Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(95,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bj (of order \(6\), 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: | \(2.68297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 95.4 | ||
Root | \(1.26217 - 1.18614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.95 |
Dual form | 336.2.bj.f.191.4 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.26217 | − | 1.18614i | 0.728714 | − | 0.684819i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.87228 | − | 1.65831i | 1.28452 | − | 0.741620i | 0.306851 | − | 0.951757i | \(-0.400725\pi\) |
0.977672 | + | 0.210138i | \(0.0673912\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | + | 2.00000i | 0.654654 | + | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.186141 | − | 2.99422i | 0.0620469 | − | 0.998073i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.65831 | + | 2.87228i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.65831 | − | 5.50000i | 0.428174 | − | 1.42009i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.87228 | + | 1.65831i | 0.696631 | + | 0.402200i | 0.806091 | − | 0.591791i | \(-0.201579\pi\) |
−0.109461 | + | 0.993991i | \(0.534912\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.06218 | + | 3.50000i | −1.39076 | + | 0.802955i | −0.993399 | − | 0.114708i | \(-0.963407\pi\) |
−0.397360 | + | 0.917663i | \(0.630073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.55842 | + | 0.469882i | 0.994729 | + | 0.102537i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.65831 | − | 2.87228i | −0.345782 | − | 0.598912i | 0.639713 | − | 0.768613i | \(-0.279053\pi\) |
−0.985496 | + | 0.169701i | \(0.945720\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 5.19615i | 0.600000 | − | 1.03923i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.31662 | − | 4.00000i | −0.638285 | − | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.63325i | − | 1.23176i | −0.787839 | − | 0.615882i | \(-0.788800\pi\) | ||
0.787839 | − | 0.615882i | \(-0.211200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.59808 | + | 1.50000i | 0.466628 | + | 0.269408i | 0.714827 | − | 0.699301i | \(-0.246505\pi\) |
−0.248199 | + | 0.968709i | \(0.579839\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.31386 | + | 5.59230i | 0.228714 | + | 0.973494i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.29156 | + | 2.87228i | 1.40153 | + | 0.485504i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | + | 0.866025i | 0.0821995 | + | 0.142374i | 0.904194 | − | 0.427121i | \(-0.140472\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.04868 | + | 4.74456i | −0.808435 | + | 0.759738i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.63325i | 1.03594i | 0.855399 | + | 0.517970i | \(0.173312\pi\) | ||||
−0.855399 | + | 0.517970i | \(0.826688\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000i | 0.304997i | 0.988304 | + | 0.152499i | \(0.0487319\pi\) | ||||
−0.988304 | + | 0.152499i | \(0.951268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.43070 | − | 8.90892i | −0.660490 | − | 1.32806i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.97494 | − | 8.61684i | −0.725669 | − | 1.25690i | −0.958698 | − | 0.284426i | \(-0.908197\pi\) |
0.233029 | − | 0.972470i | \(-0.425136\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.59230 | − | 1.31386i | 0.783078 | − | 0.183977i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.87228 | − | 1.65831i | −0.394538 | − | 0.227787i | 0.289586 | − | 0.957152i | \(-0.406482\pi\) |
−0.684125 | + | 0.729365i | \(0.739816\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.0000i | 1.48324i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.50000 | + | 11.6082i | −0.463586 | + | 1.53754i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.65831 | − | 2.87228i | 0.215894 | − | 0.373939i | −0.737655 | − | 0.675178i | \(-0.764067\pi\) |
0.953549 | + | 0.301239i | \(0.0974001\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.50000 | − | 2.59808i | −0.192055 | − | 0.332650i | 0.753876 | − | 0.657017i | \(-0.228182\pi\) |
−0.945931 | + | 0.324367i | \(0.894849\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.31084 | − | 4.81386i | 0.795092 | − | 0.606489i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.4891 | + | 6.63325i | −1.42505 | + | 0.822753i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.79423 | + | 4.50000i | 0.952217 | + | 0.549762i | 0.893769 | − | 0.448528i | \(-0.148052\pi\) |
0.0584478 | + | 0.998290i | \(0.481385\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.50000 | − | 1.65831i | −0.662122 | − | 0.199637i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.2665 | 1.57444 | 0.787222 | − | 0.616670i | \(-0.211519\pi\) | ||||
0.787222 | + | 0.616670i | \(0.211519\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.50000 | + | 6.06218i | −0.409644 | + | 0.709524i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.37686 | − | 10.1168i | −0.274456 | − | 1.16819i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.61684 | + | 1.65831i | −0.981981 | + | 0.188982i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.79423 | + | 4.50000i | −0.876919 | + | 0.506290i | −0.869641 | − | 0.493684i | \(-0.835650\pi\) |
−0.00727784 | + | 0.999974i | \(0.502317\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.93070 | − | 1.11469i | −0.992300 | − | 0.123855i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.2665 | −1.45619 | −0.728094 | − | 0.685478i | \(-0.759593\pi\) | ||||
−0.728094 | + | 0.685478i | \(0.759593\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.0000 | 1.19312 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.86797 | − | 8.37228i | −0.843535 | − | 0.897603i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.87228 | + | 1.65831i | −0.304461 | + | 0.175781i | −0.644445 | − | 0.764650i | \(-0.722912\pi\) |
0.339984 | + | 0.940431i | \(0.389578\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.92820 | − | 8.00000i | −0.726273 | − | 0.838628i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.05842 | − | 1.18843i | 0.524534 | − | 0.123235i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.6082 | + | 20.1060i | −1.19097 | + | 2.06283i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.29156 | + | 5.50000i | 0.833333 | + | 0.552771i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.87228 | + | 1.65831i | 0.285803 | + | 0.165008i | 0.636047 | − | 0.771650i | \(-0.280568\pi\) |
−0.350245 | + | 0.936658i | \(0.613902\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.52628 | − | 5.50000i | 0.938652 | − | 0.541931i | 0.0491146 | − | 0.998793i | \(-0.484360\pi\) |
0.889538 | + | 0.456862i | \(0.151027\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.8723 | − | 6.20965i | 1.35380 | − | 0.606000i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.65831 | + | 2.87228i | 0.160315 | + | 0.277674i | 0.934982 | − | 0.354696i | \(-0.115416\pi\) |
−0.774667 | + | 0.632370i | \(0.782082\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.50000 | + | 4.33013i | −0.239457 | + | 0.414751i | −0.960558 | − | 0.278078i | \(-0.910303\pi\) |
0.721102 | + | 0.692829i | \(0.243636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.65831 | + | 0.500000i | 0.157400 | + | 0.0474579i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.63325i | − | 0.624004i | −0.950082 | − | 0.312002i | \(-0.899000\pi\) | ||
0.950082 | − | 0.312002i | \(-0.101000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.52628 | − | 5.50000i | −0.888330 | − | 0.512878i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.744563 | + | 11.9769i | −0.0688348 | + | 1.10726i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.65831 | + | 8.61684i | 0.152017 | + | 0.789905i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.86797 | + | 8.37228i | 0.709431 | + | 0.754903i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 3.31662i | − | 0.296648i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000i | 0.177471i | 0.996055 | + | 0.0887357i | \(0.0282826\pi\) | ||||
−0.996055 | + | 0.0887357i | \(0.971717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.37228 | + | 2.52434i | 0.208868 | + | 0.222256i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.29156 | − | 14.3614i | −0.724437 | − | 1.25476i | −0.959205 | − | 0.282711i | \(-0.908766\pi\) |
0.234768 | − | 0.972051i | \(-0.424567\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.5000 | − | 6.06218i | −1.51744 | − | 0.525657i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.1595 | − | 5.98913i | −1.39079 | − | 0.515462i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.3614 | + | 8.29156i | 1.22698 | + | 0.708396i | 0.966397 | − | 0.257056i | \(-0.0827525\pi\) |
0.260581 | + | 0.965452i | \(0.416086\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.0000i | − | 0.848189i | −0.905618 | − | 0.424094i | \(-0.860592\pi\) | ||
0.905618 | − | 0.424094i | \(-0.139408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.5000 | − | 4.97494i | −1.38955 | − | 0.418965i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.63325 | − | 11.4891i | 0.554700 | − | 0.960769i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.0000 | − | 19.0526i | −0.913500 | − | 1.58223i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.95565 | + | 9.93070i | 0.573693 | + | 0.819071i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.3614 | − | 8.29156i | 1.17653 | − | 0.679271i | 0.221322 | − | 0.975201i | \(-0.428963\pi\) |
0.955210 | + | 0.295929i | \(0.0956293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.06218 | + | 3.50000i | 0.493333 | + | 0.284826i | 0.725956 | − | 0.687741i | \(-0.241398\pi\) |
−0.232623 | + | 0.972567i | \(0.574731\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.50000 | − | 8.29156i | 0.444649 | − | 0.670333i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.94987 | 0.799193 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.50000 | + | 2.59808i | −0.119713 | + | 0.207349i | −0.919654 | − | 0.392730i | \(-0.871531\pi\) |
0.799941 | + | 0.600079i | \(0.204864\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.59230 | + | 1.31386i | −0.443498 | + | 0.104196i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.87228 | − | 8.29156i | 0.226367 | − | 0.653467i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.06218 | − | 3.50000i | 0.474826 | − | 0.274141i | −0.243432 | − | 0.969918i | \(-0.578273\pi\) |
0.718258 | + | 0.695777i | \(0.244940\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.0475 | + | 13.8839i | 1.01575 | + | 1.08086i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.63325 | 0.513296 | 0.256648 | − | 0.966505i | \(-0.417382\pi\) | ||||
0.256648 | + | 0.966505i | \(0.417382\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.35135 | + | 18.8030i | 0.715116 | + | 1.43790i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.61684 | − | 4.97494i | 0.655127 | − | 0.378237i | −0.135291 | − | 0.990806i | \(-0.543197\pi\) |
0.790418 | + | 0.612568i | \(0.209864\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.5885 | − | 3.00000i | 1.17838 | − | 0.226779i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.31386 | − | 5.59230i | −0.0987557 | − | 0.420343i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.65831 | + | 2.87228i | −0.123948 | + | 0.214684i | −0.921321 | − | 0.388802i | \(-0.872889\pi\) |
0.797373 | + | 0.603487i | \(0.206222\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.0000 | 1.33793 | 0.668965 | − | 0.743294i | \(-0.266738\pi\) | ||||
0.668965 | + | 0.743294i | \(0.266738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.97494 | − | 1.50000i | −0.367758 | − | 0.110883i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.87228 | + | 1.65831i | 0.211174 | + | 0.121922i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.52628 | + | 5.50000i | −0.696631 | + | 0.402200i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.25544 | − | 13.5615i | 0.164059 | − | 0.986451i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.97494 | − | 8.61684i | −0.359974 | − | 0.623493i | 0.627982 | − | 0.778228i | \(-0.283881\pi\) |
−0.987956 | + | 0.154735i | \(0.950548\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.50000 | − | 2.59808i | 0.107972 | − | 0.187014i | −0.806976 | − | 0.590584i | \(-0.798898\pi\) |
0.914949 | + | 0.403570i | \(0.132231\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.63325 | + | 22.0000i | −0.475017 | + | 1.57545i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.8997i | 1.41780i | 0.705310 | + | 0.708899i | \(0.250808\pi\) | ||||
−0.705310 | + | 0.708899i | \(0.749192\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.866025 | − | 0.500000i | −0.0613909 | − | 0.0354441i | 0.468990 | − | 0.883203i | \(-0.344618\pi\) |
−0.530381 | + | 0.847759i | \(0.677951\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.1753 | − | 3.56529i | 1.07038 | − | 0.251476i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.2665 | − | 11.4891i | 0.931126 | − | 0.806379i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.0000 | + | 19.0526i | 0.768273 | + | 1.33069i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.90892 | + | 4.43070i | −0.619213 | + | 0.307955i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 23.2164i | − | 1.60591i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 26.0000i | − | 1.78991i | −0.446153 | − | 0.894957i | \(-0.647206\pi\) | ||
0.446153 | − | 0.894957i | \(-0.352794\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.7446 | − | 15.7359i | 1.14732 | − | 1.07821i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.31662 | + | 5.74456i | 0.226192 | + | 0.391776i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.50000 | + | 7.79423i | 0.101827 | + | 0.529107i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.77300 | + | 11.8030i | 0.187382 | + | 0.797572i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.4891 | − | 6.63325i | −0.772842 | − | 0.446201i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 14.0000i | − | 0.937509i | −0.883328 | − | 0.468755i | \(-0.844703\pi\) | ||
0.883328 | − | 0.468755i | \(-0.155297\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.0000 | − | 9.94987i | −1.00000 | − | 0.663325i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.65831 | + | 2.87228i | −0.110066 | + | 0.190640i | −0.915797 | − | 0.401642i | \(-0.868440\pi\) |
0.805731 | + | 0.592282i | \(0.201773\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.5000 | − | 25.1147i | −0.958187 | − | 1.65963i | −0.726900 | − | 0.686743i | \(-0.759040\pi\) |
−0.231287 | − | 0.972886i | \(-0.574293\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.90892 | + | 12.3139i | −0.586164 | + | 0.810192i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.3614 | − | 8.29156i | 0.940847 | − | 0.543198i | 0.0506213 | − | 0.998718i | \(-0.483880\pi\) |
0.890226 | + | 0.455520i | \(0.150547\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −28.5788 | − | 16.5000i | −1.86428 | − | 1.07634i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.50000 | + | 14.9248i | −0.292306 | + | 0.969471i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.63325 | −0.429069 | −0.214535 | − | 0.976716i | \(-0.568823\pi\) | ||||
−0.214535 | + | 0.976716i | \(0.568823\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.50000 | + | 16.4545i | −0.611949 | + | 1.05993i | 0.378963 | + | 0.925412i | \(0.376281\pi\) |
−0.990912 | + | 0.134515i | \(0.957053\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.5942 | + | 9.18614i | −0.807921 | + | 0.589291i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.61684 | + | 21.5581i | 0.550510 | + | 1.37729i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.2487 | − | 14.0000i | 1.54291 | − | 0.890799i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.7446 | + | 15.7359i | −1.06114 | + | 0.997224i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.8997 | −1.25606 | −0.628031 | − | 0.778189i | \(-0.716139\pi\) | ||||
−0.628031 | + | 0.778189i | \(0.716139\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.0000 | 0.691564 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.8839 | − | 13.0475i | 0.869441 | − | 0.817069i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.1060 | + | 11.6082i | −1.25418 | + | 0.724099i | −0.971936 | − | 0.235245i | \(-0.924411\pi\) |
−0.282240 | + | 0.959344i | \(0.591077\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.866025 | + | 2.50000i | −0.0538122 | + | 0.155342i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.8614 | − | 1.23472i | −1.22939 | − | 0.0764271i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.65831 | − | 2.87228i | 0.102256 | − | 0.177112i | −0.810358 | − | 0.585935i | \(-0.800727\pi\) |
0.912614 | + | 0.408823i | \(0.134061\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.0000 | −0.675725 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.65831 | + | 5.50000i | −0.101487 | + | 0.336595i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.3614 | − | 8.29156i | −0.875630 | − | 0.505545i | −0.00641522 | − | 0.999979i | \(-0.502042\pi\) |
−0.869215 | + | 0.494434i | \(0.835375\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.7224 | + | 8.50000i | −0.894324 | + | 0.516338i | −0.875354 | − | 0.483482i | \(-0.839372\pi\) |
−0.0189696 | + | 0.999820i | \(0.506039\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.2337 | − | 1.87953i | −1.10355 | − | 0.113754i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.94987 | + | 17.2337i | 0.600000 | + | 1.03923i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.50000 | − | 11.2583i | 0.390547 | − | 0.676448i | −0.601975 | − | 0.798515i | \(-0.705619\pi\) |
0.992522 | + | 0.122068i | \(0.0389525\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.97494 | − | 7.50000i | 0.297842 | − | 0.449013i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.63325i | 0.395706i | 0.980232 | + | 0.197853i | \(0.0633969\pi\) | ||||
−0.980232 | + | 0.197853i | \(0.936603\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.9904 | + | 7.50000i | 0.772198 | + | 0.445829i | 0.833658 | − | 0.552281i | \(-0.186242\pi\) |
−0.0614601 | + | 0.998110i | \(0.519576\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.19702 | + | 39.1461i | 0.544784 | + | 2.31881i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.2665 | + | 11.4891i | −0.783097 | + | 0.678182i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.00000 | − | 5.19615i | −0.176471 | − | 0.305656i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.0974 | − | 9.48913i | 0.591917 | − | 0.556262i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.2665i | 0.775037i | 0.921862 | + | 0.387519i | \(0.126668\pi\) | ||||
−0.921862 | + | 0.387519i | \(0.873332\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 11.0000i | − | 0.640445i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.9891 | − | 2.89303i | 0.985809 | − | 0.167871i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.63325 | + | 11.4891i | 0.383611 | + | 0.664433i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | + | 3.46410i | −0.230556 | + | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.59230 | − | 1.31386i | 0.321269 | − | 0.0754792i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.61684 | − | 4.97494i | −0.493399 | − | 0.284864i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.00000i | 0.342438i | 0.985233 | + | 0.171219i | \(0.0547706\pi\) | ||||
−0.985233 | + | 0.171219i | \(0.945229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.50000 | − | 18.2414i | 0.312884 | − | 1.03772i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.97494 | + | 8.61684i | −0.282103 | + | 0.488616i | −0.971902 | − | 0.235384i | \(-0.924365\pi\) |
0.689800 | + | 0.724000i | \(0.257699\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.50000 | + | 7.79423i | 0.254355 | + | 0.440556i | 0.964720 | − | 0.263278i | \(-0.0848035\pi\) |
−0.710365 | + | 0.703833i | \(0.751470\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.1436 | − | 24.2921i | 0.571529 | − | 1.36871i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.8505 | + | 14.9248i | −1.45191 | + | 0.838261i | −0.998590 | − | 0.0530866i | \(-0.983094\pi\) |
−0.453321 | + | 0.891348i | \(0.649761\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.0526 | + | 11.0000i | 1.06674 | + | 0.615882i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.50000 | + | 1.65831i | 0.306980 | + | 0.0925580i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.2164 | −1.29179 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0000 | + | 20.7846i | −0.665640 | + | 1.15292i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.98072 | + | 8.43070i | 0.109534 | + | 0.466219i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.61684 | − | 24.8747i | 0.475062 | − | 1.37139i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.7224 | + | 8.50000i | −0.809218 | + | 0.467202i | −0.846684 | − | 0.532096i | \(-0.821405\pi\) |
0.0374662 | + | 0.999298i | \(0.488071\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.68614 | − | 1.33591i | 0.147200 | − | 0.0732073i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 29.8496 | 1.63086 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.0000 | 1.52526 | 0.762629 | − | 0.646837i | \(-0.223908\pi\) | ||||
0.762629 | + | 0.646837i | \(0.223908\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.86797 | − | 8.37228i | −0.427329 | − | 0.454720i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.61684 | + | 4.97494i | −0.466628 | + | 0.269408i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −18.5475 | + | 4.35758i | −0.998566 | + | 0.234604i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.9248 | − | 25.8505i | 0.801206 | − | 1.38773i | −0.117617 | − | 0.993059i | \(-0.537526\pi\) |
0.918823 | − | 0.394670i | \(-0.129141\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.00000 | −0.428230 | −0.214115 | − | 0.976808i | \(-0.568687\pi\) | ||||
−0.214115 | + | 0.976808i | \(0.568687\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.2665 | + | 16.0000i | 0.708113 | + | 0.854017i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.5951 | − | 18.2414i | −1.68164 | − | 0.970894i | −0.960574 | − | 0.278024i | \(-0.910320\pi\) |
−0.721063 | − | 0.692869i | \(-0.756346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 38.1051 | − | 22.0000i | 2.02241 | − | 1.16764i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.3139 | + | 8.90892i | 0.651719 | + | 0.471510i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.2414 | − | 31.5951i | −0.962746 | − | 1.66753i | −0.715552 | − | 0.698559i | \(-0.753825\pi\) |
−0.247194 | − | 0.968966i | \(-0.579509\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | − | 25.9808i | 0.789474 | − | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.2164i | 1.21520i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.866025 | + | 0.500000i | 0.0452062 | + | 0.0260998i | 0.522433 | − | 0.852680i | \(-0.325025\pi\) |
−0.477227 | + | 0.878780i | \(0.658358\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.8614 | + | 1.23472i | 1.03394 | + | 0.0642768i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.65831 | − | 8.61684i | −0.0860953 | − | 0.447364i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.50000 | + | 11.2583i | 0.336557 | + | 0.582934i | 0.983783 | − | 0.179364i | \(-0.0574041\pi\) |
−0.647225 | + | 0.762299i | \(0.724071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.93398 | − | 4.18614i | −0.203150 | − | 0.216171i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.5330i | 1.36652i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0000i | 1.23280i | 0.787434 | + | 0.616399i | \(0.211409\pi\) | ||||
−0.787434 | + | 0.616399i | \(0.788591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.37228 | + | 2.52434i | 0.121536 | + | 0.129326i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.29156 | + | 14.3614i | 0.423679 | + | 0.733834i | 0.996296 | − | 0.0859894i | \(-0.0274051\pi\) |
−0.572617 | + | 0.819823i | \(0.694072\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.0000 | + | 19.0526i | −1.12122 | + | 0.971008i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.98844 | + | 0.372281i | 0.304409 | + | 0.0189241i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.87228 | + | 1.65831i | 0.145630 | + | 0.0840798i | 0.571045 | − | 0.820919i | \(-0.306538\pi\) |
−0.425414 | + | 0.904999i | \(0.639872\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 11.0000i | − | 0.556294i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.5000 | − | 8.29156i | −1.38719 | − | 0.418254i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.9248 | + | 25.8505i | −0.750949 | + | 1.30068i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.50000 | − | 11.2583i | −0.326226 | − | 0.565039i | 0.655534 | − | 0.755166i | \(-0.272444\pi\) |
−0.981760 | + | 0.190126i | \(0.939110\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −29.2786 | + | 13.1060i | −1.46576 | + | 0.656119i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.3614 | − | 8.29156i | 0.717174 | − | 0.414061i | −0.0965374 | − | 0.995329i | \(-0.530777\pi\) |
0.813712 | + | 0.581269i | \(0.197443\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.3923 | − | 6.00000i | −0.517678 | − | 0.298881i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −27.5000 | + | 11.6082i | −1.36649 | + | 0.576815i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.31662 | −0.164399 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.50000 | − | 12.9904i | 0.370851 | − | 0.642333i | −0.618846 | − | 0.785513i | \(-0.712399\pi\) |
0.989697 | + | 0.143180i | \(0.0457327\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27.9615 | − | 6.56930i | 1.37924 | − | 0.324040i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.61684 | − | 1.65831i | 0.424007 | − | 0.0816002i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.1051 | + | 22.0000i | −1.87051 | + | 1.07994i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.8614 | − | 12.6217i | −0.580856 | − | 0.618087i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.5330 | 1.29622 | 0.648111 | − | 0.761546i | \(-0.275559\pi\) | ||||
0.648111 | + | 0.761546i | \(0.275559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.00000 | 0.389896 | 0.194948 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −26.7268 | + | 13.2921i | −1.29950 | + | 0.646285i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.2337 | − | 9.94987i | 0.835957 | − | 0.482640i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.59808 | − | 7.50000i | 0.125730 | − | 0.362950i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.25544 | − | 22.3692i | −0.253735 | − | 1.07999i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.6082 | − | 20.1060i | 0.559147 | − | 0.968470i | −0.438421 | − | 0.898770i | \(-0.644462\pi\) |
0.997568 | − | 0.0697009i | \(-0.0222045\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.0000 | −0.961139 | −0.480569 | − | 0.876957i | \(-0.659570\pi\) | ||||
−0.480569 | + | 0.876957i | \(0.659570\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −36.4829 | − | 11.0000i | −1.74922 | − | 0.527410i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.1060 | + | 11.6082i | 0.961799 | + | 0.555295i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.79423 | − | 4.50000i | 0.371998 | − | 0.214773i | −0.302333 | − | 0.953202i | \(-0.597765\pi\) |
0.674331 | + | 0.738429i | \(0.264432\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.5584 | + | 4.28384i | 0.978972 | + | 0.203992i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.9248 | + | 25.8505i | 0.709099 | + | 1.22820i | 0.965192 | + | 0.261544i | \(0.0842315\pi\) |
−0.256092 | + | 0.966652i | \(0.582435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.50000 | + | 9.52628i | −0.260725 | + | 0.451589i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.29156 | − | 27.5000i | 0.392177 | − | 1.30071i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 19.8997i | − | 0.939127i | −0.882899 | − | 0.469564i | \(-0.844411\pi\) | ||
0.882899 | − | 0.469564i | \(-0.155589\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.0526 | − | 11.0000i | −0.897150 | − | 0.517970i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.8030 | − | 2.77300i | 0.554553 | − | 0.130287i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −33.1662 | − | 11.4891i | −1.55486 | − | 0.538619i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.50000 | − | 2.59808i | −0.0701670 | − | 0.121533i | 0.828807 | − | 0.559534i | \(-0.189020\pi\) |
−0.898974 | + | 0.438001i | \(0.855687\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.89303 | − | 16.9891i | −0.135035 | − | 0.792984i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 33.1662i | − | 1.54471i | −0.635193 | − | 0.772353i | \(-0.719080\pi\) | ||
0.635193 | − | 0.772353i | \(-0.280920\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.0000i | 1.76601i | 0.469364 | + | 0.883005i | \(0.344483\pi\) | ||||
−0.469364 | + | 0.883005i | \(0.655517\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.5584 | − | 11.8020i | 0.582383 | − | 0.547302i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.65831 | − | 2.87228i | −0.0767375 | − | 0.132913i | 0.825103 | − | 0.564982i | \(-0.191117\pi\) |
−0.901841 | + | 0.432069i | \(0.857784\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.50000 | + | 23.3827i | 0.207791 | + | 1.07971i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.18843 | + | 5.05842i | 0.0547600 | + | 0.233080i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.74456 | − | 3.31662i | −0.264135 | − | 0.152499i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 42.0000i | 1.92709i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.50000 | + | 8.29156i | −0.251828 | + | 0.379645i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.29156 | − | 14.3614i | 0.378851 | − | 0.656189i | −0.612044 | − | 0.790824i | \(-0.709653\pi\) |
0.990895 | + | 0.134634i | \(0.0429859\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | − | 3.46410i | −0.0911922 | − | 0.157949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.20965 | − | 13.8723i | −0.282549 | − | 0.631211i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.9783 | − | 13.2665i | 1.04339 | − | 0.602401i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.7224 | + | 8.50000i | 0.667137 | + | 0.385172i | 0.794991 | − | 0.606621i | \(-0.207476\pi\) |
−0.127854 | + | 0.991793i | \(0.540809\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.50000 | − | 11.6082i | 0.158275 | − | 0.524940i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.63325 | −0.299354 | −0.149677 | − | 0.988735i | \(-0.547823\pi\) | ||||
−0.149677 | + | 0.988735i | \(0.547823\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.0000 | − | 19.0526i | 0.495415 | − | 0.858084i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 32.9364 | + | 2.04755i | 1.48038 | + | 0.0920304i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.9783 | + | 26.5330i | 1.03072 | + | 1.19017i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.3109 | − | 17.5000i | 1.35690 | − | 0.783408i | 0.367697 | − | 0.929946i | \(-0.380146\pi\) |
0.989205 | + | 0.146538i | \(0.0468131\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.37228 | − | 7.86797i | 0.374046 | − | 0.351515i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.0000 | 0.489494 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.78651 | − | 3.55842i | 0.168165 | − | 0.158035i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.3614 | − | 8.29156i | 0.636558 | − | 0.367517i | −0.146729 | − | 0.989177i | \(-0.546875\pi\) |
0.783287 | + | 0.621660i | \(0.213541\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.1865 | + | 3.50000i | −0.804525 | + | 0.154831i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 34.1060 | + | 12.6405i | 1.50582 | + | 0.558093i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.2414 | − | 31.5951i | 0.803814 | − | 1.39225i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.0000 | 1.45134 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.97494 | − | 16.5000i | 0.218376 | − | 0.724270i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.1060 | + | 11.6082i | 0.880859 | + | 0.508564i | 0.870941 | − | 0.491387i | \(-0.163510\pi\) |
0.00991713 | + | 0.999951i | \(0.496843\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.4545 | + | 9.50000i | −0.719504 | + | 0.415406i | −0.814570 | − | 0.580065i | \(-0.803027\pi\) |
0.0950659 | + | 0.995471i | \(0.469694\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.1168 | − | 22.2766i | 0.703397 | − | 0.972231i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.97494 | + | 8.61684i | 0.216712 | + | 0.375356i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.00000 | − | 10.3923i | 0.260870 | − | 0.451839i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.29156 | − | 5.50000i | −0.359823 | − | 0.238680i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 26.5330i | − | 1.14927i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.52628 | + | 5.50000i | 0.411857 | + | 0.237786i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.31386 | + | 5.59230i | 0.0566972 | + | 0.241325i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.2414 | − | 14.3614i | −0.785714 | − | 0.618590i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.5000 | − | 32.0429i | −0.795377 | − | 1.37763i | −0.922599 | − | 0.385759i | \(-0.873939\pi\) |
0.127222 | − | 0.991874i | \(-0.459394\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.7190 | − | 21.3505i | 0.974967 | − | 0.916239i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.5831i | 0.710343i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.0000i | 1.71028i | 0.518400 | + | 0.855138i | \(0.326528\pi\) | ||||
−0.518400 | + | 0.855138i | \(0.673472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.05842 | + | 4.00772i | −0.343925 | + | 0.171045i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.2164 | + | 40.2119i | 0.989051 | + | 1.71309i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.5000 | − | 7.79423i | −0.956797 | − | 0.331444i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.59230 | − | 1.31386i | 0.237380 | − | 0.0557702i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.87228 | + | 1.65831i | 0.121702 | + | 0.0702650i | 0.559615 | − | 0.828752i | \(-0.310949\pi\) |
−0.437913 | + | 0.899017i | \(0.644282\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.00000i | − | 0.338364i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.50000 | + | 18.2414i | −0.232210 | + | 0.770154i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.97494 | + | 8.61684i | −0.209669 | + | 0.363157i | −0.951610 | − | 0.307308i | \(-0.900572\pi\) |
0.741942 | + | 0.670465i | \(0.233905\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.0000 | − | 19.0526i | −0.462773 | − | 0.801547i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.2390 | − | 19.7921i | −0.555988 | − | 0.831190i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.8505 | + | 14.9248i | −1.08371 | + | 0.625681i | −0.931895 | − | 0.362728i | \(-0.881845\pi\) |
−0.151816 | + | 0.988409i | \(0.548512\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.33013 | − | 2.50000i | −0.181210 | − | 0.104622i | 0.406651 | − | 0.913584i | \(-0.366697\pi\) |
−0.587861 | + | 0.808962i | \(0.700030\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.5000 | − | 4.97494i | −0.689297 | − | 0.207831i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.8997 | −0.829877 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.5000 | + | 30.3109i | −0.728535 | + | 1.26186i | 0.228968 | + | 0.973434i | \(0.426465\pi\) |
−0.957503 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.18843 | − | 5.05842i | −0.0493895 | − | 0.210221i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.9783 | − | 26.5330i | −0.953298 | − | 1.10077i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.52628 | − | 5.50000i | 0.394538 | − | 0.227787i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.7228 | + | 35.6357i | 0.732748 | + | 1.47335i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.5330 | −1.09513 | −0.547567 | − | 0.836762i | \(-0.684446\pi\) | ||||
−0.547567 | + | 0.836762i | \(0.684446\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.0000 | −0.865290 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.6039 | + | 25.1168i | 0.970935 | + | 1.03317i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.87228 | − | 1.65831i | 0.117950 | − | 0.0680987i | −0.439864 | − | 0.898064i | \(-0.644973\pi\) |
0.557815 | + | 0.829966i | \(0.311640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.0526 | + | 22.0000i | 0.781079 | + | 0.901912i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.68614 | + | 0.396143i | −0.0690091 | + | 0.0162131i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.97494 | + | 8.61684i | −0.203270 | + | 0.352075i | −0.949580 | − | 0.313524i | \(-0.898490\pi\) |
0.746310 | + | 0.665599i | \(0.231824\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.0000 | −0.652654 | −0.326327 | − | 0.945257i | \(-0.605811\pi\) | ||||
−0.326327 | + | 0.945257i | \(0.605811\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.9248 | − | 22.5000i | 0.607785 | − | 0.916271i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.06218 | + | 3.50000i | −0.246056 | + | 0.142061i | −0.617957 | − | 0.786212i | \(-0.712039\pi\) |
0.371901 | + | 0.928272i | \(0.378706\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.11684 | − | 30.2372i | 0.126301 | − | 1.22527i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.8997 | + | 34.4674i | 0.805058 | + | 1.39440i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.500000 | + | 0.866025i | −0.0201948 | + | 0.0349784i | −0.875946 | − | 0.482409i | \(-0.839762\pi\) |
0.855751 | + | 0.517387i | \(0.173095\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 36.4829 | + | 11.0000i | 1.47113 | + | 0.443563i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.63325i | 0.267045i | 0.991046 | + | 0.133522i | \(0.0426288\pi\) | ||||
−0.991046 | + | 0.133522i | \(0.957371\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.6506 | + | 12.5000i | 0.870212 | + | 0.502417i | 0.867419 | − | 0.497579i | \(-0.165777\pi\) |
0.00279365 | + | 0.999996i | \(0.499111\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.98913 | + | 16.1595i | −0.240335 | + | 0.648460i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.29156 | − | 2.87228i | −0.332194 | − | 0.115076i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −27.5379 | − | 29.3030i | −1.09976 | − | 1.17025i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.31662i | 0.132242i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 18.0000i | − | 0.716569i | −0.933613 | − | 0.358284i | \(-0.883362\pi\) | ||
0.933613 | − | 0.358284i | \(-0.116638\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −30.8397 | − | 32.8164i | −1.22577 | − | 1.30433i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.31662 | + | 5.74456i | 0.131616 | + | 0.227966i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.00000 | − | 27.7128i | 0.158486 | − | 1.09802i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.46943 | − | 39.7228i | 0.0976893 | − | 1.57141i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.5951 | + | 18.2414i | 1.24793 | + | 0.720493i | 0.970696 | − | 0.240309i | \(-0.0772487\pi\) |
0.277235 | + | 0.960802i | \(0.410582\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.00000i | − | 0.0788723i | −0.999222 | − | 0.0394362i | \(-0.987444\pi\) | ||
0.999222 | − | 0.0394362i | \(-0.0125562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.0000 | + | 3.31662i | 0.433125 | + | 0.130592i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.65831 | − | 2.87228i | 0.0651950 | − | 0.112921i | −0.831585 | − | 0.555397i | \(-0.812566\pi\) |
0.896780 | + | 0.442476i | \(0.145900\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.50000 | + | 9.52628i | 0.215894 | + | 0.373939i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.1383 | + | 8.05842i | 0.436545 | + | 0.315834i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.87228 | + | 1.65831i | −0.112401 | + | 0.0648948i | −0.555147 | − | 0.831753i | \(-0.687338\pi\) |
0.442746 | + | 0.896647i | \(0.354005\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −47.6314 | − | 27.5000i | −1.86111 | − | 1.07451i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.5000 | + | 11.6082i | 0.682740 | + | 0.452878i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.5330 | −1.03358 | −0.516789 | − | 0.856113i | \(-0.672873\pi\) | ||||
−0.516789 | + | 0.856113i | \(0.672873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.5000 | + | 33.7750i | −0.758462 | + | 1.31369i | 0.185173 | + | 0.982706i | \(0.440716\pi\) |
−0.943635 | + | 0.330989i | \(0.892618\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.3692 | + | 5.25544i | −0.868747 | + | 0.204104i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −60.3179 | + | 11.6082i | −2.33903 | + | 0.450146i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.0526 | + | 11.0000i | −0.737718 | + | 0.425922i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.6060 | − | 17.6704i | −0.642024 | − | 0.683176i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.94987 | 0.384111 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.0000 | 1.54189 | 0.770943 | − | 0.636904i | \(-0.219785\pi\) | ||||
0.770943 | + | 0.636904i | \(0.219785\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −30.7345 | + | 5.23369i | −1.18297 | + | 0.201445i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.61684 | + | 4.97494i | −0.331172 | + | 0.191202i | −0.656361 | − | 0.754447i | \(-0.727905\pi\) |
0.325189 | + | 0.945649i | \(0.394572\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.8564 | + | 16.0000i | 0.531760 | + | 0.614024i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.31386 | + | 5.59230i | 0.0503472 | + | 0.214297i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.6082 | − | 20.1060i | 0.444175 | − | 0.769334i | −0.553819 | − | 0.832637i | \(-0.686830\pi\) |
0.997994 | + | 0.0633033i | \(0.0201635\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 55.0000 | 2.10144 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −48.0911 | − | 14.5000i | −1.83479 | − | 0.553210i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.4891 | + | 6.63325i | 0.437701 | + | 0.252707i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.5788 | + | 16.5000i | −1.08719 | + | 0.627690i | −0.932827 | − | 0.360325i | \(-0.882666\pi\) |
−0.154363 | + | 0.988014i | \(0.549333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.36141 | + | 26.1094i | 0.127689 | + | 0.991814i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.5831 | − | 28.7228i | −0.629034 | − | 1.08952i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.0000 | + | 19.0526i | −0.416655 | + | 0.721667i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.29156 | − | 27.5000i | 0.313616 | − | 1.04015i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.2665i | − | 0.501069i | −0.968108 | − | 0.250534i | \(-0.919394\pi\) | ||
0.968108 | − | 0.250534i | \(-0.0806063\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.06218 | − | 3.50000i | −0.228639 | − | 0.132005i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −55.6426 | + | 13.0727i | −2.09562 | + | 0.492348i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.65831 | + | 8.61684i | 0.0623673 | + | 0.324070i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.5000 | + | 28.5788i | 0.619671 | + | 1.07330i | 0.989546 | + | 0.144219i | \(0.0460671\pi\) |
−0.369875 | + | 0.929081i | \(0.620600\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0232 | + | 24.1753i | 0.450904 | + | 0.906643i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 9.94987i | − | 0.372626i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 44.0000i | − | 1.64551i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.37228 | + | 7.86797i | −0.312669 | + | 0.293835i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.6082 | + | 20.1060i | 0.432912 | + | 0.749826i | 0.997123 | − | 0.0758050i | \(-0.0241526\pi\) |
−0.564210 | + | 0.825631i | \(0.690819\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.5000 | + | 9.52628i | 1.02415 | + | 0.354777i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.52673 | + | 32.0367i | 0.279922 | + | 1.19146i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −34.4674 | − | 19.8997i | −1.28009 | − | 0.739058i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 10.0000i | − | 0.370879i | −0.982656 | − | 0.185440i | \(-0.940629\pi\) | ||
0.982656 | − | 0.185440i | \(-0.0593710\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.00000 | + | 26.5330i | −0.185185 | + | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.31662 | + | 5.74456i | −0.122670 | + | 0.212470i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.50000 | − | 6.06218i | −0.129275 | − | 0.223912i | 0.794121 | − | 0.607760i | \(-0.207932\pi\) |
−0.923396 | + | 0.383849i | \(0.874598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 36.4468 | + | 16.9891i | 1.34436 | + | 0.626653i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.8505 | + | 14.9248i | −0.952217 | + | 0.549762i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.8468 | + | 15.5000i | 0.987575 | + | 0.570177i | 0.904549 | − | 0.426371i | \(-0.140208\pi\) |
0.0830265 | + | 0.996547i | \(0.473541\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.0000 | − | 46.4327i | 0.514303 | − | 1.70575i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.2665 | 0.486701 | 0.243350 | − | 0.969938i | \(-0.421754\pi\) | ||||
0.243350 | + | 0.969938i | \(0.421754\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.5000 | − | 47.6314i | 1.00752 | − | 1.74508i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.46943 | + | 39.7228i | −0.0903519 | + | 1.45338i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.87228 | + | 8.29156i | −0.104951 | + | 0.302967i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.33013 | − | 2.50000i | 0.158009 | − | 0.0912263i | −0.418911 | − | 0.908027i | \(-0.637588\pi\) |
0.576919 | + | 0.816801i | \(0.304255\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −25.1168 | + | 23.6039i | −0.915309 | + | 0.860174i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.2164 | 0.844930 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.0000 | −1.74459 | −0.872295 | − | 0.488980i | \(-0.837369\pi\) | ||||
−0.872295 | + | 0.488980i | \(0.837369\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.8839 | − | 13.0475i | 0.503952 | − | 0.473596i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.1060 | + | 11.6082i | −0.728841 | + | 0.420796i | −0.817998 | − | 0.575221i | \(-0.804916\pi\) |
0.0891571 | + | 0.996018i | \(0.471583\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.9904 | + | 2.50000i | −0.470283 | + | 0.0905061i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.04755 | − | 32.9364i | 0.0740292 | − | 1.19082i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.63325 | + | 11.4891i | −0.239513 | + | 0.414848i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.0000 | −0.576975 | −0.288487 | − | 0.957484i | \(-0.593152\pi\) | ||||
−0.288487 | + | 0.957484i | \(0.593152\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.6082 | + | 38.5000i | −0.418059 | + | 1.38654i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.3614 | + | 8.29156i | 0.516544 | + | 0.298227i | 0.735519 | − | 0.677504i | \(-0.236938\pi\) |
−0.218976 | + | 0.975730i | \(0.570272\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.5885 | − | 9.00000i | 0.559954 | − | 0.323290i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.87228 | + | 4.18265i | 0.0671677 | + | 0.150052i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.2164 | − | 40.2119i | −0.831813 | − | 1.44074i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.0000 | + | 38.1051i | −0.787222 | + | 1.36351i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −26.5330 | + | 22.0000i | −0.948212 | + | 0.786216i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.94987i | 0.355126i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.9711 | + | 22.5000i | 1.38917 | + | 0.802038i | 0.993222 | − | 0.116234i | \(-0.0370822\pi\) |
0.395949 | + | 0.918272i | \(0.370416\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.31386 | − | 5.59230i | −0.0467746 | − | 0.199091i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.2665 | − | 11.4891i | 0.471702 | − | 0.408506i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00000 | + | 10.3923i | 0.213066 | + | 0.369042i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.8839 | + | 13.0475i | −0.492410 | + | 0.462749i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.63325i | 0.234962i | 0.993075 | + | 0.117481i | \(0.0374819\pi\) | ||||
−0.993075 | + | 0.117481i | \(0.962518\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 33.0000i | − | 1.16746i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.43070 | + | 8.90892i | 0.156551 | + | 0.314781i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.6082 | − | 20.1060i | −0.409644 | − | 0.709524i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.50000 | − | 28.5788i | −0.193850 | − | 1.00727i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.9615 | + | 6.56930i | −0.984291 | + | 0.231250i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.87228 | − | 1.65831i | −0.100984 | − | 0.0583032i | 0.448657 | − | 0.893704i | \(-0.351902\pi\) |
−0.549641 | + | 0.835401i | \(0.685236\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30.0000i | − | 1.05344i | −0.850038 | − | 0.526721i | \(-0.823421\pi\) | ||
0.850038 | − | 0.526721i | \(-0.176579\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.50000 | + | 28.1913i | −0.298108 | + | 0.988712i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.6082 | − | 20.1060i | 0.406617 | − | 0.704281i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.00000 | − | 12.1244i | −0.244899 | − | 0.424178i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.2434 | + | 19.2554i | −0.882075 | + | 0.672839i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.5951 | + | 18.2414i | −1.10268 | + | 0.636631i | −0.936923 | − | 0.349537i | \(-0.886339\pi\) |
−0.165754 | + | 0.986167i | \(0.553006\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.9904 | − | 7.50000i | −0.452816 | − | 0.261434i | 0.256203 | − | 0.966623i | \(-0.417529\pi\) |
−0.709019 | + | 0.705190i | \(0.750862\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 33.0000 | + | 9.94987i | 1.14891 | + | 0.346410i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.7995 | 1.38396 | 0.691982 | − | 0.721915i | \(-0.256738\pi\) | ||||
0.691982 | + | 0.721915i | \(0.256738\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.5000 | + | 25.1147i | −0.503606 | + | 0.872271i | 0.496385 | + | 0.868102i | \(0.334660\pi\) |
−0.999991 | + | 0.00416865i | \(0.998673\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.14987 | − | 21.9198i | −0.178647 | − | 0.760390i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.3614 | + | 18.2414i | −0.497593 | + | 0.632028i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.0526 | − | 11.0000i | 0.659341 | − | 0.380671i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.61684 | − | 15.3672i | −0.0904514 | − | 0.531170i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.2665 | 0.458010 | 0.229005 | − | 0.973425i | \(-0.426453\pi\) | ||||
0.229005 | + | 0.973425i | \(0.426453\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.0000 | −0.517241 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.86797 | + | 8.37228i | 0.270987 | + | 0.288357i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.61684 | − | 4.97494i | 0.296428 | − | 0.171143i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.2921 | − | 5.94215i | 0.868023 | − | 0.203934i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.65831 | − | 2.87228i | 0.0568462 | − | 0.0984605i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.0000 | −0.684787 | −0.342393 | − | 0.939557i | \(-0.611238\pi\) | ||||
−0.342393 | + | 0.939557i | \(0.611238\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 58.0409 | + | 38.5000i | 1.98496 | + | 1.31667i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.3614 | − | 8.29156i | −0.490576 | − | 0.283234i | 0.234237 | − | 0.972179i | \(-0.424741\pi\) |
−0.724814 | + | 0.688945i | \(0.758074\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.7224 | − | 8.50000i | 0.502323 | − | 0.290016i | −0.227349 | − | 0.973813i | \(-0.573006\pi\) |
0.729672 | + | 0.683797i | \(0.239673\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.11684 | + | 30.2372i | −0.106222 | + | 1.03048i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.2414 | + | 31.5951i | 0.620946 | + | 1.07551i | 0.989310 | + | 0.145828i | \(0.0465846\pi\) |
−0.368364 | + | 0.929682i | \(0.620082\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.5000 | − | 28.5788i | 0.561017 | − | 0.971710i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.94987 | − | 3.00000i | −0.337915 | − | 0.101885i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 29.8496i | − | 1.01258i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.1769 | − | 18.0000i | −1.05639 | − | 0.609907i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.48913 | − | 23.9538i | 0.0503993 | − | 0.810712i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.63325 | − | 5.74456i | 0.224245 | − | 0.194202i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.5000 | + | 19.9186i | 0.388327 | + | 0.672603i | 0.992225 | − | 0.124459i | \(-0.0397196\pi\) |
−0.603897 | + | 0.797062i | \(0.706386\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.7359 | + | 16.7446i | 0.530760 | + | 0.564780i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 6.00000i | − | 0.201916i | −0.994891 | − | 0.100958i | \(-0.967809\pi\) | ||
0.994891 | − | 0.100958i | \(-0.0321908\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.0475 | − | 13.8839i | −0.438589 | − | 0.466701i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.6082 | − | 20.1060i | −0.389765 | − | 0.675092i | 0.602653 | − | 0.798003i | \(-0.294110\pi\) |
−0.992418 | + | 0.122911i | \(0.960777\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00000 | + | 3.46410i | −0.134156 | + | 0.116182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.0116 | − | 23.8030i | 0.603411 | − | 0.797430i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 60.3179 | + | 34.8246i | 2.01846 | + | 1.16536i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.0000i | 0.367689i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.0000 | + | 6.63325i | 0.734559 | + | 0.221478i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.94987 | − | 17.2337i | 0.331847 | − | 0.574776i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.50000 | − | 9.52628i | −0.183232 | − | 0.317366i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.939764 | + | 9.11684i | −0.0312734 | + | 0.303390i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 51.7011 | − | 29.8496i | 1.71860 | − | 0.992235i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.8993 | + | 26.5000i | 1.52406 | + | 0.879918i | 0.999594 | + | 0.0284883i | \(0.00906934\pi\) |
0.524469 | + | 0.851430i | \(0.324264\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.50000 | − | 8.29156i | 0.182423 | − | 0.275014i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.5330 | −0.879077 | −0.439539 | − | 0.898224i | \(-0.644858\pi\) | ||||
−0.439539 | + | 0.898224i | \(0.644858\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.0000 | − | 38.1051i | 0.728094 | − | 1.26110i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.7769 | + | 3.94158i | −0.554627 | + | 0.130305i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.3614 | − | 41.4578i | 0.474255 | − | 1.36906i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.9186 | + | 11.5000i | −0.657053 | + | 0.379350i | −0.791153 | − | 0.611618i | \(-0.790519\pi\) |
0.134100 | + | 0.990968i | \(0.457186\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.11684 | + | 7.57301i | 0.234508 | + | 0.249539i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −53.0660 | −1.74669 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.6950 | − | 29.5475i | −0.482646 | − | 0.970469i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.1060 | − | 11.6082i | 0.659655 | − | 0.380852i | −0.132490 | − | 0.991184i | \(-0.542297\pi\) |
0.792146 | + | 0.610332i | \(0.208964\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.1865 | − | 45.5000i | −0.596040 | − | 1.49120i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.94158 | + | 16.7769i | 0.129041 | + | 0.549251i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.2414 | + | 31.5951i | −0.596559 | + | 1.03327i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.9248 | + | 4.50000i | 0.487053 | + | 0.146852i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.61684 | + | 4.97494i | 0.280901 | + | 0.162178i | 0.633831 | − | 0.773471i | \(-0.281481\pi\) |
−0.352930 | + | 0.935650i | \(0.614815\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.0526 | − | 11.0000i | 0.620437 | − | 0.358209i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.0109 | − | 42.6925i | −0.520834 | − | 1.38879i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.97494 | + | 8.61684i | 0.161664 | + | 0.280010i | 0.935465 | − | 0.353418i | \(-0.114981\pi\) |
−0.773802 | + | 0.633428i | \(0.781647\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.0000 | − | 24.2487i | 0.454459 | − | 0.787146i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.9248 | + | 49.5000i | −0.483970 | + | 1.60515i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 19.8997i | − | 0.644616i | −0.946635 | − | 0.322308i | \(-0.895541\pi\) | ||
0.946635 | − | 0.322308i | \(-0.104459\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.5788 | − | 16.5000i | −0.924789 | − | 0.533927i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37.0951 | − | 8.71516i | 1.19911 | − | 0.281721i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.29156 | + | 43.0842i | 0.267749 | + | 1.39126i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0000 | − | 19.0526i | −0.354839 | − | 0.614599i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.90892 | − | 4.43070i | 0.287086 | − | 0.142777i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 9.94987i | − | 0.320298i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.00000i | 0.0643157i | 0.999483 | + | 0.0321578i | \(0.0102379\pi\) | ||||
−0.999483 | + | 0.0321578i | \(0.989762\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29.3030 | + | 27.5379i | −0.941347 | + | 0.884644i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.29156 | − | 14.3614i | −0.266089 | − | 0.460879i | 0.701759 | − | 0.712414i | \(-0.252398\pi\) |
−0.967848 | + | 0.251535i | \(0.919065\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.0000 | − | 17.3205i | 0.641171 | − | 0.555270i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.50744 | + | 40.4674i | 0.304482 | + | 1.29599i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.87228 | + | 1.65831i | 0.0918924 | + | 0.0530541i | 0.545242 | − | 0.838279i | \(-0.316438\pi\) |
−0.453350 | + | 0.891333i | \(0.649771\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 11.0000i | − | 0.351562i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.5000 | + | 8.29156i | 0.399094 | + | 0.264729i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.1913 | + | 48.8288i | −0.899163 | + | 1.55740i | −0.0705972 | + | 0.997505i | \(0.522490\pi\) |
−0.828566 | + | 0.559891i | \(0.810843\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.0000 | + | 57.1577i | 1.05147 | + | 1.82120i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18.6290 | − | 41.6168i | −0.592966 | − | 1.32468i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.74456 | − | 3.31662i | 0.182666 | − | 0.105463i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.2391 | − | 21.5000i | −1.18294 | − | 0.682970i | −0.226246 | − | 0.974070i | \(-0.572645\pi\) |
−0.956693 | + | 0.291100i | \(0.905979\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.50000 | + | 28.1913i | −0.269739 | + | 0.894624i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.31662 | −0.105144 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.50000 | − | 4.33013i | 0.0791758 | − | 0.137136i | −0.823719 | − | 0.566999i | \(-0.808104\pi\) |
0.902895 | + | 0.429862i | \(0.141438\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.80579 | − | 4.87228i | 0.0571326 | − | 0.154152i |
(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 | 336.2.bj.f.95.4 | yes | 8 | |
3.2 | odd | 2 | inner | 336.2.bj.f.95.2 | yes | 8 | |
4.3 | odd | 2 | inner | 336.2.bj.f.95.1 | ✓ | 8 | |
7.2 | even | 3 | inner | 336.2.bj.f.191.3 | yes | 8 | |
7.3 | odd | 6 | 2352.2.h.j.2255.4 | 4 | |||
7.4 | even | 3 | 2352.2.h.i.2255.1 | 4 | |||
12.11 | even | 2 | inner | 336.2.bj.f.95.3 | yes | 8 | |
21.2 | odd | 6 | inner | 336.2.bj.f.191.1 | yes | 8 | |
21.11 | odd | 6 | 2352.2.h.i.2255.3 | 4 | |||
21.17 | even | 6 | 2352.2.h.j.2255.2 | 4 | |||
28.3 | even | 6 | 2352.2.h.j.2255.1 | 4 | |||
28.11 | odd | 6 | 2352.2.h.i.2255.4 | 4 | |||
28.23 | odd | 6 | inner | 336.2.bj.f.191.2 | yes | 8 | |
84.11 | even | 6 | 2352.2.h.i.2255.2 | 4 | |||
84.23 | even | 6 | inner | 336.2.bj.f.191.4 | yes | 8 | |
84.59 | odd | 6 | 2352.2.h.j.2255.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.bj.f.95.1 | ✓ | 8 | 4.3 | odd | 2 | inner | |
336.2.bj.f.95.2 | yes | 8 | 3.2 | odd | 2 | inner | |
336.2.bj.f.95.3 | yes | 8 | 12.11 | even | 2 | inner | |
336.2.bj.f.95.4 | yes | 8 | 1.1 | even | 1 | trivial | |
336.2.bj.f.191.1 | yes | 8 | 21.2 | odd | 6 | inner | |
336.2.bj.f.191.2 | yes | 8 | 28.23 | odd | 6 | inner | |
336.2.bj.f.191.3 | yes | 8 | 7.2 | even | 3 | inner | |
336.2.bj.f.191.4 | yes | 8 | 84.23 | even | 6 | inner | |
2352.2.h.i.2255.1 | 4 | 7.4 | even | 3 | |||
2352.2.h.i.2255.2 | 4 | 84.11 | even | 6 | |||
2352.2.h.i.2255.3 | 4 | 21.11 | odd | 6 | |||
2352.2.h.i.2255.4 | 4 | 28.11 | odd | 6 | |||
2352.2.h.j.2255.1 | 4 | 28.3 | even | 6 | |||
2352.2.h.j.2255.2 | 4 | 21.17 | even | 6 | |||
2352.2.h.j.2255.3 | 4 | 84.59 | odd | 6 | |||
2352.2.h.j.2255.4 | 4 | 7.3 | odd | 6 |