Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(163,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.163");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.d (of order \(2\), degree \(1\), 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: | \(8.82836056527\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1919698923024.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 2x^{6} + 12x^{5} - 36x^{4} + 48x^{3} + 32x^{2} - 192x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 163.2 | ||
Root | \(1.81766 - 0.834343i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.163 |
Dual form | 324.3.d.g.163.1 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.81766 | + | 0.834343i | −0.908828 | + | 0.417171i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.60775 | − | 3.03310i | 0.651936 | − | 0.758274i | ||||
\(5\) | 6.14806 | 1.22961 | 0.614806 | − | 0.788678i | \(-0.289234\pi\) | ||||
0.614806 | + | 0.788678i | \(0.289234\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.590679i | − | 0.0843828i | −0.999110 | − | 0.0421914i | \(-0.986566\pi\) | ||
0.999110 | − | 0.0421914i | \(-0.0134339\pi\) | |||||||
\(8\) | −2.20934 | + | 7.68888i | −0.276168 | + | 0.961109i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −11.1751 | + | 5.12959i | −1.11751 | + | 0.512959i | ||||
\(11\) | 17.4596i | 1.58724i | 0.608414 | + | 0.793620i | \(0.291806\pi\) | ||||
−0.608414 | + | 0.793620i | \(0.708194\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.78451 | 0.137270 | 0.0686350 | − | 0.997642i | \(-0.478136\pi\) | ||||
0.0686350 | + | 0.997642i | \(0.478136\pi\) | |||||||
\(14\) | 0.492829 | + | 1.07365i | 0.0352021 | + | 0.0766894i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.39933 | − | 15.8191i | −0.149958 | − | 0.988692i | ||||
\(17\) | 16.9171 | 0.995123 | 0.497562 | − | 0.867429i | \(-0.334229\pi\) | ||||
0.497562 | + | 0.867429i | \(0.334229\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 19.5058i | − | 1.02662i | −0.858203 | − | 0.513310i | \(-0.828419\pi\) | ||
0.858203 | − | 0.513310i | \(-0.171581\pi\) | |||||||
\(20\) | 16.0326 | − | 18.6477i | 0.801629 | − | 0.932383i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −14.5673 | − | 31.7356i | −0.662151 | − | 1.44253i | ||||
\(23\) | 7.93023i | 0.344793i | 0.985028 | + | 0.172396i | \(0.0551510\pi\) | ||||
−0.985028 | + | 0.172396i | \(0.944849\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.7987 | 0.511947 | ||||||||
\(26\) | −3.24362 | + | 1.48889i | −0.124755 | + | 0.0572651i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.79159 | − | 1.54034i | −0.0639852 | − | 0.0550122i | ||||
\(29\) | 6.35035 | 0.218977 | 0.109489 | − | 0.993988i | \(-0.465079\pi\) | ||||
0.109489 | + | 0.993988i | \(0.465079\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 31.9342i | 1.03014i | 0.857149 | + | 0.515068i | \(0.172233\pi\) | ||||
−0.857149 | + | 0.515068i | \(0.827767\pi\) | |||||||
\(32\) | 17.5597 | + | 26.7518i | 0.548740 | + | 0.835993i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −30.7495 | + | 14.1147i | −0.904396 | + | 0.415137i | ||||
\(35\) | − | 3.63153i | − | 0.103758i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 58.2834 | 1.57523 | 0.787614 | − | 0.616169i | \(-0.211316\pi\) | ||||
0.787614 | + | 0.616169i | \(0.211316\pi\) | |||||||
\(38\) | 16.2745 | + | 35.4548i | 0.428276 | + | 0.933021i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13.5832 | + | 47.2717i | −0.339579 | + | 1.18179i | ||||
\(41\) | −5.33896 | −0.130219 | −0.0651093 | − | 0.997878i | \(-0.520740\pi\) | ||||
−0.0651093 | + | 0.997878i | \(0.520740\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 39.1818i | 0.911204i | 0.890184 | + | 0.455602i | \(0.150576\pi\) | ||||
−0.890184 | + | 0.455602i | \(0.849424\pi\) | |||||||
\(44\) | 52.9567 | + | 45.5303i | 1.20356 | + | 1.03478i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.61653 | − | 14.4144i | −0.143838 | − | 0.313357i | ||||
\(47\) | − | 11.1327i | − | 0.236865i | −0.992962 | − | 0.118433i | \(-0.962213\pi\) | ||
0.992962 | − | 0.118433i | \(-0.0377870\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.6511 | 0.992880 | ||||||||
\(50\) | −23.2636 | + | 10.6785i | −0.465271 | + | 0.213569i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.65355 | − | 5.41259i | 0.0894913 | − | 0.104088i | ||||
\(53\) | −35.8770 | −0.676925 | −0.338462 | − | 0.940980i | \(-0.609907\pi\) | ||||
−0.338462 | + | 0.940980i | \(0.609907\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 107.343i | 1.95169i | ||||||||
\(56\) | 4.54166 | + | 1.30501i | 0.0811011 | + | 0.0233038i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.5427 | + | 5.29836i | −0.199013 | + | 0.0913511i | ||||
\(59\) | 24.1303i | 0.408988i | 0.978868 | + | 0.204494i | \(0.0655549\pi\) | ||||
−0.978868 | + | 0.204494i | \(0.934445\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 75.8921 | 1.24413 | 0.622066 | − | 0.782965i | \(-0.286294\pi\) | ||||
0.622066 | + | 0.782965i | \(0.286294\pi\) | |||||||
\(62\) | −26.6441 | − | 58.0454i | −0.429743 | − | 0.936216i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −54.2376 | − | 33.9747i | −0.847463 | − | 0.530855i | ||||
\(65\) | 10.9713 | 0.168789 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 36.7426i | − | 0.548396i | −0.961673 | − | 0.274198i | \(-0.911588\pi\) | ||
0.961673 | − | 0.274198i | \(-0.0884124\pi\) | |||||||
\(68\) | 44.1155 | − | 51.3112i | 0.648757 | − | 0.754576i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.02994 | + | 6.60088i | 0.0432849 | + | 0.0942983i | ||||
\(71\) | 87.8370i | 1.23714i | 0.785730 | + | 0.618570i | \(0.212288\pi\) | ||||
−0.785730 | + | 0.618570i | \(0.787712\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −60.0423 | −0.822498 | −0.411249 | − | 0.911523i | \(-0.634907\pi\) | ||||
−0.411249 | + | 0.911523i | \(0.634907\pi\) | |||||||
\(74\) | −105.939 | + | 48.6283i | −1.43161 | + | 0.657140i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −59.1629 | − | 50.8661i | −0.778459 | − | 0.669291i | ||||
\(77\) | 10.3130 | 0.133936 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 37.1630i | − | 0.470418i | −0.971945 | − | 0.235209i | \(-0.924423\pi\) | ||
0.971945 | − | 0.235209i | \(-0.0755775\pi\) | |||||||
\(80\) | −14.7512 | − | 97.2567i | −0.184391 | − | 1.21571i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.70439 | − | 4.45452i | 0.118346 | − | 0.0543234i | ||||
\(83\) | − | 76.2427i | − | 0.918587i | −0.888285 | − | 0.459294i | \(-0.848103\pi\) | ||
0.888285 | − | 0.459294i | \(-0.151897\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 104.007 | 1.22362 | ||||||||
\(86\) | −32.6910 | − | 71.2190i | −0.380128 | − | 0.828127i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −134.245 | − | 38.5743i | −1.52551 | − | 0.438344i | ||||
\(89\) | 27.5873 | 0.309969 | 0.154985 | − | 0.987917i | \(-0.450467\pi\) | ||||
0.154985 | + | 0.987917i | \(0.450467\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.05407i | − | 0.0115832i | ||||||
\(92\) | 24.0531 | + | 20.6800i | 0.261447 | + | 0.224783i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.28846 | + | 20.2354i | 0.0988134 | + | 0.215270i | ||||
\(95\) | − | 119.923i | − | 1.26234i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −26.1171 | −0.269248 | −0.134624 | − | 0.990897i | \(-0.542983\pi\) | ||||
−0.134624 | + | 0.990897i | \(0.542983\pi\) | |||||||
\(98\) | −88.4309 | + | 40.5917i | −0.902357 | + | 0.414201i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 33.3757 | − | 38.8196i | 0.333757 | − | 0.388196i | ||||
\(101\) | −25.7663 | −0.255112 | −0.127556 | − | 0.991831i | \(-0.540713\pi\) | ||||
−0.127556 | + | 0.991831i | \(0.540713\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 19.6237i | − | 0.190522i | −0.995452 | − | 0.0952609i | \(-0.969631\pi\) | ||
0.995452 | − | 0.0952609i | \(-0.0303685\pi\) | |||||||
\(104\) | −3.94259 | + | 13.7209i | −0.0379096 | + | 0.131931i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 65.2121 | − | 29.9337i | 0.615208 | − | 0.282394i | ||||
\(107\) | − | 183.200i | − | 1.71215i | −0.516850 | − | 0.856076i | \(-0.672895\pi\) | ||
0.516850 | − | 0.856076i | \(-0.327105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 100.841 | 0.925147 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(110\) | −89.5608 | − | 195.112i | −0.814189 | − | 1.77375i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.34400 | + | 1.41724i | −0.0834286 | + | 0.0126539i | ||||
\(113\) | −18.2497 | −0.161502 | −0.0807508 | − | 0.996734i | \(-0.525732\pi\) | ||||
−0.0807508 | + | 0.996734i | \(0.525732\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 48.7555i | 0.423961i | ||||||||
\(116\) | 16.5601 | − | 19.2612i | 0.142759 | − | 0.166045i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −20.1329 | − | 43.8606i | −0.170618 | − | 0.371700i | ||||
\(119\) | − | 9.99258i | − | 0.0839713i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −183.839 | −1.51933 | ||||||||
\(122\) | −137.946 | + | 63.3200i | −1.13070 | + | 0.519016i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 96.8595 | + | 83.2763i | 0.781125 | + | 0.671583i | ||||
\(125\) | −75.0146 | −0.600117 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 164.386i | − | 1.29438i | −0.762331 | − | 0.647188i | \(-0.775945\pi\) | ||
0.762331 | − | 0.647188i | \(-0.224055\pi\) | |||||||
\(128\) | 126.932 | + | 16.5016i | 0.991655 | + | 0.128919i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −19.9420 | + | 9.15380i | −0.153400 | + | 0.0704139i | ||||
\(131\) | 142.514i | 1.08789i | 0.839120 | + | 0.543947i | \(0.183071\pi\) | ||||
−0.839120 | + | 0.543947i | \(0.816929\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.5217 | −0.0866290 | ||||||||
\(134\) | 30.6559 | + | 66.7853i | 0.228775 | + | 0.498398i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −37.3757 | + | 130.073i | −0.274821 | + | 0.956422i | ||||
\(137\) | −6.16352 | −0.0449892 | −0.0224946 | − | 0.999747i | \(-0.507161\pi\) | ||||
−0.0224946 | + | 0.999747i | \(0.507161\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 119.128i | 0.857039i | 0.903533 | + | 0.428519i | \(0.140965\pi\) | ||||
−0.903533 | + | 0.428519i | \(0.859035\pi\) | |||||||
\(140\) | −11.0148 | − | 9.47011i | −0.0786771 | − | 0.0676437i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −73.2861 | − | 159.657i | −0.516099 | − | 1.12435i | ||||
\(143\) | 31.1569i | 0.217880i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 39.0423 | 0.269257 | ||||||||
\(146\) | 109.136 | − | 50.0959i | 0.747509 | − | 0.343122i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 151.988 | − | 176.779i | 1.02695 | − | 1.19445i | ||||
\(149\) | −206.730 | −1.38745 | −0.693726 | − | 0.720239i | \(-0.744032\pi\) | ||||
−0.693726 | + | 0.720239i | \(0.744032\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 147.134i | − | 0.974398i | −0.873291 | − | 0.487199i | \(-0.838019\pi\) | ||
0.873291 | − | 0.487199i | \(-0.161981\pi\) | |||||||
\(152\) | 149.977 | + | 43.0949i | 0.986694 | + | 0.283519i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −18.7456 | + | 8.60461i | −0.121724 | + | 0.0558741i | ||||
\(155\) | 196.334i | 1.26667i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −62.8790 | −0.400503 | −0.200251 | − | 0.979745i | \(-0.564176\pi\) | ||||
−0.200251 | + | 0.979745i | \(0.564176\pi\) | |||||||
\(158\) | 31.0067 | + | 67.5496i | 0.196245 | + | 0.427529i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 107.958 | + | 164.472i | 0.674738 | + | 1.02795i | ||||
\(161\) | 4.68422 | 0.0290946 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 143.325i | − | 0.879292i | −0.898171 | − | 0.439646i | \(-0.855104\pi\) | ||
0.898171 | − | 0.439646i | \(-0.144896\pi\) | |||||||
\(164\) | −13.9227 | + | 16.1936i | −0.0848942 | + | 0.0987413i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 63.6126 | + | 138.583i | 0.383208 | + | 0.834838i | ||||
\(167\) | − | 173.818i | − | 1.04083i | −0.853915 | − | 0.520413i | \(-0.825778\pi\) | ||
0.853915 | − | 0.520413i | \(-0.174222\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −165.816 | −0.981157 | ||||||||
\(170\) | −189.050 | + | 86.7777i | −1.11206 | + | 0.510457i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 118.842 | + | 102.176i | 0.690942 | + | 0.594047i | ||||
\(173\) | −251.612 | −1.45440 | −0.727201 | − | 0.686425i | \(-0.759179\pi\) | ||||
−0.727201 | + | 0.686425i | \(0.759179\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 7.55991i | − | 0.0431995i | ||||||
\(176\) | 276.195 | − | 41.8915i | 1.56929 | − | 0.238020i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −50.1442 | + | 23.0172i | −0.281709 | + | 0.129310i | ||||
\(179\) | − | 96.0059i | − | 0.536346i | −0.963371 | − | 0.268173i | \(-0.913580\pi\) | ||
0.963371 | − | 0.268173i | \(-0.0864199\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −328.757 | −1.81634 | −0.908170 | − | 0.418603i | \(-0.862520\pi\) | ||||
−0.908170 | + | 0.418603i | \(0.862520\pi\) | |||||||
\(182\) | 0.879458 | + | 1.91594i | 0.00483219 | + | 0.0105272i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −60.9745 | − | 17.5206i | −0.331383 | − | 0.0952206i | ||||
\(185\) | 358.330 | 1.93692 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 295.366i | 1.57950i | ||||||||
\(188\) | −33.7664 | − | 29.0312i | −0.179609 | − | 0.154421i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 100.057 | + | 217.978i | 0.526614 | + | 1.14725i | ||||
\(191\) | − | 0.406356i | − | 0.00212752i | −0.999999 | − | 0.00106376i | \(-0.999661\pi\) | ||
0.999999 | − | 0.00106376i | \(-0.000338605\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 62.4459 | 0.323554 | 0.161777 | − | 0.986827i | \(-0.448277\pi\) | ||||
0.161777 | + | 0.986827i | \(0.448277\pi\) | |||||||
\(194\) | 47.4718 | − | 21.7906i | 0.244700 | − | 0.112323i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 126.870 | − | 147.563i | 0.647294 | − | 0.752875i | ||||
\(197\) | 207.861 | 1.05513 | 0.527566 | − | 0.849514i | \(-0.323105\pi\) | ||||
0.527566 | + | 0.849514i | \(0.323105\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 299.128i | 1.50316i | 0.659643 | + | 0.751579i | \(0.270707\pi\) | ||||
−0.659643 | + | 0.751579i | \(0.729293\pi\) | |||||||
\(200\) | −28.2766 | + | 98.4073i | −0.141383 | + | 0.492037i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 46.8342 | − | 21.4979i | 0.231852 | − | 0.106425i | ||||
\(203\) | − | 3.75102i | − | 0.0184779i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −32.8243 | −0.160118 | ||||||||
\(206\) | 16.3729 | + | 35.6692i | 0.0794802 | + | 0.173152i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.28163 | − | 28.2293i | −0.0205848 | − | 0.135718i | ||||
\(209\) | 340.564 | 1.62949 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 163.672i | − | 0.775697i | −0.921723 | − | 0.387848i | \(-0.873218\pi\) | ||
0.921723 | − | 0.387848i | \(-0.126782\pi\) | |||||||
\(212\) | −93.5581 | + | 108.818i | −0.441312 | + | 0.513294i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 152.852 | + | 332.995i | 0.714261 | + | 1.55605i | ||||
\(215\) | 240.892i | 1.12043i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.8629 | 0.0869257 | ||||||||
\(218\) | −183.294 | + | 84.1359i | −0.840799 | + | 0.385945i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 325.581 | + | 279.923i | 1.47991 | + | 1.27238i | ||||
\(221\) | 30.1887 | 0.136601 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 381.837i | − | 1.71228i | −0.516748 | − | 0.856138i | \(-0.672857\pi\) | ||
0.516748 | − | 0.856138i | \(-0.327143\pi\) | |||||||
\(224\) | 15.8017 | − | 10.3721i | 0.0705434 | − | 0.0463042i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 33.1717 | − | 15.2265i | 0.146777 | − | 0.0673739i | ||||
\(227\) | − | 59.5216i | − | 0.262210i | −0.991369 | − | 0.131105i | \(-0.958148\pi\) | ||
0.991369 | − | 0.131105i | \(-0.0418525\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −128.873 | −0.562765 | −0.281383 | − | 0.959596i | \(-0.590793\pi\) | ||||
−0.281383 | + | 0.959596i | \(0.590793\pi\) | |||||||
\(230\) | −40.6788 | − | 88.6208i | −0.176864 | − | 0.385308i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.0301 | + | 48.8270i | −0.0604745 | + | 0.210461i | ||||
\(233\) | −14.9939 | −0.0643513 | −0.0321757 | − | 0.999482i | \(-0.510244\pi\) | ||||
−0.0321757 | + | 0.999482i | \(0.510244\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 68.4443i | − | 0.291252i | ||||||
\(236\) | 73.1895 | + | 62.9256i | 0.310125 | + | 0.266634i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.33723 | + | 18.1631i | 0.0350304 | + | 0.0763154i | ||||
\(239\) | 364.012i | 1.52306i | 0.648128 | + | 0.761532i | \(0.275552\pi\) | ||||
−0.648128 | + | 0.761532i | \(0.724448\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 81.0471 | 0.336295 | 0.168147 | − | 0.985762i | \(-0.446222\pi\) | ||||
0.168147 | + | 0.985762i | \(0.446222\pi\) | |||||||
\(242\) | 334.156 | − | 153.385i | 1.38081 | − | 0.633820i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 197.907 | − | 230.188i | 0.811095 | − | 0.943393i | ||||
\(245\) | 299.110 | 1.22086 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 34.8082i | − | 0.140924i | ||||||
\(248\) | −245.538 | − | 70.5536i | −0.990073 | − | 0.284490i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 136.351 | − | 62.5878i | 0.545403 | − | 0.250351i | ||||
\(251\) | 281.883i | 1.12304i | 0.827463 | + | 0.561520i | \(0.189783\pi\) | ||||
−0.827463 | + | 0.561520i | \(0.810217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −138.459 | −0.547268 | ||||||||
\(254\) | 137.154 | + | 298.797i | 0.539976 | + | 1.17636i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −244.486 | + | 75.9104i | −0.955025 | + | 0.296525i | ||||
\(257\) | −75.3127 | −0.293046 | −0.146523 | − | 0.989207i | \(-0.546808\pi\) | ||||
−0.146523 | + | 0.989207i | \(0.546808\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 34.4268i | − | 0.132922i | ||||||
\(260\) | 28.6103 | − | 33.2769i | 0.110040 | − | 0.127988i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −118.905 | − | 259.041i | −0.453838 | − | 0.988708i | ||||
\(263\) | − | 122.299i | − | 0.465017i | −0.972594 | − | 0.232508i | \(-0.925307\pi\) | ||
0.972594 | − | 0.232508i | \(-0.0746933\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −220.574 | −0.832355 | ||||||||
\(266\) | 20.9424 | − | 9.61301i | 0.0787309 | − | 0.0361391i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −111.444 | − | 95.8152i | −0.415835 | − | 0.357520i | ||||
\(269\) | −280.452 | −1.04257 | −0.521287 | − | 0.853382i | \(-0.674548\pi\) | ||||
−0.521287 | + | 0.853382i | \(0.674548\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 81.4468i | 0.300542i | 0.988645 | + | 0.150271i | \(0.0480146\pi\) | ||||
−0.988645 | + | 0.150271i | \(0.951985\pi\) | |||||||
\(272\) | −40.5897 | − | 267.613i | −0.149227 | − | 0.983871i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.2032 | − | 5.14249i | 0.0408874 | − | 0.0187682i | ||||
\(275\) | 223.460i | 0.812582i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −449.723 | −1.62355 | −0.811774 | − | 0.583972i | \(-0.801498\pi\) | ||||
−0.811774 | + | 0.583972i | \(0.801498\pi\) | |||||||
\(278\) | −99.3939 | − | 216.534i | −0.357532 | − | 0.778901i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 27.9224 | + | 8.02330i | 0.0997229 | + | 0.0286546i | ||||
\(281\) | −75.7297 | −0.269501 | −0.134750 | − | 0.990880i | \(-0.543023\pi\) | ||||
−0.134750 | + | 0.990880i | \(0.543023\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 371.884i | − | 1.31408i | −0.753856 | − | 0.657039i | \(-0.771809\pi\) | ||
0.753856 | − | 0.657039i | \(-0.228191\pi\) | |||||||
\(284\) | 266.418 | + | 229.056i | 0.938091 | + | 0.806537i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −25.9955 | − | 56.6325i | −0.0908934 | − | 0.198016i | ||||
\(287\) | 3.15361i | 0.0109882i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.81196 | −0.00972996 | ||||||||
\(290\) | −70.9655 | + | 32.5747i | −0.244709 | + | 0.112326i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −156.575 | + | 182.114i | −0.536216 | + | 0.623678i | ||||
\(293\) | −132.789 | −0.453206 | −0.226603 | − | 0.973987i | \(-0.572762\pi\) | ||||
−0.226603 | + | 0.973987i | \(0.572762\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 148.354i | 0.502897i | ||||||||
\(296\) | −128.768 | + | 448.134i | −0.435027 | + | 1.51397i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 375.765 | − | 172.484i | 1.26096 | − | 0.578806i | ||||
\(299\) | 14.1516i | 0.0473297i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.1439 | 0.0768899 | ||||||||
\(302\) | 122.760 | + | 267.439i | 0.406491 | + | 0.885560i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −308.563 | + | 46.8008i | −1.01501 | + | 0.153950i | ||||
\(305\) | 466.589 | 1.52980 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 336.514i | − | 1.09614i | −0.836434 | − | 0.548068i | \(-0.815363\pi\) | ||
0.836434 | − | 0.548068i | \(-0.184637\pi\) | |||||||
\(308\) | 26.8938 | − | 31.2805i | 0.0873175 | − | 0.101560i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −163.809 | − | 356.867i | −0.528417 | − | 1.15118i | ||||
\(311\) | − | 351.267i | − | 1.12948i | −0.825270 | − | 0.564738i | \(-0.808977\pi\) | ||
0.825270 | − | 0.564738i | \(-0.191023\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 190.860 | 0.609776 | 0.304888 | − | 0.952388i | \(-0.401381\pi\) | ||||
0.304888 | + | 0.952388i | \(0.401381\pi\) | |||||||
\(314\) | 114.292 | − | 52.4626i | 0.363988 | − | 0.167078i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −112.719 | − | 96.9117i | −0.356706 | − | 0.306683i | ||||
\(317\) | −405.594 | −1.27948 | −0.639738 | − | 0.768593i | \(-0.720957\pi\) | ||||
−0.639738 | + | 0.768593i | \(0.720957\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 110.875i | 0.347570i | ||||||||
\(320\) | −333.456 | − | 208.879i | −1.04205 | − | 0.652746i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.51430 | + | 3.90825i | −0.0264419 | + | 0.0121374i | ||||
\(323\) | − | 329.981i | − | 1.02161i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.8393 | 0.0702749 | ||||||||
\(326\) | 119.582 | + | 260.515i | 0.366815 | + | 0.799125i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.7956 | − | 41.0506i | 0.0359622 | − | 0.125154i | ||||
\(329\) | −6.57584 | −0.0199874 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 443.525i | − | 1.33996i | −0.742381 | − | 0.669978i | \(-0.766304\pi\) | ||
0.742381 | − | 0.669978i | \(-0.233696\pi\) | |||||||
\(332\) | −231.251 | − | 198.822i | −0.696541 | − | 0.598860i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 145.024 | + | 315.941i | 0.434203 | + | 0.945931i | ||||
\(335\) | − | 225.896i | − | 0.674315i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 508.479 | 1.50884 | 0.754420 | − | 0.656392i | \(-0.227918\pi\) | ||||
0.754420 | + | 0.656392i | \(0.227918\pi\) | |||||||
\(338\) | 301.396 | − | 138.347i | 0.891703 | − | 0.409310i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 271.225 | − | 315.464i | 0.797719 | − | 0.927836i | ||||
\(341\) | −557.560 | −1.63507 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 57.6805i | − | 0.168165i | ||||||
\(344\) | −301.264 | − | 86.5659i | −0.875767 | − | 0.251645i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 457.343 | − | 209.930i | 1.32180 | − | 0.606735i | ||||
\(347\) | − | 569.006i | − | 1.63979i | −0.572517 | − | 0.819893i | \(-0.694033\pi\) | ||
0.572517 | − | 0.819893i | \(-0.305967\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 413.802 | 1.18568 | 0.592840 | − | 0.805320i | \(-0.298007\pi\) | ||||
0.592840 | + | 0.805320i | \(0.298007\pi\) | |||||||
\(350\) | 6.30755 | + | 13.7413i | 0.0180216 | + | 0.0392609i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −467.076 | + | 306.586i | −1.32692 | + | 0.870982i | ||||
\(353\) | 124.614 | 0.353014 | 0.176507 | − | 0.984299i | \(-0.443520\pi\) | ||||
0.176507 | + | 0.984299i | \(0.443520\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 540.027i | 1.52120i | ||||||||
\(356\) | 71.9406 | − | 83.6748i | 0.202080 | − | 0.235042i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 80.1018 | + | 174.506i | 0.223748 | + | 0.487446i | ||||
\(359\) | − | 303.196i | − | 0.844557i | −0.906466 | − | 0.422278i | \(-0.861230\pi\) | ||
0.906466 | − | 0.422278i | \(-0.138770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.4752 | −0.0539480 | ||||||||
\(362\) | 597.568 | − | 274.296i | 1.65074 | − | 0.757724i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.19710 | − | 2.74875i | −0.00878325 | − | 0.00755152i | ||||
\(365\) | −369.144 | −1.01135 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 710.800i | 1.93678i | 0.249433 | + | 0.968392i | \(0.419756\pi\) | ||||
−0.249433 | + | 0.968392i | \(0.580244\pi\) | |||||||
\(368\) | 125.449 | − | 19.0273i | 0.340894 | − | 0.0517045i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −651.321 | + | 298.970i | −1.76033 | + | 0.808027i | ||||
\(371\) | 21.1918i | 0.0571208i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −333.481 | −0.894051 | −0.447025 | − | 0.894521i | \(-0.647517\pi\) | ||||
−0.447025 | + | 0.894521i | \(0.647517\pi\) | |||||||
\(374\) | −246.437 | − | 536.874i | −0.658921 | − | 1.43549i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 85.5977 | + | 24.5959i | 0.227653 | + | 0.0654146i | ||||
\(377\) | 11.3323 | 0.0300590 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 662.686i | 1.74851i | 0.485465 | + | 0.874256i | \(0.338650\pi\) | ||||
−0.485465 | + | 0.874256i | \(0.661350\pi\) | |||||||
\(380\) | −363.737 | − | 312.728i | −0.957203 | − | 0.822968i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.339040 | + | 0.738615i | 0.000887539 | + | 0.00193355i | ||||
\(383\) | 80.7145i | 0.210743i | 0.994433 | + | 0.105371i | \(0.0336031\pi\) | ||||
−0.994433 | + | 0.105371i | \(0.966397\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 63.4052 | 0.164689 | ||||||||
\(386\) | −113.505 | + | 52.1013i | −0.294055 | + | 0.134977i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −68.1066 | + | 79.2155i | −0.175533 | + | 0.204164i | ||||
\(389\) | −692.013 | −1.77895 | −0.889476 | − | 0.456981i | \(-0.848931\pi\) | ||||
−0.889476 | + | 0.456981i | \(0.848931\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 134.156i | 0.343111i | ||||||||
\(392\) | −107.487 | + | 374.072i | −0.274201 | + | 0.954266i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −377.819 | + | 173.427i | −0.958933 | + | 0.440170i | ||||
\(395\) | − | 228.481i | − | 0.578432i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 657.713 | 1.65671 | 0.828354 | − | 0.560206i | \(-0.189278\pi\) | ||||
0.828354 | + | 0.560206i | \(0.189278\pi\) | |||||||
\(398\) | −249.576 | − | 543.713i | −0.627074 | − | 1.36611i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −30.7082 | − | 202.463i | −0.0767706 | − | 0.506158i | ||||
\(401\) | 592.866 | 1.47847 | 0.739235 | − | 0.673448i | \(-0.235187\pi\) | ||||
0.739235 | + | 0.673448i | \(0.235187\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 56.9869i | 0.141407i | ||||||||
\(404\) | −67.1918 | + | 78.1515i | −0.166316 | + | 0.193444i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.12963 | + | 6.81806i | 0.00770846 | + | 0.0167933i | ||||
\(407\) | 1017.61i | 2.50026i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 323.188 | 0.790191 | 0.395095 | − | 0.918640i | \(-0.370712\pi\) | ||||
0.395095 | + | 0.918640i | \(0.370712\pi\) | |||||||
\(410\) | 59.6632 | − | 27.3867i | 0.145520 | − | 0.0667968i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −59.5207 | − | 51.1737i | −0.144468 | − | 0.124208i | ||||
\(413\) | 14.2533 | 0.0345115 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 468.745i | − | 1.12951i | ||||||
\(416\) | 31.3354 | + | 47.7388i | 0.0753256 | + | 0.114757i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −619.028 | + | 284.147i | −1.48093 | + | 0.679777i | ||||
\(419\) | 257.203i | 0.613849i | 0.951734 | + | 0.306924i | \(0.0992998\pi\) | ||||
−0.951734 | + | 0.306924i | \(0.900700\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −83.9811 | −0.199480 | −0.0997400 | − | 0.995014i | \(-0.531801\pi\) | ||||
−0.0997400 | + | 0.995014i | \(0.531801\pi\) | |||||||
\(422\) | 136.559 | + | 297.499i | 0.323598 | + | 0.704975i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 79.2646 | − | 275.854i | 0.186945 | − | 0.650599i | ||||
\(425\) | 216.516 | 0.509450 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 44.8279i | − | 0.104983i | ||||||
\(428\) | −555.664 | − | 477.740i | −1.29828 | − | 1.11621i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −200.986 | − | 437.859i | −0.467410 | − | 1.01828i | ||||
\(431\) | − | 144.348i | − | 0.334914i | −0.985879 | − | 0.167457i | \(-0.946445\pi\) | ||
0.985879 | − | 0.167457i | \(-0.0535555\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 395.353 | 0.913057 | 0.456528 | − | 0.889709i | \(-0.349093\pi\) | ||||
0.456528 | + | 0.889709i | \(0.349093\pi\) | |||||||
\(434\) | −34.2862 | + | 15.7381i | −0.0790005 | + | 0.0362629i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 262.968 | − | 305.860i | 0.603137 | − | 0.701514i | ||||
\(437\) | 154.685 | 0.353971 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 224.908i | 0.512320i | 0.966634 | + | 0.256160i | \(0.0824574\pi\) | ||||
−0.966634 | + | 0.256160i | \(0.917543\pi\) | |||||||
\(440\) | −825.346 | − | 237.157i | −1.87579 | − | 0.538994i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −54.8727 | + | 25.1877i | −0.124146 | + | 0.0569858i | ||||
\(443\) | − | 426.297i | − | 0.962296i | −0.876639 | − | 0.481148i | \(-0.840220\pi\) | ||
0.876639 | − | 0.481148i | \(-0.159780\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 169.608 | 0.381142 | ||||||||
\(446\) | 318.583 | + | 694.049i | 0.714312 | + | 1.55616i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −20.0682 | + | 32.0370i | −0.0447950 | + | 0.0715113i | ||||
\(449\) | 406.744 | 0.905888 | 0.452944 | − | 0.891539i | \(-0.350374\pi\) | ||||
0.452944 | + | 0.891539i | \(0.350374\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 93.2163i | − | 0.206688i | ||||||
\(452\) | −47.5905 | + | 55.3530i | −0.105289 | + | 0.122462i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 49.6614 | + | 108.190i | 0.109386 | + | 0.238303i | ||||
\(455\) | − | 6.48051i | − | 0.0142429i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 319.200 | 0.698468 | 0.349234 | − | 0.937035i | \(-0.386442\pi\) | ||||
0.349234 | + | 0.937035i | \(0.386442\pi\) | |||||||
\(458\) | 234.247 | − | 107.524i | 0.511457 | − | 0.234770i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 147.880 | + | 127.142i | 0.321479 | + | 0.276396i | ||||
\(461\) | 587.776 | 1.27500 | 0.637501 | − | 0.770450i | \(-0.279968\pi\) | ||||
0.637501 | + | 0.770450i | \(0.279968\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 265.683i | 0.573829i | 0.957956 | + | 0.286914i | \(0.0926296\pi\) | ||||
−0.957956 | + | 0.286914i | \(0.907370\pi\) | |||||||
\(464\) | −15.2366 | − | 100.457i | −0.0328375 | − | 0.216501i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 27.2537 | − | 12.5100i | 0.0584843 | − | 0.0268455i | ||||
\(467\) | 794.598i | 1.70149i | 0.525575 | + | 0.850747i | \(0.323850\pi\) | ||||
−0.525575 | + | 0.850747i | \(0.676150\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.7031 | −0.0462752 | ||||||||
\(470\) | 57.1060 | + | 124.408i | 0.121502 | + | 0.264698i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −185.535 | − | 53.3121i | −0.393082 | − | 0.112949i | ||||
\(473\) | −684.099 | −1.44630 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 249.648i | − | 0.525574i | ||||||
\(476\) | −30.3084 | − | 26.0581i | −0.0636732 | − | 0.0547439i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −303.711 | − | 661.649i | −0.635378 | − | 1.38420i | ||||
\(479\) | − | 661.601i | − | 1.38121i | −0.723230 | − | 0.690607i | \(-0.757344\pi\) | ||
0.723230 | − | 0.690607i | \(-0.242656\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 104.007 | 0.216231 | ||||||||
\(482\) | −147.316 | + | 67.6210i | −0.305634 | + | 0.140293i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −479.405 | + | 557.601i | −0.990506 | + | 1.15207i | ||||
\(485\) | −160.569 | −0.331071 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 57.1525i | − | 0.117356i | −0.998277 | − | 0.0586781i | \(-0.981311\pi\) | ||
0.998277 | − | 0.0586781i | \(-0.0186886\pi\) | |||||||
\(488\) | −167.672 | + | 583.525i | −0.343589 | + | 1.19575i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −543.679 | + | 249.560i | −1.10955 | + | 0.509306i | ||||
\(491\) | − | 56.1878i | − | 0.114435i | −0.998362 | − | 0.0572177i | \(-0.981777\pi\) | ||
0.998362 | − | 0.0572177i | \(-0.0182229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 107.429 | 0.217910 | ||||||||
\(494\) | 29.0420 | + | 63.2694i | 0.0587895 | + | 0.128076i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 505.170 | − | 76.6208i | 1.01849 | − | 0.154477i | ||||
\(497\) | 51.8835 | 0.104393 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 603.013i | 1.20844i | 0.796816 | + | 0.604222i | \(0.206516\pi\) | ||||
−0.796816 | + | 0.604222i | \(0.793484\pi\) | |||||||
\(500\) | −195.619 | + | 227.526i | −0.391238 | + | 0.455053i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −235.187 | − | 512.366i | −0.468500 | − | 1.02065i | ||||
\(503\) | − | 549.354i | − | 1.09216i | −0.837734 | − | 0.546078i | \(-0.816120\pi\) | ||
0.837734 | − | 0.546078i | \(-0.183880\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −158.413 | −0.313688 | ||||||||
\(506\) | 251.671 | − | 115.522i | 0.497373 | − | 0.228305i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −498.597 | − | 428.676i | −0.981491 | − | 0.843850i | ||||
\(509\) | −238.928 | −0.469407 | −0.234704 | − | 0.972067i | \(-0.575412\pi\) | ||||
−0.234704 | + | 0.972067i | \(0.575412\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.4658i | 0.0694046i | ||||||||
\(512\) | 381.057 | − | 341.964i | 0.744252 | − | 0.667899i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 136.893 | − | 62.8366i | 0.266328 | − | 0.122250i | ||||
\(515\) | − | 120.648i | − | 0.234268i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 194.372 | 0.375962 | ||||||||
\(518\) | 28.7238 | + | 62.5761i | 0.0554513 | + | 0.120803i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −24.2393 | + | 84.3568i | −0.0466141 | + | 0.162225i | ||||
\(521\) | 567.711 | 1.08966 | 0.544828 | − | 0.838548i | \(-0.316595\pi\) | ||||
0.544828 | + | 0.838548i | \(0.316595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 941.999i | 1.80114i | 0.434706 | + | 0.900572i | \(0.356852\pi\) | ||||
−0.434706 | + | 0.900572i | \(0.643148\pi\) | |||||||
\(524\) | 432.259 | + | 371.640i | 0.824921 | + | 0.709237i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 102.040 | + | 222.298i | 0.193992 | + | 0.422620i | ||||
\(527\) | 540.234i | 1.02511i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 466.111 | 0.881118 | ||||||||
\(530\) | 400.928 | − | 184.034i | 0.756468 | − | 0.347235i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −30.0456 | + | 34.9463i | −0.0564766 | + | 0.0656885i | ||||
\(533\) | −9.52743 | −0.0178751 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1126.33i | − | 2.10528i | ||||||
\(536\) | 282.509 | + | 81.1769i | 0.527069 | + | 0.151449i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 509.766 | − | 233.993i | 0.947520 | − | 0.434932i | ||||
\(539\) | 849.430i | 1.57594i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −242.245 | −0.447772 | −0.223886 | − | 0.974615i | \(-0.571874\pi\) | ||||
−0.223886 | + | 0.974615i | \(0.571874\pi\) | |||||||
\(542\) | −67.9545 | − | 148.042i | −0.125377 | − | 0.273141i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 297.059 | + | 452.562i | 0.546064 | + | 0.831916i | ||||
\(545\) | 619.977 | 1.13757 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 196.880i | 0.359927i | 0.983673 | + | 0.179964i | \(0.0575980\pi\) | ||||
−0.983673 | + | 0.179964i | \(0.942402\pi\) | |||||||
\(548\) | −16.0729 | + | 18.6945i | −0.0293301 | + | 0.0341141i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −186.442 | − | 406.173i | −0.338986 | − | 0.738497i | ||||
\(551\) | − | 123.868i | − | 0.224807i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.9514 | −0.0396952 | ||||||||
\(554\) | 817.441 | − | 375.223i | 1.47553 | − | 0.677297i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 361.328 | + | 310.657i | 0.649870 | + | 0.558735i | ||||
\(557\) | −958.121 | −1.72015 | −0.860073 | − | 0.510171i | \(-0.829582\pi\) | ||||
−0.860073 | + | 0.510171i | \(0.829582\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 69.9202i | 0.125081i | ||||||||
\(560\) | −57.4475 | + | 8.71325i | −0.102585 | + | 0.0155594i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 137.651 | − | 63.1845i | 0.244930 | − | 0.112428i | ||||
\(563\) | − | 191.419i | − | 0.339999i | −0.985444 | − | 0.169999i | \(-0.945623\pi\) | ||
0.985444 | − | 0.169999i | \(-0.0543766\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −112.200 | −0.198584 | ||||||||
\(566\) | 310.279 | + | 675.957i | 0.548196 | + | 1.19427i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −675.368 | − | 194.062i | −1.18903 | − | 0.341658i | ||||
\(569\) | 456.430 | 0.802162 | 0.401081 | − | 0.916043i | \(-0.368635\pi\) | ||||
0.401081 | + | 0.916043i | \(0.368635\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 973.140i | − | 1.70427i | −0.523320 | − | 0.852136i | \(-0.675307\pi\) | ||
0.523320 | − | 0.852136i | \(-0.324693\pi\) | |||||||
\(572\) | 94.5018 | + | 81.2492i | 0.165213 | + | 0.142044i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.63120 | − | 5.73219i | −0.00458396 | − | 0.00998639i | ||||
\(575\) | 101.496i | 0.176515i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 138.527 | 0.240081 | 0.120040 | − | 0.992769i | \(-0.461698\pi\) | ||||
0.120040 | + | 0.992769i | \(0.461698\pi\) | |||||||
\(578\) | 5.11118 | − | 2.34614i | 0.00884286 | − | 0.00405906i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 101.812 | − | 118.419i | 0.175539 | − | 0.204171i | ||||
\(581\) | −45.0350 | −0.0775129 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 626.400i | − | 1.07444i | ||||||
\(584\) | 132.654 | − | 461.658i | 0.227147 | − | 0.790510i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 241.365 | − | 110.792i | 0.411886 | − | 0.189064i | ||||
\(587\) | 716.847i | 1.22120i | 0.791937 | + | 0.610602i | \(0.209073\pi\) | ||||
−0.791937 | + | 0.610602i | \(0.790927\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 622.902 | 1.05756 | ||||||||
\(590\) | −123.778 | − | 269.657i | −0.209794 | − | 0.457046i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −139.841 | − | 921.990i | −0.236218 | − | 1.55742i | ||||
\(593\) | −542.129 | −0.914214 | −0.457107 | − | 0.889412i | \(-0.651114\pi\) | ||||
−0.457107 | + | 0.889412i | \(0.651114\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 61.4350i | − | 0.103252i | ||||||
\(596\) | −539.100 | + | 627.033i | −0.904531 | + | 1.05207i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.8073 | − | 25.7227i | −0.0197446 | − | 0.0430145i | ||||
\(599\) | 283.510i | 0.473305i | 0.971594 | + | 0.236653i | \(0.0760504\pi\) | ||||
−0.971594 | + | 0.236653i | \(0.923950\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −754.848 | −1.25599 | −0.627993 | − | 0.778219i | \(-0.716123\pi\) | ||||
−0.627993 | + | 0.778219i | \(0.716123\pi\) | |||||||
\(602\) | −42.0676 | + | 19.3099i | −0.0698797 | + | 0.0320763i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −446.272 | − | 383.688i | −0.738860 | − | 0.635245i | ||||
\(605\) | −1130.25 | −1.86819 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 89.1690i | 0.146901i | 0.997299 | + | 0.0734506i | \(0.0234011\pi\) | ||||
−0.997299 | + | 0.0734506i | \(0.976599\pi\) | |||||||
\(608\) | 521.814 | − | 342.515i | 0.858247 | − | 0.563348i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −848.098 | + | 389.295i | −1.39032 | + | 0.638189i | ||||
\(611\) | − | 19.8664i | − | 0.0325145i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −316.779 | −0.516769 | −0.258385 | − | 0.966042i | \(-0.583190\pi\) | ||||
−0.258385 | + | 0.966042i | \(0.583190\pi\) | |||||||
\(614\) | 280.768 | + | 611.667i | 0.457277 | + | 0.996200i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.7851 | + | 79.2957i | −0.0369887 | + | 0.128727i | ||||
\(617\) | 1069.87 | 1.73398 | 0.866992 | − | 0.498323i | \(-0.166051\pi\) | ||||
0.866992 | + | 0.498323i | \(0.166051\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 668.043i | − | 1.07923i | −0.841912 | − | 0.539615i | \(-0.818570\pi\) | ||
0.841912 | − | 0.539615i | \(-0.181430\pi\) | |||||||
\(620\) | 595.498 | + | 511.988i | 0.960481 | + | 0.825787i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 293.077 | + | 638.483i | 0.471185 | + | 1.02650i | ||||
\(623\) | − | 16.2952i | − | 0.0261561i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −781.161 | −1.24986 | ||||||||
\(626\) | −346.917 | + | 159.242i | −0.554181 | + | 0.254381i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −163.972 | + | 190.718i | −0.261102 | + | 0.303691i | ||||
\(629\) | 985.986 | 1.56755 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 150.631i | − | 0.238718i | −0.992851 | − | 0.119359i | \(-0.961916\pi\) | ||
0.992851 | − | 0.119359i | \(-0.0380839\pi\) | |||||||
\(632\) | 285.742 | + | 82.1059i | 0.452123 | + | 0.129914i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 737.230 | − | 338.404i | 1.16282 | − | 0.533761i | ||||
\(635\) | − | 1010.65i | − | 1.59158i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 86.8184 | 0.136293 | ||||||||
\(638\) | −92.5075 | − | 201.532i | −0.144996 | − | 0.315881i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 780.385 | + | 101.453i | 1.21935 | + | 0.158520i | ||||
\(641\) | 703.042 | 1.09679 | 0.548395 | − | 0.836220i | \(-0.315239\pi\) | ||||
0.548395 | + | 0.836220i | \(0.315239\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 856.853i | 1.33259i | 0.745690 | + | 0.666293i | \(0.232120\pi\) | ||||
−0.745690 | + | 0.666293i | \(0.767880\pi\) | |||||||
\(644\) | 12.2153 | − | 14.2077i | 0.0189678 | − | 0.0220616i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 275.317 | + | 599.792i | 0.426188 | + | 0.928470i | ||||
\(647\) | 156.257i | 0.241510i | 0.992682 | + | 0.120755i | \(0.0385316\pi\) | ||||
−0.992682 | + | 0.120755i | \(0.961468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −421.306 | −0.649162 | ||||||||
\(650\) | −41.5141 | + | 19.0558i | −0.0638678 | + | 0.0293167i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −434.717 | − | 373.754i | −0.666744 | − | 0.573242i | ||||
\(653\) | −883.545 | −1.35306 | −0.676528 | − | 0.736417i | \(-0.736516\pi\) | ||||
−0.676528 | + | 0.736417i | \(0.736516\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 876.185i | 1.33769i | ||||||||
\(656\) | 12.8099 | + | 84.4574i | 0.0195273 | + | 0.128746i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.9526 | − | 5.48650i | 0.0181651 | − | 0.00833815i | ||||
\(659\) | − | 438.246i | − | 0.665017i | −0.943100 | − | 0.332509i | \(-0.892105\pi\) | ||
0.943100 | − | 0.332509i | \(-0.107895\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −467.848 | −0.707788 | −0.353894 | − | 0.935285i | \(-0.615143\pi\) | ||||
−0.353894 | + | 0.935285i | \(0.615143\pi\) | |||||||
\(662\) | 370.052 | + | 806.176i | 0.558991 | + | 1.21779i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 586.221 | + | 168.446i | 0.882863 | + | 0.253684i | ||||
\(665\) | −70.8359 | −0.106520 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 50.3597i | 0.0755018i | ||||||||
\(668\) | −527.206 | − | 453.273i | −0.789231 | − | 0.678552i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 188.474 | + | 410.600i | 0.281305 | + | 0.612836i | ||||
\(671\) | 1325.05i | 1.97474i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −546.603 | −0.812189 | −0.406094 | − | 0.913831i | \(-0.633110\pi\) | ||||
−0.406094 | + | 0.913831i | \(0.633110\pi\) | |||||||
\(674\) | −924.240 | + | 424.246i | −1.37128 | + | 0.629444i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −432.405 | + | 502.934i | −0.639652 | + | 0.743986i | ||||
\(677\) | 455.212 | 0.672396 | 0.336198 | − | 0.941791i | \(-0.390859\pi\) | ||||
0.336198 | + | 0.941791i | \(0.390859\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.4268i | 0.0227199i | ||||||||
\(680\) | −229.788 | + | 799.699i | −0.337923 | + | 1.17603i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1013.45 | − | 465.196i | 1.48600 | − | 0.682105i | ||||
\(683\) | 123.214i | 0.180400i | 0.995924 | + | 0.0902002i | \(0.0287507\pi\) | ||||
−0.995924 | + | 0.0902002i | \(0.971249\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.8937 | −0.0553193 | ||||||||
\(686\) | 48.1253 | + | 104.843i | 0.0701535 | + | 0.152833i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 619.819 | − | 94.0101i | 0.900900 | − | 0.136643i | ||||
\(689\) | −64.0229 | −0.0929215 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 188.593i | 0.272928i | 0.990645 | + | 0.136464i | \(0.0435737\pi\) | ||||
−0.990645 | + | 0.136464i | \(0.956426\pi\) | |||||||
\(692\) | −656.139 | + | 763.162i | −0.948177 | + | 1.10283i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 474.746 | + | 1034.26i | 0.684071 | + | 1.49028i | ||||
\(695\) | 732.409i | 1.05383i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −90.3197 | −0.129584 | ||||||||
\(698\) | −752.150 | + | 345.253i | −1.07758 | + | 0.494631i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −22.9299 | − | 19.7143i | −0.0327570 | − | 0.0281633i | ||||
\(701\) | 810.064 | 1.15558 | 0.577792 | − | 0.816184i | \(-0.303915\pi\) | ||||
0.577792 | + | 0.816184i | \(0.303915\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1136.86i | − | 1.61716i | ||||||
\(704\) | 593.186 | − | 946.969i | 0.842594 | − | 1.34513i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −226.505 | + | 103.971i | −0.320829 | + | 0.147267i | ||||
\(707\) | 15.2196i | 0.0215270i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1303.64 | 1.83870 | 0.919349 | − | 0.393442i | \(-0.128716\pi\) | ||||
0.919349 | + | 0.393442i | \(0.128716\pi\) | |||||||
\(710\) | −450.568 | − | 981.583i | −0.634602 | − | 1.38251i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −60.9497 | + | 212.115i | −0.0856035 | + | 0.297914i | ||||
\(713\) | −253.246 | −0.355183 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 191.554i | 0.267908i | ||||||||
\(716\) | −291.195 | − | 250.359i | −0.406697 | − | 0.349663i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 252.969 | + | 551.106i | 0.352325 | + | 0.767557i | ||||
\(719\) | − | 788.981i | − | 1.09733i | −0.836042 | − | 0.548666i | \(-0.815136\pi\) | ||
0.836042 | − | 0.548666i | \(-0.184864\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.5913 | −0.0160768 | ||||||||
\(722\) | 35.3993 | − | 16.2490i | 0.0490294 | − | 0.0225056i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −857.315 | + | 997.152i | −1.18414 | + | 1.37728i | ||||
\(725\) | 81.2759 | 0.112105 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 268.671i | 0.369561i | 0.982780 | + | 0.184780i | \(0.0591574\pi\) | ||||
−0.982780 | + | 0.184780i | \(0.940843\pi\) | |||||||
\(728\) | 8.10464 | + | 2.32881i | 0.0111327 | + | 0.00319891i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 670.977 | − | 307.992i | 0.919146 | − | 0.421907i | ||||
\(731\) | 662.842i | 0.906760i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 73.6686 | 0.100503 | 0.0502514 | − | 0.998737i | \(-0.483998\pi\) | ||||
0.0502514 | + | 0.998737i | \(0.483998\pi\) | |||||||
\(734\) | −593.050 | − | 1291.99i | −0.807971 | − | 1.76020i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −212.148 | + | 139.252i | −0.288244 | + | 0.189202i | ||||
\(737\) | 641.512 | 0.870437 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 448.249i | − | 0.606562i | −0.952901 | − | 0.303281i | \(-0.901918\pi\) | ||
0.952901 | − | 0.303281i | \(-0.0980820\pi\) | |||||||
\(740\) | 934.433 | − | 1086.85i | 1.26275 | − | 1.46871i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.6812 | − | 38.5194i | −0.0238292 | − | 0.0519130i | ||||
\(743\) | − | 758.179i | − | 1.02043i | −0.860047 | − | 0.510215i | \(-0.829566\pi\) | ||
0.860047 | − | 0.510215i | \(-0.170434\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1270.99 | −1.70603 | ||||||||
\(746\) | 606.153 | − | 278.237i | 0.812538 | − | 0.372972i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 895.874 | + | 770.240i | 1.19769 | + | 1.02973i | ||||
\(749\) | −108.213 | −0.144476 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1318.18i | 1.75524i | 0.479361 | + | 0.877618i | \(0.340868\pi\) | ||||
−0.479361 | + | 0.877618i | \(0.659132\pi\) | |||||||
\(752\) | −176.109 | + | 26.7110i | −0.234187 | + | 0.0355199i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20.5981 | + | 9.45498i | −0.0273185 | + | 0.0125398i | ||||
\(755\) | − | 904.589i | − | 1.19813i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 587.874 | 0.776583 | 0.388292 | − | 0.921537i | \(-0.373065\pi\) | ||||
0.388292 | + | 0.921537i | \(0.373065\pi\) | |||||||
\(758\) | −552.907 | − | 1204.54i | −0.729429 | − | 1.58910i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 922.071 | + | 264.950i | 1.21325 | + | 0.348619i | ||||
\(761\) | −376.992 | −0.495391 | −0.247695 | − | 0.968838i | \(-0.579673\pi\) | ||||
−0.247695 | + | 0.968838i | \(0.579673\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 59.5647i | − | 0.0780664i | ||||||
\(764\) | −1.23252 | − | 1.05967i | −0.00161324 | − | 0.00138701i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −67.3435 | − | 146.711i | −0.0879158 | − | 0.191529i | ||||
\(767\) | 43.0607i | 0.0561418i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1287.88 | −1.67474 | −0.837372 | − | 0.546633i | \(-0.815909\pi\) | ||||
−0.837372 | + | 0.546633i | \(0.815909\pi\) | |||||||
\(770\) | −115.249 | + | 52.9017i | −0.149674 | + | 0.0687035i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 162.843 | − | 189.404i | 0.210937 | − | 0.245343i | ||||
\(773\) | −778.578 | −1.00722 | −0.503608 | − | 0.863932i | \(-0.667994\pi\) | ||||
−0.503608 | + | 0.863932i | \(0.667994\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 408.715i | 0.527375i | ||||||||
\(776\) | 57.7015 | − | 200.811i | 0.0743577 | − | 0.258777i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1257.84 | − | 577.376i | 1.61676 | − | 0.742128i | ||||
\(779\) | 104.141i | 0.133685i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1533.60 | −1.96364 | ||||||||
\(782\) | −111.932 | − | 243.850i | −0.143136 | − | 0.311829i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −116.730 | − | 769.615i | −0.148890 | − | 0.981652i | ||||
\(785\) | −386.584 | −0.492463 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 450.660i | − | 0.572631i | −0.958135 | − | 0.286315i | \(-0.907570\pi\) | ||
0.958135 | − | 0.286315i | \(-0.0924305\pi\) | |||||||
\(788\) | 542.048 | − | 630.462i | 0.687878 | − | 0.800078i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 190.631 | + | 415.299i | 0.241305 | + | 0.525695i | ||||
\(791\) | 10.7797i | 0.0136280i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 135.430 | 0.170782 | ||||||||
\(794\) | −1195.50 | + | 548.758i | −1.50566 | + | 0.691131i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 907.285 | + | 780.051i | 1.13981 | + | 0.979963i | ||||
\(797\) | −365.782 | −0.458948 | −0.229474 | − | 0.973315i | \(-0.573701\pi\) | ||||
−0.229474 | + | 0.973315i | \(0.573701\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 188.332i | − | 0.235710i | ||||||
\(800\) | 224.741 | + | 342.387i | 0.280926 | + | 0.427984i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1077.63 | + | 494.653i | −1.34367 | + | 0.616775i | ||||
\(803\) | − | 1048.32i | − | 1.30550i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.7989 | 0.0357750 | ||||||||
\(806\) | −47.5466 | − | 103.583i | −0.0589908 | − | 0.128514i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 56.9265 | − | 198.114i | 0.0704536 | − | 0.245190i | ||||
\(809\) | −1167.70 | −1.44339 | −0.721695 | − | 0.692212i | \(-0.756636\pi\) | ||||
−0.721695 | + | 0.692212i | \(0.756636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 810.121i | − | 0.998916i | −0.866338 | − | 0.499458i | \(-0.833533\pi\) | ||
0.866338 | − | 0.499458i | \(-0.166467\pi\) | |||||||
\(812\) | −11.3772 | − | 9.78170i | −0.0140113 | − | 0.0120464i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −849.033 | − | 1849.66i | −1.04304 | − | 2.27231i | ||||
\(815\) | − | 881.168i | − | 1.08119i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 764.271 | 0.935460 | ||||||||
\(818\) | −587.445 | + | 269.650i | −0.718148 | + | 0.329645i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −85.5973 | + | 99.5591i | −0.104387 | + | 0.121414i | ||||
\(821\) | −561.026 | −0.683344 | −0.341672 | − | 0.939819i | \(-0.610993\pi\) | ||||
−0.341672 | + | 0.939819i | \(0.610993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1173.22i | − | 1.42555i | −0.701394 | − | 0.712773i | \(-0.747439\pi\) | ||
0.701394 | − | 0.712773i | \(-0.252561\pi\) | |||||||
\(824\) | 150.885 | + | 43.3556i | 0.183112 | + | 0.0526160i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −25.9075 | + | 11.8921i | −0.0313650 | + | 0.0143972i | ||||
\(827\) | 267.739i | 0.323747i | 0.986811 | + | 0.161874i | \(0.0517537\pi\) | ||||
−0.986811 | + | 0.161874i | \(0.948246\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −432.474 | −0.521682 | −0.260841 | − | 0.965382i | \(-0.584000\pi\) | ||||
−0.260841 | + | 0.965382i | \(0.584000\pi\) | |||||||
\(830\) | 391.094 | + | 852.017i | 0.471197 | + | 1.02653i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −96.7876 | − | 60.6282i | −0.116331 | − | 0.0728705i | ||||
\(833\) | 823.035 | 0.988037 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1068.64i | − | 1.27981i | ||||||
\(836\) | 888.103 | − | 1032.96i | 1.06232 | − | 1.23560i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −214.595 | − | 467.506i | −0.256080 | − | 0.557883i | ||||
\(839\) | − | 530.126i | − | 0.631855i | −0.948783 | − | 0.315927i | \(-0.897684\pi\) | ||
0.948783 | − | 0.315927i | \(-0.102316\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −800.673 | −0.952049 | ||||||||
\(842\) | 152.649 | − | 70.0690i | 0.181293 | − | 0.0832173i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −496.433 | − | 426.815i | −0.588191 | − | 0.505705i | ||||
\(845\) | −1019.44 | −1.20644 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 108.590i | 0.128205i | ||||||||
\(848\) | 86.0809 | + | 567.541i | 0.101510 | + | 0.669271i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −393.552 | + | 180.649i | −0.463002 | + | 0.212528i | ||||
\(851\) | 462.201i | 0.543127i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −176.774 | −0.207238 | −0.103619 | − | 0.994617i | \(-0.533042\pi\) | ||||
−0.103619 | + | 0.994617i | \(0.533042\pi\) | |||||||
\(854\) | 37.4018 | + | 81.4816i | 0.0437960 | + | 0.0954118i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1408.60 | + | 404.752i | 1.64557 | + | 0.472841i | ||||
\(857\) | −389.717 | −0.454746 | −0.227373 | − | 0.973808i | \(-0.573014\pi\) | ||||
−0.227373 | + | 0.973808i | \(0.573014\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 581.137i | − | 0.676527i | −0.941051 | − | 0.338263i | \(-0.890161\pi\) | ||
0.941051 | − | 0.338263i | \(-0.109839\pi\) | |||||||
\(860\) | 730.648 | + | 628.185i | 0.849591 | + | 0.730447i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 120.436 | + | 262.375i | 0.139716 | + | 0.304379i | ||||
\(863\) | − | 827.326i | − | 0.958663i | −0.877634 | − | 0.479331i | \(-0.840879\pi\) | ||
0.877634 | − | 0.479331i | \(-0.159121\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1546.92 | −1.78835 | ||||||||
\(866\) | −718.617 | + | 329.860i | −0.829811 | + | 0.380901i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 49.1896 | − | 57.2129i | 0.0566700 | − | 0.0659135i | ||||
\(869\) | 648.853 | 0.746666 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 65.5675i | − | 0.0752784i | ||||||
\(872\) | −222.792 | + | 775.354i | −0.255496 | + | 0.889167i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −281.165 | + | 129.060i | −0.321699 | + | 0.147666i | ||||
\(875\) | 44.3096i | 0.0506395i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 559.629 | 0.638118 | 0.319059 | − | 0.947735i | \(-0.396633\pi\) | ||||
0.319059 | + | 0.947735i | \(0.396633\pi\) | |||||||
\(878\) | −187.651 | − | 408.806i | −0.213725 | − | 0.465611i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1698.07 | − | 257.551i | 1.92962 | − | 0.292672i | ||||
\(881\) | 957.127 | 1.08641 | 0.543205 | − | 0.839600i | \(-0.317211\pi\) | ||||
0.543205 | + | 0.839600i | \(0.317211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 625.252i | 0.708100i | 0.935227 | + | 0.354050i | \(0.115196\pi\) | ||||
−0.935227 | + | 0.354050i | \(0.884804\pi\) | |||||||
\(884\) | 78.7245 | − | 91.5653i | 0.0890549 | − | 0.103581i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 355.678 | + | 774.861i | 0.401442 | + | 0.874561i | ||||
\(887\) | − | 1063.69i | − | 1.19920i | −0.800298 | − | 0.599602i | \(-0.795325\pi\) | ||
0.800298 | − | 0.599602i | \(-0.204675\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −97.0992 | −0.109223 | ||||||||
\(890\) | −308.289 | + | 141.511i | −0.346393 | + | 0.159002i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1158.15 | − | 995.735i | −1.29837 | − | 1.11629i | ||||
\(893\) | −217.151 | −0.243171 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 590.251i | − | 0.659498i | ||||||
\(896\) | 9.74715 | − | 74.9760i | 0.0108785 | − | 0.0836786i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −739.320 | + | 339.363i | −0.823296 | + | 0.377910i | ||||
\(899\) | 202.793i | 0.225577i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −606.935 | −0.673624 | ||||||||
\(902\) | 77.7743 | + | 169.435i | 0.0862243 | + | 0.187844i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 40.3198 | − | 140.320i | 0.0446016 | − | 0.155221i | ||||
\(905\) | −2021.22 | −2.23339 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 239.262i | − | 0.263795i | −0.991263 | − | 0.131898i | \(-0.957893\pi\) | ||
0.991263 | − | 0.131898i | \(-0.0421070\pi\) | |||||||
\(908\) | −180.535 | − | 155.217i | −0.198827 | − | 0.170944i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.40696 | + | 11.7793i | 0.00594172 | + | 0.0129443i | ||||
\(911\) | 203.001i | 0.222834i | 0.993774 | + | 0.111417i | \(0.0355389\pi\) | ||||
−0.993774 | + | 0.111417i | \(0.964461\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1331.17 | 1.45802 | ||||||||
\(914\) | −580.196 | + | 266.322i | −0.634788 | + | 0.291381i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −336.069 | + | 390.885i | −0.366887 | + | 0.426730i | ||||
\(917\) | 84.1801 | 0.0917994 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 878.708i | 0.956156i | 0.878317 | + | 0.478078i | \(0.158666\pi\) | ||||
−0.878317 | + | 0.478078i | \(0.841334\pi\) | |||||||
\(920\) | −374.875 | − | 107.718i | −0.407473 | − | 0.117084i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1068.37 | + | 490.406i | −1.15876 | + | 0.531894i | ||||
\(923\) | 156.746i | 0.169822i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 745.950 | 0.806432 | ||||||||
\(926\) | −221.670 | − | 482.920i | −0.239385 | − | 0.521512i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 111.510 | + | 169.883i | 0.120162 | + | 0.183064i | ||||
\(929\) | 600.518 | 0.646413 | 0.323207 | − | 0.946328i | \(-0.395239\pi\) | ||||
0.323207 | + | 0.946328i | \(0.395239\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 948.977i | − | 1.01931i | ||||||
\(932\) | −39.1001 | + | 45.4778i | −0.0419529 | + | 0.0487959i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −662.967 | − | 1444.31i | −0.709815 | − | 1.54637i | ||||
\(935\) | 1815.93i | 1.94217i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −184.325 | −0.196718 | −0.0983589 | − | 0.995151i | \(-0.531359\pi\) | ||||
−0.0983589 | + | 0.995151i | \(0.531359\pi\) | |||||||
\(938\) | 39.4487 | − | 18.1078i | 0.0420562 | − | 0.0193047i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −207.598 | − | 178.485i | −0.220849 | − | 0.189878i | ||||
\(941\) | −755.173 | −0.802522 | −0.401261 | − | 0.915964i | \(-0.631428\pi\) | ||||
−0.401261 | + | 0.915964i | \(0.631428\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 42.3392i | − | 0.0448984i | ||||||
\(944\) | 381.719 | − | 57.8966i | 0.404363 | − | 0.0613311i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1243.46 | − | 570.773i | 1.31444 | − | 0.603354i | ||||
\(947\) | − | 889.079i | − | 0.938837i | −0.882976 | − | 0.469419i | \(-0.844464\pi\) | ||
0.882976 | − | 0.469419i | \(-0.155536\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −107.146 | −0.112904 | ||||||||
\(950\) | 208.292 | + | 453.774i | 0.219255 | + | 0.477657i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 76.8317 | + | 22.0770i | 0.0807056 | + | 0.0231902i | ||||
\(953\) | −15.5920 | −0.0163610 | −0.00818050 | − | 0.999967i | \(-0.502604\pi\) | ||||
−0.00818050 | + | 0.999967i | \(0.502604\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2.49830i | − | 0.00261602i | ||||||
\(956\) | 1104.08 | + | 949.251i | 1.15490 | + | 0.992940i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 552.002 | + | 1202.56i | 0.576203 | + | 1.25529i | ||||
\(959\) | 3.64066i | 0.00379631i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −58.7941 | −0.0611801 | ||||||||
\(962\) | −189.050 | + | 86.7777i | −0.196517 | + | 0.0902056i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 211.350 | − | 245.824i | 0.219243 | − | 0.255004i | ||||
\(965\) | 383.921 | 0.397846 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 979.095i | 1.01251i | 0.862384 | + | 0.506254i | \(0.168970\pi\) | ||||
−0.862384 | + | 0.506254i | \(0.831030\pi\) | |||||||
\(968\) | 406.163 | − | 1413.51i | 0.419590 | − | 1.46024i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 291.860 | − | 133.970i | 0.300886 | − | 0.138113i | ||||
\(971\) | − | 67.3838i | − | 0.0693963i | −0.999398 | − | 0.0346982i | \(-0.988953\pi\) | ||
0.999398 | − | 0.0346982i | \(-0.0110470\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 70.3667 | 0.0723193 | ||||||||
\(974\) | 47.6847 | + | 103.883i | 0.0489576 | + | 0.106657i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −182.090 | − | 1200.54i | −0.186568 | − | 1.23006i | ||||
\(977\) | 707.420 | 0.724074 | 0.362037 | − | 0.932164i | \(-0.382081\pi\) | ||||
0.362037 | + | 0.932164i | \(0.382081\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 481.664i | 0.491995i | ||||||||
\(980\) | 780.002 | − | 907.229i | 0.795921 | − | 0.925744i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 46.8799 | + | 102.130i | 0.0477392 | + | 0.104002i | ||||
\(983\) | − | 391.246i | − | 0.398012i | −0.979998 | − | 0.199006i | \(-0.936229\pi\) | ||
0.979998 | − | 0.199006i | \(-0.0637713\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1277.94 | 1.29740 | ||||||||
\(986\) | −195.270 | + | 89.6329i | −0.198042 | + | 0.0909056i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −105.577 | − | 90.7710i | −0.106859 | − | 0.0918735i | ||||
\(989\) | −310.720 | −0.314176 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 104.988i | 0.105941i | 0.998596 | + | 0.0529706i | \(0.0168690\pi\) | ||||
−0.998596 | + | 0.0529706i | \(0.983131\pi\) | |||||||
\(992\) | −854.297 | + | 560.755i | −0.861186 | + | 0.565277i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −94.3063 | + | 43.2886i | −0.0948756 | + | 0.0435499i | ||||
\(995\) | 1839.06i | 1.84830i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 78.0055 | 0.0782402 | 0.0391201 | − | 0.999235i | \(-0.487545\pi\) | ||||
0.0391201 | + | 0.999235i | \(0.487545\pi\) | |||||||
\(998\) | −503.120 | − | 1096.07i | −0.504128 | − | 1.09827i | ||||
\(999\) | 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 | 324.3.d.g.163.2 | 8 | ||
3.2 | odd | 2 | 324.3.d.i.163.7 | 8 | |||
4.3 | odd | 2 | inner | 324.3.d.g.163.1 | 8 | ||
9.2 | odd | 6 | 36.3.f.c.31.3 | yes | 16 | ||
9.4 | even | 3 | 108.3.f.c.19.5 | 16 | |||
9.5 | odd | 6 | 36.3.f.c.7.4 | yes | 16 | ||
9.7 | even | 3 | 108.3.f.c.91.6 | 16 | |||
12.11 | even | 2 | 324.3.d.i.163.8 | 8 | |||
36.7 | odd | 6 | 108.3.f.c.91.5 | 16 | |||
36.11 | even | 6 | 36.3.f.c.31.4 | yes | 16 | ||
36.23 | even | 6 | 36.3.f.c.7.3 | ✓ | 16 | ||
36.31 | odd | 6 | 108.3.f.c.19.6 | 16 | |||
72.5 | odd | 6 | 576.3.o.g.511.7 | 16 | |||
72.11 | even | 6 | 576.3.o.g.319.7 | 16 | |||
72.13 | even | 6 | 1728.3.o.g.127.8 | 16 | |||
72.29 | odd | 6 | 576.3.o.g.319.2 | 16 | |||
72.43 | odd | 6 | 1728.3.o.g.1279.8 | 16 | |||
72.59 | even | 6 | 576.3.o.g.511.2 | 16 | |||
72.61 | even | 6 | 1728.3.o.g.1279.7 | 16 | |||
72.67 | odd | 6 | 1728.3.o.g.127.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.c.7.3 | ✓ | 16 | 36.23 | even | 6 | ||
36.3.f.c.7.4 | yes | 16 | 9.5 | odd | 6 | ||
36.3.f.c.31.3 | yes | 16 | 9.2 | odd | 6 | ||
36.3.f.c.31.4 | yes | 16 | 36.11 | even | 6 | ||
108.3.f.c.19.5 | 16 | 9.4 | even | 3 | |||
108.3.f.c.19.6 | 16 | 36.31 | odd | 6 | |||
108.3.f.c.91.5 | 16 | 36.7 | odd | 6 | |||
108.3.f.c.91.6 | 16 | 9.7 | even | 3 | |||
324.3.d.g.163.1 | 8 | 4.3 | odd | 2 | inner | ||
324.3.d.g.163.2 | 8 | 1.1 | even | 1 | trivial | ||
324.3.d.i.163.7 | 8 | 3.2 | odd | 2 | |||
324.3.d.i.163.8 | 8 | 12.11 | even | 2 | |||
576.3.o.g.319.2 | 16 | 72.29 | odd | 6 | |||
576.3.o.g.319.7 | 16 | 72.11 | even | 6 | |||
576.3.o.g.511.2 | 16 | 72.59 | even | 6 | |||
576.3.o.g.511.7 | 16 | 72.5 | odd | 6 | |||
1728.3.o.g.127.7 | 16 | 72.67 | odd | 6 | |||
1728.3.o.g.127.8 | 16 | 72.13 | even | 6 | |||
1728.3.o.g.1279.7 | 16 | 72.61 | even | 6 | |||
1728.3.o.g.1279.8 | 16 | 72.43 | odd | 6 |