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: | 8.0.8275904784.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 4x^{4} - 18x^{3} + 45x^{2} - 81x + 81 \) |
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 | 95.3 | ||
Root | \(-1.37009 - 1.05965i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.95 |
Dual form | 336.2.bj.e.191.3 |
$q$-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 | ||||||||
\(3\) | −0.232633 | + | 1.71636i | −0.134311 | + | 0.990939i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.581054 | + | 0.335472i | −0.259855 | + | 0.150028i | −0.624269 | − | 0.781210i | \(-0.714603\pi\) |
0.364413 | + | 0.931237i | \(0.381270\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63746 | − | 0.209313i | −0.996866 | − | 0.0791130i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.89176 | − | 0.798564i | −0.963921 | − | 0.266188i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.62440 | + | 4.54559i | −0.791285 | + | 1.37055i | 0.133886 | + | 0.990997i | \(0.457254\pi\) |
−0.925171 | + | 0.379550i | \(0.876079\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.440617 | − | 1.07534i | −0.113767 | − | 0.277651i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.64607 | − | 2.10506i | −0.884301 | − | 0.510552i | −0.0122271 | − | 0.999925i | \(-0.503892\pi\) |
−0.872074 | + | 0.489374i | \(0.837225\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.13746 | + | 0.656712i | −0.260951 | + | 0.150660i | −0.624768 | − | 0.780810i | \(-0.714807\pi\) |
0.363817 | + | 0.931470i | \(0.381473\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.972818 | − | 4.47813i | 0.212286 | − | 0.977208i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.60273 | + | 2.77600i | 0.334191 | + | 0.578836i | 0.983329 | − | 0.181834i | \(-0.0582035\pi\) |
−0.649138 | + | 0.760671i | \(0.724870\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.27492 | + | 3.94027i | −0.454983 | + | 0.788054i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.04334 | − | 4.77753i | 0.393241 | − | 0.919435i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.22295i | − | 1.15557i | −0.816188 | − | 0.577786i | \(-0.803917\pi\) | ||
0.816188 | − | 0.577786i | \(-0.196083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 0.866025i | −0.269408 | − | 0.155543i | 0.359211 | − | 0.933257i | \(-0.383046\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.19133 | − | 5.56186i | −1.25185 | − | 0.968195i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.60273 | − | 0.763171i | 0.270910 | − | 0.128999i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.13746 | + | 5.43424i | 0.515795 | + | 0.893383i | 0.999832 | + | 0.0183356i | \(0.00583672\pi\) |
−0.484037 | + | 0.875048i | \(0.660830\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.465267 | + | 3.43271i | −0.0745023 | + | 0.549674i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.76212i | 1.52459i | 0.647231 | + | 0.762294i | \(0.275927\pi\) | ||||
−0.647231 | + | 0.762294i | \(0.724073\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.55505i | 1.45713i | 0.684976 | + | 0.728566i | \(0.259813\pi\) | ||||
−0.684976 | + | 0.728566i | \(0.740187\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.94817 | − | 0.506096i | 0.290416 | − | 0.0754443i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.80818 | − | 8.32801i | −0.701345 | − | 1.21476i | −0.967995 | − | 0.250971i | \(-0.919250\pi\) |
0.266650 | − | 0.963793i | \(-0.414083\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.91238 | + | 1.10411i | 0.987482 | + | 0.157730i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.46123 | − | 5.76825i | 0.624697 | − | 0.807716i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.1974 | + | 5.88748i | 1.40072 | + | 0.808707i | 0.994467 | − | 0.105053i | \(-0.0335011\pi\) |
0.406255 | + | 0.913760i | \(0.366834\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.52165i | − | 0.474859i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.862541 | − | 2.10506i | −0.114246 | − | 0.278822i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.78651 | − | 6.55842i | 0.492961 | − | 0.853834i | −0.507006 | − | 0.861942i | \(-0.669248\pi\) |
0.999967 | + | 0.00810892i | \(0.00258118\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.86254 | + | 3.22602i | 0.238474 | + | 0.413049i | 0.960277 | − | 0.279050i | \(-0.0900195\pi\) |
−0.721803 | + | 0.692099i | \(0.756686\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.45976 | + | 2.71146i | 0.939841 | + | 0.341612i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.16211 | + | 0.670944i | −0.144142 | + | 0.0832203i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.58762 | + | 1.49397i | 0.316129 | + | 0.182517i | 0.649666 | − | 0.760220i | \(-0.274909\pi\) |
−0.333537 | + | 0.942737i | \(0.608242\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.13746 | + | 2.10506i | −0.618477 | + | 0.253419i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.08668 | 0.485000 | 0.242500 | − | 0.970151i | \(-0.422033\pi\) | ||||
0.242500 | + | 0.970151i | \(0.422033\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.137459 | + | 0.238085i | −0.0160883 | + | 0.0278658i | −0.873957 | − | 0.486002i | \(-0.838455\pi\) |
0.857869 | + | 0.513868i | \(0.171788\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.23369 | − | 4.82121i | −0.719805 | − | 0.556705i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.87319 | − | 11.4395i | 0.897233 | − | 1.30365i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.50000 | + | 2.59808i | −0.506290 | + | 0.292306i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.72459 | + | 4.61852i | 0.858288 | + | 0.513169i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.04334 | 0.224286 | 0.112143 | − | 0.993692i | \(-0.464229\pi\) | ||||
0.112143 | + | 0.993692i | \(0.464229\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.82475 | 0.306387 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.6808 | + | 1.44767i | 1.14510 | + | 0.155206i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.1003 | + | 6.98612i | −1.28263 | + | 0.740527i | −0.977329 | − | 0.211728i | \(-0.932091\pi\) |
−0.305302 | + | 0.952256i | \(0.598757\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.27492 | − | 0.418627i | −0.552962 | − | 0.0438840i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.83536 | − | 2.37307i | 0.190318 | − | 0.246076i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.440617 | − | 0.763171i | 0.0452063 | − | 0.0782997i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.27492 | −0.332517 | −0.166259 | − | 0.986082i | \(-0.553169\pi\) | ||||
−0.166259 | + | 0.986082i | \(0.553169\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.2191 | − | 11.0490i | 1.12756 | − | 1.11047i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.48396 | + | 1.43411i | 0.247163 | + | 0.142700i | 0.618465 | − | 0.785813i | \(-0.287755\pi\) |
−0.371301 | + | 0.928512i | \(0.621088\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.6873 | − | 8.47971i | 1.44718 | − | 0.835531i | 0.448869 | − | 0.893597i | \(-0.351827\pi\) |
0.998313 | + | 0.0580665i | \(0.0184936\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.937026 | + | 2.92839i | 0.0914444 | + | 0.285781i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.82985 | − | 10.0976i | −0.563593 | − | 0.976171i | −0.997179 | − | 0.0750592i | \(-0.976085\pi\) |
0.433586 | − | 0.901112i | \(-0.357248\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.41238 | + | 12.8386i | −0.709977 | + | 1.22972i | 0.254888 | + | 0.966970i | \(0.417961\pi\) |
−0.964865 | + | 0.262745i | \(0.915372\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0570 | + | 4.12081i | −0.954565 | + | 0.391130i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.76212i | − | 0.918343i | −0.888348 | − | 0.459172i | \(-0.848146\pi\) | ||
0.888348 | − | 0.459172i | \(-0.151854\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.86254 | − | 1.07534i | −0.173683 | − | 0.100276i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.78353 | − | 1.59713i | −0.534687 | − | 0.147655i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.17574 | + | 6.31518i | 0.841138 | + | 0.578911i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.27492 | − | 14.3326i | −0.752265 | − | 1.30296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.7553 | − | 2.27100i | −1.51077 | − | 0.204769i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 6.40740i | − | 0.573095i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.418627i | 0.0371471i | 0.999827 | + | 0.0185736i | \(0.00591249\pi\) | ||||
−0.999827 | + | 0.0185736i | \(0.994088\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.3999 | − | 2.22282i | −1.44393 | − | 0.195709i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.62440 | + | 4.54559i | 0.229295 | + | 0.397150i | 0.957599 | − | 0.288104i | \(-0.0930247\pi\) |
−0.728305 | + | 0.685253i | \(0.759691\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.13746 | − | 1.49397i | 0.272052 | − | 0.129543i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.415433 | + | 3.46149i | 0.0357547 | + | 0.297917i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.2624 | + | 7.65706i | 1.13309 | + | 0.654187i | 0.944709 | − | 0.327910i | \(-0.106344\pi\) |
0.188376 | + | 0.982097i | \(0.439678\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.9715i | 1.18505i | 0.805553 | + | 0.592523i | \(0.201868\pi\) | ||||
−0.805553 | + | 0.592523i | \(0.798132\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.4124 | − | 6.31518i | 1.29796 | − | 0.531834i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.24879 | + | 9.09118i | −0.438926 | + | 0.760242i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.08762 | + | 3.61587i | 0.173368 | + | 0.300282i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.50310 | + | 11.6073i | −0.288931 | + | 0.957350i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.1003 | + | 6.98612i | −0.991296 | + | 0.572325i | −0.905662 | − | 0.424001i | \(-0.860625\pi\) |
−0.0856347 | + | 0.996327i | \(0.527292\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.77492 | − | 3.91150i | −0.551335 | − | 0.318313i | 0.198325 | − | 0.980136i | \(-0.436450\pi\) |
−0.749660 | + | 0.661823i | \(0.769783\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.86254 | + | 8.99895i | 0.716494 | + | 0.727522i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.16211 | 0.0933428 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6873 | − | 20.2430i | 0.932748 | − | 1.61557i | 0.154145 | − | 0.988048i | \(-0.450738\pi\) |
0.778602 | − | 0.627518i | \(-0.215929\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.4773 | + | 16.1328i | −0.989512 | + | 1.27941i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.64607 | − | 7.65706i | −0.287350 | − | 0.603461i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.86254 | + | 1.07534i | −0.145886 | + | 0.0842270i | −0.571166 | − | 0.820835i | \(-0.693509\pi\) |
0.425281 | + | 0.905062i | \(0.360175\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.04440 | + | 0.819253i | 0.470556 | + | 0.0637787i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.9952 | −1.62466 | −0.812328 | − | 0.583201i | \(-0.801800\pi\) | ||||
−0.812328 | + | 0.583201i | \(0.801800\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.81369 | − | 0.990722i | 0.291640 | − | 0.0757624i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.4245 | + | 8.32801i | −1.09668 | + | 0.633167i | −0.935346 | − | 0.353734i | \(-0.884912\pi\) |
−0.161331 | + | 0.986900i | \(0.551579\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.82475 | − | 9.91613i | 0.515903 | − | 0.749589i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.3757 | + | 8.02470i | 0.779887 | + | 0.603174i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.01363 | + | 13.8800i | −0.598967 | + | 1.03744i | 0.394007 | + | 0.919107i | \(0.371088\pi\) |
−0.992974 | + | 0.118333i | \(0.962245\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0997 | −1.12235 | −0.561175 | − | 0.827697i | \(-0.689650\pi\) | ||||
−0.561175 | + | 0.827697i | \(0.689650\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.97029 | + | 2.44631i | −0.441336 | + | 0.180836i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.64607 | − | 2.10506i | −0.268064 | − | 0.154767i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.1375 | − | 11.0490i | 1.39947 | − | 0.807984i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.38923 | + | 12.1728i | −0.464748 | + | 0.885443i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.97029 | + | 10.3408i | 0.431995 | + | 0.748237i | 0.997045 | − | 0.0768197i | \(-0.0244766\pi\) |
−0.565050 | + | 0.825056i | \(0.691143\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.04983 | − | 15.6748i | 0.651421 | − | 1.12829i | −0.331357 | − | 0.943506i | \(-0.607506\pi\) |
0.982778 | − | 0.184789i | \(-0.0591603\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.881234 | − | 2.15068i | −0.0631065 | − | 0.154013i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.07835i | 0.504311i | 0.967687 | + | 0.252156i | \(0.0811395\pi\) | ||||
−0.967687 | + | 0.252156i | \(0.918861\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.1375 | − | 12.7811i | −1.56928 | − | 0.906026i | −0.996253 | − | 0.0864917i | \(-0.972434\pi\) |
−0.573030 | − | 0.819534i | \(-0.694232\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.16615 | + | 4.09374i | −0.223323 | + | 0.288750i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.30255 | + | 16.4128i | −0.0914208 | + | 1.15195i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.27492 | − | 5.67232i | −0.228730 | − | 0.396172i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.41789 | − | 9.30742i | −0.168055 | − | 0.646910i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 6.89389i | − | 0.476860i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.6460i | 1.07712i | 0.842589 | + | 0.538558i | \(0.181031\pi\) | ||||
−0.842589 | + | 0.538558i | \(0.818969\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.950700 | + | 7.01421i | −0.0651409 | + | 0.480606i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.20545 | − | 5.55200i | −0.218610 | − | 0.378644i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.77492 | + | 2.59808i | 0.256258 | + | 0.176369i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.376662 | − | 0.291315i | −0.0254525 | − | 0.0196852i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.29214 | − | 4.21012i | −0.490522 | − | 0.283203i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 11.7633i | − | 0.787727i | −0.919169 | − | 0.393864i | \(-0.871138\pi\) | ||
0.919169 | − | 0.393864i | \(-0.128862\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.72508 | − | 9.57767i | 0.648339 | − | 0.638511i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.50563 | − | 6.07193i | 0.232677 | − | 0.403008i | −0.725918 | − | 0.687781i | \(-0.758585\pi\) |
0.958595 | + | 0.284773i | \(0.0919182\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.13746 | − | 14.0945i | −0.537738 | − | 0.931390i | −0.999025 | − | 0.0441392i | \(-0.985945\pi\) |
0.461287 | − | 0.887251i | \(-0.347388\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.8027 | + | 16.1744i | 1.17133 | + | 1.06420i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.2624 | − | 7.65706i | 0.868850 | − | 0.501631i | 0.00188417 | − | 0.999998i | \(-0.499400\pi\) |
0.866966 | + | 0.498367i | \(0.166067\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.58762 | + | 3.22602i | 0.364496 | + | 0.210442i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.41238 | − | 8.32801i | −0.221658 | − | 0.540962i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.73512 | 0.565028 | 0.282514 | − | 0.959263i | \(-0.408832\pi\) | ||||
0.282514 | + | 0.959263i | \(0.408832\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.50000 | + | 6.06218i | −0.225455 | + | 0.390499i | −0.956456 | − | 0.291877i | \(-0.905720\pi\) |
0.731001 | + | 0.682376i | \(0.239053\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.72402 | + | 12.1837i | −0.623796 | + | 0.781587i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.38686 | + | 1.67736i | −0.280266 | + | 0.107163i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.27492 | + | 1.31342i | −0.144750 | + | 0.0835712i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.475350 | + | 3.50711i | −0.0301241 | + | 0.222254i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.7785 | 0.680331 | 0.340165 | − | 0.940366i | \(-0.389517\pi\) | ||||
0.340165 | + | 0.940366i | \(0.389517\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.8248 | −1.05776 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.657132 | + | 4.84828i | −0.0411512 | + | 0.303611i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.3924 | − | 11.1962i | 1.20967 | − | 0.698402i | 0.246981 | − | 0.969020i | \(-0.420561\pi\) |
0.962687 | + | 0.270618i | \(0.0872281\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.13746 | − | 14.9893i | −0.443500 | − | 0.931389i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.96942 | + | 17.9953i | −0.307600 | + | 1.11388i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.17574 | − | 15.8928i | 0.565800 | − | 0.979995i | −0.431175 | − | 0.902269i | \(-0.641901\pi\) |
0.996975 | − | 0.0777261i | \(-0.0247660\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.90033 | −0.485313 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.17574 | − | 22.3937i | −0.561546 | − | 1.37047i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.581054 | − | 0.335472i | −0.0354275 | − | 0.0204541i | 0.482182 | − | 0.876071i | \(-0.339845\pi\) |
−0.517609 | + | 0.855617i | \(0.673178\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.0498 | − | 10.4211i | 1.09645 | − | 0.633035i | 0.161163 | − | 0.986928i | \(-0.448475\pi\) |
0.935286 | + | 0.353892i | \(0.115142\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.94564 | − | 8.95625i | 0.117755 | − | 0.542057i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.9406 | − | 20.6817i | −0.720044 | − | 1.24715i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.86254 | + | 4.95807i | −0.171993 | + | 0.297901i | −0.939117 | − | 0.343598i | \(-0.888354\pi\) |
0.767123 | + | 0.641500i | \(0.221687\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.64607 | + | 3.70219i | 0.218284 | + | 0.221644i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.68378i | 0.160101i | 0.996791 | + | 0.0800503i | \(0.0255081\pi\) | ||||
−0.996791 | + | 0.0800503i | \(0.974492\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.2371 | + | 9.37451i | 0.965197 | + | 0.557257i | 0.897769 | − | 0.440467i | \(-0.145187\pi\) |
0.0674284 | + | 0.997724i | \(0.478521\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.20737 | + | 0.933795i | 0.0715185 | + | 0.0553132i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.04334 | − | 25.7472i | 0.120615 | − | 1.51981i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.362541 | + | 0.627940i | 0.0213260 | + | 0.0369377i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.761855 | − | 5.62093i | 0.0446608 | − | 0.329505i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.0634i | 1.34738i | 0.739014 | + | 0.673690i | \(0.235291\pi\) | ||||
−0.739014 | + | 0.673690i | \(0.764709\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.08106i | 0.295831i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.3541 | + | 21.8263i | 0.948963 | + | 1.26649i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.20545 | + | 5.55200i | 0.185376 | + | 0.321081i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | − | 25.2011i | 0.115278 | − | 1.45256i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.03930 | + | 3.92974i | −0.174604 | + | 0.225758i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.16448 | − | 1.24966i | −0.123938 | − | 0.0715554i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3205i | 0.988534i | 0.869310 | + | 0.494267i | \(0.164563\pi\) | ||||
−0.869310 | + | 0.494267i | \(0.835437\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.1375 | + | 27.1813i | 0.633588 | + | 1.54629i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.48396 | − | 4.30234i | 0.140852 | − | 0.243964i | −0.786965 | − | 0.616997i | \(-0.788349\pi\) |
0.927818 | + | 0.373034i | \(0.121682\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.77492 | + | 16.9307i | 0.552511 | + | 0.956977i | 0.998093 | + | 0.0617357i | \(0.0196636\pi\) |
−0.445582 | + | 0.895241i | \(0.647003\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.24414 | + | 0.927030i | −0.295474 | + | 0.0522322i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.87319 | − | 4.54559i | 0.442202 | − | 0.255306i | −0.262329 | − | 0.964979i | \(-0.584491\pi\) |
0.704531 | + | 0.709673i | \(0.251157\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.2870 | + | 16.3315i | 1.58377 | + | 0.914388i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.6873 | − | 7.65706i | 1.04302 | − | 0.427376i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.52967 | 0.307679 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.54983 | + | 7.88054i | −0.252379 | + | 0.437134i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.3113 | − | 15.7090i | −1.12322 | − | 0.868708i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.9382 | + | 22.9712i | 0.603043 | + | 1.26644i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.96221 | − | 1.13288i | 0.107853 | − | 0.0622689i | −0.445103 | − | 0.895479i | \(-0.646833\pi\) |
0.552956 | + | 0.833210i | \(0.313500\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.73320 | − | 18.2200i | −0.259378 | − | 0.998449i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00473 | −0.109530 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.82475 | 0.0994006 | 0.0497003 | − | 0.998764i | \(-0.484173\pi\) | ||||
0.0497003 | + | 0.998764i | \(0.484173\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.7553 | + | 2.27100i | 0.910022 | + | 0.123344i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.87319 | − | 4.54559i | 0.426357 | − | 0.246157i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0000 | − | 4.35890i | −0.971909 | − | 0.235358i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.27895 | − | 2.94663i | 0.122695 | − | 0.158641i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.48396 | − | 4.30234i | 0.133346 | − | 0.230962i | −0.791618 | − | 0.611016i | \(-0.790761\pi\) |
0.924964 | + | 0.380054i | \(0.124095\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.5498 | 1.10001 | 0.550004 | − | 0.835162i | \(-0.314626\pi\) | ||||
0.550004 | + | 0.835162i | \(0.314626\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.08668 | − | 9.55505i | 0.218131 | − | 0.510011i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.64607 | − | 2.10506i | −0.194061 | − | 0.112041i | 0.399821 | − | 0.916593i | \(-0.369072\pi\) |
−0.593882 | + | 0.804552i | \(0.702405\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.37459 | + | 1.37097i | −0.126030 | + | 0.0727634i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.9737 | + | 14.2797i | −0.686640 | + | 0.755763i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.1437 | + | 24.4975i | 0.746474 | + | 1.29293i | 0.949503 | + | 0.313758i | \(0.101588\pi\) |
−0.203030 | + | 0.979173i | \(0.565079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.63746 | + | 14.9605i | −0.454603 | + | 0.787396i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 26.5248 | − | 10.8685i | 1.39219 | − | 0.570447i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 0.184454i | − | 0.00965476i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.59967 | − | 2.65562i | −0.240101 | − | 0.138622i | 0.375122 | − | 0.926975i | \(-0.377601\pi\) |
−0.615223 | + | 0.788353i | \(0.710934\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.79568 | − | 28.2297i | 0.405827 | − | 1.46958i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.6629 | − | 17.6624i | −1.33235 | − | 0.916988i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.58762 | − | 6.21395i | −0.185760 | − | 0.321746i | 0.758072 | − | 0.652171i | \(-0.226141\pi\) |
−0.943832 | + | 0.330425i | \(0.892808\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.9974 | + | 1.49058i | 0.567903 | + | 0.0769730i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.4459i | − | 0.640996i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3923i | 0.533817i | 0.963722 | + | 0.266908i | \(0.0860021\pi\) | ||||
−0.963722 | + | 0.266908i | \(0.913998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.718513 | − | 0.0973866i | −0.0368105 | − | 0.00498927i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.92694 | + | 6.80166i | 0.200657 | + | 0.347549i | 0.948740 | − | 0.316056i | \(-0.102359\pi\) |
−0.748083 | + | 0.663605i | \(0.769026\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.737127 | + | 9.28819i | −0.0375675 | + | 0.473370i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.63032 | − | 27.6309i | 0.387871 | − | 1.40456i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.77610 | − | 5.64423i | −0.495668 | − | 0.286174i | 0.231255 | − | 0.972893i | \(-0.425717\pi\) |
−0.726923 | + | 0.686719i | \(0.759050\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 13.4953i | − | 0.682488i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.41238 | + | 3.44695i | −0.424348 | + | 0.173875i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.74316 | − | 3.01925i | 0.0877081 | − | 0.151915i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.6873 | + | 27.1712i | 0.787323 | + | 1.36368i | 0.927602 | + | 0.373571i | \(0.121867\pi\) |
−0.140279 | + | 0.990112i | \(0.544800\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.83430 | + | 5.73255i | 0.0918299 | + | 0.286986i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00237 | − | 0.578717i | 0.0500558 | − | 0.0288997i | −0.474763 | − | 0.880114i | \(-0.657466\pi\) |
0.524819 | + | 0.851214i | \(0.324133\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.00000 | − | 1.73205i | −0.149441 | − | 0.0862796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.03779 | − | 0.0922270i | −0.300020 | − | 0.00458280i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −32.9357 | −1.63256 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.7749 | − | 27.3230i | 0.780019 | − | 1.35103i | −0.151910 | − | 0.988394i | \(-0.548542\pi\) |
0.931930 | − | 0.362639i | \(-0.118124\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.2275 | + | 20.9818i | −0.800445 | + | 1.03495i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.3595 | + | 16.5050i | −0.558965 | + | 0.812158i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.18729 | + | 0.685484i | −0.0582819 | + | 0.0336491i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −23.9801 | − | 3.25024i | −1.17431 | − | 0.159165i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.3787 | 1.67951 | 0.839755 | − | 0.542965i | \(-0.182698\pi\) | ||||
0.839755 | + | 0.542965i | \(0.182698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0997 | −0.930861 | −0.465430 | − | 0.885084i | \(-0.654100\pi\) | ||||
−0.465430 | + | 0.885084i | \(0.654100\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.25366 | + | 27.9223i | 0.352685 | + | 1.35763i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.5890 | − | 9.57767i | 0.804685 | − | 0.464585i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.23713 | − | 8.89834i | −0.205049 | − | 0.430621i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.3827 | − | 11.1237i | −0.694401 | − | 0.537058i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.721492 | − | 1.24966i | 0.0347530 | − | 0.0601940i | −0.848126 | − | 0.529795i | \(-0.822269\pi\) |
0.882879 | + | 0.469601i | \(0.155602\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.69178 | + | 2.74194i | −0.320846 | + | 0.131466i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.64607 | − | 2.10506i | −0.174415 | − | 0.100699i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.3248 | + | 8.27040i | −0.683683 | + | 0.394725i | −0.801241 | − | 0.598341i | \(-0.795827\pi\) |
0.117558 | + | 0.993066i | \(0.462493\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.1073 | − | 8.71280i | −0.909869 | − | 0.414895i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.90527 | + | 5.03208i | 0.138034 | + | 0.239081i | 0.926752 | − | 0.375673i | \(-0.122588\pi\) |
−0.788719 | + | 0.614754i | \(0.789255\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.68729 | − | 8.11863i | 0.222199 | − | 0.384860i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.17574 | − | 22.3937i | −0.433997 | − | 1.05918i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.1297i | 0.714013i | 0.934102 | + | 0.357007i | \(0.116203\pi\) | ||||
−0.934102 | + | 0.357007i | \(0.883797\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −44.3746 | − | 25.6197i | −2.08952 | − | 1.20638i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.28960 | − | 10.7182i | 0.389480 | − | 0.503586i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.20545 | − | 1.52634i | 0.150274 | − | 0.0715560i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.32475 | + | 14.4189i | 0.389415 | + | 0.674487i | 0.992371 | − | 0.123287i | \(-0.0393437\pi\) |
−0.602956 | + | 0.797775i | \(0.706010\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.5071 | + | 13.1178i | −0.817163 | + | 0.612288i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 12.4459i | − | 0.579663i | −0.957078 | − | 0.289832i | \(-0.906401\pi\) | ||
0.957078 | − | 0.289832i | \(-0.0935993\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.8997i | 0.971291i | 0.874156 | + | 0.485646i | \(0.161415\pi\) | ||||
−0.874156 | + | 0.485646i | \(0.838585\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.270345 | + | 1.99459i | −0.0125370 | + | 0.0924971i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.92694 | + | 6.80166i | 0.181717 | + | 0.314744i | 0.942465 | − | 0.334304i | \(-0.108501\pi\) |
−0.760748 | + | 0.649047i | \(0.775168\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.51204 | − | 4.48190i | −0.300698 | − | 0.206955i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.0253 | + | 24.7688i | 1.47565 | + | 1.14128i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −43.4333 | − | 25.0762i | −1.99707 | − | 1.15301i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5.97586i | − | 0.274191i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.7870 | − | 25.1685i | −1.13492 | − | 1.15239i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.4679 | + | 28.5232i | −0.752436 | + | 1.30326i | 0.194202 | + | 0.980961i | \(0.437788\pi\) |
−0.946639 | + | 0.322296i | \(0.895545\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.27492 | + | 10.8685i | 0.286112 | + | 0.495560i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.9905 | − | 4.47667i | 0.636588 | − | 0.203695i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.90290 | − | 1.09864i | 0.0864065 | − | 0.0498868i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.77492 | + | 5.64355i | 0.442944 | + | 0.255734i | 0.704846 | − | 0.709361i | \(-0.251016\pi\) |
−0.261902 | + | 0.965095i | \(0.584350\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.41238 | − | 3.44695i | −0.0638698 | − | 0.155876i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.69178 | −0.301996 | −0.150998 | − | 0.988534i | \(-0.548249\pi\) | ||||
−0.150998 | + | 0.988534i | \(0.548249\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.0997 | + | 22.6893i | −0.589979 | + | 1.02187i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.81226 | + | 10.1838i | −0.126402 | + | 0.457726i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.7785 | − | 0.855398i | −0.483480 | − | 0.0383698i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.31271 | + | 1.91259i | −0.148297 | + | 0.0856194i | −0.572313 | − | 0.820036i | \(-0.693954\pi\) |
0.424015 | + | 0.905655i | \(0.360620\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.88418 | − | 36.0352i | 0.218209 | − | 1.60993i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.92442 | −0.0856356 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.09370 | − | 15.4472i | 0.0929845 | − | 0.686035i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.1974 | − | 5.88748i | 0.451992 | − | 0.260958i | −0.256679 | − | 0.966497i | \(-0.582628\pi\) |
0.708671 | + | 0.705539i | \(0.249295\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.412376 | − | 0.599168i | 0.0182424 | − | 0.0265056i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.813241 | + | 6.77613i | 0.0359055 | + | 0.299173i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.68941 | + | 9.85435i | −0.250705 | + | 0.434234i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 50.4743 | 2.21986 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.9382 | − | 26.6950i | −0.480134 | − | 1.17178i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.8467 | + | 16.0773i | 1.21999 | + | 0.704359i | 0.964915 | − | 0.262563i | \(-0.0845678\pi\) |
0.255071 | + | 0.966922i | \(0.417901\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.96221 | + | 2.86493i | −0.216982 | + | 0.125275i | −0.604552 | − | 0.796566i | \(-0.706648\pi\) |
0.387570 | + | 0.921840i | \(0.373315\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.4320 | + | 14.0205i | 0.673506 | + | 0.611906i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.64607 | + | 6.31518i | 0.158825 | + | 0.275093i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.36254 | − | 11.0202i | 0.276632 | − | 0.479141i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.1870 | + | 15.9416i | −0.702456 | + | 0.691808i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.5242i | 0.845689i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.77492 | + | 3.91150i | 0.292905 | + | 0.169109i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.9588 | − | 16.9832i | −0.947593 | − | 0.732879i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.1597 | + | 28.5232i | −0.997557 | + | 1.22858i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.1375 | + | 29.6829i | 0.736797 | + | 1.27617i | 0.953930 | + | 0.300028i | \(0.0969959\pi\) |
−0.217134 | + | 0.976142i | \(0.569671\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.51269 | − | 25.9164i | 0.150744 | − | 1.11218i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 9.94658i | − | 0.426064i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.30136i | 0.183913i | 0.995763 | + | 0.0919563i | \(0.0293120\pi\) | ||||
−0.995763 | + | 0.0919563i | \(0.970688\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.80985 | − | 10.8162i | −0.119921 | − | 0.461626i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.08668 | + | 7.07835i | 0.174099 | + | 0.301548i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.4124 | − | 5.91041i | 0.527828 | − | 0.251336i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.46123 | − | 5.76825i | 0.189369 | − | 0.244848i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.8138 | − | 11.4395i | −0.839536 | − | 0.484706i | 0.0175705 | − | 0.999846i | \(-0.494407\pi\) |
−0.857106 | + | 0.515139i | \(0.827740\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.1101i | 0.808271i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.5120 | + | 35.4171i | 0.612699 | + | 1.49531i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.1653 | + | 26.2671i | −0.639142 | + | 1.10703i | 0.346479 | + | 0.938058i | \(0.387377\pi\) |
−0.985621 | + | 0.168969i | \(0.945956\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.27492 | + | 5.67232i | 0.137777 | + | 0.238636i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19.4066 | − | 13.7980i | −0.814999 | − | 0.579462i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.5272 | + | 15.8928i | −1.15400 | + | 0.666263i | −0.949859 | − | 0.312679i | \(-0.898774\pi\) |
−0.204142 | + | 0.978941i | \(0.565440\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.9622 | + | 6.32904i | 0.458754 | + | 0.264862i | 0.711520 | − | 0.702666i | \(-0.248007\pi\) |
−0.252766 | + | 0.967527i | \(0.581340\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.1375 | + | 7.84152i | −0.799479 | + | 0.327584i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.5843 | −0.608206 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.95017 | − | 3.37779i | 0.0811865 | − | 0.140619i | −0.822573 | − | 0.568659i | \(-0.807462\pi\) |
0.903760 | + | 0.428040i | \(0.140796\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.7982 | + | 19.1792i | 1.03058 | + | 0.797061i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.38923 | − | 0.427699i | −0.223583 | − | 0.0177439i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −53.5241 | + | 30.9021i | −2.21674 | + | 1.27984i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.89634 | − | 1.01219i | 0.161094 | − | 0.0418490i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.04334 | −0.0843378 | −0.0421689 | − | 0.999110i | \(-0.513427\pi\) | ||||
−0.0421689 | + | 0.999110i | \(0.513427\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.27492 | 0.0937363 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.1490 | − | 1.64666i | −0.499742 | − | 0.0677346i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.48396 | − | 1.43411i | 0.102004 | − | 0.0588920i | −0.448130 | − | 0.893968i | \(-0.647910\pi\) |
0.550134 | + | 0.835076i | \(0.314577\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.45017 | − | 0.591258i | −0.305427 | − | 0.0242392i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27.0868 | − | 35.0225i | 1.10859 | − | 1.43337i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.2624 | − | 22.9712i | 0.541888 | − | 0.938577i | −0.456908 | − | 0.889514i | \(-0.651043\pi\) |
0.998796 | − | 0.0490632i | \(-0.0156236\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.9244 | −1.42460 | −0.712298 | − | 0.701877i | \(-0.752346\pi\) | ||||
−0.712298 | + | 0.701877i | \(0.752346\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.28977 | − | 6.38658i | −0.256139 | − | 0.260082i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.61635 | + | 5.55200i | 0.390960 | + | 0.225721i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.9502 | − | 8.63148i | 0.606809 | − | 0.350341i | −0.164907 | − | 0.986309i | \(-0.552732\pi\) |
0.771715 | + | 0.635968i | \(0.219399\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −27.8672 | − | 6.05379i | −1.12923 | − | 0.245312i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.61635 | − | 16.6560i | −0.389036 | − | 0.673830i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.58762 | + | 13.1422i | −0.306461 | + | 0.530806i | −0.977586 | − | 0.210538i | \(-0.932478\pi\) |
0.671124 | + | 0.741345i | \(0.265812\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.4976 | − | 4.30136i | 0.423304 | − | 0.173447i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.9188i | 0.962935i | 0.876464 | + | 0.481468i | \(0.159896\pi\) | ||||
−0.876464 | + | 0.481468i | \(0.840104\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.9622 | + | 9.79314i | 0.681769 | + | 0.393619i | 0.800521 | − | 0.599305i | \(-0.204556\pi\) |
−0.118752 | + | 0.992924i | \(0.537889\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.5373 | − | 1.98474i | 0.663621 | − | 0.0796449i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 33.3764 | − | 15.8928i | 1.33720 | − | 0.636733i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.22508 | − | 15.9783i | −0.369003 | − | 0.639132i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.8324 | + | 1.60375i | 0.472540 | + | 0.0640476i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 26.4181i | − | 1.05336i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 28.3616i | − | 1.12906i | −0.825413 | − | 0.564529i | \(-0.809058\pi\) | ||
0.825413 | − | 0.564529i | \(-0.190942\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.8541 | − | 3.63978i | −1.06736 | − | 0.144668i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.140438 | − | 0.243245i | −0.00557309 | − | 0.00965288i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.8248 | + | 2.20822i | 0.547757 | + | 0.0874929i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.8177 | − | 3.26348i | −0.467502 | − | 0.129101i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.1003 | − | 6.98612i | −0.477934 | − | 0.275935i | 0.241621 | − | 0.970371i | \(-0.422321\pi\) |
−0.719555 | + | 0.694436i | \(0.755654\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.62685i | − | 0.103593i | −0.998658 | − | 0.0517964i | \(-0.983505\pi\) | ||
0.998658 | − | 0.0517964i | \(-0.0164947\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.2749 | − | 4.21012i | 0.404574 | − | 0.165773i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.3058 | − | 26.5104i | 0.601732 | − | 1.04223i | −0.390827 | − | 0.920464i | \(-0.627811\pi\) |
0.992559 | − | 0.121766i | \(-0.0388557\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.8746 | + | 34.4238i | 0.780146 | + | 1.35125i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.33740 | + | 5.87471i | −0.209189 | + | 0.230248i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.4301 | − | 16.9915i | 1.15169 | − | 0.664928i | 0.202391 | − | 0.979305i | \(-0.435129\pi\) |
0.949298 | + | 0.314377i | \(0.101795\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.04983 | − | 1.76082i | −0.119167 | − | 0.0688010i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.587624 | − | 0.578717i | 0.0229254 | − | 0.0225779i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.2552 | 1.29544 | 0.647720 | − | 0.761879i | \(-0.275723\pi\) | ||||
0.647720 | + | 0.761879i | \(0.275723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.8625 | + | 18.8145i | −0.422504 | + | 0.731798i | −0.996184 | − | 0.0872815i | \(-0.972182\pi\) |
0.573680 | + | 0.819080i | \(0.305515\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.92246 | − | 11.5365i | 0.346520 | − | 0.448040i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.32185 | + | 1.92060i | −0.0512592 | + | 0.0744778i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.2749 | − | 9.97368i | 0.668887 | − | 0.386182i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.1900 | + | 2.73653i | 0.780590 | + | 0.105800i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.5522 | −0.754804 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.72508 | 0.182139 | 0.0910693 | − | 0.995845i | \(-0.470972\pi\) | ||||
0.0910693 | + | 0.995845i | \(0.470972\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.1763 | + | 18.9198i | 0.545647 | + | 0.728223i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.2359 | − | 19.1888i | 1.27736 | − | 0.737484i | 0.300998 | − | 0.953625i | \(-0.402680\pi\) |
0.976362 | + | 0.216140i | \(0.0693469\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.63746 | + | 0.685484i | 0.331475 | + | 0.0263065i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.60607 | + | 7.42945i | 0.368106 | + | 0.284697i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.3708 | − | 31.8191i | 0.702938 | − | 1.21752i | −0.264492 | − | 0.964388i | \(-0.585204\pi\) |
0.967430 | − | 0.253137i | \(-0.0814623\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.2749 | −0.392584 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.0842 | − | 10.6879i | 0.995175 | − | 0.407770i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.3948 | + | 11.7750i | 0.776981 | + | 0.448590i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.23713 | − | 4.17836i | 0.275313 | − | 0.158952i | −0.355986 | − | 0.934491i | \(-0.615855\pi\) |
0.631300 | + | 0.775539i | \(0.282522\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −31.9026 | + | 26.7930i | −1.21188 | + | 1.01778i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.68704 | − | 8.11820i | −0.177790 | − | 0.307941i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.5498 | − | 35.5934i | 0.778380 | − | 1.34819i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.0570 | + | 24.5443i | 0.380390 | + | 0.928352i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8.90672i | − | 0.336402i | −0.985753 | − | 0.168201i | \(-0.946204\pi\) | ||
0.985753 | − | 0.168201i | \(-0.0537958\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.13746 | − | 4.12081i | −0.269194 | − | 0.155419i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.83686 | + | 8.83988i | −0.257491 | + | 0.332929i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.25116 | − | 4.30234i | −0.235099 | − | 0.161806i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.68729 | − | 15.0468i | −0.326258 | − | 0.565096i | 0.655508 | − | 0.755188i | \(-0.272455\pi\) |
−0.981766 | + | 0.190093i | \(0.939121\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.0877 | − | 3.91948i | 0.565832 | − | 0.146992i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5.55200i | − | 0.207924i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 7.04329i | − | 0.263404i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.03208 | + | 14.9926i | −0.0758895 | + | 0.559908i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.68941 | + | 9.85435i | 0.212179 | + | 0.367505i | 0.952396 | − | 0.304863i | \(-0.0986106\pi\) |
−0.740217 | + | 0.672368i | \(0.765277\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.5120 | + | 19.2906i | −1.50875 | + | 0.718421i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.59064 | − | 7.41752i | −0.356680 | − | 0.275860i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.5201 | + | 14.1567i | 0.910654 | + | 0.525766i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.5479i | 1.20713i | 0.797312 | + | 0.603567i | \(0.206254\pi\) | ||||
−0.797312 | + | 0.603567i | \(0.793746\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.6495 | − | 19.5242i | −0.690722 | − | 0.723120i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.1139 | − | 34.8384i | 0.743941 | − | 1.28854i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.8625 | − | 22.2786i | −0.475089 | − | 0.822878i | 0.524504 | − | 0.851408i | \(-0.324251\pi\) |
−0.999593 | + | 0.0285300i | \(0.990917\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.85842 | − | 7.91964i | −0.0685487 | − | 0.292120i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.5819 | + | 7.84152i | −0.500296 | + | 0.288846i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.3368 | − | 16.3603i | −1.04239 | − | 0.601822i | −0.121878 | − | 0.992545i | \(-0.538892\pi\) |
−0.920508 | + | 0.390723i | \(0.872225\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.72508 | − | 4.21012i | −0.0633725 | − | 0.154663i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.4702 | −0.640921 | −0.320460 | − | 0.947262i | \(-0.603838\pi\) | ||||
−0.320460 | + | 0.947262i | \(0.603838\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.68729 | − | 8.11863i | 0.171729 | − | 0.297444i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.90886 | − | 1.63174i | −0.216194 | − | 0.0597023i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.2624 | + | 27.8522i | 0.484598 | + | 1.01770i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.5997 | − | 13.0479i | 0.824674 | − | 0.476126i | −0.0273518 | − | 0.999626i | \(-0.508707\pi\) |
0.852025 | + | 0.523500i | \(0.175374\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.50743 | + | 18.4997i | −0.0913759 | + | 0.674166i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.24879 | 0.191023 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.0997 | 0.548807 | 0.274403 | − | 0.961615i | \(-0.411520\pi\) | ||||
0.274403 | + | 0.961615i | \(0.411520\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.91400 | − | 28.8773i | 0.142069 | − | 1.04818i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.3330 | + | 18.0901i | −1.13582 | + | 0.655767i | −0.945392 | − | 0.325934i | \(-0.894321\pi\) |
−0.190429 | + | 0.981701i | \(0.560988\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.2371 | − | 32.3098i | 0.805038 | − | 1.16969i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.16851 | − | 2.25575i | −0.295333 | − | 0.0815567i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.57301 | − | 13.1168i | 0.273446 | − | 0.473622i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.17525 | −0.222685 | −0.111343 | − | 0.993782i | \(-0.535515\pi\) | ||||
−0.111343 | + | 0.993782i | \(0.535515\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.7054 | + | 35.8890i | 0.529602 | + | 1.29251i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.12766 | − | 2.96046i | −0.184429 | − | 0.106480i | 0.404943 | − | 0.914342i | \(-0.367291\pi\) |
−0.589372 | + | 0.807862i | \(0.700625\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.82475 | − | 3.94027i | 0.245152 | − | 0.141539i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27.3874 | − | 8.76342i | 0.982517 | − | 0.314386i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.41090 | − | 11.1040i | −0.229694 | − | 0.397842i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.7251 | + | 18.5764i | −0.383774 | + | 0.664715i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29.7303 | − | 12.7156i | −1.06247 | − | 0.454419i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.6830i | 0.559751i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.23713 | − | 0.714256i | −0.0440988 | − | 0.0254605i | 0.477788 | − | 0.878475i | \(-0.341439\pi\) |
−0.521887 | + | 0.853014i | \(0.674772\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.1432 | + | 19.4460i | 0.895122 | + | 0.692298i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.04334 | + | 25.7472i | −0.0726529 | + | 0.915465i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.72508 | + | 6.45203i | 0.132282 | + | 0.229118i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.83788 | − | 13.5598i | 0.0651829 | − | 0.480916i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 0.855398i | − | 0.0302997i | −0.999885 | − | 0.0151499i | \(-0.995177\pi\) | ||
0.999885 | − | 0.0151499i | \(-0.00482254\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.4860i | 1.43229i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40.5701 | − | 10.5393i | 1.43347 | − | 0.372389i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.721492 | − | 1.24966i | −0.0254609 | − | 0.0440996i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.68729 | + | 3.22602i | 0.165205 | + | 0.113702i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.710962 | − | 0.919255i | 0.0250271 | − | 0.0323593i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.2351 | + | 11.6827i | 0.711427 | + | 0.410743i | 0.811589 | − | 0.584228i | \(-0.198603\pi\) |
−0.100162 | + | 0.994971i | \(0.531936\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.7370i | 0.763288i | 0.924309 | + | 0.381644i | \(0.124642\pi\) | ||||
−0.924309 | + | 0.381644i | \(0.875358\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.6873 | + | 33.4043i | 0.480034 | + | 1.17154i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.721492 | − | 1.24966i | 0.0252728 | − | 0.0437737i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.27492 | − | 10.8685i | −0.219532 | − | 0.380240i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.9195 | + | 5.42293i | 0.521330 | + | 0.189493i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.6790 | − | 6.74287i | 0.407600 | − | 0.235328i | −0.282158 | − | 0.959368i | \(-0.591050\pi\) |
0.689758 | + | 0.724040i | \(0.257717\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.58762 | − | 3.22602i | −0.194772 | − | 0.112452i | 0.399442 | − | 0.916758i | \(-0.369204\pi\) |
−0.594215 | + | 0.804306i | \(0.702537\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 38.2749 | − | 15.6830i | 1.33256 | − | 0.546013i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.6870 | −0.962770 | −0.481385 | − | 0.876509i | \(-0.659866\pi\) | ||||
−0.481385 | + | 0.876509i | \(0.659866\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.6873 | − | 23.7071i | 0.475379 | − | 0.823381i | −0.524223 | − | 0.851581i | \(-0.675644\pi\) |
0.999602 | + | 0.0281999i | \(0.00897749\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.84389 | − | 6.06656i | −0.272102 | − | 0.210446i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.8788 | − | 18.5766i | −0.792703 | − | 0.643642i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.1993 | − | 7.04329i | 0.422175 | − | 0.243743i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.20247 | + | 5.39670i | −0.248954 | + | 0.186537i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.17337 | −0.282176 | −0.141088 | − | 0.989997i | \(-0.545060\pi\) | ||||
−0.141088 | + | 0.989997i | \(0.545060\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.72508 | −0.335348 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.60632 | − | 0.624336i | −0.158650 | − | 0.0215033i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.22949 | − | 3.01925i | 0.179900 | − | 0.103865i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.8248 | + | 39.5336i | 0.646826 | + | 1.35839i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.8673 | + | 25.6879i | −0.681844 | + | 0.881606i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.0570 | + | 17.4192i | −0.344749 | + | 0.597122i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.4502 | 0.802918 | 0.401459 | − | 0.915877i | \(-0.368503\pi\) | ||||
0.401459 | + | 0.915877i | \(0.368503\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.88360 | + | 1.85505i | −0.0644178 | + | 0.0634413i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.7487 | − | 9.66989i | −0.572126 | − | 0.330317i | 0.185872 | − | 0.982574i | \(-0.440489\pi\) |
−0.757998 | + | 0.652257i | \(0.773822\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.51204 | − | 3.75973i | 0.222188 | − | 0.128280i | −0.384775 | − | 0.923010i | \(-0.625721\pi\) |
0.606963 | + | 0.794730i | \(0.292388\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 43.7160 | + | 9.49676i | 1.48984 | + | 0.323649i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.60273 | + | 2.77600i | 0.0545574 | + | 0.0944962i | 0.892014 | − | 0.452007i | \(-0.149292\pi\) |
−0.837457 | + | 0.546503i | \(0.815959\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.58762 | − | 9.67805i | 0.189985 | − | 0.329064i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.16211 | + | 0.476171i | −0.0394673 | + | 0.0161716i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 27.2735i | − | 0.925191i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.17525 | + | 2.98793i | 0.175357 | + | 0.101242i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.47029 | + | 2.61523i | 0.320521 | + | 0.0885122i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.34115 | + | 16.8993i | −0.0453393 | + | 0.571299i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.41238 | − | 9.37451i | −0.182763 | − | 0.316555i | 0.760057 | − | 0.649856i | \(-0.225171\pi\) |
−0.942820 | + | 0.333301i | \(0.891837\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −39.5851 | − | 5.36532i | −1.33517 | − | 0.180968i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.4160i | 1.49641i | 0.663465 | + | 0.748207i | \(0.269085\pi\) | ||||
−0.663465 | + | 0.748207i | \(0.730915\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 38.1051i | − | 1.28234i | −0.767399 | − | 0.641170i | \(-0.778449\pi\) | ||
0.767399 | − | 0.641170i | \(-0.221551\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.72092 | − | 1.18203i | −0.293151 | − | 0.0397334i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.721492 | − | 1.24966i | −0.0242253 | − | 0.0419595i | 0.853659 | − | 0.520833i | \(-0.174379\pi\) |
−0.877884 | + | 0.478874i | \(0.841045\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.0876242 | − | 1.10411i | 0.00293882 | − | 0.0370307i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −41.2663 | + | 22.9920i | −1.38247 | + | 0.770261i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.9382 | + | 6.31518i | 0.366033 | + | 0.211329i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 10.7534i | − | 0.359446i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.2749 | + | 4.21012i | −0.343070 | + | 0.140572i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.38923 | + | 9.33442i | −0.179741 | + | 0.311320i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.7870 | − | 42.9323i | −0.825773 | − | 1.43028i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 42.7887 | + | 9.29532i | 1.42392 | + | 0.309329i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.77373 | − | 5.06551i | 0.291649 | − | 0.168383i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.51204 | + | 2.02768i | 0.116616 | + | 0.0673280i | 0.557173 | − | 0.830396i | \(-0.311886\pi\) |
−0.440558 | + | 0.897724i | \(0.645219\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.03779 | − | 6.13072i | −0.200261 | − | 0.203343i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.9037 | 1.25580 | 0.627902 | − | 0.778292i | \(-0.283914\pi\) | ||||
0.627902 | + | 0.778292i | \(0.283914\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.36254 | + | 9.28819i | −0.177474 | + | 0.307394i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.64839 | − | 3.42430i | 0.0875532 | − | 0.113204i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.97029 | − | 12.5381i | −0.197156 | − | 0.414045i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.1375 | − | 19.7093i | 1.12609 | − | 0.650149i | 0.183142 | − | 0.983086i | \(-0.441373\pi\) |
0.942949 | + | 0.332938i | \(0.108040\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.7282 | − | 4.02933i | −0.979577 | − | 0.132771i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.17337 | 0.269030 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.5498 | −0.938713 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −49.2438 | + | 12.7926i | −1.61738 | + | 0.420163i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.8788 | + | 13.2091i | −0.750628 | + | 0.433375i | −0.825921 | − | 0.563786i | \(-0.809344\pi\) |
0.0752926 | + | 0.997161i | \(0.476011\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.58762 | + | 3.28356i | −0.281448 | + | 0.107614i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.80651 | + | 5.26423i | 0.222835 | + | 0.172343i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.41327 | + | 12.8402i | −0.242440 | + | 0.419918i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.8248 | −1.62770 | −0.813852 | − | 0.581072i | \(-0.802633\pi\) | ||||
−0.813852 | + | 0.581072i | \(0.802633\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.3330 | + | 12.8386i | −1.02251 | + | 0.418972i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.4895 | − | 10.0976i | −0.570143 | − | 0.329172i | 0.187064 | − | 0.982348i | \(-0.440103\pi\) |
−0.757206 | + | 0.653176i | \(0.773436\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.0997 | + | 15.6460i | −0.882487 | + | 0.509504i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.371151 | − | 9.21648i | −0.0120735 | − | 0.299812i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.1003 | + | 20.9584i | 0.393207 | + | 0.681055i | 0.992871 | − | 0.119197i | \(-0.0380321\pi\) |
−0.599663 | + | 0.800252i | \(0.704699\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.274917 | + | 0.476171i | −0.00892419 | + | 0.0154572i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.97029 | + | 14.5707i | 0.193600 | + | 0.472486i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 50.5214i | − | 1.63655i | −0.574828 | − | 0.818274i | \(-0.694931\pi\) | ||
0.574828 | − | 0.818274i | \(-0.305069\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.93812 | − | 4.00573i | −0.224512 | − | 0.129622i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −34.6112 | + | 44.7513i | −1.11882 | + | 1.44660i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.3764 | − | 22.9712i | −1.07778 | − | 0.741778i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.79496 | + | 33.8554i | 0.283414 | + | 1.09097i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.1439i | 0.390925i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 9.02134i | − | 0.290107i | −0.989424 | − | 0.145053i | \(-0.953665\pi\) | ||
0.989424 | − | 0.145053i | \(-0.0463354\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.28639 | + | 9.49089i | −0.0413247 | + | 0.304891i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.50563 | − | 6.07193i | −0.112501 | − | 0.194858i | 0.804277 | − | 0.594255i | \(-0.202553\pi\) |
−0.916778 | + | 0.399397i | \(0.869219\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.92442 | − | 36.8492i | 0.0937526 | − | 1.18133i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.4674 | − | 9.64242i | −0.399276 | − | 0.308805i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.8193 | + | 20.1030i | 1.11397 | + | 0.643151i | 0.939855 | − | 0.341575i | \(-0.110960\pi\) |
0.174115 | + | 0.984725i | \(0.444294\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 73.3374i | − | 2.34387i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 31.6873 | − | 31.2070i | 1.01170 | − | 0.996362i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.1870 | + | 28.0367i | −0.516285 | + | 0.894232i | 0.483536 | + | 0.875324i | \(0.339352\pi\) |
−0.999821 | + | 0.0189076i | \(0.993981\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.37459 | − | 4.11290i | −0.0756606 | − | 0.131048i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −41.9714 | + | 13.4300i | −1.33596 | + | 0.427482i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.5248 | + | 15.3141i | −0.843441 | + | 0.486961i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.5997 | + | 7.85177i | 0.432008 | + | 0.249420i | 0.700202 | − | 0.713945i | \(-0.253093\pi\) |
−0.268194 | + | 0.963365i | \(0.586427\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.48796 | + | 3.63140i | 0.0472188 | + | 0.115239i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.1508 | 0.543716 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.86254 | + | 11.8863i | −0.217339 | + | 0.376442i | −0.953994 | − | 0.299827i | \(-0.903071\pi\) |
0.736655 | + | 0.676269i | \(0.236404\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32.3731 | − | 3.88528i | 1.02424 | − | 0.122925i |
(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.e.95.3 | ✓ | 8 | |
3.2 | odd | 2 | inner | 336.2.bj.e.95.4 | yes | 8 | |
4.3 | odd | 2 | 336.2.bj.g.95.2 | yes | 8 | ||
7.2 | even | 3 | 336.2.bj.g.191.1 | yes | 8 | ||
7.3 | odd | 6 | 2352.2.h.m.2255.2 | 8 | |||
7.4 | even | 3 | 2352.2.h.n.2255.7 | 8 | |||
12.11 | even | 2 | 336.2.bj.g.95.1 | yes | 8 | ||
21.2 | odd | 6 | 336.2.bj.g.191.2 | yes | 8 | ||
21.11 | odd | 6 | 2352.2.h.n.2255.1 | 8 | |||
21.17 | even | 6 | 2352.2.h.m.2255.8 | 8 | |||
28.3 | even | 6 | 2352.2.h.m.2255.7 | 8 | |||
28.11 | odd | 6 | 2352.2.h.n.2255.2 | 8 | |||
28.23 | odd | 6 | inner | 336.2.bj.e.191.4 | yes | 8 | |
84.11 | even | 6 | 2352.2.h.n.2255.8 | 8 | |||
84.23 | even | 6 | inner | 336.2.bj.e.191.3 | yes | 8 | |
84.59 | odd | 6 | 2352.2.h.m.2255.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.bj.e.95.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
336.2.bj.e.95.4 | yes | 8 | 3.2 | odd | 2 | inner | |
336.2.bj.e.191.3 | yes | 8 | 84.23 | even | 6 | inner | |
336.2.bj.e.191.4 | yes | 8 | 28.23 | odd | 6 | inner | |
336.2.bj.g.95.1 | yes | 8 | 12.11 | even | 2 | ||
336.2.bj.g.95.2 | yes | 8 | 4.3 | odd | 2 | ||
336.2.bj.g.191.1 | yes | 8 | 7.2 | even | 3 | ||
336.2.bj.g.191.2 | yes | 8 | 21.2 | odd | 6 | ||
2352.2.h.m.2255.1 | 8 | 84.59 | odd | 6 | |||
2352.2.h.m.2255.2 | 8 | 7.3 | odd | 6 | |||
2352.2.h.m.2255.7 | 8 | 28.3 | even | 6 | |||
2352.2.h.m.2255.8 | 8 | 21.17 | even | 6 | |||
2352.2.h.n.2255.1 | 8 | 21.11 | odd | 6 | |||
2352.2.h.n.2255.2 | 8 | 28.11 | odd | 6 | |||
2352.2.h.n.2255.7 | 8 | 7.4 | even | 3 | |||
2352.2.h.n.2255.8 | 8 | 84.11 | even | 6 |