Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,4,Mod(17,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 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("1008.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bt (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: | \(59.4739252858\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 593.7 | ||
Root | \(-4.21355 + 2.43270i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.593 |
Dual form | 1008.4.bt.a.17.7 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 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 | ||||||||
\(7\) | −2.53897 | + | 18.3454i | −0.137091 | + | 0.990558i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 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 | \(-0.969887\pi\) | ||
0.995528 | − | 0.0944620i | \(-0.0301131\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −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 | \(0.213492\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −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 | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 119.620i | − | 0.765961i | −0.923756 | − | 0.382981i | \(-0.874898\pi\) | ||
0.923756 | − | 0.382981i | \(-0.125102\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −85.6311 | + | 49.4391i | −0.496123 | + | 0.286437i | −0.727111 | − | 0.686520i | \(-0.759137\pi\) |
0.230988 | + | 0.972957i | \(0.425804\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 186.590 | + | 145.150i | 0.901129 | + | 0.700994i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −47.0949 | + | 81.5708i | −0.209253 | + | 0.362437i | −0.951479 | − | 0.307712i | \(-0.900437\pi\) |
0.742227 | + | 0.670149i | \(0.233770\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 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 | \(-0.502830\pi\) | ||||
−0.00889133 | + | 0.999960i | \(0.502830\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −28.6747 | + | 49.6660i | −0.0889921 | + | 0.154139i | −0.907085 | − | 0.420947i | \(-0.861698\pi\) |
0.818093 | + | 0.575086i | \(0.195031\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −330.107 | − | 93.1568i | −0.962412 | − | 0.271594i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 407.058 | − | 235.015i | 1.05497 | − | 0.609090i | 0.130937 | − | 0.991391i | \(-0.458202\pi\) |
0.924038 | + | 0.382301i | \(0.124868\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 690.718i | − | 1.69339i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 112.979 | + | 195.685i | 0.249299 | + | 0.431798i | 0.963331 | − | 0.268314i | \(-0.0864666\pi\) |
−0.714033 | + | 0.700112i | \(0.753133\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 370.650 | + | 213.995i | 0.777982 | + | 0.449168i | 0.835715 | − | 0.549164i | \(-0.185054\pi\) |
−0.0577325 | + | 0.998332i | \(0.518387\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −97.8884 | − | 56.5159i | −0.186793 | − | 0.107845i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 81.9267 | + | 141.901i | 0.149387 | + | 0.258746i | 0.931001 | − | 0.365016i | \(-0.118937\pi\) |
−0.781614 | + | 0.623762i | \(0.785603\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 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 | 0.140741 | − | 0.990046i | \(-0.455051\pi\) |
0.927776 | + | 0.373138i | \(0.121718\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 377.379 | + | 928.422i | 0.558523 | + | 1.37407i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 267.408 | − | 463.165i | 0.380833 | − | 0.659622i | −0.610349 | − | 0.792133i | \(-0.708971\pi\) |
0.991182 | + | 0.132511i | \(0.0423040\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −438.520 | −0.579926 | −0.289963 | − | 0.957038i | \(-0.593643\pi\) | ||||
−0.289963 | + | 0.957038i | \(0.593643\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −879.684 | −1.12253 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 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 | ||||||||
\(91\) | 162.454 | + | 22.4833i | 0.187140 | + | 0.0258999i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1811.23 | − | 1045.71i | 1.95608 | − | 1.12935i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1381.00i | − | 1.44555i | −0.691081 | − | 0.722777i | \(-0.742865\pi\) | ||
0.691081 | − | 0.722777i | \(-0.257135\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −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 | \(0.994598\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 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 | \(0.970765\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 120.145i | 0.100020i | 0.998749 | + | 0.0500102i | \(0.0159254\pi\) | ||||
−0.998749 | + | 0.0500102i | \(0.984075\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1038.77 | + | 599.735i | −0.842312 | + | 0.486309i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1182.42 | − | 480.622i | 0.910859 | − | 0.370240i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 798.612 | − | 1383.24i | 0.600009 | − | 1.03925i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1111.41 | 0.795262 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −884.302 | −0.617867 | −0.308934 | − | 0.951084i | \(-0.599972\pi\) | ||||
−0.308934 | + | 0.951084i | \(0.599972\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 803.439 | − | 1391.60i | 0.535853 | − | 0.928125i | −0.463268 | − | 0.886218i | \(-0.653323\pi\) |
0.999122 | − | 0.0419070i | \(-0.0133433\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1863.21 | + | 2395.16i | −1.21474 | + | 1.56156i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −615.297 | + | 355.242i | −0.383711 | + | 0.221535i | −0.679431 | − | 0.733739i | \(-0.737773\pi\) |
0.295721 | + | 0.955274i | \(0.404440\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −239.593 | − | 414.987i | −0.140110 | − | 0.242678i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1322.31 | − | 763.435i | −0.757322 | − | 0.437240i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2079.39 | + | 1200.54i | 1.14329 | + | 0.660079i | 0.947243 | − | 0.320516i | \(-0.103856\pi\) |
0.196046 | + | 0.980595i | \(0.437190\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1233.99 | + | 2137.33i | 0.665035 | + | 1.15188i | 0.979276 | + | 0.202532i | \(0.0649169\pi\) |
−0.314240 | + | 0.949343i | \(0.601750\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1262.12i | 0.654036i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2109.74 | − | 1218.06i | 1.07246 | − | 0.619184i | 0.143606 | − | 0.989635i | \(-0.454130\pi\) |
0.928852 | + | 0.370451i | \(0.120797\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1068.59 | − | 1373.67i | 0.523083 | − | 0.672424i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1638.50 | − | 2837.97i | 0.787347 | − | 1.36372i | −0.140240 | − | 0.990118i | \(-0.544787\pi\) |
0.927587 | − | 0.373607i | \(-0.121879\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 365.585 | 0.169400 | 0.0847000 | − | 0.996406i | \(-0.473007\pi\) | ||||
0.0847000 | + | 0.996406i | \(0.473007\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2118.58 | 0.964308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 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 | ||||||||
\(175\) | 650.739 | − | 264.508i | 0.281093 | − | 0.114257i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 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 | \(0.227985\pi\) | ||||
−0.754282 | + | 0.656551i | \(0.772015\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 601.135 | + | 1041.20i | 0.238899 | + | 0.413786i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3229.69 | − | 1864.66i | −1.26299 | − | 0.729186i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 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 | \(0.791395\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5317.81i | − | 1.92324i | −0.274384 | − | 0.961620i | \(-0.588474\pi\) | ||
0.274384 | − | 0.961620i | \(-0.411526\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2155.80 | − | 1244.65i | 0.767942 | − | 0.443371i | −0.0641982 | − | 0.997937i | \(-0.520449\pi\) |
0.832140 | + | 0.554566i | \(0.187116\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2194.48 | + | 303.711i | 0.758729 | + | 0.105007i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1655.20 | − | 2866.88i | 0.563922 | − | 0.976741i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8866.38 | 2.93445 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3454.31 | 1.12704 | 0.563519 | − | 0.826103i | \(-0.309447\pi\) | ||||
0.563519 | + | 0.826103i | \(0.309447\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −32.0013 | + | 55.4279i | −0.0101510 | + | 0.0175821i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −689.566 | − | 1696.46i | −0.215718 | − | 0.530706i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −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 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 302.747 | + | 524.374i | 0.0885201 | + | 0.153321i | 0.906886 | − | 0.421377i | \(-0.138453\pi\) |
−0.818366 | + | 0.574698i | \(0.805120\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1912.98 | − | 1104.46i | −0.552023 | − | 0.318711i | 0.197914 | − | 0.980219i | \(-0.436583\pi\) |
−0.749938 | + | 0.661509i | \(0.769917\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2065.77 | − | 1192.67i | −0.580829 | − | 0.335342i | 0.180634 | − | 0.983550i | \(-0.442185\pi\) |
−0.761463 | + | 0.648209i | \(0.775518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 366.013 | + | 633.953i | 0.101600 | + | 0.175977i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 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 | −0.762037 | − | 0.647534i | \(-0.775800\pi\) |
0.179762 | + | 0.983710i | \(0.442467\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3136.58 | + | 3054.54i | −0.817913 | + | 0.796521i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 725.465 | − | 1256.54i | 0.186883 | − | 0.323692i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1306.11 | 0.328451 | 0.164226 | − | 0.986423i | \(-0.447488\pi\) | ||||
0.164226 | + | 0.986423i | \(0.447488\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5085.03 | −1.26361 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −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 | ||||||||
\(259\) | −1376.88 | − | 1071.08i | −0.330328 | − | 0.256964i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −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 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −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 | \(0.798853\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −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 | \(0.843142\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 321.256i | 0.0682011i | 0.999418 | + | 0.0341006i | \(0.0108566\pi\) | ||||
−0.999418 | + | 0.0341006i | \(0.989143\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5891.40 | + | 3401.40i | −1.23748 | + | 0.714460i | −0.968579 | − | 0.248707i | \(-0.919994\pi\) |
−0.268903 | + | 0.963167i | \(0.586661\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −658.474 | + | 4757.82i | −0.135430 | + | 0.978556i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 81.7017 | − | 141.511i | 0.0166297 | − | 0.0288035i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −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 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −416.067 | + | 720.649i | −0.0804741 | + | 0.139385i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.7308 | − | 91.9871i | 0.00243785 | − | 0.0176148i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 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 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2340.89 | − | 4054.55i | −0.426817 | − | 0.739268i | 0.569772 | − | 0.821803i | \(-0.307032\pi\) |
−0.996588 | + | 0.0825352i | \(0.973698\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −850.477 | − | 491.023i | −0.153584 | − | 0.0886718i | 0.421238 | − | 0.906950i | \(-0.361596\pi\) |
−0.574823 | + | 0.818278i | \(0.694929\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4269.80 | − | 2465.17i | −0.756516 | − | 0.436775i | 0.0715272 | − | 0.997439i | \(-0.477213\pi\) |
−0.828044 | + | 0.560664i | \(0.810546\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3236.50 | − | 5605.79i | −0.568055 | − | 0.983899i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11292.0i | − | 1.94522i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −290.868 | + | 167.933i | −0.0496445 | + | 0.0286623i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −838.338 | − | 652.148i | −0.140483 | − | 0.109283i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2017.25 | + | 3493.99i | −0.334980 | + | 0.580202i | −0.983481 | − | 0.181012i | \(-0.942063\pi\) |
0.648501 | + | 0.761214i | \(0.275396\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2091.48 | 0.341104 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2771.62 | 0.448011 | 0.224006 | − | 0.974588i | \(-0.428087\pi\) | ||||
0.224006 | + | 0.974588i | \(0.428087\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2675.30 | + | 4633.76i | −0.424856 | + | 0.735872i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2547.13 | − | 5819.43i | 0.400968 | − | 0.916092i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −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 | \(0.0325634\pi\) | ||||
−0.994772 | + | 0.102122i | \(0.967437\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 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 | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −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 | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 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 | \(0.395183\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3277.93 | + | 8064.33i | 0.458711 | + | 1.12851i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3048.56 | + | 5280.25i | −0.423186 | + | 0.732979i | −0.996249 | − | 0.0865320i | \(-0.972422\pi\) |
0.573063 | + | 0.819511i | \(0.305755\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1059.27 | −0.144708 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9922.24 | 1.34478 | 0.672389 | − | 0.740198i | \(-0.265268\pi\) | ||||
0.672389 | + | 0.740198i | \(0.265268\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −609.532 | + | 1055.74i | −0.0813202 | + | 0.140851i | −0.903817 | − | 0.427919i | \(-0.859247\pi\) |
0.822497 | + | 0.568769i | \(0.192580\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12671.5 | + | 1753.71i | 1.67740 | + | 0.232149i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11374.6 | + | 6567.15i | −1.48256 | + | 0.855958i | −0.999804 | − | 0.0197949i | \(-0.993699\pi\) |
−0.482759 | + | 0.875753i | \(0.660365\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6476.19i | 0.837634i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3413.29 | − | 5911.99i | −0.434788 | − | 0.753075i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2697.68 | + | 1557.51i | 0.341040 | + | 0.196900i | 0.660732 | − | 0.750622i | \(-0.270246\pi\) |
−0.319692 | + | 0.947522i | \(0.603579\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9724.47 | + | 5614.42i | 1.21101 | + | 0.699179i | 0.962980 | − | 0.269572i | \(-0.0868822\pi\) |
0.248034 | + | 0.968751i | \(0.420216\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 437.797 | + | 758.287i | 0.0541147 | + | 0.0937295i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5096.90i | 0.620747i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10739.4 | + | 6200.41i | −1.29836 | + | 0.749610i | −0.980121 | − | 0.198399i | \(-0.936426\pi\) |
−0.318242 | + | 0.948010i | \(0.603092\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3876.78 | + | 1575.81i | −0.461898 | + | 0.187749i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2798.71 | + | 4847.51i | −0.331044 | + | 0.573385i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8260.19 | −0.963095 | −0.481547 | − | 0.876420i | \(-0.659925\pi\) | ||||
−0.481547 | + | 0.876420i | \(0.659925\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5571.81 | 0.645020 | 0.322510 | − | 0.946566i | \(-0.395473\pi\) | ||||
0.322510 | + | 0.946566i | \(0.395473\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1306.96 | + | 2263.72i | −0.149169 | + | 0.258368i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4866.89 | + | 6256.40i | −0.551582 | + | 0.709060i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −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 | \(-0.829195\pi\) | ||
0.859452 | − | 0.511216i | \(-0.170805\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −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 | \(0.514138\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 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 | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14114.0i | 1.48348i | 0.670689 | + | 0.741738i | \(0.265998\pi\) | ||||
−0.670689 | + | 0.741738i | \(0.734002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12153.9 | − | 7017.03i | 1.26896 | − | 0.732637i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1285.34 | − | 1652.31i | 0.132435 | − | 0.170245i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4486.87 | − | 7771.49i | 0.459271 | − | 0.795481i | −0.539651 | − | 0.841889i | \(-0.681444\pi\) |
0.998923 | + | 0.0464073i | \(0.0147772\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −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 | \(-0.705820\pi\) | ||||
−0.602479 | + | 0.798135i | \(0.705820\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2532.46 | − | 4386.34i | 0.250938 | − | 0.434638i | −0.712846 | − | 0.701320i | \(-0.752594\pi\) |
0.963784 | + | 0.266683i | \(0.0859276\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2811.24 | + | 1142.69i | −0.276783 | + | 0.112505i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −234.981 | + | 135.666i | −0.0228423 | + | 0.0131880i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6214.52i | − | 0.600299i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7606.85 | − | 13175.5i | −0.725607 | − | 1.25679i | −0.958724 | − | 0.284340i | \(-0.908226\pi\) |
0.233116 | − | 0.972449i | \(-0.425108\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 722.332 | + | 417.038i | 0.0684730 | + | 0.0395329i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15265.9 | − | 8813.75i | −1.42925 | − | 0.825179i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7905.92 | + | 13693.5i | 0.735629 | + | 1.27415i | 0.954447 | + | 0.298382i | \(0.0964468\pi\) |
−0.218817 | + | 0.975766i | \(0.570220\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 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 | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1464.93 | − | 202.744i | −0.132216 | − | 0.0182984i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5262.33 | + | 9114.62i | −0.472092 | + | 0.817688i | −0.999490 | − | 0.0319305i | \(-0.989834\pi\) |
0.527398 | + | 0.849619i | \(0.323168\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7790.82 | 0.690607 | 0.345304 | − | 0.938491i | \(-0.387776\pi\) | ||||
0.345304 | + | 0.938491i | \(0.387776\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9108.83 | −0.802649 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 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 | ||||||||
\(511\) | 5366.74 | + | 13203.2i | 0.464600 | + | 1.14300i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19815.6 | + | 11440.5i | −1.69549 | + | 0.978892i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3103.35i | 0.263994i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 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 | \(0.561564\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5901.47 | + | 3407.21i | 0.487803 | + | 0.281633i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1668.28 | − | 2889.55i | −0.137115 | − | 0.237491i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2296.59i | − | 0.186635i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 249.371 | − | 143.975i | 0.0201519 | − | 0.0116347i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17990.4 | + | 4565.93i | −1.43767 | + | 0.364876i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8380.42 | + | 14515.3i | −0.665993 | + | 1.15353i | 0.313022 | + | 0.949746i | \(0.398659\pi\) |
−0.979015 | + | 0.203788i | \(0.934675\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12157.0 | −0.955503 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5869.79 | −0.458819 | −0.229410 | − | 0.973330i | \(-0.573680\pi\) | ||||
−0.229410 | + | 0.973330i | \(0.573680\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9799.82 | − | 16973.8i | 0.757688 | − | 1.31235i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7818.00 | + | 6081.67i | 0.601185 | + | 0.467666i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18756.5 | + | 10829.1i | −1.42682 | + | 0.823774i | −0.996868 | − | 0.0790779i | \(-0.974802\pi\) |
−0.429951 | + | 0.902852i | \(0.641469\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.4019i | 0.00335957i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4795.36 | − | 8305.80i | −0.358970 | − | 0.621755i | 0.628819 | − | 0.777552i | \(-0.283539\pi\) |
−0.987789 | + | 0.155797i | \(0.950205\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1328.11 | + | 766.787i | 0.0988923 | + | 0.0570955i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14405.5 | + | 8317.01i | 1.06135 | + | 0.612772i | 0.925806 | − | 0.377999i | \(-0.123388\pi\) |
0.135546 | + | 0.990771i | \(0.456721\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3165.51 | + | 5482.83i | 0.232001 | + | 0.401838i | 0.958397 | − | 0.285439i | \(-0.0921394\pi\) |
−0.726396 | + | 0.687277i | \(0.758806\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3564.14i | 0.258495i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8431.94 | − | 4868.18i | 0.608364 | − | 0.351239i | −0.163961 | − | 0.986467i | \(-0.552427\pi\) |
0.772325 | + | 0.635228i | \(0.219094\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1113.39 | − | 8044.83i | 0.0795028 | − | 0.574450i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12717.4 | − | 22027.1i | 0.903430 | − | 1.56479i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10940.3 | −0.769255 | −0.384628 | − | 0.923072i | \(-0.625670\pi\) | ||||
−0.384628 | + | 0.923072i | \(0.625670\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16201.1 | −1.13337 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 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 | ||||||||
\(595\) | 2233.49 | − | 16138.2i | 0.153889 | − | 1.11193i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −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 | \(-0.854416\pi\) | ||
0.897218 | − | 0.441587i | \(-0.145584\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −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 | \(0.758320\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 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 | \(0.735981\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7360.91i | 0.480290i | 0.970737 | + | 0.240145i | \(0.0771950\pi\) | ||||
−0.970737 | + | 0.240145i | \(0.922805\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19878.5 | + | 11476.9i | −1.29077 | + | 0.745225i | −0.978790 | − | 0.204864i | \(-0.934325\pi\) |
−0.311978 | + | 0.950089i | \(0.600991\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 374.930 | + | 291.660i | 0.0241112 | + | 0.0187562i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9463.74 | − | 16391.7i | 0.605679 | − | 1.04907i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6491.31 | 0.411487 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21126.0 | −1.33282 | −0.666412 | − | 0.745584i | \(-0.732171\pi\) | ||||
−0.666412 | + | 0.745584i | \(0.732171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5643.77 | + | 9775.29i | −0.352703 | + | 0.610899i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −824.929 | + | 2923.19i | −0.0513106 | + | 0.181823i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15447.5 | + | 8918.61i | −0.951855 | + | 0.549554i | −0.893657 | − | 0.448751i | \(-0.851869\pi\) |
−0.0581985 | + | 0.998305i | \(0.518536\pi\) | |||||||
\(642\) | 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 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13149.2 | + | 22775.1i | 0.798993 | + | 1.38390i | 0.920273 | + | 0.391277i | \(0.127967\pi\) |
−0.121280 | + | 0.992618i | \(0.538700\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10589.1 | + | 6113.64i | 0.640462 | + | 0.369771i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8203.79 | + | 4736.46i | 0.491637 | + | 0.283847i | 0.725253 | − | 0.688482i | \(-0.241723\pi\) |
−0.233616 | + | 0.972329i | \(0.575056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10255.4 | − | 17762.8i | −0.611771 | − | 1.05962i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 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 | −0.953320 | − | 0.301962i | \(-0.902359\pi\) |
−0.215153 | + | 0.976580i | \(0.569025\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14585.4 | + | 35882.7i | 0.850521 | + | 2.09244i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5620.37 | + | 9734.77i | −0.326269 | + | 0.565115i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23159.9 | 1.33245 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4873.86 | −0.279158 | −0.139579 | − | 0.990211i | \(-0.544575\pi\) | ||||
−0.139579 | + | 0.990211i | \(0.544575\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 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 | ||||||||
\(679\) | 25334.9 | + | 3506.30i | 1.43191 | + | 0.198173i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 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 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −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 | \(0.453879\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16934.1 | − | 9776.90i | −0.924239 | − | 0.533610i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8936.75 | − | 15478.9i | −0.485658 | − | 0.841184i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33929.0i | 1.82807i | 0.405631 | + | 0.914037i | \(0.367052\pi\) | ||||
−0.405631 | + | 0.914037i | \(0.632948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13365.3 | + | 7716.46i | −0.717044 | + | 0.413986i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12243.6 | − | 4976.68i | 0.651296 | − | 0.264734i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9593.62 | + | 16616.6i | −0.508175 | + | 0.880185i | 0.491780 | + | 0.870719i | \(0.336346\pi\) |
−0.999955 | + | 0.00946553i | \(0.996987\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9291.63 | 0.488043 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6116.49 | −0.319922 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6883.43 | + | 11922.4i | −0.357036 | + | 0.618404i | −0.987464 | − | 0.157844i | \(-0.949546\pi\) |
0.630429 | + | 0.776247i | \(0.282879\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20384.3 | − | 26204.0i | 1.05291 | − | 1.35352i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −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 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 172.782 | + | 299.267i | 0.00874222 | + | 0.0151420i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2256.76 | + | 1302.94i | 0.113718 | + | 0.0656553i | 0.555780 | − | 0.831329i | \(-0.312420\pi\) |
−0.442062 | + | 0.896984i | \(0.645753\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7678.71 | + | 4433.30i | 0.383784 | + | 0.221578i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16871.7 | + | 29222.7i | 0.839833 | + | 1.45463i | 0.890034 | + | 0.455894i | \(0.150680\pi\) |
−0.0502016 | + | 0.998739i | \(0.515986\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 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 | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −256.528 | + | 329.768i | −0.0125145 | + | 0.0160874i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3757.62 | + | 6508.39i | −0.182580 | + | 0.316238i | −0.942758 | − | 0.333477i | \(-0.891778\pi\) |
0.760178 | + | 0.649714i | \(0.225111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 31502.0 | 1.51851 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23917.4 | 1.14834 | 0.574169 | − | 0.818737i | \(-0.305325\pi\) | ||||
0.574169 | + | 0.818737i | \(0.305325\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −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 | ||||||||
\(763\) | 16340.7 | − | 6642.07i | 0.775327 | − | 0.315150i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1732.85 | − | 1000.46i | 0.0815769 | − | 0.0470985i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2013.08i | 0.0943999i | 0.998885 | + | 0.0471999i | \(0.0150298\pi\) | ||||
−0.998885 | + | 0.0471999i | \(0.984970\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −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 | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36800.7 | + | 21246.9i | 1.69258 | + | 0.977213i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2160.54 | + | 3742.17i | 0.0989888 | + | 0.171454i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 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 | \(0.558379\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2204.11 | − | 305.045i | −0.0990761 | − | 0.0137119i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1894.99 | − | 3282.21i | 0.0848586 | − | 0.146979i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 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 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20821.3 | − | 36063.5i | 0.915028 | − | 1.58487i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8364.97 | − | 20579.4i | −0.366244 | − | 0.901029i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17128.3 | − | 9889.03i | 0.744375 | − | 0.429765i | −0.0792832 | − | 0.996852i | \(-0.525263\pi\) |
0.823658 | + | 0.567087i | \(0.191930\pi\) | |||||||
\(810\) | 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 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20914.4 | − | 36224.8i | −0.898896 | − | 1.55693i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −711.499 | − | 410.784i | −0.0304678 | − | 0.0175906i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9958.57 | − | 5749.58i | −0.423333 | − | 0.244411i | 0.273169 | − | 0.961966i | \(-0.411928\pi\) |
−0.696502 | + | 0.717555i | \(0.745261\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 596.549 | + | 1033.25i | 0.0252666 | + | 0.0437630i | 0.878382 | − | 0.477959i | \(-0.158623\pi\) |
−0.853116 | + | 0.521722i | \(0.825290\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 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 | −0.725738 | − | 0.687972i | \(-0.758501\pi\) |
0.232932 | + | 0.972493i | \(0.425168\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5815.07 | + | 22912.2i | 0.241873 | + | 0.953015i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2333.22 | − | 4041.26i | 0.0967000 | − | 0.167489i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11623.6 | 0.478297 | 0.239149 | − | 0.970983i | \(-0.423132\pi\) | ||||
0.239149 | + | 0.970983i | \(0.423132\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10080.1 | 0.413303 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13521.2 | − | 23419.3i | 0.550464 | − | 0.953432i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23348.4 | + | 18162.9i | 0.947178 | + | 0.736816i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7665.24 | − | 4425.53i | 0.308767 | − | 0.178267i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1019.82i | − | 0.0409354i | −0.999791 | − | 0.0204677i | \(-0.993484\pi\) | ||
0.999791 | − | 0.0204677i | \(-0.00651553\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −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 | \(0.930903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 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 | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 28940.6i | − | 1.12974i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1256.57 | − | 725.483i | 0.0488833 | − | 0.0282228i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2821.84 | + | 20389.3i | −0.109024 | + | 0.787753i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15935.8 | + | 27601.6i | −0.613583 | + | 1.06276i | 0.377048 | + | 0.926194i | \(0.376939\pi\) |
−0.990631 | + | 0.136564i | \(0.956394\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 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 | \(-0.505137\pi\) | ||||
−0.0161377 | + | 0.999870i | \(0.505137\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3940.07 | + | 6824.39i | −0.149148 | + | 0.258332i | −0.930913 | − | 0.365241i | \(-0.880986\pi\) |
0.781765 | + | 0.623574i | \(0.214320\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2245.22 | − | 16222.9i | 0.0847043 | − | 0.612034i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8137.73 | + | 4698.32i | −0.304948 | + | 0.176062i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 22462.4i | − | 0.838923i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5913.91 | + | 10243.2i | 0.219399 | + | 0.380011i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28053.3 | − | 16196.6i | −1.03728 | − | 0.598875i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 35346.4 | + | 20407.2i | 1.29829 | + | 0.749569i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10646.6 | + | 18440.4i | 0.389762 | + | 0.675088i | 0.992417 | − | 0.122914i | \(-0.0392239\pi\) |
−0.602655 | + | 0.798002i | \(0.705891\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 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 | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23489.5 | + | 18272.6i | 0.845901 | + | 0.658032i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6098.61 | − | 10563.1i | 0.218906 | − | 0.379156i | −0.735568 | − | 0.677451i | \(-0.763085\pi\) |
0.954474 | + | 0.298295i | \(0.0964179\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 707.119 | 0.0252168 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3572.46 | 0.126986 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 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 | ||||||||
\(931\) | −39209.6 | − | 40262.6i | −1.38028 | − | 1.41735i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −41224.9 | + | 23801.2i | −1.44192 | + | 0.832495i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14448.0i | 0.503730i | 0.967762 | + | 0.251865i | \(0.0810439\pi\) | ||||
−0.967762 | + | 0.251865i | \(0.918956\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −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 | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −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 | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12686.9i | 0.431236i | 0.976478 | + | 0.215618i | \(0.0691766\pi\) | ||||
−0.976478 | + | 0.215618i | \(0.930823\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6072.91 | − | 3506.20i | 0.205775 | − | 0.118804i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4954.83 | − | 12189.8i | −0.166840 | − | 0.410458i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10007.0 | + | 17332.7i | −0.335908 | + | 0.581810i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8992.17 | 0.299967 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16129.8 | −0.536401 | −0.268200 | − | 0.963363i | \(-0.586429\pi\) | ||||
−0.268200 | + | 0.963363i | \(0.586429\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26382.4 | + | 45695.6i | −0.871937 | + | 1.51024i | −0.0119472 | + | 0.999929i | \(0.503803\pi\) |
−0.859990 | + | 0.510311i | \(0.829530\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28103.5 | + | 3889.47i | 0.925956 | + | 0.128151i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46759.5 | + | 26996.6i | −1.53118 | + | 0.884030i | −0.531877 | + | 0.846821i | \(0.678513\pi\) |
−0.999308 | + | 0.0372085i | \(0.988153\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1387.91i | − | 0.0453093i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26119.2 | + | 45239.8i | 0.847480 | + | 1.46788i | 0.883450 | + | 0.468526i | \(0.155215\pi\) |
−0.0359696 | + | 0.999353i | \(0.511452\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −58784.4 | − | 33939.2i | −1.90155 | − | 1.09786i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 408.057 | + | 235.592i | 0.0131198 | + | 0.00757471i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4812.21 | − | 8334.99i | −0.154253 | − | 0.267174i | 0.778534 | − | 0.627603i | \(-0.215964\pi\) |
−0.932787 | + | 0.360429i | \(0.882630\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 31774.3i | − | 1.01237i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25023.0 | + | 14447.0i | −0.794871 | + | 0.458919i | −0.841675 | − | 0.539985i | \(-0.818430\pi\) |
0.0468034 | + | 0.998904i | \(0.485097\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1008.4.bt.a.593.7 | 16 | ||
3.2 | odd | 2 | inner | 1008.4.bt.a.593.2 | 16 | ||
4.3 | odd | 2 | 63.4.p.a.26.1 | yes | 16 | ||
7.3 | odd | 6 | inner | 1008.4.bt.a.17.2 | 16 | ||
12.11 | even | 2 | 63.4.p.a.26.8 | yes | 16 | ||
21.17 | even | 6 | inner | 1008.4.bt.a.17.7 | 16 | ||
28.3 | even | 6 | 63.4.p.a.17.8 | yes | 16 | ||
28.11 | odd | 6 | 441.4.p.c.80.8 | 16 | |||
28.19 | even | 6 | 441.4.c.a.440.16 | 16 | |||
28.23 | odd | 6 | 441.4.c.a.440.15 | 16 | |||
28.27 | even | 2 | 441.4.p.c.215.1 | 16 | |||
84.11 | even | 6 | 441.4.p.c.80.1 | 16 | |||
84.23 | even | 6 | 441.4.c.a.440.2 | 16 | |||
84.47 | odd | 6 | 441.4.c.a.440.1 | 16 | |||
84.59 | odd | 6 | 63.4.p.a.17.1 | ✓ | 16 | ||
84.83 | odd | 2 | 441.4.p.c.215.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.p.a.17.1 | ✓ | 16 | 84.59 | odd | 6 | ||
63.4.p.a.17.8 | yes | 16 | 28.3 | even | 6 | ||
63.4.p.a.26.1 | yes | 16 | 4.3 | odd | 2 | ||
63.4.p.a.26.8 | yes | 16 | 12.11 | even | 2 | ||
441.4.c.a.440.1 | 16 | 84.47 | odd | 6 | |||
441.4.c.a.440.2 | 16 | 84.23 | even | 6 | |||
441.4.c.a.440.15 | 16 | 28.23 | odd | 6 | |||
441.4.c.a.440.16 | 16 | 28.19 | even | 6 | |||
441.4.p.c.80.1 | 16 | 84.11 | even | 6 | |||
441.4.p.c.80.8 | 16 | 28.11 | odd | 6 | |||
441.4.p.c.215.1 | 16 | 28.27 | even | 2 | |||
441.4.p.c.215.8 | 16 | 84.83 | odd | 2 | |||
1008.4.bt.a.17.2 | 16 | 7.3 | odd | 6 | inner | ||
1008.4.bt.a.17.7 | 16 | 21.17 | even | 6 | inner | ||
1008.4.bt.a.593.2 | 16 | 3.2 | odd | 2 | inner | ||
1008.4.bt.a.593.7 | 16 | 1.1 | even | 1 | trivial |