Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(177,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 98) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 177.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.177 |
Dual form | 784.2.i.m.753.2 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | + | 1.22474i | 0.408248 | + | 0.707107i | 0.994694 | − | 0.102882i | \(-0.0328064\pi\) |
−0.586445 | + | 0.809989i | \(0.699473\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.41421 | − | 2.44949i | 0.632456 | − | 1.09545i | −0.354593 | − | 0.935021i | \(-0.615380\pi\) |
0.987048 | − | 0.160424i | \(-0.0512862\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.00000 | 1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.707107 | − | 1.22474i | −0.171499 | − | 0.297044i | 0.767445 | − | 0.641114i | \(-0.221528\pi\) |
−0.938944 | + | 0.344070i | \(0.888194\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.53553 | − | 6.12372i | 0.811107 | − | 1.40488i | −0.100983 | − | 0.994888i | \(-0.532199\pi\) |
0.912090 | − | 0.409991i | \(-0.134468\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.50000 | − | 2.59808i | −0.300000 | − | 0.519615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.24264 | − | 7.34847i | −0.762001 | − | 1.31982i | −0.941818 | − | 0.336124i | \(-0.890884\pi\) |
0.179817 | − | 0.983700i | \(-0.442449\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.41421 | − | 2.44949i | 0.246183 | − | 0.426401i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | + | 8.66025i | −0.821995 | + | 1.42374i | 0.0821995 | + | 0.996616i | \(0.473806\pi\) |
−0.904194 | + | 0.427121i | \(0.859528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.89949 | 1.54604 | 0.773021 | − | 0.634381i | \(-0.218745\pi\) | ||||
0.773021 | + | 0.634381i | \(0.218745\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.41421 | − | 2.44949i | −0.210819 | − | 0.365148i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.41421 | + | 2.44949i | −0.206284 | + | 0.357295i | −0.950541 | − | 0.310599i | \(-0.899470\pi\) |
0.744257 | + | 0.667893i | \(0.232804\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | − | 1.73205i | 0.140028 | − | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | + | 1.73205i | 0.137361 | + | 0.237915i | 0.926497 | − | 0.376303i | \(-0.122805\pi\) |
−0.789136 | + | 0.614218i | \(0.789471\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.65685 | −0.762770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.0000 | 1.32453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.707107 | + | 1.22474i | 0.0920575 | + | 0.159448i | 0.908377 | − | 0.418153i | \(-0.137322\pi\) |
−0.816319 | + | 0.577601i | \(0.803989\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.41421 | − | 2.44949i | 0.181071 | − | 0.313625i | −0.761174 | − | 0.648547i | \(-0.775377\pi\) |
0.942246 | + | 0.334922i | \(0.108710\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00000 | + | 10.3923i | 0.733017 | + | 1.26962i | 0.955588 | + | 0.294706i | \(0.0952216\pi\) |
−0.222571 | + | 0.974916i | \(0.571445\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.65685 | −0.681005 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.707107 | − | 1.22474i | −0.0827606 | − | 0.143346i | 0.821674 | − | 0.569958i | \(-0.193040\pi\) |
−0.904435 | + | 0.426612i | \(0.859707\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.12132 | − | 3.67423i | 0.244949 | − | 0.424264i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.00000 | + | 3.46410i | −0.225018 | + | 0.389742i | −0.956325 | − | 0.292306i | \(-0.905577\pi\) |
0.731307 | + | 0.682048i | \(0.238911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.50000 | + | 4.33013i | 0.277778 | + | 0.481125i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.89949 | 1.08661 | 0.543305 | − | 0.839535i | \(-0.317173\pi\) | ||||
0.543305 | + | 0.839535i | \(0.317173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.41421 | + | 2.44949i | 0.151620 | + | 0.262613i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.53553 | + | 6.12372i | −0.374766 | + | 0.649113i | −0.990292 | − | 0.139003i | \(-0.955610\pi\) |
0.615526 | + | 0.788116i | \(0.288944\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.00000 | − | 10.3923i | 0.622171 | − | 1.07763i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.0000 | − | 17.3205i | −1.02598 | − | 1.77705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.89949 | −1.00514 | −0.502571 | − | 0.864536i | \(-0.667612\pi\) | ||||
−0.502571 | + | 0.864536i | \(0.667612\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.24264 | + | 7.34847i | 0.422159 | + | 0.731200i | 0.996150 | − | 0.0876610i | \(-0.0279392\pi\) |
−0.573992 | + | 0.818861i | \(0.694606\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.41421 | + | 2.44949i | −0.139347 | + | 0.241355i | −0.927249 | − | 0.374444i | \(-0.877834\pi\) |
0.787903 | + | 0.615800i | \(0.211167\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.00000 | + | 3.46410i | −0.193347 | + | 0.334887i | −0.946357 | − | 0.323122i | \(-0.895268\pi\) |
0.753010 | + | 0.658009i | \(0.228601\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | + | 1.73205i | 0.0957826 | + | 0.165900i | 0.909935 | − | 0.414751i | \(-0.136131\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.1421 | −1.34231 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.65685 | + | 9.79796i | 0.527504 | + | 0.913664i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.00000 | + | 12.1244i | 0.631169 | + | 1.09322i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.41421 | − | 2.44949i | −0.124515 | − | 0.215666i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.36396 | + | 11.0227i | −0.556022 | + | 0.963058i | 0.441801 | + | 0.897113i | \(0.354340\pi\) |
−0.997823 | + | 0.0659452i | \(0.978994\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.00000 | − | 13.8564i | 0.688530 | − | 1.19257i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | − | 10.3923i | −0.512615 | − | 0.887875i | −0.999893 | − | 0.0146279i | \(-0.995344\pi\) |
0.487278 | − | 0.873247i | \(-0.337990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.89949 | 0.839664 | 0.419832 | − | 0.907602i | \(-0.362089\pi\) | ||||
0.419832 | + | 0.907602i | \(0.362089\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00000 | −0.336861 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.82843 | − | 4.89898i | 0.234888 | − | 0.406838i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.00000 | + | 8.66025i | −0.409616 | + | 0.709476i | −0.994847 | − | 0.101391i | \(-0.967671\pi\) |
0.585231 | + | 0.810867i | \(0.301004\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | − | 13.8564i | −0.651031 | − | 1.12762i | −0.982873 | − | 0.184284i | \(-0.941004\pi\) |
0.331842 | − | 0.943335i | \(-0.392330\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.41421 | −0.114332 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.0000 | −1.92773 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.65685 | − | 9.79796i | −0.451466 | − | 0.781962i | 0.547011 | − | 0.837125i | \(-0.315765\pi\) |
−0.998477 | + | 0.0551630i | \(0.982432\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.41421 | + | 2.44949i | −0.112154 | + | 0.194257i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.00000 | − | 8.66025i | 0.391630 | − | 0.678323i | −0.601035 | − | 0.799223i | \(-0.705245\pi\) |
0.992665 | + | 0.120900i | \(0.0385779\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.00000 | − | 6.92820i | −0.311400 | − | 0.539360i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.7990 | −1.53209 | −0.766046 | − | 0.642786i | \(-0.777779\pi\) | ||||
−0.766046 | + | 0.642786i | \(0.777779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.53553 | − | 6.12372i | −0.270369 | − | 0.468293i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.48528 | + | 14.6969i | −0.645124 | + | 1.11739i | 0.339149 | + | 0.940733i | \(0.389861\pi\) |
−0.984273 | + | 0.176655i | \(0.943472\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.00000 | + | 1.73205i | −0.0751646 | + | 0.130189i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000 | + | 10.3923i | 0.448461 | + | 0.776757i | 0.998286 | − | 0.0585225i | \(-0.0186389\pi\) |
−0.549825 | + | 0.835280i | \(0.685306\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.00000 | 0.295689 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.1421 | + | 24.4949i | 1.03975 | + | 1.80090i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.41421 | + | 2.44949i | −0.103418 | + | 0.179124i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.00000 | + | 3.46410i | −0.144715 | + | 0.250654i | −0.929267 | − | 0.369410i | \(-0.879560\pi\) |
0.784552 | + | 0.620063i | \(0.212893\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.00000 | + | 13.8564i | 0.575853 | + | 0.997406i | 0.995948 | + | 0.0899262i | \(0.0286631\pi\) |
−0.420096 | + | 0.907480i | \(0.638004\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.24264 | − | 7.34847i | −0.300753 | − | 0.520919i | 0.675554 | − | 0.737311i | \(-0.263905\pi\) |
−0.976307 | + | 0.216391i | \(0.930571\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.48528 | + | 14.6969i | −0.598506 | + | 1.03664i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.0000 | − | 24.2487i | 0.977802 | − | 1.69360i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00000 | + | 3.46410i | 0.139010 | + | 0.240772i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.1421 | −0.978232 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.48528 | + | 14.6969i | 0.581402 | + | 1.00702i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.82843 | + | 4.89898i | −0.192897 | + | 0.334108i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.00000 | − | 1.73205i | 0.0675737 | − | 0.117041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.6066 | + | 18.3712i | 0.703985 | + | 1.21934i | 0.967057 | + | 0.254561i | \(0.0819311\pi\) |
−0.263072 | + | 0.964776i | \(0.584736\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.48528 | + | 14.6969i | −0.560723 | + | 0.971201i | 0.436710 | + | 0.899602i | \(0.356143\pi\) |
−0.997434 | + | 0.0715988i | \(0.977190\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.0000 | + | 20.7846i | −0.786146 | + | 1.36165i | 0.142166 | + | 0.989843i | \(0.454593\pi\) |
−0.928312 | + | 0.371802i | \(0.878740\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | + | 6.92820i | 0.260931 | + | 0.451946i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.65685 | −0.367452 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.6066 | − | 18.3712i | −0.683231 | − | 1.18339i | −0.973989 | − | 0.226595i | \(-0.927241\pi\) |
0.290758 | − | 0.956797i | \(-0.406093\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.94975 | − | 8.57321i | 0.317526 | − | 0.549972i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.00000 | + | 12.1244i | 0.443607 | + | 0.768350i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.89949 | 0.624851 | 0.312425 | − | 0.949942i | \(-0.398859\pi\) | ||||
0.312425 | + | 0.949942i | \(0.398859\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | 0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.82843 | − | 4.89898i | −0.177123 | − | 0.306786i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.36396 | − | 11.0227i | 0.396973 | − | 0.687577i | −0.596378 | − | 0.802704i | \(-0.703394\pi\) |
0.993351 | + | 0.115126i | \(0.0367273\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | − | 1.73205i | 0.0618984 | − | 0.107211i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | + | 10.3923i | 0.369976 | + | 0.640817i | 0.989561 | − | 0.144112i | \(-0.0460326\pi\) |
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.65685 | 0.347498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.0000 | −0.611990 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.65685 | − | 9.79796i | −0.344904 | − | 0.597392i | 0.640432 | − | 0.768015i | \(-0.278755\pi\) |
−0.985336 | + | 0.170623i | \(0.945422\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.3137 | + | 19.5959i | −0.687259 | + | 1.19037i | 0.285462 | + | 0.958390i | \(0.407853\pi\) |
−0.972721 | + | 0.231977i | \(0.925480\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.00000 | + | 5.19615i | −0.180907 | + | 0.313340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.00000 | + | 1.73205i | 0.0600842 | + | 0.104069i | 0.894503 | − | 0.447062i | \(-0.147530\pi\) |
−0.834419 | + | 0.551131i | \(0.814196\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.48528 | −0.508001 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0000 | 0.954480 | 0.477240 | − | 0.878773i | \(-0.341637\pi\) | ||||
0.477240 | + | 0.878773i | \(0.341637\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.707107 | + | 1.22474i | 0.0420331 | + | 0.0728035i | 0.886277 | − | 0.463156i | \(-0.153283\pi\) |
−0.844243 | + | 0.535960i | \(0.819950\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.1421 | − | 24.4949i | 0.837708 | − | 1.45095i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.50000 | − | 12.9904i | 0.441176 | − | 0.764140i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.00000 | − | 12.1244i | −0.410347 | − | 0.710742i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.7990 | 1.15667 | 0.578335 | − | 0.815800i | \(-0.303703\pi\) | ||||
0.578335 | + | 0.815800i | \(0.303703\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.65685 | − | 9.79796i | −0.328244 | − | 0.568535i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.00000 | + | 10.3923i | −0.344691 | + | 0.597022i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.00000 | − | 6.92820i | −0.229039 | − | 0.396708i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.89949 | −0.564994 | −0.282497 | − | 0.959268i | \(-0.591163\pi\) | ||||
−0.282497 | + | 0.959268i | \(0.591163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.65685 | + | 9.79796i | 0.320771 | + | 0.555591i | 0.980647 | − | 0.195783i | \(-0.0627248\pi\) |
−0.659877 | + | 0.751374i | \(0.729391\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.36396 | − | 11.0227i | 0.359712 | − | 0.623040i | −0.628200 | − | 0.778052i | \(-0.716208\pi\) |
0.987913 | + | 0.155012i | \(0.0495415\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.00000 | + | 8.66025i | −0.280828 | + | 0.486408i | −0.971589 | − | 0.236675i | \(-0.923942\pi\) |
0.690761 | + | 0.723083i | \(0.257276\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.00000 | − | 3.46410i | −0.111979 | − | 0.193952i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.65685 | −0.315735 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.0000 | −0.556415 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.41421 | + | 2.44949i | −0.0782062 | + | 0.135457i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.00000 | − | 8.66025i | 0.274825 | − | 0.476011i | −0.695266 | − | 0.718752i | \(-0.744713\pi\) |
0.970091 | + | 0.242742i | \(0.0780468\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.00000 | + | 8.66025i | 0.273998 | + | 0.474579i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.9411 | 1.85440 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.48528 | − | 14.6969i | −0.460857 | − | 0.798228i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.48528 | + | 14.6969i | −0.459504 | + | 0.795884i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.00000 | + | 13.8564i | −0.430706 | + | 0.746004i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0000 | − | 25.9808i | −0.805242 | − | 1.39472i | −0.916127 | − | 0.400887i | \(-0.868702\pi\) |
0.110885 | − | 0.993833i | \(-0.464631\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.707107 | − | 1.22474i | −0.0376355 | − | 0.0651866i | 0.846594 | − | 0.532239i | \(-0.178649\pi\) |
−0.884230 | + | 0.467052i | \(0.845316\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.9706 | − | 29.3939i | 0.900704 | − | 1.56007i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.0000 | + | 27.7128i | −0.844448 | + | 1.46263i | 0.0416523 | + | 0.999132i | \(0.486738\pi\) |
−0.886100 | + | 0.463494i | \(0.846596\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.5000 | − | 26.8468i | −0.815789 | − | 1.41299i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.89949 | 0.519589 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.00000 | −0.209370 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.1421 | − | 24.4949i | −0.738213 | − | 1.27862i | −0.953299 | − | 0.302028i | \(-0.902336\pi\) |
0.215086 | − | 0.976595i | \(-0.430997\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.94975 | − | 8.57321i | 0.257674 | − | 0.446304i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.00000 | + | 8.66025i | −0.258890 | + | 0.448411i | −0.965945 | − | 0.258748i | \(-0.916690\pi\) |
0.707055 | + | 0.707159i | \(0.250023\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.00000 | + | 6.92820i | 0.206559 | + | 0.357771i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.0000 | 1.33553 | 0.667765 | − | 0.744372i | \(-0.267251\pi\) | ||||
0.667765 | + | 0.744372i | \(0.267251\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.3137 | − | 19.5959i | −0.579619 | − | 1.00393i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.3848 | − | 31.8434i | 0.939418 | − | 1.62712i | 0.172859 | − | 0.984947i | \(-0.444700\pi\) |
0.766559 | − | 0.642173i | \(-0.221967\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.00000 | + | 1.73205i | −0.0508329 | + | 0.0880451i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.0000 | − | 22.5167i | −0.659126 | − | 1.14164i | −0.980842 | − | 0.194804i | \(-0.937593\pi\) |
0.321716 | − | 0.946836i | \(-0.395740\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.65685 | 0.286079 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.0000 | −0.907980 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.65685 | + | 9.79796i | 0.284627 | + | 0.492989i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.3137 | − | 19.5959i | 0.567819 | − | 0.983491i | −0.428963 | − | 0.903322i | \(-0.641121\pi\) |
0.996781 | − | 0.0801687i | \(-0.0255459\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.00000 | − | 15.5885i | 0.449439 | − | 0.778450i | −0.548911 | − | 0.835881i | \(-0.684957\pi\) |
0.998350 | + | 0.0574304i | \(0.0182907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.1421 | 0.702728 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.0000 | 0.991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0919 | + | 33.0681i | 0.944033 | + | 1.63511i | 0.757676 | + | 0.652631i | \(0.226335\pi\) |
0.186357 | + | 0.982482i | \(0.440332\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.48528 | − | 14.6969i | 0.418548 | − | 0.724947i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.0000 | − | 24.2487i | 0.687233 | − | 1.19032i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.00000 | + | 12.1244i | 0.342791 | + | 0.593732i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.89949 | −0.483622 | −0.241811 | − | 0.970323i | \(-0.577741\pi\) | ||||
−0.241811 | + | 0.970323i | \(0.577741\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.0000 | 1.46211 | 0.731055 | − | 0.682318i | \(-0.239028\pi\) | ||||
0.731055 | + | 0.682318i | \(0.239028\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.41421 | + | 2.44949i | 0.0687614 | + | 0.119098i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.12132 | + | 3.67423i | −0.102899 | + | 0.178227i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000 | + | 10.3923i | 0.289010 | + | 0.500580i | 0.973574 | − | 0.228373i | \(-0.0733406\pi\) |
−0.684564 | + | 0.728953i | \(0.740007\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.6985 | 1.42722 | 0.713609 | − | 0.700544i | \(-0.247059\pi\) | ||||
0.713609 | + | 0.700544i | \(0.247059\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.00000 | 0.383571 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.1421 | + | 24.4949i | 0.676510 | + | 1.17175i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.48528 | − | 14.6969i | 0.404980 | − | 0.701447i | −0.589339 | − | 0.807886i | \(-0.700612\pi\) |
0.994319 | + | 0.106439i | \(0.0339450\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.00000 | + | 3.46410i | −0.0950229 | + | 0.164584i | −0.909618 | − | 0.415445i | \(-0.863626\pi\) |
0.814595 | + | 0.580030i | \(0.196959\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0000 | + | 17.3205i | 0.474045 | + | 0.821071i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.1421 | −0.668900 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.89949 | − | 17.1464i | −0.466149 | − | 0.807394i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.3137 | − | 19.5959i | 0.531564 | − | 0.920697i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.0000 | + | 20.7846i | −0.561336 | + | 0.972263i | 0.436044 | + | 0.899925i | \(0.356379\pi\) |
−0.997380 | + | 0.0723376i | \(0.976954\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.00000 | − | 6.92820i | −0.186704 | − | 0.323381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.5980 | −1.84426 | −0.922131 | − | 0.386878i | \(-0.873553\pi\) | ||||
−0.922131 | + | 0.386878i | \(0.873553\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.9706 | − | 29.3939i | −0.786991 | − | 1.36311i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.2635 | + | 28.1691i | −0.752583 | + | 1.30351i | 0.193984 | + | 0.981005i | \(0.437859\pi\) |
−0.946567 | + | 0.322507i | \(0.895474\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.00000 | − | 13.8564i | 0.368621 | − | 0.638470i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.00000 | + | 3.46410i | 0.0919601 | + | 0.159280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.2132 | −0.973329 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | 0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.5563 | + | 26.9444i | 0.710788 | + | 1.23112i | 0.964562 | + | 0.263857i | \(0.0849947\pi\) |
−0.253774 | + | 0.967264i | \(0.581672\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.0000 | + | 24.2487i | −0.635707 | + | 1.10108i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.00000 | + | 10.3923i | 0.271886 | + | 0.470920i | 0.969345 | − | 0.245705i | \(-0.0790193\pi\) |
−0.697459 | + | 0.716625i | \(0.745686\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.1421 | 0.639529 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.41421 | − | 2.44949i | −0.0636930 | − | 0.110319i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.82843 | + | 4.89898i | −0.127128 | + | 0.220193i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.00000 | + | 3.46410i | −0.0895323 | + | 0.155074i | −0.907314 | − | 0.420455i | \(-0.861871\pi\) |
0.817781 | + | 0.575529i | \(0.195204\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.0000 | − | 24.2487i | −0.625474 | − | 1.08335i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.5980 | 1.76559 | 0.882793 | − | 0.469762i | \(-0.155660\pi\) | ||||
0.882793 | + | 0.469762i | \(0.155660\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0000 | 1.06799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.19239 | − | 15.9217i | −0.408248 | − | 0.707107i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.3137 | − | 19.5959i | 0.501471 | − | 0.868574i | −0.498527 | − | 0.866874i | \(-0.666126\pi\) |
0.999999 | − | 0.00169976i | \(-0.000541051\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.0000 | − | 34.6410i | 0.883022 | − | 1.52944i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.00000 | + | 6.92820i | 0.176261 | + | 0.305293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.65685 | 0.248788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.0000 | −1.05348 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.707107 | − | 1.22474i | −0.0309789 | − | 0.0536570i | 0.850120 | − | 0.526589i | \(-0.176529\pi\) |
−0.881099 | + | 0.472931i | \(0.843196\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.36396 | + | 11.0227i | −0.278277 | + | 0.481989i | −0.970957 | − | 0.239256i | \(-0.923097\pi\) |
0.692680 | + | 0.721245i | \(0.256430\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.00000 | + | 10.3923i | −0.261364 | + | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.41421 | 0.0613716 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.65685 | + | 9.79796i | 0.244567 | + | 0.423603i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.48528 | + | 14.6969i | −0.366167 | + | 0.634220i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.00000 | + | 8.66025i | −0.214967 | + | 0.372333i | −0.953262 | − | 0.302144i | \(-0.902298\pi\) |
0.738296 | + | 0.674477i | \(0.235631\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.65685 | 0.242313 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.0000 | 1.11168 | 0.555840 | − | 0.831289i | \(-0.312397\pi\) | ||||
0.555840 | + | 0.831289i | \(0.312397\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.41421 | − | 2.44949i | −0.0603572 | − | 0.104542i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.07107 | − | 12.2474i | 0.301238 | − | 0.521759i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −20.0000 | + | 34.6410i | −0.848953 | + | 1.47043i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.0000 | + | 25.9808i | 0.635570 | + | 1.10084i | 0.986394 | + | 0.164399i | \(0.0525683\pi\) |
−0.350824 | + | 0.936442i | \(0.614098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.707107 | + | 1.22474i | 0.0298010 | + | 0.0516168i | 0.880541 | − | 0.473970i | \(-0.157179\pi\) |
−0.850740 | + | 0.525586i | \(0.823846\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.9706 | + | 29.3939i | −0.713957 | + | 1.23661i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.00000 | + | 8.66025i | −0.209611 | + | 0.363057i | −0.951592 | − | 0.307364i | \(-0.900553\pi\) |
0.741981 | + | 0.670421i | \(0.233886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.00000 | − | 1.73205i | −0.0418487 | − | 0.0724841i | 0.844342 | − | 0.535804i | \(-0.179991\pi\) |
−0.886191 | + | 0.463320i | \(0.846658\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.65685 | −0.236318 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.6066 | − | 18.3712i | −0.441559 | − | 0.764802i | 0.556247 | − | 0.831017i | \(-0.312241\pi\) |
−0.997805 | + | 0.0662152i | \(0.978908\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.3137 | + | 19.5959i | −0.470182 | + | 0.814379i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.00000 | − | 3.46410i | 0.0828315 | − | 0.143468i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.6985 | −1.22579 | −0.612894 | − | 0.790165i | \(-0.709995\pi\) | ||||
−0.612894 | + | 0.790165i | \(0.709995\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −60.0000 | −2.47226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.41421 | + | 2.44949i | 0.0581730 | + | 0.100759i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.53553 | + | 6.12372i | −0.145187 | + | 0.251471i | −0.929443 | − | 0.368967i | \(-0.879712\pi\) |
0.784256 | + | 0.620438i | \(0.213045\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.00000 | − | 10.3923i | 0.245564 | − | 0.425329i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.00000 | − | 13.8564i | −0.326871 | − | 0.566157i | 0.655018 | − | 0.755613i | \(-0.272661\pi\) |
−0.981889 | + | 0.189456i | \(0.939328\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.6985 | −1.21143 | −0.605713 | − | 0.795683i | \(-0.707112\pi\) | ||||
−0.605713 | + | 0.795683i | \(0.707112\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.89949 | − | 17.1464i | −0.402472 | − | 0.697101i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.48528 | − | 14.6969i | 0.344407 | − | 0.596530i | −0.640839 | − | 0.767675i | \(-0.721413\pi\) |
0.985246 | + | 0.171145i | \(0.0547467\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.0000 | + | 25.9808i | 0.605844 | + | 1.04935i | 0.991917 | + | 0.126885i | \(0.0404979\pi\) |
−0.386073 | + | 0.922468i | \(0.626169\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 39.5980 | 1.59674 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.0000 | −1.04672 | −0.523360 | − | 0.852111i | \(-0.675322\pi\) | ||||
−0.523360 | + | 0.852111i | \(0.675322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.19239 | − | 15.9217i | −0.369473 | − | 0.639946i | 0.620010 | − | 0.784594i | \(-0.287129\pi\) |
−0.989483 | + | 0.144647i | \(0.953795\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.3137 | + | 19.5959i | −0.454003 | + | 0.786357i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5000 | − | 26.8468i | 0.620000 | − | 1.07387i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.0000 | − | 17.3205i | −0.399362 | − | 0.691714i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.1421 | 0.563884 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.0000 | −1.75161 | −0.875806 | − | 0.482663i | \(-0.839670\pi\) | ||||
−0.875806 | + | 0.482663i | \(0.839670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.48528 | + | 14.6969i | 0.337260 | + | 0.584151i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.6274 | + | 39.1918i | −0.897942 | + | 1.55528i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | − | 10.3923i | 0.237356 | − | 0.411113i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.0000 | − | 22.5167i | −0.513469 | − | 0.889355i | −0.999878 | − | 0.0156233i | \(-0.995027\pi\) |
0.486409 | − | 0.873731i | \(-0.338307\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.89949 | 0.390398 | 0.195199 | − | 0.980764i | \(-0.437465\pi\) | ||||
0.195199 | + | 0.980764i | \(0.437465\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.24264 | − | 7.34847i | −0.166795 | − | 0.288898i | 0.770496 | − | 0.637445i | \(-0.220009\pi\) |
−0.937291 | + | 0.348547i | \(0.886675\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.41421 | − | 2.44949i | 0.0555127 | − | 0.0961509i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.00000 | − | 15.5885i | 0.352197 | − | 0.610023i | −0.634437 | − | 0.772975i | \(-0.718768\pi\) |
0.986634 | + | 0.162951i | \(0.0521013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.0000 | + | 31.1769i | 0.703318 | + | 1.21818i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.41421 | −0.0551737 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.0000 | −1.16863 | −0.584317 | − | 0.811525i | \(-0.698638\pi\) | ||||
−0.584317 | + | 0.811525i | \(0.698638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.24264 | + | 7.34847i | 0.165020 | + | 0.285822i | 0.936662 | − | 0.350234i | \(-0.113898\pi\) |
−0.771643 | + | 0.636056i | \(0.780565\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.00000 | + | 6.92820i | −0.154881 | + | 0.268261i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.65685 | −0.218380 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.0000 | −0.462566 | −0.231283 | − | 0.972887i | \(-0.574292\pi\) | ||||
−0.231283 | + | 0.972887i | \(0.574292\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.48528 | − | 14.6969i | −0.326599 | − | 0.565685i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.48528 | + | 14.6969i | −0.326116 | + | 0.564849i | −0.981738 | − | 0.190240i | \(-0.939073\pi\) |
0.655622 | + | 0.755090i | \(0.272407\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.0000 | + | 25.9808i | −0.574801 | + | 0.995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.00000 | + | 10.3923i | 0.229584 | + | 0.397650i | 0.957685 | − | 0.287819i | \(-0.0929302\pi\) |
−0.728101 | + | 0.685470i | \(0.759597\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −33.9411 | −1.29682 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.0000 | −0.915657 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.36396 | + | 11.0227i | −0.242096 | + | 0.419323i | −0.961311 | − | 0.275464i | \(-0.911168\pi\) |
0.719215 | + | 0.694788i | \(0.244502\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.0000 | − | 24.2487i | 0.531050 | − | 0.919806i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.00000 | − | 12.1244i | −0.265144 | − | 0.459243i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −33.9411 | −1.28377 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.3553 | + | 61.2372i | 1.33345 | + | 2.30961i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.65685 | + | 9.79796i | −0.213049 | + | 0.369012i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.00000 | + | 8.66025i | −0.187779 | + | 0.325243i | −0.944509 | − | 0.328484i | \(-0.893462\pi\) |
0.756730 | + | 0.653727i | \(0.226796\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.00000 | + | 3.46410i | 0.0750059 | + | 0.129914i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.9411 | 1.27111 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.48528 | + | 14.6969i | 0.316889 | + | 0.548867i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.41421 | + | 2.44949i | −0.0527413 | + | 0.0913506i | −0.891191 | − | 0.453629i | \(-0.850129\pi\) |
0.838449 | + | 0.544979i | \(0.183463\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.0000 | − | 25.9808i | 0.557856 | − | 0.966235i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.00000 | − | 5.19615i | −0.111417 | − | 0.192980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.7990 | −0.734304 | −0.367152 | − | 0.930161i | \(-0.619667\pi\) | ||||
−0.367152 | + | 0.930161i | \(0.619667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.41421 | + | 2.44949i | 0.0523066 | + | 0.0905977i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.2132 | − | 36.7423i | 0.783528 | − | 1.35711i | −0.146347 | − | 0.989233i | \(-0.546752\pi\) |
0.929875 | − | 0.367876i | \(-0.119915\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.0000 | − | 20.7846i | 0.442026 | − | 0.765611i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0000 | − | 25.9808i | −0.551784 | − | 0.955718i | −0.998146 | − | 0.0608653i | \(-0.980614\pi\) |
0.446362 | − | 0.894852i | \(-0.352719\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.0000 | −0.586983 | −0.293492 | − | 0.955962i | \(-0.594817\pi\) | ||||
−0.293492 | + | 0.955962i | \(0.594817\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.1421 | + | 24.4949i | 0.518128 | + | 0.897424i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.94975 | − | 8.57321i | 0.181102 | − | 0.313678i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.00000 | + | 3.46410i | −0.0729810 | + | 0.126407i | −0.900207 | − | 0.435463i | \(-0.856585\pi\) |
0.827225 | + | 0.561870i | \(0.189918\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.00000 | + | 12.1244i | 0.255094 | + | 0.441836i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −45.2548 | −1.64699 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.65685 | + | 9.79796i | 0.205331 | + | 0.355643i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.53553 | + | 6.12372i | −0.128163 | + | 0.221985i | −0.922965 | − | 0.384884i | \(-0.874241\pi\) |
0.794802 | + | 0.606869i | \(0.207575\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.00000 | + | 3.46410i | −0.0723102 | + | 0.125245i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.6985 | −1.07095 | −0.535477 | − | 0.844550i | \(-0.679868\pi\) | ||||
−0.535477 | + | 0.844550i | \(0.679868\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000 | 0.648254 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.0416 | + | 41.6413i | 0.864717 | + | 1.49773i | 0.867328 | + | 0.497738i | \(0.165836\pi\) |
−0.00261021 | + | 0.999997i | \(0.500831\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.7279 | + | 22.0454i | −0.457200 | + | 0.791894i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.0000 | − | 60.6218i | 1.25401 | − | 2.17200i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0000 | − | 20.7846i | −0.429394 | − | 0.743732i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.3137 | 0.404319 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32.0000 | −1.14213 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.707107 | + | 1.22474i | 0.0252056 | + | 0.0436574i | 0.878353 | − | 0.478012i | \(-0.158643\pi\) |
−0.853147 | + | 0.521670i | \(0.825309\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.48528 | + | 14.6969i | −0.302084 | + | 0.523225i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.00000 | + | 6.92820i | 0.141865 | + | 0.245718i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00000 | 0.141510 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.53553 | + | 6.12372i | 0.124922 | + | 0.216371i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.41421 | + | 2.44949i | −0.0499065 | + | 0.0864406i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.00000 | − | 13.8564i | 0.281613 | − | 0.487769i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.00000 | + | 13.8564i | 0.281265 | + | 0.487165i | 0.971697 | − | 0.236232i | \(-0.0759127\pi\) |
−0.690432 | + | 0.723398i | \(0.742579\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.6985 | −1.04285 | −0.521427 | − | 0.853296i | \(-0.674600\pi\) | ||||
−0.521427 | + | 0.853296i | \(0.674600\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −32.0000 | −1.12229 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.1421 | − | 24.4949i | −0.495377 | − | 0.858019i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.07107 | + | 12.2474i | −0.247385 | + | 0.428484i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.00000 | − | 15.5885i | 0.314102 | − | 0.544041i | −0.665144 | − | 0.746715i | \(-0.731630\pi\) |
0.979246 | + | 0.202674i | \(0.0649632\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0000 | + | 34.6410i | 0.697156 | + | 1.20751i | 0.969448 | + | 0.245295i | \(0.0788849\pi\) |
−0.272292 | + | 0.962215i | \(0.587782\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.48528 | −0.295420 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.5563 | − | 26.9444i | −0.540294 | − | 0.935817i | −0.998887 | − | 0.0471706i | \(-0.984980\pi\) |
0.458593 | − | 0.888647i | \(-0.348354\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.41421 | + | 2.44949i | −0.0490585 | + | 0.0849719i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.0000 | + | 48.4974i | −0.968980 | + | 1.67832i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.0000 | − | 41.5692i | −0.829561 | − | 1.43684i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.7990 | 0.683537 | 0.341769 | − | 0.939784i | \(-0.388974\pi\) | ||||
0.341769 | + | 0.939784i | \(0.388974\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.3137 | + | 19.5959i | 0.389665 | + | 0.674919i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.3848 | + | 31.8434i | −0.632456 | + | 1.09545i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.00000 | + | 1.73205i | −0.0343199 | + | 0.0594438i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.0000 | − | 34.6410i | −0.685591 | − | 1.18748i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.0000 | −0.683986 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.19239 | + | 15.9217i | 0.314006 | + | 0.543874i | 0.979226 | − | 0.202773i | \(-0.0649955\pi\) |
−0.665220 | + | 0.746648i | \(0.731662\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.4350 | − | 23.2702i | 0.458397 | − | 0.793967i | −0.540479 | − | 0.841357i | \(-0.681757\pi\) |
0.998876 | + | 0.0473900i | \(0.0150904\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.00000 | + | 3.46410i | −0.0680808 | + | 0.117919i | −0.898056 | − | 0.439880i | \(-0.855021\pi\) |
0.829976 | + | 0.557800i | \(0.188354\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.0000 | + | 41.5692i | 0.816024 | + | 1.41340i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.2132 | 0.720438 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000 | 0.271381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.94975 | + | 8.57321i | −0.167524 | + | 0.290159i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.0000 | − | 39.8372i | 0.776655 | − | 1.34521i | −0.157205 | − | 0.987566i | \(-0.550248\pi\) |
0.933860 | − | 0.357640i | \(-0.116418\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.0000 | + | 24.2487i | 0.472208 | + | 0.817889i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.6985 | −1.00057 | −0.500284 | − | 0.865862i | \(-0.666771\pi\) | ||||
−0.500284 | + | 0.865862i | \(0.666771\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.0000 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.82843 | + | 4.89898i | 0.0950765 | + | 0.164677i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.3848 | − | 31.8434i | 0.617300 | − | 1.06920i | −0.372676 | − | 0.927962i | \(-0.621560\pi\) |
0.989976 | − | 0.141234i | \(-0.0451070\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.00000 | − | 8.66025i | 0.167506 | − | 0.290129i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.0000 | + | 17.3205i | 0.334637 | + | 0.579609i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33.9411 | 1.13453 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.48528 | − | 14.6969i | −0.283000 | − | 0.490170i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.41421 | − | 2.44949i | 0.0471143 | − | 0.0816043i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.0000 | − | 38.1051i | −0.730498 | − | 1.26526i | −0.956671 | − | 0.291172i | \(-0.905955\pi\) |
0.226173 | − | 0.974087i | \(-0.427379\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.48528 | 0.281439 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.0000 | 1.32526 | 0.662630 | − | 0.748947i | \(-0.269440\pi\) | ||||
0.662630 | + | 0.748947i | \(0.269440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.89949 | − | 17.1464i | −0.327625 | − | 0.567464i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.65685 | − | 9.79796i | 0.187010 | − | 0.323911i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | + | 27.7128i | −0.527791 | + | 0.914161i | 0.471684 | + | 0.881768i | \(0.343646\pi\) |
−0.999475 | + | 0.0323936i | \(0.989687\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.00000 | − | 12.1244i | −0.230658 | − | 0.399511i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.0000 | 0.986394 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.41421 | + | 2.44949i | 0.0464489 | + | 0.0804518i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.2635 | − | 28.1691i | 0.533587 | − | 0.924199i | −0.465644 | − | 0.884972i | \(-0.654177\pi\) |
0.999230 | − | 0.0392269i | \(-0.0124895\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.00000 | + | 13.8564i | −0.261908 | + | 0.453638i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.00000 | + | 6.92820i | 0.130814 | + | 0.226576i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.89949 | −0.323402 | −0.161701 | − | 0.986840i | \(-0.551698\pi\) | ||||
−0.161701 | + | 0.986840i | \(0.551698\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.0000 | 0.587408 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.5563 | − | 26.9444i | −0.507122 | − | 0.878362i | −0.999966 | − | 0.00824396i | \(-0.997376\pi\) |
0.492844 | − | 0.870118i | \(-0.335957\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.7990 | + | 34.2929i | −0.644744 | + | 1.11673i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.00000 | + | 15.5885i | −0.292461 | + | 0.506557i | −0.974391 | − | 0.224860i | \(-0.927807\pi\) |
0.681930 | + | 0.731417i | \(0.261141\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.1421 | −0.458590 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.65685 | + | 9.79796i | 0.183052 | + | 0.317055i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.82843 | − | 4.89898i | 0.0914301 | − | 0.158362i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.5000 | + | 35.5070i | −0.661290 | + | 1.14539i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.00000 | + | 3.46410i | 0.0644491 | + | 0.111629i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 45.2548 | 1.45680 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.0000 | 0.385894 | 0.192947 | − | 0.981209i | \(-0.438195\pi\) | ||||
0.192947 | + | 0.981209i | \(0.438195\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.07107 | − | 12.2474i | −0.227155 | − | 0.393445i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.2635 | + | 28.1691i | −0.521919 | + | 0.903990i | 0.477756 | + | 0.878493i | \(0.341450\pi\) |
−0.999675 | + | 0.0254978i | \(0.991883\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.00000 | − | 10.3923i | −0.191957 | − | 0.332479i | 0.753942 | − | 0.656941i | \(-0.228150\pi\) |
−0.945899 | + | 0.324462i | \(0.894817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.1421 | 0.451985 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.0416 | − | 41.6413i | −0.766809 | − | 1.32815i | −0.939285 | − | 0.343138i | \(-0.888510\pi\) |
0.172476 | − | 0.985014i | \(-0.444823\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.82843 | − | 4.89898i | 0.0901212 | − | 0.156094i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.00000 | − | 6.92820i | 0.127193 | − | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | − | 13.8564i | −0.254128 | − | 0.440163i | 0.710530 | − | 0.703667i | \(-0.248455\pi\) |
−0.964658 | + | 0.263504i | \(0.915122\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.1421 | 0.448787 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.0000 | −0.760851 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.5563 | − | 26.9444i | −0.492675 | − | 0.853337i | 0.507290 | − | 0.861775i | \(-0.330647\pi\) |
−0.999964 | + | 0.00843818i | \(0.997314\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28.2843 | + | 48.9898i | −0.894875 | + | 1.54997i |
(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 | 784.2.i.m.177.2 | 4 | ||
4.3 | odd | 2 | 98.2.c.c.79.1 | 4 | |||
7.2 | even | 3 | 784.2.a.l.1.1 | 2 | |||
7.3 | odd | 6 | inner | 784.2.i.m.753.1 | 4 | ||
7.4 | even | 3 | inner | 784.2.i.m.753.2 | 4 | ||
7.5 | odd | 6 | 784.2.a.l.1.2 | 2 | |||
7.6 | odd | 2 | inner | 784.2.i.m.177.1 | 4 | ||
12.11 | even | 2 | 882.2.g.l.667.1 | 4 | |||
21.2 | odd | 6 | 7056.2.a.cl.1.2 | 2 | |||
21.5 | even | 6 | 7056.2.a.cl.1.1 | 2 | |||
28.3 | even | 6 | 98.2.c.c.67.2 | 4 | |||
28.11 | odd | 6 | 98.2.c.c.67.1 | 4 | |||
28.19 | even | 6 | 98.2.a.b.1.1 | ✓ | 2 | ||
28.23 | odd | 6 | 98.2.a.b.1.2 | yes | 2 | ||
28.27 | even | 2 | 98.2.c.c.79.2 | 4 | |||
56.5 | odd | 6 | 3136.2.a.bm.1.1 | 2 | |||
56.19 | even | 6 | 3136.2.a.bn.1.2 | 2 | |||
56.37 | even | 6 | 3136.2.a.bm.1.2 | 2 | |||
56.51 | odd | 6 | 3136.2.a.bn.1.1 | 2 | |||
84.11 | even | 6 | 882.2.g.l.361.1 | 4 | |||
84.23 | even | 6 | 882.2.a.n.1.2 | 2 | |||
84.47 | odd | 6 | 882.2.a.n.1.1 | 2 | |||
84.59 | odd | 6 | 882.2.g.l.361.2 | 4 | |||
84.83 | odd | 2 | 882.2.g.l.667.2 | 4 | |||
140.19 | even | 6 | 2450.2.a.bj.1.2 | 2 | |||
140.23 | even | 12 | 2450.2.c.v.99.2 | 4 | |||
140.47 | odd | 12 | 2450.2.c.v.99.4 | 4 | |||
140.79 | odd | 6 | 2450.2.a.bj.1.1 | 2 | |||
140.103 | odd | 12 | 2450.2.c.v.99.1 | 4 | |||
140.107 | even | 12 | 2450.2.c.v.99.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.2.a.b.1.1 | ✓ | 2 | 28.19 | even | 6 | ||
98.2.a.b.1.2 | yes | 2 | 28.23 | odd | 6 | ||
98.2.c.c.67.1 | 4 | 28.11 | odd | 6 | |||
98.2.c.c.67.2 | 4 | 28.3 | even | 6 | |||
98.2.c.c.79.1 | 4 | 4.3 | odd | 2 | |||
98.2.c.c.79.2 | 4 | 28.27 | even | 2 | |||
784.2.a.l.1.1 | 2 | 7.2 | even | 3 | |||
784.2.a.l.1.2 | 2 | 7.5 | odd | 6 | |||
784.2.i.m.177.1 | 4 | 7.6 | odd | 2 | inner | ||
784.2.i.m.177.2 | 4 | 1.1 | even | 1 | trivial | ||
784.2.i.m.753.1 | 4 | 7.3 | odd | 6 | inner | ||
784.2.i.m.753.2 | 4 | 7.4 | even | 3 | inner | ||
882.2.a.n.1.1 | 2 | 84.47 | odd | 6 | |||
882.2.a.n.1.2 | 2 | 84.23 | even | 6 | |||
882.2.g.l.361.1 | 4 | 84.11 | even | 6 | |||
882.2.g.l.361.2 | 4 | 84.59 | odd | 6 | |||
882.2.g.l.667.1 | 4 | 12.11 | even | 2 | |||
882.2.g.l.667.2 | 4 | 84.83 | odd | 2 | |||
2450.2.a.bj.1.1 | 2 | 140.79 | odd | 6 | |||
2450.2.a.bj.1.2 | 2 | 140.19 | even | 6 | |||
2450.2.c.v.99.1 | 4 | 140.103 | odd | 12 | |||
2450.2.c.v.99.2 | 4 | 140.23 | even | 12 | |||
2450.2.c.v.99.3 | 4 | 140.107 | even | 12 | |||
2450.2.c.v.99.4 | 4 | 140.47 | odd | 12 | |||
3136.2.a.bm.1.1 | 2 | 56.5 | odd | 6 | |||
3136.2.a.bm.1.2 | 2 | 56.37 | even | 6 | |||
3136.2.a.bn.1.1 | 2 | 56.51 | odd | 6 | |||
3136.2.a.bn.1.2 | 2 | 56.19 | even | 6 | |||
7056.2.a.cl.1.1 | 2 | 21.5 | even | 6 | |||
7056.2.a.cl.1.2 | 2 | 21.2 | odd | 6 |