Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(80,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.80");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.p (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: | \(26.0198423125\) |
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: | \( x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} + \cdots + 810000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 215.8 | ||
Root | \(4.21355 + 2.43270i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.215 |
Dual form | 441.4.p.c.80.8 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.21355 | + | 2.43270i | 1.48972 | + | 0.860088i | 0.999931 | − | 0.0117558i | \(-0.00374206\pi\) |
0.489785 | + | 0.871843i | \(0.337075\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.83601 | + | 13.5724i | 0.979502 | + | 1.69655i | ||||
\(5\) | 6.38217 | − | 11.0542i | 0.570839 | − | 0.988721i | −0.425642 | − | 0.904892i | \(-0.639952\pi\) |
0.996480 | − | 0.0838295i | \(-0.0267151\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 37.3274i | 1.64965i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 53.7832 | − | 31.0517i | 1.70077 | − | 0.981942i | ||||
\(11\) | 46.8633 | − | 27.0565i | 1.28453 | − | 0.741623i | 0.306856 | − | 0.951756i | \(-0.400723\pi\) |
0.977673 | + | 0.210133i | \(0.0673897\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.85528i | 0.188924i | 0.995528 | + | 0.0944620i | \(0.0301131\pi\) | ||||
−0.995528 | + | 0.0944620i | \(0.969887\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −28.1181 | + | 48.7020i | −0.439345 | + | 0.760968i | ||||
\(17\) | −34.4587 | − | 59.6841i | −0.491615 | − | 0.851502i | 0.508339 | − | 0.861157i | \(-0.330260\pi\) |
−0.999953 | + | 0.00965543i | \(0.996927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 141.898 | + | 81.9246i | 1.71334 | + | 0.989199i | 0.929960 | + | 0.367660i | \(0.119841\pi\) |
0.783383 | + | 0.621540i | \(0.213492\pi\) | |||||||
\(20\) | 200.043 | 2.23655 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 263.281 | 2.55144 | ||||||||
\(23\) | −81.3807 | − | 46.9852i | −0.737785 | − | 0.425960i | 0.0834783 | − | 0.996510i | \(-0.473397\pi\) |
−0.821263 | + | 0.570549i | \(0.806730\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −18.9642 | − | 32.8469i | −0.151713 | − | 0.262775i | ||||
\(26\) | −21.5422 | + | 37.3122i | −0.162491 | + | 0.281443i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 119.620i | 0.765961i | 0.923756 | + | 0.382981i | \(0.125102\pi\) | ||||
−0.923756 | + | 0.382981i | \(0.874898\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −85.6311 | + | 49.4391i | −0.496123 | + | 0.286437i | −0.727111 | − | 0.686520i | \(-0.759137\pi\) |
0.230988 | + | 0.972957i | \(0.425804\pi\) | |||||||
\(32\) | 21.6577 | − | 12.5041i | 0.119643 | − | 0.0690760i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 335.310i | − | 1.69133i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −47.0949 | + | 81.5708i | −0.209253 | + | 0.362437i | −0.951479 | − | 0.307712i | \(-0.900437\pi\) |
0.742227 | + | 0.670149i | \(0.233770\pi\) | |||||||
\(38\) | 398.595 | + | 690.387i | 1.70160 | + | 2.94725i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 412.626 | + | 238.230i | 1.63105 | + | 0.941686i | ||||
\(41\) | 259.347 | 0.987883 | 0.493941 | − | 0.869495i | \(-0.335556\pi\) | ||||
0.493941 | + | 0.869495i | \(0.335556\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.01418 | 0.0177827 | 0.00889133 | − | 0.999960i | \(-0.497170\pi\) | ||||
0.00889133 | + | 0.999960i | \(0.497170\pi\) | |||||||
\(44\) | 734.443 | + | 424.031i | 2.51640 | + | 1.45284i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −228.601 | − | 395.949i | −0.732727 | − | 1.26912i | ||||
\(47\) | 28.6747 | − | 49.6660i | 0.0889921 | − | 0.154139i | −0.818093 | − | 0.575086i | \(-0.804969\pi\) |
0.907085 | + | 0.420947i | \(0.138302\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 184.536i | − | 0.521947i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −120.187 | + | 69.3901i | −0.320518 | + | 0.185051i | ||||
\(53\) | −407.058 | + | 235.015i | −1.05497 | + | 0.609090i | −0.924038 | − | 0.382301i | \(-0.875132\pi\) |
−0.130937 | + | 0.991391i | \(0.541798\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 690.718i | − | 1.69339i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −290.999 | + | 504.025i | −0.658794 | + | 1.14106i | ||||
\(59\) | −112.979 | − | 195.685i | −0.249299 | − | 0.431798i | 0.714033 | − | 0.700112i | \(-0.246867\pi\) |
−0.963331 | + | 0.268314i | \(0.913533\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −370.650 | − | 213.995i | −0.777982 | − | 0.449168i | 0.0577325 | − | 0.998332i | \(-0.481613\pi\) |
−0.835715 | + | 0.549164i | \(0.814946\pi\) | |||||||
\(62\) | −481.082 | −0.985442 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 571.564 | 1.11634 | ||||||||
\(65\) | 97.8884 | + | 56.5159i | 0.186793 | + | 0.107845i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −81.9267 | − | 141.901i | −0.149387 | − | 0.258746i | 0.781614 | − | 0.623762i | \(-0.214397\pi\) |
−0.931001 | + | 0.365016i | \(0.881063\pi\) | |||||||
\(68\) | 540.037 | − | 935.372i | 0.963075 | − | 1.66809i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 79.8529i | 0.133476i | 0.997771 | + | 0.0667380i | \(0.0212592\pi\) | ||||
−0.997771 | + | 0.0667380i | \(0.978741\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −666.447 | + | 384.774i | −1.06852 | + | 0.616909i | −0.927776 | − | 0.373138i | \(-0.878282\pi\) |
−0.140741 | + | 0.990046i | \(0.544949\pi\) | |||||||
\(74\) | −396.874 | + | 229.135i | −0.623454 | + | 0.359952i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2567.85i | 3.87569i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −267.408 | + | 463.165i | −0.380833 | + | 0.659622i | −0.991182 | − | 0.132511i | \(-0.957696\pi\) |
0.610349 | + | 0.792133i | \(0.291029\pi\) | |||||||
\(80\) | 358.909 | + | 621.648i | 0.501590 | + | 0.868780i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1092.77 | + | 630.912i | 1.47166 | + | 0.849666i | ||||
\(83\) | 438.520 | 0.579926 | 0.289963 | − | 0.957038i | \(-0.406357\pi\) | ||||
0.289963 | + | 0.957038i | \(0.406357\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −879.684 | −1.12253 | ||||||||
\(86\) | 21.1275 | + | 12.1980i | 0.0264911 | + | 0.0152947i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1009.95 | + | 1749.29i | 1.22342 | + | 2.11903i | ||||
\(89\) | 12.8242 | − | 22.2121i | 0.0152737 | − | 0.0264548i | −0.858288 | − | 0.513169i | \(-0.828471\pi\) |
0.873561 | + | 0.486714i | \(0.161805\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 1472.71i | − | 1.66892i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 241.644 | − | 139.513i | 0.265146 | − | 0.153082i | ||||
\(95\) | 1811.23 | − | 1045.71i | 1.95608 | − | 1.12935i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1381.00i | 1.44555i | 0.691081 | + | 0.722777i | \(0.257135\pi\) | ||||
−0.691081 | + | 0.722777i | \(0.742865\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 297.207 | − | 514.777i | 0.297207 | − | 0.514777i | ||||
\(101\) | −356.808 | − | 618.009i | −0.351522 | − | 0.608854i | 0.634994 | − | 0.772517i | \(-0.281002\pi\) |
−0.986516 | + | 0.163663i | \(0.947669\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1552.42 | − | 896.288i | −1.48509 | − | 0.857416i | −0.485232 | − | 0.874385i | \(-0.661265\pi\) |
−0.999856 | + | 0.0169695i | \(0.994598\pi\) | |||||||
\(104\) | −330.544 | −0.311659 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2286.88 | −2.09548 | ||||||||
\(107\) | 19.5366 | + | 11.2794i | 0.0176511 | + | 0.0101909i | 0.508800 | − | 0.860885i | \(-0.330089\pi\) |
−0.491148 | + | 0.871076i | \(0.663423\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −476.210 | − | 824.820i | −0.418465 | − | 0.724802i | 0.577320 | − | 0.816518i | \(-0.304098\pi\) |
−0.995785 | + | 0.0917154i | \(0.970765\pi\) | |||||||
\(110\) | 1680.31 | − | 2910.37i | 1.45646 | − | 2.52267i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 120.145i | − | 0.100020i | −0.998749 | − | 0.0500102i | \(-0.984075\pi\) | ||
0.998749 | − | 0.0500102i | \(-0.0159254\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1038.77 | + | 599.735i | −0.842312 | + | 0.486309i | ||||
\(116\) | −1623.53 | + | 937.344i | −1.29949 | + | 0.750260i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1099.37i | − | 0.857674i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 798.612 | − | 1383.24i | 0.600009 | − | 1.03925i | ||||
\(122\) | −1041.17 | − | 1803.36i | −0.772648 | − | 1.33827i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1342.01 | − | 774.812i | −0.971906 | − | 0.561130i | ||||
\(125\) | 1111.41 | 0.795262 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 884.302 | 0.617867 | 0.308934 | − | 0.951084i | \(-0.400028\pi\) | ||||
0.308934 | + | 0.951084i | \(0.400028\pi\) | |||||||
\(128\) | 2235.05 | + | 1290.41i | 1.54338 | + | 0.891071i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 274.972 | + | 476.265i | 0.185512 | + | 0.321317i | ||||
\(131\) | −803.439 | + | 1391.60i | −0.535853 | + | 0.928125i | 0.463268 | + | 0.886218i | \(0.346677\pi\) |
−0.999122 | + | 0.0419070i | \(0.986657\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 797.210i | − | 0.513944i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2227.85 | − | 1286.25i | 1.40468 | − | 0.810994i | ||||
\(137\) | 615.297 | − | 355.242i | 0.383711 | − | 0.221535i | −0.295721 | − | 0.955274i | \(-0.595560\pi\) |
0.679431 | + | 0.733739i | \(0.262227\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1531.91i | − | 0.934782i | −0.884051 | − | 0.467391i | \(-0.845194\pi\) | ||
0.884051 | − | 0.467391i | \(-0.154806\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −194.258 | + | 336.464i | −0.114801 | + | 0.198841i | ||||
\(143\) | 239.593 | + | 414.987i | 0.140110 | + | 0.242678i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1322.31 | + | 763.435i | 0.757322 | + | 0.437240i | ||||
\(146\) | −3744.15 | −2.12238 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1476.15 | −0.819854 | ||||||||
\(149\) | −2079.39 | − | 1200.54i | −1.14329 | − | 0.660079i | −0.196046 | − | 0.980595i | \(-0.562810\pi\) |
−0.947243 | + | 0.320516i | \(0.896144\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1233.99 | − | 2137.33i | −0.665035 | − | 1.15188i | −0.979276 | − | 0.202532i | \(-0.935083\pi\) |
0.314240 | − | 0.949343i | \(-0.398250\pi\) | |||||||
\(152\) | −3058.03 | + | 5296.67i | −1.63184 | + | 2.82642i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1262.12i | 0.654036i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2109.74 | + | 1218.06i | −1.07246 | + | 0.619184i | −0.928852 | − | 0.370451i | \(-0.879203\pi\) |
−0.143606 | + | 0.989635i | \(0.545870\pi\) | |||||||
\(158\) | −2253.48 | + | 1301.05i | −1.13466 | + | 0.655099i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 319.213i | − | 0.157725i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1638.50 | + | 2837.97i | −0.787347 | + | 1.36372i | 0.140240 | + | 0.990118i | \(0.455213\pi\) |
−0.927587 | + | 0.373607i | \(0.878121\pi\) | |||||||
\(164\) | 2032.25 | + | 3519.95i | 0.967633 | + | 1.67599i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1847.73 | + | 1066.79i | 0.863924 | + | 0.498787i | ||||
\(167\) | −365.585 | −0.169400 | −0.0847000 | − | 0.996406i | \(-0.526993\pi\) | ||||
−0.0847000 | + | 0.996406i | \(0.526993\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2118.58 | 0.964308 | ||||||||
\(170\) | −3706.59 | − | 2140.00i | −1.67225 | − | 0.965475i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 39.2912 | + | 68.0543i | 0.0174182 | + | 0.0301691i | ||||
\(173\) | 1046.47 | − | 1812.53i | 0.459892 | − | 0.796557i | −0.539062 | − | 0.842266i | \(-0.681221\pi\) |
0.998955 | + | 0.0457089i | \(0.0145547\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3043.11i | 1.30331i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 108.071 | − | 62.3946i | 0.0455070 | − | 0.0262735i | ||||
\(179\) | 1524.01 | − | 879.890i | 0.636370 | − | 0.367408i | −0.146845 | − | 0.989160i | \(-0.546912\pi\) |
0.783215 | + | 0.621751i | \(0.213578\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3197.54i | − | 1.31310i | −0.754282 | − | 0.656551i | \(-0.772015\pi\) | ||
0.754282 | − | 0.656551i | \(-0.227985\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1753.84 | − | 3037.73i | 0.702687 | − | 1.21709i | ||||
\(185\) | 601.135 | + | 1041.20i | 0.238899 | + | 0.413786i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3229.69 | − | 1864.66i | −1.26299 | − | 0.729186i | ||||
\(188\) | 898.780 | 0.348672 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10175.6 | 3.88535 | ||||||||
\(191\) | 475.772 | + | 274.687i | 0.180239 | + | 0.104061i | 0.587405 | − | 0.809293i | \(-0.300150\pi\) |
−0.407166 | + | 0.913354i | \(0.633483\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 352.238 | + | 610.094i | 0.131371 | + | 0.227542i | 0.924205 | − | 0.381896i | \(-0.124729\pi\) |
−0.792834 | + | 0.609437i | \(0.791395\pi\) | |||||||
\(194\) | −3359.54 | + | 5818.90i | −1.24330 | + | 2.15347i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5317.81i | 1.92324i | 0.274384 | + | 0.961620i | \(0.411526\pi\) | ||||
−0.274384 | + | 0.961620i | \(0.588474\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2155.80 | − | 1244.65i | 0.767942 | − | 0.443371i | −0.0641982 | − | 0.997937i | \(-0.520449\pi\) |
0.832140 | + | 0.554566i | \(0.187116\pi\) | |||||||
\(200\) | 1226.09 | − | 707.883i | 0.433488 | − | 0.250274i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 3472.02i | − | 1.20936i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1655.20 | − | 2866.88i | 0.563922 | − | 0.976741i | ||||
\(206\) | −4360.79 | − | 7553.11i | −1.47491 | − | 2.55461i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −431.269 | − | 248.993i | −0.143765 | − | 0.0830029i | ||||
\(209\) | 8866.38 | 2.93445 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3454.31 | −1.12704 | −0.563519 | − | 0.826103i | \(-0.690553\pi\) | ||||
−0.563519 | + | 0.826103i | \(0.690553\pi\) | |||||||
\(212\) | −6379.42 | − | 3683.16i | −2.06670 | − | 1.19321i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 54.8789 | + | 95.0530i | 0.0175301 | + | 0.0303630i | ||||
\(215\) | 32.0013 | − | 55.4279i | 0.0101510 | − | 0.0175821i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 4633.90i | − | 1.43967i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9374.68 | − | 5412.47i | 2.87291 | − | 1.65868i | ||||
\(221\) | 528.520 | − | 305.141i | 0.160869 | − | 0.0928778i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3896.38i | 1.17005i | 0.811016 | + | 0.585024i | \(0.198915\pi\) | ||||
−0.811016 | + | 0.585024i | \(0.801085\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 292.277 | − | 506.238i | 0.0860263 | − | 0.149002i | ||||
\(227\) | −302.747 | − | 524.374i | −0.0885201 | − | 0.153321i | 0.818366 | − | 0.574698i | \(-0.194880\pi\) |
−0.906886 | + | 0.421377i | \(0.861547\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1912.98 | + | 1104.46i | 0.552023 | + | 0.318711i | 0.749938 | − | 0.661509i | \(-0.230083\pi\) |
−0.197914 | + | 0.980219i | \(0.563417\pi\) | |||||||
\(230\) | −5835.89 | −1.67307 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4465.10 | −1.26357 | ||||||||
\(233\) | 2065.77 | + | 1192.67i | 0.580829 | + | 0.335342i | 0.761463 | − | 0.648209i | \(-0.224482\pi\) |
−0.180634 | + | 0.983550i | \(0.557815\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −366.013 | − | 633.953i | −0.101600 | − | 0.175977i | ||||
\(236\) | 1770.61 | − | 3066.79i | 0.488377 | − | 0.845893i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3017.95i | 0.816798i | 0.912803 | + | 0.408399i | \(0.133913\pi\) | ||||
−0.912803 | + | 0.408399i | \(0.866087\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2178.48 | − | 1257.75i | 0.582275 | − | 0.336176i | −0.179762 | − | 0.983710i | \(-0.557533\pi\) |
0.762037 | + | 0.647534i | \(0.224200\pi\) | |||||||
\(242\) | 6729.99 | − | 3885.56i | 1.78769 | − | 1.03212i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 6707.47i | − | 1.75984i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −725.465 | + | 1256.54i | −0.186883 | + | 0.323692i | ||||
\(248\) | −1845.44 | − | 3196.39i | −0.472521 | − | 0.818431i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4682.99 | + | 2703.73i | 1.18471 | + | 0.683995i | ||||
\(251\) | −1306.11 | −0.328451 | −0.164226 | − | 0.986423i | \(-0.552512\pi\) | ||||
−0.164226 | + | 0.986423i | \(0.552512\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5085.03 | −1.26361 | ||||||||
\(254\) | 3726.05 | + | 2151.24i | 0.920447 | + | 0.531420i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3992.09 | + | 6914.50i | 0.974630 | + | 1.68811i | ||||
\(257\) | −3735.91 | + | 6470.79i | −0.906770 | + | 1.57057i | −0.0882460 | + | 0.996099i | \(0.528126\pi\) |
−0.818524 | + | 0.574473i | \(0.805207\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1771.44i | 0.422538i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6770.66 | + | 3909.04i | −1.59654 | + | 0.921762i | ||||
\(263\) | −1330.77 | + | 768.318i | −0.312010 | + | 0.180139i | −0.647825 | − | 0.761789i | \(-0.724321\pi\) |
0.335816 | + | 0.941928i | \(0.390988\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5999.62i | 1.39077i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1283.96 | − | 2223.88i | 0.292650 | − | 0.506884i | ||||
\(269\) | −1958.09 | − | 3391.52i | −0.443818 | − | 0.768715i | 0.554151 | − | 0.832416i | \(-0.313043\pi\) |
−0.997969 | + | 0.0637010i | \(0.979710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3117.42 | − | 1799.84i | −0.698780 | − | 0.403441i | 0.108113 | − | 0.994139i | \(-0.465519\pi\) |
−0.806893 | + | 0.590698i | \(0.798853\pi\) | |||||||
\(272\) | 3875.65 | 0.863955 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3456.78 | 0.762159 | ||||||||
\(275\) | −1777.45 | − | 1026.21i | −0.389760 | − | 0.225028i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −142.040 | − | 246.021i | −0.0308100 | − | 0.0533645i | 0.850209 | − | 0.526445i | \(-0.176475\pi\) |
−0.881019 | + | 0.473080i | \(0.843142\pi\) | |||||||
\(278\) | 3726.67 | − | 6454.77i | 0.803995 | − | 1.39256i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 321.256i | − | 0.0682011i | −0.999418 | − | 0.0341006i | \(-0.989143\pi\) | ||
0.999418 | − | 0.0341006i | \(-0.0108566\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5891.40 | + | 3401.40i | −1.23748 | + | 0.714460i | −0.968579 | − | 0.248707i | \(-0.919994\pi\) |
−0.268903 | + | 0.963167i | \(0.586661\pi\) | |||||||
\(284\) | −1083.79 | + | 625.728i | −0.226448 | + | 0.130740i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2331.43i | 0.482029i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 81.7017 | − | 141.511i | 0.0166297 | − | 0.0288035i | ||||
\(290\) | 3714.41 | + | 6433.55i | 0.752130 | + | 1.30273i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10444.6 | − | 6030.18i | −2.09323 | − | 1.20853i | ||||
\(293\) | −3180.05 | −0.634063 | −0.317031 | − | 0.948415i | \(-0.602686\pi\) | ||||
−0.317031 | + | 0.948415i | \(0.602686\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2884.20 | −0.569237 | ||||||||
\(296\) | −3044.83 | − | 1757.93i | −0.597895 | − | 0.345195i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5841.07 | − | 10117.0i | −1.13545 | − | 1.96666i | ||||
\(299\) | 416.067 | − | 720.649i | 0.0804741 | − | 0.139385i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 12007.6i | − | 2.28795i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7979.78 | + | 4607.13i | −1.50550 | + | 0.869200i | ||||
\(305\) | −4731.11 | + | 2731.51i | −0.888204 | + | 0.512805i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2976.39i | 0.553328i | 0.960967 | + | 0.276664i | \(0.0892289\pi\) | ||||
−0.960967 | + | 0.276664i | \(0.910771\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3070.34 | + | 5317.99i | −0.562528 | + | 0.974328i | ||||
\(311\) | 2340.89 | + | 4054.55i | 0.426817 | + | 0.739268i | 0.996588 | − | 0.0825352i | \(-0.0263017\pi\) |
−0.569772 | + | 0.821803i | \(0.692968\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 850.477 | + | 491.023i | 0.153584 | + | 0.0886718i | 0.574823 | − | 0.818278i | \(-0.305071\pi\) |
−0.421238 | + | 0.906950i | \(0.638404\pi\) | |||||||
\(314\) | −11852.7 | −2.13021 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8381.66 | −1.49211 | ||||||||
\(317\) | 4269.80 | + | 2465.17i | 0.756516 | + | 0.436775i | 0.828044 | − | 0.560664i | \(-0.189454\pi\) |
−0.0715272 | + | 0.997439i | \(0.522787\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3236.50 | + | 5605.79i | 0.568055 | + | 0.983899i | ||||
\(320\) | 3647.82 | − | 6318.21i | 0.637248 | − | 1.10375i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11292.0i | − | 1.94522i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 290.868 | − | 167.933i | 0.0496445 | − | 0.0286623i | ||||
\(326\) | −13807.8 | + | 7971.96i | −2.34585 | + | 1.35437i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9680.75i | 1.62966i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2017.25 | − | 3493.99i | 0.334980 | − | 0.580202i | −0.648501 | − | 0.761214i | \(-0.724604\pi\) |
0.983481 | + | 0.181012i | \(0.0579372\pi\) | |||||||
\(332\) | 3436.25 | + | 5951.76i | 0.568038 | + | 0.983871i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1540.41 | − | 889.356i | −0.252358 | − | 0.145699i | ||||
\(335\) | −2091.48 | −0.341104 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2771.62 | 0.448011 | 0.224006 | − | 0.974588i | \(-0.428087\pi\) | ||||
0.224006 | + | 0.974588i | \(0.428087\pi\) | |||||||
\(338\) | 8926.76 | + | 5153.87i | 1.43654 | + | 0.829389i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6893.21 | − | 11939.4i | −1.09952 | − | 1.90443i | ||||
\(341\) | −2675.30 | + | 4633.76i | −0.424856 | + | 0.735872i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 187.166i | 0.0293352i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8818.68 | − | 5091.47i | 1.37022 | − | 0.791095i | ||||
\(347\) | −3743.15 | + | 2161.11i | −0.579085 | + | 0.334335i | −0.760770 | − | 0.649022i | \(-0.775178\pi\) |
0.181685 | + | 0.983357i | \(0.441845\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1331.65i | − | 0.204245i | −0.994772 | − | 0.102122i | \(-0.967437\pi\) | ||
0.994772 | − | 0.102122i | \(-0.0325634\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 676.635 | − | 1171.97i | 0.102457 | − | 0.177460i | ||||
\(353\) | 5674.26 | + | 9828.10i | 0.855553 | + | 1.48186i | 0.876131 | + | 0.482073i | \(0.160116\pi\) |
−0.0205782 | + | 0.999788i | \(0.506551\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 882.713 | + | 509.634i | 0.131970 | + | 0.0761932i | ||||
\(356\) | 401.962 | 0.0598425 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8562.02 | 1.26401 | ||||||||
\(359\) | −7247.49 | − | 4184.34i | −1.06548 | − | 0.615156i | −0.138538 | − | 0.990357i | \(-0.544240\pi\) |
−0.926943 | + | 0.375201i | \(0.877574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9993.77 | + | 17309.7i | 1.45703 | + | 2.52365i | ||||
\(362\) | 7778.64 | − | 13473.0i | 1.12938 | − | 1.95615i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9822.76i | 1.40862i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2351.31 | + | 1357.53i | −0.334434 | + | 0.193086i | −0.657808 | − | 0.753186i | \(-0.728516\pi\) |
0.323374 | + | 0.946271i | \(0.395183\pi\) | |||||||
\(368\) | 4576.54 | − | 2642.27i | 0.648285 | − | 0.374287i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5849.52i | 0.821897i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3048.56 | + | 5280.25i | −0.423186 | + | 0.732979i | −0.996249 | − | 0.0865320i | \(-0.972422\pi\) |
0.573063 | + | 0.819511i | \(0.305755\pi\) | |||||||
\(374\) | −9072.32 | − | 15713.7i | −1.25433 | − | 2.17256i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1853.90 | + | 1070.35i | 0.254276 | + | 0.146806i | ||||
\(377\) | −1059.27 | −0.144708 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9922.24 | −1.34478 | −0.672389 | − | 0.740198i | \(-0.734732\pi\) | ||||
−0.672389 | + | 0.740198i | \(0.734732\pi\) | |||||||
\(380\) | 28385.6 | + | 16388.4i | 3.83198 | + | 2.21239i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1336.46 | + | 2314.82i | 0.179003 | + | 0.310043i | ||||
\(383\) | 609.532 | − | 1055.74i | 0.0813202 | − | 0.140851i | −0.822497 | − | 0.568769i | \(-0.807420\pi\) |
0.903817 | + | 0.427919i | \(0.140753\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3427.55i | 0.451963i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18743.4 | + | 10821.5i | −2.45245 | + | 1.41592i | ||||
\(389\) | 11374.6 | − | 6567.15i | 1.48256 | − | 0.855958i | 0.482759 | − | 0.875753i | \(-0.339635\pi\) |
0.999804 | + | 0.0197949i | \(0.00630133\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6476.19i | 0.837634i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12936.6 | + | 22406.9i | −1.65416 | + | 2.86508i | ||||
\(395\) | 3413.29 | + | 5911.99i | 0.434788 | + | 0.753075i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2697.68 | − | 1557.51i | −0.341040 | − | 0.196900i | 0.319692 | − | 0.947522i | \(-0.396421\pi\) |
−0.660732 | + | 0.750622i | \(0.729754\pi\) | |||||||
\(398\) | 12111.4 | 1.52535 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2132.94 | 0.266618 | ||||||||
\(401\) | −9724.47 | − | 5614.42i | −1.21101 | − | 0.699179i | −0.248034 | − | 0.968751i | \(-0.579784\pi\) |
−0.962980 | + | 0.269572i | \(0.913118\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −437.797 | − | 758.287i | −0.0541147 | − | 0.0937295i | ||||
\(404\) | 5591.90 | − | 9685.46i | 0.688633 | − | 1.19275i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5096.90i | 0.620747i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10739.4 | − | 6200.41i | 1.29836 | − | 0.749610i | 0.318242 | − | 0.948010i | \(-0.396908\pi\) |
0.980121 | + | 0.198399i | \(0.0635743\pi\) | |||||||
\(410\) | 13948.5 | − | 8053.18i | 1.68017 | − | 0.970044i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 28093.3i | − | 3.35936i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2798.71 | − | 4847.51i | 0.331044 | − | 0.573385i | ||||
\(416\) | 110.727 | + | 191.785i | 0.0130501 | + | 0.0226035i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 37359.0 | + | 21569.2i | 4.37150 | + | 2.52389i | ||||
\(419\) | 8260.19 | 0.963095 | 0.481547 | − | 0.876420i | \(-0.340075\pi\) | ||||
0.481547 | + | 0.876420i | \(0.340075\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5571.81 | 0.645020 | 0.322510 | − | 0.946566i | \(-0.395473\pi\) | ||||
0.322510 | + | 0.946566i | \(0.395473\pi\) | |||||||
\(422\) | −14554.9 | − | 8403.30i | −1.67896 | − | 0.969351i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8772.49 | − | 15194.4i | −1.00479 | − | 1.74034i | ||||
\(425\) | −1306.96 | + | 2263.72i | −0.149169 | + | 0.258368i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 353.543i | 0.0399279i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 269.678 | − | 155.699i | 0.0302443 | − | 0.0174616i | ||||
\(431\) | −6094.88 | + | 3518.88i | −0.681160 | + | 0.393268i | −0.800292 | − | 0.599611i | \(-0.795322\pi\) |
0.119132 | + | 0.992878i | \(0.461989\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9212.26i | 1.02243i | 0.859452 | + | 0.511216i | \(0.170805\pi\) | ||||
−0.859452 | + | 0.511216i | \(0.829195\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7463.18 | − | 12926.6i | 0.819774 | − | 1.41989i | ||||
\(437\) | −7698.48 | − | 13334.2i | −0.842719 | − | 1.45963i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7345.30 | + | 4240.81i | 0.798570 | + | 0.461054i | 0.842971 | − | 0.537959i | \(-0.180805\pi\) |
−0.0444012 | + | 0.999014i | \(0.514138\pi\) | |||||||
\(440\) | 25782.7 | 2.79350 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2969.26 | 0.319532 | ||||||||
\(443\) | 11305.9 | + | 6527.49i | 1.21255 | + | 0.700068i | 0.963315 | − | 0.268374i | \(-0.0864863\pi\) |
0.249239 | + | 0.968442i | \(0.419820\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −163.692 | − | 283.523i | −0.0174376 | − | 0.0302029i | ||||
\(446\) | −9478.70 | + | 16417.6i | −1.00634 | + | 1.74304i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 14114.0i | − | 1.48348i | −0.670689 | − | 0.741738i | \(-0.734002\pi\) | ||
0.670689 | − | 0.741738i | \(-0.265998\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12153.9 | − | 7017.03i | 1.26896 | − | 0.732637i | ||||
\(452\) | 1630.66 | − | 941.459i | 0.169689 | − | 0.0979702i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 2945.97i | − | 0.304540i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4486.87 | − | 7771.49i | 0.459271 | − | 0.795481i | −0.539651 | − | 0.841889i | \(-0.681444\pi\) |
0.998923 | + | 0.0464073i | \(0.0147772\pi\) | |||||||
\(458\) | 5373.63 | + | 9307.40i | 0.548238 | + | 0.949577i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −16279.7 | − | 9399.06i | −1.65009 | − | 0.952682i | ||||
\(461\) | −955.010 | −0.0964842 | −0.0482421 | − | 0.998836i | \(-0.515362\pi\) | ||||
−0.0482421 | + | 0.998836i | \(0.515362\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12004.5 | 1.20496 | 0.602479 | − | 0.798135i | \(-0.294180\pi\) | ||||
0.602479 | + | 0.798135i | \(0.294180\pi\) | |||||||
\(464\) | −5825.73 | − | 3363.49i | −0.582872 | − | 0.336521i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5802.82 | + | 10050.8i | 0.576846 | + | 0.999127i | ||||
\(467\) | −2532.46 | + | 4386.34i | −0.250938 | + | 0.434638i | −0.963784 | − | 0.266683i | \(-0.914072\pi\) |
0.712846 | + | 0.701320i | \(0.247406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 3561.59i | − | 0.349540i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7304.43 | − | 4217.21i | 0.712317 | − | 0.411256i | ||||
\(473\) | 234.981 | − | 135.666i | 0.0228423 | − | 0.0131880i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6214.52i | − | 0.600299i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7341.75 | + | 12716.3i | −0.702518 | + | 1.21680i | ||||
\(479\) | 7606.85 | + | 13175.5i | 0.725607 | + | 1.25679i | 0.958724 | + | 0.284340i | \(0.0917744\pi\) |
−0.233116 | + | 0.972449i | \(0.574892\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −722.332 | − | 417.038i | −0.0684730 | − | 0.0395329i | ||||
\(482\) | 12238.8 | 1.15656 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 25031.7 | 2.35084 | ||||||||
\(485\) | 15265.9 | + | 8813.75i | 1.42925 | + | 0.825179i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7905.92 | − | 13693.5i | −0.735629 | − | 1.27415i | −0.954447 | − | 0.298382i | \(-0.903553\pi\) |
0.218817 | − | 0.975766i | \(-0.429780\pi\) | |||||||
\(488\) | 7987.88 | − | 13835.4i | 0.740972 | − | 1.28340i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18064.2i | 1.66034i | 0.557512 | + | 0.830169i | \(0.311756\pi\) | ||||
−0.557512 | + | 0.830169i | \(0.688244\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7139.42 | − | 4121.94i | 0.652217 | − | 0.376558i | ||||
\(494\) | −6113.57 | + | 3529.67i | −0.556806 | + | 0.321472i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 5560.54i | − | 0.503378i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5262.33 | − | 9114.62i | 0.472092 | − | 0.817688i | −0.527398 | − | 0.849619i | \(-0.676832\pi\) |
0.999490 | + | 0.0319305i | \(0.0101655\pi\) | |||||||
\(500\) | 8709.04 | + | 15084.5i | 0.778960 | + | 1.34920i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5503.38 | − | 3177.38i | −0.489299 | − | 0.282497i | ||||
\(503\) | −7790.82 | −0.690607 | −0.345304 | − | 0.938491i | \(-0.612224\pi\) | ||||
−0.345304 | + | 0.938491i | \(0.612224\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9108.83 | −0.802649 | ||||||||
\(506\) | −21426.0 | − | 12370.3i | −1.88242 | − | 1.08681i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6929.41 | + | 12002.1i | 0.605202 | + | 1.04824i | ||||
\(509\) | 5098.24 | − | 8830.41i | 0.443960 | − | 0.768961i | −0.554019 | − | 0.832504i | \(-0.686907\pi\) |
0.997979 | + | 0.0635430i | \(0.0202400\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 18199.6i | 1.57093i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −31482.9 | + | 18176.7i | −2.70166 | + | 1.55980i | ||||
\(515\) | −19815.6 | + | 11440.5i | −1.69549 | + | 0.978892i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3103.35i | − | 0.263994i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2109.59 | + | 3653.92i | −0.177907 | + | 0.308144i | ||||
\(521\) | 963.789 | + | 1669.33i | 0.0810449 | + | 0.140374i | 0.903699 | − | 0.428168i | \(-0.140841\pi\) |
−0.822654 | + | 0.568542i | \(0.807508\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6716.70 | + | 3877.89i | 0.561569 | + | 0.324222i | 0.753775 | − | 0.657133i | \(-0.228231\pi\) |
−0.192206 | + | 0.981355i | \(0.561564\pi\) | |||||||
\(524\) | −25183.0 | −2.09948 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7476.33 | −0.619741 | ||||||||
\(527\) | 5901.47 | + | 3407.21i | 0.487803 | + | 0.281633i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1668.28 | − | 2889.55i | −0.137115 | − | 0.237491i | ||||
\(530\) | −14595.2 | + | 25279.7i | −1.19618 | + | 2.07185i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2296.59i | 0.186635i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 249.371 | − | 143.975i | 0.0201519 | − | 0.0116347i | ||||
\(536\) | 5296.80 | − | 3058.11i | 0.426841 | − | 0.246437i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 19053.8i | − | 1.52689i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8380.42 | + | 14515.3i | −0.665993 | + | 1.15353i | 0.313022 | + | 0.949746i | \(0.398659\pi\) |
−0.979015 | + | 0.203788i | \(0.934675\pi\) | |||||||
\(542\) | −8756.93 | − | 15167.4i | −0.693989 | − | 1.20202i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1492.59 | − | 861.748i | −0.117637 | − | 0.0679176i | ||||
\(545\) | −12157.0 | −0.955503 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5869.79 | 0.458819 | 0.229410 | − | 0.973330i | \(-0.426320\pi\) | ||||
0.229410 | + | 0.973330i | \(0.426320\pi\) | |||||||
\(548\) | 9642.95 | + | 5567.36i | 0.751690 | + | 0.433989i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4992.91 | − | 8647.97i | −0.387088 | − | 0.670456i | ||||
\(551\) | −9799.82 | + | 16973.8i | −0.757688 | + | 1.31235i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 1382.16i | − | 0.105997i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20791.6 | − | 12004.1i | 1.58590 | − | 0.915621i | ||||
\(557\) | 18756.5 | − | 10829.1i | 1.42682 | − | 0.823774i | 0.429951 | − | 0.902852i | \(-0.358531\pi\) |
0.996868 | + | 0.0790779i | \(0.0251976\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.4019i | 0.00335957i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 781.517 | − | 1353.63i | 0.0586589 | − | 0.101600i | ||||
\(563\) | 4795.36 | + | 8305.80i | 0.358970 | + | 0.621755i | 0.987789 | − | 0.155797i | \(-0.0497946\pi\) |
−0.628819 | + | 0.777552i | \(0.716461\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1328.11 | − | 766.787i | −0.0988923 | − | 0.0570955i | ||||
\(566\) | −33098.3 | −2.45799 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2980.70 | −0.220189 | ||||||||
\(569\) | −14405.5 | − | 8317.01i | −1.06135 | − | 0.612772i | −0.135546 | − | 0.990771i | \(-0.543279\pi\) |
−0.925806 | + | 0.377999i | \(0.876612\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3165.51 | − | 5482.83i | −0.232001 | − | 0.401838i | 0.726396 | − | 0.687277i | \(-0.241194\pi\) |
−0.958397 | + | 0.285439i | \(0.907861\pi\) | |||||||
\(572\) | −3754.91 | + | 6503.69i | −0.274477 | + | 0.475408i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3564.14i | 0.258495i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8431.94 | + | 4868.18i | −0.608364 | + | 0.351239i | −0.772325 | − | 0.635228i | \(-0.780906\pi\) |
0.163961 | + | 0.986467i | \(0.447573\pi\) | |||||||
\(578\) | 688.509 | − | 397.511i | 0.0495470 | − | 0.0286060i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 23929.1i | 1.71311i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12717.4 | + | 22027.1i | −0.903430 | + | 1.56479i | ||||
\(584\) | −14362.6 | − | 24876.8i | −1.01769 | − | 1.76268i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13399.3 | − | 7736.09i | −0.944573 | − | 0.545350i | ||||
\(587\) | 10940.3 | 0.769255 | 0.384628 | − | 0.923072i | \(-0.374330\pi\) | ||||
0.384628 | + | 0.923072i | \(0.374330\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16201.1 | −1.13337 | ||||||||
\(590\) | −12152.7 | − | 7016.39i | −0.848001 | − | 0.489594i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2648.44 | − | 4587.23i | −0.183869 | − | 0.318470i | ||||
\(593\) | 12430.4 | − | 21530.0i | 0.860799 | − | 1.49095i | −0.0103608 | − | 0.999946i | \(-0.503298\pi\) |
0.871159 | − | 0.491000i | \(-0.163369\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 37629.6i | − | 2.58619i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3506.24 | − | 2024.33i | 0.239767 | − | 0.138430i | ||||
\(599\) | −20207.8 | + | 11667.0i | −1.37841 | + | 0.795825i | −0.991968 | − | 0.126488i | \(-0.959629\pi\) |
−0.386442 | + | 0.922314i | \(0.626296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13012.4i | 0.883175i | 0.897218 | + | 0.441587i | \(0.145584\pi\) | ||||
−0.897218 | + | 0.441587i | \(0.854416\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19339.1 | − | 33496.2i | 1.30281 | − | 2.25653i | ||||
\(605\) | −10193.8 | − | 17656.1i | −0.685017 | − | 1.18648i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7355.69 | − | 4246.81i | −0.491859 | − | 0.283975i | 0.233486 | − | 0.972360i | \(-0.424987\pi\) |
−0.725345 | + | 0.688385i | \(0.758320\pi\) | |||||||
\(608\) | 4097.57 | 0.273320 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −26579.7 | −1.76423 | ||||||||
\(611\) | 439.806 | + | 253.922i | 0.0291205 | + | 0.0168127i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4569.79 | + | 7915.11i | 0.301097 | + | 0.521514i | 0.976385 | − | 0.216040i | \(-0.0693140\pi\) |
−0.675288 | + | 0.737554i | \(0.735981\pi\) | |||||||
\(614\) | −7240.66 | + | 12541.2i | −0.475911 | + | 0.824302i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7360.91i | − | 0.480290i | −0.970737 | − | 0.240145i | \(-0.922805\pi\) | ||
0.970737 | − | 0.240145i | \(-0.0771950\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19878.5 | + | 11476.9i | −1.29077 | + | 0.745225i | −0.978790 | − | 0.204864i | \(-0.934325\pi\) |
−0.311978 | + | 0.950089i | \(0.600991\pi\) | |||||||
\(620\) | −17129.9 | + | 9889.96i | −1.10960 | + | 0.640629i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22778.7i | 1.46840i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9463.74 | − | 16391.7i | 0.605679 | − | 1.04907i | ||||
\(626\) | 2389.02 | + | 4137.91i | 0.152531 | + | 0.264192i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −33064.0 | − | 19089.5i | −2.10095 | − | 1.21298i | ||||
\(629\) | 6491.31 | 0.411487 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21126.0 | 1.33282 | 0.666412 | − | 0.745584i | \(-0.267829\pi\) | ||||
0.666412 | + | 0.745584i | \(0.267829\pi\) | |||||||
\(632\) | −17288.7 | − | 9981.66i | −1.08815 | − | 0.628242i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11994.0 | + | 20774.2i | 0.751330 | + | 1.30134i | ||||
\(635\) | 5643.77 | − | 9775.29i | 0.352703 | − | 0.610899i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 31493.7i | 1.95431i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 28529.0 | − | 16471.2i | 1.76204 | − | 1.01732i | ||||
\(641\) | 15447.5 | − | 8918.61i | 0.951855 | − | 0.549554i | 0.0581985 | − | 0.998305i | \(-0.481464\pi\) |
0.893657 | + | 0.448751i | \(0.148131\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 25449.0i | − | 1.56082i | −0.625266 | − | 0.780412i | \(-0.715009\pi\) | ||
0.625266 | − | 0.780412i | \(-0.284991\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 27470.1 | − | 47579.6i | 1.67306 | − | 2.89782i | ||||
\(647\) | −13149.2 | − | 22775.1i | −0.798993 | − | 1.38390i | −0.920273 | − | 0.391277i | \(-0.872033\pi\) |
0.121280 | − | 0.992618i | \(-0.461300\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10589.1 | − | 6113.64i | −0.640462 | − | 0.369771i | ||||
\(650\) | 1634.12 | 0.0986083 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −51357.4 | −3.08483 | ||||||||
\(653\) | −8203.79 | − | 4736.46i | −0.491637 | − | 0.283847i | 0.233616 | − | 0.972329i | \(-0.424944\pi\) |
−0.725253 | + | 0.688482i | \(0.758277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10255.4 | + | 17762.8i | 0.611771 | + | 1.05962i | ||||
\(656\) | −7292.34 | + | 12630.7i | −0.434022 | + | 0.751747i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 22384.5i | − | 1.32318i | −0.749865 | − | 0.661591i | \(-0.769882\pi\) | ||
0.749865 | − | 0.661591i | \(-0.230118\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19857.3 | − | 11464.6i | 1.16847 | − | 0.674618i | 0.215153 | − | 0.976580i | \(-0.430975\pi\) |
0.953320 | + | 0.301962i | \(0.0976415\pi\) | |||||||
\(662\) | 16999.6 | − | 9814.73i | 0.998049 | − | 0.576224i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16368.8i | 0.956677i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5620.37 | − | 9734.77i | 0.326269 | − | 0.565115i | ||||
\(668\) | −2864.73 | − | 4961.85i | −0.165928 | − | 0.287395i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8812.56 | − | 5087.93i | −0.508147 | − | 0.293379i | ||||
\(671\) | −23159.9 | −1.33245 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4873.86 | −0.279158 | −0.139579 | − | 0.990211i | \(-0.544575\pi\) | ||||
−0.139579 | + | 0.990211i | \(0.544575\pi\) | |||||||
\(674\) | 11678.4 | + | 6742.51i | 0.667409 | + | 0.385329i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16601.3 | + | 28754.2i | 0.944541 | + | 1.63599i | ||||
\(677\) | 8123.71 | − | 14070.7i | 0.461181 | − | 0.798789i | −0.537839 | − | 0.843048i | \(-0.680759\pi\) |
0.999020 | + | 0.0442583i | \(0.0140925\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 32836.3i | − | 1.85179i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −22545.1 | + | 13016.4i | −1.26583 | + | 0.730827i | ||||
\(683\) | 18786.2 | − | 10846.2i | 1.05247 | − | 0.607641i | 0.129127 | − | 0.991628i | \(-0.458783\pi\) |
0.923339 | + | 0.383987i | \(0.125449\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 9068.85i | − | 0.505844i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −140.989 | + | 244.200i | −0.00781273 | + | 0.0135320i | ||||
\(689\) | −2081.12 | − | 3604.61i | −0.115072 | − | 0.199310i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19499.9 | + | 11258.3i | 1.07353 | + | 0.619803i | 0.929144 | − | 0.369718i | \(-0.120546\pi\) |
0.144387 | + | 0.989521i | \(0.453879\pi\) | |||||||
\(692\) | 32800.5 | 1.80186 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21029.2 | −1.15023 | ||||||||
\(695\) | −16934.1 | − | 9776.90i | −0.924239 | − | 0.533610i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8936.75 | − | 15478.9i | −0.485658 | − | 0.841184i | ||||
\(698\) | 3239.49 | − | 5610.97i | 0.175669 | − | 0.304267i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 33929.0i | − | 1.82807i | −0.405631 | − | 0.914037i | \(-0.632948\pi\) | ||
0.405631 | − | 0.914037i | \(-0.367052\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13365.3 | + | 7716.46i | −0.717044 | + | 0.413986i | ||||
\(704\) | 26785.4 | − | 15464.5i | 1.43397 | − | 0.827901i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 55214.9i | 2.94340i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9593.62 | + | 16616.6i | −0.508175 | + | 0.880185i | 0.491780 | + | 0.870719i | \(0.336346\pi\) |
−0.999955 | + | 0.00946553i | \(0.996987\pi\) | |||||||
\(710\) | 2479.57 | + | 4294.74i | 0.131066 | + | 0.227012i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 829.121 | + | 478.693i | 0.0436413 | + | 0.0251963i | ||||
\(713\) | 9291.63 | 0.488043 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6116.49 | 0.319922 | ||||||||
\(716\) | 23884.4 | + | 13789.7i | 1.24665 | + | 0.719754i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20358.4 | − | 35261.8i | −1.05818 | − | 1.83281i | ||||
\(719\) | 6883.43 | − | 11922.4i | 0.357036 | − | 0.618404i | −0.630429 | − | 0.776247i | \(-0.717121\pi\) |
0.987464 | + | 0.157844i | \(0.0504542\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 97247.2i | 5.01269i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 43398.2 | − | 25056.0i | 2.22774 | − | 1.28618i | ||||
\(725\) | 3929.15 | − | 2268.49i | 0.201276 | − | 0.116207i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12226.1i | − | 0.623717i | −0.950129 | − | 0.311858i | \(-0.899049\pi\) | ||
0.950129 | − | 0.311858i | \(-0.100951\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −23895.8 | + | 41388.7i | −1.21154 | + | 2.09845i | ||||
\(731\) | −172.782 | − | 299.267i | −0.00874222 | − | 0.0151420i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2256.76 | − | 1302.94i | −0.113718 | − | 0.0656553i | 0.442062 | − | 0.896984i | \(-0.354247\pi\) |
−0.555780 | + | 0.831329i | \(0.687580\pi\) | |||||||
\(734\) | −13209.8 | −0.664282 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2350.03 | −0.117695 | ||||||||
\(737\) | −7678.71 | − | 4433.30i | −0.383784 | − | 0.221578i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16871.7 | − | 29222.7i | −0.839833 | − | 1.45463i | −0.890034 | − | 0.455894i | \(-0.849320\pi\) |
0.0502016 | − | 0.998739i | \(-0.484014\pi\) | |||||||
\(740\) | −9421.01 | + | 16317.7i | −0.468004 | + | 0.810607i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 14586.9i | − | 0.720244i | −0.932905 | − | 0.360122i | \(-0.882735\pi\) | ||
0.932905 | − | 0.360122i | \(-0.117265\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26542.0 | + | 15324.0i | −1.30527 | + | 0.753597i | ||||
\(746\) | −25690.5 | + | 14832.4i | −1.26085 | + | 0.727953i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 58446.1i | − | 2.85695i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3757.62 | − | 6508.39i | 0.182580 | − | 0.316238i | −0.760178 | − | 0.649714i | \(-0.774889\pi\) |
0.942758 | + | 0.333477i | \(0.108222\pi\) | |||||||
\(752\) | 1612.55 | + | 2793.02i | 0.0781965 | + | 0.135440i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4463.28 | − | 2576.88i | −0.215574 | − | 0.124462i | ||||
\(755\) | −31502.0 | −1.51851 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23917.4 | 1.14834 | 0.574169 | − | 0.818737i | \(-0.305325\pi\) | ||||
0.574169 | + | 0.818737i | \(0.305325\pi\) | |||||||
\(758\) | −41807.9 | − | 24137.8i | −2.00334 | − | 1.15663i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 39033.7 | + | 67608.4i | 1.86303 | + | 3.22686i | ||||
\(761\) | −6099.27 | + | 10564.2i | −0.290537 | + | 0.503224i | −0.973937 | − | 0.226820i | \(-0.927167\pi\) |
0.683400 | + | 0.730044i | \(0.260500\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 8609.80i | 0.407712i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5136.59 | − | 2965.61i | 0.242288 | − | 0.139885i | ||||
\(767\) | 1732.85 | − | 1000.46i | 0.0815769 | − | 0.0470985i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2013.08i | − | 0.0943999i | −0.998885 | − | 0.0471999i | \(-0.984970\pi\) | ||
0.998885 | − | 0.0471999i | \(-0.0150298\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5520.28 | + | 9561.41i | −0.257357 | + | 0.445755i | ||||
\(773\) | −15139.1 | − | 26221.7i | −0.704418 | − | 1.22009i | −0.966901 | − | 0.255152i | \(-0.917875\pi\) |
0.262483 | − | 0.964937i | \(-0.415459\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3247.85 | + | 1875.14i | 0.150537 | + | 0.0869125i | ||||
\(776\) | −51549.0 | −2.38467 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 63903.5 | 2.94480 | ||||||||
\(779\) | 36800.7 | + | 21246.9i | 1.69258 | + | 0.977213i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2160.54 | + | 3742.17i | 0.0989888 | + | 0.171454i | ||||
\(782\) | −15754.6 | + | 27287.8i | −0.720439 | + | 1.24784i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 31095.5i | 1.41382i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24839.3 | + | 14341.0i | −1.12507 | + | 0.649557i | −0.942689 | − | 0.333671i | \(-0.891712\pi\) |
−0.182377 | + | 0.983229i | \(0.558379\pi\) | |||||||
\(788\) | −72175.3 | + | 41670.4i | −3.26287 | + | 1.88382i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 33214.0i | 1.49582i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1894.99 | − | 3282.21i | 0.0848586 | − | 0.146979i | ||||
\(794\) | −7577.89 | − | 13125.3i | −0.338702 | − | 0.586649i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 33785.7 | + | 19506.2i | 1.50440 | + | 0.868566i | ||||
\(797\) | 27108.9 | 1.20483 | 0.602413 | − | 0.798184i | \(-0.294206\pi\) | ||||
0.602413 | + | 0.798184i | \(0.294206\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3952.36 | −0.174999 | ||||||||
\(800\) | −821.441 | − | 474.259i | −0.0363029 | − | 0.0209595i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −27316.4 | − | 47313.3i | −1.20271 | − | 2.08316i | ||||
\(803\) | −20821.3 | + | 36063.5i | −0.915028 | + | 1.58487i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 4260.11i | − | 0.186174i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 23068.7 | − | 13318.7i | 1.00440 | − | 0.579890i | ||||
\(809\) | −17128.3 | + | 9889.03i | −0.744375 | + | 0.429765i | −0.823658 | − | 0.567087i | \(-0.808070\pi\) |
0.0792832 | + | 0.996852i | \(0.474737\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 44456.6i | − | 1.92488i | −0.271487 | − | 0.962442i | \(-0.587516\pi\) | ||
0.271487 | − | 0.962442i | \(-0.412484\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12399.2 | + | 21476.1i | −0.533897 | + | 0.924736i | ||||
\(815\) | 20914.4 | + | 36224.8i | 0.898896 | + | 1.55693i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 711.499 | + | 410.784i | 0.0304678 | + | 0.0175906i | ||||
\(818\) | 60334.8 | 2.57892 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 51880.6 | 2.20945 | ||||||||
\(821\) | 9958.57 | + | 5749.58i | 0.423333 | + | 0.244411i | 0.696502 | − | 0.717555i | \(-0.254739\pi\) |
−0.273169 | + | 0.961966i | \(0.588072\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −596.549 | − | 1033.25i | −0.0252666 | − | 0.0437630i | 0.853116 | − | 0.521722i | \(-0.174710\pi\) |
−0.878382 | + | 0.477959i | \(0.841377\pi\) | |||||||
\(824\) | 33456.1 | − | 57947.6i | 1.41444 | − | 2.44988i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 29552.9i | − | 1.24263i | −0.783561 | − | 0.621315i | \(-0.786599\pi\) | ||
0.783561 | − | 0.621315i | \(-0.213401\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11762.7 | − | 6791.21i | 0.492806 | − | 0.284521i | −0.232932 | − | 0.972493i | \(-0.574832\pi\) |
0.725738 | + | 0.687972i | \(0.241499\pi\) | |||||||
\(830\) | 23585.0 | − | 13616.8i | 0.986323 | − | 0.569454i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5061.36i | 0.210903i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2333.22 | + | 4041.26i | −0.0967000 | + | 0.167489i | ||||
\(836\) | 69477.1 | + | 120338.i | 2.87430 | + | 4.97843i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34804.7 | + | 20094.5i | 1.43474 | + | 0.828346i | ||||
\(839\) | −11623.6 | −0.478297 | −0.239149 | − | 0.970983i | \(-0.576868\pi\) | ||||
−0.239149 | + | 0.970983i | \(0.576868\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10080.1 | 0.413303 | ||||||||
\(842\) | 23477.1 | + | 13554.5i | 0.960896 | + | 0.554774i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −27068.1 | − | 46883.2i | −1.10393 | − | 1.91207i | ||||
\(845\) | 13521.2 | − | 23419.3i | 0.550464 | − | 0.953432i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 26432.7i | − | 1.07040i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11013.9 | + | 6358.87i | −0.444439 | + | 0.256597i | ||||
\(851\) | 7665.24 | − | 4425.53i | 0.308767 | − | 0.178267i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1019.82i | 0.0409354i | 0.999791 | + | 0.0204677i | \(0.00651553\pi\) | ||||
−0.999791 | + | 0.0204677i | \(0.993484\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −421.032 | + | 729.249i | −0.0168114 | + | 0.0291182i | ||||
\(857\) | −4299.43 | − | 7446.83i | −0.171372 | − | 0.296825i | 0.767528 | − | 0.641016i | \(-0.221487\pi\) |
−0.938900 | + | 0.344191i | \(0.888153\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32182.1 | − | 18580.4i | −1.27828 | − | 0.738013i | −0.301745 | − | 0.953389i | \(-0.597569\pi\) |
−0.976531 | + | 0.215375i | \(0.930903\pi\) | |||||||
\(860\) | 1003.05 | 0.0397718 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −34241.4 | −1.35298 | ||||||||
\(863\) | 10634.2 | + | 6139.68i | 0.419459 | + | 0.242175i | 0.694846 | − | 0.719159i | \(-0.255473\pi\) |
−0.275387 | + | 0.961334i | \(0.588806\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13357.5 | − | 23135.8i | −0.525049 | − | 0.909411i | ||||
\(866\) | −22410.6 | + | 38816.3i | −0.879381 | + | 1.52313i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28940.6i | 1.12974i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1256.57 | − | 725.483i | 0.0488833 | − | 0.0282228i | ||||
\(872\) | 30788.4 | − | 17775.7i | 1.19567 | − | 0.690322i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 74912.3i | − | 2.89925i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15935.8 | + | 27601.6i | −0.613583 | + | 1.06276i | 0.377048 | + | 0.926194i | \(0.376939\pi\) |
−0.990631 | + | 0.136564i | \(0.956394\pi\) | |||||||
\(878\) | 20633.2 | + | 35737.8i | 0.793094 | + | 1.37368i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 33639.3 | + | 19421.7i | 1.28861 | + | 0.743982i | ||||
\(881\) | 29427.6 | 1.12536 | 0.562679 | − | 0.826676i | \(-0.309771\pi\) | ||||
0.562679 | + | 0.826676i | \(0.309771\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 846.860 | 0.0322753 | 0.0161377 | − | 0.999870i | \(-0.494863\pi\) | ||||
0.0161377 | + | 0.999870i | \(0.494863\pi\) | |||||||
\(884\) | 8282.97 | + | 4782.18i | 0.315143 | + | 0.181948i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31758.8 | + | 55007.8i | 1.20424 | + | 2.08580i | ||||
\(887\) | 3940.07 | − | 6824.39i | 0.149148 | − | 0.258332i | −0.781765 | − | 0.623574i | \(-0.785680\pi\) |
0.930913 | + | 0.365241i | \(0.119014\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 1592.85i | − | 0.0599916i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −52883.1 | + | 30532.1i | −1.98504 | + | 1.14606i | ||||
\(893\) | 8137.73 | − | 4698.32i | 0.304948 | − | 0.176062i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 22462.4i | − | 0.838923i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 34335.1 | − | 59470.1i | 1.27592 | − | 2.20996i | ||||
\(899\) | −5913.91 | − | 10243.2i | −0.219399 | − | 0.380011i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28053.3 | + | 16196.6i | 1.03728 | + | 0.598875i | ||||
\(902\) | 68281.2 | 2.52053 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4484.71 | 0.164999 | ||||||||
\(905\) | −35346.4 | − | 20407.2i | −1.29829 | − | 0.749569i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10646.6 | − | 18440.4i | −0.389762 | − | 0.675088i | 0.602655 | − | 0.798002i | \(-0.294109\pi\) |
−0.992417 | + | 0.122914i | \(0.960776\pi\) | |||||||
\(908\) | 4744.67 | − | 8218.00i | 0.173411 | − | 0.300357i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14634.3i | 0.532225i | 0.963942 | + | 0.266112i | \(0.0857393\pi\) | ||||
−0.963942 | + | 0.266112i | \(0.914261\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20550.5 | − | 11864.8i | 0.744931 | − | 0.430086i | ||||
\(914\) | 37811.3 | − | 21830.4i | 1.36837 | − | 0.790027i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 34618.2i | 1.24871i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6098.61 | + | 10563.1i | −0.218906 | + | 0.379156i | −0.954474 | − | 0.298295i | \(-0.903582\pi\) |
0.735568 | + | 0.677451i | \(0.236915\pi\) | |||||||
\(920\) | −22386.5 | − | 38774.6i | −0.802242 | − | 1.38952i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4023.98 | − | 2323.25i | −0.143734 | − | 0.0829849i | ||||
\(923\) | −707.119 | −0.0252168 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3572.46 | 0.126986 | ||||||||
\(926\) | 50581.5 | + | 29203.2i | 1.79504 | + | 1.03637i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1495.74 | + | 2590.70i | 0.0529095 | + | 0.0916420i | ||||
\(929\) | 12348.1 | − | 21387.5i | 0.436091 | − | 0.755331i | −0.561293 | − | 0.827617i | \(-0.689696\pi\) |
0.997384 | + | 0.0722858i | \(0.0230294\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 37383.2i | 1.31387i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21341.3 | + | 12321.4i | −0.747653 | + | 0.431658i | ||||
\(935\) | −41224.9 | + | 23801.2i | −1.44192 | + | 0.832495i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 14448.0i | − | 0.503730i | −0.967762 | − | 0.251865i | \(-0.918956\pi\) | ||
0.967762 | − | 0.251865i | \(-0.0810439\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5736.17 | − | 9935.33i | 0.199035 | − | 0.344739i | ||||
\(941\) | −15580.4 | − | 26986.0i | −0.539752 | − | 0.934878i | −0.998917 | − | 0.0465268i | \(-0.985185\pi\) |
0.459165 | − | 0.888351i | \(-0.348149\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21105.9 | − | 12185.5i | −0.728845 | − | 0.420799i | ||||
\(944\) | 12707.0 | 0.438113 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1320.14 | 0.0453715 | ||||||||
\(947\) | −8887.48 | − | 5131.19i | −0.304968 | − | 0.176073i | 0.339705 | − | 0.940532i | \(-0.389673\pi\) |
−0.644672 | + | 0.764459i | \(0.723006\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3407.28 | − | 5901.58i | −0.116549 | − | 0.201869i | ||||
\(950\) | 15118.0 | − | 26185.2i | 0.516310 | − | 0.894274i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 12686.9i | − | 0.431236i | −0.976478 | − | 0.215618i | \(-0.930823\pi\) | ||
0.976478 | − | 0.215618i | \(-0.0691766\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6072.91 | − | 3506.20i | 0.205775 | − | 0.118804i | ||||
\(956\) | −40960.7 | + | 23648.7i | −1.38574 | + | 0.800055i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 74020.6i | 2.49634i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10007.0 | + | 17332.7i | −0.335908 | + | 0.581810i | ||||
\(962\) | −2029.05 | − | 3514.43i | −0.0680035 | − | 0.117785i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 34141.2 | + | 19711.4i | 1.14068 | + | 0.658571i | ||||
\(965\) | 8992.17 | 0.299967 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16129.8 | 0.536401 | 0.268200 | − | 0.963363i | \(-0.413571\pi\) | ||||
0.268200 | + | 0.963363i | \(0.413571\pi\) | |||||||
\(968\) | 51632.7 | + | 29810.1i | 1.71440 | + | 0.989808i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 42882.3 | + | 74274.4i | 1.41945 | + | 2.45856i | ||||
\(971\) | 26382.4 | − | 45695.6i | 0.871937 | − | 1.51024i | 0.0119472 | − | 0.999929i | \(-0.496197\pi\) |
0.859990 | − | 0.510311i | \(-0.170470\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 76930.8i | − | 2.53082i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20844.0 | − | 12034.3i | 0.683606 | − | 0.394680i | ||||
\(977\) | 46759.5 | − | 26996.6i | 1.53118 | − | 0.884030i | 0.531877 | − | 0.846821i | \(-0.321487\pi\) |
0.999308 | − | 0.0372085i | \(-0.0118466\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1387.91i | − | 0.0453093i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −43944.7 | + | 76114.4i | −1.42804 | + | 2.47343i | ||||
\(983\) | −26119.2 | − | 45239.8i | −0.847480 | − | 1.46788i | −0.883450 | − | 0.468526i | \(-0.844785\pi\) |
0.0359696 | − | 0.999353i | \(-0.488548\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 58784.4 | + | 33939.2i | 1.90155 | + | 1.09786i | ||||
\(986\) | 40109.7 | 1.29549 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22739.0 | −0.732211 | ||||||||
\(989\) | −408.057 | − | 235.592i | −0.0131198 | − | 0.00757471i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4812.21 | + | 8334.99i | 0.154253 | + | 0.267174i | 0.932787 | − | 0.360429i | \(-0.117370\pi\) |
−0.778534 | + | 0.627603i | \(0.784036\pi\) | |||||||
\(992\) | −1236.38 | + | 2141.48i | −0.0395718 | + | 0.0685403i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 31774.3i | − | 1.01237i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25023.0 | − | 14447.0i | 0.794871 | − | 0.458919i | −0.0468034 | − | 0.998904i | \(-0.514903\pi\) |
0.841675 | + | 0.539985i | \(0.181570\pi\) | |||||||
\(998\) | 44346.2 | − | 25603.3i | 1.40657 | − | 0.812082i | ||||
\(999\) | 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 | 441.4.p.c.215.8 | 16 | ||
3.2 | odd | 2 | inner | 441.4.p.c.215.1 | 16 | ||
7.2 | even | 3 | 441.4.c.a.440.1 | 16 | |||
7.3 | odd | 6 | inner | 441.4.p.c.80.1 | 16 | ||
7.4 | even | 3 | 63.4.p.a.17.1 | ✓ | 16 | ||
7.5 | odd | 6 | 441.4.c.a.440.2 | 16 | |||
7.6 | odd | 2 | 63.4.p.a.26.8 | yes | 16 | ||
21.2 | odd | 6 | 441.4.c.a.440.16 | 16 | |||
21.5 | even | 6 | 441.4.c.a.440.15 | 16 | |||
21.11 | odd | 6 | 63.4.p.a.17.8 | yes | 16 | ||
21.17 | even | 6 | inner | 441.4.p.c.80.8 | 16 | ||
21.20 | even | 2 | 63.4.p.a.26.1 | yes | 16 | ||
28.11 | odd | 6 | 1008.4.bt.a.17.7 | 16 | |||
28.27 | even | 2 | 1008.4.bt.a.593.2 | 16 | |||
84.11 | even | 6 | 1008.4.bt.a.17.2 | 16 | |||
84.83 | odd | 2 | 1008.4.bt.a.593.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.p.a.17.1 | ✓ | 16 | 7.4 | even | 3 | ||
63.4.p.a.17.8 | yes | 16 | 21.11 | odd | 6 | ||
63.4.p.a.26.1 | yes | 16 | 21.20 | even | 2 | ||
63.4.p.a.26.8 | yes | 16 | 7.6 | odd | 2 | ||
441.4.c.a.440.1 | 16 | 7.2 | even | 3 | |||
441.4.c.a.440.2 | 16 | 7.5 | odd | 6 | |||
441.4.c.a.440.15 | 16 | 21.5 | even | 6 | |||
441.4.c.a.440.16 | 16 | 21.2 | odd | 6 | |||
441.4.p.c.80.1 | 16 | 7.3 | odd | 6 | inner | ||
441.4.p.c.80.8 | 16 | 21.17 | even | 6 | inner | ||
441.4.p.c.215.1 | 16 | 3.2 | odd | 2 | inner | ||
441.4.p.c.215.8 | 16 | 1.1 | even | 1 | trivial | ||
1008.4.bt.a.17.2 | 16 | 84.11 | even | 6 | |||
1008.4.bt.a.17.7 | 16 | 28.11 | odd | 6 | |||
1008.4.bt.a.593.2 | 16 | 28.27 | even | 2 | |||
1008.4.bt.a.593.7 | 16 | 84.83 | odd | 2 |