Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(149,700)]
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, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.r (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.58952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 149.1 | ||
Root | \(-0.617942 - 0.356769i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 700.149 |
Dual form | 700.2.r.d.249.1 |
$q$-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 | ||||||||
\(3\) | −2.77509 | + | 1.60220i | −1.60220 | + | 0.925031i | −0.611155 | + | 0.791511i | \(0.709295\pi\) |
−0.991046 | + | 0.133520i | \(0.957372\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.15715 | + | 1.53189i | 0.815327 | + | 0.579001i | ||||
\(8\) | 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 | ||||||||
\(13\) | 0.204402i | 0.0566908i | 0.999598 | + | 0.0283454i | \(0.00902383\pi\) | ||||
−0.999598 | + | 0.0283454i | \(0.990976\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.38537 | − | 2.53189i | 1.06361 | − | 0.614074i | 0.137180 | − | 0.990546i | \(-0.456196\pi\) |
0.926428 | + | 0.376472i | \(0.122863\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.531894 | − | 0.921267i | 0.122025 | − | 0.211353i | −0.798541 | − | 0.601940i | \(-0.794395\pi\) |
0.920566 | + | 0.390587i | \(0.127728\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.44070 | − | 0.794959i | −1.84191 | − | 0.173474i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.85383 | − | 1.07031i | −0.386549 | − | 0.223174i | 0.294115 | − | 0.955770i | \(-0.404975\pi\) |
−0.680664 | + | 0.732596i | \(0.738309\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.6770i | 2.63214i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.47259 | 1.38763 | 0.693813 | − | 0.720156i | \(-0.255930\pi\) | ||||
0.693813 | + | 0.720156i | \(0.255930\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 11.6676 | + | 6.73630i | 2.03107 | + | 1.17264i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.19130 | − | 5.30660i | −1.51104 | − | 0.872400i | −0.999917 | − | 0.0128933i | \(-0.995896\pi\) |
−0.511124 | − | 0.859507i | \(-0.670771\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 8.26819i | 1.26089i | 0.776235 | + | 0.630444i | \(0.217127\pi\) | ||||
−0.776235 | + | 0.630444i | \(0.782873\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.83033 | + | 1.63409i | 0.412847 | + | 0.238357i | 0.692012 | − | 0.721886i | \(-0.256724\pi\) |
−0.279165 | + | 0.960243i | \(0.590058\pi\) | |||||||
\(48\) | 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 | ||||||||
\(53\) | 4.91642 | − | 2.83850i | 0.675322 | − | 0.389897i | −0.122768 | − | 0.992435i | \(-0.539177\pi\) |
0.798090 | + | 0.602538i | \(0.205844\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.40880i | 0.451507i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.602201 | + | 1.04304i | 0.0783999 | + | 0.135793i | 0.902560 | − | 0.430565i | \(-0.141686\pi\) |
−0.824160 | + | 0.566357i | \(0.808352\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 17.4817 | − | 8.01100i | 2.20249 | − | 1.00929i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.7463 | − | 6.20440i | 1.31287 | − | 0.757988i | 0.330303 | − | 0.943875i | \(-0.392849\pi\) |
0.982571 | + | 0.185887i | \(0.0595157\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | −3.46410 | + | 2.00000i | −0.405442 | + | 0.234082i | −0.688830 | − | 0.724923i | \(-0.741875\pi\) |
0.283387 | + | 0.959006i | \(0.408542\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.04304 | − | 11.0748i | 0.118866 | − | 1.26209i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.27471 | − | 5.67196i | 0.368433 | − | 0.638146i | −0.620887 | − | 0.783900i | \(-0.713228\pi\) |
0.989321 | + | 0.145754i | \(0.0465609\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0110 | − | 19.0716i | −1.22344 | − | 2.11907i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.88139i | 0.426038i | 0.977048 | + | 0.213019i | \(0.0683297\pi\) | ||||
−0.977048 | + | 0.213019i | \(0.931670\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20.7371 | + | 11.9726i | −2.22325 | + | 1.28360i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.63409 | + | 8.02649i | −0.491213 | + | 0.850806i | −0.999949 | − | 0.0101167i | \(-0.996780\pi\) |
0.508736 | + | 0.860923i | \(0.330113\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.313121 | + | 0.440925i | −0.0328241 | + | 0.0462215i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −23.5122 | − | 13.5748i | −2.43810 | − | 1.40764i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.33198i | − | 0.135242i | −0.997711 | − | 0.0676209i | \(-0.978459\pi\) | ||
0.997711 | − | 0.0676209i | \(-0.0215408\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | −8.43576 | − | 4.87039i | −0.831200 | − | 0.479894i | 0.0230631 | − | 0.999734i | \(-0.492658\pi\) |
−0.854264 | + | 0.519840i | \(0.825991\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.53848 | + | 4.92969i | 0.825446 | + | 0.476571i | 0.852291 | − | 0.523068i | \(-0.175213\pi\) |
−0.0268449 | + | 0.999640i | \(0.508546\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.03841 | − | 3.53063i | −0.195245 | − | 0.338173i | 0.751736 | − | 0.659464i | \(-0.229217\pi\) |
−0.946981 | + | 0.321291i | \(0.895883\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 34.0090 | 3.22799 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.21744i | 0.208599i | 0.994546 | + | 0.104300i | \(0.0332601\pi\) | ||||
−0.994546 | + | 0.104300i | \(0.966740\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.28659 | + | 0.742815i | 0.118946 | + | 0.0686732i | ||||
\(118\) | 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 | ||||||||
\(123\) | −29.2756 | + | 16.9023i | −2.63969 | + | 1.52403i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.54942i | − | 0.581167i | −0.956850 | − | 0.290583i | \(-0.906151\pi\) | ||
0.956850 | − | 0.290583i | \(-0.0938494\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | 2.55866 | − | 1.17251i | 0.221864 | − | 0.101669i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.7967 | − | 8.54290i | 1.26417 | − | 0.729869i | 0.290292 | − | 0.956938i | \(-0.406248\pi\) |
0.973879 | + | 0.227069i | \(0.0729144\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.740780 | −0.0628322 | −0.0314161 | − | 0.999506i | \(-0.510002\pi\) | ||||
−0.0314161 | + | 0.999506i | \(0.510002\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.4726 | −0.881951 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.744250 | − | 0.429693i | 0.0622373 | − | 0.0359327i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.9901 | − | 14.6451i | −1.40132 | − | 1.20791i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.20889 | + | 14.2182i | −0.672498 | + | 1.16480i | 0.304695 | + | 0.952450i | \(0.401445\pi\) |
−0.977193 | + | 0.212351i | \(0.931888\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | − | 36.8046i | − | 2.97547i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.21480 | − | 4.74281i | 0.655612 | − | 0.378518i | −0.134991 | − | 0.990847i | \(-0.543101\pi\) |
0.790603 | + | 0.612329i | \(0.209767\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | −7.67245 | − | 4.42969i | −0.600953 | − | 0.346960i | 0.168463 | − | 0.985708i | \(-0.446119\pi\) |
−0.769416 | + | 0.638748i | \(0.779453\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.33198i | − | 0.644748i | −0.946612 | − | 0.322374i | \(-0.895519\pi\) | ||
0.946612 | − | 0.322374i | \(-0.104481\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9582 | 0.996786 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.86591 | − | 6.69594i | −0.295633 | − | 0.512052i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.8872 | + | 9.17251i | 1.20789 | + | 0.697373i | 0.962297 | − | 0.272001i | \(-0.0876855\pi\) |
0.245588 | + | 0.969374i | \(0.421019\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.34233 | − | 1.92969i | −0.251225 | − | 0.145045i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.14061 | − | 3.70765i | −0.159997 | − | 0.277123i | 0.774870 | − | 0.632120i | \(-0.217815\pi\) |
−0.934867 | + | 0.354997i | \(0.884482\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.93621 | 0.218247 | 0.109123 | − | 0.994028i | \(-0.465196\pi\) | ||||
0.109123 | + | 0.994028i | \(0.465196\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 5.30324i | − | 0.392026i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.4379 | − | 10.6451i | −1.34831 | − | 0.778447i | ||||
\(188\) | 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 | ||||||||
\(193\) | 6.13648 | − | 3.54290i | 0.441713 | − | 0.255023i | −0.262611 | − | 0.964902i | \(-0.584584\pi\) |
0.704324 | + | 0.709879i | \(0.251250\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.48563i | 0.390835i | 0.980720 | + | 0.195417i | \(0.0626062\pi\) | ||||
−0.980720 | + | 0.195417i | \(0.937394\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.04290 | + | 13.9307i | 0.570146 | + | 0.987522i | 0.996550 | + | 0.0829891i | \(0.0264467\pi\) |
−0.426405 | + | 0.904533i | \(0.640220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.8814 | + | 34.4356i | −1.40233 | + | 2.42890i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.1195 | + | 11.4472i | 1.13137 | + | 0.803437i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.4740 | + | 7.77919i | −0.936505 | + | 0.540691i | ||||
\(208\) | 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 | ||||||||
\(213\) | 1.64063 | − | 0.947216i | 0.112414 | − | 0.0649022i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.10191 | + | 22.3176i | −0.142687 | + | 1.51502i | ||||
\(218\) | 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 | ||||||||
\(223\) | − | 15.4856i | − | 1.03699i | −0.855079 | − | 0.518497i | \(-0.826492\pi\) | ||
0.855079 | − | 0.518497i | \(-0.173508\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.27579 | − | 1.89128i | 0.217422 | − | 0.125529i | −0.387334 | − | 0.921939i | \(-0.626604\pi\) |
0.604756 | + | 0.796411i | \(0.293271\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.60220 | + | 9.70330i | −0.370204 | + | 0.641212i | −0.989597 | − | 0.143869i | \(-0.954045\pi\) |
0.619393 | + | 0.785081i | \(0.287379\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.8495 | + | 32.4047i | 0.977025 | + | 2.13208i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.3448 | + | 5.97259i | 0.677712 | + | 0.391277i | 0.798993 | − | 0.601341i | \(-0.205367\pi\) |
−0.121280 | + | 0.992618i | \(0.538700\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.9870i | 1.36325i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.3450 | −0.992587 | −0.496293 | − | 0.868155i | \(-0.665306\pi\) | ||||
−0.496293 | + | 0.868155i | \(0.665306\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 25.5793 | + | 14.7682i | 1.64091 | + | 0.947380i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.188308 | + | 0.108720i | 0.0119818 | + | 0.00691768i | ||||
\(248\) | 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 | ||||||||
\(253\) | 9.00000i | 0.565825i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.0139 | − | 6.93621i | −0.749405 | − | 0.432669i | 0.0760740 | − | 0.997102i | \(-0.475761\pi\) |
−0.825479 | + | 0.564433i | \(0.809095\pi\) | |||||||
\(258\) | 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 | ||||||||
\(263\) | 2.99606 | − | 1.72978i | 0.184745 | − | 0.106663i | −0.404775 | − | 0.914416i | \(-0.632650\pi\) |
0.589520 | + | 0.807754i | \(0.299317\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 29.6990i | − | 1.81755i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.8320 | + | 22.2256i | 0.782379 | + | 1.35512i | 0.930552 | + | 0.366159i | \(0.119328\pi\) |
−0.148173 | + | 0.988962i | \(0.547339\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 0.162491 | − | 1.72529i | 0.00983439 | − | 0.104419i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.7180 | + | 9.07479i | −0.944403 | + | 0.545251i | −0.891338 | − | 0.453340i | \(-0.850232\pi\) |
−0.0530653 | + | 0.998591i | \(0.516899\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −24.7323 | + | 14.2792i | −1.47018 | + | 0.848810i | −0.999440 | − | 0.0334610i | \(-0.989347\pi\) |
−0.470742 | + | 0.882271i | \(0.656014\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.7567 | + | 16.1606i | 1.34328 | + | 0.953929i | ||||
\(288\) | 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 | ||||||||
\(293\) | − | 25.5494i | − | 1.49261i | −0.665603 | − | 0.746306i | \(-0.731825\pi\) | ||
0.665603 | − | 0.746306i | \(-0.268175\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 49.7996 | − | 28.7518i | 2.88966 | − | 1.66835i | ||||
\(298\) | 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 | ||||||||
\(303\) | 17.1816 | + | 9.91981i | 0.987058 | + | 0.569878i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.1145i | 0.577267i | 0.957440 | + | 0.288634i | \(0.0932009\pi\) | ||||
−0.957440 | + | 0.288634i | \(0.906799\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | −7.45925 | − | 4.30660i | −0.421622 | − | 0.243424i | 0.274149 | − | 0.961687i | \(-0.411604\pi\) |
−0.695771 | + | 0.718264i | \(0.744937\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.77025 | + | 3.90880i | 0.380255 | + | 0.219540i | 0.677929 | − | 0.735127i | \(-0.262878\pi\) |
−0.297674 | + | 0.954667i | \(0.596211\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.7089 | − | 27.2086i | −0.879529 | − | 1.52339i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −31.5934 | −1.76337 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.38680i | − | 0.299729i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.3136 | + | 6.53189i | 0.625642 | + | 0.361215i | ||||
\(328\) | 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 | ||||||||
\(333\) | −66.8041 | + | 38.5694i | −3.66084 | + | 2.11359i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.29020i | 0.0702815i | 0.999382 | + | 0.0351408i | \(0.0111880\pi\) | ||||
−0.999382 | + | 0.0351408i | \(0.988812\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | −5.14868 | + | 17.7902i | −0.278003 | + | 0.960580i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.19221 | − | 4.72978i | 0.439781 | − | 0.253908i | −0.263724 | − | 0.964598i | \(-0.584951\pi\) |
0.703505 | + | 0.710691i | \(0.251617\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.5494 | −0.832341 | −0.416171 | − | 0.909287i | \(-0.636628\pi\) | ||||
−0.416171 | + | 0.909287i | \(0.636628\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.79560 | −0.149218 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.1086 | − | 7.56827i | 0.697702 | − | 0.402818i | −0.108789 | − | 0.994065i | \(-0.534697\pi\) |
0.806491 | + | 0.591246i | \(0.201364\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −39.0283 | + | 17.8848i | −2.06560 | + | 0.946562i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.15947 | − | 8.93646i | 0.272306 | − | 0.471648i | −0.697146 | − | 0.716930i | \(-0.745547\pi\) |
0.969452 | + | 0.245281i | \(0.0788802\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.93418 | + | 15.4744i | 0.470220 | + | 0.814445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 21.3958i | − | 1.12299i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.5332 | + | 8.96811i | −0.810827 | + | 0.468131i | −0.847243 | − | 0.531205i | \(-0.821739\pi\) |
0.0364158 | + | 0.999337i | \(0.488406\pi\) | |||||||
\(368\) | 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 | ||||||||
\(373\) | 14.0221 | + | 8.09568i | 0.726038 | + | 0.419179i | 0.816971 | − | 0.576679i | \(-0.195651\pi\) |
−0.0909327 | + | 0.995857i | \(0.528985\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.52741i | 0.0786656i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.6002 | 0.647227 | 0.323614 | − | 0.946189i | \(-0.395102\pi\) | ||||
0.323614 | + | 0.946189i | \(0.395102\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.4935 | + | 18.1752i | 0.537597 | + | 0.931146i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.1425 | − | 7.58783i | −0.671551 | − | 0.387720i | 0.125113 | − | 0.992142i | \(-0.460071\pi\) |
−0.796664 | + | 0.604422i | \(0.793404\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 52.0436 | + | 30.0474i | 2.64552 | + | 1.52739i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.6197 | − | 25.3221i | −0.741249 | − | 1.28388i | −0.951927 | − | 0.306326i | \(-0.900900\pi\) |
0.210677 | − | 0.977556i | \(-0.432433\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.8396 | −0.548183 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 54.5036i | 2.74934i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.75854 | + | 5.63409i | 0.489767 | + | 0.282767i | 0.724478 | − | 0.689298i | \(-0.242081\pi\) |
−0.234711 | + | 0.972065i | \(0.575414\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | −1.49979 | + | 0.865905i | −0.0747100 | + | 0.0431338i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.6222i | 2.21184i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.89576 | − | 13.6759i | −0.390420 | − | 0.676228i | 0.602085 | − | 0.798432i | \(-0.294337\pi\) |
−0.992505 | + | 0.122204i | \(0.961004\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −27.3749 | + | 47.4147i | −1.35030 | + | 2.33879i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.298792 | + | 3.17251i | −0.0147026 | + | 0.156109i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.05573 | − | 1.18688i | 0.100670 | − | 0.0581217i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.4726 | 0.658179 | 0.329090 | − | 0.944299i | \(-0.393258\pi\) | ||||
0.329090 | + | 0.944299i | \(0.393258\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.8396 | −1.30808 | −0.654041 | − | 0.756459i | \(-0.726928\pi\) | ||||
−0.654041 | + | 0.756459i | \(0.726928\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.5714 | − | 11.8769i | 1.00022 | − | 0.577475i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.98063 | + | 1.82413i | −0.192636 | + | 0.0882756i | ||||
\(428\) | 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 | ||||||||
\(433\) | 0.910136i | 0.0437383i | 0.999761 | + | 0.0218692i | \(0.00696173\pi\) | ||||
−0.999761 | + | 0.0218692i | \(0.993038\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.97208 | + | 1.13858i | −0.0943373 | + | 0.0544656i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.9517 | + | 32.8253i | −0.904515 | + | 1.56667i | −0.0829488 | + | 0.996554i | \(0.526434\pi\) |
−0.821566 | + | 0.570113i | \(0.806900\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 49.9827 | + | 9.49916i | 2.38013 | + | 0.452341i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.95946 | + | 3.44070i | 0.283143 | + | 0.163472i | 0.634845 | − | 0.772639i | \(-0.281064\pi\) |
−0.351703 | + | 0.936112i | \(0.614397\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 52.6091i | − | 2.48833i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.43754 | −0.303807 | −0.151903 | − | 0.988395i | \(-0.548540\pi\) | ||||
−0.151903 | + | 0.988395i | \(0.548540\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.1770 | − | 38.4117i | −1.04427 | − | 1.80874i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.46361 | + | 0.845015i | 0.0687664 | + | 0.0397023i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.04907 | − | 4.64713i | −0.376520 | − | 0.217384i | 0.299783 | − | 0.954007i | \(-0.403086\pi\) |
−0.676303 | + | 0.736624i | \(0.736419\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | − | 29.6091i | − | 1.37605i | −0.725685 | − | 0.688027i | \(-0.758477\pi\) | ||
0.725685 | − | 0.688027i | \(-0.241523\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.5719 | − | 13.0319i | −1.04450 | − | 0.603044i | −0.123398 | − | 0.992357i | \(-0.539379\pi\) |
−0.921105 | + | 0.389313i | \(0.872712\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | 30.1055 | − | 17.3814i | 1.38425 | − | 0.799197i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 41.2615i | − | 1.88923i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.552784 | − | 0.957450i | −0.0252573 | − | 0.0437470i | 0.853120 | − | 0.521714i | \(-0.174707\pi\) |
−0.878378 | + | 0.477967i | \(0.841374\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.08468 | − | 1.87872i | 0.0494570 | − | 0.0856621i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.7967 | + | 10.5079i | 0.673275 | + | 0.478124i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.49585 | + | 2.59568i | −0.203727 | + | 0.117622i | −0.598393 | − | 0.801203i | \(-0.704194\pi\) |
0.394666 | + | 0.918825i | \(0.370860\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 32.7701 | − | 18.9198i | 1.47589 | − | 0.852105i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.27530 | − | 0.905651i | −0.0572051 | − | 0.0406240i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.0364 | + | 22.5797i | −0.583588 | + | 1.01080i | 0.411461 | + | 0.911427i | \(0.365019\pi\) |
−0.995050 | + | 0.0993776i | \(0.968315\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.3495 | + | 23.1220i | 0.596412 | + | 1.03302i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.80864i | 0.392758i | 0.980528 | + | 0.196379i | \(0.0629182\pi\) | ||||
−0.980528 | + | 0.196379i | \(0.937082\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −35.9603 | + | 20.7617i | −1.59705 | + | 0.922058i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.0090 | + | 19.0681i | −0.487964 | + | 0.845178i | −0.999904 | − | 0.0138427i | \(-0.995594\pi\) |
0.511940 | + | 0.859021i | \(0.328927\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.5364 | − | 0.992334i | −0.466102 | − | 0.0438983i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.6002 | + | 7.27471i | 0.556311 | + | 0.321186i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 13.7408i | − | 0.604319i | ||||||
\(518\) | 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 | ||||||||
\(523\) | 3.97609 | + | 2.29560i | 0.173862 | + | 0.100380i | 0.584406 | − | 0.811462i | \(-0.301328\pi\) |
−0.410543 | + | 0.911841i | \(0.634661\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 37.1554 | + | 21.4517i | 1.61852 | + | 0.934451i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.20889 | − | 15.9503i | −0.400386 | − | 0.693490i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.75382 | 0.379883 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.15632i | 0.0934005i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.8808 | + | 6.85939i | 0.512695 | + | 0.296004i | ||||
\(538\) | 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 | ||||||||
\(543\) | −8.14826 | + | 4.70440i | −0.349675 | + | 0.201885i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.3581i | 0.485635i | 0.970072 | + | 0.242818i | \(0.0780717\pi\) | ||||
−0.970072 | + | 0.242818i | \(0.921928\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | 15.7529 | − | 7.21877i | 0.669881 | − | 0.306973i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.1991 | + | 8.19788i | −0.601637 | + | 0.347355i | −0.769685 | − | 0.638423i | \(-0.779587\pi\) |
0.168048 | + | 0.985779i | \(0.446254\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.69003 | −0.0714807 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 68.2223 | 2.88035 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.21964 | + | 2.43621i | −0.177837 | + | 0.102674i | −0.586276 | − | 0.810111i | \(-0.699407\pi\) |
0.408439 | + | 0.912786i | \(0.366073\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.46330 | − | 58.0081i | 0.229437 | − | 2.43611i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.9277 | + | 32.7837i | −0.793489 | + | 1.37436i | 0.130306 | + | 0.991474i | \(0.458404\pi\) |
−0.923794 | + | 0.382889i | \(0.874929\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 38.2772i | 1.59905i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.2850 | + | 21.5265i | −1.55219 | + | 0.896160i | −0.554231 | + | 0.832363i | \(0.686988\pi\) |
−0.997963 | + | 0.0637967i | \(0.979679\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | −20.6706 | − | 11.9342i | −0.856089 | − | 0.494263i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.67699i | 0.234315i | 0.993113 | + | 0.117157i | \(0.0373782\pi\) | ||||
−0.993113 | + | 0.117157i | \(0.962622\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.01304 | 0.371376 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.78908 | − | 15.2231i | −0.361534 | − | 0.626196i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.74675 | − | 4.47259i | −0.318121 | − | 0.183667i | 0.332434 | − | 0.943127i | \(-0.392130\pi\) |
−0.650555 | + | 0.759459i | \(0.725464\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −44.6396 | − | 25.7727i | −1.82698 | − | 1.05481i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.6132 | − | 21.8467i | −0.515362 | − | 0.892632i | −0.999841 | − | 0.0178298i | \(-0.994324\pi\) |
0.484479 | − | 0.874803i | \(-0.339009\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.3409 | 0.625770 | 0.312885 | − | 0.949791i | \(-0.398705\pi\) | ||||
0.312885 | + | 0.949791i | \(0.398705\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 90.1895i | − | 3.67280i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.1313 | + | 10.4681i | 0.735926 | + | 0.424887i | 0.820586 | − | 0.571523i | \(-0.193647\pi\) |
−0.0846599 | + | 0.996410i | \(0.526980\pi\) | |||||||
\(608\) | 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 | ||||||||
\(613\) | −4.60634 | + | 2.65947i | −0.186048 | + | 0.107415i | −0.590131 | − | 0.807307i | \(-0.700924\pi\) |
0.404083 | + | 0.914722i | \(0.367591\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.6262i | 1.15245i | 0.817291 | + | 0.576225i | \(0.195475\pi\) | ||||
−0.817291 | + | 0.576225i | \(0.804525\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.7812 | − | 18.6736i | −0.433334 | − | 0.750557i | 0.563824 | − | 0.825895i | \(-0.309330\pi\) |
−0.997158 | + | 0.0753383i | \(0.975996\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.6386 | − | 25.3548i | 0.587426 | − | 1.01745i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.2922 | + | 10.2154i | −0.893117 | + | 0.409272i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.4119 | − | 7.16599i | 0.495682 | − | 0.286182i | ||||
\(628\) | 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 | ||||||||
\(633\) | −46.0670 | + | 26.5968i | −1.83100 | + | 1.05713i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.35090 | + | 0.471473i | −0.0535246 | + | 0.0186804i | ||||
\(638\) | 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 | ||||||||
\(643\) | − | 16.4816i | − | 0.649969i | −0.945719 | − | 0.324985i | \(-0.894641\pi\) | ||
0.945719 | − | 0.324985i | \(-0.105359\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.2276 | − | 15.7199i | 1.07043 | − | 0.618013i | 0.142131 | − | 0.989848i | \(-0.454605\pi\) |
0.928299 | + | 0.371835i | \(0.121271\pi\) | |||||||
\(648\) | 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 | ||||||||
\(653\) | −35.4008 | − | 20.4387i | −1.38534 | − | 0.799827i | −0.392555 | − | 0.919729i | \(-0.628409\pi\) |
−0.992786 | + | 0.119902i | \(0.961742\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.0728i | 1.13424i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 46.6860 | 1.81863 | 0.909313 | − | 0.416112i | \(-0.136608\pi\) | ||||
0.909313 | + | 0.416112i | \(0.136608\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | −2.87235 | − | 1.65835i | −0.111553 | − | 0.0644050i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.8529 | − | 7.99797i | −0.536386 | − | 0.309682i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.8111 | + | 42.9741i | 0.959252 | + | 1.66147i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.95822 | 0.268619 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.1936i | 1.85773i | 0.370423 | + | 0.928863i | \(0.379213\pi\) | ||||
−0.370423 | + | 0.928863i | \(0.620787\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.1990 | − | 23.2089i | −1.54497 | − | 0.891990i | −0.998514 | − | 0.0545037i | \(-0.982642\pi\) |
−0.546458 | − | 0.837486i | \(-0.684024\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | 37.7149 | − | 21.7747i | 1.44312 | − | 0.833186i | 0.445064 | − | 0.895499i | \(-0.353181\pi\) |
0.998057 | + | 0.0623127i | \(0.0198476\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 35.9034i | − | 1.36980i | ||||||
\(688\) | 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 | ||||||||
\(693\) | −65.9191 | − | 46.8122i | −2.50406 | − | 1.77825i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.2631 | − | 26.7100i | 1.75234 | − | 1.01171i | ||||
\(698\) | 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 | ||||||||
\(703\) | −9.77760 | + | 5.64510i | −0.368769 | + | 0.212909i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.53597 | − | 16.3086i | 0.0577663 | − | 0.613349i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.53841 | − | 14.7890i | 0.320667 | − | 0.555411i | −0.659959 | − | 0.751302i | \(-0.729426\pi\) |
0.980626 | + | 0.195890i | \(0.0627597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.8012 | − | 41.2249i | −0.892615 | − | 1.54605i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 18.1365i | − | 0.679219i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 42.5838 | − | 24.5858i | 1.59032 | − | 0.918173i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.6231 | − | 23.5959i | 0.508056 | − | 0.879978i | −0.491901 | − | 0.870651i | \(-0.663698\pi\) |
0.999957 | − | 0.00932687i | \(-0.00296888\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7363 | − | 23.4289i | −0.399841 | − | 0.872536i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −39.9496 | − | 23.0649i | −1.48574 | − | 0.857793i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 19.9232i | − | 0.738910i | −0.929249 | − | 0.369455i | \(-0.879544\pi\) | ||
0.929249 | − | 0.369455i | \(-0.120456\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.5804 | −1.05853 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.9342 | + | 36.2591i | 0.774279 | + | 1.34109i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.9876 | − | 15.5813i | −0.996811 | − | 0.575509i | −0.0895075 | − | 0.995986i | \(-0.528529\pi\) |
−0.907303 | + | 0.420477i | \(0.861863\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −45.1819 | − | 26.0858i | −1.66430 | − | 0.960883i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.950583 | + | 1.64646i | 0.0349678 | + | 0.0605659i | 0.882980 | − | 0.469411i | \(-0.155534\pi\) |
−0.848012 | + | 0.529977i | \(0.822200\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.696765 | −0.0255963 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.0660i | 1.32313i | 0.749886 | + | 0.661567i | \(0.230108\pi\) | ||||
−0.749886 | + | 0.661567i | \(0.769892\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.4312 | + | 14.1054i | 0.893890 | + | 0.516088i | ||||
\(748\) | 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 | ||||||||
\(753\) | 53.8861 | − | 31.1112i | 1.96372 | − | 1.13375i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.9542i | 0.543518i | 0.962365 | + | 0.271759i | \(0.0876053\pi\) | ||||
−0.962365 | + | 0.271759i | \(0.912395\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 1.01139 | − | 10.7387i | 0.0366149 | − | 0.388769i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.213199 | + | 0.123091i | −0.00769819 | + | 0.00444455i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.3189 | −1.30969 | −0.654847 | − | 0.755761i | \(-0.727267\pi\) | ||||
−0.654847 | + | 0.755761i | \(0.727267\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 44.4528 | 1.60093 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −41.1089 | + | 23.7343i | −1.47859 | + | 0.853662i | −0.999707 | − | 0.0242187i | \(-0.992290\pi\) |
−0.478879 | + | 0.877881i | \(0.658957\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 73.3625 | + | 52.0981i | 2.63186 | + | 1.86901i | ||||
\(778\) | 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 | ||||||||
\(783\) | 102.203i | 3.65242i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.82901 | + | 3.94273i | −0.243428 | + | 0.140543i | −0.616751 | − | 0.787158i | \(-0.711552\pi\) |
0.373323 | + | 0.927701i | \(0.378218\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | −0.292960 | − | 0.169141i | −0.0104033 | − | 0.00600636i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.6132i | 1.19064i | 0.803488 | + | 0.595320i | \(0.202975\pi\) | ||||
−0.803488 | + | 0.595320i | \(0.797025\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.5494 | 0.585476 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 33.6815 | + | 58.3380i | 1.19008 | + | 2.06127i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.5645 | + | 8.40880i | 0.513969 | + | 0.296740i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −71.2199 | − | 41.1188i | −2.50706 | − | 1.44745i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.59568 | − | 7.95995i | −0.161576 | − | 0.279857i | 0.773858 | − | 0.633359i | \(-0.218324\pi\) |
−0.935434 | + | 0.353502i | \(0.884991\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.6483 | 0.760173 | 0.380086 | − | 0.924951i | \(-0.375894\pi\) | ||||
0.380086 | + | 0.924951i | \(0.375894\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 63.0530i | − | 2.21136i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.61721 | + | 4.39780i | 0.266493 | + | 0.153860i | ||||
\(818\) | 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 | ||||||||
\(823\) | 9.91066 | − | 5.72192i | 0.345464 | − | 0.199454i | −0.317222 | − | 0.948351i | \(-0.602750\pi\) |
0.662686 | + | 0.748898i | \(0.269417\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 9.82658i | − | 0.341704i | −0.985297 | − | 0.170852i | \(-0.945348\pi\) | ||
0.985297 | − | 0.170852i | \(-0.0546519\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.1287 | + | 33.1319i | 0.664367 | + | 1.15072i | 0.979457 | + | 0.201655i | \(0.0646321\pi\) |
−0.315090 | + | 0.949062i | \(0.602035\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.0793 | − | 50.3668i | 1.00875 | − | 1.74720i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.8487 | + | 23.1431i | 0.930253 | + | 0.801860i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −100.355 | + | 57.9398i | −3.46876 | + | 2.00269i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.6900 | −1.05954 | −0.529769 | − | 0.848142i | \(-0.677721\pi\) | ||||
−0.529769 | + | 0.848142i | \(0.677721\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.8396 | 0.925504 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 51.4402 | − | 29.6990i | 1.77169 | − | 1.02289i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.0597 | + | 7.35939i | −0.551819 | + | 0.252872i | ||||
\(848\) | 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 | ||||||||
\(853\) | 39.4569i | 1.35098i | 0.737370 | + | 0.675489i | \(0.236067\pi\) | ||||
−0.737370 | + | 0.675489i | \(0.763933\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.5192 | − | 19.9297i | 1.17915 | − | 0.680785i | 0.223336 | − | 0.974742i | \(-0.428305\pi\) |
0.955819 | + | 0.293956i | \(0.0949720\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.75719 | + | 16.8999i | −0.332911 | + | 0.576619i | −0.983081 | − | 0.183170i | \(-0.941364\pi\) |
0.650170 | + | 0.759788i | \(0.274697\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −89.0444 | − | 8.38635i | −3.03463 | − | 0.285806i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.8502 | + | 18.9661i | 1.11823 | + | 0.645613i | 0.940949 | − | 0.338547i | \(-0.109935\pi\) |
0.177284 | + | 0.984160i | \(0.443269\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.6923i | 0.940479i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.5364 | −0.934108 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.26819 | + | 2.19657i | 0.0429710 | + | 0.0744279i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.38404 | − | 4.84053i | −0.283757 | − | 0.163827i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.47881 | + | 5.47259i | 0.320077 | + | 0.184796i | 0.651427 | − | 0.758712i | \(-0.274171\pi\) |
−0.331350 | + | 0.943508i | \(0.607504\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 23.2511i | 0.782461i | 0.920293 | + | 0.391231i | \(0.127951\pi\) | ||||
−0.920293 | + | 0.391231i | \(0.872049\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.1260 | − | 11.6197i | −0.675763 | − | 0.390152i | 0.122494 | − | 0.992469i | \(-0.460911\pi\) |
−0.798257 | + | 0.602317i | \(0.794244\pi\) | |||||||
\(888\) | 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 | ||||||||
\(893\) | 3.01088 | − | 1.73833i | 0.100755 | − | 0.0581710i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.40207i | 0.0468137i | ||||||||
\(898\) | 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 | ||||||||
\(903\) | 6.57287 | − | 69.7893i | 0.218731 | − | 2.32244i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.3012 | − | 22.1132i | 1.27177 | − | 0.734257i | 0.296449 | − | 0.955049i | \(-0.404197\pi\) |
0.975321 | + | 0.220792i | \(0.0708641\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | 14.1326 | − | 8.15947i | 0.467721 | − | 0.270039i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 40.9106 | − | 18.7473i | 1.35099 | − | 0.619090i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.6581 | + | 28.8527i | −0.549501 | + | 0.951764i | 0.448807 | + | 0.893628i | \(0.351849\pi\) |
−0.998309 | + | 0.0581356i | \(0.981484\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.2055 | − | 28.0688i | −0.533990 | − | 0.924898i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 0.120842i | − | 0.00397755i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −61.3127 | + | 35.3989i | −2.01377 | + | 1.16265i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.62421 | + | 11.4735i | −0.217333 | + | 0.376432i | −0.953992 | − | 0.299833i | \(-0.903069\pi\) |
0.736659 | + | 0.676265i | \(0.236402\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.31557 | + | 1.39032i | 0.239758 | + | 0.0455658i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 94.8293 | + | 54.7497i | 3.10457 | + | 1.79243i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.1365i | 0.331146i | 0.986197 | + | 0.165573i | \(0.0529474\pi\) | ||||
−0.986197 | + | 0.165573i | \(0.947053\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | −19.5568 | − | 11.2911i | −0.636856 | − | 0.367689i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.3342 | − | 11.1626i | −0.628278 | − | 0.362736i | 0.151807 | − | 0.988410i | \(-0.451491\pi\) |
−0.780085 | + | 0.625674i | \(0.784824\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.408803 | − | 0.708068i | −0.0132703 | − | 0.0229849i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.0507 | −0.812326 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 47.4685i | − | 1.53766i | −0.639455 | − | 0.768828i | \(-0.720840\pi\) | ||
0.639455 | − | 0.768828i | \(-0.279160\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 87.1872 | + | 50.3376i | 2.81836 | + | 1.62718i | ||||
\(958\) | 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 | ||||||||
\(963\) | 62.0593 | − | 35.8299i | 1.99983 | − | 1.15460i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 21.3189i | − | 0.685571i | −0.939414 | − | 0.342785i | \(-0.888630\pi\) | ||
0.939414 | − | 0.342785i | \(-0.111370\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | −1.59797 | − | 1.13480i | −0.0512287 | − | 0.0363799i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.59315 | − | 0.919807i | 0.0509695 | − | 0.0294272i | −0.474299 | − | 0.880364i | \(-0.657298\pi\) |
0.525268 | + | 0.850937i | \(0.323965\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.9672 | 1.24540 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.6311 | −0.946050 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.85190 | + | 5.68800i | −0.314227 | + | 0.181419i | −0.648816 | − | 0.760945i | \(-0.724736\pi\) |
0.334590 | + | 0.942364i | \(0.391402\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.5910 | − | 16.0429i | −0.719078 | − | 0.510651i | ||||
\(988\) | 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 | ||||||||
\(993\) | 70.8135i | 2.24720i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.89160 | + | 5.71092i | −0.313270 | + | 0.180867i | −0.648389 | − | 0.761309i | \(-0.724557\pi\) |
0.335119 | + | 0.942176i | \(0.391224\pi\) | |||||||
\(998\) | 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.r.d.149.1 | 12 | ||
5.2 | odd | 4 | 700.2.i.e.401.3 | yes | 6 | ||
5.3 | odd | 4 | 700.2.i.d.401.1 | ✓ | 6 | ||
5.4 | even | 2 | inner | 700.2.r.d.149.6 | 12 | ||
7.2 | even | 3 | 4900.2.e.t.2549.1 | 6 | |||
7.4 | even | 3 | inner | 700.2.r.d.249.6 | 12 | ||
7.5 | odd | 6 | 4900.2.e.s.2549.6 | 6 | |||
35.2 | odd | 12 | 4900.2.a.ba.1.1 | 3 | |||
35.4 | even | 6 | inner | 700.2.r.d.249.1 | 12 | ||
35.9 | even | 6 | 4900.2.e.t.2549.6 | 6 | |||
35.12 | even | 12 | 4900.2.a.bd.1.3 | 3 | |||
35.18 | odd | 12 | 700.2.i.d.501.1 | yes | 6 | ||
35.19 | odd | 6 | 4900.2.e.s.2549.1 | 6 | |||
35.23 | odd | 12 | 4900.2.a.bc.1.3 | 3 | |||
35.32 | odd | 12 | 700.2.i.e.501.3 | yes | 6 | ||
35.33 | even | 12 | 4900.2.a.bb.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
700.2.i.d.401.1 | ✓ | 6 | 5.3 | odd | 4 | ||
700.2.i.d.501.1 | yes | 6 | 35.18 | odd | 12 | ||
700.2.i.e.401.3 | yes | 6 | 5.2 | odd | 4 | ||
700.2.i.e.501.3 | yes | 6 | 35.32 | odd | 12 | ||
700.2.r.d.149.1 | 12 | 1.1 | even | 1 | trivial | ||
700.2.r.d.149.6 | 12 | 5.4 | even | 2 | inner | ||
700.2.r.d.249.1 | 12 | 35.4 | even | 6 | inner | ||
700.2.r.d.249.6 | 12 | 7.4 | even | 3 | inner | ||
4900.2.a.ba.1.1 | 3 | 35.2 | odd | 12 | |||
4900.2.a.bb.1.1 | 3 | 35.33 | even | 12 | |||
4900.2.a.bc.1.3 | 3 | 35.23 | odd | 12 | |||
4900.2.a.bd.1.3 | 3 | 35.12 | even | 12 | |||
4900.2.e.s.2549.1 | 6 | 35.19 | odd | 6 | |||
4900.2.e.s.2549.6 | 6 | 7.5 | odd | 6 | |||
4900.2.e.t.2549.1 | 6 | 7.2 | even | 3 | |||
4900.2.e.t.2549.6 | 6 | 35.9 | even | 6 |