Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [352,2,Mod(97,352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(352, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("352.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 352 = 2^{5} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 352.m (of order \(5\), degree \(4\), 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: | \(2.81073415115\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 257.3 | ||
Root | \(1.66582 - 1.21029i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 352.257 |
Dual form | 352.2.m.e.289.3 |
$q$-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 \(\left(\mathbb{Z}/352\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(287\) | \(321\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 | ||||||||
\(3\) | 0.945302 | − | 2.90934i | 0.545770 | − | 1.67971i | −0.173381 | − | 0.984855i | \(-0.555469\pi\) |
0.719151 | − | 0.694854i | \(-0.244531\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.43185 | + | 1.76684i | −1.08756 | + | 0.790156i | −0.978985 | − | 0.203933i | \(-0.934628\pi\) |
−0.108572 | + | 0.994089i | \(0.534628\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.483582 | − | 1.48831i | −0.182777 | − | 0.562529i | 0.817126 | − | 0.576459i | \(-0.195566\pi\) |
−0.999903 | + | 0.0139295i | \(0.995566\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.14361 | − | 3.73705i | −1.71454 | − | 1.24568i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.21473 | − | 0.815786i | −0.969278 | − | 0.245969i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.95884 | − | 2.14973i | −0.820635 | − | 0.596226i | 0.0962591 | − | 0.995356i | \(-0.469312\pi\) |
−0.916894 | + | 0.399130i | \(0.869312\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.84151 | + | 8.74528i | 0.733676 | + | 2.25802i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.62100 | − | 2.63081i | 0.878222 | − | 0.638065i | −0.0545588 | − | 0.998511i | \(-0.517375\pi\) |
0.932780 | + | 0.360445i | \(0.117375\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.848695 | − | 2.61201i | 0.194704 | − | 0.599237i | −0.805276 | − | 0.592900i | \(-0.797983\pi\) |
0.999980 | − | 0.00633684i | \(-0.00201709\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.78714 | −1.04464 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.77580 | 0.995823 | 0.497911 | − | 0.867228i | \(-0.334101\pi\) | ||||
0.497911 | + | 0.867228i | \(0.334101\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.24708 | − | 3.83811i | 0.249416 | − | 0.767622i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.31014 | + | 6.03767i | −1.59929 | + | 1.16195i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.53580 | + | 4.72671i | 0.285191 | + | 0.877728i | 0.986341 | + | 0.164715i | \(0.0526703\pi\) |
−0.701150 | + | 0.713014i | \(0.747330\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.394554 | − | 0.286660i | −0.0708640 | − | 0.0514857i | 0.551789 | − | 0.833984i | \(-0.313945\pi\) |
−0.622653 | + | 0.782498i | \(0.713945\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.41229 | + | 8.58158i | −0.942159 | + | 1.49386i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.80561 | + | 2.76494i | 0.643266 | + | 0.467360i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.28946 | − | 10.1239i | −0.540784 | − | 1.66436i | −0.730809 | − | 0.682581i | \(-0.760857\pi\) |
0.190026 | − | 0.981779i | \(-0.439143\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.05128 | + | 6.57614i | −1.44937 | + | 1.05303i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.87558 | + | 11.9278i | −0.605264 | + | 1.86281i | −0.110302 | + | 0.993898i | \(0.535182\pi\) |
−0.494962 | + | 0.868914i | \(0.664818\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.45745 | 1.13725 | 0.568625 | − | 0.822597i | \(-0.307476\pi\) | ||||
0.568625 | + | 0.822597i | \(0.307476\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 19.1113 | 2.84894 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.10162 | − | 9.54579i | 0.452417 | − | 1.39240i | −0.421724 | − | 0.906724i | \(-0.638575\pi\) |
0.874141 | − | 0.485673i | \(-0.161425\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.68190 | − | 2.67505i | 0.525985 | − | 0.382150i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.23099 | − | 13.0216i | −0.592456 | − | 1.82339i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.26078 | + | 3.09564i | 0.585263 | + | 0.425218i | 0.840618 | − | 0.541629i | \(-0.182192\pi\) |
−0.255355 | + | 0.966847i | \(0.582192\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.25911 | − | 3.69605i | 1.24850 | − | 0.498376i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.79696 | − | 4.93828i | −0.900280 | − | 0.654091i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.76079 | − | 8.49684i | −0.359424 | − | 1.10619i | −0.953399 | − | 0.301711i | \(-0.902442\pi\) |
0.593975 | − | 0.804483i | \(-0.297558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.75109 | + | 1.27224i | −0.224204 | + | 0.162894i | −0.694217 | − | 0.719766i | \(-0.744249\pi\) |
0.470013 | + | 0.882659i | \(0.344249\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.07455 | + | 9.46248i | −0.387356 | + | 1.19216i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.9937 | 1.36360 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.709392 | 0.0866661 | 0.0433330 | − | 0.999061i | \(-0.486202\pi\) | ||||
0.0433330 | + | 0.999061i | \(0.486202\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.51457 | − | 13.8944i | 0.543490 | − | 1.67269i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.654053 | + | 0.475198i | −0.0776218 | + | 0.0563956i | −0.625919 | − | 0.779888i | \(-0.715276\pi\) |
0.548298 | + | 0.836283i | \(0.315276\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.163185 | − | 0.502230i | −0.0190993 | − | 0.0587816i | 0.941053 | − | 0.338260i | \(-0.109838\pi\) |
−0.960152 | + | 0.279479i | \(0.909838\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.98751 | − | 7.25635i | −1.15326 | − | 0.837891i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.340441 | + | 5.17903i | 0.0387969 | + | 0.590205i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.70380 | − | 3.41751i | −0.529219 | − | 0.384500i | 0.290846 | − | 0.956770i | \(-0.406063\pi\) |
−0.820066 | + | 0.572269i | \(0.806063\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.81598 | + | 11.7444i | 0.423998 | + | 1.30493i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.73701 | − | 4.16818i | 0.629718 | − | 0.457517i | −0.226584 | − | 0.973992i | \(-0.572756\pi\) |
0.856303 | + | 0.516474i | \(0.172756\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.15750 | + | 12.7955i | −0.450944 | + | 1.38786i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.2034 | 1.62998 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.76282 | 0.822857 | 0.411429 | − | 0.911442i | \(-0.365030\pi\) | ||||
0.411429 | + | 0.911442i | \(0.365030\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.76862 | + | 5.44325i | −0.185402 | + | 0.570608i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.20696 | + | 0.876911i | −0.125156 | + | 0.0909315i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.55112 | + | 7.85154i | 0.261739 | + | 0.805551i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.93665 | − | 2.13360i | −0.298172 | − | 0.216634i | 0.428633 | − | 0.903479i | \(-0.358995\pi\) |
−0.726805 | + | 0.686844i | \(0.758995\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.4867 | + | 16.2097i | 1.35546 | + | 1.62914i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.995345 | + | 0.723160i | 0.0990405 | + | 0.0719571i | 0.636203 | − | 0.771521i | \(-0.280504\pi\) |
−0.537163 | + | 0.843479i | \(0.680504\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.792654 | − | 2.43954i | −0.0781025 | − | 0.240375i | 0.904380 | − | 0.426727i | \(-0.140333\pi\) |
−0.982483 | + | 0.186352i | \(0.940333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.6416 | − | 8.45812i | 1.13610 | − | 0.825428i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.22154 | + | 12.9926i | −0.408112 | + | 1.25604i | 0.510157 | + | 0.860081i | \(0.329587\pi\) |
−0.918269 | + | 0.395957i | \(0.870413\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.935861 | 0.0896393 | 0.0448196 | − | 0.998995i | \(-0.485729\pi\) | ||||
0.0448196 | + | 0.998995i | \(0.485729\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −32.5634 | −3.09078 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.992485 | + | 3.05455i | −0.0933651 | + | 0.287348i | −0.986824 | − | 0.161796i | \(-0.948271\pi\) |
0.893459 | + | 0.449145i | \(0.148271\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.6140 | + | 8.43808i | −1.08301 | + | 0.786855i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.18551 | + | 22.1147i | 0.664300 | + | 2.04451i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.66652 | − | 4.11697i | −0.519449 | − | 0.377402i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.66899 | + | 5.24507i | 0.878999 | + | 0.476824i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 31.0385 | + | 22.5508i | 2.79865 | + | 2.03334i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.895788 | − | 2.75695i | −0.0801217 | − | 0.246589i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.21981 | + | 5.97204i | −0.729391 | + | 0.529933i | −0.889371 | − | 0.457187i | \(-0.848857\pi\) |
0.159980 | + | 0.987120i | \(0.448857\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.04954 | − | 21.6963i | 0.620677 | − | 1.91025i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.01348 | −0.263289 | −0.131644 | − | 0.991297i | \(-0.542026\pi\) | ||||
−0.131644 | + | 0.991297i | \(0.542026\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.29791 | −0.372676 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.54140 | − | 29.3654i | 0.821193 | − | 2.52737i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.839676 | + | 0.610060i | −0.0717383 | + | 0.0521209i | −0.623076 | − | 0.782161i | \(-0.714117\pi\) |
0.551338 | + | 0.834282i | \(0.314117\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.906933 | − | 2.79125i | −0.0769250 | − | 0.236751i | 0.905198 | − | 0.424989i | \(-0.139722\pi\) |
−0.982123 | + | 0.188239i | \(0.939722\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.8400 | − | 18.0473i | −2.09191 | − | 1.51986i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.75817 | + | 9.32457i | 0.648770 | + | 0.779760i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0862 | − | 8.78114i | −1.00370 | − | 0.729234i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.30214 | − | 13.2406i | −0.354834 | − | 1.09207i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.95118 | + | 7.22996i | −0.815233 | + | 0.592301i | −0.915343 | − | 0.402675i | \(-0.868080\pi\) |
0.100110 | + | 0.994976i | \(0.468080\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.23702 | − | 19.1956i | 0.507561 | − | 1.56211i | −0.288861 | − | 0.957371i | \(-0.593276\pi\) |
0.796422 | − | 0.604741i | \(-0.206724\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −28.4565 | −2.30057 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.46598 | 0.117750 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.08041 | + | 12.5582i | −0.325652 | + | 1.00226i | 0.645493 | + | 0.763766i | \(0.276652\pi\) |
−0.971145 | + | 0.238489i | \(0.923348\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.0340 | − | 9.46974i | 1.03366 | − | 0.750999i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.30949 | − | 7.10788i | −0.182013 | − | 0.560179i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.84035 | + | 2.06364i | 0.222474 | + | 0.161637i | 0.693439 | − | 0.720515i | \(-0.256094\pi\) |
−0.470966 | + | 0.882151i | \(0.656094\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.00042 | − | 30.4318i | −0.155733 | − | 2.36911i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.09764 | − | 5.88328i | −0.626614 | − | 0.455262i | 0.228612 | − | 0.973518i | \(-0.426581\pi\) |
−0.855225 | + | 0.518256i | \(0.826581\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.116211 | + | 0.357661i | 0.00893933 | + | 0.0275124i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.1266 | + | 10.2636i | −1.08029 | + | 0.784875i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.775536 | + | 2.38686i | −0.0589629 | + | 0.181469i | −0.976200 | − | 0.216873i | \(-0.930414\pi\) |
0.917237 | + | 0.398342i | \(0.130414\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.31538 | −0.477398 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.3300 | −2.05425 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.19007 | − | 15.9734i | 0.387924 | − | 1.19391i | −0.546412 | − | 0.837516i | \(-0.684007\pi\) |
0.934337 | − | 0.356392i | \(-0.115993\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.80422 | − | 3.49047i | 0.357095 | − | 0.259444i | −0.394745 | − | 0.918791i | \(-0.629167\pi\) |
0.751839 | + | 0.659346i | \(0.229167\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.04607 | + | 6.29716i | 0.151250 | + | 0.465500i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.8868 | + | 18.8079i | 1.90324 | + | 1.38278i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.7867 | + | 5.50339i | −1.00818 | + | 0.402447i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.0046 | + | 9.44838i | 0.945943 | + | 0.687268i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.14500 | + | 6.60162i | 0.155207 | + | 0.477677i | 0.998182 | − | 0.0602757i | \(-0.0191980\pi\) |
−0.842975 | + | 0.537952i | \(0.819198\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.96054 | + | 2.15096i | −0.213104 | + | 0.154829i | −0.689217 | − | 0.724555i | \(-0.742045\pi\) |
0.476113 | + | 0.879384i | \(0.342045\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.3924 | − | 31.9844i | 0.744212 | − | 2.29045i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.5687 | 1.25172 | 0.625859 | − | 0.779936i | \(-0.284749\pi\) | ||||
0.625859 | + | 0.779936i | \(0.284749\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.12699 | 0.505219 | 0.252609 | − | 0.967568i | \(-0.418711\pi\) | ||||
0.252609 | + | 0.967568i | \(0.418711\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.670590 | − | 2.06386i | 0.0472998 | − | 0.145574i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.29214 | − | 4.57151i | 0.441622 | − | 0.320857i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.6497 | − | 35.8542i | −0.813653 | − | 2.50417i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −24.5649 | − | 17.8474i | −1.70738 | − | 1.24048i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.85917 | + | 7.70457i | −0.336116 | + | 0.532936i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.5962 | + | 12.0578i | 1.14253 | + | 0.830096i | 0.987470 | − | 0.157810i | \(-0.0504432\pi\) |
0.155059 | + | 0.987905i | \(0.450443\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.764234 | + | 2.35207i | 0.0523644 | + | 0.161161i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.1354 | + | 13.1761i | −1.23682 | + | 0.898605i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.235841 | + | 0.725844i | −0.0160099 | + | 0.0492735i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.61542 | −0.109160 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.3695 | −1.10113 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.92982 | − | 5.93937i | 0.129230 | − | 0.397730i | −0.865418 | − | 0.501051i | \(-0.832947\pi\) |
0.994648 | + | 0.103321i | \(0.0329469\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −20.7577 | + | 15.0814i | −1.38385 | + | 1.00542i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.86911 | + | 14.9856i | 0.323174 | + | 0.994628i | 0.972258 | + | 0.233911i | \(0.0751524\pi\) |
−0.649084 | + | 0.760717i | \(0.724848\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.5330 | + | 9.83230i | 0.894286 | + | 0.649737i | 0.936992 | − | 0.349351i | \(-0.113598\pi\) |
−0.0427060 | + | 0.999088i | \(0.513598\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.3894 | + | 3.90528i | 1.01255 | + | 0.256949i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.48338 | + | 6.89008i | 0.621277 | + | 0.451384i | 0.853367 | − | 0.521310i | \(-0.174557\pi\) |
−0.232090 | + | 0.972694i | \(0.574557\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.32325 | + | 28.6940i | 0.608182 | + | 1.87179i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.3892 | + | 10.4544i | −0.934681 | + | 0.679085i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.83369 | + | 24.1096i | −0.506719 | + | 1.55952i | 0.291142 | + | 0.956680i | \(0.405965\pi\) |
−0.797861 | + | 0.602841i | \(0.794035\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.25667 | 0.0809490 | 0.0404745 | − | 0.999181i | \(-0.487113\pi\) | ||||
0.0404745 | + | 0.999181i | \(0.487113\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.96000 | 0.446484 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.22742 | + | 13.0107i | −0.270080 | + | 0.831221i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.12626 | + | 5.90408i | −0.517062 | + | 0.375667i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.70345 | − | 20.6311i | −0.424814 | − | 1.30744i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.6517 | − | 13.5513i | −1.17729 | − | 0.855349i | −0.185424 | − | 0.982659i | \(-0.559366\pi\) |
−0.991863 | + | 0.127309i | \(0.959366\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.3529 | − | 3.89603i | −0.965229 | − | 0.244941i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 33.2963 | + | 24.1912i | 2.08510 | + | 1.51491i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.66741 | − | 5.13176i | −0.104010 | − | 0.320111i | 0.885487 | − | 0.464665i | \(-0.153825\pi\) |
−0.989497 | + | 0.144554i | \(0.953825\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.4768 | + | 9.79149i | −0.837409 | + | 0.608413i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.76441 | − | 30.0518i | 0.604402 | − | 1.86016i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.3375 | −1.00742 | −0.503708 | − | 0.863874i | \(-0.668031\pi\) | ||||
−0.503708 | + | 0.863874i | \(0.668031\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.8311 | −0.972495 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.33821 | − | 22.5847i | 0.449091 | − | 1.38216i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.3600 | − | 16.2455i | 1.36331 | − | 0.990503i | 0.365084 | − | 0.930974i | \(-0.381040\pi\) |
0.998227 | − | 0.0595289i | \(-0.0189599\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.23475 | − | 28.4216i | −0.560971 | − | 1.72649i | −0.679629 | − | 0.733556i | \(-0.737859\pi\) |
0.118658 | − | 0.992935i | \(-0.462141\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.1644 | + | 10.2910i | 0.857268 | + | 0.622842i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.14010 | + | 11.3211i | −0.430564 | + | 0.682691i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.3993 | + | 14.0944i | 1.16559 | + | 0.846852i | 0.990475 | − | 0.137696i | \(-0.0439696\pi\) |
0.175117 | + | 0.984548i | \(0.443970\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.958169 | + | 2.94894i | 0.0573641 | + | 0.176548i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.29029 | + | 6.74979i | −0.554212 | + | 0.402659i | −0.829336 | − | 0.558750i | \(-0.811281\pi\) |
0.275124 | + | 0.961409i | \(0.411281\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.07083 | + | 15.6064i | −0.301430 | + | 0.927706i | 0.679556 | + | 0.733624i | \(0.262173\pi\) |
−0.980985 | + | 0.194082i | \(0.937827\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 25.2544 | 1.49594 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.6265 | 1.15852 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.937189 | − | 2.88437i | 0.0551288 | − | 0.169669i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.98339 | + | 6.52682i | −0.526616 | + | 0.382609i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.19334 | + | 15.9835i | 0.303398 | + | 0.933764i | 0.980270 | + | 0.197663i | \(0.0633352\pi\) |
−0.676872 | + | 0.736101i | \(0.736665\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.7264 | + | 15.7852i | 1.26496 | + | 0.919048i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 31.6403 | − | 12.6302i | 1.83596 | − | 0.732877i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.1308 | − | 10.2667i | −0.817207 | − | 0.593736i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.60629 | − | 11.0990i | −0.207863 | − | 0.639737i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.04482 | − | 2.21219i | 0.174920 | − | 0.127087i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.01054 | − | 6.18780i | 0.115123 | − | 0.354312i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.3071 | 0.702403 | 0.351201 | − | 0.936300i | \(-0.385773\pi\) | ||||
0.351201 | + | 0.936300i | \(0.385773\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.84675 | −0.446386 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.12870 | + | 15.7845i | −0.290822 | + | 0.895057i | 0.693771 | + | 0.720195i | \(0.255948\pi\) |
−0.984593 | + | 0.174862i | \(0.944052\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.4719 | − | 13.4206i | 1.04410 | − | 0.758580i | 0.0730148 | − | 0.997331i | \(-0.476738\pi\) |
0.971081 | + | 0.238751i | \(0.0767380\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.24188 | − | 28.4436i | −0.520721 | − | 1.60261i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.85676 | + | 2.80210i | 0.216617 | + | 0.157382i | 0.690803 | − | 0.723043i | \(-0.257257\pi\) |
−0.474185 | + | 0.880425i | \(0.657257\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.08120 | − | 16.4480i | −0.0605357 | − | 0.920911i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 33.8091 | + | 24.5638i | 1.88704 | + | 1.37102i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.79859 | − | 11.6909i | −0.211359 | − | 0.650497i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.9408 | + | 8.67550i | −0.662356 | + | 0.481230i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.884672 | − | 2.72274i | 0.0489224 | − | 0.150568i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.7070 | −0.865956 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.4925 | −1.78595 | −0.892976 | − | 0.450105i | \(-0.851387\pi\) | ||||
−0.892976 | + | 0.450105i | \(0.851387\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.9139 | + | 64.3664i | −1.14607 | + | 3.52726i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.72514 | + | 1.25338i | −0.0942542 | + | 0.0684797i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.93504 | − | 9.03312i | −0.159882 | − | 0.492066i | 0.838741 | − | 0.544531i | \(-0.183292\pi\) |
−0.998623 | + | 0.0524650i | \(0.983292\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.94854 | + | 5.77495i | 0.431705 | + | 0.313652i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.03453 | + | 1.24341i | 0.0560230 | + | 0.0673343i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.6241 | − | 10.6250i | −0.789625 | − | 0.573696i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.5705 | + | 41.7657i | 0.730611 | + | 2.24859i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.9950 | − | 21.0661i | 1.55653 | − | 1.13089i | 0.617749 | − | 0.786376i | \(-0.288045\pi\) |
0.938783 | − | 0.344510i | \(-0.111955\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.03407 | − | 24.7263i | 0.430054 | − | 1.32357i | −0.468017 | − | 0.883720i | \(-0.655031\pi\) |
0.898071 | − | 0.439851i | \(-0.144969\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 37.5677 | 2.00522 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.3264 | −0.868969 | −0.434484 | − | 0.900679i | \(-0.643069\pi\) | ||||
−0.434484 | + | 0.900679i | \(0.643069\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.750960 | − | 2.31122i | 0.0398568 | − | 0.122667i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −17.3342 | + | 12.5941i | −0.917425 | + | 0.666548i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.38640 | − | 7.34459i | −0.125949 | − | 0.387633i | 0.868123 | − | 0.496348i | \(-0.165326\pi\) |
−0.994073 | + | 0.108716i | \(0.965326\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.26899 | + | 6.73432i | 0.487842 | + | 0.354438i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.3998 | − | 23.1722i | 1.28066 | − | 1.21623i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.28420 | + | 0.933028i | 0.0672182 | + | 0.0488369i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.92708 | − | 5.93094i | −0.100593 | − | 0.309592i | 0.888078 | − | 0.459692i | \(-0.152040\pi\) |
−0.988671 | + | 0.150100i | \(0.952040\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 64.5094 | − | 46.8688i | 3.35823 | − | 2.43989i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.54684 | − | 7.83836i | 0.132225 | − | 0.406948i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.84081 | 0.250648 | 0.125324 | − | 0.992116i | \(-0.460003\pi\) | ||||
0.125324 | + | 0.992116i | \(0.460003\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.86770 | −0.457926 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.61694 | − | 17.2871i | 0.289287 | − | 0.890333i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.0664 | + | 8.04021i | −0.568443 | + | 0.412998i | −0.834539 | − | 0.550949i | \(-0.814266\pi\) |
0.266096 | + | 0.963946i | \(0.414266\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.60450 | + | 29.5596i | 0.492054 | + | 1.51439i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.30686 | − | 6.76183i | −0.475558 | − | 0.345513i | 0.324045 | − | 0.946042i | \(-0.394957\pi\) |
−0.799604 | + | 0.600528i | \(0.794957\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.97843 | − | 11.9931i | −0.508548 | − | 0.611225i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −38.3582 | − | 27.8689i | −1.94986 | − | 1.41666i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.87359 | + | 8.84400i | 0.145697 | + | 0.448408i | 0.997100 | − | 0.0761033i | \(-0.0242479\pi\) |
−0.851403 | + | 0.524512i | \(0.824248\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.2932 | − | 12.5642i | 0.874553 | − | 0.635400i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.84865 | + | 8.76723i | −0.143695 | + | 0.442248i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.4772 | 0.879371 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 38.3379 | 1.92413 | 0.962063 | − | 0.272828i | \(-0.0879589\pi\) | ||||
0.962063 | + | 0.272828i | \(0.0879589\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.06282 | + | 12.5041i | −0.203395 | + | 0.625987i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.0065 | + | 10.1763i | −0.699453 | + | 0.508182i | −0.879754 | − | 0.475429i | \(-0.842293\pi\) |
0.180301 | + | 0.983611i | \(0.442293\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.551182 | + | 1.69637i | 0.0274564 | + | 0.0845020i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −30.0304 | − | 21.8184i | −1.49222 | − | 1.08416i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.31577 | + | 35.2291i | 0.114789 | + | 1.74624i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.17834 | − | 1.58266i | −0.107712 | − | 0.0782573i | 0.532625 | − | 0.846351i | \(-0.321205\pi\) |
−0.640337 | + | 0.768094i | \(0.721205\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.981125 | + | 3.01959i | 0.0483953 | + | 0.148946i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.3109 | + | 8.21784i | −0.556572 | + | 0.404374i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.58702 | + | 20.2728i | −0.323344 | + | 0.995152i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.97803 | −0.439656 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.3425 | 0.651824 | 0.325912 | − | 0.945400i | \(-0.394329\pi\) | ||||
0.325912 | + | 0.945400i | \(0.394329\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.54615 | − | 20.1470i | 0.319040 | − | 0.981903i | −0.655020 | − | 0.755612i | \(-0.727340\pi\) |
0.974060 | − | 0.226291i | \(-0.0726602\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −51.6267 | + | 37.5090i | −2.51017 | + | 1.82375i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.58168 | − | 17.1786i | −0.270751 | − | 0.833286i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.74029 | + | 1.99094i | 0.132612 | + | 0.0963481i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 34.4622 | − | 13.7566i | 1.66385 | − | 0.664175i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.0809 | + | 10.2304i | 0.678253 | + | 0.492780i | 0.872778 | − | 0.488118i | \(-0.162316\pi\) |
−0.194524 | + | 0.980898i | \(0.562316\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.27401 | + | 3.92101i | 0.0612252 | + | 0.188432i | 0.976991 | − | 0.213281i | \(-0.0684150\pi\) |
−0.915766 | + | 0.401713i | \(0.868415\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −36.9724 | + | 26.8620i | −1.77269 | + | 1.28794i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.05319 | − | 12.4744i | 0.193891 | − | 0.596734i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.8478 | 1.47229 | 0.736143 | − | 0.676826i | \(-0.236645\pi\) | ||||
0.736143 | + | 0.676826i | \(0.236645\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −28.9351 | −1.37786 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.89223 | − | 8.90137i | 0.137414 | − | 0.422917i | −0.858544 | − | 0.512740i | \(-0.828630\pi\) |
0.995958 | + | 0.0898236i | \(0.0286303\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.8780 | + | 13.7157i | −0.894904 | + | 0.650186i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.6275 | + | 35.7859i | 0.549964 | + | 1.69261i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.98291 | + | 2.16721i | 0.140772 | + | 0.102277i | 0.655943 | − | 0.754811i | \(-0.272271\pi\) |
−0.515170 | + | 0.857088i | \(0.672271\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.1895 | − | 35.1831i | 1.04486 | − | 1.65671i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −49.9506 | − | 36.2912i | −2.34688 | − | 1.70511i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.31635 | − | 16.3621i | −0.249234 | − | 0.767065i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.0090 | + | 18.8966i | −1.21665 | + | 0.883946i | −0.995817 | − | 0.0913659i | \(-0.970877\pi\) |
−0.220830 | + | 0.975312i | \(0.570877\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.2070 | + | 43.7248i | −0.663128 | + | 2.04090i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.41140 | −0.158885 | −0.0794423 | − | 0.996839i | \(-0.525314\pi\) | ||||
−0.0794423 | + | 0.996839i | \(0.525314\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.72640 | 0.173181 | 0.0865903 | − | 0.996244i | \(-0.472403\pi\) | ||||
0.0865903 | + | 0.996244i | \(0.472403\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.38579 | − | 4.26503i | 0.0642646 | − | 0.197786i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.56111 | − | 1.13421i | 0.0722394 | − | 0.0524850i | −0.551079 | − | 0.834453i | \(-0.685784\pi\) |
0.623319 | + | 0.781968i | \(0.285784\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.343049 | − | 1.05580i | −0.0158406 | − | 0.0487522i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.6789 | + | 23.7426i | 1.50576 | + | 1.09400i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.9737 | − | 6.08368i | −1.10231 | − | 0.279728i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.96681 | − | 6.51477i | −0.411426 | − | 0.298918i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.3472 | − | 31.8455i | −0.473767 | − | 1.45811i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.8844 | − | 16.6265i | 1.04562 | − | 0.759685i | 0.0742424 | − | 0.997240i | \(-0.476346\pi\) |
0.971374 | + | 0.237555i | \(0.0763461\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0306 | + | 37.0265i | −0.548550 | + | 1.68826i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.8624 | −1.04028 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.9112 | 0.495453 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.60225 | + | 11.0866i | −0.163234 | + | 0.502382i | −0.998902 | − | 0.0468530i | \(-0.985081\pi\) |
0.835668 | + | 0.549235i | \(0.185081\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.68882 | − | 6.31279i | 0.392922 | − | 0.285474i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.74067 | + | 17.6680i | 0.259073 | + | 0.797344i | 0.993000 | + | 0.118116i | \(0.0376854\pi\) |
−0.733927 | + | 0.679228i | \(0.762315\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.9962 | + | 13.0750i | 0.810509 | + | 0.588869i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −61.4377 | − | 15.5907i | −2.76142 | − | 0.700751i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.02353 | + | 0.743639i | 0.0459117 | + | 0.0333568i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.14606 | + | 3.52720i | 0.0513045 | + | 0.157899i | 0.973426 | − | 0.229001i | \(-0.0735459\pi\) |
−0.922122 | + | 0.386900i | \(0.873546\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.7712 | + | 17.9973i | −1.10669 | + | 0.804060i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.60505 | − | 29.5613i | 0.428268 | − | 1.31807i | −0.471562 | − | 0.881833i | \(-0.656310\pi\) |
0.899830 | − | 0.436240i | \(-0.143690\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.69824 | −0.164570 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.15041 | 0.0510917 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.0394 | − | 37.0535i | 0.533637 | − | 1.64237i | −0.212938 | − | 0.977066i | \(-0.568303\pi\) |
0.746575 | − | 0.665301i | \(-0.231697\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.668563 | + | 0.485739i | −0.0295755 | + | 0.0214878i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.71770 | + | 26.8303i | 0.384896 | + | 1.18459i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.23790 | + | 4.53210i | 0.274875 | + | 0.199708i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.7582 | + | 28.1569i | −0.781004 | + | 1.23834i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.21106 | + | 4.51260i | 0.272635 | + | 0.198081i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.59202 | − | 11.0551i | −0.157369 | − | 0.484333i | 0.841024 | − | 0.540998i | \(-0.181953\pi\) |
−0.998393 | + | 0.0566650i | \(0.981953\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.3623 | − | 10.4348i | 0.628019 | − | 0.456283i | −0.227694 | − | 0.973733i | \(-0.573119\pi\) |
0.855713 | + | 0.517450i | \(0.173119\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.96994 | + | 18.3736i | −0.260550 | + | 0.801889i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.18283 | −0.0950855 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.191763 | −0.00833752 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.5527 | + | 54.0217i | −0.761723 | + | 2.34434i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 37.1088 | − | 26.9611i | 1.60736 | − | 1.16781i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.6897 | − | 39.0548i | −0.548622 | − | 1.68848i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −41.5659 | − | 30.1994i | −1.79370 | − | 1.30320i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.0186 | + | 5.59594i | −0.603823 | + | 0.241034i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.6289 | + | 14.2613i | 0.843914 | + | 0.613139i | 0.923461 | − | 0.383692i | \(-0.125348\pi\) |
−0.0795476 | + | 0.996831i | \(0.525348\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.61352 | − | 17.2767i | −0.240899 | − | 0.741412i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.27587 | + | 1.65352i | −0.0974878 | + | 0.0708290i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.56209 | + | 7.88530i | −0.109547 | + | 0.337151i | −0.990771 | − | 0.135548i | \(-0.956720\pi\) |
0.881224 | + | 0.472700i | \(0.156720\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.7614 | 0.587320 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.6497 | 0.581495 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.81165 | + | 8.65338i | −0.119564 | + | 0.367979i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 79.1894 | − | 57.5345i | 3.36140 | − | 2.44220i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.9681 | − | 39.9116i | −0.549474 | − | 1.69111i | −0.710107 | − | 0.704094i | \(-0.751354\pi\) |
0.160633 | − | 0.987014i | \(-0.448646\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.0654 | − | 16.0315i | −0.933268 | − | 0.678059i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.97861 | + | 45.3126i | 0.125757 | + | 1.91310i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.4232 | − | 19.9241i | −1.15575 | − | 0.839701i | −0.166515 | − | 0.986039i | \(-0.553251\pi\) |
−0.989235 | + | 0.146338i | \(0.953251\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.98334 | − | 9.18178i | −0.125510 | − | 0.386280i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.6340 | − | 11.3588i | 0.656566 | − | 0.477023i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.34770 | + | 16.4585i | −0.224187 | + | 0.689977i | 0.774186 | + | 0.632958i | \(0.218159\pi\) |
−0.998373 | + | 0.0570187i | \(0.981841\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.8559 | 0.663551 | 0.331775 | − | 0.943358i | \(-0.392352\pi\) | ||||
0.331775 | + | 0.943358i | \(0.392352\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.2340 | 0.887065 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.95579 | − | 18.3300i | 0.248374 | − | 0.764416i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.3438 | − | 16.9603i | 0.971816 | − | 0.706066i | 0.0159512 | − | 0.999873i | \(-0.494922\pi\) |
0.955865 | + | 0.293807i | \(0.0949224\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.45927 | + | 10.6465i | 0.143762 | + | 0.442455i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.97787 | − | 6.52280i | −0.372465 | − | 0.270612i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.1719 | − | 13.4275i | −0.462692 | − | 0.556111i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −56.5473 | − | 41.0840i | −2.33794 | − | 1.69862i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.44600 | + | 25.9941i | 0.348604 | + | 1.07289i | 0.959626 | + | 0.281279i | \(0.0907585\pi\) |
−0.611022 | + | 0.791613i | \(0.709241\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.08362 | + | 0.787293i | −0.0446496 | + | 0.0324398i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.6077 | − | 51.1133i | 0.683150 | − | 2.10252i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.4666 | −1.37431 | −0.687154 | − | 0.726512i | \(-0.741140\pi\) | ||||
−0.687154 | + | 0.726512i | \(0.741140\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.0542 | 0.863137 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.73716 | − | 20.7348i | 0.275733 | − | 0.848620i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.7397 | − | 9.98248i | 0.561389 | − | 0.407873i | −0.270578 | − | 0.962698i | \(-0.587215\pi\) |
0.831967 | + | 0.554825i | \(0.187215\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.00907725 | + | 0.0279369i | 0.000370269 | + | 0.00113957i | 0.951241 | − | 0.308447i | \(-0.0998093\pi\) |
−0.950871 | + | 0.309587i | \(0.899809\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.64884 | − | 2.65104i | −0.148592 | − | 0.107959i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −32.7807 | + | 4.32836i | −1.33273 | + | 0.175973i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.0371 | + | 15.2844i | 0.853870 | + | 0.620373i | 0.926210 | − | 0.377007i | \(-0.123047\pi\) |
−0.0723401 | + | 0.997380i | \(0.523047\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.35210 | − | 22.6274i | −0.297922 | − | 0.916910i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.6980 | + | 21.5769i | −1.20145 | + | 0.872907i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.39248 | + | 28.9071i | −0.379359 | + | 1.16755i | 0.561132 | + | 0.827726i | \(0.310366\pi\) |
−0.940491 | + | 0.339820i | \(0.889634\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −115.325 | −4.65034 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.3795 | 0.900966 | 0.450483 | − | 0.892785i | \(-0.351252\pi\) | ||||
0.450483 | + | 0.892785i | \(0.351252\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.13465 | − | 21.9582i | 0.286766 | − | 0.882575i | −0.699098 | − | 0.715026i | \(-0.746415\pi\) |
0.985864 | − | 0.167549i | \(-0.0535852\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −39.6875 | + | 28.8347i | −1.59261 | + | 1.15710i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.75396 | − | 11.5535i | −0.150399 | − | 0.462881i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.3740 | + | 16.9822i | 0.934960 | + | 0.679288i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.8218 | + | 21.4201i | 0.711735 | + | 0.855437i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −38.5452 | − | 28.0047i | −1.53690 | − | 1.11662i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.28529 | + | 28.5772i | 0.369641 | + | 1.13764i | 0.947023 | + | 0.321165i | \(0.104074\pi\) |
−0.577382 | + | 0.816474i | \(0.695926\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 50.7688 | − | 36.8857i | 2.01788 | − | 1.46607i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.43769 | − | 29.0462i | 0.374523 | − | 1.15266i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.6448 | −0.659490 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.14004 | 0.203337 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1148 | − | 34.2078i | 0.439007 | − | 1.35113i | −0.449917 | − | 0.893070i | \(-0.648546\pi\) |
0.888924 | − | 0.458055i | \(-0.151454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.7433 | + | 10.7117i | −0.581420 | + | 0.422426i | −0.839236 | − | 0.543768i | \(-0.816997\pi\) |
0.257816 | + | 0.966194i | \(0.416997\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.1904 | + | 65.2175i | 0.834373 | + | 2.56794i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.00098 | − | 6.53959i | −0.353865 | − | 0.257098i | 0.396624 | − | 0.917981i | \(-0.370182\pi\) |
−0.750489 | + | 0.660883i | \(0.770182\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.94359 | + | 29.5673i | 0.0762927 | + | 1.16062i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.88879 | + | 1.37228i | 0.0740273 | + | 0.0537840i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.11131 | − | 15.7310i | −0.200021 | − | 0.615601i | −0.999881 | − | 0.0154150i | \(-0.995093\pi\) |
0.799860 | − | 0.600186i | \(-0.204907\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.32833 | − | 5.32434i | 0.286341 | − | 0.208039i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.03750 | + | 3.19311i | −0.0404769 | + | 0.124575i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.0957 | −1.01655 | −0.508273 | − | 0.861196i | \(-0.669716\pi\) | ||||
−0.508273 | + | 0.861196i | \(0.669716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.3262 | 0.596121 | 0.298061 | − | 0.954547i | \(-0.403660\pi\) | ||||
0.298061 | + | 0.954547i | \(0.403660\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.4741 | + | 47.6244i | −0.600965 | + | 1.84958i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.4519 | − | 7.59373i | 0.405306 | − | 0.294472i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.33468 | + | 22.5738i | 0.284000 | + | 0.874062i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.4554 | − | 11.2290i | −0.597540 | − | 0.434138i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.66715 | − | 2.66140i | 0.257383 | − | 0.102742i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.8605 | − | 18.7888i | −0.996851 | − | 0.724254i | −0.0354400 | − | 0.999372i | \(-0.511283\pi\) |
−0.961411 | + | 0.275117i | \(0.911283\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.8099 | + | 39.4247i | 0.493052 | + | 1.51746i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.1028 | + | 7.34015i | −0.388284 | + | 0.282105i | −0.764752 | − | 0.644325i | \(-0.777138\pi\) |
0.376468 | + | 0.926430i | \(0.377138\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.75535 | + | 5.40243i | −0.0673643 | + | 0.207326i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 48.2009 | 1.84706 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.0471 | −0.996665 | −0.498332 | − | 0.866986i | \(-0.666054\pi\) | ||||
−0.498332 | + | 0.866986i | \(0.666054\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.964085 | − | 2.96715i | 0.0368358 | − | 0.113369i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.3983 | − | 30.0776i | 1.57944 | − | 1.14753i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.95220 | − | 18.3190i | −0.226761 | − | 0.697898i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.5824 | + | 27.3052i | 1.42970 | + | 1.03874i | 0.990072 | + | 0.140562i | \(0.0448910\pi\) |
0.439632 | + | 0.898178i | \(0.355109\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.6032 | − | 27.9112i | 0.668690 | − | 1.06026i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.13723 | + | 5.18550i | 0.270730 | + | 0.196697i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.3463 | + | 53.3866i | 0.657040 | + | 2.02216i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.0102 | − | 21.0772i | 1.09727 | − | 0.797212i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.80323 | + | 24.0159i | −0.294724 | + | 0.907067i | 0.688590 | + | 0.725151i | \(0.258230\pi\) |
−0.983314 | + | 0.181916i | \(0.941770\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.2355 | −1.10264 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 92.2939 | 3.47599 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.594958 | − | 1.83109i | 0.0223757 | − | 0.0688653i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.69638 | − | 3.41212i | 0.176376 | − | 0.128145i | −0.496094 | − | 0.868269i | \(-0.665233\pi\) |
0.672471 | + | 0.740124i | \(0.265233\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.4231 | + | 35.1567i | 0.428400 | + | 1.31848i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.88431 | − | 1.36903i | −0.0705680 | − | 0.0512706i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −35.3417 | − | 8.96850i | −1.32171 | − | 0.335403i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 62.7379 | + | 45.5817i | 2.34299 | + | 1.70228i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.80299 | − | 30.1705i | −0.365590 | − | 1.12517i | −0.949611 | − | 0.313431i | \(-0.898522\pi\) |
0.584021 | − | 0.811738i | \(-0.301478\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.24748 | + | 2.35944i | −0.120943 | + | 0.0878700i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.18793 | − | 3.65607i | 0.0441796 | − | 0.135971i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.0569 | 0.744895 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 51.2435 | 1.90052 | 0.950258 | − | 0.311464i | \(-0.100819\pi\) | ||||
0.950258 | + | 0.311464i | \(0.100819\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.86865 | + | 14.9842i | −0.180320 | + | 0.554969i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.0034 | − | 19.6191i | 0.998758 | − | 0.725640i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.5510 | + | 41.7056i | 0.500517 | + | 1.54043i | 0.808179 | + | 0.588936i | \(0.200453\pi\) |
−0.307663 | + | 0.951495i | \(0.599547\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 33.8562 | + | 24.5980i | 1.24881 | + | 0.907311i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.28050 | − | 0.578712i | −0.0840035 | − | 0.0213171i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.1036 | − | 18.2388i | −0.923450 | − | 0.670926i | 0.0209304 | − | 0.999781i | \(-0.493337\pi\) |
−0.944380 | + | 0.328855i | \(0.893337\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.49519 | + | 29.2232i | 0.348815 | + | 1.07354i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.2293 | + | 13.9709i | −0.705455 | + | 0.512543i | −0.881704 | − | 0.471802i | \(-0.843604\pi\) |
0.176249 | + | 0.984346i | \(0.443604\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.4256 | − | 35.1644i | 0.418601 | − | 1.28832i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −45.0857 | −1.64960 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.3785 | 0.781152 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.1914 | + | 40.5989i | −0.481360 | + | 1.48147i | 0.355825 | + | 0.934553i | \(0.384200\pi\) |
−0.837185 | + | 0.546921i | \(0.815800\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −57.0568 | + | 41.4542i | −2.07927 | + | 1.51068i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.7480 | + | 57.7006i | 0.682311 | + | 2.09994i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.5386 | − | 14.1956i | −0.710143 | − | 0.515949i | 0.173077 | − | 0.984908i | \(-0.444629\pi\) |
−0.883220 | + | 0.468959i | \(0.844629\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25.8480 | + | 40.9839i | −0.938223 | + | 1.48762i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.0292 | − | 8.01318i | −0.399808 | − | 0.290477i | 0.369655 | − | 0.929169i | \(-0.379476\pi\) |
−0.769463 | + | 0.638692i | \(0.779476\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.452566 | − | 1.39285i | −0.0163840 | − | 0.0504247i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 69.2020 | − | 50.2782i | 2.50200 | − | 1.81781i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.0971 | + | 31.0758i | −0.364586 | + | 1.12208i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.6960 | 0.638135 | 0.319068 | − | 0.947732i | \(-0.396630\pi\) | ||||
0.319068 | + | 0.947732i | \(0.396630\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.5063 | −0.594458 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.52978 | + | 26.2520i | −0.306795 | + | 0.944217i | 0.672207 | + | 0.740364i | \(0.265347\pi\) |
−0.979001 | + | 0.203854i | \(0.934653\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.59227 | + | 1.15685i | −0.0571962 | + | 0.0415554i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.7471 | + | 48.4646i | 0.564924 | + | 1.73866i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.8664 | + | 20.2462i | 0.998419 | + | 0.725394i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.49026 | − | 0.994064i | 0.0891087 | − | 0.0355704i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −41.3010 | − | 30.0070i | −1.47598 | − | 1.07236i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.2654 | − | 37.7492i | −0.437773 | − | 1.34733i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.2622 | − | 11.8152i | 0.579684 | − | 0.421165i | −0.258926 | − | 0.965897i | \(-0.583369\pi\) |
0.838610 | + | 0.544732i | \(0.183369\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.4439 | + | 47.5314i | −0.549817 | + | 1.69216i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.02608 | 0.178707 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.91616 | 0.281111 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.9651 | + | 46.0580i | −0.530759 | + | 1.63351i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.8947 | + | 7.91546i | −0.385910 | + | 0.280380i | −0.763778 | − | 0.645480i | \(-0.776658\pi\) |
0.377867 | + | 0.925860i | \(0.376658\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.8822 | − | 42.7251i | −0.491118 | − | 1.51150i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −39.9290 | − | 29.0101i | −1.41082 | − | 1.02502i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.114882 | + | 1.74766i | 0.00405409 | + | 0.0616735i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.1748 | + | 13.2048i | 0.640579 | + | 0.465408i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.1267 | − | 80.4096i | −0.919702 | − | 2.83055i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.03614 | + | 5.11205i | −0.247377 | + | 0.179730i | −0.704564 | − | 0.709641i | \(-0.748857\pi\) |
0.457186 | + | 0.889371i | \(0.348857\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.88841 | − | 11.9673i | 0.136541 | − | 0.420229i | −0.859286 | − | 0.511496i | \(-0.829092\pi\) |
0.995826 | + | 0.0912667i | \(0.0290916\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −91.4178 | −3.20616 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.5534 | −0.369671 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.32910 | − | 19.4790i | 0.221427 | − | 0.681482i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 29.4388 | − | 21.3886i | 1.02868 | − | 0.747377i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.6940 | − | 32.9126i | −0.373222 | − | 1.14866i | −0.944670 | − | 0.328021i | \(-0.893618\pi\) |
0.571448 | − | 0.820638i | \(-0.306382\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.3875 | − | 27.1636i | −1.30325 | − | 0.946864i | −0.303265 | − | 0.952906i | \(-0.598077\pi\) |
−0.999982 | + | 0.00604174i | \(0.998077\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 26.1875 | + | 31.4749i | 0.911732 | + | 1.09581i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.1882 | + | 7.40218i | 0.354279 | + | 0.257399i | 0.750662 | − | 0.660686i | \(-0.229735\pi\) |
−0.396383 | + | 0.918085i | \(0.629735\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.99844 | − | 30.7720i | −0.347260 | − | 1.06876i | −0.960363 | − | 0.278754i | \(-0.910079\pi\) |
0.613102 | − | 0.790003i | \(-0.289921\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 59.3437 | − | 43.1157i | 2.05861 | − | 1.49567i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.29458 | − | 19.3727i | 0.218094 | − | 0.671226i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.0871 | 1.04121 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.00956 | 0.173156 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.12705 | + | 21.9348i | −0.246053 | + | 0.757274i | 0.749408 | + | 0.662108i | \(0.230338\pi\) |
−0.995461 | + | 0.0951658i | \(0.969662\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.47837 | − | 2.52719i | 0.119944 | − | 0.0871444i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.8553 | + | 33.4092i | 0.373877 | + | 1.15067i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.914540 | − | 0.664452i | −0.0314611 | − | 0.0228578i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.13055 | − | 16.9269i | 0.107567 | − | 0.581615i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40.6109 | + | 29.5056i | 1.39376 | + | 1.01263i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.7098 | − | 48.3497i | −0.538524 | − | 1.65741i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.9288 | − | 26.8303i | 1.26442 | − | 0.918652i | 0.265451 | − | 0.964124i | \(-0.414479\pi\) |
0.998966 | + | 0.0454720i | \(0.0144792\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.2196 | − | 49.9189i | 0.554700 | − | 1.70719i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.6018 | 0.874541 | 0.437271 | − | 0.899330i | \(-0.355945\pi\) | ||||
0.437271 | + | 0.899330i | \(0.355945\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.93870 | −0.134387 | −0.0671934 | − | 0.997740i | \(-0.521404\pi\) | ||||
−0.0671934 | + | 0.997740i | \(0.521404\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.5530 | − | 57.1001i | 0.632283 | − | 1.94597i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.1595 | − | 15.3733i | 0.720278 | − | 0.523313i | −0.166195 | − | 0.986093i | \(-0.553148\pi\) |
0.886473 | + | 0.462780i | \(0.153148\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.33121 | − | 7.17473i | −0.0792635 | − | 0.243948i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.50569 | − | 5.45320i | −0.254907 | − | 0.185201i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.3335 | + | 14.8237i | 0.418385 | + | 0.502859i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.09898 | − | 1.52500i | −0.0711212 | − | 0.0516726i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.13161 | + | 21.9488i | 0.241368 | + | 0.742856i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.67002 | + | 2.66643i | −0.124069 | + | 0.0901416i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.55847 | + | 17.1072i | −0.187696 | + | 0.577669i | −0.999984 | − | 0.00558706i | \(-0.998222\pi\) |
0.812288 | + | 0.583256i | \(0.198222\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 51.4106 | 1.73404 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.1327 | −0.442453 | −0.221227 | − | 0.975222i | \(-0.571006\pi\) | ||||
−0.221227 | + | 0.975222i | \(0.571006\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.62752 | − | 23.4751i | 0.256687 | − | 0.790000i | −0.736806 | − | 0.676104i | \(-0.763667\pi\) |
0.993493 | − | 0.113896i | \(-0.0363330\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 66.4624 | − | 48.2878i | 2.23411 | − | 1.62318i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.29062 | + | 22.4382i | 0.244795 | + | 0.753401i | 0.995670 | + | 0.0929571i | \(0.0296320\pi\) |
−0.750875 | + | 0.660444i | \(0.770368\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.8632 | + | 9.34568i | 0.431419 | + | 0.313444i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.68645 | − | 40.8681i | −0.0899993 | − | 1.36913i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.3014 | − | 16.2029i | −0.746288 | − | 0.542210i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.6010 | + | 48.0150i | 0.521484 | + | 1.60496i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −43.2271 | + | 31.4063i | −1.44331 | + | 1.04863i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.749004 | − | 2.30520i | 0.0249807 | − | 0.0768826i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.5723 | 0.785307 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −35.6999 | −1.18802 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.51603 | + | 16.9766i | −0.183359 | + | 0.564321i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.5903 | + | 28.0375i | −1.28137 | + | 0.930970i | −0.999593 | − | 0.0285104i | \(-0.990924\pi\) |
−0.281776 | + | 0.959480i | \(0.590924\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.41718 | − | 7.43932i | −0.0801728 | − | 0.246747i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.798318 | + | 0.580012i | 0.0264494 | + | 0.0192166i | 0.600931 | − | 0.799301i | \(-0.294796\pi\) |
−0.574482 | + | 0.818517i | \(0.694796\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.8433 | + | 8.71940i | −0.722907 | + | 0.288570i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.1018 | − | 11.6987i | −0.532310 | − | 0.386746i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.45726 | + | 4.48500i | 0.0481231 | + | 0.148108i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.1448 | + | 11.7299i | −0.532569 | + | 0.386934i | −0.821318 | − | 0.570471i | \(-0.806761\pi\) |
0.288749 | + | 0.957405i | \(0.406761\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.6339 | − | 35.8055i | 0.383350 | − | 1.17983i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.95678 | 0.0973238 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −42.9589 | −1.41248 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.03958 | + | 15.5102i | −0.165522 | + | 0.509423i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.8609 | + | 15.8829i | −0.717234 | + | 0.521101i | −0.885499 | − | 0.464641i | \(-0.846183\pi\) |
0.168265 | + | 0.985742i | \(0.446183\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.86247 | − | 11.8875i | −0.126587 | − | 0.389596i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 41.0743 | + | 29.8423i | 1.34471 | + | 0.976992i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.8036 | − | 37.7424i | 0.778462 | − | 1.23431i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.9858 | − | 23.2391i | −1.04493 | − | 0.759187i | −0.0736894 | − | 0.997281i | \(-0.523477\pi\) |
−0.971242 | + | 0.238094i | \(0.923477\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.5837 | − | 66.4277i | −0.704357 | − | 2.16779i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.4808 | + | 14.1536i | −0.635055 | + | 0.461395i | −0.858148 | − | 0.513402i | \(-0.828385\pi\) |
0.223092 | + | 0.974797i | \(0.428385\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.5090 | + | 56.9648i | −0.602736 | + | 1.85503i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −48.3190 | −1.57182 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.6471 | −1.12588 | −0.562940 | − | 0.826498i | \(-0.690330\pi\) | ||||
−0.562940 | + | 0.826498i | \(0.690330\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.596820 | + | 1.83682i | −0.0193736 | + | 0.0596258i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.7981 | − | 8.57180i | 0.382579 | − | 0.277960i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.283275 | + | 0.871831i | 0.00917618 | + | 0.0282414i | 0.955540 | − | 0.294862i | \(-0.0952738\pi\) |
−0.946364 | + | 0.323104i | \(0.895274\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.8803 | − | 12.2643i | −0.546235 | − | 0.396863i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −48.8749 | − | 12.4027i | −1.57990 | − | 0.400923i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.31401 | + | 0.954686i | 0.0424317 | + | 0.0308284i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.50603 | − | 29.2565i | −0.306646 | − | 0.943760i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 70.2679 | − | 51.0526i | 2.26435 | − | 1.64515i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.39919 | − | 10.4616i | 0.109424 | − | 0.336772i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.8240 | 1.31281 | 0.656406 | − | 0.754408i | \(-0.272076\pi\) | ||||
0.656406 | + | 0.754408i | \(0.272076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −37.6035 | −1.20800 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.2726 | + | 47.0041i | −0.490120 | + | 1.50843i | 0.334306 | + | 0.942465i | \(0.391498\pi\) |
−0.824426 | + | 0.565970i | \(0.808502\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.71568 | + | 2.69960i | −0.119119 | + | 0.0865452i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.9523 | + | 42.9408i | 0.446832 | + | 1.37521i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.0475 | + | 13.8388i | 0.609383 | + | 0.442743i | 0.849197 | − | 0.528076i | \(-0.177086\pi\) |
−0.239814 | + | 0.970819i | \(0.577086\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.9554 | − | 6.33280i | −0.797577 | − | 0.202397i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.81371 | − | 3.49736i | −0.153690 | − | 0.111662i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.79966 | + | 5.53878i | 0.0574002 | + | 0.176660i | 0.975646 | − | 0.219352i | \(-0.0703942\pi\) |
−0.918246 | + | 0.396011i | \(0.870394\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42.7244 | + | 31.0411i | −1.36131 | + | 0.989052i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.8479 | + | 45.6971i | −0.472613 | + | 1.45455i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 35.6153 | 1.13250 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.3008 | −0.454280 | −0.227140 | − | 0.973862i | \(-0.572938\pi\) | ||||
−0.227140 | + | 0.973862i | \(0.572938\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30.7153 | + | 94.5318i | −0.974719 | + | 2.99988i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.3318 | + | 12.5923i | −0.549454 | + | 0.399202i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.73706 | − | 26.8899i | −0.276705 | − | 0.851612i | −0.988763 | − | 0.149491i | \(-0.952237\pi\) |
0.712058 | − | 0.702121i | \(-0.247763\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 88.4606 | + | 64.2704i | 2.79877 | + | 2.03343i |
(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 | 352.2.m.e.257.3 | ✓ | 12 | |
4.3 | odd | 2 | 352.2.m.f.257.1 | yes | 12 | ||
8.3 | odd | 2 | 704.2.m.n.257.3 | 12 | |||
8.5 | even | 2 | 704.2.m.m.257.1 | 12 | |||
11.3 | even | 5 | inner | 352.2.m.e.289.3 | yes | 12 | |
11.5 | even | 5 | 3872.2.a.bq.1.5 | 6 | |||
11.6 | odd | 10 | 3872.2.a.bp.1.5 | 6 | |||
44.3 | odd | 10 | 352.2.m.f.289.1 | yes | 12 | ||
44.27 | odd | 10 | 3872.2.a.bn.1.2 | 6 | |||
44.39 | even | 10 | 3872.2.a.bo.1.2 | 6 | |||
88.3 | odd | 10 | 704.2.m.n.641.3 | 12 | |||
88.5 | even | 10 | 7744.2.a.du.1.2 | 6 | |||
88.27 | odd | 10 | 7744.2.a.dv.1.5 | 6 | |||
88.61 | odd | 10 | 7744.2.a.dt.1.2 | 6 | |||
88.69 | even | 10 | 704.2.m.m.641.1 | 12 | |||
88.83 | even | 10 | 7744.2.a.dw.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
352.2.m.e.257.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
352.2.m.e.289.3 | yes | 12 | 11.3 | even | 5 | inner | |
352.2.m.f.257.1 | yes | 12 | 4.3 | odd | 2 | ||
352.2.m.f.289.1 | yes | 12 | 44.3 | odd | 10 | ||
704.2.m.m.257.1 | 12 | 8.5 | even | 2 | |||
704.2.m.m.641.1 | 12 | 88.69 | even | 10 | |||
704.2.m.n.257.3 | 12 | 8.3 | odd | 2 | |||
704.2.m.n.641.3 | 12 | 88.3 | odd | 10 | |||
3872.2.a.bn.1.2 | 6 | 44.27 | odd | 10 | |||
3872.2.a.bo.1.2 | 6 | 44.39 | even | 10 | |||
3872.2.a.bp.1.5 | 6 | 11.6 | odd | 10 | |||
3872.2.a.bq.1.5 | 6 | 11.5 | even | 5 | |||
7744.2.a.dt.1.2 | 6 | 88.61 | odd | 10 | |||
7744.2.a.du.1.2 | 6 | 88.5 | even | 10 | |||
7744.2.a.dv.1.5 | 6 | 88.27 | odd | 10 | |||
7744.2.a.dw.1.5 | 6 | 88.83 | even | 10 |