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: | \(95\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
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 | ||||||||
\(3\) | −1.94136 | −1.12085 | −0.560424 | − | 0.828206i | \(-0.689362\pi\) | ||||
−0.560424 | + | 0.828206i | \(0.689362\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.368072 | −0.164607 | −0.0823033 | − | 0.996607i | \(-0.526228\pi\) | ||||
−0.0823033 | + | 0.996607i | \(0.526228\pi\) | |||||||
\(6\) | −1.94136 | −0.792559 | ||||||||
\(7\) | −3.56861 | −1.34881 | −0.674403 | − | 0.738363i | \(-0.735599\pi\) | ||||
−0.674403 | + | 0.738363i | \(0.735599\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.768897 | 0.256299 | ||||||||
\(10\) | −0.368072 | −0.116395 | ||||||||
\(11\) | −1.91905 | −0.578616 | −0.289308 | − | 0.957236i | \(-0.593425\pi\) | ||||
−0.289308 | + | 0.957236i | \(0.593425\pi\) | |||||||
\(12\) | −1.94136 | −0.560424 | ||||||||
\(13\) | −3.88960 | −1.07878 | −0.539391 | − | 0.842056i | \(-0.681345\pi\) | ||||
−0.539391 | + | 0.842056i | \(0.681345\pi\) | |||||||
\(14\) | −3.56861 | −0.953750 | ||||||||
\(15\) | 0.714562 | 0.184499 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.31804 | −0.562208 | −0.281104 | − | 0.959677i | \(-0.590701\pi\) | ||||
−0.281104 | + | 0.959677i | \(0.590701\pi\) | |||||||
\(18\) | 0.768897 | 0.181231 | ||||||||
\(19\) | 2.22922 | 0.511418 | 0.255709 | − | 0.966754i | \(-0.417691\pi\) | ||||
0.255709 | + | 0.966754i | \(0.417691\pi\) | |||||||
\(20\) | −0.368072 | −0.0823033 | ||||||||
\(21\) | 6.92797 | 1.51181 | ||||||||
\(22\) | −1.91905 | −0.409143 | ||||||||
\(23\) | 3.88295 | 0.809651 | 0.404825 | − | 0.914394i | \(-0.367332\pi\) | ||||
0.404825 | + | 0.914394i | \(0.367332\pi\) | |||||||
\(24\) | −1.94136 | −0.396279 | ||||||||
\(25\) | −4.86452 | −0.972905 | ||||||||
\(26\) | −3.88960 | −0.762814 | ||||||||
\(27\) | 4.33138 | 0.833575 | ||||||||
\(28\) | −3.56861 | −0.674403 | ||||||||
\(29\) | −6.88751 | −1.27898 | −0.639489 | − | 0.768800i | \(-0.720854\pi\) | ||||
−0.639489 | + | 0.768800i | \(0.720854\pi\) | |||||||
\(30\) | 0.714562 | 0.130460 | ||||||||
\(31\) | 3.30935 | 0.594376 | 0.297188 | − | 0.954819i | \(-0.403951\pi\) | ||||
0.297188 | + | 0.954819i | \(0.403951\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.72558 | 0.648540 | ||||||||
\(34\) | −2.31804 | −0.397541 | ||||||||
\(35\) | 1.31350 | 0.222023 | ||||||||
\(36\) | 0.768897 | 0.128149 | ||||||||
\(37\) | −3.47882 | −0.571914 | −0.285957 | − | 0.958242i | \(-0.592311\pi\) | ||||
−0.285957 | + | 0.958242i | \(0.592311\pi\) | |||||||
\(38\) | 2.22922 | 0.361627 | ||||||||
\(39\) | 7.55113 | 1.20915 | ||||||||
\(40\) | −0.368072 | −0.0581973 | ||||||||
\(41\) | −9.31768 | −1.45518 | −0.727589 | − | 0.686013i | \(-0.759359\pi\) | ||||
−0.727589 | + | 0.686013i | \(0.759359\pi\) | |||||||
\(42\) | 6.92797 | 1.06901 | ||||||||
\(43\) | −9.31761 | −1.42092 | −0.710461 | − | 0.703737i | \(-0.751514\pi\) | ||||
−0.710461 | + | 0.703737i | \(0.751514\pi\) | |||||||
\(44\) | −1.91905 | −0.289308 | ||||||||
\(45\) | −0.283009 | −0.0421885 | ||||||||
\(46\) | 3.88295 | 0.572509 | ||||||||
\(47\) | −7.12346 | −1.03906 | −0.519532 | − | 0.854451i | \(-0.673894\pi\) | ||||
−0.519532 | + | 0.854451i | \(0.673894\pi\) | |||||||
\(48\) | −1.94136 | −0.280212 | ||||||||
\(49\) | 5.73496 | 0.819280 | ||||||||
\(50\) | −4.86452 | −0.687947 | ||||||||
\(51\) | 4.50017 | 0.630149 | ||||||||
\(52\) | −3.88960 | −0.539391 | ||||||||
\(53\) | 8.17762 | 1.12328 | 0.561641 | − | 0.827381i | \(-0.310170\pi\) | ||||
0.561641 | + | 0.827381i | \(0.310170\pi\) | |||||||
\(54\) | 4.33138 | 0.589427 | ||||||||
\(55\) | 0.706349 | 0.0952441 | ||||||||
\(56\) | −3.56861 | −0.476875 | ||||||||
\(57\) | −4.32773 | −0.573221 | ||||||||
\(58\) | −6.88751 | −0.904374 | ||||||||
\(59\) | −5.71449 | −0.743964 | −0.371982 | − | 0.928240i | \(-0.621322\pi\) | ||||
−0.371982 | + | 0.928240i | \(0.621322\pi\) | |||||||
\(60\) | 0.714562 | 0.0922495 | ||||||||
\(61\) | 2.14757 | 0.274968 | 0.137484 | − | 0.990504i | \(-0.456098\pi\) | ||||
0.137484 | + | 0.990504i | \(0.456098\pi\) | |||||||
\(62\) | 3.30935 | 0.420288 | ||||||||
\(63\) | −2.74389 | −0.345698 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.43165 | 0.177575 | ||||||||
\(66\) | 3.72558 | 0.458587 | ||||||||
\(67\) | −8.17728 | −0.999014 | −0.499507 | − | 0.866310i | \(-0.666485\pi\) | ||||
−0.499507 | + | 0.866310i | \(0.666485\pi\) | |||||||
\(68\) | −2.31804 | −0.281104 | ||||||||
\(69\) | −7.53822 | −0.907495 | ||||||||
\(70\) | 1.31350 | 0.156994 | ||||||||
\(71\) | −10.1180 | −1.20079 | −0.600396 | − | 0.799703i | \(-0.704990\pi\) | ||||
−0.600396 | + | 0.799703i | \(0.704990\pi\) | |||||||
\(72\) | 0.768897 | 0.0906154 | ||||||||
\(73\) | −7.91677 | −0.926587 | −0.463294 | − | 0.886205i | \(-0.653333\pi\) | ||||
−0.463294 | + | 0.886205i | \(0.653333\pi\) | |||||||
\(74\) | −3.47882 | −0.404404 | ||||||||
\(75\) | 9.44381 | 1.09048 | ||||||||
\(76\) | 2.22922 | 0.255709 | ||||||||
\(77\) | 6.84834 | 0.780441 | ||||||||
\(78\) | 7.55113 | 0.854998 | ||||||||
\(79\) | 10.7209 | 1.20619 | 0.603097 | − | 0.797668i | \(-0.293933\pi\) | ||||
0.603097 | + | 0.797668i | \(0.293933\pi\) | |||||||
\(80\) | −0.368072 | −0.0411517 | ||||||||
\(81\) | −10.7155 | −1.19061 | ||||||||
\(82\) | −9.31768 | −1.02897 | ||||||||
\(83\) | −5.44583 | −0.597757 | −0.298879 | − | 0.954291i | \(-0.596613\pi\) | ||||
−0.298879 | + | 0.954291i | \(0.596613\pi\) | |||||||
\(84\) | 6.92797 | 0.755903 | ||||||||
\(85\) | 0.853206 | 0.0925432 | ||||||||
\(86\) | −9.31761 | −1.00474 | ||||||||
\(87\) | 13.3712 | 1.43354 | ||||||||
\(88\) | −1.91905 | −0.204572 | ||||||||
\(89\) | −3.11259 | −0.329934 | −0.164967 | − | 0.986299i | \(-0.552752\pi\) | ||||
−0.164967 | + | 0.986299i | \(0.552752\pi\) | |||||||
\(90\) | −0.283009 | −0.0298318 | ||||||||
\(91\) | 13.8805 | 1.45507 | ||||||||
\(92\) | 3.88295 | 0.404825 | ||||||||
\(93\) | −6.42465 | −0.666205 | ||||||||
\(94\) | −7.12346 | −0.734729 | ||||||||
\(95\) | −0.820512 | −0.0841828 | ||||||||
\(96\) | −1.94136 | −0.198140 | ||||||||
\(97\) | 4.37204 | 0.443913 | 0.221957 | − | 0.975057i | \(-0.428756\pi\) | ||||
0.221957 | + | 0.975057i | \(0.428756\pi\) | |||||||
\(98\) | 5.73496 | 0.579318 | ||||||||
\(99\) | −1.47555 | −0.148299 | ||||||||
\(100\) | −4.86452 | −0.486452 | ||||||||
\(101\) | 18.6342 | 1.85417 | 0.927087 | − | 0.374847i | \(-0.122305\pi\) | ||||
0.927087 | + | 0.374847i | \(0.122305\pi\) | |||||||
\(102\) | 4.50017 | 0.445583 | ||||||||
\(103\) | 3.72595 | 0.367129 | 0.183564 | − | 0.983008i | \(-0.441236\pi\) | ||||
0.183564 | + | 0.983008i | \(0.441236\pi\) | |||||||
\(104\) | −3.88960 | −0.381407 | ||||||||
\(105\) | −2.54999 | −0.248853 | ||||||||
\(106\) | 8.17762 | 0.794281 | ||||||||
\(107\) | 2.10121 | 0.203132 | 0.101566 | − | 0.994829i | \(-0.467615\pi\) | ||||
0.101566 | + | 0.994829i | \(0.467615\pi\) | |||||||
\(108\) | 4.33138 | 0.416788 | ||||||||
\(109\) | −8.20290 | −0.785695 | −0.392848 | − | 0.919604i | \(-0.628510\pi\) | ||||
−0.392848 | + | 0.919604i | \(0.628510\pi\) | |||||||
\(110\) | 0.706349 | 0.0673477 | ||||||||
\(111\) | 6.75365 | 0.641028 | ||||||||
\(112\) | −3.56861 | −0.337202 | ||||||||
\(113\) | 11.9151 | 1.12088 | 0.560441 | − | 0.828194i | \(-0.310632\pi\) | ||||
0.560441 | + | 0.828194i | \(0.310632\pi\) | |||||||
\(114\) | −4.32773 | −0.405329 | ||||||||
\(115\) | −1.42920 | −0.133274 | ||||||||
\(116\) | −6.88751 | −0.639489 | ||||||||
\(117\) | −2.99070 | −0.276491 | ||||||||
\(118\) | −5.71449 | −0.526062 | ||||||||
\(119\) | 8.27218 | 0.758310 | ||||||||
\(120\) | 0.714562 | 0.0652302 | ||||||||
\(121\) | −7.31724 | −0.665203 | ||||||||
\(122\) | 2.14757 | 0.194432 | ||||||||
\(123\) | 18.0890 | 1.63103 | ||||||||
\(124\) | 3.30935 | 0.297188 | ||||||||
\(125\) | 3.63085 | 0.324753 | ||||||||
\(126\) | −2.74389 | −0.244445 | ||||||||
\(127\) | 17.7895 | 1.57856 | 0.789282 | − | 0.614031i | \(-0.210453\pi\) | ||||
0.789282 | + | 0.614031i | \(0.210453\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 18.0889 | 1.59264 | ||||||||
\(130\) | 1.43165 | 0.125564 | ||||||||
\(131\) | 2.29304 | 0.200344 | 0.100172 | − | 0.994970i | \(-0.468061\pi\) | ||||
0.100172 | + | 0.994970i | \(0.468061\pi\) | |||||||
\(132\) | 3.72558 | 0.324270 | ||||||||
\(133\) | −7.95520 | −0.689804 | ||||||||
\(134\) | −8.17728 | −0.706409 | ||||||||
\(135\) | −1.59426 | −0.137212 | ||||||||
\(136\) | −2.31804 | −0.198771 | ||||||||
\(137\) | 16.5841 | 1.41688 | 0.708438 | − | 0.705773i | \(-0.249400\pi\) | ||||
0.708438 | + | 0.705773i | \(0.249400\pi\) | |||||||
\(138\) | −7.53822 | −0.641696 | ||||||||
\(139\) | −17.5563 | −1.48910 | −0.744551 | − | 0.667566i | \(-0.767336\pi\) | ||||
−0.744551 | + | 0.667566i | \(0.767336\pi\) | |||||||
\(140\) | 1.31350 | 0.111011 | ||||||||
\(141\) | 13.8292 | 1.16463 | ||||||||
\(142\) | −10.1180 | −0.849088 | ||||||||
\(143\) | 7.46435 | 0.624200 | ||||||||
\(144\) | 0.768897 | 0.0640747 | ||||||||
\(145\) | 2.53510 | 0.210528 | ||||||||
\(146\) | −7.91677 | −0.655196 | ||||||||
\(147\) | −11.1336 | −0.918288 | ||||||||
\(148\) | −3.47882 | −0.285957 | ||||||||
\(149\) | 13.8344 | 1.13336 | 0.566678 | − | 0.823939i | \(-0.308228\pi\) | ||||
0.566678 | + | 0.823939i | \(0.308228\pi\) | |||||||
\(150\) | 9.44381 | 0.771084 | ||||||||
\(151\) | 11.7706 | 0.957882 | 0.478941 | − | 0.877847i | \(-0.341021\pi\) | ||||
0.478941 | + | 0.877847i | \(0.341021\pi\) | |||||||
\(152\) | 2.22922 | 0.180813 | ||||||||
\(153\) | −1.78234 | −0.144093 | ||||||||
\(154\) | 6.84834 | 0.551855 | ||||||||
\(155\) | −1.21808 | −0.0978383 | ||||||||
\(156\) | 7.55113 | 0.604575 | ||||||||
\(157\) | −2.56113 | −0.204400 | −0.102200 | − | 0.994764i | \(-0.532588\pi\) | ||||
−0.102200 | + | 0.994764i | \(0.532588\pi\) | |||||||
\(158\) | 10.7209 | 0.852908 | ||||||||
\(159\) | −15.8757 | −1.25903 | ||||||||
\(160\) | −0.368072 | −0.0290986 | ||||||||
\(161\) | −13.8567 | −1.09206 | ||||||||
\(162\) | −10.7155 | −0.841888 | ||||||||
\(163\) | 3.03303 | 0.237565 | 0.118783 | − | 0.992920i | \(-0.462101\pi\) | ||||
0.118783 | + | 0.992920i | \(0.462101\pi\) | |||||||
\(164\) | −9.31768 | −0.727589 | ||||||||
\(165\) | −1.37128 | −0.106754 | ||||||||
\(166\) | −5.44583 | −0.422678 | ||||||||
\(167\) | −7.10238 | −0.549599 | −0.274799 | − | 0.961502i | \(-0.588611\pi\) | ||||
−0.274799 | + | 0.961502i | \(0.588611\pi\) | |||||||
\(168\) | 6.92797 | 0.534504 | ||||||||
\(169\) | 2.12900 | 0.163769 | ||||||||
\(170\) | 0.853206 | 0.0654379 | ||||||||
\(171\) | 1.71404 | 0.131076 | ||||||||
\(172\) | −9.31761 | −0.710461 | ||||||||
\(173\) | 21.0730 | 1.60215 | 0.801074 | − | 0.598565i | \(-0.204262\pi\) | ||||
0.801074 | + | 0.598565i | \(0.204262\pi\) | |||||||
\(174\) | 13.3712 | 1.01367 | ||||||||
\(175\) | 17.3596 | 1.31226 | ||||||||
\(176\) | −1.91905 | −0.144654 | ||||||||
\(177\) | 11.0939 | 0.833870 | ||||||||
\(178\) | −3.11259 | −0.233298 | ||||||||
\(179\) | −12.6317 | −0.944141 | −0.472070 | − | 0.881561i | \(-0.656493\pi\) | ||||
−0.472070 | + | 0.881561i | \(0.656493\pi\) | |||||||
\(180\) | −0.283009 | −0.0210943 | ||||||||
\(181\) | 24.3889 | 1.81282 | 0.906408 | − | 0.422403i | \(-0.138813\pi\) | ||||
0.906408 | + | 0.422403i | \(0.138813\pi\) | |||||||
\(182\) | 13.8805 | 1.02889 | ||||||||
\(183\) | −4.16922 | −0.308198 | ||||||||
\(184\) | 3.88295 | 0.286255 | ||||||||
\(185\) | 1.28045 | 0.0941409 | ||||||||
\(186\) | −6.42465 | −0.471078 | ||||||||
\(187\) | 4.44845 | 0.325303 | ||||||||
\(188\) | −7.12346 | −0.519532 | ||||||||
\(189\) | −15.4570 | −1.12433 | ||||||||
\(190\) | −0.820512 | −0.0595262 | ||||||||
\(191\) | −11.7067 | −0.847068 | −0.423534 | − | 0.905880i | \(-0.639211\pi\) | ||||
−0.423534 | + | 0.905880i | \(0.639211\pi\) | |||||||
\(192\) | −1.94136 | −0.140106 | ||||||||
\(193\) | 21.1088 | 1.51944 | 0.759721 | − | 0.650249i | \(-0.225335\pi\) | ||||
0.759721 | + | 0.650249i | \(0.225335\pi\) | |||||||
\(194\) | 4.37204 | 0.313894 | ||||||||
\(195\) | −2.77936 | −0.199034 | ||||||||
\(196\) | 5.73496 | 0.409640 | ||||||||
\(197\) | −0.835550 | −0.0595304 | −0.0297652 | − | 0.999557i | \(-0.509476\pi\) | ||||
−0.0297652 | + | 0.999557i | \(0.509476\pi\) | |||||||
\(198\) | −1.47555 | −0.104863 | ||||||||
\(199\) | −19.2997 | −1.36812 | −0.684061 | − | 0.729425i | \(-0.739788\pi\) | ||||
−0.684061 | + | 0.729425i | \(0.739788\pi\) | |||||||
\(200\) | −4.86452 | −0.343974 | ||||||||
\(201\) | 15.8751 | 1.11974 | ||||||||
\(202\) | 18.6342 | 1.31110 | ||||||||
\(203\) | 24.5788 | 1.72509 | ||||||||
\(204\) | 4.50017 | 0.315075 | ||||||||
\(205\) | 3.42958 | 0.239532 | ||||||||
\(206\) | 3.72595 | 0.259599 | ||||||||
\(207\) | 2.98559 | 0.207513 | ||||||||
\(208\) | −3.88960 | −0.269695 | ||||||||
\(209\) | −4.27799 | −0.295915 | ||||||||
\(210\) | −2.54999 | −0.175966 | ||||||||
\(211\) | −18.5858 | −1.27950 | −0.639751 | − | 0.768582i | \(-0.720962\pi\) | ||||
−0.639751 | + | 0.768582i | \(0.720962\pi\) | |||||||
\(212\) | 8.17762 | 0.561641 | ||||||||
\(213\) | 19.6428 | 1.34590 | ||||||||
\(214\) | 2.10121 | 0.143636 | ||||||||
\(215\) | 3.42955 | 0.233893 | ||||||||
\(216\) | 4.33138 | 0.294713 | ||||||||
\(217\) | −11.8098 | −0.801699 | ||||||||
\(218\) | −8.20290 | −0.555570 | ||||||||
\(219\) | 15.3693 | 1.03856 | ||||||||
\(220\) | 0.706349 | 0.0476220 | ||||||||
\(221\) | 9.01626 | 0.606499 | ||||||||
\(222\) | 6.75365 | 0.453275 | ||||||||
\(223\) | 8.83295 | 0.591498 | 0.295749 | − | 0.955266i | \(-0.404431\pi\) | ||||
0.295749 | + | 0.955266i | \(0.404431\pi\) | |||||||
\(224\) | −3.56861 | −0.238438 | ||||||||
\(225\) | −3.74032 | −0.249354 | ||||||||
\(226\) | 11.9151 | 0.792583 | ||||||||
\(227\) | 3.08551 | 0.204792 | 0.102396 | − | 0.994744i | \(-0.467349\pi\) | ||||
0.102396 | + | 0.994744i | \(0.467349\pi\) | |||||||
\(228\) | −4.32773 | −0.286611 | ||||||||
\(229\) | 17.5736 | 1.16130 | 0.580648 | − | 0.814154i | \(-0.302799\pi\) | ||||
0.580648 | + | 0.814154i | \(0.302799\pi\) | |||||||
\(230\) | −1.42920 | −0.0942389 | ||||||||
\(231\) | −13.2951 | −0.874756 | ||||||||
\(232\) | −6.88751 | −0.452187 | ||||||||
\(233\) | −10.1255 | −0.663340 | −0.331670 | − | 0.943395i | \(-0.607612\pi\) | ||||
−0.331670 | + | 0.943395i | \(0.607612\pi\) | |||||||
\(234\) | −2.99070 | −0.195508 | ||||||||
\(235\) | 2.62194 | 0.171037 | ||||||||
\(236\) | −5.71449 | −0.371982 | ||||||||
\(237\) | −20.8132 | −1.35196 | ||||||||
\(238\) | 8.27218 | 0.536206 | ||||||||
\(239\) | −1.16044 | −0.0750628 | −0.0375314 | − | 0.999295i | \(-0.511949\pi\) | ||||
−0.0375314 | + | 0.999295i | \(0.511949\pi\) | |||||||
\(240\) | 0.714562 | 0.0461247 | ||||||||
\(241\) | 5.78703 | 0.372775 | 0.186388 | − | 0.982476i | \(-0.440322\pi\) | ||||
0.186388 | + | 0.982476i | \(0.440322\pi\) | |||||||
\(242\) | −7.31724 | −0.470370 | ||||||||
\(243\) | 7.80852 | 0.500917 | ||||||||
\(244\) | 2.14757 | 0.137484 | ||||||||
\(245\) | −2.11088 | −0.134859 | ||||||||
\(246\) | 18.0890 | 1.15331 | ||||||||
\(247\) | −8.67077 | −0.551708 | ||||||||
\(248\) | 3.30935 | 0.210144 | ||||||||
\(249\) | 10.5723 | 0.669995 | ||||||||
\(250\) | 3.63085 | 0.229635 | ||||||||
\(251\) | −13.1024 | −0.827015 | −0.413507 | − | 0.910501i | \(-0.635696\pi\) | ||||
−0.413507 | + | 0.910501i | \(0.635696\pi\) | |||||||
\(252\) | −2.74389 | −0.172849 | ||||||||
\(253\) | −7.45158 | −0.468477 | ||||||||
\(254\) | 17.7895 | 1.11621 | ||||||||
\(255\) | −1.65638 | −0.103727 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.17694 | 0.510063 | 0.255032 | − | 0.966933i | \(-0.417914\pi\) | ||||
0.255032 | + | 0.966933i | \(0.417914\pi\) | |||||||
\(258\) | 18.0889 | 1.12616 | ||||||||
\(259\) | 12.4145 | 0.771401 | ||||||||
\(260\) | 1.43165 | 0.0887873 | ||||||||
\(261\) | −5.29578 | −0.327801 | ||||||||
\(262\) | 2.29304 | 0.141665 | ||||||||
\(263\) | 4.43350 | 0.273381 | 0.136691 | − | 0.990614i | \(-0.456353\pi\) | ||||
0.136691 | + | 0.990614i | \(0.456353\pi\) | |||||||
\(264\) | 3.72558 | 0.229294 | ||||||||
\(265\) | −3.00995 | −0.184900 | ||||||||
\(266\) | −7.95520 | −0.487765 | ||||||||
\(267\) | 6.04267 | 0.369805 | ||||||||
\(268\) | −8.17728 | −0.499507 | ||||||||
\(269\) | 16.2099 | 0.988338 | 0.494169 | − | 0.869366i | \(-0.335472\pi\) | ||||
0.494169 | + | 0.869366i | \(0.335472\pi\) | |||||||
\(270\) | −1.59426 | −0.0970236 | ||||||||
\(271\) | −8.15583 | −0.495431 | −0.247716 | − | 0.968833i | \(-0.579680\pi\) | ||||
−0.247716 | + | 0.968833i | \(0.579680\pi\) | |||||||
\(272\) | −2.31804 | −0.140552 | ||||||||
\(273\) | −26.9470 | −1.63091 | ||||||||
\(274\) | 16.5841 | 1.00188 | ||||||||
\(275\) | 9.33527 | 0.562938 | ||||||||
\(276\) | −7.53822 | −0.453747 | ||||||||
\(277\) | −2.96226 | −0.177985 | −0.0889926 | − | 0.996032i | \(-0.528365\pi\) | ||||
−0.0889926 | + | 0.996032i | \(0.528365\pi\) | |||||||
\(278\) | −17.5563 | −1.05295 | ||||||||
\(279\) | 2.54455 | 0.152338 | ||||||||
\(280\) | 1.31350 | 0.0784969 | ||||||||
\(281\) | −15.8704 | −0.946747 | −0.473374 | − | 0.880862i | \(-0.656964\pi\) | ||||
−0.473374 | + | 0.880862i | \(0.656964\pi\) | |||||||
\(282\) | 13.8292 | 0.823519 | ||||||||
\(283\) | 21.7775 | 1.29454 | 0.647268 | − | 0.762263i | \(-0.275912\pi\) | ||||
0.647268 | + | 0.762263i | \(0.275912\pi\) | |||||||
\(284\) | −10.1180 | −0.600396 | ||||||||
\(285\) | 1.59291 | 0.0943561 | ||||||||
\(286\) | 7.46435 | 0.441376 | ||||||||
\(287\) | 33.2512 | 1.96275 | ||||||||
\(288\) | 0.768897 | 0.0453077 | ||||||||
\(289\) | −11.6267 | −0.683922 | ||||||||
\(290\) | 2.53510 | 0.148866 | ||||||||
\(291\) | −8.48772 | −0.497559 | ||||||||
\(292\) | −7.91677 | −0.463294 | ||||||||
\(293\) | 26.2240 | 1.53203 | 0.766013 | − | 0.642826i | \(-0.222238\pi\) | ||||
0.766013 | + | 0.642826i | \(0.222238\pi\) | |||||||
\(294\) | −11.1336 | −0.649328 | ||||||||
\(295\) | 2.10334 | 0.122461 | ||||||||
\(296\) | −3.47882 | −0.202202 | ||||||||
\(297\) | −8.31215 | −0.482320 | ||||||||
\(298\) | 13.8344 | 0.801403 | ||||||||
\(299\) | −15.1031 | −0.873436 | ||||||||
\(300\) | 9.44381 | 0.545239 | ||||||||
\(301\) | 33.2509 | 1.91655 | ||||||||
\(302\) | 11.7706 | 0.677325 | ||||||||
\(303\) | −36.1758 | −2.07825 | ||||||||
\(304\) | 2.22922 | 0.127854 | ||||||||
\(305\) | −0.790461 | −0.0452616 | ||||||||
\(306\) | −1.78234 | −0.101889 | ||||||||
\(307\) | 20.0487 | 1.14424 | 0.572121 | − | 0.820170i | \(-0.306121\pi\) | ||||
0.572121 | + | 0.820170i | \(0.306121\pi\) | |||||||
\(308\) | 6.84834 | 0.390221 | ||||||||
\(309\) | −7.23343 | −0.411496 | ||||||||
\(310\) | −1.21808 | −0.0691822 | ||||||||
\(311\) | −25.0170 | −1.41858 | −0.709291 | − | 0.704916i | \(-0.750985\pi\) | ||||
−0.709291 | + | 0.704916i | \(0.750985\pi\) | |||||||
\(312\) | 7.55113 | 0.427499 | ||||||||
\(313\) | 29.9847 | 1.69484 | 0.847418 | − | 0.530926i | \(-0.178156\pi\) | ||||
0.847418 | + | 0.530926i | \(0.178156\pi\) | |||||||
\(314\) | −2.56113 | −0.144533 | ||||||||
\(315\) | 1.00995 | 0.0569042 | ||||||||
\(316\) | 10.7209 | 0.603097 | ||||||||
\(317\) | −20.8808 | −1.17278 | −0.586392 | − | 0.810027i | \(-0.699452\pi\) | ||||
−0.586392 | + | 0.810027i | \(0.699452\pi\) | |||||||
\(318\) | −15.8757 | −0.890267 | ||||||||
\(319\) | 13.2175 | 0.740037 | ||||||||
\(320\) | −0.368072 | −0.0205758 | ||||||||
\(321\) | −4.07922 | −0.227680 | ||||||||
\(322\) | −13.8567 | −0.772205 | ||||||||
\(323\) | −5.16742 | −0.287523 | ||||||||
\(324\) | −10.7155 | −0.595305 | ||||||||
\(325\) | 18.9211 | 1.04955 | ||||||||
\(326\) | 3.03303 | 0.167984 | ||||||||
\(327\) | 15.9248 | 0.880644 | ||||||||
\(328\) | −9.31768 | −0.514483 | ||||||||
\(329\) | 25.4208 | 1.40150 | ||||||||
\(330\) | −1.37128 | −0.0754865 | ||||||||
\(331\) | −5.96917 | −0.328095 | −0.164048 | − | 0.986452i | \(-0.552455\pi\) | ||||
−0.164048 | + | 0.986452i | \(0.552455\pi\) | |||||||
\(332\) | −5.44583 | −0.298879 | ||||||||
\(333\) | −2.67485 | −0.146581 | ||||||||
\(334\) | −7.10238 | −0.388625 | ||||||||
\(335\) | 3.00983 | 0.164444 | ||||||||
\(336\) | 6.92797 | 0.377952 | ||||||||
\(337\) | −24.3089 | −1.32419 | −0.662096 | − | 0.749419i | \(-0.730333\pi\) | ||||
−0.662096 | + | 0.749419i | \(0.730333\pi\) | |||||||
\(338\) | 2.12900 | 0.115802 | ||||||||
\(339\) | −23.1316 | −1.25634 | ||||||||
\(340\) | 0.853206 | 0.0462716 | ||||||||
\(341\) | −6.35081 | −0.343916 | ||||||||
\(342\) | 1.71404 | 0.0926846 | ||||||||
\(343\) | 4.51443 | 0.243756 | ||||||||
\(344\) | −9.31761 | −0.502372 | ||||||||
\(345\) | 2.77461 | 0.149380 | ||||||||
\(346\) | 21.0730 | 1.13289 | ||||||||
\(347\) | 9.89764 | 0.531333 | 0.265667 | − | 0.964065i | \(-0.414408\pi\) | ||||
0.265667 | + | 0.964065i | \(0.414408\pi\) | |||||||
\(348\) | 13.3712 | 0.716770 | ||||||||
\(349\) | −6.73425 | −0.360476 | −0.180238 | − | 0.983623i | \(-0.557687\pi\) | ||||
−0.180238 | + | 0.983623i | \(0.557687\pi\) | |||||||
\(350\) | 17.3596 | 0.927908 | ||||||||
\(351\) | −16.8474 | −0.899246 | ||||||||
\(352\) | −1.91905 | −0.102286 | ||||||||
\(353\) | −10.7229 | −0.570723 | −0.285361 | − | 0.958420i | \(-0.592114\pi\) | ||||
−0.285361 | + | 0.958420i | \(0.592114\pi\) | |||||||
\(354\) | 11.0939 | 0.589635 | ||||||||
\(355\) | 3.72417 | 0.197658 | ||||||||
\(356\) | −3.11259 | −0.164967 | ||||||||
\(357\) | −16.0593 | −0.849950 | ||||||||
\(358\) | −12.6317 | −0.667608 | ||||||||
\(359\) | 11.2548 | 0.594006 | 0.297003 | − | 0.954877i | \(-0.404013\pi\) | ||||
0.297003 | + | 0.954877i | \(0.404013\pi\) | |||||||
\(360\) | −0.283009 | −0.0149159 | ||||||||
\(361\) | −14.0306 | −0.738452 | ||||||||
\(362\) | 24.3889 | 1.28185 | ||||||||
\(363\) | 14.2054 | 0.745592 | ||||||||
\(364\) | 13.8805 | 0.727534 | ||||||||
\(365\) | 2.91394 | 0.152522 | ||||||||
\(366\) | −4.16922 | −0.217929 | ||||||||
\(367\) | 23.1135 | 1.20651 | 0.603256 | − | 0.797547i | \(-0.293870\pi\) | ||||
0.603256 | + | 0.797547i | \(0.293870\pi\) | |||||||
\(368\) | 3.88295 | 0.202413 | ||||||||
\(369\) | −7.16434 | −0.372961 | ||||||||
\(370\) | 1.28045 | 0.0665676 | ||||||||
\(371\) | −29.1827 | −1.51509 | ||||||||
\(372\) | −6.42465 | −0.333103 | ||||||||
\(373\) | 0.504509 | 0.0261225 | 0.0130613 | − | 0.999915i | \(-0.495842\pi\) | ||||
0.0130613 | + | 0.999915i | \(0.495842\pi\) | |||||||
\(374\) | 4.44845 | 0.230024 | ||||||||
\(375\) | −7.04881 | −0.363999 | ||||||||
\(376\) | −7.12346 | −0.367364 | ||||||||
\(377\) | 26.7897 | 1.37974 | ||||||||
\(378\) | −15.4570 | −0.795023 | ||||||||
\(379\) | 0.664947 | 0.0341560 | 0.0170780 | − | 0.999854i | \(-0.494564\pi\) | ||||
0.0170780 | + | 0.999854i | \(0.494564\pi\) | |||||||
\(380\) | −0.820512 | −0.0420914 | ||||||||
\(381\) | −34.5359 | −1.76933 | ||||||||
\(382\) | −11.7067 | −0.598968 | ||||||||
\(383\) | −22.9062 | −1.17045 | −0.585227 | − | 0.810870i | \(-0.698995\pi\) | ||||
−0.585227 | + | 0.810870i | \(0.698995\pi\) | |||||||
\(384\) | −1.94136 | −0.0990699 | ||||||||
\(385\) | −2.52068 | −0.128466 | ||||||||
\(386\) | 21.1088 | 1.07441 | ||||||||
\(387\) | −7.16428 | −0.364181 | ||||||||
\(388\) | 4.37204 | 0.221957 | ||||||||
\(389\) | −7.85157 | −0.398090 | −0.199045 | − | 0.979990i | \(-0.563784\pi\) | ||||
−0.199045 | + | 0.979990i | \(0.563784\pi\) | |||||||
\(390\) | −2.77936 | −0.140738 | ||||||||
\(391\) | −9.00084 | −0.455192 | ||||||||
\(392\) | 5.73496 | 0.289659 | ||||||||
\(393\) | −4.45163 | −0.224555 | ||||||||
\(394\) | −0.835550 | −0.0420944 | ||||||||
\(395\) | −3.94606 | −0.198548 | ||||||||
\(396\) | −1.47555 | −0.0741493 | ||||||||
\(397\) | −0.347756 | −0.0174534 | −0.00872668 | − | 0.999962i | \(-0.502778\pi\) | ||||
−0.00872668 | + | 0.999962i | \(0.502778\pi\) | |||||||
\(398\) | −19.2997 | −0.967408 | ||||||||
\(399\) | 15.4440 | 0.773165 | ||||||||
\(400\) | −4.86452 | −0.243226 | ||||||||
\(401\) | −9.74717 | −0.486750 | −0.243375 | − | 0.969932i | \(-0.578255\pi\) | ||||
−0.243375 | + | 0.969932i | \(0.578255\pi\) | |||||||
\(402\) | 15.8751 | 0.791777 | ||||||||
\(403\) | −12.8720 | −0.641202 | ||||||||
\(404\) | 18.6342 | 0.927087 | ||||||||
\(405\) | 3.94407 | 0.195982 | ||||||||
\(406\) | 24.5788 | 1.21983 | ||||||||
\(407\) | 6.67603 | 0.330919 | ||||||||
\(408\) | 4.50017 | 0.222791 | ||||||||
\(409\) | 16.0797 | 0.795091 | 0.397545 | − | 0.917582i | \(-0.369862\pi\) | ||||
0.397545 | + | 0.917582i | \(0.369862\pi\) | |||||||
\(410\) | 3.42958 | 0.169375 | ||||||||
\(411\) | −32.1958 | −1.58810 | ||||||||
\(412\) | 3.72595 | 0.183564 | ||||||||
\(413\) | 20.3928 | 1.00346 | ||||||||
\(414\) | 2.98559 | 0.146734 | ||||||||
\(415\) | 2.00446 | 0.0983949 | ||||||||
\(416\) | −3.88960 | −0.190703 | ||||||||
\(417\) | 34.0831 | 1.66906 | ||||||||
\(418\) | −4.27799 | −0.209243 | ||||||||
\(419\) | −25.0498 | −1.22376 | −0.611881 | − | 0.790949i | \(-0.709587\pi\) | ||||
−0.611881 | + | 0.790949i | \(0.709587\pi\) | |||||||
\(420\) | −2.54999 | −0.124427 | ||||||||
\(421\) | 28.5639 | 1.39212 | 0.696061 | − | 0.717983i | \(-0.254934\pi\) | ||||
0.696061 | + | 0.717983i | \(0.254934\pi\) | |||||||
\(422\) | −18.5858 | −0.904744 | ||||||||
\(423\) | −5.47721 | −0.266311 | ||||||||
\(424\) | 8.17762 | 0.397140 | ||||||||
\(425\) | 11.2762 | 0.546975 | ||||||||
\(426\) | 19.6428 | 0.951698 | ||||||||
\(427\) | −7.66384 | −0.370879 | ||||||||
\(428\) | 2.10121 | 0.101566 | ||||||||
\(429\) | −14.4910 | −0.699633 | ||||||||
\(430\) | 3.42955 | 0.165388 | ||||||||
\(431\) | 35.7111 | 1.72014 | 0.860071 | − | 0.510174i | \(-0.170419\pi\) | ||||
0.860071 | + | 0.510174i | \(0.170419\pi\) | |||||||
\(432\) | 4.33138 | 0.208394 | ||||||||
\(433\) | −31.9940 | −1.53753 | −0.768767 | − | 0.639529i | \(-0.779130\pi\) | ||||
−0.768767 | + | 0.639529i | \(0.779130\pi\) | |||||||
\(434\) | −11.8098 | −0.566887 | ||||||||
\(435\) | −4.92155 | −0.235970 | ||||||||
\(436\) | −8.20290 | −0.392848 | ||||||||
\(437\) | 8.65594 | 0.414070 | ||||||||
\(438\) | 15.3693 | 0.734375 | ||||||||
\(439\) | −17.7250 | −0.845966 | −0.422983 | − | 0.906138i | \(-0.639017\pi\) | ||||
−0.422983 | + | 0.906138i | \(0.639017\pi\) | |||||||
\(440\) | 0.706349 | 0.0336739 | ||||||||
\(441\) | 4.40959 | 0.209981 | ||||||||
\(442\) | 9.01626 | 0.428860 | ||||||||
\(443\) | 10.9315 | 0.519370 | 0.259685 | − | 0.965693i | \(-0.416381\pi\) | ||||
0.259685 | + | 0.965693i | \(0.416381\pi\) | |||||||
\(444\) | 6.75365 | 0.320514 | ||||||||
\(445\) | 1.14566 | 0.0543093 | ||||||||
\(446\) | 8.83295 | 0.418252 | ||||||||
\(447\) | −26.8576 | −1.27032 | ||||||||
\(448\) | −3.56861 | −0.168601 | ||||||||
\(449\) | 17.7727 | 0.838744 | 0.419372 | − | 0.907814i | \(-0.362250\pi\) | ||||
0.419372 | + | 0.907814i | \(0.362250\pi\) | |||||||
\(450\) | −3.74032 | −0.176320 | ||||||||
\(451\) | 17.8811 | 0.841989 | ||||||||
\(452\) | 11.9151 | 0.560441 | ||||||||
\(453\) | −22.8511 | −1.07364 | ||||||||
\(454\) | 3.08551 | 0.144810 | ||||||||
\(455\) | −5.10901 | −0.239514 | ||||||||
\(456\) | −4.32773 | −0.202664 | ||||||||
\(457\) | 21.9371 | 1.02618 | 0.513088 | − | 0.858336i | \(-0.328502\pi\) | ||||
0.513088 | + | 0.858336i | \(0.328502\pi\) | |||||||
\(458\) | 17.5736 | 0.821161 | ||||||||
\(459\) | −10.0403 | −0.468643 | ||||||||
\(460\) | −1.42920 | −0.0666370 | ||||||||
\(461\) | −31.8456 | −1.48320 | −0.741599 | − | 0.670843i | \(-0.765932\pi\) | ||||
−0.741599 | + | 0.670843i | \(0.765932\pi\) | |||||||
\(462\) | −13.2951 | −0.618546 | ||||||||
\(463\) | −21.8179 | −1.01397 | −0.506983 | − | 0.861956i | \(-0.669239\pi\) | ||||
−0.506983 | + | 0.861956i | \(0.669239\pi\) | |||||||
\(464\) | −6.88751 | −0.319745 | ||||||||
\(465\) | 2.36473 | 0.109662 | ||||||||
\(466\) | −10.1255 | −0.469052 | ||||||||
\(467\) | 10.0246 | 0.463881 | 0.231941 | − | 0.972730i | \(-0.425492\pi\) | ||||
0.231941 | + | 0.972730i | \(0.425492\pi\) | |||||||
\(468\) | −2.99070 | −0.138245 | ||||||||
\(469\) | 29.1815 | 1.34748 | ||||||||
\(470\) | 2.62194 | 0.120941 | ||||||||
\(471\) | 4.97208 | 0.229101 | ||||||||
\(472\) | −5.71449 | −0.263031 | ||||||||
\(473\) | 17.8810 | 0.822168 | ||||||||
\(474\) | −20.8132 | −0.955980 | ||||||||
\(475\) | −10.8441 | −0.497561 | ||||||||
\(476\) | 8.27218 | 0.379155 | ||||||||
\(477\) | 6.28775 | 0.287896 | ||||||||
\(478\) | −1.16044 | −0.0530774 | ||||||||
\(479\) | −7.55660 | −0.345270 | −0.172635 | − | 0.984986i | \(-0.555228\pi\) | ||||
−0.172635 | + | 0.984986i | \(0.555228\pi\) | |||||||
\(480\) | 0.714562 | 0.0326151 | ||||||||
\(481\) | 13.5312 | 0.616970 | ||||||||
\(482\) | 5.78703 | 0.263592 | ||||||||
\(483\) | 26.9009 | 1.22404 | ||||||||
\(484\) | −7.31724 | −0.332602 | ||||||||
\(485\) | −1.60922 | −0.0730711 | ||||||||
\(486\) | 7.80852 | 0.354201 | ||||||||
\(487\) | −11.7964 | −0.534545 | −0.267272 | − | 0.963621i | \(-0.586122\pi\) | ||||
−0.267272 | + | 0.963621i | \(0.586122\pi\) | |||||||
\(488\) | 2.14757 | 0.0972160 | ||||||||
\(489\) | −5.88821 | −0.266274 | ||||||||
\(490\) | −2.11088 | −0.0953597 | ||||||||
\(491\) | −40.3707 | −1.82190 | −0.910952 | − | 0.412513i | \(-0.864651\pi\) | ||||
−0.910952 | + | 0.412513i | \(0.864651\pi\) | |||||||
\(492\) | 18.0890 | 0.815516 | ||||||||
\(493\) | 15.9655 | 0.719052 | ||||||||
\(494\) | −8.67077 | −0.390116 | ||||||||
\(495\) | 0.543109 | 0.0244110 | ||||||||
\(496\) | 3.30935 | 0.148594 | ||||||||
\(497\) | 36.1073 | 1.61964 | ||||||||
\(498\) | 10.5723 | 0.473758 | ||||||||
\(499\) | −18.8301 | −0.842950 | −0.421475 | − | 0.906840i | \(-0.638487\pi\) | ||||
−0.421475 | + | 0.906840i | \(0.638487\pi\) | |||||||
\(500\) | 3.63085 | 0.162377 | ||||||||
\(501\) | 13.7883 | 0.616016 | ||||||||
\(502\) | −13.1024 | −0.584788 | ||||||||
\(503\) | 0.944486 | 0.0421125 | 0.0210563 | − | 0.999778i | \(-0.493297\pi\) | ||||
0.0210563 | + | 0.999778i | \(0.493297\pi\) | |||||||
\(504\) | −2.74389 | −0.122223 | ||||||||
\(505\) | −6.85873 | −0.305209 | ||||||||
\(506\) | −7.45158 | −0.331263 | ||||||||
\(507\) | −4.13316 | −0.183560 | ||||||||
\(508\) | 17.7895 | 0.789282 | ||||||||
\(509\) | −16.5720 | −0.734542 | −0.367271 | − | 0.930114i | \(-0.619708\pi\) | ||||
−0.367271 | + | 0.930114i | \(0.619708\pi\) | |||||||
\(510\) | −1.65638 | −0.0733459 | ||||||||
\(511\) | 28.2518 | 1.24979 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 9.65560 | 0.426305 | ||||||||
\(514\) | 8.17694 | 0.360669 | ||||||||
\(515\) | −1.37142 | −0.0604319 | ||||||||
\(516\) | 18.0889 | 0.796318 | ||||||||
\(517\) | 13.6703 | 0.601219 | ||||||||
\(518\) | 12.4145 | 0.545463 | ||||||||
\(519\) | −40.9103 | −1.79576 | ||||||||
\(520\) | 1.43165 | 0.0627821 | ||||||||
\(521\) | 38.4143 | 1.68296 | 0.841480 | − | 0.540289i | \(-0.181685\pi\) | ||||
0.841480 | + | 0.540289i | \(0.181685\pi\) | |||||||
\(522\) | −5.29578 | −0.231790 | ||||||||
\(523\) | 9.89196 | 0.432545 | 0.216273 | − | 0.976333i | \(-0.430610\pi\) | ||||
0.216273 | + | 0.976333i | \(0.430610\pi\) | |||||||
\(524\) | 2.29304 | 0.100172 | ||||||||
\(525\) | −33.7013 | −1.47084 | ||||||||
\(526\) | 4.43350 | 0.193310 | ||||||||
\(527\) | −7.67121 | −0.334163 | ||||||||
\(528\) | 3.72558 | 0.162135 | ||||||||
\(529\) | −7.92271 | −0.344466 | ||||||||
\(530\) | −3.00995 | −0.130744 | ||||||||
\(531\) | −4.39386 | −0.190677 | ||||||||
\(532\) | −7.95520 | −0.344902 | ||||||||
\(533\) | 36.2421 | 1.56982 | ||||||||
\(534\) | 6.04267 | 0.261492 | ||||||||
\(535\) | −0.773396 | −0.0334368 | ||||||||
\(536\) | −8.17728 | −0.353205 | ||||||||
\(537\) | 24.5228 | 1.05824 | ||||||||
\(538\) | 16.2099 | 0.698860 | ||||||||
\(539\) | −11.0057 | −0.474049 | ||||||||
\(540\) | −1.59426 | −0.0686060 | ||||||||
\(541\) | 20.9733 | 0.901714 | 0.450857 | − | 0.892596i | \(-0.351118\pi\) | ||||
0.450857 | + | 0.892596i | \(0.351118\pi\) | |||||||
\(542\) | −8.15583 | −0.350323 | ||||||||
\(543\) | −47.3478 | −2.03189 | ||||||||
\(544\) | −2.31804 | −0.0993853 | ||||||||
\(545\) | 3.01925 | 0.129331 | ||||||||
\(546\) | −26.9470 | −1.15323 | ||||||||
\(547\) | −1.97621 | −0.0844968 | −0.0422484 | − | 0.999107i | \(-0.513452\pi\) | ||||
−0.0422484 | + | 0.999107i | \(0.513452\pi\) | |||||||
\(548\) | 16.5841 | 0.708438 | ||||||||
\(549\) | 1.65126 | 0.0704741 | ||||||||
\(550\) | 9.33527 | 0.398057 | ||||||||
\(551\) | −15.3538 | −0.654092 | ||||||||
\(552\) | −7.53822 | −0.320848 | ||||||||
\(553\) | −38.2586 | −1.62692 | ||||||||
\(554\) | −2.96226 | −0.125855 | ||||||||
\(555\) | −2.48583 | −0.105518 | ||||||||
\(556\) | −17.5563 | −0.744551 | ||||||||
\(557\) | −19.3740 | −0.820904 | −0.410452 | − | 0.911882i | \(-0.634629\pi\) | ||||
−0.410452 | + | 0.911882i | \(0.634629\pi\) | |||||||
\(558\) | 2.54455 | 0.107719 | ||||||||
\(559\) | 36.2418 | 1.53286 | ||||||||
\(560\) | 1.31350 | 0.0555057 | ||||||||
\(561\) | −8.63606 | −0.364615 | ||||||||
\(562\) | −15.8704 | −0.669451 | ||||||||
\(563\) | −11.2287 | −0.473234 | −0.236617 | − | 0.971603i | \(-0.576039\pi\) | ||||
−0.236617 | + | 0.971603i | \(0.576039\pi\) | |||||||
\(564\) | 13.8292 | 0.582316 | ||||||||
\(565\) | −4.38563 | −0.184505 | ||||||||
\(566\) | 21.7775 | 0.915375 | ||||||||
\(567\) | 38.2394 | 1.60590 | ||||||||
\(568\) | −10.1180 | −0.424544 | ||||||||
\(569\) | 32.8491 | 1.37710 | 0.688552 | − | 0.725187i | \(-0.258247\pi\) | ||||
0.688552 | + | 0.725187i | \(0.258247\pi\) | |||||||
\(570\) | 1.59291 | 0.0667198 | ||||||||
\(571\) | −3.99094 | −0.167016 | −0.0835078 | − | 0.996507i | \(-0.526612\pi\) | ||||
−0.0835078 | + | 0.996507i | \(0.526612\pi\) | |||||||
\(572\) | 7.46435 | 0.312100 | ||||||||
\(573\) | 22.7270 | 0.949434 | ||||||||
\(574\) | 33.2512 | 1.38788 | ||||||||
\(575\) | −18.8887 | −0.787713 | ||||||||
\(576\) | 0.768897 | 0.0320374 | ||||||||
\(577\) | 28.4674 | 1.18511 | 0.592557 | − | 0.805529i | \(-0.298118\pi\) | ||||
0.592557 | + | 0.805529i | \(0.298118\pi\) | |||||||
\(578\) | −11.6267 | −0.483606 | ||||||||
\(579\) | −40.9798 | −1.70306 | ||||||||
\(580\) | 2.53510 | 0.105264 | ||||||||
\(581\) | 19.4340 | 0.806259 | ||||||||
\(582\) | −8.48772 | −0.351827 | ||||||||
\(583\) | −15.6933 | −0.649949 | ||||||||
\(584\) | −7.91677 | −0.327598 | ||||||||
\(585\) | 1.10079 | 0.0455122 | ||||||||
\(586\) | 26.2240 | 1.08331 | ||||||||
\(587\) | 6.07953 | 0.250929 | 0.125464 | − | 0.992098i | \(-0.459958\pi\) | ||||
0.125464 | + | 0.992098i | \(0.459958\pi\) | |||||||
\(588\) | −11.1336 | −0.459144 | ||||||||
\(589\) | 7.37726 | 0.303975 | ||||||||
\(590\) | 2.10334 | 0.0865933 | ||||||||
\(591\) | 1.62211 | 0.0667245 | ||||||||
\(592\) | −3.47882 | −0.142978 | ||||||||
\(593\) | −23.6754 | −0.972231 | −0.486116 | − | 0.873894i | \(-0.661587\pi\) | ||||
−0.486116 | + | 0.873894i | \(0.661587\pi\) | |||||||
\(594\) | −8.31215 | −0.341052 | ||||||||
\(595\) | −3.04476 | −0.124823 | ||||||||
\(596\) | 13.8344 | 0.566678 | ||||||||
\(597\) | 37.4678 | 1.53346 | ||||||||
\(598\) | −15.1031 | −0.617613 | ||||||||
\(599\) | −18.2448 | −0.745462 | −0.372731 | − | 0.927939i | \(-0.621579\pi\) | ||||
−0.372731 | + | 0.927939i | \(0.621579\pi\) | |||||||
\(600\) | 9.44381 | 0.385542 | ||||||||
\(601\) | 29.9960 | 1.22356 | 0.611781 | − | 0.791027i | \(-0.290453\pi\) | ||||
0.611781 | + | 0.791027i | \(0.290453\pi\) | |||||||
\(602\) | 33.2509 | 1.35521 | ||||||||
\(603\) | −6.28748 | −0.256046 | ||||||||
\(604\) | 11.7706 | 0.478941 | ||||||||
\(605\) | 2.69327 | 0.109497 | ||||||||
\(606\) | −36.1758 | −1.46954 | ||||||||
\(607\) | −35.7697 | −1.45185 | −0.725923 | − | 0.687776i | \(-0.758587\pi\) | ||||
−0.725923 | + | 0.687776i | \(0.758587\pi\) | |||||||
\(608\) | 2.22922 | 0.0904067 | ||||||||
\(609\) | −47.7164 | −1.93357 | ||||||||
\(610\) | −0.790461 | −0.0320048 | ||||||||
\(611\) | 27.7074 | 1.12092 | ||||||||
\(612\) | −1.78234 | −0.0720467 | ||||||||
\(613\) | 4.85430 | 0.196063 | 0.0980317 | − | 0.995183i | \(-0.468745\pi\) | ||||
0.0980317 | + | 0.995183i | \(0.468745\pi\) | |||||||
\(614\) | 20.0487 | 0.809101 | ||||||||
\(615\) | −6.65806 | −0.268479 | ||||||||
\(616\) | 6.84834 | 0.275928 | ||||||||
\(617\) | 2.80918 | 0.113093 | 0.0565467 | − | 0.998400i | \(-0.481991\pi\) | ||||
0.0565467 | + | 0.998400i | \(0.481991\pi\) | |||||||
\(618\) | −7.23343 | −0.290971 | ||||||||
\(619\) | −12.8612 | −0.516937 | −0.258468 | − | 0.966020i | \(-0.583218\pi\) | ||||
−0.258468 | + | 0.966020i | \(0.583218\pi\) | |||||||
\(620\) | −1.21808 | −0.0489192 | ||||||||
\(621\) | 16.8185 | 0.674905 | ||||||||
\(622\) | −25.0170 | −1.00309 | ||||||||
\(623\) | 11.1076 | 0.445017 | ||||||||
\(624\) | 7.55113 | 0.302287 | ||||||||
\(625\) | 22.9862 | 0.919448 | ||||||||
\(626\) | 29.9847 | 1.19843 | ||||||||
\(627\) | 8.30513 | 0.331675 | ||||||||
\(628\) | −2.56113 | −0.102200 | ||||||||
\(629\) | 8.06405 | 0.321535 | ||||||||
\(630\) | 1.00995 | 0.0402373 | ||||||||
\(631\) | −9.72097 | −0.386986 | −0.193493 | − | 0.981102i | \(-0.561982\pi\) | ||||
−0.193493 | + | 0.981102i | \(0.561982\pi\) | |||||||
\(632\) | 10.7209 | 0.426454 | ||||||||
\(633\) | 36.0819 | 1.43413 | ||||||||
\(634\) | −20.8808 | −0.829283 | ||||||||
\(635\) | −6.54782 | −0.259842 | ||||||||
\(636\) | −15.8757 | −0.629514 | ||||||||
\(637\) | −22.3067 | −0.883824 | ||||||||
\(638\) | 13.2175 | 0.523285 | ||||||||
\(639\) | −7.77973 | −0.307762 | ||||||||
\(640\) | −0.368072 | −0.0145493 | ||||||||
\(641\) | 34.6409 | 1.36823 | 0.684116 | − | 0.729373i | \(-0.260188\pi\) | ||||
0.684116 | + | 0.729373i | \(0.260188\pi\) | |||||||
\(642\) | −4.07922 | −0.160994 | ||||||||
\(643\) | 23.1065 | 0.911230 | 0.455615 | − | 0.890177i | \(-0.349419\pi\) | ||||
0.455615 | + | 0.890177i | \(0.349419\pi\) | |||||||
\(644\) | −13.8567 | −0.546031 | ||||||||
\(645\) | −6.65800 | −0.262159 | ||||||||
\(646\) | −5.16742 | −0.203310 | ||||||||
\(647\) | 40.9944 | 1.61166 | 0.805828 | − | 0.592150i | \(-0.201721\pi\) | ||||
0.805828 | + | 0.592150i | \(0.201721\pi\) | |||||||
\(648\) | −10.7155 | −0.420944 | ||||||||
\(649\) | 10.9664 | 0.430469 | ||||||||
\(650\) | 18.9211 | 0.742145 | ||||||||
\(651\) | 22.9271 | 0.898582 | ||||||||
\(652\) | 3.03303 | 0.118783 | ||||||||
\(653\) | 1.79881 | 0.0703928 | 0.0351964 | − | 0.999380i | \(-0.488794\pi\) | ||||
0.0351964 | + | 0.999380i | \(0.488794\pi\) | |||||||
\(654\) | 15.9248 | 0.622710 | ||||||||
\(655\) | −0.844004 | −0.0329780 | ||||||||
\(656\) | −9.31768 | −0.363794 | ||||||||
\(657\) | −6.08718 | −0.237483 | ||||||||
\(658\) | 25.4208 | 0.991007 | ||||||||
\(659\) | 15.7513 | 0.613584 | 0.306792 | − | 0.951777i | \(-0.400744\pi\) | ||||
0.306792 | + | 0.951777i | \(0.400744\pi\) | |||||||
\(660\) | −1.37128 | −0.0533770 | ||||||||
\(661\) | 24.2869 | 0.944651 | 0.472326 | − | 0.881424i | \(-0.343415\pi\) | ||||
0.472326 | + | 0.881424i | \(0.343415\pi\) | |||||||
\(662\) | −5.96917 | −0.231998 | ||||||||
\(663\) | −17.5039 | −0.679793 | ||||||||
\(664\) | −5.44583 | −0.211339 | ||||||||
\(665\) | 2.92809 | 0.113546 | ||||||||
\(666\) | −2.67485 | −0.103648 | ||||||||
\(667\) | −26.7438 | −1.03553 | ||||||||
\(668\) | −7.10238 | −0.274799 | ||||||||
\(669\) | −17.1480 | −0.662979 | ||||||||
\(670\) | 3.00983 | 0.116280 | ||||||||
\(671\) | −4.12130 | −0.159101 | ||||||||
\(672\) | 6.92797 | 0.267252 | ||||||||
\(673\) | 34.8560 | 1.34360 | 0.671799 | − | 0.740733i | \(-0.265522\pi\) | ||||
0.671799 | + | 0.740733i | \(0.265522\pi\) | |||||||
\(674\) | −24.3089 | −0.936346 | ||||||||
\(675\) | −21.0701 | −0.810989 | ||||||||
\(676\) | 2.12900 | 0.0818846 | ||||||||
\(677\) | 10.3717 | 0.398619 | 0.199309 | − | 0.979937i | \(-0.436130\pi\) | ||||
0.199309 | + | 0.979937i | \(0.436130\pi\) | |||||||
\(678\) | −23.1316 | −0.888365 | ||||||||
\(679\) | −15.6021 | −0.598753 | ||||||||
\(680\) | 0.853206 | 0.0327190 | ||||||||
\(681\) | −5.99009 | −0.229541 | ||||||||
\(682\) | −6.35081 | −0.243185 | ||||||||
\(683\) | −35.2014 | −1.34694 | −0.673472 | − | 0.739213i | \(-0.735198\pi\) | ||||
−0.673472 | + | 0.739213i | \(0.735198\pi\) | |||||||
\(684\) | 1.71404 | 0.0655379 | ||||||||
\(685\) | −6.10414 | −0.233227 | ||||||||
\(686\) | 4.51443 | 0.172362 | ||||||||
\(687\) | −34.1168 | −1.30164 | ||||||||
\(688\) | −9.31761 | −0.355230 | ||||||||
\(689\) | −31.8077 | −1.21178 | ||||||||
\(690\) | 2.77461 | 0.105627 | ||||||||
\(691\) | 41.0402 | 1.56124 | 0.780622 | − | 0.625003i | \(-0.214902\pi\) | ||||
0.780622 | + | 0.625003i | \(0.214902\pi\) | |||||||
\(692\) | 21.0730 | 0.801074 | ||||||||
\(693\) | 5.26567 | 0.200026 | ||||||||
\(694\) | 9.89764 | 0.375709 | ||||||||
\(695\) | 6.46196 | 0.245116 | ||||||||
\(696\) | 13.3712 | 0.506833 | ||||||||
\(697\) | 21.5988 | 0.818113 | ||||||||
\(698\) | −6.73425 | −0.254895 | ||||||||
\(699\) | 19.6572 | 0.743503 | ||||||||
\(700\) | 17.3596 | 0.656130 | ||||||||
\(701\) | 6.41561 | 0.242314 | 0.121157 | − | 0.992633i | \(-0.461339\pi\) | ||||
0.121157 | + | 0.992633i | \(0.461339\pi\) | |||||||
\(702\) | −16.8474 | −0.635863 | ||||||||
\(703\) | −7.75504 | −0.292487 | ||||||||
\(704\) | −1.91905 | −0.0723270 | ||||||||
\(705\) | −5.09015 | −0.191706 | ||||||||
\(706\) | −10.7229 | −0.403562 | ||||||||
\(707\) | −66.4982 | −2.50092 | ||||||||
\(708\) | 11.0939 | 0.416935 | ||||||||
\(709\) | 23.0074 | 0.864062 | 0.432031 | − | 0.901859i | \(-0.357797\pi\) | ||||
0.432031 | + | 0.901859i | \(0.357797\pi\) | |||||||
\(710\) | 3.72417 | 0.139766 | ||||||||
\(711\) | 8.24326 | 0.309146 | ||||||||
\(712\) | −3.11259 | −0.116649 | ||||||||
\(713\) | 12.8500 | 0.481237 | ||||||||
\(714\) | −16.0593 | −0.601005 | ||||||||
\(715\) | −2.74742 | −0.102748 | ||||||||
\(716\) | −12.6317 | −0.472070 | ||||||||
\(717\) | 2.25284 | 0.0841340 | ||||||||
\(718\) | 11.2548 | 0.420026 | ||||||||
\(719\) | 38.7884 | 1.44656 | 0.723282 | − | 0.690553i | \(-0.242633\pi\) | ||||
0.723282 | + | 0.690553i | \(0.242633\pi\) | |||||||
\(720\) | −0.283009 | −0.0105471 | ||||||||
\(721\) | −13.2965 | −0.495186 | ||||||||
\(722\) | −14.0306 | −0.522164 | ||||||||
\(723\) | −11.2347 | −0.417824 | ||||||||
\(724\) | 24.3889 | 0.906408 | ||||||||
\(725\) | 33.5044 | 1.24432 | ||||||||
\(726\) | 14.2054 | 0.527213 | ||||||||
\(727\) | 2.79495 | 0.103659 | 0.0518295 | − | 0.998656i | \(-0.483495\pi\) | ||||
0.0518295 | + | 0.998656i | \(0.483495\pi\) | |||||||
\(728\) | 13.8805 | 0.514444 | ||||||||
\(729\) | 16.9873 | 0.629159 | ||||||||
\(730\) | 2.91394 | 0.107850 | ||||||||
\(731\) | 21.5986 | 0.798854 | ||||||||
\(732\) | −4.16922 | −0.154099 | ||||||||
\(733\) | −42.3818 | −1.56541 | −0.782704 | − | 0.622394i | \(-0.786160\pi\) | ||||
−0.782704 | + | 0.622394i | \(0.786160\pi\) | |||||||
\(734\) | 23.1135 | 0.853133 | ||||||||
\(735\) | 4.09798 | 0.151156 | ||||||||
\(736\) | 3.88295 | 0.143127 | ||||||||
\(737\) | 15.6926 | 0.578045 | ||||||||
\(738\) | −7.16434 | −0.263723 | ||||||||
\(739\) | 0.853744 | 0.0314055 | 0.0157027 | − | 0.999877i | \(-0.495001\pi\) | ||||
0.0157027 | + | 0.999877i | \(0.495001\pi\) | |||||||
\(740\) | 1.28045 | 0.0470704 | ||||||||
\(741\) | 16.8331 | 0.618380 | ||||||||
\(742\) | −29.1827 | −1.07133 | ||||||||
\(743\) | −1.78970 | −0.0656577 | −0.0328288 | − | 0.999461i | \(-0.510452\pi\) | ||||
−0.0328288 | + | 0.999461i | \(0.510452\pi\) | |||||||
\(744\) | −6.42465 | −0.235539 | ||||||||
\(745\) | −5.09204 | −0.186558 | ||||||||
\(746\) | 0.504509 | 0.0184714 | ||||||||
\(747\) | −4.18728 | −0.153205 | ||||||||
\(748\) | 4.44845 | 0.162651 | ||||||||
\(749\) | −7.49840 | −0.273985 | ||||||||
\(750\) | −7.04881 | −0.257386 | ||||||||
\(751\) | −33.0545 | −1.20617 | −0.603087 | − | 0.797675i | \(-0.706063\pi\) | ||||
−0.603087 | + | 0.797675i | \(0.706063\pi\) | |||||||
\(752\) | −7.12346 | −0.259766 | ||||||||
\(753\) | 25.4365 | 0.926957 | ||||||||
\(754\) | 26.7897 | 0.975622 | ||||||||
\(755\) | −4.33244 | −0.157674 | ||||||||
\(756\) | −15.4570 | −0.562166 | ||||||||
\(757\) | −10.6843 | −0.388327 | −0.194164 | − | 0.980969i | \(-0.562199\pi\) | ||||
−0.194164 | + | 0.980969i | \(0.562199\pi\) | |||||||
\(758\) | 0.664947 | 0.0241520 | ||||||||
\(759\) | 14.4662 | 0.525091 | ||||||||
\(760\) | −0.820512 | −0.0297631 | ||||||||
\(761\) | −35.5396 | −1.28831 | −0.644154 | − | 0.764896i | \(-0.722791\pi\) | ||||
−0.644154 | + | 0.764896i | \(0.722791\pi\) | |||||||
\(762\) | −34.5359 | −1.25111 | ||||||||
\(763\) | 29.2729 | 1.05975 | ||||||||
\(764\) | −11.7067 | −0.423534 | ||||||||
\(765\) | 0.656027 | 0.0237187 | ||||||||
\(766\) | −22.9062 | −0.827636 | ||||||||
\(767\) | 22.2271 | 0.802574 | ||||||||
\(768\) | −1.94136 | −0.0700530 | ||||||||
\(769\) | 17.0629 | 0.615303 | 0.307651 | − | 0.951499i | \(-0.400457\pi\) | ||||
0.307651 | + | 0.951499i | \(0.400457\pi\) | |||||||
\(770\) | −2.52068 | −0.0908391 | ||||||||
\(771\) | −15.8744 | −0.571703 | ||||||||
\(772\) | 21.1088 | 0.759721 | ||||||||
\(773\) | −31.2002 | −1.12219 | −0.561097 | − | 0.827750i | \(-0.689621\pi\) | ||||
−0.561097 | + | 0.827750i | \(0.689621\pi\) | |||||||
\(774\) | −7.16428 | −0.257515 | ||||||||
\(775\) | −16.0984 | −0.578272 | ||||||||
\(776\) | 4.37204 | 0.156947 | ||||||||
\(777\) | −24.1011 | −0.864623 | ||||||||
\(778\) | −7.85157 | −0.281492 | ||||||||
\(779\) | −20.7712 | −0.744204 | ||||||||
\(780\) | −2.77936 | −0.0995170 | ||||||||
\(781\) | 19.4171 | 0.694797 | ||||||||
\(782\) | −9.00084 | −0.321869 | ||||||||
\(783\) | −29.8324 | −1.06612 | ||||||||
\(784\) | 5.73496 | 0.204820 | ||||||||
\(785\) | 0.942678 | 0.0336456 | ||||||||
\(786\) | −4.45163 | −0.158784 | ||||||||
\(787\) | 23.6894 | 0.844436 | 0.422218 | − | 0.906494i | \(-0.361252\pi\) | ||||
0.422218 | + | 0.906494i | \(0.361252\pi\) | |||||||
\(788\) | −0.835550 | −0.0297652 | ||||||||
\(789\) | −8.60703 | −0.306418 | ||||||||
\(790\) | −3.94606 | −0.140394 | ||||||||
\(791\) | −42.5205 | −1.51185 | ||||||||
\(792\) | −1.47555 | −0.0524315 | ||||||||
\(793\) | −8.35320 | −0.296631 | ||||||||
\(794\) | −0.347756 | −0.0123414 | ||||||||
\(795\) | 5.84341 | 0.207244 | ||||||||
\(796\) | −19.2997 | −0.684061 | ||||||||
\(797\) | −20.3125 | −0.719506 | −0.359753 | − | 0.933048i | \(-0.617139\pi\) | ||||
−0.359753 | + | 0.933048i | \(0.617139\pi\) | |||||||
\(798\) | 15.4440 | 0.546710 | ||||||||
\(799\) | 16.5125 | 0.584170 | ||||||||
\(800\) | −4.86452 | −0.171987 | ||||||||
\(801\) | −2.39326 | −0.0845617 | ||||||||
\(802\) | −9.74717 | −0.344185 | ||||||||
\(803\) | 15.1927 | 0.536138 | ||||||||
\(804\) | 15.8751 | 0.559871 | ||||||||
\(805\) | 5.10027 | 0.179761 | ||||||||
\(806\) | −12.8720 | −0.453398 | ||||||||
\(807\) | −31.4694 | −1.10778 | ||||||||
\(808\) | 18.6342 | 0.655549 | ||||||||
\(809\) | 27.5303 | 0.967912 | 0.483956 | − | 0.875092i | \(-0.339199\pi\) | ||||
0.483956 | + | 0.875092i | \(0.339199\pi\) | |||||||
\(810\) | 3.94407 | 0.138580 | ||||||||
\(811\) | −36.7980 | −1.29215 | −0.646076 | − | 0.763273i | \(-0.723591\pi\) | ||||
−0.646076 | + | 0.763273i | \(0.723591\pi\) | |||||||
\(812\) | 24.5788 | 0.862547 | ||||||||
\(813\) | 15.8334 | 0.555303 | ||||||||
\(814\) | 6.67603 | 0.233995 | ||||||||
\(815\) | −1.11637 | −0.0391048 | ||||||||
\(816\) | 4.50017 | 0.157537 | ||||||||
\(817\) | −20.7710 | −0.726685 | ||||||||
\(818\) | 16.0797 | 0.562214 | ||||||||
\(819\) | 10.6726 | 0.372932 | ||||||||
\(820\) | 3.42958 | 0.119766 | ||||||||
\(821\) | −36.7610 | −1.28297 | −0.641483 | − | 0.767137i | \(-0.721681\pi\) | ||||
−0.641483 | + | 0.767137i | \(0.721681\pi\) | |||||||
\(822\) | −32.1958 | −1.12296 | ||||||||
\(823\) | −42.2714 | −1.47349 | −0.736744 | − | 0.676172i | \(-0.763638\pi\) | ||||
−0.736744 | + | 0.676172i | \(0.763638\pi\) | |||||||
\(824\) | 3.72595 | 0.129800 | ||||||||
\(825\) | −18.1232 | −0.630968 | ||||||||
\(826\) | 20.3928 | 0.709556 | ||||||||
\(827\) | −10.7708 | −0.374536 | −0.187268 | − | 0.982309i | \(-0.559963\pi\) | ||||
−0.187268 | + | 0.982309i | \(0.559963\pi\) | |||||||
\(828\) | 2.98559 | 0.103756 | ||||||||
\(829\) | −39.5879 | −1.37494 | −0.687472 | − | 0.726211i | \(-0.741279\pi\) | ||||
−0.687472 | + | 0.726211i | \(0.741279\pi\) | |||||||
\(830\) | 2.00446 | 0.0695757 | ||||||||
\(831\) | 5.75084 | 0.199494 | ||||||||
\(832\) | −3.88960 | −0.134848 | ||||||||
\(833\) | −13.2939 | −0.460606 | ||||||||
\(834\) | 34.0831 | 1.18020 | ||||||||
\(835\) | 2.61418 | 0.0904676 | ||||||||
\(836\) | −4.27799 | −0.147957 | ||||||||
\(837\) | 14.3341 | 0.495458 | ||||||||
\(838\) | −25.0498 | −0.865331 | ||||||||
\(839\) | 27.4820 | 0.948784 | 0.474392 | − | 0.880314i | \(-0.342668\pi\) | ||||
0.474392 | + | 0.880314i | \(0.342668\pi\) | |||||||
\(840\) | −2.54999 | −0.0879830 | ||||||||
\(841\) | 18.4378 | 0.635785 | ||||||||
\(842\) | 28.5639 | 0.984379 | ||||||||
\(843\) | 30.8102 | 1.06116 | ||||||||
\(844\) | −18.5858 | −0.639751 | ||||||||
\(845\) | −0.783625 | −0.0269575 | ||||||||
\(846\) | −5.47721 | −0.188310 | ||||||||
\(847\) | 26.1124 | 0.897231 | ||||||||
\(848\) | 8.17762 | 0.280821 | ||||||||
\(849\) | −42.2780 | −1.45098 | ||||||||
\(850\) | 11.2762 | 0.386770 | ||||||||
\(851\) | −13.5081 | −0.463051 | ||||||||
\(852\) | 19.6428 | 0.672952 | ||||||||
\(853\) | 9.70272 | 0.332215 | 0.166107 | − | 0.986108i | \(-0.446880\pi\) | ||||
0.166107 | + | 0.986108i | \(0.446880\pi\) | |||||||
\(854\) | −7.66384 | −0.262251 | ||||||||
\(855\) | −0.630889 | −0.0215760 | ||||||||
\(856\) | 2.10121 | 0.0718179 | ||||||||
\(857\) | 14.3097 | 0.488809 | 0.244405 | − | 0.969673i | \(-0.421407\pi\) | ||||
0.244405 | + | 0.969673i | \(0.421407\pi\) | |||||||
\(858\) | −14.4910 | −0.494715 | ||||||||
\(859\) | −20.8000 | −0.709685 | −0.354843 | − | 0.934926i | \(-0.615466\pi\) | ||||
−0.354843 | + | 0.934926i | \(0.615466\pi\) | |||||||
\(860\) | 3.42955 | 0.116947 | ||||||||
\(861\) | −64.5526 | −2.19995 | ||||||||
\(862\) | 35.7111 | 1.21632 | ||||||||
\(863\) | 13.1248 | 0.446774 | 0.223387 | − | 0.974730i | \(-0.428289\pi\) | ||||
0.223387 | + | 0.974730i | \(0.428289\pi\) | |||||||
\(864\) | 4.33138 | 0.147357 | ||||||||
\(865\) | −7.75637 | −0.263724 | ||||||||
\(866\) | −31.9940 | −1.08720 | ||||||||
\(867\) | 22.5716 | 0.766572 | ||||||||
\(868\) | −11.8098 | −0.400849 | ||||||||
\(869\) | −20.5739 | −0.697923 | ||||||||
\(870\) | −4.92155 | −0.166856 | ||||||||
\(871\) | 31.8064 | 1.07772 | ||||||||
\(872\) | −8.20290 | −0.277785 | ||||||||
\(873\) | 3.36165 | 0.113774 | ||||||||
\(874\) | 8.65594 | 0.292791 | ||||||||
\(875\) | −12.9571 | −0.438029 | ||||||||
\(876\) | 15.3693 | 0.519282 | ||||||||
\(877\) | 38.4578 | 1.29863 | 0.649314 | − | 0.760520i | \(-0.275056\pi\) | ||||
0.649314 | + | 0.760520i | \(0.275056\pi\) | |||||||
\(878\) | −17.7250 | −0.598188 | ||||||||
\(879\) | −50.9104 | −1.71717 | ||||||||
\(880\) | 0.706349 | 0.0238110 | ||||||||
\(881\) | −58.5360 | −1.97213 | −0.986064 | − | 0.166368i | \(-0.946796\pi\) | ||||
−0.986064 | + | 0.166368i | \(0.946796\pi\) | |||||||
\(882\) | 4.40959 | 0.148479 | ||||||||
\(883\) | 0.460368 | 0.0154926 | 0.00774631 | − | 0.999970i | \(-0.497534\pi\) | ||||
0.00774631 | + | 0.999970i | \(0.497534\pi\) | |||||||
\(884\) | 9.01626 | 0.303250 | ||||||||
\(885\) | −4.08336 | −0.137261 | ||||||||
\(886\) | 10.9315 | 0.367250 | ||||||||
\(887\) | −36.3069 | −1.21907 | −0.609533 | − | 0.792761i | \(-0.708643\pi\) | ||||
−0.609533 | + | 0.792761i | \(0.708643\pi\) | |||||||
\(888\) | 6.75365 | 0.226638 | ||||||||
\(889\) | −63.4838 | −2.12918 | ||||||||
\(890\) | 1.14566 | 0.0384025 | ||||||||
\(891\) | 20.5636 | 0.688906 | ||||||||
\(892\) | 8.83295 | 0.295749 | ||||||||
\(893\) | −15.8797 | −0.531395 | ||||||||
\(894\) | −26.8576 | −0.898251 | ||||||||
\(895\) | 4.64939 | 0.155412 | ||||||||
\(896\) | −3.56861 | −0.119219 | ||||||||
\(897\) | 29.3207 | 0.978989 | ||||||||
\(898\) | 17.7727 | 0.593082 | ||||||||
\(899\) | −22.7932 | −0.760194 | ||||||||
\(900\) | −3.74032 | −0.124677 | ||||||||
\(901\) | −18.9561 | −0.631518 | ||||||||
\(902\) | 17.8811 | 0.595376 | ||||||||
\(903\) | −64.5521 | −2.14816 | ||||||||
\(904\) | 11.9151 | 0.396292 | ||||||||
\(905\) | −8.97688 | −0.298402 | ||||||||
\(906\) | −22.8511 | −0.759178 | ||||||||
\(907\) | −14.0232 | −0.465634 | −0.232817 | − | 0.972521i | \(-0.574794\pi\) | ||||
−0.232817 | + | 0.972521i | \(0.574794\pi\) | |||||||
\(908\) | 3.08551 | 0.102396 | ||||||||
\(909\) | 14.3278 | 0.475223 | ||||||||
\(910\) | −5.10901 | −0.169362 | ||||||||
\(911\) | −39.7705 | −1.31765 | −0.658827 | − | 0.752294i | \(-0.728947\pi\) | ||||
−0.658827 | + | 0.752294i | \(0.728947\pi\) | |||||||
\(912\) | −4.32773 | −0.143305 | ||||||||
\(913\) | 10.4508 | 0.345872 | ||||||||
\(914\) | 21.9371 | 0.725615 | ||||||||
\(915\) | 1.53457 | 0.0507314 | ||||||||
\(916\) | 17.5736 | 0.580648 | ||||||||
\(917\) | −8.18296 | −0.270225 | ||||||||
\(918\) | −10.0403 | −0.331380 | ||||||||
\(919\) | −48.0695 | −1.58567 | −0.792833 | − | 0.609439i | \(-0.791395\pi\) | ||||
−0.792833 | + | 0.609439i | \(0.791395\pi\) | |||||||
\(920\) | −1.42920 | −0.0471194 | ||||||||
\(921\) | −38.9219 | −1.28252 | ||||||||
\(922\) | −31.8456 | −1.04878 | ||||||||
\(923\) | 39.3552 | 1.29539 | ||||||||
\(924\) | −13.2951 | −0.437378 | ||||||||
\(925\) | 16.9228 | 0.556418 | ||||||||
\(926\) | −21.8179 | −0.716982 | ||||||||
\(927\) | 2.86487 | 0.0940948 | ||||||||
\(928\) | −6.88751 | −0.226094 | ||||||||
\(929\) | −39.0133 | −1.27998 | −0.639992 | − | 0.768382i | \(-0.721062\pi\) | ||||
−0.639992 | + | 0.768382i | \(0.721062\pi\) | |||||||
\(930\) | 2.36473 | 0.0775426 | ||||||||
\(931\) | 12.7845 | 0.418994 | ||||||||
\(932\) | −10.1255 | −0.331670 | ||||||||
\(933\) | 48.5670 | 1.59001 | ||||||||
\(934\) | 10.0246 | 0.328014 | ||||||||
\(935\) | −1.63735 | −0.0535470 | ||||||||
\(936\) | −2.99070 | −0.0977542 | ||||||||
\(937\) | −5.51911 | −0.180301 | −0.0901507 | − | 0.995928i | \(-0.528735\pi\) | ||||
−0.0901507 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(938\) | 29.1815 | 0.952810 | ||||||||
\(939\) | −58.2113 | −1.89965 | ||||||||
\(940\) | 2.62194 | 0.0855184 | ||||||||
\(941\) | −22.1329 | −0.721512 | −0.360756 | − | 0.932660i | \(-0.617481\pi\) | ||||
−0.360756 | + | 0.932660i | \(0.617481\pi\) | |||||||
\(942\) | 4.97208 | 0.161999 | ||||||||
\(943\) | −36.1801 | −1.17819 | ||||||||
\(944\) | −5.71449 | −0.185991 | ||||||||
\(945\) | 5.68929 | 0.185073 | ||||||||
\(946\) | 17.8810 | 0.581361 | ||||||||
\(947\) | −3.45336 | −0.112219 | −0.0561095 | − | 0.998425i | \(-0.517870\pi\) | ||||
−0.0561095 | + | 0.998425i | \(0.517870\pi\) | |||||||
\(948\) | −20.8132 | −0.675980 | ||||||||
\(949\) | 30.7931 | 0.999585 | ||||||||
\(950\) | −10.8441 | −0.351829 | ||||||||
\(951\) | 40.5373 | 1.31451 | ||||||||
\(952\) | 8.27218 | 0.268103 | ||||||||
\(953\) | −49.4303 | −1.60120 | −0.800602 | − | 0.599197i | \(-0.795487\pi\) | ||||
−0.800602 | + | 0.599197i | \(0.795487\pi\) | |||||||
\(954\) | 6.28775 | 0.203573 | ||||||||
\(955\) | 4.30891 | 0.139433 | ||||||||
\(956\) | −1.16044 | −0.0375314 | ||||||||
\(957\) | −25.6600 | −0.829469 | ||||||||
\(958\) | −7.55660 | −0.244143 | ||||||||
\(959\) | −59.1822 | −1.91109 | ||||||||
\(960\) | 0.714562 | 0.0230624 | ||||||||
\(961\) | −20.0482 | −0.646717 | ||||||||
\(962\) | 13.5312 | 0.436264 | ||||||||
\(963\) | 1.61561 | 0.0520624 | ||||||||
\(964\) | 5.78703 | 0.186388 | ||||||||
\(965\) | −7.76954 | −0.250110 | ||||||||
\(966\) | 26.9009 | 0.865524 | ||||||||
\(967\) | −24.6541 | −0.792824 | −0.396412 | − | 0.918073i | \(-0.629745\pi\) | ||||
−0.396412 | + | 0.918073i | \(0.629745\pi\) | |||||||
\(968\) | −7.31724 | −0.235185 | ||||||||
\(969\) | 10.0319 | 0.322270 | ||||||||
\(970\) | −1.60922 | −0.0516690 | ||||||||
\(971\) | 13.1696 | 0.422632 | 0.211316 | − | 0.977418i | \(-0.432225\pi\) | ||||
0.211316 | + | 0.977418i | \(0.432225\pi\) | |||||||
\(972\) | 7.80852 | 0.250458 | ||||||||
\(973\) | 62.6514 | 2.00851 | ||||||||
\(974\) | −11.7964 | −0.377980 | ||||||||
\(975\) | −36.7327 | −1.17639 | ||||||||
\(976\) | 2.14757 | 0.0687421 | ||||||||
\(977\) | 29.3879 | 0.940202 | 0.470101 | − | 0.882613i | \(-0.344218\pi\) | ||||
0.470101 | + | 0.882613i | \(0.344218\pi\) | |||||||
\(978\) | −5.88821 | −0.188284 | ||||||||
\(979\) | 5.97322 | 0.190905 | ||||||||
\(980\) | −2.11088 | −0.0674295 | ||||||||
\(981\) | −6.30718 | −0.201373 | ||||||||
\(982\) | −40.3707 | −1.28828 | ||||||||
\(983\) | 36.5176 | 1.16473 | 0.582366 | − | 0.812927i | \(-0.302127\pi\) | ||||
0.582366 | + | 0.812927i | \(0.302127\pi\) | |||||||
\(984\) | 18.0890 | 0.576657 | ||||||||
\(985\) | 0.307542 | 0.00979911 | ||||||||
\(986\) | 15.9655 | 0.508446 | ||||||||
\(987\) | −49.3511 | −1.57086 | ||||||||
\(988\) | −8.67077 | −0.275854 | ||||||||
\(989\) | −36.1798 | −1.15045 | ||||||||
\(990\) | 0.543109 | 0.0172612 | ||||||||
\(991\) | −50.2638 | −1.59668 | −0.798342 | − | 0.602205i | \(-0.794289\pi\) | ||||
−0.798342 | + | 0.602205i | \(0.794289\pi\) | |||||||
\(992\) | 3.30935 | 0.105072 | ||||||||
\(993\) | 11.5883 | 0.367745 | ||||||||
\(994\) | 36.1073 | 1.14526 | ||||||||
\(995\) | 7.10368 | 0.225202 | ||||||||
\(996\) | 10.5723 | 0.334997 | ||||||||
\(997\) | −32.6714 | −1.03472 | −0.517358 | − | 0.855769i | \(-0.673084\pi\) | ||||
−0.517358 | + | 0.855769i | \(0.673084\pi\) | |||||||
\(998\) | −18.8301 | −0.596055 | ||||||||
\(999\) | −15.0681 | −0.476733 |
(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.g.1.19 | ✓ | 95 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.g.1.19 | ✓ | 95 | 1.1 | even | 1 | trivial |