Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1805) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.820249\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.820249 | −0.580004 | −0.290002 | − | 0.957026i | \(-0.593656\pi\) | ||||
−0.290002 | + | 0.957026i | \(0.593656\pi\) | |||||||
\(3\) | 2.32719 | 1.34360 | 0.671802 | − | 0.740731i | \(-0.265520\pi\) | ||||
0.671802 | + | 0.740731i | \(0.265520\pi\) | |||||||
\(4\) | −1.32719 | −0.663596 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.90888 | −0.779296 | ||||||||
\(7\) | 0.561717 | 0.212309 | 0.106154 | − | 0.994350i | \(-0.466146\pi\) | ||||
0.106154 | + | 0.994350i | \(0.466146\pi\) | |||||||
\(8\) | 2.72913 | 0.964892 | ||||||||
\(9\) | 2.41582 | 0.805273 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.111092 | −0.0334955 | −0.0167478 | − | 0.999860i | \(-0.505331\pi\) | ||||
−0.0167478 | + | 0.999860i | \(0.505331\pi\) | |||||||
\(12\) | −3.08863 | −0.891610 | ||||||||
\(13\) | −6.89045 | −1.91107 | −0.955534 | − | 0.294882i | \(-0.904720\pi\) | ||||
−0.955534 | + | 0.294882i | \(0.904720\pi\) | |||||||
\(14\) | −0.460748 | −0.123140 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.415819 | 0.103955 | ||||||||
\(17\) | 3.81167 | 0.924465 | 0.462233 | − | 0.886759i | \(-0.347048\pi\) | ||||
0.462233 | + | 0.886759i | \(0.347048\pi\) | |||||||
\(18\) | −1.98157 | −0.467061 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.30722 | 0.285259 | ||||||||
\(22\) | 0.0911232 | 0.0194275 | ||||||||
\(23\) | 4.04243 | 0.842906 | 0.421453 | − | 0.906850i | \(-0.361520\pi\) | ||||
0.421453 | + | 0.906850i | \(0.361520\pi\) | |||||||
\(24\) | 6.35120 | 1.29643 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.65189 | 1.10843 | ||||||||
\(27\) | −1.35950 | −0.261636 | ||||||||
\(28\) | −0.745506 | −0.140887 | ||||||||
\(29\) | 9.29239 | 1.72555 | 0.862776 | − | 0.505586i | \(-0.168724\pi\) | ||||
0.862776 | + | 0.505586i | \(0.168724\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.18987 | −0.752524 | −0.376262 | − | 0.926513i | \(-0.622791\pi\) | ||||
−0.376262 | + | 0.926513i | \(0.622791\pi\) | |||||||
\(32\) | −5.79933 | −1.02519 | ||||||||
\(33\) | −0.258532 | −0.0450047 | ||||||||
\(34\) | −3.12652 | −0.536193 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.20625 | −0.534376 | ||||||||
\(37\) | −2.68669 | −0.441690 | −0.220845 | − | 0.975309i | \(-0.570881\pi\) | ||||
−0.220845 | + | 0.975309i | \(0.570881\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.0354 | −2.56772 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0988 | −1.57716 | −0.788580 | − | 0.614932i | \(-0.789183\pi\) | ||||
−0.788580 | + | 0.614932i | \(0.789183\pi\) | |||||||
\(42\) | −1.07225 | −0.165451 | ||||||||
\(43\) | 9.63192 | 1.46885 | 0.734427 | − | 0.678688i | \(-0.237451\pi\) | ||||
0.734427 | + | 0.678688i | \(0.237451\pi\) | |||||||
\(44\) | 0.147440 | 0.0222275 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.31580 | −0.488888 | ||||||||
\(47\) | −2.12652 | −0.310185 | −0.155092 | − | 0.987900i | \(-0.549567\pi\) | ||||
−0.155092 | + | 0.987900i | \(0.549567\pi\) | |||||||
\(48\) | 0.967690 | 0.139674 | ||||||||
\(49\) | −6.68447 | −0.954925 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.87048 | 1.24212 | ||||||||
\(52\) | 9.14494 | 1.26818 | ||||||||
\(53\) | 5.74455 | 0.789075 | 0.394537 | − | 0.918880i | \(-0.370905\pi\) | ||||
0.394537 | + | 0.918880i | \(0.370905\pi\) | |||||||
\(54\) | 1.11513 | 0.151750 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.53300 | 0.204855 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.62207 | −1.00083 | ||||||||
\(59\) | 7.89903 | 1.02837 | 0.514183 | − | 0.857680i | \(-0.328095\pi\) | ||||
0.514183 | + | 0.857680i | \(0.328095\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.56575 | 0.712622 | 0.356311 | − | 0.934367i | \(-0.384034\pi\) | ||||
0.356311 | + | 0.934367i | \(0.384034\pi\) | |||||||
\(62\) | 3.43674 | 0.436467 | ||||||||
\(63\) | 1.35701 | 0.170967 | ||||||||
\(64\) | 3.92526 | 0.490657 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.212061 | 0.0261029 | ||||||||
\(67\) | 10.6534 | 1.30152 | 0.650762 | − | 0.759282i | \(-0.274450\pi\) | ||||
0.650762 | + | 0.759282i | \(0.274450\pi\) | |||||||
\(68\) | −5.05881 | −0.613471 | ||||||||
\(69\) | 9.40752 | 1.13253 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.64050 | −0.788082 | −0.394041 | − | 0.919093i | \(-0.628923\pi\) | ||||
−0.394041 | + | 0.919093i | \(0.628923\pi\) | |||||||
\(72\) | 6.59307 | 0.777001 | ||||||||
\(73\) | 8.45825 | 0.989964 | 0.494982 | − | 0.868903i | \(-0.335175\pi\) | ||||
0.494982 | + | 0.868903i | \(0.335175\pi\) | |||||||
\(74\) | 2.20376 | 0.256182 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0624023 | −0.00711140 | ||||||||
\(78\) | 13.1530 | 1.48929 | ||||||||
\(79\) | −6.27087 | −0.705528 | −0.352764 | − | 0.935712i | \(-0.614758\pi\) | ||||
−0.352764 | + | 0.935712i | \(0.614758\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.4113 | −1.15681 | ||||||||
\(82\) | 8.28349 | 0.914759 | ||||||||
\(83\) | 8.16132 | 0.895822 | 0.447911 | − | 0.894078i | \(-0.352168\pi\) | ||||
0.447911 | + | 0.894078i | \(0.352168\pi\) | |||||||
\(84\) | −1.73493 | −0.189297 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.90057 | −0.851941 | ||||||||
\(87\) | 21.6252 | 2.31846 | ||||||||
\(88\) | −0.303184 | −0.0323196 | ||||||||
\(89\) | 1.16741 | 0.123745 | 0.0618726 | − | 0.998084i | \(-0.480293\pi\) | ||||
0.0618726 | + | 0.998084i | \(0.480293\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.87048 | −0.405737 | ||||||||
\(92\) | −5.36508 | −0.559348 | ||||||||
\(93\) | −9.75064 | −1.01109 | ||||||||
\(94\) | 1.74428 | 0.179908 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −13.4961 | −1.37744 | ||||||||
\(97\) | 8.24746 | 0.837402 | 0.418701 | − | 0.908124i | \(-0.362485\pi\) | ||||
0.418701 | + | 0.908124i | \(0.362485\pi\) | |||||||
\(98\) | 5.48294 | 0.553860 | ||||||||
\(99\) | −0.268378 | −0.0269730 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.7400 | −1.16817 | −0.584087 | − | 0.811691i | \(-0.698547\pi\) | ||||
−0.584087 | + | 0.811691i | \(0.698547\pi\) | |||||||
\(102\) | −7.27601 | −0.720432 | ||||||||
\(103\) | 19.4676 | 1.91820 | 0.959099 | − | 0.283069i | \(-0.0913526\pi\) | ||||
0.959099 | + | 0.283069i | \(0.0913526\pi\) | |||||||
\(104\) | −18.8049 | −1.84397 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.71196 | −0.457666 | ||||||||
\(107\) | −16.5648 | −1.60138 | −0.800690 | − | 0.599079i | \(-0.795534\pi\) | ||||
−0.800690 | + | 0.599079i | \(0.795534\pi\) | |||||||
\(108\) | 1.80432 | 0.173621 | ||||||||
\(109\) | 14.0588 | 1.34659 | 0.673295 | − | 0.739374i | \(-0.264878\pi\) | ||||
0.673295 | + | 0.739374i | \(0.264878\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.25245 | −0.593456 | ||||||||
\(112\) | 0.233572 | 0.0220705 | ||||||||
\(113\) | −8.88950 | −0.836254 | −0.418127 | − | 0.908389i | \(-0.637313\pi\) | ||||
−0.418127 | + | 0.908389i | \(0.637313\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.3328 | −1.14507 | ||||||||
\(117\) | −16.6461 | −1.53893 | ||||||||
\(118\) | −6.47917 | −0.596456 | ||||||||
\(119\) | 2.14108 | 0.196272 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9877 | −0.998878 | ||||||||
\(122\) | −4.56531 | −0.413323 | ||||||||
\(123\) | −23.5017 | −2.11908 | ||||||||
\(124\) | 5.56076 | 0.499371 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.11308 | −0.0991613 | ||||||||
\(127\) | 7.76469 | 0.689005 | 0.344503 | − | 0.938785i | \(-0.388048\pi\) | ||||
0.344503 | + | 0.938785i | \(0.388048\pi\) | |||||||
\(128\) | 8.37897 | 0.740603 | ||||||||
\(129\) | 22.4153 | 1.97356 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.58042 | −0.400193 | −0.200097 | − | 0.979776i | \(-0.564126\pi\) | ||||
−0.200097 | + | 0.979776i | \(0.564126\pi\) | |||||||
\(132\) | 0.343122 | 0.0298649 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.73847 | −0.754889 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.4025 | 0.892009 | ||||||||
\(137\) | −1.19518 | −0.102111 | −0.0510554 | − | 0.998696i | \(-0.516259\pi\) | ||||
−0.0510554 | + | 0.998696i | \(0.516259\pi\) | |||||||
\(138\) | −7.71651 | −0.656873 | ||||||||
\(139\) | 8.06036 | 0.683670 | 0.341835 | − | 0.939760i | \(-0.388952\pi\) | ||||
0.341835 | + | 0.939760i | \(0.388952\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.94881 | −0.416765 | ||||||||
\(142\) | 5.44686 | 0.457091 | ||||||||
\(143\) | 0.765474 | 0.0640122 | ||||||||
\(144\) | 1.00454 | 0.0837119 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.93787 | −0.574183 | ||||||||
\(147\) | −15.5560 | −1.28304 | ||||||||
\(148\) | 3.56575 | 0.293103 | ||||||||
\(149\) | 9.89499 | 0.810629 | 0.405315 | − | 0.914177i | \(-0.367162\pi\) | ||||
0.405315 | + | 0.914177i | \(0.367162\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.7413 | −1.68790 | −0.843951 | − | 0.536421i | \(-0.819776\pi\) | ||||
−0.843951 | + | 0.536421i | \(0.819776\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.20830 | 0.744447 | ||||||||
\(154\) | 0.0511854 | 0.00412464 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 21.2820 | 1.70393 | ||||||||
\(157\) | 12.9092 | 1.03026 | 0.515131 | − | 0.857111i | \(-0.327743\pi\) | ||||
0.515131 | + | 0.857111i | \(0.327743\pi\) | |||||||
\(158\) | 5.14368 | 0.409209 | ||||||||
\(159\) | 13.3687 | 1.06020 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.27070 | 0.178956 | ||||||||
\(162\) | 8.53984 | 0.670953 | ||||||||
\(163\) | 7.93134 | 0.621231 | 0.310615 | − | 0.950536i | \(-0.399465\pi\) | ||||
0.310615 | + | 0.950536i | \(0.399465\pi\) | |||||||
\(164\) | 13.4030 | 1.04660 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.69432 | −0.519580 | ||||||||
\(167\) | −5.69132 | −0.440408 | −0.220204 | − | 0.975454i | \(-0.570672\pi\) | ||||
−0.220204 | + | 0.975454i | \(0.570672\pi\) | |||||||
\(168\) | 3.56757 | 0.275244 | ||||||||
\(169\) | 34.4783 | 2.65218 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.7834 | −0.974725 | ||||||||
\(173\) | 7.12043 | 0.541357 | 0.270678 | − | 0.962670i | \(-0.412752\pi\) | ||||
0.270678 | + | 0.962670i | \(0.412752\pi\) | |||||||
\(174\) | −17.7380 | −1.34472 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.0461942 | −0.00348202 | ||||||||
\(177\) | 18.3826 | 1.38172 | ||||||||
\(178\) | −0.957567 | −0.0717727 | ||||||||
\(179\) | −2.37647 | −0.177626 | −0.0888129 | − | 0.996048i | \(-0.528307\pi\) | ||||
−0.0888129 | + | 0.996048i | \(0.528307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.1766 | 1.49971 | 0.749857 | − | 0.661600i | \(-0.230122\pi\) | ||||
0.749857 | + | 0.661600i | \(0.230122\pi\) | |||||||
\(182\) | 3.17476 | 0.235329 | ||||||||
\(183\) | 12.9526 | 0.957482 | ||||||||
\(184\) | 11.0323 | 0.813313 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.99795 | 0.586438 | ||||||||
\(187\) | −0.423446 | −0.0309655 | ||||||||
\(188\) | 2.82230 | 0.205837 | ||||||||
\(189\) | −0.763655 | −0.0555477 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.88950 | 0.715579 | 0.357789 | − | 0.933802i | \(-0.383531\pi\) | ||||
0.357789 | + | 0.933802i | \(0.383531\pi\) | |||||||
\(192\) | 9.13482 | 0.659249 | ||||||||
\(193\) | 4.55092 | 0.327582 | 0.163791 | − | 0.986495i | \(-0.447628\pi\) | ||||
0.163791 | + | 0.986495i | \(0.447628\pi\) | |||||||
\(194\) | −6.76497 | −0.485697 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.87158 | 0.633684 | ||||||||
\(197\) | 12.4701 | 0.888457 | 0.444229 | − | 0.895914i | \(-0.353478\pi\) | ||||
0.444229 | + | 0.895914i | \(0.353478\pi\) | |||||||
\(198\) | 0.220137 | 0.0156445 | ||||||||
\(199\) | −19.9932 | −1.41728 | −0.708642 | − | 0.705569i | \(-0.750692\pi\) | ||||
−0.708642 | + | 0.705569i | \(0.750692\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.7926 | 1.74873 | ||||||||
\(202\) | 9.62973 | 0.677546 | ||||||||
\(203\) | 5.21969 | 0.366350 | ||||||||
\(204\) | −11.7728 | −0.824263 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −15.9683 | −1.11256 | ||||||||
\(207\) | 9.76579 | 0.678769 | ||||||||
\(208\) | −2.86518 | −0.198664 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8102 | 1.15726 | 0.578631 | − | 0.815589i | \(-0.303587\pi\) | ||||
0.578631 | + | 0.815589i | \(0.303587\pi\) | |||||||
\(212\) | −7.62412 | −0.523627 | ||||||||
\(213\) | −15.4537 | −1.05887 | ||||||||
\(214\) | 13.5873 | 0.928806 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.71025 | −0.252451 | ||||||||
\(217\) | −2.35352 | −0.159768 | ||||||||
\(218\) | −11.5317 | −0.781027 | ||||||||
\(219\) | 19.6840 | 1.33012 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.2641 | −1.76672 | ||||||||
\(222\) | 5.12857 | 0.344207 | ||||||||
\(223\) | 1.88641 | 0.126324 | 0.0631618 | − | 0.998003i | \(-0.479882\pi\) | ||||
0.0631618 | + | 0.998003i | \(0.479882\pi\) | |||||||
\(224\) | −3.25758 | −0.217656 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.29160 | 0.485030 | ||||||||
\(227\) | 10.7044 | 0.710479 | 0.355239 | − | 0.934775i | \(-0.384399\pi\) | ||||
0.355239 | + | 0.934775i | \(0.384399\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.34388 | 0.551379 | 0.275690 | − | 0.961247i | \(-0.411094\pi\) | ||||
0.275690 | + | 0.961247i | \(0.411094\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.145222 | −0.00955491 | ||||||||
\(232\) | 25.3601 | 1.66497 | ||||||||
\(233\) | 2.14436 | 0.140481 | 0.0702407 | − | 0.997530i | \(-0.477623\pi\) | ||||
0.0702407 | + | 0.997530i | \(0.477623\pi\) | |||||||
\(234\) | 13.6539 | 0.892586 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.4835 | −0.682419 | ||||||||
\(237\) | −14.5935 | −0.947951 | ||||||||
\(238\) | −1.75622 | −0.113839 | ||||||||
\(239\) | 25.0796 | 1.62227 | 0.811134 | − | 0.584861i | \(-0.198851\pi\) | ||||
0.811134 | + | 0.584861i | \(0.198851\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3527 | 0.731294 | 0.365647 | − | 0.930754i | \(-0.380848\pi\) | ||||
0.365647 | + | 0.930754i | \(0.380848\pi\) | |||||||
\(242\) | 9.01262 | 0.579353 | ||||||||
\(243\) | −20.1505 | −1.29266 | ||||||||
\(244\) | −7.38682 | −0.472893 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 19.2773 | 1.22907 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −11.4347 | −0.726104 | ||||||||
\(249\) | 18.9930 | 1.20363 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.92245 | −0.436941 | −0.218471 | − | 0.975844i | \(-0.570107\pi\) | ||||
−0.218471 | + | 0.975844i | \(0.570107\pi\) | |||||||
\(252\) | −1.80101 | −0.113453 | ||||||||
\(253\) | −0.449082 | −0.0282336 | ||||||||
\(254\) | −6.36898 | −0.399626 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.7234 | −0.920210 | ||||||||
\(257\) | −1.89721 | −0.118345 | −0.0591724 | − | 0.998248i | \(-0.518846\pi\) | ||||
−0.0591724 | + | 0.998248i | \(0.518846\pi\) | |||||||
\(258\) | −18.3861 | −1.14467 | ||||||||
\(259\) | −1.50916 | −0.0937747 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.4487 | 1.38954 | ||||||||
\(262\) | 3.75709 | 0.232114 | ||||||||
\(263\) | 11.5446 | 0.711868 | 0.355934 | − | 0.934511i | \(-0.384163\pi\) | ||||
0.355934 | + | 0.934511i | \(0.384163\pi\) | |||||||
\(264\) | −0.705568 | −0.0434247 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.71678 | 0.166265 | ||||||||
\(268\) | −14.1391 | −0.863685 | ||||||||
\(269\) | −3.02056 | −0.184167 | −0.0920833 | − | 0.995751i | \(-0.529353\pi\) | ||||
−0.0920833 | + | 0.995751i | \(0.529353\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.81150 | 0.535260 | 0.267630 | − | 0.963522i | \(-0.413759\pi\) | ||||
0.267630 | + | 0.963522i | \(0.413759\pi\) | |||||||
\(272\) | 1.58496 | 0.0961025 | ||||||||
\(273\) | −9.00735 | −0.545150 | ||||||||
\(274\) | 0.980343 | 0.0592247 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.4856 | −0.751543 | ||||||||
\(277\) | 9.68919 | 0.582167 | 0.291083 | − | 0.956698i | \(-0.405984\pi\) | ||||
0.291083 | + | 0.956698i | \(0.405984\pi\) | |||||||
\(278\) | −6.61150 | −0.396531 | ||||||||
\(279\) | −10.1220 | −0.605987 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.6762 | −1.11413 | −0.557063 | − | 0.830470i | \(-0.688072\pi\) | ||||
−0.557063 | + | 0.830470i | \(0.688072\pi\) | |||||||
\(282\) | 4.05926 | 0.241726 | ||||||||
\(283\) | 7.46451 | 0.443719 | 0.221859 | − | 0.975079i | \(-0.428787\pi\) | ||||
0.221859 | + | 0.975079i | \(0.428787\pi\) | |||||||
\(284\) | 8.81321 | 0.522968 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.627880 | −0.0371273 | ||||||||
\(287\) | −5.67264 | −0.334845 | ||||||||
\(288\) | −14.0101 | −0.825554 | ||||||||
\(289\) | −2.47118 | −0.145364 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.1934 | 1.12514 | ||||||||
\(292\) | −11.2257 | −0.656935 | ||||||||
\(293\) | 3.73771 | 0.218359 | 0.109180 | − | 0.994022i | \(-0.465178\pi\) | ||||
0.109180 | + | 0.994022i | \(0.465178\pi\) | |||||||
\(294\) | 12.7598 | 0.744169 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.33232 | −0.426183 | ||||||||
\(297\) | 0.151030 | 0.00876364 | ||||||||
\(298\) | −8.11636 | −0.470168 | ||||||||
\(299\) | −27.8542 | −1.61085 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.41041 | 0.311851 | ||||||||
\(302\) | 17.0130 | 0.978989 | ||||||||
\(303\) | −27.3212 | −1.56956 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.55310 | −0.431782 | ||||||||
\(307\) | −23.2825 | −1.32880 | −0.664402 | − | 0.747375i | \(-0.731314\pi\) | ||||
−0.664402 | + | 0.747375i | \(0.731314\pi\) | |||||||
\(308\) | 0.0828198 | 0.00471909 | ||||||||
\(309\) | 45.3048 | 2.57730 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.4553 | 1.33003 | 0.665013 | − | 0.746832i | \(-0.268426\pi\) | ||||
0.665013 | + | 0.746832i | \(0.268426\pi\) | |||||||
\(312\) | −43.7626 | −2.47757 | ||||||||
\(313\) | 15.0079 | 0.848297 | 0.424148 | − | 0.905593i | \(-0.360573\pi\) | ||||
0.424148 | + | 0.905593i | \(0.360573\pi\) | |||||||
\(314\) | −10.5887 | −0.597556 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.32265 | 0.468186 | ||||||||
\(317\) | 19.3000 | 1.08400 | 0.541998 | − | 0.840380i | \(-0.317668\pi\) | ||||
0.541998 | + | 0.840380i | \(0.317668\pi\) | |||||||
\(318\) | −10.9656 | −0.614923 | ||||||||
\(319\) | −1.03231 | −0.0577983 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −38.5495 | −2.15162 | ||||||||
\(322\) | −1.86254 | −0.103795 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 13.8178 | 0.767653 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.50568 | −0.360316 | ||||||||
\(327\) | 32.7175 | 1.80928 | ||||||||
\(328\) | −27.5608 | −1.52179 | ||||||||
\(329\) | −1.19450 | −0.0658550 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.1303 | 1.05150 | 0.525748 | − | 0.850641i | \(-0.323786\pi\) | ||||
0.525748 | + | 0.850641i | \(0.323786\pi\) | |||||||
\(332\) | −10.8316 | −0.594463 | ||||||||
\(333\) | −6.49056 | −0.355681 | ||||||||
\(334\) | 4.66830 | 0.255438 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.543568 | 0.0296540 | ||||||||
\(337\) | −25.5100 | −1.38962 | −0.694810 | − | 0.719193i | \(-0.744511\pi\) | ||||
−0.694810 | + | 0.719193i | \(0.744511\pi\) | |||||||
\(338\) | −28.2808 | −1.53827 | ||||||||
\(339\) | −20.6876 | −1.12359 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.465462 | 0.0252062 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.68680 | −0.415048 | ||||||||
\(344\) | 26.2867 | 1.41728 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.84053 | −0.313989 | ||||||||
\(347\) | 34.3847 | 1.84587 | 0.922933 | − | 0.384960i | \(-0.125785\pi\) | ||||
0.922933 | + | 0.384960i | \(0.125785\pi\) | |||||||
\(348\) | −28.7007 | −1.53852 | ||||||||
\(349\) | −28.6428 | −1.53321 | −0.766607 | − | 0.642117i | \(-0.778057\pi\) | ||||
−0.766607 | + | 0.642117i | \(0.778057\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.36758 | 0.500004 | ||||||||
\(352\) | 0.644259 | 0.0343391 | ||||||||
\(353\) | −23.5203 | −1.25186 | −0.625930 | − | 0.779879i | \(-0.715281\pi\) | ||||
−0.625930 | + | 0.779879i | \(0.715281\pi\) | |||||||
\(354\) | −15.0783 | −0.801401 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.54938 | −0.0821167 | ||||||||
\(357\) | 4.98270 | 0.263712 | ||||||||
\(358\) | 1.94930 | 0.103024 | ||||||||
\(359\) | 9.77437 | 0.515871 | 0.257936 | − | 0.966162i | \(-0.416958\pi\) | ||||
0.257936 | + | 0.966162i | \(0.416958\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −16.5498 | −0.869839 | ||||||||
\(363\) | −25.5704 | −1.34210 | ||||||||
\(364\) | 5.13687 | 0.269245 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10.6243 | −0.555343 | ||||||||
\(367\) | 2.03857 | 0.106412 | 0.0532062 | − | 0.998584i | \(-0.483056\pi\) | ||||
0.0532062 | + | 0.998584i | \(0.483056\pi\) | |||||||
\(368\) | 1.68092 | 0.0876240 | ||||||||
\(369\) | −24.3968 | −1.27004 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.22681 | 0.167528 | ||||||||
\(372\) | 12.9410 | 0.670958 | ||||||||
\(373\) | 12.9613 | 0.671110 | 0.335555 | − | 0.942021i | \(-0.391076\pi\) | ||||
0.335555 | + | 0.942021i | \(0.391076\pi\) | |||||||
\(374\) | 0.347331 | 0.0179601 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.80354 | −0.299295 | ||||||||
\(377\) | −64.0287 | −3.29765 | ||||||||
\(378\) | 0.626387 | 0.0322179 | ||||||||
\(379\) | −6.82911 | −0.350788 | −0.175394 | − | 0.984498i | \(-0.556120\pi\) | ||||
−0.175394 | + | 0.984498i | \(0.556120\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.0699 | 0.925750 | ||||||||
\(382\) | −8.11185 | −0.415038 | ||||||||
\(383\) | 17.1311 | 0.875356 | 0.437678 | − | 0.899132i | \(-0.355801\pi\) | ||||
0.437678 | + | 0.899132i | \(0.355801\pi\) | |||||||
\(384\) | 19.4995 | 0.995077 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.73289 | −0.189999 | ||||||||
\(387\) | 23.2690 | 1.18283 | ||||||||
\(388\) | −10.9460 | −0.555696 | ||||||||
\(389\) | 18.4370 | 0.934794 | 0.467397 | − | 0.884048i | \(-0.345192\pi\) | ||||
0.467397 | + | 0.884048i | \(0.345192\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.4084 | 0.779237 | ||||||||
\(392\) | −18.2428 | −0.921399 | ||||||||
\(393\) | −10.6595 | −0.537701 | ||||||||
\(394\) | −10.2286 | −0.515308 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.356189 | 0.0178992 | ||||||||
\(397\) | 3.44622 | 0.172961 | 0.0864805 | − | 0.996254i | \(-0.472438\pi\) | ||||
0.0864805 | + | 0.996254i | \(0.472438\pi\) | |||||||
\(398\) | 16.3994 | 0.822030 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.4272 | −0.620585 | −0.310293 | − | 0.950641i | \(-0.600427\pi\) | ||||
−0.310293 | + | 0.950641i | \(0.600427\pi\) | |||||||
\(402\) | −20.3361 | −1.01427 | ||||||||
\(403\) | 28.8701 | 1.43812 | ||||||||
\(404\) | 15.5812 | 0.775196 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.28145 | −0.212485 | ||||||||
\(407\) | 0.298470 | 0.0147946 | ||||||||
\(408\) | 24.2087 | 1.19851 | ||||||||
\(409\) | −2.53190 | −0.125194 | −0.0625972 | − | 0.998039i | \(-0.519938\pi\) | ||||
−0.0625972 | + | 0.998039i | \(0.519938\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.78141 | −0.137197 | ||||||||
\(412\) | −25.8372 | −1.27291 | ||||||||
\(413\) | 4.43702 | 0.218331 | ||||||||
\(414\) | −8.01038 | −0.393689 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 39.9600 | 1.95920 | ||||||||
\(417\) | 18.7580 | 0.918583 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.647537 | 0.0316342 | 0.0158171 | − | 0.999875i | \(-0.494965\pi\) | ||||
0.0158171 | + | 0.999875i | \(0.494965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.37148 | −0.213053 | −0.106526 | − | 0.994310i | \(-0.533973\pi\) | ||||
−0.106526 | + | 0.994310i | \(0.533973\pi\) | |||||||
\(422\) | −13.7886 | −0.671217 | ||||||||
\(423\) | −5.13728 | −0.249783 | ||||||||
\(424\) | 15.6776 | 0.761372 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.6759 | 0.614149 | ||||||||
\(427\) | 3.12638 | 0.151296 | ||||||||
\(428\) | 21.9847 | 1.06267 | ||||||||
\(429\) | 1.78141 | 0.0860071 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.0094 | −1.44550 | −0.722752 | − | 0.691107i | \(-0.757123\pi\) | ||||
−0.722752 | + | 0.691107i | \(0.757123\pi\) | |||||||
\(432\) | −0.565306 | −0.0271983 | ||||||||
\(433\) | 17.6077 | 0.846173 | 0.423086 | − | 0.906089i | \(-0.360947\pi\) | ||||
0.423086 | + | 0.906089i | \(0.360947\pi\) | |||||||
\(434\) | 1.93047 | 0.0926658 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.6587 | −0.893591 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −16.1458 | −0.771474 | ||||||||
\(439\) | −25.8827 | −1.23532 | −0.617658 | − | 0.786447i | \(-0.711918\pi\) | ||||
−0.617658 | + | 0.786447i | \(0.711918\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.1485 | −0.768975 | ||||||||
\(442\) | 21.5431 | 1.02470 | ||||||||
\(443\) | −11.8766 | −0.564273 | −0.282136 | − | 0.959374i | \(-0.591043\pi\) | ||||
−0.282136 | + | 0.959374i | \(0.591043\pi\) | |||||||
\(444\) | 8.29819 | 0.393815 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.54733 | −0.0732681 | ||||||||
\(447\) | 23.0275 | 1.08917 | ||||||||
\(448\) | 2.20488 | 0.104171 | ||||||||
\(449\) | −29.4524 | −1.38995 | −0.694973 | − | 0.719035i | \(-0.744584\pi\) | ||||
−0.694973 | + | 0.719035i | \(0.744584\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.12189 | 0.0528278 | ||||||||
\(452\) | 11.7981 | 0.554934 | ||||||||
\(453\) | −48.2689 | −2.26787 | ||||||||
\(454\) | −8.78031 | −0.412080 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.3329 | −1.13825 | −0.569123 | − | 0.822253i | \(-0.692717\pi\) | ||||
−0.569123 | + | 0.822253i | \(0.692717\pi\) | |||||||
\(458\) | −6.84406 | −0.319802 | ||||||||
\(459\) | −5.18197 | −0.241874 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.5042 | 1.60702 | 0.803511 | − | 0.595290i | \(-0.202963\pi\) | ||||
0.803511 | + | 0.595290i | \(0.202963\pi\) | |||||||
\(462\) | 0.119118 | 0.00554188 | ||||||||
\(463\) | 4.89328 | 0.227410 | 0.113705 | − | 0.993515i | \(-0.463728\pi\) | ||||
0.113705 | + | 0.993515i | \(0.463728\pi\) | |||||||
\(464\) | 3.86395 | 0.179379 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.75891 | −0.0814798 | ||||||||
\(467\) | −15.6840 | −0.725769 | −0.362885 | − | 0.931834i | \(-0.618208\pi\) | ||||
−0.362885 | + | 0.931834i | \(0.618208\pi\) | |||||||
\(468\) | 22.0925 | 1.02123 | ||||||||
\(469\) | 5.98421 | 0.276325 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.0421 | 1.38427 | ||||||||
\(472\) | 21.5575 | 0.992262 | ||||||||
\(473\) | −1.07003 | −0.0492000 | ||||||||
\(474\) | 11.9703 | 0.549815 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.84162 | −0.130245 | ||||||||
\(477\) | 13.8778 | 0.635421 | ||||||||
\(478\) | −20.5716 | −0.940921 | ||||||||
\(479\) | 15.1666 | 0.692981 | 0.346490 | − | 0.938054i | \(-0.387373\pi\) | ||||
0.346490 | + | 0.938054i | \(0.387373\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.5125 | 0.844098 | ||||||||
\(482\) | −9.31208 | −0.424153 | ||||||||
\(483\) | 5.28436 | 0.240447 | ||||||||
\(484\) | 14.5827 | 0.662851 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 16.5285 | 0.749746 | ||||||||
\(487\) | 14.8366 | 0.672312 | 0.336156 | − | 0.941806i | \(-0.390873\pi\) | ||||
0.336156 | + | 0.941806i | \(0.390873\pi\) | |||||||
\(488\) | 15.1896 | 0.687603 | ||||||||
\(489\) | 18.4577 | 0.834688 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.7022 | 0.979408 | 0.489704 | − | 0.871889i | \(-0.337105\pi\) | ||||
0.489704 | + | 0.871889i | \(0.337105\pi\) | |||||||
\(492\) | 31.1913 | 1.40621 | ||||||||
\(493\) | 35.4195 | 1.59521 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.74223 | −0.0782283 | ||||||||
\(497\) | −3.73008 | −0.167317 | ||||||||
\(498\) | −15.5790 | −0.698110 | ||||||||
\(499\) | −20.5764 | −0.921124 | −0.460562 | − | 0.887627i | \(-0.652352\pi\) | ||||
−0.460562 | + | 0.887627i | \(0.652352\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.2448 | −0.591734 | ||||||||
\(502\) | 5.67813 | 0.253427 | ||||||||
\(503\) | 34.8559 | 1.55415 | 0.777074 | − | 0.629409i | \(-0.216703\pi\) | ||||
0.777074 | + | 0.629409i | \(0.216703\pi\) | |||||||
\(504\) | 3.70344 | 0.164964 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.368359 | 0.0163756 | ||||||||
\(507\) | 80.2376 | 3.56348 | ||||||||
\(508\) | −10.3052 | −0.457221 | ||||||||
\(509\) | 30.7078 | 1.36110 | 0.680551 | − | 0.732701i | \(-0.261741\pi\) | ||||
0.680551 | + | 0.732701i | \(0.261741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.75114 | 0.210178 | ||||||||
\(512\) | −4.68111 | −0.206878 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.55619 | 0.0686404 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −29.7494 | −1.30964 | ||||||||
\(517\) | 0.236239 | 0.0103898 | ||||||||
\(518\) | 1.23789 | 0.0543897 | ||||||||
\(519\) | 16.5706 | 0.727369 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.9533 | 0.479874 | 0.239937 | − | 0.970788i | \(-0.422873\pi\) | ||||
0.239937 | + | 0.970788i | \(0.422873\pi\) | |||||||
\(522\) | −18.4135 | −0.805939 | ||||||||
\(523\) | −4.44485 | −0.194360 | −0.0971799 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971799 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(524\) | 6.07909 | 0.265566 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.46941 | −0.412886 | ||||||||
\(527\) | −15.9704 | −0.695682 | ||||||||
\(528\) | −0.107503 | −0.00467845 | ||||||||
\(529\) | −6.65873 | −0.289510 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.0826 | 0.828115 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 69.5849 | 3.01406 | ||||||||
\(534\) | −2.22844 | −0.0964341 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 29.0746 | 1.25583 | ||||||||
\(537\) | −5.53050 | −0.238659 | ||||||||
\(538\) | 2.47761 | 0.106817 | ||||||||
\(539\) | 0.742592 | 0.0319857 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.38522 | 0.274522 | 0.137261 | − | 0.990535i | \(-0.456170\pi\) | ||||
0.137261 | + | 0.990535i | \(0.456170\pi\) | |||||||
\(542\) | −7.22762 | −0.310453 | ||||||||
\(543\) | 46.9548 | 2.01502 | ||||||||
\(544\) | −22.1051 | −0.947749 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.38827 | 0.316189 | ||||||||
\(547\) | 10.6627 | 0.455904 | 0.227952 | − | 0.973672i | \(-0.426797\pi\) | ||||
0.227952 | + | 0.973672i | \(0.426797\pi\) | |||||||
\(548\) | 1.58623 | 0.0677603 | ||||||||
\(549\) | 13.4459 | 0.573855 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 25.6743 | 1.09277 | ||||||||
\(553\) | −3.52245 | −0.149790 | ||||||||
\(554\) | −7.94755 | −0.337659 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.6976 | −0.453681 | ||||||||
\(557\) | 3.06585 | 0.129904 | 0.0649521 | − | 0.997888i | \(-0.479311\pi\) | ||||
0.0649521 | + | 0.997888i | \(0.479311\pi\) | |||||||
\(558\) | 8.30254 | 0.351475 | ||||||||
\(559\) | −66.3683 | −2.80708 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.985440 | −0.0416053 | ||||||||
\(562\) | 15.3191 | 0.646198 | ||||||||
\(563\) | −35.1561 | −1.48165 | −0.740827 | − | 0.671696i | \(-0.765566\pi\) | ||||
−0.740827 | + | 0.671696i | \(0.765566\pi\) | |||||||
\(564\) | 6.56802 | 0.276564 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.12276 | −0.257359 | ||||||||
\(567\) | −5.84819 | −0.245601 | ||||||||
\(568\) | −18.1228 | −0.760414 | ||||||||
\(569\) | 42.2302 | 1.77038 | 0.885190 | − | 0.465229i | \(-0.154028\pi\) | ||||
0.885190 | + | 0.465229i | \(0.154028\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.3462 | −1.01886 | −0.509429 | − | 0.860513i | \(-0.670143\pi\) | ||||
−0.509429 | + | 0.860513i | \(0.670143\pi\) | |||||||
\(572\) | −1.01593 | −0.0424782 | ||||||||
\(573\) | 23.0148 | 0.961455 | ||||||||
\(574\) | 4.65298 | 0.194211 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9.48271 | 0.395113 | ||||||||
\(577\) | 9.74424 | 0.405658 | 0.202829 | − | 0.979214i | \(-0.434986\pi\) | ||||
0.202829 | + | 0.979214i | \(0.434986\pi\) | |||||||
\(578\) | 2.02699 | 0.0843115 | ||||||||
\(579\) | 10.5909 | 0.440141 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.58435 | 0.190191 | ||||||||
\(582\) | −15.7434 | −0.652584 | ||||||||
\(583\) | −0.638174 | −0.0264305 | ||||||||
\(584\) | 23.0836 | 0.955208 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.06585 | −0.126649 | ||||||||
\(587\) | −15.9708 | −0.659186 | −0.329593 | − | 0.944123i | \(-0.606911\pi\) | ||||
−0.329593 | + | 0.944123i | \(0.606911\pi\) | |||||||
\(588\) | 20.6459 | 0.851421 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.0203 | 1.19373 | ||||||||
\(592\) | −1.11718 | −0.0459157 | ||||||||
\(593\) | 0.404153 | 0.0165966 | 0.00829829 | − | 0.999966i | \(-0.497359\pi\) | ||||
0.00829829 | + | 0.999966i | \(0.497359\pi\) | |||||||
\(594\) | −0.123882 | −0.00508294 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.1325 | −0.537930 | ||||||||
\(597\) | −46.5281 | −1.90427 | ||||||||
\(598\) | 22.8474 | 0.934299 | ||||||||
\(599\) | −17.0426 | −0.696342 | −0.348171 | − | 0.937431i | \(-0.613197\pi\) | ||||
−0.348171 | + | 0.937431i | \(0.613197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.819125 | 0.0334128 | 0.0167064 | − | 0.999860i | \(-0.494682\pi\) | ||||
0.0167064 | + | 0.999860i | \(0.494682\pi\) | |||||||
\(602\) | −4.43788 | −0.180875 | ||||||||
\(603\) | 25.7368 | 1.04808 | ||||||||
\(604\) | 27.5276 | 1.12008 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 22.4102 | 0.910353 | ||||||||
\(607\) | 18.2675 | 0.741455 | 0.370728 | − | 0.928742i | \(-0.379108\pi\) | ||||
0.370728 | + | 0.928742i | \(0.379108\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.1472 | 0.492230 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.6527 | 0.592784 | ||||||||
\(612\) | −12.2212 | −0.494012 | ||||||||
\(613\) | −27.6822 | −1.11807 | −0.559037 | − | 0.829142i | \(-0.688829\pi\) | ||||
−0.559037 | + | 0.829142i | \(0.688829\pi\) | |||||||
\(614\) | 19.0975 | 0.770712 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.170304 | −0.00686173 | ||||||||
\(617\) | 40.1940 | 1.61815 | 0.809075 | − | 0.587706i | \(-0.199969\pi\) | ||||
0.809075 | + | 0.587706i | \(0.199969\pi\) | |||||||
\(618\) | −37.1612 | −1.49484 | ||||||||
\(619\) | 46.3862 | 1.86442 | 0.932209 | − | 0.361920i | \(-0.117879\pi\) | ||||
0.932209 | + | 0.361920i | \(0.117879\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.49569 | −0.220535 | ||||||||
\(622\) | −19.2392 | −0.771420 | ||||||||
\(623\) | 0.655753 | 0.0262722 | ||||||||
\(624\) | −6.66782 | −0.266926 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.3102 | −0.492015 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.1329 | −0.683678 | ||||||||
\(629\) | −10.2408 | −0.408327 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −47.5023 | −1.89104 | −0.945519 | − | 0.325568i | \(-0.894444\pi\) | ||||
−0.945519 | + | 0.325568i | \(0.894444\pi\) | |||||||
\(632\) | −17.1140 | −0.680759 | ||||||||
\(633\) | 39.1206 | 1.55490 | ||||||||
\(634\) | −15.8308 | −0.628722 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −17.7428 | −0.703547 | ||||||||
\(637\) | 46.0590 | 1.82493 | ||||||||
\(638\) | 0.846752 | 0.0335232 | ||||||||
\(639\) | −16.0422 | −0.634621 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.1626 | −0.519891 | −0.259946 | − | 0.965623i | \(-0.583705\pi\) | ||||
−0.259946 | + | 0.965623i | \(0.583705\pi\) | |||||||
\(642\) | 31.6202 | 1.24795 | ||||||||
\(643\) | 35.4538 | 1.39816 | 0.699081 | − | 0.715042i | \(-0.253593\pi\) | ||||
0.699081 | + | 0.715042i | \(0.253593\pi\) | |||||||
\(644\) | −3.01366 | −0.118755 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.38283 | −0.132993 | −0.0664964 | − | 0.997787i | \(-0.521182\pi\) | ||||
−0.0664964 | + | 0.997787i | \(0.521182\pi\) | |||||||
\(648\) | −28.4137 | −1.11619 | ||||||||
\(649\) | −0.877520 | −0.0344457 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.47710 | −0.214664 | ||||||||
\(652\) | −10.5264 | −0.412246 | ||||||||
\(653\) | 0.621795 | 0.0243327 | 0.0121664 | − | 0.999926i | \(-0.496127\pi\) | ||||
0.0121664 | + | 0.999926i | \(0.496127\pi\) | |||||||
\(654\) | −26.8365 | −1.04939 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.19925 | −0.163953 | ||||||||
\(657\) | 20.4336 | 0.797191 | ||||||||
\(658\) | 0.979789 | 0.0381961 | ||||||||
\(659\) | −11.6203 | −0.452664 | −0.226332 | − | 0.974050i | \(-0.572673\pi\) | ||||
−0.226332 | + | 0.974050i | \(0.572673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.2897 | −0.516911 | −0.258456 | − | 0.966023i | \(-0.583214\pi\) | ||||
−0.258456 | + | 0.966023i | \(0.583214\pi\) | |||||||
\(662\) | −15.6916 | −0.609871 | ||||||||
\(663\) | −61.1216 | −2.37377 | ||||||||
\(664\) | 22.2733 | 0.864371 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.32388 | 0.206296 | ||||||||
\(667\) | 37.5638 | 1.45448 | ||||||||
\(668\) | 7.55347 | 0.292253 | ||||||||
\(669\) | 4.39004 | 0.169729 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.618311 | −0.0238696 | ||||||||
\(672\) | −7.58101 | −0.292444 | ||||||||
\(673\) | 23.9351 | 0.922630 | 0.461315 | − | 0.887236i | \(-0.347378\pi\) | ||||
0.461315 | + | 0.887236i | \(0.347378\pi\) | |||||||
\(674\) | 20.9246 | 0.805985 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −45.7593 | −1.75997 | ||||||||
\(677\) | 3.71727 | 0.142866 | 0.0714331 | − | 0.997445i | \(-0.477243\pi\) | ||||
0.0714331 | + | 0.997445i | \(0.477243\pi\) | |||||||
\(678\) | 16.9690 | 0.651689 | ||||||||
\(679\) | 4.63273 | 0.177788 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.9113 | 0.954603 | ||||||||
\(682\) | −0.381795 | −0.0146197 | ||||||||
\(683\) | 1.40634 | 0.0538120 | 0.0269060 | − | 0.999638i | \(-0.491435\pi\) | ||||
0.0269060 | + | 0.999638i | \(0.491435\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.30509 | 0.240729 | ||||||||
\(687\) | 19.4178 | 0.740836 | ||||||||
\(688\) | 4.00513 | 0.152694 | ||||||||
\(689\) | −39.5826 | −1.50798 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.20762 | 0.0839820 | 0.0419910 | − | 0.999118i | \(-0.486630\pi\) | ||||
0.0419910 | + | 0.999118i | \(0.486630\pi\) | |||||||
\(692\) | −9.45018 | −0.359242 | ||||||||
\(693\) | −0.150753 | −0.00572662 | ||||||||
\(694\) | −28.2040 | −1.07061 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 59.0178 | 2.23706 | ||||||||
\(697\) | −38.4931 | −1.45803 | ||||||||
\(698\) | 23.4942 | 0.889270 | ||||||||
\(699\) | 4.99033 | 0.188751 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.95566 | −0.149403 | −0.0747016 | − | 0.997206i | \(-0.523800\pi\) | ||||
−0.0747016 | + | 0.997206i | \(0.523800\pi\) | |||||||
\(702\) | −7.68375 | −0.290004 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.436065 | −0.0164348 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.2925 | 0.726084 | ||||||||
\(707\) | −6.59456 | −0.248014 | ||||||||
\(708\) | −24.3972 | −0.916902 | ||||||||
\(709\) | −31.8658 | −1.19674 | −0.598372 | − | 0.801218i | \(-0.704186\pi\) | ||||
−0.598372 | + | 0.801218i | \(0.704186\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.1493 | −0.568143 | ||||||||
\(712\) | 3.18601 | 0.119401 | ||||||||
\(713\) | −16.9373 | −0.634306 | ||||||||
\(714\) | −4.08705 | −0.152954 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.15403 | 0.117872 | ||||||||
\(717\) | 58.3651 | 2.17969 | ||||||||
\(718\) | −8.01742 | −0.299207 | ||||||||
\(719\) | −34.2360 | −1.27679 | −0.638393 | − | 0.769710i | \(-0.720401\pi\) | ||||
−0.638393 | + | 0.769710i | \(0.720401\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.9353 | 0.407251 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.4200 | 0.982570 | ||||||||
\(724\) | −26.7782 | −0.995203 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 20.9741 | 0.778421 | ||||||||
\(727\) | 29.5181 | 1.09477 | 0.547383 | − | 0.836882i | \(-0.315624\pi\) | ||||
0.547383 | + | 0.836882i | \(0.315624\pi\) | |||||||
\(728\) | −10.5630 | −0.391492 | ||||||||
\(729\) | −15.6603 | −0.580011 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.7137 | 1.35790 | ||||||||
\(732\) | −17.1905 | −0.635381 | ||||||||
\(733\) | −28.2212 | −1.04237 | −0.521187 | − | 0.853442i | \(-0.674511\pi\) | ||||
−0.521187 | + | 0.853442i | \(0.674511\pi\) | |||||||
\(734\) | −1.67213 | −0.0617195 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −23.4434 | −0.864135 | ||||||||
\(737\) | −1.18351 | −0.0435952 | ||||||||
\(738\) | 20.0114 | 0.736630 | ||||||||
\(739\) | −24.0957 | −0.886373 | −0.443187 | − | 0.896429i | \(-0.646152\pi\) | ||||
−0.443187 | + | 0.896429i | \(0.646152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.64679 | −0.0971667 | ||||||||
\(743\) | −12.9103 | −0.473632 | −0.236816 | − | 0.971554i | \(-0.576104\pi\) | ||||
−0.236816 | + | 0.971554i | \(0.576104\pi\) | |||||||
\(744\) | −26.6107 | −0.975596 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.6315 | −0.389247 | ||||||||
\(747\) | 19.7163 | 0.721381 | ||||||||
\(748\) | 0.561994 | 0.0205485 | ||||||||
\(749\) | −9.30473 | −0.339987 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.7129 | 1.37616 | 0.688082 | − | 0.725633i | \(-0.258453\pi\) | ||||
0.688082 | + | 0.725633i | \(0.258453\pi\) | |||||||
\(752\) | −0.884246 | −0.0322451 | ||||||||
\(753\) | −16.1099 | −0.587076 | ||||||||
\(754\) | 52.5195 | 1.91265 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.01352 | 0.0368612 | ||||||||
\(757\) | 34.7933 | 1.26458 | 0.632292 | − | 0.774730i | \(-0.282114\pi\) | ||||
0.632292 | + | 0.774730i | \(0.282114\pi\) | |||||||
\(758\) | 5.60157 | 0.203458 | ||||||||
\(759\) | −1.04510 | −0.0379347 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.00019 | 0.145007 | 0.0725034 | − | 0.997368i | \(-0.476901\pi\) | ||||
0.0725034 | + | 0.997368i | \(0.476901\pi\) | |||||||
\(762\) | −14.8218 | −0.536939 | ||||||||
\(763\) | 7.89707 | 0.285893 | ||||||||
\(764\) | −13.1253 | −0.474855 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.0517 | −0.507710 | ||||||||
\(767\) | −54.4279 | −1.96528 | ||||||||
\(768\) | −34.2641 | −1.23640 | ||||||||
\(769\) | −9.59479 | −0.345997 | −0.172998 | − | 0.984922i | \(-0.555346\pi\) | ||||
−0.172998 | + | 0.984922i | \(0.555346\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.41517 | −0.159009 | ||||||||
\(772\) | −6.03994 | −0.217382 | ||||||||
\(773\) | −2.23562 | −0.0804096 | −0.0402048 | − | 0.999191i | \(-0.512801\pi\) | ||||
−0.0402048 | + | 0.999191i | \(0.512801\pi\) | |||||||
\(774\) | −19.0864 | −0.686045 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 22.5083 | 0.808003 | ||||||||
\(777\) | −3.51210 | −0.125996 | ||||||||
\(778\) | −15.1230 | −0.542184 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.737707 | 0.0263972 | ||||||||
\(782\) | −12.6387 | −0.451960 | ||||||||
\(783\) | −12.6330 | −0.451467 | ||||||||
\(784\) | −2.77953 | −0.0992689 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.74346 | 0.311869 | ||||||||
\(787\) | −19.6480 | −0.700376 | −0.350188 | − | 0.936679i | \(-0.613882\pi\) | ||||
−0.350188 | + | 0.936679i | \(0.613882\pi\) | |||||||
\(788\) | −16.5502 | −0.589576 | ||||||||
\(789\) | 26.8664 | 0.956469 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.99338 | −0.177544 | ||||||||
\(792\) | −0.732438 | −0.0260261 | ||||||||
\(793\) | −38.3506 | −1.36187 | ||||||||
\(794\) | −2.82676 | −0.100318 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.5349 | 0.940503 | ||||||||
\(797\) | 15.8851 | 0.562680 | 0.281340 | − | 0.959608i | \(-0.409221\pi\) | ||||
0.281340 | + | 0.959608i | \(0.409221\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.10558 | −0.286755 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.82025 | 0.0996486 | ||||||||
\(802\) | 10.1934 | 0.359942 | ||||||||
\(803\) | −0.939645 | −0.0331593 | ||||||||
\(804\) | −32.9045 | −1.16045 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −23.6807 | −0.834117 | ||||||||
\(807\) | −7.02942 | −0.247447 | ||||||||
\(808\) | −32.0400 | −1.12716 | ||||||||
\(809\) | 9.82989 | 0.345600 | 0.172800 | − | 0.984957i | \(-0.444718\pi\) | ||||
0.172800 | + | 0.984957i | \(0.444718\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.0667 | 1.02067 | 0.510335 | − | 0.859976i | \(-0.329521\pi\) | ||||
0.510335 | + | 0.859976i | \(0.329521\pi\) | |||||||
\(812\) | −6.92752 | −0.243108 | ||||||||
\(813\) | 20.5060 | 0.719178 | ||||||||
\(814\) | −0.244820 | −0.00858094 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.68851 | 0.129124 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 2.07679 | 0.0726133 | ||||||||
\(819\) | −9.35038 | −0.326729 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.14446 | 0.319144 | 0.159572 | − | 0.987186i | \(-0.448989\pi\) | ||||
0.159572 | + | 0.987186i | \(0.448989\pi\) | |||||||
\(822\) | 2.28145 | 0.0795746 | ||||||||
\(823\) | −25.8030 | −0.899436 | −0.449718 | − | 0.893171i | \(-0.648476\pi\) | ||||
−0.449718 | + | 0.893171i | \(0.648476\pi\) | |||||||
\(824\) | 53.1295 | 1.85085 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.63946 | −0.126633 | ||||||||
\(827\) | −4.28552 | −0.149022 | −0.0745110 | − | 0.997220i | \(-0.523740\pi\) | ||||
−0.0745110 | + | 0.997220i | \(0.523740\pi\) | |||||||
\(828\) | −12.9611 | −0.450428 | ||||||||
\(829\) | 5.70557 | 0.198163 | 0.0990813 | − | 0.995079i | \(-0.468410\pi\) | ||||
0.0990813 | + | 0.995079i | \(0.468410\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.5486 | 0.782202 | ||||||||
\(832\) | −27.0468 | −0.937679 | ||||||||
\(833\) | −25.4790 | −0.882795 | ||||||||
\(834\) | −15.3862 | −0.532781 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.69614 | 0.196887 | ||||||||
\(838\) | −0.531142 | −0.0183480 | ||||||||
\(839\) | −15.5188 | −0.535769 | −0.267884 | − | 0.963451i | \(-0.586325\pi\) | ||||
−0.267884 | + | 0.963451i | \(0.586325\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.3484 | 1.97753 | ||||||||
\(842\) | 3.58570 | 0.123571 | ||||||||
\(843\) | −43.4630 | −1.49695 | ||||||||
\(844\) | −22.3104 | −0.767954 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.21385 | 0.144875 | ||||||||
\(847\) | −6.17195 | −0.212071 | ||||||||
\(848\) | 2.38869 | 0.0820280 | ||||||||
\(849\) | 17.3713 | 0.596183 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.8608 | −0.372303 | ||||||||
\(852\) | 20.5100 | 0.702662 | ||||||||
\(853\) | 49.8235 | 1.70592 | 0.852962 | − | 0.521972i | \(-0.174804\pi\) | ||||
0.852962 | + | 0.521972i | \(0.174804\pi\) | |||||||
\(854\) | −2.56441 | −0.0877523 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −45.2074 | −1.54516 | ||||||||
\(857\) | 43.1178 | 1.47288 | 0.736438 | − | 0.676505i | \(-0.236506\pi\) | ||||
0.736438 | + | 0.676505i | \(0.236506\pi\) | |||||||
\(858\) | −1.46120 | −0.0498844 | ||||||||
\(859\) | 17.9279 | 0.611691 | 0.305845 | − | 0.952081i | \(-0.401061\pi\) | ||||
0.305845 | + | 0.952081i | \(0.401061\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.2013 | −0.449900 | ||||||||
\(862\) | 24.6152 | 0.838398 | ||||||||
\(863\) | −55.6045 | −1.89280 | −0.946399 | − | 0.322999i | \(-0.895309\pi\) | ||||
−0.946399 | + | 0.322999i | \(0.895309\pi\) | |||||||
\(864\) | 7.88419 | 0.268226 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.4427 | −0.490784 | ||||||||
\(867\) | −5.75091 | −0.195311 | ||||||||
\(868\) | 3.12357 | 0.106021 | ||||||||
\(869\) | 0.696644 | 0.0236320 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −73.4069 | −2.48730 | ||||||||
\(872\) | 38.3683 | 1.29931 | ||||||||
\(873\) | 19.9244 | 0.674337 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −26.1244 | −0.882661 | ||||||||
\(877\) | −12.1639 | −0.410744 | −0.205372 | − | 0.978684i | \(-0.565840\pi\) | ||||
−0.205372 | + | 0.978684i | \(0.565840\pi\) | |||||||
\(878\) | 21.2303 | 0.716488 | ||||||||
\(879\) | 8.69836 | 0.293388 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.8330 | 0.971408 | 0.485704 | − | 0.874123i | \(-0.338563\pi\) | ||||
0.485704 | + | 0.874123i | \(0.338563\pi\) | |||||||
\(882\) | 13.2458 | 0.446009 | ||||||||
\(883\) | 0.648525 | 0.0218246 | 0.0109123 | − | 0.999940i | \(-0.496526\pi\) | ||||
0.0109123 | + | 0.999940i | \(0.496526\pi\) | |||||||
\(884\) | 34.8575 | 1.17238 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.74174 | 0.327280 | ||||||||
\(887\) | −45.2362 | −1.51888 | −0.759441 | − | 0.650577i | \(-0.774527\pi\) | ||||
−0.759441 | + | 0.650577i | \(0.774527\pi\) | |||||||
\(888\) | −17.0637 | −0.572621 | ||||||||
\(889\) | 4.36156 | 0.146282 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.15661 | 0.0387479 | ||||||||
\(892\) | −2.50363 | −0.0838277 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −18.8883 | −0.631720 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.70661 | 0.157237 | ||||||||
\(897\) | −64.8220 | −2.16434 | ||||||||
\(898\) | 24.1583 | 0.806174 | ||||||||
\(899\) | −38.9339 | −1.29852 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.8963 | 0.729472 | ||||||||
\(902\) | −0.920230 | −0.0306403 | ||||||||
\(903\) | 12.5911 | 0.419004 | ||||||||
\(904\) | −24.2606 | −0.806894 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 39.5925 | 1.31537 | ||||||||
\(907\) | 15.1528 | 0.503142 | 0.251571 | − | 0.967839i | \(-0.419053\pi\) | ||||
0.251571 | + | 0.967839i | \(0.419053\pi\) | |||||||
\(908\) | −14.2068 | −0.471471 | ||||||||
\(909\) | −28.3617 | −0.940699 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.7373 | 1.05150 | 0.525752 | − | 0.850638i | \(-0.323784\pi\) | ||||
0.525752 | + | 0.850638i | \(0.323784\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.906658 | −0.0300060 | ||||||||
\(914\) | 19.9591 | 0.660187 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.0739 | −0.365893 | ||||||||
\(917\) | −2.57290 | −0.0849646 | ||||||||
\(918\) | 4.25051 | 0.140288 | ||||||||
\(919\) | 5.31327 | 0.175269 | 0.0876343 | − | 0.996153i | \(-0.472069\pi\) | ||||
0.0876343 | + | 0.996153i | \(0.472069\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −54.1829 | −1.78539 | ||||||||
\(922\) | −28.3021 | −0.932079 | ||||||||
\(923\) | 45.7560 | 1.50608 | ||||||||
\(924\) | 0.192737 | 0.00634059 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.01371 | −0.131899 | ||||||||
\(927\) | 47.0302 | 1.54467 | ||||||||
\(928\) | −53.8896 | −1.76901 | ||||||||
\(929\) | −3.54458 | −0.116294 | −0.0581469 | − | 0.998308i | \(-0.518519\pi\) | ||||
−0.0581469 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.84597 | −0.0932228 | ||||||||
\(933\) | 54.5849 | 1.78703 | ||||||||
\(934\) | 12.8648 | 0.420949 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −45.4292 | −1.48490 | ||||||||
\(937\) | −31.2800 | −1.02187 | −0.510936 | − | 0.859619i | \(-0.670701\pi\) | ||||
−0.510936 | + | 0.859619i | \(0.670701\pi\) | |||||||
\(938\) | −4.90854 | −0.160270 | ||||||||
\(939\) | 34.9263 | 1.13978 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.5106 | 1.48360 | 0.741802 | − | 0.670619i | \(-0.233971\pi\) | ||||
0.741802 | + | 0.670619i | \(0.233971\pi\) | |||||||
\(942\) | −24.6420 | −0.802879 | ||||||||
\(943\) | −40.8235 | −1.32940 | ||||||||
\(944\) | 3.28457 | 0.106903 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.877691 | 0.0285362 | ||||||||
\(947\) | 21.0071 | 0.682640 | 0.341320 | − | 0.939947i | \(-0.389126\pi\) | ||||
0.341320 | + | 0.939947i | \(0.389126\pi\) | |||||||
\(948\) | 19.3684 | 0.629056 | ||||||||
\(949\) | −58.2812 | −1.89189 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 44.9148 | 1.45646 | ||||||||
\(952\) | 5.84327 | 0.189382 | ||||||||
\(953\) | 32.6629 | 1.05806 | 0.529028 | − | 0.848604i | \(-0.322557\pi\) | ||||
0.529028 | + | 0.848604i | \(0.322557\pi\) | |||||||
\(954\) | −11.3833 | −0.368546 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −33.2855 | −1.07653 | ||||||||
\(957\) | −2.40238 | −0.0776580 | ||||||||
\(958\) | −12.4404 | −0.401932 | ||||||||
\(959\) | −0.671351 | −0.0216791 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.4450 | −0.433708 | ||||||||
\(962\) | −15.1849 | −0.489580 | ||||||||
\(963\) | −40.0176 | −1.28955 | ||||||||
\(964\) | −15.0673 | −0.485284 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.33449 | −0.139460 | ||||||||
\(967\) | 21.8080 | 0.701299 | 0.350650 | − | 0.936507i | \(-0.385961\pi\) | ||||
0.350650 | + | 0.936507i | \(0.385961\pi\) | |||||||
\(968\) | −29.9867 | −0.963809 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55.8370 | 1.79189 | 0.895947 | − | 0.444162i | \(-0.146498\pi\) | ||||
0.895947 | + | 0.444162i | \(0.146498\pi\) | |||||||
\(972\) | 26.7436 | 0.857801 | ||||||||
\(973\) | 4.52764 | 0.145149 | ||||||||
\(974\) | −12.1697 | −0.389943 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.31435 | 0.0740804 | ||||||||
\(977\) | −0.543879 | −0.0174002 | −0.00870012 | − | 0.999962i | \(-0.502769\pi\) | ||||
−0.00870012 | + | 0.999962i | \(0.502769\pi\) | |||||||
\(978\) | −15.1400 | −0.484122 | ||||||||
\(979\) | −0.129690 | −0.00414491 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.9635 | 1.08437 | ||||||||
\(982\) | −17.8012 | −0.568060 | ||||||||
\(983\) | −11.0176 | −0.351407 | −0.175704 | − | 0.984443i | \(-0.556220\pi\) | ||||
−0.175704 | + | 0.984443i | \(0.556220\pi\) | |||||||
\(984\) | −64.1392 | −2.04468 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −29.0528 | −0.925230 | ||||||||
\(987\) | −2.77983 | −0.0884830 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.9364 | 1.23811 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.1970 | 0.895707 | 0.447854 | − | 0.894107i | \(-0.352189\pi\) | ||||
0.447854 | + | 0.894107i | \(0.352189\pi\) | |||||||
\(992\) | 24.2984 | 0.771477 | ||||||||
\(993\) | 44.5198 | 1.41279 | ||||||||
\(994\) | 3.05959 | 0.0970445 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −25.2073 | −0.798724 | ||||||||
\(997\) | 30.5688 | 0.968123 | 0.484062 | − | 0.875034i | \(-0.339161\pi\) | ||||
0.484062 | + | 0.875034i | \(0.339161\pi\) | |||||||
\(998\) | 16.8777 | 0.534256 | ||||||||
\(999\) | 3.65256 | 0.115562 |
(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 | 9025.2.a.bo.1.2 | 4 | ||
5.4 | even | 2 | 1805.2.a.j.1.3 | ✓ | 4 | ||
19.18 | odd | 2 | 9025.2.a.bh.1.3 | 4 | |||
95.94 | odd | 2 | 1805.2.a.n.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.a.j.1.3 | ✓ | 4 | 5.4 | even | 2 | ||
1805.2.a.n.1.2 | yes | 4 | 95.94 | odd | 2 | ||
9025.2.a.bh.1.3 | 4 | 19.18 | odd | 2 | |||
9025.2.a.bo.1.2 | 4 | 1.1 | even | 1 | trivial |