Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(74\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.38029 | −1.68312 | −0.841560 | − | 0.540164i | \(-0.818362\pi\) | ||||
−0.841560 | + | 0.540164i | \(0.818362\pi\) | |||||||
\(3\) | 3.05182 | 1.76197 | 0.880986 | − | 0.473143i | \(-0.156881\pi\) | ||||
0.880986 | + | 0.473143i | \(0.156881\pi\) | |||||||
\(4\) | 3.66578 | 1.83289 | ||||||||
\(5\) | 3.97493 | 1.77764 | 0.888822 | − | 0.458252i | \(-0.151524\pi\) | ||||
0.888822 | + | 0.458252i | \(0.151524\pi\) | |||||||
\(6\) | −7.26423 | −2.96561 | ||||||||
\(7\) | −3.90026 | −1.47416 | −0.737079 | − | 0.675806i | \(-0.763796\pi\) | ||||
−0.737079 | + | 0.675806i | \(0.763796\pi\) | |||||||
\(8\) | −3.96504 | −1.40185 | ||||||||
\(9\) | 6.31363 | 2.10454 | ||||||||
\(10\) | −9.46150 | −2.99199 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 11.1873 | 3.22950 | ||||||||
\(13\) | −2.36196 | −0.655090 | −0.327545 | − | 0.944836i | \(-0.606221\pi\) | ||||
−0.327545 | + | 0.944836i | \(0.606221\pi\) | |||||||
\(14\) | 9.28375 | 2.48119 | ||||||||
\(15\) | 12.1308 | 3.13216 | ||||||||
\(16\) | 2.10639 | 0.526598 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −15.0283 | −3.54220 | ||||||||
\(19\) | −1.59876 | −0.366782 | −0.183391 | − | 0.983040i | \(-0.558707\pi\) | ||||
−0.183391 | + | 0.983040i | \(0.558707\pi\) | |||||||
\(20\) | 14.5712 | 3.25823 | ||||||||
\(21\) | −11.9029 | −2.59743 | ||||||||
\(22\) | 2.38029 | 0.507480 | ||||||||
\(23\) | −7.86563 | −1.64010 | −0.820049 | − | 0.572293i | \(-0.806054\pi\) | ||||
−0.820049 | + | 0.572293i | \(0.806054\pi\) | |||||||
\(24\) | −12.1006 | −2.47003 | ||||||||
\(25\) | 10.8001 | 2.16002 | ||||||||
\(26\) | 5.62215 | 1.10259 | ||||||||
\(27\) | 10.1126 | 1.94617 | ||||||||
\(28\) | −14.2975 | −2.70197 | ||||||||
\(29\) | 0.964418 | 0.179088 | 0.0895440 | − | 0.995983i | \(-0.471459\pi\) | ||||
0.0895440 | + | 0.995983i | \(0.471459\pi\) | |||||||
\(30\) | −28.8748 | −5.27180 | ||||||||
\(31\) | −9.21807 | −1.65561 | −0.827807 | − | 0.561013i | \(-0.810412\pi\) | ||||
−0.827807 | + | 0.561013i | \(0.810412\pi\) | |||||||
\(32\) | 2.91626 | 0.515527 | ||||||||
\(33\) | −3.05182 | −0.531254 | ||||||||
\(34\) | 2.38029 | 0.408216 | ||||||||
\(35\) | −15.5033 | −2.62053 | ||||||||
\(36\) | 23.1444 | 3.85740 | ||||||||
\(37\) | −1.49961 | −0.246535 | −0.123267 | − | 0.992373i | \(-0.539337\pi\) | ||||
−0.123267 | + | 0.992373i | \(0.539337\pi\) | |||||||
\(38\) | 3.80552 | 0.617337 | ||||||||
\(39\) | −7.20829 | −1.15425 | ||||||||
\(40\) | −15.7608 | −2.49200 | ||||||||
\(41\) | 3.86568 | 0.603718 | 0.301859 | − | 0.953353i | \(-0.402393\pi\) | ||||
0.301859 | + | 0.953353i | \(0.402393\pi\) | |||||||
\(42\) | 28.3324 | 4.37178 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −3.66578 | −0.552637 | ||||||||
\(45\) | 25.0963 | 3.74113 | ||||||||
\(46\) | 18.7225 | 2.76048 | ||||||||
\(47\) | −2.85316 | −0.416176 | −0.208088 | − | 0.978110i | \(-0.566724\pi\) | ||||
−0.208088 | + | 0.978110i | \(0.566724\pi\) | |||||||
\(48\) | 6.42834 | 0.927851 | ||||||||
\(49\) | 8.21201 | 1.17314 | ||||||||
\(50\) | −25.7074 | −3.63557 | ||||||||
\(51\) | −3.05182 | −0.427341 | ||||||||
\(52\) | −8.65843 | −1.20071 | ||||||||
\(53\) | −1.34902 | −0.185302 | −0.0926511 | − | 0.995699i | \(-0.529534\pi\) | ||||
−0.0926511 | + | 0.995699i | \(0.529534\pi\) | |||||||
\(54\) | −24.0710 | −3.27564 | ||||||||
\(55\) | −3.97493 | −0.535980 | ||||||||
\(56\) | 15.4647 | 2.06656 | ||||||||
\(57\) | −4.87915 | −0.646259 | ||||||||
\(58\) | −2.29559 | −0.301426 | ||||||||
\(59\) | 2.01671 | 0.262553 | 0.131276 | − | 0.991346i | \(-0.458092\pi\) | ||||
0.131276 | + | 0.991346i | \(0.458092\pi\) | |||||||
\(60\) | 44.4689 | 5.74090 | ||||||||
\(61\) | −12.8259 | −1.64219 | −0.821095 | − | 0.570791i | \(-0.806637\pi\) | ||||
−0.821095 | + | 0.570791i | \(0.806637\pi\) | |||||||
\(62\) | 21.9417 | 2.78660 | ||||||||
\(63\) | −24.6248 | −3.10243 | ||||||||
\(64\) | −11.1543 | −1.39429 | ||||||||
\(65\) | −9.38863 | −1.16452 | ||||||||
\(66\) | 7.26423 | 0.894164 | ||||||||
\(67\) | −11.7066 | −1.43018 | −0.715092 | − | 0.699031i | \(-0.753615\pi\) | ||||
−0.715092 | + | 0.699031i | \(0.753615\pi\) | |||||||
\(68\) | −3.66578 | −0.444541 | ||||||||
\(69\) | −24.0045 | −2.88981 | ||||||||
\(70\) | 36.9023 | 4.41066 | ||||||||
\(71\) | −14.7818 | −1.75427 | −0.877136 | − | 0.480242i | \(-0.840549\pi\) | ||||
−0.877136 | + | 0.480242i | \(0.840549\pi\) | |||||||
\(72\) | −25.0338 | −2.95026 | ||||||||
\(73\) | −12.9346 | −1.51388 | −0.756941 | − | 0.653484i | \(-0.773307\pi\) | ||||
−0.756941 | + | 0.653484i | \(0.773307\pi\) | |||||||
\(74\) | 3.56951 | 0.414948 | ||||||||
\(75\) | 32.9600 | 3.80589 | ||||||||
\(76\) | −5.86072 | −0.672271 | ||||||||
\(77\) | 3.90026 | 0.444476 | ||||||||
\(78\) | 17.1578 | 1.94274 | ||||||||
\(79\) | −4.39387 | −0.494349 | −0.247175 | − | 0.968971i | \(-0.579502\pi\) | ||||
−0.247175 | + | 0.968971i | \(0.579502\pi\) | |||||||
\(80\) | 8.37277 | 0.936104 | ||||||||
\(81\) | 11.9210 | 1.32456 | ||||||||
\(82\) | −9.20144 | −1.01613 | ||||||||
\(83\) | 8.69222 | 0.954095 | 0.477048 | − | 0.878877i | \(-0.341707\pi\) | ||||
0.477048 | + | 0.878877i | \(0.341707\pi\) | |||||||
\(84\) | −43.6334 | −4.76080 | ||||||||
\(85\) | −3.97493 | −0.431142 | ||||||||
\(86\) | 2.38029 | 0.256673 | ||||||||
\(87\) | 2.94323 | 0.315548 | ||||||||
\(88\) | 3.96504 | 0.422675 | ||||||||
\(89\) | 1.42217 | 0.150749 | 0.0753747 | − | 0.997155i | \(-0.475985\pi\) | ||||
0.0753747 | + | 0.997155i | \(0.475985\pi\) | |||||||
\(90\) | −59.7364 | −6.29677 | ||||||||
\(91\) | 9.21225 | 0.965706 | ||||||||
\(92\) | −28.8337 | −3.00612 | ||||||||
\(93\) | −28.1319 | −2.91714 | ||||||||
\(94\) | 6.79135 | 0.700474 | ||||||||
\(95\) | −6.35498 | −0.652007 | ||||||||
\(96\) | 8.89992 | 0.908344 | ||||||||
\(97\) | 11.4040 | 1.15790 | 0.578949 | − | 0.815364i | \(-0.303463\pi\) | ||||
0.578949 | + | 0.815364i | \(0.303463\pi\) | |||||||
\(98\) | −19.5470 | −1.97454 | ||||||||
\(99\) | −6.31363 | −0.634544 | ||||||||
\(100\) | 39.5908 | 3.95908 | ||||||||
\(101\) | 5.68020 | 0.565201 | 0.282600 | − | 0.959238i | \(-0.408803\pi\) | ||||
0.282600 | + | 0.959238i | \(0.408803\pi\) | |||||||
\(102\) | 7.26423 | 0.719266 | ||||||||
\(103\) | 4.40880 | 0.434412 | 0.217206 | − | 0.976126i | \(-0.430306\pi\) | ||||
0.217206 | + | 0.976126i | \(0.430306\pi\) | |||||||
\(104\) | 9.36528 | 0.918341 | ||||||||
\(105\) | −47.3132 | −4.61730 | ||||||||
\(106\) | 3.21106 | 0.311886 | ||||||||
\(107\) | 14.6001 | 1.41144 | 0.705721 | − | 0.708490i | \(-0.250623\pi\) | ||||
0.705721 | + | 0.708490i | \(0.250623\pi\) | |||||||
\(108\) | 37.0706 | 3.56712 | ||||||||
\(109\) | −4.62433 | −0.442930 | −0.221465 | − | 0.975168i | \(-0.571084\pi\) | ||||
−0.221465 | + | 0.975168i | \(0.571084\pi\) | |||||||
\(110\) | 9.46150 | 0.902118 | ||||||||
\(111\) | −4.57656 | −0.434387 | ||||||||
\(112\) | −8.21547 | −0.776289 | ||||||||
\(113\) | −11.6118 | −1.09235 | −0.546175 | − | 0.837671i | \(-0.683917\pi\) | ||||
−0.546175 | + | 0.837671i | \(0.683917\pi\) | |||||||
\(114\) | 11.6138 | 1.08773 | ||||||||
\(115\) | −31.2654 | −2.91551 | ||||||||
\(116\) | 3.53535 | 0.328249 | ||||||||
\(117\) | −14.9125 | −1.37866 | ||||||||
\(118\) | −4.80035 | −0.441908 | ||||||||
\(119\) | 3.90026 | 0.357536 | ||||||||
\(120\) | −48.0991 | −4.39083 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 30.5294 | 2.76400 | ||||||||
\(123\) | 11.7974 | 1.06373 | ||||||||
\(124\) | −33.7914 | −3.03456 | ||||||||
\(125\) | 23.0550 | 2.06210 | ||||||||
\(126\) | 58.6141 | 5.22176 | ||||||||
\(127\) | 6.65479 | 0.590517 | 0.295259 | − | 0.955417i | \(-0.404594\pi\) | ||||
0.295259 | + | 0.955417i | \(0.404594\pi\) | |||||||
\(128\) | 20.7180 | 1.83123 | ||||||||
\(129\) | −3.05182 | −0.268698 | ||||||||
\(130\) | 22.3477 | 1.96002 | ||||||||
\(131\) | 14.5751 | 1.27343 | 0.636714 | − | 0.771100i | \(-0.280293\pi\) | ||||
0.636714 | + | 0.771100i | \(0.280293\pi\) | |||||||
\(132\) | −11.1873 | −0.973731 | ||||||||
\(133\) | 6.23559 | 0.540694 | ||||||||
\(134\) | 27.8650 | 2.40717 | ||||||||
\(135\) | 40.1970 | 3.45960 | ||||||||
\(136\) | 3.96504 | 0.340000 | ||||||||
\(137\) | 15.3841 | 1.31435 | 0.657176 | − | 0.753737i | \(-0.271751\pi\) | ||||
0.657176 | + | 0.753737i | \(0.271751\pi\) | |||||||
\(138\) | 57.1377 | 4.86389 | ||||||||
\(139\) | 6.88297 | 0.583806 | 0.291903 | − | 0.956448i | \(-0.405712\pi\) | ||||
0.291903 | + | 0.956448i | \(0.405712\pi\) | |||||||
\(140\) | −56.8316 | −4.80315 | ||||||||
\(141\) | −8.70735 | −0.733291 | ||||||||
\(142\) | 35.1849 | 2.95265 | ||||||||
\(143\) | 2.36196 | 0.197517 | ||||||||
\(144\) | 13.2990 | 1.10825 | ||||||||
\(145\) | 3.83350 | 0.318355 | ||||||||
\(146\) | 30.7881 | 2.54804 | ||||||||
\(147\) | 25.0616 | 2.06705 | ||||||||
\(148\) | −5.49725 | −0.451872 | ||||||||
\(149\) | −11.4889 | −0.941210 | −0.470605 | − | 0.882344i | \(-0.655964\pi\) | ||||
−0.470605 | + | 0.882344i | \(0.655964\pi\) | |||||||
\(150\) | −78.4543 | −6.40577 | ||||||||
\(151\) | −21.3416 | −1.73676 | −0.868379 | − | 0.495901i | \(-0.834838\pi\) | ||||
−0.868379 | + | 0.495901i | \(0.834838\pi\) | |||||||
\(152\) | 6.33917 | 0.514175 | ||||||||
\(153\) | −6.31363 | −0.510427 | ||||||||
\(154\) | −9.28375 | −0.748106 | ||||||||
\(155\) | −36.6412 | −2.94309 | ||||||||
\(156\) | −26.4240 | −2.11561 | ||||||||
\(157\) | 20.3915 | 1.62742 | 0.813711 | − | 0.581269i | \(-0.197444\pi\) | ||||
0.813711 | + | 0.581269i | \(0.197444\pi\) | |||||||
\(158\) | 10.4587 | 0.832049 | ||||||||
\(159\) | −4.11697 | −0.326497 | ||||||||
\(160\) | 11.5920 | 0.916424 | ||||||||
\(161\) | 30.6780 | 2.41776 | ||||||||
\(162\) | −28.3755 | −2.22939 | ||||||||
\(163\) | −12.5323 | −0.981602 | −0.490801 | − | 0.871272i | \(-0.663296\pi\) | ||||
−0.490801 | + | 0.871272i | \(0.663296\pi\) | |||||||
\(164\) | 14.1707 | 1.10655 | ||||||||
\(165\) | −12.1308 | −0.944381 | ||||||||
\(166\) | −20.6900 | −1.60586 | ||||||||
\(167\) | −3.54501 | −0.274321 | −0.137161 | − | 0.990549i | \(-0.543798\pi\) | ||||
−0.137161 | + | 0.990549i | \(0.543798\pi\) | |||||||
\(168\) | 47.1955 | 3.64121 | ||||||||
\(169\) | −7.42115 | −0.570857 | ||||||||
\(170\) | 9.46150 | 0.725664 | ||||||||
\(171\) | −10.0940 | −0.771908 | ||||||||
\(172\) | −3.66578 | −0.279513 | ||||||||
\(173\) | 13.1932 | 1.00306 | 0.501531 | − | 0.865140i | \(-0.332770\pi\) | ||||
0.501531 | + | 0.865140i | \(0.332770\pi\) | |||||||
\(174\) | −7.00575 | −0.531105 | ||||||||
\(175\) | −42.1232 | −3.18421 | ||||||||
\(176\) | −2.10639 | −0.158775 | ||||||||
\(177\) | 6.15463 | 0.462611 | ||||||||
\(178\) | −3.38517 | −0.253729 | ||||||||
\(179\) | 1.48020 | 0.110635 | 0.0553176 | − | 0.998469i | \(-0.482383\pi\) | ||||
0.0553176 | + | 0.998469i | \(0.482383\pi\) | |||||||
\(180\) | 91.9974 | 6.85708 | ||||||||
\(181\) | −25.6135 | −1.90384 | −0.951919 | − | 0.306350i | \(-0.900892\pi\) | ||||
−0.951919 | + | 0.306350i | \(0.900892\pi\) | |||||||
\(182\) | −21.9278 | −1.62540 | ||||||||
\(183\) | −39.1424 | −2.89349 | ||||||||
\(184\) | 31.1876 | 2.29918 | ||||||||
\(185\) | −5.96086 | −0.438251 | ||||||||
\(186\) | 66.9621 | 4.90990 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −10.4591 | −0.762806 | ||||||||
\(189\) | −39.4418 | −2.86897 | ||||||||
\(190\) | 15.1267 | 1.09741 | ||||||||
\(191\) | 12.1222 | 0.877133 | 0.438566 | − | 0.898699i | \(-0.355486\pi\) | ||||
0.438566 | + | 0.898699i | \(0.355486\pi\) | |||||||
\(192\) | −34.0411 | −2.45670 | ||||||||
\(193\) | −9.89823 | −0.712490 | −0.356245 | − | 0.934393i | \(-0.615943\pi\) | ||||
−0.356245 | + | 0.934393i | \(0.615943\pi\) | |||||||
\(194\) | −27.1448 | −1.94888 | ||||||||
\(195\) | −28.6525 | −2.05184 | ||||||||
\(196\) | 30.1034 | 2.15025 | ||||||||
\(197\) | 2.71823 | 0.193666 | 0.0968329 | − | 0.995301i | \(-0.469129\pi\) | ||||
0.0968329 | + | 0.995301i | \(0.469129\pi\) | |||||||
\(198\) | 15.0283 | 1.06801 | ||||||||
\(199\) | −14.7913 | −1.04852 | −0.524262 | − | 0.851557i | \(-0.675659\pi\) | ||||
−0.524262 | + | 0.851557i | \(0.675659\pi\) | |||||||
\(200\) | −42.8229 | −3.02803 | ||||||||
\(201\) | −35.7263 | −2.51994 | ||||||||
\(202\) | −13.5205 | −0.951300 | ||||||||
\(203\) | −3.76148 | −0.264004 | ||||||||
\(204\) | −11.1873 | −0.783269 | ||||||||
\(205\) | 15.3658 | 1.07320 | ||||||||
\(206\) | −10.4942 | −0.731168 | ||||||||
\(207\) | −49.6607 | −3.45166 | ||||||||
\(208\) | −4.97521 | −0.344969 | ||||||||
\(209\) | 1.59876 | 0.110589 | ||||||||
\(210\) | 112.619 | 7.77147 | ||||||||
\(211\) | −19.8747 | −1.36823 | −0.684115 | − | 0.729374i | \(-0.739811\pi\) | ||||
−0.684115 | + | 0.729374i | \(0.739811\pi\) | |||||||
\(212\) | −4.94522 | −0.339639 | ||||||||
\(213\) | −45.1113 | −3.09098 | ||||||||
\(214\) | −34.7524 | −2.37562 | ||||||||
\(215\) | −3.97493 | −0.271088 | ||||||||
\(216\) | −40.0970 | −2.72825 | ||||||||
\(217\) | 35.9528 | 2.44064 | ||||||||
\(218\) | 11.0072 | 0.745504 | ||||||||
\(219\) | −39.4741 | −2.66742 | ||||||||
\(220\) | −14.5712 | −0.982393 | ||||||||
\(221\) | 2.36196 | 0.158883 | ||||||||
\(222\) | 10.8935 | 0.731126 | ||||||||
\(223\) | 14.0860 | 0.943267 | 0.471633 | − | 0.881795i | \(-0.343665\pi\) | ||||
0.471633 | + | 0.881795i | \(0.343665\pi\) | |||||||
\(224\) | −11.3742 | −0.759969 | ||||||||
\(225\) | 68.1878 | 4.54585 | ||||||||
\(226\) | 27.6395 | 1.83856 | ||||||||
\(227\) | −22.6709 | −1.50472 | −0.752361 | − | 0.658751i | \(-0.771085\pi\) | ||||
−0.752361 | + | 0.658751i | \(0.771085\pi\) | |||||||
\(228\) | −17.8859 | −1.18452 | ||||||||
\(229\) | −3.14716 | −0.207970 | −0.103985 | − | 0.994579i | \(-0.533159\pi\) | ||||
−0.103985 | + | 0.994579i | \(0.533159\pi\) | |||||||
\(230\) | 74.4206 | 4.90715 | ||||||||
\(231\) | 11.9029 | 0.783153 | ||||||||
\(232\) | −3.82396 | −0.251055 | ||||||||
\(233\) | 4.30236 | 0.281857 | 0.140928 | − | 0.990020i | \(-0.454991\pi\) | ||||
0.140928 | + | 0.990020i | \(0.454991\pi\) | |||||||
\(234\) | 35.4962 | 2.32046 | ||||||||
\(235\) | −11.3411 | −0.739813 | ||||||||
\(236\) | 7.39281 | 0.481231 | ||||||||
\(237\) | −13.4093 | −0.871029 | ||||||||
\(238\) | −9.28375 | −0.601776 | ||||||||
\(239\) | −0.153053 | −0.00990016 | −0.00495008 | − | 0.999988i | \(-0.501576\pi\) | ||||
−0.00495008 | + | 0.999988i | \(0.501576\pi\) | |||||||
\(240\) | 25.5522 | 1.64939 | ||||||||
\(241\) | 23.4689 | 1.51176 | 0.755882 | − | 0.654708i | \(-0.227208\pi\) | ||||
0.755882 | + | 0.654708i | \(0.227208\pi\) | |||||||
\(242\) | −2.38029 | −0.153011 | ||||||||
\(243\) | 6.04303 | 0.387660 | ||||||||
\(244\) | −47.0170 | −3.00996 | ||||||||
\(245\) | 32.6422 | 2.08543 | ||||||||
\(246\) | −28.0812 | −1.79039 | ||||||||
\(247\) | 3.77622 | 0.240275 | ||||||||
\(248\) | 36.5501 | 2.32093 | ||||||||
\(249\) | 26.5271 | 1.68109 | ||||||||
\(250\) | −54.8776 | −3.47076 | ||||||||
\(251\) | 15.2463 | 0.962337 | 0.481168 | − | 0.876628i | \(-0.340213\pi\) | ||||
0.481168 | + | 0.876628i | \(0.340213\pi\) | |||||||
\(252\) | −90.2691 | −5.68642 | ||||||||
\(253\) | 7.86563 | 0.494508 | ||||||||
\(254\) | −15.8403 | −0.993911 | ||||||||
\(255\) | −12.1308 | −0.759660 | ||||||||
\(256\) | −27.0063 | −1.68789 | ||||||||
\(257\) | 20.3984 | 1.27242 | 0.636208 | − | 0.771518i | \(-0.280502\pi\) | ||||
0.636208 | + | 0.771518i | \(0.280502\pi\) | |||||||
\(258\) | 7.26423 | 0.452251 | ||||||||
\(259\) | 5.84888 | 0.363432 | ||||||||
\(260\) | −34.4167 | −2.13443 | ||||||||
\(261\) | 6.08898 | 0.376898 | ||||||||
\(262\) | −34.6929 | −2.14333 | ||||||||
\(263\) | −2.05878 | −0.126950 | −0.0634750 | − | 0.997983i | \(-0.520218\pi\) | ||||
−0.0634750 | + | 0.997983i | \(0.520218\pi\) | |||||||
\(264\) | 12.1006 | 0.744741 | ||||||||
\(265\) | −5.36227 | −0.329402 | ||||||||
\(266\) | −14.8425 | −0.910053 | ||||||||
\(267\) | 4.34020 | 0.265616 | ||||||||
\(268\) | −42.9137 | −2.62137 | ||||||||
\(269\) | 4.84407 | 0.295348 | 0.147674 | − | 0.989036i | \(-0.452821\pi\) | ||||
0.147674 | + | 0.989036i | \(0.452821\pi\) | |||||||
\(270\) | −95.6804 | −5.82293 | ||||||||
\(271\) | 12.1618 | 0.738778 | 0.369389 | − | 0.929275i | \(-0.379567\pi\) | ||||
0.369389 | + | 0.929275i | \(0.379567\pi\) | |||||||
\(272\) | −2.10639 | −0.127719 | ||||||||
\(273\) | 28.1142 | 1.70155 | ||||||||
\(274\) | −36.6186 | −2.21221 | ||||||||
\(275\) | −10.8001 | −0.651270 | ||||||||
\(276\) | −87.9954 | −5.29670 | ||||||||
\(277\) | 5.80183 | 0.348598 | 0.174299 | − | 0.984693i | \(-0.444234\pi\) | ||||
0.174299 | + | 0.984693i | \(0.444234\pi\) | |||||||
\(278\) | −16.3835 | −0.982615 | ||||||||
\(279\) | −58.1995 | −3.48431 | ||||||||
\(280\) | 61.4711 | 3.67360 | ||||||||
\(281\) | −15.6759 | −0.935143 | −0.467571 | − | 0.883955i | \(-0.654871\pi\) | ||||
−0.467571 | + | 0.883955i | \(0.654871\pi\) | |||||||
\(282\) | 20.7260 | 1.23422 | ||||||||
\(283\) | −7.14727 | −0.424861 | −0.212431 | − | 0.977176i | \(-0.568138\pi\) | ||||
−0.212431 | + | 0.977176i | \(0.568138\pi\) | |||||||
\(284\) | −54.1867 | −3.21539 | ||||||||
\(285\) | −19.3943 | −1.14882 | ||||||||
\(286\) | −5.62215 | −0.332445 | ||||||||
\(287\) | −15.0771 | −0.889976 | ||||||||
\(288\) | 18.4122 | 1.08495 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −9.12484 | −0.535829 | ||||||||
\(291\) | 34.8029 | 2.04018 | ||||||||
\(292\) | −47.4155 | −2.77478 | ||||||||
\(293\) | −11.1213 | −0.649712 | −0.324856 | − | 0.945763i | \(-0.605316\pi\) | ||||
−0.324856 | + | 0.945763i | \(0.605316\pi\) | |||||||
\(294\) | −59.6539 | −3.47909 | ||||||||
\(295\) | 8.01627 | 0.466725 | ||||||||
\(296\) | 5.94603 | 0.345606 | ||||||||
\(297\) | −10.1126 | −0.586793 | ||||||||
\(298\) | 27.3470 | 1.58417 | ||||||||
\(299\) | 18.5783 | 1.07441 | ||||||||
\(300\) | 120.824 | 6.97578 | ||||||||
\(301\) | 3.90026 | 0.224807 | ||||||||
\(302\) | 50.7993 | 2.92317 | ||||||||
\(303\) | 17.3350 | 0.995867 | ||||||||
\(304\) | −3.36762 | −0.193147 | ||||||||
\(305\) | −50.9822 | −2.91923 | ||||||||
\(306\) | 15.0283 | 0.859109 | ||||||||
\(307\) | 14.0856 | 0.803909 | 0.401954 | − | 0.915660i | \(-0.368331\pi\) | ||||
0.401954 | + | 0.915660i | \(0.368331\pi\) | |||||||
\(308\) | 14.2975 | 0.814675 | ||||||||
\(309\) | 13.4549 | 0.765422 | ||||||||
\(310\) | 87.2167 | 4.95358 | ||||||||
\(311\) | −25.5009 | −1.44602 | −0.723012 | − | 0.690836i | \(-0.757243\pi\) | ||||
−0.723012 | + | 0.690836i | \(0.757243\pi\) | |||||||
\(312\) | 28.5812 | 1.61809 | ||||||||
\(313\) | 4.50851 | 0.254836 | 0.127418 | − | 0.991849i | \(-0.459331\pi\) | ||||
0.127418 | + | 0.991849i | \(0.459331\pi\) | |||||||
\(314\) | −48.5378 | −2.73915 | ||||||||
\(315\) | −97.8819 | −5.51502 | ||||||||
\(316\) | −16.1070 | −0.906088 | ||||||||
\(317\) | 14.2330 | 0.799403 | 0.399702 | − | 0.916645i | \(-0.369114\pi\) | ||||
0.399702 | + | 0.916645i | \(0.369114\pi\) | |||||||
\(318\) | 9.79959 | 0.549534 | ||||||||
\(319\) | −0.964418 | −0.0539970 | ||||||||
\(320\) | −44.3377 | −2.47856 | ||||||||
\(321\) | 44.5568 | 2.48692 | ||||||||
\(322\) | −73.0225 | −4.06939 | ||||||||
\(323\) | 1.59876 | 0.0889576 | ||||||||
\(324\) | 43.6999 | 2.42777 | ||||||||
\(325\) | −25.5094 | −1.41501 | ||||||||
\(326\) | 29.8304 | 1.65215 | ||||||||
\(327\) | −14.1126 | −0.780430 | ||||||||
\(328\) | −15.3276 | −0.846325 | ||||||||
\(329\) | 11.1281 | 0.613510 | ||||||||
\(330\) | 28.8748 | 1.58951 | ||||||||
\(331\) | 9.36883 | 0.514958 | 0.257479 | − | 0.966284i | \(-0.417108\pi\) | ||||
0.257479 | + | 0.966284i | \(0.417108\pi\) | |||||||
\(332\) | 31.8638 | 1.74875 | ||||||||
\(333\) | −9.46800 | −0.518843 | ||||||||
\(334\) | 8.43816 | 0.461716 | ||||||||
\(335\) | −46.5328 | −2.54236 | ||||||||
\(336\) | −25.0722 | −1.36780 | ||||||||
\(337\) | 0.168606 | 0.00918457 | 0.00459229 | − | 0.999989i | \(-0.498538\pi\) | ||||
0.00459229 | + | 0.999989i | \(0.498538\pi\) | |||||||
\(338\) | 17.6645 | 0.960821 | ||||||||
\(339\) | −35.4373 | −1.92469 | ||||||||
\(340\) | −14.5712 | −0.790236 | ||||||||
\(341\) | 9.21807 | 0.499186 | ||||||||
\(342\) | 24.0267 | 1.29921 | ||||||||
\(343\) | −4.72715 | −0.255242 | ||||||||
\(344\) | 3.96504 | 0.213781 | ||||||||
\(345\) | −95.4164 | −5.13705 | ||||||||
\(346\) | −31.4037 | −1.68827 | ||||||||
\(347\) | −1.46974 | −0.0788999 | −0.0394500 | − | 0.999222i | \(-0.512561\pi\) | ||||
−0.0394500 | + | 0.999222i | \(0.512561\pi\) | |||||||
\(348\) | 10.7893 | 0.578365 | ||||||||
\(349\) | 3.46448 | 0.185449 | 0.0927246 | − | 0.995692i | \(-0.470442\pi\) | ||||
0.0927246 | + | 0.995692i | \(0.470442\pi\) | |||||||
\(350\) | 100.265 | 5.35941 | ||||||||
\(351\) | −23.8856 | −1.27492 | ||||||||
\(352\) | −2.91626 | −0.155437 | ||||||||
\(353\) | −20.1359 | −1.07173 | −0.535863 | − | 0.844305i | \(-0.680014\pi\) | ||||
−0.535863 | + | 0.844305i | \(0.680014\pi\) | |||||||
\(354\) | −14.6498 | −0.778629 | ||||||||
\(355\) | −58.7565 | −3.11847 | ||||||||
\(356\) | 5.21335 | 0.276307 | ||||||||
\(357\) | 11.9029 | 0.629968 | ||||||||
\(358\) | −3.52330 | −0.186212 | ||||||||
\(359\) | −20.8177 | −1.09871 | −0.549357 | − | 0.835588i | \(-0.685127\pi\) | ||||
−0.549357 | + | 0.835588i | \(0.685127\pi\) | |||||||
\(360\) | −99.5078 | −5.24452 | ||||||||
\(361\) | −16.4440 | −0.865471 | ||||||||
\(362\) | 60.9676 | 3.20439 | ||||||||
\(363\) | 3.05182 | 0.160179 | ||||||||
\(364\) | 33.7701 | 1.77003 | ||||||||
\(365\) | −51.4142 | −2.69114 | ||||||||
\(366\) | 93.1704 | 4.87009 | ||||||||
\(367\) | −7.37707 | −0.385080 | −0.192540 | − | 0.981289i | \(-0.561672\pi\) | ||||
−0.192540 | + | 0.981289i | \(0.561672\pi\) | |||||||
\(368\) | −16.5681 | −0.863672 | ||||||||
\(369\) | 24.4065 | 1.27055 | ||||||||
\(370\) | 14.1886 | 0.737629 | ||||||||
\(371\) | 5.26153 | 0.273165 | ||||||||
\(372\) | −103.125 | −5.34681 | ||||||||
\(373\) | 14.1880 | 0.734626 | 0.367313 | − | 0.930097i | \(-0.380278\pi\) | ||||
0.367313 | + | 0.930097i | \(0.380278\pi\) | |||||||
\(374\) | −2.38029 | −0.123082 | ||||||||
\(375\) | 70.3598 | 3.63336 | ||||||||
\(376\) | 11.3129 | 0.583419 | ||||||||
\(377\) | −2.27792 | −0.117319 | ||||||||
\(378\) | 93.8829 | 4.82882 | ||||||||
\(379\) | 7.83499 | 0.402457 | 0.201228 | − | 0.979544i | \(-0.435507\pi\) | ||||
0.201228 | + | 0.979544i | \(0.435507\pi\) | |||||||
\(380\) | −23.2960 | −1.19506 | ||||||||
\(381\) | 20.3093 | 1.04047 | ||||||||
\(382\) | −28.8544 | −1.47632 | ||||||||
\(383\) | 2.35115 | 0.120138 | 0.0600690 | − | 0.998194i | \(-0.480868\pi\) | ||||
0.0600690 | + | 0.998194i | \(0.480868\pi\) | |||||||
\(384\) | 63.2278 | 3.22658 | ||||||||
\(385\) | 15.5033 | 0.790120 | ||||||||
\(386\) | 23.5607 | 1.19921 | ||||||||
\(387\) | −6.31363 | −0.320940 | ||||||||
\(388\) | 41.8045 | 2.12230 | ||||||||
\(389\) | −32.0897 | −1.62701 | −0.813506 | − | 0.581557i | \(-0.802444\pi\) | ||||
−0.813506 | + | 0.581557i | \(0.802444\pi\) | |||||||
\(390\) | 68.2012 | 3.45350 | ||||||||
\(391\) | 7.86563 | 0.397782 | ||||||||
\(392\) | −32.5610 | −1.64458 | ||||||||
\(393\) | 44.4805 | 2.24374 | ||||||||
\(394\) | −6.47018 | −0.325963 | ||||||||
\(395\) | −17.4653 | −0.878777 | ||||||||
\(396\) | −23.1444 | −1.16305 | ||||||||
\(397\) | −31.7177 | −1.59187 | −0.795933 | − | 0.605385i | \(-0.793019\pi\) | ||||
−0.795933 | + | 0.605385i | \(0.793019\pi\) | |||||||
\(398\) | 35.2075 | 1.76479 | ||||||||
\(399\) | 19.0299 | 0.952688 | ||||||||
\(400\) | 22.7492 | 1.13746 | ||||||||
\(401\) | −5.42740 | −0.271031 | −0.135516 | − | 0.990775i | \(-0.543269\pi\) | ||||
−0.135516 | + | 0.990775i | \(0.543269\pi\) | |||||||
\(402\) | 85.0391 | 4.24136 | ||||||||
\(403\) | 21.7727 | 1.08458 | ||||||||
\(404\) | 20.8224 | 1.03595 | ||||||||
\(405\) | 47.3853 | 2.35459 | ||||||||
\(406\) | 8.95341 | 0.444350 | ||||||||
\(407\) | 1.49961 | 0.0743331 | ||||||||
\(408\) | 12.1006 | 0.599070 | ||||||||
\(409\) | 15.6985 | 0.776240 | 0.388120 | − | 0.921609i | \(-0.373125\pi\) | ||||
0.388120 | + | 0.921609i | \(0.373125\pi\) | |||||||
\(410\) | −36.5751 | −1.80632 | ||||||||
\(411\) | 46.9496 | 2.31585 | ||||||||
\(412\) | 16.1617 | 0.796230 | ||||||||
\(413\) | −7.86567 | −0.387045 | ||||||||
\(414\) | 118.207 | 5.80955 | ||||||||
\(415\) | 34.5510 | 1.69604 | ||||||||
\(416\) | −6.88810 | −0.337717 | ||||||||
\(417\) | 21.0056 | 1.02865 | ||||||||
\(418\) | −3.80552 | −0.186134 | ||||||||
\(419\) | 15.9083 | 0.777169 | 0.388584 | − | 0.921413i | \(-0.372964\pi\) | ||||
0.388584 | + | 0.921413i | \(0.372964\pi\) | |||||||
\(420\) | −173.440 | −8.46300 | ||||||||
\(421\) | −1.80478 | −0.0879595 | −0.0439797 | − | 0.999032i | \(-0.514004\pi\) | ||||
−0.0439797 | + | 0.999032i | \(0.514004\pi\) | |||||||
\(422\) | 47.3075 | 2.30290 | ||||||||
\(423\) | −18.0138 | −0.875861 | ||||||||
\(424\) | 5.34893 | 0.259767 | ||||||||
\(425\) | −10.8001 | −0.523882 | ||||||||
\(426\) | 107.378 | 5.20248 | ||||||||
\(427\) | 50.0244 | 2.42085 | ||||||||
\(428\) | 53.5206 | 2.58702 | ||||||||
\(429\) | 7.20829 | 0.348019 | ||||||||
\(430\) | 9.46150 | 0.456274 | ||||||||
\(431\) | −32.0777 | −1.54513 | −0.772564 | − | 0.634936i | \(-0.781026\pi\) | ||||
−0.772564 | + | 0.634936i | \(0.781026\pi\) | |||||||
\(432\) | 21.3011 | 1.02485 | ||||||||
\(433\) | 9.38697 | 0.451109 | 0.225555 | − | 0.974231i | \(-0.427581\pi\) | ||||
0.225555 | + | 0.974231i | \(0.427581\pi\) | |||||||
\(434\) | −85.5782 | −4.10789 | ||||||||
\(435\) | 11.6992 | 0.560932 | ||||||||
\(436\) | −16.9518 | −0.811842 | ||||||||
\(437\) | 12.5753 | 0.601558 | ||||||||
\(438\) | 93.9599 | 4.48958 | ||||||||
\(439\) | −32.6210 | −1.55692 | −0.778458 | − | 0.627697i | \(-0.783998\pi\) | ||||
−0.778458 | + | 0.627697i | \(0.783998\pi\) | |||||||
\(440\) | 15.7608 | 0.751366 | ||||||||
\(441\) | 51.8476 | 2.46893 | ||||||||
\(442\) | −5.62215 | −0.267418 | ||||||||
\(443\) | 12.7123 | 0.603980 | 0.301990 | − | 0.953311i | \(-0.402349\pi\) | ||||
0.301990 | + | 0.953311i | \(0.402349\pi\) | |||||||
\(444\) | −16.7767 | −0.796185 | ||||||||
\(445\) | 5.65302 | 0.267979 | ||||||||
\(446\) | −33.5287 | −1.58763 | ||||||||
\(447\) | −35.0622 | −1.65838 | ||||||||
\(448\) | 43.5048 | 2.05541 | ||||||||
\(449\) | 20.3201 | 0.958964 | 0.479482 | − | 0.877552i | \(-0.340825\pi\) | ||||
0.479482 | + | 0.877552i | \(0.340825\pi\) | |||||||
\(450\) | −162.307 | −7.65121 | ||||||||
\(451\) | −3.86568 | −0.182028 | ||||||||
\(452\) | −42.5665 | −2.00216 | ||||||||
\(453\) | −65.1309 | −3.06012 | ||||||||
\(454\) | 53.9634 | 2.53263 | ||||||||
\(455\) | 36.6181 | 1.71668 | ||||||||
\(456\) | 19.3460 | 0.905961 | ||||||||
\(457\) | −4.61745 | −0.215995 | −0.107998 | − | 0.994151i | \(-0.534444\pi\) | ||||
−0.107998 | + | 0.994151i | \(0.534444\pi\) | |||||||
\(458\) | 7.49116 | 0.350039 | ||||||||
\(459\) | −10.1126 | −0.472016 | ||||||||
\(460\) | −114.612 | −5.34381 | ||||||||
\(461\) | 27.2776 | 1.27044 | 0.635222 | − | 0.772330i | \(-0.280909\pi\) | ||||
0.635222 | + | 0.772330i | \(0.280909\pi\) | |||||||
\(462\) | −28.3324 | −1.31814 | ||||||||
\(463\) | 4.16878 | 0.193739 | 0.0968697 | − | 0.995297i | \(-0.469117\pi\) | ||||
0.0968697 | + | 0.995297i | \(0.469117\pi\) | |||||||
\(464\) | 2.03144 | 0.0943074 | ||||||||
\(465\) | −111.823 | −5.18565 | ||||||||
\(466\) | −10.2409 | −0.474399 | ||||||||
\(467\) | −31.7833 | −1.47076 | −0.735378 | − | 0.677657i | \(-0.762996\pi\) | ||||
−0.735378 | + | 0.677657i | \(0.762996\pi\) | |||||||
\(468\) | −54.6661 | −2.52694 | ||||||||
\(469\) | 45.6586 | 2.10832 | ||||||||
\(470\) | 26.9952 | 1.24519 | ||||||||
\(471\) | 62.2314 | 2.86747 | ||||||||
\(472\) | −7.99633 | −0.368061 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 31.9181 | 1.46605 | ||||||||
\(475\) | −17.2668 | −0.792255 | ||||||||
\(476\) | 14.2975 | 0.655325 | ||||||||
\(477\) | −8.51722 | −0.389977 | ||||||||
\(478\) | 0.364310 | 0.0166632 | ||||||||
\(479\) | 5.27876 | 0.241193 | 0.120596 | − | 0.992702i | \(-0.461519\pi\) | ||||
0.120596 | + | 0.992702i | \(0.461519\pi\) | |||||||
\(480\) | 35.3766 | 1.61471 | ||||||||
\(481\) | 3.54203 | 0.161503 | ||||||||
\(482\) | −55.8627 | −2.54448 | ||||||||
\(483\) | 93.6238 | 4.26003 | ||||||||
\(484\) | 3.66578 | 0.166626 | ||||||||
\(485\) | 45.3300 | 2.05833 | ||||||||
\(486\) | −14.3842 | −0.652479 | ||||||||
\(487\) | 38.2290 | 1.73232 | 0.866161 | − | 0.499765i | \(-0.166580\pi\) | ||||
0.866161 | + | 0.499765i | \(0.166580\pi\) | |||||||
\(488\) | 50.8553 | 2.30211 | ||||||||
\(489\) | −38.2462 | −1.72955 | ||||||||
\(490\) | −77.6979 | −3.51003 | ||||||||
\(491\) | −36.5482 | −1.64940 | −0.824698 | − | 0.565573i | \(-0.808655\pi\) | ||||
−0.824698 | + | 0.565573i | \(0.808655\pi\) | |||||||
\(492\) | 43.2466 | 1.94971 | ||||||||
\(493\) | −0.964418 | −0.0434352 | ||||||||
\(494\) | −8.98849 | −0.404411 | ||||||||
\(495\) | −25.0963 | −1.12799 | ||||||||
\(496\) | −19.4169 | −0.871843 | ||||||||
\(497\) | 57.6527 | 2.58608 | ||||||||
\(498\) | −63.1423 | −2.82947 | ||||||||
\(499\) | 31.4483 | 1.40782 | 0.703911 | − | 0.710289i | \(-0.251436\pi\) | ||||
0.703911 | + | 0.710289i | \(0.251436\pi\) | |||||||
\(500\) | 84.5146 | 3.77961 | ||||||||
\(501\) | −10.8188 | −0.483346 | ||||||||
\(502\) | −36.2906 | −1.61973 | ||||||||
\(503\) | 17.7669 | 0.792185 | 0.396093 | − | 0.918211i | \(-0.370366\pi\) | ||||
0.396093 | + | 0.918211i | \(0.370366\pi\) | |||||||
\(504\) | 97.6383 | 4.34916 | ||||||||
\(505\) | 22.5784 | 1.00473 | ||||||||
\(506\) | −18.7225 | −0.832316 | ||||||||
\(507\) | −22.6480 | −1.00583 | ||||||||
\(508\) | 24.3950 | 1.08235 | ||||||||
\(509\) | −30.8069 | −1.36549 | −0.682746 | − | 0.730656i | \(-0.739215\pi\) | ||||
−0.682746 | + | 0.730656i | \(0.739215\pi\) | |||||||
\(510\) | 28.8748 | 1.27860 | ||||||||
\(511\) | 50.4483 | 2.23170 | ||||||||
\(512\) | 22.8467 | 1.00969 | ||||||||
\(513\) | −16.1677 | −0.713821 | ||||||||
\(514\) | −48.5540 | −2.14163 | ||||||||
\(515\) | 17.5247 | 0.772230 | ||||||||
\(516\) | −11.1873 | −0.492494 | ||||||||
\(517\) | 2.85316 | 0.125482 | ||||||||
\(518\) | −13.9220 | −0.611699 | ||||||||
\(519\) | 40.2634 | 1.76737 | ||||||||
\(520\) | 37.2263 | 1.63248 | ||||||||
\(521\) | 42.6343 | 1.86784 | 0.933921 | − | 0.357479i | \(-0.116364\pi\) | ||||
0.933921 | + | 0.357479i | \(0.116364\pi\) | |||||||
\(522\) | −14.4935 | −0.634365 | ||||||||
\(523\) | 35.0044 | 1.53064 | 0.765318 | − | 0.643652i | \(-0.222582\pi\) | ||||
0.765318 | + | 0.643652i | \(0.222582\pi\) | |||||||
\(524\) | 53.4290 | 2.33406 | ||||||||
\(525\) | −128.552 | −5.61049 | ||||||||
\(526\) | 4.90050 | 0.213672 | ||||||||
\(527\) | 9.21807 | 0.401545 | ||||||||
\(528\) | −6.42834 | −0.279758 | ||||||||
\(529\) | 38.8682 | 1.68992 | ||||||||
\(530\) | 12.7638 | 0.554422 | ||||||||
\(531\) | 12.7327 | 0.552554 | ||||||||
\(532\) | 22.8583 | 0.991034 | ||||||||
\(533\) | −9.13058 | −0.395489 | ||||||||
\(534\) | −10.3309 | −0.447064 | ||||||||
\(535\) | 58.0343 | 2.50904 | ||||||||
\(536\) | 46.4170 | 2.00491 | ||||||||
\(537\) | 4.51730 | 0.194936 | ||||||||
\(538\) | −11.5303 | −0.497107 | ||||||||
\(539\) | −8.21201 | −0.353716 | ||||||||
\(540\) | 147.353 | 6.34108 | ||||||||
\(541\) | 29.1385 | 1.25276 | 0.626382 | − | 0.779516i | \(-0.284535\pi\) | ||||
0.626382 | + | 0.779516i | \(0.284535\pi\) | |||||||
\(542\) | −28.9486 | −1.24345 | ||||||||
\(543\) | −78.1679 | −3.35451 | ||||||||
\(544\) | −2.91626 | −0.125034 | ||||||||
\(545\) | −18.3814 | −0.787372 | ||||||||
\(546\) | −66.9199 | −2.86391 | ||||||||
\(547\) | −11.9893 | −0.512627 | −0.256314 | − | 0.966594i | \(-0.582508\pi\) | ||||
−0.256314 | + | 0.966594i | \(0.582508\pi\) | |||||||
\(548\) | 56.3948 | 2.40906 | ||||||||
\(549\) | −80.9781 | −3.45606 | ||||||||
\(550\) | 25.7074 | 1.09617 | ||||||||
\(551\) | −1.54188 | −0.0656862 | ||||||||
\(552\) | 95.1790 | 4.05109 | ||||||||
\(553\) | 17.1372 | 0.728749 | ||||||||
\(554\) | −13.8100 | −0.586732 | ||||||||
\(555\) | −18.1915 | −0.772186 | ||||||||
\(556\) | 25.2315 | 1.07005 | ||||||||
\(557\) | −28.2150 | −1.19551 | −0.597753 | − | 0.801680i | \(-0.703940\pi\) | ||||
−0.597753 | + | 0.801680i | \(0.703940\pi\) | |||||||
\(558\) | 138.532 | 5.86451 | ||||||||
\(559\) | 2.36196 | 0.0999003 | ||||||||
\(560\) | −32.6560 | −1.37997 | ||||||||
\(561\) | 3.05182 | 0.128848 | ||||||||
\(562\) | 37.3131 | 1.57396 | ||||||||
\(563\) | 34.6634 | 1.46089 | 0.730445 | − | 0.682971i | \(-0.239313\pi\) | ||||
0.730445 | + | 0.682971i | \(0.239313\pi\) | |||||||
\(564\) | −31.9192 | −1.34404 | ||||||||
\(565\) | −46.1563 | −1.94181 | ||||||||
\(566\) | 17.0126 | 0.715092 | ||||||||
\(567\) | −46.4951 | −1.95261 | ||||||||
\(568\) | 58.6103 | 2.45923 | ||||||||
\(569\) | −10.3241 | −0.432811 | −0.216405 | − | 0.976304i | \(-0.569433\pi\) | ||||
−0.216405 | + | 0.976304i | \(0.569433\pi\) | |||||||
\(570\) | 46.1640 | 1.93360 | ||||||||
\(571\) | −36.3862 | −1.52271 | −0.761357 | − | 0.648333i | \(-0.775467\pi\) | ||||
−0.761357 | + | 0.648333i | \(0.775467\pi\) | |||||||
\(572\) | 8.65843 | 0.362027 | ||||||||
\(573\) | 36.9949 | 1.54548 | ||||||||
\(574\) | 35.8880 | 1.49794 | ||||||||
\(575\) | −84.9496 | −3.54264 | ||||||||
\(576\) | −70.4243 | −2.93435 | ||||||||
\(577\) | 34.3389 | 1.42955 | 0.714774 | − | 0.699355i | \(-0.246529\pi\) | ||||
0.714774 | + | 0.699355i | \(0.246529\pi\) | |||||||
\(578\) | −2.38029 | −0.0990070 | ||||||||
\(579\) | −30.2077 | −1.25539 | ||||||||
\(580\) | 14.0528 | 0.583509 | ||||||||
\(581\) | −33.9019 | −1.40649 | ||||||||
\(582\) | −82.8410 | −3.43387 | ||||||||
\(583\) | 1.34902 | 0.0558707 | ||||||||
\(584\) | 51.2863 | 2.12224 | ||||||||
\(585\) | −59.2763 | −2.45078 | ||||||||
\(586\) | 26.4719 | 1.09354 | ||||||||
\(587\) | −24.1098 | −0.995119 | −0.497560 | − | 0.867430i | \(-0.665770\pi\) | ||||
−0.497560 | + | 0.867430i | \(0.665770\pi\) | |||||||
\(588\) | 91.8704 | 3.78867 | ||||||||
\(589\) | 14.7375 | 0.607249 | ||||||||
\(590\) | −19.0811 | −0.785555 | ||||||||
\(591\) | 8.29556 | 0.341234 | ||||||||
\(592\) | −3.15877 | −0.129825 | ||||||||
\(593\) | 8.82363 | 0.362343 | 0.181172 | − | 0.983452i | \(-0.442011\pi\) | ||||
0.181172 | + | 0.983452i | \(0.442011\pi\) | |||||||
\(594\) | 24.0710 | 0.987643 | ||||||||
\(595\) | 15.5033 | 0.635572 | ||||||||
\(596\) | −42.1159 | −1.72513 | ||||||||
\(597\) | −45.1403 | −1.84747 | ||||||||
\(598\) | −44.2218 | −1.80836 | ||||||||
\(599\) | 6.75030 | 0.275810 | 0.137905 | − | 0.990445i | \(-0.455963\pi\) | ||||
0.137905 | + | 0.990445i | \(0.455963\pi\) | |||||||
\(600\) | −130.688 | −5.33531 | ||||||||
\(601\) | −8.35200 | −0.340685 | −0.170342 | − | 0.985385i | \(-0.554487\pi\) | ||||
−0.170342 | + | 0.985385i | \(0.554487\pi\) | |||||||
\(602\) | −9.28375 | −0.378377 | ||||||||
\(603\) | −73.9108 | −3.00988 | ||||||||
\(604\) | −78.2338 | −3.18329 | ||||||||
\(605\) | 3.97493 | 0.161604 | ||||||||
\(606\) | −41.2622 | −1.67616 | ||||||||
\(607\) | 28.7901 | 1.16855 | 0.584277 | − | 0.811554i | \(-0.301378\pi\) | ||||
0.584277 | + | 0.811554i | \(0.301378\pi\) | |||||||
\(608\) | −4.66242 | −0.189086 | ||||||||
\(609\) | −11.4794 | −0.465168 | ||||||||
\(610\) | 121.352 | 4.91341 | ||||||||
\(611\) | 6.73905 | 0.272633 | ||||||||
\(612\) | −23.1444 | −0.935556 | ||||||||
\(613\) | 4.21447 | 0.170221 | 0.0851105 | − | 0.996372i | \(-0.472876\pi\) | ||||
0.0851105 | + | 0.996372i | \(0.472876\pi\) | |||||||
\(614\) | −33.5279 | −1.35307 | ||||||||
\(615\) | 46.8938 | 1.89094 | ||||||||
\(616\) | −15.4647 | −0.623090 | ||||||||
\(617\) | 1.09186 | 0.0439568 | 0.0219784 | − | 0.999758i | \(-0.493003\pi\) | ||||
0.0219784 | + | 0.999758i | \(0.493003\pi\) | |||||||
\(618\) | −32.0265 | −1.28830 | ||||||||
\(619\) | −45.6057 | −1.83305 | −0.916523 | − | 0.399982i | \(-0.869017\pi\) | ||||
−0.916523 | + | 0.399982i | \(0.869017\pi\) | |||||||
\(620\) | −134.319 | −5.39437 | ||||||||
\(621\) | −79.5421 | −3.19191 | ||||||||
\(622\) | 60.6995 | 2.43383 | ||||||||
\(623\) | −5.54682 | −0.222229 | ||||||||
\(624\) | −15.1835 | −0.607826 | ||||||||
\(625\) | 37.6416 | 1.50566 | ||||||||
\(626\) | −10.7316 | −0.428919 | ||||||||
\(627\) | 4.87915 | 0.194854 | ||||||||
\(628\) | 74.7510 | 2.98289 | ||||||||
\(629\) | 1.49961 | 0.0597935 | ||||||||
\(630\) | 232.987 | 9.28243 | ||||||||
\(631\) | 23.7457 | 0.945300 | 0.472650 | − | 0.881250i | \(-0.343297\pi\) | ||||
0.472650 | + | 0.881250i | \(0.343297\pi\) | |||||||
\(632\) | 17.4219 | 0.693006 | ||||||||
\(633\) | −60.6541 | −2.41078 | ||||||||
\(634\) | −33.8786 | −1.34549 | ||||||||
\(635\) | 26.4524 | 1.04973 | ||||||||
\(636\) | −15.0919 | −0.598434 | ||||||||
\(637\) | −19.3964 | −0.768515 | ||||||||
\(638\) | 2.29559 | 0.0908835 | ||||||||
\(639\) | −93.3265 | −3.69194 | ||||||||
\(640\) | 82.3528 | 3.25528 | ||||||||
\(641\) | −42.5926 | −1.68230 | −0.841152 | − | 0.540798i | \(-0.818122\pi\) | ||||
−0.841152 | + | 0.540798i | \(0.818122\pi\) | |||||||
\(642\) | −106.058 | −4.18578 | ||||||||
\(643\) | 41.9483 | 1.65428 | 0.827140 | − | 0.561995i | \(-0.189966\pi\) | ||||
0.827140 | + | 0.561995i | \(0.189966\pi\) | |||||||
\(644\) | 112.459 | 4.43150 | ||||||||
\(645\) | −12.1308 | −0.477650 | ||||||||
\(646\) | −3.80552 | −0.149726 | ||||||||
\(647\) | 1.43468 | 0.0564031 | 0.0282015 | − | 0.999602i | \(-0.491022\pi\) | ||||
0.0282015 | + | 0.999602i | \(0.491022\pi\) | |||||||
\(648\) | −47.2674 | −1.85684 | ||||||||
\(649\) | −2.01671 | −0.0791626 | ||||||||
\(650\) | 60.7198 | 2.38163 | ||||||||
\(651\) | 109.722 | 4.30033 | ||||||||
\(652\) | −45.9405 | −1.79917 | ||||||||
\(653\) | 19.7425 | 0.772582 | 0.386291 | − | 0.922377i | \(-0.373756\pi\) | ||||
0.386291 | + | 0.922377i | \(0.373756\pi\) | |||||||
\(654\) | 33.5921 | 1.31356 | ||||||||
\(655\) | 57.9349 | 2.26370 | ||||||||
\(656\) | 8.14264 | 0.317917 | ||||||||
\(657\) | −81.6643 | −3.18603 | ||||||||
\(658\) | −26.4880 | −1.03261 | ||||||||
\(659\) | 3.20854 | 0.124987 | 0.0624935 | − | 0.998045i | \(-0.480095\pi\) | ||||
0.0624935 | + | 0.998045i | \(0.480095\pi\) | |||||||
\(660\) | −44.4689 | −1.73095 | ||||||||
\(661\) | −22.3124 | −0.867852 | −0.433926 | − | 0.900949i | \(-0.642872\pi\) | ||||
−0.433926 | + | 0.900949i | \(0.642872\pi\) | |||||||
\(662\) | −22.3005 | −0.866735 | ||||||||
\(663\) | 7.20829 | 0.279947 | ||||||||
\(664\) | −34.4650 | −1.33750 | ||||||||
\(665\) | 24.7861 | 0.961162 | ||||||||
\(666\) | 22.5366 | 0.873275 | ||||||||
\(667\) | −7.58576 | −0.293722 | ||||||||
\(668\) | −12.9952 | −0.502801 | ||||||||
\(669\) | 42.9879 | 1.66201 | ||||||||
\(670\) | 110.761 | 4.27909 | ||||||||
\(671\) | 12.8259 | 0.495139 | ||||||||
\(672\) | −34.7120 | −1.33904 | ||||||||
\(673\) | 12.6503 | 0.487634 | 0.243817 | − | 0.969821i | \(-0.421600\pi\) | ||||
0.243817 | + | 0.969821i | \(0.421600\pi\) | |||||||
\(674\) | −0.401332 | −0.0154587 | ||||||||
\(675\) | 109.217 | 4.20377 | ||||||||
\(676\) | −27.2043 | −1.04632 | ||||||||
\(677\) | −16.9413 | −0.651108 | −0.325554 | − | 0.945524i | \(-0.605551\pi\) | ||||
−0.325554 | + | 0.945524i | \(0.605551\pi\) | |||||||
\(678\) | 84.3510 | 3.23948 | ||||||||
\(679\) | −44.4784 | −1.70692 | ||||||||
\(680\) | 15.7608 | 0.604399 | ||||||||
\(681\) | −69.1877 | −2.65128 | ||||||||
\(682\) | −21.9417 | −0.840190 | ||||||||
\(683\) | −43.1401 | −1.65071 | −0.825356 | − | 0.564613i | \(-0.809025\pi\) | ||||
−0.825356 | + | 0.564613i | \(0.809025\pi\) | |||||||
\(684\) | −37.0024 | −1.41482 | ||||||||
\(685\) | 61.1508 | 2.33645 | ||||||||
\(686\) | 11.2520 | 0.429603 | ||||||||
\(687\) | −9.60458 | −0.366438 | ||||||||
\(688\) | −2.10639 | −0.0803055 | ||||||||
\(689\) | 3.18633 | 0.121390 | ||||||||
\(690\) | 227.119 | 8.64626 | ||||||||
\(691\) | 36.3015 | 1.38098 | 0.690488 | − | 0.723344i | \(-0.257396\pi\) | ||||
0.690488 | + | 0.723344i | \(0.257396\pi\) | |||||||
\(692\) | 48.3635 | 1.83850 | ||||||||
\(693\) | 24.6248 | 0.935418 | ||||||||
\(694\) | 3.49841 | 0.132798 | ||||||||
\(695\) | 27.3594 | 1.03780 | ||||||||
\(696\) | −11.6701 | −0.442352 | ||||||||
\(697\) | −3.86568 | −0.146423 | ||||||||
\(698\) | −8.24646 | −0.312133 | ||||||||
\(699\) | 13.1300 | 0.496624 | ||||||||
\(700\) | −154.414 | −5.83631 | ||||||||
\(701\) | 33.0039 | 1.24654 | 0.623270 | − | 0.782007i | \(-0.285804\pi\) | ||||
0.623270 | + | 0.782007i | \(0.285804\pi\) | |||||||
\(702\) | 56.8546 | 2.14584 | ||||||||
\(703\) | 2.39753 | 0.0904245 | ||||||||
\(704\) | 11.1543 | 0.420395 | ||||||||
\(705\) | −34.6111 | −1.30353 | ||||||||
\(706\) | 47.9293 | 1.80384 | ||||||||
\(707\) | −22.1542 | −0.833195 | ||||||||
\(708\) | 22.5615 | 0.847915 | ||||||||
\(709\) | 22.8500 | 0.858148 | 0.429074 | − | 0.903269i | \(-0.358840\pi\) | ||||
0.429074 | + | 0.903269i | \(0.358840\pi\) | |||||||
\(710\) | 139.858 | 5.24876 | ||||||||
\(711\) | −27.7413 | −1.04038 | ||||||||
\(712\) | −5.63896 | −0.211329 | ||||||||
\(713\) | 72.5060 | 2.71537 | ||||||||
\(714\) | −28.3324 | −1.06031 | ||||||||
\(715\) | 9.38863 | 0.351115 | ||||||||
\(716\) | 5.42608 | 0.202782 | ||||||||
\(717\) | −0.467090 | −0.0174438 | ||||||||
\(718\) | 49.5521 | 1.84927 | ||||||||
\(719\) | 29.6910 | 1.10729 | 0.553643 | − | 0.832754i | \(-0.313237\pi\) | ||||
0.553643 | + | 0.832754i | \(0.313237\pi\) | |||||||
\(720\) | 52.8626 | 1.97007 | ||||||||
\(721\) | −17.1955 | −0.640393 | ||||||||
\(722\) | 39.1414 | 1.45669 | ||||||||
\(723\) | 71.6229 | 2.66368 | ||||||||
\(724\) | −93.8936 | −3.48953 | ||||||||
\(725\) | 10.4158 | 0.386833 | ||||||||
\(726\) | −7.26423 | −0.269601 | ||||||||
\(727\) | −45.0486 | −1.67076 | −0.835380 | − | 0.549673i | \(-0.814752\pi\) | ||||
−0.835380 | + | 0.549673i | \(0.814752\pi\) | |||||||
\(728\) | −36.5270 | −1.35378 | ||||||||
\(729\) | −17.3208 | −0.641512 | ||||||||
\(730\) | 122.381 | 4.52951 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −143.488 | −5.30346 | ||||||||
\(733\) | −13.0921 | −0.483568 | −0.241784 | − | 0.970330i | \(-0.577733\pi\) | ||||
−0.241784 | + | 0.970330i | \(0.577733\pi\) | |||||||
\(734\) | 17.5596 | 0.648135 | ||||||||
\(735\) | 99.6182 | 3.67447 | ||||||||
\(736\) | −22.9383 | −0.845515 | ||||||||
\(737\) | 11.7066 | 0.431216 | ||||||||
\(738\) | −58.0945 | −2.13849 | ||||||||
\(739\) | 53.4062 | 1.96458 | 0.982290 | − | 0.187369i | \(-0.0599959\pi\) | ||||
0.982290 | + | 0.187369i | \(0.0599959\pi\) | |||||||
\(740\) | −21.8512 | −0.803267 | ||||||||
\(741\) | 11.5243 | 0.423357 | ||||||||
\(742\) | −12.5240 | −0.459769 | ||||||||
\(743\) | 10.2612 | 0.376446 | 0.188223 | − | 0.982126i | \(-0.439727\pi\) | ||||
0.188223 | + | 0.982126i | \(0.439727\pi\) | |||||||
\(744\) | 111.544 | 4.08941 | ||||||||
\(745\) | −45.6677 | −1.67314 | ||||||||
\(746\) | −33.7715 | −1.23646 | ||||||||
\(747\) | 54.8795 | 2.00793 | ||||||||
\(748\) | 3.66578 | 0.134034 | ||||||||
\(749\) | −56.9440 | −2.08069 | ||||||||
\(750\) | −167.477 | −6.11538 | ||||||||
\(751\) | −40.3234 | −1.47142 | −0.735710 | − | 0.677296i | \(-0.763152\pi\) | ||||
−0.735710 | + | 0.677296i | \(0.763152\pi\) | |||||||
\(752\) | −6.00988 | −0.219158 | ||||||||
\(753\) | 46.5290 | 1.69561 | ||||||||
\(754\) | 5.42210 | 0.197461 | ||||||||
\(755\) | −84.8316 | −3.08734 | ||||||||
\(756\) | −144.585 | −5.25851 | ||||||||
\(757\) | 51.9570 | 1.88841 | 0.944204 | − | 0.329362i | \(-0.106834\pi\) | ||||
0.944204 | + | 0.329362i | \(0.106834\pi\) | |||||||
\(758\) | −18.6496 | −0.677382 | ||||||||
\(759\) | 24.0045 | 0.871309 | ||||||||
\(760\) | 25.1978 | 0.914019 | ||||||||
\(761\) | −35.5671 | −1.28931 | −0.644653 | − | 0.764475i | \(-0.722998\pi\) | ||||
−0.644653 | + | 0.764475i | \(0.722998\pi\) | |||||||
\(762\) | −48.3419 | −1.75124 | ||||||||
\(763\) | 18.0361 | 0.652949 | ||||||||
\(764\) | 44.4374 | 1.60769 | ||||||||
\(765\) | −25.0963 | −0.907357 | ||||||||
\(766\) | −5.59641 | −0.202207 | ||||||||
\(767\) | −4.76338 | −0.171996 | ||||||||
\(768\) | −82.4184 | −2.97402 | ||||||||
\(769\) | −33.3934 | −1.20420 | −0.602099 | − | 0.798421i | \(-0.705669\pi\) | ||||
−0.602099 | + | 0.798421i | \(0.705669\pi\) | |||||||
\(770\) | −36.9023 | −1.32987 | ||||||||
\(771\) | 62.2522 | 2.24196 | ||||||||
\(772\) | −36.2848 | −1.30592 | ||||||||
\(773\) | 50.8929 | 1.83049 | 0.915246 | − | 0.402895i | \(-0.131996\pi\) | ||||
0.915246 | + | 0.402895i | \(0.131996\pi\) | |||||||
\(774\) | 15.0283 | 0.540180 | ||||||||
\(775\) | −99.5560 | −3.57616 | ||||||||
\(776\) | −45.2172 | −1.62320 | ||||||||
\(777\) | 17.8497 | 0.640356 | ||||||||
\(778\) | 76.3828 | 2.73845 | ||||||||
\(779\) | −6.18031 | −0.221433 | ||||||||
\(780\) | −105.034 | −3.76081 | ||||||||
\(781\) | 14.7818 | 0.528933 | ||||||||
\(782\) | −18.7225 | −0.669515 | ||||||||
\(783\) | 9.75278 | 0.348536 | ||||||||
\(784\) | 17.2977 | 0.617776 | ||||||||
\(785\) | 81.0550 | 2.89298 | ||||||||
\(786\) | −105.877 | −3.77649 | ||||||||
\(787\) | −45.8519 | −1.63444 | −0.817222 | − | 0.576323i | \(-0.804487\pi\) | ||||
−0.817222 | + | 0.576323i | \(0.804487\pi\) | |||||||
\(788\) | 9.96444 | 0.354968 | ||||||||
\(789\) | −6.28305 | −0.223682 | ||||||||
\(790\) | 41.5726 | 1.47909 | ||||||||
\(791\) | 45.2892 | 1.61030 | ||||||||
\(792\) | 25.0338 | 0.889538 | ||||||||
\(793\) | 30.2943 | 1.07578 | ||||||||
\(794\) | 75.4973 | 2.67930 | ||||||||
\(795\) | −16.3647 | −0.580396 | ||||||||
\(796\) | −54.2215 | −1.92183 | ||||||||
\(797\) | 20.4179 | 0.723238 | 0.361619 | − | 0.932326i | \(-0.382224\pi\) | ||||
0.361619 | + | 0.932326i | \(0.382224\pi\) | |||||||
\(798\) | −45.2968 | −1.60349 | ||||||||
\(799\) | 2.85316 | 0.100938 | ||||||||
\(800\) | 31.4959 | 1.11355 | ||||||||
\(801\) | 8.97904 | 0.317259 | ||||||||
\(802\) | 12.9188 | 0.456178 | ||||||||
\(803\) | 12.9346 | 0.456452 | ||||||||
\(804\) | −130.965 | −4.61878 | ||||||||
\(805\) | 121.943 | 4.29793 | ||||||||
\(806\) | −51.8254 | −1.82547 | ||||||||
\(807\) | 14.7833 | 0.520395 | ||||||||
\(808\) | −22.5222 | −0.792329 | ||||||||
\(809\) | 41.1287 | 1.44601 | 0.723004 | − | 0.690844i | \(-0.242761\pi\) | ||||
0.723004 | + | 0.690844i | \(0.242761\pi\) | |||||||
\(810\) | −112.791 | −3.96306 | ||||||||
\(811\) | −46.5188 | −1.63350 | −0.816748 | − | 0.576995i | \(-0.804225\pi\) | ||||
−0.816748 | + | 0.576995i | \(0.804225\pi\) | |||||||
\(812\) | −13.7888 | −0.483891 | ||||||||
\(813\) | 37.1157 | 1.30170 | ||||||||
\(814\) | −3.56951 | −0.125111 | ||||||||
\(815\) | −49.8149 | −1.74494 | ||||||||
\(816\) | −6.42834 | −0.225037 | ||||||||
\(817\) | 1.59876 | 0.0559337 | ||||||||
\(818\) | −37.3669 | −1.30650 | ||||||||
\(819\) | 58.1627 | 2.03237 | ||||||||
\(820\) | 56.3277 | 1.96705 | ||||||||
\(821\) | −5.67947 | −0.198215 | −0.0991074 | − | 0.995077i | \(-0.531599\pi\) | ||||
−0.0991074 | + | 0.995077i | \(0.531599\pi\) | |||||||
\(822\) | −111.754 | −3.89785 | ||||||||
\(823\) | 28.7627 | 1.00261 | 0.501303 | − | 0.865272i | \(-0.332854\pi\) | ||||
0.501303 | + | 0.865272i | \(0.332854\pi\) | |||||||
\(824\) | −17.4811 | −0.608983 | ||||||||
\(825\) | −32.9600 | −1.14752 | ||||||||
\(826\) | 18.7226 | 0.651442 | ||||||||
\(827\) | 43.1493 | 1.50045 | 0.750225 | − | 0.661183i | \(-0.229945\pi\) | ||||
0.750225 | + | 0.661183i | \(0.229945\pi\) | |||||||
\(828\) | −182.045 | −6.32651 | ||||||||
\(829\) | 9.70305 | 0.337001 | 0.168500 | − | 0.985702i | \(-0.446108\pi\) | ||||
0.168500 | + | 0.985702i | \(0.446108\pi\) | |||||||
\(830\) | −82.2414 | −2.85464 | ||||||||
\(831\) | 17.7062 | 0.614220 | ||||||||
\(832\) | 26.3461 | 0.913387 | ||||||||
\(833\) | −8.21201 | −0.284529 | ||||||||
\(834\) | −49.9995 | −1.73134 | ||||||||
\(835\) | −14.0912 | −0.487646 | ||||||||
\(836\) | 5.86072 | 0.202697 | ||||||||
\(837\) | −93.2188 | −3.22211 | ||||||||
\(838\) | −37.8663 | −1.30807 | ||||||||
\(839\) | 4.36840 | 0.150814 | 0.0754069 | − | 0.997153i | \(-0.475974\pi\) | ||||
0.0754069 | + | 0.997153i | \(0.475974\pi\) | |||||||
\(840\) | 187.599 | 6.47278 | ||||||||
\(841\) | −28.0699 | −0.967928 | ||||||||
\(842\) | 4.29589 | 0.148046 | ||||||||
\(843\) | −47.8399 | −1.64769 | ||||||||
\(844\) | −72.8563 | −2.50782 | ||||||||
\(845\) | −29.4986 | −1.01478 | ||||||||
\(846\) | 42.8781 | 1.47418 | ||||||||
\(847\) | −3.90026 | −0.134014 | ||||||||
\(848\) | −2.84157 | −0.0975798 | ||||||||
\(849\) | −21.8122 | −0.748593 | ||||||||
\(850\) | 25.7074 | 0.881755 | ||||||||
\(851\) | 11.7954 | 0.404341 | ||||||||
\(852\) | −165.368 | −5.66542 | ||||||||
\(853\) | −41.9248 | −1.43548 | −0.717739 | − | 0.696313i | \(-0.754823\pi\) | ||||
−0.717739 | + | 0.696313i | \(0.754823\pi\) | |||||||
\(854\) | −119.073 | −4.07458 | ||||||||
\(855\) | −40.1230 | −1.37218 | ||||||||
\(856\) | −57.8899 | −1.97864 | ||||||||
\(857\) | −39.5453 | −1.35084 | −0.675421 | − | 0.737432i | \(-0.736038\pi\) | ||||
−0.675421 | + | 0.737432i | \(0.736038\pi\) | |||||||
\(858\) | −17.1578 | −0.585758 | ||||||||
\(859\) | −52.1191 | −1.77828 | −0.889140 | − | 0.457636i | \(-0.848696\pi\) | ||||
−0.889140 | + | 0.457636i | \(0.848696\pi\) | |||||||
\(860\) | −14.5712 | −0.496875 | ||||||||
\(861\) | −46.0128 | −1.56811 | ||||||||
\(862\) | 76.3543 | 2.60064 | ||||||||
\(863\) | 8.91404 | 0.303438 | 0.151719 | − | 0.988424i | \(-0.451519\pi\) | ||||
0.151719 | + | 0.988424i | \(0.451519\pi\) | |||||||
\(864\) | 29.4910 | 1.00331 | ||||||||
\(865\) | 52.4422 | 1.78309 | ||||||||
\(866\) | −22.3437 | −0.759271 | ||||||||
\(867\) | 3.05182 | 0.103645 | ||||||||
\(868\) | 131.795 | 4.47342 | ||||||||
\(869\) | 4.39387 | 0.149052 | ||||||||
\(870\) | −27.8474 | −0.944115 | ||||||||
\(871\) | 27.6504 | 0.936898 | ||||||||
\(872\) | 18.3357 | 0.620924 | ||||||||
\(873\) | 72.0004 | 2.43684 | ||||||||
\(874\) | −29.9328 | −1.01249 | ||||||||
\(875\) | −89.9204 | −3.03987 | ||||||||
\(876\) | −144.704 | −4.88908 | ||||||||
\(877\) | −8.22514 | −0.277743 | −0.138872 | − | 0.990310i | \(-0.544348\pi\) | ||||
−0.138872 | + | 0.990310i | \(0.544348\pi\) | |||||||
\(878\) | 77.6475 | 2.62048 | ||||||||
\(879\) | −33.9402 | −1.14477 | ||||||||
\(880\) | −8.37277 | −0.282246 | ||||||||
\(881\) | 16.0690 | 0.541378 | 0.270689 | − | 0.962667i | \(-0.412748\pi\) | ||||
0.270689 | + | 0.962667i | \(0.412748\pi\) | |||||||
\(882\) | −123.412 | −4.15551 | ||||||||
\(883\) | 7.52160 | 0.253122 | 0.126561 | − | 0.991959i | \(-0.459606\pi\) | ||||
0.126561 | + | 0.991959i | \(0.459606\pi\) | |||||||
\(884\) | 8.65843 | 0.291215 | ||||||||
\(885\) | 24.4643 | 0.822357 | ||||||||
\(886\) | −30.2590 | −1.01657 | ||||||||
\(887\) | −25.5521 | −0.857954 | −0.428977 | − | 0.903315i | \(-0.641126\pi\) | ||||
−0.428977 | + | 0.903315i | \(0.641126\pi\) | |||||||
\(888\) | 18.1462 | 0.608948 | ||||||||
\(889\) | −25.9554 | −0.870516 | ||||||||
\(890\) | −13.4558 | −0.451040 | ||||||||
\(891\) | −11.9210 | −0.399369 | ||||||||
\(892\) | 51.6361 | 1.72890 | ||||||||
\(893\) | 4.56153 | 0.152646 | ||||||||
\(894\) | 83.4582 | 2.79126 | ||||||||
\(895\) | 5.88369 | 0.196670 | ||||||||
\(896\) | −80.8057 | −2.69953 | ||||||||
\(897\) | 56.6977 | 1.89308 | ||||||||
\(898\) | −48.3677 | −1.61405 | ||||||||
\(899\) | −8.89007 | −0.296500 | ||||||||
\(900\) | 249.962 | 8.33205 | ||||||||
\(901\) | 1.34902 | 0.0449424 | ||||||||
\(902\) | 9.20144 | 0.306374 | ||||||||
\(903\) | 11.9029 | 0.396104 | ||||||||
\(904\) | 46.0414 | 1.53132 | ||||||||
\(905\) | −101.812 | −3.38435 | ||||||||
\(906\) | 155.031 | 5.15055 | ||||||||
\(907\) | −5.17575 | −0.171858 | −0.0859290 | − | 0.996301i | \(-0.527386\pi\) | ||||
−0.0859290 | + | 0.996301i | \(0.527386\pi\) | |||||||
\(908\) | −83.1067 | −2.75799 | ||||||||
\(909\) | 35.8626 | 1.18949 | ||||||||
\(910\) | −87.1617 | −2.88938 | ||||||||
\(911\) | −44.6776 | −1.48024 | −0.740118 | − | 0.672477i | \(-0.765230\pi\) | ||||
−0.740118 | + | 0.672477i | \(0.765230\pi\) | |||||||
\(912\) | −10.2774 | −0.340319 | ||||||||
\(913\) | −8.69222 | −0.287670 | ||||||||
\(914\) | 10.9909 | 0.363546 | ||||||||
\(915\) | −155.589 | −5.14360 | ||||||||
\(916\) | −11.5368 | −0.381187 | ||||||||
\(917\) | −56.8465 | −1.87724 | ||||||||
\(918\) | 24.0710 | 0.794460 | ||||||||
\(919\) | 23.1495 | 0.763632 | 0.381816 | − | 0.924238i | \(-0.375299\pi\) | ||||
0.381816 | + | 0.924238i | \(0.375299\pi\) | |||||||
\(920\) | 123.969 | 4.08712 | ||||||||
\(921\) | 42.9868 | 1.41646 | ||||||||
\(922\) | −64.9286 | −2.13831 | ||||||||
\(923\) | 34.9139 | 1.14921 | ||||||||
\(924\) | 43.6334 | 1.43543 | ||||||||
\(925\) | −16.1960 | −0.532520 | ||||||||
\(926\) | −9.92290 | −0.326087 | ||||||||
\(927\) | 27.8355 | 0.914239 | ||||||||
\(928\) | 2.81250 | 0.0923247 | ||||||||
\(929\) | −32.7003 | −1.07286 | −0.536432 | − | 0.843944i | \(-0.680228\pi\) | ||||
−0.536432 | + | 0.843944i | \(0.680228\pi\) | |||||||
\(930\) | 266.170 | 8.72806 | ||||||||
\(931\) | −13.1291 | −0.430288 | ||||||||
\(932\) | 15.7715 | 0.516613 | ||||||||
\(933\) | −77.8243 | −2.54785 | ||||||||
\(934\) | 75.6535 | 2.47546 | ||||||||
\(935\) | 3.97493 | 0.129994 | ||||||||
\(936\) | 59.1289 | 1.93269 | ||||||||
\(937\) | 20.7841 | 0.678986 | 0.339493 | − | 0.940609i | \(-0.389744\pi\) | ||||
0.339493 | + | 0.940609i | \(0.389744\pi\) | |||||||
\(938\) | −108.681 | −3.54855 | ||||||||
\(939\) | 13.7592 | 0.449013 | ||||||||
\(940\) | −41.5741 | −1.35600 | ||||||||
\(941\) | 3.80983 | 0.124197 | 0.0620985 | − | 0.998070i | \(-0.480221\pi\) | ||||
0.0620985 | + | 0.998070i | \(0.480221\pi\) | |||||||
\(942\) | −148.129 | −4.82630 | ||||||||
\(943\) | −30.4060 | −0.990156 | ||||||||
\(944\) | 4.24798 | 0.138260 | ||||||||
\(945\) | −156.778 | −5.10000 | ||||||||
\(946\) | −2.38029 | −0.0773899 | ||||||||
\(947\) | −7.08098 | −0.230101 | −0.115050 | − | 0.993360i | \(-0.536703\pi\) | ||||
−0.115050 | + | 0.993360i | \(0.536703\pi\) | |||||||
\(948\) | −49.1556 | −1.59650 | ||||||||
\(949\) | 30.5510 | 0.991728 | ||||||||
\(950\) | 41.1000 | 1.33346 | ||||||||
\(951\) | 43.4365 | 1.40853 | ||||||||
\(952\) | −15.4647 | −0.501214 | ||||||||
\(953\) | 18.6112 | 0.602874 | 0.301437 | − | 0.953486i | \(-0.402534\pi\) | ||||
0.301437 | + | 0.953486i | \(0.402534\pi\) | |||||||
\(954\) | 20.2735 | 0.656377 | ||||||||
\(955\) | 48.1850 | 1.55923 | ||||||||
\(956\) | −0.561058 | −0.0181459 | ||||||||
\(957\) | −2.94323 | −0.0951412 | ||||||||
\(958\) | −12.5650 | −0.405956 | ||||||||
\(959\) | −60.0020 | −1.93756 | ||||||||
\(960\) | −135.311 | −4.36714 | ||||||||
\(961\) | 53.9728 | 1.74106 | ||||||||
\(962\) | −8.43105 | −0.271828 | ||||||||
\(963\) | 92.1794 | 2.97044 | ||||||||
\(964\) | 86.0318 | 2.77090 | ||||||||
\(965\) | −39.3448 | −1.26655 | ||||||||
\(966\) | −222.852 | −7.17014 | ||||||||
\(967\) | −5.20828 | −0.167487 | −0.0837435 | − | 0.996487i | \(-0.526688\pi\) | ||||
−0.0837435 | + | 0.996487i | \(0.526688\pi\) | |||||||
\(968\) | −3.96504 | −0.127441 | ||||||||
\(969\) | 4.87915 | 0.156741 | ||||||||
\(970\) | −107.899 | −3.46441 | ||||||||
\(971\) | −27.7112 | −0.889294 | −0.444647 | − | 0.895706i | \(-0.646671\pi\) | ||||
−0.444647 | + | 0.895706i | \(0.646671\pi\) | |||||||
\(972\) | 22.1524 | 0.710539 | ||||||||
\(973\) | −26.8454 | −0.860623 | ||||||||
\(974\) | −90.9961 | −2.91570 | ||||||||
\(975\) | −77.8502 | −2.49320 | ||||||||
\(976\) | −27.0164 | −0.864774 | ||||||||
\(977\) | 41.0935 | 1.31470 | 0.657349 | − | 0.753586i | \(-0.271678\pi\) | ||||
0.657349 | + | 0.753586i | \(0.271678\pi\) | |||||||
\(978\) | 91.0371 | 2.91105 | ||||||||
\(979\) | −1.42217 | −0.0454527 | ||||||||
\(980\) | 119.659 | 3.82237 | ||||||||
\(981\) | −29.1963 | −0.932165 | ||||||||
\(982\) | 86.9953 | 2.77613 | ||||||||
\(983\) | −28.8589 | −0.920456 | −0.460228 | − | 0.887801i | \(-0.652232\pi\) | ||||
−0.460228 | + | 0.887801i | \(0.652232\pi\) | |||||||
\(984\) | −46.7771 | −1.49120 | ||||||||
\(985\) | 10.8048 | 0.344269 | ||||||||
\(986\) | 2.29559 | 0.0731066 | ||||||||
\(987\) | 33.9609 | 1.08099 | ||||||||
\(988\) | 13.8428 | 0.440398 | ||||||||
\(989\) | 7.86563 | 0.250113 | ||||||||
\(990\) | 59.7364 | 1.89855 | ||||||||
\(991\) | −21.6667 | −0.688266 | −0.344133 | − | 0.938921i | \(-0.611827\pi\) | ||||
−0.344133 | + | 0.938921i | \(0.611827\pi\) | |||||||
\(992\) | −26.8823 | −0.853514 | ||||||||
\(993\) | 28.5920 | 0.907341 | ||||||||
\(994\) | −137.230 | −4.35267 | ||||||||
\(995\) | −58.7942 | −1.86390 | ||||||||
\(996\) | 97.2426 | 3.08125 | ||||||||
\(997\) | −26.4028 | −0.836185 | −0.418092 | − | 0.908405i | \(-0.637301\pi\) | ||||
−0.418092 | + | 0.908405i | \(0.637301\pi\) | |||||||
\(998\) | −74.8562 | −2.36953 | ||||||||
\(999\) | −15.1650 | −0.479800 |
(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 | 8041.2.a.h.1.9 | ✓ | 74 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.h.1.9 | ✓ | 74 | 1.1 | even | 1 | trivial |