Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,2,Mod(241,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1232.241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.bn (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.83756952902\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 241.3 | ||
Root | \(-1.29724 + 0.347596i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.241 |
Dual form | 1232.2.bn.b.593.3 |
$q$-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 \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.35034 | − | 0.779618i | −0.779618 | − | 0.450113i | 0.0566769 | − | 0.998393i | \(-0.481950\pi\) |
−0.836295 | + | 0.548280i | \(0.815283\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.882559 | − | 0.509546i | 0.394692 | − | 0.227876i | −0.289499 | − | 0.957178i | \(-0.593489\pi\) |
0.684191 | + | 0.729303i | \(0.260155\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.25578 | + | 1.38256i | −0.852604 | + | 0.522558i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.284392 | − | 0.492581i | −0.0947972 | − | 0.164194i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.510616 | − | 3.27708i | 0.153957 | − | 0.988078i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.167247 | −0.0463859 | −0.0231929 | − | 0.999731i | \(-0.507383\pi\) | ||||
−0.0231929 | + | 0.999731i | \(0.507383\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.58900 | −0.410279 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.47616 | + | 2.55678i | −0.358021 | + | 0.620111i | −0.987630 | − | 0.156801i | \(-0.949882\pi\) |
0.629609 | + | 0.776912i | \(0.283215\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.155850 | + | 0.269940i | 0.0357545 | + | 0.0619286i | 0.883349 | − | 0.468716i | \(-0.155283\pi\) |
−0.847594 | + | 0.530645i | \(0.821950\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.12393 | − | 0.108278i | 0.899915 | − | 0.0236281i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.237719 | − | 0.411742i | −0.0495679 | − | 0.0858541i | 0.840177 | − | 0.542312i | \(-0.182451\pi\) |
−0.889745 | + | 0.456458i | \(0.849118\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.98073 | + | 3.43072i | −0.396145 | + | 0.686144i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56458i | 1.07090i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.89701i | − | 0.352266i | −0.984366 | − | 0.176133i | \(-0.943641\pi\) | ||
0.984366 | − | 0.176133i | \(-0.0563589\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.20834 | + | 1.27498i | 0.396629 | + | 0.228994i | 0.685028 | − | 0.728516i | \(-0.259790\pi\) |
−0.288400 | + | 0.957510i | \(0.593123\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.24438 | + | 4.02708i | −0.564774 | + | 0.701025i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.28638 | + | 2.36961i | −0.217438 | + | 0.400537i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.04667 | − | 5.27699i | −0.500870 | − | 0.867532i | −0.999999 | − | 0.00100474i | \(-0.999680\pi\) |
0.499130 | − | 0.866527i | \(-0.333653\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.225839 | + | 0.130388i | 0.0361633 | + | 0.0208789i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.2084 | −1.59428 | −0.797138 | − | 0.603797i | \(-0.793654\pi\) | ||||
−0.797138 | + | 0.603797i | \(0.793654\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.1222i | 1.54363i | 0.635848 | + | 0.771814i | \(0.280650\pi\) | ||||
−0.635848 | + | 0.771814i | \(0.719350\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.501985 | − | 0.289821i | −0.0748315 | − | 0.0432040i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.28968 | − | 1.89930i | 0.479849 | − | 0.277041i | −0.240505 | − | 0.970648i | \(-0.577313\pi\) |
0.720354 | + | 0.693607i | \(0.243980\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.17706 | − | 6.23749i | 0.453866 | − | 0.891070i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.98663 | − | 2.30168i | 0.558239 | − | 0.322300i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.21079 | + | 7.29330i | −0.578396 | + | 1.00181i | 0.417268 | + | 0.908784i | \(0.362988\pi\) |
−0.995664 | + | 0.0930275i | \(0.970346\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.21917 | − | 3.15240i | −0.164393 | − | 0.425070i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.486014i | − | 0.0643742i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.40617 | − | 3.12126i | −0.703824 | − | 0.406353i | 0.104946 | − | 0.994478i | \(-0.466533\pi\) |
−0.808770 | + | 0.588125i | \(0.799866\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.93960 | + | 10.2877i | 0.760488 | + | 1.31720i | 0.942599 | + | 0.333926i | \(0.108374\pi\) |
−0.182111 | + | 0.983278i | \(0.558293\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.32255 | + | 0.717964i | 0.166625 | + | 0.0904550i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.147605 | + | 0.0852198i | −0.0183081 | + | 0.0105702i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.19151 | + | 8.99196i | −0.634244 | + | 1.09854i | 0.352431 | + | 0.935838i | \(0.385355\pi\) |
−0.986675 | + | 0.162705i | \(0.947978\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.741321i | 0.0892445i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.5206 | −1.72328 | −0.861639 | − | 0.507522i | \(-0.830561\pi\) | ||||
−0.861639 | + | 0.507522i | \(0.830561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.85385 | + | 8.40712i | −0.568101 | + | 0.983979i | 0.428653 | + | 0.903469i | \(0.358988\pi\) |
−0.996754 | + | 0.0805099i | \(0.974345\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.34930 | − | 3.08842i | 0.617684 | − | 0.356620i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.37892 | + | 8.09833i | 0.385064 | + | 0.922890i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.06709 | + | 3.50284i | −0.682601 | + | 0.394100i | −0.800834 | − | 0.598886i | \(-0.795610\pi\) |
0.118233 | + | 0.992986i | \(0.462277\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.48507 | − | 6.03631i | 0.387230 | − | 0.670702i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.6915 | 1.61261 | 0.806303 | − | 0.591502i | \(-0.201465\pi\) | ||||
0.806303 | + | 0.591502i | \(0.201465\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00868i | 0.326337i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.47894 | + | 2.56161i | −0.158559 | + | 0.274633i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.97639 | − | 3.45047i | 0.633496 | − | 0.365749i | −0.148609 | − | 0.988896i | \(-0.547480\pi\) |
0.782105 | + | 0.623147i | \(0.214146\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.377271 | − | 0.231228i | 0.0395488 | − | 0.0242393i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.98800 | − | 3.44332i | −0.206146 | − | 0.357055i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.275094 | + | 0.158826i | 0.0282240 | + | 0.0162952i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0218i | 1.11909i | 0.828799 | + | 0.559547i | \(0.189025\pi\) | ||||
−0.828799 | + | 0.559547i | \(0.810975\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.75944 | + | 0.680455i | −0.176831 | + | 0.0683883i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.66752 | + | 4.62028i | −0.265428 | + | 0.459735i | −0.967676 | − | 0.252198i | \(-0.918847\pi\) |
0.702248 | + | 0.711933i | \(0.252180\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7849 | − | 6.22664i | 1.06266 | − | 0.613529i | 0.136496 | − | 0.990641i | \(-0.456416\pi\) |
0.926168 | + | 0.377112i | \(0.123083\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.58444 | − | 2.19689i | 0.349805 | − | 0.214395i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.28227 | + | 3.62707i | −0.607330 | + | 0.350642i | −0.771920 | − | 0.635720i | \(-0.780703\pi\) |
0.164590 | + | 0.986362i | \(0.447370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.01103 | + | 0.583716i | 0.0968387 | + | 0.0559098i | 0.547637 | − | 0.836716i | \(-0.315527\pi\) |
−0.450799 | + | 0.892626i | \(0.648861\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.50096i | 0.901791i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.40135 | −0.790333 | −0.395166 | − | 0.918610i | \(-0.629313\pi\) | ||||
−0.395166 | + | 0.918610i | \(0.629313\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.419602 | − | 0.242258i | −0.0391281 | − | 0.0225906i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0475636 | + | 0.0823825i | 0.00439725 | + | 0.00761626i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.205017 | − | 7.80841i | −0.0187939 | − | 0.715796i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4785 | − | 3.34666i | −0.952595 | − | 0.304242i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.7847 | + | 7.95862i | 1.24293 | + | 0.717604i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.13254i | 0.816839i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.53324i | − | 0.313525i | −0.987636 | − | 0.156762i | \(-0.949894\pi\) | ||
0.987636 | − | 0.156762i | \(-0.0501057\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.89149 | − | 13.6685i | 0.694807 | − | 1.20344i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.98984 | + | 12.1068i | 0.610705 | + | 1.05777i | 0.991122 | + | 0.132957i | \(0.0424473\pi\) |
−0.380417 | + | 0.924815i | \(0.624219\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.724772 | − | 0.393453i | −0.0628457 | − | 0.0341167i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.83541 | + | 4.91107i | 0.244033 | + | 0.422677i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.50529 | − | 6.07134i | 0.299477 | − | 0.518709i | −0.676539 | − | 0.736406i | \(-0.736521\pi\) |
0.976016 | + | 0.217697i | \(0.0698545\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.4615 | −0.972148 | −0.486074 | − | 0.873918i | \(-0.661571\pi\) | ||||
−0.486074 | + | 0.873918i | \(0.661571\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.92291 | −0.498799 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.0853989 | + | 0.548081i | −0.00714141 | + | 0.0458328i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.966613 | − | 1.67422i | −0.0802729 | − | 0.139037i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.15297 | + | 5.94583i | −0.754924 | + | 0.490403i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.2602 | − | 7.07841i | 1.00439 | − | 0.579886i | 0.0948474 | − | 0.995492i | \(-0.469764\pi\) |
0.909545 | + | 0.415606i | \(0.136430\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.1819 | − | 11.6520i | −1.64238 | − | 0.948228i | −0.979985 | − | 0.199072i | \(-0.936207\pi\) |
−0.662394 | − | 0.749156i | \(-0.730459\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.67923 | 0.135758 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.59865 | 0.208728 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.49234 | + | 2.01630i | 0.278719 | + | 0.160919i | 0.632843 | − | 0.774280i | \(-0.281888\pi\) |
−0.354124 | + | 0.935198i | \(0.615221\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.3720 | − | 6.56561i | 0.901856 | − | 0.520687i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.10550 | + | 0.600137i | 0.0871255 | + | 0.0472974i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.76994 | − | 4.79768i | −0.216958 | − | 0.375783i | 0.736918 | − | 0.675982i | \(-0.236280\pi\) |
−0.953877 | + | 0.300199i | \(0.902947\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.811371 | + | 5.20730i | −0.0631652 | + | 0.405388i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.2252 | −1.64245 | −0.821226 | − | 0.570603i | \(-0.806709\pi\) | ||||
−0.821226 | + | 0.570603i | \(0.806709\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9720 | −0.997848 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0886450 | − | 0.153538i | 0.00677885 | − | 0.0117413i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.53277 | − | 13.0471i | −0.572706 | − | 0.991956i | −0.996287 | − | 0.0860973i | \(-0.972560\pi\) |
0.423581 | − | 0.905858i | \(-0.360773\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.275094 | − | 10.4774i | −0.0207951 | − | 0.792018i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.86677 | + | 8.42950i | 0.365809 | + | 0.633600i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.08088 | + | 1.87214i | −0.0807887 | + | 0.139930i | −0.903589 | − | 0.428401i | \(-0.859077\pi\) |
0.822800 | + | 0.568331i | \(0.192411\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.39285i | 0.400848i | 0.979709 | + | 0.200424i | \(0.0642319\pi\) | ||||
−0.979709 | + | 0.200424i | \(0.935768\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 18.5225i | − | 1.36922i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.37774 | − | 3.10484i | −0.395379 | − | 0.228272i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.62504 | + | 6.14303i | 0.557598 | + | 0.449223i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.69335 | − | 12.5524i | −0.559609 | − | 0.913056i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | + | 5.19615i | 0.217072 | + | 0.375980i | 0.953912 | − | 0.300088i | \(-0.0970159\pi\) |
−0.736839 | + | 0.676068i | \(0.763683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.31348 | + | 4.79979i | 0.598417 | + | 0.345496i | 0.768419 | − | 0.639947i | \(-0.221044\pi\) |
−0.170001 | + | 0.985444i | \(0.554377\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.265756 | 0.0190311 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 14.8180i | − | 1.05574i | −0.849325 | − | 0.527870i | \(-0.822991\pi\) | ||
0.849325 | − | 0.527870i | \(-0.177009\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.55962 | − | 2.05515i | −0.252335 | − | 0.145686i | 0.368498 | − | 0.929629i | \(-0.379872\pi\) |
−0.620833 | + | 0.783943i | \(0.713205\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.0206 | − | 8.09479i | 0.988936 | − | 0.570963i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.62273 | + | 4.27923i | 0.184079 | + | 0.300343i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00947 | + | 5.20162i | −0.629249 | + | 0.363297i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.135211 | + | 0.234192i | −0.00939780 | + | 0.0162775i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.964197 | − | 0.372898i | 0.0666949 | − | 0.0257939i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 7.52456i | − | 0.518012i | −0.965876 | − | 0.259006i | \(-0.916605\pi\) | ||
0.965876 | − | 0.259006i | \(-0.0833950\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.6077 | + | 11.3205i | 1.34350 | + | 0.775669i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.15775 | + | 8.93348i | 0.351755 | + | 0.609258i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.74425 | + | 0.177076i | −0.457830 | + | 0.0120207i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.1087 | − | 7.56830i | 0.885803 | − | 0.511418i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.246883 | − | 0.427613i | 0.0166071 | − | 0.0287644i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.5885i | − | 0.909951i | −0.890504 | − | 0.454975i | \(-0.849648\pi\) | ||
0.890504 | − | 0.454975i | \(-0.150352\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.25321 | 0.150214 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8318 | − | 18.7611i | 0.718929 | − | 1.24522i | −0.242496 | − | 0.970152i | \(-0.577966\pi\) |
0.961425 | − | 0.275069i | \(-0.0887006\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.0355 | − | 15.0316i | 1.72047 | − | 0.993317i | 0.802527 | − | 0.596616i | \(-0.203489\pi\) |
0.917948 | − | 0.396700i | \(-0.129845\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.75091 | − | 13.5697i | 0.115201 | − | 0.892824i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.0223 | − | 8.09580i | 0.918633 | − | 0.530373i | 0.0354345 | − | 0.999372i | \(-0.488718\pi\) |
0.883199 | + | 0.468999i | \(0.155385\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.93556 | − | 3.35248i | 0.126262 | − | 0.218692i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.9235 | 0.709558 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 26.0701i | − | 1.68633i | −0.537652 | − | 0.843167i | \(-0.680689\pi\) | ||
0.537652 | − | 0.843167i | \(-0.319311\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.60221 | − | 11.4354i | 0.425286 | − | 0.736617i | −0.571161 | − | 0.820838i | \(-0.693507\pi\) |
0.996447 | + | 0.0842210i | \(0.0268402\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.04515 | − | 2.91282i | 0.323647 | − | 0.186858i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.374342 | − | 7.12381i | −0.0239159 | − | 0.455124i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0260654 | − | 0.0451466i | −0.00165850 | − | 0.00287261i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.8386 | − | 11.4538i | −1.25722 | − | 0.725855i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.9829i | 1.82939i | 0.404149 | + | 0.914693i | \(0.367568\pi\) | ||||
−0.404149 | + | 0.914693i | \(0.632432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.47070 | + | 0.568783i | −0.0924618 | + | 0.0357591i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.34562 | − | 4.06274i | 0.146889 | − | 0.254419i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.05007 | − | 3.49301i | 0.377393 | − | 0.217888i | −0.299290 | − | 0.954162i | \(-0.596750\pi\) |
0.676683 | + | 0.736274i | \(0.263417\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.1684 | + | 7.69151i | 0.880379 | + | 0.477927i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.934431 | + | 0.539494i | −0.0578398 | + | 0.0333938i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.87174 | + | 2.23535i | 0.238741 | + | 0.137837i | 0.614598 | − | 0.788840i | \(-0.289318\pi\) |
−0.375857 | + | 0.926678i | \(0.622652\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.58235i | 0.527210i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.7602 | −0.658513 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.92024 | + | 1.10865i | 0.117079 | + | 0.0675956i | 0.557396 | − | 0.830247i | \(-0.311801\pi\) |
−0.440317 | + | 0.897842i | \(0.645134\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.2561 | − | 19.4961i | −0.683759 | − | 1.18431i | −0.973825 | − | 0.227299i | \(-0.927011\pi\) |
0.290066 | − | 0.957007i | \(-0.406323\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.689713 | + | 0.0181091i | −0.0417433 | + | 0.00109601i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.2314 | + | 8.24279i | 0.616974 | + | 0.497059i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.1880 | − | 12.2329i | −1.27306 | − | 0.735004i | −0.297500 | − | 0.954722i | \(-0.596153\pi\) |
−0.975563 | + | 0.219718i | \(0.929486\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 1.45038i | − | 0.0868319i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.3532i | 0.677273i | 0.940917 | + | 0.338636i | \(0.109966\pi\) | ||||
−0.940917 | + | 0.338636i | \(0.890034\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.8268 | + | 18.7526i | −0.643589 | + | 1.11473i | 0.341037 | + | 0.940050i | \(0.389222\pi\) |
−0.984626 | + | 0.174679i | \(0.944111\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.247646 | − | 0.428936i | −0.0146693 | − | 0.0254080i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.0278 | − | 14.1137i | 1.35929 | − | 0.833102i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.14191 | + | 7.17400i | 0.243642 | + | 0.422000i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.59279 | − | 14.8831i | 0.503718 | − | 0.872465i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.1233 | 0.708249 | 0.354124 | − | 0.935198i | \(-0.384779\pi\) | ||||
0.354124 | + | 0.935198i | \(0.384779\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.36169 | −0.370392 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.2356 | + | 2.84136i | 1.05814 | + | 0.164873i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.0397577 | + | 0.0688624i | 0.00229925 | + | 0.00398242i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.9946 | − | 22.8335i | −0.806636 | − | 1.31610i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.20410 | − | 4.15929i | 0.413865 | − | 0.238945i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.4841 | + | 6.05300i | 0.600318 | + | 0.346594i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.65817 | −0.551221 | −0.275610 | − | 0.961269i | \(-0.588880\pi\) | ||||
−0.275610 | + | 0.961269i | \(0.588880\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.4176 | −1.10463 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.3094 | + | 8.83890i | 0.868118 | + | 0.501208i | 0.866722 | − | 0.498791i | \(-0.166223\pi\) |
0.00139530 | + | 0.999999i | \(0.499556\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.9505 | + | 14.4052i | −1.41028 | + | 0.814228i | −0.995415 | − | 0.0956530i | \(-0.969506\pi\) |
−0.414869 | + | 0.909881i | \(0.636173\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.53306 | − | 0.0402519i | 0.0863782 | − | 0.00226794i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.17280 | − | 8.95955i | −0.290533 | − | 0.503218i | 0.683403 | − | 0.730042i | \(-0.260499\pi\) |
−0.973936 | + | 0.226823i | \(0.927166\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.21666 | − | 0.968644i | −0.348066 | − | 0.0542337i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.3109 | 0.631314 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.920239 | −0.0512034 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.331270 | − | 0.573776i | 0.0183755 | − | 0.0318274i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.910151 | − | 1.57643i | −0.0503315 | − | 0.0871766i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.79489 | + | 8.83257i | −0.264351 | + | 0.486955i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.4224 | − | 23.2483i | −0.737763 | − | 1.27784i | −0.953500 | − | 0.301392i | \(-0.902549\pi\) |
0.215737 | − | 0.976451i | \(-0.430785\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.73290 | + | 3.00147i | −0.0949622 | + | 0.164479i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.5813i | 0.578116i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 14.5505i | − | 0.792614i | −0.918118 | − | 0.396307i | \(-0.870292\pi\) | ||
0.918118 | − | 0.396307i | \(-0.129708\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.3447 | + | 6.54984i | 0.616158 | + | 0.355739i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.30584 | − | 6.58587i | 0.287327 | − | 0.356645i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.45696 | + | 18.4629i | 0.0786683 | + | 0.996901i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.377737 | + | 0.654259i | 0.0203367 | + | 0.0352241i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.7179 | + | 14.2709i | 1.32693 | + | 0.766101i | 0.984823 | − | 0.173562i | \(-0.0555278\pi\) |
0.342102 | + | 0.939663i | \(0.388861\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.6026 | −1.85224 | −0.926118 | − | 0.377235i | \(-0.876875\pi\) | ||||
−0.926118 | + | 0.377235i | \(0.876875\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 0.930656i | − | 0.0496748i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.6534 | − | 8.46017i | −0.779924 | − | 0.450289i | 0.0564792 | − | 0.998404i | \(-0.482013\pi\) |
−0.836403 | + | 0.548114i | \(0.815346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.8153 | + | 7.39891i | −0.680164 | + | 0.392693i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.81073 | + | 10.7038i | −0.307537 | + | 0.566507i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.2848 | + | 15.1755i | −1.38726 | + | 0.800934i | −0.993006 | − | 0.118067i | \(-0.962330\pi\) |
−0.394254 | + | 0.919002i | \(0.628997\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.45142 | − | 16.3703i | 0.497443 | − | 0.861597i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.5405 | + | 12.6884i | 0.605717 | + | 0.665968i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.89304i | 0.517825i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.0875 | + | 8.71075i | 0.787559 | + | 0.454698i | 0.839103 | − | 0.543973i | \(-0.183081\pi\) |
−0.0515432 | + | 0.998671i | \(0.516414\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.90317 | + | 5.02844i | 0.151133 | + | 0.261770i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.584817 | − | 22.2737i | −0.0303622 | − | 1.15639i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.92596 | − | 4.57606i | 0.410391 | − | 0.236939i | −0.280567 | − | 0.959834i | \(-0.590522\pi\) |
0.690958 | + | 0.722895i | \(0.257189\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.11989 | − | 12.3320i | 0.367670 | − | 0.636822i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.317269i | 0.0163402i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.15382 | 0.316100 | 0.158050 | − | 0.987431i | \(-0.449479\pi\) | ||||
0.158050 | + | 0.987431i | \(0.449479\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.75458 | + | 4.77107i | −0.141121 | + | 0.244429i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.2281 | + | 6.48253i | −0.573728 | + | 0.331242i | −0.758637 | − | 0.651514i | \(-0.774134\pi\) |
0.184909 | + | 0.982756i | \(0.440801\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.10857 | + | 5.42553i | 0.362286 | + | 0.276511i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.98603 | − | 2.87868i | 0.253454 | − | 0.146332i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.58323 | + | 4.47429i | −0.130975 | + | 0.226856i | −0.924053 | − | 0.382265i | \(-0.875144\pi\) |
0.793078 | + | 0.609121i | \(0.208477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.40365 | 0.0709854 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 21.7976i | − | 1.09954i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.56971 | + | 6.18292i | −0.179612 | + | 0.311097i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.01690 | − | 4.62856i | 0.402357 | − | 0.232301i | −0.285144 | − | 0.958485i | \(-0.592041\pi\) |
0.687500 | + | 0.726184i | \(0.258708\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.671943 | + | 1.09634i | 0.0336392 | + | 0.0548856i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.4624 | + | 26.7816i | 0.772155 | + | 1.33741i | 0.936380 | + | 0.350988i | \(0.114154\pi\) |
−0.164225 | + | 0.986423i | \(0.552512\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.369337 | − | 0.213237i | −0.0183980 | − | 0.0106221i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 7.10320i | − | 0.352961i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.8488 | + | 7.28968i | −0.934301 | + | 0.361336i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.9198 | + | 20.6458i | −0.589399 | + | 1.02087i | 0.404913 | + | 0.914355i | \(0.367302\pi\) |
−0.994311 | + | 0.106513i | \(0.966031\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.46665 | + | 5.46557i | −0.466955 | + | 0.269597i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.5104 | − | 0.433497i | 0.812426 | − | 0.0213310i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.9662 | − | 7.48601i | 0.636484 | − | 0.367474i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.4768 | + | 8.93556i | 0.757904 | + | 0.437576i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.03426i | 0.245940i | 0.992410 | + | 0.122970i | \(0.0392418\pi\) | ||||
−0.992410 | + | 0.122970i | \(0.960758\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.9250 | −0.824872 | −0.412436 | − | 0.910987i | \(-0.635322\pi\) | ||||
−0.412436 | + | 0.910987i | \(0.635322\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.87112 | − | 1.08029i | −0.0909767 | − | 0.0525254i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.84773 | − | 10.1286i | −0.283657 | − | 0.491308i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.6218 | − | 14.9949i | −1.33671 | − | 0.725654i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.542611 | − | 0.673516i | 0.0261975 | − | 0.0325177i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.19535 | + | 2.99953i | 0.250251 | + | 0.144482i | 0.619879 | − | 0.784697i | \(-0.287182\pi\) |
−0.369628 | + | 0.929180i | \(0.620515\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.1175i | 1.73570i | 0.496829 | + | 0.867849i | \(0.334498\pi\) | ||||
−0.496829 | + | 0.867849i | \(0.665502\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.01436i | 0.144527i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0740971 | − | 0.128340i | 0.00354455 | − | 0.00613934i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.67481 | − | 9.82906i | −0.270844 | − | 0.469116i | 0.698234 | − | 0.715869i | \(-0.253969\pi\) |
−0.969078 | + | 0.246754i | \(0.920636\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.97600 | + | 0.208931i | −0.189333 | + | 0.00994909i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.37538 | − | 4.11428i | −0.112858 | − | 0.195475i | 0.804064 | − | 0.594543i | \(-0.202667\pi\) |
−0.916921 | + | 0.399068i | \(0.869334\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.51634 | − | 6.09048i | 0.166691 | − | 0.288717i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.0738 | −1.04406 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.33297 | 0.346064 | 0.173032 | − | 0.984916i | \(-0.444644\pi\) | ||||
0.173032 | + | 0.984916i | \(0.444644\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.21255 | + | 33.4536i | −0.245449 | + | 1.57527i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.1682 | + | 31.4683i | 0.853619 | + | 1.47851i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.215143 | − | 0.396310i | 0.0100860 | − | 0.0185793i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.7066 | + | 6.75879i | −0.547610 | + | 0.316163i | −0.748158 | − | 0.663521i | \(-0.769061\pi\) |
0.200547 | + | 0.979684i | \(0.435728\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.2274 | − | 8.21420i | −0.664079 | − | 0.383406i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.5730 | −0.865033 | −0.432516 | − | 0.901626i | \(-0.642374\pi\) | ||||
−0.432516 | + | 0.901626i | \(0.642374\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.2849 | −1.31451 | −0.657256 | − | 0.753667i | \(-0.728283\pi\) | ||||
−0.657256 | + | 0.753667i | \(0.728283\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.50905 | − | 2.02595i | −0.162728 | − | 0.0939513i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.6881 | − | 10.7896i | 0.864782 | − | 0.499282i | −0.000828665 | − | 1.00000i | \(-0.500264\pi\) |
0.865611 | + | 0.500717i | \(0.166930\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.721025 | − | 27.4614i | −0.0332938 | − | 1.26805i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.14389 | − | 5.44538i | −0.144863 | − | 0.250910i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.1714 | + | 5.16859i | 1.52522 | + | 0.237652i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.23479 | −0.0566559 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.79005 | 0.219321 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.46780 | − | 6.00641i | 0.158448 | − | 0.274440i | −0.775861 | − | 0.630904i | \(-0.782684\pi\) |
0.934309 | + | 0.356464i | \(0.116018\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.509546 | + | 0.882559i | 0.0232333 | + | 0.0402412i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.02492 | − | 1.67225i | −0.0466355 | − | 0.0760902i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.61611 | + | 9.72738i | 0.255014 | + | 0.441698i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.08702 | + | 10.5430i | −0.275829 | + | 0.477750i | −0.970344 | − | 0.241728i | \(-0.922286\pi\) |
0.694515 | + | 0.719478i | \(0.255619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.63798i | 0.390623i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.37152i | − | 0.107025i | −0.998567 | − | 0.0535125i | \(-0.982958\pi\) | ||
0.998567 | − | 0.0535125i | \(-0.0170417\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.85024 | + | 2.80029i | 0.218444 | + | 0.126119i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.20609 | + | 1.49706i | −0.0542097 | + | 0.0672878i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.7552 | − | 20.0756i | 1.46927 | − | 0.900513i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.96446 | − | 3.40255i | −0.0879413 | − | 0.152319i | 0.818699 | − | 0.574222i | \(-0.194695\pi\) |
−0.906641 | + | 0.421903i | \(0.861362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28.6611 | + | 16.5475i | 1.28048 | + | 0.739288i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.8703 | 0.885971 | 0.442986 | − | 0.896529i | \(-0.353919\pi\) | ||||
0.442986 | + | 0.896529i | \(0.353919\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.43689i | 0.241938i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.5166 | + | 10.1132i | 0.777940 | + | 0.449144i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.2438 | − | 7.64634i | 0.587023 | − | 0.338918i | −0.176896 | − | 0.984229i | \(-0.556606\pi\) |
0.763920 | + | 0.645312i | \(0.223272\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.674129 | − | 25.6753i | −0.0298217 | − | 1.13581i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.50210 | + | 0.867240i | −0.0663195 | + | 0.0382896i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.34552 | − | 10.9908i | 0.279617 | − | 0.484311i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.54439 | − | 11.7504i | −0.199862 | − | 0.516780i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.4907i | 1.03113i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.121861 | − | 0.0703565i | −0.00533883 | − | 0.00308237i | 0.497328 | − | 0.867562i | \(-0.334314\pi\) |
−0.502667 | + | 0.864480i | \(0.667648\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.56153 | + | 7.90081i | 0.199462 | + | 0.345478i | 0.948354 | − | 0.317214i | \(-0.102747\pi\) |
−0.748892 | + | 0.662692i | \(0.769414\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.79691 | + | 14.3625i | −0.340285 | + | 0.626831i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.51971 | + | 3.76416i | −0.284003 | + | 0.163969i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3870 | − | 19.7228i | 0.495086 | − | 0.857514i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.55064i | 0.154085i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.70731 | 0.0739519 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.69632 | + | 6.40221i | −0.159806 | + | 0.276792i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.91910 | − | 1.68534i | 0.125969 | − | 0.0727280i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.8185 | − | 13.5965i | −0.810571 | − | 0.585641i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.6730 | + | 12.5129i | −0.931797 | + | 0.537973i | −0.887379 | − | 0.461040i | \(-0.847476\pi\) |
−0.0444172 | + | 0.999013i | \(0.514143\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.20437 | − | 7.28217i | 0.180427 | − | 0.312508i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.18972 | 0.0509620 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.7246i | 1.57023i | 0.619348 | + | 0.785116i | \(0.287397\pi\) | ||||
−0.619348 | + | 0.785116i | \(0.712603\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.37835 | − | 5.85147i | 0.144184 | − | 0.249735i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.512080 | − | 0.295649i | 0.0218153 | − | 0.0125951i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.84313 | − | 16.2897i | 0.376048 | − | 0.692710i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.84117 | + | 8.38516i | 0.205496 | + | 0.355930i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.5815 | − | 19.3883i | −1.42290 | − | 0.821509i | −0.426350 | − | 0.904558i | \(-0.640201\pi\) |
−0.996545 | + | 0.0830490i | \(0.973534\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.69291i | − | 0.0716025i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.50716 | − | 14.2398i | −0.232512 | − | 0.601204i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.6247 | − | 37.4550i | 0.911371 | − | 1.57854i | 0.0992415 | − | 0.995063i | \(-0.468358\pi\) |
0.812129 | − | 0.583477i | \(-0.198308\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.41469 | + | 4.28087i | −0.311938 | + | 0.180098i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.484025 | + | 18.4349i | 0.0203271 | + | 0.774193i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.4783 | + | 10.6685i | −0.774651 | + | 0.447245i | −0.834531 | − | 0.550961i | \(-0.814261\pi\) |
0.0598803 | + | 0.998206i | \(0.480928\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.5677 | − | 11.2974i | −0.818883 | − | 0.472782i | 0.0311482 | − | 0.999515i | \(-0.490084\pi\) |
−0.850031 | + | 0.526733i | \(0.823417\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 9.35542i | − | 0.390828i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.88343 | 0.0785443 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.3358 | − | 16.9370i | −1.22126 | − | 0.705097i | −0.256077 | − | 0.966656i | \(-0.582430\pi\) |
−0.965187 | + | 0.261559i | \(0.915763\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.48400 | − | 12.9627i | −0.311025 | − | 0.538710i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.1409 | + | 20.3119i | −1.37491 | + | 0.842681i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.7506 | + | 17.5232i | 0.900819 | + | 0.725736i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0839553 | + | 0.0484716i | 0.00347112 | + | 0.00200405i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.07819i | 0.250874i | 0.992102 | + | 0.125437i | \(0.0400332\pi\) | ||||
−0.992102 | + | 0.125437i | \(0.959967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.794825i | 0.0327502i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.5524 | + | 20.0093i | −0.475202 | + | 0.823074i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.809196 | − | 1.40157i | −0.0332297 | − | 0.0575555i | 0.848932 | − | 0.528502i | \(-0.177246\pi\) |
−0.882162 | + | 0.470946i | \(0.843913\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.15968 | − | 6.78692i | −0.170530 | − | 0.278236i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.20446 | + | 5.55029i | 0.131150 | + | 0.227158i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.63955 | − | 4.57184i | 0.107849 | − | 0.186800i | −0.807050 | − | 0.590484i | \(-0.798937\pi\) |
0.914899 | + | 0.403684i | \(0.132270\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.7945 | −1.33771 | −0.668857 | − | 0.743391i | \(-0.733216\pi\) | ||||
−0.668857 | + | 0.743391i | \(0.733216\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.90569 | 0.240498 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.9532 | + | 2.38567i | −0.445311 | + | 0.0969912i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.332910 | − | 0.576616i | −0.0135124 | − | 0.0234041i | 0.859190 | − | 0.511656i | \(-0.170968\pi\) |
−0.872703 | + | 0.488252i | \(0.837635\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.205404 | − | 7.82314i | −0.00832337 | − | 0.317009i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.550188 | + | 0.317651i | −0.0222582 | + | 0.0128508i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.71908 | + | 2.14721i | 0.150212 | + | 0.0867251i | 0.573222 | − | 0.819400i | \(-0.305693\pi\) |
−0.423010 | + | 0.906125i | \(0.639027\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.2211 | 0.654098 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.9913 | −1.24766 | −0.623831 | − | 0.781559i | \(-0.714425\pi\) | ||||
−0.623831 | + | 0.781559i | \(0.714425\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.685357 | + | 0.395691i | 0.0275468 | + | 0.0159042i | 0.513710 | − | 0.857964i | \(-0.328271\pi\) |
−0.486163 | + | 0.873868i | \(0.661604\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.29117 | − | 1.32281i | 0.0919414 | − | 0.0530824i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.71092 | + | 16.0462i | −0.348996 | + | 0.642877i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.25019 | − | 9.09359i | −0.210007 | − | 0.363744i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.59271 | − | 0.248167i | −0.0636067 | − | 0.00991083i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.9895 | 0.717288 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.3677 | 1.36816 | 0.684078 | − | 0.729409i | \(-0.260205\pi\) | ||||
0.684078 | + | 0.729409i | \(0.260205\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.86628 | + | 10.1607i | −0.233164 | + | 0.403852i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.80035 | − | 3.11830i | −0.0714447 | − | 0.123746i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.531353 | + | 1.04320i | −0.0210530 | + | 0.0413331i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.12954 | + | 7.15257i | 0.163362 | + | 0.282951i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.47939 | + | 4.29443i | −0.0979301 | + | 0.169620i | −0.910828 | − | 0.412787i | \(-0.864556\pi\) |
0.812898 | + | 0.582407i | \(0.197889\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 48.1404i | 1.89847i | 0.314562 | + | 0.949237i | \(0.398142\pi\) | ||||
−0.314562 | + | 0.949237i | \(0.601858\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 16.0843i | − | 0.633318i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.74160 | + | 1.58286i | 0.107783 | + | 0.0622287i | 0.552923 | − | 0.833233i | \(-0.313513\pi\) |
−0.445139 | + | 0.895461i | \(0.646846\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.9891 | + | 16.1227i | −0.509867 | + | 0.632872i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.24507 | + | 5.01883i | 0.362343 | + | 0.196703i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.0606 | + | 19.1575i | 0.432833 | + | 0.749689i | 0.997116 | − | 0.0758922i | \(-0.0241805\pi\) |
−0.564283 | + | 0.825582i | \(0.690847\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.3379 | + | 7.12329i | 0.482081 | + | 0.278330i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.52158 | 0.215417 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 24.6258i | − | 0.959286i | −0.877464 | − | 0.479643i | \(-0.840766\pi\) | ||
0.877464 | − | 0.479643i | \(-0.159234\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.0205 | + | 13.8682i | 0.934289 | + | 0.539412i | 0.888166 | − | 0.459524i | \(-0.151980\pi\) |
0.0461236 | + | 0.998936i | \(0.485313\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.666750 | + | 0.384948i | −0.0258944 | + | 0.0149502i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.840136 | + | 0.0220585i | −0.0325791 | + | 0.000855394i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.781078 | + | 0.450956i | −0.0302435 | + | 0.0174611i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.5938 | + | 18.3490i | −0.409580 | + | 0.709414i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.7465 | − | 14.2115i | 1.41858 | − | 0.548629i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.9518i | 0.614897i | 0.951565 | + | 0.307449i | \(0.0994752\pi\) | ||||
−0.951565 | + | 0.307449i | \(0.900525\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.0905 | − | 11.0219i | −0.734793 | − | 0.424233i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.52574 | + | 13.0350i | 0.289238 | + | 0.500974i | 0.973628 | − | 0.228141i | \(-0.0732649\pi\) |
−0.684390 | + | 0.729116i | \(0.739932\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.2383 | − | 24.8627i | −0.584792 | − | 0.954143i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −29.2531 | + | 16.8893i | −1.12098 | + | 0.647198i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.64673 | + | 4.58427i | −0.101274 | + | 0.175412i | −0.912210 | − | 0.409723i | \(-0.865625\pi\) |
0.810936 | + | 0.585135i | \(0.198959\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 7.14442i | − | 0.272974i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −46.8756 | −1.78842 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.704240 | − | 1.21978i | 0.0268294 | − | 0.0464699i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.4089 | − | 13.5151i | 0.890517 | − | 0.514140i | 0.0164055 | − | 0.999865i | \(-0.494778\pi\) |
0.874112 | + | 0.485725i | \(0.161444\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.02814 | − | 3.96749i | 0.115030 | − | 0.150712i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.1154 | + | 5.84014i | −0.383699 | + | 0.221529i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.0692 | − | 26.1005i | 0.570785 | − | 0.988629i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.2465 | −0.954911 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 19.9250i | − | 0.752555i | −0.926507 | − | 0.376278i | \(-0.877204\pi\) | ||
0.926507 | − | 0.376278i | \(-0.122796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.949649 | − | 1.64484i | 0.0358167 | − | 0.0620363i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.22731 | + | 3.01799i | −0.196872 | + | 0.113664i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.370479 | − | 14.1103i | −0.0139333 | − | 0.530673i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.98412 | − | 8.63276i | −0.187183 | − | 0.324210i | 0.757127 | − | 0.653268i | \(-0.226602\pi\) |
−0.944310 | + | 0.329058i | \(0.893269\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.45086 | + | 1.99236i | 0.129417 | + | 0.0747192i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.21235i | − | 0.0454029i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.203903 | + | 0.527228i | 0.00762553 | + | 0.0197172i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.3247 | + | 35.2034i | −0.759040 | + | 1.31470i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.6817 | + | 20.6008i | −1.33070 | + | 0.768282i | −0.985407 | − | 0.170212i | \(-0.945555\pi\) |
−0.345295 | + | 0.938494i | \(0.612221\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.7195 | + | 28.9566i | −0.585426 | + | 1.07840i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.8304 | + | 10.2944i | −0.663121 | + | 0.382853i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.50811 | + | 3.75746i | 0.241705 | + | 0.139549i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 0.0415718i | − | 0.00154181i | −1.00000 | 0.000770906i | \(-0.999755\pi\) | |||
1.00000 | 0.000770906i | \(-0.000245387\pi\) | ||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.9940 | −1.11089 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.8804 | − | 14.9420i | −0.957221 | − | 0.552652i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.40404 | + | 7.62803i | 0.162667 | + | 0.281748i | 0.935824 | − | 0.352467i | \(-0.114657\pi\) |
−0.773157 | + | 0.634214i | \(0.781324\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.04836 | + | 9.91140i | −0.186212 | + | 0.365587i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.8165 | + | 21.6045i | 0.987800 | + | 0.795810i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.4003 | + | 16.3969i | 1.04472 | + | 0.603170i | 0.921167 | − | 0.389167i | \(-0.127237\pi\) |
0.123555 | + | 0.992338i | \(0.460571\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0812842i | 0.00298605i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.7575i | 0.944952i | 0.881344 | + | 0.472476i | \(0.156640\pi\) | ||||
−0.881344 | + | 0.472476i | \(0.843360\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.21355 | − | 12.4942i | 0.264284 | − | 0.457753i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.17815 | − | 7.23678i | −0.152871 | − | 0.264780i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.15676 | − | 16.8675i | 0.334581 | − | 0.616324i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.73290 | + | 9.92967i | 0.209196 | + | 0.362339i | 0.951462 | − | 0.307767i | \(-0.0995819\pi\) |
−0.742265 | + | 0.670106i | \(0.766249\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.5956 | − | 39.1367i | 0.823430 | − | 1.42622i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.7489 | −0.864313 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.9741 | 0.798661 | 0.399331 | − | 0.916807i | \(-0.369243\pi\) | ||||
0.399331 | + | 0.916807i | \(0.369243\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.42937 | + | 0.378530i | 0.0881805 | + | 0.0137398i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.0047 | + | 22.5249i | 0.471421 | + | 0.816526i | 0.999466 | − | 0.0326910i | \(-0.0104077\pi\) |
−0.528044 | + | 0.849217i | \(0.677074\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.08767 | + | 0.0810696i | −0.111781 | + | 0.00293492i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.48202 | − | 0.855644i | 0.0535825 | − | 0.0309359i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.904164 | + | 0.522020i | 0.0326475 | + | 0.0188490i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.8753 | −1.47400 | −0.737001 | − | 0.675891i | \(-0.763759\pi\) | ||||
−0.737001 | + | 0.675891i | \(0.763759\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.8929 | −0.392296 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.8229 | + | 23.5691i | 1.46830 | + | 0.847722i | 0.999369 | − | 0.0355144i | \(-0.0113070\pi\) |
0.468928 | + | 0.883236i | \(0.344640\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.74822 | + | 5.05078i | −0.314245 | + | 0.181430i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.1356 | − | 21.4321i | −0.471239 | − | 0.768871i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.59097 | − | 2.75565i | −0.0570025 | − | 0.0987313i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.41445 | + | 47.5852i | −0.265310 | + | 1.70273i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.5561 | 0.377243 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.10960 | 0.146678 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.0746 | + | 20.9137i | −0.430411 | + | 0.745494i | −0.996909 | − | 0.0785692i | \(-0.974965\pi\) |
0.566497 | + | 0.824064i | \(0.308298\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.48543 | − | 6.03695i | −0.124085 | − | 0.214921i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.9516 | − | 11.6154i | 0.673840 | − | 0.412995i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.993379 | − | 1.72058i | −0.0352759 | − | 0.0610997i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.69096 | − | 11.5891i | 0.237304 | − | 0.411022i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 20.3073i | − | 0.719321i | −0.933083 | − | 0.359660i | \(-0.882893\pi\) | ||
0.933083 | − | 0.359660i | \(-0.117107\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.2147i | 0.396746i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.39927 | − | 1.96257i | −0.120107 | − | 0.0693440i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.0724 | + | 20.1993i | 0.884785 | + | 0.712818i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.28147 | − | 0.0336460i | 0.0451657 | − | 0.00118587i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.72865 | − | 2.99410i | −0.0608513 | − | 0.105397i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.4501 | − | 13.5389i | −0.824461 | − | 0.476003i | 0.0274911 | − | 0.999622i | \(-0.491248\pi\) |
−0.851953 | + | 0.523619i | \(0.824582\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.5808 | −0.828033 | −0.414016 | − | 0.910269i | \(-0.635874\pi\) | ||||
−0.414016 | + | 0.910269i | \(0.635874\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 35.1018i | 1.23107i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.88927 | − | 2.82282i | −0.171264 | − | 0.0988792i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.73240 | + | 1.57755i | −0.0955947 | + | 0.0551916i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.221191 | − | 0.120077i | −0.00772905 | − | 0.00419583i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.4247 | − | 16.9884i | 1.02693 | − | 0.592898i | 0.110826 | − | 0.993840i | \(-0.464650\pi\) |
0.916104 | + | 0.400942i | \(0.131317\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.90033 | + | 10.2197i | −0.205673 | + | 0.356235i | −0.950347 | − | 0.311193i | \(-0.899272\pi\) |
0.744674 | + | 0.667428i | \(0.232605\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.38957 | − | 19.1071i | −0.257272 | − | 0.665224i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17.0595i | − | 0.593217i | −0.954999 | − | 0.296609i | \(-0.904144\pi\) | ||
0.954999 | − | 0.296609i | \(-0.0958557\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.7387 | − | 12.5508i | −0.755015 | − | 0.435908i | 0.0724880 | − | 0.997369i | \(-0.476906\pi\) |
−0.827503 | + | 0.561461i | \(0.810239\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.0740 | + | 33.0371i | 0.661669 | + | 1.14604i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.2581 | + | 17.3306i | 0.390069 | + | 0.600469i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.7324 | + | 10.8152i | −0.648263 | + | 0.374275i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.09474 | + | 12.2884i | −0.245230 | + | 0.424751i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 41.1030i | − | 1.41903i | −0.704688 | − | 0.709517i | \(-0.748913\pi\) | ||
0.704688 | − | 0.709517i | \(-0.251087\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.4014 | 0.875909 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.85113 | − | 15.3306i | 0.304849 | − | 0.528014i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.4486 | + | 6.60984i | −0.393843 | + | 0.227385i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.2642 | − | 6.93787i | 0.971170 | − | 0.238388i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.2398 | − | 16.8816i | 1.00351 | − | 0.579375i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.44851 | + | 2.50888i | −0.0496541 | + | 0.0860035i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.7195 | 1.80508 | 0.902541 | − | 0.430605i | \(-0.141700\pi\) | ||||
0.902541 | + | 0.430605i | \(0.141700\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 0.180675i | − | 0.00617894i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.9387 | + | 18.9464i | −0.373659 | + | 0.647197i | −0.990125 | − | 0.140184i | \(-0.955230\pi\) |
0.616466 | + | 0.787382i | \(0.288564\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.8529 | + | 6.84326i | −0.404415 | + | 0.233489i | −0.688387 | − | 0.725344i | \(-0.741681\pi\) |
0.283972 | + | 0.958832i | \(0.408348\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −42.0985 | + | 1.10534i | −1.43471 | + | 0.0376697i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.0240 | + | 26.0223i | 0.511423 | + | 0.885810i | 0.999912 | + | 0.0132402i | \(0.00421461\pi\) |
−0.488490 | + | 0.872570i | \(0.662452\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.2962 | − | 7.67658i | −0.452085 | − | 0.261012i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 12.9164i | − | 0.438665i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.38113 | + | 21.6710i | 0.284310 | + | 0.735137i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.868263 | − | 1.50388i | 0.0294200 | − | 0.0509569i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.42913 | − | 3.13451i | 0.183748 | − | 0.106087i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.6263 | − | 20.6010i | −0.426846 | − | 0.696440i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.2786 | + | 7.08908i | −0.414620 | + | 0.239381i | −0.692773 | − | 0.721156i | \(-0.743611\pi\) |
0.278153 | + | 0.960537i | \(0.410278\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.3705 | − | 9.45151i | −0.552163 | − | 0.318792i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.3264i | 0.752196i | 0.926580 | + | 0.376098i | \(0.122734\pi\) | ||||
−0.926580 | + | 0.376098i | \(0.877266\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.45618 | 0.149962 | 0.0749812 | − | 0.997185i | \(-0.476110\pi\) | ||||
0.0749812 | + | 0.997185i | \(0.476110\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.59043 | + | 4.95969i | 0.288764 | + | 0.166718i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.50070 | + | 7.79545i | 0.151119 | + | 0.261746i | 0.931639 | − | 0.363385i | \(-0.118379\pi\) |
−0.780520 | + | 0.625131i | \(0.785046\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.88492 | + | 7.97021i | 0.163835 | + | 0.267312i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.0020 | − | 14.5031i | −0.603089 | − | 0.485872i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.02539 | + | 0.592012i | 0.0343135 | + | 0.0198109i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.20303i | 0.0736391i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 0.123983i | − | 0.00413968i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.41866 | − | 4.18924i | 0.0806667 | − | 0.139719i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.4316 | − | 21.5321i | −0.414156 | − | 0.717339i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.09601 | + | 41.7434i | 0.0364730 | + | 1.38913i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.74791 | + | 4.75951i | 0.0913435 | + | 0.158212i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.6872 | − | 18.5107i | 0.354862 | − | 0.614638i | −0.632233 | − | 0.774779i | \(-0.717861\pi\) |
0.987094 | + | 0.160140i | \(0.0511947\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.03448 | 0.100647 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.4299 | 0.941924 | 0.470962 | − | 0.882153i | \(-0.343907\pi\) | ||||
0.470962 | + | 0.882153i | \(0.343907\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.50174 | − | 48.1454i | 0.248271 | − | 1.59338i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.43805 | − | 16.3472i | −0.312012 | − | 0.540421i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.5058 | − | 17.6463i | −1.07344 | − | 0.582732i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.2320 | + | 10.5263i | −0.601419 | + | 0.347229i | −0.769600 | − | 0.638527i | \(-0.779544\pi\) |
0.168181 | + | 0.985756i | \(0.446211\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.0418 | + | 7.52968i | 0.429741 | + | 0.248111i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.42852 | 0.0799357 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.1385 | 0.793669 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.13425 | − | 3.54161i | −0.201475 | − | 0.116322i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.8055 | − | 6.23858i | 0.354518 | − | 0.204681i | −0.312155 | − | 0.950031i | \(-0.601051\pi\) |
0.666674 | + | 0.745350i | \(0.267718\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.17890 | − | 0.114497i | 0.0714104 | − | 0.00375248i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.7819 | − | 23.8710i | −0.451200 | − | 0.781501i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.85970 | + | 1.53628i | 0.322447 | + | 0.0502418i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.2128 | 1.41170 | 0.705850 | − | 0.708362i | \(-0.250565\pi\) | ||||
0.705850 | + | 0.708362i | \(0.250565\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 44.9221 | 1.46598 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.73754 | − | 13.4018i | 0.252236 | − | 0.436886i | −0.711905 | − | 0.702276i | \(-0.752167\pi\) |
0.964141 | + | 0.265390i | \(0.0855006\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.42672 | + | 4.20321i | 0.0790249 | + | 0.136875i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.1859 | − | 7.15816i | −0.428937 | − | 0.232855i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.7488 | + | 29.0098i | 0.544264 | + | 0.942693i | 0.998653 | + | 0.0518895i | \(0.0165244\pi\) |
−0.454389 | + | 0.890803i | \(0.650142\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.811791 | − | 1.40606i | 0.0263518 | − | 0.0456427i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.1312i | 0.523091i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.4820i | 0.825444i | 0.910857 | + | 0.412722i | \(0.135422\pi\) | ||||
−0.910857 | + | 0.412722i | \(0.864578\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.29535 | + | 3.05727i | 0.171354 | + | 0.0989311i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.63942 | + | 6.15462i | 0.246947 | + | 0.198951i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.486833 | + | 18.5419i | 0.0157207 | + | 0.598748i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.2488 | − | 21.2156i | −0.395124 | − | 0.684374i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.57325 | + | 2.06302i | 0.115146 | + | 0.0664798i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.78285 | 0.314921 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 39.6417i | − | 1.27479i | −0.770537 | − | 0.637395i | \(-0.780012\pi\) | ||
0.770537 | − | 0.637395i | \(-0.219988\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.24263 | + | 0.717434i | 0.0399191 | + | 0.0230473i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.5082 | − | 9.53101i | 0.529773 | − | 0.305865i | −0.211151 | − | 0.977454i | \(-0.567721\pi\) |
0.740924 | + | 0.671589i | \(0.234388\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.8545 | − | 15.8461i | 0.828857 | − | 0.508004i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.894652 | + | 0.516528i | −0.0286518 | + | 0.0165421i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.8348 | + | 41.2832i | −0.762544 | + | 1.32077i | 0.178991 | + | 0.983851i | \(0.442717\pi\) |
−0.941535 | + | 0.336915i | \(0.890617\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.25583 | − | 21.3470i | −0.263857 | − | 0.682252i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 0.664016i | − | 0.0212004i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.2377 | − | 23.2312i | −1.28338 | − | 0.740961i | −0.305917 | − | 0.952058i | \(-0.598963\pi\) |
−0.977465 | + | 0.211097i | \(0.932296\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.55046 | − | 13.0778i | −0.240578 | − | 0.416693i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.3608 | − | 8.18877i | 0.425278 | − | 0.260651i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.16775 | − | 2.40625i | 0.132527 | − | 0.0765144i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.28588 | + | 12.6195i | −0.231444 | + | 0.400872i | −0.958233 | − | 0.285988i | \(-0.907678\pi\) |
0.726790 | + | 0.686860i | \(0.241012\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 41.8575i | 1.32831i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.18877 | −0.132793 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.05848 | + | 3.56539i | −0.0651927 | + | 0.112917i | −0.896779 | − | 0.442478i | \(-0.854100\pi\) |
0.831587 | + | 0.555395i | \(0.187433\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 29.3642 | − | 16.9534i | 0.929043 | − | 0.536383i |
(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 | 1232.2.bn.b.241.3 | 16 | ||
4.3 | odd | 2 | 154.2.i.a.87.3 | ✓ | 16 | ||
7.5 | odd | 6 | inner | 1232.2.bn.b.593.4 | 16 | ||
11.10 | odd | 2 | inner | 1232.2.bn.b.241.4 | 16 | ||
12.11 | even | 2 | 1386.2.bk.c.703.6 | 16 | |||
28.3 | even | 6 | 1078.2.c.b.1077.6 | 16 | |||
28.11 | odd | 6 | 1078.2.c.b.1077.3 | 16 | |||
28.19 | even | 6 | 154.2.i.a.131.7 | yes | 16 | ||
28.23 | odd | 6 | 1078.2.i.c.901.6 | 16 | |||
28.27 | even | 2 | 1078.2.i.c.1011.2 | 16 | |||
44.43 | even | 2 | 154.2.i.a.87.7 | yes | 16 | ||
77.54 | even | 6 | inner | 1232.2.bn.b.593.3 | 16 | ||
84.47 | odd | 6 | 1386.2.bk.c.901.2 | 16 | |||
132.131 | odd | 2 | 1386.2.bk.c.703.2 | 16 | |||
308.87 | odd | 6 | 1078.2.c.b.1077.14 | 16 | |||
308.131 | odd | 6 | 154.2.i.a.131.3 | yes | 16 | ||
308.219 | even | 6 | 1078.2.i.c.901.2 | 16 | |||
308.263 | even | 6 | 1078.2.c.b.1077.11 | 16 | |||
308.307 | odd | 2 | 1078.2.i.c.1011.6 | 16 | |||
924.131 | even | 6 | 1386.2.bk.c.901.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.i.a.87.3 | ✓ | 16 | 4.3 | odd | 2 | ||
154.2.i.a.87.7 | yes | 16 | 44.43 | even | 2 | ||
154.2.i.a.131.3 | yes | 16 | 308.131 | odd | 6 | ||
154.2.i.a.131.7 | yes | 16 | 28.19 | even | 6 | ||
1078.2.c.b.1077.3 | 16 | 28.11 | odd | 6 | |||
1078.2.c.b.1077.6 | 16 | 28.3 | even | 6 | |||
1078.2.c.b.1077.11 | 16 | 308.263 | even | 6 | |||
1078.2.c.b.1077.14 | 16 | 308.87 | odd | 6 | |||
1078.2.i.c.901.2 | 16 | 308.219 | even | 6 | |||
1078.2.i.c.901.6 | 16 | 28.23 | odd | 6 | |||
1078.2.i.c.1011.2 | 16 | 28.27 | even | 2 | |||
1078.2.i.c.1011.6 | 16 | 308.307 | odd | 2 | |||
1232.2.bn.b.241.3 | 16 | 1.1 | even | 1 | trivial | ||
1232.2.bn.b.241.4 | 16 | 11.10 | odd | 2 | inner | ||
1232.2.bn.b.593.3 | 16 | 77.54 | even | 6 | inner | ||
1232.2.bn.b.593.4 | 16 | 7.5 | odd | 6 | inner | ||
1386.2.bk.c.703.2 | 16 | 132.131 | odd | 2 | |||
1386.2.bk.c.703.6 | 16 | 12.11 | even | 2 | |||
1386.2.bk.c.901.2 | 16 | 84.47 | odd | 6 | |||
1386.2.bk.c.901.6 | 16 | 924.131 | even | 6 |