Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,3,Mod(325,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.325");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.z (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: | \(48.0655186332\) |
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: | \( x^{16} - 12x^{14} + 114x^{12} - 336x^{10} + 755x^{8} - 336x^{6} + 114x^{4} - 12x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{6}\cdot 7^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.4 | ||
Root | \(-0.293380 + 0.169383i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.901 |
Dual form | 1764.3.z.n.325.4 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(5\) | −3.68448 | − | 2.12723i | −0.736896 | − | 0.425447i | 0.0840439 | − | 0.996462i | \(-0.473216\pi\) |
−0.820940 | + | 0.571015i | \(0.806550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.48935 | + | 16.4360i | 0.862668 | + | 1.49418i | 0.869344 | + | 0.494207i | \(0.164542\pi\) |
−0.00667619 | + | 0.999978i | \(0.502125\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.46088i | − | 0.343145i | −0.985171 | − | 0.171572i | \(-0.945115\pi\) | ||
0.985171 | − | 0.171572i | \(-0.0548848\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11.0534 | + | 6.38170i | −0.650202 | + | 0.375394i | −0.788534 | − | 0.614992i | \(-0.789159\pi\) |
0.138332 | + | 0.990386i | \(0.455826\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.11475 | − | 4.68506i | −0.427092 | − | 0.246582i | 0.271015 | − | 0.962575i | \(-0.412641\pi\) |
−0.698107 | + | 0.715993i | \(0.745974\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.53562 | − | 14.7841i | 0.371114 | − | 0.642788i | −0.618623 | − | 0.785688i | \(-0.712309\pi\) |
0.989737 | + | 0.142900i | \(0.0456426\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.44975 | − | 5.97514i | −0.137990 | − | 0.239006i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 20.8862 | 0.720212 | 0.360106 | − | 0.932911i | \(-0.382741\pi\) | ||||
0.360106 | + | 0.932911i | \(0.382741\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −13.5116 | + | 7.80092i | −0.435858 | + | 0.251642i | −0.701839 | − | 0.712336i | \(-0.747637\pi\) |
0.265981 | + | 0.963978i | \(0.414304\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −22.8492 | + | 39.5760i | −0.617547 | + | 1.06962i | 0.372385 | + | 0.928078i | \(0.378540\pi\) |
−0.989932 | + | 0.141545i | \(0.954793\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 63.3894i | − | 1.54608i | −0.634355 | − | 0.773042i | \(-0.718734\pi\) | ||
0.634355 | − | 0.773042i | \(-0.281266\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.20101 | 0.0511863 | 0.0255931 | − | 0.999672i | \(-0.491853\pi\) | ||||
0.0255931 | + | 0.999672i | \(0.491853\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 43.8434 | + | 25.3130i | 0.932839 | + | 0.538575i | 0.887708 | − | 0.460406i | \(-0.152296\pi\) |
0.0451306 | + | 0.998981i | \(0.485630\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −18.9787 | − | 32.8721i | −0.358089 | − | 0.620228i | 0.629553 | − | 0.776958i | \(-0.283238\pi\) |
−0.987641 | + | 0.156730i | \(0.949905\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 80.7443i | − | 1.46808i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 58.5813 | − | 33.8220i | 0.992904 | − | 0.573253i | 0.0867630 | − | 0.996229i | \(-0.472348\pi\) |
0.906141 | + | 0.422976i | \(0.139014\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −54.8814 | − | 31.6858i | −0.899695 | − | 0.519439i | −0.0225940 | − | 0.999745i | \(-0.507193\pi\) |
−0.877101 | + | 0.480305i | \(0.840526\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.48935 | + | 16.4360i | −0.145990 | + | 0.252862i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.6985 | − | 23.7265i | −0.204455 | − | 0.354126i | 0.745504 | − | 0.666501i | \(-0.232209\pi\) |
−0.949959 | + | 0.312375i | \(0.898876\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.1638 | 0.213574 | 0.106787 | − | 0.994282i | \(-0.465944\pi\) | ||||
0.106787 | + | 0.994282i | \(0.465944\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −72.5860 | + | 41.9075i | −0.994329 | + | 0.574076i | −0.906565 | − | 0.422066i | \(-0.861305\pi\) |
−0.0877632 | + | 0.996141i | \(0.527972\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −66.5980 | + | 115.351i | −0.843012 | + | 1.46014i | 0.0443238 | + | 0.999017i | \(0.485887\pi\) |
−0.887336 | + | 0.461123i | \(0.847447\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 109.761i | 1.32242i | 0.750200 | + | 0.661211i | \(0.229957\pi\) | ||||
−0.750200 | + | 0.661211i | \(0.770043\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 54.3015 | 0.638841 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −69.2645 | − | 39.9899i | −0.778252 | − | 0.449324i | 0.0575582 | − | 0.998342i | \(-0.481669\pi\) |
−0.835811 | + | 0.549018i | \(0.815002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.9324 | + | 34.5240i | 0.209815 | + | 0.363410i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 119.547i | − | 1.23245i | −0.787572 | − | 0.616223i | \(-0.788662\pi\) | ||
0.787572 | − | 0.616223i | \(-0.211338\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −127.846 | + | 73.8118i | −1.26580 | + | 0.730810i | −0.974191 | − | 0.225727i | \(-0.927524\pi\) |
−0.291610 | + | 0.956537i | \(0.594191\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −159.577 | − | 92.1319i | −1.54929 | − | 0.894485i | −0.998196 | − | 0.0600435i | \(-0.980876\pi\) |
−0.551097 | − | 0.834441i | \(-0.685791\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −23.6994 | + | 41.0486i | −0.221490 | + | 0.383632i | −0.955261 | − | 0.295766i | \(-0.904425\pi\) |
0.733771 | + | 0.679397i | \(0.237759\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −49.4472 | − | 85.6451i | −0.453644 | − | 0.785735i | 0.544965 | − | 0.838459i | \(-0.316543\pi\) |
−0.998609 | + | 0.0527240i | \(0.983210\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −187.880 | −1.66265 | −0.831325 | − | 0.555786i | \(-0.812417\pi\) | ||||
−0.831325 | + | 0.555786i | \(0.812417\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −62.8986 | + | 36.3145i | −0.546944 | + | 0.315779i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −119.595 | + | 207.145i | −0.988392 | + | 1.71195i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 135.715i | 1.08572i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −22.9949 | −0.181063 | −0.0905313 | − | 0.995894i | \(-0.528857\pi\) | ||||
−0.0905313 | + | 0.995894i | \(0.528857\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −124.532 | − | 71.8984i | −0.950623 | − | 0.548843i | −0.0573487 | − | 0.998354i | \(-0.518265\pi\) |
−0.893274 | + | 0.449512i | \(0.851598\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −33.2367 | − | 57.5676i | −0.242604 | − | 0.420202i | 0.718852 | − | 0.695164i | \(-0.244668\pi\) |
−0.961455 | + | 0.274962i | \(0.911335\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 246.268i | − | 1.77171i | −0.463961 | − | 0.885856i | \(-0.653572\pi\) | ||
0.463961 | − | 0.885856i | \(-0.346428\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 73.3193 | − | 42.3309i | 0.512722 | − | 0.296020i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −76.9546 | − | 44.4297i | −0.530721 | − | 0.306412i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 39.8648 | − | 69.0479i | 0.267549 | − | 0.463409i | −0.700679 | − | 0.713477i | \(-0.747120\pi\) |
0.968228 | + | 0.250068i | \(0.0804528\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.2965 | − | 28.2263i | −0.107924 | − | 0.186929i | 0.807005 | − | 0.590544i | \(-0.201087\pi\) |
−0.914929 | + | 0.403615i | \(0.867754\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 66.3775 | 0.428242 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −220.515 | + | 127.314i | −1.40455 | + | 0.810919i | −0.994856 | − | 0.101302i | \(-0.967699\pi\) |
−0.409698 | + | 0.912221i | \(0.634366\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −121.497 | + | 210.440i | −0.745383 | + | 1.29104i | 0.204632 | + | 0.978839i | \(0.434400\pi\) |
−0.950015 | + | 0.312203i | \(0.898933\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 144.224i | − | 0.863619i | −0.901965 | − | 0.431809i | \(-0.857875\pi\) | ||
0.901965 | − | 0.431809i | \(-0.142125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 149.101 | 0.882252 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 289.593 | + | 167.196i | 1.67395 | + | 0.966453i | 0.965395 | + | 0.260793i | \(0.0839839\pi\) |
0.708550 | + | 0.705660i | \(0.249349\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −58.7956 | − | 101.837i | −0.328467 | − | 0.568922i | 0.653741 | − | 0.756719i | \(-0.273199\pi\) |
−0.982208 | + | 0.187797i | \(0.939865\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 173.481i | − | 0.958459i | −0.877690 | − | 0.479230i | \(-0.840916\pi\) | ||
0.877690 | − | 0.479230i | \(-0.159084\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 168.375 | − | 97.2114i | 0.910135 | − | 0.525467i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −209.780 | − | 121.116i | −1.12182 | − | 0.647681i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −130.991 | + | 226.884i | −0.685819 | + | 1.18787i | 0.287360 | + | 0.957823i | \(0.407222\pi\) |
−0.973179 | + | 0.230050i | \(0.926111\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.7990 | − | 25.6326i | −0.0766787 | − | 0.132811i | 0.825136 | − | 0.564934i | \(-0.191098\pi\) |
−0.901815 | + | 0.432122i | \(0.857765\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 237.282 | 1.20448 | 0.602238 | − | 0.798317i | \(-0.294276\pi\) | ||||
0.602238 | + | 0.798317i | \(0.294276\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.5871 | − | 14.7727i | 0.128579 | − | 0.0742349i | −0.434331 | − | 0.900753i | \(-0.643015\pi\) |
0.562910 | + | 0.826518i | \(0.309682\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −134.844 | + | 233.557i | −0.657777 | + | 1.13930i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 177.832i | − | 0.850873i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −157.990 | −0.748767 | −0.374384 | − | 0.927274i | \(-0.622146\pi\) | ||||
−0.374384 | + | 0.927274i | \(0.622146\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.10957 | − | 4.68206i | −0.0377189 | − | 0.0217770i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.4680 | + | 49.3081i | 0.128815 | + | 0.223114i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 225.779i | − | 1.01246i | −0.862397 | − | 0.506232i | \(-0.831038\pi\) | ||
0.862397 | − | 0.506232i | \(-0.168962\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −124.902 | + | 72.1122i | −0.550229 | + | 0.317675i | −0.749214 | − | 0.662328i | \(-0.769569\pi\) |
0.198985 | + | 0.980002i | \(0.436235\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −107.880 | − | 62.2845i | −0.471092 | − | 0.271985i | 0.245605 | − | 0.969370i | \(-0.421013\pi\) |
−0.716697 | + | 0.697385i | \(0.754347\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 213.486 | − | 369.769i | 0.916251 | − | 1.58699i | 0.111190 | − | 0.993799i | \(-0.464534\pi\) |
0.805060 | − | 0.593193i | \(-0.202133\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −107.693 | − | 186.530i | −0.458270 | − | 0.793747i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.5160 | 0.119314 | 0.0596568 | − | 0.998219i | \(-0.480999\pi\) | ||||
0.0596568 | + | 0.998219i | \(0.480999\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −203.548 | + | 117.518i | −0.844597 | + | 0.487628i | −0.858824 | − | 0.512271i | \(-0.828805\pi\) |
0.0142272 | + | 0.999899i | \(0.495471\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.8995 | + | 36.1990i | −0.0846133 | + | 0.146555i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 193.568i | − | 0.771186i | −0.922669 | − | 0.385593i | \(-0.873997\pi\) | ||
0.922669 | − | 0.385593i | \(-0.126003\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 323.990 | 1.28059 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −128.586 | − | 74.2394i | −0.500336 | − | 0.288869i | 0.228516 | − | 0.973540i | \(-0.426613\pi\) |
−0.728852 | + | 0.684671i | \(0.759946\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 223.882 | + | 387.774i | 0.851261 | + | 1.47443i | 0.880071 | + | 0.474842i | \(0.157495\pi\) |
−0.0288108 | + | 0.999585i | \(0.509172\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 161.489i | 0.609391i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −158.803 | + | 91.6849i | −0.590345 | + | 0.340836i | −0.765234 | − | 0.643752i | \(-0.777377\pi\) |
0.174889 | + | 0.984588i | \(0.444043\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −116.984 | − | 67.5407i | −0.431675 | − | 0.249228i | 0.268385 | − | 0.963312i | \(-0.413510\pi\) |
−0.700060 | + | 0.714084i | \(0.746843\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 65.4717 | − | 113.400i | 0.238079 | − | 0.412365i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.3015 | − | 17.8427i | −0.0371896 | − | 0.0644143i | 0.846832 | − | 0.531861i | \(-0.178507\pi\) |
−0.884021 | + | 0.467447i | \(0.845174\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −241.001 | −0.857654 | −0.428827 | − | 0.903387i | \(-0.641073\pi\) | ||||
−0.428827 | + | 0.903387i | \(0.641073\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 76.8765 | − | 44.3847i | 0.271648 | − | 0.156836i | −0.357988 | − | 0.933726i | \(-0.616537\pi\) |
0.629637 | + | 0.776890i | \(0.283204\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −63.0477 | + | 109.202i | −0.218158 | + | 0.377861i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 275.258i | 0.939446i | 0.882814 | + | 0.469723i | \(0.155646\pi\) | ||||
−0.882814 | + | 0.469723i | \(0.844354\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −287.789 | −0.975556 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −65.9503 | − | 38.0764i | −0.220570 | − | 0.127346i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 134.806 | + | 233.491i | 0.441988 | + | 0.765545i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 366.196i | − | 1.19282i | −0.802680 | − | 0.596410i | \(-0.796593\pi\) | ||
0.802680 | − | 0.596410i | \(-0.203407\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −256.062 | + | 147.837i | −0.823350 | + | 0.475361i | −0.851570 | − | 0.524240i | \(-0.824349\pi\) |
0.0282202 | + | 0.999602i | \(0.491016\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 200.791 | + | 115.927i | 0.641504 | + | 0.370373i | 0.785194 | − | 0.619250i | \(-0.212563\pi\) |
−0.143689 | + | 0.989623i | \(0.545897\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −154.691 | + | 267.932i | −0.487983 | + | 0.845212i | −0.999904 | − | 0.0138204i | \(-0.995601\pi\) |
0.511921 | + | 0.859033i | \(0.328934\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 198.196 | + | 343.285i | 0.621304 | + | 1.07613i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 119.595 | 0.370262 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.6544 | + | 15.3889i | −0.0820135 | + | 0.0473505i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 116.593 | − | 201.945i | 0.352244 | − | 0.610105i | −0.634398 | − | 0.773007i | \(-0.718752\pi\) |
0.986642 | + | 0.162901i | \(0.0520852\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 116.560i | 0.347939i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 172.894 | 0.513040 | 0.256520 | − | 0.966539i | \(-0.417424\pi\) | ||||
0.256520 | + | 0.966539i | \(0.417424\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −256.432 | − | 148.051i | −0.752001 | − | 0.434168i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −232.465 | − | 402.641i | −0.669928 | − | 1.16035i | −0.977924 | − | 0.208962i | \(-0.932992\pi\) |
0.307996 | − | 0.951388i | \(-0.400342\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 426.071i | 1.22083i | 0.792080 | + | 0.610417i | \(0.208998\pi\) | ||||
−0.792080 | + | 0.610417i | \(0.791002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 349.655 | − | 201.873i | 0.990524 | − | 0.571880i | 0.0850934 | − | 0.996373i | \(-0.472881\pi\) |
0.905431 | + | 0.424493i | \(0.139548\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −55.8706 | − | 32.2569i | −0.157382 | − | 0.0908646i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 37.0516 | − | 64.1752i | 0.103208 | − | 0.178761i | −0.809797 | − | 0.586710i | \(-0.800423\pi\) |
0.913005 | + | 0.407949i | \(0.133756\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −136.601 | − | 236.599i | −0.378395 | − | 0.655399i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 356.589 | 0.976955 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 264.136 | − | 152.499i | 0.719718 | − | 0.415529i | −0.0949312 | − | 0.995484i | \(-0.530263\pi\) |
0.814649 | + | 0.579955i | \(0.196930\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 64.7035 | − | 112.070i | 0.173468 | − | 0.300455i | −0.766162 | − | 0.642647i | \(-0.777836\pi\) |
0.939630 | + | 0.342192i | \(0.111169\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 93.1707i | − | 0.247137i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −276.804 | −0.730354 | −0.365177 | − | 0.930938i | \(-0.618991\pi\) | ||||
−0.365177 | + | 0.930938i | \(0.618991\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 573.297 | + | 330.993i | 1.49686 | + | 0.864212i | 0.999993 | − | 0.00361454i | \(-0.00115055\pi\) |
0.496866 | + | 0.867827i | \(0.334484\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −204.045 | − | 353.416i | −0.524537 | − | 0.908525i | −0.999592 | − | 0.0285687i | \(-0.990905\pi\) |
0.475055 | − | 0.879956i | \(-0.342428\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 217.887i | 0.557256i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 490.758 | − | 283.339i | 1.24242 | − | 0.717314i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 614.993 | + | 355.066i | 1.54910 | + | 0.894373i | 0.998211 | + | 0.0597948i | \(0.0190446\pi\) |
0.550889 | + | 0.834578i | \(0.314289\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −336.800 | + | 583.355i | −0.839900 | + | 1.45475i | 0.0500773 | + | 0.998745i | \(0.484053\pi\) |
−0.889978 | + | 0.456004i | \(0.849280\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.7990 | + | 60.2736i | 0.0863499 | + | 0.149562i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −867.298 | −2.13095 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −256.703 | + | 148.207i | −0.627635 | + | 0.362365i | −0.779835 | − | 0.625985i | \(-0.784697\pi\) |
0.152201 | + | 0.988350i | \(0.451364\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 233.487 | − | 404.412i | 0.562620 | − | 0.974487i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 357.803i | 0.853945i | 0.904265 | + | 0.426973i | \(0.140420\pi\) | ||||
−0.904265 | + | 0.426973i | \(0.859580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 185.186 | 0.439871 | 0.219936 | − | 0.975514i | \(-0.429415\pi\) | ||||
0.219936 | + | 0.975514i | \(0.429415\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 76.2631 | + | 44.0305i | 0.179443 | + | 0.103601i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −360.643 | − | 624.652i | −0.836759 | − | 1.44931i | −0.892590 | − | 0.450869i | \(-0.851114\pi\) |
0.0558311 | − | 0.998440i | \(-0.482219\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 585.095i | 1.35126i | 0.737242 | + | 0.675629i | \(0.236128\pi\) | ||||
−0.737242 | + | 0.675629i | \(0.763872\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −138.529 | + | 79.9797i | −0.317000 | + | 0.183020i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −131.893 | − | 76.1482i | −0.300439 | − | 0.173458i | 0.342201 | − | 0.939627i | \(-0.388828\pi\) |
−0.642640 | + | 0.766168i | \(0.722161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 358.736 | − | 621.348i | 0.809787 | − | 1.40259i | −0.103224 | − | 0.994658i | \(-0.532916\pi\) |
0.913011 | − | 0.407934i | \(-0.133751\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 170.136 | + | 294.684i | 0.382327 | + | 0.662210i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.3522 | −0.0297376 | −0.0148688 | − | 0.999889i | \(-0.504733\pi\) | ||||
−0.0148688 | + | 0.999889i | \(0.504733\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1041.87 | − | 601.524i | 2.31013 | − | 1.33376i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 277.095 | − | 479.943i | 0.606336 | − | 1.05020i | −0.385503 | − | 0.922707i | \(-0.625972\pi\) |
0.991839 | − | 0.127498i | \(-0.0406946\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 336.103i | − | 0.729074i | −0.931189 | − | 0.364537i | \(-0.881227\pi\) | ||
0.931189 | − | 0.364537i | \(-0.118773\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −481.186 | −1.03928 | −0.519639 | − | 0.854386i | \(-0.673934\pi\) | ||||
−0.519639 | + | 0.854386i | \(0.673934\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −334.899 | − | 193.354i | −0.717128 | − | 0.414034i | 0.0965670 | − | 0.995326i | \(-0.469214\pi\) |
−0.813695 | + | 0.581293i | \(0.802547\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.8862 | + | 36.1759i | 0.0441568 | + | 0.0764818i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 64.6490i | 0.136103i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −232.474 | + | 134.219i | −0.485332 | + | 0.280206i | −0.722636 | − | 0.691229i | \(-0.757070\pi\) |
0.237304 | + | 0.971435i | \(0.423736\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 176.544 | + | 101.928i | 0.367036 | + | 0.211908i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −254.305 | + | 440.469i | −0.524340 | + | 0.908184i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 42.8995 | + | 74.3041i | 0.0880893 | + | 0.152575i | 0.906703 | − | 0.421769i | \(-0.138591\pi\) |
−0.818614 | + | 0.574344i | \(0.805257\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 465.122 | 0.947295 | 0.473647 | − | 0.880715i | \(-0.342937\pi\) | ||||
0.473647 | + | 0.880715i | \(0.342937\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −230.864 | + | 133.289i | −0.468283 | + | 0.270364i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 427.784 | − | 740.943i | 0.857282 | − | 1.48486i | −0.0172292 | − | 0.999852i | \(-0.505485\pi\) |
0.874511 | − | 0.485005i | \(-0.161182\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 432.245i | 0.859335i | 0.902987 | + | 0.429667i | \(0.141369\pi\) | ||||
−0.902987 | + | 0.429667i | \(0.858631\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 628.060 | 1.24368 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −231.752 | − | 133.802i | −0.455308 | − | 0.262872i | 0.254761 | − | 0.967004i | \(-0.418003\pi\) |
−0.710069 | + | 0.704132i | \(0.751336\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 391.972 | + | 678.916i | 0.761111 | + | 1.31828i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 960.816i | 1.85844i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −290.703 | + | 167.838i | −0.557972 | + | 0.322145i | −0.752331 | − | 0.658785i | \(-0.771071\pi\) |
0.194359 | + | 0.980930i | \(0.437737\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 840.091 | + | 485.027i | 1.60629 | + | 0.927393i | 0.990190 | + | 0.139727i | \(0.0446224\pi\) |
0.616102 | + | 0.787666i | \(0.288711\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 99.5663 | − | 172.454i | 0.188930 | − | 0.327237i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 118.786 | + | 205.744i | 0.224549 | + | 0.388930i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −282.773 | −0.530531 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 174.640 | − | 100.828i | 0.326430 | − | 0.188464i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 175.090 | − | 303.265i | 0.323642 | − | 0.560565i | −0.657594 | − | 0.753372i | \(-0.728426\pi\) |
0.981237 | + | 0.192807i | \(0.0617593\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 420.743i | 0.772006i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −648.794 | −1.18609 | −0.593047 | − | 0.805167i | \(-0.702075\pi\) | ||||
−0.593047 | + | 0.805167i | \(0.702075\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −169.486 | − | 97.8528i | −0.307597 | − | 0.177591i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 439.371 | + | 761.013i | 0.788817 | + | 1.36627i | 0.926692 | + | 0.375822i | \(0.122640\pi\) |
−0.137875 | + | 0.990450i | \(0.544027\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.81845i | − | 0.0175643i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −508.828 | + | 293.772i | −0.903780 | + | 0.521798i | −0.878425 | − | 0.477881i | \(-0.841405\pi\) |
−0.0253555 | + | 0.999678i | \(0.508072\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 692.238 | + | 399.664i | 1.22520 | + | 0.707369i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 52.1195 | − | 90.2737i | 0.0915985 | − | 0.158653i | −0.816585 | − | 0.577225i | \(-0.804136\pi\) |
0.908184 | + | 0.418571i | \(0.137469\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 235.693 | + | 408.233i | 0.412773 | + | 0.714944i | 0.995192 | − | 0.0979450i | \(-0.0312269\pi\) |
−0.582419 | + | 0.812889i | \(0.697894\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −117.783 | −0.204840 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 411.347 | − | 237.491i | 0.712907 | − | 0.411597i | −0.0992296 | − | 0.995065i | \(-0.531638\pi\) |
0.812136 | + | 0.583468i | \(0.198304\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 360.191 | − | 623.869i | 0.617823 | − | 1.07010i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 539.013i | − | 0.918251i | −0.888371 | − | 0.459125i | \(-0.848163\pi\) | ||
0.888371 | − | 0.459125i | \(-0.151837\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 146.191 | 0.248202 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 89.8901 | + | 51.8981i | 0.151585 | + | 0.0875178i | 0.573874 | − | 0.818944i | \(-0.305440\pi\) |
−0.422289 | + | 0.906461i | \(0.638773\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 275.095 | + | 476.479i | 0.459257 | + | 0.795457i | 0.998922 | − | 0.0464229i | \(-0.0147822\pi\) |
−0.539664 | + | 0.841880i | \(0.681449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 848.487i | 1.41179i | 0.708315 | + | 0.705896i | \(0.249456\pi\) | ||||
−0.708315 | + | 0.705896i | \(0.750544\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 881.294 | − | 508.815i | 1.45668 | − | 0.841017i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −515.032 | − | 297.354i | −0.848488 | − | 0.489875i | 0.0116523 | − | 0.999932i | \(-0.496291\pi\) |
−0.860140 | + | 0.510057i | \(0.829624\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 112.918 | − | 195.580i | 0.184809 | − | 0.320099i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −258.754 | − | 448.175i | −0.422111 | − | 0.731117i | 0.574035 | − | 0.818831i | \(-0.305377\pi\) |
−0.996146 | + | 0.0877137i | \(0.972044\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 681.421 | 1.10441 | 0.552205 | − | 0.833708i | \(-0.313786\pi\) | ||||
0.552205 | + | 0.833708i | \(0.313786\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 774.084 | − | 446.918i | 1.25054 | − | 0.721999i | 0.279323 | − | 0.960197i | \(-0.409890\pi\) |
0.971217 | + | 0.238198i | \(0.0765567\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 202.455 | − | 350.662i | 0.323928 | − | 0.561059i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 583.268i | − | 0.927295i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −949.588 | −1.50489 | −0.752447 | − | 0.658653i | \(-0.771127\pi\) | ||||
−0.752447 | + | 0.658653i | \(0.771127\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 84.7244 | + | 48.9156i | 0.133424 | + | 0.0770325i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −215.394 | − | 373.073i | −0.336028 | − | 0.582017i | 0.647654 | − | 0.761935i | \(-0.275750\pi\) |
−0.983682 | + | 0.179917i | \(0.942417\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 540.999i | 0.841368i | 0.907207 | + | 0.420684i | \(0.138210\pi\) | ||||
−0.907207 | + | 0.420684i | \(0.861790\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −85.8353 | + | 49.5570i | −0.132667 | + | 0.0765951i | −0.564864 | − | 0.825184i | \(-0.691072\pi\) |
0.432198 | + | 0.901779i | \(0.357738\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1111.80 | + | 641.897i | 1.71309 | + | 0.989055i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 414.622 | − | 718.147i | 0.634950 | − | 1.09977i | −0.351576 | − | 0.936159i | \(-0.614354\pi\) |
0.986526 | − | 0.163606i | \(-0.0523126\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 305.889 | + | 529.816i | 0.467007 | + | 0.808879i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 584.716 | 0.887278 | 0.443639 | − | 0.896206i | \(-0.353687\pi\) | ||||
0.443639 | + | 0.896206i | \(0.353687\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −333.657 | + | 192.637i | −0.504776 | + | 0.291433i | −0.730684 | − | 0.682716i | \(-0.760799\pi\) |
0.225908 | + | 0.974149i | \(0.427465\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 178.276 | − | 308.784i | 0.267281 | − | 0.462944i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1202.71i | − | 1.79241i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 797.266 | 1.18465 | 0.592323 | − | 0.805701i | \(-0.298211\pi\) | ||||
0.592323 | + | 0.805701i | \(0.298211\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 415.605 | + | 239.950i | 0.613893 | + | 0.354431i | 0.774487 | − | 0.632589i | \(-0.218008\pi\) |
−0.160595 | + | 0.987020i | \(0.551341\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −535.170 | − | 926.942i | −0.783559 | − | 1.35716i | −0.929856 | − | 0.367923i | \(-0.880069\pi\) |
0.146298 | − | 0.989241i | \(-0.453264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 282.809i | 0.412860i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −146.639 | + | 84.6618i | −0.212828 | + | 0.122876i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.9344 | − | 14.9732i | −0.0375317 | − | 0.0216690i | 0.481117 | − | 0.876657i | \(-0.340231\pi\) |
−0.518648 | + | 0.854988i | \(0.673565\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −523.870 | + | 907.369i | −0.753769 | + | 1.30557i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 404.533 | + | 700.671i | 0.580391 | + | 1.00527i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −396.453 | −0.565554 | −0.282777 | − | 0.959186i | \(-0.591256\pi\) | ||||
−0.282777 | + | 0.959186i | \(0.591256\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 370.832 | − | 214.100i | 0.527499 | − | 0.304552i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 173.749 | − | 300.942i | 0.245062 | − | 0.424459i | −0.717087 | − | 0.696983i | \(-0.754525\pi\) |
0.962149 | + | 0.272524i | \(0.0878584\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 266.343i | 0.373552i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −360.191 | −0.503764 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 910.047 | + | 525.416i | 1.26571 | + | 0.730760i | 0.974174 | − | 0.225799i | \(-0.0724994\pi\) |
0.291539 | + | 0.956559i | \(0.405833\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −72.0519 | − | 124.798i | −0.0993820 | − | 0.172135i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.3417i | 0.0651193i | 0.999470 | + | 0.0325596i | \(0.0103659\pi\) | ||||
−0.999470 | + | 0.0325596i | \(0.989634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.3287 | + | 14.0462i | −0.0332814 | + | 0.0192150i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −53.9898 | − | 31.1710i | −0.0736559 | − | 0.0425252i | 0.462720 | − | 0.886505i | \(-0.346874\pi\) |
−0.536376 | + | 0.843979i | \(0.680207\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 259.979 | − | 450.297i | 0.352754 | − | 0.610987i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −669.176 | − | 1159.05i | −0.905515 | − | 1.56840i | −0.820224 | − | 0.572042i | \(-0.806151\pi\) |
−0.0852911 | − | 0.996356i | \(-0.527182\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −242.908 | −0.326929 | −0.163464 | − | 0.986549i | \(-0.552267\pi\) | ||||
−0.163464 | + | 0.986549i | \(0.552267\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −293.762 | + | 169.604i | −0.394312 | + | 0.227656i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 496.291 | − | 859.602i | 0.660841 | − | 1.14461i | −0.319554 | − | 0.947568i | \(-0.603533\pi\) |
0.980395 | − | 0.197042i | \(-0.0631335\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 138.666i | 0.183663i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 780.060 | 1.03046 | 0.515231 | − | 0.857051i | \(-0.327706\pi\) | ||||
0.515231 | + | 0.857051i | \(0.327706\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 402.349 | + | 232.296i | 0.528711 | + | 0.305251i | 0.740491 | − | 0.672066i | \(-0.234593\pi\) |
−0.211781 | + | 0.977317i | \(0.567926\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −150.876 | − | 261.325i | −0.196709 | − | 0.340710i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 611.409i | 0.795071i | 0.917587 | + | 0.397535i | \(0.130134\pi\) | ||||
−0.917587 | + | 0.397535i | \(0.869866\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 204.128 | − | 117.853i | 0.264072 | − | 0.152462i | −0.362119 | − | 0.932132i | \(-0.617947\pi\) |
0.626191 | + | 0.779670i | \(0.284613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 93.2231 | + | 53.8224i | 0.120288 | + | 0.0694482i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −296.983 | + | 514.390i | −0.381236 | + | 0.660321i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 143.894 | + | 249.232i | 0.184244 | + | 0.319120i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1083.31 | 1.38001 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 515.266 | − | 297.489i | 0.654722 | − | 0.378004i | −0.135541 | − | 0.990772i | \(-0.543277\pi\) |
0.790263 | + | 0.612768i | \(0.209944\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −141.347 | + | 244.820i | −0.178243 | + | 0.308726i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 547.544i | 0.687006i | 0.939152 | + | 0.343503i | \(0.111614\pi\) | ||||
−0.939152 | + | 0.343503i | \(0.888386\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −646.161 | −0.808712 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1377.59 | − | 795.350i | −1.71555 | − | 0.990474i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 256.069 | + | 443.524i | 0.316525 | + | 0.548237i | 0.979760 | − | 0.200174i | \(-0.0641506\pi\) |
−0.663236 | + | 0.748411i | \(0.730817\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1615.33i | − | 1.99178i | −0.0905851 | − | 0.995889i | \(-0.528874\pi\) | ||
0.0905851 | − | 0.995889i | \(-0.471126\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 895.310 | − | 516.907i | 1.09854 | − | 0.634242i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.8607 | − | 10.3119i | −0.0218613 | − | 0.0126216i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 490.777 | − | 850.050i | 0.597779 | − | 1.03538i | −0.395369 | − | 0.918522i | \(-0.629383\pi\) |
0.993148 | − | 0.116861i | \(-0.0372833\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 678.276 | + | 1174.81i | 0.824151 | + | 1.42747i | 0.902566 | + | 0.430551i | \(0.141681\pi\) |
−0.0784154 | + | 0.996921i | \(0.524986\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −601.883 | −0.727791 | −0.363896 | − | 0.931440i | \(-0.618554\pi\) | ||||
−0.363896 | + | 0.931440i | \(0.618554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 154.783 | − | 89.3641i | 0.186711 | − | 0.107798i | −0.403731 | − | 0.914878i | \(-0.632287\pi\) |
0.590442 | + | 0.807080i | \(0.298954\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −306.799 | + | 531.391i | −0.367424 | + | 0.636397i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 852.989i | 1.01667i | 0.861158 | + | 0.508337i | \(0.169739\pi\) | ||||
−0.861158 | + | 0.508337i | \(0.830261\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −404.769 | −0.481295 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −549.358 | − | 317.172i | −0.650127 | − | 0.375351i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 390.065 | + | 675.612i | 0.458361 | + | 0.793904i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 855.303i | 1.00270i | 0.865245 | + | 0.501350i | \(0.167163\pi\) | ||||
−0.865245 | + | 0.501350i | \(0.832837\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1251.22 | + | 722.394i | −1.46000 | + | 0.842933i | −0.999011 | − | 0.0444708i | \(-0.985840\pi\) |
−0.460992 | + | 0.887404i | \(0.652506\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −367.259 | − | 212.037i | −0.427543 | − | 0.246842i | 0.270756 | − | 0.962648i | \(-0.412726\pi\) |
−0.698299 | + | 0.715806i | \(0.746060\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −674.602 | + | 1168.44i | −0.781694 | + | 1.35393i | 0.149261 | + | 0.988798i | \(0.452311\pi\) |
−0.930955 | + | 0.365135i | \(0.881023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −711.332 | − | 1232.06i | −0.822349 | − | 1.42435i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2527.89 | −2.90896 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −105.841 | + | 61.1074i | −0.121517 | + | 0.0701577i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −321.829 | + | 557.424i | −0.366966 | + | 0.635603i | −0.989090 | − | 0.147315i | \(-0.952937\pi\) |
0.622124 | + | 0.782919i | \(0.286270\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1206.54i | 1.36951i | 0.728774 | + | 0.684754i | \(0.240091\pi\) | ||||
−0.728774 | + | 0.684754i | \(0.759909\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 652.754 | 0.739245 | 0.369623 | − | 0.929182i | \(-0.379487\pi\) | ||||
0.369623 | + | 0.929182i | \(0.379487\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −910.418 | − | 525.630i | −1.02640 | − | 0.592593i | −0.110450 | − | 0.993882i | \(-0.535229\pi\) |
−0.915952 | + | 0.401289i | \(0.868562\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −237.186 | − | 410.818i | −0.265606 | − | 0.460042i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 500.288i | 0.558981i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −282.205 | + | 162.931i | −0.313910 | + | 0.181236i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 419.560 | + | 242.233i | 0.465660 | + | 0.268849i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −369.035 | + | 639.187i | −0.407773 | + | 0.706284i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −143.080 | − | 247.822i | −0.157751 | − | 0.273233i | 0.776306 | − | 0.630356i | \(-0.217091\pi\) |
−0.934057 | + | 0.357123i | \(0.883758\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 713.465 | 0.783167 | 0.391583 | − | 0.920143i | \(-0.371927\pi\) | ||||
0.391583 | + | 0.920143i | \(0.371927\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1804.04 | + | 1041.56i | −1.97594 | + | 1.14081i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −170.698 | + | 295.658i | −0.185744 | + | 0.321718i | −0.943827 | − | 0.330440i | \(-0.892803\pi\) |
0.758083 | + | 0.652158i | \(0.226136\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 67.6439i | − | 0.0732870i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 315.296 | 0.340861 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −79.5587 | − | 45.9332i | −0.0856390 | − | 0.0494437i | 0.456569 | − | 0.889688i | \(-0.349078\pi\) |
−0.542208 | + | 0.840244i | \(0.682412\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 515.286 | + | 892.501i | 0.551108 | + | 0.954547i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 906.902i | − | 0.967879i | −0.875102 | − | 0.483939i | \(-0.839206\pi\) | ||
0.875102 | − | 0.483939i | \(-0.160794\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 337.880 | − | 195.075i | 0.359064 | − | 0.207306i | −0.309606 | − | 0.950865i | \(-0.600197\pi\) |
0.668670 | + | 0.743559i | \(0.266864\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −937.158 | − | 541.068i | −0.993804 | − | 0.573773i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 304.757 | − | 527.854i | 0.321813 | − | 0.557396i | −0.659049 | − | 0.752100i | \(-0.729041\pi\) |
0.980862 | + | 0.194704i | \(0.0623745\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 186.945 | + | 323.798i | 0.196991 | + | 0.341199i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 110.441 | 0.115887 | 0.0579437 | − | 0.998320i | \(-0.481546\pi\) | ||||
0.0579437 | + | 0.998320i | \(0.481546\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 965.269 | − | 557.299i | 1.01075 | − | 0.583559i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −358.791 | + | 621.445i | −0.373352 | + | 0.646665i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 125.924i | 0.130491i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1125.53 | −1.16394 | −0.581969 | − | 0.813211i | \(-0.697717\pi\) | ||||
−0.581969 | + | 0.813211i | \(0.697717\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 977.849 | + | 564.562i | 1.00705 | + | 0.581423i | 0.910328 | − | 0.413888i | \(-0.135830\pi\) |
0.0967262 | + | 0.995311i | \(0.469163\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −756.430 | − | 1310.18i | −0.774238 | − | 1.34102i | −0.935222 | − | 0.354062i | \(-0.884800\pi\) |
0.160984 | − | 0.986957i | \(-0.448533\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1517.91i | − | 1.55047i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −501.830 | + | 289.731i | −0.510508 | + | 0.294742i | −0.733043 | − | 0.680183i | \(-0.761900\pi\) |
0.222534 | + | 0.974925i | \(0.428567\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −874.259 | − | 504.754i | −0.887573 | − | 0.512440i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.7870 | − | 32.5400i | 0.0189959 | − | 0.0329019i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −86.3768 | − | 149.609i | −0.0871612 | − | 0.150968i | 0.819149 | − | 0.573581i | \(-0.194446\pi\) |
−0.906310 | + | 0.422613i | \(0.861113\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −125.700 | −0.126332 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −333.267 | + | 192.412i | −0.334270 | + | 0.192991i | −0.657735 | − | 0.753249i | \(-0.728485\pi\) |
0.323465 | + | 0.946240i | \(0.395152\pi\) | |||||||
\(998\) | 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 | 1764.3.z.n.901.4 | 16 | ||
3.2 | odd | 2 | inner | 1764.3.z.n.901.5 | 16 | ||
7.2 | even | 3 | 1764.3.d.g.685.5 | yes | 8 | ||
7.3 | odd | 6 | inner | 1764.3.z.n.325.4 | 16 | ||
7.4 | even | 3 | inner | 1764.3.z.n.325.6 | 16 | ||
7.5 | odd | 6 | 1764.3.d.g.685.3 | ✓ | 8 | ||
7.6 | odd | 2 | inner | 1764.3.z.n.901.6 | 16 | ||
21.2 | odd | 6 | 1764.3.d.g.685.4 | yes | 8 | ||
21.5 | even | 6 | 1764.3.d.g.685.6 | yes | 8 | ||
21.11 | odd | 6 | inner | 1764.3.z.n.325.3 | 16 | ||
21.17 | even | 6 | inner | 1764.3.z.n.325.5 | 16 | ||
21.20 | even | 2 | inner | 1764.3.z.n.901.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.3.d.g.685.3 | ✓ | 8 | 7.5 | odd | 6 | ||
1764.3.d.g.685.4 | yes | 8 | 21.2 | odd | 6 | ||
1764.3.d.g.685.5 | yes | 8 | 7.2 | even | 3 | ||
1764.3.d.g.685.6 | yes | 8 | 21.5 | even | 6 | ||
1764.3.z.n.325.3 | 16 | 21.11 | odd | 6 | inner | ||
1764.3.z.n.325.4 | 16 | 7.3 | odd | 6 | inner | ||
1764.3.z.n.325.5 | 16 | 21.17 | even | 6 | inner | ||
1764.3.z.n.325.6 | 16 | 7.4 | even | 3 | inner | ||
1764.3.z.n.901.3 | 16 | 21.20 | even | 2 | inner | ||
1764.3.z.n.901.4 | 16 | 1.1 | even | 1 | trivial | ||
1764.3.z.n.901.5 | 16 | 3.2 | odd | 2 | inner | ||
1764.3.z.n.901.6 | 16 | 7.6 | odd | 2 | inner |