Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2695,2,Mod(1,2695)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2695, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2695.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2695 = 5 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2695.a (trivial) |
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: | yes |
Analytic conductor: | \(21.5196833447\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 56x^{6} - 92x^{5} - 86x^{4} + 116x^{3} + 31x^{2} - 30x - 7 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-2.25931\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2695.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.25931 | 1.59757 | 0.798785 | − | 0.601616i | \(-0.205476\pi\) | ||||
0.798785 | + | 0.601616i | \(0.205476\pi\) | |||||||
\(3\) | −2.89439 | −1.67107 | −0.835537 | − | 0.549434i | \(-0.814843\pi\) | ||||
−0.835537 | + | 0.549434i | \(0.814843\pi\) | |||||||
\(4\) | 3.10446 | 1.55223 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −6.53930 | −2.66966 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.49532 | 0.882227 | ||||||||
\(9\) | 5.37747 | 1.79249 | ||||||||
\(10\) | 2.25931 | 0.714455 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −8.98551 | −2.59389 | ||||||||
\(13\) | −5.18923 | −1.43923 | −0.719617 | − | 0.694371i | \(-0.755683\pi\) | ||||
−0.719617 | + | 0.694371i | \(0.755683\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.89439 | −0.747327 | ||||||||
\(16\) | −0.571242 | −0.142811 | ||||||||
\(17\) | −1.23865 | −0.300416 | −0.150208 | − | 0.988654i | \(-0.547994\pi\) | ||||
−0.150208 | + | 0.988654i | \(0.547994\pi\) | |||||||
\(18\) | 12.1493 | 2.86363 | ||||||||
\(19\) | −0.0890109 | −0.0204205 | −0.0102102 | − | 0.999948i | \(-0.503250\pi\) | ||||
−0.0102102 | + | 0.999948i | \(0.503250\pi\) | |||||||
\(20\) | 3.10446 | 0.694179 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.25931 | 0.481686 | ||||||||
\(23\) | −6.56566 | −1.36904 | −0.684518 | − | 0.728996i | \(-0.739987\pi\) | ||||
−0.684518 | + | 0.728996i | \(0.739987\pi\) | |||||||
\(24\) | −7.22241 | −1.47427 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −11.7241 | −2.29928 | ||||||||
\(27\) | −6.88131 | −1.32431 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.308703 | −0.0573247 | −0.0286624 | − | 0.999589i | \(-0.509125\pi\) | ||||
−0.0286624 | + | 0.999589i | \(0.509125\pi\) | |||||||
\(30\) | −6.53930 | −1.19391 | ||||||||
\(31\) | 7.01096 | 1.25921 | 0.629603 | − | 0.776917i | \(-0.283218\pi\) | ||||
0.629603 | + | 0.776917i | \(0.283218\pi\) | |||||||
\(32\) | −6.28124 | −1.11038 | ||||||||
\(33\) | −2.89439 | −0.503848 | ||||||||
\(34\) | −2.79849 | −0.479936 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 16.6941 | 2.78236 | ||||||||
\(37\) | −0.545621 | −0.0896996 | −0.0448498 | − | 0.998994i | \(-0.514281\pi\) | ||||
−0.0448498 | + | 0.998994i | \(0.514281\pi\) | |||||||
\(38\) | −0.201103 | −0.0326232 | ||||||||
\(39\) | 15.0196 | 2.40507 | ||||||||
\(40\) | 2.49532 | 0.394544 | ||||||||
\(41\) | −9.60425 | −1.49993 | −0.749966 | − | 0.661476i | \(-0.769930\pi\) | ||||
−0.749966 | + | 0.661476i | \(0.769930\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.61867 | 0.399343 | 0.199671 | − | 0.979863i | \(-0.436013\pi\) | ||||
0.199671 | + | 0.979863i | \(0.436013\pi\) | |||||||
\(44\) | 3.10446 | 0.468015 | ||||||||
\(45\) | 5.37747 | 0.801626 | ||||||||
\(46\) | −14.8338 | −2.18713 | ||||||||
\(47\) | −10.1126 | −1.47507 | −0.737535 | − | 0.675309i | \(-0.764010\pi\) | ||||
−0.737535 | + | 0.675309i | \(0.764010\pi\) | |||||||
\(48\) | 1.65340 | 0.238647 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.25931 | 0.319514 | ||||||||
\(51\) | 3.58513 | 0.502018 | ||||||||
\(52\) | −16.1098 | −2.23402 | ||||||||
\(53\) | −4.66178 | −0.640345 | −0.320172 | − | 0.947359i | \(-0.603741\pi\) | ||||
−0.320172 | + | 0.947359i | \(0.603741\pi\) | |||||||
\(54\) | −15.5470 | −2.11568 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.257632 | 0.0341242 | ||||||||
\(58\) | −0.697455 | −0.0915803 | ||||||||
\(59\) | 11.5718 | 1.50652 | 0.753262 | − | 0.657721i | \(-0.228479\pi\) | ||||
0.753262 | + | 0.657721i | \(0.228479\pi\) | |||||||
\(60\) | −8.98551 | −1.16002 | ||||||||
\(61\) | 3.97047 | 0.508367 | 0.254183 | − | 0.967156i | \(-0.418193\pi\) | ||||
0.254183 | + | 0.967156i | \(0.418193\pi\) | |||||||
\(62\) | 15.8399 | 2.01167 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0488 | −1.63110 | ||||||||
\(65\) | −5.18923 | −0.643645 | ||||||||
\(66\) | −6.53930 | −0.804932 | ||||||||
\(67\) | −2.15100 | −0.262787 | −0.131393 | − | 0.991330i | \(-0.541945\pi\) | ||||
−0.131393 | + | 0.991330i | \(0.541945\pi\) | |||||||
\(68\) | −3.84534 | −0.466315 | ||||||||
\(69\) | 19.0036 | 2.28776 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.8329 | −1.76034 | −0.880170 | − | 0.474659i | \(-0.842572\pi\) | ||||
−0.880170 | + | 0.474659i | \(0.842572\pi\) | |||||||
\(72\) | 13.4185 | 1.58138 | ||||||||
\(73\) | 4.27711 | 0.500598 | 0.250299 | − | 0.968169i | \(-0.419471\pi\) | ||||
0.250299 | + | 0.968169i | \(0.419471\pi\) | |||||||
\(74\) | −1.23273 | −0.143301 | ||||||||
\(75\) | −2.89439 | −0.334215 | ||||||||
\(76\) | −0.276331 | −0.0316973 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 33.9339 | 3.84226 | ||||||||
\(79\) | 5.28131 | 0.594194 | 0.297097 | − | 0.954847i | \(-0.403981\pi\) | ||||
0.297097 | + | 0.954847i | \(0.403981\pi\) | |||||||
\(80\) | −0.571242 | −0.0638668 | ||||||||
\(81\) | 3.78476 | 0.420529 | ||||||||
\(82\) | −21.6989 | −2.39625 | ||||||||
\(83\) | −9.15911 | −1.00534 | −0.502671 | − | 0.864478i | \(-0.667649\pi\) | ||||
−0.502671 | + | 0.864478i | \(0.667649\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.23865 | −0.134350 | ||||||||
\(86\) | 5.91637 | 0.637978 | ||||||||
\(87\) | 0.893506 | 0.0957939 | ||||||||
\(88\) | 2.49532 | 0.266002 | ||||||||
\(89\) | −12.3013 | −1.30393 | −0.651966 | − | 0.758248i | \(-0.726056\pi\) | ||||
−0.651966 | + | 0.758248i | \(0.726056\pi\) | |||||||
\(90\) | 12.1493 | 1.28065 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −20.3828 | −2.12506 | ||||||||
\(93\) | −20.2924 | −2.10423 | ||||||||
\(94\) | −22.8474 | −2.35653 | ||||||||
\(95\) | −0.0890109 | −0.00913232 | ||||||||
\(96\) | 18.1803 | 1.85552 | ||||||||
\(97\) | −19.0137 | −1.93055 | −0.965277 | − | 0.261229i | \(-0.915872\pi\) | ||||
−0.965277 | + | 0.261229i | \(0.915872\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.37747 | 0.540456 | ||||||||
\(100\) | 3.10446 | 0.310446 | ||||||||
\(101\) | −15.5111 | −1.54341 | −0.771706 | − | 0.635979i | \(-0.780597\pi\) | ||||
−0.771706 | + | 0.635979i | \(0.780597\pi\) | |||||||
\(102\) | 8.09989 | 0.802009 | ||||||||
\(103\) | 16.8800 | 1.66323 | 0.831616 | − | 0.555352i | \(-0.187416\pi\) | ||||
0.831616 | + | 0.555352i | \(0.187416\pi\) | |||||||
\(104\) | −12.9488 | −1.26973 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.5324 | −1.02300 | ||||||||
\(107\) | −20.1474 | −1.94772 | −0.973860 | − | 0.227149i | \(-0.927060\pi\) | ||||
−0.973860 | + | 0.227149i | \(0.927060\pi\) | |||||||
\(108\) | −21.3628 | −2.05563 | ||||||||
\(109\) | −16.7050 | −1.60005 | −0.800026 | − | 0.599965i | \(-0.795181\pi\) | ||||
−0.800026 | + | 0.599965i | \(0.795181\pi\) | |||||||
\(110\) | 2.25931 | 0.215416 | ||||||||
\(111\) | 1.57924 | 0.149895 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2463 | 1.05796 | 0.528980 | − | 0.848634i | \(-0.322575\pi\) | ||||
0.528980 | + | 0.848634i | \(0.322575\pi\) | |||||||
\(114\) | 0.582069 | 0.0545157 | ||||||||
\(115\) | −6.56566 | −0.612251 | ||||||||
\(116\) | −0.958357 | −0.0889812 | ||||||||
\(117\) | −27.9049 | −2.57981 | ||||||||
\(118\) | 26.1443 | 2.40678 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −7.22241 | −0.659312 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.97050 | 0.812151 | ||||||||
\(123\) | 27.7984 | 2.50650 | ||||||||
\(124\) | 21.7653 | 1.95458 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.35425 | −0.120170 | −0.0600849 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600849 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(128\) | −16.9187 | −1.49541 | ||||||||
\(129\) | −7.57943 | −0.667332 | ||||||||
\(130\) | −11.7241 | −1.02827 | ||||||||
\(131\) | 7.97900 | 0.697129 | 0.348564 | − | 0.937285i | \(-0.386669\pi\) | ||||
0.348564 | + | 0.937285i | \(0.386669\pi\) | |||||||
\(132\) | −8.98551 | −0.782088 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.85977 | −0.419820 | ||||||||
\(135\) | −6.88131 | −0.592249 | ||||||||
\(136\) | −3.09082 | −0.265036 | ||||||||
\(137\) | 12.6254 | 1.07866 | 0.539328 | − | 0.842095i | \(-0.318678\pi\) | ||||
0.539328 | + | 0.842095i | \(0.318678\pi\) | |||||||
\(138\) | 42.9348 | 3.65486 | ||||||||
\(139\) | 18.0063 | 1.52727 | 0.763635 | − | 0.645648i | \(-0.223413\pi\) | ||||
0.763635 | + | 0.645648i | \(0.223413\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 29.2697 | 2.46495 | ||||||||
\(142\) | −33.5120 | −2.81227 | ||||||||
\(143\) | −5.18923 | −0.433945 | ||||||||
\(144\) | −3.07184 | −0.255986 | ||||||||
\(145\) | −0.308703 | −0.0256364 | ||||||||
\(146\) | 9.66330 | 0.799741 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.69386 | −0.139234 | ||||||||
\(149\) | −1.46846 | −0.120301 | −0.0601506 | − | 0.998189i | \(-0.519158\pi\) | ||||
−0.0601506 | + | 0.998189i | \(0.519158\pi\) | |||||||
\(150\) | −6.53930 | −0.533932 | ||||||||
\(151\) | 3.06680 | 0.249573 | 0.124786 | − | 0.992184i | \(-0.460175\pi\) | ||||
0.124786 | + | 0.992184i | \(0.460175\pi\) | |||||||
\(152\) | −0.222110 | −0.0180155 | ||||||||
\(153\) | −6.66079 | −0.538493 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.01096 | 0.563134 | ||||||||
\(156\) | 46.6279 | 3.73322 | ||||||||
\(157\) | 0.0106622 | 0.000850937 0 | 0.000425469 | − | 1.00000i | \(-0.499865\pi\) | ||||
0.000425469 | 1.00000i | \(0.499865\pi\) | ||||||||
\(158\) | 11.9321 | 0.949267 | ||||||||
\(159\) | 13.4930 | 1.07006 | ||||||||
\(160\) | −6.28124 | −0.496576 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.55093 | 0.671824 | ||||||||
\(163\) | −24.7147 | −1.93580 | −0.967902 | − | 0.251326i | \(-0.919133\pi\) | ||||
−0.967902 | + | 0.251326i | \(0.919133\pi\) | |||||||
\(164\) | −29.8160 | −2.32824 | ||||||||
\(165\) | −2.89439 | −0.225328 | ||||||||
\(166\) | −20.6932 | −1.60611 | ||||||||
\(167\) | 8.51313 | 0.658766 | 0.329383 | − | 0.944196i | \(-0.393159\pi\) | ||||
0.329383 | + | 0.944196i | \(0.393159\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.9281 | 1.07139 | ||||||||
\(170\) | −2.79849 | −0.214634 | ||||||||
\(171\) | −0.478653 | −0.0366035 | ||||||||
\(172\) | 8.12955 | 0.619872 | ||||||||
\(173\) | 15.1992 | 1.15558 | 0.577788 | − | 0.816187i | \(-0.303916\pi\) | ||||
0.577788 | + | 0.816187i | \(0.303916\pi\) | |||||||
\(174\) | 2.01870 | 0.153037 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.571242 | −0.0430590 | ||||||||
\(177\) | −33.4933 | −2.51751 | ||||||||
\(178\) | −27.7923 | −2.08312 | ||||||||
\(179\) | 20.0498 | 1.49859 | 0.749297 | − | 0.662234i | \(-0.230392\pi\) | ||||
0.749297 | + | 0.662234i | \(0.230392\pi\) | |||||||
\(180\) | 16.6941 | 1.24431 | ||||||||
\(181\) | −18.1470 | −1.34886 | −0.674429 | − | 0.738340i | \(-0.735610\pi\) | ||||
−0.674429 | + | 0.738340i | \(0.735610\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.4921 | −0.849518 | ||||||||
\(184\) | −16.3834 | −1.20780 | ||||||||
\(185\) | −0.545621 | −0.0401149 | ||||||||
\(186\) | −45.8468 | −3.36165 | ||||||||
\(187\) | −1.23865 | −0.0905789 | ||||||||
\(188\) | −31.3941 | −2.28965 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.201103 | −0.0145895 | ||||||||
\(191\) | 11.9314 | 0.863326 | 0.431663 | − | 0.902035i | \(-0.357927\pi\) | ||||
0.431663 | + | 0.902035i | \(0.357927\pi\) | |||||||
\(192\) | 37.7681 | 2.72568 | ||||||||
\(193\) | −6.85826 | −0.493668 | −0.246834 | − | 0.969058i | \(-0.579390\pi\) | ||||
−0.246834 | + | 0.969058i | \(0.579390\pi\) | |||||||
\(194\) | −42.9579 | −3.08420 | ||||||||
\(195\) | 15.0196 | 1.07558 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.70609 | 0.335295 | 0.167647 | − | 0.985847i | \(-0.446383\pi\) | ||||
0.167647 | + | 0.985847i | \(0.446383\pi\) | |||||||
\(198\) | 12.1493 | 0.863416 | ||||||||
\(199\) | 4.68345 | 0.332001 | 0.166000 | − | 0.986126i | \(-0.446915\pi\) | ||||
0.166000 | + | 0.986126i | \(0.446915\pi\) | |||||||
\(200\) | 2.49532 | 0.176445 | ||||||||
\(201\) | 6.22583 | 0.439136 | ||||||||
\(202\) | −35.0443 | −2.46571 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 11.1299 | 0.779248 | ||||||||
\(205\) | −9.60425 | −0.670790 | ||||||||
\(206\) | 38.1370 | 2.65713 | ||||||||
\(207\) | −35.3066 | −2.45398 | ||||||||
\(208\) | 2.96431 | 0.205538 | ||||||||
\(209\) | −0.0890109 | −0.00615701 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.21950 | −0.428168 | −0.214084 | − | 0.976815i | \(-0.568677\pi\) | ||||
−0.214084 | + | 0.976815i | \(0.568677\pi\) | |||||||
\(212\) | −14.4723 | −0.993963 | ||||||||
\(213\) | 42.9321 | 2.94166 | ||||||||
\(214\) | −45.5191 | −3.11162 | ||||||||
\(215\) | 2.61867 | 0.178592 | ||||||||
\(216\) | −17.1710 | −1.16834 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −37.7418 | −2.55620 | ||||||||
\(219\) | −12.3796 | −0.836537 | ||||||||
\(220\) | 3.10446 | 0.209303 | ||||||||
\(221\) | 6.42763 | 0.432369 | ||||||||
\(222\) | 3.56798 | 0.239467 | ||||||||
\(223\) | −9.98943 | −0.668942 | −0.334471 | − | 0.942406i | \(-0.608558\pi\) | ||||
−0.334471 | + | 0.942406i | \(0.608558\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.37747 | 0.358498 | ||||||||
\(226\) | 25.4088 | 1.69017 | ||||||||
\(227\) | 2.41877 | 0.160539 | 0.0802697 | − | 0.996773i | \(-0.474422\pi\) | ||||
0.0802697 | + | 0.996773i | \(0.474422\pi\) | |||||||
\(228\) | 0.799808 | 0.0529686 | ||||||||
\(229\) | 3.38871 | 0.223932 | 0.111966 | − | 0.993712i | \(-0.464285\pi\) | ||||
0.111966 | + | 0.993712i | \(0.464285\pi\) | |||||||
\(230\) | −14.8338 | −0.978114 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.770312 | −0.0505735 | ||||||||
\(233\) | 15.2101 | 0.996446 | 0.498223 | − | 0.867049i | \(-0.333986\pi\) | ||||
0.498223 | + | 0.867049i | \(0.333986\pi\) | |||||||
\(234\) | −63.0457 | −4.12143 | ||||||||
\(235\) | −10.1126 | −0.659671 | ||||||||
\(236\) | 35.9243 | 2.33847 | ||||||||
\(237\) | −15.2862 | −0.992943 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.6034 | −1.07398 | −0.536992 | − | 0.843587i | \(-0.680439\pi\) | ||||
−0.536992 | + | 0.843587i | \(0.680439\pi\) | |||||||
\(240\) | 1.65340 | 0.106726 | ||||||||
\(241\) | −11.7656 | −0.757891 | −0.378946 | − | 0.925419i | \(-0.623713\pi\) | ||||
−0.378946 | + | 0.925419i | \(0.623713\pi\) | |||||||
\(242\) | 2.25931 | 0.145234 | ||||||||
\(243\) | 9.68938 | 0.621574 | ||||||||
\(244\) | 12.3262 | 0.789102 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 62.8051 | 4.00431 | ||||||||
\(247\) | 0.461898 | 0.0293899 | ||||||||
\(248\) | 17.4946 | 1.11091 | ||||||||
\(249\) | 26.5100 | 1.68000 | ||||||||
\(250\) | 2.25931 | 0.142891 | ||||||||
\(251\) | −4.73206 | −0.298685 | −0.149342 | − | 0.988786i | \(-0.547716\pi\) | ||||
−0.149342 | + | 0.988786i | \(0.547716\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.56566 | −0.412780 | ||||||||
\(254\) | −3.05965 | −0.191980 | ||||||||
\(255\) | 3.58513 | 0.224509 | ||||||||
\(256\) | −12.1269 | −0.757930 | ||||||||
\(257\) | 7.62211 | 0.475454 | 0.237727 | − | 0.971332i | \(-0.423598\pi\) | ||||
0.237727 | + | 0.971332i | \(0.423598\pi\) | |||||||
\(258\) | −17.1243 | −1.06611 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −16.1098 | −0.999085 | ||||||||
\(261\) | −1.66004 | −0.102754 | ||||||||
\(262\) | 18.0270 | 1.11371 | ||||||||
\(263\) | 25.1797 | 1.55265 | 0.776325 | − | 0.630333i | \(-0.217082\pi\) | ||||
0.776325 | + | 0.630333i | \(0.217082\pi\) | |||||||
\(264\) | −7.22241 | −0.444508 | ||||||||
\(265\) | −4.66178 | −0.286371 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.6046 | 2.17897 | ||||||||
\(268\) | −6.67770 | −0.407906 | ||||||||
\(269\) | 10.5440 | 0.642877 | 0.321438 | − | 0.946930i | \(-0.395834\pi\) | ||||
0.321438 | + | 0.946930i | \(0.395834\pi\) | |||||||
\(270\) | −15.5470 | −0.946159 | ||||||||
\(271\) | 18.6620 | 1.13363 | 0.566817 | − | 0.823844i | \(-0.308175\pi\) | ||||
0.566817 | + | 0.823844i | \(0.308175\pi\) | |||||||
\(272\) | 0.707568 | 0.0429026 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 28.5245 | 1.72323 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 58.9958 | 3.55113 | ||||||||
\(277\) | 2.97955 | 0.179024 | 0.0895119 | − | 0.995986i | \(-0.471469\pi\) | ||||
0.0895119 | + | 0.995986i | \(0.471469\pi\) | |||||||
\(278\) | 40.6816 | 2.43992 | ||||||||
\(279\) | 37.7012 | 2.25711 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.6873 | −1.23410 | −0.617051 | − | 0.786923i | \(-0.711673\pi\) | ||||
−0.617051 | + | 0.786923i | \(0.711673\pi\) | |||||||
\(282\) | 66.1292 | 3.93793 | ||||||||
\(283\) | 31.0609 | 1.84638 | 0.923188 | − | 0.384349i | \(-0.125574\pi\) | ||||
0.923188 | + | 0.384349i | \(0.125574\pi\) | |||||||
\(284\) | −46.0481 | −2.73245 | ||||||||
\(285\) | 0.257632 | 0.0152608 | ||||||||
\(286\) | −11.7241 | −0.693258 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −33.7772 | −1.99034 | ||||||||
\(289\) | −15.4658 | −0.909750 | ||||||||
\(290\) | −0.697455 | −0.0409560 | ||||||||
\(291\) | 55.0331 | 3.22610 | ||||||||
\(292\) | 13.2781 | 0.777044 | ||||||||
\(293\) | 4.89906 | 0.286206 | 0.143103 | − | 0.989708i | \(-0.454292\pi\) | ||||
0.143103 | + | 0.989708i | \(0.454292\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.5718 | 0.673738 | ||||||||
\(296\) | −1.36150 | −0.0791354 | ||||||||
\(297\) | −6.88131 | −0.399294 | ||||||||
\(298\) | −3.31770 | −0.192189 | ||||||||
\(299\) | 34.0707 | 1.97036 | ||||||||
\(300\) | −8.98551 | −0.518779 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.92884 | 0.398710 | ||||||||
\(303\) | 44.8951 | 2.57916 | ||||||||
\(304\) | 0.0508468 | 0.00291626 | ||||||||
\(305\) | 3.97047 | 0.227348 | ||||||||
\(306\) | −15.0488 | −0.860281 | ||||||||
\(307\) | 11.2937 | 0.644564 | 0.322282 | − | 0.946644i | \(-0.395550\pi\) | ||||
0.322282 | + | 0.946644i | \(0.395550\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −48.8571 | −2.77938 | ||||||||
\(310\) | 15.8399 | 0.899646 | ||||||||
\(311\) | −9.94078 | −0.563690 | −0.281845 | − | 0.959460i | \(-0.590946\pi\) | ||||
−0.281845 | + | 0.959460i | \(0.590946\pi\) | |||||||
\(312\) | 37.4787 | 2.12182 | ||||||||
\(313\) | −23.9712 | −1.35493 | −0.677465 | − | 0.735555i | \(-0.736921\pi\) | ||||
−0.677465 | + | 0.735555i | \(0.736921\pi\) | |||||||
\(314\) | 0.0240892 | 0.00135943 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.3956 | 0.922327 | ||||||||
\(317\) | −3.53943 | −0.198794 | −0.0993971 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993971 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(318\) | 30.4848 | 1.70950 | ||||||||
\(319\) | −0.308703 | −0.0172841 | ||||||||
\(320\) | −13.0488 | −0.729448 | ||||||||
\(321\) | 58.3143 | 3.25478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.110253 | 0.00613465 | ||||||||
\(324\) | 11.7496 | 0.652758 | ||||||||
\(325\) | −5.18923 | −0.287847 | ||||||||
\(326\) | −55.8381 | −3.09258 | ||||||||
\(327\) | 48.3508 | 2.67381 | ||||||||
\(328\) | −23.9656 | −1.32328 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.53930 | −0.359977 | ||||||||
\(331\) | 21.7702 | 1.19660 | 0.598300 | − | 0.801272i | \(-0.295843\pi\) | ||||
0.598300 | + | 0.801272i | \(0.295843\pi\) | |||||||
\(332\) | −28.4341 | −1.56052 | ||||||||
\(333\) | −2.93406 | −0.160786 | ||||||||
\(334\) | 19.2338 | 1.05242 | ||||||||
\(335\) | −2.15100 | −0.117522 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.9441 | 0.868533 | 0.434266 | − | 0.900784i | \(-0.357008\pi\) | ||||
0.434266 | + | 0.900784i | \(0.357008\pi\) | |||||||
\(338\) | 31.4679 | 1.71163 | ||||||||
\(339\) | −32.5511 | −1.76793 | ||||||||
\(340\) | −3.84534 | −0.208543 | ||||||||
\(341\) | 7.01096 | 0.379665 | ||||||||
\(342\) | −1.08142 | −0.0584767 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.53440 | 0.352311 | ||||||||
\(345\) | 19.0036 | 1.02312 | ||||||||
\(346\) | 34.3397 | 1.84612 | ||||||||
\(347\) | 29.9536 | 1.60799 | 0.803996 | − | 0.594634i | \(-0.202703\pi\) | ||||
0.803996 | + | 0.594634i | \(0.202703\pi\) | |||||||
\(348\) | 2.77386 | 0.148694 | ||||||||
\(349\) | −7.06337 | −0.378094 | −0.189047 | − | 0.981968i | \(-0.560540\pi\) | ||||
−0.189047 | + | 0.981968i | \(0.560540\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 35.7087 | 1.90599 | ||||||||
\(352\) | −6.28124 | −0.334791 | ||||||||
\(353\) | −10.9105 | −0.580705 | −0.290353 | − | 0.956920i | \(-0.593773\pi\) | ||||
−0.290353 | + | 0.956920i | \(0.593773\pi\) | |||||||
\(354\) | −75.6717 | −4.02190 | ||||||||
\(355\) | −14.8329 | −0.787248 | ||||||||
\(356\) | −38.1888 | −2.02400 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 45.2987 | 2.39411 | ||||||||
\(359\) | −4.29511 | −0.226687 | −0.113344 | − | 0.993556i | \(-0.536156\pi\) | ||||
−0.113344 | + | 0.993556i | \(0.536156\pi\) | |||||||
\(360\) | 13.4185 | 0.707216 | ||||||||
\(361\) | −18.9921 | −0.999583 | ||||||||
\(362\) | −40.9997 | −2.15489 | ||||||||
\(363\) | −2.89439 | −0.151916 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.27711 | 0.223874 | ||||||||
\(366\) | −25.9641 | −1.35717 | ||||||||
\(367\) | −18.9852 | −0.991018 | −0.495509 | − | 0.868603i | \(-0.665018\pi\) | ||||
−0.495509 | + | 0.868603i | \(0.665018\pi\) | |||||||
\(368\) | 3.75058 | 0.195513 | ||||||||
\(369\) | −51.6466 | −2.68861 | ||||||||
\(370\) | −1.23273 | −0.0640863 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −62.9971 | −3.26624 | ||||||||
\(373\) | 16.7806 | 0.868869 | 0.434434 | − | 0.900704i | \(-0.356948\pi\) | ||||
0.434434 | + | 0.900704i | \(0.356948\pi\) | |||||||
\(374\) | −2.79849 | −0.144706 | ||||||||
\(375\) | −2.89439 | −0.149465 | ||||||||
\(376\) | −25.2341 | −1.30135 | ||||||||
\(377\) | 1.60193 | 0.0825037 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.4327 | 0.844089 | 0.422045 | − | 0.906575i | \(-0.361313\pi\) | ||||
0.422045 | + | 0.906575i | \(0.361313\pi\) | |||||||
\(380\) | −0.276331 | −0.0141755 | ||||||||
\(381\) | 3.91971 | 0.200813 | ||||||||
\(382\) | 26.9567 | 1.37922 | ||||||||
\(383\) | −22.3089 | −1.13993 | −0.569966 | − | 0.821668i | \(-0.693044\pi\) | ||||
−0.569966 | + | 0.821668i | \(0.693044\pi\) | |||||||
\(384\) | 48.9691 | 2.49894 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.4949 | −0.788670 | ||||||||
\(387\) | 14.0818 | 0.715818 | ||||||||
\(388\) | −59.0275 | −2.99666 | ||||||||
\(389\) | 8.54367 | 0.433181 | 0.216591 | − | 0.976263i | \(-0.430506\pi\) | ||||
0.216591 | + | 0.976263i | \(0.430506\pi\) | |||||||
\(390\) | 33.9339 | 1.71831 | ||||||||
\(391\) | 8.13255 | 0.411281 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.0943 | −1.16495 | ||||||||
\(394\) | 10.6325 | 0.535657 | ||||||||
\(395\) | 5.28131 | 0.265732 | ||||||||
\(396\) | 16.6941 | 0.838912 | ||||||||
\(397\) | 24.6326 | 1.23627 | 0.618137 | − | 0.786070i | \(-0.287888\pi\) | ||||
0.618137 | + | 0.786070i | \(0.287888\pi\) | |||||||
\(398\) | 10.5813 | 0.530395 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.571242 | −0.0285621 | ||||||||
\(401\) | 1.08299 | 0.0540820 | 0.0270410 | − | 0.999634i | \(-0.491392\pi\) | ||||
0.0270410 | + | 0.999634i | \(0.491392\pi\) | |||||||
\(402\) | 14.0660 | 0.701551 | ||||||||
\(403\) | −36.3815 | −1.81229 | ||||||||
\(404\) | −48.1536 | −2.39573 | ||||||||
\(405\) | 3.78476 | 0.188066 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.545621 | −0.0270455 | ||||||||
\(408\) | 8.94602 | 0.442894 | ||||||||
\(409\) | 20.8402 | 1.03048 | 0.515241 | − | 0.857045i | \(-0.327702\pi\) | ||||
0.515241 | + | 0.857045i | \(0.327702\pi\) | |||||||
\(410\) | −21.6989 | −1.07163 | ||||||||
\(411\) | −36.5426 | −1.80252 | ||||||||
\(412\) | 52.4032 | 2.58172 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −79.7685 | −3.92041 | ||||||||
\(415\) | −9.15911 | −0.449603 | ||||||||
\(416\) | 32.5948 | 1.59809 | ||||||||
\(417\) | −52.1170 | −2.55218 | ||||||||
\(418\) | −0.201103 | −0.00983626 | ||||||||
\(419\) | −10.1828 | −0.497463 | −0.248731 | − | 0.968573i | \(-0.580014\pi\) | ||||
−0.248731 | + | 0.968573i | \(0.580014\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.4719 | 1.33890 | 0.669449 | − | 0.742858i | \(-0.266530\pi\) | ||||
0.669449 | + | 0.742858i | \(0.266530\pi\) | |||||||
\(422\) | −14.0518 | −0.684029 | ||||||||
\(423\) | −54.3800 | −2.64405 | ||||||||
\(424\) | −11.6326 | −0.564930 | ||||||||
\(425\) | −1.23865 | −0.0600833 | ||||||||
\(426\) | 96.9967 | 4.69951 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −62.5467 | −3.02331 | ||||||||
\(429\) | 15.0196 | 0.725155 | ||||||||
\(430\) | 5.91637 | 0.285313 | ||||||||
\(431\) | 29.7975 | 1.43530 | 0.717648 | − | 0.696406i | \(-0.245219\pi\) | ||||
0.717648 | + | 0.696406i | \(0.245219\pi\) | |||||||
\(432\) | 3.93090 | 0.189125 | ||||||||
\(433\) | −7.88526 | −0.378942 | −0.189471 | − | 0.981886i | \(-0.560677\pi\) | ||||
−0.189471 | + | 0.981886i | \(0.560677\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.893506 | 0.0428403 | ||||||||
\(436\) | −51.8602 | −2.48365 | ||||||||
\(437\) | 0.584415 | 0.0279564 | ||||||||
\(438\) | −27.9693 | −1.33643 | ||||||||
\(439\) | 34.7141 | 1.65682 | 0.828408 | − | 0.560126i | \(-0.189247\pi\) | ||||
0.828408 | + | 0.560126i | \(0.189247\pi\) | |||||||
\(440\) | 2.49532 | 0.118960 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.5220 | 0.690740 | ||||||||
\(443\) | −0.195671 | −0.00929662 | −0.00464831 | − | 0.999989i | \(-0.501480\pi\) | ||||
−0.00464831 | + | 0.999989i | \(0.501480\pi\) | |||||||
\(444\) | 4.90269 | 0.232671 | ||||||||
\(445\) | −12.3013 | −0.583136 | ||||||||
\(446\) | −22.5692 | −1.06868 | ||||||||
\(447\) | 4.25030 | 0.201032 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.5122 | 0.543296 | 0.271648 | − | 0.962397i | \(-0.412431\pi\) | ||||
0.271648 | + | 0.962397i | \(0.412431\pi\) | |||||||
\(450\) | 12.1493 | 0.572726 | ||||||||
\(451\) | −9.60425 | −0.452247 | ||||||||
\(452\) | 34.9136 | 1.64220 | ||||||||
\(453\) | −8.87650 | −0.417054 | ||||||||
\(454\) | 5.46474 | 0.256473 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.642873 | 0.0301053 | ||||||||
\(457\) | −5.36664 | −0.251041 | −0.125521 | − | 0.992091i | \(-0.540060\pi\) | ||||
−0.125521 | + | 0.992091i | \(0.540060\pi\) | |||||||
\(458\) | 7.65614 | 0.357748 | ||||||||
\(459\) | 8.52352 | 0.397844 | ||||||||
\(460\) | −20.3828 | −0.950355 | ||||||||
\(461\) | −29.5146 | −1.37463 | −0.687317 | − | 0.726358i | \(-0.741212\pi\) | ||||
−0.687317 | + | 0.726358i | \(0.741212\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.6366 | −1.09848 | −0.549242 | − | 0.835663i | \(-0.685084\pi\) | ||||
−0.549242 | + | 0.835663i | \(0.685084\pi\) | |||||||
\(464\) | 0.176344 | 0.00818658 | ||||||||
\(465\) | −20.2924 | −0.941039 | ||||||||
\(466\) | 34.3642 | 1.59189 | ||||||||
\(467\) | −25.7195 | −1.19016 | −0.595078 | − | 0.803668i | \(-0.702879\pi\) | ||||
−0.595078 | + | 0.803668i | \(0.702879\pi\) | |||||||
\(468\) | −86.6298 | −4.00446 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −22.8474 | −1.05387 | ||||||||
\(471\) | −0.0308605 | −0.00142198 | ||||||||
\(472\) | 28.8754 | 1.32910 | ||||||||
\(473\) | 2.61867 | 0.120406 | ||||||||
\(474\) | −34.5361 | −1.58630 | ||||||||
\(475\) | −0.0890109 | −0.00408410 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.0686 | −1.14781 | ||||||||
\(478\) | −37.5121 | −1.71576 | ||||||||
\(479\) | 36.5837 | 1.67155 | 0.835776 | − | 0.549071i | \(-0.185018\pi\) | ||||
0.835776 | + | 0.549071i | \(0.185018\pi\) | |||||||
\(480\) | 18.1803 | 0.829815 | ||||||||
\(481\) | 2.83136 | 0.129099 | ||||||||
\(482\) | −26.5822 | −1.21078 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.10446 | 0.141112 | ||||||||
\(485\) | −19.0137 | −0.863370 | ||||||||
\(486\) | 21.8913 | 0.993008 | ||||||||
\(487\) | 4.85250 | 0.219888 | 0.109944 | − | 0.993938i | \(-0.464933\pi\) | ||||
0.109944 | + | 0.993938i | \(0.464933\pi\) | |||||||
\(488\) | 9.90758 | 0.448495 | ||||||||
\(489\) | 71.5339 | 3.23487 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.0213 | −0.813290 | −0.406645 | − | 0.913586i | \(-0.633301\pi\) | ||||
−0.406645 | + | 0.913586i | \(0.633301\pi\) | |||||||
\(492\) | 86.2991 | 3.89066 | ||||||||
\(493\) | 0.382375 | 0.0172213 | ||||||||
\(494\) | 1.04357 | 0.0469524 | ||||||||
\(495\) | 5.37747 | 0.241699 | ||||||||
\(496\) | −4.00496 | −0.179828 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 59.8942 | 2.68392 | ||||||||
\(499\) | −0.419359 | −0.0187731 | −0.00938655 | − | 0.999956i | \(-0.502988\pi\) | ||||
−0.00938655 | + | 0.999956i | \(0.502988\pi\) | |||||||
\(500\) | 3.10446 | 0.138836 | ||||||||
\(501\) | −24.6403 | −1.10085 | ||||||||
\(502\) | −10.6912 | −0.477170 | ||||||||
\(503\) | −37.0947 | −1.65397 | −0.826986 | − | 0.562223i | \(-0.809946\pi\) | ||||
−0.826986 | + | 0.562223i | \(0.809946\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.5111 | −0.690235 | ||||||||
\(506\) | −14.8338 | −0.659445 | ||||||||
\(507\) | −40.3133 | −1.79038 | ||||||||
\(508\) | −4.20420 | −0.186531 | ||||||||
\(509\) | −30.1531 | −1.33651 | −0.668256 | − | 0.743931i | \(-0.732959\pi\) | ||||
−0.668256 | + | 0.743931i | \(0.732959\pi\) | |||||||
\(510\) | 8.09989 | 0.358669 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 6.43897 | 0.284565 | ||||||||
\(513\) | 0.612511 | 0.0270430 | ||||||||
\(514\) | 17.2207 | 0.759571 | ||||||||
\(515\) | 16.8800 | 0.743820 | ||||||||
\(516\) | −23.5301 | −1.03585 | ||||||||
\(517\) | −10.1126 | −0.444750 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −43.9925 | −1.93105 | ||||||||
\(520\) | −12.9488 | −0.567841 | ||||||||
\(521\) | −13.1706 | −0.577012 | −0.288506 | − | 0.957478i | \(-0.593159\pi\) | ||||
−0.288506 | + | 0.957478i | \(0.593159\pi\) | |||||||
\(522\) | −3.75054 | −0.164157 | ||||||||
\(523\) | −27.6655 | −1.20973 | −0.604864 | − | 0.796328i | \(-0.706773\pi\) | ||||
−0.604864 | + | 0.796328i | \(0.706773\pi\) | |||||||
\(524\) | 24.7705 | 1.08210 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 56.8887 | 2.48047 | ||||||||
\(527\) | −8.68412 | −0.378286 | ||||||||
\(528\) | 1.65340 | 0.0719548 | ||||||||
\(529\) | 20.1079 | 0.874258 | ||||||||
\(530\) | −10.5324 | −0.457498 | ||||||||
\(531\) | 62.2271 | 2.70043 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 49.8387 | 2.15875 | ||||||||
\(534\) | 80.4417 | 3.48105 | ||||||||
\(535\) | −20.1474 | −0.871047 | ||||||||
\(536\) | −5.36743 | −0.231838 | ||||||||
\(537\) | −58.0319 | −2.50426 | ||||||||
\(538\) | 23.8220 | 1.02704 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −21.3628 | −0.919307 | ||||||||
\(541\) | 13.5889 | 0.584233 | 0.292117 | − | 0.956383i | \(-0.405640\pi\) | ||||
0.292117 | + | 0.956383i | \(0.405640\pi\) | |||||||
\(542\) | 42.1631 | 1.81106 | ||||||||
\(543\) | 52.5245 | 2.25404 | ||||||||
\(544\) | 7.78025 | 0.333575 | ||||||||
\(545\) | −16.7050 | −0.715565 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.8660 | 1.40525 | 0.702624 | − | 0.711562i | \(-0.252012\pi\) | ||||
0.702624 | + | 0.711562i | \(0.252012\pi\) | |||||||
\(548\) | 39.1949 | 1.67432 | ||||||||
\(549\) | 21.3511 | 0.911242 | ||||||||
\(550\) | 2.25931 | 0.0963371 | ||||||||
\(551\) | 0.0274779 | 0.00117060 | ||||||||
\(552\) | 47.4199 | 2.01832 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.73171 | 0.286003 | ||||||||
\(555\) | 1.57924 | 0.0670350 | ||||||||
\(556\) | 55.8997 | 2.37068 | ||||||||
\(557\) | 35.3570 | 1.49812 | 0.749062 | − | 0.662500i | \(-0.230505\pi\) | ||||
0.749062 | + | 0.662500i | \(0.230505\pi\) | |||||||
\(558\) | 85.1786 | 3.60590 | ||||||||
\(559\) | −13.5889 | −0.574748 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.58513 | 0.151364 | ||||||||
\(562\) | −46.7390 | −1.97157 | ||||||||
\(563\) | −24.3034 | −1.02426 | −0.512132 | − | 0.858907i | \(-0.671144\pi\) | ||||
−0.512132 | + | 0.858907i | \(0.671144\pi\) | |||||||
\(564\) | 90.8666 | 3.82617 | ||||||||
\(565\) | 11.2463 | 0.473134 | ||||||||
\(566\) | 70.1760 | 2.94972 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −37.0127 | −1.55302 | ||||||||
\(569\) | −45.3206 | −1.89994 | −0.949969 | − | 0.312345i | \(-0.898886\pi\) | ||||
−0.949969 | + | 0.312345i | \(0.898886\pi\) | |||||||
\(570\) | 0.582069 | 0.0243802 | ||||||||
\(571\) | 19.9418 | 0.834537 | 0.417269 | − | 0.908783i | \(-0.362987\pi\) | ||||
0.417269 | + | 0.908783i | \(0.362987\pi\) | |||||||
\(572\) | −16.1098 | −0.673583 | ||||||||
\(573\) | −34.5341 | −1.44268 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.56566 | −0.273807 | ||||||||
\(576\) | −70.1693 | −2.92372 | ||||||||
\(577\) | −11.6234 | −0.483887 | −0.241944 | − | 0.970290i | \(-0.577785\pi\) | ||||
−0.241944 | + | 0.970290i | \(0.577785\pi\) | |||||||
\(578\) | −34.9419 | −1.45339 | ||||||||
\(579\) | 19.8504 | 0.824956 | ||||||||
\(580\) | −0.958357 | −0.0397936 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 124.337 | 5.15392 | ||||||||
\(583\) | −4.66178 | −0.193071 | ||||||||
\(584\) | 10.6727 | 0.441641 | ||||||||
\(585\) | −27.9049 | −1.15373 | ||||||||
\(586\) | 11.0685 | 0.457234 | ||||||||
\(587\) | 9.03748 | 0.373017 | 0.186508 | − | 0.982453i | \(-0.440283\pi\) | ||||
0.186508 | + | 0.982453i | \(0.440283\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.624052 | −0.0257136 | ||||||||
\(590\) | 26.1443 | 1.07634 | ||||||||
\(591\) | −13.6212 | −0.560303 | ||||||||
\(592\) | 0.311682 | 0.0128101 | ||||||||
\(593\) | −2.98060 | −0.122399 | −0.0611993 | − | 0.998126i | \(-0.519493\pi\) | ||||
−0.0611993 | + | 0.998126i | \(0.519493\pi\) | |||||||
\(594\) | −15.5470 | −0.637900 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.55878 | −0.186735 | ||||||||
\(597\) | −13.5557 | −0.554798 | ||||||||
\(598\) | 76.9762 | 3.14779 | ||||||||
\(599\) | −39.2979 | −1.60567 | −0.802834 | − | 0.596202i | \(-0.796676\pi\) | ||||
−0.802834 | + | 0.596202i | \(0.796676\pi\) | |||||||
\(600\) | −7.22241 | −0.294853 | ||||||||
\(601\) | −20.4001 | −0.832138 | −0.416069 | − | 0.909333i | \(-0.636593\pi\) | ||||
−0.416069 | + | 0.909333i | \(0.636593\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.5669 | −0.471042 | ||||||||
\(604\) | 9.52076 | 0.387394 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 101.432 | 4.12039 | ||||||||
\(607\) | 6.70707 | 0.272231 | 0.136116 | − | 0.990693i | \(-0.456538\pi\) | ||||
0.136116 | + | 0.990693i | \(0.456538\pi\) | |||||||
\(608\) | 0.559099 | 0.0226744 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.97050 | 0.363205 | ||||||||
\(611\) | 52.4765 | 2.12297 | ||||||||
\(612\) | −20.6782 | −0.835866 | ||||||||
\(613\) | −2.52305 | −0.101905 | −0.0509524 | − | 0.998701i | \(-0.516226\pi\) | ||||
−0.0509524 | + | 0.998701i | \(0.516226\pi\) | |||||||
\(614\) | 25.5159 | 1.02974 | ||||||||
\(615\) | 27.7984 | 1.12094 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.2173 | −0.451591 | −0.225795 | − | 0.974175i | \(-0.572498\pi\) | ||||
−0.225795 | + | 0.974175i | \(0.572498\pi\) | |||||||
\(618\) | −110.383 | −4.44026 | ||||||||
\(619\) | −14.5132 | −0.583337 | −0.291668 | − | 0.956520i | \(-0.594210\pi\) | ||||
−0.291668 | + | 0.956520i | \(0.594210\pi\) | |||||||
\(620\) | 21.7653 | 0.874114 | ||||||||
\(621\) | 45.1804 | 1.81303 | ||||||||
\(622\) | −22.4593 | −0.900535 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −8.57985 | −0.343469 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −54.1582 | −2.16460 | ||||||||
\(627\) | 0.257632 | 0.0102888 | ||||||||
\(628\) | 0.0331004 | 0.00132085 | ||||||||
\(629\) | 0.675833 | 0.0269472 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.8572 | 1.86535 | 0.932677 | − | 0.360713i | \(-0.117467\pi\) | ||||
0.932677 | + | 0.360713i | \(0.117467\pi\) | |||||||
\(632\) | 13.1785 | 0.524214 | ||||||||
\(633\) | 18.0016 | 0.715501 | ||||||||
\(634\) | −7.99665 | −0.317588 | ||||||||
\(635\) | −1.35425 | −0.0537416 | ||||||||
\(636\) | 41.8885 | 1.66099 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.697455 | −0.0276125 | ||||||||
\(639\) | −79.7634 | −3.15539 | ||||||||
\(640\) | −16.9187 | −0.668768 | ||||||||
\(641\) | 2.35168 | 0.0928858 | 0.0464429 | − | 0.998921i | \(-0.485211\pi\) | ||||
0.0464429 | + | 0.998921i | \(0.485211\pi\) | |||||||
\(642\) | 131.750 | 5.19975 | ||||||||
\(643\) | −6.05724 | −0.238874 | −0.119437 | − | 0.992842i | \(-0.538109\pi\) | ||||
−0.119437 | + | 0.992842i | \(0.538109\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.57943 | −0.298440 | ||||||||
\(646\) | 0.249096 | 0.00980053 | ||||||||
\(647\) | −26.7941 | −1.05338 | −0.526692 | − | 0.850056i | \(-0.676568\pi\) | ||||
−0.526692 | + | 0.850056i | \(0.676568\pi\) | |||||||
\(648\) | 9.44417 | 0.371002 | ||||||||
\(649\) | 11.5718 | 0.454234 | ||||||||
\(650\) | −11.7241 | −0.459855 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −76.7258 | −3.00482 | ||||||||
\(653\) | 14.2400 | 0.557254 | 0.278627 | − | 0.960399i | \(-0.410121\pi\) | ||||
0.278627 | + | 0.960399i | \(0.410121\pi\) | |||||||
\(654\) | 109.239 | 4.27159 | ||||||||
\(655\) | 7.97900 | 0.311766 | ||||||||
\(656\) | 5.48636 | 0.214206 | ||||||||
\(657\) | 23.0000 | 0.897317 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.0130 | −0.390050 | −0.195025 | − | 0.980798i | \(-0.562479\pi\) | ||||
−0.195025 | + | 0.980798i | \(0.562479\pi\) | |||||||
\(660\) | −8.98551 | −0.349760 | ||||||||
\(661\) | −8.61490 | −0.335081 | −0.167540 | − | 0.985865i | \(-0.553582\pi\) | ||||
−0.167540 | + | 0.985865i | \(0.553582\pi\) | |||||||
\(662\) | 49.1856 | 1.91165 | ||||||||
\(663\) | −18.6040 | −0.722521 | ||||||||
\(664\) | −22.8549 | −0.886941 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.62894 | −0.256866 | ||||||||
\(667\) | 2.02684 | 0.0784796 | ||||||||
\(668\) | 26.4287 | 1.02256 | ||||||||
\(669\) | 28.9133 | 1.11785 | ||||||||
\(670\) | −4.85977 | −0.187749 | ||||||||
\(671\) | 3.97047 | 0.153278 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.3364 | −1.78614 | −0.893069 | − | 0.449920i | \(-0.851452\pi\) | ||||
−0.893069 | + | 0.449920i | \(0.851452\pi\) | |||||||
\(674\) | 36.0227 | 1.38754 | ||||||||
\(675\) | −6.88131 | −0.264862 | ||||||||
\(676\) | 43.2393 | 1.66305 | ||||||||
\(677\) | 5.52562 | 0.212367 | 0.106183 | − | 0.994347i | \(-0.466137\pi\) | ||||
0.106183 | + | 0.994347i | \(0.466137\pi\) | |||||||
\(678\) | −73.5428 | −2.82439 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.09082 | −0.118527 | ||||||||
\(681\) | −7.00086 | −0.268273 | ||||||||
\(682\) | 15.8399 | 0.606541 | ||||||||
\(683\) | −5.69730 | −0.218001 | −0.109001 | − | 0.994042i | \(-0.534765\pi\) | ||||
−0.109001 | + | 0.994042i | \(0.534765\pi\) | |||||||
\(684\) | −1.48596 | −0.0568171 | ||||||||
\(685\) | 12.6254 | 0.482390 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.80824 | −0.374208 | ||||||||
\(688\) | −1.49589 | −0.0570304 | ||||||||
\(689\) | 24.1911 | 0.921606 | ||||||||
\(690\) | 42.9348 | 1.63450 | ||||||||
\(691\) | −24.7075 | −0.939917 | −0.469958 | − | 0.882689i | \(-0.655731\pi\) | ||||
−0.469958 | + | 0.882689i | \(0.655731\pi\) | |||||||
\(692\) | 47.1855 | 1.79372 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 67.6743 | 2.56888 | ||||||||
\(695\) | 18.0063 | 0.683016 | ||||||||
\(696\) | 2.22958 | 0.0845120 | ||||||||
\(697\) | 11.8963 | 0.450604 | ||||||||
\(698\) | −15.9583 | −0.604031 | ||||||||
\(699\) | −44.0239 | −1.66514 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.97453 | 0.0745771 | 0.0372885 | − | 0.999305i | \(-0.488128\pi\) | ||||
0.0372885 | + | 0.999305i | \(0.488128\pi\) | |||||||
\(702\) | 80.6769 | 3.04495 | ||||||||
\(703\) | 0.0485662 | 0.00183171 | ||||||||
\(704\) | −13.0488 | −0.491794 | ||||||||
\(705\) | 29.2697 | 1.10236 | ||||||||
\(706\) | −24.6501 | −0.927717 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −103.979 | −3.90776 | ||||||||
\(709\) | 4.47721 | 0.168145 | 0.0840725 | − | 0.996460i | \(-0.473207\pi\) | ||||
0.0840725 | + | 0.996460i | \(0.473207\pi\) | |||||||
\(710\) | −33.5120 | −1.25768 | ||||||||
\(711\) | 28.4001 | 1.06509 | ||||||||
\(712\) | −30.6956 | −1.15036 | ||||||||
\(713\) | −46.0316 | −1.72390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.18923 | −0.194066 | ||||||||
\(716\) | 62.2439 | 2.32616 | ||||||||
\(717\) | 48.0566 | 1.79471 | ||||||||
\(718\) | −9.70396 | −0.362149 | ||||||||
\(719\) | 3.98375 | 0.148569 | 0.0742843 | − | 0.997237i | \(-0.476333\pi\) | ||||
0.0742843 | + | 0.997237i | \(0.476333\pi\) | |||||||
\(720\) | −3.07184 | −0.114481 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −42.9089 | −1.59690 | ||||||||
\(723\) | 34.0543 | 1.26649 | ||||||||
\(724\) | −56.3367 | −2.09374 | ||||||||
\(725\) | −0.308703 | −0.0114649 | ||||||||
\(726\) | −6.53930 | −0.242696 | ||||||||
\(727\) | −2.98387 | −0.110666 | −0.0553329 | − | 0.998468i | \(-0.517622\pi\) | ||||
−0.0553329 | + | 0.998468i | \(0.517622\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.3991 | −1.45922 | ||||||||
\(730\) | 9.66330 | 0.357655 | ||||||||
\(731\) | −3.24361 | −0.119969 | ||||||||
\(732\) | −35.6767 | −1.31865 | ||||||||
\(733\) | −0.613761 | −0.0226698 | −0.0113349 | − | 0.999936i | \(-0.503608\pi\) | ||||
−0.0113349 | + | 0.999936i | \(0.503608\pi\) | |||||||
\(734\) | −42.8933 | −1.58322 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 41.2405 | 1.52015 | ||||||||
\(737\) | −2.15100 | −0.0792332 | ||||||||
\(738\) | −116.685 | −4.29525 | ||||||||
\(739\) | 1.30551 | 0.0480241 | 0.0240120 | − | 0.999712i | \(-0.492356\pi\) | ||||
0.0240120 | + | 0.999712i | \(0.492356\pi\) | |||||||
\(740\) | −1.69386 | −0.0622676 | ||||||||
\(741\) | −1.33691 | −0.0491126 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.9550 | 0.695392 | 0.347696 | − | 0.937607i | \(-0.386964\pi\) | ||||
0.347696 | + | 0.937607i | \(0.386964\pi\) | |||||||
\(744\) | −50.6360 | −1.85641 | ||||||||
\(745\) | −1.46846 | −0.0538003 | ||||||||
\(746\) | 37.9126 | 1.38808 | ||||||||
\(747\) | −49.2528 | −1.80207 | ||||||||
\(748\) | −3.84534 | −0.140599 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −6.53930 | −0.238782 | ||||||||
\(751\) | −36.1767 | −1.32011 | −0.660053 | − | 0.751219i | \(-0.729466\pi\) | ||||
−0.660053 | + | 0.751219i | \(0.729466\pi\) | |||||||
\(752\) | 5.77673 | 0.210656 | ||||||||
\(753\) | 13.6964 | 0.499125 | ||||||||
\(754\) | 3.61925 | 0.131805 | ||||||||
\(755\) | 3.06680 | 0.111612 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.78039 | −0.355474 | −0.177737 | − | 0.984078i | \(-0.556878\pi\) | ||||
−0.177737 | + | 0.984078i | \(0.556878\pi\) | |||||||
\(758\) | 37.1264 | 1.34849 | ||||||||
\(759\) | 19.0036 | 0.689786 | ||||||||
\(760\) | −0.222110 | −0.00805678 | ||||||||
\(761\) | −39.8118 | −1.44318 | −0.721589 | − | 0.692322i | \(-0.756588\pi\) | ||||
−0.721589 | + | 0.692322i | \(0.756588\pi\) | |||||||
\(762\) | 8.85582 | 0.320813 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 37.0406 | 1.34008 | ||||||||
\(765\) | −6.66079 | −0.240821 | ||||||||
\(766\) | −50.4026 | −1.82112 | ||||||||
\(767\) | −60.0489 | −2.16824 | ||||||||
\(768\) | 35.0999 | 1.26656 | ||||||||
\(769\) | −10.0809 | −0.363527 | −0.181764 | − | 0.983342i | \(-0.558181\pi\) | ||||
−0.181764 | + | 0.983342i | \(0.558181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.0613 | −0.794519 | ||||||||
\(772\) | −21.2912 | −0.766287 | ||||||||
\(773\) | 46.0264 | 1.65545 | 0.827727 | − | 0.561130i | \(-0.189633\pi\) | ||||
0.827727 | + | 0.561130i | \(0.189633\pi\) | |||||||
\(774\) | 31.8151 | 1.14357 | ||||||||
\(775\) | 7.01096 | 0.251841 | ||||||||
\(776\) | −47.4453 | −1.70319 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19.3028 | 0.692037 | ||||||||
\(779\) | 0.854883 | 0.0306294 | ||||||||
\(780\) | 46.6279 | 1.66955 | ||||||||
\(781\) | −14.8329 | −0.530762 | ||||||||
\(782\) | 18.3739 | 0.657050 | ||||||||
\(783\) | 2.12428 | 0.0759157 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0106622 | 0.000380551 0 | ||||||||
\(786\) | −52.1771 | −1.86110 | ||||||||
\(787\) | 11.3150 | 0.403336 | 0.201668 | − | 0.979454i | \(-0.435364\pi\) | ||||
0.201668 | + | 0.979454i | \(0.435364\pi\) | |||||||
\(788\) | 14.6099 | 0.520455 | ||||||||
\(789\) | −72.8799 | −2.59459 | ||||||||
\(790\) | 11.9321 | 0.424525 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 13.4185 | 0.476805 | ||||||||
\(793\) | −20.6037 | −0.731658 | ||||||||
\(794\) | 55.6525 | 1.97503 | ||||||||
\(795\) | 13.4930 | 0.478547 | ||||||||
\(796\) | 14.5396 | 0.515342 | ||||||||
\(797\) | −5.13243 | −0.181800 | −0.0909001 | − | 0.995860i | \(-0.528974\pi\) | ||||
−0.0909001 | + | 0.995860i | \(0.528974\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.5259 | 0.443135 | ||||||||
\(800\) | −6.28124 | −0.222075 | ||||||||
\(801\) | −66.1497 | −2.33728 | ||||||||
\(802\) | 2.44681 | 0.0863998 | ||||||||
\(803\) | 4.27711 | 0.150936 | ||||||||
\(804\) | 19.3278 | 0.681640 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −82.1969 | −2.89526 | ||||||||
\(807\) | −30.5183 | −1.07429 | ||||||||
\(808\) | −38.7051 | −1.36164 | ||||||||
\(809\) | 21.3222 | 0.749647 | 0.374824 | − | 0.927096i | \(-0.377703\pi\) | ||||
0.374824 | + | 0.927096i | \(0.377703\pi\) | |||||||
\(810\) | 8.55093 | 0.300449 | ||||||||
\(811\) | −12.5828 | −0.441843 | −0.220922 | − | 0.975292i | \(-0.570907\pi\) | ||||
−0.220922 | + | 0.975292i | \(0.570907\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −54.0149 | −1.89439 | ||||||||
\(814\) | −1.23273 | −0.0432070 | ||||||||
\(815\) | −24.7147 | −0.865718 | ||||||||
\(816\) | −2.04798 | −0.0716935 | ||||||||
\(817\) | −0.233090 | −0.00815478 | ||||||||
\(818\) | 47.0844 | 1.64627 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29.8160 | −1.04122 | ||||||||
\(821\) | 31.0379 | 1.08323 | 0.541616 | − | 0.840626i | \(-0.317813\pi\) | ||||
0.541616 | + | 0.840626i | \(0.317813\pi\) | |||||||
\(822\) | −82.5610 | −2.87965 | ||||||||
\(823\) | 17.5694 | 0.612432 | 0.306216 | − | 0.951962i | \(-0.400937\pi\) | ||||
0.306216 | + | 0.951962i | \(0.400937\pi\) | |||||||
\(824\) | 42.1208 | 1.46735 | ||||||||
\(825\) | −2.89439 | −0.100770 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.9112 | 1.04012 | 0.520058 | − | 0.854131i | \(-0.325910\pi\) | ||||
0.520058 | + | 0.854131i | \(0.325910\pi\) | |||||||
\(828\) | −109.608 | −3.80915 | ||||||||
\(829\) | 37.7004 | 1.30939 | 0.654694 | − | 0.755894i | \(-0.272798\pi\) | ||||
0.654694 | + | 0.755894i | \(0.272798\pi\) | |||||||
\(830\) | −20.6932 | −0.718272 | ||||||||
\(831\) | −8.62396 | −0.299162 | ||||||||
\(832\) | 67.7130 | 2.34753 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −117.748 | −4.07729 | ||||||||
\(835\) | 8.51313 | 0.294609 | ||||||||
\(836\) | −0.276331 | −0.00955710 | ||||||||
\(837\) | −48.2446 | −1.66758 | ||||||||
\(838\) | −23.0061 | −0.794732 | ||||||||
\(839\) | 35.1426 | 1.21326 | 0.606628 | − | 0.794985i | \(-0.292522\pi\) | ||||
0.606628 | + | 0.794985i | \(0.292522\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9047 | −0.996714 | ||||||||
\(842\) | 62.0674 | 2.13898 | ||||||||
\(843\) | 59.8771 | 2.06228 | ||||||||
\(844\) | −19.3082 | −0.664616 | ||||||||
\(845\) | 13.9281 | 0.479142 | ||||||||
\(846\) | −122.861 | −4.22405 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.66301 | 0.0914480 | ||||||||
\(849\) | −89.9021 | −3.08543 | ||||||||
\(850\) | −2.79849 | −0.0959872 | ||||||||
\(851\) | 3.58237 | 0.122802 | ||||||||
\(852\) | 133.281 | 4.56613 | ||||||||
\(853\) | 44.6401 | 1.52845 | 0.764223 | − | 0.644952i | \(-0.223123\pi\) | ||||
0.764223 | + | 0.644952i | \(0.223123\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.478653 | −0.0163696 | ||||||||
\(856\) | −50.2741 | −1.71833 | ||||||||
\(857\) | −42.8895 | −1.46508 | −0.732538 | − | 0.680726i | \(-0.761664\pi\) | ||||
−0.732538 | + | 0.680726i | \(0.761664\pi\) | |||||||
\(858\) | 33.9339 | 1.15849 | ||||||||
\(859\) | −10.8330 | −0.369616 | −0.184808 | − | 0.982775i | \(-0.559166\pi\) | ||||
−0.184808 | + | 0.982775i | \(0.559166\pi\) | |||||||
\(860\) | 8.12955 | 0.277215 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 67.3217 | 2.29298 | ||||||||
\(863\) | −11.0789 | −0.377130 | −0.188565 | − | 0.982061i | \(-0.560384\pi\) | ||||
−0.188565 | + | 0.982061i | \(0.560384\pi\) | |||||||
\(864\) | 43.2232 | 1.47048 | ||||||||
\(865\) | 15.1992 | 0.516790 | ||||||||
\(866\) | −17.8152 | −0.605386 | ||||||||
\(867\) | 44.7638 | 1.52026 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.28131 | 0.179156 | ||||||||
\(870\) | 2.01870 | 0.0684404 | ||||||||
\(871\) | 11.1620 | 0.378211 | ||||||||
\(872\) | −41.6844 | −1.41161 | ||||||||
\(873\) | −102.246 | −3.46050 | ||||||||
\(874\) | 1.32037 | 0.0446623 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −38.4320 | −1.29850 | ||||||||
\(877\) | −37.4882 | −1.26589 | −0.632943 | − | 0.774198i | \(-0.718153\pi\) | ||||
−0.632943 | + | 0.774198i | \(0.718153\pi\) | |||||||
\(878\) | 78.4298 | 2.64688 | ||||||||
\(879\) | −14.1798 | −0.478272 | ||||||||
\(880\) | −0.571242 | −0.0192566 | ||||||||
\(881\) | −35.2942 | −1.18909 | −0.594546 | − | 0.804062i | \(-0.702668\pi\) | ||||
−0.594546 | + | 0.804062i | \(0.702668\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.3090 | 0.683451 | 0.341725 | − | 0.939800i | \(-0.388989\pi\) | ||||
0.341725 | + | 0.939800i | \(0.388989\pi\) | |||||||
\(884\) | 19.9543 | 0.671137 | ||||||||
\(885\) | −33.4933 | −1.12587 | ||||||||
\(886\) | −0.442081 | −0.0148520 | ||||||||
\(887\) | −56.0806 | −1.88300 | −0.941502 | − | 0.337008i | \(-0.890585\pi\) | ||||
−0.941502 | + | 0.337008i | \(0.890585\pi\) | |||||||
\(888\) | 3.94070 | 0.132241 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −27.7923 | −0.931601 | ||||||||
\(891\) | 3.78476 | 0.126794 | ||||||||
\(892\) | −31.0118 | −1.03835 | ||||||||
\(893\) | 0.900129 | 0.0301217 | ||||||||
\(894\) | 9.60272 | 0.321163 | ||||||||
\(895\) | 20.0498 | 0.670192 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −98.6139 | −3.29262 | ||||||||
\(898\) | 26.0097 | 0.867954 | ||||||||
\(899\) | −2.16431 | −0.0721836 | ||||||||
\(900\) | 16.6941 | 0.556471 | ||||||||
\(901\) | 5.77431 | 0.192370 | ||||||||
\(902\) | −21.6989 | −0.722496 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 28.0630 | 0.933362 | ||||||||
\(905\) | −18.1470 | −0.603227 | ||||||||
\(906\) | −20.0547 | −0.666274 | ||||||||
\(907\) | −8.12019 | −0.269626 | −0.134813 | − | 0.990871i | \(-0.543043\pi\) | ||||
−0.134813 | + | 0.990871i | \(0.543043\pi\) | |||||||
\(908\) | 7.50898 | 0.249194 | ||||||||
\(909\) | −83.4105 | −2.76655 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.4761 | −1.63922 | −0.819608 | − | 0.572925i | \(-0.805809\pi\) | ||||
−0.819608 | + | 0.572925i | \(0.805809\pi\) | |||||||
\(912\) | −0.147170 | −0.00487329 | ||||||||
\(913\) | −9.15911 | −0.303122 | ||||||||
\(914\) | −12.1249 | −0.401056 | ||||||||
\(915\) | −11.4921 | −0.379916 | ||||||||
\(916\) | 10.5201 | 0.347595 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 19.2572 | 0.635584 | ||||||||
\(919\) | 8.42669 | 0.277971 | 0.138985 | − | 0.990294i | \(-0.455616\pi\) | ||||
0.138985 | + | 0.990294i | \(0.455616\pi\) | |||||||
\(920\) | −16.3834 | −0.540145 | ||||||||
\(921\) | −32.6883 | −1.07711 | ||||||||
\(922\) | −66.6826 | −2.19607 | ||||||||
\(923\) | 76.9713 | 2.53354 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.545621 | −0.0179399 | ||||||||
\(926\) | −53.4022 | −1.75491 | ||||||||
\(927\) | 90.7714 | 2.98132 | ||||||||
\(928\) | 1.93904 | 0.0636521 | ||||||||
\(929\) | 31.8919 | 1.04634 | 0.523169 | − | 0.852229i | \(-0.324749\pi\) | ||||
0.523169 | + | 0.852229i | \(0.324749\pi\) | |||||||
\(930\) | −45.8468 | −1.50338 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 47.2191 | 1.54671 | ||||||||
\(933\) | 28.7725 | 0.941968 | ||||||||
\(934\) | −58.1081 | −1.90136 | ||||||||
\(935\) | −1.23865 | −0.0405081 | ||||||||
\(936\) | −69.6316 | −2.27598 | ||||||||
\(937\) | −27.4103 | −0.895457 | −0.447728 | − | 0.894170i | \(-0.647767\pi\) | ||||
−0.447728 | + | 0.894170i | \(0.647767\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 69.3818 | 2.26419 | ||||||||
\(940\) | −31.3941 | −1.02396 | ||||||||
\(941\) | 40.2446 | 1.31194 | 0.655968 | − | 0.754789i | \(-0.272261\pi\) | ||||
0.655968 | + | 0.754789i | \(0.272261\pi\) | |||||||
\(942\) | −0.0697234 | −0.00227171 | ||||||||
\(943\) | 63.0583 | 2.05346 | ||||||||
\(944\) | −6.61032 | −0.215147 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.91637 | 0.192358 | ||||||||
\(947\) | 47.3761 | 1.53952 | 0.769758 | − | 0.638336i | \(-0.220377\pi\) | ||||
0.769758 | + | 0.638336i | \(0.220377\pi\) | |||||||
\(948\) | −47.4553 | −1.54128 | ||||||||
\(949\) | −22.1949 | −0.720478 | ||||||||
\(950\) | −0.201103 | −0.00652463 | ||||||||
\(951\) | 10.2445 | 0.332200 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.8245 | −1.54919 | −0.774593 | − | 0.632460i | \(-0.782045\pi\) | ||||
−0.774593 | + | 0.632460i | \(0.782045\pi\) | |||||||
\(954\) | −56.6376 | −1.83371 | ||||||||
\(955\) | 11.9314 | 0.386091 | ||||||||
\(956\) | −51.5446 | −1.66707 | ||||||||
\(957\) | 0.893506 | 0.0288829 | ||||||||
\(958\) | 82.6537 | 2.67042 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 37.7681 | 1.21896 | ||||||||
\(961\) | 18.1536 | 0.585599 | ||||||||
\(962\) | 6.39690 | 0.206244 | ||||||||
\(963\) | −108.342 | −3.49127 | ||||||||
\(964\) | −36.5260 | −1.17642 | ||||||||
\(965\) | −6.85826 | −0.220775 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.607859 | −0.0195474 | −0.00977371 | − | 0.999952i | \(-0.503111\pi\) | ||||
−0.00977371 | + | 0.999952i | \(0.503111\pi\) | |||||||
\(968\) | 2.49532 | 0.0802025 | ||||||||
\(969\) | −0.319115 | −0.0102515 | ||||||||
\(970\) | −42.9579 | −1.37929 | ||||||||
\(971\) | −23.5739 | −0.756523 | −0.378262 | − | 0.925699i | \(-0.623478\pi\) | ||||
−0.378262 | + | 0.925699i | \(0.623478\pi\) | |||||||
\(972\) | 30.0803 | 0.964826 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 10.9633 | 0.351286 | ||||||||
\(975\) | 15.0196 | 0.481013 | ||||||||
\(976\) | −2.26810 | −0.0726001 | ||||||||
\(977\) | −54.3184 | −1.73780 | −0.868900 | − | 0.494988i | \(-0.835172\pi\) | ||||
−0.868900 | + | 0.494988i | \(0.835172\pi\) | |||||||
\(978\) | 161.617 | 5.16794 | ||||||||
\(979\) | −12.3013 | −0.393150 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −89.8308 | −2.86808 | ||||||||
\(982\) | −40.7156 | −1.29929 | ||||||||
\(983\) | 20.6054 | 0.657209 | 0.328604 | − | 0.944468i | \(-0.393422\pi\) | ||||
0.328604 | + | 0.944468i | \(0.393422\pi\) | |||||||
\(984\) | 69.3658 | 2.21130 | ||||||||
\(985\) | 4.70609 | 0.149948 | ||||||||
\(986\) | 0.863901 | 0.0275122 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.43394 | 0.0456198 | ||||||||
\(989\) | −17.1933 | −0.546715 | ||||||||
\(990\) | 12.1493 | 0.386131 | ||||||||
\(991\) | 34.9827 | 1.11126 | 0.555630 | − | 0.831429i | \(-0.312477\pi\) | ||||
0.555630 | + | 0.831429i | \(0.312477\pi\) | |||||||
\(992\) | −44.0375 | −1.39819 | ||||||||
\(993\) | −63.0114 | −1.99961 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.68345 | 0.148475 | ||||||||
\(996\) | 82.2992 | 2.60775 | ||||||||
\(997\) | −18.0226 | −0.570783 | −0.285391 | − | 0.958411i | \(-0.592124\pi\) | ||||
−0.285391 | + | 0.958411i | \(0.592124\pi\) | |||||||
\(998\) | −0.947461 | −0.0299913 | ||||||||
\(999\) | 3.75459 | 0.118790 |
(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 | 2695.2.a.u.1.10 | ✓ | 10 | |
7.6 | odd | 2 | 2695.2.a.v.1.10 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2695.2.a.u.1.10 | ✓ | 10 | 1.1 | even | 1 | trivial | |
2695.2.a.v.1.10 | yes | 10 | 7.6 | odd | 2 |