Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,3,Mod(251,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.251");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.j (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: | \(18.3924178443\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 3 x^{18} - 19 x^{16} - 66 x^{14} + 109 x^{12} + 813 x^{10} + 981 x^{8} - 5346 x^{6} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{12} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 251.7 | ||
Root | \(-0.185238 - 1.72212i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.251 |
Dual form | 675.3.j.e.476.7 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.15863 | + | 0.668935i | 0.579314 | + | 0.334467i | 0.760861 | − | 0.648915i | \(-0.224777\pi\) |
−0.181547 | + | 0.983382i | \(0.558110\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.10505 | − | 1.91401i | −0.276263 | − | 0.478502i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.10376 | + | 7.10792i | −0.586251 | + | 1.01542i | 0.408467 | + | 0.912773i | \(0.366064\pi\) |
−0.994718 | + | 0.102644i | \(0.967270\pi\) | |||||||
\(8\) | − | 8.30831i | − | 1.03854i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.67242 | + | 3.27497i | 0.515675 | + | 0.297725i | 0.735163 | − | 0.677890i | \(-0.237106\pi\) |
−0.219489 | + | 0.975615i | \(0.570439\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.749233 | − | 1.29771i | −0.0576333 | − | 0.0998238i | 0.835769 | − | 0.549081i | \(-0.185022\pi\) |
−0.893403 | + | 0.449257i | \(0.851689\pi\) | |||||||
\(14\) | −9.50946 | + | 5.49029i | −0.679247 | + | 0.392164i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.13750 | − | 1.97021i | 0.0710939 | − | 0.123138i | ||||
\(17\) | 15.1237i | 0.889630i | 0.895622 | + | 0.444815i | \(0.146731\pi\) | ||||
−0.895622 | + | 0.444815i | \(0.853269\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.9980 | 1.36831 | 0.684157 | − | 0.729334i | \(-0.260170\pi\) | ||||
0.684157 | + | 0.729334i | \(0.260170\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.38149 | + | 7.58896i | 0.199158 | + | 0.344953i | ||||
\(23\) | −20.1010 | + | 11.6053i | −0.873958 | + | 0.504580i | −0.868661 | − | 0.495406i | \(-0.835019\pi\) |
−0.00529637 | + | 0.999986i | \(0.501686\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 2.00475i | − | 0.0771058i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 18.1395 | 0.647839 | ||||||||
\(29\) | 6.96344 | + | 4.02034i | 0.240119 | + | 0.138633i | 0.615231 | − | 0.788347i | \(-0.289063\pi\) |
−0.375113 | + | 0.926979i | \(0.622396\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.5107 | + | 38.9897i | 0.726152 | + | 1.25773i | 0.958498 | + | 0.285099i | \(0.0920264\pi\) |
−0.232346 | + | 0.972633i | \(0.574640\pi\) | |||||||
\(32\) | −26.1449 | + | 15.0948i | −0.817029 | + | 0.471712i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10.1168 | + | 17.5228i | −0.297552 | + | 0.515375i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 62.8487 | 1.69861 | 0.849307 | − | 0.527900i | \(-0.177020\pi\) | ||||
0.849307 | + | 0.527900i | \(0.177020\pi\) | |||||||
\(38\) | 30.1220 | + | 17.3909i | 0.792684 | + | 0.457657i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.97361 | + | 5.75827i | −0.243259 | + | 0.140446i | −0.616674 | − | 0.787219i | \(-0.711520\pi\) |
0.373415 | + | 0.927664i | \(0.378187\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21.3253 | + | 36.9366i | −0.495938 | + | 0.858990i | −0.999989 | − | 0.00468401i | \(-0.998509\pi\) |
0.504051 | + | 0.863674i | \(0.331842\pi\) | |||||||
\(44\) | − | 14.4761i | − | 0.329002i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −31.0528 | −0.675062 | ||||||||
\(47\) | 14.2898 | + | 8.25020i | 0.304037 | + | 0.175536i | 0.644255 | − | 0.764811i | \(-0.277167\pi\) |
−0.340218 | + | 0.940347i | \(0.610501\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.18167 | − | 15.9031i | −0.187381 | − | 0.324553i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.65588 | + | 2.86808i | −0.0318439 | + | 0.0551553i | ||||
\(53\) | 66.0119i | 1.24551i | 0.782418 | + | 0.622754i | \(0.213986\pi\) | ||||
−0.782418 | + | 0.622754i | \(0.786014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 59.0548 | + | 34.0953i | 1.05455 | + | 0.608845i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.37870 | + | 9.31617i | 0.0927361 | + | 0.160624i | ||||
\(59\) | 0.373843 | − | 0.215838i | 0.00633632 | − | 0.00365828i | −0.496828 | − | 0.867849i | \(-0.665502\pi\) |
0.503165 | + | 0.864190i | \(0.332169\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.7923 | − | 27.3530i | 0.258890 | − | 0.448410i | −0.707055 | − | 0.707158i | \(-0.749977\pi\) |
0.965945 | + | 0.258748i | \(0.0833101\pi\) | |||||||
\(62\) | 60.2328i | 0.971496i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −49.4897 | −0.773277 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 47.9785 | + | 83.1011i | 0.716096 | + | 1.24032i | 0.962535 | + | 0.271157i | \(0.0874062\pi\) |
−0.246439 | + | 0.969158i | \(0.579260\pi\) | |||||||
\(68\) | 28.9469 | − | 16.7125i | 0.425690 | − | 0.245772i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 84.2523i | − | 1.18665i | −0.804962 | − | 0.593326i | \(-0.797814\pi\) | ||
0.804962 | − | 0.593326i | \(-0.202186\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 63.5769 | 0.870916 | 0.435458 | − | 0.900209i | \(-0.356586\pi\) | ||||
0.435458 | + | 0.900209i | \(0.356586\pi\) | |||||||
\(74\) | 72.8183 | + | 42.0417i | 0.984031 | + | 0.568131i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −28.7292 | − | 49.7604i | −0.378015 | − | 0.654741i | ||||
\(77\) | −46.5565 | + | 26.8794i | −0.604630 | + | 0.349083i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.06687 | + | 15.7043i | −0.114771 | + | 0.198788i | −0.917688 | − | 0.397302i | \(-0.869947\pi\) |
0.802917 | + | 0.596090i | \(0.203280\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −15.4076 | −0.187898 | ||||||||
\(83\) | −87.4333 | − | 50.4796i | −1.05341 | − | 0.608188i | −0.129810 | − | 0.991539i | \(-0.541437\pi\) |
−0.923603 | + | 0.383351i | \(0.874770\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −49.4163 | + | 28.5305i | −0.574608 | + | 0.331750i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 27.2095 | − | 47.1282i | 0.309199 | − | 0.535548i | ||||
\(89\) | − | 86.3067i | − | 0.969738i | −0.874587 | − | 0.484869i | \(-0.838867\pi\) | ||
0.874587 | − | 0.484869i | \(-0.161133\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.2987 | 0.135150 | ||||||||
\(92\) | 44.4254 | + | 25.6490i | 0.482885 | + | 0.278794i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.0377 | + | 19.1178i | 0.117422 | + | 0.203381i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −34.5230 | + | 59.7956i | −0.355907 | + | 0.616450i | −0.987273 | − | 0.159036i | \(-0.949161\pi\) |
0.631365 | + | 0.775485i | \(0.282495\pi\) | |||||||
\(98\) | − | 24.5677i | − | 0.250691i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −30.1891 | − | 17.4297i | −0.298902 | − | 0.172571i | 0.343048 | − | 0.939318i | \(-0.388541\pi\) |
−0.641949 | + | 0.766747i | \(0.721874\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.0058 | − | 19.0625i | −0.106852 | − | 0.185073i | 0.807641 | − | 0.589674i | \(-0.200744\pi\) |
−0.914493 | + | 0.404601i | \(0.867410\pi\) | |||||||
\(104\) | −10.7818 | + | 6.22486i | −0.103671 | + | 0.0598544i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −44.1576 | + | 76.4833i | −0.416582 | + | 0.721540i | ||||
\(107\) | 99.8598i | 0.933269i | 0.884450 | + | 0.466635i | \(0.154534\pi\) | ||||
−0.884450 | + | 0.466635i | \(0.845466\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.7865 | 0.108133 | 0.0540664 | − | 0.998537i | \(-0.482782\pi\) | ||||
0.0540664 | + | 0.998537i | \(0.482782\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.33607 | + | 16.1706i | 0.0833578 | + | 0.144380i | ||||
\(113\) | −11.7278 | + | 6.77103i | −0.103786 | + | 0.0599206i | −0.550994 | − | 0.834509i | \(-0.685751\pi\) |
0.447209 | + | 0.894430i | \(0.352418\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 17.7708i | − | 0.153196i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.577527 | 0.00489430 | ||||||||
\(119\) | −107.498 | − | 62.0640i | −0.903345 | − | 0.521547i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −39.0491 | − | 67.6350i | −0.322720 | − | 0.558967i | ||||
\(122\) | 36.5947 | − | 21.1280i | 0.299957 | − | 0.173180i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 49.7511 | − | 86.1714i | 0.401218 | − | 0.694930i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.1983 | 0.103924 | 0.0519620 | − | 0.998649i | \(-0.483453\pi\) | ||||
0.0519620 | + | 0.998649i | \(0.483453\pi\) | |||||||
\(128\) | 47.2396 | + | 27.2738i | 0.369059 | + | 0.213076i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −184.044 | + | 106.258i | −1.40491 | + | 0.811127i | −0.994892 | − | 0.100949i | \(-0.967812\pi\) |
−0.410022 | + | 0.912076i | \(0.634479\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −106.689 | + | 184.792i | −0.802176 | + | 1.38941i | ||||
\(134\) | 128.378i | 0.958043i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 125.652 | 0.923915 | ||||||||
\(137\) | −129.866 | − | 74.9783i | −0.947929 | − | 0.547287i | −0.0554918 | − | 0.998459i | \(-0.517673\pi\) |
−0.892437 | + | 0.451172i | \(0.851006\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.80453 | + | 4.85759i | 0.0201765 | + | 0.0349467i | 0.875937 | − | 0.482425i | \(-0.160244\pi\) |
−0.855761 | + | 0.517372i | \(0.826911\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 56.3593 | − | 97.6171i | 0.396896 | − | 0.687445i | ||||
\(143\) | − | 9.81487i | − | 0.0686355i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 73.6620 | + | 42.5288i | 0.504534 | + | 0.291293i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −69.4512 | − | 120.293i | −0.469265 | − | 0.812790i | ||||
\(149\) | −97.4936 | + | 56.2879i | −0.654319 | + | 0.377771i | −0.790109 | − | 0.612966i | \(-0.789976\pi\) |
0.135790 | + | 0.990738i | \(0.456643\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 30.3786 | − | 52.6172i | 0.201183 | − | 0.348458i | −0.747727 | − | 0.664006i | \(-0.768855\pi\) |
0.948910 | + | 0.315548i | \(0.102188\pi\) | |||||||
\(152\) | − | 215.999i | − | 1.42105i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −71.9222 | −0.467028 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −147.499 | − | 255.475i | −0.939482 | − | 1.62723i | −0.766439 | − | 0.642317i | \(-0.777973\pi\) |
−0.173043 | − | 0.984914i | \(-0.555360\pi\) | |||||||
\(158\) | −21.0103 | + | 12.1303i | −0.132976 | + | 0.0767740i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 190.502i | − | 1.18324i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.8284 | −0.121647 | −0.0608235 | − | 0.998149i | \(-0.519373\pi\) | ||||
−0.0608235 | + | 0.998149i | \(0.519373\pi\) | |||||||
\(164\) | 22.0427 | + | 12.7264i | 0.134407 | + | 0.0775999i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −67.5351 | − | 116.974i | −0.406838 | − | 0.704664i | ||||
\(167\) | 87.7198 | − | 50.6451i | 0.525268 | − | 0.303264i | −0.213819 | − | 0.976873i | \(-0.568590\pi\) |
0.739087 | + | 0.673609i | \(0.235257\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 83.3773 | − | 144.414i | 0.493357 | − | 0.854519i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 94.2625 | 0.548038 | ||||||||
\(173\) | 95.8461 | + | 55.3368i | 0.554024 | + | 0.319866i | 0.750743 | − | 0.660594i | \(-0.229696\pi\) |
−0.196720 | + | 0.980460i | \(0.563029\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.9048 | − | 7.45058i | 0.0733226 | − | 0.0423328i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 57.7335 | − | 99.9974i | 0.324346 | − | 0.561783i | ||||
\(179\) | − | 55.1312i | − | 0.307995i | −0.988071 | − | 0.153998i | \(-0.950785\pi\) | ||
0.988071 | − | 0.153998i | \(-0.0492148\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −27.6183 | −0.152587 | −0.0762935 | − | 0.997085i | \(-0.524309\pi\) | ||||
−0.0762935 | + | 0.997085i | \(0.524309\pi\) | |||||||
\(182\) | 14.2496 | + | 8.22702i | 0.0782946 | + | 0.0452034i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 96.4207 | + | 167.006i | 0.524026 | + | 0.907639i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −49.5297 | + | 85.7880i | −0.264865 | + | 0.458760i | ||||
\(188\) | − | 36.4676i | − | 0.193977i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 225.953 | + | 130.454i | 1.18300 | + | 0.683004i | 0.956706 | − | 0.291055i | \(-0.0940064\pi\) |
0.226292 | + | 0.974060i | \(0.427340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 57.8659 | + | 100.227i | 0.299823 | + | 0.519309i | 0.976095 | − | 0.217343i | \(-0.0697390\pi\) |
−0.676272 | + | 0.736652i | \(0.736406\pi\) | |||||||
\(194\) | −79.9987 | + | 46.1873i | −0.412365 | + | 0.238079i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −20.2925 | + | 35.1476i | −0.103533 | + | 0.179324i | ||||
\(197\) | − | 179.618i | − | 0.911768i | −0.890039 | − | 0.455884i | \(-0.849323\pi\) | ||
0.890039 | − | 0.455884i | \(-0.150677\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 132.649 | 0.666577 | 0.333289 | − | 0.942825i | \(-0.391842\pi\) | ||||
0.333289 | + | 0.942825i | \(0.391842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −23.3186 | − | 40.3890i | −0.115439 | − | 0.199946i | ||||
\(203\) | −57.1526 | + | 32.9970i | −0.281540 | + | 0.162547i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 29.4485i | − | 0.142954i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.40902 | −0.0163895 | ||||||||
\(209\) | 147.471 | + | 85.1427i | 0.705605 | + | 0.407381i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 174.674 | + | 302.545i | 0.827841 | + | 1.43386i | 0.899729 | + | 0.436450i | \(0.143764\pi\) |
−0.0718877 | + | 0.997413i | \(0.522902\pi\) | |||||||
\(212\) | 126.347 | − | 72.9467i | 0.595978 | − | 0.344088i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −66.7997 | + | 115.700i | −0.312148 | + | 0.540656i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −369.514 | −1.70283 | ||||||||
\(218\) | 13.6562 | + | 7.88438i | 0.0626429 | + | 0.0361669i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.6262 | − | 11.3312i | 0.0888063 | − | 0.0512723i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 70.9086 | − | 122.817i | 0.317976 | − | 0.550750i | −0.662090 | − | 0.749424i | \(-0.730330\pi\) |
0.980066 | + | 0.198674i | \(0.0636636\pi\) | |||||||
\(224\) | − | 247.781i | − | 1.10617i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.1175 | −0.0801660 | ||||||||
\(227\) | 117.695 | + | 67.9512i | 0.518480 | + | 0.299344i | 0.736312 | − | 0.676642i | \(-0.236565\pi\) |
−0.217833 | + | 0.975986i | \(0.569899\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −102.326 | − | 177.233i | −0.446837 | − | 0.773944i | 0.551342 | − | 0.834280i | \(-0.314116\pi\) |
−0.998178 | + | 0.0603360i | \(0.980783\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 33.4023 | − | 57.8544i | 0.143975 | − | 0.249373i | ||||
\(233\) | − | 270.050i | − | 1.15901i | −0.814967 | − | 0.579507i | \(-0.803245\pi\) | ||
0.814967 | − | 0.579507i | \(-0.196755\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.826233 | − | 0.477026i | −0.00350099 | − | 0.00202130i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −83.0336 | − | 143.818i | −0.348881 | − | 0.604279i | ||||
\(239\) | 318.573 | − | 183.928i | 1.33294 | − | 0.769575i | 0.347193 | − | 0.937794i | \(-0.387135\pi\) |
0.985750 | + | 0.168219i | \(0.0538016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.7054 | + | 34.1307i | −0.0817650 | + | 0.141621i | −0.904008 | − | 0.427515i | \(-0.859389\pi\) |
0.822243 | + | 0.569136i | \(0.192722\pi\) | |||||||
\(242\) | − | 104.485i | − | 0.431757i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −69.8052 | −0.286087 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.4785 | − | 33.7378i | −0.0788605 | − | 0.136590i | ||||
\(248\) | 323.938 | − | 187.026i | 1.30620 | − | 0.754137i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 80.2388i | 0.319677i | 0.987143 | + | 0.159838i | \(0.0510973\pi\) | ||||
−0.987143 | + | 0.159838i | \(0.948903\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −152.029 | −0.600904 | ||||||||
\(254\) | 15.2920 | + | 8.82883i | 0.0602046 | + | 0.0347592i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 135.468 | + | 234.638i | 0.529173 | + | 0.916554i | ||||
\(257\) | −112.839 | + | 65.1474i | −0.439061 | + | 0.253492i | −0.703199 | − | 0.710993i | \(-0.748246\pi\) |
0.264138 | + | 0.964485i | \(0.414912\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −257.916 | + | 446.723i | −0.995814 | + | 1.72480i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −284.318 | −1.08518 | ||||||||
\(263\) | −281.249 | − | 162.379i | −1.06939 | − | 0.617411i | −0.141374 | − | 0.989956i | \(-0.545152\pi\) |
−0.928014 | + | 0.372545i | \(0.878485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −247.227 | + | 142.737i | −0.929424 | + | 0.536603i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 106.037 | − | 183.662i | 0.395662 | − | 0.685307i | ||||
\(269\) | 353.608i | 1.31453i | 0.753660 | + | 0.657264i | \(0.228286\pi\) | ||||
−0.753660 | + | 0.657264i | \(0.771714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −332.793 | −1.22802 | −0.614010 | − | 0.789298i | \(-0.710444\pi\) | ||||
−0.614010 | + | 0.789298i | \(0.710444\pi\) | |||||||
\(272\) | 29.7969 | + | 17.2033i | 0.109547 | + | 0.0632473i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −100.311 | − | 173.744i | −0.366099 | − | 0.634102i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 42.0119 | − | 72.7668i | 0.151668 | − | 0.262696i | −0.780173 | − | 0.625564i | \(-0.784869\pi\) |
0.931841 | + | 0.362868i | \(0.118202\pi\) | |||||||
\(278\) | 7.50419i | 0.0269935i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 322.954 | + | 186.458i | 1.14930 | + | 0.663551i | 0.948718 | − | 0.316125i | \(-0.102382\pi\) |
0.200586 | + | 0.979676i | \(0.435715\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 80.2796 | + | 139.048i | 0.283674 | + | 0.491337i | 0.972287 | − | 0.233792i | \(-0.0751135\pi\) |
−0.688613 | + | 0.725129i | \(0.741780\pi\) | |||||||
\(284\) | −161.260 | + | 93.1033i | −0.567816 | + | 0.327828i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.56551 | − | 11.3718i | 0.0229563 | − | 0.0397615i | ||||
\(287\) | − | 94.5221i | − | 0.329345i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 60.2734 | 0.208559 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −70.2558 | − | 121.687i | −0.240602 | − | 0.416735i | ||||
\(293\) | −276.729 | + | 159.770i | −0.944467 | + | 0.545288i | −0.891358 | − | 0.453300i | \(-0.850247\pi\) |
−0.0531095 | + | 0.998589i | \(0.516913\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 522.166i | − | 1.76408i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −150.612 | −0.505409 | ||||||||
\(299\) | 30.1207 | + | 17.3902i | 0.100738 | + | 0.0581612i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −175.028 | − | 303.157i | −0.581489 | − | 1.00717i | ||||
\(302\) | 70.3949 | − | 40.6425i | 0.233096 | − | 0.134578i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 29.5728 | − | 51.2215i | 0.0972789 | − | 0.168492i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 336.649 | 1.09658 | 0.548288 | − | 0.836289i | \(-0.315280\pi\) | ||||
0.548288 | + | 0.836289i | \(0.315280\pi\) | |||||||
\(308\) | 102.895 | + | 59.4063i | 0.334074 | + | 0.192878i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 263.046 | − | 151.869i | 0.845806 | − | 0.488326i | −0.0134276 | − | 0.999910i | \(-0.504274\pi\) |
0.859234 | + | 0.511584i | \(0.170941\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −114.618 | + | 198.525i | −0.366193 | + | 0.634265i | −0.988967 | − | 0.148137i | \(-0.952672\pi\) |
0.622774 | + | 0.782402i | \(0.286006\pi\) | |||||||
\(314\) | − | 394.668i | − | 1.25690i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 40.0775 | 0.126828 | ||||||||
\(317\) | −372.001 | − | 214.775i | −1.17351 | − | 0.677524i | −0.219002 | − | 0.975724i | \(-0.570280\pi\) |
−0.954503 | + | 0.298201i | \(0.903614\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.3330 | + | 45.6102i | 0.0825487 | + | 0.142979i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 127.433 | − | 220.721i | 0.395756 | − | 0.685469i | ||||
\(323\) | 393.186i | 1.21729i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −22.9738 | − | 13.2639i | −0.0704718 | − | 0.0406869i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 47.8415 | + | 82.8638i | 0.145858 | + | 0.252634i | ||||
\(329\) | −117.283 | + | 67.7136i | −0.356485 | + | 0.205816i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 137.447 | − | 238.065i | 0.415248 | − | 0.719230i | −0.580207 | − | 0.814469i | \(-0.697028\pi\) |
0.995454 | + | 0.0952390i | \(0.0303615\pi\) | |||||||
\(332\) | 223.131i | 0.672080i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 135.513 | 0.405727 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 128.494 | + | 222.557i | 0.381287 | + | 0.660408i | 0.991246 | − | 0.132024i | \(-0.0421477\pi\) |
−0.609960 | + | 0.792432i | \(0.708814\pi\) | |||||||
\(338\) | 193.207 | − | 111.548i | 0.571617 | − | 0.330023i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 294.888i | 0.864774i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −251.451 | −0.733093 | ||||||||
\(344\) | 306.880 | + | 177.177i | 0.892094 | + | 0.515051i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 74.0333 | + | 128.229i | 0.213969 | + | 0.370605i | ||||
\(347\) | 221.381 | − | 127.814i | 0.637986 | − | 0.368341i | −0.145853 | − | 0.989306i | \(-0.546593\pi\) |
0.783838 | + | 0.620965i | \(0.213259\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 146.497 | − | 253.740i | 0.419761 | − | 0.727048i | −0.576154 | − | 0.817341i | \(-0.695447\pi\) |
0.995915 | + | 0.0902933i | \(0.0287804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −197.740 | −0.561762 | ||||||||
\(353\) | −33.2985 | − | 19.2249i | −0.0943301 | − | 0.0544615i | 0.452093 | − | 0.891971i | \(-0.350678\pi\) |
−0.546423 | + | 0.837509i | \(0.684011\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −165.192 | + | 95.3734i | −0.464022 | + | 0.267903i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 36.8792 | − | 63.8766i | 0.103014 | − | 0.178426i | ||||
\(359\) | − | 168.269i | − | 0.468716i | −0.972150 | − | 0.234358i | \(-0.924701\pi\) | ||
0.972150 | − | 0.234358i | \(-0.0752988\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 314.895 | 0.872286 | ||||||||
\(362\) | −31.9993 | − | 18.4748i | −0.0883959 | − | 0.0510354i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.5907 | − | 23.5398i | −0.0373371 | − | 0.0646698i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.5376 | + | 40.7684i | −0.0641353 | + | 0.111086i | −0.896310 | − | 0.443428i | \(-0.853762\pi\) |
0.832175 | + | 0.554513i | \(0.187096\pi\) | |||||||
\(368\) | 52.8044i | 0.143490i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −469.207 | − | 270.897i | −1.26471 | − | 0.730180i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 128.563 | + | 222.678i | 0.344674 | + | 0.596993i | 0.985294 | − | 0.170865i | \(-0.0546562\pi\) |
−0.640621 | + | 0.767858i | \(0.721323\pi\) | |||||||
\(374\) | −114.773 | + | 66.2643i | −0.306880 | + | 0.177177i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 68.5452 | − | 118.724i | 0.182301 | − | 0.315755i | ||||
\(377\) | − | 12.0487i | − | 0.0319594i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −194.506 | −0.513210 | −0.256605 | − | 0.966516i | \(-0.582604\pi\) | ||||
−0.256605 | + | 0.966516i | \(0.582604\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 174.530 | + | 302.295i | 0.456885 | + | 0.791348i | ||||
\(383\) | −178.271 | + | 102.925i | −0.465460 | + | 0.268733i | −0.714337 | − | 0.699802i | \(-0.753272\pi\) |
0.248877 | + | 0.968535i | \(0.419938\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 154.834i | 0.401124i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 152.599 | 0.393297 | ||||||||
\(389\) | −296.754 | − | 171.331i | −0.762863 | − | 0.440439i | 0.0674597 | − | 0.997722i | \(-0.478511\pi\) |
−0.830323 | + | 0.557283i | \(0.811844\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −175.516 | − | 304.002i | −0.448889 | − | 0.777499i | ||||
\(392\) | −132.128 | + | 76.2842i | −0.337061 | + | 0.194602i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 120.153 | − | 208.111i | 0.304957 | − | 0.528201i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 332.225 | 0.836838 | 0.418419 | − | 0.908254i | \(-0.362584\pi\) | ||||
0.418419 | + | 0.908254i | \(0.362584\pi\) | |||||||
\(398\) | 153.691 | + | 88.7334i | 0.386158 | + | 0.222948i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −414.101 | + | 239.081i | −1.03267 | + | 0.596213i | −0.917749 | − | 0.397161i | \(-0.869995\pi\) |
−0.114923 | + | 0.993374i | \(0.536662\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.7315 | − | 58.4247i | 0.0837011 | − | 0.144975i | ||||
\(404\) | 77.0429i | 0.190700i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −88.2915 | −0.217467 | ||||||||
\(407\) | 356.504 | + | 205.828i | 0.875932 | + | 0.505719i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 91.4354 | + | 158.371i | 0.223559 | + | 0.387215i | 0.955886 | − | 0.293738i | \(-0.0948993\pi\) |
−0.732327 | + | 0.680953i | \(0.761566\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −24.3239 | + | 42.1302i | −0.0590386 | + | 0.102258i | ||||
\(413\) | 3.54299i | 0.00857868i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 39.1773 | + | 22.6190i | 0.0941762 | + | 0.0543727i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 113.910 | + | 197.298i | 0.272511 | + | 0.472004i | ||||
\(419\) | −352.311 | + | 203.407i | −0.840839 | + | 0.485459i | −0.857549 | − | 0.514402i | \(-0.828014\pi\) |
0.0167104 | + | 0.999860i | \(0.494681\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −224.098 | + | 388.148i | −0.532298 | + | 0.921968i | 0.466991 | + | 0.884262i | \(0.345338\pi\) |
−0.999289 | + | 0.0377055i | \(0.987995\pi\) | |||||||
\(422\) | 467.383i | 1.10754i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 548.447 | 1.29351 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 129.615 | + | 224.500i | 0.303549 | + | 0.525762i | ||||
\(428\) | 191.132 | − | 110.350i | 0.446571 | − | 0.257828i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 254.466i | − | 0.590409i | −0.955434 | − | 0.295204i | \(-0.904612\pi\) | ||
0.955434 | − | 0.295204i | \(-0.0953877\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 82.9913 | 0.191666 | 0.0958329 | − | 0.995397i | \(-0.469449\pi\) | ||||
0.0958329 | + | 0.995397i | \(0.469449\pi\) | |||||||
\(434\) | −428.130 | − | 247.181i | −0.986474 | − | 0.569541i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.0247 | − | 22.5594i | −0.0298731 | − | 0.0517418i | ||||
\(437\) | −522.586 | + | 301.715i | −1.19585 | + | 0.690424i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 129.457 | − | 224.226i | 0.294891 | − | 0.510765i | −0.680069 | − | 0.733148i | \(-0.738050\pi\) |
0.974959 | + | 0.222383i | \(0.0713835\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.3193 | 0.0685957 | ||||||||
\(443\) | 142.835 | + | 82.4657i | 0.322426 | + | 0.186153i | 0.652473 | − | 0.757812i | \(-0.273731\pi\) |
−0.330047 | + | 0.943964i | \(0.607065\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 164.313 | − | 94.8664i | 0.368416 | − | 0.212705i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 203.094 | − | 351.769i | 0.453335 | − | 0.785198i | ||||
\(449\) | 628.421i | 1.39960i | 0.714338 | + | 0.699800i | \(0.246728\pi\) | ||||
−0.714338 | + | 0.699800i | \(0.753272\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −75.4327 | −0.167256 | ||||||||
\(452\) | 25.9196 | + | 14.9647i | 0.0573443 | + | 0.0331077i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 90.9097 | + | 157.460i | 0.200242 | + | 0.346829i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −374.823 | + | 649.213i | −0.820183 | + | 1.42060i | 0.0853634 | + | 0.996350i | \(0.472795\pi\) |
−0.905546 | + | 0.424248i | \(0.860538\pi\) | |||||||
\(458\) | − | 273.796i | − | 0.597809i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −325.037 | − | 187.660i | −0.705069 | − | 0.407072i | 0.104163 | − | 0.994560i | \(-0.466784\pi\) |
−0.809233 | + | 0.587488i | \(0.800117\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −82.4936 | − | 142.883i | −0.178172 | − | 0.308603i | 0.763082 | − | 0.646301i | \(-0.223685\pi\) |
−0.941254 | + | 0.337698i | \(0.890352\pi\) | |||||||
\(464\) | 15.8419 | − | 9.14630i | 0.0341420 | − | 0.0197119i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 180.646 | − | 312.888i | 0.387652 | − | 0.671434i | ||||
\(467\) | 751.743i | 1.60973i | 0.593460 | + | 0.804864i | \(0.297762\pi\) | ||||
−0.593460 | + | 0.804864i | \(0.702238\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −787.568 | −1.67925 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.79325 | − | 3.10600i | −0.00379926 | − | 0.00658052i | ||||
\(473\) | −241.933 | + | 139.680i | −0.511485 | + | 0.295306i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 274.336i | 0.576337i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 492.144 | 1.02959 | ||||||||
\(479\) | −23.9669 | − | 13.8373i | −0.0500352 | − | 0.0288879i | 0.474774 | − | 0.880108i | \(-0.342530\pi\) |
−0.524809 | + | 0.851220i | \(0.675863\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −47.0883 | − | 81.5594i | −0.0978967 | − | 0.169562i | ||||
\(482\) | −45.6624 | + | 26.3632i | −0.0947353 | + | 0.0546955i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −86.3027 | + | 149.481i | −0.178311 | + | 0.308844i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 690.293 | 1.41744 | 0.708720 | − | 0.705490i | \(-0.249273\pi\) | ||||
0.708720 | + | 0.705490i | \(0.249273\pi\) | |||||||
\(488\) | −227.257 | − | 131.207i | −0.465691 | − | 0.268867i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 308.987 | − | 178.394i | 0.629302 | − | 0.363328i | −0.151180 | − | 0.988506i | \(-0.548307\pi\) |
0.780482 | + | 0.625179i | \(0.214974\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −60.8025 | + | 105.313i | −0.123332 | + | 0.213617i | ||||
\(494\) | − | 52.1195i | − | 0.105505i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 102.424 | 0.206500 | ||||||||
\(497\) | 598.859 | + | 345.751i | 1.20495 | + | 0.695676i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.4485 | + | 31.9538i | 0.0369710 | + | 0.0640356i | 0.883919 | − | 0.467640i | \(-0.154896\pi\) |
−0.846948 | + | 0.531676i | \(0.821562\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −53.6745 | + | 92.9670i | −0.106921 | + | 0.185193i | ||||
\(503\) | 283.649i | 0.563914i | 0.959427 | + | 0.281957i | \(0.0909836\pi\) | ||||
−0.959427 | + | 0.281957i | \(0.909016\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −176.145 | − | 101.697i | −0.348112 | − | 0.200983i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.5849 | − | 25.2617i | −0.0287104 | − | 0.0497278i | ||||
\(509\) | 833.302 | − | 481.107i | 1.63714 | − | 0.945201i | 0.655324 | − | 0.755348i | \(-0.272532\pi\) |
0.981813 | − | 0.189853i | \(-0.0608012\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −260.904 | + | 451.899i | −0.510576 | + | 0.884343i | ||||
\(512\) | 144.287i | 0.281811i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −174.318 | −0.339139 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 54.0383 | + | 93.5971i | 0.104523 | + | 0.181039i | ||||
\(518\) | −597.658 | + | 345.058i | −1.15378 | + | 0.666135i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 643.651i | 1.23541i | 0.786408 | + | 0.617707i | \(0.211938\pi\) | ||||
−0.786408 | + | 0.617707i | \(0.788062\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 539.982 | 1.03247 | 0.516235 | − | 0.856447i | \(-0.327333\pi\) | ||||
0.516235 | + | 0.856447i | \(0.327333\pi\) | |||||||
\(524\) | 406.756 | + | 234.841i | 0.776252 | + | 0.448169i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −217.242 | − | 376.274i | −0.413008 | − | 0.715350i | ||||
\(527\) | −589.669 | + | 340.445i | −1.11892 | + | 0.646006i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.86759 | − | 8.43092i | 0.00920150 | − | 0.0159375i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 471.590 | 0.886447 | ||||||||
\(533\) | 14.9451 | + | 8.62857i | 0.0280396 | + | 0.0161887i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 690.430 | − | 398.620i | 1.28812 | − | 0.743694i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −236.541 | + | 409.700i | −0.439667 | + | 0.761525i | ||||
\(539\) | − | 120.279i | − | 0.223152i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 726.214 | 1.34235 | 0.671177 | − | 0.741297i | \(-0.265789\pi\) | ||||
0.671177 | + | 0.741297i | \(0.265789\pi\) | |||||||
\(542\) | −385.584 | − | 222.617i | −0.711409 | − | 0.410732i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −228.289 | − | 395.408i | −0.419649 | − | 0.726854i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 314.233 | − | 544.268i | 0.574467 | − | 0.995006i | −0.421632 | − | 0.906767i | \(-0.638543\pi\) |
0.996099 | − | 0.0882392i | \(-0.0281240\pi\) | |||||||
\(548\) | 331.420i | 0.604781i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 181.035 | + | 104.521i | 0.328558 | + | 0.189693i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −74.4165 | − | 128.893i | −0.134569 | − | 0.233080i | ||||
\(554\) | 97.3525 | − | 56.2065i | 0.175726 | − | 0.101456i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.19831 | − | 10.7358i | 0.0111480 | − | 0.0193090i | ||||
\(557\) | − | 821.989i | − | 1.47574i | −0.674941 | − | 0.737872i | \(-0.735831\pi\) | ||
0.674941 | − | 0.737872i | \(-0.264169\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 63.9106 | 0.114330 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 249.456 | + | 432.071i | 0.443872 | + | 0.768809i | ||||
\(563\) | 763.584 | − | 440.856i | 1.35628 | − | 0.783047i | 0.367158 | − | 0.930159i | \(-0.380331\pi\) |
0.989120 | + | 0.147111i | \(0.0469976\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 214.807i | 0.379518i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −699.994 | −1.23238 | ||||||||
\(569\) | −238.573 | − | 137.740i | −0.419284 | − | 0.242074i | 0.275487 | − | 0.961305i | \(-0.411161\pi\) |
−0.694771 | + | 0.719231i | \(0.744494\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 216.022 | + | 374.161i | 0.378322 | + | 0.655273i | 0.990818 | − | 0.135200i | \(-0.0431678\pi\) |
−0.612496 | + | 0.790474i | \(0.709834\pi\) | |||||||
\(572\) | −18.7857 | + | 10.8460i | −0.0328422 | + | 0.0189615i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 63.2291 | − | 109.516i | 0.110155 | − | 0.190794i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1060.42 | −1.83782 | −0.918911 | − | 0.394466i | \(-0.870930\pi\) | ||||
−0.918911 | + | 0.394466i | \(0.870930\pi\) | |||||||
\(578\) | 69.8345 | + | 40.3190i | 0.120821 | + | 0.0697560i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 717.610 | − | 414.312i | 1.23513 | − | 0.713102i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −216.187 | + | 374.447i | −0.370819 | + | 0.642277i | ||||
\(584\) | − | 528.216i | − | 0.904480i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −427.501 | −0.729525 | ||||||||
\(587\) | −149.127 | − | 86.0987i | −0.254050 | − | 0.146676i | 0.367567 | − | 0.929997i | \(-0.380191\pi\) |
−0.621617 | + | 0.783321i | \(0.713524\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 585.233 | + | 1013.65i | 0.993604 | + | 1.72097i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 71.4906 | − | 123.825i | 0.120761 | − | 0.209164i | ||||
\(593\) | − | 534.948i | − | 0.902104i | −0.892498 | − | 0.451052i | \(-0.851049\pi\) | ||
0.892498 | − | 0.451052i | \(-0.148951\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 215.471 | + | 124.402i | 0.361529 | + | 0.208729i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 23.2658 | + | 40.2976i | 0.0389060 | + | 0.0673872i | ||||
\(599\) | 646.293 | − | 373.137i | 1.07895 | − | 0.622934i | 0.148339 | − | 0.988937i | \(-0.452607\pi\) |
0.930614 | + | 0.366003i | \(0.119274\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −134.353 | + | 232.706i | −0.223549 | + | 0.387199i | −0.955883 | − | 0.293747i | \(-0.905098\pi\) |
0.732334 | + | 0.680946i | \(0.238431\pi\) | |||||||
\(602\) | − | 468.329i | − | 0.777956i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −134.280 | −0.222317 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −255.867 | − | 443.175i | −0.421527 | − | 0.730107i | 0.574562 | − | 0.818461i | \(-0.305173\pi\) |
−0.996089 | + | 0.0883543i | \(0.971839\pi\) | |||||||
\(608\) | −679.716 | + | 392.434i | −1.11795 | + | 0.645451i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 24.7253i | − | 0.0404669i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −606.924 | −0.990088 | −0.495044 | − | 0.868868i | \(-0.664848\pi\) | ||||
−0.495044 | + | 0.868868i | \(0.664848\pi\) | |||||||
\(614\) | 390.051 | + | 225.196i | 0.635263 | + | 0.366769i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 223.322 | + | 386.806i | 0.362536 | + | 0.627931i | ||||
\(617\) | 710.901 | − | 410.439i | 1.15219 | − | 0.665217i | 0.202769 | − | 0.979227i | \(-0.435006\pi\) |
0.949420 | + | 0.314010i | \(0.101673\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −292.071 | + | 505.881i | −0.471843 | + | 0.817256i | −0.999481 | − | 0.0322136i | \(-0.989744\pi\) |
0.527638 | + | 0.849469i | \(0.323078\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 406.363 | 0.653317 | ||||||||
\(623\) | 613.461 | + | 354.182i | 0.984688 | + | 0.568510i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −265.600 | + | 153.344i | −0.424282 | + | 0.244959i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −325.988 | + | 564.628i | −0.519089 | + | 0.899088i | ||||
\(629\) | 950.505i | 1.51114i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −273.744 | −0.433825 | −0.216913 | − | 0.976191i | \(-0.569599\pi\) | ||||
−0.216913 | + | 0.976191i | \(0.569599\pi\) | |||||||
\(632\) | 130.476 | + | 75.3304i | 0.206449 | + | 0.119194i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −287.341 | − | 497.689i | −0.453219 | − | 0.784998i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.7584 | + | 23.8303i | −0.0215988 | + | 0.0374102i | ||||
\(638\) | 70.4603i | 0.110439i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −641.498 | − | 370.369i | −1.00078 | − | 0.577799i | −0.0922990 | − | 0.995731i | \(-0.529422\pi\) |
−0.908478 | + | 0.417932i | \(0.862755\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.2027 | + | 60.9729i | 0.0547476 | + | 0.0948256i | 0.892100 | − | 0.451837i | \(-0.149231\pi\) |
−0.837353 | + | 0.546663i | \(0.815898\pi\) | |||||||
\(644\) | −364.622 | + | 210.515i | −0.566184 | + | 0.326886i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −263.016 | + | 455.556i | −0.407145 | + | 0.705196i | ||||
\(647\) | 470.408i | 0.727060i | 0.931582 | + | 0.363530i | \(0.118429\pi\) | ||||
−0.931582 | + | 0.363530i | \(0.881571\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.82746 | 0.00435664 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.9115 | + | 37.9518i | 0.0336066 | + | 0.0582083i | ||||
\(653\) | 208.519 | − | 120.389i | 0.319325 | − | 0.184362i | −0.331767 | − | 0.943362i | \(-0.607645\pi\) |
0.651092 | + | 0.758999i | \(0.274311\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 26.2002i | 0.0399393i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −181.184 | −0.275355 | ||||||||
\(659\) | −616.489 | − | 355.930i | −0.935491 | − | 0.540106i | −0.0469470 | − | 0.998897i | \(-0.514949\pi\) |
−0.888544 | + | 0.458791i | \(0.848283\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 216.848 | + | 375.592i | 0.328060 | + | 0.568217i | 0.982127 | − | 0.188220i | \(-0.0602717\pi\) |
−0.654067 | + | 0.756437i | \(0.726938\pi\) | |||||||
\(662\) | 318.500 | − | 183.886i | 0.481118 | − | 0.277774i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −419.400 | + | 726.422i | −0.631627 | + | 1.09401i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −186.630 | −0.279805 | ||||||||
\(668\) | −193.870 | − | 111.931i | −0.290225 | − | 0.167561i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 179.161 | − | 103.438i | 0.267006 | − | 0.154156i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 543.562 | − | 941.477i | 0.807671 | − | 1.39893i | −0.106803 | − | 0.994280i | \(-0.534061\pi\) |
0.914473 | − | 0.404646i | \(-0.132605\pi\) | |||||||
\(674\) | 343.815i | 0.510112i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −368.545 | −0.545185 | ||||||||
\(677\) | −740.549 | − | 427.556i | −1.09387 | − | 0.631545i | −0.159265 | − | 0.987236i | \(-0.550912\pi\) |
−0.934604 | + | 0.355691i | \(0.884246\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −283.348 | − | 490.774i | −0.417302 | − | 0.722789i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −197.261 | + | 341.666i | −0.289239 | + | 0.500976i | ||||
\(683\) | 96.8904i | 0.141860i | 0.997481 | + | 0.0709300i | \(0.0225967\pi\) | ||||
−0.997481 | + | 0.0709300i | \(0.977403\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −291.338 | − | 168.204i | −0.424691 | − | 0.245196i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 48.5152 | + | 84.0309i | 0.0705163 | + | 0.122138i | ||||
\(689\) | 85.6643 | − | 49.4583i | 0.124331 | − | 0.0717827i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 410.189 | − | 710.468i | 0.593616 | − | 1.02817i | −0.400125 | − | 0.916461i | \(-0.631033\pi\) |
0.993741 | − | 0.111712i | \(-0.0356335\pi\) | |||||||
\(692\) | − | 244.600i | − | 0.353469i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 341.998 | 0.492792 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −87.0863 | − | 150.838i | −0.124945 | − | 0.216410i | ||||
\(698\) | 339.471 | − | 195.993i | 0.486347 | − | 0.280793i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1180.09i | 1.68343i | 0.539919 | + | 0.841717i | \(0.318455\pi\) | ||||
−0.539919 | + | 0.841717i | \(0.681545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1633.94 | 2.32424 | ||||||||
\(704\) | −280.727 | − | 162.078i | −0.398759 | − | 0.230224i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −25.7204 | − | 44.5491i | −0.0364312 | − | 0.0631007i | ||||
\(707\) | 247.777 | − | 143.054i | 0.350463 | − | 0.202340i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 450.319 | − | 779.975i | 0.635146 | − | 1.10011i | −0.351338 | − | 0.936249i | \(-0.614273\pi\) |
0.986484 | − | 0.163857i | \(-0.0523936\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −717.062 | −1.00711 | ||||||||
\(713\) | −904.977 | − | 522.489i | −1.26925 | − | 0.732803i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −105.522 | + | 60.9229i | −0.147376 | + | 0.0850878i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 112.561 | − | 194.961i | 0.156770 | − | 0.271534i | ||||
\(719\) | 710.264i | 0.987850i | 0.869505 | + | 0.493925i | \(0.164438\pi\) | ||||
−0.869505 | + | 0.493925i | \(0.835562\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 180.660 | 0.250569 | ||||||||
\(722\) | 364.846 | + | 210.644i | 0.505327 | + | 0.291751i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 30.5196 | + | 52.8616i | 0.0421542 | + | 0.0730132i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 177.728 | − | 307.833i | 0.244467 | − | 0.423429i | −0.717515 | − | 0.696543i | \(-0.754720\pi\) |
0.961982 | + | 0.273114i | \(0.0880537\pi\) | |||||||
\(728\) | − | 102.181i | − | 0.140359i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −558.618 | − | 322.518i | −0.764183 | − | 0.441201i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −661.951 | − | 1146.53i | −0.903071 | − | 1.56416i | −0.823486 | − | 0.567337i | \(-0.807974\pi\) |
−0.0795852 | − | 0.996828i | \(-0.525360\pi\) | |||||||
\(734\) | −54.5428 | + | 31.4903i | −0.0743089 | + | 0.0429023i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 350.360 | − | 606.842i | 0.476033 | − | 0.824513i | ||||
\(737\) | 628.513i | 0.852799i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1145.75 | 1.55040 | 0.775202 | − | 0.631713i | \(-0.217648\pi\) | ||||
0.775202 | + | 0.631713i | \(0.217648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −362.425 | − | 627.738i | −0.488443 | − | 0.846008i | ||||
\(743\) | 686.107 | − | 396.124i | 0.923428 | − | 0.533141i | 0.0387008 | − | 0.999251i | \(-0.487678\pi\) |
0.884727 | + | 0.466110i | \(0.154345\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 344.002i | 0.461129i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 218.932 | 0.292690 | ||||||||
\(749\) | −709.795 | − | 409.801i | −0.947657 | − | 0.547130i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 159.251 | + | 275.830i | 0.212051 | + | 0.367284i | 0.952356 | − | 0.304987i | \(-0.0986523\pi\) |
−0.740305 | + | 0.672271i | \(0.765319\pi\) | |||||||
\(752\) | 32.5093 | − | 18.7692i | 0.0432304 | − | 0.0249591i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.05979 | − | 13.9600i | 0.0106894 | − | 0.0185146i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 174.964 | 0.231128 | 0.115564 | − | 0.993300i | \(-0.463132\pi\) | ||||
0.115564 | + | 0.993300i | \(0.463132\pi\) | |||||||
\(758\) | −225.361 | − | 130.112i | −0.297310 | − | 0.171652i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1032.43 | − | 596.072i | 1.35667 | − | 0.783275i | 0.367498 | − | 0.930024i | \(-0.380214\pi\) |
0.989174 | + | 0.146749i | \(0.0468810\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −48.3689 | + | 83.7773i | −0.0633930 | + | 0.109800i | ||||
\(764\) | − | 576.634i | − | 0.754756i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −275.400 | −0.359530 | ||||||||
\(767\) | −0.560191 | − | 0.323427i | −0.000730367 | − | 0.000421677i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −424.901 | − | 735.950i | −0.552537 | − | 0.957022i | −0.998091 | − | 0.0617670i | \(-0.980326\pi\) |
0.445553 | − | 0.895255i | \(-0.353007\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 127.890 | − | 221.511i | 0.165660 | − | 0.286932i | ||||
\(773\) | − | 344.791i | − | 0.446042i | −0.974814 | − | 0.223021i | \(-0.928408\pi\) | ||
0.974814 | − | 0.223021i | \(-0.0715919\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 496.801 | + | 286.828i | 0.640207 | + | 0.369624i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −229.218 | − | 397.018i | −0.294625 | − | 0.510305i | ||||
\(779\) | −259.294 | + | 149.703i | −0.332855 | + | 0.192174i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 275.924 | − | 477.915i | 0.353296 | − | 0.611926i | ||||
\(782\) | − | 469.634i | − | 0.600555i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −41.7767 | −0.0532866 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −625.961 | − | 1084.20i | −0.795376 | − | 1.37763i | −0.922600 | − | 0.385758i | \(-0.873940\pi\) |
0.127224 | − | 0.991874i | \(-0.459393\pi\) | |||||||
\(788\) | −343.791 | + | 198.488i | −0.436283 | + | 0.251888i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 111.147i | − | 0.140514i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −47.3284 | −0.0596827 | ||||||||
\(794\) | 384.925 | + | 222.237i | 0.484792 | + | 0.279895i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −146.584 | − | 253.891i | −0.184151 | − | 0.318959i | ||||
\(797\) | 375.640 | − | 216.876i | 0.471318 | − | 0.272115i | −0.245473 | − | 0.969403i | \(-0.578943\pi\) |
0.716791 | + | 0.697288i | \(0.245610\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −124.774 | + | 216.114i | −0.156162 | + | 0.270481i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −639.719 | −0.797655 | ||||||||
\(803\) | 360.635 | + | 208.213i | 0.449109 | + | 0.259293i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 78.1647 | − | 45.1284i | 0.0969785 | − | 0.0559905i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −144.811 | + | 250.820i | −0.179222 | + | 0.310421i | ||||
\(809\) | − | 900.166i | − | 1.11269i | −0.830951 | − | 0.556345i | \(-0.812203\pi\) | ||
0.830951 | − | 0.556345i | \(-0.187797\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −112.379 | −0.138569 | −0.0692844 | − | 0.997597i | \(-0.522072\pi\) | ||||
−0.0692844 | + | 0.997597i | \(0.522072\pi\) | |||||||
\(812\) | 126.313 | + | 72.9270i | 0.155558 | + | 0.0898116i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 275.371 | + | 476.956i | 0.338293 | + | 0.585941i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −554.416 | + | 960.276i | −0.678599 | + | 1.17537i | ||||
\(818\) | 244.657i | 0.299092i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1244.40 | − | 718.457i | −1.51572 | − | 0.875100i | −0.999830 | − | 0.0184448i | \(-0.994128\pi\) |
−0.515889 | − | 0.856656i | \(-0.672538\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.2627 | − | 61.0768i | −0.0428465 | − | 0.0742123i | 0.843807 | − | 0.536647i | \(-0.180309\pi\) |
−0.886653 | + | 0.462435i | \(0.846976\pi\) | |||||||
\(824\) | −158.377 | + | 91.4393i | −0.192206 | + | 0.110970i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.37003 | + | 4.10501i | −0.00286929 | + | 0.00496975i | ||||
\(827\) | − | 1406.58i | − | 1.70082i | −0.526122 | − | 0.850409i | \(-0.676354\pi\) | ||
0.526122 | − | 0.850409i | \(-0.323646\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 771.482 | 0.930618 | 0.465309 | − | 0.885148i | \(-0.345943\pi\) | ||||
0.465309 | + | 0.885148i | \(0.345943\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 37.0793 | + | 64.2233i | 0.0445665 | + | 0.0771915i | ||||
\(833\) | 240.514 | − | 138.861i | 0.288732 | − | 0.166700i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 376.349i | − | 0.450178i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −544.264 | −0.649480 | ||||||||
\(839\) | 552.639 | + | 319.066i | 0.658687 | + | 0.380293i | 0.791777 | − | 0.610811i | \(-0.209156\pi\) |
−0.133089 | + | 0.991104i | \(0.542490\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −388.174 | − | 672.336i | −0.461562 | − | 0.799449i | ||||
\(842\) | −519.292 | + | 299.813i | −0.616736 | + | 0.356073i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 386.049 | − | 668.657i | 0.457404 | − | 0.792247i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 640.992 | 0.756780 | ||||||||
\(848\) | 130.057 | + | 75.0887i | 0.153370 | + | 0.0885480i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1263.32 | + | 729.380i | −1.48452 | + | 0.857086i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −185.429 | + | 321.173i | −0.217385 | + | 0.376521i | −0.954008 | − | 0.299782i | \(-0.903086\pi\) |
0.736623 | + | 0.676304i | \(0.236419\pi\) | |||||||
\(854\) | 346.817i | 0.406108i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 829.666 | 0.969236 | ||||||||
\(857\) | −562.649 | − | 324.846i | −0.656533 | − | 0.379050i | 0.134421 | − | 0.990924i | \(-0.457082\pi\) |
−0.790955 | + | 0.611875i | \(0.790416\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.4224 | + | 44.0328i | 0.0295953 | + | 0.0512606i | 0.880444 | − | 0.474151i | \(-0.157245\pi\) |
−0.850848 | + | 0.525411i | \(0.823911\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 170.221 | − | 294.832i | 0.197472 | − | 0.342032i | ||||
\(863\) | − | 254.583i | − | 0.294997i | −0.989062 | − | 0.147499i | \(-0.952878\pi\) | ||
0.989062 | − | 0.147499i | \(-0.0471222\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 96.1561 | + | 55.5157i | 0.111035 | + | 0.0641059i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 408.333 | + | 707.253i | 0.470429 | + | 0.814808i | ||||
\(869\) | −102.862 | + | 59.3875i | −0.118369 | + | 0.0683401i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 71.8941 | − | 124.524i | 0.0825420 | − | 0.142967i | ||||
\(872\) | − | 97.9257i | − | 0.112300i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −807.311 | −0.923697 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −285.665 | − | 494.786i | −0.325729 | − | 0.564180i | 0.655930 | − | 0.754821i | \(-0.272277\pi\) |
−0.981660 | + | 0.190642i | \(0.938943\pi\) | |||||||
\(878\) | 299.985 | − | 173.196i | 0.341669 | − | 0.197263i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 671.733i | − | 0.762466i | −0.924479 | − | 0.381233i | \(-0.875499\pi\) | ||
0.924479 | − | 0.381233i | \(-0.124501\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −858.151 | −0.971858 | −0.485929 | − | 0.873998i | \(-0.661519\pi\) | ||||
−0.485929 | + | 0.873998i | \(0.661519\pi\) | |||||||
\(884\) | −43.3760 | − | 25.0431i | −0.0490678 | − | 0.0283293i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 110.328 | + | 191.094i | 0.124524 | + | 0.215682i | ||||
\(887\) | 1364.45 | − | 787.767i | 1.53828 | − | 0.888125i | 0.539337 | − | 0.842090i | \(-0.318675\pi\) |
0.998940 | − | 0.0460349i | \(-0.0146585\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −54.1628 | + | 93.8127i | −0.0609255 | + | 0.105526i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −313.431 | −0.351380 | ||||||||
\(893\) | 371.505 | + | 214.488i | 0.416019 | + | 0.240189i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −387.719 | + | 223.850i | −0.432723 | + | 0.249833i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −420.372 | + | 728.106i | −0.468121 | + | 0.810809i | ||||
\(899\) | 362.003i | 0.402673i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −998.345 | −1.10804 | ||||||||
\(902\) | −87.3984 | − | 50.4595i | −0.0968941 | − | 0.0559418i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 56.2558 | + | 97.4379i | 0.0622299 | + | 0.107785i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 547.384 | − | 948.097i | 0.603511 | − | 1.04531i | −0.388774 | − | 0.921333i | \(-0.627101\pi\) |
0.992285 | − | 0.123978i | \(-0.0395652\pi\) | |||||||
\(908\) | − | 300.359i | − | 0.330791i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 695.184 | + | 401.365i | 0.763100 | + | 0.440576i | 0.830408 | − | 0.557156i | \(-0.188108\pi\) |
−0.0673079 | + | 0.997732i | \(0.521441\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −330.639 | − | 572.683i | −0.362145 | − | 0.627254i | ||||
\(914\) | −868.562 | + | 501.465i | −0.950287 | + | 0.548648i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −226.150 | + | 391.704i | −0.246889 | + | 0.427624i | ||||
\(917\) | − | 1744.22i | − | 1.90210i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1294.88 | −1.40901 | −0.704506 | − | 0.709698i | \(-0.748831\pi\) | ||||
−0.704506 | + | 0.709698i | \(0.748831\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −251.065 | − | 434.857i | −0.272305 | − | 0.471645i | ||||
\(923\) | −109.335 | + | 63.1246i | −0.118456 | + | 0.0683907i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 220.731i | − | 0.238371i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −242.745 | −0.261579 | ||||||||
\(929\) | −450.703 | − | 260.214i | −0.485149 | − | 0.280101i | 0.237411 | − | 0.971409i | \(-0.423701\pi\) |
−0.722560 | + | 0.691309i | \(0.757035\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −238.705 | − | 413.449i | −0.256396 | − | 0.444091i | ||||
\(932\) | −516.879 | + | 298.420i | −0.554591 | + | 0.320193i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −502.867 | + | 870.990i | −0.538401 | + | 0.932538i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −255.010 | −0.272155 | −0.136078 | − | 0.990698i | \(-0.543450\pi\) | ||||
−0.136078 | + | 0.990698i | \(0.543450\pi\) | |||||||
\(938\) | −912.499 | − | 526.831i | −0.972813 | − | 0.561654i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 528.359 | − | 305.048i | 0.561487 | − | 0.324175i | −0.192255 | − | 0.981345i | \(-0.561580\pi\) |
0.753742 | + | 0.657170i | \(0.228247\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 133.653 | − | 231.494i | 0.141732 | − | 0.245487i | ||||
\(944\) | − | 0.982067i | − | 0.00104033i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −373.747 | −0.395081 | ||||||||
\(947\) | 915.897 | + | 528.793i | 0.967156 | + | 0.558388i | 0.898368 | − | 0.439244i | \(-0.144754\pi\) |
0.0687878 | + | 0.997631i | \(0.478087\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.6339 | − | 82.5043i | −0.0501938 | − | 0.0869382i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −515.647 | + | 893.127i | −0.541646 | + | 0.938159i | ||||
\(953\) | 605.977i | 0.635862i | 0.948114 | + | 0.317931i | \(0.102988\pi\) | ||||
−0.948114 | + | 0.317931i | \(0.897012\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −704.081 | − | 406.501i | −0.736486 | − | 0.425211i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18.5125 | − | 32.0645i | −0.0193241 | − | 0.0334703i | ||||
\(959\) | 1065.88 | − | 615.386i | 1.11145 | − | 0.641695i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −532.964 | + | 923.121i | −0.554593 | + | 0.960584i | ||||
\(962\) | − | 125.996i | − | 0.130973i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 87.1019 | 0.0903547 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 447.513 | + | 775.116i | 0.462785 | + | 0.801567i | 0.999099 | − | 0.0424516i | \(-0.0135168\pi\) |
−0.536313 | + | 0.844019i | \(0.680184\pi\) | |||||||
\(968\) | −561.933 | + | 324.432i | −0.580509 | + | 0.335157i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1442.25i | 1.48532i | 0.669666 | + | 0.742662i | \(0.266437\pi\) | ||||
−0.669666 | + | 0.742662i | \(0.733563\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −46.0364 | −0.0473139 | ||||||||
\(974\) | 799.794 | + | 461.761i | 0.821143 | + | 0.474087i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −35.9275 | − | 62.2282i | −0.0368109 | − | 0.0637584i | ||||
\(977\) | −316.520 | + | 182.743i | −0.323972 | + | 0.187045i | −0.653161 | − | 0.757219i | \(-0.726558\pi\) |
0.329190 | + | 0.944264i | \(0.393224\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 282.652 | − | 489.568i | 0.288715 | − | 0.500069i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 477.335 | 0.486085 | ||||||||
\(983\) | 617.048 | + | 356.253i | 0.627719 | + | 0.362414i | 0.779868 | − | 0.625944i | \(-0.215286\pi\) |
−0.152149 | + | 0.988358i | \(0.548619\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −140.895 | + | 81.3458i | −0.142896 | + | 0.0825008i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −43.0497 | + | 74.5642i | −0.0435725 | + | 0.0754698i | ||||
\(989\) | − | 989.951i | − | 1.00096i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 831.784 | 0.839338 | 0.419669 | − | 0.907677i | \(-0.362146\pi\) | ||||
0.419669 | + | 0.907677i | \(0.362146\pi\) | |||||||
\(992\) | −1177.08 | − | 679.589i | −1.18657 | − | 0.685069i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 462.570 | + | 801.194i | 0.465362 | + | 0.806031i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 439.170 | − | 760.664i | 0.440491 | − | 0.762953i | −0.557235 | − | 0.830355i | \(-0.688138\pi\) |
0.997726 | + | 0.0674021i | \(0.0214710\pi\) | |||||||
\(998\) | 49.3634i | 0.0494623i | ||||||||
\(999\) | 0 | 0 |
(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 | 675.3.j.e.251.7 | 20 | ||
3.2 | odd | 2 | 225.3.j.e.101.4 | 20 | |||
5.2 | odd | 4 | 135.3.h.a.89.4 | 20 | |||
5.3 | odd | 4 | 135.3.h.a.89.7 | 20 | |||
5.4 | even | 2 | inner | 675.3.j.e.251.4 | 20 | ||
9.4 | even | 3 | 225.3.j.e.176.4 | 20 | |||
9.5 | odd | 6 | inner | 675.3.j.e.476.7 | 20 | ||
15.2 | even | 4 | 45.3.h.a.29.7 | yes | 20 | ||
15.8 | even | 4 | 45.3.h.a.29.4 | yes | 20 | ||
15.14 | odd | 2 | 225.3.j.e.101.7 | 20 | |||
45.2 | even | 12 | 405.3.d.a.404.8 | 20 | |||
45.4 | even | 6 | 225.3.j.e.176.7 | 20 | |||
45.7 | odd | 12 | 405.3.d.a.404.13 | 20 | |||
45.13 | odd | 12 | 45.3.h.a.14.7 | yes | 20 | ||
45.14 | odd | 6 | inner | 675.3.j.e.476.4 | 20 | ||
45.22 | odd | 12 | 45.3.h.a.14.4 | ✓ | 20 | ||
45.23 | even | 12 | 135.3.h.a.44.4 | 20 | |||
45.32 | even | 12 | 135.3.h.a.44.7 | 20 | |||
45.38 | even | 12 | 405.3.d.a.404.14 | 20 | |||
45.43 | odd | 12 | 405.3.d.a.404.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.h.a.14.4 | ✓ | 20 | 45.22 | odd | 12 | ||
45.3.h.a.14.7 | yes | 20 | 45.13 | odd | 12 | ||
45.3.h.a.29.4 | yes | 20 | 15.8 | even | 4 | ||
45.3.h.a.29.7 | yes | 20 | 15.2 | even | 4 | ||
135.3.h.a.44.4 | 20 | 45.23 | even | 12 | |||
135.3.h.a.44.7 | 20 | 45.32 | even | 12 | |||
135.3.h.a.89.4 | 20 | 5.2 | odd | 4 | |||
135.3.h.a.89.7 | 20 | 5.3 | odd | 4 | |||
225.3.j.e.101.4 | 20 | 3.2 | odd | 2 | |||
225.3.j.e.101.7 | 20 | 15.14 | odd | 2 | |||
225.3.j.e.176.4 | 20 | 9.4 | even | 3 | |||
225.3.j.e.176.7 | 20 | 45.4 | even | 6 | |||
405.3.d.a.404.7 | 20 | 45.43 | odd | 12 | |||
405.3.d.a.404.8 | 20 | 45.2 | even | 12 | |||
405.3.d.a.404.13 | 20 | 45.7 | odd | 12 | |||
405.3.d.a.404.14 | 20 | 45.38 | even | 12 | |||
675.3.j.e.251.4 | 20 | 5.4 | even | 2 | inner | ||
675.3.j.e.251.7 | 20 | 1.1 | even | 1 | trivial | ||
675.3.j.e.476.4 | 20 | 45.14 | odd | 6 | inner | ||
675.3.j.e.476.7 | 20 | 9.5 | odd | 6 | inner |