Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [704,2,Mod(257,704)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(704, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("704.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 704 = 2^{6} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 704.m (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.62146830230\) |
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: | no (minimal twist has level 352) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 257.3 | ||
Root | \(1.66582 - 1.21029i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 704.257 |
Dual form | 704.2.m.n.641.3 |
$q$-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 \(\left(\mathbb{Z}/704\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(321\) | \(639\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 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 | 0.108572 | − | 0.994089i | \(-0.465372\pi\) |
0.978985 | + | 0.203933i | \(0.0653723\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.483582 | + | 1.48831i | 0.182777 | + | 0.562529i | 0.999903 | − | 0.0139295i | \(-0.00443405\pi\) |
−0.817126 | + | 0.576459i | \(0.804434\pi\) | |||||||
\(8\) | 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 | 0.916894 | − | 0.399130i | \(-0.130688\pi\) |
−0.0962591 | + | 0.995356i | \(0.530688\pi\) | |||||||
\(14\) | 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 | \(-0.665899\pi\) | ||||
−0.497911 | + | 0.867228i | \(0.665899\pi\) | |||||||
\(24\) | 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 | \(-0.947330\pi\) |
0.701150 | − | 0.713014i | \(-0.252670\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.394554 | + | 0.286660i | 0.0708640 | + | 0.0514857i | 0.622653 | − | 0.782498i | \(-0.286055\pi\) |
−0.551789 | + | 0.833984i | \(0.686055\pi\) | |||||||
\(32\) | 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 | \(0.239143\pi\) |
−0.190026 | + | 0.981779i | \(0.560857\pi\) | |||||||
\(38\) | 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 | \(0.361425\pi\) |
−0.874141 | + | 0.485673i | \(0.838575\pi\) | |||||||
\(48\) | 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 | 0.255355 | − | 0.966847i | \(-0.417808\pi\) |
−0.840618 | + | 0.541629i | \(0.817808\pi\) | |||||||
\(54\) | 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 | −0.470013 | − | 0.882659i | \(-0.655751\pi\) |
0.694217 | + | 0.719766i | \(0.255751\pi\) | |||||||
\(62\) | 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 | −0.548298 | − | 0.836283i | \(-0.684724\pi\) |
0.625919 | + | 0.779888i | \(0.284724\pi\) | |||||||
\(72\) | 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 | 0.820066 | − | 0.572269i | \(-0.193937\pi\) |
−0.290846 | + | 0.956770i | \(0.593937\pi\) | |||||||
\(80\) | 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 | 0.537163 | − | 0.843479i | \(-0.319496\pi\) |
−0.636203 | + | 0.771521i | \(0.719496\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.792654 | + | 2.43954i | 0.0781025 | + | 0.240375i | 0.982483 | − | 0.186352i | \(-0.0596665\pi\) |
−0.904380 | + | 0.426727i | \(0.859667\pi\) | |||||||
\(104\) | 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 | \(-0.514271\pi\) | ||||
−0.0448196 | + | 0.998995i | \(0.514271\pi\) | |||||||
\(110\) | 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 | −0.159980 | − | 0.987120i | \(-0.551143\pi\) |
0.889371 | + | 0.457187i | \(0.151143\pi\) | |||||||
\(128\) | 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 | −0.100110 | − | 0.994976i | \(-0.531920\pi\) |
0.915343 | + | 0.402675i | \(0.131920\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.23702 | + | 19.1956i | −0.507561 | + | 1.56211i | 0.288861 | + | 0.957371i | \(0.406724\pi\) |
−0.796422 | + | 0.604741i | \(0.793276\pi\) | |||||||
\(152\) | 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 | \(-0.723348\pi\) |
0.971145 | − | 0.238489i | \(-0.0766520\pi\) | |||||||
\(158\) | 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 | 0.855225 | − | 0.518256i | \(-0.173419\pi\) |
−0.228612 | + | 0.973518i | \(0.573419\pi\) | |||||||
\(168\) | 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 | −0.917237 | − | 0.398342i | \(-0.869586\pi\) |
0.976200 | + | 0.216873i | \(0.0695857\pi\) | |||||||
\(174\) | 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 | −0.751839 | − | 0.659346i | \(-0.770833\pi\) |
0.394745 | + | 0.918791i | \(0.370833\pi\) | |||||||
\(182\) | 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 | 0.842975 | − | 0.537952i | \(-0.180802\pi\) |
−0.998182 | + | 0.0602757i | \(0.980802\pi\) | |||||||
\(192\) | 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 | \(-0.715251\pi\) | ||||
−0.625859 | + | 0.779936i | \(0.715251\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.12699 | −0.505219 | −0.252609 | − | 0.967568i | \(-0.581289\pi\) | ||||
−0.252609 | + | 0.967568i | \(0.581289\pi\) | |||||||
\(200\) | 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 | −0.994648 | − | 0.103321i | \(-0.967053\pi\) |
0.865418 | + | 0.501051i | \(0.167053\pi\) | |||||||
\(224\) | 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 | 0.0427060 | − | 0.999088i | \(-0.486402\pi\) |
−0.936992 | + | 0.349351i | \(0.886402\pi\) | |||||||
\(230\) | 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 | \(-0.594035\pi\) |
0.797861 | − | 0.602841i | \(-0.205965\pi\) | |||||||
\(240\) | 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 | \(-0.331969\pi\) | ||||
0.503708 | + | 0.863874i | \(0.331969\pi\) | |||||||
\(264\) | 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 | \(0.618960\pi\) |
−0.998227 | + | 0.0595289i | \(0.981040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.23475 | + | 28.4216i | 0.560971 | + | 1.72649i | 0.679629 | + | 0.733556i | \(0.262141\pi\) |
−0.118658 | + | 0.992935i | \(0.537859\pi\) | |||||||
\(272\) | 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 | −0.175117 | − | 0.984548i | \(-0.556030\pi\) |
−0.990475 | + | 0.137696i | \(0.956030\pi\) | |||||||
\(278\) | 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 | \(-0.936665\pi\) |
0.676872 | − | 0.736101i | \(-0.263335\pi\) | |||||||
\(294\) | 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 | \(-0.744052\pi\) |
0.984593 | − | 0.174862i | \(-0.0559479\pi\) | |||||||
\(312\) | 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 | 0.474185 | − | 0.880425i | \(-0.342743\pi\) |
−0.690803 | + | 0.723043i | \(0.742743\pi\) | |||||||
\(318\) | 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 | \(0.344969\pi\) |
−0.898071 | + | 0.439851i | \(0.855031\pi\) | |||||||
\(350\) | 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 | 0.994073 | − | 0.108716i | \(-0.0346739\pi\) |
−0.868123 | + | 0.496348i | \(0.834674\pi\) | |||||||
\(360\) | 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 | 0.988671 | − | 0.150100i | \(-0.0479596\pi\) |
−0.888078 | + | 0.459692i | \(0.847960\pi\) | |||||||
\(368\) | 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 | \(-0.539997\pi\) | ||||
−0.125324 | + | 0.992116i | \(0.539997\pi\) | |||||||
\(374\) | 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 | 0.799604 | − | 0.600528i | \(-0.205043\pi\) |
−0.324045 | + | 0.946042i | \(0.605043\pi\) | |||||||
\(384\) | 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 | 0.851403 | − | 0.524512i | \(-0.175752\pi\) |
−0.997100 | + | 0.0761033i | \(0.975752\pi\) | |||||||
\(390\) | 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 | \(-0.912041\pi\) | ||||
−0.962063 | + | 0.272828i | \(0.912041\pi\) | |||||||
\(398\) | 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 | \(0.272660\pi\) |
−0.974060 | + | 0.226291i | \(0.927340\pi\) | |||||||
\(422\) | 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 | 0.194524 | − | 0.980898i | \(-0.437684\pi\) |
−0.872778 | + | 0.488118i | \(0.837684\pi\) | |||||||
\(432\) | 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 | \(-0.763355\pi\) | ||||
−0.736143 | + | 0.676826i | \(0.763355\pi\) | |||||||
\(440\) | 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 | \(-0.474686\pi\) | ||||
0.0794423 | + | 0.996839i | \(0.474686\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.72640 | −0.173181 | −0.0865903 | − | 0.996244i | \(-0.527597\pi\) | ||||
−0.0865903 | + | 0.996244i | \(0.527597\pi\) | |||||||
\(464\) | 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 | −0.971374 | − | 0.237555i | \(-0.923654\pi\) |
−0.0742424 | + | 0.997240i | \(0.523654\pi\) | |||||||
\(480\) | 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 | −0.835668 | − | 0.549235i | \(-0.814919\pi\) |
0.998902 | + | 0.0468530i | \(0.0149192\pi\) | |||||||
\(488\) | 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 | \(0.343690\pi\) |
−0.899830 | + | 0.436240i | \(0.856310\pi\) | |||||||
\(504\) | 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 | \(0.431697\pi\) |
−0.746575 | + | 0.665301i | \(0.768303\pi\) | |||||||
\(510\) | 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 | 0.0795476 | − | 0.996831i | \(-0.474652\pi\) |
−0.923461 | + | 0.383692i | \(0.874652\pi\) | |||||||
\(542\) | 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 | \(0.248646\pi\) |
−0.160633 | + | 0.987014i | \(0.551354\pi\) | |||||||
\(558\) | 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 | −0.831967 | − | 0.554825i | \(-0.812785\pi\) |
0.270578 | + | 0.962698i | \(0.412785\pi\) | |||||||
\(600\) | 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 | 0.0723401 | − | 0.997380i | \(-0.476953\pi\) |
−0.926210 | + | 0.377007i | \(0.876953\pi\) | |||||||
\(608\) | 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 | \(-0.689634\pi\) |
0.940491 | − | 0.339820i | \(-0.110366\pi\) | |||||||
\(614\) | 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 | \(-0.895926\pi\) |
0.577382 | − | 0.816474i | \(-0.304074\pi\) | |||||||
\(632\) | 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 | 0.750489 | − | 0.660883i | \(-0.229818\pi\) |
−0.396624 | + | 0.917981i | \(0.629818\pi\) | |||||||
\(648\) | 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 | \(0.00490693\pi\) |
−0.799860 | + | 0.600186i | \(0.795093\pi\) | |||||||
\(654\) | 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 | \(-0.596340\pi\) | ||||
−0.298061 | + | 0.954547i | \(0.596340\pi\) | |||||||
\(662\) | 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 | −0.376468 | − | 0.926430i | \(-0.622862\pi\) |
0.764752 | + | 0.644325i | \(0.222862\pi\) | |||||||
\(678\) | 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 | \(-0.741770\pi\) |
0.983314 | − | 0.181916i | \(-0.0582300\pi\) | |||||||
\(702\) | 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 | −0.672471 | − | 0.740124i | \(-0.734767\pi\) |
0.496094 | + | 0.868269i | \(0.334767\pi\) | |||||||
\(710\) | 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 | \(0.101478\pi\) |
−0.584021 | + | 0.811738i | \(0.698522\pi\) | |||||||
\(720\) | 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 | \(-0.899181\pi\) | ||||
−0.950258 | + | 0.311464i | \(0.899181\pi\) | |||||||
\(728\) | 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 | \(-0.799547\pi\) |
0.307663 | − | 0.951495i | \(-0.400453\pi\) | |||||||
\(734\) | 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 | −0.176249 | − | 0.984346i | \(-0.556396\pi\) |
0.881704 | + | 0.471802i | \(0.156396\pi\) | |||||||
\(744\) | 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 | \(-0.615800\pi\) |
0.837185 | − | 0.546921i | \(-0.184200\pi\) | |||||||
\(752\) | 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 | 0.883220 | − | 0.468959i | \(-0.155371\pi\) |
−0.173077 | + | 0.984908i | \(0.555371\pi\) | |||||||
\(758\) | 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 | \(-0.734653\pi\) |
0.979001 | − | 0.203854i | \(-0.0653467\pi\) | |||||||
\(774\) | 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 | −0.377867 | − | 0.925860i | \(-0.623342\pi\) |
0.763778 | + | 0.645480i | \(0.223342\pi\) | |||||||
\(798\) | 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 | \(0.106382\pi\) |
−0.571448 | + | 0.820638i | \(0.693618\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.3875 | + | 27.1636i | 1.30325 | + | 0.946864i | 0.999982 | − | 0.00604174i | \(-0.00192316\pi\) |
0.303265 | + | 0.952906i | \(0.401923\pi\) | |||||||
\(824\) | 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 | \(0.0899213\pi\) |
−0.613102 | + | 0.790003i | \(0.710079\pi\) | |||||||
\(830\) | 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 | \(-0.769662\pi\) |
0.995461 | − | 0.0951658i | \(-0.0303381\pi\) | |||||||
\(840\) | 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 | −0.998966 | − | 0.0454720i | \(-0.985521\pi\) |
−0.265451 | + | 0.964124i | \(0.585521\pi\) | |||||||
\(854\) | 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 | −0.886473 | − | 0.462780i | \(-0.846852\pi\) |
0.166195 | + | 0.986093i | \(0.446852\pi\) | |||||||
\(864\) | 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 | −0.812288 | − | 0.583256i | \(-0.801778\pi\) |
0.999984 | + | 0.00558706i | \(0.00177843\pi\) | |||||||
\(878\) | 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 | \(-0.970368\pi\) |
0.750875 | − | 0.660444i | \(-0.229632\pi\) | |||||||
\(888\) | 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 | 0.574482 | − | 0.818517i | \(-0.305204\pi\) |
−0.600931 | + | 0.799301i | \(0.705204\pi\) | |||||||
\(912\) | 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 | −0.288749 | − | 0.957405i | \(-0.593239\pi\) |
0.821318 | + | 0.570471i | \(0.193239\pi\) | |||||||
\(920\) | 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 | −0.223092 | − | 0.974797i | \(-0.571615\pi\) |
0.858148 | + | 0.513402i | \(0.171615\pi\) | |||||||
\(942\) | 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 | \(-0.727924\pi\) | ||||
−0.656406 | + | 0.754408i | \(0.727924\pi\) | |||||||
\(968\) | 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 | 0.918246 | − | 0.396011i | \(-0.129606\pi\) |
−0.975646 | + | 0.219352i | \(0.929606\pi\) | |||||||
\(984\) | 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 | \(-0.427062\pi\) | ||||
0.227140 | + | 0.973862i | \(0.427062\pi\) | |||||||
\(992\) | 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 | \(0.0477634\pi\) |
−0.712058 | + | 0.702121i | \(0.752237\pi\) | |||||||
\(998\) | 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 | 704.2.m.n.257.3 | 12 | ||
4.3 | odd | 2 | 704.2.m.m.257.1 | 12 | |||
8.3 | odd | 2 | 352.2.m.e.257.3 | ✓ | 12 | ||
8.5 | even | 2 | 352.2.m.f.257.1 | yes | 12 | ||
11.3 | even | 5 | inner | 704.2.m.n.641.3 | 12 | ||
11.5 | even | 5 | 7744.2.a.dv.1.5 | 6 | |||
11.6 | odd | 10 | 7744.2.a.dw.1.5 | 6 | |||
44.3 | odd | 10 | 704.2.m.m.641.1 | 12 | |||
44.27 | odd | 10 | 7744.2.a.du.1.2 | 6 | |||
44.39 | even | 10 | 7744.2.a.dt.1.2 | 6 | |||
88.3 | odd | 10 | 352.2.m.e.289.3 | yes | 12 | ||
88.5 | even | 10 | 3872.2.a.bn.1.2 | 6 | |||
88.27 | odd | 10 | 3872.2.a.bq.1.5 | 6 | |||
88.61 | odd | 10 | 3872.2.a.bo.1.2 | 6 | |||
88.69 | even | 10 | 352.2.m.f.289.1 | yes | 12 | ||
88.83 | even | 10 | 3872.2.a.bp.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
352.2.m.e.257.3 | ✓ | 12 | 8.3 | odd | 2 | ||
352.2.m.e.289.3 | yes | 12 | 88.3 | odd | 10 | ||
352.2.m.f.257.1 | yes | 12 | 8.5 | even | 2 | ||
352.2.m.f.289.1 | yes | 12 | 88.69 | even | 10 | ||
704.2.m.m.257.1 | 12 | 4.3 | odd | 2 | |||
704.2.m.m.641.1 | 12 | 44.3 | odd | 10 | |||
704.2.m.n.257.3 | 12 | 1.1 | even | 1 | trivial | ||
704.2.m.n.641.3 | 12 | 11.3 | even | 5 | inner | ||
3872.2.a.bn.1.2 | 6 | 88.5 | even | 10 | |||
3872.2.a.bo.1.2 | 6 | 88.61 | odd | 10 | |||
3872.2.a.bp.1.5 | 6 | 88.83 | even | 10 | |||
3872.2.a.bq.1.5 | 6 | 88.27 | odd | 10 | |||
7744.2.a.dt.1.2 | 6 | 44.39 | even | 10 | |||
7744.2.a.du.1.2 | 6 | 44.27 | odd | 10 | |||
7744.2.a.dv.1.5 | 6 | 11.5 | even | 5 | |||
7744.2.a.dw.1.5 | 6 | 11.6 | odd | 10 |