Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.516772\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.516772 | −0.298358 | −0.149179 | − | 0.988810i | \(-0.547663\pi\) | ||||
−0.149179 | + | 0.988810i | \(0.547663\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.53195 | −0.685110 | −0.342555 | − | 0.939498i | \(-0.611292\pi\) | ||||
−0.342555 | + | 0.939498i | \(0.611292\pi\) | |||||||
\(6\) | 0.516772 | 0.210971 | ||||||||
\(7\) | −0.576902 | −0.218049 | −0.109024 | − | 0.994039i | \(-0.534773\pi\) | ||||
−0.109024 | + | 0.994039i | \(0.534773\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.73295 | −0.910982 | ||||||||
\(10\) | 1.53195 | 0.484446 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.516772 | −0.149179 | ||||||||
\(13\) | 6.31699 | 1.75202 | 0.876009 | − | 0.482295i | \(-0.160197\pi\) | ||||
0.876009 | + | 0.482295i | \(0.160197\pi\) | |||||||
\(14\) | 0.576902 | 0.154184 | ||||||||
\(15\) | 0.791670 | 0.204408 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.519591 | −0.126019 | −0.0630097 | − | 0.998013i | \(-0.520070\pi\) | ||||
−0.0630097 | + | 0.998013i | \(0.520070\pi\) | |||||||
\(18\) | 2.73295 | 0.644162 | ||||||||
\(19\) | −0.276328 | −0.0633940 | −0.0316970 | − | 0.999498i | \(-0.510091\pi\) | ||||
−0.0316970 | + | 0.999498i | \(0.510091\pi\) | |||||||
\(20\) | −1.53195 | −0.342555 | ||||||||
\(21\) | 0.298127 | 0.0650566 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −1.50740 | −0.314316 | −0.157158 | − | 0.987574i | \(-0.550233\pi\) | ||||
−0.157158 | + | 0.987574i | \(0.550233\pi\) | |||||||
\(24\) | 0.516772 | 0.105486 | ||||||||
\(25\) | −2.65312 | −0.530624 | ||||||||
\(26\) | −6.31699 | −1.23886 | ||||||||
\(27\) | 2.96263 | 0.570158 | ||||||||
\(28\) | −0.576902 | −0.109024 | ||||||||
\(29\) | −2.50711 | −0.465558 | −0.232779 | − | 0.972530i | \(-0.574782\pi\) | ||||
−0.232779 | + | 0.972530i | \(0.574782\pi\) | |||||||
\(30\) | −0.791670 | −0.144539 | ||||||||
\(31\) | −0.621065 | −0.111546 | −0.0557732 | − | 0.998443i | \(-0.517762\pi\) | ||||
−0.0557732 | + | 0.998443i | \(0.517762\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.516772 | −0.0899585 | ||||||||
\(34\) | 0.519591 | 0.0891092 | ||||||||
\(35\) | 0.883787 | 0.149387 | ||||||||
\(36\) | −2.73295 | −0.455491 | ||||||||
\(37\) | −4.65628 | −0.765488 | −0.382744 | − | 0.923854i | \(-0.625021\pi\) | ||||
−0.382744 | + | 0.923854i | \(0.625021\pi\) | |||||||
\(38\) | 0.276328 | 0.0448263 | ||||||||
\(39\) | −3.26444 | −0.522729 | ||||||||
\(40\) | 1.53195 | 0.242223 | ||||||||
\(41\) | 6.59498 | 1.02996 | 0.514981 | − | 0.857201i | \(-0.327799\pi\) | ||||
0.514981 | + | 0.857201i | \(0.327799\pi\) | |||||||
\(42\) | −0.298127 | −0.0460020 | ||||||||
\(43\) | −8.04854 | −1.22739 | −0.613695 | − | 0.789543i | \(-0.710318\pi\) | ||||
−0.613695 | + | 0.789543i | \(0.710318\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 4.18674 | 0.624123 | ||||||||
\(46\) | 1.50740 | 0.222255 | ||||||||
\(47\) | 1.94410 | 0.283577 | 0.141788 | − | 0.989897i | \(-0.454715\pi\) | ||||
0.141788 | + | 0.989897i | \(0.454715\pi\) | |||||||
\(48\) | −0.516772 | −0.0745896 | ||||||||
\(49\) | −6.66718 | −0.952455 | ||||||||
\(50\) | 2.65312 | 0.375208 | ||||||||
\(51\) | 0.268510 | 0.0375990 | ||||||||
\(52\) | 6.31699 | 0.876009 | ||||||||
\(53\) | 11.6545 | 1.60087 | 0.800435 | − | 0.599419i | \(-0.204602\pi\) | ||||
0.800435 | + | 0.599419i | \(0.204602\pi\) | |||||||
\(54\) | −2.96263 | −0.403162 | ||||||||
\(55\) | −1.53195 | −0.206568 | ||||||||
\(56\) | 0.576902 | 0.0770918 | ||||||||
\(57\) | 0.142799 | 0.0189141 | ||||||||
\(58\) | 2.50711 | 0.329199 | ||||||||
\(59\) | 8.08984 | 1.05321 | 0.526604 | − | 0.850111i | \(-0.323465\pi\) | ||||
0.526604 | + | 0.850111i | \(0.323465\pi\) | |||||||
\(60\) | 0.791670 | 0.102204 | ||||||||
\(61\) | 2.60152 | 0.333090 | 0.166545 | − | 0.986034i | \(-0.446739\pi\) | ||||
0.166545 | + | 0.986034i | \(0.446739\pi\) | |||||||
\(62\) | 0.621065 | 0.0788753 | ||||||||
\(63\) | 1.57664 | 0.198638 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.67733 | −1.20033 | ||||||||
\(66\) | 0.516772 | 0.0636102 | ||||||||
\(67\) | 5.29122 | 0.646425 | 0.323212 | − | 0.946326i | \(-0.395237\pi\) | ||||
0.323212 | + | 0.946326i | \(0.395237\pi\) | |||||||
\(68\) | −0.519591 | −0.0630097 | ||||||||
\(69\) | 0.778984 | 0.0937787 | ||||||||
\(70\) | −0.883787 | −0.105633 | ||||||||
\(71\) | 14.1174 | 1.67542 | 0.837711 | − | 0.546114i | \(-0.183893\pi\) | ||||
0.837711 | + | 0.546114i | \(0.183893\pi\) | |||||||
\(72\) | 2.73295 | 0.322081 | ||||||||
\(73\) | −2.91021 | −0.340615 | −0.170307 | − | 0.985391i | \(-0.554476\pi\) | ||||
−0.170307 | + | 0.985391i | \(0.554476\pi\) | |||||||
\(74\) | 4.65628 | 0.541282 | ||||||||
\(75\) | 1.37106 | 0.158316 | ||||||||
\(76\) | −0.276328 | −0.0316970 | ||||||||
\(77\) | −0.576902 | −0.0657441 | ||||||||
\(78\) | 3.26444 | 0.369626 | ||||||||
\(79\) | −5.82588 | −0.655463 | −0.327732 | − | 0.944771i | \(-0.606284\pi\) | ||||
−0.327732 | + | 0.944771i | \(0.606284\pi\) | |||||||
\(80\) | −1.53195 | −0.171277 | ||||||||
\(81\) | 6.66784 | 0.740871 | ||||||||
\(82\) | −6.59498 | −0.728294 | ||||||||
\(83\) | −0.321166 | −0.0352525 | −0.0176263 | − | 0.999845i | \(-0.505611\pi\) | ||||
−0.0176263 | + | 0.999845i | \(0.505611\pi\) | |||||||
\(84\) | 0.298127 | 0.0325283 | ||||||||
\(85\) | 0.795989 | 0.0863371 | ||||||||
\(86\) | 8.04854 | 0.867896 | ||||||||
\(87\) | 1.29560 | 0.138903 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 7.65030 | 0.810930 | 0.405465 | − | 0.914111i | \(-0.367110\pi\) | ||||
0.405465 | + | 0.914111i | \(0.367110\pi\) | |||||||
\(90\) | −4.18674 | −0.441322 | ||||||||
\(91\) | −3.64429 | −0.382025 | ||||||||
\(92\) | −1.50740 | −0.157158 | ||||||||
\(93\) | 0.320949 | 0.0332808 | ||||||||
\(94\) | −1.94410 | −0.200519 | ||||||||
\(95\) | 0.423321 | 0.0434319 | ||||||||
\(96\) | 0.516772 | 0.0527428 | ||||||||
\(97\) | −6.38659 | −0.648460 | −0.324230 | − | 0.945978i | \(-0.605105\pi\) | ||||
−0.324230 | + | 0.945978i | \(0.605105\pi\) | |||||||
\(98\) | 6.66718 | 0.673487 | ||||||||
\(99\) | −2.73295 | −0.274671 | ||||||||
\(100\) | −2.65312 | −0.265312 | ||||||||
\(101\) | −11.6653 | −1.16074 | −0.580369 | − | 0.814353i | \(-0.697092\pi\) | ||||
−0.580369 | + | 0.814353i | \(0.697092\pi\) | |||||||
\(102\) | −0.268510 | −0.0265865 | ||||||||
\(103\) | 0.865809 | 0.0853107 | 0.0426554 | − | 0.999090i | \(-0.486418\pi\) | ||||
0.0426554 | + | 0.999090i | \(0.486418\pi\) | |||||||
\(104\) | −6.31699 | −0.619432 | ||||||||
\(105\) | −0.456716 | −0.0445709 | ||||||||
\(106\) | −11.6545 | −1.13199 | ||||||||
\(107\) | −9.28437 | −0.897554 | −0.448777 | − | 0.893644i | \(-0.648140\pi\) | ||||
−0.448777 | + | 0.893644i | \(0.648140\pi\) | |||||||
\(108\) | 2.96263 | 0.285079 | ||||||||
\(109\) | −5.26206 | −0.504013 | −0.252007 | − | 0.967725i | \(-0.581091\pi\) | ||||
−0.252007 | + | 0.967725i | \(0.581091\pi\) | |||||||
\(110\) | 1.53195 | 0.146066 | ||||||||
\(111\) | 2.40624 | 0.228390 | ||||||||
\(112\) | −0.576902 | −0.0545121 | ||||||||
\(113\) | 16.7854 | 1.57904 | 0.789519 | − | 0.613726i | \(-0.210330\pi\) | ||||
0.789519 | + | 0.613726i | \(0.210330\pi\) | |||||||
\(114\) | −0.142799 | −0.0133743 | ||||||||
\(115\) | 2.30927 | 0.215341 | ||||||||
\(116\) | −2.50711 | −0.232779 | ||||||||
\(117\) | −17.2640 | −1.59606 | ||||||||
\(118\) | −8.08984 | −0.744730 | ||||||||
\(119\) | 0.299753 | 0.0274783 | ||||||||
\(120\) | −0.791670 | −0.0722693 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.60152 | −0.235530 | ||||||||
\(123\) | −3.40810 | −0.307298 | ||||||||
\(124\) | −0.621065 | −0.0557732 | ||||||||
\(125\) | 11.7242 | 1.04865 | ||||||||
\(126\) | −1.57664 | −0.140459 | ||||||||
\(127\) | −8.14472 | −0.722727 | −0.361363 | − | 0.932425i | \(-0.617689\pi\) | ||||
−0.361363 | + | 0.932425i | \(0.617689\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.15926 | 0.366202 | ||||||||
\(130\) | 9.67733 | 0.848758 | ||||||||
\(131\) | 3.53403 | 0.308770 | 0.154385 | − | 0.988011i | \(-0.450660\pi\) | ||||
0.154385 | + | 0.988011i | \(0.450660\pi\) | |||||||
\(132\) | −0.516772 | −0.0449792 | ||||||||
\(133\) | 0.159414 | 0.0138230 | ||||||||
\(134\) | −5.29122 | −0.457091 | ||||||||
\(135\) | −4.53860 | −0.390621 | ||||||||
\(136\) | 0.519591 | 0.0445546 | ||||||||
\(137\) | −15.4462 | −1.31965 | −0.659827 | − | 0.751418i | \(-0.729370\pi\) | ||||
−0.659827 | + | 0.751418i | \(0.729370\pi\) | |||||||
\(138\) | −0.778984 | −0.0663116 | ||||||||
\(139\) | 6.61303 | 0.560910 | 0.280455 | − | 0.959867i | \(-0.409515\pi\) | ||||
0.280455 | + | 0.959867i | \(0.409515\pi\) | |||||||
\(140\) | 0.883787 | 0.0746936 | ||||||||
\(141\) | −1.00466 | −0.0846075 | ||||||||
\(142\) | −14.1174 | −1.18470 | ||||||||
\(143\) | 6.31699 | 0.528253 | ||||||||
\(144\) | −2.73295 | −0.227746 | ||||||||
\(145\) | 3.84077 | 0.318958 | ||||||||
\(146\) | 2.91021 | 0.240851 | ||||||||
\(147\) | 3.44541 | 0.284173 | ||||||||
\(148\) | −4.65628 | −0.382744 | ||||||||
\(149\) | −12.3628 | −1.01280 | −0.506398 | − | 0.862300i | \(-0.669023\pi\) | ||||
−0.506398 | + | 0.862300i | \(0.669023\pi\) | |||||||
\(150\) | −1.37106 | −0.111947 | ||||||||
\(151\) | −20.4592 | −1.66495 | −0.832474 | − | 0.554063i | \(-0.813076\pi\) | ||||
−0.832474 | + | 0.554063i | \(0.813076\pi\) | |||||||
\(152\) | 0.276328 | 0.0224132 | ||||||||
\(153\) | 1.42002 | 0.114801 | ||||||||
\(154\) | 0.576902 | 0.0464881 | ||||||||
\(155\) | 0.951441 | 0.0764216 | ||||||||
\(156\) | −3.26444 | −0.261365 | ||||||||
\(157\) | −21.3362 | −1.70282 | −0.851408 | − | 0.524505i | \(-0.824251\pi\) | ||||
−0.851408 | + | 0.524505i | \(0.824251\pi\) | |||||||
\(158\) | 5.82588 | 0.463482 | ||||||||
\(159\) | −6.02273 | −0.477633 | ||||||||
\(160\) | 1.53195 | 0.121111 | ||||||||
\(161\) | 0.869625 | 0.0685360 | ||||||||
\(162\) | −6.66784 | −0.523875 | ||||||||
\(163\) | −24.0912 | −1.88697 | −0.943483 | − | 0.331421i | \(-0.892472\pi\) | ||||
−0.943483 | + | 0.331421i | \(0.892472\pi\) | |||||||
\(164\) | 6.59498 | 0.514981 | ||||||||
\(165\) | 0.791670 | 0.0616314 | ||||||||
\(166\) | 0.321166 | 0.0249273 | ||||||||
\(167\) | 21.8326 | 1.68946 | 0.844729 | − | 0.535195i | \(-0.179762\pi\) | ||||
0.844729 | + | 0.535195i | \(0.179762\pi\) | |||||||
\(168\) | −0.298127 | −0.0230010 | ||||||||
\(169\) | 26.9044 | 2.06957 | ||||||||
\(170\) | −0.795989 | −0.0610496 | ||||||||
\(171\) | 0.755190 | 0.0577508 | ||||||||
\(172\) | −8.04854 | −0.613695 | ||||||||
\(173\) | −19.7187 | −1.49919 | −0.749594 | − | 0.661898i | \(-0.769751\pi\) | ||||
−0.749594 | + | 0.661898i | \(0.769751\pi\) | |||||||
\(174\) | −1.29560 | −0.0982194 | ||||||||
\(175\) | 1.53059 | 0.115702 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −4.18060 | −0.314233 | ||||||||
\(178\) | −7.65030 | −0.573414 | ||||||||
\(179\) | −17.8912 | −1.33725 | −0.668625 | − | 0.743600i | \(-0.733117\pi\) | ||||
−0.668625 | + | 0.743600i | \(0.733117\pi\) | |||||||
\(180\) | 4.18674 | 0.312061 | ||||||||
\(181\) | −21.6524 | −1.60941 | −0.804703 | − | 0.593677i | \(-0.797676\pi\) | ||||
−0.804703 | + | 0.593677i | \(0.797676\pi\) | |||||||
\(182\) | 3.64429 | 0.270132 | ||||||||
\(183\) | −1.34439 | −0.0993803 | ||||||||
\(184\) | 1.50740 | 0.111127 | ||||||||
\(185\) | 7.13321 | 0.524444 | ||||||||
\(186\) | −0.320949 | −0.0235331 | ||||||||
\(187\) | −0.519591 | −0.0379963 | ||||||||
\(188\) | 1.94410 | 0.141788 | ||||||||
\(189\) | −1.70915 | −0.124322 | ||||||||
\(190\) | −0.423321 | −0.0307110 | ||||||||
\(191\) | 6.58409 | 0.476408 | 0.238204 | − | 0.971215i | \(-0.423441\pi\) | ||||
0.238204 | + | 0.971215i | \(0.423441\pi\) | |||||||
\(192\) | −0.516772 | −0.0372948 | ||||||||
\(193\) | 14.5978 | 1.05077 | 0.525386 | − | 0.850864i | \(-0.323921\pi\) | ||||
0.525386 | + | 0.850864i | \(0.323921\pi\) | |||||||
\(194\) | 6.38659 | 0.458531 | ||||||||
\(195\) | 5.00097 | 0.358127 | ||||||||
\(196\) | −6.66718 | −0.476227 | ||||||||
\(197\) | 1.00000 | 0.0712470 | ||||||||
\(198\) | 2.73295 | 0.194222 | ||||||||
\(199\) | −22.2655 | −1.57836 | −0.789178 | − | 0.614164i | \(-0.789493\pi\) | ||||
−0.789178 | + | 0.614164i | \(0.789493\pi\) | |||||||
\(200\) | 2.65312 | 0.187604 | ||||||||
\(201\) | −2.73435 | −0.192866 | ||||||||
\(202\) | 11.6653 | 0.820766 | ||||||||
\(203\) | 1.44636 | 0.101514 | ||||||||
\(204\) | 0.268510 | 0.0187995 | ||||||||
\(205\) | −10.1032 | −0.705638 | ||||||||
\(206\) | −0.865809 | −0.0603238 | ||||||||
\(207\) | 4.11966 | 0.286336 | ||||||||
\(208\) | 6.31699 | 0.438005 | ||||||||
\(209\) | −0.276328 | −0.0191140 | ||||||||
\(210\) | 0.456716 | 0.0315164 | ||||||||
\(211\) | −12.5295 | −0.862563 | −0.431281 | − | 0.902217i | \(-0.641938\pi\) | ||||
−0.431281 | + | 0.902217i | \(0.641938\pi\) | |||||||
\(212\) | 11.6545 | 0.800435 | ||||||||
\(213\) | −7.29546 | −0.499876 | ||||||||
\(214\) | 9.28437 | 0.634667 | ||||||||
\(215\) | 12.3300 | 0.840897 | ||||||||
\(216\) | −2.96263 | −0.201581 | ||||||||
\(217\) | 0.358294 | 0.0243226 | ||||||||
\(218\) | 5.26206 | 0.356391 | ||||||||
\(219\) | 1.50392 | 0.101625 | ||||||||
\(220\) | −1.53195 | −0.103284 | ||||||||
\(221\) | −3.28225 | −0.220788 | ||||||||
\(222\) | −2.40624 | −0.161496 | ||||||||
\(223\) | −13.6319 | −0.912860 | −0.456430 | − | 0.889759i | \(-0.650872\pi\) | ||||
−0.456430 | + | 0.889759i | \(0.650872\pi\) | |||||||
\(224\) | 0.576902 | 0.0385459 | ||||||||
\(225\) | 7.25084 | 0.483389 | ||||||||
\(226\) | −16.7854 | −1.11655 | ||||||||
\(227\) | 7.51079 | 0.498508 | 0.249254 | − | 0.968438i | \(-0.419815\pi\) | ||||
0.249254 | + | 0.968438i | \(0.419815\pi\) | |||||||
\(228\) | 0.142799 | 0.00945707 | ||||||||
\(229\) | −13.1694 | −0.870258 | −0.435129 | − | 0.900368i | \(-0.643297\pi\) | ||||
−0.435129 | + | 0.900368i | \(0.643297\pi\) | |||||||
\(230\) | −2.30927 | −0.152269 | ||||||||
\(231\) | 0.298127 | 0.0196153 | ||||||||
\(232\) | 2.50711 | 0.164600 | ||||||||
\(233\) | −8.17542 | −0.535590 | −0.267795 | − | 0.963476i | \(-0.586295\pi\) | ||||
−0.267795 | + | 0.963476i | \(0.586295\pi\) | |||||||
\(234\) | 17.2640 | 1.12858 | ||||||||
\(235\) | −2.97827 | −0.194281 | ||||||||
\(236\) | 8.08984 | 0.526604 | ||||||||
\(237\) | 3.01065 | 0.195563 | ||||||||
\(238\) | −0.299753 | −0.0194301 | ||||||||
\(239\) | 2.81584 | 0.182141 | 0.0910707 | − | 0.995844i | \(-0.470971\pi\) | ||||
0.0910707 | + | 0.995844i | \(0.470971\pi\) | |||||||
\(240\) | 0.791670 | 0.0511021 | ||||||||
\(241\) | 8.59567 | 0.553696 | 0.276848 | − | 0.960914i | \(-0.410710\pi\) | ||||
0.276848 | + | 0.960914i | \(0.410710\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −12.3336 | −0.791203 | ||||||||
\(244\) | 2.60152 | 0.166545 | ||||||||
\(245\) | 10.2138 | 0.652536 | ||||||||
\(246\) | 3.40810 | 0.217293 | ||||||||
\(247\) | −1.74556 | −0.111067 | ||||||||
\(248\) | 0.621065 | 0.0394376 | ||||||||
\(249\) | 0.165970 | 0.0105179 | ||||||||
\(250\) | −11.7242 | −0.741505 | ||||||||
\(251\) | −7.11696 | −0.449218 | −0.224609 | − | 0.974449i | \(-0.572111\pi\) | ||||
−0.224609 | + | 0.974449i | \(0.572111\pi\) | |||||||
\(252\) | 1.57664 | 0.0993192 | ||||||||
\(253\) | −1.50740 | −0.0947697 | ||||||||
\(254\) | 8.14472 | 0.511045 | ||||||||
\(255\) | −0.411345 | −0.0257594 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.33665 | 0.145756 | 0.0728780 | − | 0.997341i | \(-0.476782\pi\) | ||||
0.0728780 | + | 0.997341i | \(0.476782\pi\) | |||||||
\(258\) | −4.15926 | −0.258944 | ||||||||
\(259\) | 2.68622 | 0.166914 | ||||||||
\(260\) | −9.67733 | −0.600163 | ||||||||
\(261\) | 6.85179 | 0.424115 | ||||||||
\(262\) | −3.53403 | −0.218333 | ||||||||
\(263\) | −28.6230 | −1.76497 | −0.882485 | − | 0.470341i | \(-0.844131\pi\) | ||||
−0.882485 | + | 0.470341i | \(0.844131\pi\) | |||||||
\(264\) | 0.516772 | 0.0318051 | ||||||||
\(265\) | −17.8542 | −1.09677 | ||||||||
\(266\) | −0.159414 | −0.00977432 | ||||||||
\(267\) | −3.95346 | −0.241948 | ||||||||
\(268\) | 5.29122 | 0.323212 | ||||||||
\(269\) | −14.6174 | −0.891240 | −0.445620 | − | 0.895222i | \(-0.647017\pi\) | ||||
−0.445620 | + | 0.895222i | \(0.647017\pi\) | |||||||
\(270\) | 4.53860 | 0.276211 | ||||||||
\(271\) | 32.6618 | 1.98406 | 0.992031 | − | 0.125993i | \(-0.0402117\pi\) | ||||
0.992031 | + | 0.125993i | \(0.0402117\pi\) | |||||||
\(272\) | −0.519591 | −0.0315048 | ||||||||
\(273\) | 1.88327 | 0.113980 | ||||||||
\(274\) | 15.4462 | 0.933136 | ||||||||
\(275\) | −2.65312 | −0.159989 | ||||||||
\(276\) | 0.778984 | 0.0468894 | ||||||||
\(277\) | 13.4119 | 0.805841 | 0.402921 | − | 0.915235i | \(-0.367995\pi\) | ||||
0.402921 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(278\) | −6.61303 | −0.396623 | ||||||||
\(279\) | 1.69734 | 0.101617 | ||||||||
\(280\) | −0.883787 | −0.0528164 | ||||||||
\(281\) | −2.23914 | −0.133576 | −0.0667879 | − | 0.997767i | \(-0.521275\pi\) | ||||
−0.0667879 | + | 0.997767i | \(0.521275\pi\) | |||||||
\(282\) | 1.00466 | 0.0598265 | ||||||||
\(283\) | 20.1113 | 1.19549 | 0.597747 | − | 0.801685i | \(-0.296063\pi\) | ||||
0.597747 | + | 0.801685i | \(0.296063\pi\) | |||||||
\(284\) | 14.1174 | 0.837711 | ||||||||
\(285\) | −0.218761 | −0.0129583 | ||||||||
\(286\) | −6.31699 | −0.373532 | ||||||||
\(287\) | −3.80466 | −0.224582 | ||||||||
\(288\) | 2.73295 | 0.161040 | ||||||||
\(289\) | −16.7300 | −0.984119 | ||||||||
\(290\) | −3.84077 | −0.225538 | ||||||||
\(291\) | 3.30041 | 0.193474 | ||||||||
\(292\) | −2.91021 | −0.170307 | ||||||||
\(293\) | 12.4760 | 0.728853 | 0.364427 | − | 0.931232i | \(-0.381265\pi\) | ||||
0.364427 | + | 0.931232i | \(0.381265\pi\) | |||||||
\(294\) | −3.44541 | −0.200941 | ||||||||
\(295\) | −12.3933 | −0.721563 | ||||||||
\(296\) | 4.65628 | 0.270641 | ||||||||
\(297\) | 2.96263 | 0.171909 | ||||||||
\(298\) | 12.3628 | 0.716155 | ||||||||
\(299\) | −9.52226 | −0.550687 | ||||||||
\(300\) | 1.37106 | 0.0791581 | ||||||||
\(301\) | 4.64322 | 0.267631 | ||||||||
\(302\) | 20.4592 | 1.17730 | ||||||||
\(303\) | 6.02829 | 0.346316 | ||||||||
\(304\) | −0.276328 | −0.0158485 | ||||||||
\(305\) | −3.98540 | −0.228203 | ||||||||
\(306\) | −1.42002 | −0.0811769 | ||||||||
\(307\) | −1.25071 | −0.0713820 | −0.0356910 | − | 0.999363i | \(-0.511363\pi\) | ||||
−0.0356910 | + | 0.999363i | \(0.511363\pi\) | |||||||
\(308\) | −0.576902 | −0.0328721 | ||||||||
\(309\) | −0.447426 | −0.0254532 | ||||||||
\(310\) | −0.951441 | −0.0540382 | ||||||||
\(311\) | 8.37779 | 0.475061 | 0.237531 | − | 0.971380i | \(-0.423662\pi\) | ||||
0.237531 | + | 0.971380i | \(0.423662\pi\) | |||||||
\(312\) | 3.26444 | 0.184813 | ||||||||
\(313\) | 15.4365 | 0.872525 | 0.436263 | − | 0.899819i | \(-0.356302\pi\) | ||||
0.436263 | + | 0.899819i | \(0.356302\pi\) | |||||||
\(314\) | 21.3362 | 1.20407 | ||||||||
\(315\) | −2.41534 | −0.136089 | ||||||||
\(316\) | −5.82588 | −0.327732 | ||||||||
\(317\) | −31.9865 | −1.79654 | −0.898271 | − | 0.439441i | \(-0.855177\pi\) | ||||
−0.898271 | + | 0.439441i | \(0.855177\pi\) | |||||||
\(318\) | 6.02273 | 0.337738 | ||||||||
\(319\) | −2.50711 | −0.140371 | ||||||||
\(320\) | −1.53195 | −0.0856387 | ||||||||
\(321\) | 4.79791 | 0.267793 | ||||||||
\(322\) | −0.869625 | −0.0484623 | ||||||||
\(323\) | 0.143578 | 0.00798887 | ||||||||
\(324\) | 6.66784 | 0.370435 | ||||||||
\(325\) | −16.7597 | −0.929663 | ||||||||
\(326\) | 24.0912 | 1.33429 | ||||||||
\(327\) | 2.71928 | 0.150377 | ||||||||
\(328\) | −6.59498 | −0.364147 | ||||||||
\(329\) | −1.12156 | −0.0618335 | ||||||||
\(330\) | −0.791670 | −0.0435800 | ||||||||
\(331\) | 8.82597 | 0.485119 | 0.242560 | − | 0.970137i | \(-0.422013\pi\) | ||||
0.242560 | + | 0.970137i | \(0.422013\pi\) | |||||||
\(332\) | −0.321166 | −0.0176263 | ||||||||
\(333\) | 12.7254 | 0.697346 | ||||||||
\(334\) | −21.8326 | −1.19463 | ||||||||
\(335\) | −8.10589 | −0.442872 | ||||||||
\(336\) | 0.298127 | 0.0162642 | ||||||||
\(337\) | −15.7719 | −0.859149 | −0.429575 | − | 0.903031i | \(-0.641336\pi\) | ||||
−0.429575 | + | 0.903031i | \(0.641336\pi\) | |||||||
\(338\) | −26.9044 | −1.46341 | ||||||||
\(339\) | −8.67423 | −0.471120 | ||||||||
\(340\) | 0.795989 | 0.0431686 | ||||||||
\(341\) | −0.621065 | −0.0336325 | ||||||||
\(342\) | −0.755190 | −0.0408360 | ||||||||
\(343\) | 7.88463 | 0.425730 | ||||||||
\(344\) | 8.04854 | 0.433948 | ||||||||
\(345\) | −1.19337 | −0.0642487 | ||||||||
\(346\) | 19.7187 | 1.06009 | ||||||||
\(347\) | −15.0085 | −0.805701 | −0.402851 | − | 0.915266i | \(-0.631981\pi\) | ||||
−0.402851 | + | 0.915266i | \(0.631981\pi\) | |||||||
\(348\) | 1.29560 | 0.0694516 | ||||||||
\(349\) | 10.9213 | 0.584604 | 0.292302 | − | 0.956326i | \(-0.405579\pi\) | ||||
0.292302 | + | 0.956326i | \(0.405579\pi\) | |||||||
\(350\) | −1.53059 | −0.0818136 | ||||||||
\(351\) | 18.7149 | 0.998927 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 11.9233 | 0.634615 | 0.317307 | − | 0.948323i | \(-0.397221\pi\) | ||||
0.317307 | + | 0.948323i | \(0.397221\pi\) | |||||||
\(354\) | 4.18060 | 0.222197 | ||||||||
\(355\) | −21.6271 | −1.14785 | ||||||||
\(356\) | 7.65030 | 0.405465 | ||||||||
\(357\) | −0.154904 | −0.00819840 | ||||||||
\(358\) | 17.8912 | 0.945578 | ||||||||
\(359\) | −20.8521 | −1.10053 | −0.550265 | − | 0.834990i | \(-0.685473\pi\) | ||||
−0.550265 | + | 0.834990i | \(0.685473\pi\) | |||||||
\(360\) | −4.18674 | −0.220661 | ||||||||
\(361\) | −18.9236 | −0.995981 | ||||||||
\(362\) | 21.6524 | 1.13802 | ||||||||
\(363\) | −0.516772 | −0.0271235 | ||||||||
\(364\) | −3.64429 | −0.191013 | ||||||||
\(365\) | 4.45831 | 0.233359 | ||||||||
\(366\) | 1.34439 | 0.0702725 | ||||||||
\(367\) | −11.8600 | −0.619086 | −0.309543 | − | 0.950885i | \(-0.600176\pi\) | ||||
−0.309543 | + | 0.950885i | \(0.600176\pi\) | |||||||
\(368\) | −1.50740 | −0.0785789 | ||||||||
\(369\) | −18.0237 | −0.938278 | ||||||||
\(370\) | −7.13321 | −0.370838 | ||||||||
\(371\) | −6.72352 | −0.349068 | ||||||||
\(372\) | 0.320949 | 0.0166404 | ||||||||
\(373\) | −29.1370 | −1.50866 | −0.754329 | − | 0.656497i | \(-0.772037\pi\) | ||||
−0.754329 | + | 0.656497i | \(0.772037\pi\) | |||||||
\(374\) | 0.519591 | 0.0268674 | ||||||||
\(375\) | −6.05875 | −0.312872 | ||||||||
\(376\) | −1.94410 | −0.100259 | ||||||||
\(377\) | −15.8374 | −0.815666 | ||||||||
\(378\) | 1.70915 | 0.0879090 | ||||||||
\(379\) | 8.69451 | 0.446607 | 0.223303 | − | 0.974749i | \(-0.428316\pi\) | ||||
0.223303 | + | 0.974749i | \(0.428316\pi\) | |||||||
\(380\) | 0.423321 | 0.0217159 | ||||||||
\(381\) | 4.20896 | 0.215632 | ||||||||
\(382\) | −6.58409 | −0.336871 | ||||||||
\(383\) | −17.0555 | −0.871496 | −0.435748 | − | 0.900069i | \(-0.643516\pi\) | ||||
−0.435748 | + | 0.900069i | \(0.643516\pi\) | |||||||
\(384\) | 0.516772 | 0.0263714 | ||||||||
\(385\) | 0.883787 | 0.0450419 | ||||||||
\(386\) | −14.5978 | −0.743008 | ||||||||
\(387\) | 21.9962 | 1.11813 | ||||||||
\(388\) | −6.38659 | −0.324230 | ||||||||
\(389\) | 23.0914 | 1.17078 | 0.585389 | − | 0.810752i | \(-0.300942\pi\) | ||||
0.585389 | + | 0.810752i | \(0.300942\pi\) | |||||||
\(390\) | −5.00097 | −0.253234 | ||||||||
\(391\) | 0.783234 | 0.0396099 | ||||||||
\(392\) | 6.66718 | 0.336744 | ||||||||
\(393\) | −1.82629 | −0.0921241 | ||||||||
\(394\) | −1.00000 | −0.0503793 | ||||||||
\(395\) | 8.92498 | 0.449064 | ||||||||
\(396\) | −2.73295 | −0.137336 | ||||||||
\(397\) | 14.3188 | 0.718640 | 0.359320 | − | 0.933214i | \(-0.383009\pi\) | ||||
0.359320 | + | 0.933214i | \(0.383009\pi\) | |||||||
\(398\) | 22.2655 | 1.11607 | ||||||||
\(399\) | −0.0823808 | −0.00412420 | ||||||||
\(400\) | −2.65312 | −0.132656 | ||||||||
\(401\) | −33.6253 | −1.67917 | −0.839584 | − | 0.543230i | \(-0.817201\pi\) | ||||
−0.839584 | + | 0.543230i | \(0.817201\pi\) | |||||||
\(402\) | 2.73435 | 0.136377 | ||||||||
\(403\) | −3.92326 | −0.195431 | ||||||||
\(404\) | −11.6653 | −0.580369 | ||||||||
\(405\) | −10.2148 | −0.507578 | ||||||||
\(406\) | −1.44636 | −0.0717814 | ||||||||
\(407\) | −4.65628 | −0.230803 | ||||||||
\(408\) | −0.268510 | −0.0132932 | ||||||||
\(409\) | −14.1008 | −0.697239 | −0.348620 | − | 0.937264i | \(-0.613350\pi\) | ||||
−0.348620 | + | 0.937264i | \(0.613350\pi\) | |||||||
\(410\) | 10.1032 | 0.498961 | ||||||||
\(411\) | 7.98214 | 0.393730 | ||||||||
\(412\) | 0.865809 | 0.0426554 | ||||||||
\(413\) | −4.66705 | −0.229650 | ||||||||
\(414\) | −4.11966 | −0.202470 | ||||||||
\(415\) | 0.492011 | 0.0241519 | ||||||||
\(416\) | −6.31699 | −0.309716 | ||||||||
\(417\) | −3.41743 | −0.167352 | ||||||||
\(418\) | 0.276328 | 0.0135156 | ||||||||
\(419\) | −11.0166 | −0.538196 | −0.269098 | − | 0.963113i | \(-0.586726\pi\) | ||||
−0.269098 | + | 0.963113i | \(0.586726\pi\) | |||||||
\(420\) | −0.456716 | −0.0222855 | ||||||||
\(421\) | 9.64998 | 0.470311 | 0.235156 | − | 0.971958i | \(-0.424440\pi\) | ||||
0.235156 | + | 0.971958i | \(0.424440\pi\) | |||||||
\(422\) | 12.5295 | 0.609924 | ||||||||
\(423\) | −5.31313 | −0.258333 | ||||||||
\(424\) | −11.6545 | −0.565993 | ||||||||
\(425\) | 1.37854 | 0.0668690 | ||||||||
\(426\) | 7.29546 | 0.353466 | ||||||||
\(427\) | −1.50082 | −0.0726298 | ||||||||
\(428\) | −9.28437 | −0.448777 | ||||||||
\(429\) | −3.26444 | −0.157609 | ||||||||
\(430\) | −12.3300 | −0.594604 | ||||||||
\(431\) | −12.9828 | −0.625359 | −0.312680 | − | 0.949859i | \(-0.601227\pi\) | ||||
−0.312680 | + | 0.949859i | \(0.601227\pi\) | |||||||
\(432\) | 2.96263 | 0.142539 | ||||||||
\(433\) | 10.5182 | 0.505475 | 0.252737 | − | 0.967535i | \(-0.418669\pi\) | ||||
0.252737 | + | 0.967535i | \(0.418669\pi\) | |||||||
\(434\) | −0.358294 | −0.0171986 | ||||||||
\(435\) | −1.98480 | −0.0951639 | ||||||||
\(436\) | −5.26206 | −0.252007 | ||||||||
\(437\) | 0.416538 | 0.0199257 | ||||||||
\(438\) | −1.50392 | −0.0718600 | ||||||||
\(439\) | −7.20297 | −0.343779 | −0.171889 | − | 0.985116i | \(-0.554987\pi\) | ||||
−0.171889 | + | 0.985116i | \(0.554987\pi\) | |||||||
\(440\) | 1.53195 | 0.0730330 | ||||||||
\(441\) | 18.2211 | 0.867669 | ||||||||
\(442\) | 3.28225 | 0.156121 | ||||||||
\(443\) | −20.2810 | −0.963580 | −0.481790 | − | 0.876287i | \(-0.660013\pi\) | ||||
−0.481790 | + | 0.876287i | \(0.660013\pi\) | |||||||
\(444\) | 2.40624 | 0.114195 | ||||||||
\(445\) | −11.7199 | −0.555576 | ||||||||
\(446\) | 13.6319 | 0.645490 | ||||||||
\(447\) | 6.38872 | 0.302176 | ||||||||
\(448\) | −0.576902 | −0.0272561 | ||||||||
\(449\) | −31.5168 | −1.48737 | −0.743685 | − | 0.668531i | \(-0.766924\pi\) | ||||
−0.743685 | + | 0.668531i | \(0.766924\pi\) | |||||||
\(450\) | −7.25084 | −0.341808 | ||||||||
\(451\) | 6.59498 | 0.310545 | ||||||||
\(452\) | 16.7854 | 0.789519 | ||||||||
\(453\) | 10.5728 | 0.496752 | ||||||||
\(454\) | −7.51079 | −0.352499 | ||||||||
\(455\) | 5.58287 | 0.261729 | ||||||||
\(456\) | −0.142799 | −0.00668716 | ||||||||
\(457\) | −31.8248 | −1.48870 | −0.744351 | − | 0.667788i | \(-0.767241\pi\) | ||||
−0.744351 | + | 0.667788i | \(0.767241\pi\) | |||||||
\(458\) | 13.1694 | 0.615366 | ||||||||
\(459\) | −1.53935 | −0.0718509 | ||||||||
\(460\) | 2.30927 | 0.107670 | ||||||||
\(461\) | −15.4987 | −0.721847 | −0.360923 | − | 0.932595i | \(-0.617538\pi\) | ||||
−0.360923 | + | 0.932595i | \(0.617538\pi\) | |||||||
\(462\) | −0.298127 | −0.0138701 | ||||||||
\(463\) | 39.0742 | 1.81593 | 0.907965 | − | 0.419045i | \(-0.137635\pi\) | ||||
0.907965 | + | 0.419045i | \(0.137635\pi\) | |||||||
\(464\) | −2.50711 | −0.116389 | ||||||||
\(465\) | −0.491678 | −0.0228010 | ||||||||
\(466\) | 8.17542 | 0.378719 | ||||||||
\(467\) | 30.6437 | 1.41802 | 0.709010 | − | 0.705199i | \(-0.249142\pi\) | ||||
0.709010 | + | 0.705199i | \(0.249142\pi\) | |||||||
\(468\) | −17.2640 | −0.798029 | ||||||||
\(469\) | −3.05251 | −0.140952 | ||||||||
\(470\) | 2.97827 | 0.137378 | ||||||||
\(471\) | 11.0260 | 0.508049 | ||||||||
\(472\) | −8.08984 | −0.372365 | ||||||||
\(473\) | −8.04854 | −0.370072 | ||||||||
\(474\) | −3.01065 | −0.138284 | ||||||||
\(475\) | 0.733132 | 0.0336384 | ||||||||
\(476\) | 0.299753 | 0.0137392 | ||||||||
\(477\) | −31.8512 | −1.45836 | ||||||||
\(478\) | −2.81584 | −0.128793 | ||||||||
\(479\) | −12.4403 | −0.568412 | −0.284206 | − | 0.958763i | \(-0.591730\pi\) | ||||
−0.284206 | + | 0.958763i | \(0.591730\pi\) | |||||||
\(480\) | −0.791670 | −0.0361346 | ||||||||
\(481\) | −29.4137 | −1.34115 | ||||||||
\(482\) | −8.59567 | −0.391522 | ||||||||
\(483\) | −0.449398 | −0.0204483 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 9.78396 | 0.444267 | ||||||||
\(486\) | 12.3336 | 0.559465 | ||||||||
\(487\) | −40.5024 | −1.83534 | −0.917670 | − | 0.397344i | \(-0.869932\pi\) | ||||
−0.917670 | + | 0.397344i | \(0.869932\pi\) | |||||||
\(488\) | −2.60152 | −0.117765 | ||||||||
\(489\) | 12.4496 | 0.562992 | ||||||||
\(490\) | −10.2138 | −0.461413 | ||||||||
\(491\) | 13.4456 | 0.606792 | 0.303396 | − | 0.952865i | \(-0.401880\pi\) | ||||
0.303396 | + | 0.952865i | \(0.401880\pi\) | |||||||
\(492\) | −3.40810 | −0.153649 | ||||||||
\(493\) | 1.30267 | 0.0586693 | ||||||||
\(494\) | 1.74556 | 0.0785365 | ||||||||
\(495\) | 4.18674 | 0.188180 | ||||||||
\(496\) | −0.621065 | −0.0278866 | ||||||||
\(497\) | −8.14433 | −0.365323 | ||||||||
\(498\) | −0.165970 | −0.00743727 | ||||||||
\(499\) | −42.6557 | −1.90953 | −0.954765 | − | 0.297361i | \(-0.903893\pi\) | ||||
−0.954765 | + | 0.297361i | \(0.903893\pi\) | |||||||
\(500\) | 11.7242 | 0.524323 | ||||||||
\(501\) | −11.2825 | −0.504064 | ||||||||
\(502\) | 7.11696 | 0.317645 | ||||||||
\(503\) | 30.9713 | 1.38094 | 0.690471 | − | 0.723360i | \(-0.257404\pi\) | ||||
0.690471 | + | 0.723360i | \(0.257404\pi\) | |||||||
\(504\) | −1.57664 | −0.0702293 | ||||||||
\(505\) | 17.8706 | 0.795233 | ||||||||
\(506\) | 1.50740 | 0.0670123 | ||||||||
\(507\) | −13.9034 | −0.617473 | ||||||||
\(508\) | −8.14472 | −0.361363 | ||||||||
\(509\) | −26.5455 | −1.17661 | −0.588305 | − | 0.808639i | \(-0.700205\pi\) | ||||
−0.588305 | + | 0.808639i | \(0.700205\pi\) | |||||||
\(510\) | 0.411345 | 0.0182147 | ||||||||
\(511\) | 1.67891 | 0.0742706 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.818657 | −0.0361446 | ||||||||
\(514\) | −2.33665 | −0.103065 | ||||||||
\(515\) | −1.32638 | −0.0584472 | ||||||||
\(516\) | 4.15926 | 0.183101 | ||||||||
\(517\) | 1.94410 | 0.0855016 | ||||||||
\(518\) | −2.68622 | −0.118026 | ||||||||
\(519\) | 10.1901 | 0.447295 | ||||||||
\(520\) | 9.67733 | 0.424379 | ||||||||
\(521\) | −8.49955 | −0.372372 | −0.186186 | − | 0.982515i | \(-0.559613\pi\) | ||||
−0.186186 | + | 0.982515i | \(0.559613\pi\) | |||||||
\(522\) | −6.85179 | −0.299895 | ||||||||
\(523\) | 36.7026 | 1.60489 | 0.802445 | − | 0.596726i | \(-0.203532\pi\) | ||||
0.802445 | + | 0.596726i | \(0.203532\pi\) | |||||||
\(524\) | 3.53403 | 0.154385 | ||||||||
\(525\) | −0.790967 | −0.0345206 | ||||||||
\(526\) | 28.6230 | 1.24802 | ||||||||
\(527\) | 0.322700 | 0.0140570 | ||||||||
\(528\) | −0.516772 | −0.0224896 | ||||||||
\(529\) | −20.7277 | −0.901206 | ||||||||
\(530\) | 17.8542 | 0.775535 | ||||||||
\(531\) | −22.1091 | −0.959453 | ||||||||
\(532\) | 0.159414 | 0.00691148 | ||||||||
\(533\) | 41.6604 | 1.80451 | ||||||||
\(534\) | 3.95346 | 0.171083 | ||||||||
\(535\) | 14.2232 | 0.614923 | ||||||||
\(536\) | −5.29122 | −0.228546 | ||||||||
\(537\) | 9.24566 | 0.398980 | ||||||||
\(538\) | 14.6174 | 0.630202 | ||||||||
\(539\) | −6.66718 | −0.287176 | ||||||||
\(540\) | −4.53860 | −0.195310 | ||||||||
\(541\) | 38.4107 | 1.65140 | 0.825701 | − | 0.564107i | \(-0.190780\pi\) | ||||
0.825701 | + | 0.564107i | \(0.190780\pi\) | |||||||
\(542\) | −32.6618 | −1.40294 | ||||||||
\(543\) | 11.1893 | 0.480180 | ||||||||
\(544\) | 0.519591 | 0.0222773 | ||||||||
\(545\) | 8.06122 | 0.345305 | ||||||||
\(546\) | −1.88327 | −0.0805963 | ||||||||
\(547\) | −16.5291 | −0.706732 | −0.353366 | − | 0.935485i | \(-0.614963\pi\) | ||||
−0.353366 | + | 0.935485i | \(0.614963\pi\) | |||||||
\(548\) | −15.4462 | −0.659827 | ||||||||
\(549\) | −7.10981 | −0.303439 | ||||||||
\(550\) | 2.65312 | 0.113129 | ||||||||
\(551\) | 0.692784 | 0.0295136 | ||||||||
\(552\) | −0.778984 | −0.0331558 | ||||||||
\(553\) | 3.36097 | 0.142923 | ||||||||
\(554\) | −13.4119 | −0.569816 | ||||||||
\(555\) | −3.68624 | −0.156472 | ||||||||
\(556\) | 6.61303 | 0.280455 | ||||||||
\(557\) | −0.664297 | −0.0281472 | −0.0140736 | − | 0.999901i | \(-0.504480\pi\) | ||||
−0.0140736 | + | 0.999901i | \(0.504480\pi\) | |||||||
\(558\) | −1.69734 | −0.0718540 | ||||||||
\(559\) | −50.8425 | −2.15041 | ||||||||
\(560\) | 0.883787 | 0.0373468 | ||||||||
\(561\) | 0.268510 | 0.0113365 | ||||||||
\(562\) | 2.23914 | 0.0944524 | ||||||||
\(563\) | −9.28117 | −0.391155 | −0.195577 | − | 0.980688i | \(-0.562658\pi\) | ||||
−0.195577 | + | 0.980688i | \(0.562658\pi\) | |||||||
\(564\) | −1.00466 | −0.0423037 | ||||||||
\(565\) | −25.7145 | −1.08182 | ||||||||
\(566\) | −20.1113 | −0.845342 | ||||||||
\(567\) | −3.84669 | −0.161546 | ||||||||
\(568\) | −14.1174 | −0.592351 | ||||||||
\(569\) | −11.2214 | −0.470424 | −0.235212 | − | 0.971944i | \(-0.575578\pi\) | ||||
−0.235212 | + | 0.971944i | \(0.575578\pi\) | |||||||
\(570\) | 0.218761 | 0.00916288 | ||||||||
\(571\) | 27.4537 | 1.14890 | 0.574451 | − | 0.818539i | \(-0.305215\pi\) | ||||
0.574451 | + | 0.818539i | \(0.305215\pi\) | |||||||
\(572\) | 6.31699 | 0.264127 | ||||||||
\(573\) | −3.40247 | −0.142140 | ||||||||
\(574\) | 3.80466 | 0.158803 | ||||||||
\(575\) | 3.99933 | 0.166783 | ||||||||
\(576\) | −2.73295 | −0.113873 | ||||||||
\(577\) | 46.9132 | 1.95302 | 0.976511 | − | 0.215468i | \(-0.0691277\pi\) | ||||
0.976511 | + | 0.215468i | \(0.0691277\pi\) | |||||||
\(578\) | 16.7300 | 0.695877 | ||||||||
\(579\) | −7.54373 | −0.313507 | ||||||||
\(580\) | 3.84077 | 0.159479 | ||||||||
\(581\) | 0.185281 | 0.00768676 | ||||||||
\(582\) | −3.30041 | −0.136807 | ||||||||
\(583\) | 11.6545 | 0.482681 | ||||||||
\(584\) | 2.91021 | 0.120426 | ||||||||
\(585\) | 26.4476 | 1.09347 | ||||||||
\(586\) | −12.4760 | −0.515377 | ||||||||
\(587\) | −16.4191 | −0.677688 | −0.338844 | − | 0.940843i | \(-0.610036\pi\) | ||||
−0.338844 | + | 0.940843i | \(0.610036\pi\) | |||||||
\(588\) | 3.44541 | 0.142086 | ||||||||
\(589\) | 0.171618 | 0.00707138 | ||||||||
\(590\) | 12.3933 | 0.510222 | ||||||||
\(591\) | −0.516772 | −0.0212572 | ||||||||
\(592\) | −4.65628 | −0.191372 | ||||||||
\(593\) | −9.46890 | −0.388841 | −0.194421 | − | 0.980918i | \(-0.562283\pi\) | ||||
−0.194421 | + | 0.980918i | \(0.562283\pi\) | |||||||
\(594\) | −2.96263 | −0.121558 | ||||||||
\(595\) | −0.459208 | −0.0188257 | ||||||||
\(596\) | −12.3628 | −0.506398 | ||||||||
\(597\) | 11.5062 | 0.470916 | ||||||||
\(598\) | 9.52226 | 0.389394 | ||||||||
\(599\) | 3.39030 | 0.138524 | 0.0692619 | − | 0.997599i | \(-0.477936\pi\) | ||||
0.0692619 | + | 0.997599i | \(0.477936\pi\) | |||||||
\(600\) | −1.37106 | −0.0559733 | ||||||||
\(601\) | −21.3548 | −0.871082 | −0.435541 | − | 0.900169i | \(-0.643443\pi\) | ||||
−0.435541 | + | 0.900169i | \(0.643443\pi\) | |||||||
\(602\) | −4.64322 | −0.189243 | ||||||||
\(603\) | −14.4606 | −0.588882 | ||||||||
\(604\) | −20.4592 | −0.832474 | ||||||||
\(605\) | −1.53195 | −0.0622827 | ||||||||
\(606\) | −6.02829 | −0.244882 | ||||||||
\(607\) | 28.0450 | 1.13831 | 0.569156 | − | 0.822229i | \(-0.307270\pi\) | ||||
0.569156 | + | 0.822229i | \(0.307270\pi\) | |||||||
\(608\) | 0.276328 | 0.0112066 | ||||||||
\(609\) | −0.747436 | −0.0302876 | ||||||||
\(610\) | 3.98540 | 0.161364 | ||||||||
\(611\) | 12.2809 | 0.496831 | ||||||||
\(612\) | 1.42002 | 0.0574007 | ||||||||
\(613\) | 35.1970 | 1.42160 | 0.710798 | − | 0.703397i | \(-0.248334\pi\) | ||||
0.710798 | + | 0.703397i | \(0.248334\pi\) | |||||||
\(614\) | 1.25071 | 0.0504747 | ||||||||
\(615\) | 5.22105 | 0.210533 | ||||||||
\(616\) | 0.576902 | 0.0232441 | ||||||||
\(617\) | −25.6256 | −1.03165 | −0.515823 | − | 0.856695i | \(-0.672514\pi\) | ||||
−0.515823 | + | 0.856695i | \(0.672514\pi\) | |||||||
\(618\) | 0.447426 | 0.0179981 | ||||||||
\(619\) | 32.1193 | 1.29099 | 0.645493 | − | 0.763767i | \(-0.276652\pi\) | ||||
0.645493 | + | 0.763767i | \(0.276652\pi\) | |||||||
\(620\) | 0.951441 | 0.0382108 | ||||||||
\(621\) | −4.46588 | −0.179209 | ||||||||
\(622\) | −8.37779 | −0.335919 | ||||||||
\(623\) | −4.41347 | −0.176822 | ||||||||
\(624\) | −3.26444 | −0.130682 | ||||||||
\(625\) | −4.69534 | −0.187813 | ||||||||
\(626\) | −15.4365 | −0.616968 | ||||||||
\(627\) | 0.142799 | 0.00570283 | ||||||||
\(628\) | −21.3362 | −0.851408 | ||||||||
\(629\) | 2.41936 | 0.0964664 | ||||||||
\(630\) | 2.41534 | 0.0962295 | ||||||||
\(631\) | 3.17376 | 0.126345 | 0.0631726 | − | 0.998003i | \(-0.479878\pi\) | ||||
0.0631726 | + | 0.998003i | \(0.479878\pi\) | |||||||
\(632\) | 5.82588 | 0.231741 | ||||||||
\(633\) | 6.47487 | 0.257353 | ||||||||
\(634\) | 31.9865 | 1.27035 | ||||||||
\(635\) | 12.4773 | 0.495147 | ||||||||
\(636\) | −6.02273 | −0.238817 | ||||||||
\(637\) | −42.1165 | −1.66872 | ||||||||
\(638\) | 2.50711 | 0.0992573 | ||||||||
\(639\) | −38.5820 | −1.52628 | ||||||||
\(640\) | 1.53195 | 0.0605557 | ||||||||
\(641\) | 25.0824 | 0.990696 | 0.495348 | − | 0.868695i | \(-0.335041\pi\) | ||||
0.495348 | + | 0.868695i | \(0.335041\pi\) | |||||||
\(642\) | −4.79791 | −0.189358 | ||||||||
\(643\) | 9.69035 | 0.382150 | 0.191075 | − | 0.981575i | \(-0.438803\pi\) | ||||
0.191075 | + | 0.981575i | \(0.438803\pi\) | |||||||
\(644\) | 0.869625 | 0.0342680 | ||||||||
\(645\) | −6.37179 | −0.250889 | ||||||||
\(646\) | −0.143578 | −0.00564899 | ||||||||
\(647\) | 42.4143 | 1.66748 | 0.833739 | − | 0.552159i | \(-0.186196\pi\) | ||||
0.833739 | + | 0.552159i | \(0.186196\pi\) | |||||||
\(648\) | −6.66784 | −0.261937 | ||||||||
\(649\) | 8.08984 | 0.317554 | ||||||||
\(650\) | 16.7597 | 0.657371 | ||||||||
\(651\) | −0.185156 | −0.00725684 | ||||||||
\(652\) | −24.0912 | −0.943483 | ||||||||
\(653\) | 38.4602 | 1.50506 | 0.752531 | − | 0.658557i | \(-0.228833\pi\) | ||||
0.752531 | + | 0.658557i | \(0.228833\pi\) | |||||||
\(654\) | −2.71928 | −0.106332 | ||||||||
\(655\) | −5.41397 | −0.211541 | ||||||||
\(656\) | 6.59498 | 0.257491 | ||||||||
\(657\) | 7.95346 | 0.310294 | ||||||||
\(658\) | 1.12156 | 0.0437229 | ||||||||
\(659\) | 30.3041 | 1.18048 | 0.590239 | − | 0.807228i | \(-0.299033\pi\) | ||||
0.590239 | + | 0.807228i | \(0.299033\pi\) | |||||||
\(660\) | 0.791670 | 0.0308157 | ||||||||
\(661\) | −13.8645 | −0.539265 | −0.269633 | − | 0.962963i | \(-0.586902\pi\) | ||||
−0.269633 | + | 0.962963i | \(0.586902\pi\) | |||||||
\(662\) | −8.82597 | −0.343031 | ||||||||
\(663\) | 1.69618 | 0.0658740 | ||||||||
\(664\) | 0.321166 | 0.0124637 | ||||||||
\(665\) | −0.244215 | −0.00947025 | ||||||||
\(666\) | −12.7254 | −0.493098 | ||||||||
\(667\) | 3.77922 | 0.146332 | ||||||||
\(668\) | 21.8326 | 0.844729 | ||||||||
\(669\) | 7.04459 | 0.272360 | ||||||||
\(670\) | 8.10589 | 0.313158 | ||||||||
\(671\) | 2.60152 | 0.100430 | ||||||||
\(672\) | −0.298127 | −0.0115005 | ||||||||
\(673\) | −39.5240 | −1.52354 | −0.761770 | − | 0.647848i | \(-0.775669\pi\) | ||||
−0.761770 | + | 0.647848i | \(0.775669\pi\) | |||||||
\(674\) | 15.7719 | 0.607510 | ||||||||
\(675\) | −7.86021 | −0.302540 | ||||||||
\(676\) | 26.9044 | 1.03478 | ||||||||
\(677\) | −13.6994 | −0.526509 | −0.263255 | − | 0.964726i | \(-0.584796\pi\) | ||||
−0.263255 | + | 0.964726i | \(0.584796\pi\) | |||||||
\(678\) | 8.67423 | 0.333132 | ||||||||
\(679\) | 3.68444 | 0.141396 | ||||||||
\(680\) | −0.795989 | −0.0305248 | ||||||||
\(681\) | −3.88136 | −0.148734 | ||||||||
\(682\) | 0.621065 | 0.0237818 | ||||||||
\(683\) | −15.0292 | −0.575076 | −0.287538 | − | 0.957769i | \(-0.592837\pi\) | ||||
−0.287538 | + | 0.957769i | \(0.592837\pi\) | |||||||
\(684\) | 0.755190 | 0.0288754 | ||||||||
\(685\) | 23.6628 | 0.904108 | ||||||||
\(686\) | −7.88463 | −0.301037 | ||||||||
\(687\) | 6.80558 | 0.259649 | ||||||||
\(688\) | −8.04854 | −0.306848 | ||||||||
\(689\) | 73.6215 | 2.80475 | ||||||||
\(690\) | 1.19337 | 0.0454307 | ||||||||
\(691\) | −10.5598 | −0.401714 | −0.200857 | − | 0.979621i | \(-0.564373\pi\) | ||||
−0.200857 | + | 0.979621i | \(0.564373\pi\) | |||||||
\(692\) | −19.7187 | −0.749594 | ||||||||
\(693\) | 1.57664 | 0.0598917 | ||||||||
\(694\) | 15.0085 | 0.569717 | ||||||||
\(695\) | −10.1308 | −0.384285 | ||||||||
\(696\) | −1.29560 | −0.0491097 | ||||||||
\(697\) | −3.42669 | −0.129795 | ||||||||
\(698\) | −10.9213 | −0.413377 | ||||||||
\(699\) | 4.22483 | 0.159798 | ||||||||
\(700\) | 1.53059 | 0.0578509 | ||||||||
\(701\) | −37.1615 | −1.40357 | −0.701785 | − | 0.712389i | \(-0.747613\pi\) | ||||
−0.701785 | + | 0.712389i | \(0.747613\pi\) | |||||||
\(702\) | −18.7149 | −0.706348 | ||||||||
\(703\) | 1.28666 | 0.0485274 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 1.53909 | 0.0579654 | ||||||||
\(706\) | −11.9233 | −0.448740 | ||||||||
\(707\) | 6.72972 | 0.253097 | ||||||||
\(708\) | −4.18060 | −0.157117 | ||||||||
\(709\) | −1.26847 | −0.0476384 | −0.0238192 | − | 0.999716i | \(-0.507583\pi\) | ||||
−0.0238192 | + | 0.999716i | \(0.507583\pi\) | |||||||
\(710\) | 21.6271 | 0.811651 | ||||||||
\(711\) | 15.9218 | 0.597115 | ||||||||
\(712\) | −7.65030 | −0.286707 | ||||||||
\(713\) | 0.936196 | 0.0350608 | ||||||||
\(714\) | 0.154904 | 0.00579714 | ||||||||
\(715\) | −9.67733 | −0.361912 | ||||||||
\(716\) | −17.8912 | −0.668625 | ||||||||
\(717\) | −1.45515 | −0.0543434 | ||||||||
\(718\) | 20.8521 | 0.778193 | ||||||||
\(719\) | 17.0687 | 0.636555 | 0.318278 | − | 0.947998i | \(-0.396896\pi\) | ||||
0.318278 | + | 0.947998i | \(0.396896\pi\) | |||||||
\(720\) | 4.18674 | 0.156031 | ||||||||
\(721\) | −0.499487 | −0.0186019 | ||||||||
\(722\) | 18.9236 | 0.704265 | ||||||||
\(723\) | −4.44200 | −0.165200 | ||||||||
\(724\) | −21.6524 | −0.804703 | ||||||||
\(725\) | 6.65166 | 0.247036 | ||||||||
\(726\) | 0.516772 | 0.0191792 | ||||||||
\(727\) | −20.0266 | −0.742747 | −0.371373 | − | 0.928484i | \(-0.621113\pi\) | ||||
−0.371373 | + | 0.928484i | \(0.621113\pi\) | |||||||
\(728\) | 3.64429 | 0.135066 | ||||||||
\(729\) | −13.6298 | −0.504809 | ||||||||
\(730\) | −4.45831 | −0.165009 | ||||||||
\(731\) | 4.18195 | 0.154675 | ||||||||
\(732\) | −1.34439 | −0.0496901 | ||||||||
\(733\) | 46.0965 | 1.70261 | 0.851306 | − | 0.524669i | \(-0.175811\pi\) | ||||
0.851306 | + | 0.524669i | \(0.175811\pi\) | |||||||
\(734\) | 11.8600 | 0.437760 | ||||||||
\(735\) | −5.27821 | −0.194690 | ||||||||
\(736\) | 1.50740 | 0.0555637 | ||||||||
\(737\) | 5.29122 | 0.194904 | ||||||||
\(738\) | 18.0237 | 0.663463 | ||||||||
\(739\) | −13.0612 | −0.480462 | −0.240231 | − | 0.970716i | \(-0.577223\pi\) | ||||
−0.240231 | + | 0.970716i | \(0.577223\pi\) | |||||||
\(740\) | 7.13321 | 0.262222 | ||||||||
\(741\) | 0.902058 | 0.0331379 | ||||||||
\(742\) | 6.72352 | 0.246828 | ||||||||
\(743\) | −15.6807 | −0.575269 | −0.287635 | − | 0.957740i | \(-0.592869\pi\) | ||||
−0.287635 | + | 0.957740i | \(0.592869\pi\) | |||||||
\(744\) | −0.320949 | −0.0117666 | ||||||||
\(745\) | 18.9391 | 0.693877 | ||||||||
\(746\) | 29.1370 | 1.06678 | ||||||||
\(747\) | 0.877729 | 0.0321144 | ||||||||
\(748\) | −0.519591 | −0.0189981 | ||||||||
\(749\) | 5.35618 | 0.195710 | ||||||||
\(750\) | 6.05875 | 0.221234 | ||||||||
\(751\) | −45.7780 | −1.67046 | −0.835231 | − | 0.549899i | \(-0.814666\pi\) | ||||
−0.835231 | + | 0.549899i | \(0.814666\pi\) | |||||||
\(752\) | 1.94410 | 0.0708941 | ||||||||
\(753\) | 3.67784 | 0.134028 | ||||||||
\(754\) | 15.8374 | 0.576763 | ||||||||
\(755\) | 31.3426 | 1.14067 | ||||||||
\(756\) | −1.70915 | −0.0621610 | ||||||||
\(757\) | 10.3839 | 0.377409 | 0.188705 | − | 0.982034i | \(-0.439571\pi\) | ||||
0.188705 | + | 0.982034i | \(0.439571\pi\) | |||||||
\(758\) | −8.69451 | −0.315799 | ||||||||
\(759\) | 0.778984 | 0.0282753 | ||||||||
\(760\) | −0.423321 | −0.0153555 | ||||||||
\(761\) | 27.5237 | 0.997735 | 0.498867 | − | 0.866678i | \(-0.333749\pi\) | ||||
0.498867 | + | 0.866678i | \(0.333749\pi\) | |||||||
\(762\) | −4.20896 | −0.152475 | ||||||||
\(763\) | 3.03569 | 0.109899 | ||||||||
\(764\) | 6.58409 | 0.238204 | ||||||||
\(765\) | −2.17540 | −0.0786516 | ||||||||
\(766\) | 17.0555 | 0.616240 | ||||||||
\(767\) | 51.1035 | 1.84524 | ||||||||
\(768\) | −0.516772 | −0.0186474 | ||||||||
\(769\) | 1.39711 | 0.0503811 | 0.0251905 | − | 0.999683i | \(-0.491981\pi\) | ||||
0.0251905 | + | 0.999683i | \(0.491981\pi\) | |||||||
\(770\) | −0.883787 | −0.0318495 | ||||||||
\(771\) | −1.20751 | −0.0434875 | ||||||||
\(772\) | 14.5978 | 0.525386 | ||||||||
\(773\) | −8.08782 | −0.290899 | −0.145449 | − | 0.989366i | \(-0.546463\pi\) | ||||
−0.145449 | + | 0.989366i | \(0.546463\pi\) | |||||||
\(774\) | −21.9962 | −0.790638 | ||||||||
\(775\) | 1.64776 | 0.0591893 | ||||||||
\(776\) | 6.38659 | 0.229265 | ||||||||
\(777\) | −1.38816 | −0.0498001 | ||||||||
\(778\) | −23.0914 | −0.827865 | ||||||||
\(779\) | −1.82238 | −0.0652935 | ||||||||
\(780\) | 5.00097 | 0.179064 | ||||||||
\(781\) | 14.1174 | 0.505159 | ||||||||
\(782\) | −0.783234 | −0.0280084 | ||||||||
\(783\) | −7.42762 | −0.265441 | ||||||||
\(784\) | −6.66718 | −0.238114 | ||||||||
\(785\) | 32.6861 | 1.16662 | ||||||||
\(786\) | 1.82629 | 0.0651416 | ||||||||
\(787\) | 46.0364 | 1.64102 | 0.820510 | − | 0.571632i | \(-0.193689\pi\) | ||||
0.820510 | + | 0.571632i | \(0.193689\pi\) | |||||||
\(788\) | 1.00000 | 0.0356235 | ||||||||
\(789\) | 14.7916 | 0.526594 | ||||||||
\(790\) | −8.92498 | −0.317536 | ||||||||
\(791\) | −9.68354 | −0.344307 | ||||||||
\(792\) | 2.73295 | 0.0971110 | ||||||||
\(793\) | 16.4338 | 0.583580 | ||||||||
\(794\) | −14.3188 | −0.508155 | ||||||||
\(795\) | 9.22653 | 0.327231 | ||||||||
\(796\) | −22.2655 | −0.789178 | ||||||||
\(797\) | 26.9455 | 0.954459 | 0.477229 | − | 0.878779i | \(-0.341641\pi\) | ||||
0.477229 | + | 0.878779i | \(0.341641\pi\) | |||||||
\(798\) | 0.0823808 | 0.00291625 | ||||||||
\(799\) | −1.01014 | −0.0357361 | ||||||||
\(800\) | 2.65312 | 0.0938020 | ||||||||
\(801\) | −20.9079 | −0.738743 | ||||||||
\(802\) | 33.6253 | 1.18735 | ||||||||
\(803\) | −2.91021 | −0.102699 | ||||||||
\(804\) | −2.73435 | −0.0964332 | ||||||||
\(805\) | −1.33222 | −0.0469547 | ||||||||
\(806\) | 3.92326 | 0.138191 | ||||||||
\(807\) | 7.55388 | 0.265909 | ||||||||
\(808\) | 11.6653 | 0.410383 | ||||||||
\(809\) | −19.8717 | −0.698651 | −0.349325 | − | 0.937001i | \(-0.613589\pi\) | ||||
−0.349325 | + | 0.937001i | \(0.613589\pi\) | |||||||
\(810\) | 10.2148 | 0.358912 | ||||||||
\(811\) | −24.2933 | −0.853054 | −0.426527 | − | 0.904475i | \(-0.640263\pi\) | ||||
−0.426527 | + | 0.904475i | \(0.640263\pi\) | |||||||
\(812\) | 1.44636 | 0.0507571 | ||||||||
\(813\) | −16.8787 | −0.591962 | ||||||||
\(814\) | 4.65628 | 0.163203 | ||||||||
\(815\) | 36.9065 | 1.29278 | ||||||||
\(816\) | 0.268510 | 0.00939974 | ||||||||
\(817\) | 2.22404 | 0.0778092 | ||||||||
\(818\) | 14.1008 | 0.493023 | ||||||||
\(819\) | 9.95964 | 0.348018 | ||||||||
\(820\) | −10.1032 | −0.352819 | ||||||||
\(821\) | −23.7798 | −0.829921 | −0.414961 | − | 0.909839i | \(-0.636205\pi\) | ||||
−0.414961 | + | 0.909839i | \(0.636205\pi\) | |||||||
\(822\) | −7.98214 | −0.278409 | ||||||||
\(823\) | −55.4091 | −1.93144 | −0.965721 | − | 0.259584i | \(-0.916415\pi\) | ||||
−0.965721 | + | 0.259584i | \(0.916415\pi\) | |||||||
\(824\) | −0.865809 | −0.0301619 | ||||||||
\(825\) | 1.37106 | 0.0477342 | ||||||||
\(826\) | 4.66705 | 0.162387 | ||||||||
\(827\) | 10.1210 | 0.351941 | 0.175971 | − | 0.984395i | \(-0.443694\pi\) | ||||
0.175971 | + | 0.984395i | \(0.443694\pi\) | |||||||
\(828\) | 4.11966 | 0.143168 | ||||||||
\(829\) | 27.9017 | 0.969066 | 0.484533 | − | 0.874773i | \(-0.338990\pi\) | ||||
0.484533 | + | 0.874773i | \(0.338990\pi\) | |||||||
\(830\) | −0.492011 | −0.0170779 | ||||||||
\(831\) | −6.93088 | −0.240430 | ||||||||
\(832\) | 6.31699 | 0.219002 | ||||||||
\(833\) | 3.46421 | 0.120028 | ||||||||
\(834\) | 3.41743 | 0.118336 | ||||||||
\(835\) | −33.4465 | −1.15746 | ||||||||
\(836\) | −0.276328 | −0.00955701 | ||||||||
\(837\) | −1.83998 | −0.0635991 | ||||||||
\(838\) | 11.0166 | 0.380562 | ||||||||
\(839\) | 11.6786 | 0.403190 | 0.201595 | − | 0.979469i | \(-0.435388\pi\) | ||||
0.201595 | + | 0.979469i | \(0.435388\pi\) | |||||||
\(840\) | 0.456716 | 0.0157582 | ||||||||
\(841\) | −22.7144 | −0.783256 | ||||||||
\(842\) | −9.64998 | −0.332560 | ||||||||
\(843\) | 1.15712 | 0.0398535 | ||||||||
\(844\) | −12.5295 | −0.431281 | ||||||||
\(845\) | −41.2162 | −1.41788 | ||||||||
\(846\) | 5.31313 | 0.182669 | ||||||||
\(847\) | −0.576902 | −0.0198226 | ||||||||
\(848\) | 11.6545 | 0.400218 | ||||||||
\(849\) | −10.3930 | −0.356686 | ||||||||
\(850\) | −1.37854 | −0.0472835 | ||||||||
\(851\) | 7.01890 | 0.240605 | ||||||||
\(852\) | −7.29546 | −0.249938 | ||||||||
\(853\) | −41.6239 | −1.42518 | −0.712588 | − | 0.701583i | \(-0.752477\pi\) | ||||
−0.712588 | + | 0.701583i | \(0.752477\pi\) | |||||||
\(854\) | 1.50082 | 0.0513570 | ||||||||
\(855\) | −1.15691 | −0.0395657 | ||||||||
\(856\) | 9.28437 | 0.317333 | ||||||||
\(857\) | −16.7955 | −0.573724 | −0.286862 | − | 0.957972i | \(-0.592612\pi\) | ||||
−0.286862 | + | 0.957972i | \(0.592612\pi\) | |||||||
\(858\) | 3.26444 | 0.111446 | ||||||||
\(859\) | 50.5448 | 1.72457 | 0.862283 | − | 0.506427i | \(-0.169034\pi\) | ||||
0.862283 | + | 0.506427i | \(0.169034\pi\) | |||||||
\(860\) | 12.3300 | 0.420449 | ||||||||
\(861\) | 1.96614 | 0.0670059 | ||||||||
\(862\) | 12.9828 | 0.442196 | ||||||||
\(863\) | 6.29987 | 0.214450 | 0.107225 | − | 0.994235i | \(-0.465803\pi\) | ||||
0.107225 | + | 0.994235i | \(0.465803\pi\) | |||||||
\(864\) | −2.96263 | −0.100791 | ||||||||
\(865\) | 30.2082 | 1.02711 | ||||||||
\(866\) | −10.5182 | −0.357424 | ||||||||
\(867\) | 8.64561 | 0.293620 | ||||||||
\(868\) | 0.358294 | 0.0121613 | ||||||||
\(869\) | −5.82588 | −0.197630 | ||||||||
\(870\) | 1.98480 | 0.0672911 | ||||||||
\(871\) | 33.4246 | 1.13255 | ||||||||
\(872\) | 5.26206 | 0.178196 | ||||||||
\(873\) | 17.4542 | 0.590736 | ||||||||
\(874\) | −0.416538 | −0.0140896 | ||||||||
\(875\) | −6.76373 | −0.228656 | ||||||||
\(876\) | 1.50392 | 0.0508127 | ||||||||
\(877\) | 25.5113 | 0.861456 | 0.430728 | − | 0.902482i | \(-0.358257\pi\) | ||||
0.430728 | + | 0.902482i | \(0.358257\pi\) | |||||||
\(878\) | 7.20297 | 0.243088 | ||||||||
\(879\) | −6.44722 | −0.217459 | ||||||||
\(880\) | −1.53195 | −0.0516421 | ||||||||
\(881\) | −27.9488 | −0.941620 | −0.470810 | − | 0.882235i | \(-0.656038\pi\) | ||||
−0.470810 | + | 0.882235i | \(0.656038\pi\) | |||||||
\(882\) | −18.2211 | −0.613535 | ||||||||
\(883\) | −22.1577 | −0.745665 | −0.372833 | − | 0.927899i | \(-0.621613\pi\) | ||||
−0.372833 | + | 0.927899i | \(0.621613\pi\) | |||||||
\(884\) | −3.28225 | −0.110394 | ||||||||
\(885\) | 6.40449 | 0.215284 | ||||||||
\(886\) | 20.2810 | 0.681354 | ||||||||
\(887\) | 8.67845 | 0.291394 | 0.145697 | − | 0.989329i | \(-0.453458\pi\) | ||||
0.145697 | + | 0.989329i | \(0.453458\pi\) | |||||||
\(888\) | −2.40624 | −0.0807480 | ||||||||
\(889\) | 4.69871 | 0.157590 | ||||||||
\(890\) | 11.7199 | 0.392852 | ||||||||
\(891\) | 6.66784 | 0.223381 | ||||||||
\(892\) | −13.6319 | −0.456430 | ||||||||
\(893\) | −0.537210 | −0.0179771 | ||||||||
\(894\) | −6.38872 | −0.213671 | ||||||||
\(895\) | 27.4084 | 0.916163 | ||||||||
\(896\) | 0.576902 | 0.0192730 | ||||||||
\(897\) | 4.92084 | 0.164302 | ||||||||
\(898\) | 31.5168 | 1.05173 | ||||||||
\(899\) | 1.55707 | 0.0519314 | ||||||||
\(900\) | 7.25084 | 0.241695 | ||||||||
\(901\) | −6.05558 | −0.201741 | ||||||||
\(902\) | −6.59498 | −0.219589 | ||||||||
\(903\) | −2.39949 | −0.0798499 | ||||||||
\(904\) | −16.7854 | −0.558274 | ||||||||
\(905\) | 33.1704 | 1.10262 | ||||||||
\(906\) | −10.5728 | −0.351256 | ||||||||
\(907\) | −22.6484 | −0.752027 | −0.376013 | − | 0.926614i | \(-0.622705\pi\) | ||||
−0.376013 | + | 0.926614i | \(0.622705\pi\) | |||||||
\(908\) | 7.51079 | 0.249254 | ||||||||
\(909\) | 31.8806 | 1.05741 | ||||||||
\(910\) | −5.58287 | −0.185070 | ||||||||
\(911\) | 30.7384 | 1.01841 | 0.509204 | − | 0.860646i | \(-0.329940\pi\) | ||||
0.509204 | + | 0.860646i | \(0.329940\pi\) | |||||||
\(912\) | 0.142799 | 0.00472853 | ||||||||
\(913\) | −0.321166 | −0.0106290 | ||||||||
\(914\) | 31.8248 | 1.05267 | ||||||||
\(915\) | 2.05954 | 0.0680864 | ||||||||
\(916\) | −13.1694 | −0.435129 | ||||||||
\(917\) | −2.03879 | −0.0673268 | ||||||||
\(918\) | 1.53935 | 0.0508063 | ||||||||
\(919\) | −22.1039 | −0.729141 | −0.364570 | − | 0.931176i | \(-0.618784\pi\) | ||||
−0.364570 | + | 0.931176i | \(0.618784\pi\) | |||||||
\(920\) | −2.30927 | −0.0761344 | ||||||||
\(921\) | 0.646334 | 0.0212974 | ||||||||
\(922\) | 15.4987 | 0.510423 | ||||||||
\(923\) | 89.1792 | 2.93537 | ||||||||
\(924\) | 0.298127 | 0.00980766 | ||||||||
\(925\) | 12.3537 | 0.406187 | ||||||||
\(926\) | −39.0742 | −1.28406 | ||||||||
\(927\) | −2.36621 | −0.0777166 | ||||||||
\(928\) | 2.50711 | 0.0822998 | ||||||||
\(929\) | −5.23732 | −0.171831 | −0.0859154 | − | 0.996302i | \(-0.527381\pi\) | ||||
−0.0859154 | + | 0.996302i | \(0.527381\pi\) | |||||||
\(930\) | 0.491678 | 0.0161228 | ||||||||
\(931\) | 1.84233 | 0.0603799 | ||||||||
\(932\) | −8.17542 | −0.267795 | ||||||||
\(933\) | −4.32941 | −0.141739 | ||||||||
\(934\) | −30.6437 | −1.00269 | ||||||||
\(935\) | 0.795989 | 0.0260316 | ||||||||
\(936\) | 17.2640 | 0.564291 | ||||||||
\(937\) | −8.29459 | −0.270973 | −0.135486 | − | 0.990779i | \(-0.543260\pi\) | ||||
−0.135486 | + | 0.990779i | \(0.543260\pi\) | |||||||
\(938\) | 3.05251 | 0.0996681 | ||||||||
\(939\) | −7.97718 | −0.260325 | ||||||||
\(940\) | −2.97827 | −0.0971406 | ||||||||
\(941\) | −50.7882 | −1.65565 | −0.827825 | − | 0.560987i | \(-0.810422\pi\) | ||||
−0.827825 | + | 0.560987i | \(0.810422\pi\) | |||||||
\(942\) | −11.0260 | −0.359245 | ||||||||
\(943\) | −9.94130 | −0.323733 | ||||||||
\(944\) | 8.08984 | 0.263302 | ||||||||
\(945\) | 2.61833 | 0.0851743 | ||||||||
\(946\) | 8.04854 | 0.261681 | ||||||||
\(947\) | −26.3951 | −0.857724 | −0.428862 | − | 0.903370i | \(-0.641085\pi\) | ||||
−0.428862 | + | 0.903370i | \(0.641085\pi\) | |||||||
\(948\) | 3.01065 | 0.0977815 | ||||||||
\(949\) | −18.3838 | −0.596763 | ||||||||
\(950\) | −0.733132 | −0.0237859 | ||||||||
\(951\) | 16.5297 | 0.536014 | ||||||||
\(952\) | −0.299753 | −0.00971506 | ||||||||
\(953\) | 49.6464 | 1.60820 | 0.804102 | − | 0.594492i | \(-0.202647\pi\) | ||||
0.804102 | + | 0.594492i | \(0.202647\pi\) | |||||||
\(954\) | 31.8512 | 1.03122 | ||||||||
\(955\) | −10.0865 | −0.326392 | ||||||||
\(956\) | 2.81584 | 0.0910707 | ||||||||
\(957\) | 1.29560 | 0.0418809 | ||||||||
\(958\) | 12.4403 | 0.401928 | ||||||||
\(959\) | 8.91092 | 0.287749 | ||||||||
\(960\) | 0.791670 | 0.0255510 | ||||||||
\(961\) | −30.6143 | −0.987557 | ||||||||
\(962\) | 29.4137 | 0.948336 | ||||||||
\(963\) | 25.3737 | 0.817656 | ||||||||
\(964\) | 8.59567 | 0.276848 | ||||||||
\(965\) | −22.3631 | −0.719895 | ||||||||
\(966\) | 0.449398 | 0.0144591 | ||||||||
\(967\) | −8.50184 | −0.273401 | −0.136700 | − | 0.990612i | \(-0.543650\pi\) | ||||
−0.136700 | + | 0.990612i | \(0.543650\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −0.0741969 | −0.00238355 | ||||||||
\(970\) | −9.78396 | −0.314144 | ||||||||
\(971\) | 10.7205 | 0.344037 | 0.172018 | − | 0.985094i | \(-0.444971\pi\) | ||||
0.172018 | + | 0.985094i | \(0.444971\pi\) | |||||||
\(972\) | −12.3336 | −0.395601 | ||||||||
\(973\) | −3.81507 | −0.122306 | ||||||||
\(974\) | 40.5024 | 1.29778 | ||||||||
\(975\) | 8.66097 | 0.277373 | ||||||||
\(976\) | 2.60152 | 0.0832725 | ||||||||
\(977\) | 36.3637 | 1.16338 | 0.581690 | − | 0.813411i | \(-0.302392\pi\) | ||||
0.581690 | + | 0.813411i | \(0.302392\pi\) | |||||||
\(978\) | −12.4496 | −0.398096 | ||||||||
\(979\) | 7.65030 | 0.244505 | ||||||||
\(980\) | 10.2138 | 0.326268 | ||||||||
\(981\) | 14.3809 | 0.459147 | ||||||||
\(982\) | −13.4456 | −0.429067 | ||||||||
\(983\) | 16.5642 | 0.528315 | 0.264157 | − | 0.964480i | \(-0.414906\pi\) | ||||
0.264157 | + | 0.964480i | \(0.414906\pi\) | |||||||
\(984\) | 3.40810 | 0.108646 | ||||||||
\(985\) | −1.53195 | −0.0488121 | ||||||||
\(986\) | −1.30267 | −0.0414855 | ||||||||
\(987\) | 0.579589 | 0.0184485 | ||||||||
\(988\) | −1.74556 | −0.0555337 | ||||||||
\(989\) | 12.1324 | 0.385788 | ||||||||
\(990\) | −4.18674 | −0.133063 | ||||||||
\(991\) | 6.84666 | 0.217491 | 0.108746 | − | 0.994070i | \(-0.465317\pi\) | ||||
0.108746 | + | 0.994070i | \(0.465317\pi\) | |||||||
\(992\) | 0.621065 | 0.0197188 | ||||||||
\(993\) | −4.56101 | −0.144739 | ||||||||
\(994\) | 8.14433 | 0.258323 | ||||||||
\(995\) | 34.1096 | 1.08135 | ||||||||
\(996\) | 0.165970 | 0.00525895 | ||||||||
\(997\) | 27.3637 | 0.866616 | 0.433308 | − | 0.901246i | \(-0.357346\pi\) | ||||
0.433308 | + | 0.901246i | \(0.357346\pi\) | |||||||
\(998\) | 42.6557 | 1.35024 | ||||||||
\(999\) | −13.7948 | −0.436449 |
(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 | 4334.2.a.a.1.6 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.a.1.6 | ✓ | 15 | 1.1 | even | 1 | trivial |