Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(401,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, 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("700.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.i (of order \(3\), degree \(2\), 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: | \(5.58952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1783323.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 401.1 | ||
Root | \(0.356769 - 0.617942i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 700.401 |
Dual form | 700.2.i.d.501.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.60220 | − | 2.77509i | −0.925031 | − | 1.60220i | −0.791511 | − | 0.611155i | \(-0.790705\pi\) |
−0.133520 | − | 0.991046i | \(-0.542628\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.53189 | − | 2.15715i | 0.579001 | − | 0.815327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.63409 | + | 6.29444i | −1.21136 | + | 2.09815i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.10220 | − | 3.64112i | −0.633837 | − | 1.09784i | −0.986760 | − | 0.162186i | \(-0.948146\pi\) |
0.352923 | − | 0.935652i | \(-0.385188\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.204402 | −0.0566908 | −0.0283454 | − | 0.999598i | \(-0.509024\pi\) | ||||
−0.0283454 | + | 0.999598i | \(0.509024\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.53189 | − | 4.38537i | −0.614074 | − | 1.06361i | −0.990546 | − | 0.137180i | \(-0.956196\pi\) |
0.376472 | − | 0.926428i | \(-0.377137\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.531894 | + | 0.921267i | −0.122025 | + | 0.211353i | −0.920566 | − | 0.390587i | \(-0.872272\pi\) |
0.798541 | + | 0.601940i | \(0.205605\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.44070 | − | 0.794959i | −1.84191 | − | 0.173474i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.07031 | − | 1.85383i | 0.223174 | − | 0.386549i | −0.732596 | − | 0.680664i | \(-0.761691\pi\) |
0.955770 | + | 0.294115i | \(0.0950247\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.6770 | 2.63214 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.47259 | −1.38763 | −0.693813 | − | 0.720156i | \(-0.744070\pi\) | ||||
−0.693813 | + | 0.720156i | \(0.744070\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.23630 | + | 7.33748i | 0.760861 | + | 1.31785i | 0.942407 | + | 0.334468i | \(0.108557\pi\) |
−0.181546 | + | 0.983382i | \(0.558110\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.73630 | + | 11.6676i | −1.17264 | + | 2.03107i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.30660 | + | 9.19130i | −0.872400 | + | 1.51104i | −0.0128933 | + | 0.999917i | \(0.504104\pi\) |
−0.859507 | + | 0.511124i | \(0.829229\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.327492 | + | 0.567233i | 0.0524407 | + | 0.0908300i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.5494 | 1.64754 | 0.823771 | − | 0.566923i | \(-0.191866\pi\) | ||||
0.823771 | + | 0.566923i | \(0.191866\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.26819 | −1.26089 | −0.630444 | − | 0.776235i | \(-0.717127\pi\) | ||||
−0.630444 | + | 0.776235i | \(0.717127\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.63409 | − | 2.83033i | 0.238357 | − | 0.412847i | −0.721886 | − | 0.692012i | \(-0.756724\pi\) |
0.960243 | + | 0.279165i | \(0.0900578\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.30660 | − | 6.60905i | −0.329515 | − | 0.944150i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.11320 | + | 14.0525i | −1.13608 | + | 1.96774i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.83850 | + | 4.91642i | 0.389897 | + | 0.675322i | 0.992435 | − | 0.122768i | \(-0.0391771\pi\) |
−0.602538 | + | 0.798090i | \(0.705844\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.40880 | 0.451507 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.602201 | − | 1.04304i | −0.0783999 | − | 0.135793i | 0.824160 | − | 0.566357i | \(-0.191648\pi\) |
−0.902560 | + | 0.430565i | \(0.858314\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.827492 | + | 1.43326i | −0.105950 | + | 0.183510i | −0.914126 | − | 0.405431i | \(-0.867122\pi\) |
0.808176 | + | 0.588941i | \(0.200455\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.01100 | + | 17.4817i | 1.00929 | + | 2.20249i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.20440 | − | 10.7463i | −0.757988 | − | 1.31287i | −0.943875 | − | 0.330303i | \(-0.892849\pi\) |
0.185887 | − | 0.982571i | \(-0.440484\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.85939 | −0.825773 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.591197 | −0.0701622 | −0.0350811 | − | 0.999384i | \(-0.511169\pi\) | ||||
−0.0350811 | + | 0.999384i | \(0.511169\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | − | 3.46410i | −0.234082 | − | 0.405442i | 0.724923 | − | 0.688830i | \(-0.241875\pi\) |
−0.959006 | + | 0.283387i | \(0.908542\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.0748 | − | 1.04304i | −1.26209 | − | 0.118866i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.27471 | + | 5.67196i | −0.368433 | + | 0.638146i | −0.989321 | − | 0.145754i | \(-0.953439\pi\) |
0.620887 | + | 0.783900i | \(0.286772\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0110 | − | 19.0716i | −1.22344 | − | 2.11907i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.88139 | −0.426038 | −0.213019 | − | 0.977048i | \(-0.568330\pi\) | ||||
−0.213019 | + | 0.977048i | \(0.568330\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.9726 | + | 20.7371i | 1.28360 | + | 2.22325i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.63409 | − | 8.02649i | 0.491213 | − | 0.850806i | −0.508736 | − | 0.860923i | \(-0.669887\pi\) |
0.999949 | + | 0.0101167i | \(0.00322032\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.313121 | + | 0.440925i | −0.0328241 | + | 0.0462215i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.5748 | − | 23.5122i | 1.40764 | − | 2.43810i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.33198 | −0.135242 | −0.0676209 | − | 0.997711i | \(-0.521541\pi\) | ||||
−0.0676209 | + | 0.997711i | \(0.521541\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 30.5584 | 3.07123 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.09568 | − | 5.36188i | −0.308032 | − | 0.533527i | 0.669900 | − | 0.742451i | \(-0.266337\pi\) |
−0.977932 | + | 0.208925i | \(0.933004\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.87039 | − | 8.43576i | 0.479894 | − | 0.831200i | −0.519840 | − | 0.854264i | \(-0.674009\pi\) |
0.999734 | + | 0.0230631i | \(0.00734186\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.92969 | − | 8.53848i | 0.476571 | − | 0.825446i | −0.523068 | − | 0.852291i | \(-0.675213\pi\) |
0.999640 | + | 0.0268449i | \(0.00854603\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.03841 | + | 3.53063i | 0.195245 | + | 0.338173i | 0.946981 | − | 0.321291i | \(-0.104117\pi\) |
−0.751736 | + | 0.659464i | \(0.770783\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 34.0090 | 3.22799 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.21744 | −0.208599 | −0.104300 | − | 0.994546i | \(-0.533260\pi\) | ||||
−0.104300 | + | 0.994546i | \(0.533260\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.742815 | − | 1.28659i | 0.0686732 | − | 0.118946i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.3385 | − | 1.25624i | −1.22274 | − | 0.115159i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.33850 | + | 5.78245i | −0.303500 | + | 0.525677i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.9023 | − | 29.2756i | −1.52403 | − | 2.63969i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.54942 | −0.581167 | −0.290583 | − | 0.956850i | \(-0.593849\pi\) | ||||
−0.290583 | + | 0.956850i | \(0.593849\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.2473 | + | 22.9450i | 1.16636 | + | 2.02019i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.50448 | − | 14.7302i | 0.743040 | − | 1.28698i | −0.208065 | − | 0.978115i | \(-0.566716\pi\) |
0.951105 | − | 0.308868i | \(-0.0999503\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.17251 | + | 2.55866i | 0.101669 | + | 0.221864i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.54290 | − | 14.7967i | −0.729869 | − | 1.26417i | −0.956938 | − | 0.290292i | \(-0.906248\pi\) |
0.227069 | − | 0.973879i | \(-0.427086\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.740780 | 0.0628322 | 0.0314161 | − | 0.999506i | \(-0.489998\pi\) | ||||
0.0314161 | + | 0.999506i | \(0.489998\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.4726 | −0.881951 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.429693 | + | 0.744250i | 0.0359327 | + | 0.0622373i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.6451 | + | 16.9901i | −1.20791 | + | 1.40132i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.20889 | − | 14.2182i | 0.672498 | − | 1.16480i | −0.304695 | − | 0.952450i | \(-0.598555\pi\) |
0.977193 | − | 0.212351i | \(-0.0681120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.263705 | − | 0.456750i | −0.0214600 | − | 0.0371698i | 0.855096 | − | 0.518470i | \(-0.173498\pi\) |
−0.876556 | + | 0.481300i | \(0.840165\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 36.8046 | 2.97547 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.74281 | − | 8.21480i | −0.378518 | − | 0.655612i | 0.612329 | − | 0.790603i | \(-0.290233\pi\) |
−0.990847 | + | 0.134991i | \(0.956899\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.09568 | − | 15.7542i | 0.721334 | − | 1.24939i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.35939 | − | 5.14868i | −0.185946 | − | 0.405773i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.42969 | − | 7.67245i | 0.346960 | − | 0.600953i | −0.638748 | − | 0.769416i | \(-0.720547\pi\) |
0.985708 | + | 0.168463i | \(0.0538805\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.33198 | −0.644748 | −0.322374 | − | 0.946612i | \(-0.604481\pi\) | ||||
−0.322374 | + | 0.946612i | \(0.604481\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9582 | −0.996786 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.86591 | − | 6.69594i | −0.295633 | − | 0.512052i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.17251 | + | 15.8872i | −0.697373 | + | 1.20789i | 0.272001 | + | 0.962297i | \(0.412314\pi\) |
−0.969374 | + | 0.245588i | \(0.921019\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.92969 | + | 3.34233i | −0.145045 | + | 0.251225i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.14061 | + | 3.70765i | 0.159997 | + | 0.277123i | 0.934867 | − | 0.354997i | \(-0.115518\pi\) |
−0.774870 | + | 0.632120i | \(0.782185\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.93621 | 0.218247 | 0.109123 | − | 0.994028i | \(-0.465196\pi\) | ||||
0.109123 | + | 0.994028i | \(0.465196\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.30324 | 0.392026 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.6451 | + | 18.4379i | −0.778447 | + | 1.34831i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 20.9517 | − | 29.5033i | 1.52401 | − | 2.14605i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.97259 | − | 10.3448i | 0.432162 | − | 0.748526i | −0.564898 | − | 0.825161i | \(-0.691084\pi\) |
0.997059 | + | 0.0766353i | \(0.0244177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.54290 | + | 6.13648i | 0.255023 | + | 0.441713i | 0.964902 | − | 0.262611i | \(-0.0845835\pi\) |
−0.709879 | + | 0.704324i | \(0.751250\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.48563 | 0.390835 | 0.195417 | − | 0.980720i | \(-0.437394\pi\) | ||||
0.195417 | + | 0.980720i | \(0.437394\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.04290 | − | 13.9307i | −0.570146 | − | 0.987522i | −0.996550 | − | 0.0829891i | \(-0.973553\pi\) |
0.426405 | − | 0.904533i | \(-0.359780\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.8814 | + | 34.4356i | −1.40233 | + | 2.42890i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.4472 | + | 16.1195i | −0.803437 | + | 1.13137i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.77919 | + | 13.4740i | 0.540691 | + | 0.936505i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.47259 | 0.309376 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.6002 | 1.14280 | 0.571401 | − | 0.820671i | \(-0.306400\pi\) | ||||
0.571401 | + | 0.820671i | \(0.306400\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.947216 | + | 1.64063i | 0.0649022 | + | 0.112414i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.3176 | + | 2.10191i | 1.51502 | + | 0.142687i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.40880 | + | 11.1004i | −0.433067 | + | 0.750094i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.517523 | + | 0.896376i | 0.0348124 | + | 0.0602968i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.4856 | 1.03699 | 0.518497 | − | 0.855079i | \(-0.326492\pi\) | ||||
0.518497 | + | 0.855079i | \(0.326492\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.89128 | − | 3.27579i | −0.125529 | − | 0.217422i | 0.796411 | − | 0.604756i | \(-0.206729\pi\) |
−0.921939 | + | 0.387334i | \(0.873396\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.60220 | − | 9.70330i | 0.370204 | − | 0.641212i | −0.619393 | − | 0.785081i | \(-0.712621\pi\) |
0.989597 | + | 0.143869i | \(0.0459545\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.8495 | + | 32.4047i | 0.977025 | + | 2.13208i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.97259 | + | 10.3448i | −0.391277 | + | 0.677712i | −0.992618 | − | 0.121280i | \(-0.961300\pi\) |
0.601341 | + | 0.798993i | \(0.294633\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.9870 | 1.36325 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.3450 | 0.992587 | 0.496293 | − | 0.868155i | \(-0.334694\pi\) | ||||
0.496293 | + | 0.868155i | \(0.334694\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.19788 | + | 12.4671i | 0.463656 | + | 0.803076i | 0.999140 | − | 0.0414694i | \(-0.0132039\pi\) |
−0.535483 | + | 0.844546i | \(0.679871\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7682 | + | 25.5793i | −0.947380 | + | 1.64091i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.108720 | − | 0.188308i | 0.00691768 | − | 0.0119818i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.21877 | + | 10.7712i | 0.394099 | + | 0.682599i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.4178 | −1.22564 | −0.612819 | − | 0.790223i | \(-0.709965\pi\) | ||||
−0.612819 | + | 0.790223i | \(0.709965\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.00000 | −0.565825 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.93621 | + | 12.0139i | −0.432669 | + | 0.749405i | −0.997102 | − | 0.0760740i | \(-0.975761\pi\) |
0.564433 | + | 0.825479i | \(0.309095\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.6979 | + | 25.5272i | 0.726871 | + | 1.58619i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27.1561 | − | 47.0357i | 1.68092 | − | 2.91144i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.72978 | + | 2.99606i | 0.106663 | + | 0.184745i | 0.914416 | − | 0.404775i | \(-0.132650\pi\) |
−0.807754 | + | 0.589520i | \(0.799317\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −29.6990 | −1.81755 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.8320 | − | 22.2256i | −0.782379 | − | 1.35512i | −0.930552 | − | 0.366159i | \(-0.880672\pi\) |
0.148173 | − | 0.988962i | \(-0.452661\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.83850 | + | 17.0408i | −0.597646 | + | 1.03515i | 0.395522 | + | 0.918457i | \(0.370564\pi\) |
−0.993168 | + | 0.116697i | \(0.962769\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.72529 | + | 0.162491i | 0.104419 | + | 0.00983439i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.07479 | + | 15.7180i | 0.545251 | + | 0.944403i | 0.998591 | + | 0.0530653i | \(0.0168991\pi\) |
−0.453340 | + | 0.891338i | \(0.649768\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −61.5804 | −3.68672 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.5364 | −1.10579 | −0.552894 | − | 0.833252i | \(-0.686476\pi\) | ||||
−0.552894 | + | 0.833252i | \(0.686476\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.2792 | − | 24.7323i | −0.848810 | − | 1.47018i | −0.882271 | − | 0.470742i | \(-0.843986\pi\) |
0.0334610 | − | 0.999440i | \(-0.489347\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.1606 | − | 22.7567i | 0.953929 | − | 1.34328i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.32097 | + | 7.48415i | −0.254175 | + | 0.440244i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.13409 | + | 3.69636i | 0.125103 | + | 0.216684i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.5494 | 1.49261 | 0.746306 | − | 0.665603i | \(-0.231825\pi\) | ||||
0.746306 | + | 0.665603i | \(0.231825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −28.7518 | − | 49.7996i | −1.66835 | − | 2.88966i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.218772 | + | 0.378925i | −0.0126519 | + | 0.0219138i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.6660 | + | 17.8357i | −0.730055 | + | 1.02803i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.91981 | + | 17.1816i | −0.569878 | + | 0.987058i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.1145 | 0.577267 | 0.288634 | − | 0.957440i | \(-0.406799\pi\) | ||||
0.288634 | + | 0.957440i | \(0.406799\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −31.2134 | −1.77567 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.0858 | − | 29.5935i | −0.968847 | − | 1.67809i | −0.698905 | − | 0.715215i | \(-0.746329\pi\) |
−0.269942 | − | 0.962877i | \(-0.587005\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.30660 | − | 7.45925i | 0.243424 | − | 0.421622i | −0.718264 | − | 0.695771i | \(-0.755063\pi\) |
0.961687 | + | 0.274149i | \(0.0883962\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.90880 | − | 6.77025i | 0.219540 | − | 0.380255i | −0.735127 | − | 0.677929i | \(-0.762878\pi\) |
0.954667 | + | 0.297674i | \(0.0962109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.7089 | + | 27.2086i | 0.879529 | + | 1.52339i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −31.5934 | −1.76337 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.38680 | 0.299729 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.53189 | − | 11.3136i | 0.361215 | − | 0.625642i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.60220 | − | 7.86076i | −0.198596 | − | 0.433378i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.0494 | − | 19.1382i | 0.607331 | − | 1.05193i | −0.384348 | − | 0.923188i | \(-0.625574\pi\) |
0.991678 | − | 0.128739i | \(-0.0410931\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −38.5694 | − | 66.8041i | −2.11359 | − | 3.66084i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.29020 | 0.0702815 | 0.0351408 | − | 0.999382i | \(-0.488812\pi\) | ||||
0.0351408 | + | 0.999382i | \(0.488812\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.55278 | + | 6.15360i | 0.192961 | + | 0.334218i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.8111 | − | 30.8497i | 0.964524 | − | 1.67061i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.7902 | − | 5.14868i | −0.960580 | − | 0.278003i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.72978 | − | 8.19221i | −0.253908 | − | 0.439781i | 0.710691 | − | 0.703505i | \(-0.248383\pi\) |
−0.964598 | + | 0.263724i | \(0.915049\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.5494 | 0.832341 | 0.416171 | − | 0.909287i | \(-0.363372\pi\) | ||||
0.416171 | + | 0.909287i | \(0.363372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.79560 | −0.149218 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.56827 | + | 13.1086i | 0.402818 | + | 0.697702i | 0.994065 | − | 0.108789i | \(-0.0346972\pi\) |
−0.591246 | + | 0.806491i | \(0.701364\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.8848 | + | 39.0283i | 0.946562 | + | 2.06560i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.15947 | + | 8.93646i | −0.272306 | + | 0.471648i | −0.969452 | − | 0.245281i | \(-0.921120\pi\) |
0.697146 | + | 0.716930i | \(0.254453\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.93418 | + | 15.4744i | 0.470220 | + | 0.814445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.3958 | 1.12299 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.96811 | + | 15.5332i | 0.468131 | + | 0.810827i | 0.999337 | − | 0.0364158i | \(-0.0115941\pi\) |
−0.531205 | + | 0.847243i | \(0.678261\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −38.3376 | + | 66.4026i | −1.99577 | + | 3.45678i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.9537 | + | 1.40837i | 0.776359 | + | 0.0731188i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.09568 | + | 14.0221i | −0.419179 | + | 0.726038i | −0.995857 | − | 0.0909327i | \(-0.971015\pi\) |
0.576679 | + | 0.816971i | \(0.304349\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.52741 | 0.0786656 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.6002 | −0.647227 | −0.323614 | − | 0.946189i | \(-0.604898\pi\) | ||||
−0.323614 | + | 0.946189i | \(0.604898\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.4935 | + | 18.1752i | 0.537597 | + | 0.931146i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.58783 | − | 13.1425i | 0.387720 | − | 0.671551i | −0.604422 | − | 0.796664i | \(-0.706596\pi\) |
0.992142 | + | 0.125113i | \(0.0399294\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 30.0474 | − | 52.0436i | 1.52739 | − | 2.64552i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.6197 | + | 25.3221i | 0.741249 | + | 1.28388i | 0.951927 | + | 0.306326i | \(0.0990998\pi\) |
−0.210677 | + | 0.977556i | \(0.567567\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.8396 | −0.548183 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −54.5036 | −2.74934 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.63409 | − | 9.75854i | 0.282767 | − | 0.489767i | −0.689298 | − | 0.724478i | \(-0.742081\pi\) |
0.972065 | + | 0.234711i | \(0.0754143\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.22192 | − | 7.35330i | 0.261423 | − | 0.368126i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.01100 | − | 15.6075i | 0.449988 | − | 0.779402i | −0.548397 | − | 0.836218i | \(-0.684762\pi\) |
0.998385 | + | 0.0568162i | \(0.0180949\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.865905 | − | 1.49979i | −0.0431338 | − | 0.0747100i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.6222 | 2.21184 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.89576 | + | 13.6759i | 0.390420 | + | 0.676228i | 0.992505 | − | 0.122204i | \(-0.0389963\pi\) |
−0.602085 | + | 0.798432i | \(0.705663\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −27.3749 | + | 47.4147i | −1.35030 | + | 2.33879i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.17251 | − | 0.298792i | −0.156109 | − | 0.0147026i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.18688 | − | 2.05573i | −0.0581217 | − | 0.100670i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.4726 | −0.658179 | −0.329090 | − | 0.944299i | \(-0.606742\pi\) | ||||
−0.329090 | + | 0.944299i | \(0.606742\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.8396 | −1.30808 | −0.654041 | − | 0.756459i | \(-0.726928\pi\) | ||||
−0.654041 | + | 0.756459i | \(0.726928\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.8769 | + | 20.5714i | 0.577475 | + | 1.00022i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.82413 | + | 3.98063i | 0.0882756 | + | 0.192636i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.37691 | − | 2.38488i | 0.0664778 | − | 0.115143i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.02537 | − | 13.9004i | −0.386569 | − | 0.669557i | 0.605417 | − | 0.795909i | \(-0.293006\pi\) |
−0.991985 | + | 0.126352i | \(0.959673\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.910136 | −0.0437383 | −0.0218692 | − | 0.999761i | \(-0.506962\pi\) | ||||
−0.0218692 | + | 0.999761i | \(0.506962\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.13858 | + | 1.97208i | 0.0544656 | + | 0.0943373i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.9517 | − | 32.8253i | 0.904515 | − | 1.56667i | 0.0829488 | − | 0.996554i | \(-0.473566\pi\) |
0.821566 | − | 0.570113i | \(-0.193100\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 49.9827 | + | 9.49916i | 2.38013 | + | 0.452341i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.44070 | + | 5.95946i | −0.163472 | + | 0.283143i | −0.936112 | − | 0.351703i | \(-0.885603\pi\) |
0.772639 | + | 0.634845i | \(0.218936\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −52.6091 | −2.48833 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.43754 | 0.303807 | 0.151903 | − | 0.988395i | \(-0.451460\pi\) | ||||
0.151903 | + | 0.988395i | \(0.451460\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.1770 | − | 38.4117i | −1.04427 | − | 1.80874i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.845015 | + | 1.46361i | −0.0397023 | + | 0.0687664i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.64713 | + | 8.04907i | −0.217384 | + | 0.376520i | −0.954007 | − | 0.299783i | \(-0.903086\pi\) |
0.736624 | + | 0.676303i | \(0.236419\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −34.6287 | − | 59.9787i | −1.61633 | − | 2.79956i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.29020 | 0.432688 | 0.216344 | − | 0.976317i | \(-0.430587\pi\) | ||||
0.216344 | + | 0.976317i | \(0.430587\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.6091 | 1.37605 | 0.688027 | − | 0.725685i | \(-0.258477\pi\) | ||||
0.688027 | + | 0.725685i | \(0.258477\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.0319 | + | 22.5719i | −0.603044 | + | 1.04450i | 0.389313 | + | 0.921105i | \(0.372712\pi\) |
−0.992357 | + | 0.123398i | \(0.960621\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.6860 | − | 3.07842i | −1.50930 | − | 0.142148i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.1979 | + | 26.3235i | −0.700281 | + | 1.21292i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.3814 | + | 30.1055i | 0.799197 | + | 1.38425i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −41.2615 | −1.88923 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.552784 | + | 0.957450i | 0.0252573 | + | 0.0437470i | 0.878378 | − | 0.477967i | \(-0.158626\pi\) |
−0.853120 | + | 0.521714i | \(0.825293\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.08468 | − | 1.87872i | 0.0494570 | − | 0.0856621i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.5079 | + | 14.7967i | −0.478124 | + | 0.673275i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.59568 | + | 4.49585i | 0.117622 | + | 0.203727i | 0.918825 | − | 0.394666i | \(-0.129140\pi\) |
−0.801203 | + | 0.598393i | \(0.795806\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −28.3890 | −1.28380 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.6640 | −1.29359 | −0.646793 | − | 0.762666i | \(-0.723890\pi\) | ||||
−0.646793 | + | 0.762666i | \(0.723890\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.9198 | + | 32.7701i | 0.852105 | + | 1.47589i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.905651 | + | 1.27530i | −0.0406240 | + | 0.0572051i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.0364 | − | 22.5797i | 0.583588 | − | 1.01080i | −0.411461 | − | 0.911427i | \(-0.634981\pi\) |
0.995050 | − | 0.0993776i | \(-0.0316852\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.3495 | + | 23.1220i | 0.596412 | + | 1.03302i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.80864 | −0.392758 | −0.196379 | − | 0.980528i | \(-0.562918\pi\) | ||||
−0.196379 | + | 0.980528i | \(0.562918\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.7617 | + | 35.9603i | 0.922058 | + | 1.59705i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.0090 | − | 19.0681i | 0.487964 | − | 0.845178i | −0.511940 | − | 0.859021i | \(-0.671073\pi\) |
0.999904 | + | 0.0138427i | \(0.00440640\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.5364 | − | 0.992334i | −0.466102 | − | 0.0438983i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.27471 | + | 12.6002i | −0.321186 | + | 0.556311i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.7408 | −0.604319 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 58.7848 | 2.58037 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.54942 | + | 13.0760i | 0.330746 | + | 0.572869i | 0.982658 | − | 0.185426i | \(-0.0593663\pi\) |
−0.651912 | + | 0.758294i | \(0.726033\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.29560 | + | 3.97609i | −0.100380 | + | 0.173862i | −0.911841 | − | 0.410543i | \(-0.865339\pi\) |
0.811462 | + | 0.584406i | \(0.198672\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.4517 | − | 37.1554i | 0.934451 | − | 1.61852i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.20889 | + | 15.9503i | 0.400386 | + | 0.693490i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.75382 | 0.379883 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.15632 | −0.0934005 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.85939 | − | 11.8808i | 0.296004 | − | 0.512695i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.2154 | + | 22.2922i | −0.827666 | + | 0.960192i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.83850 | + | 11.8446i | −0.294010 | + | 0.509240i | −0.974754 | − | 0.223281i | \(-0.928323\pi\) |
0.680744 | + | 0.732521i | \(0.261657\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.70440 | − | 8.14826i | −0.201885 | − | 0.349675i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.3581 | 0.485635 | 0.242818 | − | 0.970072i | \(-0.421928\pi\) | ||||
0.242818 | + | 0.970072i | \(0.421928\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.01437 | − | 10.4172i | −0.256687 | − | 0.444595i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.97463 | − | 6.88425i | 0.169325 | − | 0.293279i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.21877 | + | 15.7529i | 0.306973 | + | 0.669881i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.19788 | + | 14.1991i | 0.347355 | + | 0.601637i | 0.985779 | − | 0.168048i | \(-0.0537464\pi\) |
−0.638423 | + | 0.769685i | \(0.720413\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.69003 | 0.0714807 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 68.2223 | 2.88035 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.43621 | − | 4.21964i | −0.102674 | − | 0.177837i | 0.810111 | − | 0.586276i | \(-0.199407\pi\) |
−0.912786 | + | 0.408439i | \(0.866073\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −58.0081 | − | 5.46330i | −2.43611 | − | 0.229437i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.9277 | − | 32.7837i | 0.793489 | − | 1.37436i | −0.130306 | − | 0.991474i | \(-0.541596\pi\) |
0.923794 | − | 0.382889i | \(-0.125071\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.8704 | + | 36.1486i | 0.873399 | + | 1.51277i | 0.858459 | + | 0.512882i | \(0.171422\pi\) |
0.0149398 | + | 0.999888i | \(0.495244\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −38.2772 | −1.59905 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.5265 | + | 37.2850i | 0.896160 | + | 1.55219i | 0.832363 | + | 0.554231i | \(0.186988\pi\) |
0.0637967 | + | 0.997963i | \(0.479679\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.3529 | − | 19.6637i | 0.471809 | − | 0.817197i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.94588 | + | 8.37275i | −0.246677 | + | 0.347360i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.9342 | − | 20.6706i | 0.494263 | − | 0.856089i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.67699 | 0.234315 | 0.117157 | − | 0.993113i | \(-0.462622\pi\) | ||||
0.117157 | + | 0.993113i | \(0.462622\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.01304 | −0.371376 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.78908 | − | 15.2231i | −0.361534 | − | 0.626196i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.47259 | − | 7.74675i | 0.183667 | − | 0.318121i | −0.759459 | − | 0.650555i | \(-0.774536\pi\) |
0.943127 | + | 0.332434i | \(0.107870\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.7727 | + | 44.6396i | −1.05481 | + | 1.82698i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.6132 | + | 21.8467i | 0.515362 | + | 0.892632i | 0.999841 | + | 0.0178298i | \(0.00567570\pi\) |
−0.484479 | + | 0.874803i | \(0.660991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.3409 | 0.625770 | 0.312885 | − | 0.949791i | \(-0.398705\pi\) | ||||
0.312885 | + | 0.949791i | \(0.398705\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 90.1895 | 3.67280 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.4681 | − | 18.1313i | 0.424887 | − | 0.735926i | −0.571523 | − | 0.820586i | \(-0.693647\pi\) |
0.996410 | + | 0.0846599i | \(0.0269804\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 63.0739 | + | 5.94040i | 2.55588 | + | 0.240717i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.334011 | + | 0.578525i | −0.0135127 | + | 0.0234046i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.65947 | − | 4.60634i | −0.107415 | − | 0.186048i | 0.807307 | − | 0.590131i | \(-0.200924\pi\) |
−0.914722 | + | 0.404083i | \(0.867591\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.6262 | 1.15245 | 0.576225 | − | 0.817291i | \(-0.304525\pi\) | ||||
0.576225 | + | 0.817291i | \(0.304525\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.7812 | + | 18.6736i | 0.433334 | + | 0.750557i | 0.997158 | − | 0.0753383i | \(-0.0240037\pi\) |
−0.563824 | + | 0.825895i | \(0.690670\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.6386 | − | 25.3548i | 0.587426 | − | 1.01745i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.2154 | − | 22.2922i | −0.409272 | − | 0.893117i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.16599 | − | 12.4119i | −0.286182 | − | 0.495682i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 53.7430 | 2.14287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.1365 | −1.00067 | −0.500335 | − | 0.865832i | \(-0.666790\pi\) | ||||
−0.500335 | + | 0.865832i | \(0.666790\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.5968 | − | 46.0670i | −1.05713 | − | 1.83100i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.471473 | + | 1.35090i | 0.0186804 | + | 0.0535246i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.14847 | − | 3.72125i | 0.0849920 | − | 0.147210i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.0539 | − | 38.1985i | −0.871077 | − | 1.50875i | −0.860884 | − | 0.508801i | \(-0.830089\pi\) |
−0.0101927 | − | 0.999948i | \(-0.503244\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.4816 | 0.649969 | 0.324985 | − | 0.945719i | \(-0.394641\pi\) | ||||
0.324985 | + | 0.945719i | \(0.394641\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.7199 | − | 27.2276i | −0.618013 | − | 1.07043i | −0.989848 | − | 0.142131i | \(-0.954605\pi\) |
0.371835 | − | 0.928299i | \(-0.378729\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.53189 | + | 4.38537i | −0.0993855 | + | 0.172141i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29.9243 | − | 65.3011i | −1.17283 | − | 2.55935i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.4387 | − | 35.4008i | 0.799827 | − | 1.38534i | −0.119902 | − | 0.992786i | \(-0.538258\pi\) |
0.919729 | − | 0.392555i | \(-0.128409\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.0728 | 1.13424 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.6860 | −1.81863 | −0.909313 | − | 0.416112i | \(-0.863392\pi\) | ||||
−0.909313 | + | 0.416112i | \(0.863392\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.0637877 | − | 0.110484i | −0.00248106 | − | 0.00429731i | 0.864782 | − | 0.502147i | \(-0.167456\pi\) |
−0.867263 | + | 0.497850i | \(0.834123\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.65835 | − | 2.87235i | 0.0644050 | − | 0.111553i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.99797 | + | 13.8529i | −0.309682 | + | 0.536386i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.8111 | − | 42.9741i | −0.959252 | − | 1.66147i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.95822 | 0.268619 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.1936 | −1.85773 | −0.928863 | − | 0.370423i | \(-0.879213\pi\) | ||||
−0.928863 | + | 0.370423i | \(0.879213\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.2089 | + | 40.1990i | −0.891990 | + | 1.54497i | −0.0545037 | + | 0.998514i | \(0.517358\pi\) |
−0.837486 | + | 0.546458i | \(0.815976\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.04045 | + | 2.87328i | −0.0783052 | + | 0.110266i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.06042 | + | 10.4970i | −0.232236 | + | 0.402244i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.7747 | + | 37.7149i | 0.833186 | + | 1.44312i | 0.895499 | + | 0.445064i | \(0.146819\pi\) |
−0.0623127 | + | 0.998057i | \(0.519848\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −35.9034 | −1.36980 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.580193 | − | 1.00492i | −0.0221036 | − | 0.0382845i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.0474 | − | 22.5987i | 0.496346 | − | 0.859696i | −0.503645 | − | 0.863911i | \(-0.668008\pi\) |
0.999991 | + | 0.00421436i | \(0.00134147\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 46.8122 | − | 65.9191i | 1.77825 | − | 2.50406i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.7100 | − | 46.2631i | −1.01171 | − | 1.75234i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 38.2772 | 1.44778 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.7277 | 0.820645 | 0.410323 | − | 0.911940i | \(-0.365416\pi\) | ||||
0.410323 | + | 0.911940i | \(0.365416\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.64510 | − | 9.77760i | −0.212909 | − | 0.368769i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.3086 | − | 1.53597i | −0.613349 | − | 0.0577663i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.53841 | + | 14.7890i | −0.320667 | + | 0.555411i | −0.980626 | − | 0.195890i | \(-0.937240\pi\) |
0.659959 | + | 0.751302i | \(0.270574\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.8012 | − | 41.2249i | −0.892615 | − | 1.54605i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.1365 | 0.679219 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.5858 | − | 42.5838i | −0.918173 | − | 1.59032i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.6231 | + | 23.5959i | −0.508056 | + | 0.879978i | 0.491901 | + | 0.870651i | \(0.336302\pi\) |
−0.999957 | + | 0.00932687i | \(0.997031\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7363 | − | 23.4289i | −0.399841 | − | 0.872536i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.0649 | − | 39.9496i | 0.857793 | − | 1.48574i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.9232 | −0.738910 | −0.369455 | − | 0.929249i | \(-0.620456\pi\) | ||||
−0.369455 | + | 0.929249i | \(0.620456\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.5804 | 1.05853 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.9342 | + | 36.2591i | 0.774279 | + | 1.34109i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.5813 | − | 26.9876i | 0.575509 | − | 0.996811i | −0.420477 | − | 0.907303i | \(-0.638137\pi\) |
0.995986 | − | 0.0895075i | \(-0.0285293\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26.0858 | + | 45.1819i | −0.960883 | + | 1.66430i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.950583 | − | 1.64646i | −0.0349678 | − | 0.0605659i | 0.848012 | − | 0.529977i | \(-0.177800\pi\) |
−0.882980 | + | 0.469411i | \(0.844466\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.696765 | −0.0255963 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.0660 | −1.32313 | −0.661567 | − | 0.749886i | \(-0.730108\pi\) | ||||
−0.661567 | + | 0.749886i | \(0.730108\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.1054 | − | 24.4312i | 0.516088 | − | 0.893890i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.8670 | − | 23.7141i | −0.397072 | − | 0.866496i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.384761 | − | 0.666425i | 0.0140401 | − | 0.0243182i | −0.858920 | − | 0.512110i | \(-0.828864\pi\) |
0.872960 | + | 0.487792i | \(0.162197\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.1112 | + | 53.8861i | 1.13375 | + | 1.96372i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.9542 | 0.543518 | 0.271759 | − | 0.962365i | \(-0.412395\pi\) | ||||
0.271759 | + | 0.962365i | \(0.412395\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.4198 | + | 24.9758i | 0.523406 | + | 0.906565i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.58580 | + | 16.6031i | −0.347485 | + | 0.601861i | −0.985802 | − | 0.167912i | \(-0.946298\pi\) |
0.638317 | + | 0.769773i | \(0.279631\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.7387 | + | 1.01139i | 0.388769 | + | 0.0366149i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.123091 | + | 0.213199i | 0.00444455 | + | 0.00769819i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.3189 | 1.30969 | 0.654847 | − | 0.755761i | \(-0.272733\pi\) | ||||
0.654847 | + | 0.755761i | \(0.272733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 44.4528 | 1.60093 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.7343 | − | 41.1089i | −0.853662 | − | 1.47859i | −0.877881 | − | 0.478879i | \(-0.841043\pi\) |
0.0242187 | − | 0.999707i | \(-0.492290\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 52.0981 | − | 73.3625i | 1.86901 | − | 2.63186i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.61117 | + | 9.71883i | −0.201041 | + | 0.348213i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.24281 | + | 2.15262i | 0.0444714 | + | 0.0770267i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −102.203 | −3.65242 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.94273 | + | 6.82901i | 0.140543 | + | 0.243428i | 0.927701 | − | 0.373323i | \(-0.121782\pi\) |
−0.787158 | + | 0.616751i | \(0.788448\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.54290 | − | 9.60058i | 0.197332 | − | 0.341790i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.39688 | + | 4.78335i | −0.120779 | + | 0.170076i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.169141 | − | 0.292960i | 0.00600636 | − | 0.0104033i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.6132 | 1.19064 | 0.595320 | − | 0.803488i | \(-0.297025\pi\) | ||||
0.595320 | + | 0.803488i | \(0.297025\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.5494 | −0.585476 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 33.6815 | + | 58.3380i | 1.19008 | + | 2.06127i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.40880 | + | 14.5645i | −0.296740 | + | 0.513969i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −41.1188 | + | 71.2199i | −1.44745 | + | 2.50706i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.59568 | + | 7.95995i | 0.161576 | + | 0.279857i | 0.935434 | − | 0.353502i | \(-0.115009\pi\) |
−0.773858 | + | 0.633359i | \(0.781676\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.6483 | 0.760173 | 0.380086 | − | 0.924951i | \(-0.375894\pi\) | ||||
0.380086 | + | 0.924951i | \(0.375894\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 63.0530 | 2.21136 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.39780 | − | 7.61721i | 0.153860 | − | 0.266493i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.63746 | − | 3.57329i | −0.0572175 | − | 0.124861i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.1307 | + | 27.9392i | −0.562966 | + | 0.975086i | 0.434269 | + | 0.900783i | \(0.357007\pi\) |
−0.997236 | + | 0.0743032i | \(0.976327\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.72192 | + | 9.91066i | 0.199454 | + | 0.345464i | 0.948351 | − | 0.317222i | \(-0.102750\pi\) |
−0.748898 | + | 0.662686i | \(0.769417\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.82658 | −0.341704 | −0.170852 | − | 0.985297i | \(-0.554652\pi\) | ||||
−0.170852 | + | 0.985297i | \(0.554652\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.1287 | − | 33.1319i | −0.664367 | − | 1.15072i | −0.979457 | − | 0.201655i | \(-0.935368\pi\) |
0.315090 | − | 0.949062i | \(-0.397965\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.0793 | − | 50.3668i | 1.00875 | − | 1.74720i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23.1431 | + | 26.8487i | −0.801860 | + | 0.930253i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 57.9398 | + | 100.355i | 2.00269 | + | 3.46876i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.6900 | 1.05954 | 0.529769 | − | 0.848142i | \(-0.322279\pi\) | ||||
0.529769 | + | 0.848142i | \(0.322279\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.8396 | 0.925504 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.6990 | + | 51.4402i | 1.02289 | + | 1.77169i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.35939 | + | 16.0597i | 0.252872 | + | 0.551819i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −45.7563 | + | 79.2522i | −1.57035 | + | 2.71993i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.3594 | + | 19.6750i | 0.389395 | + | 0.674451i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.4569 | −1.35098 | −0.675489 | − | 0.737370i | \(-0.736067\pi\) | ||||
−0.675489 | + | 0.737370i | \(0.736067\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.9297 | − | 34.5192i | −0.680785 | − | 1.17915i | −0.974742 | − | 0.223336i | \(-0.928305\pi\) |
0.293956 | − | 0.955819i | \(-0.405028\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.75719 | − | 16.8999i | 0.332911 | − | 0.576619i | −0.650170 | − | 0.759788i | \(-0.725303\pi\) |
0.983081 | + | 0.183170i | \(0.0586358\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −89.0444 | − | 8.38635i | −3.03463 | − | 0.285806i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.9661 | + | 32.8502i | −0.645613 | + | 1.11823i | 0.338547 | + | 0.940949i | \(0.390065\pi\) |
−0.984160 | + | 0.177284i | \(0.943269\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.6923 | 0.940479 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.5364 | 0.934108 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.26819 | + | 2.19657i | 0.0429710 | + | 0.0744279i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.84053 | − | 8.38404i | 0.163827 | − | 0.283757i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.47259 | − | 9.47881i | 0.184796 | − | 0.320077i | −0.758712 | − | 0.651427i | \(-0.774171\pi\) |
0.943508 | + | 0.331350i | \(0.107504\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −40.9353 | − | 70.9020i | −1.38071 | − | 2.39147i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.2592 | −0.547787 | −0.273894 | − | 0.961760i | \(-0.588312\pi\) | ||||
−0.273894 | + | 0.961760i | \(0.588312\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.2511 | −0.782461 | −0.391231 | − | 0.920293i | \(-0.627951\pi\) | ||||
−0.391231 | + | 0.920293i | \(0.627951\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.6197 | + | 20.1260i | −0.390152 | + | 0.675763i | −0.992469 | − | 0.122494i | \(-0.960911\pi\) |
0.602317 | + | 0.798257i | \(0.294244\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.0330 | + | 14.1281i | −0.336496 | + | 0.473841i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −46.2947 | + | 80.1847i | −1.55093 | + | 2.68629i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.73833 | + | 3.01088i | 0.0581710 | + | 0.100755i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.40207 | 0.0468137 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31.6561 | − | 54.8300i | −1.05579 | − | 1.82868i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.3735 | − | 24.8957i | 0.478852 | − | 0.829396i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 69.7893 | + | 6.57287i | 2.32244 | + | 0.218731i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.1132 | − | 38.3012i | −0.734257 | − | 1.27177i | −0.955049 | − | 0.296449i | \(-0.904197\pi\) |
0.220792 | − | 0.975321i | \(-0.429136\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 45.0000 | 1.49256 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.4218 | −0.908526 | −0.454263 | − | 0.890868i | \(-0.650097\pi\) | ||||
−0.454263 | + | 0.890868i | \(0.650097\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.15947 | + | 14.1326i | 0.270039 | + | 0.467721i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.7473 | − | 40.9106i | −0.619090 | − | 1.35099i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.6581 | − | 28.8527i | 0.549501 | − | 0.951764i | −0.448807 | − | 0.893628i | \(-0.648151\pi\) |
0.998309 | − | 0.0581356i | \(-0.0185156\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.2055 | − | 28.0688i | −0.533990 | − | 0.924898i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.120842 | 0.00397755 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 35.3989 | + | 61.3127i | 1.16265 | + | 2.01377i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.62421 | − | 11.4735i | 0.217333 | − | 0.376432i | −0.736659 | − | 0.676265i | \(-0.763598\pi\) |
0.953992 | + | 0.299833i | \(0.0969308\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.31557 | + | 1.39032i | 0.239758 | + | 0.0455658i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −54.7497 | + | 94.8293i | −1.79243 | + | 3.10457i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.1365 | 0.331146 | 0.165573 | − | 0.986197i | \(-0.447053\pi\) | ||||
0.165573 | + | 0.986197i | \(0.447053\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.6002 | −0.900697 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.4342 | + | 28.4648i | 0.535739 | + | 0.927927i | 0.999127 | + | 0.0417716i | \(0.0133002\pi\) |
−0.463388 | + | 0.886155i | \(0.653366\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.2911 | − | 19.5568i | 0.367689 | − | 0.636856i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.1626 | + | 19.3342i | −0.362736 | + | 0.628278i | −0.988410 | − | 0.151807i | \(-0.951491\pi\) |
0.625674 | + | 0.780085i | \(0.284824\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.408803 | + | 0.708068i | 0.0132703 | + | 0.0229849i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.0507 | −0.812326 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.4685 | 1.53766 | 0.768828 | − | 0.639455i | \(-0.220840\pi\) | ||||
0.768828 | + | 0.639455i | \(0.220840\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 50.3376 | − | 87.1872i | 1.62718 | − | 2.81836i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −45.0056 | − | 4.23870i | −1.45331 | − | 0.136875i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.3924 | + | 35.3207i | −0.657819 | + | 1.13938i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 35.8299 | + | 62.0593i | 1.15460 | + | 1.99983i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.3189 | −0.685571 | −0.342785 | − | 0.939414i | \(-0.611370\pi\) | ||||
−0.342785 | + | 0.939414i | \(0.611370\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.63073 | − | 14.9489i | −0.277259 | − | 0.480227i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.7812 | − | 25.6018i | 0.474352 | − | 0.821602i | −0.525217 | − | 0.850969i | \(-0.676016\pi\) |
0.999569 | + | 0.0293666i | \(0.00934901\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.13480 | − | 1.59797i | 0.0363799 | − | 0.0512287i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.919807 | − | 1.59315i | −0.0294272 | − | 0.0509695i | 0.850937 | − | 0.525268i | \(-0.176035\pi\) |
−0.880364 | + | 0.474299i | \(0.842702\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −38.9672 | −1.24540 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.6311 | −0.946050 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.68800 | − | 9.85190i | −0.181419 | − | 0.314227i | 0.760945 | − | 0.648816i | \(-0.224736\pi\) |
−0.942364 | + | 0.334590i | \(0.891402\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.0429 | + | 22.5910i | −0.510651 | + | 0.719078i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.84950 | + | 15.3278i | −0.281398 | + | 0.487395i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.89576 | − | 6.74766i | −0.123753 | − | 0.214347i | 0.797492 | − | 0.603330i | \(-0.206160\pi\) |
−0.921245 | + | 0.388983i | \(0.872826\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −70.8135 | −2.24720 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.71092 | + | 9.89160i | 0.180867 | + | 0.313270i | 0.942176 | − | 0.335119i | \(-0.108776\pi\) |
−0.761309 | + | 0.648389i | \(0.775443\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −72.5784 | + | 125.709i | −2.29628 | + | 3.97727i |
(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 | 700.2.i.d.401.1 | ✓ | 6 | |
5.2 | odd | 4 | 700.2.r.d.149.1 | 12 | |||
5.3 | odd | 4 | 700.2.r.d.149.6 | 12 | |||
5.4 | even | 2 | 700.2.i.e.401.3 | yes | 6 | ||
7.2 | even | 3 | 4900.2.a.bc.1.3 | 3 | |||
7.4 | even | 3 | inner | 700.2.i.d.501.1 | yes | 6 | |
7.5 | odd | 6 | 4900.2.a.bb.1.1 | 3 | |||
35.2 | odd | 12 | 4900.2.e.t.2549.1 | 6 | |||
35.4 | even | 6 | 700.2.i.e.501.3 | yes | 6 | ||
35.9 | even | 6 | 4900.2.a.ba.1.1 | 3 | |||
35.12 | even | 12 | 4900.2.e.s.2549.6 | 6 | |||
35.18 | odd | 12 | 700.2.r.d.249.1 | 12 | |||
35.19 | odd | 6 | 4900.2.a.bd.1.3 | 3 | |||
35.23 | odd | 12 | 4900.2.e.t.2549.6 | 6 | |||
35.32 | odd | 12 | 700.2.r.d.249.6 | 12 | |||
35.33 | even | 12 | 4900.2.e.s.2549.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
700.2.i.d.401.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
700.2.i.d.501.1 | yes | 6 | 7.4 | even | 3 | inner | |
700.2.i.e.401.3 | yes | 6 | 5.4 | even | 2 | ||
700.2.i.e.501.3 | yes | 6 | 35.4 | even | 6 | ||
700.2.r.d.149.1 | 12 | 5.2 | odd | 4 | |||
700.2.r.d.149.6 | 12 | 5.3 | odd | 4 | |||
700.2.r.d.249.1 | 12 | 35.18 | odd | 12 | |||
700.2.r.d.249.6 | 12 | 35.32 | odd | 12 | |||
4900.2.a.ba.1.1 | 3 | 35.9 | even | 6 | |||
4900.2.a.bb.1.1 | 3 | 7.5 | odd | 6 | |||
4900.2.a.bc.1.3 | 3 | 7.2 | even | 3 | |||
4900.2.a.bd.1.3 | 3 | 35.19 | odd | 6 | |||
4900.2.e.s.2549.1 | 6 | 35.33 | even | 12 | |||
4900.2.e.s.2549.6 | 6 | 35.12 | even | 12 | |||
4900.2.e.t.2549.1 | 6 | 35.2 | odd | 12 | |||
4900.2.e.t.2549.6 | 6 | 35.23 | odd | 12 |