0.253801i | 0.991915 | + | 0.126900i | \(0.0405028\pi\) | ||||
−0.991915 | + | 0.126900i | \(0.959497\pi\) | |||||||
\(954\) | −25.3067 | −0.819333 | ||||||||
\(955\) | −1.72345 | − | 12.2667i | −0.0557695 | − | 0.396941i | ||||
\(956\) | 72.6405 | 2.34936 | ||||||||
\(957\) | − | 6.11753i | − | 0.197752i | ||||||
\(958\) | 76.6089i | 2.47512i | ||||||||
\(959\) | −13.5669 | −0.438099 | ||||||||
\(960\) | −28.4701 | + | 4.00000i | −0.918869 | + | 0.129099i | ||||
\(961\) | −6.30021 | −0.203233 | ||||||||
\(962\) | − | 3.80642i | − | 0.122724i | ||||||
\(963\) | − | 8.83654i | − | 0.284753i | ||||||
\(964\) | 3.45091 | 0.111146 | ||||||||
\(965\) | 20.6321 | − | 2.89877i | 0.664170 | − | 0.0933146i | ||||
\(966\) | 5.59210 | 0.179923 | ||||||||
\(967\) | 29.5783i | 0.951174i | 0.879669 | + | 0.475587i | \(0.157764\pi\) | ||||
−0.879669 | + | 0.475587i | \(0.842236\pi\) | |||||||
\(968\) | − | 2.00000i | − | 0.0642824i | ||||||
\(969\) | −0.719004 | −0.0230977 | ||||||||
\(970\) | 5.88739 | + | 41.9037i | 0.189033 | + | 1.34545i | ||||
\(971\) | 13.3749 | 0.429220 | 0.214610 | − | 0.976700i | \(-0.431152\pi\) | ||||
0.214610 | + | 0.976700i | \(0.431152\pi\) | |||||||
\(972\) | − | 2.90321i | − | 0.0931206i | ||||||
\(973\) | − | 6.01429i | − | 0.192809i | ||||||
\(974\) | 27.5843 | 0.883857 | ||||||||
\(975\) | 6.30174 | − | 1.80642i | 0.201817 | − | 0.0578519i | ||||
\(976\) | 1.44107 | 0.0461275 | ||||||||
\(977\) | − | 57.1245i | − | 1.82757i | −0.406194 | − | 0.913787i | \(-0.633144\pi\) | ||
0.406194 | − | 0.913787i | \(-0.366856\pi\) | |||||||
\(978\) | − | 2.90321i | − | 0.0928345i | ||||||
\(979\) | −11.3620 | −0.363130 | ||||||||
\(980\) | 0.903212 | + | 6.42864i | 0.0288520 | + | 0.205355i | ||||
\(981\) | 3.39853 | 0.108507 | ||||||||
\(982\) | 36.3749i | 1.16077i | ||||||||
\(983\) | − | 11.4924i | − | 0.366551i | −0.983062 | − | 0.183275i | \(-0.941330\pi\) | ||
0.983062 | − | 0.183275i | \(-0.0586700\pi\) | |||||||
\(984\) | −5.37778 | −0.171438 | ||||||||
\(985\) | 59.8578 | − | 8.40990i | 1.90723 | − | 0.267962i | ||||
\(986\) | 25.7812 | 0.821042 | ||||||||
\(987\) | − | 1.59210i | − | 0.0506772i | ||||||
\(988\) | 1.43801i | 0.0457491i | ||||||||
\(989\) | −15.4494 | −0.491262 | ||||||||
\(990\) | −4.90321 | + | 0.688892i | −0.155834 | + | 0.0218944i | ||||
\(991\) | 23.4987 | 0.746461 | 0.373231 | − | 0.927739i | \(-0.378250\pi\) | ||||
0.373231 | + | 0.927739i | \(0.378250\pi\) | |||||||
\(992\) | 35.0420i | 1.11258i | ||||||||
\(993\) | 32.5210i | 1.03202i | ||||||||
\(994\) | −10.9032 | −0.345829 | ||||||||
\(995\) | 1.26317 | + | 8.99063i | 0.0400451 | + | 0.285022i | ||||
\(996\) | −19.5067 | −0.618093 | ||||||||
\(997\) | − | 24.3970i | − | 0.772661i | −0.922360 | − | 0.386330i | \(-0.873742\pi\) | ||
0.922360 | − | 0.386330i | \(-0.126258\pi\) | |||||||
\(998\) | 82.5106i | 2.61183i | ||||||||
\(999\) | 1.31111 | 0.0414816 |
(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 | 1155.2.c.c.694.6 | yes | 6 | |
5.2 | odd | 4 | 5775.2.a.bu.1.1 | 3 | |||
5.3 | odd | 4 | 5775.2.a.bt.1.3 | 3 | |||
5.4 | even | 2 | inner | 1155.2.c.c.694.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.c.c.694.1 | ✓ | 6 | 5.4 | even | 2 | inner | |
1155.2.c.c.694.6 | yes | 6 | 1.1 | even | 1 | trivial | |
5775.2.a.bt.1.3 | 3 | 5.3 | odd | 4 | |||
5775.2.a.bu.1.1 | 3 | 5.2 | odd | 4 |