Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(2155,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3234.2155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.e (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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2155.5 | ||
Character | \(\chi\) | \(=\) | 3234.2155 |
Dual form | 3234.2.e.c.2155.20 |
$q$-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 \(\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(1079\) | \(2059\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 0.942563i | − | 0.421527i | −0.977537 | − | 0.210764i | \(-0.932405\pi\) | ||
0.977537 | − | 0.210764i | \(-0.0675950\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.942563 | −0.298065 | ||||||||
\(11\) | 1.67140 | − | 2.86468i | 0.503948 | − | 0.863734i | ||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 2.81702 | 0.781301 | 0.390651 | − | 0.920539i | \(-0.372250\pi\) | ||||
0.390651 | + | 0.920539i | \(0.372250\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.942563 | −0.243369 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.30608 | 1.04438 | 0.522188 | − | 0.852830i | \(-0.325116\pi\) | ||||
0.522188 | + | 0.852830i | \(0.325116\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 2.51637 | 0.577295 | 0.288648 | − | 0.957435i | \(-0.406794\pi\) | ||||
0.288648 | + | 0.957435i | \(0.406794\pi\) | |||||||
\(20\) | 0.942563i | 0.210764i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.86468 | − | 1.67140i | −0.610752 | − | 0.356345i | ||||
\(23\) | 4.33514 | 0.903938 | 0.451969 | − | 0.892034i | \(-0.350722\pi\) | ||||
0.451969 | + | 0.892034i | \(0.350722\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 4.11157 | 0.822315 | ||||||||
\(26\) | − | 2.81702i | − | 0.552463i | ||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.01022i | 1.48746i | 0.668480 | + | 0.743730i | \(0.266945\pi\) | ||||
−0.668480 | + | 0.743730i | \(0.733055\pi\) | |||||||
\(30\) | 0.942563i | 0.172088i | ||||||||
\(31\) | 6.05783i | 1.08802i | 0.839079 | + | 0.544009i | \(0.183094\pi\) | ||||
−0.839079 | + | 0.544009i | \(0.816906\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −2.86468 | − | 1.67140i | −0.498677 | − | 0.290954i | ||||
\(34\) | − | 4.30608i | − | 0.738486i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.4379 | 1.71599 | 0.857993 | − | 0.513662i | \(-0.171711\pi\) | ||||
0.857993 | + | 0.513662i | \(0.171711\pi\) | |||||||
\(38\) | − | 2.51637i | − | 0.408209i | ||||||
\(39\) | − | 2.81702i | − | 0.451084i | ||||||
\(40\) | 0.942563 | 0.149032 | ||||||||
\(41\) | −5.20158 | −0.812351 | −0.406175 | − | 0.913795i | \(-0.633138\pi\) | ||||
−0.406175 | + | 0.913795i | \(0.633138\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.3608i | 1.73250i | 0.499608 | + | 0.866251i | \(0.333477\pi\) | ||||
−0.499608 | + | 0.866251i | \(0.666523\pi\) | |||||||
\(44\) | −1.67140 | + | 2.86468i | −0.251974 | + | 0.431867i | ||||
\(45\) | 0.942563i | 0.140509i | ||||||||
\(46\) | − | 4.33514i | − | 0.639181i | ||||||
\(47\) | 8.96951i | 1.30834i | 0.756349 | + | 0.654169i | \(0.226981\pi\) | ||||
−0.756349 | + | 0.654169i | \(0.773019\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 4.11157i | − | 0.581464i | ||||||
\(51\) | − | 4.30608i | − | 0.602971i | ||||||
\(52\) | −2.81702 | −0.390651 | ||||||||
\(53\) | 4.55271 | 0.625363 | 0.312682 | − | 0.949858i | \(-0.398773\pi\) | ||||
0.312682 | + | 0.949858i | \(0.398773\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.70014 | − | 1.57540i | −0.364087 | − | 0.212428i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.51637i | − | 0.333302i | ||||||
\(58\) | 8.01022 | 1.05179 | ||||||||
\(59\) | − | 13.4801i | − | 1.75496i | −0.479613 | − | 0.877480i | \(-0.659223\pi\) | ||
0.479613 | − | 0.877480i | \(-0.340777\pi\) | |||||||
\(60\) | 0.942563 | 0.121684 | ||||||||
\(61\) | −2.41499 | −0.309208 | −0.154604 | − | 0.987976i | \(-0.549410\pi\) | ||||
−0.154604 | + | 0.987976i | \(0.549410\pi\) | |||||||
\(62\) | 6.05783 | 0.769345 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 2.65522i | − | 0.329340i | ||||||
\(66\) | −1.67140 | + | 2.86468i | −0.205736 | + | 0.352618i | ||||
\(67\) | −2.22408 | −0.271715 | −0.135857 | − | 0.990728i | \(-0.543379\pi\) | ||||
−0.135857 | + | 0.990728i | \(0.543379\pi\) | |||||||
\(68\) | −4.30608 | −0.522188 | ||||||||
\(69\) | − | 4.33514i | − | 0.521889i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.80437 | −0.570173 | −0.285087 | − | 0.958502i | \(-0.592022\pi\) | ||||
−0.285087 | + | 0.958502i | \(0.592022\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | 4.63368 | 0.542331 | 0.271165 | − | 0.962533i | \(-0.412591\pi\) | ||||
0.271165 | + | 0.962533i | \(0.412591\pi\) | |||||||
\(74\) | − | 10.4379i | − | 1.21338i | ||||||
\(75\) | − | 4.11157i | − | 0.474764i | ||||||
\(76\) | −2.51637 | −0.288648 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.81702 | −0.318965 | ||||||||
\(79\) | 9.26447i | 1.04233i | 0.853455 | + | 0.521167i | \(0.174503\pi\) | ||||
−0.853455 | + | 0.521167i | \(0.825497\pi\) | |||||||
\(80\) | − | 0.942563i | − | 0.105382i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.20158i | 0.574419i | ||||||||
\(83\) | 8.84143 | 0.970473 | 0.485237 | − | 0.874383i | \(-0.338733\pi\) | ||||
0.485237 | + | 0.874383i | \(0.338733\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 4.05875i | − | 0.440233i | ||||||
\(86\) | 11.3608 | 1.22506 | ||||||||
\(87\) | 8.01022 | 0.858786 | ||||||||
\(88\) | 2.86468 | + | 1.67140i | 0.305376 | + | 0.178172i | ||||
\(89\) | − | 11.5356i | − | 1.22277i | −0.791334 | − | 0.611384i | \(-0.790613\pi\) | ||
0.791334 | − | 0.611384i | \(-0.209387\pi\) | |||||||
\(90\) | 0.942563 | 0.0993549 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.33514 | −0.451969 | ||||||||
\(93\) | 6.05783 | 0.628168 | ||||||||
\(94\) | 8.96951 | 0.925134 | ||||||||
\(95\) | − | 2.37184i | − | 0.243346i | ||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | − | 12.5496i | − | 1.27422i | −0.770772 | − | 0.637112i | \(-0.780129\pi\) | ||
0.770772 | − | 0.637112i | \(-0.219871\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.67140 | + | 2.86468i | −0.167983 | + | 0.287911i | ||||
\(100\) | −4.11157 | −0.411157 | ||||||||
\(101\) | −8.65999 | −0.861701 | −0.430851 | − | 0.902423i | \(-0.641786\pi\) | ||||
−0.430851 | + | 0.902423i | \(0.641786\pi\) | |||||||
\(102\) | −4.30608 | −0.426365 | ||||||||
\(103\) | − | 11.4902i | − | 1.13216i | −0.824351 | − | 0.566079i | \(-0.808460\pi\) | ||
0.824351 | − | 0.566079i | \(-0.191540\pi\) | |||||||
\(104\) | 2.81702i | 0.276232i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 4.55271i | − | 0.442198i | ||||||
\(107\) | − | 8.51031i | − | 0.822723i | −0.911472 | − | 0.411361i | \(-0.865053\pi\) | ||
0.911472 | − | 0.411361i | \(-0.134947\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | 0.950748i | 0.0910651i | 0.998963 | + | 0.0455326i | \(0.0144985\pi\) | ||||
−0.998963 | + | 0.0455326i | \(0.985502\pi\) | |||||||
\(110\) | −1.57540 | + | 2.70014i | −0.150209 | + | 0.257449i | ||||
\(111\) | − | 10.4379i | − | 0.990725i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.55994 | −0.805251 | −0.402626 | − | 0.915365i | \(-0.631902\pi\) | ||||
−0.402626 | + | 0.915365i | \(0.631902\pi\) | |||||||
\(114\) | −2.51637 | −0.235680 | ||||||||
\(115\) | − | 4.08614i | − | 0.381035i | ||||||
\(116\) | − | 8.01022i | − | 0.743730i | ||||||
\(117\) | −2.81702 | −0.260434 | ||||||||
\(118\) | −13.4801 | −1.24094 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 0.942563i | − | 0.0860438i | ||||||
\(121\) | −5.41281 | − | 9.57609i | −0.492074 | − | 0.870554i | ||||
\(122\) | 2.41499i | 0.218643i | ||||||||
\(123\) | 5.20158i | 0.469011i | ||||||||
\(124\) | − | 6.05783i | − | 0.544009i | ||||||
\(125\) | − | 8.58823i | − | 0.768155i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.4372i | 1.28109i | 0.767919 | + | 0.640547i | \(0.221292\pi\) | ||||
−0.767919 | + | 0.640547i | \(0.778708\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 11.3608 | 1.00026 | ||||||||
\(130\) | −2.65522 | −0.232878 | ||||||||
\(131\) | 9.54305 | 0.833780 | 0.416890 | − | 0.908957i | \(-0.363120\pi\) | ||||
0.416890 | + | 0.908957i | \(0.363120\pi\) | |||||||
\(132\) | 2.86468 | + | 1.67140i | 0.249339 | + | 0.145477i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.22408i | 0.192131i | ||||||||
\(135\) | 0.942563 | 0.0811229 | ||||||||
\(136\) | 4.30608i | 0.369243i | ||||||||
\(137\) | 18.7883 | 1.60519 | 0.802595 | − | 0.596525i | \(-0.203452\pi\) | ||||
0.802595 | + | 0.596525i | \(0.203452\pi\) | |||||||
\(138\) | −4.33514 | −0.369031 | ||||||||
\(139\) | −19.9086 | −1.68863 | −0.844315 | − | 0.535848i | \(-0.819992\pi\) | ||||
−0.844315 | + | 0.535848i | \(0.819992\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.96951 | 0.755369 | ||||||||
\(142\) | 4.80437i | 0.403173i | ||||||||
\(143\) | 4.70838 | − | 8.06987i | 0.393735 | − | 0.674837i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 7.55014 | 0.627005 | ||||||||
\(146\) | − | 4.63368i | − | 0.383486i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.4379 | −0.857993 | ||||||||
\(149\) | 3.86561i | 0.316683i | 0.987384 | + | 0.158341i | \(0.0506147\pi\) | ||||
−0.987384 | + | 0.158341i | \(0.949385\pi\) | |||||||
\(150\) | −4.11157 | −0.335709 | ||||||||
\(151\) | − | 1.64273i | − | 0.133684i | −0.997764 | − | 0.0668418i | \(-0.978708\pi\) | ||
0.997764 | − | 0.0668418i | \(-0.0212923\pi\) | |||||||
\(152\) | 2.51637i | 0.204105i | ||||||||
\(153\) | −4.30608 | −0.348126 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.70989 | 0.458629 | ||||||||
\(156\) | 2.81702i | 0.225542i | ||||||||
\(157\) | − | 4.01593i | − | 0.320506i | −0.987076 | − | 0.160253i | \(-0.948769\pi\) | ||
0.987076 | − | 0.160253i | \(-0.0512311\pi\) | |||||||
\(158\) | 9.26447 | 0.737042 | ||||||||
\(159\) | − | 4.55271i | − | 0.361054i | ||||||
\(160\) | −0.942563 | −0.0745162 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 12.6206 | 0.988520 | 0.494260 | − | 0.869314i | \(-0.335439\pi\) | ||||
0.494260 | + | 0.869314i | \(0.335439\pi\) | |||||||
\(164\) | 5.20158 | 0.406175 | ||||||||
\(165\) | −1.57540 | + | 2.70014i | −0.122645 | + | 0.210206i | ||||
\(166\) | − | 8.84143i | − | 0.686228i | ||||||
\(167\) | −15.1392 | −1.17150 | −0.585752 | − | 0.810490i | \(-0.699201\pi\) | ||||
−0.585752 | + | 0.810490i | \(0.699201\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.06439 | −0.389569 | ||||||||
\(170\) | −4.05875 | −0.311292 | ||||||||
\(171\) | −2.51637 | −0.192432 | ||||||||
\(172\) | − | 11.3608i | − | 0.866251i | ||||||
\(173\) | −7.73438 | −0.588034 | −0.294017 | − | 0.955800i | \(-0.594992\pi\) | ||||
−0.294017 | + | 0.955800i | \(0.594992\pi\) | |||||||
\(174\) | − | 8.01022i | − | 0.607253i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.67140 | − | 2.86468i | 0.125987 | − | 0.215934i | ||||
\(177\) | −13.4801 | −1.01323 | ||||||||
\(178\) | −11.5356 | −0.864627 | ||||||||
\(179\) | 16.8680 | 1.26078 | 0.630388 | − | 0.776280i | \(-0.282896\pi\) | ||||
0.630388 | + | 0.776280i | \(0.282896\pi\) | |||||||
\(180\) | − | 0.942563i | − | 0.0702545i | ||||||
\(181\) | − | 1.82684i | − | 0.135788i | −0.997693 | − | 0.0678938i | \(-0.978372\pi\) | ||
0.997693 | − | 0.0678938i | \(-0.0216279\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.41499i | 0.178522i | ||||||||
\(184\) | 4.33514i | 0.319591i | ||||||||
\(185\) | − | 9.83841i | − | 0.723334i | ||||||
\(186\) | − | 6.05783i | − | 0.444182i | ||||||
\(187\) | 7.19720 | − | 12.3355i | 0.526311 | − | 0.902064i | ||||
\(188\) | − | 8.96951i | − | 0.654169i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.37184 | −0.172071 | ||||||||
\(191\) | −14.2909 | −1.03406 | −0.517028 | − | 0.855968i | \(-0.672962\pi\) | ||||
−0.517028 | + | 0.855968i | \(0.672962\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 3.68856i | 0.265509i | 0.991149 | + | 0.132754i | \(0.0423821\pi\) | ||||
−0.991149 | + | 0.132754i | \(0.957618\pi\) | |||||||
\(194\) | −12.5496 | −0.901012 | ||||||||
\(195\) | −2.65522 | −0.190144 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.22462i | 0.0872507i | 0.999048 | + | 0.0436253i | \(0.0138908\pi\) | ||||
−0.999048 | + | 0.0436253i | \(0.986109\pi\) | |||||||
\(198\) | 2.86468 | + | 1.67140i | 0.203584 | + | 0.118782i | ||||
\(199\) | 12.8195i | 0.908752i | 0.890810 | + | 0.454376i | \(0.150138\pi\) | ||||
−0.890810 | + | 0.454376i | \(0.849862\pi\) | |||||||
\(200\) | 4.11157i | 0.290732i | ||||||||
\(201\) | 2.22408i | 0.156874i | ||||||||
\(202\) | 8.65999i | 0.609315i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.30608i | 0.301486i | ||||||||
\(205\) | 4.90282i | 0.342428i | ||||||||
\(206\) | −11.4902 | −0.800557 | ||||||||
\(207\) | −4.33514 | −0.301313 | ||||||||
\(208\) | 2.81702 | 0.195325 | ||||||||
\(209\) | 4.20588 | − | 7.20861i | 0.290927 | − | 0.498630i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0672i | 1.17495i | 0.809241 | + | 0.587476i | \(0.199878\pi\) | ||||
−0.809241 | + | 0.587476i | \(0.800122\pi\) | |||||||
\(212\) | −4.55271 | −0.312682 | ||||||||
\(213\) | 4.80437i | 0.329190i | ||||||||
\(214\) | −8.51031 | −0.581753 | ||||||||
\(215\) | 10.7083 | 0.730297 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.950748 | 0.0643928 | ||||||||
\(219\) | − | 4.63368i | − | 0.313115i | ||||||
\(220\) | 2.70014 | + | 1.57540i | 0.182044 | + | 0.106214i | ||||
\(221\) | 12.1303 | 0.815973 | ||||||||
\(222\) | −10.4379 | −0.700548 | ||||||||
\(223\) | − | 8.56595i | − | 0.573619i | −0.957988 | − | 0.286809i | \(-0.907405\pi\) | ||
0.957988 | − | 0.286809i | \(-0.0925946\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.11157 | −0.274105 | ||||||||
\(226\) | 8.55994i | 0.569398i | ||||||||
\(227\) | −16.9377 | −1.12419 | −0.562097 | − | 0.827071i | \(-0.690005\pi\) | ||||
−0.562097 | + | 0.827071i | \(0.690005\pi\) | |||||||
\(228\) | 2.51637i | 0.166651i | ||||||||
\(229\) | 0.723697i | 0.0478233i | 0.999714 | + | 0.0239116i | \(0.00761203\pi\) | ||||
−0.999714 | + | 0.0239116i | \(0.992388\pi\) | |||||||
\(230\) | −4.08614 | −0.269432 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.01022 | −0.525897 | ||||||||
\(233\) | − | 13.7409i | − | 0.900199i | −0.892978 | − | 0.450100i | \(-0.851388\pi\) | ||
0.892978 | − | 0.450100i | \(-0.148612\pi\) | |||||||
\(234\) | 2.81702i | 0.184154i | ||||||||
\(235\) | 8.45433 | 0.551499 | ||||||||
\(236\) | 13.4801i | 0.877480i | ||||||||
\(237\) | 9.26447 | 0.601792 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.273841i | 0.0177133i | 0.999961 | + | 0.00885667i | \(0.00281920\pi\) | ||||
−0.999961 | + | 0.00885667i | \(0.997181\pi\) | |||||||
\(240\) | −0.942563 | −0.0608422 | ||||||||
\(241\) | −0.693253 | −0.0446563 | −0.0223282 | − | 0.999751i | \(-0.507108\pi\) | ||||
−0.0223282 | + | 0.999751i | \(0.507108\pi\) | |||||||
\(242\) | −9.57609 | + | 5.41281i | −0.615574 | + | 0.347949i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 2.41499 | 0.154604 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.20158 | 0.331641 | ||||||||
\(247\) | 7.08867 | 0.451041 | ||||||||
\(248\) | −6.05783 | −0.384673 | ||||||||
\(249\) | − | 8.84143i | − | 0.560303i | ||||||
\(250\) | −8.58823 | −0.543168 | ||||||||
\(251\) | 4.79326i | 0.302548i | 0.988492 | + | 0.151274i | \(0.0483376\pi\) | ||||
−0.988492 | + | 0.151274i | \(0.951662\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.24577 | − | 12.4188i | 0.455538 | − | 0.780763i | ||||
\(254\) | 14.4372 | 0.905870 | ||||||||
\(255\) | −4.05875 | −0.254169 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.9768i | 0.996605i | 0.867003 | + | 0.498302i | \(0.166043\pi\) | ||||
−0.867003 | + | 0.498302i | \(0.833957\pi\) | |||||||
\(258\) | − | 11.3608i | − | 0.707291i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.65522i | 0.164670i | ||||||||
\(261\) | − | 8.01022i | − | 0.495820i | ||||||
\(262\) | − | 9.54305i | − | 0.589572i | ||||||
\(263\) | − | 17.1219i | − | 1.05578i | −0.849312 | − | 0.527891i | \(-0.822983\pi\) | ||
0.849312 | − | 0.527891i | \(-0.177017\pi\) | |||||||
\(264\) | 1.67140 | − | 2.86468i | 0.102868 | − | 0.176309i | ||||
\(265\) | − | 4.29122i | − | 0.263607i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.5356 | −0.705965 | ||||||||
\(268\) | 2.22408 | 0.135857 | ||||||||
\(269\) | − | 11.8794i | − | 0.724300i | −0.932120 | − | 0.362150i | \(-0.882043\pi\) | ||
0.932120 | − | 0.362150i | \(-0.117957\pi\) | |||||||
\(270\) | − | 0.942563i | − | 0.0573626i | ||||||
\(271\) | −12.9150 | −0.784531 | −0.392266 | − | 0.919852i | \(-0.628309\pi\) | ||||
−0.392266 | + | 0.919852i | \(0.628309\pi\) | |||||||
\(272\) | 4.30608 | 0.261094 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 18.7883i | − | 1.13504i | ||||||
\(275\) | 6.87211 | − | 11.7784i | 0.414404 | − | 0.710262i | ||||
\(276\) | 4.33514i | 0.260945i | ||||||||
\(277\) | 21.4574i | 1.28925i | 0.764499 | + | 0.644625i | \(0.222987\pi\) | ||||
−0.764499 | + | 0.644625i | \(0.777013\pi\) | |||||||
\(278\) | 19.9086i | 1.19404i | ||||||||
\(279\) | − | 6.05783i | − | 0.362673i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.770084i | − | 0.0459393i | −0.999736 | − | 0.0229697i | \(-0.992688\pi\) | ||
0.999736 | − | 0.0229697i | \(-0.00731212\pi\) | |||||||
\(282\) | − | 8.96951i | − | 0.534126i | ||||||
\(283\) | −16.7151 | −0.993609 | −0.496804 | − | 0.867863i | \(-0.665493\pi\) | ||||
−0.496804 | + | 0.867863i | \(0.665493\pi\) | |||||||
\(284\) | 4.80437 | 0.285087 | ||||||||
\(285\) | −2.37184 | −0.140496 | ||||||||
\(286\) | −8.06987 | − | 4.70838i | −0.477181 | − | 0.278413i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 1.54228 | 0.0907225 | ||||||||
\(290\) | − | 7.55014i | − | 0.443359i | ||||||
\(291\) | −12.5496 | −0.735673 | ||||||||
\(292\) | −4.63368 | −0.271165 | ||||||||
\(293\) | 24.6448 | 1.43976 | 0.719881 | − | 0.694097i | \(-0.244196\pi\) | ||||
0.719881 | + | 0.694097i | \(0.244196\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.7058 | −0.739763 | ||||||||
\(296\) | 10.4379i | 0.606692i | ||||||||
\(297\) | 2.86468 | + | 1.67140i | 0.166226 | + | 0.0969847i | ||||
\(298\) | 3.86561 | 0.223929 | ||||||||
\(299\) | 12.2122 | 0.706248 | ||||||||
\(300\) | 4.11157i | 0.237382i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.64273 | −0.0945285 | ||||||||
\(303\) | 8.65999i | 0.497504i | ||||||||
\(304\) | 2.51637 | 0.144324 | ||||||||
\(305\) | 2.27628i | 0.130340i | ||||||||
\(306\) | 4.30608i | 0.246162i | ||||||||
\(307\) | −15.2768 | −0.871893 | −0.435947 | − | 0.899973i | \(-0.643586\pi\) | ||||
−0.435947 | + | 0.899973i | \(0.643586\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.4902 | −0.653652 | ||||||||
\(310\) | − | 5.70989i | − | 0.324300i | ||||||
\(311\) | 24.0083i | 1.36139i | 0.732569 | + | 0.680693i | \(0.238321\pi\) | ||||
−0.732569 | + | 0.680693i | \(0.761679\pi\) | |||||||
\(312\) | 2.81702 | 0.159482 | ||||||||
\(313\) | − | 1.80468i | − | 0.102007i | −0.998698 | − | 0.0510034i | \(-0.983758\pi\) | ||
0.998698 | − | 0.0510034i | \(-0.0162419\pi\) | |||||||
\(314\) | −4.01593 | −0.226632 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 9.26447i | − | 0.521167i | ||||||
\(317\) | −21.4013 | −1.20202 | −0.601009 | − | 0.799242i | \(-0.705235\pi\) | ||||
−0.601009 | + | 0.799242i | \(0.705235\pi\) | |||||||
\(318\) | −4.55271 | −0.255303 | ||||||||
\(319\) | 22.9467 | + | 13.3883i | 1.28477 | + | 0.749602i | ||||
\(320\) | 0.942563i | 0.0526909i | ||||||||
\(321\) | −8.51031 | −0.474999 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.8357 | 0.602914 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 11.5824 | 0.642476 | ||||||||
\(326\) | − | 12.6206i | − | 0.698989i | ||||||
\(327\) | 0.950748 | 0.0525765 | ||||||||
\(328\) | − | 5.20158i | − | 0.287209i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.70014 | + | 1.57540i | 0.148638 | + | 0.0867232i | ||||
\(331\) | −24.5734 | −1.35068 | −0.675338 | − | 0.737508i | \(-0.736002\pi\) | ||||
−0.675338 | + | 0.737508i | \(0.736002\pi\) | |||||||
\(332\) | −8.84143 | −0.485237 | ||||||||
\(333\) | −10.4379 | −0.571995 | ||||||||
\(334\) | 15.1392i | 0.828379i | ||||||||
\(335\) | 2.09634i | 0.114535i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.4718i | 1.82332i | 0.410940 | + | 0.911662i | \(0.365201\pi\) | ||||
−0.410940 | + | 0.911662i | \(0.634799\pi\) | |||||||
\(338\) | 5.06439i | 0.275467i | ||||||||
\(339\) | 8.55994i | 0.464912i | ||||||||
\(340\) | 4.05875i | 0.220116i | ||||||||
\(341\) | 17.3538 | + | 10.1251i | 0.939759 | + | 0.548304i | ||||
\(342\) | 2.51637i | 0.136070i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11.3608 | −0.612532 | ||||||||
\(345\) | −4.08614 | −0.219990 | ||||||||
\(346\) | 7.73438i | 0.415803i | ||||||||
\(347\) | − | 19.4917i | − | 1.04637i | −0.852220 | − | 0.523184i | \(-0.824744\pi\) | ||
0.852220 | − | 0.523184i | \(-0.175256\pi\) | |||||||
\(348\) | −8.01022 | −0.429393 | ||||||||
\(349\) | −7.90787 | −0.423299 | −0.211649 | − | 0.977346i | \(-0.567883\pi\) | ||||
−0.211649 | + | 0.977346i | \(0.567883\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.81702i | 0.150361i | ||||||||
\(352\) | −2.86468 | − | 1.67140i | −0.152688 | − | 0.0890862i | ||||
\(353\) | − | 24.9608i | − | 1.32853i | −0.747498 | − | 0.664265i | \(-0.768745\pi\) | ||
0.747498 | − | 0.664265i | \(-0.231255\pi\) | |||||||
\(354\) | 13.4801i | 0.716459i | ||||||||
\(355\) | 4.52842i | 0.240343i | ||||||||
\(356\) | 11.5356i | 0.611384i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 16.8680i | − | 0.891504i | ||||||
\(359\) | − | 36.2082i | − | 1.91099i | −0.295001 | − | 0.955497i | \(-0.595320\pi\) | ||
0.295001 | − | 0.955497i | \(-0.404680\pi\) | |||||||
\(360\) | −0.942563 | −0.0496774 | ||||||||
\(361\) | −12.6679 | −0.666730 | ||||||||
\(362\) | −1.82684 | −0.0960164 | ||||||||
\(363\) | −9.57609 | + | 5.41281i | −0.502614 | + | 0.284099i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 4.36753i | − | 0.228607i | ||||||
\(366\) | 2.41499 | 0.126234 | ||||||||
\(367\) | 3.99407i | 0.208489i | 0.994552 | + | 0.104244i | \(0.0332424\pi\) | ||||
−0.994552 | + | 0.104244i | \(0.966758\pi\) | |||||||
\(368\) | 4.33514 | 0.225985 | ||||||||
\(369\) | 5.20158 | 0.270784 | ||||||||
\(370\) | −9.83841 | −0.511474 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.05783 | −0.314084 | ||||||||
\(373\) | 13.7307i | 0.710951i | 0.934686 | + | 0.355476i | \(0.115681\pi\) | ||||
−0.934686 | + | 0.355476i | \(0.884319\pi\) | |||||||
\(374\) | −12.3355 | − | 7.19720i | −0.637855 | − | 0.372158i | ||||
\(375\) | −8.58823 | −0.443495 | ||||||||
\(376\) | −8.96951 | −0.462567 | ||||||||
\(377\) | 22.5650i | 1.16215i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.64244 | 0.495299 | 0.247649 | − | 0.968850i | \(-0.420342\pi\) | ||||
0.247649 | + | 0.968850i | \(0.420342\pi\) | |||||||
\(380\) | 2.37184i | 0.121673i | ||||||||
\(381\) | 14.4372 | 0.739639 | ||||||||
\(382\) | 14.2909i | 0.731188i | ||||||||
\(383\) | − | 7.81472i | − | 0.399313i | −0.979866 | − | 0.199657i | \(-0.936017\pi\) | ||
0.979866 | − | 0.199657i | \(-0.0639827\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.68856 | 0.187743 | ||||||||
\(387\) | − | 11.3608i | − | 0.577501i | ||||||
\(388\) | 12.5496i | 0.637112i | ||||||||
\(389\) | 12.9955 | 0.658896 | 0.329448 | − | 0.944174i | \(-0.393137\pi\) | ||||
0.329448 | + | 0.944174i | \(0.393137\pi\) | |||||||
\(390\) | 2.65522i | 0.134452i | ||||||||
\(391\) | 18.6674 | 0.944052 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 9.54305i | − | 0.481383i | ||||||
\(394\) | 1.22462 | 0.0616956 | ||||||||
\(395\) | 8.73235 | 0.439372 | ||||||||
\(396\) | 1.67140 | − | 2.86468i | 0.0839913 | − | 0.143956i | ||||
\(397\) | − | 32.8955i | − | 1.65098i | −0.564417 | − | 0.825490i | \(-0.690899\pi\) | ||
0.564417 | − | 0.825490i | \(-0.309101\pi\) | |||||||
\(398\) | 12.8195 | 0.642585 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.11157 | 0.205579 | ||||||||
\(401\) | 28.0768 | 1.40209 | 0.701045 | − | 0.713117i | \(-0.252717\pi\) | ||||
0.701045 | + | 0.713117i | \(0.252717\pi\) | |||||||
\(402\) | 2.22408 | 0.110927 | ||||||||
\(403\) | 17.0650i | 0.850070i | ||||||||
\(404\) | 8.65999 | 0.430851 | ||||||||
\(405\) | − | 0.942563i | − | 0.0468363i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.4460 | − | 29.9014i | 0.864767 | − | 1.48216i | ||||
\(408\) | 4.30608 | 0.213182 | ||||||||
\(409\) | −39.1324 | −1.93497 | −0.967485 | − | 0.252928i | \(-0.918607\pi\) | ||||
−0.967485 | + | 0.252928i | \(0.918607\pi\) | |||||||
\(410\) | 4.90282 | 0.242133 | ||||||||
\(411\) | − | 18.7883i | − | 0.926757i | ||||||
\(412\) | 11.4902i | 0.566079i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.33514i | 0.213060i | ||||||||
\(415\) | − | 8.33361i | − | 0.409081i | ||||||
\(416\) | − | 2.81702i | − | 0.138116i | ||||||
\(417\) | 19.9086i | 0.974931i | ||||||||
\(418\) | −7.20861 | − | 4.20588i | −0.352584 | − | 0.205716i | ||||
\(419\) | 27.5652i | 1.34665i | 0.739347 | + | 0.673324i | \(0.235134\pi\) | ||||
−0.739347 | + | 0.673324i | \(0.764866\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.46286 | −0.314980 | −0.157490 | − | 0.987521i | \(-0.550340\pi\) | ||||
−0.157490 | + | 0.987521i | \(0.550340\pi\) | |||||||
\(422\) | 17.0672 | 0.830817 | ||||||||
\(423\) | − | 8.96951i | − | 0.436112i | ||||||
\(424\) | 4.55271i | 0.221099i | ||||||||
\(425\) | 17.7047 | 0.858807 | ||||||||
\(426\) | 4.80437 | 0.232772 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.51031i | 0.411361i | ||||||||
\(429\) | −8.06987 | − | 4.70838i | −0.389617 | − | 0.227323i | ||||
\(430\) | − | 10.7083i | − | 0.516398i | ||||||
\(431\) | 5.81850i | 0.280267i | 0.990133 | + | 0.140134i | \(0.0447532\pi\) | ||||
−0.990133 | + | 0.140134i | \(0.955247\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 27.1792i | − | 1.30615i | −0.757293 | − | 0.653075i | \(-0.773478\pi\) | ||
0.757293 | − | 0.653075i | \(-0.226522\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 7.55014i | − | 0.362001i | ||||||
\(436\) | − | 0.950748i | − | 0.0455326i | ||||||
\(437\) | 10.9088 | 0.521839 | ||||||||
\(438\) | −4.63368 | −0.221406 | ||||||||
\(439\) | 24.3998 | 1.16454 | 0.582270 | − | 0.812996i | \(-0.302165\pi\) | ||||
0.582270 | + | 0.812996i | \(0.302165\pi\) | |||||||
\(440\) | 1.57540 | − | 2.70014i | 0.0751045 | − | 0.128724i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 12.1303i | − | 0.576980i | ||||||
\(443\) | 7.40742 | 0.351937 | 0.175969 | − | 0.984396i | \(-0.443694\pi\) | ||||
0.175969 | + | 0.984396i | \(0.443694\pi\) | |||||||
\(444\) | 10.4379i | 0.495362i | ||||||||
\(445\) | −10.8730 | −0.515429 | ||||||||
\(446\) | −8.56595 | −0.405610 | ||||||||
\(447\) | 3.86561 | 0.182837 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.04219 | −0.379535 | −0.189767 | − | 0.981829i | \(-0.560773\pi\) | ||||
−0.189767 | + | 0.981829i | \(0.560773\pi\) | |||||||
\(450\) | 4.11157i | 0.193821i | ||||||||
\(451\) | −8.69395 | + | 14.9009i | −0.409382 | + | 0.701655i | ||||
\(452\) | 8.55994 | 0.402626 | ||||||||
\(453\) | −1.64273 | −0.0771822 | ||||||||
\(454\) | 16.9377i | 0.794926i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.51637 | 0.117840 | ||||||||
\(457\) | 18.1058i | 0.846953i | 0.905907 | + | 0.423476i | \(0.139190\pi\) | ||||
−0.905907 | + | 0.423476i | \(0.860810\pi\) | |||||||
\(458\) | 0.723697 | 0.0338162 | ||||||||
\(459\) | 4.30608i | 0.200990i | ||||||||
\(460\) | 4.08614i | 0.190517i | ||||||||
\(461\) | 17.1197 | 0.797343 | 0.398672 | − | 0.917094i | \(-0.369471\pi\) | ||||
0.398672 | + | 0.917094i | \(0.369471\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.4136 | 1.32049 | 0.660245 | − | 0.751050i | \(-0.270452\pi\) | ||||
0.660245 | + | 0.751050i | \(0.270452\pi\) | |||||||
\(464\) | 8.01022i | 0.371865i | ||||||||
\(465\) | − | 5.70989i | − | 0.264790i | ||||||
\(466\) | −13.7409 | −0.636537 | ||||||||
\(467\) | 20.6667i | 0.956341i | 0.878267 | + | 0.478171i | \(0.158700\pi\) | ||||
−0.878267 | + | 0.478171i | \(0.841300\pi\) | |||||||
\(468\) | 2.81702 | 0.130217 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 8.45433i | − | 0.389969i | ||||||
\(471\) | −4.01593 | −0.185044 | ||||||||
\(472\) | 13.4801 | 0.620472 | ||||||||
\(473\) | 32.5450 | + | 18.9885i | 1.49642 | + | 0.873091i | ||||
\(474\) | − | 9.26447i | − | 0.425531i | ||||||
\(475\) | 10.3463 | 0.474719 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.55271 | −0.208454 | ||||||||
\(478\) | 0.273841 | 0.0125252 | ||||||||
\(479\) | 20.7439 | 0.947811 | 0.473906 | − | 0.880576i | \(-0.342844\pi\) | ||||
0.473906 | + | 0.880576i | \(0.342844\pi\) | |||||||
\(480\) | 0.942563i | 0.0430219i | ||||||||
\(481\) | 29.4039 | 1.34070 | ||||||||
\(482\) | 0.693253i | 0.0315768i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.41281 | + | 9.57609i | 0.246037 | + | 0.435277i | ||||
\(485\) | −11.8288 | −0.537120 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −36.2719 | −1.64364 | −0.821818 | − | 0.569750i | \(-0.807040\pi\) | ||||
−0.821818 | + | 0.569750i | \(0.807040\pi\) | |||||||
\(488\) | − | 2.41499i | − | 0.109322i | ||||||
\(489\) | − | 12.6206i | − | 0.570723i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 0.584864i | − | 0.0263945i | −0.999913 | − | 0.0131973i | \(-0.995799\pi\) | ||
0.999913 | − | 0.0131973i | \(-0.00420094\pi\) | |||||||
\(492\) | − | 5.20158i | − | 0.234505i | ||||||
\(493\) | 34.4926i | 1.55347i | ||||||||
\(494\) | − | 7.08867i | − | 0.318934i | ||||||
\(495\) | 2.70014 | + | 1.57540i | 0.121362 | + | 0.0708092i | ||||
\(496\) | 6.05783i | 0.272005i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −8.84143 | −0.396194 | ||||||||
\(499\) | −21.6453 | −0.968979 | −0.484489 | − | 0.874797i | \(-0.660995\pi\) | ||||
−0.484489 | + | 0.874797i | \(0.660995\pi\) | |||||||
\(500\) | 8.58823i | 0.384078i | ||||||||
\(501\) | 15.1392i | 0.676368i | ||||||||
\(502\) | 4.79326 | 0.213934 | ||||||||
\(503\) | −31.5510 | −1.40679 | −0.703395 | − | 0.710800i | \(-0.748333\pi\) | ||||
−0.703395 | + | 0.710800i | \(0.748333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.16259i | 0.363230i | ||||||||
\(506\) | −12.4188 | − | 7.24577i | −0.552083 | − | 0.322114i | ||||
\(507\) | 5.06439i | 0.224918i | ||||||||
\(508\) | − | 14.4372i | − | 0.640547i | ||||||
\(509\) | 21.2731i | 0.942914i | 0.881889 | + | 0.471457i | \(0.156272\pi\) | ||||
−0.881889 | + | 0.471457i | \(0.843728\pi\) | |||||||
\(510\) | 4.05875i | 0.179724i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 2.51637i | 0.111101i | ||||||||
\(514\) | 15.9768 | 0.704706 | ||||||||
\(515\) | −10.8302 | −0.477235 | ||||||||
\(516\) | −11.3608 | −0.500131 | ||||||||
\(517\) | 25.6948 | + | 14.9917i | 1.13006 | + | 0.659333i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.73438i | 0.339501i | ||||||||
\(520\) | 2.65522 | 0.116439 | ||||||||
\(521\) | − | 9.14346i | − | 0.400582i | −0.979736 | − | 0.200291i | \(-0.935811\pi\) | ||
0.979736 | − | 0.200291i | \(-0.0641888\pi\) | |||||||
\(522\) | −8.01022 | −0.350598 | ||||||||
\(523\) | −27.9801 | −1.22349 | −0.611743 | − | 0.791057i | \(-0.709531\pi\) | ||||
−0.611743 | + | 0.791057i | \(0.709531\pi\) | |||||||
\(524\) | −9.54305 | −0.416890 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.1219 | −0.746550 | ||||||||
\(527\) | 26.0855i | 1.13630i | ||||||||
\(528\) | −2.86468 | − | 1.67140i | −0.124669 | − | 0.0727386i | ||||
\(529\) | −4.20659 | −0.182895 | ||||||||
\(530\) | −4.29122 | −0.186399 | ||||||||
\(531\) | 13.4801i | 0.584987i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.6530 | −0.634690 | ||||||||
\(534\) | 11.5356i | 0.499193i | ||||||||
\(535\) | −8.02151 | −0.346800 | ||||||||
\(536\) | − | 2.22408i | − | 0.0960656i | ||||||
\(537\) | − | 16.8680i | − | 0.727910i | ||||||
\(538\) | −11.8794 | −0.512157 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.942563 | −0.0405615 | ||||||||
\(541\) | − | 27.1482i | − | 1.16719i | −0.812044 | − | 0.583597i | \(-0.801645\pi\) | ||
0.812044 | − | 0.583597i | \(-0.198355\pi\) | |||||||
\(542\) | 12.9150i | 0.554748i | ||||||||
\(543\) | −1.82684 | −0.0783970 | ||||||||
\(544\) | − | 4.30608i | − | 0.184621i | ||||||
\(545\) | 0.896140 | 0.0383864 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.17032i | 0.349337i | 0.984627 | + | 0.174669i | \(0.0558854\pi\) | ||||
−0.984627 | + | 0.174669i | \(0.944115\pi\) | |||||||
\(548\) | −18.7883 | −0.802595 | ||||||||
\(549\) | 2.41499 | 0.103069 | ||||||||
\(550\) | −11.7784 | − | 6.87211i | −0.502231 | − | 0.293028i | ||||
\(551\) | 20.1567i | 0.858704i | ||||||||
\(552\) | 4.33514 | 0.184516 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 21.4574 | 0.911638 | ||||||||
\(555\) | −9.83841 | −0.417617 | ||||||||
\(556\) | 19.9086 | 0.844315 | ||||||||
\(557\) | − | 15.2398i | − | 0.645732i | −0.946445 | − | 0.322866i | \(-0.895354\pi\) | ||
0.946445 | − | 0.322866i | \(-0.104646\pi\) | |||||||
\(558\) | −6.05783 | −0.256448 | ||||||||
\(559\) | 32.0036i | 1.35361i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.3355 | − | 7.19720i | −0.520807 | − | 0.303866i | ||||
\(562\) | −0.770084 | −0.0324840 | ||||||||
\(563\) | −28.1605 | −1.18683 | −0.593413 | − | 0.804898i | \(-0.702220\pi\) | ||||
−0.593413 | + | 0.804898i | \(0.702220\pi\) | |||||||
\(564\) | −8.96951 | −0.377684 | ||||||||
\(565\) | 8.06828i | 0.339435i | ||||||||
\(566\) | 16.7151i | 0.702587i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 4.80437i | − | 0.201587i | ||||||
\(569\) | − | 45.8500i | − | 1.92213i | −0.276317 | − | 0.961067i | \(-0.589114\pi\) | ||
0.276317 | − | 0.961067i | \(-0.410886\pi\) | |||||||
\(570\) | 2.37184i | 0.0993454i | ||||||||
\(571\) | − | 36.4708i | − | 1.52626i | −0.646247 | − | 0.763128i | \(-0.723663\pi\) | ||
0.646247 | − | 0.763128i | \(-0.276337\pi\) | |||||||
\(572\) | −4.70838 | + | 8.06987i | −0.196867 | + | 0.337418i | ||||
\(573\) | 14.2909i | 0.597013i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.8242 | 0.743322 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 38.2106i | 1.59073i | 0.606132 | + | 0.795364i | \(0.292720\pi\) | ||||
−0.606132 | + | 0.795364i | \(0.707280\pi\) | |||||||
\(578\) | − | 1.54228i | − | 0.0641505i | ||||||
\(579\) | 3.68856 | 0.153291 | ||||||||
\(580\) | −7.55014 | −0.313502 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 12.5496i | 0.520199i | ||||||||
\(583\) | 7.60942 | − | 13.0421i | 0.315150 | − | 0.540148i | ||||
\(584\) | 4.63368i | 0.191743i | ||||||||
\(585\) | 2.65522i | 0.109780i | ||||||||
\(586\) | − | 24.6448i | − | 1.01807i | ||||||
\(587\) | 21.0138i | 0.867333i | 0.901074 | + | 0.433666i | \(0.142780\pi\) | ||||
−0.901074 | + | 0.433666i | \(0.857220\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.2438i | 0.628108i | ||||||||
\(590\) | 12.7058i | 0.523092i | ||||||||
\(591\) | 1.22462 | 0.0503742 | ||||||||
\(592\) | 10.4379 | 0.428996 | ||||||||
\(593\) | −2.35790 | −0.0968272 | −0.0484136 | − | 0.998827i | \(-0.515417\pi\) | ||||
−0.0484136 | + | 0.998827i | \(0.515417\pi\) | |||||||
\(594\) | 1.67140 | − | 2.86468i | 0.0685786 | − | 0.117539i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 3.86561i | − | 0.158341i | ||||||
\(597\) | 12.8195 | 0.524668 | ||||||||
\(598\) | − | 12.2122i | − | 0.499393i | ||||||
\(599\) | −18.4896 | −0.755464 | −0.377732 | − | 0.925915i | \(-0.623296\pi\) | ||||
−0.377732 | + | 0.925915i | \(0.623296\pi\) | |||||||
\(600\) | 4.11157 | 0.167854 | ||||||||
\(601\) | 21.1149 | 0.861293 | 0.430647 | − | 0.902521i | \(-0.358286\pi\) | ||||
0.430647 | + | 0.902521i | \(0.358286\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.22408 | 0.0905715 | ||||||||
\(604\) | 1.64273i | 0.0668418i | ||||||||
\(605\) | −9.02607 | + | 5.10192i | −0.366962 | + | 0.207422i | ||||
\(606\) | 8.65999 | 0.351788 | ||||||||
\(607\) | −33.2254 | −1.34858 | −0.674290 | − | 0.738467i | \(-0.735550\pi\) | ||||
−0.674290 | + | 0.738467i | \(0.735550\pi\) | |||||||
\(608\) | − | 2.51637i | − | 0.102052i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.27628 | 0.0921641 | ||||||||
\(611\) | 25.2673i | 1.02221i | ||||||||
\(612\) | 4.30608 | 0.174063 | ||||||||
\(613\) | 10.4600i | 0.422473i | 0.977435 | + | 0.211237i | \(0.0677491\pi\) | ||||
−0.977435 | + | 0.211237i | \(0.932251\pi\) | |||||||
\(614\) | 15.2768i | 0.616522i | ||||||||
\(615\) | 4.90282 | 0.197701 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.7531 | 1.60040 | 0.800200 | − | 0.599733i | \(-0.204727\pi\) | ||||
0.800200 | + | 0.599733i | \(0.204727\pi\) | |||||||
\(618\) | 11.4902i | 0.462202i | ||||||||
\(619\) | − | 17.0154i | − | 0.683907i | −0.939717 | − | 0.341953i | \(-0.888911\pi\) | ||
0.939717 | − | 0.341953i | \(-0.111089\pi\) | |||||||
\(620\) | −5.70989 | −0.229315 | ||||||||
\(621\) | 4.33514i | 0.173963i | ||||||||
\(622\) | 24.0083 | 0.962646 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 2.81702i | − | 0.112771i | ||||||
\(625\) | 12.4629 | 0.498517 | ||||||||
\(626\) | −1.80468 | −0.0721296 | ||||||||
\(627\) | −7.20861 | − | 4.20588i | −0.287884 | − | 0.167967i | ||||
\(628\) | 4.01593i | 0.160253i | ||||||||
\(629\) | 44.9465 | 1.79213 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.4904 | 1.49247 | 0.746234 | − | 0.665684i | \(-0.231860\pi\) | ||||
0.746234 | + | 0.665684i | \(0.231860\pi\) | |||||||
\(632\) | −9.26447 | −0.368521 | ||||||||
\(633\) | 17.0672 | 0.678359 | ||||||||
\(634\) | 21.4013i | 0.849955i | ||||||||
\(635\) | 13.6080 | 0.540015 | ||||||||
\(636\) | 4.55271i | 0.180527i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.3883 | − | 22.9467i | 0.530049 | − | 0.908470i | ||||
\(639\) | 4.80437 | 0.190058 | ||||||||
\(640\) | 0.942563 | 0.0372581 | ||||||||
\(641\) | −23.9255 | −0.945000 | −0.472500 | − | 0.881331i | \(-0.656648\pi\) | ||||
−0.472500 | + | 0.881331i | \(0.656648\pi\) | |||||||
\(642\) | 8.51031i | 0.335875i | ||||||||
\(643\) | − | 0.155057i | − | 0.00611485i | −0.999995 | − | 0.00305742i | \(-0.999027\pi\) | ||
0.999995 | − | 0.00305742i | \(-0.000973210\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 10.7083i | − | 0.421637i | ||||||
\(646\) | − | 10.8357i | − | 0.426324i | ||||||
\(647\) | − | 37.0329i | − | 1.45591i | −0.685624 | − | 0.727956i | \(-0.740471\pi\) | ||
0.685624 | − | 0.727956i | \(-0.259529\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −38.6162 | − | 22.5307i | −1.51582 | − | 0.884408i | ||||
\(650\) | − | 11.5824i | − | 0.454299i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.6206 | −0.494260 | ||||||||
\(653\) | 2.65522 | 0.103907 | 0.0519534 | − | 0.998650i | \(-0.483455\pi\) | ||||
0.0519534 | + | 0.998650i | \(0.483455\pi\) | |||||||
\(654\) | − | 0.950748i | − | 0.0371772i | ||||||
\(655\) | − | 8.99493i | − | 0.351461i | ||||||
\(656\) | −5.20158 | −0.203088 | ||||||||
\(657\) | −4.63368 | −0.180777 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 13.6694i | − | 0.532485i | −0.963906 | − | 0.266243i | \(-0.914218\pi\) | ||
0.963906 | − | 0.266243i | \(-0.0857823\pi\) | |||||||
\(660\) | 1.57540 | − | 2.70014i | 0.0613225 | − | 0.105103i | ||||
\(661\) | − | 16.4336i | − | 0.639195i | −0.947553 | − | 0.319597i | \(-0.896452\pi\) | ||
0.947553 | − | 0.319597i | \(-0.103548\pi\) | |||||||
\(662\) | 24.5734i | 0.955072i | ||||||||
\(663\) | − | 12.1303i | − | 0.471102i | ||||||
\(664\) | 8.84143i | 0.343114i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.4379i | 0.404462i | ||||||||
\(667\) | 34.7254i | 1.34457i | ||||||||
\(668\) | 15.1392 | 0.585752 | ||||||||
\(669\) | −8.56595 | −0.331179 | ||||||||
\(670\) | 2.09634 | 0.0809885 | ||||||||
\(671\) | −4.03643 | + | 6.91819i | −0.155825 | + | 0.267074i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 48.3352i | − | 1.86318i | −0.363506 | − | 0.931592i | \(-0.618420\pi\) | ||
0.363506 | − | 0.931592i | \(-0.381580\pi\) | |||||||
\(674\) | 33.4718 | 1.28929 | ||||||||
\(675\) | 4.11157i | 0.158255i | ||||||||
\(676\) | 5.06439 | 0.194784 | ||||||||
\(677\) | 39.1427 | 1.50437 | 0.752187 | − | 0.658950i | \(-0.228999\pi\) | ||||
0.752187 | + | 0.658950i | \(0.228999\pi\) | |||||||
\(678\) | 8.55994 | 0.328742 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.05875 | 0.155646 | ||||||||
\(681\) | 16.9377i | 0.649054i | ||||||||
\(682\) | 10.1251 | − | 17.3538i | 0.387710 | − | 0.664510i | ||||
\(683\) | −4.64928 | −0.177900 | −0.0889500 | − | 0.996036i | \(-0.528351\pi\) | ||||
−0.0889500 | + | 0.996036i | \(0.528351\pi\) | |||||||
\(684\) | 2.51637 | 0.0962159 | ||||||||
\(685\) | − | 17.7091i | − | 0.676631i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.723697 | 0.0276108 | ||||||||
\(688\) | 11.3608i | 0.433126i | ||||||||
\(689\) | 12.8251 | 0.488597 | ||||||||
\(690\) | 4.08614i | 0.155557i | ||||||||
\(691\) | 7.45733i | 0.283690i | 0.989889 | + | 0.141845i | \(0.0453035\pi\) | ||||
−0.989889 | + | 0.141845i | \(0.954696\pi\) | |||||||
\(692\) | 7.73438 | 0.294017 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.4917 | −0.739894 | ||||||||
\(695\) | 18.7652i | 0.711803i | ||||||||
\(696\) | 8.01022i | 0.303627i | ||||||||
\(697\) | −22.3984 | −0.848400 | ||||||||
\(698\) | 7.90787i | 0.299317i | ||||||||
\(699\) | −13.7409 | −0.519730 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 34.1129i | − | 1.28843i | −0.764845 | − | 0.644214i | \(-0.777185\pi\) | ||
0.764845 | − | 0.644214i | \(-0.222815\pi\) | |||||||
\(702\) | 2.81702 | 0.106322 | ||||||||
\(703\) | 26.2657 | 0.990630 | ||||||||
\(704\) | −1.67140 | + | 2.86468i | −0.0629934 | + | 0.107967i | ||||
\(705\) | − | 8.45433i | − | 0.318408i | ||||||
\(706\) | −24.9608 | −0.939412 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 13.4801 | 0.506613 | ||||||||
\(709\) | −14.9868 | −0.562840 | −0.281420 | − | 0.959585i | \(-0.590805\pi\) | ||||
−0.281420 | + | 0.959585i | \(0.590805\pi\) | |||||||
\(710\) | 4.52842 | 0.169948 | ||||||||
\(711\) | − | 9.26447i | − | 0.347445i | ||||||
\(712\) | 11.5356 | 0.432313 | ||||||||
\(713\) | 26.2615i | 0.983502i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.60636 | − | 4.43795i | −0.284462 | − | 0.165970i | ||||
\(716\) | −16.8680 | −0.630388 | ||||||||
\(717\) | 0.273841 | 0.0102268 | ||||||||
\(718\) | −36.2082 | −1.35128 | ||||||||
\(719\) | − | 28.1244i | − | 1.04886i | −0.851452 | − | 0.524432i | \(-0.824278\pi\) | ||
0.851452 | − | 0.524432i | \(-0.175722\pi\) | |||||||
\(720\) | 0.942563i | 0.0351273i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.6679i | 0.471449i | ||||||||
\(723\) | 0.693253i | 0.0257823i | ||||||||
\(724\) | 1.82684i | 0.0678938i | ||||||||
\(725\) | 32.9346i | 1.22316i | ||||||||
\(726\) | 5.41281 | + | 9.57609i | 0.200888 | + | 0.355402i | ||||
\(727\) | 27.0175i | 1.00202i | 0.865441 | + | 0.501012i | \(0.167039\pi\) | ||||
−0.865441 | + | 0.501012i | \(0.832961\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −4.36753 | −0.161650 | ||||||||
\(731\) | 48.9204i | 1.80939i | ||||||||
\(732\) | − | 2.41499i | − | 0.0892608i | ||||||
\(733\) | −7.00127 | −0.258598 | −0.129299 | − | 0.991606i | \(-0.541273\pi\) | ||||
−0.129299 | + | 0.991606i | \(0.541273\pi\) | |||||||
\(734\) | 3.99407 | 0.147424 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 4.33514i | − | 0.159795i | ||||||
\(737\) | −3.71734 | + | 6.37128i | −0.136930 | + | 0.234689i | ||||
\(738\) | − | 5.20158i | − | 0.191473i | ||||||
\(739\) | 41.7535i | 1.53593i | 0.640494 | + | 0.767963i | \(0.278730\pi\) | ||||
−0.640494 | + | 0.767963i | \(0.721270\pi\) | |||||||
\(740\) | 9.83841i | 0.361667i | ||||||||
\(741\) | − | 7.08867i | − | 0.260409i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.1614i | 1.62013i | 0.586343 | + | 0.810063i | \(0.300567\pi\) | ||||
−0.586343 | + | 0.810063i | \(0.699433\pi\) | |||||||
\(744\) | 6.05783i | 0.222091i | ||||||||
\(745\) | 3.64358 | 0.133490 | ||||||||
\(746\) | 13.7307 | 0.502718 | ||||||||
\(747\) | −8.84143 | −0.323491 | ||||||||
\(748\) | −7.19720 | + | 12.3355i | −0.263156 | + | 0.451032i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8.58823i | 0.313598i | ||||||||
\(751\) | −11.8651 | −0.432965 | −0.216482 | − | 0.976287i | \(-0.569458\pi\) | ||||
−0.216482 | + | 0.976287i | \(0.569458\pi\) | |||||||
\(752\) | 8.96951i | 0.327084i | ||||||||
\(753\) | 4.79326 | 0.174676 | ||||||||
\(754\) | 22.5650 | 0.821767 | ||||||||
\(755\) | −1.54838 | −0.0563512 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.4503 | 1.54288 | 0.771441 | − | 0.636301i | \(-0.219536\pi\) | ||||
0.771441 | + | 0.636301i | \(0.219536\pi\) | |||||||
\(758\) | − | 9.64244i | − | 0.350229i | ||||||
\(759\) | −12.4188 | − | 7.24577i | −0.450774 | − | 0.263005i | ||||
\(760\) | 2.37184 | 0.0860357 | ||||||||
\(761\) | −8.21277 | −0.297713 | −0.148856 | − | 0.988859i | \(-0.547559\pi\) | ||||
−0.148856 | + | 0.988859i | \(0.547559\pi\) | |||||||
\(762\) | − | 14.4372i | − | 0.523004i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 14.2909 | 0.517028 | ||||||||
\(765\) | 4.05875i | 0.146744i | ||||||||
\(766\) | −7.81472 | −0.282357 | ||||||||
\(767\) | − | 37.9737i | − | 1.37115i | ||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 35.8809 | 1.29390 | 0.646950 | − | 0.762533i | \(-0.276044\pi\) | ||||
0.646950 | + | 0.762533i | \(0.276044\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.9768 | 0.575390 | ||||||||
\(772\) | − | 3.68856i | − | 0.132754i | ||||||
\(773\) | − | 16.9090i | − | 0.608175i | −0.952644 | − | 0.304088i | \(-0.901648\pi\) | ||
0.952644 | − | 0.304088i | \(-0.0983516\pi\) | |||||||
\(774\) | −11.3608 | −0.408355 | ||||||||
\(775\) | 24.9072i | 0.894694i | ||||||||
\(776\) | 12.5496 | 0.450506 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 12.9955i | − | 0.465910i | ||||||
\(779\) | −13.0891 | −0.468966 | ||||||||
\(780\) | 2.65522 | 0.0950721 | ||||||||
\(781\) | −8.03004 | + | 13.7630i | −0.287337 | + | 0.492478i | ||||
\(782\) | − | 18.6674i | − | 0.667546i | ||||||
\(783\) | −8.01022 | −0.286262 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.78527 | −0.135102 | ||||||||
\(786\) | −9.54305 | −0.340389 | ||||||||
\(787\) | 35.6858 | 1.27206 | 0.636030 | − | 0.771664i | \(-0.280575\pi\) | ||||
0.636030 | + | 0.771664i | \(0.280575\pi\) | |||||||
\(788\) | − | 1.22462i | − | 0.0436253i | ||||||
\(789\) | −17.1219 | −0.609556 | ||||||||
\(790\) | − | 8.73235i | − | 0.310683i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.86468 | − | 1.67140i | −0.101792 | − | 0.0593908i | ||||
\(793\) | −6.80309 | −0.241585 | ||||||||
\(794\) | −32.8955 | −1.16742 | ||||||||
\(795\) | −4.29122 | −0.152194 | ||||||||
\(796\) | − | 12.8195i | − | 0.454376i | ||||||
\(797\) | 25.7624i | 0.912550i | 0.889839 | + | 0.456275i | \(0.150817\pi\) | ||||
−0.889839 | + | 0.456275i | \(0.849183\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.6234i | 1.36640i | ||||||||
\(800\) | − | 4.11157i | − | 0.145366i | ||||||
\(801\) | 11.5356i | 0.407589i | ||||||||
\(802\) | − | 28.0768i | − | 0.991427i | ||||||
\(803\) | 7.74475 | − | 13.2740i | 0.273306 | − | 0.468430i | ||||
\(804\) | − | 2.22408i | − | 0.0784372i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.0650 | 0.601090 | ||||||||
\(807\) | −11.8794 | −0.418175 | ||||||||
\(808\) | − | 8.65999i | − | 0.304657i | ||||||
\(809\) | − | 23.2691i | − | 0.818099i | −0.912512 | − | 0.409050i | \(-0.865860\pi\) | ||
0.912512 | − | 0.409050i | \(-0.134140\pi\) | |||||||
\(810\) | −0.942563 | −0.0331183 | ||||||||
\(811\) | 1.49575 | 0.0525229 | 0.0262614 | − | 0.999655i | \(-0.491640\pi\) | ||||
0.0262614 | + | 0.999655i | \(0.491640\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.9150i | 0.452949i | ||||||||
\(814\) | −29.9014 | − | 17.4460i | −1.04804 | − | 0.611482i | ||||
\(815\) | − | 11.8957i | − | 0.416688i | ||||||
\(816\) | − | 4.30608i | − | 0.150743i | ||||||
\(817\) | 28.5880i | 1.00017i | ||||||||
\(818\) | 39.1324i | 1.36823i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 4.90282i | − | 0.171214i | ||||||
\(821\) | 34.5952i | 1.20738i | 0.797219 | + | 0.603690i | \(0.206303\pi\) | ||||
−0.797219 | + | 0.603690i | \(0.793697\pi\) | |||||||
\(822\) | −18.7883 | −0.655316 | ||||||||
\(823\) | −33.5957 | −1.17107 | −0.585537 | − | 0.810646i | \(-0.699116\pi\) | ||||
−0.585537 | + | 0.810646i | \(0.699116\pi\) | |||||||
\(824\) | 11.4902 | 0.400278 | ||||||||
\(825\) | −11.7784 | − | 6.87211i | −0.410070 | − | 0.239256i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5.10053i | − | 0.177363i | −0.996060 | − | 0.0886814i | \(-0.971735\pi\) | ||
0.996060 | − | 0.0886814i | \(-0.0282653\pi\) | |||||||
\(828\) | 4.33514 | 0.150656 | ||||||||
\(829\) | − | 12.6217i | − | 0.438370i | −0.975683 | − | 0.219185i | \(-0.929660\pi\) | ||
0.975683 | − | 0.219185i | \(-0.0703398\pi\) | |||||||
\(830\) | −8.33361 | −0.289264 | ||||||||
\(831\) | 21.4574 | 0.744349 | ||||||||
\(832\) | −2.81702 | −0.0976626 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 19.9086 | 0.689380 | ||||||||
\(835\) | 14.2696i | 0.493821i | ||||||||
\(836\) | −4.20588 | + | 7.20861i | −0.145463 | + | 0.249315i | ||||
\(837\) | −6.05783 | −0.209389 | ||||||||
\(838\) | 27.5652 | 0.952224 | ||||||||
\(839\) | − | 18.2805i | − | 0.631114i | −0.948907 | − | 0.315557i | \(-0.897809\pi\) | ||
0.948907 | − | 0.315557i | \(-0.102191\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −35.1636 | −1.21254 | ||||||||
\(842\) | 6.46286i | 0.222725i | ||||||||
\(843\) | −0.770084 | −0.0265231 | ||||||||
\(844\) | − | 17.0672i | − | 0.587476i | ||||||
\(845\) | 4.77351i | 0.164214i | ||||||||
\(846\) | −8.96951 | −0.308378 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.55271 | 0.156341 | ||||||||
\(849\) | 16.7151i | 0.573660i | ||||||||
\(850\) | − | 17.7047i | − | 0.607268i | ||||||
\(851\) | 45.2499 | 1.55115 | ||||||||
\(852\) | − | 4.80437i | − | 0.164595i | ||||||
\(853\) | 48.9693 | 1.67668 | 0.838338 | − | 0.545150i | \(-0.183527\pi\) | ||||
0.838338 | + | 0.545150i | \(0.183527\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.37184i | 0.0811152i | ||||||||
\(856\) | 8.51031 | 0.290876 | ||||||||
\(857\) | 34.7766 | 1.18794 | 0.593972 | − | 0.804485i | \(-0.297559\pi\) | ||||
0.593972 | + | 0.804485i | \(0.297559\pi\) | |||||||
\(858\) | −4.70838 | + | 8.06987i | −0.160742 | + | 0.275501i | ||||
\(859\) | − | 7.70241i | − | 0.262803i | −0.991329 | − | 0.131401i | \(-0.958052\pi\) | ||
0.991329 | − | 0.131401i | \(-0.0419477\pi\) | |||||||
\(860\) | −10.7083 | −0.365148 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.81850 | 0.198179 | ||||||||
\(863\) | 21.8084 | 0.742365 | 0.371183 | − | 0.928560i | \(-0.378952\pi\) | ||||
0.371183 | + | 0.928560i | \(0.378952\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 7.29014i | 0.247872i | ||||||||
\(866\) | −27.1792 | −0.923588 | ||||||||
\(867\) | − | 1.54228i | − | 0.0523787i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.5398 | + | 15.4847i | 0.900300 | + | 0.525282i | ||||
\(870\) | −7.55014 | −0.255974 | ||||||||
\(871\) | −6.26528 | −0.212291 | ||||||||
\(872\) | −0.950748 | −0.0321964 | ||||||||
\(873\) | 12.5496i | 0.424741i | ||||||||
\(874\) | − | 10.9088i | − | 0.368996i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.63368i | 0.156557i | ||||||||
\(877\) | 51.1146i | 1.72602i | 0.505189 | + | 0.863009i | \(0.331423\pi\) | ||||
−0.505189 | + | 0.863009i | \(0.668577\pi\) | |||||||
\(878\) | − | 24.3998i | − | 0.823454i | ||||||
\(879\) | − | 24.6448i | − | 0.831247i | ||||||
\(880\) | −2.70014 | − | 1.57540i | −0.0910218 | − | 0.0531069i | ||||
\(881\) | − | 14.3532i | − | 0.483573i | −0.970329 | − | 0.241787i | \(-0.922267\pi\) | ||
0.970329 | − | 0.241787i | \(-0.0777334\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.4009 | −0.450977 | −0.225488 | − | 0.974246i | \(-0.572398\pi\) | ||||
−0.225488 | + | 0.974246i | \(0.572398\pi\) | |||||||
\(884\) | −12.1303 | −0.407986 | ||||||||
\(885\) | 12.7058i | 0.427102i | ||||||||
\(886\) | − | 7.40742i | − | 0.248857i | ||||||
\(887\) | −17.5783 | −0.590223 | −0.295112 | − | 0.955463i | \(-0.595357\pi\) | ||||
−0.295112 | + | 0.955463i | \(0.595357\pi\) | |||||||
\(888\) | 10.4379 | 0.350274 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 10.8730i | 0.364464i | ||||||||
\(891\) | 1.67140 | − | 2.86468i | 0.0559942 | − | 0.0959705i | ||||
\(892\) | 8.56595i | 0.286809i | ||||||||
\(893\) | 22.5706i | 0.755297i | ||||||||
\(894\) | − | 3.86561i | − | 0.129285i | ||||||
\(895\) | − | 15.8992i | − | 0.531451i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 12.2122i | − | 0.407753i | ||||||
\(898\) | 8.04219i | 0.268372i | ||||||||
\(899\) | −48.5246 | −1.61838 | ||||||||
\(900\) | 4.11157 | 0.137052 | ||||||||
\(901\) | 19.6043 | 0.653115 | ||||||||
\(902\) | 14.9009 | + | 8.69395i | 0.496145 | + | 0.289477i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 8.55994i | − | 0.284699i | ||||||
\(905\) | −1.72191 | −0.0572382 | ||||||||
\(906\) | 1.64273i | 0.0545761i | ||||||||
\(907\) | −15.3916 | −0.511071 | −0.255535 | − | 0.966800i | \(-0.582252\pi\) | ||||
−0.255535 | + | 0.966800i | \(0.582252\pi\) | |||||||
\(908\) | 16.9377 | 0.562097 | ||||||||
\(909\) | 8.65999 | 0.287234 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.3460 | −0.607828 | −0.303914 | − | 0.952699i | \(-0.598294\pi\) | ||||
−0.303914 | + | 0.952699i | \(0.598294\pi\) | |||||||
\(912\) | − | 2.51637i | − | 0.0833254i | ||||||
\(913\) | 14.7776 | − | 25.3279i | 0.489068 | − | 0.838231i | ||||
\(914\) | 18.1058 | 0.598886 | ||||||||
\(915\) | 2.27628 | 0.0752517 | ||||||||
\(916\) | − | 0.723697i | − | 0.0239116i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.30608 | 0.142122 | ||||||||
\(919\) | − | 19.3005i | − | 0.636664i | −0.947979 | − | 0.318332i | \(-0.896877\pi\) | ||
0.947979 | − | 0.318332i | \(-0.103123\pi\) | |||||||
\(920\) | 4.08614 | 0.134716 | ||||||||
\(921\) | 15.2768i | 0.503388i | ||||||||
\(922\) | − | 17.1197i | − | 0.563807i | ||||||
\(923\) | −13.5340 | −0.445477 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.9163 | 1.41108 | ||||||||
\(926\) | − | 28.4136i | − | 0.933728i | ||||||
\(927\) | 11.4902i | 0.377386i | ||||||||
\(928\) | 8.01022 | 0.262948 | ||||||||
\(929\) | − | 26.6207i | − | 0.873397i | −0.899608 | − | 0.436698i | \(-0.856148\pi\) | ||
0.899608 | − | 0.436698i | \(-0.143852\pi\) | |||||||
\(930\) | −5.70989 | −0.187235 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 13.7409i | 0.450100i | ||||||||
\(933\) | 24.0083 | 0.785997 | ||||||||
\(934\) | 20.6667 | 0.676235 | ||||||||
\(935\) | −11.6270 | − | 6.78381i | −0.380244 | − | 0.221854i | ||||
\(936\) | − | 2.81702i | − | 0.0920772i | ||||||
\(937\) | 45.3628 | 1.48194 | 0.740969 | − | 0.671539i | \(-0.234366\pi\) | ||||
0.740969 | + | 0.671539i | \(0.234366\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.80468 | −0.0588936 | ||||||||
\(940\) | −8.45433 | −0.275750 | ||||||||
\(941\) | 47.8871 | 1.56107 | 0.780537 | − | 0.625110i | \(-0.214946\pi\) | ||||
0.780537 | + | 0.625110i | \(0.214946\pi\) | |||||||
\(942\) | 4.01593i | 0.130846i | ||||||||
\(943\) | −22.5496 | −0.734315 | ||||||||
\(944\) | − | 13.4801i | − | 0.438740i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.9885 | − | 32.5450i | 0.617368 | − | 1.05813i | ||||
\(947\) | −22.5730 | −0.733523 | −0.366762 | − | 0.930315i | \(-0.619534\pi\) | ||||
−0.366762 | + | 0.930315i | \(0.619534\pi\) | |||||||
\(948\) | −9.26447 | −0.300896 | ||||||||
\(949\) | 13.0532 | 0.423724 | ||||||||
\(950\) | − | 10.3463i | − | 0.335677i | ||||||
\(951\) | 21.4013i | 0.693986i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 44.2701i | − | 1.43405i | −0.697048 | − | 0.717025i | \(-0.745503\pi\) | ||
0.697048 | − | 0.717025i | \(-0.254497\pi\) | |||||||
\(954\) | 4.55271i | 0.147399i | ||||||||
\(955\) | 13.4701i | 0.435883i | ||||||||
\(956\) | − | 0.273841i | − | 0.00885667i | ||||||
\(957\) | 13.3883 | − | 22.9467i | 0.432783 | − | 0.741763i | ||||
\(958\) | − | 20.7439i | − | 0.670204i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.942563 | 0.0304211 | ||||||||
\(961\) | −5.69731 | −0.183784 | ||||||||
\(962\) | − | 29.4039i | − | 0.948019i | ||||||
\(963\) | 8.51031i | 0.274241i | ||||||||
\(964\) | 0.693253 | 0.0223282 | ||||||||
\(965\) | 3.47670 | 0.111919 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.65227i | 0.310396i | 0.987883 | + | 0.155198i | \(0.0496015\pi\) | ||||
−0.987883 | + | 0.155198i | \(0.950398\pi\) | |||||||
\(968\) | 9.57609 | − | 5.41281i | 0.307787 | − | 0.173974i | ||||
\(969\) | − | 10.8357i | − | 0.348092i | ||||||
\(970\) | 11.8288i | 0.379801i | ||||||||
\(971\) | 60.4441i | 1.93974i | 0.243616 | + | 0.969872i | \(0.421666\pi\) | ||||
−0.243616 | + | 0.969872i | \(0.578334\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 36.2719i | 1.16223i | ||||||||
\(975\) | − | 11.5824i | − | 0.370933i | ||||||
\(976\) | −2.41499 | −0.0773021 | ||||||||
\(977\) | −5.39548 | −0.172617 | −0.0863083 | − | 0.996268i | \(-0.527507\pi\) | ||||
−0.0863083 | + | 0.996268i | \(0.527507\pi\) | |||||||
\(978\) | −12.6206 | −0.403562 | ||||||||
\(979\) | −33.0457 | − | 19.2806i | −1.05615 | − | 0.616211i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 0.950748i | − | 0.0303550i | ||||||
\(982\) | −0.584864 | −0.0186638 | ||||||||
\(983\) | − | 21.8043i | − | 0.695449i | −0.937597 | − | 0.347724i | \(-0.886954\pi\) | ||
0.937597 | − | 0.347724i | \(-0.113046\pi\) | |||||||
\(984\) | −5.20158 | −0.165820 | ||||||||
\(985\) | 1.15428 | 0.0367785 | ||||||||
\(986\) | 34.4926 | 1.09847 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.08867 | −0.225521 | ||||||||
\(989\) | 49.2505i | 1.56608i | ||||||||
\(990\) | 1.57540 | − | 2.70014i | 0.0500696 | − | 0.0858162i | ||||
\(991\) | 9.04292 | 0.287258 | 0.143629 | − | 0.989632i | \(-0.454123\pi\) | ||||
0.143629 | + | 0.989632i | \(0.454123\pi\) | |||||||
\(992\) | 6.05783 | 0.192336 | ||||||||
\(993\) | 24.5734i | 0.779813i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.0832 | 0.383063 | ||||||||
\(996\) | 8.84143i | 0.280152i | ||||||||
\(997\) | −39.4853 | −1.25051 | −0.625256 | − | 0.780420i | \(-0.715005\pi\) | ||||
−0.625256 | + | 0.780420i | \(0.715005\pi\) | |||||||
\(998\) | 21.6453i | 0.685171i | ||||||||
\(999\) | 10.4379i | 0.330242i |
(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 | 3234.2.e.c.2155.5 | ✓ | 24 | |
7.6 | odd | 2 | 3234.2.e.d.2155.8 | yes | 24 | ||
11.10 | odd | 2 | 3234.2.e.d.2155.17 | yes | 24 | ||
77.76 | even | 2 | inner | 3234.2.e.c.2155.20 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.e.c.2155.5 | ✓ | 24 | 1.1 | even | 1 | trivial | |
3234.2.e.c.2155.20 | yes | 24 | 77.76 | even | 2 | inner | |
3234.2.e.d.2155.8 | yes | 24 | 7.6 | odd | 2 | ||
3234.2.e.d.2155.17 | yes | 24 | 11.10 | odd | 2 |