Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, 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("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.17233 | −1.25419 | −0.627097 | − | 0.778941i | \(-0.715757\pi\) | ||||
−0.627097 | + | 0.778941i | \(0.715757\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.31184 | −0.586674 | −0.293337 | − | 0.956009i | \(-0.594766\pi\) | ||||
−0.293337 | + | 0.956009i | \(0.594766\pi\) | |||||||
\(6\) | 2.17233 | 0.886849 | ||||||||
\(7\) | −2.50290 | −0.946008 | −0.473004 | − | 0.881060i | \(-0.656830\pi\) | ||||
−0.473004 | + | 0.881060i | \(0.656830\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.71901 | 0.573003 | ||||||||
\(10\) | 1.31184 | 0.414841 | ||||||||
\(11\) | −0.100565 | −0.0303215 | −0.0151608 | − | 0.999885i | \(-0.504826\pi\) | ||||
−0.0151608 | + | 0.999885i | \(0.504826\pi\) | |||||||
\(12\) | −2.17233 | −0.627097 | ||||||||
\(13\) | 2.06885 | 0.573796 | 0.286898 | − | 0.957961i | \(-0.407376\pi\) | ||||
0.286898 | + | 0.957961i | \(0.407376\pi\) | |||||||
\(14\) | 2.50290 | 0.668929 | ||||||||
\(15\) | 2.84976 | 0.735804 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.01258 | −0.488122 | −0.244061 | − | 0.969760i | \(-0.578480\pi\) | ||||
−0.244061 | + | 0.969760i | \(0.578480\pi\) | |||||||
\(18\) | −1.71901 | −0.405175 | ||||||||
\(19\) | 4.95546 | 1.13686 | 0.568430 | − | 0.822731i | \(-0.307551\pi\) | ||||
0.568430 | + | 0.822731i | \(0.307551\pi\) | |||||||
\(20\) | −1.31184 | −0.293337 | ||||||||
\(21\) | 5.43713 | 1.18648 | ||||||||
\(22\) | 0.100565 | 0.0214405 | ||||||||
\(23\) | 5.18712 | 1.08159 | 0.540795 | − | 0.841155i | \(-0.318124\pi\) | ||||
0.540795 | + | 0.841155i | \(0.318124\pi\) | |||||||
\(24\) | 2.17233 | 0.443425 | ||||||||
\(25\) | −3.27907 | −0.655813 | ||||||||
\(26\) | −2.06885 | −0.405735 | ||||||||
\(27\) | 2.78273 | 0.535537 | ||||||||
\(28\) | −2.50290 | −0.473004 | ||||||||
\(29\) | 9.97044 | 1.85146 | 0.925732 | − | 0.378180i | \(-0.123450\pi\) | ||||
0.925732 | + | 0.378180i | \(0.123450\pi\) | |||||||
\(30\) | −2.84976 | −0.520292 | ||||||||
\(31\) | −7.91975 | −1.42243 | −0.711215 | − | 0.702975i | \(-0.751855\pi\) | ||||
−0.711215 | + | 0.702975i | \(0.751855\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.218460 | 0.0380291 | ||||||||
\(34\) | 2.01258 | 0.345155 | ||||||||
\(35\) | 3.28342 | 0.554999 | ||||||||
\(36\) | 1.71901 | 0.286502 | ||||||||
\(37\) | 3.73621 | 0.614229 | 0.307114 | − | 0.951673i | \(-0.400637\pi\) | ||||
0.307114 | + | 0.951673i | \(0.400637\pi\) | |||||||
\(38\) | −4.95546 | −0.803882 | ||||||||
\(39\) | −4.49422 | −0.719652 | ||||||||
\(40\) | 1.31184 | 0.207421 | ||||||||
\(41\) | 3.49399 | 0.545670 | 0.272835 | − | 0.962061i | \(-0.412039\pi\) | ||||
0.272835 | + | 0.962061i | \(0.412039\pi\) | |||||||
\(42\) | −5.43713 | −0.838967 | ||||||||
\(43\) | 7.18482 | 1.09568 | 0.547838 | − | 0.836585i | \(-0.315451\pi\) | ||||
0.547838 | + | 0.836585i | \(0.315451\pi\) | |||||||
\(44\) | −0.100565 | −0.0151608 | ||||||||
\(45\) | −2.25507 | −0.336166 | ||||||||
\(46\) | −5.18712 | −0.764799 | ||||||||
\(47\) | −6.40829 | −0.934745 | −0.467372 | − | 0.884061i | \(-0.654799\pi\) | ||||
−0.467372 | + | 0.884061i | \(0.654799\pi\) | |||||||
\(48\) | −2.17233 | −0.313549 | ||||||||
\(49\) | −0.735476 | −0.105068 | ||||||||
\(50\) | 3.27907 | 0.463730 | ||||||||
\(51\) | 4.37198 | 0.612200 | ||||||||
\(52\) | 2.06885 | 0.286898 | ||||||||
\(53\) | −2.04402 | −0.280768 | −0.140384 | − | 0.990097i | \(-0.544834\pi\) | ||||
−0.140384 | + | 0.990097i | \(0.544834\pi\) | |||||||
\(54\) | −2.78273 | −0.378682 | ||||||||
\(55\) | 0.131926 | 0.0177889 | ||||||||
\(56\) | 2.50290 | 0.334465 | ||||||||
\(57\) | −10.7649 | −1.42584 | ||||||||
\(58\) | −9.97044 | −1.30918 | ||||||||
\(59\) | −0.710808 | −0.0925394 | −0.0462697 | − | 0.998929i | \(-0.514733\pi\) | ||||
−0.0462697 | + | 0.998929i | \(0.514733\pi\) | |||||||
\(60\) | 2.84976 | 0.367902 | ||||||||
\(61\) | −0.711142 | −0.0910524 | −0.0455262 | − | 0.998963i | \(-0.514496\pi\) | ||||
−0.0455262 | + | 0.998963i | \(0.514496\pi\) | |||||||
\(62\) | 7.91975 | 1.00581 | ||||||||
\(63\) | −4.30252 | −0.542066 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.71401 | −0.336631 | ||||||||
\(66\) | −0.218460 | −0.0268906 | ||||||||
\(67\) | 2.07100 | 0.253013 | 0.126507 | − | 0.991966i | \(-0.459623\pi\) | ||||
0.126507 | + | 0.991966i | \(0.459623\pi\) | |||||||
\(68\) | −2.01258 | −0.244061 | ||||||||
\(69\) | −11.2681 | −1.35652 | ||||||||
\(70\) | −3.28342 | −0.392444 | ||||||||
\(71\) | −12.5268 | −1.48666 | −0.743331 | − | 0.668924i | \(-0.766755\pi\) | ||||
−0.743331 | + | 0.668924i | \(0.766755\pi\) | |||||||
\(72\) | −1.71901 | −0.202587 | ||||||||
\(73\) | −4.08400 | −0.477997 | −0.238998 | − | 0.971020i | \(-0.576819\pi\) | ||||
−0.238998 | + | 0.971020i | \(0.576819\pi\) | |||||||
\(74\) | −3.73621 | −0.434325 | ||||||||
\(75\) | 7.12321 | 0.822517 | ||||||||
\(76\) | 4.95546 | 0.568430 | ||||||||
\(77\) | 0.251705 | 0.0286844 | ||||||||
\(78\) | 4.49422 | 0.508871 | ||||||||
\(79\) | 2.72361 | 0.306430 | 0.153215 | − | 0.988193i | \(-0.451037\pi\) | ||||
0.153215 | + | 0.988193i | \(0.451037\pi\) | |||||||
\(80\) | −1.31184 | −0.146669 | ||||||||
\(81\) | −11.2020 | −1.24467 | ||||||||
\(82\) | −3.49399 | −0.385847 | ||||||||
\(83\) | 7.12661 | 0.782247 | 0.391124 | − | 0.920338i | \(-0.372087\pi\) | ||||
0.391124 | + | 0.920338i | \(0.372087\pi\) | |||||||
\(84\) | 5.43713 | 0.593239 | ||||||||
\(85\) | 2.64019 | 0.286369 | ||||||||
\(86\) | −7.18482 | −0.774759 | ||||||||
\(87\) | −21.6591 | −2.32210 | ||||||||
\(88\) | 0.100565 | 0.0107203 | ||||||||
\(89\) | −9.67029 | −1.02505 | −0.512524 | − | 0.858673i | \(-0.671290\pi\) | ||||
−0.512524 | + | 0.858673i | \(0.671290\pi\) | |||||||
\(90\) | 2.25507 | 0.237706 | ||||||||
\(91\) | −5.17813 | −0.542816 | ||||||||
\(92\) | 5.18712 | 0.540795 | ||||||||
\(93\) | 17.2043 | 1.78400 | ||||||||
\(94\) | 6.40829 | 0.660964 | ||||||||
\(95\) | −6.50079 | −0.666967 | ||||||||
\(96\) | 2.17233 | 0.221712 | ||||||||
\(97\) | 13.5076 | 1.37149 | 0.685746 | − | 0.727841i | \(-0.259476\pi\) | ||||
0.685746 | + | 0.727841i | \(0.259476\pi\) | |||||||
\(98\) | 0.735476 | 0.0742943 | ||||||||
\(99\) | −0.172872 | −0.0173743 | ||||||||
\(100\) | −3.27907 | −0.327907 | ||||||||
\(101\) | −8.75991 | −0.871644 | −0.435822 | − | 0.900033i | \(-0.643542\pi\) | ||||
−0.435822 | + | 0.900033i | \(0.643542\pi\) | |||||||
\(102\) | −4.37198 | −0.432891 | ||||||||
\(103\) | 10.1373 | 0.998862 | 0.499431 | − | 0.866354i | \(-0.333542\pi\) | ||||
0.499431 | + | 0.866354i | \(0.333542\pi\) | |||||||
\(104\) | −2.06885 | −0.202868 | ||||||||
\(105\) | −7.13266 | −0.696077 | ||||||||
\(106\) | 2.04402 | 0.198533 | ||||||||
\(107\) | 9.92879 | 0.959853 | 0.479926 | − | 0.877309i | \(-0.340663\pi\) | ||||
0.479926 | + | 0.877309i | \(0.340663\pi\) | |||||||
\(108\) | 2.78273 | 0.267768 | ||||||||
\(109\) | −16.1257 | −1.54456 | −0.772279 | − | 0.635284i | \(-0.780883\pi\) | ||||
−0.772279 | + | 0.635284i | \(0.780883\pi\) | |||||||
\(110\) | −0.131926 | −0.0125786 | ||||||||
\(111\) | −8.11627 | −0.770362 | ||||||||
\(112\) | −2.50290 | −0.236502 | ||||||||
\(113\) | −11.7020 | −1.10083 | −0.550416 | − | 0.834891i | \(-0.685531\pi\) | ||||
−0.550416 | + | 0.834891i | \(0.685531\pi\) | |||||||
\(114\) | 10.7649 | 1.00822 | ||||||||
\(115\) | −6.80469 | −0.634541 | ||||||||
\(116\) | 9.97044 | 0.925732 | ||||||||
\(117\) | 3.55638 | 0.328787 | ||||||||
\(118\) | 0.710808 | 0.0654352 | ||||||||
\(119\) | 5.03729 | 0.461768 | ||||||||
\(120\) | −2.84976 | −0.260146 | ||||||||
\(121\) | −10.9899 | −0.999081 | ||||||||
\(122\) | 0.711142 | 0.0643838 | ||||||||
\(123\) | −7.59010 | −0.684376 | ||||||||
\(124\) | −7.91975 | −0.711215 | ||||||||
\(125\) | 10.8608 | 0.971423 | ||||||||
\(126\) | 4.30252 | 0.383299 | ||||||||
\(127\) | −4.84397 | −0.429833 | −0.214917 | − | 0.976632i | \(-0.568948\pi\) | ||||
−0.214917 | + | 0.976632i | \(0.568948\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −15.6078 | −1.37419 | ||||||||
\(130\) | 2.71401 | 0.238034 | ||||||||
\(131\) | 5.91413 | 0.516720 | 0.258360 | − | 0.966049i | \(-0.416818\pi\) | ||||
0.258360 | + | 0.966049i | \(0.416818\pi\) | |||||||
\(132\) | 0.218460 | 0.0190145 | ||||||||
\(133\) | −12.4030 | −1.07548 | ||||||||
\(134\) | −2.07100 | −0.178908 | ||||||||
\(135\) | −3.65051 | −0.314186 | ||||||||
\(136\) | 2.01258 | 0.172577 | ||||||||
\(137\) | 13.2312 | 1.13041 | 0.565207 | − | 0.824949i | \(-0.308796\pi\) | ||||
0.565207 | + | 0.824949i | \(0.308796\pi\) | |||||||
\(138\) | 11.2681 | 0.959207 | ||||||||
\(139\) | −5.31410 | −0.450736 | −0.225368 | − | 0.974274i | \(-0.572358\pi\) | ||||
−0.225368 | + | 0.974274i | \(0.572358\pi\) | |||||||
\(140\) | 3.28342 | 0.277499 | ||||||||
\(141\) | 13.9209 | 1.17235 | ||||||||
\(142\) | 12.5268 | 1.05123 | ||||||||
\(143\) | −0.208054 | −0.0173984 | ||||||||
\(144\) | 1.71901 | 0.143251 | ||||||||
\(145\) | −13.0797 | −1.08621 | ||||||||
\(146\) | 4.08400 | 0.337995 | ||||||||
\(147\) | 1.59770 | 0.131776 | ||||||||
\(148\) | 3.73621 | 0.307114 | ||||||||
\(149\) | −4.04539 | −0.331411 | −0.165706 | − | 0.986175i | \(-0.552990\pi\) | ||||
−0.165706 | + | 0.986175i | \(0.552990\pi\) | |||||||
\(150\) | −7.12321 | −0.581607 | ||||||||
\(151\) | 3.91908 | 0.318931 | 0.159465 | − | 0.987204i | \(-0.449023\pi\) | ||||
0.159465 | + | 0.987204i | \(0.449023\pi\) | |||||||
\(152\) | −4.95546 | −0.401941 | ||||||||
\(153\) | −3.45964 | −0.279696 | ||||||||
\(154\) | −0.251705 | −0.0202829 | ||||||||
\(155\) | 10.3895 | 0.834503 | ||||||||
\(156\) | −4.49422 | −0.359826 | ||||||||
\(157\) | 1.29450 | 0.103312 | 0.0516560 | − | 0.998665i | \(-0.483550\pi\) | ||||
0.0516560 | + | 0.998665i | \(0.483550\pi\) | |||||||
\(158\) | −2.72361 | −0.216679 | ||||||||
\(159\) | 4.44028 | 0.352137 | ||||||||
\(160\) | 1.31184 | 0.103710 | ||||||||
\(161\) | −12.9829 | −1.02319 | ||||||||
\(162\) | 11.2020 | 0.880115 | ||||||||
\(163\) | −5.00829 | −0.392280 | −0.196140 | − | 0.980576i | \(-0.562841\pi\) | ||||
−0.196140 | + | 0.980576i | \(0.562841\pi\) | |||||||
\(164\) | 3.49399 | 0.272835 | ||||||||
\(165\) | −0.286586 | −0.0223107 | ||||||||
\(166\) | −7.12661 | −0.553132 | ||||||||
\(167\) | 14.5968 | 1.12953 | 0.564765 | − | 0.825252i | \(-0.308967\pi\) | ||||
0.564765 | + | 0.825252i | \(0.308967\pi\) | |||||||
\(168\) | −5.43713 | −0.419483 | ||||||||
\(169\) | −8.71986 | −0.670758 | ||||||||
\(170\) | −2.64019 | −0.202493 | ||||||||
\(171\) | 8.51849 | 0.651425 | ||||||||
\(172\) | 7.18482 | 0.547838 | ||||||||
\(173\) | −18.7254 | −1.42367 | −0.711833 | − | 0.702348i | \(-0.752135\pi\) | ||||
−0.711833 | + | 0.702348i | \(0.752135\pi\) | |||||||
\(174\) | 21.6591 | 1.64197 | ||||||||
\(175\) | 8.20718 | 0.620405 | ||||||||
\(176\) | −0.100565 | −0.00758038 | ||||||||
\(177\) | 1.54411 | 0.116062 | ||||||||
\(178\) | 9.67029 | 0.724819 | ||||||||
\(179\) | 16.4101 | 1.22655 | 0.613276 | − | 0.789869i | \(-0.289851\pi\) | ||||
0.613276 | + | 0.789869i | \(0.289851\pi\) | |||||||
\(180\) | −2.25507 | −0.168083 | ||||||||
\(181\) | 16.1897 | 1.20337 | 0.601686 | − | 0.798732i | \(-0.294496\pi\) | ||||
0.601686 | + | 0.798732i | \(0.294496\pi\) | |||||||
\(182\) | 5.17813 | 0.383829 | ||||||||
\(183\) | 1.54483 | 0.114197 | ||||||||
\(184\) | −5.18712 | −0.382400 | ||||||||
\(185\) | −4.90132 | −0.360352 | ||||||||
\(186\) | −17.2043 | −1.26148 | ||||||||
\(187\) | 0.202395 | 0.0148006 | ||||||||
\(188\) | −6.40829 | −0.467372 | ||||||||
\(189\) | −6.96491 | −0.506622 | ||||||||
\(190\) | 6.50079 | 0.471617 | ||||||||
\(191\) | −24.9052 | −1.80208 | −0.901039 | − | 0.433738i | \(-0.857194\pi\) | ||||
−0.901039 | + | 0.433738i | \(0.857194\pi\) | |||||||
\(192\) | −2.17233 | −0.156774 | ||||||||
\(193\) | −16.9546 | −1.22042 | −0.610208 | − | 0.792241i | \(-0.708914\pi\) | ||||
−0.610208 | + | 0.792241i | \(0.708914\pi\) | |||||||
\(194\) | −13.5076 | −0.969791 | ||||||||
\(195\) | 5.89572 | 0.422201 | ||||||||
\(196\) | −0.735476 | −0.0525340 | ||||||||
\(197\) | 19.7851 | 1.40963 | 0.704815 | − | 0.709391i | \(-0.251030\pi\) | ||||
0.704815 | + | 0.709391i | \(0.251030\pi\) | |||||||
\(198\) | 0.172872 | 0.0122855 | ||||||||
\(199\) | −10.1142 | −0.716979 | −0.358490 | − | 0.933534i | \(-0.616708\pi\) | ||||
−0.358490 | + | 0.933534i | \(0.616708\pi\) | |||||||
\(200\) | 3.27907 | 0.231865 | ||||||||
\(201\) | −4.49890 | −0.317328 | ||||||||
\(202\) | 8.75991 | 0.616345 | ||||||||
\(203\) | −24.9550 | −1.75150 | ||||||||
\(204\) | 4.37198 | 0.306100 | ||||||||
\(205\) | −4.58357 | −0.320131 | ||||||||
\(206\) | −10.1373 | −0.706302 | ||||||||
\(207\) | 8.91671 | 0.619754 | ||||||||
\(208\) | 2.06885 | 0.143449 | ||||||||
\(209\) | −0.498346 | −0.0344713 | ||||||||
\(210\) | 7.13266 | 0.492200 | ||||||||
\(211\) | −25.2032 | −1.73506 | −0.867532 | − | 0.497382i | \(-0.834295\pi\) | ||||
−0.867532 | + | 0.497382i | \(0.834295\pi\) | |||||||
\(212\) | −2.04402 | −0.140384 | ||||||||
\(213\) | 27.2124 | 1.86456 | ||||||||
\(214\) | −9.92879 | −0.678718 | ||||||||
\(215\) | −9.42537 | −0.642805 | ||||||||
\(216\) | −2.78273 | −0.189341 | ||||||||
\(217\) | 19.8224 | 1.34563 | ||||||||
\(218\) | 16.1257 | 1.09217 | ||||||||
\(219\) | 8.87180 | 0.599501 | ||||||||
\(220\) | 0.131926 | 0.00889443 | ||||||||
\(221\) | −4.16373 | −0.280083 | ||||||||
\(222\) | 8.11627 | 0.544728 | ||||||||
\(223\) | 14.7802 | 0.989757 | 0.494879 | − | 0.868962i | \(-0.335213\pi\) | ||||
0.494879 | + | 0.868962i | \(0.335213\pi\) | |||||||
\(224\) | 2.50290 | 0.167232 | ||||||||
\(225\) | −5.63675 | −0.375783 | ||||||||
\(226\) | 11.7020 | 0.778405 | ||||||||
\(227\) | −10.1598 | −0.674330 | −0.337165 | − | 0.941446i | \(-0.609468\pi\) | ||||
−0.337165 | + | 0.941446i | \(0.609468\pi\) | |||||||
\(228\) | −10.7649 | −0.712922 | ||||||||
\(229\) | 19.5203 | 1.28994 | 0.644970 | − | 0.764208i | \(-0.276870\pi\) | ||||
0.644970 | + | 0.764208i | \(0.276870\pi\) | |||||||
\(230\) | 6.80469 | 0.448688 | ||||||||
\(231\) | −0.546785 | −0.0359758 | ||||||||
\(232\) | −9.97044 | −0.654592 | ||||||||
\(233\) | −9.34433 | −0.612168 | −0.306084 | − | 0.952005i | \(-0.599019\pi\) | ||||
−0.306084 | + | 0.952005i | \(0.599019\pi\) | |||||||
\(234\) | −3.55638 | −0.232488 | ||||||||
\(235\) | 8.40667 | 0.548391 | ||||||||
\(236\) | −0.710808 | −0.0462697 | ||||||||
\(237\) | −5.91658 | −0.384323 | ||||||||
\(238\) | −5.03729 | −0.326519 | ||||||||
\(239\) | 20.5513 | 1.32935 | 0.664676 | − | 0.747132i | \(-0.268570\pi\) | ||||
0.664676 | + | 0.747132i | \(0.268570\pi\) | |||||||
\(240\) | 2.84976 | 0.183951 | ||||||||
\(241\) | 6.41466 | 0.413204 | 0.206602 | − | 0.978425i | \(-0.433759\pi\) | ||||
0.206602 | + | 0.978425i | \(0.433759\pi\) | |||||||
\(242\) | 10.9899 | 0.706457 | ||||||||
\(243\) | 15.9863 | 1.02552 | ||||||||
\(244\) | −0.711142 | −0.0455262 | ||||||||
\(245\) | 0.964830 | 0.0616407 | ||||||||
\(246\) | 7.59010 | 0.483927 | ||||||||
\(247\) | 10.2521 | 0.652326 | ||||||||
\(248\) | 7.91975 | 0.502905 | ||||||||
\(249\) | −15.4813 | −0.981090 | ||||||||
\(250\) | −10.8608 | −0.686900 | ||||||||
\(251\) | 10.7601 | 0.679170 | 0.339585 | − | 0.940575i | \(-0.389713\pi\) | ||||
0.339585 | + | 0.940575i | \(0.389713\pi\) | |||||||
\(252\) | −4.30252 | −0.271033 | ||||||||
\(253\) | −0.521643 | −0.0327954 | ||||||||
\(254\) | 4.84397 | 0.303938 | ||||||||
\(255\) | −5.73536 | −0.359162 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.29400 | 0.0807178 | 0.0403589 | − | 0.999185i | \(-0.487150\pi\) | ||||
0.0403589 | + | 0.999185i | \(0.487150\pi\) | |||||||
\(258\) | 15.6078 | 0.971699 | ||||||||
\(259\) | −9.35137 | −0.581066 | ||||||||
\(260\) | −2.71401 | −0.168316 | ||||||||
\(261\) | 17.1393 | 1.06090 | ||||||||
\(262\) | −5.91413 | −0.365376 | ||||||||
\(263\) | −7.04882 | −0.434649 | −0.217324 | − | 0.976099i | \(-0.569733\pi\) | ||||
−0.217324 | + | 0.976099i | \(0.569733\pi\) | |||||||
\(264\) | −0.218460 | −0.0134453 | ||||||||
\(265\) | 2.68143 | 0.164719 | ||||||||
\(266\) | 12.4030 | 0.760479 | ||||||||
\(267\) | 21.0070 | 1.28561 | ||||||||
\(268\) | 2.07100 | 0.126507 | ||||||||
\(269\) | 26.9814 | 1.64509 | 0.822543 | − | 0.568702i | \(-0.192554\pi\) | ||||
0.822543 | + | 0.568702i | \(0.192554\pi\) | |||||||
\(270\) | 3.65051 | 0.222163 | ||||||||
\(271\) | −1.38607 | −0.0841978 | −0.0420989 | − | 0.999113i | \(-0.513404\pi\) | ||||
−0.0420989 | + | 0.999113i | \(0.513404\pi\) | |||||||
\(272\) | −2.01258 | −0.122031 | ||||||||
\(273\) | 11.2486 | 0.680797 | ||||||||
\(274\) | −13.2312 | −0.799324 | ||||||||
\(275\) | 0.329759 | 0.0198852 | ||||||||
\(276\) | −11.2681 | −0.678262 | ||||||||
\(277\) | −11.3658 | −0.682905 | −0.341453 | − | 0.939899i | \(-0.610919\pi\) | ||||
−0.341453 | + | 0.939899i | \(0.610919\pi\) | |||||||
\(278\) | 5.31410 | 0.318719 | ||||||||
\(279\) | −13.6141 | −0.815057 | ||||||||
\(280\) | −3.28342 | −0.196222 | ||||||||
\(281\) | 9.12180 | 0.544161 | 0.272080 | − | 0.962275i | \(-0.412288\pi\) | ||||
0.272080 | + | 0.962275i | \(0.412288\pi\) | |||||||
\(282\) | −13.9209 | −0.828978 | ||||||||
\(283\) | 1.86684 | 0.110972 | 0.0554860 | − | 0.998459i | \(-0.482329\pi\) | ||||
0.0554860 | + | 0.998459i | \(0.482329\pi\) | |||||||
\(284\) | −12.5268 | −0.743331 | ||||||||
\(285\) | 14.1219 | 0.836506 | ||||||||
\(286\) | 0.208054 | 0.0123025 | ||||||||
\(287\) | −8.74513 | −0.516208 | ||||||||
\(288\) | −1.71901 | −0.101294 | ||||||||
\(289\) | −12.9495 | −0.761737 | ||||||||
\(290\) | 13.0797 | 0.768064 | ||||||||
\(291\) | −29.3430 | −1.72012 | ||||||||
\(292\) | −4.08400 | −0.238998 | ||||||||
\(293\) | 5.28826 | 0.308943 | 0.154472 | − | 0.987997i | \(-0.450632\pi\) | ||||
0.154472 | + | 0.987997i | \(0.450632\pi\) | |||||||
\(294\) | −1.59770 | −0.0931795 | ||||||||
\(295\) | 0.932469 | 0.0542905 | ||||||||
\(296\) | −3.73621 | −0.217163 | ||||||||
\(297\) | −0.279845 | −0.0162383 | ||||||||
\(298\) | 4.04539 | 0.234343 | ||||||||
\(299\) | 10.7314 | 0.620612 | ||||||||
\(300\) | 7.12321 | 0.411259 | ||||||||
\(301\) | −17.9829 | −1.03652 | ||||||||
\(302\) | −3.91908 | −0.225518 | ||||||||
\(303\) | 19.0294 | 1.09321 | ||||||||
\(304\) | 4.95546 | 0.284215 | ||||||||
\(305\) | 0.932907 | 0.0534181 | ||||||||
\(306\) | 3.45964 | 0.197775 | ||||||||
\(307\) | 27.5283 | 1.57113 | 0.785563 | − | 0.618782i | \(-0.212373\pi\) | ||||
0.785563 | + | 0.618782i | \(0.212373\pi\) | |||||||
\(308\) | 0.251705 | 0.0143422 | ||||||||
\(309\) | −22.0216 | −1.25277 | ||||||||
\(310\) | −10.3895 | −0.590083 | ||||||||
\(311\) | 3.05641 | 0.173313 | 0.0866566 | − | 0.996238i | \(-0.472382\pi\) | ||||
0.0866566 | + | 0.996238i | \(0.472382\pi\) | |||||||
\(312\) | 4.49422 | 0.254435 | ||||||||
\(313\) | −21.5109 | −1.21587 | −0.607933 | − | 0.793988i | \(-0.708001\pi\) | ||||
−0.607933 | + | 0.793988i | \(0.708001\pi\) | |||||||
\(314\) | −1.29450 | −0.0730526 | ||||||||
\(315\) | 5.64423 | 0.318016 | ||||||||
\(316\) | 2.72361 | 0.153215 | ||||||||
\(317\) | −5.45734 | −0.306515 | −0.153257 | − | 0.988186i | \(-0.548976\pi\) | ||||
−0.153257 | + | 0.988186i | \(0.548976\pi\) | |||||||
\(318\) | −4.44028 | −0.248999 | ||||||||
\(319\) | −1.00268 | −0.0561392 | ||||||||
\(320\) | −1.31184 | −0.0733343 | ||||||||
\(321\) | −21.5686 | −1.20384 | ||||||||
\(322\) | 12.9829 | 0.723506 | ||||||||
\(323\) | −9.97326 | −0.554927 | ||||||||
\(324\) | −11.2020 | −0.622335 | ||||||||
\(325\) | −6.78390 | −0.376303 | ||||||||
\(326\) | 5.00829 | 0.277384 | ||||||||
\(327\) | 35.0302 | 1.93718 | ||||||||
\(328\) | −3.49399 | −0.192923 | ||||||||
\(329\) | 16.0393 | 0.884276 | ||||||||
\(330\) | 0.286586 | 0.0157760 | ||||||||
\(331\) | −10.4352 | −0.573569 | −0.286785 | − | 0.957995i | \(-0.592586\pi\) | ||||
−0.286785 | + | 0.957995i | \(0.592586\pi\) | |||||||
\(332\) | 7.12661 | 0.391124 | ||||||||
\(333\) | 6.42258 | 0.351955 | ||||||||
\(334\) | −14.5968 | −0.798699 | ||||||||
\(335\) | −2.71683 | −0.148437 | ||||||||
\(336\) | 5.43713 | 0.296620 | ||||||||
\(337\) | 28.2649 | 1.53969 | 0.769844 | − | 0.638233i | \(-0.220334\pi\) | ||||
0.769844 | + | 0.638233i | \(0.220334\pi\) | |||||||
\(338\) | 8.71986 | 0.474298 | ||||||||
\(339\) | 25.4206 | 1.38066 | ||||||||
\(340\) | 2.64019 | 0.143184 | ||||||||
\(341\) | 0.796450 | 0.0431302 | ||||||||
\(342\) | −8.51849 | −0.460627 | ||||||||
\(343\) | 19.3611 | 1.04540 | ||||||||
\(344\) | −7.18482 | −0.387380 | ||||||||
\(345\) | 14.7820 | 0.795837 | ||||||||
\(346\) | 18.7254 | 1.00668 | ||||||||
\(347\) | 4.29931 | 0.230799 | 0.115400 | − | 0.993319i | \(-0.463185\pi\) | ||||
0.115400 | + | 0.993319i | \(0.463185\pi\) | |||||||
\(348\) | −21.6591 | −1.16105 | ||||||||
\(349\) | −15.7538 | −0.843283 | −0.421642 | − | 0.906763i | \(-0.638546\pi\) | ||||
−0.421642 | + | 0.906763i | \(0.638546\pi\) | |||||||
\(350\) | −8.20718 | −0.438692 | ||||||||
\(351\) | 5.75706 | 0.307289 | ||||||||
\(352\) | 0.100565 | 0.00536014 | ||||||||
\(353\) | −32.0369 | −1.70515 | −0.852577 | − | 0.522602i | \(-0.824961\pi\) | ||||
−0.852577 | + | 0.522602i | \(0.824961\pi\) | |||||||
\(354\) | −1.54411 | −0.0820685 | ||||||||
\(355\) | 16.4333 | 0.872187 | ||||||||
\(356\) | −9.67029 | −0.512524 | ||||||||
\(357\) | −10.9426 | −0.579146 | ||||||||
\(358\) | −16.4101 | −0.867303 | ||||||||
\(359\) | −25.5931 | −1.35075 | −0.675377 | − | 0.737472i | \(-0.736019\pi\) | ||||
−0.675377 | + | 0.737472i | \(0.736019\pi\) | |||||||
\(360\) | 2.25507 | 0.118853 | ||||||||
\(361\) | 5.55659 | 0.292452 | ||||||||
\(362\) | −16.1897 | −0.850913 | ||||||||
\(363\) | 23.8736 | 1.25304 | ||||||||
\(364\) | −5.17813 | −0.271408 | ||||||||
\(365\) | 5.35758 | 0.280428 | ||||||||
\(366\) | −1.54483 | −0.0807497 | ||||||||
\(367\) | −26.2220 | −1.36878 | −0.684390 | − | 0.729116i | \(-0.739931\pi\) | ||||
−0.684390 | + | 0.729116i | \(0.739931\pi\) | |||||||
\(368\) | 5.18712 | 0.270397 | ||||||||
\(369\) | 6.00621 | 0.312671 | ||||||||
\(370\) | 4.90132 | 0.254808 | ||||||||
\(371\) | 5.11598 | 0.265609 | ||||||||
\(372\) | 17.2043 | 0.892002 | ||||||||
\(373\) | 36.7040 | 1.90046 | 0.950231 | − | 0.311546i | \(-0.100847\pi\) | ||||
0.950231 | + | 0.311546i | \(0.100847\pi\) | |||||||
\(374\) | −0.202395 | −0.0104656 | ||||||||
\(375\) | −23.5933 | −1.21835 | ||||||||
\(376\) | 6.40829 | 0.330482 | ||||||||
\(377\) | 20.6274 | 1.06236 | ||||||||
\(378\) | 6.96491 | 0.358236 | ||||||||
\(379\) | −29.0002 | −1.48964 | −0.744821 | − | 0.667265i | \(-0.767465\pi\) | ||||
−0.744821 | + | 0.667265i | \(0.767465\pi\) | |||||||
\(380\) | −6.50079 | −0.333484 | ||||||||
\(381\) | 10.5227 | 0.539094 | ||||||||
\(382\) | 24.9052 | 1.27426 | ||||||||
\(383\) | 25.2690 | 1.29118 | 0.645592 | − | 0.763683i | \(-0.276611\pi\) | ||||
0.645592 | + | 0.763683i | \(0.276611\pi\) | |||||||
\(384\) | 2.17233 | 0.110856 | ||||||||
\(385\) | −0.330197 | −0.0168284 | ||||||||
\(386\) | 16.9546 | 0.862964 | ||||||||
\(387\) | 12.3508 | 0.627826 | ||||||||
\(388\) | 13.5076 | 0.685746 | ||||||||
\(389\) | −6.33010 | −0.320949 | −0.160474 | − | 0.987040i | \(-0.551302\pi\) | ||||
−0.160474 | + | 0.987040i | \(0.551302\pi\) | |||||||
\(390\) | −5.89572 | −0.298541 | ||||||||
\(391\) | −10.4395 | −0.527948 | ||||||||
\(392\) | 0.735476 | 0.0371471 | ||||||||
\(393\) | −12.8474 | −0.648067 | ||||||||
\(394\) | −19.7851 | −0.996759 | ||||||||
\(395\) | −3.57296 | −0.179775 | ||||||||
\(396\) | −0.172872 | −0.00868716 | ||||||||
\(397\) | −13.9127 | −0.698256 | −0.349128 | − | 0.937075i | \(-0.613522\pi\) | ||||
−0.349128 | + | 0.937075i | \(0.613522\pi\) | |||||||
\(398\) | 10.1142 | 0.506981 | ||||||||
\(399\) | 26.9435 | 1.34886 | ||||||||
\(400\) | −3.27907 | −0.163953 | ||||||||
\(401\) | −32.7694 | −1.63642 | −0.818212 | − | 0.574916i | \(-0.805035\pi\) | ||||
−0.818212 | + | 0.574916i | \(0.805035\pi\) | |||||||
\(402\) | 4.49890 | 0.224385 | ||||||||
\(403\) | −16.3848 | −0.816184 | ||||||||
\(404\) | −8.75991 | −0.435822 | ||||||||
\(405\) | 14.6953 | 0.730216 | ||||||||
\(406\) | 24.9550 | 1.23850 | ||||||||
\(407\) | −0.375732 | −0.0186243 | ||||||||
\(408\) | −4.37198 | −0.216445 | ||||||||
\(409\) | −30.9075 | −1.52828 | −0.764138 | − | 0.645053i | \(-0.776835\pi\) | ||||
−0.764138 | + | 0.645053i | \(0.776835\pi\) | |||||||
\(410\) | 4.58357 | 0.226367 | ||||||||
\(411\) | −28.7424 | −1.41776 | ||||||||
\(412\) | 10.1373 | 0.499431 | ||||||||
\(413\) | 1.77908 | 0.0875430 | ||||||||
\(414\) | −8.91671 | −0.438232 | ||||||||
\(415\) | −9.34900 | −0.458924 | ||||||||
\(416\) | −2.06885 | −0.101434 | ||||||||
\(417\) | 11.5440 | 0.565311 | ||||||||
\(418\) | 0.498346 | 0.0243749 | ||||||||
\(419\) | 34.5512 | 1.68794 | 0.843968 | − | 0.536394i | \(-0.180214\pi\) | ||||
0.843968 | + | 0.536394i | \(0.180214\pi\) | |||||||
\(420\) | −7.13266 | −0.348038 | ||||||||
\(421\) | 10.0270 | 0.488687 | 0.244344 | − | 0.969689i | \(-0.421428\pi\) | ||||
0.244344 | + | 0.969689i | \(0.421428\pi\) | |||||||
\(422\) | 25.2032 | 1.22687 | ||||||||
\(423\) | −11.0159 | −0.535612 | ||||||||
\(424\) | 2.04402 | 0.0992663 | ||||||||
\(425\) | 6.59938 | 0.320117 | ||||||||
\(426\) | −27.2124 | −1.31845 | ||||||||
\(427\) | 1.77992 | 0.0861363 | ||||||||
\(428\) | 9.92879 | 0.479926 | ||||||||
\(429\) | 0.451962 | 0.0218209 | ||||||||
\(430\) | 9.42537 | 0.454532 | ||||||||
\(431\) | 12.7690 | 0.615062 | 0.307531 | − | 0.951538i | \(-0.400497\pi\) | ||||
0.307531 | + | 0.951538i | \(0.400497\pi\) | |||||||
\(432\) | 2.78273 | 0.133884 | ||||||||
\(433\) | 7.62871 | 0.366612 | 0.183306 | − | 0.983056i | \(-0.441320\pi\) | ||||
0.183306 | + | 0.983056i | \(0.441320\pi\) | |||||||
\(434\) | −19.8224 | −0.951504 | ||||||||
\(435\) | 28.4133 | 1.36231 | ||||||||
\(436\) | −16.1257 | −0.772279 | ||||||||
\(437\) | 25.7046 | 1.22962 | ||||||||
\(438\) | −8.87180 | −0.423911 | ||||||||
\(439\) | −0.892723 | −0.0426073 | −0.0213037 | − | 0.999773i | \(-0.506782\pi\) | ||||
−0.0213037 | + | 0.999773i | \(0.506782\pi\) | |||||||
\(440\) | −0.131926 | −0.00628931 | ||||||||
\(441\) | −1.26429 | −0.0602043 | ||||||||
\(442\) | 4.16373 | 0.198048 | ||||||||
\(443\) | 25.6792 | 1.22005 | 0.610027 | − | 0.792380i | \(-0.291158\pi\) | ||||
0.610027 | + | 0.792380i | \(0.291158\pi\) | |||||||
\(444\) | −8.11627 | −0.385181 | ||||||||
\(445\) | 12.6859 | 0.601370 | ||||||||
\(446\) | −14.7802 | −0.699864 | ||||||||
\(447\) | 8.78791 | 0.415654 | ||||||||
\(448\) | −2.50290 | −0.118251 | ||||||||
\(449\) | 26.4059 | 1.24617 | 0.623087 | − | 0.782153i | \(-0.285878\pi\) | ||||
0.623087 | + | 0.782153i | \(0.285878\pi\) | |||||||
\(450\) | 5.63675 | 0.265719 | ||||||||
\(451\) | −0.351374 | −0.0165455 | ||||||||
\(452\) | −11.7020 | −0.550416 | ||||||||
\(453\) | −8.51354 | −0.400001 | ||||||||
\(454\) | 10.1598 | 0.476823 | ||||||||
\(455\) | 6.79290 | 0.318456 | ||||||||
\(456\) | 10.7649 | 0.504112 | ||||||||
\(457\) | −16.0306 | −0.749880 | −0.374940 | − | 0.927049i | \(-0.622337\pi\) | ||||
−0.374940 | + | 0.927049i | \(0.622337\pi\) | |||||||
\(458\) | −19.5203 | −0.912126 | ||||||||
\(459\) | −5.60047 | −0.261407 | ||||||||
\(460\) | −6.80469 | −0.317270 | ||||||||
\(461\) | 19.3403 | 0.900767 | 0.450383 | − | 0.892835i | \(-0.351287\pi\) | ||||
0.450383 | + | 0.892835i | \(0.351287\pi\) | |||||||
\(462\) | 0.546785 | 0.0254387 | ||||||||
\(463\) | 2.26727 | 0.105369 | 0.0526844 | − | 0.998611i | \(-0.483222\pi\) | ||||
0.0526844 | + | 0.998611i | \(0.483222\pi\) | |||||||
\(464\) | 9.97044 | 0.462866 | ||||||||
\(465\) | −22.5694 | −1.04663 | ||||||||
\(466\) | 9.34433 | 0.432868 | ||||||||
\(467\) | 24.3815 | 1.12824 | 0.564121 | − | 0.825692i | \(-0.309215\pi\) | ||||
0.564121 | + | 0.825692i | \(0.309215\pi\) | |||||||
\(468\) | 3.55638 | 0.164394 | ||||||||
\(469\) | −5.18352 | −0.239353 | ||||||||
\(470\) | −8.40667 | −0.387771 | ||||||||
\(471\) | −2.81207 | −0.129573 | ||||||||
\(472\) | 0.710808 | 0.0327176 | ||||||||
\(473\) | −0.722542 | −0.0332225 | ||||||||
\(474\) | 5.91658 | 0.271758 | ||||||||
\(475\) | −16.2493 | −0.745568 | ||||||||
\(476\) | 5.03729 | 0.230884 | ||||||||
\(477\) | −3.51369 | −0.160881 | ||||||||
\(478\) | −20.5513 | −0.939994 | ||||||||
\(479\) | 23.3231 | 1.06566 | 0.532831 | − | 0.846222i | \(-0.321128\pi\) | ||||
0.532831 | + | 0.846222i | \(0.321128\pi\) | |||||||
\(480\) | −2.84976 | −0.130073 | ||||||||
\(481\) | 7.72966 | 0.352442 | ||||||||
\(482\) | −6.41466 | −0.292180 | ||||||||
\(483\) | 28.2030 | 1.28328 | ||||||||
\(484\) | −10.9899 | −0.499540 | ||||||||
\(485\) | −17.7199 | −0.804619 | ||||||||
\(486\) | −15.9863 | −0.725153 | ||||||||
\(487\) | 11.4534 | 0.519005 | 0.259503 | − | 0.965742i | \(-0.416441\pi\) | ||||
0.259503 | + | 0.965742i | \(0.416441\pi\) | |||||||
\(488\) | 0.711142 | 0.0321919 | ||||||||
\(489\) | 10.8797 | 0.491995 | ||||||||
\(490\) | −0.964830 | −0.0435866 | ||||||||
\(491\) | −18.5596 | −0.837581 | −0.418790 | − | 0.908083i | \(-0.637546\pi\) | ||||
−0.418790 | + | 0.908083i | \(0.637546\pi\) | |||||||
\(492\) | −7.59010 | −0.342188 | ||||||||
\(493\) | −20.0663 | −0.903741 | ||||||||
\(494\) | −10.2521 | −0.461264 | ||||||||
\(495\) | 0.226782 | 0.0101931 | ||||||||
\(496\) | −7.91975 | −0.355607 | ||||||||
\(497\) | 31.3535 | 1.40640 | ||||||||
\(498\) | 15.4813 | 0.693735 | ||||||||
\(499\) | 14.5750 | 0.652464 | 0.326232 | − | 0.945290i | \(-0.394221\pi\) | ||||
0.326232 | + | 0.945290i | \(0.394221\pi\) | |||||||
\(500\) | 10.8608 | 0.485712 | ||||||||
\(501\) | −31.7089 | −1.41665 | ||||||||
\(502\) | −10.7601 | −0.480246 | ||||||||
\(503\) | 35.3826 | 1.57763 | 0.788816 | − | 0.614629i | \(-0.210694\pi\) | ||||
0.788816 | + | 0.614629i | \(0.210694\pi\) | |||||||
\(504\) | 4.30252 | 0.191649 | ||||||||
\(505\) | 11.4916 | 0.511371 | ||||||||
\(506\) | 0.521643 | 0.0231899 | ||||||||
\(507\) | 18.9424 | 0.841261 | ||||||||
\(508\) | −4.84397 | −0.214917 | ||||||||
\(509\) | 18.7107 | 0.829337 | 0.414669 | − | 0.909972i | \(-0.363897\pi\) | ||||
0.414669 | + | 0.909972i | \(0.363897\pi\) | |||||||
\(510\) | 5.73536 | 0.253966 | ||||||||
\(511\) | 10.2219 | 0.452189 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 13.7897 | 0.608831 | ||||||||
\(514\) | −1.29400 | −0.0570761 | ||||||||
\(515\) | −13.2986 | −0.586007 | ||||||||
\(516\) | −15.6078 | −0.687095 | ||||||||
\(517\) | 0.644450 | 0.0283429 | ||||||||
\(518\) | 9.35137 | 0.410875 | ||||||||
\(519\) | 40.6777 | 1.78555 | ||||||||
\(520\) | 2.71401 | 0.119017 | ||||||||
\(521\) | −1.20896 | −0.0529655 | −0.0264827 | − | 0.999649i | \(-0.508431\pi\) | ||||
−0.0264827 | + | 0.999649i | \(0.508431\pi\) | |||||||
\(522\) | −17.1393 | −0.750166 | ||||||||
\(523\) | 13.4025 | 0.586052 | 0.293026 | − | 0.956104i | \(-0.405338\pi\) | ||||
0.293026 | + | 0.956104i | \(0.405338\pi\) | |||||||
\(524\) | 5.91413 | 0.258360 | ||||||||
\(525\) | −17.8287 | −0.778108 | ||||||||
\(526\) | 7.04882 | 0.307343 | ||||||||
\(527\) | 15.9391 | 0.694319 | ||||||||
\(528\) | 0.218460 | 0.00950726 | ||||||||
\(529\) | 3.90621 | 0.169835 | ||||||||
\(530\) | −2.68143 | −0.116474 | ||||||||
\(531\) | −1.22189 | −0.0530254 | ||||||||
\(532\) | −12.4030 | −0.537740 | ||||||||
\(533\) | 7.22855 | 0.313103 | ||||||||
\(534\) | −21.0070 | −0.909064 | ||||||||
\(535\) | −13.0250 | −0.563121 | ||||||||
\(536\) | −2.07100 | −0.0894538 | ||||||||
\(537\) | −35.6482 | −1.53833 | ||||||||
\(538\) | −26.9814 | −1.16325 | ||||||||
\(539\) | 0.0739632 | 0.00318582 | ||||||||
\(540\) | −3.65051 | −0.157093 | ||||||||
\(541\) | −41.9329 | −1.80284 | −0.901418 | − | 0.432950i | \(-0.857472\pi\) | ||||
−0.901418 | + | 0.432950i | \(0.857472\pi\) | |||||||
\(542\) | 1.38607 | 0.0595369 | ||||||||
\(543\) | −35.1694 | −1.50926 | ||||||||
\(544\) | 2.01258 | 0.0862886 | ||||||||
\(545\) | 21.1543 | 0.906153 | ||||||||
\(546\) | −11.2486 | −0.481396 | ||||||||
\(547\) | −31.9661 | −1.36677 | −0.683385 | − | 0.730058i | \(-0.739493\pi\) | ||||
−0.683385 | + | 0.730058i | \(0.739493\pi\) | |||||||
\(548\) | 13.2312 | 0.565207 | ||||||||
\(549\) | −1.22246 | −0.0521733 | ||||||||
\(550\) | −0.329759 | −0.0140610 | ||||||||
\(551\) | 49.4081 | 2.10486 | ||||||||
\(552\) | 11.2681 | 0.479603 | ||||||||
\(553\) | −6.81694 | −0.289886 | ||||||||
\(554\) | 11.3658 | 0.482887 | ||||||||
\(555\) | 10.6473 | 0.451952 | ||||||||
\(556\) | −5.31410 | −0.225368 | ||||||||
\(557\) | 43.1997 | 1.83043 | 0.915215 | − | 0.402967i | \(-0.132021\pi\) | ||||
0.915215 | + | 0.402967i | \(0.132021\pi\) | |||||||
\(558\) | 13.6141 | 0.576332 | ||||||||
\(559\) | 14.8643 | 0.628694 | ||||||||
\(560\) | 3.28342 | 0.138750 | ||||||||
\(561\) | −0.439669 | −0.0185628 | ||||||||
\(562\) | −9.12180 | −0.384780 | ||||||||
\(563\) | −13.9123 | −0.586332 | −0.293166 | − | 0.956062i | \(-0.594709\pi\) | ||||
−0.293166 | + | 0.956062i | \(0.594709\pi\) | |||||||
\(564\) | 13.9209 | 0.586176 | ||||||||
\(565\) | 15.3512 | 0.645830 | ||||||||
\(566\) | −1.86684 | −0.0784690 | ||||||||
\(567\) | 28.0376 | 1.17747 | ||||||||
\(568\) | 12.5268 | 0.525614 | ||||||||
\(569\) | −11.1738 | −0.468430 | −0.234215 | − | 0.972185i | \(-0.575252\pi\) | ||||
−0.234215 | + | 0.972185i | \(0.575252\pi\) | |||||||
\(570\) | −14.1219 | −0.591499 | ||||||||
\(571\) | −14.9473 | −0.625523 | −0.312762 | − | 0.949832i | \(-0.601254\pi\) | ||||
−0.312762 | + | 0.949832i | \(0.601254\pi\) | |||||||
\(572\) | −0.208054 | −0.00869918 | ||||||||
\(573\) | 54.1023 | 2.26016 | ||||||||
\(574\) | 8.74513 | 0.365015 | ||||||||
\(575\) | −17.0089 | −0.709320 | ||||||||
\(576\) | 1.71901 | 0.0716254 | ||||||||
\(577\) | 27.2187 | 1.13313 | 0.566566 | − | 0.824017i | \(-0.308272\pi\) | ||||
0.566566 | + | 0.824017i | \(0.308272\pi\) | |||||||
\(578\) | 12.9495 | 0.538629 | ||||||||
\(579\) | 36.8309 | 1.53064 | ||||||||
\(580\) | −13.0797 | −0.543103 | ||||||||
\(581\) | −17.8372 | −0.740012 | ||||||||
\(582\) | 29.3430 | 1.21631 | ||||||||
\(583\) | 0.205557 | 0.00851330 | ||||||||
\(584\) | 4.08400 | 0.168997 | ||||||||
\(585\) | −4.66541 | −0.192891 | ||||||||
\(586\) | −5.28826 | −0.218456 | ||||||||
\(587\) | −10.4117 | −0.429737 | −0.214869 | − | 0.976643i | \(-0.568932\pi\) | ||||
−0.214869 | + | 0.976643i | \(0.568932\pi\) | |||||||
\(588\) | 1.59770 | 0.0658878 | ||||||||
\(589\) | −39.2460 | −1.61710 | ||||||||
\(590\) | −0.932469 | −0.0383892 | ||||||||
\(591\) | −42.9797 | −1.76795 | ||||||||
\(592\) | 3.73621 | 0.153557 | ||||||||
\(593\) | −30.0513 | −1.23406 | −0.617030 | − | 0.786940i | \(-0.711664\pi\) | ||||
−0.617030 | + | 0.786940i | \(0.711664\pi\) | |||||||
\(594\) | 0.279845 | 0.0114822 | ||||||||
\(595\) | −6.60814 | −0.270907 | ||||||||
\(596\) | −4.04539 | −0.165706 | ||||||||
\(597\) | 21.9714 | 0.899231 | ||||||||
\(598\) | −10.7314 | −0.438839 | ||||||||
\(599\) | 12.5523 | 0.512873 | 0.256436 | − | 0.966561i | \(-0.417452\pi\) | ||||
0.256436 | + | 0.966561i | \(0.417452\pi\) | |||||||
\(600\) | −7.12321 | −0.290804 | ||||||||
\(601\) | −31.2086 | −1.27303 | −0.636513 | − | 0.771266i | \(-0.719624\pi\) | ||||
−0.636513 | + | 0.771266i | \(0.719624\pi\) | |||||||
\(602\) | 17.9829 | 0.732929 | ||||||||
\(603\) | 3.56008 | 0.144978 | ||||||||
\(604\) | 3.91908 | 0.159465 | ||||||||
\(605\) | 14.4170 | 0.586135 | ||||||||
\(606\) | −19.0294 | −0.773017 | ||||||||
\(607\) | −24.8789 | −1.00980 | −0.504901 | − | 0.863177i | \(-0.668471\pi\) | ||||
−0.504901 | + | 0.863177i | \(0.668471\pi\) | |||||||
\(608\) | −4.95546 | −0.200970 | ||||||||
\(609\) | 54.2106 | 2.19672 | ||||||||
\(610\) | −0.932907 | −0.0377723 | ||||||||
\(611\) | −13.2578 | −0.536353 | ||||||||
\(612\) | −3.45964 | −0.139848 | ||||||||
\(613\) | 30.6685 | 1.23869 | 0.619345 | − | 0.785119i | \(-0.287398\pi\) | ||||
0.619345 | + | 0.785119i | \(0.287398\pi\) | |||||||
\(614\) | −27.5283 | −1.11095 | ||||||||
\(615\) | 9.95703 | 0.401506 | ||||||||
\(616\) | −0.251705 | −0.0101415 | ||||||||
\(617\) | 30.5353 | 1.22930 | 0.614651 | − | 0.788799i | \(-0.289297\pi\) | ||||
0.614651 | + | 0.788799i | \(0.289297\pi\) | |||||||
\(618\) | 22.0216 | 0.885840 | ||||||||
\(619\) | 44.7812 | 1.79991 | 0.899954 | − | 0.435986i | \(-0.143600\pi\) | ||||
0.899954 | + | 0.435986i | \(0.143600\pi\) | |||||||
\(620\) | 10.3895 | 0.417252 | ||||||||
\(621\) | 14.4344 | 0.579231 | ||||||||
\(622\) | −3.05641 | −0.122551 | ||||||||
\(623\) | 24.2038 | 0.969705 | ||||||||
\(624\) | −4.49422 | −0.179913 | ||||||||
\(625\) | 2.14760 | 0.0859039 | ||||||||
\(626\) | 21.5109 | 0.859747 | ||||||||
\(627\) | 1.08257 | 0.0432337 | ||||||||
\(628\) | 1.29450 | 0.0516560 | ||||||||
\(629\) | −7.51941 | −0.299819 | ||||||||
\(630\) | −5.64423 | −0.224871 | ||||||||
\(631\) | −30.4326 | −1.21150 | −0.605752 | − | 0.795653i | \(-0.707128\pi\) | ||||
−0.605752 | + | 0.795653i | \(0.707128\pi\) | |||||||
\(632\) | −2.72361 | −0.108340 | ||||||||
\(633\) | 54.7497 | 2.17611 | ||||||||
\(634\) | 5.45734 | 0.216739 | ||||||||
\(635\) | 6.35454 | 0.252172 | ||||||||
\(636\) | 4.44028 | 0.176069 | ||||||||
\(637\) | −1.52159 | −0.0602876 | ||||||||
\(638\) | 1.00268 | 0.0396964 | ||||||||
\(639\) | −21.5338 | −0.851862 | ||||||||
\(640\) | 1.31184 | 0.0518552 | ||||||||
\(641\) | 33.3018 | 1.31534 | 0.657671 | − | 0.753306i | \(-0.271542\pi\) | ||||
0.657671 | + | 0.753306i | \(0.271542\pi\) | |||||||
\(642\) | 21.5686 | 0.851245 | ||||||||
\(643\) | −27.4330 | −1.08185 | −0.540926 | − | 0.841070i | \(-0.681926\pi\) | ||||
−0.540926 | + | 0.841070i | \(0.681926\pi\) | |||||||
\(644\) | −12.9829 | −0.511596 | ||||||||
\(645\) | 20.4750 | 0.806202 | ||||||||
\(646\) | 9.97326 | 0.392393 | ||||||||
\(647\) | −26.7203 | −1.05048 | −0.525242 | − | 0.850953i | \(-0.676025\pi\) | ||||
−0.525242 | + | 0.850953i | \(0.676025\pi\) | |||||||
\(648\) | 11.2020 | 0.440057 | ||||||||
\(649\) | 0.0714825 | 0.00280593 | ||||||||
\(650\) | 6.78390 | 0.266086 | ||||||||
\(651\) | −43.0607 | −1.68768 | ||||||||
\(652\) | −5.00829 | −0.196140 | ||||||||
\(653\) | 17.2176 | 0.673776 | 0.336888 | − | 0.941545i | \(-0.390626\pi\) | ||||
0.336888 | + | 0.941545i | \(0.390626\pi\) | |||||||
\(654\) | −35.0302 | −1.36979 | ||||||||
\(655\) | −7.75841 | −0.303146 | ||||||||
\(656\) | 3.49399 | 0.136418 | ||||||||
\(657\) | −7.02044 | −0.273894 | ||||||||
\(658\) | −16.0393 | −0.625278 | ||||||||
\(659\) | 7.61250 | 0.296541 | 0.148270 | − | 0.988947i | \(-0.452629\pi\) | ||||
0.148270 | + | 0.988947i | \(0.452629\pi\) | |||||||
\(660\) | −0.286586 | −0.0111553 | ||||||||
\(661\) | 12.9707 | 0.504502 | 0.252251 | − | 0.967662i | \(-0.418829\pi\) | ||||
0.252251 | + | 0.967662i | \(0.418829\pi\) | |||||||
\(662\) | 10.4352 | 0.405575 | ||||||||
\(663\) | 9.04498 | 0.351278 | ||||||||
\(664\) | −7.12661 | −0.276566 | ||||||||
\(665\) | 16.2708 | 0.630956 | ||||||||
\(666\) | −6.42258 | −0.248870 | ||||||||
\(667\) | 51.7179 | 2.00252 | ||||||||
\(668\) | 14.5968 | 0.564765 | ||||||||
\(669\) | −32.1075 | −1.24135 | ||||||||
\(670\) | 2.71683 | 0.104960 | ||||||||
\(671\) | 0.0715160 | 0.00276084 | ||||||||
\(672\) | −5.43713 | −0.209742 | ||||||||
\(673\) | 39.5644 | 1.52509 | 0.762547 | − | 0.646932i | \(-0.223948\pi\) | ||||
0.762547 | + | 0.646932i | \(0.223948\pi\) | |||||||
\(674\) | −28.2649 | −1.08872 | ||||||||
\(675\) | −9.12476 | −0.351212 | ||||||||
\(676\) | −8.71986 | −0.335379 | ||||||||
\(677\) | 16.6832 | 0.641188 | 0.320594 | − | 0.947217i | \(-0.396117\pi\) | ||||
0.320594 | + | 0.947217i | \(0.396117\pi\) | |||||||
\(678\) | −25.4206 | −0.976272 | ||||||||
\(679\) | −33.8083 | −1.29744 | ||||||||
\(680\) | −2.64019 | −0.101247 | ||||||||
\(681\) | 22.0704 | 0.845741 | ||||||||
\(682\) | −0.796450 | −0.0304977 | ||||||||
\(683\) | 47.6884 | 1.82475 | 0.912373 | − | 0.409360i | \(-0.134248\pi\) | ||||
0.912373 | + | 0.409360i | \(0.134248\pi\) | |||||||
\(684\) | 8.51849 | 0.325712 | ||||||||
\(685\) | −17.3572 | −0.663185 | ||||||||
\(686\) | −19.3611 | −0.739212 | ||||||||
\(687\) | −42.4046 | −1.61784 | ||||||||
\(688\) | 7.18482 | 0.273919 | ||||||||
\(689\) | −4.22877 | −0.161103 | ||||||||
\(690\) | −14.7820 | −0.562742 | ||||||||
\(691\) | 47.1497 | 1.79366 | 0.896829 | − | 0.442377i | \(-0.145865\pi\) | ||||
0.896829 | + | 0.442377i | \(0.145865\pi\) | |||||||
\(692\) | −18.7254 | −0.711833 | ||||||||
\(693\) | 0.432683 | 0.0164363 | ||||||||
\(694\) | −4.29931 | −0.163200 | ||||||||
\(695\) | 6.97127 | 0.264435 | ||||||||
\(696\) | 21.6591 | 0.820985 | ||||||||
\(697\) | −7.03194 | −0.266354 | ||||||||
\(698\) | 15.7538 | 0.596291 | ||||||||
\(699\) | 20.2990 | 0.767777 | ||||||||
\(700\) | 8.20718 | 0.310202 | ||||||||
\(701\) | 18.2319 | 0.688610 | 0.344305 | − | 0.938858i | \(-0.388115\pi\) | ||||
0.344305 | + | 0.938858i | \(0.388115\pi\) | |||||||
\(702\) | −5.75706 | −0.217286 | ||||||||
\(703\) | 18.5146 | 0.698292 | ||||||||
\(704\) | −0.100565 | −0.00379019 | ||||||||
\(705\) | −18.2621 | −0.687789 | ||||||||
\(706\) | 32.0369 | 1.20573 | ||||||||
\(707\) | 21.9252 | 0.824582 | ||||||||
\(708\) | 1.54411 | 0.0580312 | ||||||||
\(709\) | −30.6601 | −1.15146 | −0.575731 | − | 0.817639i | \(-0.695283\pi\) | ||||
−0.575731 | + | 0.817639i | \(0.695283\pi\) | |||||||
\(710\) | −16.4333 | −0.616729 | ||||||||
\(711\) | 4.68192 | 0.175586 | ||||||||
\(712\) | 9.67029 | 0.362410 | ||||||||
\(713\) | −41.0807 | −1.53848 | ||||||||
\(714\) | 10.9426 | 0.409518 | ||||||||
\(715\) | 0.272935 | 0.0102072 | ||||||||
\(716\) | 16.4101 | 0.613276 | ||||||||
\(717\) | −44.6441 | −1.66727 | ||||||||
\(718\) | 25.5931 | 0.955128 | ||||||||
\(719\) | −6.05972 | −0.225989 | −0.112995 | − | 0.993596i | \(-0.536044\pi\) | ||||
−0.112995 | + | 0.993596i | \(0.536044\pi\) | |||||||
\(720\) | −2.25507 | −0.0840416 | ||||||||
\(721\) | −25.3728 | −0.944932 | ||||||||
\(722\) | −5.55659 | −0.206795 | ||||||||
\(723\) | −13.9347 | −0.518239 | ||||||||
\(724\) | 16.1897 | 0.601686 | ||||||||
\(725\) | −32.6937 | −1.21421 | ||||||||
\(726\) | −23.8736 | −0.886034 | ||||||||
\(727\) | 52.9498 | 1.96380 | 0.981901 | − | 0.189397i | \(-0.0606534\pi\) | ||||
0.981901 | + | 0.189397i | \(0.0606534\pi\) | |||||||
\(728\) | 5.17813 | 0.191914 | ||||||||
\(729\) | −1.12140 | −0.0415332 | ||||||||
\(730\) | −5.35758 | −0.198293 | ||||||||
\(731\) | −14.4600 | −0.534823 | ||||||||
\(732\) | 1.54483 | 0.0570987 | ||||||||
\(733\) | −42.0710 | −1.55393 | −0.776965 | − | 0.629544i | \(-0.783242\pi\) | ||||
−0.776965 | + | 0.629544i | \(0.783242\pi\) | |||||||
\(734\) | 26.2220 | 0.967873 | ||||||||
\(735\) | −2.09593 | −0.0773094 | ||||||||
\(736\) | −5.18712 | −0.191200 | ||||||||
\(737\) | −0.208271 | −0.00767175 | ||||||||
\(738\) | −6.00621 | −0.221092 | ||||||||
\(739\) | 11.0290 | 0.405707 | 0.202853 | − | 0.979209i | \(-0.434979\pi\) | ||||
0.202853 | + | 0.979209i | \(0.434979\pi\) | |||||||
\(740\) | −4.90132 | −0.180176 | ||||||||
\(741\) | −22.2709 | −0.818144 | ||||||||
\(742\) | −5.11598 | −0.187814 | ||||||||
\(743\) | 14.0240 | 0.514489 | 0.257244 | − | 0.966346i | \(-0.417185\pi\) | ||||
0.257244 | + | 0.966346i | \(0.417185\pi\) | |||||||
\(744\) | −17.2043 | −0.630740 | ||||||||
\(745\) | 5.30692 | 0.194430 | ||||||||
\(746\) | −36.7040 | −1.34383 | ||||||||
\(747\) | 12.2507 | 0.448230 | ||||||||
\(748\) | 0.202395 | 0.00740030 | ||||||||
\(749\) | −24.8508 | −0.908029 | ||||||||
\(750\) | 23.5933 | 0.861506 | ||||||||
\(751\) | 34.0777 | 1.24351 | 0.621757 | − | 0.783210i | \(-0.286419\pi\) | ||||
0.621757 | + | 0.783210i | \(0.286419\pi\) | |||||||
\(752\) | −6.40829 | −0.233686 | ||||||||
\(753\) | −23.3744 | −0.851811 | ||||||||
\(754\) | −20.6274 | −0.751204 | ||||||||
\(755\) | −5.14123 | −0.187108 | ||||||||
\(756\) | −6.96491 | −0.253311 | ||||||||
\(757\) | −23.6972 | −0.861290 | −0.430645 | − | 0.902521i | \(-0.641714\pi\) | ||||
−0.430645 | + | 0.902521i | \(0.641714\pi\) | |||||||
\(758\) | 29.0002 | 1.05334 | ||||||||
\(759\) | 1.13318 | 0.0411318 | ||||||||
\(760\) | 6.50079 | 0.235808 | ||||||||
\(761\) | 4.04853 | 0.146759 | 0.0733795 | − | 0.997304i | \(-0.476622\pi\) | ||||
0.0733795 | + | 0.997304i | \(0.476622\pi\) | |||||||
\(762\) | −10.5227 | −0.381197 | ||||||||
\(763\) | 40.3610 | 1.46116 | ||||||||
\(764\) | −24.9052 | −0.901039 | ||||||||
\(765\) | 4.53851 | 0.164090 | ||||||||
\(766\) | −25.2690 | −0.913005 | ||||||||
\(767\) | −1.47056 | −0.0530987 | ||||||||
\(768\) | −2.17233 | −0.0783871 | ||||||||
\(769\) | 40.7296 | 1.46875 | 0.734374 | − | 0.678745i | \(-0.237476\pi\) | ||||
0.734374 | + | 0.678745i | \(0.237476\pi\) | |||||||
\(770\) | 0.330197 | 0.0118995 | ||||||||
\(771\) | −2.81100 | −0.101236 | ||||||||
\(772\) | −16.9546 | −0.610208 | ||||||||
\(773\) | −21.4110 | −0.770100 | −0.385050 | − | 0.922896i | \(-0.625816\pi\) | ||||
−0.385050 | + | 0.922896i | \(0.625816\pi\) | |||||||
\(774\) | −12.3508 | −0.443940 | ||||||||
\(775\) | 25.9694 | 0.932848 | ||||||||
\(776\) | −13.5076 | −0.484895 | ||||||||
\(777\) | 20.3142 | 0.728769 | ||||||||
\(778\) | 6.33010 | 0.226945 | ||||||||
\(779\) | 17.3143 | 0.620351 | ||||||||
\(780\) | 5.89572 | 0.211101 | ||||||||
\(781\) | 1.25976 | 0.0450778 | ||||||||
\(782\) | 10.4395 | 0.373315 | ||||||||
\(783\) | 27.7451 | 0.991527 | ||||||||
\(784\) | −0.735476 | −0.0262670 | ||||||||
\(785\) | −1.69818 | −0.0606105 | ||||||||
\(786\) | 12.8474 | 0.458253 | ||||||||
\(787\) | 25.0065 | 0.891385 | 0.445693 | − | 0.895186i | \(-0.352957\pi\) | ||||
0.445693 | + | 0.895186i | \(0.352957\pi\) | |||||||
\(788\) | 19.7851 | 0.704815 | ||||||||
\(789\) | 15.3123 | 0.545134 | ||||||||
\(790\) | 3.57296 | 0.127120 | ||||||||
\(791\) | 29.2890 | 1.04140 | ||||||||
\(792\) | 0.172872 | 0.00614275 | ||||||||
\(793\) | −1.47125 | −0.0522455 | ||||||||
\(794\) | 13.9127 | 0.493742 | ||||||||
\(795\) | −5.82495 | −0.206590 | ||||||||
\(796\) | −10.1142 | −0.358490 | ||||||||
\(797\) | −34.9899 | −1.23940 | −0.619702 | − | 0.784837i | \(-0.712747\pi\) | ||||
−0.619702 | + | 0.784837i | \(0.712747\pi\) | |||||||
\(798\) | −26.9435 | −0.953788 | ||||||||
\(799\) | 12.8972 | 0.456270 | ||||||||
\(800\) | 3.27907 | 0.115932 | ||||||||
\(801\) | −16.6233 | −0.587356 | ||||||||
\(802\) | 32.7694 | 1.15713 | ||||||||
\(803\) | 0.410708 | 0.0144936 | ||||||||
\(804\) | −4.49890 | −0.158664 | ||||||||
\(805\) | 17.0315 | 0.600281 | ||||||||
\(806\) | 16.3848 | 0.577130 | ||||||||
\(807\) | −58.6125 | −2.06326 | ||||||||
\(808\) | 8.75991 | 0.308173 | ||||||||
\(809\) | −29.7270 | −1.04515 | −0.522573 | − | 0.852595i | \(-0.675028\pi\) | ||||
−0.522573 | + | 0.852595i | \(0.675028\pi\) | |||||||
\(810\) | −14.6953 | −0.516341 | ||||||||
\(811\) | 21.0565 | 0.739395 | 0.369697 | − | 0.929152i | \(-0.379461\pi\) | ||||
0.369697 | + | 0.929152i | \(0.379461\pi\) | |||||||
\(812\) | −24.9550 | −0.875751 | ||||||||
\(813\) | 3.01100 | 0.105600 | ||||||||
\(814\) | 0.375732 | 0.0131694 | ||||||||
\(815\) | 6.57010 | 0.230140 | ||||||||
\(816\) | 4.37198 | 0.153050 | ||||||||
\(817\) | 35.6041 | 1.24563 | ||||||||
\(818\) | 30.9075 | 1.08065 | ||||||||
\(819\) | −8.90126 | −0.311035 | ||||||||
\(820\) | −4.58357 | −0.160065 | ||||||||
\(821\) | 14.8753 | 0.519153 | 0.259577 | − | 0.965723i | \(-0.416417\pi\) | ||||
0.259577 | + | 0.965723i | \(0.416417\pi\) | |||||||
\(822\) | 28.7424 | 1.00251 | ||||||||
\(823\) | 37.0263 | 1.29066 | 0.645328 | − | 0.763906i | \(-0.276721\pi\) | ||||
0.645328 | + | 0.763906i | \(0.276721\pi\) | |||||||
\(824\) | −10.1373 | −0.353151 | ||||||||
\(825\) | −0.716346 | −0.0249400 | ||||||||
\(826\) | −1.77908 | −0.0619023 | ||||||||
\(827\) | 34.3635 | 1.19493 | 0.597467 | − | 0.801893i | \(-0.296174\pi\) | ||||
0.597467 | + | 0.801893i | \(0.296174\pi\) | |||||||
\(828\) | 8.91671 | 0.309877 | ||||||||
\(829\) | −15.8069 | −0.548996 | −0.274498 | − | 0.961588i | \(-0.588512\pi\) | ||||
−0.274498 | + | 0.961588i | \(0.588512\pi\) | |||||||
\(830\) | 9.34900 | 0.324509 | ||||||||
\(831\) | 24.6903 | 0.856496 | ||||||||
\(832\) | 2.06885 | 0.0717245 | ||||||||
\(833\) | 1.48020 | 0.0512860 | ||||||||
\(834\) | −11.5440 | −0.399735 | ||||||||
\(835\) | −19.1487 | −0.662667 | ||||||||
\(836\) | −0.498346 | −0.0172357 | ||||||||
\(837\) | −22.0385 | −0.761763 | ||||||||
\(838\) | −34.5512 | −1.19355 | ||||||||
\(839\) | 37.3168 | 1.28832 | 0.644159 | − | 0.764891i | \(-0.277207\pi\) | ||||
0.644159 | + | 0.764891i | \(0.277207\pi\) | |||||||
\(840\) | 7.13266 | 0.246100 | ||||||||
\(841\) | 70.4097 | 2.42792 | ||||||||
\(842\) | −10.0270 | −0.345554 | ||||||||
\(843\) | −19.8155 | −0.682483 | ||||||||
\(844\) | −25.2032 | −0.867532 | ||||||||
\(845\) | 11.4391 | 0.393517 | ||||||||
\(846\) | 11.0159 | 0.378735 | ||||||||
\(847\) | 27.5066 | 0.945139 | ||||||||
\(848\) | −2.04402 | −0.0701919 | ||||||||
\(849\) | −4.05538 | −0.139180 | ||||||||
\(850\) | −6.59938 | −0.226357 | ||||||||
\(851\) | 19.3802 | 0.664343 | ||||||||
\(852\) | 27.2124 | 0.932282 | ||||||||
\(853\) | −39.4222 | −1.34979 | −0.674895 | − | 0.737914i | \(-0.735811\pi\) | ||||
−0.674895 | + | 0.737914i | \(0.735811\pi\) | |||||||
\(854\) | −1.77992 | −0.0609076 | ||||||||
\(855\) | −11.1749 | −0.382174 | ||||||||
\(856\) | −9.92879 | −0.339359 | ||||||||
\(857\) | −46.8985 | −1.60202 | −0.801012 | − | 0.598648i | \(-0.795705\pi\) | ||||
−0.801012 | + | 0.598648i | \(0.795705\pi\) | |||||||
\(858\) | −0.451962 | −0.0154297 | ||||||||
\(859\) | 21.0160 | 0.717055 | 0.358528 | − | 0.933519i | \(-0.383279\pi\) | ||||
0.358528 | + | 0.933519i | \(0.383279\pi\) | |||||||
\(860\) | −9.42537 | −0.321402 | ||||||||
\(861\) | 18.9973 | 0.647426 | ||||||||
\(862\) | −12.7690 | −0.434914 | ||||||||
\(863\) | 1.99957 | 0.0680661 | 0.0340331 | − | 0.999421i | \(-0.489165\pi\) | ||||
0.0340331 | + | 0.999421i | \(0.489165\pi\) | |||||||
\(864\) | −2.78273 | −0.0946704 | ||||||||
\(865\) | 24.5648 | 0.835229 | ||||||||
\(866\) | −7.62871 | −0.259234 | ||||||||
\(867\) | 28.1306 | 0.955366 | ||||||||
\(868\) | 19.8224 | 0.672815 | ||||||||
\(869\) | −0.273900 | −0.00929143 | ||||||||
\(870\) | −28.4133 | −0.963302 | ||||||||
\(871\) | 4.28460 | 0.145178 | ||||||||
\(872\) | 16.1257 | 0.546084 | ||||||||
\(873\) | 23.2197 | 0.785869 | ||||||||
\(874\) | −25.7046 | −0.869470 | ||||||||
\(875\) | −27.1836 | −0.918975 | ||||||||
\(876\) | 8.87180 | 0.299750 | ||||||||
\(877\) | −29.4135 | −0.993224 | −0.496612 | − | 0.867973i | \(-0.665423\pi\) | ||||
−0.496612 | + | 0.867973i | \(0.665423\pi\) | |||||||
\(878\) | 0.892723 | 0.0301279 | ||||||||
\(879\) | −11.4878 | −0.387475 | ||||||||
\(880\) | 0.131926 | 0.00444721 | ||||||||
\(881\) | 6.76250 | 0.227834 | 0.113917 | − | 0.993490i | \(-0.463660\pi\) | ||||
0.113917 | + | 0.993490i | \(0.463660\pi\) | |||||||
\(882\) | 1.26429 | 0.0425709 | ||||||||
\(883\) | −14.9701 | −0.503782 | −0.251891 | − | 0.967756i | \(-0.581053\pi\) | ||||
−0.251891 | + | 0.967756i | \(0.581053\pi\) | |||||||
\(884\) | −4.16373 | −0.140041 | ||||||||
\(885\) | −2.02563 | −0.0680908 | ||||||||
\(886\) | −25.6792 | −0.862709 | ||||||||
\(887\) | −26.0458 | −0.874534 | −0.437267 | − | 0.899332i | \(-0.644053\pi\) | ||||
−0.437267 | + | 0.899332i | \(0.644053\pi\) | |||||||
\(888\) | 8.11627 | 0.272364 | ||||||||
\(889\) | 12.1240 | 0.406626 | ||||||||
\(890\) | −12.6859 | −0.425233 | ||||||||
\(891\) | 1.12653 | 0.0377403 | ||||||||
\(892\) | 14.7802 | 0.494879 | ||||||||
\(893\) | −31.7560 | −1.06267 | ||||||||
\(894\) | −8.78791 | −0.293912 | ||||||||
\(895\) | −21.5275 | −0.719587 | ||||||||
\(896\) | 2.50290 | 0.0836161 | ||||||||
\(897\) | −23.3121 | −0.778368 | ||||||||
\(898\) | −26.4059 | −0.881177 | ||||||||
\(899\) | −78.9634 | −2.63358 | ||||||||
\(900\) | −5.63675 | −0.187892 | ||||||||
\(901\) | 4.11375 | 0.137049 | ||||||||
\(902\) | 0.351374 | 0.0116995 | ||||||||
\(903\) | 39.0648 | 1.29999 | ||||||||
\(904\) | 11.7020 | 0.389203 | ||||||||
\(905\) | −21.2384 | −0.705988 | ||||||||
\(906\) | 8.51354 | 0.282843 | ||||||||
\(907\) | 38.2589 | 1.27036 | 0.635182 | − | 0.772362i | \(-0.280925\pi\) | ||||
0.635182 | + | 0.772362i | \(0.280925\pi\) | |||||||
\(908\) | −10.1598 | −0.337165 | ||||||||
\(909\) | −15.0584 | −0.499455 | ||||||||
\(910\) | −6.79290 | −0.225183 | ||||||||
\(911\) | 17.7130 | 0.586859 | 0.293430 | − | 0.955981i | \(-0.405203\pi\) | ||||
0.293430 | + | 0.955981i | \(0.405203\pi\) | |||||||
\(912\) | −10.7649 | −0.356461 | ||||||||
\(913\) | −0.716688 | −0.0237189 | ||||||||
\(914\) | 16.0306 | 0.530245 | ||||||||
\(915\) | −2.02658 | −0.0669967 | ||||||||
\(916\) | 19.5203 | 0.644970 | ||||||||
\(917\) | −14.8025 | −0.488821 | ||||||||
\(918\) | 5.60047 | 0.184843 | ||||||||
\(919\) | −58.4634 | −1.92853 | −0.964264 | − | 0.264942i | \(-0.914647\pi\) | ||||
−0.964264 | + | 0.264942i | \(0.914647\pi\) | |||||||
\(920\) | 6.80469 | 0.224344 | ||||||||
\(921\) | −59.8006 | −1.97050 | ||||||||
\(922\) | −19.3403 | −0.636938 | ||||||||
\(923\) | −25.9162 | −0.853041 | ||||||||
\(924\) | −0.546785 | −0.0179879 | ||||||||
\(925\) | −12.2513 | −0.402819 | ||||||||
\(926\) | −2.26727 | −0.0745070 | ||||||||
\(927\) | 17.4262 | 0.572351 | ||||||||
\(928\) | −9.97044 | −0.327296 | ||||||||
\(929\) | 47.1093 | 1.54561 | 0.772803 | − | 0.634646i | \(-0.218854\pi\) | ||||
0.772803 | + | 0.634646i | \(0.218854\pi\) | |||||||
\(930\) | 22.5694 | 0.740078 | ||||||||
\(931\) | −3.64462 | −0.119448 | ||||||||
\(932\) | −9.34433 | −0.306084 | ||||||||
\(933\) | −6.63953 | −0.217368 | ||||||||
\(934\) | −24.3815 | −0.797788 | ||||||||
\(935\) | −0.265511 | −0.00868313 | ||||||||
\(936\) | −3.55638 | −0.116244 | ||||||||
\(937\) | 16.6377 | 0.543530 | 0.271765 | − | 0.962364i | \(-0.412393\pi\) | ||||
0.271765 | + | 0.962364i | \(0.412393\pi\) | |||||||
\(938\) | 5.18352 | 0.169248 | ||||||||
\(939\) | 46.7287 | 1.52493 | ||||||||
\(940\) | 8.40667 | 0.274195 | ||||||||
\(941\) | 46.3653 | 1.51146 | 0.755732 | − | 0.654881i | \(-0.227281\pi\) | ||||
0.755732 | + | 0.654881i | \(0.227281\pi\) | |||||||
\(942\) | 2.81207 | 0.0916222 | ||||||||
\(943\) | 18.1238 | 0.590191 | ||||||||
\(944\) | −0.710808 | −0.0231348 | ||||||||
\(945\) | 9.13687 | 0.297222 | ||||||||
\(946\) | 0.722542 | 0.0234919 | ||||||||
\(947\) | 49.7566 | 1.61687 | 0.808436 | − | 0.588585i | \(-0.200315\pi\) | ||||
0.808436 | + | 0.588585i | \(0.200315\pi\) | |||||||
\(948\) | −5.91658 | −0.192162 | ||||||||
\(949\) | −8.44920 | −0.274273 | ||||||||
\(950\) | 16.2493 | 0.527196 | ||||||||
\(951\) | 11.8551 | 0.384429 | ||||||||
\(952\) | −5.03729 | −0.163260 | ||||||||
\(953\) | −53.0218 | −1.71754 | −0.858772 | − | 0.512358i | \(-0.828772\pi\) | ||||
−0.858772 | + | 0.512358i | \(0.828772\pi\) | |||||||
\(954\) | 3.51369 | 0.113760 | ||||||||
\(955\) | 32.6718 | 1.05723 | ||||||||
\(956\) | 20.5513 | 0.664676 | ||||||||
\(957\) | 2.17815 | 0.0704094 | ||||||||
\(958\) | −23.3231 | −0.753536 | ||||||||
\(959\) | −33.1163 | −1.06938 | ||||||||
\(960\) | 2.84976 | 0.0919755 | ||||||||
\(961\) | 31.7225 | 1.02331 | ||||||||
\(962\) | −7.72966 | −0.249214 | ||||||||
\(963\) | 17.0677 | 0.549999 | ||||||||
\(964\) | 6.41466 | 0.206602 | ||||||||
\(965\) | 22.2417 | 0.715987 | ||||||||
\(966\) | −28.2030 | −0.907418 | ||||||||
\(967\) | −31.5421 | −1.01433 | −0.507163 | − | 0.861850i | \(-0.669306\pi\) | ||||
−0.507163 | + | 0.861850i | \(0.669306\pi\) | |||||||
\(968\) | 10.9899 | 0.353228 | ||||||||
\(969\) | 21.6652 | 0.695986 | ||||||||
\(970\) | 17.7199 | 0.568951 | ||||||||
\(971\) | 35.8122 | 1.14927 | 0.574634 | − | 0.818410i | \(-0.305144\pi\) | ||||
0.574634 | + | 0.818410i | \(0.305144\pi\) | |||||||
\(972\) | 15.9863 | 0.512761 | ||||||||
\(973\) | 13.3007 | 0.426400 | ||||||||
\(974\) | −11.4534 | −0.366992 | ||||||||
\(975\) | 14.7369 | 0.471957 | ||||||||
\(976\) | −0.711142 | −0.0227631 | ||||||||
\(977\) | −0.0185896 | −0.000594735 0 | −0.000297368 | − | 1.00000i | \(-0.500095\pi\) | ||||
−0.000297368 | 1.00000i | \(0.500095\pi\) | ||||||||
\(978\) | −10.8797 | −0.347893 | ||||||||
\(979\) | 0.972493 | 0.0310810 | ||||||||
\(980\) | 0.964830 | 0.0308203 | ||||||||
\(981\) | −27.7202 | −0.885037 | ||||||||
\(982\) | 18.5596 | 0.592259 | ||||||||
\(983\) | 11.2924 | 0.360172 | 0.180086 | − | 0.983651i | \(-0.442362\pi\) | ||||
0.180086 | + | 0.983651i | \(0.442362\pi\) | |||||||
\(984\) | 7.59010 | 0.241964 | ||||||||
\(985\) | −25.9550 | −0.826994 | ||||||||
\(986\) | 20.0663 | 0.639041 | ||||||||
\(987\) | −34.8427 | −1.10905 | ||||||||
\(988\) | 10.2521 | 0.326163 | ||||||||
\(989\) | 37.2685 | 1.18507 | ||||||||
\(990\) | −0.226782 | −0.00720759 | ||||||||
\(991\) | 20.6817 | 0.656974 | 0.328487 | − | 0.944508i | \(-0.393461\pi\) | ||||
0.328487 | + | 0.944508i | \(0.393461\pi\) | |||||||
\(992\) | 7.91975 | 0.251452 | ||||||||
\(993\) | 22.6686 | 0.719367 | ||||||||
\(994\) | −31.3535 | −0.994472 | ||||||||
\(995\) | 13.2683 | 0.420633 | ||||||||
\(996\) | −15.4813 | −0.490545 | ||||||||
\(997\) | 28.7917 | 0.911842 | 0.455921 | − | 0.890020i | \(-0.349310\pi\) | ||||
0.455921 | + | 0.890020i | \(0.349310\pi\) | |||||||
\(998\) | −14.5750 | −0.461362 | ||||||||
\(999\) | 10.3969 | 0.328942 |
(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 | 8002.2.a.e.1.14 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.14 | ✓ | 77 | 1.1 | even | 1 | trivial |