Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4019,2,Mod(1,4019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4019, 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("4019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4019.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: | \(32.0918765724\) |
Analytic rank: | \(0\) |
Dimension: | \(186\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.43886 | −1.72454 | −0.862268 | − | 0.506452i | \(-0.830957\pi\) | ||||
−0.862268 | + | 0.506452i | \(0.830957\pi\) | |||||||
\(3\) | −0.628245 | −0.362717 | −0.181359 | − | 0.983417i | \(-0.558049\pi\) | ||||
−0.181359 | + | 0.983417i | \(0.558049\pi\) | |||||||
\(4\) | 3.94805 | 1.97403 | ||||||||
\(5\) | 3.87591 | 1.73336 | 0.866680 | − | 0.498865i | \(-0.166250\pi\) | ||||
0.866680 | + | 0.498865i | \(0.166250\pi\) | |||||||
\(6\) | 1.53220 | 0.625519 | ||||||||
\(7\) | −4.09962 | −1.54951 | −0.774755 | − | 0.632262i | \(-0.782127\pi\) | ||||
−0.774755 | + | 0.632262i | \(0.782127\pi\) | |||||||
\(8\) | −4.75103 | −1.67974 | ||||||||
\(9\) | −2.60531 | −0.868436 | ||||||||
\(10\) | −9.45281 | −2.98924 | ||||||||
\(11\) | −2.21292 | −0.667222 | −0.333611 | − | 0.942711i | \(-0.608267\pi\) | ||||
−0.333611 | + | 0.942711i | \(0.608267\pi\) | |||||||
\(12\) | −2.48034 | −0.716013 | ||||||||
\(13\) | 1.62769 | 0.451439 | 0.225720 | − | 0.974192i | \(-0.427527\pi\) | ||||
0.225720 | + | 0.974192i | \(0.427527\pi\) | |||||||
\(14\) | 9.99840 | 2.67219 | ||||||||
\(15\) | −2.43502 | −0.628719 | ||||||||
\(16\) | 3.69100 | 0.922751 | ||||||||
\(17\) | 6.22231 | 1.50913 | 0.754566 | − | 0.656224i | \(-0.227847\pi\) | ||||
0.754566 | + | 0.656224i | \(0.227847\pi\) | |||||||
\(18\) | 6.35399 | 1.49765 | ||||||||
\(19\) | 2.20181 | 0.505130 | 0.252565 | − | 0.967580i | \(-0.418726\pi\) | ||||
0.252565 | + | 0.967580i | \(0.418726\pi\) | |||||||
\(20\) | 15.3023 | 3.42170 | ||||||||
\(21\) | 2.57556 | 0.562034 | ||||||||
\(22\) | 5.39702 | 1.15065 | ||||||||
\(23\) | 3.51792 | 0.733537 | 0.366769 | − | 0.930312i | \(-0.380464\pi\) | ||||
0.366769 | + | 0.930312i | \(0.380464\pi\) | |||||||
\(24\) | 2.98481 | 0.609271 | ||||||||
\(25\) | 10.0227 | 2.00453 | ||||||||
\(26\) | −3.96970 | −0.778523 | ||||||||
\(27\) | 3.52150 | 0.677714 | ||||||||
\(28\) | −16.1855 | −3.05877 | ||||||||
\(29\) | −1.15470 | −0.214423 | −0.107212 | − | 0.994236i | \(-0.534192\pi\) | ||||
−0.107212 | + | 0.994236i | \(0.534192\pi\) | |||||||
\(30\) | 5.93868 | 1.08425 | ||||||||
\(31\) | 5.67640 | 1.01951 | 0.509756 | − | 0.860319i | \(-0.329736\pi\) | ||||
0.509756 | + | 0.860319i | \(0.329736\pi\) | |||||||
\(32\) | 0.500206 | 0.0884247 | ||||||||
\(33\) | 1.39026 | 0.242013 | ||||||||
\(34\) | −15.1754 | −2.60255 | ||||||||
\(35\) | −15.8897 | −2.68586 | ||||||||
\(36\) | −10.2859 | −1.71432 | ||||||||
\(37\) | −11.2931 | −1.85658 | −0.928291 | − | 0.371855i | \(-0.878722\pi\) | ||||
−0.928291 | + | 0.371855i | \(0.878722\pi\) | |||||||
\(38\) | −5.36992 | −0.871116 | ||||||||
\(39\) | −1.02259 | −0.163745 | ||||||||
\(40\) | −18.4146 | −2.91160 | ||||||||
\(41\) | 6.68311 | 1.04373 | 0.521863 | − | 0.853029i | \(-0.325237\pi\) | ||||
0.521863 | + | 0.853029i | \(0.325237\pi\) | |||||||
\(42\) | −6.28144 | −0.969248 | ||||||||
\(43\) | −4.36322 | −0.665385 | −0.332693 | − | 0.943035i | \(-0.607957\pi\) | ||||
−0.332693 | + | 0.943035i | \(0.607957\pi\) | |||||||
\(44\) | −8.73674 | −1.31711 | ||||||||
\(45\) | −10.0979 | −1.50531 | ||||||||
\(46\) | −8.57973 | −1.26501 | ||||||||
\(47\) | −5.80689 | −0.847021 | −0.423511 | − | 0.905891i | \(-0.639202\pi\) | ||||
−0.423511 | + | 0.905891i | \(0.639202\pi\) | |||||||
\(48\) | −2.31885 | −0.334698 | ||||||||
\(49\) | 9.80686 | 1.40098 | ||||||||
\(50\) | −24.4439 | −3.45689 | ||||||||
\(51\) | −3.90913 | −0.547388 | ||||||||
\(52\) | 6.42619 | 0.891152 | ||||||||
\(53\) | 8.19329 | 1.12543 | 0.562717 | − | 0.826649i | \(-0.309756\pi\) | ||||
0.562717 | + | 0.826649i | \(0.309756\pi\) | |||||||
\(54\) | −8.58847 | −1.16874 | ||||||||
\(55\) | −8.57709 | −1.15654 | ||||||||
\(56\) | 19.4774 | 2.60278 | ||||||||
\(57\) | −1.38328 | −0.183219 | ||||||||
\(58\) | 2.81617 | 0.369781 | ||||||||
\(59\) | 2.69786 | 0.351232 | 0.175616 | − | 0.984459i | \(-0.443808\pi\) | ||||
0.175616 | + | 0.984459i | \(0.443808\pi\) | |||||||
\(60\) | −9.61358 | −1.24111 | ||||||||
\(61\) | −9.72805 | −1.24555 | −0.622775 | − | 0.782401i | \(-0.713995\pi\) | ||||
−0.622775 | + | 0.782401i | \(0.713995\pi\) | |||||||
\(62\) | −13.8440 | −1.75818 | ||||||||
\(63\) | 10.6808 | 1.34565 | ||||||||
\(64\) | −8.60194 | −1.07524 | ||||||||
\(65\) | 6.30877 | 0.782506 | ||||||||
\(66\) | −3.39065 | −0.417360 | ||||||||
\(67\) | −8.40586 | −1.02694 | −0.513470 | − | 0.858108i | \(-0.671640\pi\) | ||||
−0.513470 | + | 0.858108i | \(0.671640\pi\) | |||||||
\(68\) | 24.5660 | 2.97907 | ||||||||
\(69\) | −2.21012 | −0.266067 | ||||||||
\(70\) | 38.7529 | 4.63186 | ||||||||
\(71\) | −15.5834 | −1.84941 | −0.924705 | − | 0.380684i | \(-0.875689\pi\) | ||||
−0.924705 | + | 0.380684i | \(0.875689\pi\) | |||||||
\(72\) | 12.3779 | 1.45875 | ||||||||
\(73\) | 11.0703 | 1.29568 | 0.647839 | − | 0.761777i | \(-0.275673\pi\) | ||||
0.647839 | + | 0.761777i | \(0.275673\pi\) | |||||||
\(74\) | 27.5424 | 3.20174 | ||||||||
\(75\) | −6.29669 | −0.727079 | ||||||||
\(76\) | 8.69287 | 0.997140 | ||||||||
\(77\) | 9.07214 | 1.03387 | ||||||||
\(78\) | 2.49394 | 0.282384 | ||||||||
\(79\) | −5.03435 | −0.566409 | −0.283204 | − | 0.959060i | \(-0.591398\pi\) | ||||
−0.283204 | + | 0.959060i | \(0.591398\pi\) | |||||||
\(80\) | 14.3060 | 1.59946 | ||||||||
\(81\) | 5.60356 | 0.622618 | ||||||||
\(82\) | −16.2992 | −1.79994 | ||||||||
\(83\) | −9.40283 | −1.03209 | −0.516047 | − | 0.856560i | \(-0.672597\pi\) | ||||
−0.516047 | + | 0.856560i | \(0.672597\pi\) | |||||||
\(84\) | 10.1685 | 1.10947 | ||||||||
\(85\) | 24.1171 | 2.61587 | ||||||||
\(86\) | 10.6413 | 1.14748 | ||||||||
\(87\) | 0.725437 | 0.0777750 | ||||||||
\(88\) | 10.5137 | 1.12076 | ||||||||
\(89\) | 11.8335 | 1.25435 | 0.627174 | − | 0.778879i | \(-0.284212\pi\) | ||||
0.627174 | + | 0.778879i | \(0.284212\pi\) | |||||||
\(90\) | 24.6275 | 2.59597 | ||||||||
\(91\) | −6.67289 | −0.699509 | ||||||||
\(92\) | 13.8889 | 1.44802 | ||||||||
\(93\) | −3.56617 | −0.369794 | ||||||||
\(94\) | 14.1622 | 1.46072 | ||||||||
\(95\) | 8.53402 | 0.875572 | ||||||||
\(96\) | −0.314252 | −0.0320732 | ||||||||
\(97\) | −6.70100 | −0.680383 | −0.340192 | − | 0.940356i | \(-0.610492\pi\) | ||||
−0.340192 | + | 0.940356i | \(0.610492\pi\) | |||||||
\(98\) | −23.9176 | −2.41604 | ||||||||
\(99\) | 5.76535 | 0.579440 | ||||||||
\(100\) | 39.5700 | 3.95700 | ||||||||
\(101\) | 13.5965 | 1.35290 | 0.676450 | − | 0.736489i | \(-0.263518\pi\) | ||||
0.676450 | + | 0.736489i | \(0.263518\pi\) | |||||||
\(102\) | 9.53384 | 0.943991 | ||||||||
\(103\) | 1.60985 | 0.158624 | 0.0793119 | − | 0.996850i | \(-0.474728\pi\) | ||||
0.0793119 | + | 0.996850i | \(0.474728\pi\) | |||||||
\(104\) | −7.73319 | −0.758301 | ||||||||
\(105\) | 9.98264 | 0.974206 | ||||||||
\(106\) | −19.9823 | −1.94085 | ||||||||
\(107\) | 0.759987 | 0.0734708 | 0.0367354 | − | 0.999325i | \(-0.488304\pi\) | ||||
0.0367354 | + | 0.999325i | \(0.488304\pi\) | |||||||
\(108\) | 13.9031 | 1.33782 | ||||||||
\(109\) | 13.3165 | 1.27549 | 0.637744 | − | 0.770248i | \(-0.279868\pi\) | ||||
0.637744 | + | 0.770248i | \(0.279868\pi\) | |||||||
\(110\) | 20.9184 | 1.99449 | ||||||||
\(111\) | 7.09486 | 0.673414 | ||||||||
\(112\) | −15.1317 | −1.42981 | ||||||||
\(113\) | −8.56360 | −0.805596 | −0.402798 | − | 0.915289i | \(-0.631962\pi\) | ||||
−0.402798 | + | 0.915289i | \(0.631962\pi\) | |||||||
\(114\) | 3.37362 | 0.315969 | ||||||||
\(115\) | 13.6351 | 1.27148 | ||||||||
\(116\) | −4.55883 | −0.423277 | ||||||||
\(117\) | −4.24063 | −0.392046 | ||||||||
\(118\) | −6.57971 | −0.605712 | ||||||||
\(119\) | −25.5091 | −2.33842 | ||||||||
\(120\) | 11.5688 | 1.05609 | ||||||||
\(121\) | −6.10297 | −0.554815 | ||||||||
\(122\) | 23.7254 | 2.14799 | ||||||||
\(123\) | −4.19863 | −0.378578 | ||||||||
\(124\) | 22.4107 | 2.01254 | ||||||||
\(125\) | 19.4674 | 1.74122 | ||||||||
\(126\) | −26.0489 | −2.32062 | ||||||||
\(127\) | −20.8677 | −1.85171 | −0.925854 | − | 0.377882i | \(-0.876652\pi\) | ||||
−0.925854 | + | 0.377882i | \(0.876652\pi\) | |||||||
\(128\) | 19.9785 | 1.76587 | ||||||||
\(129\) | 2.74117 | 0.241347 | ||||||||
\(130\) | −15.3862 | −1.34946 | ||||||||
\(131\) | 10.0230 | 0.875715 | 0.437857 | − | 0.899044i | \(-0.355737\pi\) | ||||
0.437857 | + | 0.899044i | \(0.355737\pi\) | |||||||
\(132\) | 5.48881 | 0.477739 | ||||||||
\(133\) | −9.02659 | −0.782704 | ||||||||
\(134\) | 20.5007 | 1.77099 | ||||||||
\(135\) | 13.6490 | 1.17472 | ||||||||
\(136\) | −29.5624 | −2.53495 | ||||||||
\(137\) | −3.80142 | −0.324777 | −0.162389 | − | 0.986727i | \(-0.551920\pi\) | ||||
−0.162389 | + | 0.986727i | \(0.551920\pi\) | |||||||
\(138\) | 5.39017 | 0.458842 | ||||||||
\(139\) | 5.68409 | 0.482119 | 0.241059 | − | 0.970510i | \(-0.422505\pi\) | ||||
0.241059 | + | 0.970510i | \(0.422505\pi\) | |||||||
\(140\) | −62.7335 | −5.30195 | ||||||||
\(141\) | 3.64814 | 0.307229 | ||||||||
\(142\) | 38.0058 | 3.18938 | ||||||||
\(143\) | −3.60195 | −0.301210 | ||||||||
\(144\) | −9.61620 | −0.801350 | ||||||||
\(145\) | −4.47553 | −0.371673 | ||||||||
\(146\) | −26.9989 | −2.23444 | ||||||||
\(147\) | −6.16111 | −0.508160 | ||||||||
\(148\) | −44.5859 | −3.66494 | ||||||||
\(149\) | −9.66764 | −0.792004 | −0.396002 | − | 0.918250i | \(-0.629603\pi\) | ||||
−0.396002 | + | 0.918250i | \(0.629603\pi\) | |||||||
\(150\) | 15.3568 | 1.25387 | ||||||||
\(151\) | 19.4769 | 1.58500 | 0.792502 | − | 0.609869i | \(-0.208778\pi\) | ||||
0.792502 | + | 0.609869i | \(0.208778\pi\) | |||||||
\(152\) | −10.4609 | −0.848489 | ||||||||
\(153\) | −16.2110 | −1.31059 | ||||||||
\(154\) | −22.1257 | −1.78294 | ||||||||
\(155\) | 22.0012 | 1.76718 | ||||||||
\(156\) | −4.03722 | −0.323236 | ||||||||
\(157\) | 1.76005 | 0.140467 | 0.0702334 | − | 0.997531i | \(-0.477626\pi\) | ||||
0.0702334 | + | 0.997531i | \(0.477626\pi\) | |||||||
\(158\) | 12.2781 | 0.976793 | ||||||||
\(159\) | −5.14739 | −0.408215 | ||||||||
\(160\) | 1.93875 | 0.153272 | ||||||||
\(161\) | −14.4221 | −1.13662 | ||||||||
\(162\) | −13.6663 | −1.07373 | ||||||||
\(163\) | 8.12353 | 0.636284 | 0.318142 | − | 0.948043i | \(-0.396941\pi\) | ||||
0.318142 | + | 0.948043i | \(0.396941\pi\) | |||||||
\(164\) | 26.3853 | 2.06034 | ||||||||
\(165\) | 5.38851 | 0.419495 | ||||||||
\(166\) | 22.9322 | 1.77988 | ||||||||
\(167\) | 22.1876 | 1.71693 | 0.858464 | − | 0.512873i | \(-0.171419\pi\) | ||||
0.858464 | + | 0.512873i | \(0.171419\pi\) | |||||||
\(168\) | −12.2366 | −0.944072 | ||||||||
\(169\) | −10.3506 | −0.796203 | ||||||||
\(170\) | −58.8183 | −4.51116 | ||||||||
\(171\) | −5.73640 | −0.438673 | ||||||||
\(172\) | −17.2262 | −1.31349 | ||||||||
\(173\) | −9.30584 | −0.707510 | −0.353755 | − | 0.935338i | \(-0.615095\pi\) | ||||
−0.353755 | + | 0.935338i | \(0.615095\pi\) | |||||||
\(174\) | −1.76924 | −0.134126 | ||||||||
\(175\) | −41.0891 | −3.10605 | ||||||||
\(176\) | −8.16791 | −0.615680 | ||||||||
\(177\) | −1.69492 | −0.127398 | ||||||||
\(178\) | −28.8603 | −2.16317 | ||||||||
\(179\) | 1.19714 | 0.0894786 | 0.0447393 | − | 0.998999i | \(-0.485754\pi\) | ||||
0.0447393 | + | 0.998999i | \(0.485754\pi\) | |||||||
\(180\) | −39.8672 | −2.97152 | ||||||||
\(181\) | 20.4926 | 1.52321 | 0.761603 | − | 0.648044i | \(-0.224413\pi\) | ||||
0.761603 | + | 0.648044i | \(0.224413\pi\) | |||||||
\(182\) | 16.2743 | 1.20633 | ||||||||
\(183\) | 6.11159 | 0.451782 | ||||||||
\(184\) | −16.7137 | −1.23215 | ||||||||
\(185\) | −43.7712 | −3.21812 | ||||||||
\(186\) | 8.69739 | 0.637723 | ||||||||
\(187\) | −13.7695 | −1.00693 | ||||||||
\(188\) | −22.9259 | −1.67204 | ||||||||
\(189\) | −14.4368 | −1.05012 | ||||||||
\(190\) | −20.8133 | −1.50996 | ||||||||
\(191\) | 11.0771 | 0.801509 | 0.400754 | − | 0.916186i | \(-0.368748\pi\) | ||||
0.400754 | + | 0.916186i | \(0.368748\pi\) | |||||||
\(192\) | 5.40412 | 0.390009 | ||||||||
\(193\) | 19.4580 | 1.40061 | 0.700307 | − | 0.713841i | \(-0.253046\pi\) | ||||
0.700307 | + | 0.713841i | \(0.253046\pi\) | |||||||
\(194\) | 16.3428 | 1.17335 | ||||||||
\(195\) | −3.96345 | −0.283828 | ||||||||
\(196\) | 38.7180 | 2.76557 | ||||||||
\(197\) | 11.4181 | 0.813503 | 0.406752 | − | 0.913539i | \(-0.366661\pi\) | ||||
0.406752 | + | 0.913539i | \(0.366661\pi\) | |||||||
\(198\) | −14.0609 | −0.999265 | ||||||||
\(199\) | 20.0999 | 1.42485 | 0.712423 | − | 0.701751i | \(-0.247598\pi\) | ||||
0.712423 | + | 0.701751i | \(0.247598\pi\) | |||||||
\(200\) | −47.6180 | −3.36710 | ||||||||
\(201\) | 5.28094 | 0.372489 | ||||||||
\(202\) | −33.1599 | −2.33312 | ||||||||
\(203\) | 4.73385 | 0.332251 | ||||||||
\(204\) | −15.4335 | −1.08056 | ||||||||
\(205\) | 25.9031 | 1.80915 | ||||||||
\(206\) | −3.92621 | −0.273552 | ||||||||
\(207\) | −9.16527 | −0.637031 | ||||||||
\(208\) | 6.00780 | 0.416566 | ||||||||
\(209\) | −4.87244 | −0.337034 | ||||||||
\(210\) | −24.3463 | −1.68005 | ||||||||
\(211\) | 21.0824 | 1.45137 | 0.725685 | − | 0.688027i | \(-0.241523\pi\) | ||||
0.725685 | + | 0.688027i | \(0.241523\pi\) | |||||||
\(212\) | 32.3475 | 2.22164 | ||||||||
\(213\) | 9.79019 | 0.670813 | ||||||||
\(214\) | −1.85350 | −0.126703 | ||||||||
\(215\) | −16.9115 | −1.15335 | ||||||||
\(216\) | −16.7308 | −1.13838 | ||||||||
\(217\) | −23.2711 | −1.57974 | ||||||||
\(218\) | −32.4771 | −2.19963 | ||||||||
\(219\) | −6.95484 | −0.469965 | ||||||||
\(220\) | −33.8628 | −2.28303 | ||||||||
\(221\) | 10.1280 | 0.681281 | ||||||||
\(222\) | −17.3034 | −1.16133 | ||||||||
\(223\) | 12.6501 | 0.847111 | 0.423555 | − | 0.905870i | \(-0.360782\pi\) | ||||
0.423555 | + | 0.905870i | \(0.360782\pi\) | |||||||
\(224\) | −2.05065 | −0.137015 | ||||||||
\(225\) | −26.1122 | −1.74081 | ||||||||
\(226\) | 20.8855 | 1.38928 | ||||||||
\(227\) | 0.455889 | 0.0302584 | 0.0151292 | − | 0.999886i | \(-0.495184\pi\) | ||||
0.0151292 | + | 0.999886i | \(0.495184\pi\) | |||||||
\(228\) | −5.46125 | −0.361680 | ||||||||
\(229\) | 4.05325 | 0.267846 | 0.133923 | − | 0.990992i | \(-0.457242\pi\) | ||||
0.133923 | + | 0.990992i | \(0.457242\pi\) | |||||||
\(230\) | −33.2542 | −2.19272 | ||||||||
\(231\) | −5.69952 | −0.375001 | ||||||||
\(232\) | 5.48604 | 0.360176 | ||||||||
\(233\) | 2.02974 | 0.132973 | 0.0664865 | − | 0.997787i | \(-0.478821\pi\) | ||||
0.0664865 | + | 0.997787i | \(0.478821\pi\) | |||||||
\(234\) | 10.3423 | 0.676098 | ||||||||
\(235\) | −22.5070 | −1.46819 | ||||||||
\(236\) | 10.6513 | 0.693340 | ||||||||
\(237\) | 3.16280 | 0.205446 | ||||||||
\(238\) | 62.2132 | 4.03268 | ||||||||
\(239\) | −2.94077 | −0.190223 | −0.0951114 | − | 0.995467i | \(-0.530321\pi\) | ||||
−0.0951114 | + | 0.995467i | \(0.530321\pi\) | |||||||
\(240\) | −8.98766 | −0.580151 | ||||||||
\(241\) | −1.99108 | −0.128257 | −0.0641285 | − | 0.997942i | \(-0.520427\pi\) | ||||
−0.0641285 | + | 0.997942i | \(0.520427\pi\) | |||||||
\(242\) | 14.8843 | 0.956799 | ||||||||
\(243\) | −14.0849 | −0.903548 | ||||||||
\(244\) | −38.4068 | −2.45875 | ||||||||
\(245\) | 38.0105 | 2.42840 | ||||||||
\(246\) | 10.2399 | 0.652871 | ||||||||
\(247\) | 3.58386 | 0.228036 | ||||||||
\(248\) | −26.9687 | −1.71252 | ||||||||
\(249\) | 5.90728 | 0.374358 | ||||||||
\(250\) | −47.4784 | −3.00280 | ||||||||
\(251\) | 22.2070 | 1.40170 | 0.700848 | − | 0.713311i | \(-0.252805\pi\) | ||||
0.700848 | + | 0.713311i | \(0.252805\pi\) | |||||||
\(252\) | 42.1682 | 2.65635 | ||||||||
\(253\) | −7.78490 | −0.489432 | ||||||||
\(254\) | 50.8934 | 3.19334 | ||||||||
\(255\) | −15.1514 | −0.948821 | ||||||||
\(256\) | −31.5210 | −1.97006 | ||||||||
\(257\) | −10.2911 | −0.641943 | −0.320971 | − | 0.947089i | \(-0.604009\pi\) | ||||
−0.320971 | + | 0.947089i | \(0.604009\pi\) | |||||||
\(258\) | −6.68534 | −0.416211 | ||||||||
\(259\) | 46.2976 | 2.87679 | ||||||||
\(260\) | 24.9073 | 1.54469 | ||||||||
\(261\) | 3.00836 | 0.186213 | ||||||||
\(262\) | −24.4448 | −1.51020 | ||||||||
\(263\) | −11.3371 | −0.699076 | −0.349538 | − | 0.936922i | \(-0.613661\pi\) | ||||
−0.349538 | + | 0.936922i | \(0.613661\pi\) | |||||||
\(264\) | −6.60515 | −0.406519 | ||||||||
\(265\) | 31.7564 | 1.95078 | ||||||||
\(266\) | 22.0146 | 1.34980 | ||||||||
\(267\) | −7.43432 | −0.454973 | ||||||||
\(268\) | −33.1868 | −2.02720 | ||||||||
\(269\) | −18.4372 | −1.12414 | −0.562068 | − | 0.827091i | \(-0.689994\pi\) | ||||
−0.562068 | + | 0.827091i | \(0.689994\pi\) | |||||||
\(270\) | −33.2881 | −2.02585 | ||||||||
\(271\) | 28.4641 | 1.72907 | 0.864534 | − | 0.502574i | \(-0.167614\pi\) | ||||
0.864534 | + | 0.502574i | \(0.167614\pi\) | |||||||
\(272\) | 22.9666 | 1.39255 | ||||||||
\(273\) | 4.19221 | 0.253724 | ||||||||
\(274\) | 9.27115 | 0.560090 | ||||||||
\(275\) | −22.1794 | −1.33747 | ||||||||
\(276\) | −8.72565 | −0.525222 | ||||||||
\(277\) | 1.83137 | 0.110036 | 0.0550182 | − | 0.998485i | \(-0.482478\pi\) | ||||
0.0550182 | + | 0.998485i | \(0.482478\pi\) | |||||||
\(278\) | −13.8627 | −0.831431 | ||||||||
\(279\) | −14.7888 | −0.885380 | ||||||||
\(280\) | 75.4926 | 4.51155 | ||||||||
\(281\) | 5.63789 | 0.336328 | 0.168164 | − | 0.985759i | \(-0.446216\pi\) | ||||
0.168164 | + | 0.985759i | \(0.446216\pi\) | |||||||
\(282\) | −8.89732 | −0.529828 | ||||||||
\(283\) | 12.8735 | 0.765248 | 0.382624 | − | 0.923904i | \(-0.375020\pi\) | ||||
0.382624 | + | 0.923904i | \(0.375020\pi\) | |||||||
\(284\) | −61.5241 | −3.65078 | ||||||||
\(285\) | −5.36145 | −0.317585 | ||||||||
\(286\) | 8.78466 | 0.519448 | ||||||||
\(287\) | −27.3982 | −1.61726 | ||||||||
\(288\) | −1.30319 | −0.0767912 | ||||||||
\(289\) | 21.7172 | 1.27748 | ||||||||
\(290\) | 10.9152 | 0.640963 | ||||||||
\(291\) | 4.20986 | 0.246787 | ||||||||
\(292\) | 43.7060 | 2.55770 | ||||||||
\(293\) | 14.1162 | 0.824679 | 0.412340 | − | 0.911030i | \(-0.364712\pi\) | ||||
0.412340 | + | 0.911030i | \(0.364712\pi\) | |||||||
\(294\) | 15.0261 | 0.876340 | ||||||||
\(295\) | 10.4567 | 0.608810 | ||||||||
\(296\) | 53.6541 | 3.11858 | ||||||||
\(297\) | −7.79282 | −0.452185 | ||||||||
\(298\) | 23.5780 | 1.36584 | ||||||||
\(299\) | 5.72607 | 0.331147 | ||||||||
\(300\) | −24.8596 | −1.43527 | ||||||||
\(301\) | 17.8875 | 1.03102 | ||||||||
\(302\) | −47.5014 | −2.73340 | ||||||||
\(303\) | −8.54191 | −0.490720 | ||||||||
\(304\) | 8.12690 | 0.466109 | ||||||||
\(305\) | −37.7050 | −2.15898 | ||||||||
\(306\) | 39.5365 | 2.26015 | ||||||||
\(307\) | −21.9501 | −1.25276 | −0.626380 | − | 0.779517i | \(-0.715464\pi\) | ||||
−0.626380 | + | 0.779517i | \(0.715464\pi\) | |||||||
\(308\) | 35.8173 | 2.04088 | ||||||||
\(309\) | −1.01138 | −0.0575355 | ||||||||
\(310\) | −53.6579 | −3.04756 | ||||||||
\(311\) | −25.2490 | −1.43174 | −0.715871 | − | 0.698233i | \(-0.753970\pi\) | ||||
−0.715871 | + | 0.698233i | \(0.753970\pi\) | |||||||
\(312\) | 4.85833 | 0.275049 | ||||||||
\(313\) | 8.19362 | 0.463131 | 0.231565 | − | 0.972819i | \(-0.425615\pi\) | ||||
0.231565 | + | 0.972819i | \(0.425615\pi\) | |||||||
\(314\) | −4.29251 | −0.242240 | ||||||||
\(315\) | 41.3977 | 2.33250 | ||||||||
\(316\) | −19.8759 | −1.11811 | ||||||||
\(317\) | 31.9121 | 1.79236 | 0.896180 | − | 0.443691i | \(-0.146331\pi\) | ||||
0.896180 | + | 0.443691i | \(0.146331\pi\) | |||||||
\(318\) | 12.5538 | 0.703981 | ||||||||
\(319\) | 2.55527 | 0.143068 | ||||||||
\(320\) | −33.3403 | −1.86378 | ||||||||
\(321\) | −0.477458 | −0.0266491 | ||||||||
\(322\) | 35.1736 | 1.96015 | ||||||||
\(323\) | 13.7004 | 0.762309 | ||||||||
\(324\) | 22.1231 | 1.22906 | ||||||||
\(325\) | 16.3138 | 0.904925 | ||||||||
\(326\) | −19.8122 | −1.09729 | ||||||||
\(327\) | −8.36602 | −0.462642 | ||||||||
\(328\) | −31.7517 | −1.75319 | ||||||||
\(329\) | 23.8060 | 1.31247 | ||||||||
\(330\) | −13.1418 | −0.723435 | ||||||||
\(331\) | 11.6244 | 0.638933 | 0.319466 | − | 0.947598i | \(-0.396496\pi\) | ||||
0.319466 | + | 0.947598i | \(0.396496\pi\) | |||||||
\(332\) | −37.1228 | −2.03738 | ||||||||
\(333\) | 29.4221 | 1.61232 | ||||||||
\(334\) | −54.1125 | −2.96091 | ||||||||
\(335\) | −32.5804 | −1.78005 | ||||||||
\(336\) | 9.50641 | 0.518617 | ||||||||
\(337\) | −27.7217 | −1.51010 | −0.755049 | − | 0.655668i | \(-0.772387\pi\) | ||||
−0.755049 | + | 0.655668i | \(0.772387\pi\) | |||||||
\(338\) | 25.2438 | 1.37308 | ||||||||
\(339\) | 5.38004 | 0.292203 | ||||||||
\(340\) | 95.2156 | 5.16379 | ||||||||
\(341\) | −12.5614 | −0.680240 | ||||||||
\(342\) | 13.9903 | 0.756508 | ||||||||
\(343\) | −11.5071 | −0.621323 | ||||||||
\(344\) | 20.7298 | 1.11768 | ||||||||
\(345\) | −8.56621 | −0.461189 | ||||||||
\(346\) | 22.6957 | 1.22013 | ||||||||
\(347\) | −26.5737 | −1.42655 | −0.713276 | − | 0.700883i | \(-0.752789\pi\) | ||||
−0.713276 | + | 0.700883i | \(0.752789\pi\) | |||||||
\(348\) | 2.86406 | 0.153530 | ||||||||
\(349\) | 17.4443 | 0.933772 | 0.466886 | − | 0.884317i | \(-0.345376\pi\) | ||||
0.466886 | + | 0.884317i | \(0.345376\pi\) | |||||||
\(350\) | 100.211 | 5.35649 | ||||||||
\(351\) | 5.73191 | 0.305947 | ||||||||
\(352\) | −1.10692 | −0.0589989 | ||||||||
\(353\) | 30.8824 | 1.64371 | 0.821853 | − | 0.569699i | \(-0.192940\pi\) | ||||
0.821853 | + | 0.569699i | \(0.192940\pi\) | |||||||
\(354\) | 4.13367 | 0.219702 | ||||||||
\(355\) | −60.3999 | −3.20569 | ||||||||
\(356\) | 46.7192 | 2.47611 | ||||||||
\(357\) | 16.0260 | 0.848183 | ||||||||
\(358\) | −2.91967 | −0.154309 | ||||||||
\(359\) | 23.4050 | 1.23527 | 0.617633 | − | 0.786466i | \(-0.288092\pi\) | ||||
0.617633 | + | 0.786466i | \(0.288092\pi\) | |||||||
\(360\) | 47.9756 | 2.52854 | ||||||||
\(361\) | −14.1520 | −0.744843 | ||||||||
\(362\) | −49.9787 | −2.62682 | ||||||||
\(363\) | 3.83415 | 0.201241 | ||||||||
\(364\) | −26.3449 | −1.38085 | ||||||||
\(365\) | 42.9074 | 2.24588 | ||||||||
\(366\) | −14.9053 | −0.779114 | ||||||||
\(367\) | 28.3927 | 1.48209 | 0.741043 | − | 0.671458i | \(-0.234332\pi\) | ||||
0.741043 | + | 0.671458i | \(0.234332\pi\) | |||||||
\(368\) | 12.9847 | 0.676872 | ||||||||
\(369\) | −17.4116 | −0.906410 | ||||||||
\(370\) | 106.752 | 5.54977 | ||||||||
\(371\) | −33.5894 | −1.74387 | ||||||||
\(372\) | −14.0794 | −0.729983 | ||||||||
\(373\) | 13.6212 | 0.705281 | 0.352640 | − | 0.935759i | \(-0.385284\pi\) | ||||
0.352640 | + | 0.935759i | \(0.385284\pi\) | |||||||
\(374\) | 33.5819 | 1.73648 | ||||||||
\(375\) | −12.2303 | −0.631570 | ||||||||
\(376\) | 27.5887 | 1.42278 | ||||||||
\(377\) | −1.87950 | −0.0967991 | ||||||||
\(378\) | 35.2094 | 1.81098 | ||||||||
\(379\) | −3.96826 | −0.203836 | −0.101918 | − | 0.994793i | \(-0.532498\pi\) | ||||
−0.101918 | + | 0.994793i | \(0.532498\pi\) | |||||||
\(380\) | 33.6928 | 1.72840 | ||||||||
\(381\) | 13.1100 | 0.671646 | ||||||||
\(382\) | −27.0155 | −1.38223 | ||||||||
\(383\) | 2.84868 | 0.145561 | 0.0727804 | − | 0.997348i | \(-0.476813\pi\) | ||||
0.0727804 | + | 0.997348i | \(0.476813\pi\) | |||||||
\(384\) | −12.5514 | −0.640511 | ||||||||
\(385\) | 35.1628 | 1.79206 | ||||||||
\(386\) | −47.4553 | −2.41541 | ||||||||
\(387\) | 11.3675 | 0.577845 | ||||||||
\(388\) | −26.4559 | −1.34309 | ||||||||
\(389\) | 0.863906 | 0.0438018 | 0.0219009 | − | 0.999760i | \(-0.493028\pi\) | ||||
0.0219009 | + | 0.999760i | \(0.493028\pi\) | |||||||
\(390\) | 9.66630 | 0.489472 | ||||||||
\(391\) | 21.8896 | 1.10701 | ||||||||
\(392\) | −46.5927 | −2.35329 | ||||||||
\(393\) | −6.29690 | −0.317637 | ||||||||
\(394\) | −27.8471 | −1.40292 | ||||||||
\(395\) | −19.5127 | −0.981790 | ||||||||
\(396\) | 22.7619 | 1.14383 | ||||||||
\(397\) | 14.8634 | 0.745973 | 0.372986 | − | 0.927837i | \(-0.378334\pi\) | ||||
0.372986 | + | 0.927837i | \(0.378334\pi\) | |||||||
\(398\) | −49.0209 | −2.45720 | ||||||||
\(399\) | 5.67090 | 0.283900 | ||||||||
\(400\) | 36.9937 | 1.84969 | ||||||||
\(401\) | 28.9868 | 1.44753 | 0.723767 | − | 0.690045i | \(-0.242409\pi\) | ||||
0.723767 | + | 0.690045i | \(0.242409\pi\) | |||||||
\(402\) | −12.8795 | −0.642370 | ||||||||
\(403\) | 9.23940 | 0.460247 | ||||||||
\(404\) | 53.6796 | 2.67066 | ||||||||
\(405\) | 21.7189 | 1.07922 | ||||||||
\(406\) | −11.5452 | −0.572979 | ||||||||
\(407\) | 24.9909 | 1.23875 | ||||||||
\(408\) | 18.5724 | 0.919471 | ||||||||
\(409\) | 33.9530 | 1.67887 | 0.839434 | − | 0.543462i | \(-0.182887\pi\) | ||||
0.839434 | + | 0.543462i | \(0.182887\pi\) | |||||||
\(410\) | −63.1742 | −3.11995 | ||||||||
\(411\) | 2.38822 | 0.117802 | ||||||||
\(412\) | 6.35579 | 0.313127 | ||||||||
\(413\) | −11.0602 | −0.544237 | ||||||||
\(414\) | 22.3528 | 1.09858 | ||||||||
\(415\) | −36.4445 | −1.78899 | ||||||||
\(416\) | 0.814178 | 0.0399184 | ||||||||
\(417\) | −3.57100 | −0.174873 | ||||||||
\(418\) | 11.8832 | 0.581227 | ||||||||
\(419\) | −2.04520 | −0.0999148 | −0.0499574 | − | 0.998751i | \(-0.515909\pi\) | ||||
−0.0499574 | + | 0.998751i | \(0.515909\pi\) | |||||||
\(420\) | 39.4120 | 1.92311 | ||||||||
\(421\) | 16.2367 | 0.791329 | 0.395665 | − | 0.918395i | \(-0.370514\pi\) | ||||
0.395665 | + | 0.918395i | \(0.370514\pi\) | |||||||
\(422\) | −51.4170 | −2.50294 | ||||||||
\(423\) | 15.1287 | 0.735584 | ||||||||
\(424\) | −38.9266 | −1.89044 | ||||||||
\(425\) | 62.3642 | 3.02511 | ||||||||
\(426\) | −23.8769 | −1.15684 | ||||||||
\(427\) | 39.8813 | 1.92999 | ||||||||
\(428\) | 3.00047 | 0.145033 | ||||||||
\(429\) | 2.26290 | 0.109254 | ||||||||
\(430\) | 41.2447 | 1.98900 | ||||||||
\(431\) | 8.97949 | 0.432527 | 0.216263 | − | 0.976335i | \(-0.430613\pi\) | ||||
0.216263 | + | 0.976335i | \(0.430613\pi\) | |||||||
\(432\) | 12.9979 | 0.625361 | ||||||||
\(433\) | −9.54993 | −0.458940 | −0.229470 | − | 0.973316i | \(-0.573699\pi\) | ||||
−0.229470 | + | 0.973316i | \(0.573699\pi\) | |||||||
\(434\) | 56.7549 | 2.72432 | ||||||||
\(435\) | 2.81173 | 0.134812 | ||||||||
\(436\) | 52.5742 | 2.51785 | ||||||||
\(437\) | 7.74580 | 0.370532 | ||||||||
\(438\) | 16.9619 | 0.810471 | ||||||||
\(439\) | 35.2852 | 1.68407 | 0.842036 | − | 0.539422i | \(-0.181357\pi\) | ||||
0.842036 | + | 0.539422i | \(0.181357\pi\) | |||||||
\(440\) | 40.7500 | 1.94268 | ||||||||
\(441\) | −25.5499 | −1.21666 | ||||||||
\(442\) | −24.7007 | −1.17489 | ||||||||
\(443\) | −11.0824 | −0.526542 | −0.263271 | − | 0.964722i | \(-0.584801\pi\) | ||||
−0.263271 | + | 0.964722i | \(0.584801\pi\) | |||||||
\(444\) | 28.0109 | 1.32934 | ||||||||
\(445\) | 45.8655 | 2.17423 | ||||||||
\(446\) | −30.8518 | −1.46087 | ||||||||
\(447\) | 6.07364 | 0.287273 | ||||||||
\(448\) | 35.2647 | 1.66610 | ||||||||
\(449\) | 0.709031 | 0.0334613 | 0.0167306 | − | 0.999860i | \(-0.494674\pi\) | ||||
0.0167306 | + | 0.999860i | \(0.494674\pi\) | |||||||
\(450\) | 63.6840 | 3.00209 | ||||||||
\(451\) | −14.7892 | −0.696397 | ||||||||
\(452\) | −33.8095 | −1.59027 | ||||||||
\(453\) | −12.2362 | −0.574908 | ||||||||
\(454\) | −1.11185 | −0.0521817 | ||||||||
\(455\) | −25.8635 | −1.21250 | ||||||||
\(456\) | 6.57198 | 0.307761 | ||||||||
\(457\) | −27.5148 | −1.28709 | −0.643545 | − | 0.765408i | \(-0.722537\pi\) | ||||
−0.643545 | + | 0.765408i | \(0.722537\pi\) | |||||||
\(458\) | −9.88532 | −0.461911 | ||||||||
\(459\) | 21.9119 | 1.02276 | ||||||||
\(460\) | 53.8322 | 2.50994 | ||||||||
\(461\) | 4.35888 | 0.203013 | 0.101507 | − | 0.994835i | \(-0.467634\pi\) | ||||
0.101507 | + | 0.994835i | \(0.467634\pi\) | |||||||
\(462\) | 13.9004 | 0.646703 | ||||||||
\(463\) | 2.30016 | 0.106898 | 0.0534488 | − | 0.998571i | \(-0.482979\pi\) | ||||
0.0534488 | + | 0.998571i | \(0.482979\pi\) | |||||||
\(464\) | −4.26202 | −0.197859 | ||||||||
\(465\) | −13.8221 | −0.640986 | ||||||||
\(466\) | −4.95027 | −0.229317 | ||||||||
\(467\) | −0.847476 | −0.0392165 | −0.0196083 | − | 0.999808i | \(-0.506242\pi\) | ||||
−0.0196083 | + | 0.999808i | \(0.506242\pi\) | |||||||
\(468\) | −16.7422 | −0.773909 | ||||||||
\(469\) | 34.4608 | 1.59125 | ||||||||
\(470\) | 54.8914 | 2.53195 | ||||||||
\(471\) | −1.10574 | −0.0509497 | ||||||||
\(472\) | −12.8176 | −0.589978 | ||||||||
\(473\) | 9.65548 | 0.443960 | ||||||||
\(474\) | −7.71365 | −0.354299 | ||||||||
\(475\) | 22.0680 | 1.01255 | ||||||||
\(476\) | −100.711 | −4.61609 | ||||||||
\(477\) | −21.3461 | −0.977369 | ||||||||
\(478\) | 7.17214 | 0.328046 | ||||||||
\(479\) | −34.9972 | −1.59906 | −0.799530 | − | 0.600626i | \(-0.794918\pi\) | ||||
−0.799530 | + | 0.600626i | \(0.794918\pi\) | |||||||
\(480\) | −1.21801 | −0.0555943 | ||||||||
\(481\) | −18.3817 | −0.838134 | ||||||||
\(482\) | 4.85598 | 0.221184 | ||||||||
\(483\) | 9.06063 | 0.412273 | ||||||||
\(484\) | −24.0948 | −1.09522 | ||||||||
\(485\) | −25.9725 | −1.17935 | ||||||||
\(486\) | 34.3512 | 1.55820 | ||||||||
\(487\) | −42.1102 | −1.90819 | −0.954097 | − | 0.299498i | \(-0.903181\pi\) | ||||
−0.954097 | + | 0.299498i | \(0.903181\pi\) | |||||||
\(488\) | 46.2182 | 2.09220 | ||||||||
\(489\) | −5.10356 | −0.230791 | ||||||||
\(490\) | −92.7024 | −4.18787 | ||||||||
\(491\) | −34.7830 | −1.56973 | −0.784866 | − | 0.619665i | \(-0.787268\pi\) | ||||
−0.784866 | + | 0.619665i | \(0.787268\pi\) | |||||||
\(492\) | −16.5764 | −0.747322 | ||||||||
\(493\) | −7.18494 | −0.323593 | ||||||||
\(494\) | −8.74054 | −0.393256 | ||||||||
\(495\) | 22.3460 | 1.00438 | ||||||||
\(496\) | 20.9516 | 0.940755 | ||||||||
\(497\) | 63.8860 | 2.86568 | ||||||||
\(498\) | −14.4070 | −0.645595 | ||||||||
\(499\) | 13.9032 | 0.622391 | 0.311195 | − | 0.950346i | \(-0.399271\pi\) | ||||
0.311195 | + | 0.950346i | \(0.399271\pi\) | |||||||
\(500\) | 76.8584 | 3.43721 | ||||||||
\(501\) | −13.9392 | −0.622759 | ||||||||
\(502\) | −54.1599 | −2.41728 | ||||||||
\(503\) | −21.4824 | −0.957855 | −0.478927 | − | 0.877855i | \(-0.658974\pi\) | ||||
−0.478927 | + | 0.877855i | \(0.658974\pi\) | |||||||
\(504\) | −50.7446 | −2.26035 | ||||||||
\(505\) | 52.6987 | 2.34506 | ||||||||
\(506\) | 18.9863 | 0.844044 | ||||||||
\(507\) | 6.50273 | 0.288796 | ||||||||
\(508\) | −82.3867 | −3.65532 | ||||||||
\(509\) | −38.1621 | −1.69151 | −0.845753 | − | 0.533574i | \(-0.820848\pi\) | ||||
−0.845753 | + | 0.533574i | \(0.820848\pi\) | |||||||
\(510\) | 36.9523 | 1.63628 | ||||||||
\(511\) | −45.3839 | −2.00767 | ||||||||
\(512\) | 36.9184 | 1.63158 | ||||||||
\(513\) | 7.75369 | 0.342334 | ||||||||
\(514\) | 25.0986 | 1.10705 | ||||||||
\(515\) | 6.23965 | 0.274952 | ||||||||
\(516\) | 10.8223 | 0.476424 | ||||||||
\(517\) | 12.8502 | 0.565151 | ||||||||
\(518\) | −112.913 | −4.96113 | ||||||||
\(519\) | 5.84634 | 0.256626 | ||||||||
\(520\) | −29.9731 | −1.31441 | ||||||||
\(521\) | −30.1596 | −1.32132 | −0.660658 | − | 0.750687i | \(-0.729723\pi\) | ||||
−0.660658 | + | 0.750687i | \(0.729723\pi\) | |||||||
\(522\) | −7.33698 | −0.321131 | ||||||||
\(523\) | 30.6838 | 1.34171 | 0.670854 | − | 0.741589i | \(-0.265928\pi\) | ||||
0.670854 | + | 0.741589i | \(0.265928\pi\) | |||||||
\(524\) | 39.5714 | 1.72868 | ||||||||
\(525\) | 25.8140 | 1.12662 | ||||||||
\(526\) | 27.6496 | 1.20558 | ||||||||
\(527\) | 35.3203 | 1.53858 | ||||||||
\(528\) | 5.13145 | 0.223318 | ||||||||
\(529\) | −10.6242 | −0.461923 | ||||||||
\(530\) | −77.4496 | −3.36420 | ||||||||
\(531\) | −7.02876 | −0.305022 | ||||||||
\(532\) | −35.6374 | −1.54508 | ||||||||
\(533\) | 10.8780 | 0.471179 | ||||||||
\(534\) | 18.1313 | 0.784618 | ||||||||
\(535\) | 2.94564 | 0.127351 | ||||||||
\(536\) | 39.9365 | 1.72499 | ||||||||
\(537\) | −0.752098 | −0.0324554 | ||||||||
\(538\) | 44.9658 | 1.93861 | ||||||||
\(539\) | −21.7018 | −0.934765 | ||||||||
\(540\) | 53.8871 | 2.31893 | ||||||||
\(541\) | 37.6465 | 1.61855 | 0.809275 | − | 0.587430i | \(-0.199860\pi\) | ||||
0.809275 | + | 0.587430i | \(0.199860\pi\) | |||||||
\(542\) | −69.4199 | −2.98184 | ||||||||
\(543\) | −12.8744 | −0.552493 | ||||||||
\(544\) | 3.11244 | 0.133445 | ||||||||
\(545\) | 51.6135 | 2.21088 | ||||||||
\(546\) | −10.2242 | −0.437556 | ||||||||
\(547\) | 17.9264 | 0.766477 | 0.383238 | − | 0.923650i | \(-0.374809\pi\) | ||||
0.383238 | + | 0.923650i | \(0.374809\pi\) | |||||||
\(548\) | −15.0082 | −0.641119 | ||||||||
\(549\) | 25.3446 | 1.08168 | ||||||||
\(550\) | 54.0925 | 2.30651 | ||||||||
\(551\) | −2.54244 | −0.108312 | ||||||||
\(552\) | 10.5003 | 0.446923 | ||||||||
\(553\) | 20.6389 | 0.877656 | ||||||||
\(554\) | −4.46646 | −0.189762 | ||||||||
\(555\) | 27.4990 | 1.16727 | ||||||||
\(556\) | 22.4411 | 0.951714 | ||||||||
\(557\) | −5.15105 | −0.218257 | −0.109128 | − | 0.994028i | \(-0.534806\pi\) | ||||
−0.109128 | + | 0.994028i | \(0.534806\pi\) | |||||||
\(558\) | 36.0678 | 1.52687 | ||||||||
\(559\) | −7.10196 | −0.300381 | ||||||||
\(560\) | −58.6491 | −2.47838 | ||||||||
\(561\) | 8.65062 | 0.365229 | ||||||||
\(562\) | −13.7500 | −0.580010 | ||||||||
\(563\) | 8.56675 | 0.361045 | 0.180523 | − | 0.983571i | \(-0.442221\pi\) | ||||
0.180523 | + | 0.983571i | \(0.442221\pi\) | |||||||
\(564\) | 14.4031 | 0.606478 | ||||||||
\(565\) | −33.1917 | −1.39639 | ||||||||
\(566\) | −31.3966 | −1.31970 | ||||||||
\(567\) | −22.9725 | −0.964752 | ||||||||
\(568\) | 74.0372 | 3.10653 | ||||||||
\(569\) | 26.3362 | 1.10407 | 0.552036 | − | 0.833820i | \(-0.313851\pi\) | ||||
0.552036 | + | 0.833820i | \(0.313851\pi\) | |||||||
\(570\) | 13.0758 | 0.547687 | ||||||||
\(571\) | 34.1341 | 1.42847 | 0.714233 | − | 0.699908i | \(-0.246776\pi\) | ||||
0.714233 | + | 0.699908i | \(0.246776\pi\) | |||||||
\(572\) | −14.2207 | −0.594596 | ||||||||
\(573\) | −6.95911 | −0.290721 | ||||||||
\(574\) | 66.8204 | 2.78903 | ||||||||
\(575\) | 35.2590 | 1.47040 | ||||||||
\(576\) | 22.4107 | 0.933780 | ||||||||
\(577\) | −17.0854 | −0.711276 | −0.355638 | − | 0.934624i | \(-0.615736\pi\) | ||||
−0.355638 | + | 0.934624i | \(0.615736\pi\) | |||||||
\(578\) | −52.9652 | −2.20306 | ||||||||
\(579\) | −12.2244 | −0.508027 | ||||||||
\(580\) | −17.6696 | −0.733691 | ||||||||
\(581\) | 38.5480 | 1.59924 | ||||||||
\(582\) | −10.2673 | −0.425592 | ||||||||
\(583\) | −18.1311 | −0.750915 | ||||||||
\(584\) | −52.5952 | −2.17641 | ||||||||
\(585\) | −16.4363 | −0.679557 | ||||||||
\(586\) | −34.4276 | −1.42219 | ||||||||
\(587\) | 26.8654 | 1.10886 | 0.554428 | − | 0.832232i | \(-0.312937\pi\) | ||||
0.554428 | + | 0.832232i | \(0.312937\pi\) | |||||||
\(588\) | −24.3244 | −1.00312 | ||||||||
\(589\) | 12.4984 | 0.514986 | ||||||||
\(590\) | −25.5024 | −1.04992 | ||||||||
\(591\) | −7.17334 | −0.295072 | ||||||||
\(592\) | −41.6830 | −1.71316 | ||||||||
\(593\) | −3.42519 | −0.140656 | −0.0703278 | − | 0.997524i | \(-0.522405\pi\) | ||||
−0.0703278 | + | 0.997524i | \(0.522405\pi\) | |||||||
\(594\) | 19.0056 | 0.779810 | ||||||||
\(595\) | −98.8710 | −4.05331 | ||||||||
\(596\) | −38.1683 | −1.56344 | ||||||||
\(597\) | −12.6277 | −0.516816 | ||||||||
\(598\) | −13.9651 | −0.571076 | ||||||||
\(599\) | 2.91800 | 0.119226 | 0.0596131 | − | 0.998222i | \(-0.481013\pi\) | ||||
0.0596131 | + | 0.998222i | \(0.481013\pi\) | |||||||
\(600\) | 29.9157 | 1.22131 | ||||||||
\(601\) | 4.93129 | 0.201152 | 0.100576 | − | 0.994929i | \(-0.467931\pi\) | ||||
0.100576 | + | 0.994929i | \(0.467931\pi\) | |||||||
\(602\) | −43.6253 | −1.77803 | ||||||||
\(603\) | 21.8999 | 0.891831 | ||||||||
\(604\) | 76.8956 | 3.12884 | ||||||||
\(605\) | −23.6545 | −0.961694 | ||||||||
\(606\) | 20.8325 | 0.846264 | ||||||||
\(607\) | 11.4106 | 0.463144 | 0.231572 | − | 0.972818i | \(-0.425613\pi\) | ||||
0.231572 | + | 0.972818i | \(0.425613\pi\) | |||||||
\(608\) | 1.10136 | 0.0446660 | ||||||||
\(609\) | −2.97401 | −0.120513 | ||||||||
\(610\) | 91.9574 | 3.72325 | ||||||||
\(611\) | −9.45179 | −0.382379 | ||||||||
\(612\) | −64.0020 | −2.58713 | ||||||||
\(613\) | −46.8967 | −1.89414 | −0.947070 | − | 0.321026i | \(-0.895972\pi\) | ||||
−0.947070 | + | 0.321026i | \(0.895972\pi\) | |||||||
\(614\) | 53.5334 | 2.16043 | ||||||||
\(615\) | −16.2735 | −0.656211 | ||||||||
\(616\) | −43.1020 | −1.73663 | ||||||||
\(617\) | −38.5838 | −1.55332 | −0.776662 | − | 0.629917i | \(-0.783089\pi\) | ||||
−0.776662 | + | 0.629917i | \(0.783089\pi\) | |||||||
\(618\) | 2.46662 | 0.0992221 | ||||||||
\(619\) | 8.36777 | 0.336329 | 0.168165 | − | 0.985759i | \(-0.446216\pi\) | ||||
0.168165 | + | 0.985759i | \(0.446216\pi\) | |||||||
\(620\) | 86.8619 | 3.48846 | ||||||||
\(621\) | 12.3884 | 0.497128 | ||||||||
\(622\) | 61.5790 | 2.46909 | ||||||||
\(623\) | −48.5128 | −1.94362 | ||||||||
\(624\) | −3.77437 | −0.151096 | ||||||||
\(625\) | 25.3406 | 1.01362 | ||||||||
\(626\) | −19.9831 | −0.798686 | ||||||||
\(627\) | 3.06109 | 0.122248 | ||||||||
\(628\) | 6.94875 | 0.277285 | ||||||||
\(629\) | −70.2695 | −2.80183 | ||||||||
\(630\) | −100.963 | −4.02247 | ||||||||
\(631\) | 36.2698 | 1.44388 | 0.721939 | − | 0.691957i | \(-0.243251\pi\) | ||||
0.721939 | + | 0.691957i | \(0.243251\pi\) | |||||||
\(632\) | 23.9184 | 0.951421 | ||||||||
\(633\) | −13.2449 | −0.526437 | ||||||||
\(634\) | −77.8291 | −3.09099 | ||||||||
\(635\) | −80.8812 | −3.20967 | ||||||||
\(636\) | −20.3222 | −0.805826 | ||||||||
\(637\) | 15.9625 | 0.632457 | ||||||||
\(638\) | −6.23196 | −0.246726 | ||||||||
\(639\) | 40.5996 | 1.60610 | ||||||||
\(640\) | 77.4350 | 3.06089 | ||||||||
\(641\) | −27.1168 | −1.07105 | −0.535525 | − | 0.844520i | \(-0.679886\pi\) | ||||
−0.535525 | + | 0.844520i | \(0.679886\pi\) | |||||||
\(642\) | 1.16445 | 0.0459573 | ||||||||
\(643\) | −28.3221 | −1.11691 | −0.558457 | − | 0.829534i | \(-0.688606\pi\) | ||||
−0.558457 | + | 0.829534i | \(0.688606\pi\) | |||||||
\(644\) | −56.9393 | −2.24372 | ||||||||
\(645\) | 10.6245 | 0.418341 | ||||||||
\(646\) | −33.4133 | −1.31463 | ||||||||
\(647\) | −2.15649 | −0.0847804 | −0.0423902 | − | 0.999101i | \(-0.513497\pi\) | ||||
−0.0423902 | + | 0.999101i | \(0.513497\pi\) | |||||||
\(648\) | −26.6227 | −1.04584 | ||||||||
\(649\) | −5.97016 | −0.234349 | ||||||||
\(650\) | −39.7870 | −1.56058 | ||||||||
\(651\) | 14.6199 | 0.573000 | ||||||||
\(652\) | 32.0721 | 1.25604 | ||||||||
\(653\) | 6.52339 | 0.255280 | 0.127640 | − | 0.991821i | \(-0.459260\pi\) | ||||
0.127640 | + | 0.991821i | \(0.459260\pi\) | |||||||
\(654\) | 20.4036 | 0.797842 | ||||||||
\(655\) | 38.8483 | 1.51793 | ||||||||
\(656\) | 24.6674 | 0.963100 | ||||||||
\(657\) | −28.8415 | −1.12521 | ||||||||
\(658\) | −58.0596 | −2.26340 | ||||||||
\(659\) | −16.7915 | −0.654105 | −0.327052 | − | 0.945006i | \(-0.606055\pi\) | ||||
−0.327052 | + | 0.945006i | \(0.606055\pi\) | |||||||
\(660\) | 21.2741 | 0.828094 | ||||||||
\(661\) | −20.6732 | −0.804093 | −0.402047 | − | 0.915619i | \(-0.631701\pi\) | ||||
−0.402047 | + | 0.915619i | \(0.631701\pi\) | |||||||
\(662\) | −28.3502 | −1.10186 | ||||||||
\(663\) | −6.36285 | −0.247112 | ||||||||
\(664\) | 44.6731 | 1.73365 | ||||||||
\(665\) | −34.9862 | −1.35671 | ||||||||
\(666\) | −71.7565 | −2.78051 | ||||||||
\(667\) | −4.06216 | −0.157288 | ||||||||
\(668\) | 87.5978 | 3.38926 | ||||||||
\(669\) | −7.94733 | −0.307262 | ||||||||
\(670\) | 79.4590 | 3.06977 | ||||||||
\(671\) | 21.5274 | 0.831058 | ||||||||
\(672\) | 1.28831 | 0.0496977 | ||||||||
\(673\) | −20.3307 | −0.783691 | −0.391846 | − | 0.920031i | \(-0.628163\pi\) | ||||
−0.391846 | + | 0.920031i | \(0.628163\pi\) | |||||||
\(674\) | 67.6095 | 2.60422 | ||||||||
\(675\) | 35.2949 | 1.35850 | ||||||||
\(676\) | −40.8648 | −1.57172 | ||||||||
\(677\) | −29.8163 | −1.14593 | −0.572967 | − | 0.819578i | \(-0.694208\pi\) | ||||
−0.572967 | + | 0.819578i | \(0.694208\pi\) | |||||||
\(678\) | −13.1212 | −0.503915 | ||||||||
\(679\) | 27.4715 | 1.05426 | ||||||||
\(680\) | −114.581 | −4.39399 | ||||||||
\(681\) | −0.286410 | −0.0109752 | ||||||||
\(682\) | 30.6356 | 1.17310 | ||||||||
\(683\) | −2.96283 | −0.113369 | −0.0566847 | − | 0.998392i | \(-0.518053\pi\) | ||||
−0.0566847 | + | 0.998392i | \(0.518053\pi\) | |||||||
\(684\) | −22.6476 | −0.865953 | ||||||||
\(685\) | −14.7340 | −0.562956 | ||||||||
\(686\) | 28.0641 | 1.07149 | ||||||||
\(687\) | −2.54643 | −0.0971525 | ||||||||
\(688\) | −16.1047 | −0.613985 | ||||||||
\(689\) | 13.3361 | 0.508065 | ||||||||
\(690\) | 20.8918 | 0.795337 | ||||||||
\(691\) | −1.29240 | −0.0491651 | −0.0245825 | − | 0.999698i | \(-0.507826\pi\) | ||||
−0.0245825 | + | 0.999698i | \(0.507826\pi\) | |||||||
\(692\) | −36.7399 | −1.39664 | ||||||||
\(693\) | −23.6357 | −0.897847 | ||||||||
\(694\) | 64.8097 | 2.46014 | ||||||||
\(695\) | 22.0310 | 0.835685 | ||||||||
\(696\) | −3.44657 | −0.130642 | ||||||||
\(697\) | 41.5844 | 1.57512 | ||||||||
\(698\) | −42.5443 | −1.61032 | ||||||||
\(699\) | −1.27518 | −0.0482316 | ||||||||
\(700\) | −162.222 | −6.13141 | ||||||||
\(701\) | 40.9042 | 1.54493 | 0.772464 | − | 0.635058i | \(-0.219024\pi\) | ||||
0.772464 | + | 0.635058i | \(0.219024\pi\) | |||||||
\(702\) | −13.9793 | −0.527616 | ||||||||
\(703\) | −24.8654 | −0.937816 | ||||||||
\(704\) | 19.0354 | 0.717425 | ||||||||
\(705\) | 14.1399 | 0.532539 | ||||||||
\(706\) | −75.3180 | −2.83463 | ||||||||
\(707\) | −55.7403 | −2.09633 | ||||||||
\(708\) | −6.69162 | −0.251486 | ||||||||
\(709\) | −12.9779 | −0.487396 | −0.243698 | − | 0.969851i | \(-0.578361\pi\) | ||||
−0.243698 | + | 0.969851i | \(0.578361\pi\) | |||||||
\(710\) | 147.307 | 5.52833 | ||||||||
\(711\) | 13.1160 | 0.491890 | ||||||||
\(712\) | −56.2212 | −2.10698 | ||||||||
\(713\) | 19.9691 | 0.747850 | ||||||||
\(714\) | −39.0851 | −1.46272 | ||||||||
\(715\) | −13.9608 | −0.522105 | ||||||||
\(716\) | 4.72638 | 0.176633 | ||||||||
\(717\) | 1.84752 | 0.0689971 | ||||||||
\(718\) | −57.0815 | −2.13026 | ||||||||
\(719\) | −39.4615 | −1.47166 | −0.735832 | − | 0.677164i | \(-0.763209\pi\) | ||||
−0.735832 | + | 0.677164i | \(0.763209\pi\) | |||||||
\(720\) | −37.2715 | −1.38903 | ||||||||
\(721\) | −6.59979 | −0.245789 | ||||||||
\(722\) | 34.5148 | 1.28451 | ||||||||
\(723\) | 1.25089 | 0.0465210 | ||||||||
\(724\) | 80.9059 | 3.00685 | ||||||||
\(725\) | −11.5732 | −0.429819 | ||||||||
\(726\) | −9.35098 | −0.347047 | ||||||||
\(727\) | −14.2405 | −0.528151 | −0.264075 | − | 0.964502i | \(-0.585067\pi\) | ||||
−0.264075 | + | 0.964502i | \(0.585067\pi\) | |||||||
\(728\) | 31.7031 | 1.17500 | ||||||||
\(729\) | −7.96191 | −0.294885 | ||||||||
\(730\) | −104.645 | −3.87309 | ||||||||
\(731\) | −27.1493 | −1.00415 | ||||||||
\(732\) | 24.1289 | 0.891829 | ||||||||
\(733\) | 23.5915 | 0.871374 | 0.435687 | − | 0.900098i | \(-0.356506\pi\) | ||||
0.435687 | + | 0.900098i | \(0.356506\pi\) | |||||||
\(734\) | −69.2458 | −2.55591 | ||||||||
\(735\) | −23.8799 | −0.880823 | ||||||||
\(736\) | 1.75969 | 0.0648629 | ||||||||
\(737\) | 18.6015 | 0.685196 | ||||||||
\(738\) | 42.4644 | 1.56314 | ||||||||
\(739\) | 25.2279 | 0.928025 | 0.464013 | − | 0.885829i | \(-0.346409\pi\) | ||||
0.464013 | + | 0.885829i | \(0.346409\pi\) | |||||||
\(740\) | −172.811 | −6.35266 | ||||||||
\(741\) | −2.25154 | −0.0827124 | ||||||||
\(742\) | 81.9198 | 3.00737 | ||||||||
\(743\) | 21.3735 | 0.784117 | 0.392059 | − | 0.919940i | \(-0.371763\pi\) | ||||
0.392059 | + | 0.919940i | \(0.371763\pi\) | |||||||
\(744\) | 16.9430 | 0.621159 | ||||||||
\(745\) | −37.4709 | −1.37283 | ||||||||
\(746\) | −33.2203 | −1.21628 | ||||||||
\(747\) | 24.4973 | 0.896308 | ||||||||
\(748\) | −54.3627 | −1.98770 | ||||||||
\(749\) | −3.11566 | −0.113844 | ||||||||
\(750\) | 29.8280 | 1.08917 | ||||||||
\(751\) | −14.4616 | −0.527713 | −0.263856 | − | 0.964562i | \(-0.584994\pi\) | ||||
−0.263856 | + | 0.964562i | \(0.584994\pi\) | |||||||
\(752\) | −21.4332 | −0.781590 | ||||||||
\(753\) | −13.9514 | −0.508419 | ||||||||
\(754\) | 4.58384 | 0.166933 | ||||||||
\(755\) | 75.4905 | 2.74738 | ||||||||
\(756\) | −56.9973 | −2.07297 | ||||||||
\(757\) | 6.16797 | 0.224179 | 0.112089 | − | 0.993698i | \(-0.464246\pi\) | ||||
0.112089 | + | 0.993698i | \(0.464246\pi\) | |||||||
\(758\) | 9.67803 | 0.351522 | ||||||||
\(759\) | 4.89082 | 0.177525 | ||||||||
\(760\) | −40.5454 | −1.47074 | ||||||||
\(761\) | 17.5936 | 0.637768 | 0.318884 | − | 0.947794i | \(-0.396692\pi\) | ||||
0.318884 | + | 0.947794i | \(0.396692\pi\) | |||||||
\(762\) | −31.9735 | −1.15828 | ||||||||
\(763\) | −54.5925 | −1.97638 | ||||||||
\(764\) | 43.7328 | 1.58220 | ||||||||
\(765\) | −62.8325 | −2.27172 | ||||||||
\(766\) | −6.94754 | −0.251025 | ||||||||
\(767\) | 4.39127 | 0.158560 | ||||||||
\(768\) | 19.8029 | 0.714576 | ||||||||
\(769\) | 33.4473 | 1.20614 | 0.603070 | − | 0.797689i | \(-0.293944\pi\) | ||||
0.603070 | + | 0.797689i | \(0.293944\pi\) | |||||||
\(770\) | −85.7572 | −3.09048 | ||||||||
\(771\) | 6.46535 | 0.232844 | ||||||||
\(772\) | 76.8210 | 2.76485 | ||||||||
\(773\) | −2.14793 | −0.0772557 | −0.0386279 | − | 0.999254i | \(-0.512299\pi\) | ||||
−0.0386279 | + | 0.999254i | \(0.512299\pi\) | |||||||
\(774\) | −27.7239 | −0.996514 | ||||||||
\(775\) | 56.8927 | 2.04364 | ||||||||
\(776\) | 31.8366 | 1.14287 | ||||||||
\(777\) | −29.0862 | −1.04346 | ||||||||
\(778\) | −2.10695 | −0.0755377 | ||||||||
\(779\) | 14.7150 | 0.527218 | ||||||||
\(780\) | −15.6479 | −0.560284 | ||||||||
\(781\) | 34.4849 | 1.23397 | ||||||||
\(782\) | −53.3858 | −1.90907 | ||||||||
\(783\) | −4.06630 | −0.145318 | ||||||||
\(784\) | 36.1972 | 1.29276 | ||||||||
\(785\) | 6.82177 | 0.243480 | ||||||||
\(786\) | 15.3573 | 0.547776 | ||||||||
\(787\) | −28.2561 | −1.00722 | −0.503611 | − | 0.863931i | \(-0.667995\pi\) | ||||
−0.503611 | + | 0.863931i | \(0.667995\pi\) | |||||||
\(788\) | 45.0791 | 1.60588 | ||||||||
\(789\) | 7.12247 | 0.253567 | ||||||||
\(790\) | 47.5888 | 1.69313 | ||||||||
\(791\) | 35.1075 | 1.24828 | ||||||||
\(792\) | −27.3913 | −0.973309 | ||||||||
\(793\) | −15.8342 | −0.562290 | ||||||||
\(794\) | −36.2498 | −1.28646 | ||||||||
\(795\) | −19.9508 | −0.707582 | ||||||||
\(796\) | 79.3555 | 2.81268 | ||||||||
\(797\) | 49.1722 | 1.74177 | 0.870885 | − | 0.491487i | \(-0.163547\pi\) | ||||
0.870885 | + | 0.491487i | \(0.163547\pi\) | |||||||
\(798\) | −13.8306 | −0.489596 | ||||||||
\(799\) | −36.1323 | −1.27827 | ||||||||
\(800\) | 5.01340 | 0.177250 | ||||||||
\(801\) | −30.8299 | −1.08932 | ||||||||
\(802\) | −70.6949 | −2.49632 | ||||||||
\(803\) | −24.4977 | −0.864505 | ||||||||
\(804\) | 20.8494 | 0.735302 | ||||||||
\(805\) | −55.8989 | −1.97018 | ||||||||
\(806\) | −22.5336 | −0.793713 | ||||||||
\(807\) | 11.5831 | 0.407744 | ||||||||
\(808\) | −64.5972 | −2.27252 | ||||||||
\(809\) | 48.3023 | 1.69822 | 0.849109 | − | 0.528217i | \(-0.177139\pi\) | ||||
0.849109 | + | 0.528217i | \(0.177139\pi\) | |||||||
\(810\) | −52.9694 | −1.86115 | ||||||||
\(811\) | −23.2458 | −0.816271 | −0.408135 | − | 0.912921i | \(-0.633821\pi\) | ||||
−0.408135 | + | 0.912921i | \(0.633821\pi\) | |||||||
\(812\) | 18.6895 | 0.655872 | ||||||||
\(813\) | −17.8824 | −0.627163 | ||||||||
\(814\) | −60.9493 | −2.13627 | ||||||||
\(815\) | 31.4861 | 1.10291 | ||||||||
\(816\) | −14.4286 | −0.505103 | ||||||||
\(817\) | −9.60700 | −0.336106 | ||||||||
\(818\) | −82.8067 | −2.89527 | ||||||||
\(819\) | 17.3849 | 0.607479 | ||||||||
\(820\) | 102.267 | 3.57131 | ||||||||
\(821\) | 41.4282 | 1.44586 | 0.722928 | − | 0.690923i | \(-0.242796\pi\) | ||||
0.722928 | + | 0.690923i | \(0.242796\pi\) | |||||||
\(822\) | −5.82455 | −0.203154 | ||||||||
\(823\) | 13.4994 | 0.470560 | 0.235280 | − | 0.971928i | \(-0.424399\pi\) | ||||
0.235280 | + | 0.971928i | \(0.424399\pi\) | |||||||
\(824\) | −7.64847 | −0.266447 | ||||||||
\(825\) | 13.9341 | 0.485123 | ||||||||
\(826\) | 26.9743 | 0.938556 | ||||||||
\(827\) | −12.3354 | −0.428943 | −0.214471 | − | 0.976730i | \(-0.568803\pi\) | ||||
−0.214471 | + | 0.976730i | \(0.568803\pi\) | |||||||
\(828\) | −36.1850 | −1.25751 | ||||||||
\(829\) | 32.9824 | 1.14553 | 0.572764 | − | 0.819720i | \(-0.305871\pi\) | ||||
0.572764 | + | 0.819720i | \(0.305871\pi\) | |||||||
\(830\) | 88.8831 | 3.08518 | ||||||||
\(831\) | −1.15055 | −0.0399121 | ||||||||
\(832\) | −14.0013 | −0.485407 | ||||||||
\(833\) | 61.0214 | 2.11427 | ||||||||
\(834\) | 8.70918 | 0.301574 | ||||||||
\(835\) | 85.9971 | 2.97605 | ||||||||
\(836\) | −19.2367 | −0.665314 | ||||||||
\(837\) | 19.9895 | 0.690937 | ||||||||
\(838\) | 4.98797 | 0.172307 | ||||||||
\(839\) | 37.3200 | 1.28843 | 0.644214 | − | 0.764845i | \(-0.277184\pi\) | ||||
0.644214 | + | 0.764845i | \(0.277184\pi\) | |||||||
\(840\) | −47.4278 | −1.63642 | ||||||||
\(841\) | −27.6667 | −0.954023 | ||||||||
\(842\) | −39.5991 | −1.36468 | ||||||||
\(843\) | −3.54197 | −0.121992 | ||||||||
\(844\) | 83.2342 | 2.86504 | ||||||||
\(845\) | −40.1181 | −1.38011 | ||||||||
\(846\) | −36.8969 | −1.26854 | ||||||||
\(847\) | 25.0198 | 0.859691 | ||||||||
\(848\) | 30.2415 | 1.03850 | ||||||||
\(849\) | −8.08769 | −0.277569 | ||||||||
\(850\) | −152.098 | −5.21691 | ||||||||
\(851\) | −39.7284 | −1.36187 | ||||||||
\(852\) | 38.6522 | 1.32420 | ||||||||
\(853\) | 37.3887 | 1.28017 | 0.640083 | − | 0.768306i | \(-0.278900\pi\) | ||||
0.640083 | + | 0.768306i | \(0.278900\pi\) | |||||||
\(854\) | −97.2650 | −3.32834 | ||||||||
\(855\) | −22.2338 | −0.760379 | ||||||||
\(856\) | −3.61072 | −0.123412 | ||||||||
\(857\) | 40.6864 | 1.38982 | 0.694911 | − | 0.719095i | \(-0.255444\pi\) | ||||
0.694911 | + | 0.719095i | \(0.255444\pi\) | |||||||
\(858\) | −5.51891 | −0.188413 | ||||||||
\(859\) | 16.1103 | 0.549676 | 0.274838 | − | 0.961491i | \(-0.411376\pi\) | ||||
0.274838 | + | 0.961491i | \(0.411376\pi\) | |||||||
\(860\) | −66.7673 | −2.27675 | ||||||||
\(861\) | 17.2128 | 0.586610 | ||||||||
\(862\) | −21.8997 | −0.745908 | ||||||||
\(863\) | −37.9883 | −1.29314 | −0.646569 | − | 0.762855i | \(-0.723797\pi\) | ||||
−0.646569 | + | 0.762855i | \(0.723797\pi\) | |||||||
\(864\) | 1.76148 | 0.0599267 | ||||||||
\(865\) | −36.0686 | −1.22637 | ||||||||
\(866\) | 23.2910 | 0.791459 | ||||||||
\(867\) | −13.6437 | −0.463364 | ||||||||
\(868\) | −91.8753 | −3.11845 | ||||||||
\(869\) | 11.1406 | 0.377920 | ||||||||
\(870\) | −6.85742 | −0.232488 | ||||||||
\(871\) | −13.6821 | −0.463601 | ||||||||
\(872\) | −63.2670 | −2.14249 | ||||||||
\(873\) | 17.4582 | 0.590869 | ||||||||
\(874\) | −18.8909 | −0.638996 | ||||||||
\(875\) | −79.8090 | −2.69804 | ||||||||
\(876\) | −27.4581 | −0.927722 | ||||||||
\(877\) | −3.73410 | −0.126092 | −0.0630458 | − | 0.998011i | \(-0.520081\pi\) | ||||
−0.0630458 | + | 0.998011i | \(0.520081\pi\) | |||||||
\(878\) | −86.0558 | −2.90424 | ||||||||
\(879\) | −8.86845 | −0.299125 | ||||||||
\(880\) | −31.6581 | −1.06719 | ||||||||
\(881\) | 0.934871 | 0.0314966 | 0.0157483 | − | 0.999876i | \(-0.494987\pi\) | ||||
0.0157483 | + | 0.999876i | \(0.494987\pi\) | |||||||
\(882\) | 62.3127 | 2.09818 | ||||||||
\(883\) | 19.9915 | 0.672768 | 0.336384 | − | 0.941725i | \(-0.390796\pi\) | ||||
0.336384 | + | 0.941725i | \(0.390796\pi\) | |||||||
\(884\) | 39.9858 | 1.34487 | ||||||||
\(885\) | −6.56934 | −0.220826 | ||||||||
\(886\) | 27.0285 | 0.908041 | ||||||||
\(887\) | 7.01024 | 0.235381 | 0.117690 | − | 0.993050i | \(-0.462451\pi\) | ||||
0.117690 | + | 0.993050i | \(0.462451\pi\) | |||||||
\(888\) | −33.7079 | −1.13116 | ||||||||
\(889\) | 85.5495 | 2.86924 | ||||||||
\(890\) | −111.860 | −3.74955 | ||||||||
\(891\) | −12.4003 | −0.415424 | ||||||||
\(892\) | 49.9431 | 1.67222 | ||||||||
\(893\) | −12.7857 | −0.427856 | ||||||||
\(894\) | −14.8128 | −0.495413 | ||||||||
\(895\) | 4.64001 | 0.155099 | ||||||||
\(896\) | −81.9044 | −2.73623 | ||||||||
\(897\) | −3.59738 | −0.120113 | ||||||||
\(898\) | −1.72923 | −0.0577051 | ||||||||
\(899\) | −6.55456 | −0.218607 | ||||||||
\(900\) | −103.092 | −3.43640 | ||||||||
\(901\) | 50.9812 | 1.69843 | ||||||||
\(902\) | 36.0689 | 1.20096 | ||||||||
\(903\) | −11.2378 | −0.373969 | ||||||||
\(904\) | 40.6859 | 1.35319 | ||||||||
\(905\) | 79.4276 | 2.64026 | ||||||||
\(906\) | 29.8425 | 0.991450 | ||||||||
\(907\) | 43.6889 | 1.45066 | 0.725332 | − | 0.688399i | \(-0.241686\pi\) | ||||
0.725332 | + | 0.688399i | \(0.241686\pi\) | |||||||
\(908\) | 1.79987 | 0.0597308 | ||||||||
\(909\) | −35.4230 | −1.17491 | ||||||||
\(910\) | 63.0776 | 2.09100 | ||||||||
\(911\) | −36.8510 | −1.22093 | −0.610464 | − | 0.792044i | \(-0.709017\pi\) | ||||
−0.610464 | + | 0.792044i | \(0.709017\pi\) | |||||||
\(912\) | −5.10568 | −0.169066 | ||||||||
\(913\) | 20.8077 | 0.688636 | ||||||||
\(914\) | 67.1049 | 2.21963 | ||||||||
\(915\) | 23.6880 | 0.783101 | ||||||||
\(916\) | 16.0024 | 0.528736 | ||||||||
\(917\) | −41.0905 | −1.35693 | ||||||||
\(918\) | −53.4401 | −1.76379 | ||||||||
\(919\) | 35.8749 | 1.18340 | 0.591702 | − | 0.806157i | \(-0.298456\pi\) | ||||
0.591702 | + | 0.806157i | \(0.298456\pi\) | |||||||
\(920\) | −64.7810 | −2.13577 | ||||||||
\(921\) | 13.7901 | 0.454398 | ||||||||
\(922\) | −10.6307 | −0.350103 | ||||||||
\(923\) | −25.3649 | −0.834896 | ||||||||
\(924\) | −22.5020 | −0.740262 | ||||||||
\(925\) | −113.188 | −3.72158 | ||||||||
\(926\) | −5.60978 | −0.184349 | ||||||||
\(927\) | −4.19417 | −0.137755 | ||||||||
\(928\) | −0.577590 | −0.0189603 | ||||||||
\(929\) | 19.9934 | 0.655961 | 0.327980 | − | 0.944685i | \(-0.393632\pi\) | ||||
0.327980 | + | 0.944685i | \(0.393632\pi\) | |||||||
\(930\) | 33.7103 | 1.10540 | ||||||||
\(931\) | 21.5929 | 0.707678 | ||||||||
\(932\) | 8.01354 | 0.262492 | ||||||||
\(933\) | 15.8626 | 0.519317 | ||||||||
\(934\) | 2.06688 | 0.0676303 | ||||||||
\(935\) | −53.3694 | −1.74536 | ||||||||
\(936\) | 20.1473 | 0.658536 | ||||||||
\(937\) | −2.82509 | −0.0922918 | −0.0461459 | − | 0.998935i | \(-0.514694\pi\) | ||||
−0.0461459 | + | 0.998935i | \(0.514694\pi\) | |||||||
\(938\) | −84.0452 | −2.74417 | ||||||||
\(939\) | −5.14760 | −0.167985 | ||||||||
\(940\) | −88.8586 | −2.89825 | ||||||||
\(941\) | 5.68873 | 0.185447 | 0.0927236 | − | 0.995692i | \(-0.470443\pi\) | ||||
0.0927236 | + | 0.995692i | \(0.470443\pi\) | |||||||
\(942\) | 2.69674 | 0.0878647 | ||||||||
\(943\) | 23.5107 | 0.765613 | ||||||||
\(944\) | 9.95781 | 0.324099 | ||||||||
\(945\) | −55.9558 | −1.82024 | ||||||||
\(946\) | −23.5484 | −0.765625 | ||||||||
\(947\) | −41.8313 | −1.35933 | −0.679667 | − | 0.733521i | \(-0.737876\pi\) | ||||
−0.679667 | + | 0.733521i | \(0.737876\pi\) | |||||||
\(948\) | 12.4869 | 0.405556 | ||||||||
\(949\) | 18.0189 | 0.584920 | ||||||||
\(950\) | −53.8209 | −1.74618 | ||||||||
\(951\) | −20.0486 | −0.650119 | ||||||||
\(952\) | 121.194 | 3.92794 | ||||||||
\(953\) | 57.6205 | 1.86651 | 0.933256 | − | 0.359211i | \(-0.116954\pi\) | ||||
0.933256 | + | 0.359211i | \(0.116954\pi\) | |||||||
\(954\) | 52.0601 | 1.68551 | ||||||||
\(955\) | 42.9337 | 1.38930 | ||||||||
\(956\) | −11.6103 | −0.375505 | ||||||||
\(957\) | −1.60534 | −0.0518932 | ||||||||
\(958\) | 85.3533 | 2.75764 | ||||||||
\(959\) | 15.5844 | 0.503246 | ||||||||
\(960\) | 20.9459 | 0.676026 | ||||||||
\(961\) | 1.22149 | 0.0394028 | ||||||||
\(962\) | 44.8305 | 1.44539 | ||||||||
\(963\) | −1.98000 | −0.0638047 | ||||||||
\(964\) | −7.86090 | −0.253182 | ||||||||
\(965\) | 75.4173 | 2.42777 | ||||||||
\(966\) | −22.0976 | −0.710979 | ||||||||
\(967\) | 30.5409 | 0.982128 | 0.491064 | − | 0.871124i | \(-0.336608\pi\) | ||||
0.491064 | + | 0.871124i | \(0.336608\pi\) | |||||||
\(968\) | 28.9954 | 0.931946 | ||||||||
\(969\) | −8.60718 | −0.276502 | ||||||||
\(970\) | 63.3432 | 2.03383 | ||||||||
\(971\) | −22.4503 | −0.720465 | −0.360233 | − | 0.932863i | \(-0.617303\pi\) | ||||
−0.360233 | + | 0.932863i | \(0.617303\pi\) | |||||||
\(972\) | −55.6080 | −1.78363 | ||||||||
\(973\) | −23.3026 | −0.747047 | ||||||||
\(974\) | 102.701 | 3.29075 | ||||||||
\(975\) | −10.2490 | −0.328232 | ||||||||
\(976\) | −35.9063 | −1.14933 | ||||||||
\(977\) | −1.42834 | −0.0456966 | −0.0228483 | − | 0.999739i | \(-0.507273\pi\) | ||||
−0.0228483 | + | 0.999739i | \(0.507273\pi\) | |||||||
\(978\) | 12.4469 | 0.398008 | ||||||||
\(979\) | −26.1866 | −0.836928 | ||||||||
\(980\) | 150.067 | 4.79373 | ||||||||
\(981\) | −34.6936 | −1.10768 | ||||||||
\(982\) | 84.8309 | 2.70706 | ||||||||
\(983\) | −42.0376 | −1.34079 | −0.670396 | − | 0.742004i | \(-0.733876\pi\) | ||||
−0.670396 | + | 0.742004i | \(0.733876\pi\) | |||||||
\(984\) | 19.9478 | 0.635913 | ||||||||
\(985\) | 44.2554 | 1.41009 | ||||||||
\(986\) | 17.5231 | 0.558048 | ||||||||
\(987\) | −14.9560 | −0.476055 | ||||||||
\(988\) | 14.1493 | 0.450148 | ||||||||
\(989\) | −15.3495 | −0.488085 | ||||||||
\(990\) | −54.4988 | −1.73208 | ||||||||
\(991\) | −28.6001 | −0.908513 | −0.454257 | − | 0.890871i | \(-0.650095\pi\) | ||||
−0.454257 | + | 0.890871i | \(0.650095\pi\) | |||||||
\(992\) | 2.83937 | 0.0901500 | ||||||||
\(993\) | −7.30294 | −0.231752 | ||||||||
\(994\) | −155.809 | −4.94197 | ||||||||
\(995\) | 77.9055 | 2.46977 | ||||||||
\(996\) | 23.3222 | 0.738993 | ||||||||
\(997\) | −1.34132 | −0.0424802 | −0.0212401 | − | 0.999774i | \(-0.506761\pi\) | ||||
−0.0212401 | + | 0.999774i | \(0.506761\pi\) | |||||||
\(998\) | −33.9079 | −1.07334 | ||||||||
\(999\) | −39.7689 | −1.25823 |
(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 | 4019.2.a.b.1.16 | ✓ | 186 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4019.2.a.b.1.16 | ✓ | 186 | 1.1 | even | 1 | trivial |