Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,2,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, 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("245.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(1.95633484952\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.414214 | −0.292893 | −0.146447 | − | 0.989219i | \(-0.546784\pi\) | ||||
−0.146447 | + | 0.989219i | \(0.546784\pi\) | |||||||
\(3\) | 2.41421 | 1.39385 | 0.696923 | − | 0.717146i | \(-0.254552\pi\) | ||||
0.696923 | + | 0.717146i | \(0.254552\pi\) | |||||||
\(4\) | −1.82843 | −0.914214 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.58579 | 0.560660 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | −0.414214 | −0.130986 | ||||||||
\(11\) | 4.82843 | 1.45583 | 0.727913 | − | 0.685670i | \(-0.240491\pi\) | ||||
0.727913 | + | 0.685670i | \(0.240491\pi\) | |||||||
\(12\) | −4.41421 | −1.27427 | ||||||||
\(13\) | 0.828427 | 0.229764 | 0.114882 | − | 0.993379i | \(-0.463351\pi\) | ||||
0.114882 | + | 0.993379i | \(0.463351\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.41421 | 0.623347 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −0.828427 | −0.200923 | −0.100462 | − | 0.994941i | \(-0.532032\pi\) | ||||
−0.100462 | + | 0.994941i | \(0.532032\pi\) | |||||||
\(18\) | −1.17157 | −0.276142 | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | −1.82843 | −0.408849 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | −2.41421 | −0.503398 | −0.251699 | − | 0.967806i | \(-0.580989\pi\) | ||||
−0.251699 | + | 0.967806i | \(0.580989\pi\) | |||||||
\(24\) | 3.82843 | 0.781474 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.343146 | −0.0672964 | ||||||||
\(27\) | −0.414214 | −0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | −4.41421 | −0.780330 | ||||||||
\(33\) | 11.6569 | 2.02920 | ||||||||
\(34\) | 0.343146 | 0.0588490 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.17157 | −0.861929 | ||||||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | 1.17157 | 0.190054 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 1.58579 | 0.250735 | ||||||||
\(41\) | −2.17157 | −0.339143 | −0.169571 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169571 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.41421 | 0.978158 | 0.489079 | − | 0.872239i | \(-0.337333\pi\) | ||||
0.489079 | + | 0.872239i | \(0.337333\pi\) | |||||||
\(44\) | −8.82843 | −1.33094 | ||||||||
\(45\) | 2.82843 | 0.421637 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 2.00000 | 0.291730 | 0.145865 | − | 0.989305i | \(-0.453403\pi\) | ||||
0.145865 | + | 0.989305i | \(0.453403\pi\) | |||||||
\(48\) | 7.24264 | 1.04539 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.414214 | −0.0585786 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | −1.51472 | −0.210054 | ||||||||
\(53\) | −6.82843 | −0.937957 | −0.468978 | − | 0.883210i | \(-0.655378\pi\) | ||||
−0.468978 | + | 0.883210i | \(0.655378\pi\) | |||||||
\(54\) | 0.171573 | 0.0233481 | ||||||||
\(55\) | 4.82843 | 0.651065 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.82843 | −0.904447 | ||||||||
\(58\) | 0.414214 | 0.0543889 | ||||||||
\(59\) | −12.4853 | −1.62545 | −0.812723 | − | 0.582651i | \(-0.802016\pi\) | ||||
−0.812723 | + | 0.582651i | \(0.802016\pi\) | |||||||
\(60\) | −4.41421 | −0.569873 | ||||||||
\(61\) | −11.4853 | −1.47054 | −0.735270 | − | 0.677775i | \(-0.762945\pi\) | ||||
−0.735270 | + | 0.677775i | \(0.762945\pi\) | |||||||
\(62\) | 2.48528 | 0.315631 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | 0.828427 | 0.102754 | ||||||||
\(66\) | −4.82843 | −0.594338 | ||||||||
\(67\) | 12.4142 | 1.51664 | 0.758319 | − | 0.651884i | \(-0.226021\pi\) | ||||
0.758319 | + | 0.651884i | \(0.226021\pi\) | |||||||
\(68\) | 1.51472 | 0.183687 | ||||||||
\(69\) | −5.82843 | −0.701660 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4853 | −1.48173 | −0.740865 | − | 0.671654i | \(-0.765584\pi\) | ||||
−0.740865 | + | 0.671654i | \(0.765584\pi\) | |||||||
\(72\) | 4.48528 | 0.528595 | ||||||||
\(73\) | 4.82843 | 0.565125 | 0.282562 | − | 0.959249i | \(-0.408816\pi\) | ||||
0.282562 | + | 0.959249i | \(0.408816\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.41421 | 0.278769 | ||||||||
\(76\) | 5.17157 | 0.593220 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.828427 | −0.0938009 | ||||||||
\(79\) | 9.17157 | 1.03188 | 0.515941 | − | 0.856624i | \(-0.327442\pi\) | ||||
0.515941 | + | 0.856624i | \(0.327442\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0.899495 | 0.0993326 | ||||||||
\(83\) | −11.7279 | −1.28731 | −0.643653 | − | 0.765317i | \(-0.722582\pi\) | ||||
−0.643653 | + | 0.765317i | \(0.722582\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.828427 | −0.0898555 | ||||||||
\(86\) | −2.65685 | −0.286496 | ||||||||
\(87\) | −2.41421 | −0.258831 | ||||||||
\(88\) | 7.65685 | 0.816223 | ||||||||
\(89\) | 2.65685 | 0.281626 | 0.140813 | − | 0.990036i | \(-0.455028\pi\) | ||||
0.140813 | + | 0.990036i | \(0.455028\pi\) | |||||||
\(90\) | −1.17157 | −0.123495 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.41421 | 0.460214 | ||||||||
\(93\) | −14.4853 | −1.50205 | ||||||||
\(94\) | −0.828427 | −0.0854457 | ||||||||
\(95\) | −2.82843 | −0.290191 | ||||||||
\(96\) | −10.6569 | −1.08766 | ||||||||
\(97\) | 0.343146 | 0.0348412 | 0.0174206 | − | 0.999848i | \(-0.494455\pi\) | ||||
0.0174206 | + | 0.999848i | \(0.494455\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.6569 | 1.37257 | ||||||||
\(100\) | −1.82843 | −0.182843 | ||||||||
\(101\) | 12.3137 | 1.22526 | 0.612630 | − | 0.790370i | \(-0.290112\pi\) | ||||
0.612630 | + | 0.790370i | \(0.290112\pi\) | |||||||
\(102\) | 0.828427 | 0.0820265 | ||||||||
\(103\) | 0.414214 | 0.0408137 | 0.0204068 | − | 0.999792i | \(-0.493504\pi\) | ||||
0.0204068 | + | 0.999792i | \(0.493504\pi\) | |||||||
\(104\) | 1.31371 | 0.128820 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.82843 | 0.274721 | ||||||||
\(107\) | 2.75736 | 0.266564 | 0.133282 | − | 0.991078i | \(-0.457448\pi\) | ||||
0.133282 | + | 0.991078i | \(0.457448\pi\) | |||||||
\(108\) | 0.757359 | 0.0728769 | ||||||||
\(109\) | 3.48528 | 0.333829 | 0.166915 | − | 0.985971i | \(-0.446620\pi\) | ||||
0.166915 | + | 0.985971i | \(0.446620\pi\) | |||||||
\(110\) | −2.00000 | −0.190693 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.4853 | 1.17452 | 0.587258 | − | 0.809400i | \(-0.300207\pi\) | ||||
0.587258 | + | 0.809400i | \(0.300207\pi\) | |||||||
\(114\) | 2.82843 | 0.264906 | ||||||||
\(115\) | −2.41421 | −0.225127 | ||||||||
\(116\) | 1.82843 | 0.169765 | ||||||||
\(117\) | 2.34315 | 0.216624 | ||||||||
\(118\) | 5.17157 | 0.476082 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.82843 | 0.349486 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | 4.75736 | 0.430711 | ||||||||
\(123\) | −5.24264 | −0.472713 | ||||||||
\(124\) | 10.9706 | 0.985186 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.3137 | 1.18140 | 0.590700 | − | 0.806891i | \(-0.298852\pi\) | ||||
0.590700 | + | 0.806891i | \(0.298852\pi\) | |||||||
\(128\) | 10.5563 | 0.933058 | ||||||||
\(129\) | 15.4853 | 1.36340 | ||||||||
\(130\) | −0.343146 | −0.0300959 | ||||||||
\(131\) | 3.31371 | 0.289520 | 0.144760 | − | 0.989467i | \(-0.453759\pi\) | ||||
0.144760 | + | 0.989467i | \(0.453759\pi\) | |||||||
\(132\) | −21.3137 | −1.85512 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.14214 | −0.444213 | ||||||||
\(135\) | −0.414214 | −0.0356498 | ||||||||
\(136\) | −1.31371 | −0.112650 | ||||||||
\(137\) | 1.65685 | 0.141555 | 0.0707773 | − | 0.997492i | \(-0.477452\pi\) | ||||
0.0707773 | + | 0.997492i | \(0.477452\pi\) | |||||||
\(138\) | 2.41421 | 0.205512 | ||||||||
\(139\) | 12.1421 | 1.02988 | 0.514941 | − | 0.857225i | \(-0.327814\pi\) | ||||
0.514941 | + | 0.857225i | \(0.327814\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.82843 | 0.406627 | ||||||||
\(142\) | 5.17157 | 0.433989 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 8.48528 | 0.707107 | ||||||||
\(145\) | −1.00000 | −0.0830455 | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.82843 | −0.641330 | −0.320665 | − | 0.947193i | \(-0.603906\pi\) | ||||
−0.320665 | + | 0.947193i | \(0.603906\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 0.343146 | 0.0279248 | 0.0139624 | − | 0.999903i | \(-0.495555\pi\) | ||||
0.0139624 | + | 0.999903i | \(0.495555\pi\) | |||||||
\(152\) | −4.48528 | −0.363804 | ||||||||
\(153\) | −2.34315 | −0.189432 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | −3.65685 | −0.292783 | ||||||||
\(157\) | −5.31371 | −0.424080 | −0.212040 | − | 0.977261i | \(-0.568011\pi\) | ||||
−0.212040 | + | 0.977261i | \(0.568011\pi\) | |||||||
\(158\) | −3.79899 | −0.302231 | ||||||||
\(159\) | −16.4853 | −1.30737 | ||||||||
\(160\) | −4.41421 | −0.348974 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.92893 | 0.308686 | ||||||||
\(163\) | 23.6569 | 1.85295 | 0.926474 | − | 0.376359i | \(-0.122824\pi\) | ||||
0.926474 | + | 0.376359i | \(0.122824\pi\) | |||||||
\(164\) | 3.97056 | 0.310049 | ||||||||
\(165\) | 11.6569 | 0.907485 | ||||||||
\(166\) | 4.85786 | 0.377043 | ||||||||
\(167\) | 19.5858 | 1.51559 | 0.757797 | − | 0.652491i | \(-0.226276\pi\) | ||||
0.757797 | + | 0.652491i | \(0.226276\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3137 | −0.947208 | ||||||||
\(170\) | 0.343146 | 0.0263181 | ||||||||
\(171\) | −8.00000 | −0.611775 | ||||||||
\(172\) | −11.7279 | −0.894246 | ||||||||
\(173\) | −19.3137 | −1.46839 | −0.734197 | − | 0.678936i | \(-0.762441\pi\) | ||||
−0.734197 | + | 0.678936i | \(0.762441\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.4853 | 1.09187 | ||||||||
\(177\) | −30.1421 | −2.26562 | ||||||||
\(178\) | −1.10051 | −0.0824863 | ||||||||
\(179\) | −10.0000 | −0.747435 | −0.373718 | − | 0.927543i | \(-0.621917\pi\) | ||||
−0.373718 | + | 0.927543i | \(0.621917\pi\) | |||||||
\(180\) | −5.17157 | −0.385466 | ||||||||
\(181\) | −8.65685 | −0.643459 | −0.321729 | − | 0.946832i | \(-0.604264\pi\) | ||||
−0.321729 | + | 0.946832i | \(0.604264\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −27.7279 | −2.04971 | ||||||||
\(184\) | −3.82843 | −0.282235 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | −4.00000 | −0.292509 | ||||||||
\(188\) | −3.65685 | −0.266704 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.17157 | 0.0849948 | ||||||||
\(191\) | −7.17157 | −0.518917 | −0.259458 | − | 0.965754i | \(-0.583544\pi\) | ||||
−0.259458 | + | 0.965754i | \(0.583544\pi\) | |||||||
\(192\) | −10.0711 | −0.726817 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | −0.142136 | −0.0102047 | ||||||||
\(195\) | 2.00000 | 0.143223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.6569 | −1.68548 | −0.842741 | − | 0.538320i | \(-0.819059\pi\) | ||||
−0.842741 | + | 0.538320i | \(0.819059\pi\) | |||||||
\(198\) | −5.65685 | −0.402015 | ||||||||
\(199\) | 1.65685 | 0.117451 | 0.0587256 | − | 0.998274i | \(-0.481296\pi\) | ||||
0.0587256 | + | 0.998274i | \(0.481296\pi\) | |||||||
\(200\) | 1.58579 | 0.112132 | ||||||||
\(201\) | 29.9706 | 2.11396 | ||||||||
\(202\) | −5.10051 | −0.358870 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.65685 | 0.256031 | ||||||||
\(205\) | −2.17157 | −0.151669 | ||||||||
\(206\) | −0.171573 | −0.0119540 | ||||||||
\(207\) | −6.82843 | −0.474608 | ||||||||
\(208\) | 2.48528 | 0.172323 | ||||||||
\(209\) | −13.6569 | −0.944664 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.51472 | 0.241963 | 0.120982 | − | 0.992655i | \(-0.461396\pi\) | ||||
0.120982 | + | 0.992655i | \(0.461396\pi\) | |||||||
\(212\) | 12.4853 | 0.857493 | ||||||||
\(213\) | −30.1421 | −2.06531 | ||||||||
\(214\) | −1.14214 | −0.0780748 | ||||||||
\(215\) | 6.41421 | 0.437446 | ||||||||
\(216\) | −0.656854 | −0.0446933 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.44365 | −0.0977764 | ||||||||
\(219\) | 11.6569 | 0.787697 | ||||||||
\(220\) | −8.82843 | −0.595212 | ||||||||
\(221\) | −0.686292 | −0.0461650 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.6569 | 0.780601 | 0.390300 | − | 0.920688i | \(-0.372371\pi\) | ||||
0.390300 | + | 0.920688i | \(0.372371\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.82843 | 0.188562 | ||||||||
\(226\) | −5.17157 | −0.344008 | ||||||||
\(227\) | 26.9706 | 1.79010 | 0.895050 | − | 0.445967i | \(-0.147140\pi\) | ||||
0.895050 | + | 0.445967i | \(0.147140\pi\) | |||||||
\(228\) | 12.4853 | 0.826858 | ||||||||
\(229\) | −0.343146 | −0.0226757 | −0.0113379 | − | 0.999936i | \(-0.503609\pi\) | ||||
−0.0113379 | + | 0.999936i | \(0.503609\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.58579 | −0.104112 | ||||||||
\(233\) | −11.1716 | −0.731874 | −0.365937 | − | 0.930640i | \(-0.619251\pi\) | ||||
−0.365937 | + | 0.930640i | \(0.619251\pi\) | |||||||
\(234\) | −0.970563 | −0.0634477 | ||||||||
\(235\) | 2.00000 | 0.130466 | ||||||||
\(236\) | 22.8284 | 1.48600 | ||||||||
\(237\) | 22.1421 | 1.43829 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.31371 | 0.0849767 | 0.0424884 | − | 0.999097i | \(-0.486471\pi\) | ||||
0.0424884 | + | 0.999097i | \(0.486471\pi\) | |||||||
\(240\) | 7.24264 | 0.467510 | ||||||||
\(241\) | 16.3431 | 1.05275 | 0.526377 | − | 0.850251i | \(-0.323550\pi\) | ||||
0.526377 | + | 0.850251i | \(0.323550\pi\) | |||||||
\(242\) | −5.10051 | −0.327873 | ||||||||
\(243\) | −21.6569 | −1.38929 | ||||||||
\(244\) | 21.0000 | 1.34439 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.17157 | 0.138454 | ||||||||
\(247\) | −2.34315 | −0.149091 | ||||||||
\(248\) | −9.51472 | −0.604185 | ||||||||
\(249\) | −28.3137 | −1.79431 | ||||||||
\(250\) | −0.414214 | −0.0261972 | ||||||||
\(251\) | 13.3137 | 0.840354 | 0.420177 | − | 0.907442i | \(-0.361968\pi\) | ||||
0.420177 | + | 0.907442i | \(0.361968\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.6569 | −0.732860 | ||||||||
\(254\) | −5.51472 | −0.346024 | ||||||||
\(255\) | −2.00000 | −0.125245 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | 17.6569 | 1.10140 | 0.550702 | − | 0.834702i | \(-0.314360\pi\) | ||||
0.550702 | + | 0.834702i | \(0.314360\pi\) | |||||||
\(258\) | −6.41421 | −0.399331 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.51472 | −0.0939389 | ||||||||
\(261\) | −2.82843 | −0.175075 | ||||||||
\(262\) | −1.37258 | −0.0847985 | ||||||||
\(263\) | 19.0416 | 1.17416 | 0.587079 | − | 0.809530i | \(-0.300278\pi\) | ||||
0.587079 | + | 0.809530i | \(0.300278\pi\) | |||||||
\(264\) | 18.4853 | 1.13769 | ||||||||
\(265\) | −6.82843 | −0.419467 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.41421 | 0.392543 | ||||||||
\(268\) | −22.6985 | −1.38653 | ||||||||
\(269\) | −30.4558 | −1.85693 | −0.928463 | − | 0.371425i | \(-0.878869\pi\) | ||||
−0.928463 | + | 0.371425i | \(0.878869\pi\) | |||||||
\(270\) | 0.171573 | 0.0104416 | ||||||||
\(271\) | −0.485281 | −0.0294787 | −0.0147394 | − | 0.999891i | \(-0.504692\pi\) | ||||
−0.0147394 | + | 0.999891i | \(0.504692\pi\) | |||||||
\(272\) | −2.48528 | −0.150692 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.686292 | −0.0414604 | ||||||||
\(275\) | 4.82843 | 0.291165 | ||||||||
\(276\) | 10.6569 | 0.641467 | ||||||||
\(277\) | −12.1421 | −0.729550 | −0.364775 | − | 0.931096i | \(-0.618854\pi\) | ||||
−0.364775 | + | 0.931096i | \(0.618854\pi\) | |||||||
\(278\) | −5.02944 | −0.301646 | ||||||||
\(279\) | −16.9706 | −1.01600 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.2843 | 1.56799 | 0.783994 | − | 0.620768i | \(-0.213179\pi\) | ||||
0.783994 | + | 0.620768i | \(0.213179\pi\) | |||||||
\(282\) | −2.00000 | −0.119098 | ||||||||
\(283\) | 14.0000 | 0.832214 | 0.416107 | − | 0.909316i | \(-0.363394\pi\) | ||||
0.416107 | + | 0.909316i | \(0.363394\pi\) | |||||||
\(284\) | 22.8284 | 1.35462 | ||||||||
\(285\) | −6.82843 | −0.404481 | ||||||||
\(286\) | −1.65685 | −0.0979718 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −12.4853 | −0.735702 | ||||||||
\(289\) | −16.3137 | −0.959630 | ||||||||
\(290\) | 0.414214 | 0.0243235 | ||||||||
\(291\) | 0.828427 | 0.0485633 | ||||||||
\(292\) | −8.82843 | −0.516645 | ||||||||
\(293\) | −16.0000 | −0.934730 | −0.467365 | − | 0.884064i | \(-0.654797\pi\) | ||||
−0.467365 | + | 0.884064i | \(0.654797\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.4853 | −0.726921 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.00000 | −0.116052 | ||||||||
\(298\) | 3.24264 | 0.187841 | ||||||||
\(299\) | −2.00000 | −0.115663 | ||||||||
\(300\) | −4.41421 | −0.254855 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.142136 | −0.00817899 | ||||||||
\(303\) | 29.7279 | 1.70782 | ||||||||
\(304\) | −8.48528 | −0.486664 | ||||||||
\(305\) | −11.4853 | −0.657645 | ||||||||
\(306\) | 0.970563 | 0.0554834 | ||||||||
\(307\) | −13.2426 | −0.755797 | −0.377899 | − | 0.925847i | \(-0.623353\pi\) | ||||
−0.377899 | + | 0.925847i | \(0.623353\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 2.48528 | 0.141154 | ||||||||
\(311\) | −18.8284 | −1.06766 | −0.533831 | − | 0.845591i | \(-0.679248\pi\) | ||||
−0.533831 | + | 0.845591i | \(0.679248\pi\) | |||||||
\(312\) | 3.17157 | 0.179555 | ||||||||
\(313\) | −17.6569 | −0.998024 | −0.499012 | − | 0.866595i | \(-0.666304\pi\) | ||||
−0.499012 | + | 0.866595i | \(0.666304\pi\) | |||||||
\(314\) | 2.20101 | 0.124210 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.7696 | −0.943361 | ||||||||
\(317\) | 25.7990 | 1.44902 | 0.724508 | − | 0.689267i | \(-0.242067\pi\) | ||||
0.724508 | + | 0.689267i | \(0.242067\pi\) | |||||||
\(318\) | 6.82843 | 0.382919 | ||||||||
\(319\) | −4.82843 | −0.270340 | ||||||||
\(320\) | −4.17157 | −0.233198 | ||||||||
\(321\) | 6.65685 | 0.371549 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.34315 | 0.130376 | ||||||||
\(324\) | 17.3431 | 0.963508 | ||||||||
\(325\) | 0.828427 | 0.0459529 | ||||||||
\(326\) | −9.79899 | −0.542716 | ||||||||
\(327\) | 8.41421 | 0.465307 | ||||||||
\(328\) | −3.44365 | −0.190144 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.82843 | −0.265796 | ||||||||
\(331\) | −10.9706 | −0.602997 | −0.301498 | − | 0.953467i | \(-0.597487\pi\) | ||||
−0.301498 | + | 0.953467i | \(0.597487\pi\) | |||||||
\(332\) | 21.4437 | 1.17687 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.11270 | −0.443907 | ||||||||
\(335\) | 12.4142 | 0.678261 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.8284 | 0.807756 | 0.403878 | − | 0.914813i | \(-0.367662\pi\) | ||||
0.403878 | + | 0.914813i | \(0.367662\pi\) | |||||||
\(338\) | 5.10051 | 0.277431 | ||||||||
\(339\) | 30.1421 | 1.63710 | ||||||||
\(340\) | 1.51472 | 0.0821472 | ||||||||
\(341\) | −28.9706 | −1.56884 | ||||||||
\(342\) | 3.31371 | 0.179185 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 10.1716 | 0.548414 | ||||||||
\(345\) | −5.82843 | −0.313792 | ||||||||
\(346\) | 8.00000 | 0.430083 | ||||||||
\(347\) | 22.0711 | 1.18484 | 0.592418 | − | 0.805630i | \(-0.298173\pi\) | ||||
0.592418 | + | 0.805630i | \(0.298173\pi\) | |||||||
\(348\) | 4.41421 | 0.236627 | ||||||||
\(349\) | −26.6569 | −1.42691 | −0.713454 | − | 0.700702i | \(-0.752870\pi\) | ||||
−0.713454 | + | 0.700702i | \(0.752870\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.343146 | −0.0183158 | ||||||||
\(352\) | −21.3137 | −1.13602 | ||||||||
\(353\) | −21.1716 | −1.12685 | −0.563425 | − | 0.826168i | \(-0.690516\pi\) | ||||
−0.563425 | + | 0.826168i | \(0.690516\pi\) | |||||||
\(354\) | 12.4853 | 0.663585 | ||||||||
\(355\) | −12.4853 | −0.662650 | ||||||||
\(356\) | −4.85786 | −0.257466 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.14214 | 0.218919 | ||||||||
\(359\) | −10.0000 | −0.527780 | −0.263890 | − | 0.964553i | \(-0.585006\pi\) | ||||
−0.263890 | + | 0.964553i | \(0.585006\pi\) | |||||||
\(360\) | 4.48528 | 0.236395 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 3.58579 | 0.188465 | ||||||||
\(363\) | 29.7279 | 1.56031 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.82843 | 0.252731 | ||||||||
\(366\) | 11.4853 | 0.600345 | ||||||||
\(367\) | −11.2426 | −0.586861 | −0.293431 | − | 0.955980i | \(-0.594797\pi\) | ||||
−0.293431 | + | 0.955980i | \(0.594797\pi\) | |||||||
\(368\) | −7.24264 | −0.377549 | ||||||||
\(369\) | −6.14214 | −0.319747 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 26.4853 | 1.37320 | ||||||||
\(373\) | 12.9706 | 0.671590 | 0.335795 | − | 0.941935i | \(-0.390995\pi\) | ||||
0.335795 | + | 0.941935i | \(0.390995\pi\) | |||||||
\(374\) | 1.65685 | 0.0856739 | ||||||||
\(375\) | 2.41421 | 0.124669 | ||||||||
\(376\) | 3.17157 | 0.163561 | ||||||||
\(377\) | −0.828427 | −0.0426662 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.1716 | 1.08751 | 0.543755 | − | 0.839244i | \(-0.317002\pi\) | ||||
0.543755 | + | 0.839244i | \(0.317002\pi\) | |||||||
\(380\) | 5.17157 | 0.265296 | ||||||||
\(381\) | 32.1421 | 1.64669 | ||||||||
\(382\) | 2.97056 | 0.151987 | ||||||||
\(383\) | 16.8995 | 0.863524 | 0.431762 | − | 0.901988i | \(-0.357892\pi\) | ||||
0.431762 | + | 0.901988i | \(0.357892\pi\) | |||||||
\(384\) | 25.4853 | 1.30054 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.828427 | 0.0421658 | ||||||||
\(387\) | 18.1421 | 0.922217 | ||||||||
\(388\) | −0.627417 | −0.0318523 | ||||||||
\(389\) | 12.3431 | 0.625822 | 0.312911 | − | 0.949782i | \(-0.398696\pi\) | ||||
0.312911 | + | 0.949782i | \(0.398696\pi\) | |||||||
\(390\) | −0.828427 | −0.0419490 | ||||||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.00000 | 0.403547 | ||||||||
\(394\) | 9.79899 | 0.493666 | ||||||||
\(395\) | 9.17157 | 0.461472 | ||||||||
\(396\) | −24.9706 | −1.25482 | ||||||||
\(397\) | 28.6274 | 1.43677 | 0.718384 | − | 0.695646i | \(-0.244882\pi\) | ||||
0.718384 | + | 0.695646i | \(0.244882\pi\) | |||||||
\(398\) | −0.686292 | −0.0344007 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 7.68629 | 0.383835 | 0.191918 | − | 0.981411i | \(-0.438529\pi\) | ||||
0.191918 | + | 0.981411i | \(0.438529\pi\) | |||||||
\(402\) | −12.4142 | −0.619165 | ||||||||
\(403\) | −4.97056 | −0.247601 | ||||||||
\(404\) | −22.5147 | −1.12015 | ||||||||
\(405\) | −9.48528 | −0.471327 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −3.17157 | −0.157016 | ||||||||
\(409\) | 24.7990 | 1.22623 | 0.613116 | − | 0.789993i | \(-0.289916\pi\) | ||||
0.613116 | + | 0.789993i | \(0.289916\pi\) | |||||||
\(410\) | 0.899495 | 0.0444229 | ||||||||
\(411\) | 4.00000 | 0.197305 | ||||||||
\(412\) | −0.757359 | −0.0373124 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.82843 | 0.139010 | ||||||||
\(415\) | −11.7279 | −0.575701 | ||||||||
\(416\) | −3.65685 | −0.179292 | ||||||||
\(417\) | 29.3137 | 1.43550 | ||||||||
\(418\) | 5.65685 | 0.276686 | ||||||||
\(419\) | −23.3137 | −1.13895 | −0.569475 | − | 0.822009i | \(-0.692853\pi\) | ||||
−0.569475 | + | 0.822009i | \(0.692853\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.48528 | −0.169862 | −0.0849311 | − | 0.996387i | \(-0.527067\pi\) | ||||
−0.0849311 | + | 0.996387i | \(0.527067\pi\) | |||||||
\(422\) | −1.45584 | −0.0708694 | ||||||||
\(423\) | 5.65685 | 0.275046 | ||||||||
\(424\) | −10.8284 | −0.525875 | ||||||||
\(425\) | −0.828427 | −0.0401846 | ||||||||
\(426\) | 12.4853 | 0.604914 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.04163 | −0.243696 | ||||||||
\(429\) | 9.65685 | 0.466237 | ||||||||
\(430\) | −2.65685 | −0.128125 | ||||||||
\(431\) | −21.7990 | −1.05002 | −0.525010 | − | 0.851096i | \(-0.675938\pi\) | ||||
−0.525010 | + | 0.851096i | \(0.675938\pi\) | |||||||
\(432\) | −1.24264 | −0.0597866 | ||||||||
\(433\) | −31.7990 | −1.52816 | −0.764081 | − | 0.645120i | \(-0.776807\pi\) | ||||
−0.764081 | + | 0.645120i | \(0.776807\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.41421 | −0.115753 | ||||||||
\(436\) | −6.37258 | −0.305191 | ||||||||
\(437\) | 6.82843 | 0.326648 | ||||||||
\(438\) | −4.82843 | −0.230711 | ||||||||
\(439\) | 33.9411 | 1.61992 | 0.809961 | − | 0.586484i | \(-0.199488\pi\) | ||||
0.809961 | + | 0.586484i | \(0.199488\pi\) | |||||||
\(440\) | 7.65685 | 0.365026 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.284271 | 0.0135214 | ||||||||
\(443\) | −12.2132 | −0.580267 | −0.290133 | − | 0.956986i | \(-0.593700\pi\) | ||||
−0.290133 | + | 0.956986i | \(0.593700\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.65685 | 0.125947 | ||||||||
\(446\) | −4.82843 | −0.228633 | ||||||||
\(447\) | −18.8995 | −0.893915 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.82843 | −0.0862888 | −0.0431444 | − | 0.999069i | \(-0.513738\pi\) | ||||
−0.0431444 | + | 0.999069i | \(0.513738\pi\) | |||||||
\(450\) | −1.17157 | −0.0552285 | ||||||||
\(451\) | −10.4853 | −0.493733 | ||||||||
\(452\) | −22.8284 | −1.07376 | ||||||||
\(453\) | 0.828427 | 0.0389229 | ||||||||
\(454\) | −11.1716 | −0.524308 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −10.8284 | −0.507088 | ||||||||
\(457\) | −32.2843 | −1.51019 | −0.755097 | − | 0.655613i | \(-0.772410\pi\) | ||||
−0.755097 | + | 0.655613i | \(0.772410\pi\) | |||||||
\(458\) | 0.142136 | 0.00664156 | ||||||||
\(459\) | 0.343146 | 0.0160167 | ||||||||
\(460\) | 4.41421 | 0.205814 | ||||||||
\(461\) | 18.6863 | 0.870307 | 0.435154 | − | 0.900356i | \(-0.356694\pi\) | ||||
0.435154 | + | 0.900356i | \(0.356694\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0416 | 0.513148 | 0.256574 | − | 0.966525i | \(-0.417406\pi\) | ||||
0.256574 | + | 0.966525i | \(0.417406\pi\) | |||||||
\(464\) | −3.00000 | −0.139272 | ||||||||
\(465\) | −14.4853 | −0.671739 | ||||||||
\(466\) | 4.62742 | 0.214361 | ||||||||
\(467\) | −22.8995 | −1.05966 | −0.529831 | − | 0.848103i | \(-0.677745\pi\) | ||||
−0.529831 | + | 0.848103i | \(0.677745\pi\) | |||||||
\(468\) | −4.28427 | −0.198041 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.828427 | −0.0382125 | ||||||||
\(471\) | −12.8284 | −0.591103 | ||||||||
\(472\) | −19.7990 | −0.911322 | ||||||||
\(473\) | 30.9706 | 1.42403 | ||||||||
\(474\) | −9.17157 | −0.421264 | ||||||||
\(475\) | −2.82843 | −0.129777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.3137 | −0.884314 | ||||||||
\(478\) | −0.544156 | −0.0248891 | ||||||||
\(479\) | −24.3431 | −1.11227 | −0.556133 | − | 0.831093i | \(-0.687716\pi\) | ||||
−0.556133 | + | 0.831093i | \(0.687716\pi\) | |||||||
\(480\) | −10.6569 | −0.486417 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −6.76955 | −0.308345 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22.5147 | −1.02340 | ||||||||
\(485\) | 0.343146 | 0.0155814 | ||||||||
\(486\) | 8.97056 | 0.406913 | ||||||||
\(487\) | 15.6569 | 0.709480 | 0.354740 | − | 0.934965i | \(-0.384569\pi\) | ||||
0.354740 | + | 0.934965i | \(0.384569\pi\) | |||||||
\(488\) | −18.2132 | −0.824473 | ||||||||
\(489\) | 57.1127 | 2.58273 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.3137 | −0.600839 | −0.300420 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300420 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(492\) | 9.58579 | 0.432161 | ||||||||
\(493\) | 0.828427 | 0.0373105 | ||||||||
\(494\) | 0.970563 | 0.0436677 | ||||||||
\(495\) | 13.6569 | 0.613830 | ||||||||
\(496\) | −18.0000 | −0.808224 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 11.7279 | 0.525541 | ||||||||
\(499\) | 4.82843 | 0.216150 | 0.108075 | − | 0.994143i | \(-0.465531\pi\) | ||||
0.108075 | + | 0.994143i | \(0.465531\pi\) | |||||||
\(500\) | −1.82843 | −0.0817697 | ||||||||
\(501\) | 47.2843 | 2.11251 | ||||||||
\(502\) | −5.51472 | −0.246134 | ||||||||
\(503\) | 37.8701 | 1.68854 | 0.844271 | − | 0.535916i | \(-0.180034\pi\) | ||||
0.844271 | + | 0.535916i | \(0.180034\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.3137 | 0.547953 | ||||||||
\(506\) | 4.82843 | 0.214650 | ||||||||
\(507\) | −29.7279 | −1.32026 | ||||||||
\(508\) | −24.3431 | −1.08005 | ||||||||
\(509\) | 24.6569 | 1.09290 | 0.546448 | − | 0.837493i | \(-0.315980\pi\) | ||||
0.546448 | + | 0.837493i | \(0.315980\pi\) | |||||||
\(510\) | 0.828427 | 0.0366834 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.7574 | −1.00574 | ||||||||
\(513\) | 1.17157 | 0.0517262 | ||||||||
\(514\) | −7.31371 | −0.322594 | ||||||||
\(515\) | 0.414214 | 0.0182524 | ||||||||
\(516\) | −28.3137 | −1.24644 | ||||||||
\(517\) | 9.65685 | 0.424708 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −46.6274 | −2.04672 | ||||||||
\(520\) | 1.31371 | 0.0576099 | ||||||||
\(521\) | −18.9706 | −0.831115 | −0.415558 | − | 0.909567i | \(-0.636414\pi\) | ||||
−0.415558 | + | 0.909567i | \(0.636414\pi\) | |||||||
\(522\) | 1.17157 | 0.0512784 | ||||||||
\(523\) | 24.3431 | 1.06445 | 0.532226 | − | 0.846602i | \(-0.321356\pi\) | ||||
0.532226 | + | 0.846602i | \(0.321356\pi\) | |||||||
\(524\) | −6.05887 | −0.264683 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.88730 | −0.343903 | ||||||||
\(527\) | 4.97056 | 0.216521 | ||||||||
\(528\) | 34.9706 | 1.52190 | ||||||||
\(529\) | −17.1716 | −0.746590 | ||||||||
\(530\) | 2.82843 | 0.122859 | ||||||||
\(531\) | −35.3137 | −1.53248 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.79899 | −0.0779229 | ||||||||
\(534\) | −2.65685 | −0.114973 | ||||||||
\(535\) | 2.75736 | 0.119211 | ||||||||
\(536\) | 19.6863 | 0.850318 | ||||||||
\(537\) | −24.1421 | −1.04181 | ||||||||
\(538\) | 12.6152 | 0.543881 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.757359 | 0.0325916 | ||||||||
\(541\) | 18.6569 | 0.802121 | 0.401060 | − | 0.916052i | \(-0.368642\pi\) | ||||
0.401060 | + | 0.916052i | \(0.368642\pi\) | |||||||
\(542\) | 0.201010 | 0.00863412 | ||||||||
\(543\) | −20.8995 | −0.896883 | ||||||||
\(544\) | 3.65685 | 0.156786 | ||||||||
\(545\) | 3.48528 | 0.149293 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.10051 | 0.218082 | 0.109041 | − | 0.994037i | \(-0.465222\pi\) | ||||
0.109041 | + | 0.994037i | \(0.465222\pi\) | |||||||
\(548\) | −3.02944 | −0.129411 | ||||||||
\(549\) | −32.4853 | −1.38644 | ||||||||
\(550\) | −2.00000 | −0.0852803 | ||||||||
\(551\) | 2.82843 | 0.120495 | ||||||||
\(552\) | −9.24264 | −0.393393 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.02944 | 0.213680 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22.2010 | −0.941533 | ||||||||
\(557\) | −34.2843 | −1.45267 | −0.726336 | − | 0.687340i | \(-0.758778\pi\) | ||||
−0.726336 | + | 0.687340i | \(0.758778\pi\) | |||||||
\(558\) | 7.02944 | 0.297580 | ||||||||
\(559\) | 5.31371 | 0.224746 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.65685 | −0.407713 | ||||||||
\(562\) | −10.8873 | −0.459253 | ||||||||
\(563\) | 16.2721 | 0.685786 | 0.342893 | − | 0.939374i | \(-0.388593\pi\) | ||||
0.342893 | + | 0.939374i | \(0.388593\pi\) | |||||||
\(564\) | −8.82843 | −0.371744 | ||||||||
\(565\) | 12.4853 | 0.525260 | ||||||||
\(566\) | −5.79899 | −0.243750 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19.7990 | −0.830747 | ||||||||
\(569\) | −3.65685 | −0.153303 | −0.0766517 | − | 0.997058i | \(-0.524423\pi\) | ||||
−0.0766517 | + | 0.997058i | \(0.524423\pi\) | |||||||
\(570\) | 2.82843 | 0.118470 | ||||||||
\(571\) | 14.8284 | 0.620550 | 0.310275 | − | 0.950647i | \(-0.399579\pi\) | ||||
0.310275 | + | 0.950647i | \(0.399579\pi\) | |||||||
\(572\) | −7.31371 | −0.305802 | ||||||||
\(573\) | −17.3137 | −0.723291 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.41421 | −0.100680 | ||||||||
\(576\) | −11.7990 | −0.491625 | ||||||||
\(577\) | 23.9411 | 0.996682 | 0.498341 | − | 0.866981i | \(-0.333943\pi\) | ||||
0.498341 | + | 0.866981i | \(0.333943\pi\) | |||||||
\(578\) | 6.75736 | 0.281069 | ||||||||
\(579\) | −4.82843 | −0.200663 | ||||||||
\(580\) | 1.82843 | 0.0759213 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.343146 | −0.0142238 | ||||||||
\(583\) | −32.9706 | −1.36550 | ||||||||
\(584\) | 7.65685 | 0.316843 | ||||||||
\(585\) | 2.34315 | 0.0968772 | ||||||||
\(586\) | 6.62742 | 0.273776 | ||||||||
\(587\) | 22.2843 | 0.919770 | 0.459885 | − | 0.887978i | \(-0.347891\pi\) | ||||
0.459885 | + | 0.887978i | \(0.347891\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.9706 | 0.699260 | ||||||||
\(590\) | 5.17157 | 0.212910 | ||||||||
\(591\) | −57.1127 | −2.34930 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 43.7990 | 1.79861 | 0.899304 | − | 0.437323i | \(-0.144073\pi\) | ||||
0.899304 | + | 0.437323i | \(0.144073\pi\) | |||||||
\(594\) | 0.828427 | 0.0339908 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.3137 | 0.586312 | ||||||||
\(597\) | 4.00000 | 0.163709 | ||||||||
\(598\) | 0.828427 | 0.0338769 | ||||||||
\(599\) | 17.6569 | 0.721440 | 0.360720 | − | 0.932674i | \(-0.382531\pi\) | ||||
0.360720 | + | 0.932674i | \(0.382531\pi\) | |||||||
\(600\) | 3.82843 | 0.156295 | ||||||||
\(601\) | 8.34315 | 0.340324 | 0.170162 | − | 0.985416i | \(-0.445571\pi\) | ||||
0.170162 | + | 0.985416i | \(0.445571\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 35.1127 | 1.42990 | ||||||||
\(604\) | −0.627417 | −0.0255292 | ||||||||
\(605\) | 12.3137 | 0.500623 | ||||||||
\(606\) | −12.3137 | −0.500210 | ||||||||
\(607\) | −4.21320 | −0.171009 | −0.0855043 | − | 0.996338i | \(-0.527250\pi\) | ||||
−0.0855043 | + | 0.996338i | \(0.527250\pi\) | |||||||
\(608\) | 12.4853 | 0.506345 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.75736 | 0.192620 | ||||||||
\(611\) | 1.65685 | 0.0670291 | ||||||||
\(612\) | 4.28427 | 0.173181 | ||||||||
\(613\) | −15.4558 | −0.624256 | −0.312128 | − | 0.950040i | \(-0.601042\pi\) | ||||
−0.312128 | + | 0.950040i | \(0.601042\pi\) | |||||||
\(614\) | 5.48528 | 0.221368 | ||||||||
\(615\) | −5.24264 | −0.211404 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.3137 | −0.455473 | −0.227736 | − | 0.973723i | \(-0.573132\pi\) | ||||
−0.227736 | + | 0.973723i | \(0.573132\pi\) | |||||||
\(618\) | −0.414214 | −0.0166621 | ||||||||
\(619\) | 42.4853 | 1.70763 | 0.853814 | − | 0.520578i | \(-0.174284\pi\) | ||||
0.853814 | + | 0.520578i | \(0.174284\pi\) | |||||||
\(620\) | 10.9706 | 0.440588 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 7.79899 | 0.312711 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.00000 | 0.240192 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.31371 | 0.292315 | ||||||||
\(627\) | −32.9706 | −1.31672 | ||||||||
\(628\) | 9.71573 | 0.387700 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.14214 | 0.324133 | 0.162067 | − | 0.986780i | \(-0.448184\pi\) | ||||
0.162067 | + | 0.986780i | \(0.448184\pi\) | |||||||
\(632\) | 14.5442 | 0.578535 | ||||||||
\(633\) | 8.48528 | 0.337260 | ||||||||
\(634\) | −10.6863 | −0.424407 | ||||||||
\(635\) | 13.3137 | 0.528338 | ||||||||
\(636\) | 30.1421 | 1.19521 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.00000 | 0.0791808 | ||||||||
\(639\) | −35.3137 | −1.39699 | ||||||||
\(640\) | 10.5563 | 0.417276 | ||||||||
\(641\) | 14.5147 | 0.573297 | 0.286648 | − | 0.958036i | \(-0.407459\pi\) | ||||
0.286648 | + | 0.958036i | \(0.407459\pi\) | |||||||
\(642\) | −2.75736 | −0.108824 | ||||||||
\(643\) | −30.2843 | −1.19430 | −0.597148 | − | 0.802131i | \(-0.703699\pi\) | ||||
−0.597148 | + | 0.802131i | \(0.703699\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.4853 | 0.609732 | ||||||||
\(646\) | −0.970563 | −0.0381863 | ||||||||
\(647\) | 17.0416 | 0.669976 | 0.334988 | − | 0.942222i | \(-0.391268\pi\) | ||||
0.334988 | + | 0.942222i | \(0.391268\pi\) | |||||||
\(648\) | −15.0416 | −0.590891 | ||||||||
\(649\) | −60.2843 | −2.36636 | ||||||||
\(650\) | −0.343146 | −0.0134593 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −43.2548 | −1.69399 | ||||||||
\(653\) | −24.8284 | −0.971611 | −0.485806 | − | 0.874067i | \(-0.661474\pi\) | ||||
−0.485806 | + | 0.874067i | \(0.661474\pi\) | |||||||
\(654\) | −3.48528 | −0.136285 | ||||||||
\(655\) | 3.31371 | 0.129477 | ||||||||
\(656\) | −6.51472 | −0.254357 | ||||||||
\(657\) | 13.6569 | 0.532805 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.8284 | 1.04509 | 0.522544 | − | 0.852613i | \(-0.324983\pi\) | ||||
0.522544 | + | 0.852613i | \(0.324983\pi\) | |||||||
\(660\) | −21.3137 | −0.829635 | ||||||||
\(661\) | 26.1716 | 1.01796 | 0.508978 | − | 0.860779i | \(-0.330023\pi\) | ||||
0.508978 | + | 0.860779i | \(0.330023\pi\) | |||||||
\(662\) | 4.54416 | 0.176614 | ||||||||
\(663\) | −1.65685 | −0.0643469 | ||||||||
\(664\) | −18.5980 | −0.721742 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.41421 | 0.0934787 | ||||||||
\(668\) | −35.8112 | −1.38558 | ||||||||
\(669\) | 28.1421 | 1.08804 | ||||||||
\(670\) | −5.14214 | −0.198658 | ||||||||
\(671\) | −55.4558 | −2.14085 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.3431 | 0.707076 | 0.353538 | − | 0.935420i | \(-0.384978\pi\) | ||||
0.353538 | + | 0.935420i | \(0.384978\pi\) | |||||||
\(674\) | −6.14214 | −0.236586 | ||||||||
\(675\) | −0.414214 | −0.0159431 | ||||||||
\(676\) | 22.5147 | 0.865951 | ||||||||
\(677\) | 0.142136 | 0.00546272 | 0.00273136 | − | 0.999996i | \(-0.499131\pi\) | ||||
0.00273136 | + | 0.999996i | \(0.499131\pi\) | |||||||
\(678\) | −12.4853 | −0.479494 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.31371 | −0.0503784 | ||||||||
\(681\) | 65.1127 | 2.49512 | ||||||||
\(682\) | 12.0000 | 0.459504 | ||||||||
\(683\) | −43.2426 | −1.65463 | −0.827317 | − | 0.561736i | \(-0.810134\pi\) | ||||
−0.827317 | + | 0.561736i | \(0.810134\pi\) | |||||||
\(684\) | 14.6274 | 0.559293 | ||||||||
\(685\) | 1.65685 | 0.0633051 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.828427 | −0.0316065 | ||||||||
\(688\) | 19.2426 | 0.733619 | ||||||||
\(689\) | −5.65685 | −0.215509 | ||||||||
\(690\) | 2.41421 | 0.0919075 | ||||||||
\(691\) | −4.82843 | −0.183682 | −0.0918410 | − | 0.995774i | \(-0.529275\pi\) | ||||
−0.0918410 | + | 0.995774i | \(0.529275\pi\) | |||||||
\(692\) | 35.3137 | 1.34243 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.14214 | −0.347031 | ||||||||
\(695\) | 12.1421 | 0.460577 | ||||||||
\(696\) | −3.82843 | −0.145116 | ||||||||
\(697\) | 1.79899 | 0.0681416 | ||||||||
\(698\) | 11.0416 | 0.417932 | ||||||||
\(699\) | −26.9706 | −1.02012 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.7990 | −1.61650 | −0.808248 | − | 0.588843i | \(-0.799584\pi\) | ||||
−0.808248 | + | 0.588843i | \(0.799584\pi\) | |||||||
\(702\) | 0.142136 | 0.00536456 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −20.1421 | −0.759135 | ||||||||
\(705\) | 4.82843 | 0.181849 | ||||||||
\(706\) | 8.76955 | 0.330046 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 55.1127 | 2.07126 | ||||||||
\(709\) | 38.3137 | 1.43890 | 0.719451 | − | 0.694543i | \(-0.244394\pi\) | ||||
0.719451 | + | 0.694543i | \(0.244394\pi\) | |||||||
\(710\) | 5.17157 | 0.194086 | ||||||||
\(711\) | 25.9411 | 0.972868 | ||||||||
\(712\) | 4.21320 | 0.157896 | ||||||||
\(713\) | 14.4853 | 0.542478 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | 18.2843 | 0.683315 | ||||||||
\(717\) | 3.17157 | 0.118445 | ||||||||
\(718\) | 4.14214 | 0.154583 | ||||||||
\(719\) | −41.1127 | −1.53324 | −0.766622 | − | 0.642098i | \(-0.778064\pi\) | ||||
−0.766622 | + | 0.642098i | \(0.778064\pi\) | |||||||
\(720\) | 8.48528 | 0.316228 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.55635 | 0.169570 | ||||||||
\(723\) | 39.4558 | 1.46738 | ||||||||
\(724\) | 15.8284 | 0.588259 | ||||||||
\(725\) | −1.00000 | −0.0371391 | ||||||||
\(726\) | −12.3137 | −0.457005 | ||||||||
\(727\) | −40.4142 | −1.49888 | −0.749440 | − | 0.662072i | \(-0.769677\pi\) | ||||
−0.749440 | + | 0.662072i | \(0.769677\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | −2.00000 | −0.0740233 | ||||||||
\(731\) | −5.31371 | −0.196535 | ||||||||
\(732\) | 50.6985 | 1.87387 | ||||||||
\(733\) | −22.0000 | −0.812589 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(734\) | 4.65685 | 0.171888 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.6569 | 0.392817 | ||||||||
\(737\) | 59.9411 | 2.20796 | ||||||||
\(738\) | 2.54416 | 0.0936517 | ||||||||
\(739\) | 41.1127 | 1.51236 | 0.756178 | − | 0.654367i | \(-0.227065\pi\) | ||||
0.756178 | + | 0.654367i | \(0.227065\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.65685 | −0.207810 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.92893 | −0.0707657 | −0.0353828 | − | 0.999374i | \(-0.511265\pi\) | ||||
−0.0353828 | + | 0.999374i | \(0.511265\pi\) | |||||||
\(744\) | −22.9706 | −0.842142 | ||||||||
\(745\) | −7.82843 | −0.286811 | ||||||||
\(746\) | −5.37258 | −0.196704 | ||||||||
\(747\) | −33.1716 | −1.21368 | ||||||||
\(748\) | 7.31371 | 0.267416 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −41.6569 | −1.52008 | −0.760040 | − | 0.649876i | \(-0.774821\pi\) | ||||
−0.760040 | + | 0.649876i | \(0.774821\pi\) | |||||||
\(752\) | 6.00000 | 0.218797 | ||||||||
\(753\) | 32.1421 | 1.17132 | ||||||||
\(754\) | 0.343146 | 0.0124966 | ||||||||
\(755\) | 0.343146 | 0.0124884 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.4558 | 0.707135 | 0.353567 | − | 0.935409i | \(-0.384969\pi\) | ||||
0.353567 | + | 0.935409i | \(0.384969\pi\) | |||||||
\(758\) | −8.76955 | −0.318524 | ||||||||
\(759\) | −28.1421 | −1.02149 | ||||||||
\(760\) | −4.48528 | −0.162698 | ||||||||
\(761\) | −13.3137 | −0.482622 | −0.241311 | − | 0.970448i | \(-0.577577\pi\) | ||||
−0.241311 | + | 0.970448i | \(0.577577\pi\) | |||||||
\(762\) | −13.3137 | −0.482305 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 13.1127 | 0.474401 | ||||||||
\(765\) | −2.34315 | −0.0847166 | ||||||||
\(766\) | −7.00000 | −0.252920 | ||||||||
\(767\) | −10.3431 | −0.373469 | ||||||||
\(768\) | 9.58579 | 0.345897 | ||||||||
\(769\) | 44.6274 | 1.60931 | 0.804653 | − | 0.593745i | \(-0.202351\pi\) | ||||
0.804653 | + | 0.593745i | \(0.202351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 42.6274 | 1.53519 | ||||||||
\(772\) | 3.65685 | 0.131613 | ||||||||
\(773\) | 25.1127 | 0.903241 | 0.451620 | − | 0.892210i | \(-0.350846\pi\) | ||||
0.451620 | + | 0.892210i | \(0.350846\pi\) | |||||||
\(774\) | −7.51472 | −0.270111 | ||||||||
\(775\) | −6.00000 | −0.215526 | ||||||||
\(776\) | 0.544156 | 0.0195341 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.11270 | −0.183299 | ||||||||
\(779\) | 6.14214 | 0.220065 | ||||||||
\(780\) | −3.65685 | −0.130936 | ||||||||
\(781\) | −60.2843 | −2.15714 | ||||||||
\(782\) | −0.828427 | −0.0296245 | ||||||||
\(783\) | 0.414214 | 0.0148028 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.31371 | −0.189654 | ||||||||
\(786\) | −3.31371 | −0.118196 | ||||||||
\(787\) | −28.5563 | −1.01792 | −0.508962 | − | 0.860789i | \(-0.669971\pi\) | ||||
−0.508962 | + | 0.860789i | \(0.669971\pi\) | |||||||
\(788\) | 43.2548 | 1.54089 | ||||||||
\(789\) | 45.9706 | 1.63660 | ||||||||
\(790\) | −3.79899 | −0.135162 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 21.6569 | 0.769543 | ||||||||
\(793\) | −9.51472 | −0.337878 | ||||||||
\(794\) | −11.8579 | −0.420820 | ||||||||
\(795\) | −16.4853 | −0.584673 | ||||||||
\(796\) | −3.02944 | −0.107376 | ||||||||
\(797\) | −8.00000 | −0.283375 | −0.141687 | − | 0.989911i | \(-0.545253\pi\) | ||||
−0.141687 | + | 0.989911i | \(0.545253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.65685 | −0.0586153 | ||||||||
\(800\) | −4.41421 | −0.156066 | ||||||||
\(801\) | 7.51472 | 0.265520 | ||||||||
\(802\) | −3.18377 | −0.112423 | ||||||||
\(803\) | 23.3137 | 0.822723 | ||||||||
\(804\) | −54.7990 | −1.93261 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.05887 | 0.0725208 | ||||||||
\(807\) | −73.5269 | −2.58827 | ||||||||
\(808\) | 19.5269 | 0.686954 | ||||||||
\(809\) | −9.62742 | −0.338482 | −0.169241 | − | 0.985575i | \(-0.554132\pi\) | ||||
−0.169241 | + | 0.985575i | \(0.554132\pi\) | |||||||
\(810\) | 3.92893 | 0.138049 | ||||||||
\(811\) | 24.6274 | 0.864786 | 0.432393 | − | 0.901685i | \(-0.357669\pi\) | ||||
0.432393 | + | 0.901685i | \(0.357669\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.17157 | −0.0410889 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.6569 | 0.828663 | ||||||||
\(816\) | −6.00000 | −0.210042 | ||||||||
\(817\) | −18.1421 | −0.634713 | ||||||||
\(818\) | −10.2721 | −0.359155 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.97056 | 0.138658 | ||||||||
\(821\) | −19.9411 | −0.695950 | −0.347975 | − | 0.937504i | \(-0.613131\pi\) | ||||
−0.347975 | + | 0.937504i | \(0.613131\pi\) | |||||||
\(822\) | −1.65685 | −0.0577894 | ||||||||
\(823\) | −12.0711 | −0.420771 | −0.210385 | − | 0.977619i | \(-0.567472\pi\) | ||||
−0.210385 | + | 0.977619i | \(0.567472\pi\) | |||||||
\(824\) | 0.656854 | 0.0228826 | ||||||||
\(825\) | 11.6569 | 0.405840 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.2132 | 0.563788 | 0.281894 | − | 0.959446i | \(-0.409037\pi\) | ||||
0.281894 | + | 0.959446i | \(0.409037\pi\) | |||||||
\(828\) | 12.4853 | 0.433894 | ||||||||
\(829\) | 6.68629 | 0.232225 | 0.116112 | − | 0.993236i | \(-0.462957\pi\) | ||||
0.116112 | + | 0.993236i | \(0.462957\pi\) | |||||||
\(830\) | 4.85786 | 0.168619 | ||||||||
\(831\) | −29.3137 | −1.01688 | ||||||||
\(832\) | −3.45584 | −0.119810 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −12.1421 | −0.420448 | ||||||||
\(835\) | 19.5858 | 0.677794 | ||||||||
\(836\) | 24.9706 | 0.863625 | ||||||||
\(837\) | 2.48528 | 0.0859039 | ||||||||
\(838\) | 9.65685 | 0.333590 | ||||||||
\(839\) | 20.8284 | 0.719077 | 0.359539 | − | 0.933130i | \(-0.382934\pi\) | ||||
0.359539 | + | 0.933130i | \(0.382934\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 1.44365 | 0.0497515 | ||||||||
\(843\) | 63.4558 | 2.18554 | ||||||||
\(844\) | −6.42641 | −0.221206 | ||||||||
\(845\) | −12.3137 | −0.423604 | ||||||||
\(846\) | −2.34315 | −0.0805590 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −20.4853 | −0.703467 | ||||||||
\(849\) | 33.7990 | 1.15998 | ||||||||
\(850\) | 0.343146 | 0.0117698 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 55.1127 | 1.88813 | ||||||||
\(853\) | 53.4558 | 1.83029 | 0.915147 | − | 0.403121i | \(-0.132075\pi\) | ||||
0.915147 | + | 0.403121i | \(0.132075\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.00000 | −0.273594 | ||||||||
\(856\) | 4.37258 | 0.149452 | ||||||||
\(857\) | −22.2843 | −0.761216 | −0.380608 | − | 0.924736i | \(-0.624285\pi\) | ||||
−0.380608 | + | 0.924736i | \(0.624285\pi\) | |||||||
\(858\) | −4.00000 | −0.136558 | ||||||||
\(859\) | 46.6274 | 1.59091 | 0.795453 | − | 0.606015i | \(-0.207233\pi\) | ||||
0.795453 | + | 0.606015i | \(0.207233\pi\) | |||||||
\(860\) | −11.7279 | −0.399919 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.02944 | 0.307544 | ||||||||
\(863\) | −16.5563 | −0.563585 | −0.281792 | − | 0.959475i | \(-0.590929\pi\) | ||||
−0.281792 | + | 0.959475i | \(0.590929\pi\) | |||||||
\(864\) | 1.82843 | 0.0622044 | ||||||||
\(865\) | −19.3137 | −0.656686 | ||||||||
\(866\) | 13.1716 | 0.447588 | ||||||||
\(867\) | −39.3848 | −1.33758 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44.2843 | 1.50224 | ||||||||
\(870\) | 1.00000 | 0.0339032 | ||||||||
\(871\) | 10.2843 | 0.348469 | ||||||||
\(872\) | 5.52691 | 0.187165 | ||||||||
\(873\) | 0.970563 | 0.0328486 | ||||||||
\(874\) | −2.82843 | −0.0956730 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −21.3137 | −0.720123 | ||||||||
\(877\) | 30.8284 | 1.04100 | 0.520501 | − | 0.853861i | \(-0.325745\pi\) | ||||
0.520501 | + | 0.853861i | \(0.325745\pi\) | |||||||
\(878\) | −14.0589 | −0.474464 | ||||||||
\(879\) | −38.6274 | −1.30287 | ||||||||
\(880\) | 14.4853 | 0.488299 | ||||||||
\(881\) | −3.82843 | −0.128983 | −0.0644915 | − | 0.997918i | \(-0.520543\pi\) | ||||
−0.0644915 | + | 0.997918i | \(0.520543\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.2843 | −1.28837 | −0.644184 | − | 0.764870i | \(-0.722803\pi\) | ||||
−0.644184 | + | 0.764870i | \(0.722803\pi\) | |||||||
\(884\) | 1.25483 | 0.0422046 | ||||||||
\(885\) | −30.1421 | −1.01322 | ||||||||
\(886\) | 5.05887 | 0.169956 | ||||||||
\(887\) | 44.0711 | 1.47976 | 0.739881 | − | 0.672738i | \(-0.234882\pi\) | ||||
0.739881 | + | 0.672738i | \(0.234882\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.10051 | −0.0368890 | ||||||||
\(891\) | −45.7990 | −1.53432 | ||||||||
\(892\) | −21.3137 | −0.713636 | ||||||||
\(893\) | −5.65685 | −0.189299 | ||||||||
\(894\) | 7.82843 | 0.261822 | ||||||||
\(895\) | −10.0000 | −0.334263 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.82843 | −0.161216 | ||||||||
\(898\) | 0.757359 | 0.0252734 | ||||||||
\(899\) | 6.00000 | 0.200111 | ||||||||
\(900\) | −5.17157 | −0.172386 | ||||||||
\(901\) | 5.65685 | 0.188457 | ||||||||
\(902\) | 4.34315 | 0.144611 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.7990 | 0.658505 | ||||||||
\(905\) | −8.65685 | −0.287764 | ||||||||
\(906\) | −0.343146 | −0.0114003 | ||||||||
\(907\) | 28.2132 | 0.936804 | 0.468402 | − | 0.883515i | \(-0.344830\pi\) | ||||
0.468402 | + | 0.883515i | \(0.344830\pi\) | |||||||
\(908\) | −49.3137 | −1.63653 | ||||||||
\(909\) | 34.8284 | 1.15519 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.7990 | −1.64991 | −0.824957 | − | 0.565195i | \(-0.808801\pi\) | ||||
−0.824957 | + | 0.565195i | \(0.808801\pi\) | |||||||
\(912\) | −20.4853 | −0.678335 | ||||||||
\(913\) | −56.6274 | −1.87409 | ||||||||
\(914\) | 13.3726 | 0.442326 | ||||||||
\(915\) | −27.7279 | −0.916657 | ||||||||
\(916\) | 0.627417 | 0.0207304 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.142136 | −0.00469117 | ||||||||
\(919\) | 19.1127 | 0.630470 | 0.315235 | − | 0.949014i | \(-0.397917\pi\) | ||||
0.315235 | + | 0.949014i | \(0.397917\pi\) | |||||||
\(920\) | −3.82843 | −0.126220 | ||||||||
\(921\) | −31.9706 | −1.05347 | ||||||||
\(922\) | −7.74012 | −0.254907 | ||||||||
\(923\) | −10.3431 | −0.340449 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.57359 | −0.150298 | ||||||||
\(927\) | 1.17157 | 0.0384795 | ||||||||
\(928\) | 4.41421 | 0.144904 | ||||||||
\(929\) | −11.4853 | −0.376820 | −0.188410 | − | 0.982090i | \(-0.560333\pi\) | ||||
−0.188410 | + | 0.982090i | \(0.560333\pi\) | |||||||
\(930\) | 6.00000 | 0.196748 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.4264 | 0.669089 | ||||||||
\(933\) | −45.4558 | −1.48816 | ||||||||
\(934\) | 9.48528 | 0.310368 | ||||||||
\(935\) | −4.00000 | −0.130814 | ||||||||
\(936\) | 3.71573 | 0.121452 | ||||||||
\(937\) | −10.6274 | −0.347183 | −0.173591 | − | 0.984818i | \(-0.555537\pi\) | ||||
−0.173591 | + | 0.984818i | \(0.555537\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −42.6274 | −1.39109 | ||||||||
\(940\) | −3.65685 | −0.119273 | ||||||||
\(941\) | 10.2843 | 0.335258 | 0.167629 | − | 0.985850i | \(-0.446389\pi\) | ||||
0.167629 | + | 0.985850i | \(0.446389\pi\) | |||||||
\(942\) | 5.31371 | 0.173130 | ||||||||
\(943\) | 5.24264 | 0.170724 | ||||||||
\(944\) | −37.4558 | −1.21908 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.8284 | −0.417088 | ||||||||
\(947\) | −43.1838 | −1.40328 | −0.701642 | − | 0.712530i | \(-0.747549\pi\) | ||||
−0.701642 | + | 0.712530i | \(0.747549\pi\) | |||||||
\(948\) | −40.4853 | −1.31490 | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 1.17157 | 0.0380108 | ||||||||
\(951\) | 62.2843 | 2.01971 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.34315 | −0.0759019 | −0.0379510 | − | 0.999280i | \(-0.512083\pi\) | ||||
−0.0379510 | + | 0.999280i | \(0.512083\pi\) | |||||||
\(954\) | 8.00000 | 0.259010 | ||||||||
\(955\) | −7.17157 | −0.232067 | ||||||||
\(956\) | −2.40202 | −0.0776869 | ||||||||
\(957\) | −11.6569 | −0.376813 | ||||||||
\(958\) | 10.0833 | 0.325775 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −10.0711 | −0.325042 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.79899 | 0.251319 | ||||||||
\(964\) | −29.8823 | −0.962442 | ||||||||
\(965\) | −2.00000 | −0.0643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.5269 | −0.885206 | −0.442603 | − | 0.896718i | \(-0.645945\pi\) | ||||
−0.442603 | + | 0.896718i | \(0.645945\pi\) | |||||||
\(968\) | 19.5269 | 0.627619 | ||||||||
\(969\) | 5.65685 | 0.181724 | ||||||||
\(970\) | −0.142136 | −0.00456370 | ||||||||
\(971\) | −24.0000 | −0.770197 | −0.385098 | − | 0.922876i | \(-0.625832\pi\) | ||||
−0.385098 | + | 0.922876i | \(0.625832\pi\) | |||||||
\(972\) | 39.5980 | 1.27011 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.48528 | −0.207802 | ||||||||
\(975\) | 2.00000 | 0.0640513 | ||||||||
\(976\) | −34.4558 | −1.10290 | ||||||||
\(977\) | 21.3137 | 0.681886 | 0.340943 | − | 0.940084i | \(-0.389254\pi\) | ||||
0.340943 | + | 0.940084i | \(0.389254\pi\) | |||||||
\(978\) | −23.6569 | −0.756463 | ||||||||
\(979\) | 12.8284 | 0.409998 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.85786 | 0.314737 | ||||||||
\(982\) | 5.51472 | 0.175982 | ||||||||
\(983\) | −14.2132 | −0.453331 | −0.226665 | − | 0.973973i | \(-0.572782\pi\) | ||||
−0.226665 | + | 0.973973i | \(0.572782\pi\) | |||||||
\(984\) | −8.31371 | −0.265031 | ||||||||
\(985\) | −23.6569 | −0.753770 | ||||||||
\(986\) | −0.343146 | −0.0109280 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.28427 | 0.136301 | ||||||||
\(989\) | −15.4853 | −0.492403 | ||||||||
\(990\) | −5.65685 | −0.179787 | ||||||||
\(991\) | −15.6569 | −0.497356 | −0.248678 | − | 0.968586i | \(-0.579996\pi\) | ||||
−0.248678 | + | 0.968586i | \(0.579996\pi\) | |||||||
\(992\) | 26.4853 | 0.840909 | ||||||||
\(993\) | −26.4853 | −0.840485 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.65685 | 0.0525258 | ||||||||
\(996\) | 51.7696 | 1.64038 | ||||||||
\(997\) | −17.4558 | −0.552832 | −0.276416 | − | 0.961038i | \(-0.589147\pi\) | ||||
−0.276416 | + | 0.961038i | \(0.589147\pi\) | |||||||
\(998\) | −2.00000 | −0.0633089 | ||||||||
\(999\) | 0 | 0 |
(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 | 245.2.a.h.1.1 | 2 | ||
3.2 | odd | 2 | 2205.2.a.n.1.2 | 2 | |||
4.3 | odd | 2 | 3920.2.a.bq.1.1 | 2 | |||
5.2 | odd | 4 | 1225.2.b.g.99.2 | 4 | |||
5.3 | odd | 4 | 1225.2.b.g.99.3 | 4 | |||
5.4 | even | 2 | 1225.2.a.k.1.2 | 2 | |||
7.2 | even | 3 | 35.2.e.a.11.2 | ✓ | 4 | ||
7.3 | odd | 6 | 245.2.e.e.226.2 | 4 | |||
7.4 | even | 3 | 35.2.e.a.16.2 | yes | 4 | ||
7.5 | odd | 6 | 245.2.e.e.116.2 | 4 | |||
7.6 | odd | 2 | 245.2.a.g.1.1 | 2 | |||
21.2 | odd | 6 | 315.2.j.e.46.1 | 4 | |||
21.11 | odd | 6 | 315.2.j.e.226.1 | 4 | |||
21.20 | even | 2 | 2205.2.a.q.1.2 | 2 | |||
28.11 | odd | 6 | 560.2.q.k.401.2 | 4 | |||
28.23 | odd | 6 | 560.2.q.k.81.2 | 4 | |||
28.27 | even | 2 | 3920.2.a.bv.1.2 | 2 | |||
35.2 | odd | 12 | 175.2.k.a.74.2 | 8 | |||
35.4 | even | 6 | 175.2.e.c.51.1 | 4 | |||
35.9 | even | 6 | 175.2.e.c.151.1 | 4 | |||
35.13 | even | 4 | 1225.2.b.h.99.3 | 4 | |||
35.18 | odd | 12 | 175.2.k.a.149.2 | 8 | |||
35.23 | odd | 12 | 175.2.k.a.74.3 | 8 | |||
35.27 | even | 4 | 1225.2.b.h.99.2 | 4 | |||
35.32 | odd | 12 | 175.2.k.a.149.3 | 8 | |||
35.34 | odd | 2 | 1225.2.a.m.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.e.a.11.2 | ✓ | 4 | 7.2 | even | 3 | ||
35.2.e.a.16.2 | yes | 4 | 7.4 | even | 3 | ||
175.2.e.c.51.1 | 4 | 35.4 | even | 6 | |||
175.2.e.c.151.1 | 4 | 35.9 | even | 6 | |||
175.2.k.a.74.2 | 8 | 35.2 | odd | 12 | |||
175.2.k.a.74.3 | 8 | 35.23 | odd | 12 | |||
175.2.k.a.149.2 | 8 | 35.18 | odd | 12 | |||
175.2.k.a.149.3 | 8 | 35.32 | odd | 12 | |||
245.2.a.g.1.1 | 2 | 7.6 | odd | 2 | |||
245.2.a.h.1.1 | 2 | 1.1 | even | 1 | trivial | ||
245.2.e.e.116.2 | 4 | 7.5 | odd | 6 | |||
245.2.e.e.226.2 | 4 | 7.3 | odd | 6 | |||
315.2.j.e.46.1 | 4 | 21.2 | odd | 6 | |||
315.2.j.e.226.1 | 4 | 21.11 | odd | 6 | |||
560.2.q.k.81.2 | 4 | 28.23 | odd | 6 | |||
560.2.q.k.401.2 | 4 | 28.11 | odd | 6 | |||
1225.2.a.k.1.2 | 2 | 5.4 | even | 2 | |||
1225.2.a.m.1.2 | 2 | 35.34 | odd | 2 | |||
1225.2.b.g.99.2 | 4 | 5.2 | odd | 4 | |||
1225.2.b.g.99.3 | 4 | 5.3 | odd | 4 | |||
1225.2.b.h.99.2 | 4 | 35.27 | even | 4 | |||
1225.2.b.h.99.3 | 4 | 35.13 | even | 4 | |||
2205.2.a.n.1.2 | 2 | 3.2 | odd | 2 | |||
2205.2.a.q.1.2 | 2 | 21.20 | even | 2 | |||
3920.2.a.bq.1.1 | 2 | 4.3 | odd | 2 | |||
3920.2.a.bv.1.2 | 2 | 28.27 | even | 2 |