Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(95,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.95");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.r (of order \(6\), degree \(2\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 95.2 | ||
Root | \(0.385124 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.95 |
Dual form | 224.3.r.d.191.2 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.53177 | − | 0.884367i | −0.510590 | − | 0.294789i | 0.222486 | − | 0.974936i | \(-0.428583\pi\) |
−0.733076 | + | 0.680147i | \(0.761916\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.10168 | + | 7.10432i | 0.820336 | + | 1.42086i | 0.905432 | + | 0.424491i | \(0.139547\pi\) |
−0.0850965 | + | 0.996373i | \(0.527120\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.46804 | + | 4.37041i | −0.781149 | + | 0.624345i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.93579 | − | 5.08494i | −0.326199 | − | 0.564993i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.10155 | − | 5.25478i | −0.827413 | − | 0.477707i | 0.0255528 | − | 0.999673i | \(-0.491865\pi\) |
−0.852966 | + | 0.521966i | \(0.825199\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.87158 | −0.451660 | −0.225830 | − | 0.974167i | \(-0.572509\pi\) | ||||
−0.225830 | + | 0.974167i | \(0.572509\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 14.5096i | − | 0.967304i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.5084 | + | 23.3972i | −0.794612 | + | 1.37631i | 0.128474 | + | 0.991713i | \(0.458992\pi\) |
−0.923086 | + | 0.384595i | \(0.874341\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.6595 | − | 6.15427i | 0.561026 | − | 0.323909i | −0.192531 | − | 0.981291i | \(-0.561670\pi\) |
0.753557 | + | 0.657382i | \(0.228336\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.2408 | − | 1.85871i | 0.582897 | − | 0.0885098i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −36.2985 | + | 20.9570i | −1.57820 | + | 0.911173i | −0.583086 | + | 0.812410i | \(0.698155\pi\) |
−0.995111 | + | 0.0987627i | \(0.968512\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21.1475 | + | 36.6286i | −0.845902 | + | 1.46514i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.3039i | 0.974217i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 36.4235 | 1.25598 | 0.627992 | − | 0.778220i | \(-0.283877\pi\) | ||||
0.627992 | + | 0.778220i | \(0.283877\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.61671 | + | 3.82016i | 0.213442 | + | 0.123231i | 0.602910 | − | 0.797809i | \(-0.294008\pi\) |
−0.389468 | + | 0.921040i | \(0.627341\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.29431 | + | 16.0982i | 0.281646 | + | 0.487825i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −53.4770 | − | 20.9207i | −1.52791 | − | 0.597733i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.62842 | − | 6.28461i | −0.0980654 | − | 0.169854i | 0.812818 | − | 0.582517i | \(-0.197932\pi\) |
−0.910884 | + | 0.412663i | \(0.864599\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.99390 | + | 5.19263i | 0.230613 | + | 0.133144i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −48.1667 | −1.17480 | −0.587398 | − | 0.809298i | \(-0.699848\pi\) | ||||
−0.587398 | + | 0.809298i | \(0.699848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 23.4863i | 0.546193i | 0.961987 | + | 0.273097i | \(0.0880479\pi\) | ||||
−0.961987 | + | 0.273097i | \(0.911952\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 24.0833 | − | 41.7136i | 0.535185 | − | 0.926968i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 51.1971 | − | 29.5587i | 1.08930 | − | 0.628907i | 0.155910 | − | 0.987771i | \(-0.450169\pi\) |
0.933390 | + | 0.358864i | \(0.116836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.7990 | − | 47.7952i | 0.220387 | − | 0.975412i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 41.3835 | − | 23.8928i | 0.811441 | − | 0.468486i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.03281 | − | 3.52092i | 0.0383548 | − | 0.0664325i | −0.846211 | − | 0.532848i | \(-0.821122\pi\) |
0.884566 | + | 0.466416i | \(0.154455\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 86.2137i | − | 1.56752i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −21.7705 | −0.381939 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 23.2280 | + | 13.4107i | 0.393696 | + | 0.227300i | 0.683760 | − | 0.729707i | \(-0.260343\pi\) |
−0.290064 | + | 0.957007i | \(0.593677\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.185012 | − | 0.320450i | −0.00303298 | − | 0.00525328i | 0.864505 | − | 0.502624i | \(-0.167632\pi\) |
−0.867538 | + | 0.497371i | \(0.834299\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 38.2763 | + | 14.9740i | 0.607560 | + | 0.237683i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −24.0833 | − | 41.7136i | −0.370513 | − | 0.641747i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.80658 | + | 1.04303i | 0.0269638 | + | 0.0155676i | 0.513421 | − | 0.858137i | \(-0.328378\pi\) |
−0.486458 | + | 0.873704i | \(0.661711\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 74.1346 | 1.07442 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 121.781i | 1.71523i | 0.514291 | + | 0.857616i | \(0.328055\pi\) | ||||
−0.514291 | + | 0.857616i | \(0.671945\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 38.5726 | − | 66.8097i | 0.528392 | − | 0.915202i | −0.471060 | − | 0.882101i | \(-0.656129\pi\) |
0.999452 | − | 0.0331005i | \(-0.0105381\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 64.7863 | − | 37.4044i | 0.863817 | − | 0.498725i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 72.7332 | − | 11.0442i | 0.944587 | − | 0.143431i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −31.8785 | + | 18.4050i | −0.403525 | + | 0.232975i | −0.688004 | − | 0.725707i | \(-0.741513\pi\) |
0.284479 | + | 0.958682i | \(0.408179\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.15983 | + | 5.47298i | −0.0390102 | + | 0.0675676i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 98.2951i | 1.18428i | 0.805836 | + | 0.592139i | \(0.201716\pi\) | ||||
−0.805836 | + | 0.592139i | \(0.798284\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −221.628 | −2.60739 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −55.7924 | − | 32.2118i | −0.641292 | − | 0.370250i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.1729 | + | 26.2802i | 0.170482 | + | 0.295283i | 0.938588 | − | 0.345039i | \(-0.112134\pi\) |
−0.768107 | + | 0.640322i | \(0.778801\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 32.1060 | − | 25.6612i | 0.352814 | − | 0.281992i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.75684 | − | 11.7032i | −0.0726542 | − | 0.125841i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 87.4437 | + | 50.4857i | 0.920460 | + | 0.531428i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.87158 | −0.0605317 | −0.0302659 | − | 0.999542i | \(-0.509635\pi\) | ||||
−0.0302659 | + | 0.999542i | \(0.509635\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 61.7077i | 0.623310i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 76.6583 | − | 132.776i | 0.758993 | − | 1.31461i | −0.184372 | − | 0.982857i | \(-0.559025\pi\) |
0.943365 | − | 0.331757i | \(-0.107642\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 67.3135 | − | 38.8635i | 0.653529 | − | 0.377315i | −0.136278 | − | 0.990671i | \(-0.543514\pi\) |
0.789807 | + | 0.613356i | \(0.210181\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 63.4128 | + | 79.3389i | 0.603931 | + | 0.755609i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 142.798 | − | 82.4447i | 1.33456 | − | 0.770511i | 0.348569 | − | 0.937283i | \(-0.386668\pi\) |
0.985995 | + | 0.166772i | \(0.0533344\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −30.6298 | + | 53.0524i | −0.281008 | + | 0.486719i | −0.971633 | − | 0.236493i | \(-0.924002\pi\) |
0.690626 | + | 0.723212i | \(0.257335\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.8354i | 0.115634i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.79509 | −0.0866822 | −0.0433411 | − | 0.999060i | \(-0.513800\pi\) | ||||
−0.0433411 | + | 0.999060i | \(0.513800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −297.770 | − | 171.918i | −2.58930 | − | 1.49494i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.2377 | + | 29.8566i | 0.147331 | + | 0.255185i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −28.3911 | − | 186.974i | −0.238580 | − | 1.57121i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.27456 | − | 9.13581i | −0.0435914 | − | 0.0755026i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 73.7802 | + | 42.5970i | 0.599839 | + | 0.346317i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −141.878 | −1.13502 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 125.705i | 0.989802i | 0.868949 | + | 0.494901i | \(0.164796\pi\) | ||||
−0.868949 | + | 0.494901i | \(0.835204\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 20.7705 | − | 35.9756i | 0.161012 | − | 0.278881i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −30.8455 | + | 17.8087i | −0.235462 | + | 0.135944i | −0.613089 | − | 0.790014i | \(-0.710073\pi\) |
0.377627 | + | 0.925958i | \(0.376740\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −31.3899 | + | 80.2382i | −0.236014 | + | 0.603295i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −186.871 | + | 107.890i | −1.38423 | + | 0.799185i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 59.7500 | − | 103.490i | 0.436131 | − | 0.755402i | −0.561256 | − | 0.827642i | \(-0.689682\pi\) |
0.997387 | + | 0.0722407i | \(0.0230150\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 47.3989i | − | 0.341000i | −0.985358 | − | 0.170500i | \(-0.945462\pi\) | ||
0.985358 | − | 0.170500i | \(-0.0545382\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −104.563 | −0.741580 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 53.4405 | + | 30.8539i | 0.373709 | + | 0.215761i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 149.398 | + | 258.764i | 1.03033 | + | 1.78458i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −58.8100 | + | 63.6610i | −0.400068 | + | 0.433068i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 94.6872 | + | 164.003i | 0.635485 | + | 1.10069i | 0.986412 | + | 0.164289i | \(0.0525329\pi\) |
−0.350928 | + | 0.936403i | \(0.614134\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −212.442 | − | 122.654i | −1.40690 | − | 0.812276i | −0.411816 | − | 0.911267i | \(-0.635105\pi\) |
−0.995088 | + | 0.0989909i | \(0.968439\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 158.631 | 1.03681 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 62.6762i | 0.404363i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −110.359 | + | 191.148i | −0.702924 | + | 1.21750i | 0.264511 | + | 0.964383i | \(0.414789\pi\) |
−0.967435 | + | 0.253118i | \(0.918544\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.22758 | + | 3.59549i | −0.0391672 | + | 0.0226132i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 106.891 | − | 273.233i | 0.663921 | − | 1.69710i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −235.589 | + | 136.017i | −1.44533 | + | 0.834461i | −0.998198 | − | 0.0600075i | \(-0.980888\pi\) |
−0.447131 | + | 0.894469i | \(0.647554\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −76.2446 | + | 132.059i | −0.462088 | + | 0.800360i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 88.8674i | 0.532140i | 0.963954 | + | 0.266070i | \(0.0857252\pi\) | ||||
−0.963954 | + | 0.266070i | \(0.914275\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −134.525 | −0.796003 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −62.5881 | − | 36.1353i | −0.366012 | − | 0.211317i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 159.591 | + | 276.420i | 0.922491 | + | 1.59780i | 0.795547 | + | 0.605891i | \(0.207183\pi\) |
0.126944 | + | 0.991910i | \(0.459483\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −44.4465 | − | 292.710i | −0.253980 | − | 1.67263i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −23.7200 | − | 41.0842i | −0.134011 | − | 0.232114i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 120.755 | + | 69.7179i | 0.674608 | + | 0.389485i | 0.797820 | − | 0.602895i | \(-0.205986\pi\) |
−0.123212 | + | 0.992380i | \(0.539320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −73.1328 | −0.404048 | −0.202024 | − | 0.979381i | \(-0.564752\pi\) | ||||
−0.202024 | + | 0.979381i | \(0.564752\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.654474i | 0.00357636i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 29.7652 | − | 51.5549i | 0.160893 | − | 0.278675i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 245.895 | − | 141.967i | 1.31494 | − | 0.759183i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −114.959 | − | 143.831i | −0.608248 | − | 0.761009i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 111.101 | − | 64.1442i | 0.581680 | − | 0.335833i | −0.180121 | − | 0.983645i | \(-0.557649\pi\) |
0.761801 | + | 0.647811i | \(0.224315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −139.769 | + | 242.087i | −0.724192 | + | 1.25434i | 0.235113 | + | 0.971968i | \(0.424454\pi\) |
−0.959306 | + | 0.282370i | \(0.908879\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 85.1940i | 0.436892i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −99.0628 | −0.502857 | −0.251428 | − | 0.967876i | \(-0.580900\pi\) | ||||
−0.251428 | + | 0.967876i | \(0.580900\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 204.657 | + | 118.159i | 1.02843 | + | 0.593763i | 0.916534 | − | 0.399957i | \(-0.130975\pi\) |
0.111894 | + | 0.993720i | \(0.464308\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.84484 | − | 3.19535i | −0.00917829 | − | 0.0158973i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −199.165 | + | 159.186i | −0.981110 | + | 0.784166i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −197.564 | − | 342.191i | −0.963728 | − | 1.66923i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 213.130 | + | 123.051i | 1.02961 | + | 0.594447i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −129.357 | −0.618934 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 389.683i | − | 1.84684i | −0.383791 | − | 0.923420i | \(-0.625382\pi\) | ||
0.383791 | − | 0.923420i | \(-0.374618\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 107.699 | − | 186.541i | 0.505631 | − | 0.875779i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −166.854 | + | 96.3333i | −0.776066 | + | 0.448062i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −52.8761 | + | 8.02896i | −0.243669 | + | 0.0369998i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −118.169 | + | 68.2247i | −0.539583 | + | 0.311528i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 79.3156 | − | 137.379i | 0.358894 | − | 0.621623i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 102.219i | − | 0.458379i | −0.973382 | − | 0.229190i | \(-0.926392\pi\) | ||
0.973382 | − | 0.229190i | \(-0.0736076\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 248.339 | 1.10373 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −200.037 | − | 115.491i | −0.881219 | − | 0.508772i | −0.0101588 | − | 0.999948i | \(-0.503234\pi\) |
−0.871060 | + | 0.491176i | \(0.836567\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.40221 | + | 14.5530i | 0.0366909 | + | 0.0635504i | 0.883788 | − | 0.467888i | \(-0.154985\pi\) |
−0.847097 | + | 0.531439i | \(0.821652\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −121.178 | − | 47.4058i | −0.524578 | − | 0.205220i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 60.3074 | + | 104.455i | 0.258830 | + | 0.448307i | 0.965929 | − | 0.258808i | \(-0.0833298\pi\) |
−0.707099 | + | 0.707115i | \(0.749996\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 419.988 | + | 242.480i | 1.78718 | + | 1.03183i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 65.1073 | 0.274714 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 109.863i | 0.459679i | 0.973229 | + | 0.229840i | \(0.0738202\pi\) | ||||
−0.973229 | + | 0.229840i | \(0.926180\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −92.4493 | + | 160.127i | −0.383607 | + | 0.664427i | −0.991575 | − | 0.129535i | \(-0.958652\pi\) |
0.607968 | + | 0.793962i | \(0.291985\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 214.699 | − | 123.956i | 0.883533 | − | 0.510108i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 383.846 | − | 119.321i | 1.56672 | − | 0.487026i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −62.5881 | + | 36.1353i | −0.253393 | + | 0.146297i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 86.9289 | − | 150.565i | 0.349112 | − | 0.604680i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 224.827i | 0.895724i | 0.894103 | + | 0.447862i | \(0.147814\pi\) | ||||
−0.894103 | + | 0.447862i | \(0.852186\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 440.497 | 1.74110 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 339.484 | + | 196.001i | 1.33131 | + | 0.768631i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −89.2071 | − | 154.511i | −0.347109 | − | 0.601211i | 0.638625 | − | 0.769518i | \(-0.279503\pi\) |
−0.985735 | + | 0.168307i | \(0.946170\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 47.3067 | + | 18.5068i | 0.182651 | + | 0.0714549i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −106.932 | − | 185.211i | −0.409700 | − | 0.709622i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −249.946 | − | 144.307i | −0.950367 | − | 0.548694i | −0.0571718 | − | 0.998364i | \(-0.518208\pi\) |
−0.893195 | + | 0.449670i | \(0.851542\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.3517 | 0.125855 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 53.6736i | − | 0.201025i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −112.649 | + | 195.113i | −0.418768 | + | 0.725328i | −0.995816 | − | 0.0913828i | \(-0.970871\pi\) |
0.577048 | + | 0.816710i | \(0.304205\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 169.467 | − | 97.8417i | 0.625339 | − | 0.361039i | −0.153606 | − | 0.988132i | \(-0.549089\pi\) |
0.778945 | + | 0.627093i | \(0.215755\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −71.8730 | + | 10.9135i | −0.263271 | + | 0.0399763i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 384.951 | − | 222.251i | 1.39982 | − | 0.808187i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 67.8142 | − | 117.458i | 0.244817 | − | 0.424035i | −0.717263 | − | 0.696802i | \(-0.754606\pi\) |
0.962080 | + | 0.272767i | \(0.0879389\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 44.8607i | − | 0.160791i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −372.495 | −1.32560 | −0.662802 | − | 0.748795i | \(-0.730633\pi\) | ||||
−0.662802 | + | 0.748795i | \(0.730633\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −248.903 | − | 143.704i | −0.879517 | − | 0.507789i | −0.00901792 | − | 0.999959i | \(-0.502871\pi\) |
−0.870499 | + | 0.492170i | \(0.836204\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −89.2957 | − | 154.665i | −0.313318 | − | 0.542683i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 263.377 | − | 210.508i | 0.917691 | − | 0.733478i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −220.454 | − | 381.837i | −0.762815 | − | 1.32123i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.99390 | + | 5.19263i | 0.0309069 | + | 0.0178441i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 131.947 | 0.450332 | 0.225166 | − | 0.974320i | \(-0.427708\pi\) | ||||
0.225166 | + | 0.974320i | \(0.427708\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 220.026i | 0.745850i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 138.221 | − | 239.406i | 0.465391 | − | 0.806081i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 213.130 | − | 123.051i | 0.712809 | − | 0.411540i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −102.645 | − | 128.424i | −0.341013 | − | 0.426658i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −234.845 | + | 135.588i | −0.775068 | + | 0.447486i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.51772 | − | 2.62877i | 0.00497613 | − | 0.00861891i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 47.8253i | − | 0.155783i | −0.996962 | − | 0.0778913i | \(-0.975181\pi\) | ||
0.996962 | − | 0.0778913i | \(-0.0248187\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −137.478 | −0.444913 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 197.020 | + | 113.749i | 0.633505 | + | 0.365754i | 0.782108 | − | 0.623143i | \(-0.214144\pi\) |
−0.148604 | + | 0.988897i | \(0.547478\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −61.5483 | − | 106.605i | −0.196640 | − | 0.340591i | 0.750797 | − | 0.660533i | \(-0.229670\pi\) |
−0.947437 | + | 0.319943i | \(0.896336\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 50.6168 | + | 333.346i | 0.160688 | + | 1.05824i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 240.148 | + | 415.948i | 0.757563 | + | 1.31214i | 0.944090 | + | 0.329688i | \(0.106944\pi\) |
−0.186527 | + | 0.982450i | \(0.559723\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −331.510 | − | 191.398i | −1.03922 | − | 0.599992i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −291.646 | −0.908553 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 332.537i | 1.02953i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 124.169 | − | 215.068i | 0.382060 | − | 0.661747i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 93.8356 | − | 54.1760i | 0.286959 | − | 0.165676i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −150.764 | + | 385.380i | −0.458250 | + | 1.17137i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 410.836 | − | 237.196i | 1.24119 | − | 0.716604i | 0.271857 | − | 0.962338i | \(-0.412362\pi\) |
0.969337 | + | 0.245733i | \(0.0790287\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.3046 | + | 36.9006i | −0.0639777 | + | 0.110813i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.1126i | 0.0510825i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −305.861 | −0.907599 | −0.453799 | − | 0.891104i | \(-0.649932\pi\) | ||||
−0.453799 | + | 0.891104i | \(0.649932\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.0038 | + | 8.66246i | 0.0442590 | + | 0.0255530i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −40.1482 | − | 69.5387i | −0.117737 | − | 0.203926i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 149.836 | + | 308.542i | 0.436838 | + | 0.899540i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 304.076 | + | 526.676i | 0.881381 | + | 1.52660i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −596.404 | − | 344.334i | −1.71874 | − | 0.992317i | −0.921233 | − | 0.389012i | \(-0.872816\pi\) |
−0.797511 | − | 0.603305i | \(-0.793850\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 128.861 | 0.369228 | 0.184614 | − | 0.982811i | \(-0.440896\pi\) | ||||
0.184614 | + | 0.982811i | \(0.440896\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 154.445i | − | 0.440015i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 47.5462 | − | 82.3524i | 0.134692 | − | 0.233293i | −0.790788 | − | 0.612090i | \(-0.790329\pi\) |
0.925480 | + | 0.378797i | \(0.123662\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −865.174 | + | 499.508i | −2.43711 | + | 1.40707i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −121.865 | + | 311.510i | −0.341360 | + | 0.872576i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.3627 | + | 18.1072i | −0.0873612 | + | 0.0504380i | −0.543044 | − | 0.839704i | \(-0.682728\pi\) |
0.455683 | + | 0.890142i | \(0.349395\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −104.750 | + | 181.432i | −0.290166 | + | 0.502583i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.6586i | 0.0514011i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 632.850 | 1.73384 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.6725 | + | 11.9353i | 0.0563284 | + | 0.0325212i | 0.527900 | − | 0.849307i | \(-0.322980\pi\) |
−0.471571 | + | 0.881828i | \(0.656313\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 141.407 | + | 244.924i | 0.383217 | + | 0.663752i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.27242 | + | 28.1368i | 0.0115160 | + | 0.0758403i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 85.6886 | + | 148.417i | 0.229728 | + | 0.397901i | 0.957727 | − | 0.287677i | \(-0.0928830\pi\) |
−0.727999 | + | 0.685578i | \(0.759550\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 217.324 | + | 125.472i | 0.579531 | + | 0.334592i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −213.864 | −0.567277 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.8798i | 0.0603689i | 0.999544 | + | 0.0301845i | \(0.00960947\pi\) | ||||
−0.999544 | + | 0.0301845i | \(0.990391\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 111.169 | − | 192.551i | 0.291783 | − | 0.505383i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −489.108 | + | 282.387i | −1.27705 | + | 0.737302i | −0.976304 | − | 0.216404i | \(-0.930567\pi\) |
−0.300741 | + | 0.953706i | \(0.597234\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 376.789 | + | 471.420i | 0.978674 | + | 1.22447i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 119.426 | − | 68.9509i | 0.308595 | − | 0.178168i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −59.7609 | + | 103.509i | −0.153627 | + | 0.266090i | −0.932558 | − | 0.361020i | \(-0.882429\pi\) |
0.778931 | + | 0.627109i | \(0.215762\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1132.38i | − | 2.89611i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 62.9975 | 0.160299 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −261.511 | − | 150.983i | −0.662052 | − | 0.382236i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −262.734 | − | 455.069i | −0.661799 | − | 1.14627i | −0.980143 | − | 0.198294i | \(-0.936460\pi\) |
0.318343 | − | 0.947975i | \(-0.396874\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 119.042 | − | 95.1462i | 0.298351 | − | 0.238462i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 83.2528 | + | 144.198i | 0.207613 | + | 0.359596i | 0.950962 | − | 0.309307i | \(-0.100097\pi\) |
−0.743349 | + | 0.668904i | \(0.766764\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.8505 | − | 22.4304i | −0.0964032 | − | 0.0556584i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −51.8424 | −0.128006 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 76.2662i | 0.187386i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −237.672 | + | 411.660i | −0.581106 | + | 1.00650i | 0.414243 | + | 0.910166i | \(0.364046\pi\) |
−0.995349 | + | 0.0963383i | \(0.969287\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −183.046 | + | 105.682i | −0.445368 | + | 0.257134i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −185.622 | + | 28.1858i | −0.449449 | + | 0.0682465i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −698.319 | + | 403.175i | −1.68270 | + | 0.971506i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −41.9181 | + | 72.6042i | −0.100523 | + | 0.174111i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 370.547i | 0.884360i | 0.896926 | + | 0.442180i | \(0.145795\pi\) | ||||
−0.896926 | + | 0.442180i | \(0.854205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −248.779 | −0.590924 | −0.295462 | − | 0.955355i | \(-0.595474\pi\) | ||||
−0.295462 | + | 0.955355i | \(0.595474\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −300.608 | − | 173.556i | −0.710657 | − | 0.410298i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −571.339 | − | 989.588i | −1.34433 | − | 2.32844i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.41215 | + | 0.943656i | 0.00564907 | + | 0.00220997i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −54.5723 | − | 94.5220i | −0.127208 | − | 0.220331i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −57.1732 | − | 33.0090i | −0.132653 | − | 0.0765870i | 0.432205 | − | 0.901775i | \(-0.357736\pi\) |
−0.564858 | + | 0.825188i | \(0.691069\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 753.932 | 1.74118 | 0.870591 | − | 0.492007i | \(-0.163737\pi\) | ||||
0.870591 | + | 0.492007i | \(0.163737\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 528.489i | − | 1.21492i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −257.950 | + | 446.782i | −0.590274 | + | 1.02238i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.2488 | − | 18.6188i | 0.0734596 | − | 0.0424119i | −0.462820 | − | 0.886452i | \(-0.653162\pi\) |
0.536280 | + | 0.844040i | \(0.319829\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −274.739 | + | 85.4046i | −0.622991 | + | 0.193661i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 486.899 | − | 281.111i | 1.09909 | − | 0.634562i | 0.163111 | − | 0.986608i | \(-0.447847\pi\) |
0.935983 | + | 0.352045i | \(0.114514\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −124.469 | + | 215.586i | −0.279705 | + | 0.484463i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 334.953i | − | 0.749335i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 265.855 | 0.592105 | 0.296052 | − | 0.955172i | \(-0.404330\pi\) | ||||
0.296052 | + | 0.955172i | \(0.404330\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 438.391 | + | 253.105i | 0.972043 | + | 0.561209i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 216.942 | + | 375.754i | 0.478900 | + | 0.829480i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 313.994 | + | 122.837i | 0.690097 | + | 0.269972i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.0409 | + | 57.2285i | 0.0722995 | + | 0.125226i | 0.899909 | − | 0.436078i | \(-0.143633\pi\) |
−0.827609 | + | 0.561305i | \(0.810300\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −615.438 | − | 355.323i | −1.34082 | − | 0.774124i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 59.0572 | 0.128107 | 0.0640534 | − | 0.997946i | \(-0.479597\pi\) | ||||
0.0640534 | + | 0.997946i | \(0.479597\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 390.109i | 0.842569i | 0.906929 | + | 0.421285i | \(0.138421\pi\) | ||||
−0.906929 | + | 0.421285i | \(0.861579\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 55.4288 | − | 96.0055i | 0.119202 | − | 0.206463i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 312.811 | − | 180.601i | 0.669830 | − | 0.386727i | −0.126182 | − | 0.992007i | \(-0.540272\pi\) |
0.796012 | + | 0.605280i | \(0.206939\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.4369 | + | 2.19217i | −0.0307823 | + | 0.00467413i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 338.089 | − | 195.196i | 0.717812 | − | 0.414429i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 123.415 | − | 213.762i | 0.260921 | − | 0.451928i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 520.591i | 1.09598i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.8716 | −0.0500452 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −83.4872 | − | 48.2014i | −0.174295 | − | 0.100629i | 0.410315 | − | 0.911944i | \(-0.365419\pi\) |
−0.584609 | + | 0.811315i | \(0.698752\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.3046 | + | 36.9006i | 0.0442922 | + | 0.0767164i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −405.371 | + | 323.999i | −0.839278 | + | 0.670805i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −24.0833 | − | 41.7136i | −0.0496564 | − | 0.0860073i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 49.0925 | + | 28.3435i | 0.100806 | + | 0.0582003i | 0.549555 | − | 0.835457i | \(-0.314797\pi\) |
−0.448750 | + | 0.893658i | \(0.648130\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 481.156 | 0.983960 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 559.896i | − | 1.14032i | −0.821534 | − | 0.570159i | \(-0.806882\pi\) | ||
0.821534 | − | 0.570159i | \(-0.193118\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −492.023 | + | 852.209i | −0.998019 | + | 1.72862i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −438.391 | + | 253.105i | −0.885639 | + | 0.511324i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −532.235 | − | 665.906i | −1.07090 | − | 1.33985i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 322.766 | − | 186.349i | 0.646826 | − | 0.373445i | −0.140413 | − | 0.990093i | \(-0.544843\pi\) |
0.787239 | + | 0.616648i | \(0.211510\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 78.5914 | − | 136.124i | 0.156869 | − | 0.271705i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 648.033i | 1.28834i | 0.764884 | + | 0.644168i | \(0.222796\pi\) | ||||
−0.764884 | + | 0.644168i | \(0.777204\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1257.71 | 2.49052 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 206.061 | + | 118.969i | 0.406431 | + | 0.234653i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −210.281 | − | 364.217i | −0.413125 | − | 0.715554i | 0.582104 | − | 0.813114i | \(-0.302230\pi\) |
−0.995230 | + | 0.0975601i | \(0.968896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 81.0694 | + | 533.897i | 0.158649 | + | 1.04481i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 161.881 | + | 280.386i | 0.315558 | + | 0.546562i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 552.197 | + | 318.811i | 1.07223 | + | 0.619050i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −621.297 | −1.20173 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 564.548i | − | 1.08776i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −138.832 | + | 240.464i | −0.266472 | + | 0.461543i | −0.967948 | − | 0.251150i | \(-0.919191\pi\) |
0.701476 | + | 0.712693i | \(0.252525\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −565.536 | + | 326.512i | −1.08133 | + | 0.624307i | −0.931255 | − | 0.364368i | \(-0.881285\pi\) |
−0.150076 | + | 0.988674i | \(0.547952\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −190.782 | + | 487.672i | −0.363393 | + | 0.928898i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −178.762 | + | 103.208i | −0.339207 | + | 0.195841i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 613.889 | − | 1063.29i | 1.16047 | − | 2.01000i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 157.484i | − | 0.296580i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 282.814 | 0.530609 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1171.43 | + | 676.323i | 2.18958 | + | 1.26416i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −123.312 | − | 213.583i | −0.229632 | − | 0.397734i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −349.441 | + | 378.264i | −0.648313 | + | 0.701789i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −133.144 | − | 230.612i | −0.246107 | − | 0.426269i | 0.716336 | − | 0.697756i | \(-0.245818\pi\) |
−0.962442 | + | 0.271487i | \(0.912485\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 112.023 | + | 64.6762i | 0.206303 | + | 0.119109i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −502.535 | −0.922082 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 291.492i | − | 0.532892i | −0.963850 | − | 0.266446i | \(-0.914151\pi\) | ||
0.963850 | − | 0.266446i | \(-0.0858493\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.08631 | + | 1.88155i | −0.00197871 | + | 0.00342723i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 388.256 | − | 224.160i | 0.704640 | − | 0.406824i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 93.8752 | − | 239.962i | 0.169756 | − | 0.433927i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −91.1869 | + | 52.6468i | −0.164301 | + | 0.0948591i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 288.069 | − | 498.951i | 0.517180 | − | 0.895783i | −0.482621 | − | 0.875830i | \(-0.660315\pi\) |
0.999801 | − | 0.0199531i | \(-0.00635170\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 137.902i | − | 0.246694i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −502.205 | −0.895196 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 498.094 | + | 287.575i | 0.884714 | + | 0.510790i | 0.872210 | − | 0.489132i | \(-0.162686\pi\) |
0.0125043 | + | 0.999922i | \(0.496020\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −40.1763 | − | 69.5874i | −0.0711085 | − | 0.123164i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.64112 | − | 43.7362i | −0.0117127 | − | 0.0771362i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −428.609 | − | 742.373i | −0.753268 | − | 1.30470i | −0.946231 | − | 0.323492i | \(-0.895143\pi\) |
0.192963 | − | 0.981206i | \(-0.438190\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 255.486 | + | 147.505i | 0.447436 | + | 0.258327i | 0.706747 | − | 0.707467i | \(-0.250162\pi\) |
−0.259311 | + | 0.965794i | \(0.583495\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −226.908 | −0.396000 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1772.75i | − | 3.08305i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 283.201 | − | 490.519i | 0.490817 | − | 0.850119i | −0.509127 | − | 0.860691i | \(-0.670032\pi\) |
0.999944 | + | 0.0105718i | \(0.00336517\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 428.188 | − | 247.214i | 0.739530 | − | 0.426968i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −429.590 | − | 537.482i | −0.739398 | − | 0.925098i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −37.0034 | + | 21.3639i | −0.0634706 | + | 0.0366448i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −141.407 | + | 244.924i | −0.241722 | + | 0.418674i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 882.011i | − | 1.50257i | −0.659975 | − | 0.751287i | \(-0.729433\pi\) | ||
0.659975 | − | 0.751287i | \(-0.270567\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 94.0411 | 0.159662 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 151.741 | + | 87.6079i | 0.256754 | + | 0.148237i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 462.541 | + | 801.145i | 0.780003 | + | 1.35100i | 0.931939 | + | 0.362614i | \(0.118116\pi\) |
−0.151937 | + | 0.988390i | \(0.548551\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1211.87 | − | 968.608i | 2.03676 | − | 1.62791i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −208.992 | − | 361.984i | −0.350070 | − | 0.606339i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −131.504 | − | 75.9240i | −0.219540 | − | 0.126751i | 0.386197 | − | 0.922416i | \(-0.373788\pi\) |
−0.605737 | + | 0.795665i | \(0.707122\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 485.178 | 0.807284 | 0.403642 | − | 0.914917i | \(-0.367744\pi\) | ||||
0.403642 | + | 0.914917i | \(0.367744\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 12.2484i | − | 0.0203125i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 43.2691 | − | 74.9443i | 0.0715192 | − | 0.123875i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −327.526 | + | 189.097i | −0.539581 | + | 0.311527i | −0.744909 | − | 0.667166i | \(-0.767507\pi\) |
0.205328 | + | 0.978693i | \(0.434174\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 445.854 | − | 67.7006i | 0.732108 | − | 0.111167i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −300.608 | + | 173.556i | −0.491993 | + | 0.284052i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 307.141 | − | 531.983i | 0.501045 | − | 0.867836i | −0.498954 | − | 0.866628i | \(-0.666282\pi\) |
0.999999 | − | 0.00120729i | \(-0.000384294\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 698.877i | 1.13639i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1193.13 | 1.93377 | 0.966883 | − | 0.255220i | \(-0.0821479\pi\) | ||||
0.966883 | + | 0.255220i | \(0.0821479\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 423.076 | + | 244.263i | 0.683483 | + | 0.394609i | 0.801166 | − | 0.598442i | \(-0.204213\pi\) |
−0.117683 | + | 0.993051i | \(0.537547\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −551.250 | − | 954.792i | −0.887680 | − | 1.53751i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −197.821 | − | 77.3895i | −0.317530 | − | 0.124221i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −53.2486 | − | 92.2293i | −0.0851978 | − | 0.147567i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 198.145 | + | 114.399i | 0.316021 | + | 0.182455i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 196.057 | 0.311696 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 384.907i | 0.609995i | 0.952353 | + | 0.304998i | \(0.0986557\pi\) | ||||
−0.952353 | + | 0.304998i | \(0.901344\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −344.623 | + | 596.905i | −0.544428 | + | 0.942977i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −893.048 | + | 515.601i | −1.40637 | + | 0.811970i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −63.4070 | + | 280.633i | −0.0995401 | + | 0.440555i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 619.251 | − | 357.525i | 0.969093 | − | 0.559506i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −546.981 | + | 947.399i | −0.853325 | + | 1.47800i | 0.0248661 | + | 0.999691i | \(0.492084\pi\) |
−0.878191 | + | 0.478311i | \(0.841249\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 866.317i | 1.34731i | 0.739048 | + | 0.673653i | \(0.235276\pi\) | ||||
−0.739048 | + | 0.673653i | \(0.764724\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 340.776 | 0.528335 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.2070 | − | 18.5947i | −0.0497790 | − | 0.0287399i | 0.474904 | − | 0.880038i | \(-0.342483\pi\) |
−0.524683 | + | 0.851298i | \(0.675816\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −140.941 | − | 244.117i | −0.217166 | − | 0.376143i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 88.0945 | + | 34.4634i | 0.135322 | + | 0.0529391i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 547.956 | + | 949.088i | 0.839137 | + | 1.45343i | 0.890617 | + | 0.454754i | \(0.150273\pi\) |
−0.0514806 | + | 0.998674i | \(0.516394\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −253.037 | − | 146.091i | −0.386315 | − | 0.223039i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −452.964 | −0.689443 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 13.9021i | − | 0.0210957i | −0.999944 | − | 0.0105479i | \(-0.996642\pi\) | ||
0.999944 | − | 0.0105479i | \(-0.00335755\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 50.8103 | − | 88.0061i | 0.0768689 | − | 0.133141i | −0.825029 | − | 0.565091i | \(-0.808841\pi\) |
0.901897 | + | 0.431950i | \(0.142174\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −242.986 | + | 140.288i | −0.366495 | + | 0.211596i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −698.789 | + | 106.108i | −1.05081 | + | 0.159560i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1322.12 | + | 763.326i | −1.98219 | + | 1.14442i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −90.3988 | + | 156.575i | −0.135125 | + | 0.234044i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.88879i | 0.00579551i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −71.7077 | −0.106549 | −0.0532747 | − | 0.998580i | \(-0.516966\pi\) | ||||
−0.0532747 | + | 0.998580i | \(0.516966\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −963.475 | − | 556.262i | −1.42737 | − | 0.824092i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 524.998 | + | 909.323i | 0.775477 | + | 1.34317i | 0.934526 | + | 0.355895i | \(0.115824\pi\) |
−0.159049 | + | 0.987271i | \(0.550843\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.1060 | − | 25.6612i | 0.0472843 | − | 0.0377927i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 204.273 | + | 353.812i | 0.299961 | + | 0.519547i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −116.044 | − | 66.9981i | −0.169904 | − | 0.0980939i | 0.412637 | − | 0.910896i | \(-0.364608\pi\) |
−0.582540 | + | 0.812802i | \(0.697941\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 980.301 | 1.43110 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 29.7225i | − | 0.0432643i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.9358 | + | 20.6734i | −0.0173233 | + | 0.0300049i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 390.403 | − | 225.399i | 0.564982 | − | 0.326193i | −0.190161 | − | 0.981753i | \(-0.560901\pi\) |
0.755143 | + | 0.655560i | \(0.227568\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −269.688 | − | 337.420i | −0.389161 | − | 0.486898i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 336.737 | − | 194.415i | 0.484514 | − | 0.279734i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 650.654 | − | 1126.97i | 0.933507 | − | 1.61688i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 213.335i | − | 0.305201i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −524.776 | −0.748611 | −0.374305 | − | 0.927306i | \(-0.622119\pi\) | ||||
−0.374305 | + | 0.927306i | \(0.622119\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −77.3543 | − | 44.6605i | −0.110035 | − | 0.0635285i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −428.883 | − | 742.847i | −0.608345 | − | 1.05368i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 161.115 | + | 1061.05i | 0.227886 | + | 1.50078i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.2186 | + | 38.4837i | 0.0313379 | + | 0.0542789i | 0.881269 | − | 0.472615i | \(-0.156690\pi\) |
−0.849931 | + | 0.526894i | \(0.823357\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 187.177 | + | 108.067i | 0.263259 | + | 0.151993i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −320.236 | −0.449138 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 506.211i | 0.707987i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 97.1595 | − | 168.285i | 0.135508 | − | 0.234707i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −465.543 | + | 268.781i | −0.647487 | + | 0.373827i | −0.787493 | − | 0.616324i | \(-0.788621\pi\) |
0.140006 | + | 0.990151i | \(0.455288\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −198.224 | + | 506.695i | −0.274929 | + | 0.702767i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 283.222 | − | 163.518i | 0.391732 | − | 0.226166i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −770.268 | + | 1334.14i | −1.06244 | + | 1.84020i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 168.754i | − | 0.232124i | −0.993242 | − | 0.116062i | \(-0.962973\pi\) | ||
0.993242 | − | 0.116062i | \(-0.0370271\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −381.615 | −0.523477 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −549.515 | − | 317.262i | −0.751730 | − | 0.434012i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −100.846 | − | 174.671i | −0.137580 | − | 0.238296i | 0.789000 | − | 0.614393i | \(-0.210599\pi\) |
−0.926580 | + | 0.376097i | \(0.877266\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −693.488 | − | 156.688i | −0.943520 | − | 0.213181i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.9618 | − | 18.9863i | −0.0148735 | − | 0.0257616i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −192.074 | − | 110.894i | −0.259911 | − | 0.150059i | 0.364383 | − | 0.931249i | \(-0.381280\pi\) |
−0.624294 | + | 0.781190i | \(0.714613\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 127.827 | 0.172507 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 344.416i | 0.463547i | 0.972770 | + | 0.231774i | \(0.0744529\pi\) | ||||
−0.972770 | + | 0.231774i | \(0.925547\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −776.753 | + | 1345.38i | −1.04262 | + | 1.80587i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 499.824 | − | 288.574i | 0.669109 | − | 0.386310i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −420.510 | + | 1074.90i | −0.561429 | + | 1.43511i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1167.06 | − | 673.805i | 1.55401 | − | 0.897211i | 0.556206 | − | 0.831045i | \(-0.312257\pi\) |
0.997809 | − | 0.0661661i | \(-0.0210767\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 198.829 | − | 344.382i | 0.264050 | − | 0.457347i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2012.34i | − | 2.66536i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −796.713 | −1.05246 | −0.526230 | − | 0.850342i | \(-0.676395\pi\) | ||||
−0.526230 | + | 0.850342i | \(0.676395\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −674.740 | − | 389.561i | −0.888985 | − | 0.513256i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 407.280 | + | 705.429i | 0.535190 | + | 0.926976i | 0.999154 | + | 0.0411222i | \(0.0130933\pi\) |
−0.463964 | + | 0.885854i | \(0.653573\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −64.3758 | − | 423.958i | −0.0843720 | − | 0.555646i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 650.654 | + | 1126.97i | 0.850529 | + | 1.47316i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −136.385 | − | 78.7421i | −0.177817 | − | 0.102662i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 60.5653 | 0.0787585 | 0.0393792 | − | 0.999224i | \(-0.487462\pi\) | ||||
0.0393792 | + | 0.999224i | \(0.487462\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 315.567i | 0.409296i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 499.210 | − | 864.657i | 0.645809 | − | 1.11857i | −0.338305 | − | 0.941036i | \(-0.609854\pi\) |
0.984114 | − | 0.177537i | \(-0.0568130\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −279.854 | + | 161.574i | −0.361102 | + | 0.208482i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −56.0961 | − | 70.1846i | −0.0721958 | − | 0.0903277i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −513.433 | + | 296.431i | −0.659092 | + | 0.380527i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 639.935 | − | 1108.40i | 0.819378 | − | 1.41921i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 958.079i | 1.22360i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1810.63 | −2.30654 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 652.956 | + | 376.984i | 0.829677 | + | 0.479014i | 0.853742 | − | 0.520696i | \(-0.174327\pi\) |
−0.0240648 | + | 0.999710i | \(0.507661\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 255.240 | + | 442.089i | 0.323498 | + | 0.560315i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 53.5600 | − | 42.8086i | 0.0677117 | − | 0.0541196i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.08631 | + | 1.88155i | 0.00136988 | + | 0.00237270i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −51.0871 | − | 29.4951i | −0.0642605 | − | 0.0371008i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 335.856 | 0.421400 | 0.210700 | − | 0.977551i | \(-0.432426\pi\) | ||||
0.210700 | + | 0.977551i | \(0.432426\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1597.16i | 1.99895i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 89.0888 | − | 154.306i | 0.111222 | − | 0.192642i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −702.141 | + | 405.381i | −0.874397 | + | 0.504833i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2379.57 | − | 361.325i | 2.95599 | − | 0.448851i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 345.103 | − | 199.245i | 0.427637 | − | 0.246897i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −374.844 | + | 649.250i | −0.463343 | + | 0.802533i | −0.999125 | − | 0.0418229i | \(-0.986683\pi\) |
0.535782 | + | 0.844356i | \(0.320017\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 790.284i | − | 0.974456i | −0.873275 | − | 0.487228i | \(-0.838008\pi\) | ||
0.873275 | − | 0.487228i | \(-0.161992\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −346.112 | −0.425722 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1932.62 | − | 1115.80i | −2.37131 | − | 1.36908i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 144.541 | + | 250.352i | 0.176917 | + | 0.306429i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −224.742 | − | 87.9212i | −0.274411 | − | 0.107352i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −459.548 | − | 795.961i | −0.559742 | − | 0.969501i | −0.997518 | − | 0.0704171i | \(-0.977567\pi\) |
0.437776 | − | 0.899084i | \(-0.355766\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −841.077 | − | 485.596i | −1.02197 | − | 0.590032i | −0.107293 | − | 0.994227i | \(-0.534218\pi\) |
−0.914673 | + | 0.404196i | \(0.867552\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −786.207 | −0.952979 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 110.492i | 0.133606i | 0.997766 | + | 0.0668029i | \(0.0212799\pi\) | ||||
−0.997766 | + | 0.0668029i | \(0.978720\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 247.986 | − | 429.525i | 0.299139 | − | 0.518124i | −0.676800 | − | 0.736167i | \(-0.736634\pi\) |
0.975939 | + | 0.218043i | \(0.0699673\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −207.751 | + | 119.945i | −0.250002 | + | 0.144339i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 972.399 | + | 898.303i | 1.16735 | + | 1.07839i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −631.342 | + | 364.506i | −0.756098 | + | 0.436534i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −100.485 | + | 174.045i | −0.120054 | + | 0.207939i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 529.377i | 0.630962i | 0.948932 | + | 0.315481i | \(0.102166\pi\) | ||||
−0.948932 | + | 0.315481i | \(0.897834\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 485.672 | 0.577493 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 570.576 | + | 329.422i | 0.676840 | + | 0.390774i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −551.777 | − | 955.705i | −0.652990 | − | 1.13101i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 68.7688 | + | 26.9030i | 0.0811910 | + | 0.0317627i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 254.175 | + | 440.244i | 0.299382 | + | 0.518544i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 263.413 | + | 152.081i | 0.309533 | + | 0.178709i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1122.77 | 1.31626 | 0.658132 | − | 0.752902i | \(-0.271347\pi\) | ||||
0.658132 | + | 0.752902i | \(0.271347\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 592.861i | − | 0.693405i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 334.966 | − | 580.178i | 0.390859 | − | 0.676987i | −0.601704 | − | 0.798719i | \(-0.705511\pi\) |
0.992563 | + | 0.121732i | \(0.0388448\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 202.690 | − | 117.023i | 0.235961 | − | 0.136232i | −0.377358 | − | 0.926067i | \(-0.623167\pi\) |
0.613319 | + | 0.789835i | \(0.289834\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −589.600 | + | 89.5277i | −0.684785 | + | 0.103981i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.7766 | − | 25.8518i | 0.0518849 | − | 0.0299557i | −0.473833 | − | 0.880615i | \(-0.657130\pi\) |
0.525718 | + | 0.850659i | \(0.323797\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1309.18 | + | 2267.57i | −1.51350 | + | 2.62147i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 779.847i | 0.899478i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 386.858 | 0.445176 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.6074 | − | 6.12421i | −0.0121785 | − | 0.00703124i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.2377 | + | 29.8566i | 0.0197454 | + | 0.0342000i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 775.794 | − | 620.065i | 0.886621 | − | 0.708645i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.1626 | + | 93.8124i | 0.0617590 | + | 0.106970i | 0.895252 | − | 0.445561i | \(-0.146996\pi\) |
−0.833493 | + | 0.552530i | \(0.813662\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −202.113 | − | 116.690i | −0.229935 | − | 0.132753i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 901.643 | 1.02343 | 0.511716 | − | 0.859155i | \(-0.329010\pi\) | ||||
0.511716 | + | 0.859155i | \(0.329010\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 391.049i | 0.442864i | 0.975176 | + | 0.221432i | \(0.0710731\pi\) | ||||
−0.975176 | + | 0.221432i | \(0.928927\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 194.584 | − | 337.029i | 0.219869 | − | 0.380823i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1123.13 | − | 648.438i | 1.26621 | − | 0.731047i | 0.291941 | − | 0.956436i | \(-0.405699\pi\) |
0.974269 | + | 0.225390i | \(0.0723655\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −549.382 | − | 687.360i | −0.617978 | − | 0.773183i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 57.5186 | − | 33.2084i | 0.0645551 | − | 0.0372709i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 363.824 | − | 630.161i | 0.407417 | − | 0.705668i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1143.84i | 1.27803i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −435.287 | −0.485270 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 241.004 | + | 139.144i | 0.268080 | + | 0.154776i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 54.9199 | + | 95.1241i | 0.0609544 | + | 0.105576i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 43.6542 | + | 287.492i | 0.0483435 | + | 0.318374i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −299.967 | − | 519.558i | −0.331455 | − | 0.574098i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −399.679 | − | 230.755i | −0.440660 | − | 0.254415i | 0.263217 | − | 0.964737i | \(-0.415216\pi\) |
−0.703878 | + | 0.710321i | \(0.748550\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −900.210 | −0.990330 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 119.595i | 0.131279i | 0.997843 | + | 0.0656395i | \(0.0209087\pi\) | ||||
−0.997843 | + | 0.0656395i | \(0.979091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 516.519 | − | 894.637i | 0.565738 | − | 0.979888i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.64959 | + | 2.68444i | −0.00508152 | + | 0.00293382i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 90.8333 | − | 232.186i | 0.0990548 | − | 0.253202i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 612.884 | − | 353.849i | 0.666903 | − | 0.385037i | −0.127999 | − | 0.991774i | \(-0.540855\pi\) |
0.794902 | + | 0.606737i | \(0.207522\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −42.2951 | + | 73.2572i | −0.0459230 | + | 0.0795410i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 715.049i | − | 0.774701i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 306.929 | 0.331815 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −395.236 | − | 228.190i | −0.426361 | − | 0.246159i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 198.528 | + | 343.860i | 0.213701 | + | 0.370140i | 0.952870 | − | 0.303380i | \(-0.0981150\pi\) |
−0.739169 | + | 0.673520i | \(0.764782\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −179.033 | − | 575.933i | −0.192302 | − | 0.618618i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −201.193 | − | 348.476i | −0.215641 | − | 0.373500i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2017.16 | + | 1164.61i | 2.15739 | + | 1.24557i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1227.51 | −1.31004 | −0.655020 | − | 0.755612i | \(-0.727340\pi\) | ||||
−0.655020 | + | 0.755612i | \(0.727340\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 217.725i | 0.231869i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 343.521 | − | 594.995i | 0.365059 | − | 0.632301i | −0.623726 | − | 0.781643i | \(-0.714382\pi\) |
0.988786 | + | 0.149342i | \(0.0477154\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1748.38 | − | 1009.43i | 1.85406 | − | 1.07044i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 550.295 | − | 1406.65i | 0.582322 | − | 1.48852i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −115.670 | + | 66.7819i | −0.122143 | + | 0.0705194i | −0.559827 | − | 0.828610i | \(-0.689132\pi\) |
0.437684 | + | 0.899129i | \(0.355799\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −226.482 | + | 392.279i | −0.238653 | + | 0.413360i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 849.514i | − | 0.893285i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1030.34 | 1.08115 | 0.540575 | − | 0.841296i | \(-0.318207\pi\) | ||||
0.540575 | + | 0.841296i | \(0.318207\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 911.401 | + | 526.198i | 0.954346 | + | 0.550992i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 338.531 | + | 586.354i | 0.353742 | + | 0.612700i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 125.579 | + | 827.020i | 0.130948 | + | 0.862378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −451.313 | − | 781.697i | −0.469628 | − | 0.813420i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −838.452 | − | 484.081i | −0.870667 | − | 0.502680i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2293.15 | −2.37632 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 337.880i | − | 0.349410i | −0.984621 | − | 0.174705i | \(-0.944103\pi\) | ||
0.984621 | − | 0.174705i | \(-0.0558972\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 294.085 | − | 509.370i | 0.303493 | − | 0.525666i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1454.36 | − | 839.672i | 1.49779 | − | 0.864750i | 0.497794 | − | 0.867295i | \(-0.334143\pi\) |
0.999997 | + | 0.00254493i | \(0.000810076\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 207.153 | + | 259.179i | 0.212901 | + | 0.266371i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −380.398 | + | 219.623i | −0.390152 | + | 0.225254i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 554.679 | − | 960.733i | 0.567737 | − | 0.983350i | −0.429052 | − | 0.903280i | \(-0.641152\pi\) |
0.996789 | − | 0.0800700i | \(-0.0255144\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 318.921i | − | 0.325762i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 359.691 | 0.366657 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −360.616 | − | 208.202i | −0.366852 | − | 0.211802i | 0.305230 | − | 0.952279i | \(-0.401267\pi\) |
−0.672082 | + | 0.740476i | \(0.734600\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −406.324 | − | 703.774i | −0.412512 | − | 0.714491i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 571.754 | − | 456.983i | 0.579285 | − | 0.463002i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −492.202 | − | 852.519i | −0.497677 | − | 0.862001i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1034.76 | + | 597.420i | 1.04416 | + | 0.602846i | 0.921009 | − | 0.389542i | \(-0.127367\pi\) |
0.123151 | + | 0.992388i | \(0.460700\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −839.073 | −0.844988 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1938.60i | 1.94834i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −838.567 | + | 1452.44i | −0.841090 | + | 1.45681i | 0.0478838 | + | 0.998853i | \(0.484752\pi\) |
−0.888974 | + | 0.457958i | \(0.848581\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 165.310 | − | 95.4415i | 0.165475 | − | 0.0955371i |
(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 | 224.3.r.d.95.2 | ✓ | 12 | |
4.3 | odd | 2 | inner | 224.3.r.d.95.5 | yes | 12 | |
7.2 | even | 3 | inner | 224.3.r.d.191.5 | yes | 12 | |
7.3 | odd | 6 | 1568.3.d.l.1471.2 | 6 | |||
7.4 | even | 3 | 1568.3.d.i.1471.5 | 6 | |||
8.3 | odd | 2 | 448.3.r.f.319.2 | 12 | |||
8.5 | even | 2 | 448.3.r.f.319.5 | 12 | |||
28.3 | even | 6 | 1568.3.d.l.1471.5 | 6 | |||
28.11 | odd | 6 | 1568.3.d.i.1471.2 | 6 | |||
28.23 | odd | 6 | inner | 224.3.r.d.191.2 | yes | 12 | |
56.37 | even | 6 | 448.3.r.f.191.2 | 12 | |||
56.51 | odd | 6 | 448.3.r.f.191.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.r.d.95.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
224.3.r.d.95.5 | yes | 12 | 4.3 | odd | 2 | inner | |
224.3.r.d.191.2 | yes | 12 | 28.23 | odd | 6 | inner | |
224.3.r.d.191.5 | yes | 12 | 7.2 | even | 3 | inner | |
448.3.r.f.191.2 | 12 | 56.37 | even | 6 | |||
448.3.r.f.191.5 | 12 | 56.51 | odd | 6 | |||
448.3.r.f.319.2 | 12 | 8.3 | odd | 2 | |||
448.3.r.f.319.5 | 12 | 8.5 | even | 2 | |||
1568.3.d.i.1471.2 | 6 | 28.11 | odd | 6 | |||
1568.3.d.i.1471.5 | 6 | 7.4 | even | 3 | |||
1568.3.d.l.1471.2 | 6 | 7.3 | odd | 6 | |||
1568.3.d.l.1471.5 | 6 | 28.3 | even | 6 |