Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,2,Mod(99,1225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1225.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(9.78167424761\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.2 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1225.99 |
Dual form | 1225.2.b.g.99.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.414214i | − 0.292893i | −0.989219 | − | 0.146447i | \(-0.953216\pi\) | ||||
0.989219 | − | 0.146447i | \(-0.0467837\pi\) | |||||||
\(3\) | − 2.41421i | − 1.39385i | −0.717146 | − | 0.696923i | \(-0.754552\pi\) | ||||
0.717146 | − | 0.696923i | \(-0.245448\pi\) | |||||||
\(4\) | 1.82843 | 0.914214 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 1.58579i | − 0.560660i | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.82843 | 1.45583 | 0.727913 | − | 0.685670i | \(-0.240491\pi\) | ||||
0.727913 | + | 0.685670i | \(0.240491\pi\) | |||||||
\(12\) | − 4.41421i | − 1.27427i | ||||||||
\(13\) | − 0.828427i | − 0.229764i | −0.993379 | − | 0.114882i | \(-0.963351\pi\) | ||||
0.993379 | − | 0.114882i | \(-0.0366490\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | − 0.828427i | − 0.200923i | −0.994941 | − | 0.100462i | \(-0.967968\pi\) | ||||
0.994941 | − | 0.100462i | \(-0.0320319\pi\) | |||||||
\(18\) | 1.17157i | 0.276142i | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 2.00000i | − 0.426401i | ||||||||
\(23\) | 2.41421i | 0.503398i | 0.967806 | + | 0.251699i | \(0.0809893\pi\) | ||||
−0.967806 | + | 0.251699i | \(0.919011\pi\) | |||||||
\(24\) | −3.82843 | −0.781474 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.343146 | −0.0672964 | ||||||||
\(27\) | − 0.414214i | − 0.0797154i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | − 4.41421i | − 0.780330i | ||||||||
\(33\) | − 11.6569i | − 2.02920i | ||||||||
\(34\) | −0.343146 | −0.0588490 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.17157 | −0.861929 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | − 1.17157i | − 0.190054i | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.17157 | −0.339143 | −0.169571 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169571 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 6.41421i | − 0.978158i | −0.872239 | − | 0.489079i | \(-0.837333\pi\) | ||||
0.872239 | − | 0.489079i | \(-0.162667\pi\) | |||||||
\(44\) | 8.82843 | 1.33094 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 2.00000i | 0.291730i | 0.989305 | + | 0.145865i | \(0.0465965\pi\) | ||||
−0.989305 | + | 0.145865i | \(0.953403\pi\) | |||||||
\(48\) | − 7.24264i | − 1.04539i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | − 1.51472i | − 0.210054i | ||||||||
\(53\) | 6.82843i | 0.937957i | 0.883210 | + | 0.468978i | \(0.155378\pi\) | ||||
−0.883210 | + | 0.468978i | \(0.844622\pi\) | |||||||
\(54\) | −0.171573 | −0.0233481 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 6.82843i | − 0.904447i | ||||||||
\(58\) | − 0.414214i | − 0.0543889i | ||||||||
\(59\) | 12.4853 | 1.62545 | 0.812723 | − | 0.582651i | \(-0.197984\pi\) | ||||
0.812723 | + | 0.582651i | \(0.197984\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.4853 | −1.47054 | −0.735270 | − | 0.677775i | \(-0.762945\pi\) | ||||
−0.735270 | + | 0.677775i | \(0.762945\pi\) | |||||||
\(62\) | 2.48528i | 0.315631i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.17157 | 0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.82843 | −0.594338 | ||||||||
\(67\) | 12.4142i | 1.51664i | 0.651884 | + | 0.758319i | \(0.273979\pi\) | ||||
−0.651884 | + | 0.758319i | \(0.726021\pi\) | |||||||
\(68\) | − 1.51472i | − 0.183687i | ||||||||
\(69\) | 5.82843 | 0.701660 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4853 | −1.48173 | −0.740865 | − | 0.671654i | \(-0.765584\pi\) | ||||
−0.740865 | + | 0.671654i | \(0.765584\pi\) | |||||||
\(72\) | 4.48528i | 0.528595i | ||||||||
\(73\) | − 4.82843i | − 0.565125i | −0.959249 | − | 0.282562i | \(-0.908816\pi\) | ||||
0.959249 | − | 0.282562i | \(-0.0911844\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.17157 | 0.593220 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.828427i | 0.0938009i | ||||||||
\(79\) | −9.17157 | −1.03188 | −0.515941 | − | 0.856624i | \(-0.672558\pi\) | ||||
−0.515941 | + | 0.856624i | \(0.672558\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0.899495i | 0.0993326i | ||||||||
\(83\) | 11.7279i | 1.28731i | 0.765317 | + | 0.643653i | \(0.222582\pi\) | ||||
−0.765317 | + | 0.643653i | \(0.777418\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.65685 | −0.286496 | ||||||||
\(87\) | − 2.41421i | − 0.258831i | ||||||||
\(88\) | − 7.65685i | − 0.816223i | ||||||||
\(89\) | −2.65685 | −0.281626 | −0.140813 | − | 0.990036i | \(-0.544972\pi\) | ||||
−0.140813 | + | 0.990036i | \(0.544972\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.41421i | 0.460214i | ||||||||
\(93\) | 14.4853i | 1.50205i | ||||||||
\(94\) | 0.828427 | 0.0854457 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −10.6569 | −1.08766 | ||||||||
\(97\) | 0.343146i | 0.0348412i | 0.999848 | + | 0.0174206i | \(0.00554543\pi\) | ||||
−0.999848 | + | 0.0174206i | \(0.994455\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.6569 | −1.37257 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.3137 | 1.22526 | 0.612630 | − | 0.790370i | \(-0.290112\pi\) | ||||
0.612630 | + | 0.790370i | \(0.290112\pi\) | |||||||
\(102\) | 0.828427i | 0.0820265i | ||||||||
\(103\) | − 0.414214i | − 0.0408137i | −0.999792 | − | 0.0204068i | \(-0.993504\pi\) | ||||
0.999792 | − | 0.0204068i | \(-0.00649615\pi\) | |||||||
\(104\) | −1.31371 | −0.128820 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.82843 | 0.274721 | ||||||||
\(107\) | 2.75736i | 0.266564i | 0.991078 | + | 0.133282i | \(0.0425516\pi\) | ||||
−0.991078 | + | 0.133282i | \(0.957448\pi\) | |||||||
\(108\) | − 0.757359i | − 0.0728769i | ||||||||
\(109\) | −3.48528 | −0.333829 | −0.166915 | − | 0.985971i | \(-0.553380\pi\) | ||||
−0.166915 | + | 0.985971i | \(0.553380\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 12.4853i | − 1.17452i | −0.809400 | − | 0.587258i | \(-0.800207\pi\) | ||||
0.809400 | − | 0.587258i | \(-0.199793\pi\) | |||||||
\(114\) | −2.82843 | −0.264906 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.82843 | 0.169765 | ||||||||
\(117\) | 2.34315i | 0.216624i | ||||||||
\(118\) | − 5.17157i | − 0.476082i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | 4.75736i | 0.430711i | ||||||||
\(123\) | 5.24264i | 0.472713i | ||||||||
\(124\) | −10.9706 | −0.985186 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.3137i | 1.18140i | 0.806891 | + | 0.590700i | \(0.201148\pi\) | ||||
−0.806891 | + | 0.590700i | \(0.798852\pi\) | |||||||
\(128\) | − 10.5563i | − 0.933058i | ||||||||
\(129\) | −15.4853 | −1.36340 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.31371 | 0.289520 | 0.144760 | − | 0.989467i | \(-0.453759\pi\) | ||||
0.144760 | + | 0.989467i | \(0.453759\pi\) | |||||||
\(132\) | − 21.3137i | − 1.85512i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.14214 | 0.444213 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.31371 | −0.112650 | ||||||||
\(137\) | 1.65685i | 0.141555i | 0.997492 | + | 0.0707773i | \(0.0225480\pi\) | ||||
−0.997492 | + | 0.0707773i | \(0.977452\pi\) | |||||||
\(138\) | − 2.41421i | − 0.205512i | ||||||||
\(139\) | −12.1421 | −1.02988 | −0.514941 | − | 0.857225i | \(-0.672186\pi\) | ||||
−0.514941 | + | 0.857225i | \(0.672186\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.82843 | 0.406627 | ||||||||
\(142\) | 5.17157i | 0.433989i | ||||||||
\(143\) | − 4.00000i | − 0.334497i | ||||||||
\(144\) | −8.48528 | −0.707107 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.82843 | 0.641330 | 0.320665 | − | 0.947193i | \(-0.396094\pi\) | ||||
0.320665 | + | 0.947193i | \(0.396094\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.343146 | 0.0279248 | 0.0139624 | − | 0.999903i | \(-0.495555\pi\) | ||||
0.0139624 | + | 0.999903i | \(0.495555\pi\) | |||||||
\(152\) | − 4.48528i | − 0.363804i | ||||||||
\(153\) | 2.34315i | 0.189432i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.65685 | −0.292783 | ||||||||
\(157\) | − 5.31371i | − 0.424080i | −0.977261 | − | 0.212040i | \(-0.931989\pi\) | ||||
0.977261 | − | 0.212040i | \(-0.0680107\pi\) | |||||||
\(158\) | 3.79899i | 0.302231i | ||||||||
\(159\) | 16.4853 | 1.30737 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.92893i | 0.308686i | ||||||||
\(163\) | − 23.6569i | − 1.85295i | −0.376359 | − | 0.926474i | \(-0.622824\pi\) | ||||
0.376359 | − | 0.926474i | \(-0.377176\pi\) | |||||||
\(164\) | −3.97056 | −0.310049 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.85786 | 0.377043 | ||||||||
\(167\) | 19.5858i | 1.51559i | 0.652491 | + | 0.757797i | \(0.273724\pi\) | ||||
−0.652491 | + | 0.757797i | \(0.726276\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.3137 | 0.947208 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.00000 | −0.611775 | ||||||||
\(172\) | − 11.7279i | − 0.894246i | ||||||||
\(173\) | 19.3137i | 1.46839i | 0.678936 | + | 0.734197i | \(0.262441\pi\) | ||||
−0.678936 | + | 0.734197i | \(0.737559\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.4853 | 1.09187 | ||||||||
\(177\) | − 30.1421i | − 2.26562i | ||||||||
\(178\) | 1.10051i | 0.0824863i | ||||||||
\(179\) | 10.0000 | 0.747435 | 0.373718 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.65685 | −0.643459 | −0.321729 | − | 0.946832i | \(-0.604264\pi\) | ||||
−0.321729 | + | 0.946832i | \(0.604264\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 27.7279i | 2.04971i | ||||||||
\(184\) | 3.82843 | 0.282235 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | − 4.00000i | − 0.292509i | ||||||||
\(188\) | 3.65685i | 0.266704i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.17157 | −0.518917 | −0.259458 | − | 0.965754i | \(-0.583544\pi\) | ||||
−0.259458 | + | 0.965754i | \(0.583544\pi\) | |||||||
\(192\) | − 10.0711i | − 0.726817i | ||||||||
\(193\) | 2.00000i | 0.143963i | 0.997406 | + | 0.0719816i | \(0.0229323\pi\) | ||||
−0.997406 | + | 0.0719816i | \(0.977068\pi\) | |||||||
\(194\) | 0.142136 | 0.0102047 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 23.6569i | − 1.68548i | −0.538320 | − | 0.842741i | \(-0.680941\pi\) | ||||
0.538320 | − | 0.842741i | \(-0.319059\pi\) | |||||||
\(198\) | 5.65685i | 0.402015i | ||||||||
\(199\) | −1.65685 | −0.117451 | −0.0587256 | − | 0.998274i | \(-0.518704\pi\) | ||||
−0.0587256 | + | 0.998274i | \(0.518704\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 29.9706 | 2.11396 | ||||||||
\(202\) | − 5.10051i | − 0.358870i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.65685 | −0.256031 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.171573 | −0.0119540 | ||||||||
\(207\) | − 6.82843i | − 0.474608i | ||||||||
\(208\) | − 2.48528i | − 0.172323i | ||||||||
\(209\) | 13.6569 | 0.944664 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.51472 | 0.241963 | 0.120982 | − | 0.992655i | \(-0.461396\pi\) | ||||
0.120982 | + | 0.992655i | \(0.461396\pi\) | |||||||
\(212\) | 12.4853i | 0.857493i | ||||||||
\(213\) | 30.1421i | 2.06531i | ||||||||
\(214\) | 1.14214 | 0.0780748 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.656854 | −0.0446933 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.44365i | 0.0977764i | ||||||||
\(219\) | −11.6569 | −0.787697 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.686292 | −0.0461650 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 11.6569i | − 0.780601i | −0.920688 | − | 0.390300i | \(-0.872371\pi\) | ||||
0.920688 | − | 0.390300i | \(-0.127629\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.17157 | −0.344008 | ||||||||
\(227\) | 26.9706i | 1.79010i | 0.445967 | + | 0.895050i | \(0.352860\pi\) | ||||
−0.445967 | + | 0.895050i | \(0.647140\pi\) | |||||||
\(228\) | − 12.4853i | − 0.826858i | ||||||||
\(229\) | 0.343146 | 0.0226757 | 0.0113379 | − | 0.999936i | \(-0.496391\pi\) | ||||
0.0113379 | + | 0.999936i | \(0.496391\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 1.58579i | − 0.104112i | ||||||||
\(233\) | 11.1716i | 0.731874i | 0.930640 | + | 0.365937i | \(0.119251\pi\) | ||||
−0.930640 | + | 0.365937i | \(0.880749\pi\) | |||||||
\(234\) | 0.970563 | 0.0634477 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 22.8284 | 1.48600 | ||||||||
\(237\) | 22.1421i | 1.43829i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.31371 | −0.0849767 | −0.0424884 | − | 0.999097i | \(-0.513529\pi\) | ||||
−0.0424884 | + | 0.999097i | \(0.513529\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.3431 | 1.05275 | 0.526377 | − | 0.850251i | \(-0.323550\pi\) | ||||
0.526377 | + | 0.850251i | \(0.323550\pi\) | |||||||
\(242\) | − 5.10051i | − 0.327873i | ||||||||
\(243\) | 21.6569i | 1.38929i | ||||||||
\(244\) | −21.0000 | −1.34439 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.17157 | 0.138454 | ||||||||
\(247\) | − 2.34315i | − 0.149091i | ||||||||
\(248\) | 9.51472i | 0.604185i | ||||||||
\(249\) | 28.3137 | 1.79431 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.3137 | 0.840354 | 0.420177 | − | 0.907442i | \(-0.361968\pi\) | ||||
0.420177 | + | 0.907442i | \(0.361968\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.6569i | 0.732860i | ||||||||
\(254\) | 5.51472 | 0.346024 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | 17.6569i | 1.10140i | 0.834702 | + | 0.550702i | \(0.185640\pi\) | ||||
−0.834702 | + | 0.550702i | \(0.814360\pi\) | |||||||
\(258\) | 6.41421i | 0.399331i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.82843 | −0.175075 | ||||||||
\(262\) | − 1.37258i | − 0.0847985i | ||||||||
\(263\) | − 19.0416i | − 1.17416i | −0.809530 | − | 0.587079i | \(-0.800278\pi\) | ||||
0.809530 | − | 0.587079i | \(-0.199722\pi\) | |||||||
\(264\) | −18.4853 | −1.13769 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.41421i | 0.392543i | ||||||||
\(268\) | 22.6985i | 1.38653i | ||||||||
\(269\) | 30.4558 | 1.85693 | 0.928463 | − | 0.371425i | \(-0.121131\pi\) | ||||
0.928463 | + | 0.371425i | \(0.121131\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.485281 | −0.0294787 | −0.0147394 | − | 0.999891i | \(-0.504692\pi\) | ||||
−0.0147394 | + | 0.999891i | \(0.504692\pi\) | |||||||
\(272\) | − 2.48528i | − 0.150692i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.686292 | 0.0414604 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 10.6569 | 0.641467 | ||||||||
\(277\) | − 12.1421i | − 0.729550i | −0.931096 | − | 0.364775i | \(-0.881146\pi\) | ||||
0.931096 | − | 0.364775i | \(-0.118854\pi\) | |||||||
\(278\) | 5.02944i | 0.301646i | ||||||||
\(279\) | 16.9706 | 1.01600 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.2843 | 1.56799 | 0.783994 | − | 0.620768i | \(-0.213179\pi\) | ||||
0.783994 | + | 0.620768i | \(0.213179\pi\) | |||||||
\(282\) | − 2.00000i | − 0.119098i | ||||||||
\(283\) | − 14.0000i | − 0.832214i | −0.909316 | − | 0.416107i | \(-0.863394\pi\) | ||||
0.909316 | − | 0.416107i | \(-0.136606\pi\) | |||||||
\(284\) | −22.8284 | −1.35462 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.65685 | −0.0979718 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 12.4853i | 0.735702i | ||||||||
\(289\) | 16.3137 | 0.959630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.828427 | 0.0485633 | ||||||||
\(292\) | − 8.82843i | − 0.516645i | ||||||||
\(293\) | 16.0000i | 0.934730i | 0.884064 | + | 0.467365i | \(0.154797\pi\) | ||||
−0.884064 | + | 0.467365i | \(0.845203\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 2.00000i | − 0.116052i | ||||||||
\(298\) | − 3.24264i | − 0.187841i | ||||||||
\(299\) | 2.00000 | 0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 0.142136i | − 0.00817899i | ||||||||
\(303\) | − 29.7279i | − 1.70782i | ||||||||
\(304\) | 8.48528 | 0.486664 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.970563 | 0.0554834 | ||||||||
\(307\) | − 13.2426i | − 0.755797i | −0.925847 | − | 0.377899i | \(-0.876647\pi\) | ||||
0.925847 | − | 0.377899i | \(-0.123353\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.8284 | −1.06766 | −0.533831 | − | 0.845591i | \(-0.679248\pi\) | ||||
−0.533831 | + | 0.845591i | \(0.679248\pi\) | |||||||
\(312\) | 3.17157i | 0.179555i | ||||||||
\(313\) | 17.6569i | 0.998024i | 0.866595 | + | 0.499012i | \(0.166304\pi\) | ||||
−0.866595 | + | 0.499012i | \(0.833696\pi\) | |||||||
\(314\) | −2.20101 | −0.124210 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.7696 | −0.943361 | ||||||||
\(317\) | 25.7990i | 1.44902i | 0.689267 | + | 0.724508i | \(0.257933\pi\) | ||||
−0.689267 | + | 0.724508i | \(0.742067\pi\) | |||||||
\(318\) | − 6.82843i | − 0.382919i | ||||||||
\(319\) | 4.82843 | 0.270340 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.65685 | 0.371549 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.34315i | − 0.130376i | ||||||||
\(324\) | −17.3431 | −0.963508 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.79899 | −0.542716 | ||||||||
\(327\) | 8.41421i | 0.465307i | ||||||||
\(328\) | 3.44365i | 0.190144i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9706 | −0.602997 | −0.301498 | − | 0.953467i | \(-0.597487\pi\) | ||||
−0.301498 | + | 0.953467i | \(0.597487\pi\) | |||||||
\(332\) | 21.4437i | 1.17687i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.11270 | 0.443907 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.8284i | 0.807756i | 0.914813 | + | 0.403878i | \(0.132338\pi\) | ||||
−0.914813 | + | 0.403878i | \(0.867662\pi\) | |||||||
\(338\) | − 5.10051i | − 0.277431i | ||||||||
\(339\) | −30.1421 | −1.63710 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.9706 | −1.56884 | ||||||||
\(342\) | 3.31371i | 0.179185i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10.1716 | −0.548414 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.00000 | 0.430083 | ||||||||
\(347\) | 22.0711i | 1.18484i | 0.805630 | + | 0.592418i | \(0.201827\pi\) | ||||
−0.805630 | + | 0.592418i | \(0.798173\pi\) | |||||||
\(348\) | − 4.41421i | − 0.236627i | ||||||||
\(349\) | 26.6569 | 1.42691 | 0.713454 | − | 0.700702i | \(-0.247130\pi\) | ||||
0.713454 | + | 0.700702i | \(0.247130\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.343146 | −0.0183158 | ||||||||
\(352\) | − 21.3137i | − 1.13602i | ||||||||
\(353\) | 21.1716i | 1.12685i | 0.826168 | + | 0.563425i | \(0.190516\pi\) | ||||
−0.826168 | + | 0.563425i | \(0.809484\pi\) | |||||||
\(354\) | −12.4853 | −0.663585 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.85786 | −0.257466 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 4.14214i | − 0.218919i | ||||||||
\(359\) | 10.0000 | 0.527780 | 0.263890 | − | 0.964553i | \(-0.414994\pi\) | ||||
0.263890 | + | 0.964553i | \(0.414994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 3.58579i | 0.188465i | ||||||||
\(363\) | − 29.7279i | − 1.56031i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.4853 | 0.600345 | ||||||||
\(367\) | − 11.2426i | − 0.586861i | −0.955980 | − | 0.293431i | \(-0.905203\pi\) | ||||
0.955980 | − | 0.293431i | \(-0.0947969\pi\) | |||||||
\(368\) | 7.24264i | 0.377549i | ||||||||
\(369\) | 6.14214 | 0.319747 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 26.4853i | 1.37320i | ||||||||
\(373\) | − 12.9706i | − 0.671590i | −0.941935 | − | 0.335795i | \(-0.890995\pi\) | ||||
0.941935 | − | 0.335795i | \(-0.109005\pi\) | |||||||
\(374\) | −1.65685 | −0.0856739 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.17157 | 0.163561 | ||||||||
\(377\) | − 0.828427i | − 0.0426662i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.1716 | −1.08751 | −0.543755 | − | 0.839244i | \(-0.682998\pi\) | ||||
−0.543755 | + | 0.839244i | \(0.682998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 32.1421 | 1.64669 | ||||||||
\(382\) | 2.97056i | 0.151987i | ||||||||
\(383\) | − 16.8995i | − 0.863524i | −0.901988 | − | 0.431762i | \(-0.857892\pi\) | ||||
0.901988 | − | 0.431762i | \(-0.142108\pi\) | |||||||
\(384\) | −25.4853 | −1.30054 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.828427 | 0.0421658 | ||||||||
\(387\) | 18.1421i | 0.922217i | ||||||||
\(388\) | 0.627417i | 0.0318523i | ||||||||
\(389\) | −12.3431 | −0.625822 | −0.312911 | − | 0.949782i | \(-0.601304\pi\) | ||||
−0.312911 | + | 0.949782i | \(0.601304\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 8.00000i | − 0.403547i | ||||||||
\(394\) | −9.79899 | −0.493666 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −24.9706 | −1.25482 | ||||||||
\(397\) | 28.6274i | 1.43677i | 0.695646 | + | 0.718384i | \(0.255118\pi\) | ||||
−0.695646 | + | 0.718384i | \(0.744882\pi\) | |||||||
\(398\) | 0.686292i | 0.0344007i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.68629 | 0.383835 | 0.191918 | − | 0.981411i | \(-0.438529\pi\) | ||||
0.191918 | + | 0.981411i | \(0.438529\pi\) | |||||||
\(402\) | − 12.4142i | − 0.619165i | ||||||||
\(403\) | 4.97056i | 0.247601i | ||||||||
\(404\) | 22.5147 | 1.12015 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 3.17157i | 0.157016i | ||||||||
\(409\) | −24.7990 | −1.22623 | −0.613116 | − | 0.789993i | \(-0.710084\pi\) | ||||
−0.613116 | + | 0.789993i | \(0.710084\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.00000 | 0.197305 | ||||||||
\(412\) | − 0.757359i | − 0.0373124i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.82843 | −0.139010 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.65685 | −0.179292 | ||||||||
\(417\) | 29.3137i | 1.43550i | ||||||||
\(418\) | − 5.65685i | − 0.276686i | ||||||||
\(419\) | 23.3137 | 1.13895 | 0.569475 | − | 0.822009i | \(-0.307147\pi\) | ||||
0.569475 | + | 0.822009i | \(0.307147\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.48528 | −0.169862 | −0.0849311 | − | 0.996387i | \(-0.527067\pi\) | ||||
−0.0849311 | + | 0.996387i | \(0.527067\pi\) | |||||||
\(422\) | − 1.45584i | − 0.0708694i | ||||||||
\(423\) | − 5.65685i | − 0.275046i | ||||||||
\(424\) | 10.8284 | 0.525875 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.4853 | 0.604914 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.04163i | 0.243696i | ||||||||
\(429\) | −9.65685 | −0.466237 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.7990 | −1.05002 | −0.525010 | − | 0.851096i | \(-0.675938\pi\) | ||||
−0.525010 | + | 0.851096i | \(0.675938\pi\) | |||||||
\(432\) | − 1.24264i | − 0.0597866i | ||||||||
\(433\) | 31.7990i | 1.52816i | 0.645120 | + | 0.764081i | \(0.276807\pi\) | ||||
−0.645120 | + | 0.764081i | \(0.723193\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.37258 | −0.305191 | ||||||||
\(437\) | 6.82843i | 0.326648i | ||||||||
\(438\) | 4.82843i | 0.230711i | ||||||||
\(439\) | −33.9411 | −1.61992 | −0.809961 | − | 0.586484i | \(-0.800512\pi\) | ||||
−0.809961 | + | 0.586484i | \(0.800512\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.284271i | 0.0135214i | ||||||||
\(443\) | 12.2132i | 0.580267i | 0.956986 | + | 0.290133i | \(0.0936997\pi\) | ||||
−0.956986 | + | 0.290133i | \(0.906300\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.82843 | −0.228633 | ||||||||
\(447\) | − 18.8995i | − 0.893915i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.82843 | 0.0862888 | 0.0431444 | − | 0.999069i | \(-0.486262\pi\) | ||||
0.0431444 | + | 0.999069i | \(0.486262\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.4853 | −0.493733 | ||||||||
\(452\) | − 22.8284i | − 1.07376i | ||||||||
\(453\) | − 0.828427i | − 0.0389229i | ||||||||
\(454\) | 11.1716 | 0.524308 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −10.8284 | −0.507088 | ||||||||
\(457\) | − 32.2843i | − 1.51019i | −0.655613 | − | 0.755097i | \(-0.727590\pi\) | ||||
0.655613 | − | 0.755097i | \(-0.272410\pi\) | |||||||
\(458\) | − 0.142136i | − 0.00664156i | ||||||||
\(459\) | −0.343146 | −0.0160167 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.6863 | 0.870307 | 0.435154 | − | 0.900356i | \(-0.356694\pi\) | ||||
0.435154 | + | 0.900356i | \(0.356694\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 11.0416i | − 0.513148i | −0.966525 | − | 0.256574i | \(-0.917406\pi\) | ||||
0.966525 | − | 0.256574i | \(-0.0825937\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.62742 | 0.214361 | ||||||||
\(467\) | − 22.8995i | − 1.05966i | −0.848103 | − | 0.529831i | \(-0.822255\pi\) | ||||
0.848103 | − | 0.529831i | \(-0.177745\pi\) | |||||||
\(468\) | 4.28427i | 0.198041i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.8284 | −0.591103 | ||||||||
\(472\) | − 19.7990i | − 0.911322i | ||||||||
\(473\) | − 30.9706i | − 1.42403i | ||||||||
\(474\) | 9.17157 | 0.421264 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 19.3137i | − 0.884314i | ||||||||
\(478\) | 0.544156i | 0.0248891i | ||||||||
\(479\) | 24.3431 | 1.11227 | 0.556133 | − | 0.831093i | \(-0.312284\pi\) | ||||
0.556133 | + | 0.831093i | \(0.312284\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − 6.76955i | − 0.308345i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.5147 | 1.02340 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.97056 | 0.406913 | ||||||||
\(487\) | 15.6569i | 0.709480i | 0.934965 | + | 0.354740i | \(0.115431\pi\) | ||||
−0.934965 | + | 0.354740i | \(0.884569\pi\) | |||||||
\(488\) | 18.2132i | 0.824473i | ||||||||
\(489\) | −57.1127 | −2.58273 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.3137 | −0.600839 | −0.300420 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300420 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(492\) | 9.58579i | 0.432161i | ||||||||
\(493\) | − 0.828427i | − 0.0373105i | ||||||||
\(494\) | −0.970563 | −0.0436677 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18.0000 | −0.808224 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − 11.7279i | − 0.525541i | ||||||||
\(499\) | −4.82843 | −0.216150 | −0.108075 | − | 0.994143i | \(-0.534469\pi\) | ||||
−0.108075 | + | 0.994143i | \(0.534469\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 47.2843 | 2.11251 | ||||||||
\(502\) | − 5.51472i | − 0.246134i | ||||||||
\(503\) | − 37.8701i | − 1.68854i | −0.535916 | − | 0.844271i | \(-0.680034\pi\) | ||||
0.535916 | − | 0.844271i | \(-0.319966\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.82843 | 0.214650 | ||||||||
\(507\) | − 29.7279i | − 1.32026i | ||||||||
\(508\) | 24.3431i | 1.08005i | ||||||||
\(509\) | −24.6569 | −1.09290 | −0.546448 | − | 0.837493i | \(-0.684020\pi\) | ||||
−0.546448 | + | 0.837493i | \(0.684020\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 22.7574i | − 1.00574i | ||||||||
\(513\) | − 1.17157i | − 0.0517262i | ||||||||
\(514\) | 7.31371 | 0.322594 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −28.3137 | −1.24644 | ||||||||
\(517\) | 9.65685i | 0.424708i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 46.6274 | 2.04672 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.9706 | −0.831115 | −0.415558 | − | 0.909567i | \(-0.636414\pi\) | ||||
−0.415558 | + | 0.909567i | \(0.636414\pi\) | |||||||
\(522\) | 1.17157i | 0.0512784i | ||||||||
\(523\) | − 24.3431i | − 1.06445i | −0.846602 | − | 0.532226i | \(-0.821356\pi\) | ||||
0.846602 | − | 0.532226i | \(-0.178644\pi\) | |||||||
\(524\) | 6.05887 | 0.264683 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.88730 | −0.343903 | ||||||||
\(527\) | 4.97056i | 0.216521i | ||||||||
\(528\) | − 34.9706i | − 1.52190i | ||||||||
\(529\) | 17.1716 | 0.746590 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.3137 | −1.53248 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.79899i | 0.0779229i | ||||||||
\(534\) | 2.65685 | 0.114973 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 19.6863 | 0.850318 | ||||||||
\(537\) | − 24.1421i | − 1.04181i | ||||||||
\(538\) | − 12.6152i | − 0.543881i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.6569 | 0.802121 | 0.401060 | − | 0.916052i | \(-0.368642\pi\) | ||||
0.401060 | + | 0.916052i | \(0.368642\pi\) | |||||||
\(542\) | 0.201010i | 0.00863412i | ||||||||
\(543\) | 20.8995i | 0.896883i | ||||||||
\(544\) | −3.65685 | −0.156786 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.10051i | 0.218082i | 0.994037 | + | 0.109041i | \(0.0347780\pi\) | ||||
−0.994037 | + | 0.109041i | \(0.965222\pi\) | |||||||
\(548\) | 3.02944i | 0.129411i | ||||||||
\(549\) | 32.4853 | 1.38644 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.82843 | 0.120495 | ||||||||
\(552\) | − 9.24264i | − 0.393393i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.02944 | −0.213680 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22.2010 | −0.941533 | ||||||||
\(557\) | − 34.2843i | − 1.45267i | −0.687340 | − | 0.726336i | \(-0.741222\pi\) | ||||
0.687340 | − | 0.726336i | \(-0.258778\pi\) | |||||||
\(558\) | − 7.02944i | − 0.297580i | ||||||||
\(559\) | −5.31371 | −0.224746 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.65685 | −0.407713 | ||||||||
\(562\) | − 10.8873i | − 0.459253i | ||||||||
\(563\) | − 16.2721i | − 0.685786i | −0.939374 | − | 0.342893i | \(-0.888593\pi\) | ||||
0.939374 | − | 0.342893i | \(-0.111407\pi\) | |||||||
\(564\) | 8.82843 | 0.371744 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.79899 | −0.243750 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19.7990i | 0.830747i | ||||||||
\(569\) | 3.65685 | 0.153303 | 0.0766517 | − | 0.997058i | \(-0.475577\pi\) | ||||
0.0766517 | + | 0.997058i | \(0.475577\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.8284 | 0.620550 | 0.310275 | − | 0.950647i | \(-0.399579\pi\) | ||||
0.310275 | + | 0.950647i | \(0.399579\pi\) | |||||||
\(572\) | − 7.31371i | − 0.305802i | ||||||||
\(573\) | 17.3137i | 0.723291i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.7990 | −0.491625 | ||||||||
\(577\) | 23.9411i | 0.996682i | 0.866981 | + | 0.498341i | \(0.166057\pi\) | ||||
−0.866981 | + | 0.498341i | \(0.833943\pi\) | |||||||
\(578\) | − 6.75736i | − 0.281069i | ||||||||
\(579\) | 4.82843 | 0.200663 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − 0.343146i | − 0.0142238i | ||||||||
\(583\) | 32.9706i | 1.36550i | ||||||||
\(584\) | −7.65685 | −0.316843 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.62742 | 0.273776 | ||||||||
\(587\) | 22.2843i | 0.919770i | 0.887978 | + | 0.459885i | \(0.152109\pi\) | ||||
−0.887978 | + | 0.459885i | \(0.847891\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.9706 | −0.699260 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −57.1127 | −2.34930 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 43.7990i | − 1.79861i | −0.437323 | − | 0.899304i | \(-0.644073\pi\) | ||||
0.437323 | − | 0.899304i | \(-0.355927\pi\) | |||||||
\(594\) | −0.828427 | −0.0339908 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.3137 | 0.586312 | ||||||||
\(597\) | 4.00000i | 0.163709i | ||||||||
\(598\) | − 0.828427i | − 0.0338769i | ||||||||
\(599\) | −17.6569 | −0.721440 | −0.360720 | − | 0.932674i | \(-0.617469\pi\) | ||||
−0.360720 | + | 0.932674i | \(0.617469\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.34315 | 0.340324 | 0.170162 | − | 0.985416i | \(-0.445571\pi\) | ||||
0.170162 | + | 0.985416i | \(0.445571\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 35.1127i | − 1.42990i | ||||||||
\(604\) | 0.627417 | 0.0255292 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.3137 | −0.500210 | ||||||||
\(607\) | − 4.21320i | − 0.171009i | −0.996338 | − | 0.0855043i | \(-0.972750\pi\) | ||||
0.996338 | − | 0.0855043i | \(-0.0272501\pi\) | |||||||
\(608\) | − 12.4853i | − 0.506345i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.65685 | 0.0670291 | ||||||||
\(612\) | 4.28427i | 0.173181i | ||||||||
\(613\) | 15.4558i | 0.624256i | 0.950040 | + | 0.312128i | \(0.101042\pi\) | ||||
−0.950040 | + | 0.312128i | \(0.898958\pi\) | |||||||
\(614\) | −5.48528 | −0.221368 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 11.3137i | − 0.455473i | −0.973723 | − | 0.227736i | \(-0.926868\pi\) | ||||
0.973723 | − | 0.227736i | \(-0.0731324\pi\) | |||||||
\(618\) | 0.414214i | 0.0166621i | ||||||||
\(619\) | −42.4853 | −1.70763 | −0.853814 | − | 0.520578i | \(-0.825716\pi\) | ||||
−0.853814 | + | 0.520578i | \(0.825716\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 7.79899i | 0.312711i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.00000 | −0.240192 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.31371 | 0.292315 | ||||||||
\(627\) | − 32.9706i | − 1.31672i | ||||||||
\(628\) | − 9.71573i | − 0.387700i | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.14214 | 0.324133 | 0.162067 | − | 0.986780i | \(-0.448184\pi\) | ||||
0.162067 | + | 0.986780i | \(0.448184\pi\) | |||||||
\(632\) | 14.5442i | 0.578535i | ||||||||
\(633\) | − 8.48528i | − 0.337260i | ||||||||
\(634\) | 10.6863 | 0.424407 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 30.1421 | 1.19521 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 2.00000i | − 0.0791808i | ||||||||
\(639\) | 35.3137 | 1.39699 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.5147 | 0.573297 | 0.286648 | − | 0.958036i | \(-0.407459\pi\) | ||||
0.286648 | + | 0.958036i | \(0.407459\pi\) | |||||||
\(642\) | − 2.75736i | − 0.108824i | ||||||||
\(643\) | 30.2843i | 1.19430i | 0.802131 | + | 0.597148i | \(0.203699\pi\) | ||||
−0.802131 | + | 0.597148i | \(0.796301\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.970563 | −0.0381863 | ||||||||
\(647\) | 17.0416i | 0.669976i | 0.942222 | + | 0.334988i | \(0.108732\pi\) | ||||
−0.942222 | + | 0.334988i | \(0.891268\pi\) | |||||||
\(648\) | 15.0416i | 0.590891i | ||||||||
\(649\) | 60.2843 | 2.36636 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 43.2548i | − 1.69399i | ||||||||
\(653\) | 24.8284i | 0.971611i | 0.874067 | + | 0.485806i | \(0.161474\pi\) | ||||
−0.874067 | + | 0.485806i | \(0.838526\pi\) | |||||||
\(654\) | 3.48528 | 0.136285 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.51472 | −0.254357 | ||||||||
\(657\) | 13.6569i | 0.532805i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.8284 | −1.04509 | −0.522544 | − | 0.852613i | \(-0.675017\pi\) | ||||
−0.522544 | + | 0.852613i | \(0.675017\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.1716 | 1.01796 | 0.508978 | − | 0.860779i | \(-0.330023\pi\) | ||||
0.508978 | + | 0.860779i | \(0.330023\pi\) | |||||||
\(662\) | 4.54416i | 0.176614i | ||||||||
\(663\) | 1.65685i | 0.0643469i | ||||||||
\(664\) | 18.5980 | 0.721742 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.41421i | 0.0934787i | ||||||||
\(668\) | 35.8112i | 1.38558i | ||||||||
\(669\) | −28.1421 | −1.08804 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −55.4558 | −2.14085 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 18.3431i | − 0.707076i | −0.935420 | − | 0.353538i | \(-0.884978\pi\) | ||||
0.935420 | − | 0.353538i | \(-0.115022\pi\) | |||||||
\(674\) | 6.14214 | 0.236586 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22.5147 | 0.865951 | ||||||||
\(677\) | 0.142136i | 0.00546272i | 0.999996 | + | 0.00273136i | \(0.000869419\pi\) | ||||
−0.999996 | + | 0.00273136i | \(0.999131\pi\) | |||||||
\(678\) | 12.4853i | 0.479494i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 65.1127 | 2.49512 | ||||||||
\(682\) | 12.0000i | 0.459504i | ||||||||
\(683\) | 43.2426i | 1.65463i | 0.561736 | + | 0.827317i | \(0.310134\pi\) | ||||
−0.561736 | + | 0.827317i | \(0.689866\pi\) | |||||||
\(684\) | −14.6274 | −0.559293 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 0.828427i | − 0.0316065i | ||||||||
\(688\) | − 19.2426i | − 0.733619i | ||||||||
\(689\) | 5.65685 | 0.215509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.82843 | −0.183682 | −0.0918410 | − | 0.995774i | \(-0.529275\pi\) | ||||
−0.0918410 | + | 0.995774i | \(0.529275\pi\) | |||||||
\(692\) | 35.3137i | 1.34243i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.14214 | 0.347031 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.82843 | −0.145116 | ||||||||
\(697\) | 1.79899i | 0.0681416i | ||||||||
\(698\) | − 11.0416i | − 0.417932i | ||||||||
\(699\) | 26.9706 | 1.02012 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.7990 | −1.61650 | −0.808248 | − | 0.588843i | \(-0.799584\pi\) | ||||
−0.808248 | + | 0.588843i | \(0.799584\pi\) | |||||||
\(702\) | 0.142136i | 0.00536456i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 20.1421 | 0.759135 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.76955 | 0.330046 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − 55.1127i | − 2.07126i | ||||||||
\(709\) | −38.3137 | −1.43890 | −0.719451 | − | 0.694543i | \(-0.755606\pi\) | ||||
−0.719451 | + | 0.694543i | \(0.755606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.9411 | 0.972868 | ||||||||
\(712\) | 4.21320i | 0.157896i | ||||||||
\(713\) | − 14.4853i | − 0.542478i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.2843 | 0.683315 | ||||||||
\(717\) | 3.17157i | 0.118445i | ||||||||
\(718\) | − 4.14214i | − 0.154583i | ||||||||
\(719\) | 41.1127 | 1.53324 | 0.766622 | − | 0.642098i | \(-0.221936\pi\) | ||||
0.766622 | + | 0.642098i | \(0.221936\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.55635i | 0.169570i | ||||||||
\(723\) | − 39.4558i | − 1.46738i | ||||||||
\(724\) | −15.8284 | −0.588259 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −12.3137 | −0.457005 | ||||||||
\(727\) | − 40.4142i | − 1.49888i | −0.662072 | − | 0.749440i | \(-0.730323\pi\) | ||||
0.662072 | − | 0.749440i | \(-0.269677\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.8284 | 0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.31371 | −0.196535 | ||||||||
\(732\) | 50.6985i | 1.87387i | ||||||||
\(733\) | 22.0000i | 0.812589i | 0.913742 | + | 0.406294i | \(0.133179\pi\) | ||||
−0.913742 | + | 0.406294i | \(0.866821\pi\) | |||||||
\(734\) | −4.65685 | −0.171888 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.6569 | 0.392817 | ||||||||
\(737\) | 59.9411i | 2.20796i | ||||||||
\(738\) | − 2.54416i | − 0.0936517i | ||||||||
\(739\) | −41.1127 | −1.51236 | −0.756178 | − | 0.654367i | \(-0.772935\pi\) | ||||
−0.756178 | + | 0.654367i | \(0.772935\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.65685 | −0.207810 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.92893i | 0.0707657i | 0.999374 | + | 0.0353828i | \(0.0112651\pi\) | ||||
−0.999374 | + | 0.0353828i | \(0.988735\pi\) | |||||||
\(744\) | 22.9706 | 0.842142 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.37258 | −0.196704 | ||||||||
\(747\) | − 33.1716i | − 1.21368i | ||||||||
\(748\) | − 7.31371i | − 0.267416i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.6569 | −1.52008 | −0.760040 | − | 0.649876i | \(-0.774821\pi\) | ||||
−0.760040 | + | 0.649876i | \(0.774821\pi\) | |||||||
\(752\) | 6.00000i | 0.218797i | ||||||||
\(753\) | − 32.1421i | − 1.17132i | ||||||||
\(754\) | −0.343146 | −0.0124966 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.4558i | 0.707135i | 0.935409 | + | 0.353567i | \(0.115031\pi\) | ||||
−0.935409 | + | 0.353567i | \(0.884969\pi\) | |||||||
\(758\) | 8.76955i | 0.318524i | ||||||||
\(759\) | 28.1421 | 1.02149 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.3137 | −0.482622 | −0.241311 | − | 0.970448i | \(-0.577577\pi\) | ||||
−0.241311 | + | 0.970448i | \(0.577577\pi\) | |||||||
\(762\) | − 13.3137i | − 0.482305i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.1127 | −0.474401 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.00000 | −0.252920 | ||||||||
\(767\) | − 10.3431i | − 0.373469i | ||||||||
\(768\) | − 9.58579i | − 0.345897i | ||||||||
\(769\) | −44.6274 | −1.60931 | −0.804653 | − | 0.593745i | \(-0.797649\pi\) | ||||
−0.804653 | + | 0.593745i | \(0.797649\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 42.6274 | 1.53519 | ||||||||
\(772\) | 3.65685i | 0.131613i | ||||||||
\(773\) | − 25.1127i | − 0.903241i | −0.892210 | − | 0.451620i | \(-0.850846\pi\) | ||||
0.892210 | − | 0.451620i | \(-0.149154\pi\) | |||||||
\(774\) | 7.51472 | 0.270111 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.544156 | 0.0195341 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.11270i | 0.183299i | ||||||||
\(779\) | −6.14214 | −0.220065 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.2843 | −2.15714 | ||||||||
\(782\) | − 0.828427i | − 0.0296245i | ||||||||
\(783\) | − 0.414214i | − 0.0148028i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.31371 | −0.118196 | ||||||||
\(787\) | − 28.5563i | − 1.01792i | −0.860789 | − | 0.508962i | \(-0.830029\pi\) | ||||
0.860789 | − | 0.508962i | \(-0.169971\pi\) | |||||||
\(788\) | − 43.2548i | − 1.54089i | ||||||||
\(789\) | −45.9706 | −1.63660 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 21.6569i | 0.769543i | ||||||||
\(793\) | 9.51472i | 0.337878i | ||||||||
\(794\) | 11.8579 | 0.420820 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.02944 | −0.107376 | ||||||||
\(797\) | − 8.00000i | − 0.283375i | −0.989911 | − | 0.141687i | \(-0.954747\pi\) | ||||
0.989911 | − | 0.141687i | \(-0.0452527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.65685 | 0.0586153 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.51472 | 0.265520 | ||||||||
\(802\) | − 3.18377i | − 0.112423i | ||||||||
\(803\) | − 23.3137i | − 0.822723i | ||||||||
\(804\) | 54.7990 | 1.93261 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.05887 | 0.0725208 | ||||||||
\(807\) | − 73.5269i | − 2.58827i | ||||||||
\(808\) | − 19.5269i | − 0.686954i | ||||||||
\(809\) | 9.62742 | 0.338482 | 0.169241 | − | 0.985575i | \(-0.445868\pi\) | ||||
0.169241 | + | 0.985575i | \(0.445868\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.6274 | 0.864786 | 0.432393 | − | 0.901685i | \(-0.357669\pi\) | ||||
0.432393 | + | 0.901685i | \(0.357669\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.17157i | 0.0410889i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.00000 | −0.210042 | ||||||||
\(817\) | − 18.1421i | − 0.634713i | ||||||||
\(818\) | 10.2721i | 0.359155i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.9411 | −0.695950 | −0.347975 | − | 0.937504i | \(-0.613131\pi\) | ||||
−0.347975 | + | 0.937504i | \(0.613131\pi\) | |||||||
\(822\) | − 1.65685i | − 0.0577894i | ||||||||
\(823\) | 12.0711i | 0.420771i | 0.977619 | + | 0.210385i | \(0.0674719\pi\) | ||||
−0.977619 | + | 0.210385i | \(0.932528\pi\) | |||||||
\(824\) | −0.656854 | −0.0228826 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.2132i | 0.563788i | 0.959446 | + | 0.281894i | \(0.0909627\pi\) | ||||
−0.959446 | + | 0.281894i | \(0.909037\pi\) | |||||||
\(828\) | − 12.4853i | − 0.433894i | ||||||||
\(829\) | −6.68629 | −0.232225 | −0.116112 | − | 0.993236i | \(-0.537043\pi\) | ||||
−0.116112 | + | 0.993236i | \(0.537043\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.3137 | −1.01688 | ||||||||
\(832\) | − 3.45584i | − 0.119810i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 12.1421 | 0.420448 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 24.9706 | 0.863625 | ||||||||
\(837\) | 2.48528i | 0.0859039i | ||||||||
\(838\) | − 9.65685i | − 0.333590i | ||||||||
\(839\) | −20.8284 | −0.719077 | −0.359539 | − | 0.933130i | \(-0.617066\pi\) | ||||
−0.359539 | + | 0.933130i | \(0.617066\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 1.44365i | 0.0497515i | ||||||||
\(843\) | − 63.4558i | − 2.18554i | ||||||||
\(844\) | 6.42641 | 0.221206 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.34315 | −0.0805590 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 20.4853i | 0.703467i | ||||||||
\(849\) | −33.7990 | −1.15998 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 55.1127i | 1.88813i | ||||||||
\(853\) | − 53.4558i | − 1.83029i | −0.403121 | − | 0.915147i | \(-0.632075\pi\) | ||||
0.403121 | − | 0.915147i | \(-0.367925\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.37258 | 0.149452 | ||||||||
\(857\) | − 22.2843i | − 0.761216i | −0.924736 | − | 0.380608i | \(-0.875715\pi\) | ||||
0.924736 | − | 0.380608i | \(-0.124285\pi\) | |||||||
\(858\) | 4.00000i | 0.136558i | ||||||||
\(859\) | −46.6274 | −1.59091 | −0.795453 | − | 0.606015i | \(-0.792767\pi\) | ||||
−0.795453 | + | 0.606015i | \(0.792767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.02944i | 0.307544i | ||||||||
\(863\) | 16.5563i | 0.563585i | 0.959475 | + | 0.281792i | \(0.0909289\pi\) | ||||
−0.959475 | + | 0.281792i | \(0.909071\pi\) | |||||||
\(864\) | −1.82843 | −0.0622044 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13.1716 | 0.447588 | ||||||||
\(867\) | − 39.3848i | − 1.33758i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −44.2843 | −1.50224 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.2843 | 0.348469 | ||||||||
\(872\) | 5.52691i | 0.187165i | ||||||||
\(873\) | − 0.970563i | − 0.0328486i | ||||||||
\(874\) | 2.82843 | 0.0956730 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −21.3137 | −0.720123 | ||||||||
\(877\) | 30.8284i | 1.04100i | 0.853861 | + | 0.520501i | \(0.174255\pi\) | ||||
−0.853861 | + | 0.520501i | \(0.825745\pi\) | |||||||
\(878\) | 14.0589i | 0.474464i | ||||||||
\(879\) | 38.6274 | 1.30287 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.82843 | −0.128983 | −0.0644915 | − | 0.997918i | \(-0.520543\pi\) | ||||
−0.0644915 | + | 0.997918i | \(0.520543\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.2843i | 1.28837i | 0.764870 | + | 0.644184i | \(0.222803\pi\) | ||||
−0.764870 | + | 0.644184i | \(0.777197\pi\) | |||||||
\(884\) | −1.25483 | −0.0422046 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.05887 | 0.169956 | ||||||||
\(887\) | 44.0711i | 1.47976i | 0.672738 | + | 0.739881i | \(0.265118\pi\) | ||||
−0.672738 | + | 0.739881i | \(0.734882\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −45.7990 | −1.53432 | ||||||||
\(892\) | − 21.3137i | − 0.713636i | ||||||||
\(893\) | 5.65685i | 0.189299i | ||||||||
\(894\) | −7.82843 | −0.261822 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 4.82843i | − 0.161216i | ||||||||
\(898\) | − 0.757359i | − 0.0252734i | ||||||||
\(899\) | −6.00000 | −0.200111 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.65685 | 0.188457 | ||||||||
\(902\) | 4.34315i | 0.144611i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.7990 | −0.658505 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.343146 | −0.0114003 | ||||||||
\(907\) | 28.2132i | 0.936804i | 0.883515 | + | 0.468402i | \(0.155170\pi\) | ||||
−0.883515 | + | 0.468402i | \(0.844830\pi\) | |||||||
\(908\) | 49.3137i | 1.63653i | ||||||||
\(909\) | −34.8284 | −1.15519 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.7990 | −1.64991 | −0.824957 | − | 0.565195i | \(-0.808801\pi\) | ||||
−0.824957 | + | 0.565195i | \(0.808801\pi\) | |||||||
\(912\) | − 20.4853i | − 0.678335i | ||||||||
\(913\) | 56.6274i | 1.87409i | ||||||||
\(914\) | −13.3726 | −0.442326 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.627417 | 0.0207304 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.142136i | 0.00469117i | ||||||||
\(919\) | −19.1127 | −0.630470 | −0.315235 | − | 0.949014i | \(-0.602083\pi\) | ||||
−0.315235 | + | 0.949014i | \(0.602083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.9706 | −1.05347 | ||||||||
\(922\) | − 7.74012i | − 0.254907i | ||||||||
\(923\) | 10.3431i | 0.340449i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.57359 | −0.150298 | ||||||||
\(927\) | 1.17157i | 0.0384795i | ||||||||
\(928\) | − 4.41421i | − 0.144904i | ||||||||
\(929\) | 11.4853 | 0.376820 | 0.188410 | − | 0.982090i | \(-0.439667\pi\) | ||||
0.188410 | + | 0.982090i | \(0.439667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.4264i | 0.669089i | ||||||||
\(933\) | 45.4558i | 1.48816i | ||||||||
\(934\) | −9.48528 | −0.310368 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.71573 | 0.121452 | ||||||||
\(937\) | − 10.6274i | − 0.347183i | −0.984818 | − | 0.173591i | \(-0.944463\pi\) | ||||
0.984818 | − | 0.173591i | \(-0.0555372\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.6274 | 1.39109 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.2843 | 0.335258 | 0.167629 | − | 0.985850i | \(-0.446389\pi\) | ||||
0.167629 | + | 0.985850i | \(0.446389\pi\) | |||||||
\(942\) | 5.31371i | 0.173130i | ||||||||
\(943\) | − 5.24264i | − 0.170724i | ||||||||
\(944\) | 37.4558 | 1.21908 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.8284 | −0.417088 | ||||||||
\(947\) | − 43.1838i | − 1.40328i | −0.712530 | − | 0.701642i | \(-0.752451\pi\) | ||||
0.712530 | − | 0.701642i | \(-0.247549\pi\) | |||||||
\(948\) | 40.4853i | 1.31490i | ||||||||
\(949\) | −4.00000 | −0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 62.2843 | 2.01971 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.34315i | 0.0759019i | 0.999280 | + | 0.0379510i | \(0.0120831\pi\) | ||||
−0.999280 | + | 0.0379510i | \(0.987917\pi\) | |||||||
\(954\) | −8.00000 | −0.259010 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.40202 | −0.0776869 | ||||||||
\(957\) | − 11.6569i | − 0.376813i | ||||||||
\(958\) | − 10.0833i | − 0.325775i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 7.79899i | − 0.251319i | ||||||||
\(964\) | 29.8823 | 0.962442 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 27.5269i | − 0.885206i | −0.896718 | − | 0.442603i | \(-0.854055\pi\) | ||||
0.896718 | − | 0.442603i | \(-0.145945\pi\) | |||||||
\(968\) | − 19.5269i | − 0.627619i | ||||||||
\(969\) | −5.65685 | −0.181724 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.0000 | −0.770197 | −0.385098 | − | 0.922876i | \(-0.625832\pi\) | ||||
−0.385098 | + | 0.922876i | \(0.625832\pi\) | |||||||
\(972\) | 39.5980i | 1.27011i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 6.48528 | 0.207802 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.4558 | −1.10290 | ||||||||
\(977\) | 21.3137i | 0.681886i | 0.940084 | + | 0.340943i | \(0.110746\pi\) | ||||
−0.940084 | + | 0.340943i | \(0.889254\pi\) | |||||||
\(978\) | 23.6569i | 0.756463i | ||||||||
\(979\) | −12.8284 | −0.409998 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.85786 | 0.314737 | ||||||||
\(982\) | 5.51472i | 0.175982i | ||||||||
\(983\) | 14.2132i | 0.453331i | 0.973973 | + | 0.226665i | \(0.0727824\pi\) | ||||
−0.973973 | + | 0.226665i | \(0.927218\pi\) | |||||||
\(984\) | 8.31371 | 0.265031 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.343146 | −0.0109280 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 4.28427i | − 0.136301i | ||||||||
\(989\) | 15.4853 | 0.492403 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.6569 | −0.497356 | −0.248678 | − | 0.968586i | \(-0.579996\pi\) | ||||
−0.248678 | + | 0.968586i | \(0.579996\pi\) | |||||||
\(992\) | 26.4853i | 0.840909i | ||||||||
\(993\) | 26.4853i | 0.840485i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 51.7696 | 1.64038 | ||||||||
\(997\) | − 17.4558i | − 0.552832i | −0.961038 | − | 0.276416i | \(-0.910853\pi\) | ||||
0.961038 | − | 0.276416i | \(-0.0891468\pi\) | |||||||
\(998\) | 2.00000i | 0.0633089i | ||||||||
\(999\) | 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 | 1225.2.b.g.99.2 | 4 | ||
5.2 | odd | 4 | 1225.2.a.k.1.2 | 2 | |||
5.3 | odd | 4 | 245.2.a.h.1.1 | 2 | |||
5.4 | even | 2 | inner | 1225.2.b.g.99.3 | 4 | ||
7.2 | even | 3 | 175.2.k.a.74.2 | 8 | |||
7.4 | even | 3 | 175.2.k.a.149.3 | 8 | |||
7.6 | odd | 2 | 1225.2.b.h.99.2 | 4 | |||
15.8 | even | 4 | 2205.2.a.n.1.2 | 2 | |||
20.3 | even | 4 | 3920.2.a.bq.1.1 | 2 | |||
35.2 | odd | 12 | 175.2.e.c.151.1 | 4 | |||
35.3 | even | 12 | 245.2.e.e.226.2 | 4 | |||
35.4 | even | 6 | 175.2.k.a.149.2 | 8 | |||
35.9 | even | 6 | 175.2.k.a.74.3 | 8 | |||
35.13 | even | 4 | 245.2.a.g.1.1 | 2 | |||
35.18 | odd | 12 | 35.2.e.a.16.2 | yes | 4 | ||
35.23 | odd | 12 | 35.2.e.a.11.2 | ✓ | 4 | ||
35.27 | even | 4 | 1225.2.a.m.1.2 | 2 | |||
35.32 | odd | 12 | 175.2.e.c.51.1 | 4 | |||
35.33 | even | 12 | 245.2.e.e.116.2 | 4 | |||
35.34 | odd | 2 | 1225.2.b.h.99.3 | 4 | |||
105.23 | even | 12 | 315.2.j.e.46.1 | 4 | |||
105.53 | even | 12 | 315.2.j.e.226.1 | 4 | |||
105.83 | odd | 4 | 2205.2.a.q.1.2 | 2 | |||
140.23 | even | 12 | 560.2.q.k.81.2 | 4 | |||
140.83 | odd | 4 | 3920.2.a.bv.1.2 | 2 | |||
140.123 | even | 12 | 560.2.q.k.401.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.e.a.11.2 | ✓ | 4 | 35.23 | odd | 12 | ||
35.2.e.a.16.2 | yes | 4 | 35.18 | odd | 12 | ||
175.2.e.c.51.1 | 4 | 35.32 | odd | 12 | |||
175.2.e.c.151.1 | 4 | 35.2 | odd | 12 | |||
175.2.k.a.74.2 | 8 | 7.2 | even | 3 | |||
175.2.k.a.74.3 | 8 | 35.9 | even | 6 | |||
175.2.k.a.149.2 | 8 | 35.4 | even | 6 | |||
175.2.k.a.149.3 | 8 | 7.4 | even | 3 | |||
245.2.a.g.1.1 | 2 | 35.13 | even | 4 | |||
245.2.a.h.1.1 | 2 | 5.3 | odd | 4 | |||
245.2.e.e.116.2 | 4 | 35.33 | even | 12 | |||
245.2.e.e.226.2 | 4 | 35.3 | even | 12 | |||
315.2.j.e.46.1 | 4 | 105.23 | even | 12 | |||
315.2.j.e.226.1 | 4 | 105.53 | even | 12 | |||
560.2.q.k.81.2 | 4 | 140.23 | even | 12 | |||
560.2.q.k.401.2 | 4 | 140.123 | even | 12 | |||
1225.2.a.k.1.2 | 2 | 5.2 | odd | 4 | |||
1225.2.a.m.1.2 | 2 | 35.27 | even | 4 | |||
1225.2.b.g.99.2 | 4 | 1.1 | even | 1 | trivial | ||
1225.2.b.g.99.3 | 4 | 5.4 | even | 2 | inner | ||
1225.2.b.h.99.2 | 4 | 7.6 | odd | 2 | |||
1225.2.b.h.99.3 | 4 | 35.34 | odd | 2 | |||
2205.2.a.n.1.2 | 2 | 15.8 | even | 4 | |||
2205.2.a.q.1.2 | 2 | 105.83 | odd | 4 | |||
3920.2.a.bq.1.1 | 2 | 20.3 | even | 4 | |||
3920.2.a.bv.1.2 | 2 | 140.83 | odd | 4 |