Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.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: | \(31.9481458487\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.40 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.82225 | −1.28853 | −0.644263 | − | 0.764804i | \(-0.722836\pi\) | ||||
−0.644263 | + | 0.764804i | \(0.722836\pi\) | |||||||
\(3\) | 2.68606 | 1.55080 | 0.775398 | − | 0.631473i | \(-0.217549\pi\) | ||||
0.775398 | + | 0.631473i | \(0.217549\pi\) | |||||||
\(4\) | 1.32060 | 0.660299 | ||||||||
\(5\) | −4.13220 | −1.84797 | −0.923987 | − | 0.382423i | \(-0.875090\pi\) | ||||
−0.923987 | + | 0.382423i | \(0.875090\pi\) | |||||||
\(6\) | −4.89467 | −1.99824 | ||||||||
\(7\) | 5.17565 | 1.95621 | 0.978107 | − | 0.208105i | \(-0.0667294\pi\) | ||||
0.978107 | + | 0.208105i | \(0.0667294\pi\) | |||||||
\(8\) | 1.23804 | 0.437714 | ||||||||
\(9\) | 4.21490 | 1.40497 | ||||||||
\(10\) | 7.52990 | 2.38116 | ||||||||
\(11\) | −3.00578 | −0.906277 | −0.453138 | − | 0.891440i | \(-0.649696\pi\) | ||||
−0.453138 | + | 0.891440i | \(0.649696\pi\) | |||||||
\(12\) | 3.54720 | 1.02399 | ||||||||
\(13\) | 0.487304 | 0.135154 | 0.0675769 | − | 0.997714i | \(-0.478473\pi\) | ||||
0.0675769 | + | 0.997714i | \(0.478473\pi\) | |||||||
\(14\) | −9.43134 | −2.52063 | ||||||||
\(15\) | −11.0993 | −2.86583 | ||||||||
\(16\) | −4.89722 | −1.22430 | ||||||||
\(17\) | 1.27456 | 0.309125 | 0.154563 | − | 0.987983i | \(-0.450603\pi\) | ||||
0.154563 | + | 0.987983i | \(0.450603\pi\) | |||||||
\(18\) | −7.68061 | −1.81034 | ||||||||
\(19\) | 5.37940 | 1.23412 | 0.617059 | − | 0.786917i | \(-0.288324\pi\) | ||||
0.617059 | + | 0.786917i | \(0.288324\pi\) | |||||||
\(20\) | −5.45697 | −1.22022 | ||||||||
\(21\) | 13.9021 | 3.03369 | ||||||||
\(22\) | 5.47728 | 1.16776 | ||||||||
\(23\) | −0.0884748 | −0.0184483 | −0.00922413 | − | 0.999957i | \(-0.502936\pi\) | ||||
−0.00922413 | + | 0.999957i | \(0.502936\pi\) | |||||||
\(24\) | 3.32545 | 0.678804 | ||||||||
\(25\) | 12.0751 | 2.41501 | ||||||||
\(26\) | −0.887990 | −0.174149 | ||||||||
\(27\) | 3.26329 | 0.628021 | ||||||||
\(28\) | 6.83496 | 1.29169 | ||||||||
\(29\) | 2.32622 | 0.431968 | 0.215984 | − | 0.976397i | \(-0.430704\pi\) | ||||
0.215984 | + | 0.976397i | \(0.430704\pi\) | |||||||
\(30\) | 20.2257 | 3.69270 | ||||||||
\(31\) | 7.57211 | 1.35999 | 0.679996 | − | 0.733216i | \(-0.261982\pi\) | ||||
0.679996 | + | 0.733216i | \(0.261982\pi\) | |||||||
\(32\) | 6.44788 | 1.13983 | ||||||||
\(33\) | −8.07369 | −1.40545 | ||||||||
\(34\) | −2.32256 | −0.398316 | ||||||||
\(35\) | −21.3868 | −3.61503 | ||||||||
\(36\) | 5.56619 | 0.927698 | ||||||||
\(37\) | −4.84346 | −0.796259 | −0.398130 | − | 0.917329i | \(-0.630341\pi\) | ||||
−0.398130 | + | 0.917329i | \(0.630341\pi\) | |||||||
\(38\) | −9.80261 | −1.59019 | ||||||||
\(39\) | 1.30893 | 0.209596 | ||||||||
\(40\) | −5.11583 | −0.808884 | ||||||||
\(41\) | −1.44912 | −0.226314 | −0.113157 | − | 0.993577i | \(-0.536096\pi\) | ||||
−0.113157 | + | 0.993577i | \(0.536096\pi\) | |||||||
\(42\) | −25.3331 | −3.90898 | ||||||||
\(43\) | −10.7400 | −1.63784 | −0.818919 | − | 0.573909i | \(-0.805426\pi\) | ||||
−0.818919 | + | 0.573909i | \(0.805426\pi\) | |||||||
\(44\) | −3.96943 | −0.598413 | ||||||||
\(45\) | −17.4168 | −2.59634 | ||||||||
\(46\) | 0.161223 | 0.0237711 | ||||||||
\(47\) | 1.02412 | 0.149384 | 0.0746920 | − | 0.997207i | \(-0.476203\pi\) | ||||
0.0746920 | + | 0.997207i | \(0.476203\pi\) | |||||||
\(48\) | −13.1542 | −1.89865 | ||||||||
\(49\) | 19.7874 | 2.82677 | ||||||||
\(50\) | −22.0038 | −3.11180 | ||||||||
\(51\) | 3.42353 | 0.479390 | ||||||||
\(52\) | 0.643532 | 0.0892419 | ||||||||
\(53\) | 2.55300 | 0.350681 | 0.175341 | − | 0.984508i | \(-0.443897\pi\) | ||||
0.175341 | + | 0.984508i | \(0.443897\pi\) | |||||||
\(54\) | −5.94654 | −0.809222 | ||||||||
\(55\) | 12.4205 | 1.67478 | ||||||||
\(56\) | 6.40767 | 0.856261 | ||||||||
\(57\) | 14.4494 | 1.91387 | ||||||||
\(58\) | −4.23896 | −0.556602 | ||||||||
\(59\) | −0.415687 | −0.0541178 | −0.0270589 | − | 0.999634i | \(-0.508614\pi\) | ||||
−0.0270589 | + | 0.999634i | \(0.508614\pi\) | |||||||
\(60\) | −14.6577 | −1.89231 | ||||||||
\(61\) | −4.77911 | −0.611902 | −0.305951 | − | 0.952047i | \(-0.598974\pi\) | ||||
−0.305951 | + | 0.952047i | \(0.598974\pi\) | |||||||
\(62\) | −13.7983 | −1.75238 | ||||||||
\(63\) | 21.8149 | 2.74842 | ||||||||
\(64\) | −1.95521 | −0.244401 | ||||||||
\(65\) | −2.01364 | −0.249761 | ||||||||
\(66\) | 14.7123 | 1.81096 | ||||||||
\(67\) | −3.55935 | −0.434844 | −0.217422 | − | 0.976078i | \(-0.569765\pi\) | ||||
−0.217422 | + | 0.976078i | \(0.569765\pi\) | |||||||
\(68\) | 1.68318 | 0.204115 | ||||||||
\(69\) | −0.237648 | −0.0286095 | ||||||||
\(70\) | 38.9721 | 4.65806 | ||||||||
\(71\) | −5.50177 | −0.652940 | −0.326470 | − | 0.945208i | \(-0.605859\pi\) | ||||
−0.326470 | + | 0.945208i | \(0.605859\pi\) | |||||||
\(72\) | 5.21822 | 0.614973 | ||||||||
\(73\) | 4.20006 | 0.491580 | 0.245790 | − | 0.969323i | \(-0.420953\pi\) | ||||
0.245790 | + | 0.969323i | \(0.420953\pi\) | |||||||
\(74\) | 8.82599 | 1.02600 | ||||||||
\(75\) | 32.4343 | 3.74519 | ||||||||
\(76\) | 7.10402 | 0.814887 | ||||||||
\(77\) | −15.5569 | −1.77287 | ||||||||
\(78\) | −2.38519 | −0.270070 | ||||||||
\(79\) | 16.6252 | 1.87048 | 0.935239 | − | 0.354016i | \(-0.115184\pi\) | ||||
0.935239 | + | 0.354016i | \(0.115184\pi\) | |||||||
\(80\) | 20.2363 | 2.26248 | ||||||||
\(81\) | −3.87931 | −0.431034 | ||||||||
\(82\) | 2.64065 | 0.291611 | ||||||||
\(83\) | 11.0604 | 1.21403 | 0.607017 | − | 0.794689i | \(-0.292366\pi\) | ||||
0.607017 | + | 0.794689i | \(0.292366\pi\) | |||||||
\(84\) | 18.3591 | 2.00314 | ||||||||
\(85\) | −5.26672 | −0.571256 | ||||||||
\(86\) | 19.5710 | 2.11040 | ||||||||
\(87\) | 6.24836 | 0.669894 | ||||||||
\(88\) | −3.72128 | −0.396690 | ||||||||
\(89\) | 7.34281 | 0.778336 | 0.389168 | − | 0.921167i | \(-0.372762\pi\) | ||||
0.389168 | + | 0.921167i | \(0.372762\pi\) | |||||||
\(90\) | 31.7378 | 3.34546 | ||||||||
\(91\) | 2.52212 | 0.264390 | ||||||||
\(92\) | −0.116840 | −0.0121814 | ||||||||
\(93\) | 20.3391 | 2.10907 | ||||||||
\(94\) | −1.86621 | −0.192485 | ||||||||
\(95\) | −22.2287 | −2.28062 | ||||||||
\(96\) | 17.3194 | 1.76765 | ||||||||
\(97\) | −16.7412 | −1.69981 | −0.849906 | − | 0.526934i | \(-0.823342\pi\) | ||||
−0.849906 | + | 0.526934i | \(0.823342\pi\) | |||||||
\(98\) | −36.0576 | −3.64237 | ||||||||
\(99\) | −12.6691 | −1.27329 | ||||||||
\(100\) | 15.9463 | 1.59463 | ||||||||
\(101\) | −7.01632 | −0.698150 | −0.349075 | − | 0.937095i | \(-0.613504\pi\) | ||||
−0.349075 | + | 0.937095i | \(0.613504\pi\) | |||||||
\(102\) | −6.23853 | −0.617707 | ||||||||
\(103\) | −0.948146 | −0.0934236 | −0.0467118 | − | 0.998908i | \(-0.514874\pi\) | ||||
−0.0467118 | + | 0.998908i | \(0.514874\pi\) | |||||||
\(104\) | 0.603302 | 0.0591586 | ||||||||
\(105\) | −57.4462 | −5.60618 | ||||||||
\(106\) | −4.65220 | −0.451862 | ||||||||
\(107\) | 1.51759 | 0.146711 | 0.0733554 | − | 0.997306i | \(-0.476629\pi\) | ||||
0.0733554 | + | 0.997306i | \(0.476629\pi\) | |||||||
\(108\) | 4.30950 | 0.414682 | ||||||||
\(109\) | 14.3328 | 1.37283 | 0.686416 | − | 0.727209i | \(-0.259183\pi\) | ||||
0.686416 | + | 0.727209i | \(0.259183\pi\) | |||||||
\(110\) | −22.6332 | −2.15799 | ||||||||
\(111\) | −13.0098 | −1.23484 | ||||||||
\(112\) | −25.3463 | −2.39500 | ||||||||
\(113\) | 13.4796 | 1.26806 | 0.634028 | − | 0.773310i | \(-0.281401\pi\) | ||||
0.634028 | + | 0.773310i | \(0.281401\pi\) | |||||||
\(114\) | −26.3304 | −2.46607 | ||||||||
\(115\) | 0.365595 | 0.0340919 | ||||||||
\(116\) | 3.07200 | 0.285228 | ||||||||
\(117\) | 2.05394 | 0.189887 | ||||||||
\(118\) | 0.757486 | 0.0697322 | ||||||||
\(119\) | 6.59666 | 0.604715 | ||||||||
\(120\) | −13.7414 | −1.25441 | ||||||||
\(121\) | −1.96529 | −0.178663 | ||||||||
\(122\) | 8.70873 | 0.788452 | ||||||||
\(123\) | −3.89241 | −0.350967 | ||||||||
\(124\) | 9.99971 | 0.898001 | ||||||||
\(125\) | −29.2355 | −2.61490 | ||||||||
\(126\) | −39.7522 | −3.54140 | ||||||||
\(127\) | 3.88226 | 0.344495 | 0.172248 | − | 0.985054i | \(-0.444897\pi\) | ||||
0.172248 | + | 0.985054i | \(0.444897\pi\) | |||||||
\(128\) | −9.33286 | −0.824916 | ||||||||
\(129\) | −28.8483 | −2.53995 | ||||||||
\(130\) | 3.66935 | 0.321823 | ||||||||
\(131\) | 11.6225 | 1.01547 | 0.507733 | − | 0.861515i | \(-0.330484\pi\) | ||||
0.507733 | + | 0.861515i | \(0.330484\pi\) | |||||||
\(132\) | −10.6621 | −0.928017 | ||||||||
\(133\) | 27.8419 | 2.41420 | ||||||||
\(134\) | 6.48602 | 0.560307 | ||||||||
\(135\) | −13.4846 | −1.16057 | ||||||||
\(136\) | 1.57795 | 0.135308 | ||||||||
\(137\) | −13.7634 | −1.17589 | −0.587945 | − | 0.808901i | \(-0.700063\pi\) | ||||
−0.587945 | + | 0.808901i | \(0.700063\pi\) | |||||||
\(138\) | 0.433055 | 0.0368641 | ||||||||
\(139\) | 18.7351 | 1.58909 | 0.794545 | − | 0.607205i | \(-0.207709\pi\) | ||||
0.794545 | + | 0.607205i | \(0.207709\pi\) | |||||||
\(140\) | −28.2434 | −2.38700 | ||||||||
\(141\) | 2.75086 | 0.231664 | ||||||||
\(142\) | 10.0256 | 0.841330 | ||||||||
\(143\) | −1.46473 | −0.122487 | ||||||||
\(144\) | −20.6413 | −1.72011 | ||||||||
\(145\) | −9.61240 | −0.798266 | ||||||||
\(146\) | −7.65356 | −0.633413 | ||||||||
\(147\) | 53.1501 | 4.38374 | ||||||||
\(148\) | −6.39626 | −0.525769 | ||||||||
\(149\) | 17.0987 | 1.40078 | 0.700390 | − | 0.713760i | \(-0.253009\pi\) | ||||
0.700390 | + | 0.713760i | \(0.253009\pi\) | |||||||
\(150\) | −59.1034 | −4.82577 | ||||||||
\(151\) | 0.102087 | 0.00830775 | 0.00415387 | − | 0.999991i | \(-0.498678\pi\) | ||||
0.00415387 | + | 0.999991i | \(0.498678\pi\) | |||||||
\(152\) | 6.65992 | 0.540191 | ||||||||
\(153\) | 5.37213 | 0.434311 | ||||||||
\(154\) | 28.3485 | 2.28439 | ||||||||
\(155\) | −31.2895 | −2.51323 | ||||||||
\(156\) | 1.72856 | 0.138396 | ||||||||
\(157\) | 6.49465 | 0.518329 | 0.259165 | − | 0.965833i | \(-0.416553\pi\) | ||||
0.259165 | + | 0.965833i | \(0.416553\pi\) | |||||||
\(158\) | −30.2952 | −2.41016 | ||||||||
\(159\) | 6.85750 | 0.543835 | ||||||||
\(160\) | −26.6439 | −2.10638 | ||||||||
\(161\) | −0.457915 | −0.0360887 | ||||||||
\(162\) | 7.06908 | 0.555399 | ||||||||
\(163\) | 6.35927 | 0.498096 | 0.249048 | − | 0.968491i | \(-0.419882\pi\) | ||||
0.249048 | + | 0.968491i | \(0.419882\pi\) | |||||||
\(164\) | −1.91370 | −0.149435 | ||||||||
\(165\) | 33.3621 | 2.59724 | ||||||||
\(166\) | −20.1548 | −1.56431 | ||||||||
\(167\) | −6.02781 | −0.466446 | −0.233223 | − | 0.972423i | \(-0.574927\pi\) | ||||
−0.233223 | + | 0.972423i | \(0.574927\pi\) | |||||||
\(168\) | 17.2114 | 1.32789 | ||||||||
\(169\) | −12.7625 | −0.981733 | ||||||||
\(170\) | 9.59728 | 0.736078 | ||||||||
\(171\) | 22.6736 | 1.73390 | ||||||||
\(172\) | −14.1833 | −1.08146 | ||||||||
\(173\) | −21.1629 | −1.60898 | −0.804491 | − | 0.593965i | \(-0.797562\pi\) | ||||
−0.804491 | + | 0.593965i | \(0.797562\pi\) | |||||||
\(174\) | −11.3861 | −0.863176 | ||||||||
\(175\) | 62.4963 | 4.72427 | ||||||||
\(176\) | 14.7200 | 1.10956 | ||||||||
\(177\) | −1.11656 | −0.0839257 | ||||||||
\(178\) | −13.3804 | −1.00291 | ||||||||
\(179\) | 15.5515 | 1.16237 | 0.581186 | − | 0.813771i | \(-0.302589\pi\) | ||||
0.581186 | + | 0.813771i | \(0.302589\pi\) | |||||||
\(180\) | −23.0006 | −1.71436 | ||||||||
\(181\) | −6.44125 | −0.478774 | −0.239387 | − | 0.970924i | \(-0.576946\pi\) | ||||
−0.239387 | + | 0.970924i | \(0.576946\pi\) | |||||||
\(182\) | −4.59593 | −0.340673 | ||||||||
\(183\) | −12.8370 | −0.948935 | ||||||||
\(184\) | −0.109535 | −0.00807506 | ||||||||
\(185\) | 20.0141 | 1.47147 | ||||||||
\(186\) | −37.0630 | −2.71759 | ||||||||
\(187\) | −3.83103 | −0.280153 | ||||||||
\(188\) | 1.35246 | 0.0986381 | ||||||||
\(189\) | 16.8897 | 1.22854 | ||||||||
\(190\) | 40.5063 | 2.93864 | ||||||||
\(191\) | 5.65605 | 0.409257 | 0.204629 | − | 0.978840i | \(-0.434401\pi\) | ||||
0.204629 | + | 0.978840i | \(0.434401\pi\) | |||||||
\(192\) | −5.25181 | −0.379017 | ||||||||
\(193\) | −8.10006 | −0.583055 | −0.291528 | − | 0.956562i | \(-0.594163\pi\) | ||||
−0.291528 | + | 0.956562i | \(0.594163\pi\) | |||||||
\(194\) | 30.5067 | 2.19025 | ||||||||
\(195\) | −5.40874 | −0.387328 | ||||||||
\(196\) | 26.1312 | 1.86651 | ||||||||
\(197\) | −10.5838 | −0.754062 | −0.377031 | − | 0.926201i | \(-0.623055\pi\) | ||||
−0.377031 | + | 0.926201i | \(0.623055\pi\) | |||||||
\(198\) | 23.0862 | 1.64067 | ||||||||
\(199\) | −21.1551 | −1.49964 | −0.749822 | − | 0.661640i | \(-0.769861\pi\) | ||||
−0.749822 | + | 0.661640i | \(0.769861\pi\) | |||||||
\(200\) | 14.9494 | 1.05708 | ||||||||
\(201\) | −9.56061 | −0.674353 | ||||||||
\(202\) | 12.7855 | 0.899585 | ||||||||
\(203\) | 12.0397 | 0.845022 | ||||||||
\(204\) | 4.52111 | 0.316541 | ||||||||
\(205\) | 5.98803 | 0.418222 | ||||||||
\(206\) | 1.72776 | 0.120379 | ||||||||
\(207\) | −0.372913 | −0.0259192 | ||||||||
\(208\) | −2.38643 | −0.165469 | ||||||||
\(209\) | −16.1693 | −1.11845 | ||||||||
\(210\) | 104.681 | 7.22370 | ||||||||
\(211\) | −0.592362 | −0.0407799 | −0.0203899 | − | 0.999792i | \(-0.506491\pi\) | ||||
−0.0203899 | + | 0.999792i | \(0.506491\pi\) | |||||||
\(212\) | 3.37148 | 0.231554 | ||||||||
\(213\) | −14.7781 | −1.01258 | ||||||||
\(214\) | −2.76543 | −0.189041 | ||||||||
\(215\) | 44.3799 | 3.02668 | ||||||||
\(216\) | 4.04009 | 0.274893 | ||||||||
\(217\) | 39.1906 | 2.66043 | ||||||||
\(218\) | −26.1179 | −1.76893 | ||||||||
\(219\) | 11.2816 | 0.762340 | ||||||||
\(220\) | 16.4024 | 1.10585 | ||||||||
\(221\) | 0.621096 | 0.0417794 | ||||||||
\(222\) | 23.7071 | 1.59112 | ||||||||
\(223\) | 12.4349 | 0.832705 | 0.416352 | − | 0.909203i | \(-0.363308\pi\) | ||||
0.416352 | + | 0.909203i | \(0.363308\pi\) | |||||||
\(224\) | 33.3720 | 2.22976 | ||||||||
\(225\) | 50.8952 | 3.39301 | ||||||||
\(226\) | −24.5632 | −1.63392 | ||||||||
\(227\) | 15.8638 | 1.05292 | 0.526458 | − | 0.850201i | \(-0.323520\pi\) | ||||
0.526458 | + | 0.850201i | \(0.323520\pi\) | |||||||
\(228\) | 19.0818 | 1.26372 | ||||||||
\(229\) | 9.32802 | 0.616413 | 0.308206 | − | 0.951320i | \(-0.400271\pi\) | ||||
0.308206 | + | 0.951320i | \(0.400271\pi\) | |||||||
\(230\) | −0.666206 | −0.0439283 | ||||||||
\(231\) | −41.7866 | −2.74936 | ||||||||
\(232\) | 2.87996 | 0.189078 | ||||||||
\(233\) | 21.0202 | 1.37708 | 0.688540 | − | 0.725199i | \(-0.258252\pi\) | ||||
0.688540 | + | 0.725199i | \(0.258252\pi\) | |||||||
\(234\) | −3.74279 | −0.244674 | ||||||||
\(235\) | −4.23188 | −0.276058 | ||||||||
\(236\) | −0.548955 | −0.0357339 | ||||||||
\(237\) | 44.6562 | 2.90073 | ||||||||
\(238\) | −12.0208 | −0.779191 | ||||||||
\(239\) | −8.07536 | −0.522352 | −0.261176 | − | 0.965291i | \(-0.584110\pi\) | ||||
−0.261176 | + | 0.965291i | \(0.584110\pi\) | |||||||
\(240\) | 54.3558 | 3.50865 | ||||||||
\(241\) | 16.0756 | 1.03552 | 0.517760 | − | 0.855526i | \(-0.326766\pi\) | ||||
0.517760 | + | 0.855526i | \(0.326766\pi\) | |||||||
\(242\) | 3.58125 | 0.230212 | ||||||||
\(243\) | −20.2099 | −1.29647 | ||||||||
\(244\) | −6.31128 | −0.404038 | ||||||||
\(245\) | −81.7654 | −5.22380 | ||||||||
\(246\) | 7.09294 | 0.452230 | ||||||||
\(247\) | 2.62140 | 0.166796 | ||||||||
\(248\) | 9.37458 | 0.595287 | ||||||||
\(249\) | 29.7088 | 1.88272 | ||||||||
\(250\) | 53.2744 | 3.36937 | ||||||||
\(251\) | 3.30727 | 0.208753 | 0.104377 | − | 0.994538i | \(-0.466715\pi\) | ||||
0.104377 | + | 0.994538i | \(0.466715\pi\) | |||||||
\(252\) | 28.8087 | 1.81478 | ||||||||
\(253\) | 0.265936 | 0.0167192 | ||||||||
\(254\) | −7.07446 | −0.443891 | ||||||||
\(255\) | −14.1467 | −0.885901 | ||||||||
\(256\) | 20.9172 | 1.30733 | ||||||||
\(257\) | −2.73397 | −0.170541 | −0.0852703 | − | 0.996358i | \(-0.527175\pi\) | ||||
−0.0852703 | + | 0.996358i | \(0.527175\pi\) | |||||||
\(258\) | 52.5689 | 3.27280 | ||||||||
\(259\) | −25.0681 | −1.55765 | ||||||||
\(260\) | −2.65920 | −0.164917 | ||||||||
\(261\) | 9.80479 | 0.606901 | ||||||||
\(262\) | −21.1792 | −1.30845 | ||||||||
\(263\) | 23.8280 | 1.46930 | 0.734648 | − | 0.678448i | \(-0.237347\pi\) | ||||
0.734648 | + | 0.678448i | \(0.237347\pi\) | |||||||
\(264\) | −9.99556 | −0.615184 | ||||||||
\(265\) | −10.5495 | −0.648050 | ||||||||
\(266\) | −50.7349 | −3.11076 | ||||||||
\(267\) | 19.7232 | 1.20704 | ||||||||
\(268\) | −4.70047 | −0.287127 | ||||||||
\(269\) | 12.1682 | 0.741910 | 0.370955 | − | 0.928651i | \(-0.379030\pi\) | ||||
0.370955 | + | 0.928651i | \(0.379030\pi\) | |||||||
\(270\) | 24.5723 | 1.49542 | ||||||||
\(271\) | −20.3384 | −1.23547 | −0.617736 | − | 0.786386i | \(-0.711950\pi\) | ||||
−0.617736 | + | 0.786386i | \(0.711950\pi\) | |||||||
\(272\) | −6.24178 | −0.378463 | ||||||||
\(273\) | 6.77455 | 0.410014 | ||||||||
\(274\) | 25.0804 | 1.51516 | ||||||||
\(275\) | −36.2949 | −2.18867 | ||||||||
\(276\) | −0.313838 | −0.0188908 | ||||||||
\(277\) | 9.70253 | 0.582968 | 0.291484 | − | 0.956576i | \(-0.405851\pi\) | ||||
0.291484 | + | 0.956576i | \(0.405851\pi\) | |||||||
\(278\) | −34.1400 | −2.04758 | ||||||||
\(279\) | 31.9157 | 1.91074 | ||||||||
\(280\) | −26.4778 | −1.58235 | ||||||||
\(281\) | 26.2637 | 1.56676 | 0.783380 | − | 0.621544i | \(-0.213494\pi\) | ||||
0.783380 | + | 0.621544i | \(0.213494\pi\) | |||||||
\(282\) | −5.01275 | −0.298505 | ||||||||
\(283\) | 8.58208 | 0.510152 | 0.255076 | − | 0.966921i | \(-0.417900\pi\) | ||||
0.255076 | + | 0.966921i | \(0.417900\pi\) | |||||||
\(284\) | −7.26563 | −0.431136 | ||||||||
\(285\) | −59.7076 | −3.53678 | ||||||||
\(286\) | 2.66910 | 0.157827 | ||||||||
\(287\) | −7.50012 | −0.442718 | ||||||||
\(288\) | 27.1772 | 1.60143 | ||||||||
\(289\) | −15.3755 | −0.904442 | ||||||||
\(290\) | 17.5162 | 1.02859 | ||||||||
\(291\) | −44.9679 | −2.63606 | ||||||||
\(292\) | 5.54659 | 0.324589 | ||||||||
\(293\) | −0.133318 | −0.00778854 | −0.00389427 | − | 0.999992i | \(-0.501240\pi\) | ||||
−0.00389427 | + | 0.999992i | \(0.501240\pi\) | |||||||
\(294\) | −96.8527 | −5.64857 | ||||||||
\(295\) | 1.71770 | 0.100008 | ||||||||
\(296\) | −5.99640 | −0.348534 | ||||||||
\(297\) | −9.80874 | −0.569161 | ||||||||
\(298\) | −31.1581 | −1.80494 | ||||||||
\(299\) | −0.0431141 | −0.00249335 | ||||||||
\(300\) | 42.8326 | 2.47294 | ||||||||
\(301\) | −55.5867 | −3.20396 | ||||||||
\(302\) | −0.186029 | −0.0107047 | ||||||||
\(303\) | −18.8462 | −1.08269 | ||||||||
\(304\) | −26.3441 | −1.51094 | ||||||||
\(305\) | 19.7482 | 1.13078 | ||||||||
\(306\) | −9.78937 | −0.559621 | ||||||||
\(307\) | −26.5823 | −1.51713 | −0.758567 | − | 0.651595i | \(-0.774100\pi\) | ||||
−0.758567 | + | 0.651595i | \(0.774100\pi\) | |||||||
\(308\) | −20.5444 | −1.17062 | ||||||||
\(309\) | −2.54678 | −0.144881 | ||||||||
\(310\) | 57.0172 | 3.23836 | ||||||||
\(311\) | 19.4255 | 1.10152 | 0.550759 | − | 0.834664i | \(-0.314338\pi\) | ||||
0.550759 | + | 0.834664i | \(0.314338\pi\) | |||||||
\(312\) | 1.62050 | 0.0917430 | ||||||||
\(313\) | −5.80086 | −0.327884 | −0.163942 | − | 0.986470i | \(-0.552421\pi\) | ||||
−0.163942 | + | 0.986470i | \(0.552421\pi\) | |||||||
\(314\) | −11.8349 | −0.667881 | ||||||||
\(315\) | −90.1433 | −5.07900 | ||||||||
\(316\) | 21.9552 | 1.23508 | ||||||||
\(317\) | 31.4424 | 1.76598 | 0.882990 | − | 0.469392i | \(-0.155527\pi\) | ||||
0.882990 | + | 0.469392i | \(0.155527\pi\) | |||||||
\(318\) | −12.4961 | −0.700745 | ||||||||
\(319\) | −6.99210 | −0.391483 | ||||||||
\(320\) | 8.07932 | 0.451648 | ||||||||
\(321\) | 4.07633 | 0.227518 | ||||||||
\(322\) | 0.834436 | 0.0465013 | ||||||||
\(323\) | 6.85635 | 0.381497 | ||||||||
\(324\) | −5.12301 | −0.284612 | ||||||||
\(325\) | 5.88422 | 0.326398 | ||||||||
\(326\) | −11.5882 | −0.641810 | ||||||||
\(327\) | 38.4987 | 2.12898 | ||||||||
\(328\) | −1.79407 | −0.0990607 | ||||||||
\(329\) | 5.30051 | 0.292227 | ||||||||
\(330\) | −60.7941 | −3.34661 | ||||||||
\(331\) | 11.4177 | 0.627575 | 0.313788 | − | 0.949493i | \(-0.398402\pi\) | ||||
0.313788 | + | 0.949493i | \(0.398402\pi\) | |||||||
\(332\) | 14.6063 | 0.801625 | ||||||||
\(333\) | −20.4147 | −1.11872 | ||||||||
\(334\) | 10.9842 | 0.601027 | ||||||||
\(335\) | 14.7079 | 0.803580 | ||||||||
\(336\) | −68.0816 | −3.71416 | ||||||||
\(337\) | 26.1871 | 1.42650 | 0.713251 | − | 0.700909i | \(-0.247222\pi\) | ||||
0.713251 | + | 0.700909i | \(0.247222\pi\) | |||||||
\(338\) | 23.2565 | 1.26499 | ||||||||
\(339\) | 36.2070 | 1.96649 | ||||||||
\(340\) | −6.95521 | −0.377199 | ||||||||
\(341\) | −22.7601 | −1.23253 | ||||||||
\(342\) | −41.3171 | −2.23417 | ||||||||
\(343\) | 66.1831 | 3.57355 | ||||||||
\(344\) | −13.2966 | −0.716904 | ||||||||
\(345\) | 0.982010 | 0.0528696 | ||||||||
\(346\) | 38.5640 | 2.07321 | ||||||||
\(347\) | −28.5805 | −1.53428 | −0.767142 | − | 0.641478i | \(-0.778322\pi\) | ||||
−0.767142 | + | 0.641478i | \(0.778322\pi\) | |||||||
\(348\) | 8.25157 | 0.442330 | ||||||||
\(349\) | 24.1301 | 1.29165 | 0.645826 | − | 0.763484i | \(-0.276513\pi\) | ||||
0.645826 | + | 0.763484i | \(0.276513\pi\) | |||||||
\(350\) | −113.884 | −6.08735 | ||||||||
\(351\) | 1.59022 | 0.0848794 | ||||||||
\(352\) | −19.3809 | −1.03300 | ||||||||
\(353\) | −33.3389 | −1.77445 | −0.887224 | − | 0.461338i | \(-0.847369\pi\) | ||||
−0.887224 | + | 0.461338i | \(0.847369\pi\) | |||||||
\(354\) | 2.03465 | 0.108140 | ||||||||
\(355\) | 22.7344 | 1.20662 | ||||||||
\(356\) | 9.69690 | 0.513935 | ||||||||
\(357\) | 17.7190 | 0.937789 | ||||||||
\(358\) | −28.3387 | −1.49775 | ||||||||
\(359\) | 21.5536 | 1.13755 | 0.568777 | − | 0.822492i | \(-0.307417\pi\) | ||||
0.568777 | + | 0.822492i | \(0.307417\pi\) | |||||||
\(360\) | −21.5627 | −1.13645 | ||||||||
\(361\) | 9.93793 | 0.523049 | ||||||||
\(362\) | 11.7376 | 0.616913 | ||||||||
\(363\) | −5.27888 | −0.277070 | ||||||||
\(364\) | 3.33070 | 0.174576 | ||||||||
\(365\) | −17.3555 | −0.908427 | ||||||||
\(366\) | 23.3922 | 1.22273 | ||||||||
\(367\) | 17.4807 | 0.912487 | 0.456244 | − | 0.889855i | \(-0.349195\pi\) | ||||
0.456244 | + | 0.889855i | \(0.349195\pi\) | |||||||
\(368\) | 0.433280 | 0.0225863 | ||||||||
\(369\) | −6.10788 | −0.317964 | ||||||||
\(370\) | −36.4707 | −1.89602 | ||||||||
\(371\) | 13.2134 | 0.686007 | ||||||||
\(372\) | 26.8598 | 1.39262 | ||||||||
\(373\) | 4.90780 | 0.254116 | 0.127058 | − | 0.991895i | \(-0.459447\pi\) | ||||
0.127058 | + | 0.991895i | \(0.459447\pi\) | |||||||
\(374\) | 6.98111 | 0.360984 | ||||||||
\(375\) | −78.5282 | −4.05518 | ||||||||
\(376\) | 1.26791 | 0.0653874 | ||||||||
\(377\) | 1.13358 | 0.0583821 | ||||||||
\(378\) | −30.7772 | −1.58301 | ||||||||
\(379\) | −22.6574 | −1.16383 | −0.581917 | − | 0.813248i | \(-0.697697\pi\) | ||||
−0.581917 | + | 0.813248i | \(0.697697\pi\) | |||||||
\(380\) | −29.3552 | −1.50589 | ||||||||
\(381\) | 10.4280 | 0.534242 | ||||||||
\(382\) | −10.3067 | −0.527339 | ||||||||
\(383\) | −5.15569 | −0.263443 | −0.131722 | − | 0.991287i | \(-0.542051\pi\) | ||||
−0.131722 | + | 0.991287i | \(0.542051\pi\) | |||||||
\(384\) | −25.0686 | −1.27928 | ||||||||
\(385\) | 64.2841 | 3.27622 | ||||||||
\(386\) | 14.7603 | 0.751282 | ||||||||
\(387\) | −45.2682 | −2.30111 | ||||||||
\(388\) | −22.1084 | −1.12238 | ||||||||
\(389\) | −27.0339 | −1.37067 | −0.685336 | − | 0.728227i | \(-0.740345\pi\) | ||||
−0.685336 | + | 0.728227i | \(0.740345\pi\) | |||||||
\(390\) | 9.85608 | 0.499082 | ||||||||
\(391\) | −0.112766 | −0.00570283 | ||||||||
\(392\) | 24.4976 | 1.23732 | ||||||||
\(393\) | 31.2188 | 1.57478 | ||||||||
\(394\) | 19.2863 | 0.971629 | ||||||||
\(395\) | −68.6985 | −3.45660 | ||||||||
\(396\) | −16.7307 | −0.840751 | ||||||||
\(397\) | 20.3480 | 1.02124 | 0.510619 | − | 0.859807i | \(-0.329416\pi\) | ||||
0.510619 | + | 0.859807i | \(0.329416\pi\) | |||||||
\(398\) | 38.5499 | 1.93233 | ||||||||
\(399\) | 74.7849 | 3.74393 | ||||||||
\(400\) | −59.1341 | −2.95671 | ||||||||
\(401\) | −37.3694 | −1.86614 | −0.933068 | − | 0.359699i | \(-0.882879\pi\) | ||||
−0.933068 | + | 0.359699i | \(0.882879\pi\) | |||||||
\(402\) | 17.4218 | 0.868922 | ||||||||
\(403\) | 3.68992 | 0.183808 | ||||||||
\(404\) | −9.26574 | −0.460988 | ||||||||
\(405\) | 16.0301 | 0.796541 | ||||||||
\(406\) | −21.9394 | −1.08883 | ||||||||
\(407\) | 14.5584 | 0.721631 | ||||||||
\(408\) | 4.23847 | 0.209836 | ||||||||
\(409\) | 30.4801 | 1.50715 | 0.753573 | − | 0.657364i | \(-0.228329\pi\) | ||||
0.753573 | + | 0.657364i | \(0.228329\pi\) | |||||||
\(410\) | −10.9117 | −0.538890 | ||||||||
\(411\) | −36.9694 | −1.82356 | ||||||||
\(412\) | −1.25212 | −0.0616875 | ||||||||
\(413\) | −2.15145 | −0.105866 | ||||||||
\(414\) | 0.679540 | 0.0333976 | ||||||||
\(415\) | −45.7036 | −2.24350 | ||||||||
\(416\) | 3.14207 | 0.154053 | ||||||||
\(417\) | 50.3235 | 2.46435 | ||||||||
\(418\) | 29.4645 | 1.44116 | ||||||||
\(419\) | 21.6303 | 1.05671 | 0.528354 | − | 0.849024i | \(-0.322809\pi\) | ||||
0.528354 | + | 0.849024i | \(0.322809\pi\) | |||||||
\(420\) | −75.8633 | −3.70175 | ||||||||
\(421\) | −22.1290 | −1.07850 | −0.539251 | − | 0.842145i | \(-0.681293\pi\) | ||||
−0.539251 | + | 0.842145i | \(0.681293\pi\) | |||||||
\(422\) | 1.07943 | 0.0525459 | ||||||||
\(423\) | 4.31658 | 0.209880 | ||||||||
\(424\) | 3.16072 | 0.153498 | ||||||||
\(425\) | 15.3903 | 0.746541 | ||||||||
\(426\) | 26.9294 | 1.30473 | ||||||||
\(427\) | −24.7350 | −1.19701 | ||||||||
\(428\) | 2.00412 | 0.0968730 | ||||||||
\(429\) | −3.93434 | −0.189952 | ||||||||
\(430\) | −80.8713 | −3.89996 | ||||||||
\(431\) | 30.4676 | 1.46757 | 0.733786 | − | 0.679380i | \(-0.237751\pi\) | ||||
0.733786 | + | 0.679380i | \(0.237751\pi\) | |||||||
\(432\) | −15.9811 | −0.768889 | ||||||||
\(433\) | 20.3753 | 0.979175 | 0.489588 | − | 0.871954i | \(-0.337147\pi\) | ||||
0.489588 | + | 0.871954i | \(0.337147\pi\) | |||||||
\(434\) | −71.4151 | −3.42804 | ||||||||
\(435\) | −25.8194 | −1.23795 | ||||||||
\(436\) | 18.9278 | 0.906479 | ||||||||
\(437\) | −0.475941 | −0.0227674 | ||||||||
\(438\) | −20.5579 | −0.982294 | ||||||||
\(439\) | 27.8037 | 1.32700 | 0.663499 | − | 0.748177i | \(-0.269071\pi\) | ||||
0.663499 | + | 0.748177i | \(0.269071\pi\) | |||||||
\(440\) | 15.3771 | 0.733072 | ||||||||
\(441\) | 83.4019 | 3.97152 | ||||||||
\(442\) | −1.13179 | −0.0538339 | ||||||||
\(443\) | −13.0379 | −0.619450 | −0.309725 | − | 0.950826i | \(-0.600237\pi\) | ||||
−0.309725 | + | 0.950826i | \(0.600237\pi\) | |||||||
\(444\) | −17.1807 | −0.815360 | ||||||||
\(445\) | −30.3419 | −1.43835 | ||||||||
\(446\) | −22.6596 | −1.07296 | ||||||||
\(447\) | 45.9281 | 2.17232 | ||||||||
\(448\) | −10.1195 | −0.478101 | ||||||||
\(449\) | 2.12159 | 0.100124 | 0.0500620 | − | 0.998746i | \(-0.484058\pi\) | ||||
0.0500620 | + | 0.998746i | \(0.484058\pi\) | |||||||
\(450\) | −92.7437 | −4.37198 | ||||||||
\(451\) | 4.35572 | 0.205103 | ||||||||
\(452\) | 17.8011 | 0.837296 | ||||||||
\(453\) | 0.274212 | 0.0128836 | ||||||||
\(454\) | −28.9078 | −1.35671 | ||||||||
\(455\) | −10.4219 | −0.488585 | ||||||||
\(456\) | 17.8889 | 0.837725 | ||||||||
\(457\) | 31.2174 | 1.46029 | 0.730144 | − | 0.683294i | \(-0.239453\pi\) | ||||
0.730144 | + | 0.683294i | \(0.239453\pi\) | |||||||
\(458\) | −16.9980 | −0.794264 | ||||||||
\(459\) | 4.15925 | 0.194137 | ||||||||
\(460\) | 0.482804 | 0.0225109 | ||||||||
\(461\) | 15.8163 | 0.736636 | 0.368318 | − | 0.929700i | \(-0.379934\pi\) | ||||
0.368318 | + | 0.929700i | \(0.379934\pi\) | |||||||
\(462\) | 76.1457 | 3.54262 | ||||||||
\(463\) | −2.89470 | −0.134528 | −0.0672640 | − | 0.997735i | \(-0.521427\pi\) | ||||
−0.0672640 | + | 0.997735i | \(0.521427\pi\) | |||||||
\(464\) | −11.3920 | −0.528860 | ||||||||
\(465\) | −84.0452 | −3.89750 | ||||||||
\(466\) | −38.3041 | −1.77440 | ||||||||
\(467\) | 8.96153 | 0.414690 | 0.207345 | − | 0.978268i | \(-0.433518\pi\) | ||||
0.207345 | + | 0.978268i | \(0.433518\pi\) | |||||||
\(468\) | 2.71243 | 0.125382 | ||||||||
\(469\) | −18.4220 | −0.850647 | ||||||||
\(470\) | 7.71156 | 0.355708 | ||||||||
\(471\) | 17.4450 | 0.803823 | ||||||||
\(472\) | −0.514637 | −0.0236881 | ||||||||
\(473\) | 32.2821 | 1.48433 | ||||||||
\(474\) | −81.3747 | −3.73767 | ||||||||
\(475\) | 64.9565 | 2.98041 | ||||||||
\(476\) | 8.71154 | 0.399293 | ||||||||
\(477\) | 10.7606 | 0.492696 | ||||||||
\(478\) | 14.7153 | 0.673064 | ||||||||
\(479\) | −35.2623 | −1.61117 | −0.805587 | − | 0.592477i | \(-0.798150\pi\) | ||||
−0.805587 | + | 0.592477i | \(0.798150\pi\) | |||||||
\(480\) | −71.5670 | −3.26657 | ||||||||
\(481\) | −2.36023 | −0.107617 | ||||||||
\(482\) | −29.2938 | −1.33430 | ||||||||
\(483\) | −1.22999 | −0.0559663 | ||||||||
\(484\) | −2.59536 | −0.117971 | ||||||||
\(485\) | 69.1780 | 3.14121 | ||||||||
\(486\) | 36.8276 | 1.67053 | ||||||||
\(487\) | −9.78816 | −0.443544 | −0.221772 | − | 0.975099i | \(-0.571184\pi\) | ||||
−0.221772 | + | 0.975099i | \(0.571184\pi\) | |||||||
\(488\) | −5.91673 | −0.267838 | ||||||||
\(489\) | 17.0814 | 0.772445 | ||||||||
\(490\) | 148.997 | 6.73100 | ||||||||
\(491\) | 10.2068 | 0.460628 | 0.230314 | − | 0.973116i | \(-0.426025\pi\) | ||||
0.230314 | + | 0.973116i | \(0.426025\pi\) | |||||||
\(492\) | −5.14031 | −0.231743 | ||||||||
\(493\) | 2.96490 | 0.133532 | ||||||||
\(494\) | −4.77685 | −0.214921 | ||||||||
\(495\) | 52.3511 | 2.35301 | ||||||||
\(496\) | −37.0823 | −1.66504 | ||||||||
\(497\) | −28.4753 | −1.27729 | ||||||||
\(498\) | −54.1369 | −2.42593 | ||||||||
\(499\) | −7.89886 | −0.353601 | −0.176801 | − | 0.984247i | \(-0.556575\pi\) | ||||
−0.176801 | + | 0.984247i | \(0.556575\pi\) | |||||||
\(500\) | −38.6083 | −1.72662 | ||||||||
\(501\) | −16.1910 | −0.723362 | ||||||||
\(502\) | −6.02668 | −0.268984 | ||||||||
\(503\) | 42.0662 | 1.87564 | 0.937821 | − | 0.347120i | \(-0.112840\pi\) | ||||
0.937821 | + | 0.347120i | \(0.112840\pi\) | |||||||
\(504\) | 27.0077 | 1.20302 | ||||||||
\(505\) | 28.9928 | 1.29016 | ||||||||
\(506\) | −0.484602 | −0.0215432 | ||||||||
\(507\) | −34.2809 | −1.52247 | ||||||||
\(508\) | 5.12691 | 0.227470 | ||||||||
\(509\) | −20.1333 | −0.892394 | −0.446197 | − | 0.894935i | \(-0.647222\pi\) | ||||
−0.446197 | + | 0.894935i | \(0.647222\pi\) | |||||||
\(510\) | 25.7788 | 1.14151 | ||||||||
\(511\) | 21.7380 | 0.961634 | ||||||||
\(512\) | −19.4507 | −0.859609 | ||||||||
\(513\) | 17.5546 | 0.775053 | ||||||||
\(514\) | 4.98198 | 0.219746 | ||||||||
\(515\) | 3.91793 | 0.172645 | ||||||||
\(516\) | −38.0970 | −1.67713 | ||||||||
\(517\) | −3.07829 | −0.135383 | ||||||||
\(518\) | 45.6803 | 2.00708 | ||||||||
\(519\) | −56.8446 | −2.49520 | ||||||||
\(520\) | −2.49296 | −0.109324 | ||||||||
\(521\) | −16.0105 | −0.701434 | −0.350717 | − | 0.936482i | \(-0.614062\pi\) | ||||
−0.350717 | + | 0.936482i | \(0.614062\pi\) | |||||||
\(522\) | −17.8668 | −0.782008 | ||||||||
\(523\) | 1.35515 | 0.0592564 | 0.0296282 | − | 0.999561i | \(-0.490568\pi\) | ||||
0.0296282 | + | 0.999561i | \(0.490568\pi\) | |||||||
\(524\) | 15.3487 | 0.670511 | ||||||||
\(525\) | 167.869 | 7.32638 | ||||||||
\(526\) | −43.4206 | −1.89323 | ||||||||
\(527\) | 9.65108 | 0.420408 | ||||||||
\(528\) | 39.5386 | 1.72070 | ||||||||
\(529\) | −22.9922 | −0.999660 | ||||||||
\(530\) | 19.2238 | 0.835029 | ||||||||
\(531\) | −1.75208 | −0.0760338 | ||||||||
\(532\) | 36.7680 | 1.59409 | ||||||||
\(533\) | −0.706160 | −0.0305872 | ||||||||
\(534\) | −35.9406 | −1.55530 | ||||||||
\(535\) | −6.27097 | −0.271118 | ||||||||
\(536\) | −4.40662 | −0.190337 | ||||||||
\(537\) | 41.7722 | 1.80260 | ||||||||
\(538\) | −22.1736 | −0.955970 | ||||||||
\(539\) | −59.4765 | −2.56184 | ||||||||
\(540\) | −17.8077 | −0.766321 | ||||||||
\(541\) | 33.1080 | 1.42343 | 0.711713 | − | 0.702471i | \(-0.247920\pi\) | ||||
0.711713 | + | 0.702471i | \(0.247920\pi\) | |||||||
\(542\) | 37.0617 | 1.59194 | ||||||||
\(543\) | −17.3016 | −0.742481 | ||||||||
\(544\) | 8.21818 | 0.352352 | ||||||||
\(545\) | −59.2259 | −2.53696 | ||||||||
\(546\) | −12.3449 | −0.528314 | ||||||||
\(547\) | −26.3531 | −1.12678 | −0.563388 | − | 0.826192i | \(-0.690502\pi\) | ||||
−0.563388 | + | 0.826192i | \(0.690502\pi\) | |||||||
\(548\) | −18.1760 | −0.776439 | ||||||||
\(549\) | −20.1435 | −0.859702 | ||||||||
\(550\) | 66.1385 | 2.82015 | ||||||||
\(551\) | 12.5137 | 0.533100 | ||||||||
\(552\) | −0.294218 | −0.0125228 | ||||||||
\(553\) | 86.0462 | 3.65906 | ||||||||
\(554\) | −17.6804 | −0.751170 | ||||||||
\(555\) | 53.7590 | 2.28194 | ||||||||
\(556\) | 24.7415 | 1.04927 | ||||||||
\(557\) | 24.1858 | 1.02478 | 0.512392 | − | 0.858752i | \(-0.328760\pi\) | ||||
0.512392 | + | 0.858752i | \(0.328760\pi\) | |||||||
\(558\) | −58.1584 | −2.46204 | ||||||||
\(559\) | −5.23366 | −0.221360 | ||||||||
\(560\) | 104.736 | 4.42590 | ||||||||
\(561\) | −10.2904 | −0.434460 | ||||||||
\(562\) | −47.8590 | −2.01881 | ||||||||
\(563\) | −19.5434 | −0.823657 | −0.411828 | − | 0.911261i | \(-0.635110\pi\) | ||||
−0.411828 | + | 0.911261i | \(0.635110\pi\) | |||||||
\(564\) | 3.63278 | 0.152967 | ||||||||
\(565\) | −55.7004 | −2.34333 | ||||||||
\(566\) | −15.6387 | −0.657344 | ||||||||
\(567\) | −20.0780 | −0.843195 | ||||||||
\(568\) | −6.81142 | −0.285801 | ||||||||
\(569\) | −10.0091 | −0.419603 | −0.209802 | − | 0.977744i | \(-0.567282\pi\) | ||||
−0.209802 | + | 0.977744i | \(0.567282\pi\) | |||||||
\(570\) | 108.802 | 4.55723 | ||||||||
\(571\) | −8.28534 | −0.346731 | −0.173365 | − | 0.984858i | \(-0.555464\pi\) | ||||
−0.173365 | + | 0.984858i | \(0.555464\pi\) | |||||||
\(572\) | −1.93432 | −0.0808778 | ||||||||
\(573\) | 15.1925 | 0.634674 | ||||||||
\(574\) | 13.6671 | 0.570454 | ||||||||
\(575\) | −1.06834 | −0.0445528 | ||||||||
\(576\) | −8.24102 | −0.343376 | ||||||||
\(577\) | 9.42953 | 0.392556 | 0.196278 | − | 0.980548i | \(-0.437114\pi\) | ||||
0.196278 | + | 0.980548i | \(0.437114\pi\) | |||||||
\(578\) | 28.0180 | 1.16540 | ||||||||
\(579\) | −21.7572 | −0.904199 | ||||||||
\(580\) | −12.6941 | −0.527094 | ||||||||
\(581\) | 57.2447 | 2.37491 | ||||||||
\(582\) | 81.9427 | 3.39663 | ||||||||
\(583\) | −7.67375 | −0.317814 | ||||||||
\(584\) | 5.19984 | 0.215171 | ||||||||
\(585\) | −8.48727 | −0.350906 | ||||||||
\(586\) | 0.242939 | 0.0100357 | ||||||||
\(587\) | −21.8257 | −0.900844 | −0.450422 | − | 0.892816i | \(-0.648727\pi\) | ||||
−0.450422 | + | 0.892816i | \(0.648727\pi\) | |||||||
\(588\) | 70.1898 | 2.89458 | ||||||||
\(589\) | 40.7334 | 1.67839 | ||||||||
\(590\) | −3.13008 | −0.128863 | ||||||||
\(591\) | −28.4286 | −1.16940 | ||||||||
\(592\) | 23.7195 | 0.974864 | ||||||||
\(593\) | 39.5962 | 1.62602 | 0.813010 | − | 0.582250i | \(-0.197828\pi\) | ||||
0.813010 | + | 0.582250i | \(0.197828\pi\) | |||||||
\(594\) | 17.8740 | 0.733379 | ||||||||
\(595\) | −27.2587 | −1.11750 | ||||||||
\(596\) | 22.5805 | 0.924934 | ||||||||
\(597\) | −56.8237 | −2.32564 | ||||||||
\(598\) | 0.0785647 | 0.00321275 | ||||||||
\(599\) | 29.4004 | 1.20127 | 0.600634 | − | 0.799524i | \(-0.294915\pi\) | ||||
0.600634 | + | 0.799524i | \(0.294915\pi\) | |||||||
\(600\) | 40.1550 | 1.63932 | ||||||||
\(601\) | −24.8580 | −1.01398 | −0.506989 | − | 0.861953i | \(-0.669241\pi\) | ||||
−0.506989 | + | 0.861953i | \(0.669241\pi\) | |||||||
\(602\) | 101.293 | 4.12839 | ||||||||
\(603\) | −15.0023 | −0.610941 | ||||||||
\(604\) | 0.134816 | 0.00548560 | ||||||||
\(605\) | 8.12097 | 0.330164 | ||||||||
\(606\) | 34.3426 | 1.39507 | ||||||||
\(607\) | 24.2523 | 0.984372 | 0.492186 | − | 0.870490i | \(-0.336198\pi\) | ||||
0.492186 | + | 0.870490i | \(0.336198\pi\) | |||||||
\(608\) | 34.6857 | 1.40669 | ||||||||
\(609\) | 32.3393 | 1.31046 | ||||||||
\(610\) | −35.9862 | −1.45704 | ||||||||
\(611\) | 0.499060 | 0.0201898 | ||||||||
\(612\) | 7.09442 | 0.286775 | ||||||||
\(613\) | −17.9999 | −0.727009 | −0.363504 | − | 0.931593i | \(-0.618420\pi\) | ||||
−0.363504 | + | 0.931593i | \(0.618420\pi\) | |||||||
\(614\) | 48.4397 | 1.95487 | ||||||||
\(615\) | 16.0842 | 0.648577 | ||||||||
\(616\) | −19.2600 | −0.776009 | ||||||||
\(617\) | −30.0696 | −1.21056 | −0.605278 | − | 0.796014i | \(-0.706938\pi\) | ||||
−0.605278 | + | 0.796014i | \(0.706938\pi\) | |||||||
\(618\) | 4.64086 | 0.186683 | ||||||||
\(619\) | −43.5036 | −1.74856 | −0.874279 | − | 0.485425i | \(-0.838665\pi\) | ||||
−0.874279 | + | 0.485425i | \(0.838665\pi\) | |||||||
\(620\) | −41.3208 | −1.65948 | ||||||||
\(621\) | −0.288719 | −0.0115859 | ||||||||
\(622\) | −35.3981 | −1.41934 | ||||||||
\(623\) | 38.0038 | 1.52259 | ||||||||
\(624\) | −6.41009 | −0.256609 | ||||||||
\(625\) | 60.4316 | 2.41726 | ||||||||
\(626\) | 10.5706 | 0.422487 | ||||||||
\(627\) | −43.4316 | −1.73449 | ||||||||
\(628\) | 8.57682 | 0.342252 | ||||||||
\(629\) | −6.17326 | −0.246144 | ||||||||
\(630\) | 164.264 | 6.54443 | ||||||||
\(631\) | −32.6888 | −1.30132 | −0.650660 | − | 0.759369i | \(-0.725508\pi\) | ||||
−0.650660 | + | 0.759369i | \(0.725508\pi\) | |||||||
\(632\) | 20.5827 | 0.818734 | ||||||||
\(633\) | −1.59112 | −0.0632412 | ||||||||
\(634\) | −57.2959 | −2.27551 | ||||||||
\(635\) | −16.0423 | −0.636618 | ||||||||
\(636\) | 9.05600 | 0.359094 | ||||||||
\(637\) | 9.64247 | 0.382049 | ||||||||
\(638\) | 12.7414 | 0.504435 | ||||||||
\(639\) | −23.1894 | −0.917360 | ||||||||
\(640\) | 38.5652 | 1.52442 | ||||||||
\(641\) | 28.3515 | 1.11982 | 0.559908 | − | 0.828555i | \(-0.310837\pi\) | ||||
0.559908 | + | 0.828555i | \(0.310837\pi\) | |||||||
\(642\) | −7.42809 | −0.293163 | ||||||||
\(643\) | −5.78843 | −0.228273 | −0.114137 | − | 0.993465i | \(-0.536410\pi\) | ||||
−0.114137 | + | 0.993465i | \(0.536410\pi\) | |||||||
\(644\) | −0.604721 | −0.0238294 | ||||||||
\(645\) | 119.207 | 4.69377 | ||||||||
\(646\) | −12.4940 | −0.491569 | ||||||||
\(647\) | 25.4787 | 1.00167 | 0.500836 | − | 0.865542i | \(-0.333026\pi\) | ||||
0.500836 | + | 0.865542i | \(0.333026\pi\) | |||||||
\(648\) | −4.80274 | −0.188670 | ||||||||
\(649\) | 1.24946 | 0.0490457 | ||||||||
\(650\) | −10.7225 | −0.420572 | ||||||||
\(651\) | 105.268 | 4.12579 | ||||||||
\(652\) | 8.39803 | 0.328892 | ||||||||
\(653\) | 23.0587 | 0.902355 | 0.451178 | − | 0.892434i | \(-0.351004\pi\) | ||||
0.451178 | + | 0.892434i | \(0.351004\pi\) | |||||||
\(654\) | −70.1542 | −2.74325 | ||||||||
\(655\) | −48.0266 | −1.87655 | ||||||||
\(656\) | 7.09664 | 0.277077 | ||||||||
\(657\) | 17.7028 | 0.690653 | ||||||||
\(658\) | −9.65887 | −0.376542 | ||||||||
\(659\) | −24.6113 | −0.958721 | −0.479360 | − | 0.877618i | \(-0.659131\pi\) | ||||
−0.479360 | + | 0.877618i | \(0.659131\pi\) | |||||||
\(660\) | 44.0579 | 1.71495 | ||||||||
\(661\) | −19.8608 | −0.772497 | −0.386249 | − | 0.922395i | \(-0.626229\pi\) | ||||
−0.386249 | + | 0.922395i | \(0.626229\pi\) | |||||||
\(662\) | −20.8060 | −0.808647 | ||||||||
\(663\) | 1.66830 | 0.0647914 | ||||||||
\(664\) | 13.6932 | 0.531399 | ||||||||
\(665\) | −115.048 | −4.46138 | ||||||||
\(666\) | 37.2007 | 1.44150 | ||||||||
\(667\) | −0.205812 | −0.00796906 | ||||||||
\(668\) | −7.96031 | −0.307994 | ||||||||
\(669\) | 33.4009 | 1.29135 | ||||||||
\(670\) | −26.8015 | −1.03543 | ||||||||
\(671\) | 14.3649 | 0.554552 | ||||||||
\(672\) | 89.6390 | 3.45790 | ||||||||
\(673\) | −26.9327 | −1.03818 | −0.519090 | − | 0.854719i | \(-0.673729\pi\) | ||||
−0.519090 | + | 0.854719i | \(0.673729\pi\) | |||||||
\(674\) | −47.7195 | −1.83809 | ||||||||
\(675\) | 39.4044 | 1.51668 | ||||||||
\(676\) | −16.8542 | −0.648238 | ||||||||
\(677\) | −18.9289 | −0.727496 | −0.363748 | − | 0.931497i | \(-0.618503\pi\) | ||||
−0.363748 | + | 0.931497i | \(0.618503\pi\) | |||||||
\(678\) | −65.9782 | −2.53388 | ||||||||
\(679\) | −86.6467 | −3.32520 | ||||||||
\(680\) | −6.52041 | −0.250046 | ||||||||
\(681\) | 42.6110 | 1.63286 | ||||||||
\(682\) | 41.4746 | 1.58814 | ||||||||
\(683\) | −38.8590 | −1.48690 | −0.743448 | − | 0.668794i | \(-0.766811\pi\) | ||||
−0.743448 | + | 0.668794i | \(0.766811\pi\) | |||||||
\(684\) | 29.9428 | 1.14489 | ||||||||
\(685\) | 56.8732 | 2.17301 | ||||||||
\(686\) | −120.602 | −4.60461 | ||||||||
\(687\) | 25.0556 | 0.955930 | ||||||||
\(688\) | 52.5962 | 2.00521 | ||||||||
\(689\) | 1.24409 | 0.0473959 | ||||||||
\(690\) | −1.78947 | −0.0681239 | ||||||||
\(691\) | −43.6266 | −1.65964 | −0.829818 | − | 0.558034i | \(-0.811556\pi\) | ||||
−0.829818 | + | 0.558034i | \(0.811556\pi\) | |||||||
\(692\) | −27.9476 | −1.06241 | ||||||||
\(693\) | −65.5707 | −2.49082 | ||||||||
\(694\) | 52.0809 | 1.97696 | ||||||||
\(695\) | −77.4171 | −2.93660 | ||||||||
\(696\) | 7.73572 | 0.293222 | ||||||||
\(697\) | −1.84698 | −0.0699593 | ||||||||
\(698\) | −43.9710 | −1.66433 | ||||||||
\(699\) | 56.4615 | 2.13557 | ||||||||
\(700\) | 82.5325 | 3.11943 | ||||||||
\(701\) | −46.1568 | −1.74332 | −0.871660 | − | 0.490111i | \(-0.836956\pi\) | ||||
−0.871660 | + | 0.490111i | \(0.836956\pi\) | |||||||
\(702\) | −2.89777 | −0.109369 | ||||||||
\(703\) | −26.0549 | −0.982678 | ||||||||
\(704\) | 5.87693 | 0.221495 | ||||||||
\(705\) | −11.3671 | −0.428109 | ||||||||
\(706\) | 60.7518 | 2.28642 | ||||||||
\(707\) | −36.3141 | −1.36573 | ||||||||
\(708\) | −1.47452 | −0.0554160 | ||||||||
\(709\) | −8.25597 | −0.310060 | −0.155030 | − | 0.987910i | \(-0.549547\pi\) | ||||
−0.155030 | + | 0.987910i | \(0.549547\pi\) | |||||||
\(710\) | −41.4278 | −1.55476 | ||||||||
\(711\) | 70.0735 | 2.62796 | ||||||||
\(712\) | 9.09070 | 0.340688 | ||||||||
\(713\) | −0.669941 | −0.0250895 | ||||||||
\(714\) | −32.2885 | −1.20837 | ||||||||
\(715\) | 6.05254 | 0.226352 | ||||||||
\(716\) | 20.5373 | 0.767513 | ||||||||
\(717\) | −21.6909 | −0.810061 | ||||||||
\(718\) | −39.2760 | −1.46577 | ||||||||
\(719\) | 8.86749 | 0.330702 | 0.165351 | − | 0.986235i | \(-0.447124\pi\) | ||||
0.165351 | + | 0.986235i | \(0.447124\pi\) | |||||||
\(720\) | 85.2939 | 3.17871 | ||||||||
\(721\) | −4.90728 | −0.182757 | ||||||||
\(722\) | −18.1094 | −0.673962 | ||||||||
\(723\) | 43.1800 | 1.60588 | ||||||||
\(724\) | −8.50630 | −0.316134 | ||||||||
\(725\) | 28.0892 | 1.04321 | ||||||||
\(726\) | 9.61945 | 0.357011 | ||||||||
\(727\) | −31.0127 | −1.15020 | −0.575098 | − | 0.818085i | \(-0.695036\pi\) | ||||
−0.575098 | + | 0.818085i | \(0.695036\pi\) | |||||||
\(728\) | 3.12248 | 0.115727 | ||||||||
\(729\) | −42.6471 | −1.57952 | ||||||||
\(730\) | 31.6260 | 1.17053 | ||||||||
\(731\) | −13.6888 | −0.506297 | ||||||||
\(732\) | −16.9525 | −0.626581 | ||||||||
\(733\) | −6.91323 | −0.255346 | −0.127673 | − | 0.991816i | \(-0.540751\pi\) | ||||
−0.127673 | + | 0.991816i | \(0.540751\pi\) | |||||||
\(734\) | −31.8543 | −1.17576 | ||||||||
\(735\) | −219.626 | −8.10105 | ||||||||
\(736\) | −0.570474 | −0.0210280 | ||||||||
\(737\) | 10.6986 | 0.394088 | ||||||||
\(738\) | 11.1301 | 0.409704 | ||||||||
\(739\) | 32.2320 | 1.18568 | 0.592838 | − | 0.805322i | \(-0.298008\pi\) | ||||
0.592838 | + | 0.805322i | \(0.298008\pi\) | |||||||
\(740\) | 26.4306 | 0.971608 | ||||||||
\(741\) | 7.04123 | 0.258666 | ||||||||
\(742\) | −24.0782 | −0.883938 | ||||||||
\(743\) | −46.5143 | −1.70644 | −0.853222 | − | 0.521547i | \(-0.825355\pi\) | ||||
−0.853222 | + | 0.521547i | \(0.825355\pi\) | |||||||
\(744\) | 25.1807 | 0.923168 | ||||||||
\(745\) | −70.6552 | −2.58861 | ||||||||
\(746\) | −8.94324 | −0.327435 | ||||||||
\(747\) | 46.6184 | 1.70568 | ||||||||
\(748\) | −5.05926 | −0.184985 | ||||||||
\(749\) | 7.85451 | 0.286998 | ||||||||
\(750\) | 143.098 | 5.22520 | ||||||||
\(751\) | 41.3671 | 1.50951 | 0.754754 | − | 0.656008i | \(-0.227756\pi\) | ||||
0.754754 | + | 0.656008i | \(0.227756\pi\) | |||||||
\(752\) | −5.01536 | −0.182891 | ||||||||
\(753\) | 8.88352 | 0.323733 | ||||||||
\(754\) | −2.06566 | −0.0752269 | ||||||||
\(755\) | −0.421845 | −0.0153525 | ||||||||
\(756\) | 22.3045 | 0.811206 | ||||||||
\(757\) | −3.99613 | −0.145242 | −0.0726208 | − | 0.997360i | \(-0.523136\pi\) | ||||
−0.0726208 | + | 0.997360i | \(0.523136\pi\) | |||||||
\(758\) | 41.2875 | 1.49963 | ||||||||
\(759\) | 0.714318 | 0.0259281 | ||||||||
\(760\) | −27.5201 | −0.998258 | ||||||||
\(761\) | 18.3632 | 0.665666 | 0.332833 | − | 0.942986i | \(-0.391996\pi\) | ||||
0.332833 | + | 0.942986i | \(0.391996\pi\) | |||||||
\(762\) | −19.0024 | −0.688384 | ||||||||
\(763\) | 74.1815 | 2.68555 | ||||||||
\(764\) | 7.46937 | 0.270232 | ||||||||
\(765\) | −22.1987 | −0.802595 | ||||||||
\(766\) | 9.39496 | 0.339454 | ||||||||
\(767\) | −0.202566 | −0.00731423 | ||||||||
\(768\) | 56.1849 | 2.02740 | ||||||||
\(769\) | −18.2658 | −0.658683 | −0.329341 | − | 0.944211i | \(-0.606827\pi\) | ||||
−0.329341 | + | 0.944211i | \(0.606827\pi\) | |||||||
\(770\) | −117.142 | −4.22149 | ||||||||
\(771\) | −7.34361 | −0.264474 | ||||||||
\(772\) | −10.6969 | −0.384991 | ||||||||
\(773\) | −13.0559 | −0.469588 | −0.234794 | − | 0.972045i | \(-0.575442\pi\) | ||||
−0.234794 | + | 0.972045i | \(0.575442\pi\) | |||||||
\(774\) | 82.4899 | 2.96504 | ||||||||
\(775\) | 91.4336 | 3.28439 | ||||||||
\(776\) | −20.7263 | −0.744031 | ||||||||
\(777\) | −67.3342 | −2.41560 | ||||||||
\(778\) | 49.2625 | 1.76615 | ||||||||
\(779\) | −7.79537 | −0.279298 | ||||||||
\(780\) | −7.14277 | −0.255752 | ||||||||
\(781\) | 16.5371 | 0.591744 | ||||||||
\(782\) | 0.205488 | 0.00734824 | ||||||||
\(783\) | 7.59114 | 0.271285 | ||||||||
\(784\) | −96.9031 | −3.46083 | ||||||||
\(785\) | −26.8372 | −0.957859 | ||||||||
\(786\) | −56.8885 | −2.02914 | ||||||||
\(787\) | −42.3411 | −1.50930 | −0.754648 | − | 0.656130i | \(-0.772192\pi\) | ||||
−0.754648 | + | 0.656130i | \(0.772192\pi\) | |||||||
\(788\) | −13.9769 | −0.497906 | ||||||||
\(789\) | 64.0033 | 2.27858 | ||||||||
\(790\) | 125.186 | 4.45391 | ||||||||
\(791\) | 69.7658 | 2.48059 | ||||||||
\(792\) | −15.6848 | −0.557336 | ||||||||
\(793\) | −2.32888 | −0.0827008 | ||||||||
\(794\) | −37.0792 | −1.31589 | ||||||||
\(795\) | −28.3365 | −1.00499 | ||||||||
\(796\) | −27.9373 | −0.990213 | ||||||||
\(797\) | 54.0030 | 1.91288 | 0.956442 | − | 0.291921i | \(-0.0942945\pi\) | ||||
0.956442 | + | 0.291921i | \(0.0942945\pi\) | |||||||
\(798\) | −136.277 | −4.82415 | ||||||||
\(799\) | 1.30530 | 0.0461784 | ||||||||
\(800\) | 77.8584 | 2.75271 | ||||||||
\(801\) | 30.9492 | 1.09354 | ||||||||
\(802\) | 68.0963 | 2.40457 | ||||||||
\(803\) | −12.6244 | −0.445507 | ||||||||
\(804\) | −12.6257 | −0.445275 | ||||||||
\(805\) | 1.89219 | 0.0666911 | ||||||||
\(806\) | −6.72396 | −0.236841 | ||||||||
\(807\) | 32.6846 | 1.15055 | ||||||||
\(808\) | −8.68650 | −0.305590 | ||||||||
\(809\) | 18.9901 | 0.667655 | 0.333828 | − | 0.942634i | \(-0.391660\pi\) | ||||
0.333828 | + | 0.942634i | \(0.391660\pi\) | |||||||
\(810\) | −29.2108 | −1.02636 | ||||||||
\(811\) | −1.99008 | −0.0698810 | −0.0349405 | − | 0.999389i | \(-0.511124\pi\) | ||||
−0.0349405 | + | 0.999389i | \(0.511124\pi\) | |||||||
\(812\) | 15.8996 | 0.557967 | ||||||||
\(813\) | −54.6302 | −1.91596 | ||||||||
\(814\) | −26.5290 | −0.929840 | ||||||||
\(815\) | −26.2777 | −0.920469 | ||||||||
\(816\) | −16.7658 | −0.586919 | ||||||||
\(817\) | −57.7749 | −2.02129 | ||||||||
\(818\) | −55.5424 | −1.94200 | ||||||||
\(819\) | 10.6305 | 0.371459 | ||||||||
\(820\) | 7.90778 | 0.276152 | ||||||||
\(821\) | −13.6320 | −0.475759 | −0.237879 | − | 0.971295i | \(-0.576452\pi\) | ||||
−0.237879 | + | 0.971295i | \(0.576452\pi\) | |||||||
\(822\) | 67.3675 | 2.34971 | ||||||||
\(823\) | −21.4172 | −0.746557 | −0.373279 | − | 0.927719i | \(-0.621766\pi\) | ||||
−0.373279 | + | 0.927719i | \(0.621766\pi\) | |||||||
\(824\) | −1.17384 | −0.0408928 | ||||||||
\(825\) | −97.4903 | −3.39418 | ||||||||
\(826\) | 3.92048 | 0.136411 | ||||||||
\(827\) | −9.71569 | −0.337848 | −0.168924 | − | 0.985629i | \(-0.554029\pi\) | ||||
−0.168924 | + | 0.985629i | \(0.554029\pi\) | |||||||
\(828\) | −0.492467 | −0.0171144 | ||||||||
\(829\) | −32.0851 | −1.11436 | −0.557181 | − | 0.830391i | \(-0.688117\pi\) | ||||
−0.557181 | + | 0.830391i | \(0.688117\pi\) | |||||||
\(830\) | 83.2835 | 2.89081 | ||||||||
\(831\) | 26.0615 | 0.904065 | ||||||||
\(832\) | −0.952782 | −0.0330318 | ||||||||
\(833\) | 25.2201 | 0.873826 | ||||||||
\(834\) | −91.7021 | −3.17538 | ||||||||
\(835\) | 24.9081 | 0.861980 | ||||||||
\(836\) | −21.3531 | −0.738513 | ||||||||
\(837\) | 24.7100 | 0.854103 | ||||||||
\(838\) | −39.4158 | −1.36160 | ||||||||
\(839\) | 2.52233 | 0.0870804 | 0.0435402 | − | 0.999052i | \(-0.486136\pi\) | ||||
0.0435402 | + | 0.999052i | \(0.486136\pi\) | |||||||
\(840\) | −71.1208 | −2.45390 | ||||||||
\(841\) | −23.5887 | −0.813404 | ||||||||
\(842\) | 40.3246 | 1.38968 | ||||||||
\(843\) | 70.5457 | 2.42972 | ||||||||
\(844\) | −0.782272 | −0.0269269 | ||||||||
\(845\) | 52.7373 | 1.81422 | ||||||||
\(846\) | −7.86590 | −0.270435 | ||||||||
\(847\) | −10.1717 | −0.349503 | ||||||||
\(848\) | −12.5026 | −0.429340 | ||||||||
\(849\) | 23.0520 | 0.791141 | ||||||||
\(850\) | −28.0450 | −0.961937 | ||||||||
\(851\) | 0.428524 | 0.0146896 | ||||||||
\(852\) | −19.5159 | −0.668603 | ||||||||
\(853\) | −28.3783 | −0.971654 | −0.485827 | − | 0.874055i | \(-0.661482\pi\) | ||||
−0.485827 | + | 0.874055i | \(0.661482\pi\) | |||||||
\(854\) | 45.0734 | 1.54238 | ||||||||
\(855\) | −93.6919 | −3.20420 | ||||||||
\(856\) | 1.87884 | 0.0642173 | ||||||||
\(857\) | 20.0013 | 0.683231 | 0.341616 | − | 0.939840i | \(-0.389026\pi\) | ||||
0.341616 | + | 0.939840i | \(0.389026\pi\) | |||||||
\(858\) | 7.16936 | 0.244758 | ||||||||
\(859\) | −55.8459 | −1.90544 | −0.952719 | − | 0.303853i | \(-0.901727\pi\) | ||||
−0.952719 | + | 0.303853i | \(0.901727\pi\) | |||||||
\(860\) | 58.6080 | 1.99852 | ||||||||
\(861\) | −20.1458 | −0.686565 | ||||||||
\(862\) | −55.5196 | −1.89101 | ||||||||
\(863\) | −10.7654 | −0.366457 | −0.183229 | − | 0.983070i | \(-0.558655\pi\) | ||||
−0.183229 | + | 0.983070i | \(0.558655\pi\) | |||||||
\(864\) | 21.0413 | 0.715840 | ||||||||
\(865\) | 87.4491 | 2.97336 | ||||||||
\(866\) | −37.1289 | −1.26169 | ||||||||
\(867\) | −41.2995 | −1.40260 | ||||||||
\(868\) | 51.7551 | 1.75668 | ||||||||
\(869\) | −49.9716 | −1.69517 | ||||||||
\(870\) | 47.0495 | 1.59513 | ||||||||
\(871\) | −1.73448 | −0.0587707 | ||||||||
\(872\) | 17.7446 | 0.600907 | ||||||||
\(873\) | −70.5626 | −2.38818 | ||||||||
\(874\) | 0.867284 | 0.0293363 | ||||||||
\(875\) | −151.313 | −5.11531 | ||||||||
\(876\) | 14.8984 | 0.503372 | ||||||||
\(877\) | −13.8207 | −0.466692 | −0.233346 | − | 0.972394i | \(-0.574968\pi\) | ||||
−0.233346 | + | 0.972394i | \(0.574968\pi\) | |||||||
\(878\) | −50.6653 | −1.70987 | ||||||||
\(879\) | −0.358101 | −0.0120784 | ||||||||
\(880\) | −60.8257 | −2.05044 | ||||||||
\(881\) | −5.26645 | −0.177431 | −0.0887157 | − | 0.996057i | \(-0.528276\pi\) | ||||
−0.0887157 | + | 0.996057i | \(0.528276\pi\) | |||||||
\(882\) | −151.979 | −5.11741 | ||||||||
\(883\) | −5.43937 | −0.183049 | −0.0915247 | − | 0.995803i | \(-0.529174\pi\) | ||||
−0.0915247 | + | 0.995803i | \(0.529174\pi\) | |||||||
\(884\) | 0.820218 | 0.0275869 | ||||||||
\(885\) | 4.61384 | 0.155093 | ||||||||
\(886\) | 23.7583 | 0.798177 | ||||||||
\(887\) | 25.5993 | 0.859542 | 0.429771 | − | 0.902938i | \(-0.358594\pi\) | ||||
0.429771 | + | 0.902938i | \(0.358594\pi\) | |||||||
\(888\) | −16.1067 | −0.540504 | ||||||||
\(889\) | 20.0932 | 0.673906 | ||||||||
\(890\) | 55.2906 | 1.85335 | ||||||||
\(891\) | 11.6603 | 0.390636 | ||||||||
\(892\) | 16.4215 | 0.549834 | ||||||||
\(893\) | 5.50918 | 0.184358 | ||||||||
\(894\) | −83.6925 | −2.79910 | ||||||||
\(895\) | −64.2618 | −2.14804 | ||||||||
\(896\) | −48.3037 | −1.61371 | ||||||||
\(897\) | −0.115807 | −0.00386668 | ||||||||
\(898\) | −3.86607 | −0.129012 | ||||||||
\(899\) | 17.6144 | 0.587473 | ||||||||
\(900\) | 67.2120 | 2.24040 | ||||||||
\(901\) | 3.25394 | 0.108404 | ||||||||
\(902\) | −7.93722 | −0.264280 | ||||||||
\(903\) | −149.309 | −4.96869 | ||||||||
\(904\) | 16.6883 | 0.555045 | ||||||||
\(905\) | 26.6165 | 0.884763 | ||||||||
\(906\) | −0.499684 | −0.0166009 | ||||||||
\(907\) | −22.5912 | −0.750129 | −0.375064 | − | 0.926999i | \(-0.622379\pi\) | ||||
−0.375064 | + | 0.926999i | \(0.622379\pi\) | |||||||
\(908\) | 20.9497 | 0.695239 | ||||||||
\(909\) | −29.5731 | −0.980878 | ||||||||
\(910\) | 18.9913 | 0.629555 | ||||||||
\(911\) | 40.5238 | 1.34261 | 0.671307 | − | 0.741179i | \(-0.265733\pi\) | ||||
0.671307 | + | 0.741179i | \(0.265733\pi\) | |||||||
\(912\) | −70.7617 | −2.34315 | ||||||||
\(913\) | −33.2450 | −1.10025 | ||||||||
\(914\) | −56.8859 | −1.88162 | ||||||||
\(915\) | 53.0448 | 1.75361 | ||||||||
\(916\) | 12.3186 | 0.407017 | ||||||||
\(917\) | 60.1542 | 1.98647 | ||||||||
\(918\) | −7.57920 | −0.250151 | ||||||||
\(919\) | 56.5294 | 1.86473 | 0.932367 | − | 0.361514i | \(-0.117740\pi\) | ||||
0.932367 | + | 0.361514i | \(0.117740\pi\) | |||||||
\(920\) | 0.452622 | 0.0149225 | ||||||||
\(921\) | −71.4017 | −2.35277 | ||||||||
\(922\) | −28.8212 | −0.949175 | ||||||||
\(923\) | −2.68103 | −0.0882473 | ||||||||
\(924\) | −55.1834 | −1.81540 | ||||||||
\(925\) | −58.4850 | −1.92297 | ||||||||
\(926\) | 5.27486 | 0.173343 | ||||||||
\(927\) | −3.99634 | −0.131257 | ||||||||
\(928\) | 14.9992 | 0.492372 | ||||||||
\(929\) | −24.7082 | −0.810650 | −0.405325 | − | 0.914173i | \(-0.632842\pi\) | ||||
−0.405325 | + | 0.914173i | \(0.632842\pi\) | |||||||
\(930\) | 153.152 | 5.02204 | ||||||||
\(931\) | 106.444 | 3.48857 | ||||||||
\(932\) | 27.7592 | 0.909284 | ||||||||
\(933\) | 52.1780 | 1.70823 | ||||||||
\(934\) | −16.3301 | −0.534339 | ||||||||
\(935\) | 15.8306 | 0.517716 | ||||||||
\(936\) | 2.54286 | 0.0831159 | ||||||||
\(937\) | 40.6915 | 1.32933 | 0.664667 | − | 0.747139i | \(-0.268573\pi\) | ||||
0.664667 | + | 0.747139i | \(0.268573\pi\) | |||||||
\(938\) | 33.5694 | 1.09608 | ||||||||
\(939\) | −15.5814 | −0.508481 | ||||||||
\(940\) | −5.58862 | −0.182281 | ||||||||
\(941\) | 25.7501 | 0.839429 | 0.419715 | − | 0.907656i | \(-0.362130\pi\) | ||||
0.419715 | + | 0.907656i | \(0.362130\pi\) | |||||||
\(942\) | −31.7892 | −1.03575 | ||||||||
\(943\) | 0.128210 | 0.00417510 | ||||||||
\(944\) | 2.03571 | 0.0662567 | ||||||||
\(945\) | −69.7915 | −2.27032 | ||||||||
\(946\) | −58.8262 | −1.91260 | ||||||||
\(947\) | 53.0653 | 1.72439 | 0.862196 | − | 0.506575i | \(-0.169089\pi\) | ||||
0.862196 | + | 0.506575i | \(0.169089\pi\) | |||||||
\(948\) | 58.9728 | 1.91535 | ||||||||
\(949\) | 2.04670 | 0.0664388 | ||||||||
\(950\) | −118.367 | −3.84033 | ||||||||
\(951\) | 84.4560 | 2.73867 | ||||||||
\(952\) | 8.16694 | 0.264692 | ||||||||
\(953\) | 17.7978 | 0.576528 | 0.288264 | − | 0.957551i | \(-0.406922\pi\) | ||||
0.288264 | + | 0.957551i | \(0.406922\pi\) | |||||||
\(954\) | −19.6086 | −0.634851 | ||||||||
\(955\) | −23.3719 | −0.756297 | ||||||||
\(956\) | −10.6643 | −0.344908 | ||||||||
\(957\) | −18.7812 | −0.607109 | ||||||||
\(958\) | 64.2567 | 2.07604 | ||||||||
\(959\) | −71.2348 | −2.30029 | ||||||||
\(960\) | 21.7015 | 0.700413 | ||||||||
\(961\) | 26.3369 | 0.849576 | ||||||||
\(962\) | 4.30094 | 0.138668 | ||||||||
\(963\) | 6.39648 | 0.206124 | ||||||||
\(964\) | 21.2294 | 0.683753 | ||||||||
\(965\) | 33.4710 | 1.07747 | ||||||||
\(966\) | 2.24134 | 0.0721140 | ||||||||
\(967\) | −33.3758 | −1.07329 | −0.536647 | − | 0.843807i | \(-0.680309\pi\) | ||||
−0.536647 | + | 0.843807i | \(0.680309\pi\) | |||||||
\(968\) | −2.43311 | −0.0782031 | ||||||||
\(969\) | 18.4165 | 0.591624 | ||||||||
\(970\) | −126.060 | −4.04753 | ||||||||
\(971\) | −18.5427 | −0.595064 | −0.297532 | − | 0.954712i | \(-0.596163\pi\) | ||||
−0.297532 | + | 0.954712i | \(0.596163\pi\) | |||||||
\(972\) | −26.6892 | −0.856056 | ||||||||
\(973\) | 96.9664 | 3.10860 | ||||||||
\(974\) | 17.8365 | 0.571518 | ||||||||
\(975\) | 15.8053 | 0.506176 | ||||||||
\(976\) | 23.4043 | 0.749154 | ||||||||
\(977\) | 32.6089 | 1.04325 | 0.521626 | − | 0.853174i | \(-0.325326\pi\) | ||||
0.521626 | + | 0.853174i | \(0.325326\pi\) | |||||||
\(978\) | −31.1265 | −0.995316 | ||||||||
\(979\) | −22.0709 | −0.705388 | ||||||||
\(980\) | −107.979 | −3.44927 | ||||||||
\(981\) | 60.4112 | 1.92878 | ||||||||
\(982\) | −18.5994 | −0.593531 | ||||||||
\(983\) | −59.8324 | −1.90836 | −0.954179 | − | 0.299237i | \(-0.903268\pi\) | ||||
−0.954179 | + | 0.299237i | \(0.903268\pi\) | |||||||
\(984\) | −4.81896 | −0.153623 | ||||||||
\(985\) | 43.7342 | 1.39349 | ||||||||
\(986\) | −5.40279 | −0.172060 | ||||||||
\(987\) | 14.2375 | 0.453184 | ||||||||
\(988\) | 3.46182 | 0.110135 | ||||||||
\(989\) | 0.950222 | 0.0302153 | ||||||||
\(990\) | −95.3968 | −3.03191 | ||||||||
\(991\) | −28.0661 | −0.891551 | −0.445775 | − | 0.895145i | \(-0.647072\pi\) | ||||
−0.445775 | + | 0.895145i | \(0.647072\pi\) | |||||||
\(992\) | 48.8240 | 1.55016 | ||||||||
\(993\) | 30.6687 | 0.973241 | ||||||||
\(994\) | 51.8891 | 1.64582 | ||||||||
\(995\) | 87.4169 | 2.77130 | ||||||||
\(996\) | 39.2334 | 1.24316 | ||||||||
\(997\) | −40.7160 | −1.28949 | −0.644744 | − | 0.764399i | \(-0.723036\pi\) | ||||
−0.644744 | + | 0.764399i | \(0.723036\pi\) | |||||||
\(998\) | 14.3937 | 0.455625 | ||||||||
\(999\) | −15.8056 | −0.500068 |
(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 | 4001.2.a.b.1.40 | ✓ | 184 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.b.1.40 | ✓ | 184 | 1.1 | even | 1 | trivial |