Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3381,2,Mod(1,3381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, 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("3381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3381 = 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3381.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: | \(26.9974209234\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 15x^{6} + 11x^{5} + 75x^{4} - 35x^{3} - 141x^{2} + 37x + 80 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 483) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.74585\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3381.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.74585 | 1.94161 | 0.970804 | − | 0.239874i | \(-0.0771060\pi\) | ||||
0.970804 | + | 0.239874i | \(0.0771060\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.53968 | 2.76984 | ||||||||
\(5\) | 1.91481 | 0.856327 | 0.428163 | − | 0.903701i | \(-0.359161\pi\) | ||||
0.428163 | + | 0.903701i | \(0.359161\pi\) | |||||||
\(6\) | −2.74585 | −1.12099 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 9.71944 | 3.43634 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 5.25777 | 1.66265 | ||||||||
\(11\) | 5.32332 | 1.60504 | 0.802521 | − | 0.596624i | \(-0.203492\pi\) | ||||
0.802521 | + | 0.596624i | \(0.203492\pi\) | |||||||
\(12\) | −5.53968 | −1.59917 | ||||||||
\(13\) | 4.78352 | 1.32671 | 0.663355 | − | 0.748305i | \(-0.269132\pi\) | ||||
0.663355 | + | 0.748305i | \(0.269132\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.91481 | −0.494401 | ||||||||
\(16\) | 15.6087 | 3.90218 | ||||||||
\(17\) | −2.61781 | −0.634913 | −0.317457 | − | 0.948273i | \(-0.602829\pi\) | ||||
−0.317457 | + | 0.948273i | \(0.602829\pi\) | |||||||
\(18\) | 2.74585 | 0.647203 | ||||||||
\(19\) | −4.46024 | −1.02325 | −0.511624 | − | 0.859209i | \(-0.670956\pi\) | ||||
−0.511624 | + | 0.859209i | \(0.670956\pi\) | |||||||
\(20\) | 10.6074 | 2.37189 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.6170 | 3.11636 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −9.71944 | −1.98397 | ||||||||
\(25\) | −1.33352 | −0.266704 | ||||||||
\(26\) | 13.1348 | 2.57595 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.86099 | −1.64544 | −0.822722 | − | 0.568444i | \(-0.807546\pi\) | ||||
−0.822722 | + | 0.568444i | \(0.807546\pi\) | |||||||
\(30\) | −5.25777 | −0.959932 | ||||||||
\(31\) | −5.90898 | −1.06128 | −0.530642 | − | 0.847596i | \(-0.678049\pi\) | ||||
−0.530642 | + | 0.847596i | \(0.678049\pi\) | |||||||
\(32\) | 23.4204 | 4.14017 | ||||||||
\(33\) | −5.32332 | −0.926671 | ||||||||
\(34\) | −7.18812 | −1.23275 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.53968 | 0.923281 | ||||||||
\(37\) | −2.91929 | −0.479929 | −0.239964 | − | 0.970782i | \(-0.577136\pi\) | ||||
−0.239964 | + | 0.970782i | \(0.577136\pi\) | |||||||
\(38\) | −12.2471 | −1.98675 | ||||||||
\(39\) | −4.78352 | −0.765976 | ||||||||
\(40\) | 18.6108 | 2.94263 | ||||||||
\(41\) | −4.98968 | −0.779258 | −0.389629 | − | 0.920972i | \(-0.627397\pi\) | ||||
−0.389629 | + | 0.920972i | \(0.627397\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.45341 | −0.984136 | −0.492068 | − | 0.870557i | \(-0.663759\pi\) | ||||
−0.492068 | + | 0.870557i | \(0.663759\pi\) | |||||||
\(44\) | 29.4895 | 4.44571 | ||||||||
\(45\) | 1.91481 | 0.285442 | ||||||||
\(46\) | −2.74585 | −0.404853 | ||||||||
\(47\) | 6.94360 | 1.01283 | 0.506414 | − | 0.862291i | \(-0.330971\pi\) | ||||
0.506414 | + | 0.862291i | \(0.330971\pi\) | |||||||
\(48\) | −15.6087 | −2.25293 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.66165 | −0.517835 | ||||||||
\(51\) | 2.61781 | 0.366567 | ||||||||
\(52\) | 26.4992 | 3.67478 | ||||||||
\(53\) | 1.01228 | 0.139048 | 0.0695238 | − | 0.997580i | \(-0.477852\pi\) | ||||
0.0695238 | + | 0.997580i | \(0.477852\pi\) | |||||||
\(54\) | −2.74585 | −0.373663 | ||||||||
\(55\) | 10.1931 | 1.37444 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.46024 | 0.590773 | ||||||||
\(58\) | −24.3309 | −3.19481 | ||||||||
\(59\) | −6.15656 | −0.801515 | −0.400758 | − | 0.916184i | \(-0.631253\pi\) | ||||
−0.400758 | + | 0.916184i | \(0.631253\pi\) | |||||||
\(60\) | −10.6074 | −1.36941 | ||||||||
\(61\) | −2.24372 | −0.287279 | −0.143639 | − | 0.989630i | \(-0.545881\pi\) | ||||
−0.143639 | + | 0.989630i | \(0.545881\pi\) | |||||||
\(62\) | −16.2252 | −2.06060 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 33.0913 | 4.13641 | ||||||||
\(65\) | 9.15951 | 1.13610 | ||||||||
\(66\) | −14.6170 | −1.79923 | ||||||||
\(67\) | 9.38847 | 1.14698 | 0.573492 | − | 0.819211i | \(-0.305588\pi\) | ||||
0.573492 | + | 0.819211i | \(0.305588\pi\) | |||||||
\(68\) | −14.5019 | −1.75861 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2261 | −1.21362 | −0.606810 | − | 0.794847i | \(-0.707551\pi\) | ||||
−0.606810 | + | 0.794847i | \(0.707551\pi\) | |||||||
\(72\) | 9.71944 | 1.14545 | ||||||||
\(73\) | −3.85118 | −0.450747 | −0.225373 | − | 0.974272i | \(-0.572360\pi\) | ||||
−0.225373 | + | 0.974272i | \(0.572360\pi\) | |||||||
\(74\) | −8.01593 | −0.931833 | ||||||||
\(75\) | 1.33352 | 0.153982 | ||||||||
\(76\) | −24.7083 | −2.83424 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −13.1348 | −1.48723 | ||||||||
\(79\) | 2.97781 | 0.335030 | 0.167515 | − | 0.985870i | \(-0.446426\pi\) | ||||
0.167515 | + | 0.985870i | \(0.446426\pi\) | |||||||
\(80\) | 29.8877 | 3.34155 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −13.7009 | −1.51301 | ||||||||
\(83\) | 2.29460 | 0.251865 | 0.125932 | − | 0.992039i | \(-0.459808\pi\) | ||||
0.125932 | + | 0.992039i | \(0.459808\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.01260 | −0.543693 | ||||||||
\(86\) | −17.7201 | −1.91081 | ||||||||
\(87\) | 8.86099 | 0.949998 | ||||||||
\(88\) | 51.7397 | 5.51547 | ||||||||
\(89\) | 10.0816 | 1.06865 | 0.534325 | − | 0.845279i | \(-0.320566\pi\) | ||||
0.534325 | + | 0.845279i | \(0.320566\pi\) | |||||||
\(90\) | 5.25777 | 0.554217 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.53968 | −0.577552 | ||||||||
\(93\) | 5.90898 | 0.612732 | ||||||||
\(94\) | 19.0661 | 1.96651 | ||||||||
\(95\) | −8.54048 | −0.876235 | ||||||||
\(96\) | −23.4204 | −2.39033 | ||||||||
\(97\) | −13.2317 | −1.34347 | −0.671735 | − | 0.740791i | \(-0.734451\pi\) | ||||
−0.671735 | + | 0.740791i | \(0.734451\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.32332 | 0.535014 | ||||||||
\(100\) | −7.38728 | −0.738728 | ||||||||
\(101\) | 8.17507 | 0.813450 | 0.406725 | − | 0.913551i | \(-0.366671\pi\) | ||||
0.406725 | + | 0.913551i | \(0.366671\pi\) | |||||||
\(102\) | 7.18812 | 0.711730 | ||||||||
\(103\) | 12.1436 | 1.19655 | 0.598273 | − | 0.801293i | \(-0.295854\pi\) | ||||
0.598273 | + | 0.801293i | \(0.295854\pi\) | |||||||
\(104\) | 46.4931 | 4.55903 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.77957 | 0.269976 | ||||||||
\(107\) | 11.6601 | 1.12722 | 0.563611 | − | 0.826040i | \(-0.309412\pi\) | ||||
0.563611 | + | 0.826040i | \(0.309412\pi\) | |||||||
\(108\) | −5.53968 | −0.533056 | ||||||||
\(109\) | 0.884608 | 0.0847301 | 0.0423650 | − | 0.999102i | \(-0.486511\pi\) | ||||
0.0423650 | + | 0.999102i | \(0.486511\pi\) | |||||||
\(110\) | 27.9888 | 2.66863 | ||||||||
\(111\) | 2.91929 | 0.277087 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.00924 | −0.0949413 | −0.0474706 | − | 0.998873i | \(-0.515116\pi\) | ||||
−0.0474706 | + | 0.998873i | \(0.515116\pi\) | |||||||
\(114\) | 12.2471 | 1.14705 | ||||||||
\(115\) | −1.91481 | −0.178557 | ||||||||
\(116\) | −49.0871 | −4.55762 | ||||||||
\(117\) | 4.78352 | 0.442237 | ||||||||
\(118\) | −16.9050 | −1.55623 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −18.6108 | −1.69893 | ||||||||
\(121\) | 17.3378 | 1.57616 | ||||||||
\(122\) | −6.16091 | −0.557782 | ||||||||
\(123\) | 4.98968 | 0.449905 | ||||||||
\(124\) | −32.7339 | −2.93959 | ||||||||
\(125\) | −12.1275 | −1.08471 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.94220 | −0.172342 | −0.0861711 | − | 0.996280i | \(-0.527463\pi\) | ||||
−0.0861711 | + | 0.996280i | \(0.527463\pi\) | |||||||
\(128\) | 44.0229 | 3.89111 | ||||||||
\(129\) | 6.45341 | 0.568191 | ||||||||
\(130\) | 25.1506 | 2.20586 | ||||||||
\(131\) | 7.12385 | 0.622414 | 0.311207 | − | 0.950342i | \(-0.399267\pi\) | ||||
0.311207 | + | 0.950342i | \(0.399267\pi\) | |||||||
\(132\) | −29.4895 | −2.56673 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 25.7793 | 2.22699 | ||||||||
\(135\) | −1.91481 | −0.164800 | ||||||||
\(136\) | −25.4437 | −2.18178 | ||||||||
\(137\) | 6.12064 | 0.522921 | 0.261461 | − | 0.965214i | \(-0.415796\pi\) | ||||
0.261461 | + | 0.965214i | \(0.415796\pi\) | |||||||
\(138\) | 2.74585 | 0.233742 | ||||||||
\(139\) | 13.1313 | 1.11378 | 0.556892 | − | 0.830585i | \(-0.311994\pi\) | ||||
0.556892 | + | 0.830585i | \(0.311994\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.94360 | −0.584756 | ||||||||
\(142\) | −28.0794 | −2.35637 | ||||||||
\(143\) | 25.4642 | 2.12942 | ||||||||
\(144\) | 15.6087 | 1.30073 | ||||||||
\(145\) | −16.9671 | −1.40904 | ||||||||
\(146\) | −10.5748 | −0.875174 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −16.1720 | −1.32933 | ||||||||
\(149\) | 1.96204 | 0.160736 | 0.0803682 | − | 0.996765i | \(-0.474390\pi\) | ||||
0.0803682 | + | 0.996765i | \(0.474390\pi\) | |||||||
\(150\) | 3.66165 | 0.298972 | ||||||||
\(151\) | −15.6637 | −1.27469 | −0.637345 | − | 0.770579i | \(-0.719967\pi\) | ||||
−0.637345 | + | 0.770579i | \(0.719967\pi\) | |||||||
\(152\) | −43.3510 | −3.51623 | ||||||||
\(153\) | −2.61781 | −0.211638 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.3145 | −0.908805 | ||||||||
\(156\) | −26.4992 | −2.12163 | ||||||||
\(157\) | 17.4547 | 1.39304 | 0.696518 | − | 0.717539i | \(-0.254731\pi\) | ||||
0.696518 | + | 0.717539i | \(0.254731\pi\) | |||||||
\(158\) | 8.17661 | 0.650496 | ||||||||
\(159\) | −1.01228 | −0.0802792 | ||||||||
\(160\) | 44.8454 | 3.54534 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.74585 | 0.215734 | ||||||||
\(163\) | −11.8987 | −0.931975 | −0.465988 | − | 0.884791i | \(-0.654301\pi\) | ||||
−0.465988 | + | 0.884791i | \(0.654301\pi\) | |||||||
\(164\) | −27.6413 | −2.15842 | ||||||||
\(165\) | −10.1931 | −0.793534 | ||||||||
\(166\) | 6.30062 | 0.489023 | ||||||||
\(167\) | 9.48883 | 0.734267 | 0.367134 | − | 0.930168i | \(-0.380339\pi\) | ||||
0.367134 | + | 0.930168i | \(0.380339\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.88206 | 0.760158 | ||||||||
\(170\) | −13.7639 | −1.05564 | ||||||||
\(171\) | −4.46024 | −0.341083 | ||||||||
\(172\) | −35.7499 | −2.72590 | ||||||||
\(173\) | 5.46126 | 0.415212 | 0.207606 | − | 0.978213i | \(-0.433433\pi\) | ||||
0.207606 | + | 0.978213i | \(0.433433\pi\) | |||||||
\(174\) | 24.3309 | 1.84452 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 83.0903 | 6.26317 | ||||||||
\(177\) | 6.15656 | 0.462755 | ||||||||
\(178\) | 27.6826 | 2.07490 | ||||||||
\(179\) | −0.840159 | −0.0627964 | −0.0313982 | − | 0.999507i | \(-0.509996\pi\) | ||||
−0.0313982 | + | 0.999507i | \(0.509996\pi\) | |||||||
\(180\) | 10.6074 | 0.790630 | ||||||||
\(181\) | −17.2554 | −1.28258 | −0.641291 | − | 0.767298i | \(-0.721601\pi\) | ||||
−0.641291 | + | 0.767298i | \(0.721601\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.24372 | 0.165860 | ||||||||
\(184\) | −9.71944 | −0.716527 | ||||||||
\(185\) | −5.58988 | −0.410976 | ||||||||
\(186\) | 16.2252 | 1.18969 | ||||||||
\(187\) | −13.9355 | −1.01906 | ||||||||
\(188\) | 38.4653 | 2.80537 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −23.4509 | −1.70131 | ||||||||
\(191\) | −13.7884 | −0.997697 | −0.498849 | − | 0.866689i | \(-0.666244\pi\) | ||||
−0.498849 | + | 0.866689i | \(0.666244\pi\) | |||||||
\(192\) | −33.0913 | −2.38816 | ||||||||
\(193\) | −19.5816 | −1.40951 | −0.704756 | − | 0.709450i | \(-0.748943\pi\) | ||||
−0.704756 | + | 0.709450i | \(0.748943\pi\) | |||||||
\(194\) | −36.3321 | −2.60849 | ||||||||
\(195\) | −9.15951 | −0.655926 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.8814 | −1.34525 | −0.672623 | − | 0.739986i | \(-0.734832\pi\) | ||||
−0.672623 | + | 0.739986i | \(0.734832\pi\) | |||||||
\(198\) | 14.6170 | 1.03879 | ||||||||
\(199\) | 7.04079 | 0.499108 | 0.249554 | − | 0.968361i | \(-0.419716\pi\) | ||||
0.249554 | + | 0.968361i | \(0.419716\pi\) | |||||||
\(200\) | −12.9611 | −0.916486 | ||||||||
\(201\) | −9.38847 | −0.662212 | ||||||||
\(202\) | 22.4475 | 1.57940 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 14.5019 | 1.01533 | ||||||||
\(205\) | −9.55427 | −0.667299 | ||||||||
\(206\) | 33.3445 | 2.32322 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 74.6647 | 5.17707 | ||||||||
\(209\) | −23.7433 | −1.64236 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.1639 | −1.11277 | −0.556386 | − | 0.830924i | \(-0.687812\pi\) | ||||
−0.556386 | + | 0.830924i | \(0.687812\pi\) | |||||||
\(212\) | 5.60772 | 0.385140 | ||||||||
\(213\) | 10.2261 | 0.700683 | ||||||||
\(214\) | 32.0168 | 2.18862 | ||||||||
\(215\) | −12.3570 | −0.842742 | ||||||||
\(216\) | −9.71944 | −0.661324 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.42900 | 0.164513 | ||||||||
\(219\) | 3.85118 | 0.260239 | ||||||||
\(220\) | 56.4667 | 3.80698 | ||||||||
\(221\) | −12.5224 | −0.842345 | ||||||||
\(222\) | 8.01593 | 0.537994 | ||||||||
\(223\) | −1.72721 | −0.115662 | −0.0578312 | − | 0.998326i | \(-0.518419\pi\) | ||||
−0.0578312 | + | 0.998326i | \(0.518419\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.33352 | −0.0889014 | ||||||||
\(226\) | −2.77122 | −0.184339 | ||||||||
\(227\) | −3.06888 | −0.203688 | −0.101844 | − | 0.994800i | \(-0.532474\pi\) | ||||
−0.101844 | + | 0.994800i | \(0.532474\pi\) | |||||||
\(228\) | 24.7083 | 1.63635 | ||||||||
\(229\) | −2.87483 | −0.189974 | −0.0949872 | − | 0.995478i | \(-0.530281\pi\) | ||||
−0.0949872 | + | 0.995478i | \(0.530281\pi\) | |||||||
\(230\) | −5.25777 | −0.346687 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −86.1238 | −5.65431 | ||||||||
\(233\) | −9.06274 | −0.593720 | −0.296860 | − | 0.954921i | \(-0.595939\pi\) | ||||
−0.296860 | + | 0.954921i | \(0.595939\pi\) | |||||||
\(234\) | 13.1348 | 0.858650 | ||||||||
\(235\) | 13.2956 | 0.867312 | ||||||||
\(236\) | −34.1054 | −2.22007 | ||||||||
\(237\) | −2.97781 | −0.193429 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.5432 | 1.84630 | 0.923152 | − | 0.384436i | \(-0.125604\pi\) | ||||
0.923152 | + | 0.384436i | \(0.125604\pi\) | |||||||
\(240\) | −29.8877 | −1.92924 | ||||||||
\(241\) | 10.3623 | 0.667496 | 0.333748 | − | 0.942662i | \(-0.391687\pi\) | ||||
0.333748 | + | 0.942662i | \(0.391687\pi\) | |||||||
\(242\) | 47.6068 | 3.06028 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −12.4295 | −0.795716 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.7009 | 0.873538 | ||||||||
\(247\) | −21.3356 | −1.35755 | ||||||||
\(248\) | −57.4319 | −3.64693 | ||||||||
\(249\) | −2.29460 | −0.145414 | ||||||||
\(250\) | −33.3002 | −2.10609 | ||||||||
\(251\) | 13.6387 | 0.860865 | 0.430433 | − | 0.902623i | \(-0.358361\pi\) | ||||
0.430433 | + | 0.902623i | \(0.358361\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.32332 | −0.334674 | ||||||||
\(254\) | −5.33298 | −0.334621 | ||||||||
\(255\) | 5.01260 | 0.313901 | ||||||||
\(256\) | 54.6977 | 3.41861 | ||||||||
\(257\) | −10.9968 | −0.685962 | −0.342981 | − | 0.939342i | \(-0.611437\pi\) | ||||
−0.342981 | + | 0.939342i | \(0.611437\pi\) | |||||||
\(258\) | 17.7201 | 1.10320 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 50.7408 | 3.14681 | ||||||||
\(261\) | −8.86099 | −0.548481 | ||||||||
\(262\) | 19.5610 | 1.20848 | ||||||||
\(263\) | 8.29171 | 0.511289 | 0.255644 | − | 0.966771i | \(-0.417712\pi\) | ||||
0.255644 | + | 0.966771i | \(0.417712\pi\) | |||||||
\(264\) | −51.7397 | −3.18436 | ||||||||
\(265\) | 1.93832 | 0.119070 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.0816 | −0.616986 | ||||||||
\(268\) | 52.0092 | 3.17697 | ||||||||
\(269\) | 1.06056 | 0.0646635 | 0.0323318 | − | 0.999477i | \(-0.489707\pi\) | ||||
0.0323318 | + | 0.999477i | \(0.489707\pi\) | |||||||
\(270\) | −5.25777 | −0.319977 | ||||||||
\(271\) | 22.3153 | 1.35556 | 0.677779 | − | 0.735266i | \(-0.262943\pi\) | ||||
0.677779 | + | 0.735266i | \(0.262943\pi\) | |||||||
\(272\) | −40.8608 | −2.47755 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.8063 | 1.01531 | ||||||||
\(275\) | −7.09876 | −0.428071 | ||||||||
\(276\) | 5.53968 | 0.333450 | ||||||||
\(277\) | 24.4131 | 1.46684 | 0.733420 | − | 0.679776i | \(-0.237923\pi\) | ||||
0.733420 | + | 0.679776i | \(0.237923\pi\) | |||||||
\(278\) | 36.0566 | 2.16253 | ||||||||
\(279\) | −5.90898 | −0.353761 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.764668 | −0.0456163 | −0.0228081 | − | 0.999740i | \(-0.507261\pi\) | ||||
−0.0228081 | + | 0.999740i | \(0.507261\pi\) | |||||||
\(282\) | −19.0661 | −1.13537 | ||||||||
\(283\) | −2.82032 | −0.167650 | −0.0838252 | − | 0.996480i | \(-0.526714\pi\) | ||||
−0.0838252 | + | 0.996480i | \(0.526714\pi\) | |||||||
\(284\) | −56.6496 | −3.36153 | ||||||||
\(285\) | 8.54048 | 0.505895 | ||||||||
\(286\) | 69.9209 | 4.13451 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 23.4204 | 1.38006 | ||||||||
\(289\) | −10.1471 | −0.596885 | ||||||||
\(290\) | −46.5890 | −2.73580 | ||||||||
\(291\) | 13.2317 | 0.775653 | ||||||||
\(292\) | −21.3343 | −1.24850 | ||||||||
\(293\) | −32.2644 | −1.88490 | −0.942452 | − | 0.334342i | \(-0.891486\pi\) | ||||
−0.942452 | + | 0.334342i | \(0.891486\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.7886 | −0.686359 | ||||||||
\(296\) | −28.3739 | −1.64920 | ||||||||
\(297\) | −5.32332 | −0.308890 | ||||||||
\(298\) | 5.38746 | 0.312087 | ||||||||
\(299\) | −4.78352 | −0.276638 | ||||||||
\(300\) | 7.38728 | 0.426505 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −43.0100 | −2.47495 | ||||||||
\(303\) | −8.17507 | −0.469645 | ||||||||
\(304\) | −69.6186 | −3.99290 | ||||||||
\(305\) | −4.29628 | −0.246004 | ||||||||
\(306\) | −7.18812 | −0.410918 | ||||||||
\(307\) | 12.2320 | 0.698118 | 0.349059 | − | 0.937101i | \(-0.386501\pi\) | ||||
0.349059 | + | 0.937101i | \(0.386501\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.1436 | −0.690826 | ||||||||
\(310\) | −31.0680 | −1.76454 | ||||||||
\(311\) | −6.44397 | −0.365404 | −0.182702 | − | 0.983168i | \(-0.558484\pi\) | ||||
−0.182702 | + | 0.983168i | \(0.558484\pi\) | |||||||
\(312\) | −46.4931 | −2.63215 | ||||||||
\(313\) | 31.9752 | 1.80735 | 0.903673 | − | 0.428223i | \(-0.140860\pi\) | ||||
0.903673 | + | 0.428223i | \(0.140860\pi\) | |||||||
\(314\) | 47.9280 | 2.70473 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.4961 | 0.927979 | ||||||||
\(317\) | 14.2714 | 0.801564 | 0.400782 | − | 0.916173i | \(-0.368738\pi\) | ||||
0.400782 | + | 0.916173i | \(0.368738\pi\) | |||||||
\(318\) | −2.77957 | −0.155871 | ||||||||
\(319\) | −47.1699 | −2.64101 | ||||||||
\(320\) | 63.3633 | 3.54212 | ||||||||
\(321\) | −11.6601 | −0.650802 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.6761 | 0.649674 | ||||||||
\(324\) | 5.53968 | 0.307760 | ||||||||
\(325\) | −6.37892 | −0.353839 | ||||||||
\(326\) | −32.6719 | −1.80953 | ||||||||
\(327\) | −0.884608 | −0.0489189 | ||||||||
\(328\) | −48.4969 | −2.67779 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −27.9888 | −1.54073 | ||||||||
\(331\) | 5.19270 | 0.285416 | 0.142708 | − | 0.989765i | \(-0.454419\pi\) | ||||
0.142708 | + | 0.989765i | \(0.454419\pi\) | |||||||
\(332\) | 12.7114 | 0.697626 | ||||||||
\(333\) | −2.91929 | −0.159976 | ||||||||
\(334\) | 26.0549 | 1.42566 | ||||||||
\(335\) | 17.9771 | 0.982193 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.3455 | 1.48961 | 0.744803 | − | 0.667284i | \(-0.232543\pi\) | ||||
0.744803 | + | 0.667284i | \(0.232543\pi\) | |||||||
\(338\) | 27.1346 | 1.47593 | ||||||||
\(339\) | 1.00924 | 0.0548144 | ||||||||
\(340\) | −27.7682 | −1.50594 | ||||||||
\(341\) | −31.4554 | −1.70340 | ||||||||
\(342\) | −12.2471 | −0.662249 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −62.7236 | −3.38183 | ||||||||
\(345\) | 1.91481 | 0.103090 | ||||||||
\(346\) | 14.9958 | 0.806179 | ||||||||
\(347\) | 5.15907 | 0.276954 | 0.138477 | − | 0.990366i | \(-0.455779\pi\) | ||||
0.138477 | + | 0.990366i | \(0.455779\pi\) | |||||||
\(348\) | 49.0871 | 2.63134 | ||||||||
\(349\) | −15.1720 | −0.812140 | −0.406070 | − | 0.913842i | \(-0.633101\pi\) | ||||
−0.406070 | + | 0.913842i | \(0.633101\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.78352 | −0.255325 | ||||||||
\(352\) | 124.674 | 6.64515 | ||||||||
\(353\) | −4.97378 | −0.264728 | −0.132364 | − | 0.991201i | \(-0.542257\pi\) | ||||
−0.132364 | + | 0.991201i | \(0.542257\pi\) | |||||||
\(354\) | 16.9050 | 0.898489 | ||||||||
\(355\) | −19.5811 | −1.03925 | ||||||||
\(356\) | 55.8491 | 2.95999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.30695 | −0.121926 | ||||||||
\(359\) | 19.5574 | 1.03220 | 0.516099 | − | 0.856529i | \(-0.327384\pi\) | ||||
0.516099 | + | 0.856529i | \(0.327384\pi\) | |||||||
\(360\) | 18.6108 | 0.980877 | ||||||||
\(361\) | 0.893701 | 0.0470369 | ||||||||
\(362\) | −47.3807 | −2.49027 | ||||||||
\(363\) | −17.3378 | −0.909996 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.37427 | −0.385987 | ||||||||
\(366\) | 6.16091 | 0.322036 | ||||||||
\(367\) | 11.6525 | 0.608256 | 0.304128 | − | 0.952631i | \(-0.401635\pi\) | ||||
0.304128 | + | 0.952631i | \(0.401635\pi\) | |||||||
\(368\) | −15.6087 | −0.813662 | ||||||||
\(369\) | −4.98968 | −0.259753 | ||||||||
\(370\) | −15.3490 | −0.797954 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 32.7339 | 1.69717 | ||||||||
\(373\) | −13.2588 | −0.686516 | −0.343258 | − | 0.939241i | \(-0.611531\pi\) | ||||
−0.343258 | + | 0.939241i | \(0.611531\pi\) | |||||||
\(374\) | −38.2647 | −1.97862 | ||||||||
\(375\) | 12.1275 | 0.626259 | ||||||||
\(376\) | 67.4879 | 3.48042 | ||||||||
\(377\) | −42.3867 | −2.18303 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.81701 | −0.298800 | −0.149400 | − | 0.988777i | \(-0.547734\pi\) | ||||
−0.149400 | + | 0.988777i | \(0.547734\pi\) | |||||||
\(380\) | −47.3116 | −2.42703 | ||||||||
\(381\) | 1.94220 | 0.0995018 | ||||||||
\(382\) | −37.8610 | −1.93714 | ||||||||
\(383\) | −16.7857 | −0.857708 | −0.428854 | − | 0.903374i | \(-0.641083\pi\) | ||||
−0.428854 | + | 0.903374i | \(0.641083\pi\) | |||||||
\(384\) | −44.0229 | −2.24653 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −53.7680 | −2.73672 | ||||||||
\(387\) | −6.45341 | −0.328045 | ||||||||
\(388\) | −73.2992 | −3.72120 | ||||||||
\(389\) | 3.08411 | 0.156370 | 0.0781852 | − | 0.996939i | \(-0.475087\pi\) | ||||
0.0781852 | + | 0.996939i | \(0.475087\pi\) | |||||||
\(390\) | −25.1506 | −1.27355 | ||||||||
\(391\) | 2.61781 | 0.132389 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.12385 | −0.359351 | ||||||||
\(394\) | −51.8455 | −2.61194 | ||||||||
\(395\) | 5.70192 | 0.286895 | ||||||||
\(396\) | 29.4895 | 1.48190 | ||||||||
\(397\) | 20.6686 | 1.03733 | 0.518663 | − | 0.854979i | \(-0.326430\pi\) | ||||
0.518663 | + | 0.854979i | \(0.326430\pi\) | |||||||
\(398\) | 19.3329 | 0.969073 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.8146 | −1.04073 | ||||||||
\(401\) | 27.3184 | 1.36422 | 0.682109 | − | 0.731251i | \(-0.261063\pi\) | ||||
0.682109 | + | 0.731251i | \(0.261063\pi\) | |||||||
\(402\) | −25.7793 | −1.28576 | ||||||||
\(403\) | −28.2657 | −1.40801 | ||||||||
\(404\) | 45.2873 | 2.25313 | ||||||||
\(405\) | 1.91481 | 0.0951474 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.5403 | −0.770306 | ||||||||
\(408\) | 25.4437 | 1.25965 | ||||||||
\(409\) | −10.0609 | −0.497477 | −0.248739 | − | 0.968571i | \(-0.580016\pi\) | ||||
−0.248739 | + | 0.968571i | \(0.580016\pi\) | |||||||
\(410\) | −26.2346 | −1.29563 | ||||||||
\(411\) | −6.12064 | −0.301909 | ||||||||
\(412\) | 67.2718 | 3.31424 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.74585 | −0.134951 | ||||||||
\(415\) | 4.39371 | 0.215679 | ||||||||
\(416\) | 112.032 | 5.49281 | ||||||||
\(417\) | −13.1313 | −0.643044 | ||||||||
\(418\) | −65.1954 | −3.18881 | ||||||||
\(419\) | 17.1206 | 0.836396 | 0.418198 | − | 0.908356i | \(-0.362662\pi\) | ||||
0.418198 | + | 0.908356i | \(0.362662\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.4594 | −0.997129 | −0.498565 | − | 0.866853i | \(-0.666139\pi\) | ||||
−0.498565 | + | 0.866853i | \(0.666139\pi\) | |||||||
\(422\) | −44.3837 | −2.16057 | ||||||||
\(423\) | 6.94360 | 0.337609 | ||||||||
\(424\) | 9.83881 | 0.477815 | ||||||||
\(425\) | 3.49091 | 0.169334 | ||||||||
\(426\) | 28.0794 | 1.36045 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 64.5931 | 3.12223 | ||||||||
\(429\) | −25.4642 | −1.22942 | ||||||||
\(430\) | −33.9305 | −1.63628 | ||||||||
\(431\) | 18.0657 | 0.870194 | 0.435097 | − | 0.900383i | \(-0.356714\pi\) | ||||
0.435097 | + | 0.900383i | \(0.356714\pi\) | |||||||
\(432\) | −15.6087 | −0.750976 | ||||||||
\(433\) | 14.9439 | 0.718157 | 0.359079 | − | 0.933307i | \(-0.383091\pi\) | ||||
0.359079 | + | 0.933307i | \(0.383091\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.9671 | 0.813509 | ||||||||
\(436\) | 4.90045 | 0.234689 | ||||||||
\(437\) | 4.46024 | 0.213362 | ||||||||
\(438\) | 10.5748 | 0.505282 | ||||||||
\(439\) | 22.9749 | 1.09653 | 0.548265 | − | 0.836305i | \(-0.315288\pi\) | ||||
0.548265 | + | 0.836305i | \(0.315288\pi\) | |||||||
\(440\) | 99.0714 | 4.72305 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −34.3845 | −1.63550 | ||||||||
\(443\) | −13.6849 | −0.650187 | −0.325094 | − | 0.945682i | \(-0.605396\pi\) | ||||
−0.325094 | + | 0.945682i | \(0.605396\pi\) | |||||||
\(444\) | 16.1720 | 0.767487 | ||||||||
\(445\) | 19.3044 | 0.915114 | ||||||||
\(446\) | −4.74265 | −0.224571 | ||||||||
\(447\) | −1.96204 | −0.0928012 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.1186 | −0.902261 | −0.451130 | − | 0.892458i | \(-0.648979\pi\) | ||||
−0.451130 | + | 0.892458i | \(0.648979\pi\) | |||||||
\(450\) | −3.66165 | −0.172612 | ||||||||
\(451\) | −26.5617 | −1.25074 | ||||||||
\(452\) | −5.59087 | −0.262972 | ||||||||
\(453\) | 15.6637 | 0.735943 | ||||||||
\(454\) | −8.42667 | −0.395483 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 43.3510 | 2.03010 | ||||||||
\(457\) | −18.0657 | −0.845076 | −0.422538 | − | 0.906345i | \(-0.638861\pi\) | ||||
−0.422538 | + | 0.906345i | \(0.638861\pi\) | |||||||
\(458\) | −7.89386 | −0.368856 | ||||||||
\(459\) | 2.61781 | 0.122189 | ||||||||
\(460\) | −10.6074 | −0.494573 | ||||||||
\(461\) | −32.2584 | −1.50242 | −0.751211 | − | 0.660062i | \(-0.770530\pi\) | ||||
−0.751211 | + | 0.660062i | \(0.770530\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.3695 | 1.13255 | 0.566274 | − | 0.824217i | \(-0.308385\pi\) | ||||
0.566274 | + | 0.824217i | \(0.308385\pi\) | |||||||
\(464\) | −138.309 | −6.42083 | ||||||||
\(465\) | 11.3145 | 0.524699 | ||||||||
\(466\) | −24.8849 | −1.15277 | ||||||||
\(467\) | 33.6645 | 1.55781 | 0.778903 | − | 0.627144i | \(-0.215776\pi\) | ||||
0.778903 | + | 0.627144i | \(0.215776\pi\) | |||||||
\(468\) | 26.4992 | 1.22493 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 36.5078 | 1.68398 | ||||||||
\(471\) | −17.4547 | −0.804270 | ||||||||
\(472\) | −59.8383 | −2.75428 | ||||||||
\(473\) | −34.3536 | −1.57958 | ||||||||
\(474\) | −8.17661 | −0.375564 | ||||||||
\(475\) | 5.94782 | 0.272905 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.01228 | 0.0463492 | ||||||||
\(478\) | 78.3752 | 3.58480 | ||||||||
\(479\) | −32.7675 | −1.49718 | −0.748592 | − | 0.663030i | \(-0.769270\pi\) | ||||
−0.748592 | + | 0.663030i | \(0.769270\pi\) | |||||||
\(480\) | −44.8454 | −2.04690 | ||||||||
\(481\) | −13.9645 | −0.636726 | ||||||||
\(482\) | 28.4534 | 1.29602 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 96.0457 | 4.36571 | ||||||||
\(485\) | −25.3360 | −1.15045 | ||||||||
\(486\) | −2.74585 | −0.124554 | ||||||||
\(487\) | 21.7581 | 0.985954 | 0.492977 | − | 0.870042i | \(-0.335909\pi\) | ||||
0.492977 | + | 0.870042i | \(0.335909\pi\) | |||||||
\(488\) | −21.8077 | −0.987187 | ||||||||
\(489\) | 11.8987 | 0.538076 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.4957 | 1.69216 | 0.846078 | − | 0.533059i | \(-0.178958\pi\) | ||||
0.846078 | + | 0.533059i | \(0.178958\pi\) | |||||||
\(492\) | 27.6413 | 1.24616 | ||||||||
\(493\) | 23.1964 | 1.04471 | ||||||||
\(494\) | −58.5844 | −2.63584 | ||||||||
\(495\) | 10.1931 | 0.458147 | ||||||||
\(496\) | −92.2316 | −4.14132 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.30062 | −0.282338 | ||||||||
\(499\) | 7.62293 | 0.341249 | 0.170625 | − | 0.985336i | \(-0.445421\pi\) | ||||
0.170625 | + | 0.985336i | \(0.445421\pi\) | |||||||
\(500\) | −67.1823 | −3.00448 | ||||||||
\(501\) | −9.48883 | −0.423930 | ||||||||
\(502\) | 37.4497 | 1.67146 | ||||||||
\(503\) | 18.3255 | 0.817092 | 0.408546 | − | 0.912738i | \(-0.366036\pi\) | ||||
0.408546 | + | 0.912738i | \(0.366036\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.6537 | 0.696579 | ||||||||
\(506\) | −14.6170 | −0.649806 | ||||||||
\(507\) | −9.88206 | −0.438878 | ||||||||
\(508\) | −10.7592 | −0.477361 | ||||||||
\(509\) | −37.3481 | −1.65543 | −0.827713 | − | 0.561152i | \(-0.810358\pi\) | ||||
−0.827713 | + | 0.561152i | \(0.810358\pi\) | |||||||
\(510\) | 13.7639 | 0.609474 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 62.1458 | 2.74648 | ||||||||
\(513\) | 4.46024 | 0.196924 | ||||||||
\(514\) | −30.1956 | −1.33187 | ||||||||
\(515\) | 23.2526 | 1.02463 | ||||||||
\(516\) | 35.7499 | 1.57380 | ||||||||
\(517\) | 36.9630 | 1.62563 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.46126 | −0.239723 | ||||||||
\(520\) | 89.0253 | 3.90402 | ||||||||
\(521\) | 26.6237 | 1.16641 | 0.583204 | − | 0.812326i | \(-0.301799\pi\) | ||||
0.583204 | + | 0.812326i | \(0.301799\pi\) | |||||||
\(522\) | −24.3309 | −1.06494 | ||||||||
\(523\) | −40.8800 | −1.78756 | −0.893780 | − | 0.448506i | \(-0.851956\pi\) | ||||
−0.893780 | + | 0.448506i | \(0.851956\pi\) | |||||||
\(524\) | 39.4639 | 1.72399 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.7678 | 0.992722 | ||||||||
\(527\) | 15.4686 | 0.673823 | ||||||||
\(528\) | −83.0903 | −3.61604 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 5.32234 | 0.231188 | ||||||||
\(531\) | −6.15656 | −0.267172 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.8682 | −1.03385 | ||||||||
\(534\) | −27.6826 | −1.19794 | ||||||||
\(535\) | 22.3268 | 0.965270 | ||||||||
\(536\) | 91.2507 | 3.94143 | ||||||||
\(537\) | 0.840159 | 0.0362555 | ||||||||
\(538\) | 2.91214 | 0.125551 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −10.6074 | −0.456471 | ||||||||
\(541\) | 22.1375 | 0.951768 | 0.475884 | − | 0.879508i | \(-0.342128\pi\) | ||||
0.475884 | + | 0.879508i | \(0.342128\pi\) | |||||||
\(542\) | 61.2744 | 2.63196 | ||||||||
\(543\) | 17.2554 | 0.740499 | ||||||||
\(544\) | −61.3101 | −2.62865 | ||||||||
\(545\) | 1.69385 | 0.0725566 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.7940 | −1.06012 | −0.530058 | − | 0.847962i | \(-0.677830\pi\) | ||||
−0.530058 | + | 0.847962i | \(0.677830\pi\) | |||||||
\(548\) | 33.9064 | 1.44841 | ||||||||
\(549\) | −2.24372 | −0.0957595 | ||||||||
\(550\) | −19.4921 | −0.831147 | ||||||||
\(551\) | 39.5221 | 1.68370 | ||||||||
\(552\) | 9.71944 | 0.413687 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 67.0346 | 2.84803 | ||||||||
\(555\) | 5.58988 | 0.237277 | ||||||||
\(556\) | 72.7434 | 3.08501 | ||||||||
\(557\) | 10.5365 | 0.446445 | 0.223223 | − | 0.974767i | \(-0.428342\pi\) | ||||
0.223223 | + | 0.974767i | \(0.428342\pi\) | |||||||
\(558\) | −16.2252 | −0.686865 | ||||||||
\(559\) | −30.8700 | −1.30566 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.9355 | 0.588356 | ||||||||
\(562\) | −2.09966 | −0.0885689 | ||||||||
\(563\) | 4.12319 | 0.173772 | 0.0868859 | − | 0.996218i | \(-0.472308\pi\) | ||||
0.0868859 | + | 0.996218i | \(0.472308\pi\) | |||||||
\(564\) | −38.4653 | −1.61968 | ||||||||
\(565\) | −1.93250 | −0.0813008 | ||||||||
\(566\) | −7.74416 | −0.325511 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −99.3923 | −4.17041 | ||||||||
\(569\) | 20.0857 | 0.842038 | 0.421019 | − | 0.907052i | \(-0.361673\pi\) | ||||
0.421019 | + | 0.907052i | \(0.361673\pi\) | |||||||
\(570\) | 23.4509 | 0.982249 | ||||||||
\(571\) | 39.2874 | 1.64413 | 0.822064 | − | 0.569396i | \(-0.192823\pi\) | ||||
0.822064 | + | 0.569396i | \(0.192823\pi\) | |||||||
\(572\) | 141.064 | 5.89817 | ||||||||
\(573\) | 13.7884 | 0.576021 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.33352 | 0.0556117 | ||||||||
\(576\) | 33.0913 | 1.37880 | ||||||||
\(577\) | −6.54033 | −0.272277 | −0.136139 | − | 0.990690i | \(-0.543469\pi\) | ||||
−0.136139 | + | 0.990690i | \(0.543469\pi\) | |||||||
\(578\) | −27.8623 | −1.15892 | ||||||||
\(579\) | 19.5816 | 0.813782 | ||||||||
\(580\) | −93.9922 | −3.90281 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 36.3321 | 1.50601 | ||||||||
\(583\) | 5.38870 | 0.223177 | ||||||||
\(584\) | −37.4313 | −1.54892 | ||||||||
\(585\) | 9.15951 | 0.378699 | ||||||||
\(586\) | −88.5930 | −3.65974 | ||||||||
\(587\) | −45.0583 | −1.85976 | −0.929878 | − | 0.367868i | \(-0.880088\pi\) | ||||
−0.929878 | + | 0.367868i | \(0.880088\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.3554 | 1.08596 | ||||||||
\(590\) | −32.3697 | −1.33264 | ||||||||
\(591\) | 18.8814 | 0.776678 | ||||||||
\(592\) | −45.5665 | −1.87277 | ||||||||
\(593\) | −5.07341 | −0.208340 | −0.104170 | − | 0.994560i | \(-0.533219\pi\) | ||||
−0.104170 | + | 0.994560i | \(0.533219\pi\) | |||||||
\(594\) | −14.6170 | −0.599744 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.8691 | 0.445214 | ||||||||
\(597\) | −7.04079 | −0.288160 | ||||||||
\(598\) | −13.1348 | −0.537123 | ||||||||
\(599\) | 45.3530 | 1.85307 | 0.926536 | − | 0.376206i | \(-0.122771\pi\) | ||||
0.926536 | + | 0.376206i | \(0.122771\pi\) | |||||||
\(600\) | 12.9611 | 0.529134 | ||||||||
\(601\) | 4.71581 | 0.192362 | 0.0961810 | − | 0.995364i | \(-0.469337\pi\) | ||||
0.0961810 | + | 0.995364i | \(0.469337\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.38847 | 0.382328 | ||||||||
\(604\) | −86.7717 | −3.53069 | ||||||||
\(605\) | 33.1984 | 1.34971 | ||||||||
\(606\) | −22.4475 | −0.911867 | ||||||||
\(607\) | 31.9679 | 1.29754 | 0.648769 | − | 0.760985i | \(-0.275284\pi\) | ||||
0.648769 | + | 0.760985i | \(0.275284\pi\) | |||||||
\(608\) | −104.460 | −4.23642 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.7969 | −0.477644 | ||||||||
\(611\) | 33.2148 | 1.34373 | ||||||||
\(612\) | −14.5019 | −0.586203 | ||||||||
\(613\) | 17.4400 | 0.704396 | 0.352198 | − | 0.935926i | \(-0.385434\pi\) | ||||
0.352198 | + | 0.935926i | \(0.385434\pi\) | |||||||
\(614\) | 33.5873 | 1.35547 | ||||||||
\(615\) | 9.55427 | 0.385265 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.50110 | −0.100691 | −0.0503453 | − | 0.998732i | \(-0.516032\pi\) | ||||
−0.0503453 | + | 0.998732i | \(0.516032\pi\) | |||||||
\(618\) | −33.3445 | −1.34131 | ||||||||
\(619\) | −16.1932 | −0.650858 | −0.325429 | − | 0.945566i | \(-0.605509\pi\) | ||||
−0.325429 | + | 0.945566i | \(0.605509\pi\) | |||||||
\(620\) | −62.6790 | −2.51725 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −17.6942 | −0.709471 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −74.6647 | −2.98898 | ||||||||
\(625\) | −16.5541 | −0.662165 | ||||||||
\(626\) | 87.7991 | 3.50916 | ||||||||
\(627\) | 23.7433 | 0.948215 | ||||||||
\(628\) | 96.6935 | 3.85849 | ||||||||
\(629\) | 7.64216 | 0.304713 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.3726 | −1.01007 | −0.505033 | − | 0.863100i | \(-0.668520\pi\) | ||||
−0.505033 | + | 0.863100i | \(0.668520\pi\) | |||||||
\(632\) | 28.9426 | 1.15128 | ||||||||
\(633\) | 16.1639 | 0.642459 | ||||||||
\(634\) | 39.1872 | 1.55632 | ||||||||
\(635\) | −3.71893 | −0.147581 | ||||||||
\(636\) | −5.60772 | −0.222361 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −129.521 | −5.12780 | ||||||||
\(639\) | −10.2261 | −0.404540 | ||||||||
\(640\) | 84.2953 | 3.33206 | ||||||||
\(641\) | 2.56881 | 0.101462 | 0.0507310 | − | 0.998712i | \(-0.483845\pi\) | ||||
0.0507310 | + | 0.998712i | \(0.483845\pi\) | |||||||
\(642\) | −32.0168 | −1.26360 | ||||||||
\(643\) | −32.1446 | −1.26766 | −0.633829 | − | 0.773473i | \(-0.718518\pi\) | ||||
−0.633829 | + | 0.773473i | \(0.718518\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.3570 | 0.486558 | ||||||||
\(646\) | 32.0607 | 1.26141 | ||||||||
\(647\) | −34.5119 | −1.35680 | −0.678400 | − | 0.734692i | \(-0.737327\pi\) | ||||
−0.678400 | + | 0.734692i | \(0.737327\pi\) | |||||||
\(648\) | 9.71944 | 0.381816 | ||||||||
\(649\) | −32.7733 | −1.28647 | ||||||||
\(650\) | −17.5156 | −0.687017 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −65.9148 | −2.58142 | ||||||||
\(653\) | 20.6766 | 0.809137 | 0.404569 | − | 0.914508i | \(-0.367422\pi\) | ||||
0.404569 | + | 0.914508i | \(0.367422\pi\) | |||||||
\(654\) | −2.42900 | −0.0949814 | ||||||||
\(655\) | 13.6408 | 0.532990 | ||||||||
\(656\) | −77.8827 | −3.04081 | ||||||||
\(657\) | −3.85118 | −0.150249 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.2297 | −0.398491 | −0.199246 | − | 0.979950i | \(-0.563849\pi\) | ||||
−0.199246 | + | 0.979950i | \(0.563849\pi\) | |||||||
\(660\) | −56.4667 | −2.19796 | ||||||||
\(661\) | −4.66774 | −0.181554 | −0.0907771 | − | 0.995871i | \(-0.528935\pi\) | ||||
−0.0907771 | + | 0.995871i | \(0.528935\pi\) | |||||||
\(662\) | 14.2584 | 0.554167 | ||||||||
\(663\) | 12.5224 | 0.486328 | ||||||||
\(664\) | 22.3022 | 0.865494 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.01593 | −0.310611 | ||||||||
\(667\) | 8.86099 | 0.343099 | ||||||||
\(668\) | 52.5651 | 2.03381 | ||||||||
\(669\) | 1.72721 | 0.0667778 | ||||||||
\(670\) | 49.3624 | 1.90703 | ||||||||
\(671\) | −11.9440 | −0.461094 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.2826 | −1.39859 | −0.699296 | − | 0.714832i | \(-0.746503\pi\) | ||||
−0.699296 | + | 0.714832i | \(0.746503\pi\) | |||||||
\(674\) | 75.0867 | 2.89223 | ||||||||
\(675\) | 1.33352 | 0.0513272 | ||||||||
\(676\) | 54.7435 | 2.10552 | ||||||||
\(677\) | −39.6435 | −1.52362 | −0.761811 | − | 0.647799i | \(-0.775690\pi\) | ||||
−0.761811 | + | 0.647799i | \(0.775690\pi\) | |||||||
\(678\) | 2.77122 | 0.106428 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −48.7197 | −1.86832 | ||||||||
\(681\) | 3.06888 | 0.117600 | ||||||||
\(682\) | −86.3717 | −3.30734 | ||||||||
\(683\) | −13.8778 | −0.531019 | −0.265510 | − | 0.964108i | \(-0.585540\pi\) | ||||
−0.265510 | + | 0.964108i | \(0.585540\pi\) | |||||||
\(684\) | −24.7083 | −0.944745 | ||||||||
\(685\) | 11.7198 | 0.447792 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.87483 | 0.109682 | ||||||||
\(688\) | −100.730 | −3.84028 | ||||||||
\(689\) | 4.84227 | 0.184476 | ||||||||
\(690\) | 5.25777 | 0.200160 | ||||||||
\(691\) | −37.3305 | −1.42012 | −0.710059 | − | 0.704142i | \(-0.751332\pi\) | ||||
−0.710059 | + | 0.704142i | \(0.751332\pi\) | |||||||
\(692\) | 30.2537 | 1.15007 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.1660 | 0.537735 | ||||||||
\(695\) | 25.1439 | 0.953764 | ||||||||
\(696\) | 86.1238 | 3.26452 | ||||||||
\(697\) | 13.0621 | 0.494761 | ||||||||
\(698\) | −41.6601 | −1.57686 | ||||||||
\(699\) | 9.06274 | 0.342784 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.48359 | 0.282651 | 0.141326 | − | 0.989963i | \(-0.454864\pi\) | ||||
0.141326 | + | 0.989963i | \(0.454864\pi\) | |||||||
\(702\) | −13.1348 | −0.495742 | ||||||||
\(703\) | 13.0207 | 0.491086 | ||||||||
\(704\) | 176.155 | 6.63911 | ||||||||
\(705\) | −13.2956 | −0.500743 | ||||||||
\(706\) | −13.6572 | −0.513997 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 34.1054 | 1.28176 | ||||||||
\(709\) | 48.4901 | 1.82108 | 0.910542 | − | 0.413417i | \(-0.135665\pi\) | ||||
0.910542 | + | 0.413417i | \(0.135665\pi\) | |||||||
\(710\) | −53.7666 | −2.01783 | ||||||||
\(711\) | 2.97781 | 0.111677 | ||||||||
\(712\) | 97.9878 | 3.67225 | ||||||||
\(713\) | 5.90898 | 0.221293 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 48.7590 | 1.82348 | ||||||||
\(716\) | −4.65421 | −0.173936 | ||||||||
\(717\) | −28.5432 | −1.06596 | ||||||||
\(718\) | 53.7016 | 2.00412 | ||||||||
\(719\) | 16.1138 | 0.600943 | 0.300471 | − | 0.953791i | \(-0.402856\pi\) | ||||
0.300471 | + | 0.953791i | \(0.402856\pi\) | |||||||
\(720\) | 29.8877 | 1.11385 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.45397 | 0.0913272 | ||||||||
\(723\) | −10.3623 | −0.385379 | ||||||||
\(724\) | −95.5894 | −3.55255 | ||||||||
\(725\) | 11.8163 | 0.438847 | ||||||||
\(726\) | −47.6068 | −1.76686 | ||||||||
\(727\) | −16.2362 | −0.602167 | −0.301084 | − | 0.953598i | \(-0.597348\pi\) | ||||
−0.301084 | + | 0.953598i | \(0.597348\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −20.2486 | −0.749435 | ||||||||
\(731\) | 16.8938 | 0.624841 | ||||||||
\(732\) | 12.4295 | 0.459407 | ||||||||
\(733\) | −1.39404 | −0.0514901 | −0.0257450 | − | 0.999669i | \(-0.508196\pi\) | ||||
−0.0257450 | + | 0.999669i | \(0.508196\pi\) | |||||||
\(734\) | 31.9960 | 1.18099 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −23.4204 | −0.863286 | ||||||||
\(737\) | 49.9778 | 1.84096 | ||||||||
\(738\) | −13.7009 | −0.504338 | ||||||||
\(739\) | −8.19880 | −0.301598 | −0.150799 | − | 0.988564i | \(-0.548185\pi\) | ||||
−0.150799 | + | 0.988564i | \(0.548185\pi\) | |||||||
\(740\) | −30.9661 | −1.13834 | ||||||||
\(741\) | 21.3356 | 0.783784 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.6236 | −1.49034 | −0.745168 | − | 0.666877i | \(-0.767631\pi\) | ||||
−0.745168 | + | 0.666877i | \(0.767631\pi\) | |||||||
\(744\) | 57.4319 | 2.10556 | ||||||||
\(745\) | 3.75692 | 0.137643 | ||||||||
\(746\) | −36.4068 | −1.33295 | ||||||||
\(747\) | 2.29460 | 0.0839550 | ||||||||
\(748\) | −77.1981 | −2.82264 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 33.3002 | 1.21595 | ||||||||
\(751\) | 31.7668 | 1.15919 | 0.579594 | − | 0.814905i | \(-0.303211\pi\) | ||||
0.579594 | + | 0.814905i | \(0.303211\pi\) | |||||||
\(752\) | 108.381 | 3.95224 | ||||||||
\(753\) | −13.6387 | −0.497021 | ||||||||
\(754\) | −116.387 | −4.23858 | ||||||||
\(755\) | −29.9928 | −1.09155 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.9385 | 0.542950 | 0.271475 | − | 0.962445i | \(-0.412489\pi\) | ||||
0.271475 | + | 0.962445i | \(0.412489\pi\) | |||||||
\(758\) | −15.9726 | −0.580152 | ||||||||
\(759\) | 5.32332 | 0.193224 | ||||||||
\(760\) | −83.0087 | −3.01104 | ||||||||
\(761\) | −46.6199 | −1.68997 | −0.844985 | − | 0.534790i | \(-0.820391\pi\) | ||||
−0.844985 | + | 0.534790i | \(0.820391\pi\) | |||||||
\(762\) | 5.33298 | 0.193194 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −76.3837 | −2.76346 | ||||||||
\(765\) | −5.01260 | −0.181231 | ||||||||
\(766\) | −46.0909 | −1.66533 | ||||||||
\(767\) | −29.4500 | −1.06338 | ||||||||
\(768\) | −54.6977 | −1.97373 | ||||||||
\(769\) | 32.7623 | 1.18144 | 0.590720 | − | 0.806876i | \(-0.298844\pi\) | ||||
0.590720 | + | 0.806876i | \(0.298844\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.9968 | 0.396040 | ||||||||
\(772\) | −108.476 | −3.90413 | ||||||||
\(773\) | −39.4800 | −1.42000 | −0.709998 | − | 0.704204i | \(-0.751304\pi\) | ||||
−0.709998 | + | 0.704204i | \(0.751304\pi\) | |||||||
\(774\) | −17.7201 | −0.636936 | ||||||||
\(775\) | 7.87974 | 0.283049 | ||||||||
\(776\) | −128.604 | −4.61662 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.46849 | 0.303610 | ||||||||
\(779\) | 22.2552 | 0.797374 | ||||||||
\(780\) | −50.7408 | −1.81681 | ||||||||
\(781\) | −54.4370 | −1.94791 | ||||||||
\(782\) | 7.18812 | 0.257047 | ||||||||
\(783\) | 8.86099 | 0.316666 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33.4224 | 1.19289 | ||||||||
\(786\) | −19.5610 | −0.697719 | ||||||||
\(787\) | 20.5155 | 0.731298 | 0.365649 | − | 0.930753i | \(-0.380847\pi\) | ||||
0.365649 | + | 0.930753i | \(0.380847\pi\) | |||||||
\(788\) | −104.597 | −3.72612 | ||||||||
\(789\) | −8.29171 | −0.295193 | ||||||||
\(790\) | 15.6566 | 0.557038 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 51.7397 | 1.83849 | ||||||||
\(793\) | −10.7329 | −0.381135 | ||||||||
\(794\) | 56.7528 | 2.01408 | ||||||||
\(795\) | −1.93832 | −0.0687452 | ||||||||
\(796\) | 39.0038 | 1.38245 | ||||||||
\(797\) | −11.1887 | −0.396325 | −0.198162 | − | 0.980169i | \(-0.563497\pi\) | ||||
−0.198162 | + | 0.980169i | \(0.563497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.1770 | −0.643058 | ||||||||
\(800\) | −31.2315 | −1.10420 | ||||||||
\(801\) | 10.0816 | 0.356217 | ||||||||
\(802\) | 75.0123 | 2.64878 | ||||||||
\(803\) | −20.5011 | −0.723468 | ||||||||
\(804\) | −52.0092 | −1.83422 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −77.6133 | −2.73381 | ||||||||
\(807\) | −1.06056 | −0.0373335 | ||||||||
\(808\) | 79.4571 | 2.79529 | ||||||||
\(809\) | 8.83213 | 0.310521 | 0.155260 | − | 0.987874i | \(-0.450378\pi\) | ||||
0.155260 | + | 0.987874i | \(0.450378\pi\) | |||||||
\(810\) | 5.25777 | 0.184739 | ||||||||
\(811\) | −40.0206 | −1.40531 | −0.702657 | − | 0.711529i | \(-0.748003\pi\) | ||||
−0.702657 | + | 0.711529i | \(0.748003\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.3153 | −0.782632 | ||||||||
\(814\) | −42.6714 | −1.49563 | ||||||||
\(815\) | −22.7836 | −0.798076 | ||||||||
\(816\) | 40.8608 | 1.43041 | ||||||||
\(817\) | 28.7837 | 1.00702 | ||||||||
\(818\) | −27.6256 | −0.965906 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −52.9277 | −1.84831 | ||||||||
\(821\) | −33.6641 | −1.17488 | −0.587442 | − | 0.809266i | \(-0.699865\pi\) | ||||
−0.587442 | + | 0.809266i | \(0.699865\pi\) | |||||||
\(822\) | −16.8063 | −0.586189 | ||||||||
\(823\) | 12.3738 | 0.431323 | 0.215662 | − | 0.976468i | \(-0.430809\pi\) | ||||
0.215662 | + | 0.976468i | \(0.430809\pi\) | |||||||
\(824\) | 118.029 | 4.11174 | ||||||||
\(825\) | 7.09876 | 0.247147 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.19126 | 0.284838 | 0.142419 | − | 0.989806i | \(-0.454512\pi\) | ||||
0.142419 | + | 0.989806i | \(0.454512\pi\) | |||||||
\(828\) | −5.53968 | −0.192517 | ||||||||
\(829\) | 8.00301 | 0.277956 | 0.138978 | − | 0.990295i | \(-0.455618\pi\) | ||||
0.138978 | + | 0.990295i | \(0.455618\pi\) | |||||||
\(830\) | 12.0645 | 0.418764 | ||||||||
\(831\) | −24.4131 | −0.846881 | ||||||||
\(832\) | 158.293 | 5.48781 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −36.0566 | −1.24854 | ||||||||
\(835\) | 18.1693 | 0.628773 | ||||||||
\(836\) | −131.530 | −4.54907 | ||||||||
\(837\) | 5.90898 | 0.204244 | ||||||||
\(838\) | 47.0106 | 1.62395 | ||||||||
\(839\) | 30.7825 | 1.06273 | 0.531365 | − | 0.847143i | \(-0.321679\pi\) | ||||
0.531365 | + | 0.847143i | \(0.321679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49.5171 | 1.70749 | ||||||||
\(842\) | −56.1784 | −1.93603 | ||||||||
\(843\) | 0.764668 | 0.0263366 | ||||||||
\(844\) | −89.5431 | −3.08220 | ||||||||
\(845\) | 18.9222 | 0.650944 | ||||||||
\(846\) | 19.0661 | 0.655505 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15.8004 | 0.542589 | ||||||||
\(849\) | 2.82032 | 0.0967930 | ||||||||
\(850\) | 9.58551 | 0.328780 | ||||||||
\(851\) | 2.91929 | 0.100072 | ||||||||
\(852\) | 56.6496 | 1.94078 | ||||||||
\(853\) | −37.1025 | −1.27037 | −0.635183 | − | 0.772362i | \(-0.719075\pi\) | ||||
−0.635183 | + | 0.772362i | \(0.719075\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.54048 | −0.292078 | ||||||||
\(856\) | 113.329 | 3.87352 | ||||||||
\(857\) | −39.2181 | −1.33966 | −0.669832 | − | 0.742513i | \(-0.733634\pi\) | ||||
−0.669832 | + | 0.742513i | \(0.733634\pi\) | |||||||
\(858\) | −69.9209 | −2.38706 | ||||||||
\(859\) | 26.5529 | 0.905972 | 0.452986 | − | 0.891518i | \(-0.350359\pi\) | ||||
0.452986 | + | 0.891518i | \(0.350359\pi\) | |||||||
\(860\) | −68.4540 | −2.33426 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 49.6057 | 1.68958 | ||||||||
\(863\) | −43.5713 | −1.48318 | −0.741591 | − | 0.670852i | \(-0.765929\pi\) | ||||
−0.741591 | + | 0.670852i | \(0.765929\pi\) | |||||||
\(864\) | −23.4204 | −0.796777 | ||||||||
\(865\) | 10.4572 | 0.355557 | ||||||||
\(866\) | 41.0337 | 1.39438 | ||||||||
\(867\) | 10.1471 | 0.344612 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.8518 | 0.537737 | ||||||||
\(870\) | 46.5890 | 1.57951 | ||||||||
\(871\) | 44.9099 | 1.52171 | ||||||||
\(872\) | 8.59789 | 0.291161 | ||||||||
\(873\) | −13.2317 | −0.447824 | ||||||||
\(874\) | 12.2471 | 0.414265 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 21.3343 | 0.720821 | ||||||||
\(877\) | −56.6084 | −1.91153 | −0.955765 | − | 0.294133i | \(-0.904969\pi\) | ||||
−0.955765 | + | 0.294133i | \(0.904969\pi\) | |||||||
\(878\) | 63.0855 | 2.12903 | ||||||||
\(879\) | 32.2644 | 1.08825 | ||||||||
\(880\) | 159.102 | 5.36332 | ||||||||
\(881\) | −12.0366 | −0.405524 | −0.202762 | − | 0.979228i | \(-0.564992\pi\) | ||||
−0.202762 | + | 0.979228i | \(0.564992\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.42054 | 0.0814577 | 0.0407289 | − | 0.999170i | \(-0.487032\pi\) | ||||
0.0407289 | + | 0.999170i | \(0.487032\pi\) | |||||||
\(884\) | −69.3699 | −2.33316 | ||||||||
\(885\) | 11.7886 | 0.396270 | ||||||||
\(886\) | −37.5765 | −1.26241 | ||||||||
\(887\) | −17.2377 | −0.578786 | −0.289393 | − | 0.957210i | \(-0.593453\pi\) | ||||
−0.289393 | + | 0.957210i | \(0.593453\pi\) | |||||||
\(888\) | 28.3739 | 0.952165 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 53.0069 | 1.77679 | ||||||||
\(891\) | 5.32332 | 0.178338 | ||||||||
\(892\) | −9.56819 | −0.320367 | ||||||||
\(893\) | −30.9701 | −1.03637 | ||||||||
\(894\) | −5.38746 | −0.180184 | ||||||||
\(895\) | −1.60874 | −0.0537743 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.78352 | 0.159717 | ||||||||
\(898\) | −52.4967 | −1.75184 | ||||||||
\(899\) | 52.3594 | 1.74628 | ||||||||
\(900\) | −7.38728 | −0.246243 | ||||||||
\(901\) | −2.64997 | −0.0882832 | ||||||||
\(902\) | −72.9344 | −2.42845 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.80924 | −0.326251 | ||||||||
\(905\) | −33.0407 | −1.09831 | ||||||||
\(906\) | 43.0100 | 1.42891 | ||||||||
\(907\) | −23.1026 | −0.767110 | −0.383555 | − | 0.923518i | \(-0.625300\pi\) | ||||
−0.383555 | + | 0.923518i | \(0.625300\pi\) | |||||||
\(908\) | −17.0006 | −0.564185 | ||||||||
\(909\) | 8.17507 | 0.271150 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.5226 | −0.746209 | −0.373104 | − | 0.927789i | \(-0.621707\pi\) | ||||
−0.373104 | + | 0.927789i | \(0.621707\pi\) | |||||||
\(912\) | 69.6186 | 2.30530 | ||||||||
\(913\) | 12.2149 | 0.404254 | ||||||||
\(914\) | −49.6056 | −1.64081 | ||||||||
\(915\) | 4.29628 | 0.142031 | ||||||||
\(916\) | −15.9257 | −0.526199 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 7.18812 | 0.237243 | ||||||||
\(919\) | −15.1590 | −0.500049 | −0.250025 | − | 0.968239i | \(-0.580439\pi\) | ||||
−0.250025 | + | 0.968239i | \(0.580439\pi\) | |||||||
\(920\) | −18.6108 | −0.613581 | ||||||||
\(921\) | −12.2320 | −0.403059 | ||||||||
\(922\) | −88.5766 | −2.91712 | ||||||||
\(923\) | −48.9169 | −1.61012 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.89294 | 0.127999 | ||||||||
\(926\) | 66.9150 | 2.19896 | ||||||||
\(927\) | 12.1436 | 0.398848 | ||||||||
\(928\) | −207.527 | −6.81242 | ||||||||
\(929\) | −47.7655 | −1.56713 | −0.783567 | − | 0.621307i | \(-0.786602\pi\) | ||||
−0.783567 | + | 0.621307i | \(0.786602\pi\) | |||||||
\(930\) | 31.0680 | 1.01876 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −50.2047 | −1.64451 | ||||||||
\(933\) | 6.44397 | 0.210966 | ||||||||
\(934\) | 92.4376 | 3.02465 | ||||||||
\(935\) | −26.6837 | −0.872650 | ||||||||
\(936\) | 46.4931 | 1.51968 | ||||||||
\(937\) | 55.2717 | 1.80565 | 0.902824 | − | 0.430011i | \(-0.141490\pi\) | ||||
0.902824 | + | 0.430011i | \(0.141490\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.9752 | −1.04347 | ||||||||
\(940\) | 73.6536 | 2.40232 | ||||||||
\(941\) | −9.61902 | −0.313571 | −0.156786 | − | 0.987633i | \(-0.550113\pi\) | ||||
−0.156786 | + | 0.987633i | \(0.550113\pi\) | |||||||
\(942\) | −47.9280 | −1.56158 | ||||||||
\(943\) | 4.98968 | 0.162486 | ||||||||
\(944\) | −96.0961 | −3.12766 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −94.3298 | −3.06693 | ||||||||
\(947\) | −40.9406 | −1.33039 | −0.665195 | − | 0.746670i | \(-0.731652\pi\) | ||||
−0.665195 | + | 0.746670i | \(0.731652\pi\) | |||||||
\(948\) | −16.4961 | −0.535769 | ||||||||
\(949\) | −18.4222 | −0.598010 | ||||||||
\(950\) | 16.3318 | 0.529874 | ||||||||
\(951\) | −14.2714 | −0.462783 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.0752 | −1.29816 | −0.649081 | − | 0.760719i | \(-0.724846\pi\) | ||||
−0.649081 | + | 0.760719i | \(0.724846\pi\) | |||||||
\(954\) | 2.77957 | 0.0899920 | ||||||||
\(955\) | −26.4022 | −0.854355 | ||||||||
\(956\) | 158.120 | 5.11397 | ||||||||
\(957\) | 47.1699 | 1.52479 | ||||||||
\(958\) | −89.9746 | −2.90695 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −63.3633 | −2.04504 | ||||||||
\(961\) | 3.91599 | 0.126322 | ||||||||
\(962\) | −38.3444 | −1.23627 | ||||||||
\(963\) | 11.6601 | 0.375741 | ||||||||
\(964\) | 57.4040 | 1.84886 | ||||||||
\(965\) | −37.4949 | −1.20700 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.8542 | 1.47457 | 0.737285 | − | 0.675582i | \(-0.236107\pi\) | ||||
0.737285 | + | 0.675582i | \(0.236107\pi\) | |||||||
\(968\) | 168.513 | 5.41622 | ||||||||
\(969\) | −11.6761 | −0.375089 | ||||||||
\(970\) | −69.5689 | −2.23372 | ||||||||
\(971\) | 30.7243 | 0.985991 | 0.492996 | − | 0.870032i | \(-0.335902\pi\) | ||||
0.492996 | + | 0.870032i | \(0.335902\pi\) | |||||||
\(972\) | −5.53968 | −0.177685 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 59.7445 | 1.91434 | ||||||||
\(975\) | 6.37892 | 0.204289 | ||||||||
\(976\) | −35.0216 | −1.12101 | ||||||||
\(977\) | 0.268936 | 0.00860402 | 0.00430201 | − | 0.999991i | \(-0.498631\pi\) | ||||
0.00430201 | + | 0.999991i | \(0.498631\pi\) | |||||||
\(978\) | 32.6719 | 1.04473 | ||||||||
\(979\) | 53.6678 | 1.71523 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.884608 | 0.0282434 | ||||||||
\(982\) | 102.957 | 3.28550 | ||||||||
\(983\) | 8.59485 | 0.274133 | 0.137067 | − | 0.990562i | \(-0.456233\pi\) | ||||
0.137067 | + | 0.990562i | \(0.456233\pi\) | |||||||
\(984\) | 48.4969 | 1.54603 | ||||||||
\(985\) | −36.1542 | −1.15197 | ||||||||
\(986\) | 63.6939 | 2.02843 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −118.193 | −3.76021 | ||||||||
\(989\) | 6.45341 | 0.205207 | ||||||||
\(990\) | 27.9888 | 0.889542 | ||||||||
\(991\) | 24.2310 | 0.769722 | 0.384861 | − | 0.922975i | \(-0.374249\pi\) | ||||
0.384861 | + | 0.922975i | \(0.374249\pi\) | |||||||
\(992\) | −138.390 | −4.39390 | ||||||||
\(993\) | −5.19270 | −0.164785 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.4817 | 0.427400 | ||||||||
\(996\) | −12.7114 | −0.402775 | ||||||||
\(997\) | 37.9955 | 1.20333 | 0.601665 | − | 0.798749i | \(-0.294504\pi\) | ||||
0.601665 | + | 0.798749i | \(0.294504\pi\) | |||||||
\(998\) | 20.9314 | 0.662572 | ||||||||
\(999\) | 2.91929 | 0.0923623 |
(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 | 3381.2.a.be.1.8 | 8 | ||
7.3 | odd | 6 | 483.2.i.g.415.1 | yes | 16 | ||
7.5 | odd | 6 | 483.2.i.g.277.1 | ✓ | 16 | ||
7.6 | odd | 2 | 3381.2.a.bf.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.g.277.1 | ✓ | 16 | 7.5 | odd | 6 | ||
483.2.i.g.415.1 | yes | 16 | 7.3 | odd | 6 | ||
3381.2.a.be.1.8 | 8 | 1.1 | even | 1 | trivial | ||
3381.2.a.bf.1.8 | 8 | 7.6 | odd | 2 |