Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("825.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (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: | \(6.58765816676\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.2.c.d.199.3 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | \(-0.0467837\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 1.82843 | 0.914214 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.414214 | −0.169102 | ||||||||
\(7\) | − 2.41421i | − 0.912487i | −0.889855 | − | 0.456243i | \(-0.849195\pi\) | ||||
0.889855 | − | 0.456243i | \(-0.150805\pi\) | |||||||
\(8\) | − 1.58579i | − 0.560660i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | − 1.82843i | − 0.527821i | ||||||||
\(13\) | − 2.82843i | − 0.784465i | −0.919866 | − | 0.392232i | \(-0.871703\pi\) | ||||
0.919866 | − | 0.392232i | \(-0.128297\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | − 0.414214i | − 0.100462i | −0.998738 | − | 0.0502308i | \(-0.984004\pi\) | ||||
0.998738 | − | 0.0502308i | \(-0.0159957\pi\) | |||||||
\(18\) | 0.414214i | 0.0976311i | ||||||||
\(19\) | −3.58579 | −0.822636 | −0.411318 | − | 0.911492i | \(-0.634931\pi\) | ||||
−0.411318 | + | 0.911492i | \(0.634931\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.41421 | −0.526825 | ||||||||
\(22\) | 0.414214i | 0.0883106i | ||||||||
\(23\) | − 1.00000i | − 0.208514i | −0.994550 | − | 0.104257i | \(-0.966753\pi\) | ||||
0.994550 | − | 0.104257i | \(-0.0332465\pi\) | |||||||
\(24\) | −1.58579 | −0.323697 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.17157 | −0.229764 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − 4.41421i | − 0.834208i | ||||||||
\(29\) | −6.82843 | −1.26801 | −0.634004 | − | 0.773330i | \(-0.718590\pi\) | ||||
−0.634004 | + | 0.773330i | \(0.718590\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.48528 | 1.52400 | 0.762001 | − | 0.647576i | \(-0.224217\pi\) | ||||
0.762001 | + | 0.647576i | \(0.224217\pi\) | |||||||
\(32\) | − 4.41421i | − 0.780330i | ||||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | −0.171573 | −0.0294245 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.82843 | −0.304738 | ||||||||
\(37\) | − 5.82843i | − 0.958188i | −0.877764 | − | 0.479094i | \(-0.840965\pi\) | ||||
0.877764 | − | 0.479094i | \(-0.159035\pi\) | |||||||
\(38\) | 1.48528i | 0.240944i | ||||||||
\(39\) | −2.82843 | −0.452911 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.89949 | 1.38987 | 0.694934 | − | 0.719074i | \(-0.255434\pi\) | ||||
0.694934 | + | 0.719074i | \(0.255434\pi\) | |||||||
\(42\) | 1.00000i | 0.154303i | ||||||||
\(43\) | 0.343146i | 0.0523292i | 0.999658 | + | 0.0261646i | \(0.00832941\pi\) | ||||
−0.999658 | + | 0.0261646i | \(0.991671\pi\) | |||||||
\(44\) | −1.82843 | −0.275646 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.414214 | −0.0610725 | ||||||||
\(47\) | 9.48528i | 1.38357i | 0.722103 | + | 0.691785i | \(0.243176\pi\) | ||||
−0.722103 | + | 0.691785i | \(0.756824\pi\) | |||||||
\(48\) | − 3.00000i | − 0.433013i | ||||||||
\(49\) | 1.17157 | 0.167368 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.414214 | −0.0580015 | ||||||||
\(52\) | − 5.17157i | − 0.717168i | ||||||||
\(53\) | 3.65685i | 0.502308i | 0.967947 | + | 0.251154i | \(0.0808100\pi\) | ||||
−0.967947 | + | 0.251154i | \(0.919190\pi\) | |||||||
\(54\) | 0.414214 | 0.0563673 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.82843 | −0.511595 | ||||||||
\(57\) | 3.58579i | 0.474949i | ||||||||
\(58\) | 2.82843i | 0.371391i | ||||||||
\(59\) | −11.0000 | −1.43208 | −0.716039 | − | 0.698060i | \(-0.754047\pi\) | ||||
−0.716039 | + | 0.698060i | \(0.754047\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.17157 | 0.406078 | 0.203039 | − | 0.979171i | \(-0.434918\pi\) | ||||
0.203039 | + | 0.979171i | \(0.434918\pi\) | |||||||
\(62\) | − 3.51472i | − 0.446370i | ||||||||
\(63\) | 2.41421i | 0.304162i | ||||||||
\(64\) | 4.17157 | 0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.414214 | 0.0509862 | ||||||||
\(67\) | − 11.6569i | − 1.42411i | −0.702123 | − | 0.712056i | \(-0.747764\pi\) | ||||
0.702123 | − | 0.712056i | \(-0.252236\pi\) | |||||||
\(68\) | − 0.757359i | − 0.0918433i | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.17157 | 0.257718 | 0.128859 | − | 0.991663i | \(-0.458868\pi\) | ||||
0.128859 | + | 0.991663i | \(0.458868\pi\) | |||||||
\(72\) | 1.58579i | 0.186887i | ||||||||
\(73\) | 3.17157i | 0.371205i | 0.982625 | + | 0.185602i | \(0.0594236\pi\) | ||||
−0.982625 | + | 0.185602i | \(0.940576\pi\) | |||||||
\(74\) | −2.41421 | −0.280647 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.55635 | −0.752065 | ||||||||
\(77\) | 2.41421i | 0.275125i | ||||||||
\(78\) | 1.17157i | 0.132655i | ||||||||
\(79\) | −4.75736 | −0.535245 | −0.267622 | − | 0.963524i | \(-0.586238\pi\) | ||||
−0.267622 | + | 0.963524i | \(0.586238\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 3.68629i | − 0.407083i | ||||||||
\(83\) | − 12.4853i | − 1.37044i | −0.728337 | − | 0.685219i | \(-0.759707\pi\) | ||||
0.728337 | − | 0.685219i | \(-0.240293\pi\) | |||||||
\(84\) | −4.41421 | −0.481630 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.142136 | 0.0153269 | ||||||||
\(87\) | 6.82843i | 0.732084i | ||||||||
\(88\) | 1.58579i | 0.169045i | ||||||||
\(89\) | 7.65685 | 0.811625 | 0.405812 | − | 0.913956i | \(-0.366989\pi\) | ||||
0.405812 | + | 0.913956i | \(0.366989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.82843 | −0.715814 | ||||||||
\(92\) | − 1.82843i | − 0.190627i | ||||||||
\(93\) | − 8.48528i | − 0.879883i | ||||||||
\(94\) | 3.92893 | 0.405238 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.41421 | −0.450524 | ||||||||
\(97\) | 0.171573i | 0.0174206i | 0.999962 | + | 0.00871029i | \(0.00277261\pi\) | ||||
−0.999962 | + | 0.00871029i | \(0.997227\pi\) | |||||||
\(98\) | − 0.485281i | − 0.0490208i | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.89949 | −0.487518 | −0.243759 | − | 0.969836i | \(-0.578381\pi\) | ||||
−0.243759 | + | 0.969836i | \(0.578381\pi\) | |||||||
\(102\) | 0.171573i | 0.0169882i | ||||||||
\(103\) | 2.34315i | 0.230877i | 0.993315 | + | 0.115439i | \(0.0368273\pi\) | ||||
−0.993315 | + | 0.115439i | \(0.963173\pi\) | |||||||
\(104\) | −4.48528 | −0.439818 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.51472 | 0.147122 | ||||||||
\(107\) | 17.3137i | 1.67378i | 0.547372 | + | 0.836890i | \(0.315628\pi\) | ||||
−0.547372 | + | 0.836890i | \(0.684372\pi\) | |||||||
\(108\) | 1.82843i | 0.175940i | ||||||||
\(109\) | 17.3137 | 1.65835 | 0.829176 | − | 0.558987i | \(-0.188810\pi\) | ||||
0.829176 | + | 0.558987i | \(0.188810\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.82843 | −0.553210 | ||||||||
\(112\) | − 7.24264i | − 0.684365i | ||||||||
\(113\) | 10.0000i | 0.940721i | 0.882474 | + | 0.470360i | \(0.155876\pi\) | ||||
−0.882474 | + | 0.470360i | \(0.844124\pi\) | |||||||
\(114\) | 1.48528 | 0.139109 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.4853 | −1.15923 | ||||||||
\(117\) | 2.82843i | 0.261488i | ||||||||
\(118\) | 4.55635i | 0.419446i | ||||||||
\(119\) | −1.00000 | −0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − 1.31371i | − 0.118938i | ||||||||
\(123\) | − 8.89949i | − 0.802440i | ||||||||
\(124\) | 15.5147 | 1.39326 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | − 1.24264i | − 0.110267i | −0.998479 | − | 0.0551333i | \(-0.982442\pi\) | ||||
0.998479 | − | 0.0551333i | \(-0.0175584\pi\) | |||||||
\(128\) | − 10.5563i | − 0.933058i | ||||||||
\(129\) | 0.343146 | 0.0302123 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.17157 | 0.102361 | 0.0511804 | − | 0.998689i | \(-0.483702\pi\) | ||||
0.0511804 | + | 0.998689i | \(0.483702\pi\) | |||||||
\(132\) | 1.82843i | 0.159144i | ||||||||
\(133\) | 8.65685i | 0.750644i | ||||||||
\(134\) | −4.82843 | −0.417113 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.656854 | −0.0563248 | ||||||||
\(137\) | 16.1421i | 1.37912i | 0.724231 | + | 0.689558i | \(0.242195\pi\) | ||||
−0.724231 | + | 0.689558i | \(0.757805\pi\) | |||||||
\(138\) | 0.414214i | 0.0352602i | ||||||||
\(139\) | −14.9706 | −1.26979 | −0.634893 | − | 0.772600i | \(-0.718956\pi\) | ||||
−0.634893 | + | 0.772600i | \(0.718956\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.48528 | 0.798805 | ||||||||
\(142\) | − 0.899495i | − 0.0754839i | ||||||||
\(143\) | 2.82843i | 0.236525i | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.31371 | 0.108723 | ||||||||
\(147\) | − 1.17157i | − 0.0966297i | ||||||||
\(148\) | − 10.6569i | − 0.875988i | ||||||||
\(149\) | 17.7279 | 1.45233 | 0.726164 | − | 0.687522i | \(-0.241301\pi\) | ||||
0.726164 | + | 0.687522i | \(0.241301\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0000 | 1.13930 | 0.569652 | − | 0.821886i | \(-0.307078\pi\) | ||||
0.569652 | + | 0.821886i | \(0.307078\pi\) | |||||||
\(152\) | 5.68629i | 0.461219i | ||||||||
\(153\) | 0.414214i | 0.0334872i | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.17157 | −0.414057 | ||||||||
\(157\) | 6.00000i | 0.478852i | 0.970915 | + | 0.239426i | \(0.0769593\pi\) | ||||
−0.970915 | + | 0.239426i | \(0.923041\pi\) | |||||||
\(158\) | 1.97056i | 0.156770i | ||||||||
\(159\) | 3.65685 | 0.290007 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.41421 | −0.190267 | ||||||||
\(162\) | − 0.414214i | − 0.0325437i | ||||||||
\(163\) | 23.7990i | 1.86408i | 0.362354 | + | 0.932040i | \(0.381973\pi\) | ||||
−0.362354 | + | 0.932040i | \(0.618027\pi\) | |||||||
\(164\) | 16.2721 | 1.27064 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.17157 | −0.401392 | ||||||||
\(167\) | − 17.7990i | − 1.37733i | −0.725081 | − | 0.688664i | \(-0.758198\pi\) | ||||
0.725081 | − | 0.688664i | \(-0.241802\pi\) | |||||||
\(168\) | 3.82843i | 0.295370i | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.58579 | 0.274212 | ||||||||
\(172\) | 0.627417i | 0.0478401i | ||||||||
\(173\) | − 18.5563i | − 1.41081i | −0.708803 | − | 0.705407i | \(-0.750764\pi\) | ||||
0.708803 | − | 0.705407i | \(-0.249236\pi\) | |||||||
\(174\) | 2.82843 | 0.214423 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 11.0000i | 0.826811i | ||||||||
\(178\) | − 3.17157i | − 0.237719i | ||||||||
\(179\) | 22.7990 | 1.70408 | 0.852038 | − | 0.523480i | \(-0.175366\pi\) | ||||
0.852038 | + | 0.523480i | \(0.175366\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.9706 | 0.889765 | 0.444882 | − | 0.895589i | \(-0.353245\pi\) | ||||
0.444882 | + | 0.895589i | \(0.353245\pi\) | |||||||
\(182\) | 2.82843i | 0.209657i | ||||||||
\(183\) | − 3.17157i | − 0.234449i | ||||||||
\(184\) | −1.58579 | −0.116906 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.51472 | −0.257712 | ||||||||
\(187\) | 0.414214i | 0.0302903i | ||||||||
\(188\) | 17.3431i | 1.26488i | ||||||||
\(189\) | 2.41421 | 0.175608 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.8284 | 0.855875 | 0.427937 | − | 0.903808i | \(-0.359240\pi\) | ||||
0.427937 | + | 0.903808i | \(0.359240\pi\) | |||||||
\(192\) | − 4.17157i | − 0.301057i | ||||||||
\(193\) | 19.3137i | 1.39023i | 0.718898 | + | 0.695116i | \(0.244647\pi\) | ||||
−0.718898 | + | 0.695116i | \(0.755353\pi\) | |||||||
\(194\) | 0.0710678 | 0.00510237 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.14214 | 0.153010 | ||||||||
\(197\) | 13.2426i | 0.943499i | 0.881733 | + | 0.471750i | \(0.156377\pi\) | ||||
−0.881733 | + | 0.471750i | \(0.843623\pi\) | |||||||
\(198\) | − 0.414214i | − 0.0294369i | ||||||||
\(199\) | −5.17157 | −0.366603 | −0.183302 | − | 0.983057i | \(-0.558678\pi\) | ||||
−0.183302 | + | 0.983057i | \(0.558678\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.6569 | −0.822211 | ||||||||
\(202\) | 2.02944i | 0.142791i | ||||||||
\(203\) | 16.4853i | 1.15704i | ||||||||
\(204\) | −0.757359 | −0.0530258 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.970563 | 0.0676223 | ||||||||
\(207\) | 1.00000i | 0.0695048i | ||||||||
\(208\) | − 8.48528i | − 0.588348i | ||||||||
\(209\) | 3.58579 | 0.248034 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.31371 | 0.641182 | 0.320591 | − | 0.947218i | \(-0.396118\pi\) | ||||
0.320591 | + | 0.947218i | \(0.396118\pi\) | |||||||
\(212\) | 6.68629i | 0.459216i | ||||||||
\(213\) | − 2.17157i | − 0.148794i | ||||||||
\(214\) | 7.17157 | 0.490239 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.58579 | 0.107899 | ||||||||
\(217\) | − 20.4853i | − 1.39063i | ||||||||
\(218\) | − 7.17157i | − 0.485720i | ||||||||
\(219\) | 3.17157 | 0.214315 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.17157 | −0.0788085 | ||||||||
\(222\) | 2.41421i | 0.162031i | ||||||||
\(223\) | 26.8284i | 1.79656i | 0.439419 | + | 0.898282i | \(0.355184\pi\) | ||||
−0.439419 | + | 0.898282i | \(0.644816\pi\) | |||||||
\(224\) | −10.6569 | −0.712041 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.14214 | 0.275531 | ||||||||
\(227\) | − 1.51472i | − 0.100535i | −0.998736 | − | 0.0502677i | \(-0.983993\pi\) | ||||
0.998736 | − | 0.0502677i | \(-0.0160075\pi\) | |||||||
\(228\) | 6.55635i | 0.434205i | ||||||||
\(229\) | 19.4853 | 1.28762 | 0.643812 | − | 0.765184i | \(-0.277352\pi\) | ||||
0.643812 | + | 0.765184i | \(0.277352\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.41421 | 0.158844 | ||||||||
\(232\) | 10.8284i | 0.710921i | ||||||||
\(233\) | 14.5563i | 0.953618i | 0.879007 | + | 0.476809i | \(0.158207\pi\) | ||||
−0.879007 | + | 0.476809i | \(0.841793\pi\) | |||||||
\(234\) | 1.17157 | 0.0765881 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −20.1127 | −1.30923 | ||||||||
\(237\) | 4.75736i | 0.309024i | ||||||||
\(238\) | 0.414214i | 0.0268495i | ||||||||
\(239\) | −12.3431 | −0.798412 | −0.399206 | − | 0.916861i | \(-0.630714\pi\) | ||||
−0.399206 | + | 0.916861i | \(0.630714\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.1421 | −0.910975 | −0.455488 | − | 0.890242i | \(-0.650535\pi\) | ||||
−0.455488 | + | 0.890242i | \(0.650535\pi\) | |||||||
\(242\) | − 0.414214i | − 0.0266267i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 5.79899 | 0.371242 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.68629 | −0.235029 | ||||||||
\(247\) | 10.1421i | 0.645329i | ||||||||
\(248\) | − 13.4558i | − 0.854447i | ||||||||
\(249\) | −12.4853 | −0.791223 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.9706 | −1.57613 | −0.788064 | − | 0.615593i | \(-0.788916\pi\) | ||||
−0.788064 | + | 0.615593i | \(0.788916\pi\) | |||||||
\(252\) | 4.41421i | 0.278069i | ||||||||
\(253\) | 1.00000i | 0.0628695i | ||||||||
\(254\) | −0.514719 | −0.0322963 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | − 13.3137i | − 0.830486i | −0.909710 | − | 0.415243i | \(-0.863696\pi\) | ||||
0.909710 | − | 0.415243i | \(-0.136304\pi\) | |||||||
\(258\) | − 0.142136i | − 0.00884898i | ||||||||
\(259\) | −14.0711 | −0.874334 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.82843 | 0.422669 | ||||||||
\(262\) | − 0.485281i | − 0.0299808i | ||||||||
\(263\) | 10.9706i | 0.676474i | 0.941061 | + | 0.338237i | \(0.109831\pi\) | ||||
−0.941061 | + | 0.338237i | \(0.890169\pi\) | |||||||
\(264\) | 1.58579 | 0.0975984 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.58579 | 0.219859 | ||||||||
\(267\) | − 7.65685i | − 0.468592i | ||||||||
\(268\) | − 21.3137i | − 1.30194i | ||||||||
\(269\) | −23.7990 | −1.45105 | −0.725525 | − | 0.688196i | \(-0.758403\pi\) | ||||
−0.725525 | + | 0.688196i | \(0.758403\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.8995 | −0.662097 | −0.331049 | − | 0.943614i | \(-0.607402\pi\) | ||||
−0.331049 | + | 0.943614i | \(0.607402\pi\) | |||||||
\(272\) | − 1.24264i | − 0.0753462i | ||||||||
\(273\) | 6.82843i | 0.413275i | ||||||||
\(274\) | 6.68629 | 0.403934 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.82843 | −0.110058 | ||||||||
\(277\) | − 0.828427i | − 0.0497754i | −0.999690 | − | 0.0248877i | \(-0.992077\pi\) | ||||
0.999690 | − | 0.0248877i | \(-0.00792281\pi\) | |||||||
\(278\) | 6.20101i | 0.371912i | ||||||||
\(279\) | −8.48528 | −0.508001 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.9289 | 1.06955 | 0.534775 | − | 0.844994i | \(-0.320396\pi\) | ||||
0.534775 | + | 0.844994i | \(0.320396\pi\) | |||||||
\(282\) | − 3.92893i | − 0.233965i | ||||||||
\(283\) | − 18.8995i | − 1.12346i | −0.827321 | − | 0.561729i | \(-0.810136\pi\) | ||||
0.827321 | − | 0.561729i | \(-0.189864\pi\) | |||||||
\(284\) | 3.97056 | 0.235610 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.17157 | 0.0692766 | ||||||||
\(287\) | − 21.4853i | − 1.26824i | ||||||||
\(288\) | 4.41421i | 0.260110i | ||||||||
\(289\) | 16.8284 | 0.989907 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.171573 | 0.0100578 | ||||||||
\(292\) | 5.79899i | 0.339360i | ||||||||
\(293\) | − 20.4142i | − 1.19261i | −0.802758 | − | 0.596306i | \(-0.796635\pi\) | ||||
0.802758 | − | 0.596306i | \(-0.203365\pi\) | |||||||
\(294\) | −0.485281 | −0.0283022 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.24264 | −0.537218 | ||||||||
\(297\) | − 1.00000i | − 0.0580259i | ||||||||
\(298\) | − 7.34315i | − 0.425377i | ||||||||
\(299\) | −2.82843 | −0.163572 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.828427 | 0.0477497 | ||||||||
\(302\) | − 5.79899i | − 0.333694i | ||||||||
\(303\) | 4.89949i | 0.281469i | ||||||||
\(304\) | −10.7574 | −0.616977 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.171573 | 0.00980817 | ||||||||
\(307\) | 29.3137i | 1.67302i | 0.547950 | + | 0.836511i | \(0.315408\pi\) | ||||
−0.547950 | + | 0.836511i | \(0.684592\pi\) | |||||||
\(308\) | 4.41421i | 0.251523i | ||||||||
\(309\) | 2.34315 | 0.133297 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.34315 | 0.132868 | 0.0664338 | − | 0.997791i | \(-0.478838\pi\) | ||||
0.0664338 | + | 0.997791i | \(0.478838\pi\) | |||||||
\(312\) | 4.48528i | 0.253929i | ||||||||
\(313\) | − 1.14214i | − 0.0645573i | −0.999479 | − | 0.0322787i | \(-0.989724\pi\) | ||||
0.999479 | − | 0.0322787i | \(-0.0102764\pi\) | |||||||
\(314\) | 2.48528 | 0.140253 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.69848 | −0.489328 | ||||||||
\(317\) | 25.1716i | 1.41378i | 0.707325 | + | 0.706888i | \(0.249902\pi\) | ||||
−0.707325 | + | 0.706888i | \(0.750098\pi\) | |||||||
\(318\) | − 1.51472i | − 0.0849412i | ||||||||
\(319\) | 6.82843 | 0.382319 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.3137 | 0.966357 | ||||||||
\(322\) | 1.00000i | 0.0557278i | ||||||||
\(323\) | 1.48528i | 0.0826433i | ||||||||
\(324\) | 1.82843 | 0.101579 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.85786 | 0.545977 | ||||||||
\(327\) | − 17.3137i | − 0.957450i | ||||||||
\(328\) | − 14.1127i | − 0.779243i | ||||||||
\(329\) | 22.8995 | 1.26249 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.85786 | −0.212047 | −0.106024 | − | 0.994364i | \(-0.533812\pi\) | ||||
−0.106024 | + | 0.994364i | \(0.533812\pi\) | |||||||
\(332\) | − 22.8284i | − 1.25287i | ||||||||
\(333\) | 5.82843i | 0.319396i | ||||||||
\(334\) | −7.37258 | −0.403410 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.24264 | −0.395118 | ||||||||
\(337\) | − 24.1421i | − 1.31511i | −0.753408 | − | 0.657553i | \(-0.771592\pi\) | ||||
0.753408 | − | 0.657553i | \(-0.228408\pi\) | |||||||
\(338\) | − 2.07107i | − 0.112651i | ||||||||
\(339\) | 10.0000 | 0.543125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.48528 | −0.459504 | ||||||||
\(342\) | − 1.48528i | − 0.0803148i | ||||||||
\(343\) | − 19.7279i | − 1.06521i | ||||||||
\(344\) | 0.544156 | 0.0293389 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.68629 | −0.413218 | ||||||||
\(347\) | − 26.8284i | − 1.44023i | −0.693857 | − | 0.720113i | \(-0.744090\pi\) | ||||
0.693857 | − | 0.720113i | \(-0.255910\pi\) | |||||||
\(348\) | 12.4853i | 0.669281i | ||||||||
\(349\) | −14.4853 | −0.775379 | −0.387690 | − | 0.921790i | \(-0.626727\pi\) | ||||
−0.387690 | + | 0.921790i | \(0.626727\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.82843 | 0.150970 | ||||||||
\(352\) | 4.41421i | 0.235278i | ||||||||
\(353\) | − 12.4853i | − 0.664524i | −0.943187 | − | 0.332262i | \(-0.892188\pi\) | ||||
0.943187 | − | 0.332262i | \(-0.107812\pi\) | |||||||
\(354\) | 4.55635 | 0.242167 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.0000 | 0.741999 | ||||||||
\(357\) | 1.00000i | 0.0529256i | ||||||||
\(358\) | − 9.44365i | − 0.499112i | ||||||||
\(359\) | −32.4853 | −1.71451 | −0.857254 | − | 0.514894i | \(-0.827831\pi\) | ||||
−0.857254 | + | 0.514894i | \(0.827831\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.14214 | −0.323270 | ||||||||
\(362\) | − 4.95837i | − 0.260606i | ||||||||
\(363\) | − 1.00000i | − 0.0524864i | ||||||||
\(364\) | −12.4853 | −0.654407 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.31371 | −0.0686686 | ||||||||
\(367\) | − 21.3137i | − 1.11257i | −0.830993 | − | 0.556283i | \(-0.812227\pi\) | ||||
0.830993 | − | 0.556283i | \(-0.187773\pi\) | |||||||
\(368\) | − 3.00000i | − 0.156386i | ||||||||
\(369\) | −8.89949 | −0.463289 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.82843 | 0.458349 | ||||||||
\(372\) | − 15.5147i | − 0.804401i | ||||||||
\(373\) | 12.3431i | 0.639104i | 0.947569 | + | 0.319552i | \(0.103532\pi\) | ||||
−0.947569 | + | 0.319552i | \(0.896468\pi\) | |||||||
\(374\) | 0.171573 | 0.00887182 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.0416 | 0.775713 | ||||||||
\(377\) | 19.3137i | 0.994707i | ||||||||
\(378\) | − 1.00000i | − 0.0514344i | ||||||||
\(379\) | −14.8284 | −0.761685 | −0.380843 | − | 0.924640i | \(-0.624366\pi\) | ||||
−0.380843 | + | 0.924640i | \(0.624366\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.24264 | −0.0636624 | ||||||||
\(382\) | − 4.89949i | − 0.250680i | ||||||||
\(383\) | − 20.0000i | − 1.02195i | −0.859595 | − | 0.510976i | \(-0.829284\pi\) | ||||
0.859595 | − | 0.510976i | \(-0.170716\pi\) | |||||||
\(384\) | −10.5563 | −0.538701 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.00000 | 0.407189 | ||||||||
\(387\) | − 0.343146i | − 0.0174431i | ||||||||
\(388\) | 0.313708i | 0.0159261i | ||||||||
\(389\) | 6.34315 | 0.321610 | 0.160805 | − | 0.986986i | \(-0.448591\pi\) | ||||
0.160805 | + | 0.986986i | \(0.448591\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.414214 | −0.0209477 | ||||||||
\(392\) | − 1.85786i | − 0.0938363i | ||||||||
\(393\) | − 1.17157i | − 0.0590980i | ||||||||
\(394\) | 5.48528 | 0.276344 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.82843 | 0.0918819 | ||||||||
\(397\) | 31.9411i | 1.60308i | 0.597942 | + | 0.801540i | \(0.295985\pi\) | ||||
−0.597942 | + | 0.801540i | \(0.704015\pi\) | |||||||
\(398\) | 2.14214i | 0.107376i | ||||||||
\(399\) | 8.65685 | 0.433385 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.79899 | −0.389463 | −0.194731 | − | 0.980857i | \(-0.562384\pi\) | ||||
−0.194731 | + | 0.980857i | \(0.562384\pi\) | |||||||
\(402\) | 4.82843i | 0.240820i | ||||||||
\(403\) | − 24.0000i | − 1.19553i | ||||||||
\(404\) | −8.95837 | −0.445696 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.82843 | 0.338889 | ||||||||
\(407\) | 5.82843i | 0.288904i | ||||||||
\(408\) | 0.656854i | 0.0325191i | ||||||||
\(409\) | −24.1421 | −1.19375 | −0.596876 | − | 0.802334i | \(-0.703592\pi\) | ||||
−0.596876 | + | 0.802334i | \(0.703592\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.1421 | 0.796233 | ||||||||
\(412\) | 4.28427i | 0.211071i | ||||||||
\(413\) | 26.5563i | 1.30675i | ||||||||
\(414\) | 0.414214 | 0.0203575 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.4853 | −0.612141 | ||||||||
\(417\) | 14.9706i | 0.733112i | ||||||||
\(418\) | − 1.48528i | − 0.0726475i | ||||||||
\(419\) | 8.51472 | 0.415971 | 0.207986 | − | 0.978132i | \(-0.433309\pi\) | ||||
0.207986 | + | 0.978132i | \(0.433309\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.0000 | −1.31590 | −0.657950 | − | 0.753062i | \(-0.728576\pi\) | ||||
−0.657950 | + | 0.753062i | \(0.728576\pi\) | |||||||
\(422\) | − 3.85786i | − 0.187798i | ||||||||
\(423\) | − 9.48528i | − 0.461190i | ||||||||
\(424\) | 5.79899 | 0.281624 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.899495 | −0.0435807 | ||||||||
\(427\) | − 7.65685i | − 0.370541i | ||||||||
\(428\) | 31.6569i | 1.53019i | ||||||||
\(429\) | 2.82843 | 0.136558 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.82843 | 0.328914 | 0.164457 | − | 0.986384i | \(-0.447413\pi\) | ||||
0.164457 | + | 0.986384i | \(0.447413\pi\) | |||||||
\(432\) | 3.00000i | 0.144338i | ||||||||
\(433\) | − 9.31371i | − 0.447588i | −0.974636 | − | 0.223794i | \(-0.928156\pi\) | ||||
0.974636 | − | 0.223794i | \(-0.0718443\pi\) | |||||||
\(434\) | −8.48528 | −0.407307 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 31.6569 | 1.51609 | ||||||||
\(437\) | 3.58579i | 0.171531i | ||||||||
\(438\) | − 1.31371i | − 0.0627714i | ||||||||
\(439\) | −27.7279 | −1.32338 | −0.661691 | − | 0.749777i | \(-0.730161\pi\) | ||||
−0.661691 | + | 0.749777i | \(0.730161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.17157 | −0.0557892 | ||||||||
\(442\) | 0.485281i | 0.0230825i | ||||||||
\(443\) | − 25.9706i | − 1.23390i | −0.787003 | − | 0.616949i | \(-0.788368\pi\) | ||||
0.787003 | − | 0.616949i | \(-0.211632\pi\) | |||||||
\(444\) | −10.6569 | −0.505752 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.1127 | 0.526202 | ||||||||
\(447\) | − 17.7279i | − 0.838502i | ||||||||
\(448\) | − 10.0711i | − 0.475813i | ||||||||
\(449\) | −10.4853 | −0.494831 | −0.247416 | − | 0.968909i | \(-0.579581\pi\) | ||||
−0.247416 | + | 0.968909i | \(0.579581\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.89949 | −0.419061 | ||||||||
\(452\) | 18.2843i | 0.860020i | ||||||||
\(453\) | − 14.0000i | − 0.657777i | ||||||||
\(454\) | −0.627417 | −0.0294461 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.68629 | 0.266285 | ||||||||
\(457\) | 32.1421i | 1.50355i | 0.659422 | + | 0.751773i | \(0.270801\pi\) | ||||
−0.659422 | + | 0.751773i | \(0.729199\pi\) | |||||||
\(458\) | − 8.07107i | − 0.377136i | ||||||||
\(459\) | 0.414214 | 0.0193338 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.7696 | 1.89883 | 0.949414 | − | 0.314028i | \(-0.101679\pi\) | ||||
0.949414 | + | 0.314028i | \(0.101679\pi\) | |||||||
\(462\) | − 1.00000i | − 0.0465242i | ||||||||
\(463\) | − 1.02944i | − 0.0478420i | −0.999714 | − | 0.0239210i | \(-0.992385\pi\) | ||||
0.999714 | − | 0.0239210i | \(-0.00761502\pi\) | |||||||
\(464\) | −20.4853 | −0.951005 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.02944 | 0.279308 | ||||||||
\(467\) | − 34.6274i | − 1.60237i | −0.598420 | − | 0.801183i | \(-0.704204\pi\) | ||||
0.598420 | − | 0.801183i | \(-0.295796\pi\) | |||||||
\(468\) | 5.17157i | 0.239056i | ||||||||
\(469\) | −28.1421 | −1.29948 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.00000 | 0.276465 | ||||||||
\(472\) | 17.4437i | 0.802909i | ||||||||
\(473\) | − 0.343146i | − 0.0157779i | ||||||||
\(474\) | 1.97056 | 0.0905109 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.82843 | −0.0838058 | ||||||||
\(477\) | − 3.65685i | − 0.167436i | ||||||||
\(478\) | 5.11270i | 0.233849i | ||||||||
\(479\) | 7.51472 | 0.343356 | 0.171678 | − | 0.985153i | \(-0.445081\pi\) | ||||
0.171678 | + | 0.985153i | \(0.445081\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.4853 | −0.751664 | ||||||||
\(482\) | 5.85786i | 0.266818i | ||||||||
\(483\) | 2.41421i | 0.109851i | ||||||||
\(484\) | 1.82843 | 0.0831103 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.414214 | −0.0187891 | ||||||||
\(487\) | 10.4853i | 0.475133i | 0.971371 | + | 0.237567i | \(0.0763498\pi\) | ||||
−0.971371 | + | 0.237567i | \(0.923650\pi\) | |||||||
\(488\) | − 5.02944i | − 0.227672i | ||||||||
\(489\) | 23.7990 | 1.07623 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.14214 | 0.186932 | 0.0934660 | − | 0.995622i | \(-0.470205\pi\) | ||||
0.0934660 | + | 0.995622i | \(0.470205\pi\) | |||||||
\(492\) | − 16.2721i | − 0.733602i | ||||||||
\(493\) | 2.82843i | 0.127386i | ||||||||
\(494\) | 4.20101 | 0.189012 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 25.4558 | 1.14300 | ||||||||
\(497\) | − 5.24264i | − 0.235165i | ||||||||
\(498\) | 5.17157i | 0.231744i | ||||||||
\(499\) | −40.8284 | −1.82773 | −0.913866 | − | 0.406017i | \(-0.866918\pi\) | ||||
−0.913866 | + | 0.406017i | \(0.866918\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.7990 | −0.795200 | ||||||||
\(502\) | 10.3431i | 0.461637i | ||||||||
\(503\) | − 22.2843i | − 0.993607i | −0.867863 | − | 0.496803i | \(-0.834507\pi\) | ||||
0.867863 | − | 0.496803i | \(-0.165493\pi\) | |||||||
\(504\) | 3.82843 | 0.170532 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.414214 | 0.0184140 | ||||||||
\(507\) | − 5.00000i | − 0.222058i | ||||||||
\(508\) | − 2.27208i | − 0.100807i | ||||||||
\(509\) | 40.6274 | 1.80078 | 0.900389 | − | 0.435085i | \(-0.143282\pi\) | ||||
0.900389 | + | 0.435085i | \(0.143282\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.65685 | 0.338719 | ||||||||
\(512\) | − 22.7574i | − 1.00574i | ||||||||
\(513\) | − 3.58579i | − 0.158316i | ||||||||
\(514\) | −5.51472 | −0.243244 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.627417 | 0.0276205 | ||||||||
\(517\) | − 9.48528i | − 0.417162i | ||||||||
\(518\) | 5.82843i | 0.256086i | ||||||||
\(519\) | −18.5563 | −0.814533 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.85786 | −0.344259 | −0.172130 | − | 0.985074i | \(-0.555065\pi\) | ||||
−0.172130 | + | 0.985074i | \(0.555065\pi\) | |||||||
\(522\) | − 2.82843i | − 0.123797i | ||||||||
\(523\) | 0.213203i | 0.00932274i | 0.999989 | + | 0.00466137i | \(0.00148376\pi\) | ||||
−0.999989 | + | 0.00466137i | \(0.998516\pi\) | |||||||
\(524\) | 2.14214 | 0.0935796 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.54416 | 0.198135 | ||||||||
\(527\) | − 3.51472i | − 0.153104i | ||||||||
\(528\) | 3.00000i | 0.130558i | ||||||||
\(529\) | 22.0000 | 0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.0000 | 0.477359 | ||||||||
\(532\) | 15.8284i | 0.686249i | ||||||||
\(533\) | − 25.1716i | − 1.09030i | ||||||||
\(534\) | −3.17157 | −0.137247 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −18.4853 | −0.798443 | ||||||||
\(537\) | − 22.7990i | − 0.983849i | ||||||||
\(538\) | 9.85786i | 0.425003i | ||||||||
\(539\) | −1.17157 | −0.0504632 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.3137 | −0.486414 | −0.243207 | − | 0.969974i | \(-0.578199\pi\) | ||||
−0.243207 | + | 0.969974i | \(0.578199\pi\) | |||||||
\(542\) | 4.51472i | 0.193924i | ||||||||
\(543\) | − 11.9706i | − 0.513706i | ||||||||
\(544\) | −1.82843 | −0.0783932 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.82843 | 0.121046 | ||||||||
\(547\) | − 17.8701i | − 0.764068i | −0.924148 | − | 0.382034i | \(-0.875224\pi\) | ||||
0.924148 | − | 0.382034i | \(-0.124776\pi\) | |||||||
\(548\) | 29.5147i | 1.26081i | ||||||||
\(549\) | −3.17157 | −0.135359 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.4853 | 1.04311 | ||||||||
\(552\) | 1.58579i | 0.0674956i | ||||||||
\(553\) | 11.4853i | 0.488404i | ||||||||
\(554\) | −0.343146 | −0.0145789 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −27.3726 | −1.16086 | ||||||||
\(557\) | − 10.8284i | − 0.458815i | −0.973330 | − | 0.229408i | \(-0.926321\pi\) | ||||
0.973330 | − | 0.229408i | \(-0.0736789\pi\) | |||||||
\(558\) | 3.51472i | 0.148790i | ||||||||
\(559\) | 0.970563 | 0.0410504 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.414214 | 0.0174881 | ||||||||
\(562\) | − 7.42641i | − 0.313264i | ||||||||
\(563\) | 7.31371i | 0.308236i | 0.988052 | + | 0.154118i | \(0.0492536\pi\) | ||||
−0.988052 | + | 0.154118i | \(0.950746\pi\) | |||||||
\(564\) | 17.3431 | 0.730278 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.82843 | −0.329053 | ||||||||
\(567\) | − 2.41421i | − 0.101387i | ||||||||
\(568\) | − 3.44365i | − 0.144492i | ||||||||
\(569\) | −6.75736 | −0.283283 | −0.141642 | − | 0.989918i | \(-0.545238\pi\) | ||||
−0.141642 | + | 0.989918i | \(0.545238\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.9706 | −1.79826 | −0.899131 | − | 0.437680i | \(-0.855800\pi\) | ||||
−0.899131 | + | 0.437680i | \(0.855800\pi\) | |||||||
\(572\) | 5.17157i | 0.216234i | ||||||||
\(573\) | − 11.8284i | − 0.494140i | ||||||||
\(574\) | −8.89949 | −0.371458 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.17157 | −0.173816 | ||||||||
\(577\) | − 9.97056i | − 0.415080i | −0.978227 | − | 0.207540i | \(-0.933454\pi\) | ||||
0.978227 | − | 0.207540i | \(-0.0665457\pi\) | |||||||
\(578\) | − 6.97056i | − 0.289937i | ||||||||
\(579\) | 19.3137 | 0.802650 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.1421 | −1.25051 | ||||||||
\(582\) | − 0.0710678i | − 0.00294586i | ||||||||
\(583\) | − 3.65685i | − 0.151451i | ||||||||
\(584\) | 5.02944 | 0.208120 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.45584 | −0.349308 | ||||||||
\(587\) | − 25.3431i | − 1.04602i | −0.852325 | − | 0.523012i | \(-0.824808\pi\) | ||||
0.852325 | − | 0.523012i | \(-0.175192\pi\) | |||||||
\(588\) | − 2.14214i | − 0.0883402i | ||||||||
\(589\) | −30.4264 | −1.25370 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.2426 | 0.544729 | ||||||||
\(592\) | − 17.4853i | − 0.718641i | ||||||||
\(593\) | 35.7990i | 1.47009i | 0.678019 | + | 0.735044i | \(0.262839\pi\) | ||||
−0.678019 | + | 0.735044i | \(0.737161\pi\) | |||||||
\(594\) | −0.414214 | −0.0169954 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 32.4142 | 1.32774 | ||||||||
\(597\) | 5.17157i | 0.211658i | ||||||||
\(598\) | 1.17157i | 0.0479092i | ||||||||
\(599\) | −13.6863 | −0.559207 | −0.279603 | − | 0.960116i | \(-0.590203\pi\) | ||||
−0.279603 | + | 0.960116i | \(0.590203\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.17157 | −0.374116 | −0.187058 | − | 0.982349i | \(-0.559895\pi\) | ||||
−0.187058 | + | 0.982349i | \(0.559895\pi\) | |||||||
\(602\) | − 0.343146i | − 0.0139856i | ||||||||
\(603\) | 11.6569i | 0.474704i | ||||||||
\(604\) | 25.5980 | 1.04157 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.02944 | 0.0824403 | ||||||||
\(607\) | 30.9706i | 1.25706i | 0.777787 | + | 0.628528i | \(0.216342\pi\) | ||||
−0.777787 | + | 0.628528i | \(0.783658\pi\) | |||||||
\(608\) | 15.8284i | 0.641927i | ||||||||
\(609\) | 16.4853 | 0.668017 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.8284 | 1.08536 | ||||||||
\(612\) | 0.757359i | 0.0306144i | ||||||||
\(613\) | 42.0000i | 1.69636i | 0.529705 | + | 0.848182i | \(0.322303\pi\) | ||||
−0.529705 | + | 0.848182i | \(0.677697\pi\) | |||||||
\(614\) | 12.1421 | 0.490017 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.82843 | 0.154252 | ||||||||
\(617\) | − 38.1421i | − 1.53554i | −0.640723 | − | 0.767772i | \(-0.721365\pi\) | ||||
0.640723 | − | 0.767772i | \(-0.278635\pi\) | |||||||
\(618\) | − 0.970563i | − 0.0390418i | ||||||||
\(619\) | 6.62742 | 0.266378 | 0.133189 | − | 0.991091i | \(-0.457478\pi\) | ||||
0.133189 | + | 0.991091i | \(0.457478\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | − 0.970563i | − 0.0389160i | ||||||||
\(623\) | − 18.4853i | − 0.740597i | ||||||||
\(624\) | −8.48528 | −0.339683 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.473088 | −0.0189084 | ||||||||
\(627\) | − 3.58579i | − 0.143203i | ||||||||
\(628\) | 10.9706i | 0.437773i | ||||||||
\(629\) | −2.41421 | −0.0962610 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.6274 | −0.741546 | −0.370773 | − | 0.928724i | \(-0.620907\pi\) | ||||
−0.370773 | + | 0.928724i | \(0.620907\pi\) | |||||||
\(632\) | 7.54416i | 0.300090i | ||||||||
\(633\) | − 9.31371i | − 0.370187i | ||||||||
\(634\) | 10.4264 | 0.414086 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.68629 | 0.265129 | ||||||||
\(637\) | − 3.31371i | − 0.131294i | ||||||||
\(638\) | − 2.82843i | − 0.111979i | ||||||||
\(639\) | −2.17157 | −0.0859061 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.5147 | −1.00777 | −0.503885 | − | 0.863771i | \(-0.668097\pi\) | ||||
−0.503885 | + | 0.863771i | \(0.668097\pi\) | |||||||
\(642\) | − 7.17157i | − 0.283039i | ||||||||
\(643\) | − 0.970563i | − 0.0382753i | −0.999817 | − | 0.0191376i | \(-0.993908\pi\) | ||||
0.999817 | − | 0.0191376i | \(-0.00609207\pi\) | |||||||
\(644\) | −4.41421 | −0.173944 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.615224 | 0.0242057 | ||||||||
\(647\) | 28.6569i | 1.12662i | 0.826247 | + | 0.563309i | \(0.190472\pi\) | ||||
−0.826247 | + | 0.563309i | \(0.809528\pi\) | |||||||
\(648\) | − 1.58579i | − 0.0622956i | ||||||||
\(649\) | 11.0000 | 0.431788 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.4853 | −0.802881 | ||||||||
\(652\) | 43.5147i | 1.70417i | ||||||||
\(653\) | 23.5147i | 0.920202i | 0.887867 | + | 0.460101i | \(0.152187\pi\) | ||||
−0.887867 | + | 0.460101i | \(0.847813\pi\) | |||||||
\(654\) | −7.17157 | −0.280431 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 26.6985 | 1.04240 | ||||||||
\(657\) | − 3.17157i | − 0.123735i | ||||||||
\(658\) | − 9.48528i | − 0.369775i | ||||||||
\(659\) | 47.1127 | 1.83525 | 0.917625 | − | 0.397447i | \(-0.130104\pi\) | ||||
0.917625 | + | 0.397447i | \(0.130104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.3431 | −0.907943 | −0.453972 | − | 0.891016i | \(-0.649993\pi\) | ||||
−0.453972 | + | 0.891016i | \(0.649993\pi\) | |||||||
\(662\) | 1.59798i | 0.0621072i | ||||||||
\(663\) | 1.17157i | 0.0455001i | ||||||||
\(664\) | −19.7990 | −0.768350 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.41421 | 0.0935489 | ||||||||
\(667\) | 6.82843i | 0.264398i | ||||||||
\(668\) | − 32.5442i | − 1.25917i | ||||||||
\(669\) | 26.8284 | 1.03725 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.17157 | −0.122437 | ||||||||
\(672\) | 10.6569i | 0.411097i | ||||||||
\(673\) | − 0.343146i | − 0.0132273i | −0.999978 | − | 0.00661365i | \(-0.997895\pi\) | ||||
0.999978 | − | 0.00661365i | \(-0.00210520\pi\) | |||||||
\(674\) | −10.0000 | −0.385186 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.14214 | 0.351621 | ||||||||
\(677\) | 23.5147i | 0.903744i | 0.892083 | + | 0.451872i | \(0.149244\pi\) | ||||
−0.892083 | + | 0.451872i | \(0.850756\pi\) | |||||||
\(678\) | − 4.14214i | − 0.159078i | ||||||||
\(679\) | 0.414214 | 0.0158961 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.51472 | −0.0580441 | ||||||||
\(682\) | 3.51472i | 0.134586i | ||||||||
\(683\) | − 12.5147i | − 0.478862i | −0.970913 | − | 0.239431i | \(-0.923039\pi\) | ||||
0.970913 | − | 0.239431i | \(-0.0769610\pi\) | |||||||
\(684\) | 6.55635 | 0.250688 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.17157 | −0.311992 | ||||||||
\(687\) | − 19.4853i | − 0.743410i | ||||||||
\(688\) | 1.02944i | 0.0392469i | ||||||||
\(689\) | 10.3431 | 0.394042 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.4558 | −1.34880 | −0.674402 | − | 0.738364i | \(-0.735598\pi\) | ||||
−0.674402 | + | 0.738364i | \(0.735598\pi\) | |||||||
\(692\) | − 33.9289i | − 1.28978i | ||||||||
\(693\) | − 2.41421i | − 0.0917084i | ||||||||
\(694\) | −11.1127 | −0.421832 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 10.8284 | 0.410450 | ||||||||
\(697\) | − 3.68629i | − 0.139628i | ||||||||
\(698\) | 6.00000i | 0.227103i | ||||||||
\(699\) | 14.5563 | 0.550572 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.3848 | −1.56308 | −0.781541 | − | 0.623854i | \(-0.785566\pi\) | ||||
−0.781541 | + | 0.623854i | \(0.785566\pi\) | |||||||
\(702\) | − 1.17157i | − 0.0442182i | ||||||||
\(703\) | 20.8995i | 0.788239i | ||||||||
\(704\) | −4.17157 | −0.157222 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.17157 | −0.194635 | ||||||||
\(707\) | 11.8284i | 0.444854i | ||||||||
\(708\) | 20.1127i | 0.755881i | ||||||||
\(709\) | 29.1421 | 1.09446 | 0.547228 | − | 0.836984i | \(-0.315683\pi\) | ||||
0.547228 | + | 0.836984i | \(0.315683\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.75736 | 0.178415 | ||||||||
\(712\) | − 12.1421i | − 0.455046i | ||||||||
\(713\) | − 8.48528i | − 0.317776i | ||||||||
\(714\) | 0.414214 | 0.0155016 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 41.6863 | 1.55789 | ||||||||
\(717\) | 12.3431i | 0.460963i | ||||||||
\(718\) | 13.4558i | 0.502168i | ||||||||
\(719\) | −9.65685 | −0.360140 | −0.180070 | − | 0.983654i | \(-0.557632\pi\) | ||||
−0.180070 | + | 0.983654i | \(0.557632\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.65685 | 0.210672 | ||||||||
\(722\) | 2.54416i | 0.0946837i | ||||||||
\(723\) | 14.1421i | 0.525952i | ||||||||
\(724\) | 21.8873 | 0.813435 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.414214 | −0.0153729 | ||||||||
\(727\) | 16.9706i | 0.629403i | 0.949191 | + | 0.314702i | \(0.101904\pi\) | ||||
−0.949191 | + | 0.314702i | \(0.898096\pi\) | |||||||
\(728\) | 10.8284i | 0.401328i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.142136 | 0.00525708 | ||||||||
\(732\) | − 5.79899i | − 0.214337i | ||||||||
\(733\) | − 32.1421i | − 1.18720i | −0.804761 | − | 0.593598i | \(-0.797707\pi\) | ||||
0.804761 | − | 0.593598i | \(-0.202293\pi\) | |||||||
\(734\) | −8.82843 | −0.325863 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.41421 | −0.162710 | ||||||||
\(737\) | 11.6569i | 0.429386i | ||||||||
\(738\) | 3.68629i | 0.135694i | ||||||||
\(739\) | −20.4142 | −0.750949 | −0.375474 | − | 0.926833i | \(-0.622520\pi\) | ||||
−0.375474 | + | 0.926833i | \(0.622520\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.1421 | 0.372581 | ||||||||
\(742\) | − 3.65685i | − 0.134247i | ||||||||
\(743\) | 31.1127i | 1.14141i | 0.821154 | + | 0.570707i | \(0.193331\pi\) | ||||
−0.821154 | + | 0.570707i | \(0.806669\pi\) | |||||||
\(744\) | −13.4558 | −0.493315 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.11270 | 0.187189 | ||||||||
\(747\) | 12.4853i | 0.456813i | ||||||||
\(748\) | 0.757359i | 0.0276918i | ||||||||
\(749\) | 41.7990 | 1.52730 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.5980 | 1.15303 | 0.576513 | − | 0.817088i | \(-0.304413\pi\) | ||||
0.576513 | + | 0.817088i | \(0.304413\pi\) | |||||||
\(752\) | 28.4558i | 1.03768i | ||||||||
\(753\) | 24.9706i | 0.909978i | ||||||||
\(754\) | 8.00000 | 0.291343 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.41421 | 0.160543 | ||||||||
\(757\) | − 10.6863i | − 0.388400i | −0.980962 | − | 0.194200i | \(-0.937789\pi\) | ||||
0.980962 | − | 0.194200i | \(-0.0622111\pi\) | |||||||
\(758\) | 6.14214i | 0.223092i | ||||||||
\(759\) | 1.00000 | 0.0362977 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.17157 | −0.187469 | −0.0937347 | − | 0.995597i | \(-0.529881\pi\) | ||||
−0.0937347 | + | 0.995597i | \(0.529881\pi\) | |||||||
\(762\) | 0.514719i | 0.0186463i | ||||||||
\(763\) | − 41.7990i | − 1.51323i | ||||||||
\(764\) | 21.6274 | 0.782452 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.28427 | −0.299323 | ||||||||
\(767\) | 31.1127i | 1.12341i | ||||||||
\(768\) | − 3.97056i | − 0.143275i | ||||||||
\(769\) | 7.65685 | 0.276113 | 0.138057 | − | 0.990424i | \(-0.455914\pi\) | ||||
0.138057 | + | 0.990424i | \(0.455914\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.3137 | −0.479481 | ||||||||
\(772\) | 35.3137i | 1.27097i | ||||||||
\(773\) | 0.828427i | 0.0297965i | 0.999889 | + | 0.0148982i | \(0.00474243\pi\) | ||||
−0.999889 | + | 0.0148982i | \(0.995258\pi\) | |||||||
\(774\) | −0.142136 | −0.00510896 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.272078 | 0.00976703 | ||||||||
\(777\) | 14.0711i | 0.504797i | ||||||||
\(778\) | − 2.62742i | − 0.0941975i | ||||||||
\(779\) | −31.9117 | −1.14335 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.17157 | −0.0777050 | ||||||||
\(782\) | 0.171573i | 0.00613543i | ||||||||
\(783\) | − 6.82843i | − 0.244028i | ||||||||
\(784\) | 3.51472 | 0.125526 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.485281 | −0.0173094 | ||||||||
\(787\) | − 7.92893i | − 0.282636i | −0.989964 | − | 0.141318i | \(-0.954866\pi\) | ||||
0.989964 | − | 0.141318i | \(-0.0451340\pi\) | |||||||
\(788\) | 24.2132i | 0.862560i | ||||||||
\(789\) | 10.9706 | 0.390562 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.1421 | 0.858396 | ||||||||
\(792\) | − 1.58579i | − 0.0563485i | ||||||||
\(793\) | − 8.97056i | − 0.318554i | ||||||||
\(794\) | 13.2304 | 0.469531 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.45584 | −0.335154 | ||||||||
\(797\) | 40.9706i | 1.45125i | 0.688089 | + | 0.725626i | \(0.258450\pi\) | ||||
−0.688089 | + | 0.725626i | \(0.741550\pi\) | |||||||
\(798\) | − 3.58579i | − 0.126935i | ||||||||
\(799\) | 3.92893 | 0.138996 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.65685 | −0.270542 | ||||||||
\(802\) | 3.23045i | 0.114071i | ||||||||
\(803\) | − 3.17157i | − 0.111922i | ||||||||
\(804\) | −21.3137 | −0.751677 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.94113 | −0.350161 | ||||||||
\(807\) | 23.7990i | 0.837764i | ||||||||
\(808\) | 7.76955i | 0.273332i | ||||||||
\(809\) | −7.72792 | −0.271699 | −0.135850 | − | 0.990729i | \(-0.543376\pi\) | ||||
−0.135850 | + | 0.990729i | \(0.543376\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.2132 | 0.358634 | 0.179317 | − | 0.983791i | \(-0.442611\pi\) | ||||
0.179317 | + | 0.983791i | \(0.442611\pi\) | |||||||
\(812\) | 30.1421i | 1.05778i | ||||||||
\(813\) | 10.8995i | 0.382262i | ||||||||
\(814\) | 2.41421 | 0.0846181 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.24264 | −0.0435011 | ||||||||
\(817\) | − 1.23045i | − 0.0430479i | ||||||||
\(818\) | 10.0000i | 0.349642i | ||||||||
\(819\) | 6.82843 | 0.238605 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.7990 | 0.551389 | 0.275694 | − | 0.961245i | \(-0.411092\pi\) | ||||
0.275694 | + | 0.961245i | \(0.411092\pi\) | |||||||
\(822\) | − 6.68629i | − 0.233211i | ||||||||
\(823\) | 14.9706i | 0.521841i | 0.965360 | + | 0.260921i | \(0.0840260\pi\) | ||||
−0.965360 | + | 0.260921i | \(0.915974\pi\) | |||||||
\(824\) | 3.71573 | 0.129444 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.0000 | 0.382739 | ||||||||
\(827\) | − 12.6863i | − 0.441146i | −0.975371 | − | 0.220573i | \(-0.929207\pi\) | ||||
0.975371 | − | 0.220573i | \(-0.0707927\pi\) | |||||||
\(828\) | 1.82843i | 0.0635422i | ||||||||
\(829\) | 47.9411 | 1.66506 | 0.832532 | − | 0.553977i | \(-0.186890\pi\) | ||||
0.832532 | + | 0.553977i | \(0.186890\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.828427 | −0.0287378 | ||||||||
\(832\) | − 11.7990i | − 0.409056i | ||||||||
\(833\) | − 0.485281i | − 0.0168140i | ||||||||
\(834\) | 6.20101 | 0.214723 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.55635 | 0.226756 | ||||||||
\(837\) | 8.48528i | 0.293294i | ||||||||
\(838\) | − 3.52691i | − 0.121835i | ||||||||
\(839\) | 47.3137 | 1.63345 | 0.816725 | − | 0.577027i | \(-0.195787\pi\) | ||||
0.816725 | + | 0.577027i | \(0.195787\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.6274 | 0.607842 | ||||||||
\(842\) | 11.1838i | 0.385418i | ||||||||
\(843\) | − 17.9289i | − 0.617505i | ||||||||
\(844\) | 17.0294 | 0.586177 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.92893 | −0.135079 | ||||||||
\(847\) | − 2.41421i | − 0.0829534i | ||||||||
\(848\) | 10.9706i | 0.376731i | ||||||||
\(849\) | −18.8995 | −0.648629 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.82843 | −0.199796 | ||||||||
\(852\) | − 3.97056i | − 0.136029i | ||||||||
\(853\) | 19.1716i | 0.656422i | 0.944604 | + | 0.328211i | \(0.106446\pi\) | ||||
−0.944604 | + | 0.328211i | \(0.893554\pi\) | |||||||
\(854\) | −3.17157 | −0.108529 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27.4558 | 0.938421 | ||||||||
\(857\) | − 36.6985i | − 1.25360i | −0.779182 | − | 0.626798i | \(-0.784365\pi\) | ||||
0.779182 | − | 0.626798i | \(-0.215635\pi\) | |||||||
\(858\) | − 1.17157i | − 0.0399968i | ||||||||
\(859\) | 20.4853 | 0.698949 | 0.349474 | − | 0.936946i | \(-0.386360\pi\) | ||||
0.349474 | + | 0.936946i | \(0.386360\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.4853 | −0.732216 | ||||||||
\(862\) | − 2.82843i | − 0.0963366i | ||||||||
\(863\) | 28.6863i | 0.976493i | 0.872706 | + | 0.488246i | \(0.162363\pi\) | ||||
−0.872706 | + | 0.488246i | \(0.837637\pi\) | |||||||
\(864\) | 4.41421 | 0.150175 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.85786 | −0.131096 | ||||||||
\(867\) | − 16.8284i | − 0.571523i | ||||||||
\(868\) | − 37.4558i | − 1.27133i | ||||||||
\(869\) | 4.75736 | 0.161382 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.9706 | −1.11716 | ||||||||
\(872\) | − 27.4558i | − 0.929772i | ||||||||
\(873\) | − 0.171573i | − 0.00580686i | ||||||||
\(874\) | 1.48528 | 0.0502404 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.79899 | 0.195930 | ||||||||
\(877\) | 15.1127i | 0.510320i | 0.966899 | + | 0.255160i | \(0.0821281\pi\) | ||||
−0.966899 | + | 0.255160i | \(0.917872\pi\) | |||||||
\(878\) | 11.4853i | 0.387609i | ||||||||
\(879\) | −20.4142 | −0.688554 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.0000 | −0.808581 | −0.404290 | − | 0.914631i | \(-0.632481\pi\) | ||||
−0.404290 | + | 0.914631i | \(0.632481\pi\) | |||||||
\(882\) | 0.485281i | 0.0163403i | ||||||||
\(883\) | − 38.6274i | − 1.29992i | −0.759970 | − | 0.649958i | \(-0.774786\pi\) | ||||
0.759970 | − | 0.649958i | \(-0.225214\pi\) | |||||||
\(884\) | −2.14214 | −0.0720478 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.7574 | −0.361401 | ||||||||
\(887\) | − 22.1421i | − 0.743460i | −0.928341 | − | 0.371730i | \(-0.878765\pi\) | ||||
0.928341 | − | 0.371730i | \(-0.121235\pi\) | |||||||
\(888\) | 9.24264i | 0.310163i | ||||||||
\(889\) | −3.00000 | −0.100617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 49.0538i | 1.64244i | ||||||||
\(893\) | − 34.0122i | − 1.13817i | ||||||||
\(894\) | −7.34315 | −0.245592 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −25.4853 | −0.851403 | ||||||||
\(897\) | 2.82843i | 0.0944384i | ||||||||
\(898\) | 4.34315i | 0.144933i | ||||||||
\(899\) | −57.9411 | −1.93244 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.51472 | 0.0504626 | ||||||||
\(902\) | 3.68629i | 0.122740i | ||||||||
\(903\) | − 0.828427i | − 0.0275683i | ||||||||
\(904\) | 15.8579 | 0.527425 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.79899 | −0.192659 | ||||||||
\(907\) | − 2.48528i | − 0.0825224i | −0.999148 | − | 0.0412612i | \(-0.986862\pi\) | ||||
0.999148 | − | 0.0412612i | \(-0.0131376\pi\) | |||||||
\(908\) | − 2.76955i | − 0.0919108i | ||||||||
\(909\) | 4.89949 | 0.162506 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.5147 | 0.944735 | 0.472367 | − | 0.881402i | \(-0.343400\pi\) | ||||
0.472367 | + | 0.881402i | \(0.343400\pi\) | |||||||
\(912\) | 10.7574i | 0.356212i | ||||||||
\(913\) | 12.4853i | 0.413203i | ||||||||
\(914\) | 13.3137 | 0.440378 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 35.6274 | 1.17716 | ||||||||
\(917\) | − 2.82843i | − 0.0934029i | ||||||||
\(918\) | − 0.171573i | − 0.00566275i | ||||||||
\(919\) | −1.78680 | −0.0589410 | −0.0294705 | − | 0.999566i | \(-0.509382\pi\) | ||||
−0.0294705 | + | 0.999566i | \(0.509382\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.3137 | 0.965920 | ||||||||
\(922\) | − 16.8873i | − 0.556154i | ||||||||
\(923\) | − 6.14214i | − 0.202171i | ||||||||
\(924\) | 4.41421 | 0.145217 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.426407 | −0.0140126 | ||||||||
\(927\) | − 2.34315i | − 0.0769590i | ||||||||
\(928\) | 30.1421i | 0.989464i | ||||||||
\(929\) | 13.7990 | 0.452730 | 0.226365 | − | 0.974043i | \(-0.427316\pi\) | ||||
0.226365 | + | 0.974043i | \(0.427316\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.20101 | −0.137683 | ||||||||
\(932\) | 26.6152i | 0.871811i | ||||||||
\(933\) | − 2.34315i | − 0.0767111i | ||||||||
\(934\) | −14.3431 | −0.469322 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.48528 | 0.146606 | ||||||||
\(937\) | − 16.0000i | − 0.522697i | −0.965244 | − | 0.261349i | \(-0.915833\pi\) | ||||
0.965244 | − | 0.261349i | \(-0.0841672\pi\) | |||||||
\(938\) | 11.6569i | 0.380610i | ||||||||
\(939\) | −1.14214 | −0.0372722 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.8995 | −0.746502 | −0.373251 | − | 0.927730i | \(-0.621757\pi\) | ||||
−0.373251 | + | 0.927730i | \(0.621757\pi\) | |||||||
\(942\) | − 2.48528i | − 0.0809748i | ||||||||
\(943\) | − 8.89949i | − 0.289807i | ||||||||
\(944\) | −33.0000 | −1.07406 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.142136 | −0.00462123 | ||||||||
\(947\) | − 36.7990i | − 1.19581i | −0.801568 | − | 0.597903i | \(-0.796001\pi\) | ||||
0.801568 | − | 0.597903i | \(-0.203999\pi\) | |||||||
\(948\) | 8.69848i | 0.282514i | ||||||||
\(949\) | 8.97056 | 0.291197 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.1716 | 0.816244 | ||||||||
\(952\) | 1.58579i | 0.0513956i | ||||||||
\(953\) | 29.0416i | 0.940751i | 0.882466 | + | 0.470375i | \(0.155881\pi\) | ||||
−0.882466 | + | 0.470375i | \(0.844119\pi\) | |||||||
\(954\) | −1.51472 | −0.0490408 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −22.5685 | −0.729919 | ||||||||
\(957\) | − 6.82843i | − 0.220732i | ||||||||
\(958\) | − 3.11270i | − 0.100567i | ||||||||
\(959\) | 38.9706 | 1.25843 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.0000 | 1.32258 | ||||||||
\(962\) | 6.82843i | 0.220157i | ||||||||
\(963\) | − 17.3137i | − 0.557926i | ||||||||
\(964\) | −25.8579 | −0.832826 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.00000 | 0.0321745 | ||||||||
\(967\) | 38.0000i | 1.22200i | 0.791632 | + | 0.610999i | \(0.209232\pi\) | ||||
−0.791632 | + | 0.610999i | \(0.790768\pi\) | |||||||
\(968\) | − 1.58579i | − 0.0509691i | ||||||||
\(969\) | 1.48528 | 0.0477141 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.3137 | −1.61464 | −0.807322 | − | 0.590111i | \(-0.799084\pi\) | ||||
−0.807322 | + | 0.590111i | \(0.799084\pi\) | |||||||
\(972\) | − 1.82843i | − 0.0586468i | ||||||||
\(973\) | 36.1421i | 1.15866i | ||||||||
\(974\) | 4.34315 | 0.139163 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.51472 | 0.304559 | ||||||||
\(977\) | 60.5685i | 1.93776i | 0.247532 | + | 0.968880i | \(0.420380\pi\) | ||||
−0.247532 | + | 0.968880i | \(0.579620\pi\) | |||||||
\(978\) | − 9.85786i | − 0.315220i | ||||||||
\(979\) | −7.65685 | −0.244714 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.3137 | −0.552784 | ||||||||
\(982\) | − 1.71573i | − 0.0547511i | ||||||||
\(983\) | − 51.2843i | − 1.63571i | −0.575421 | − | 0.817857i | \(-0.695162\pi\) | ||||
0.575421 | − | 0.817857i | \(-0.304838\pi\) | |||||||
\(984\) | −14.1127 | −0.449896 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.17157 | 0.0373105 | ||||||||
\(987\) | − 22.8995i | − 0.728899i | ||||||||
\(988\) | 18.5442i | 0.589968i | ||||||||
\(989\) | 0.343146 | 0.0109114 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.2843 | −1.34320 | −0.671602 | − | 0.740912i | \(-0.734394\pi\) | ||||
−0.671602 | + | 0.740912i | \(0.734394\pi\) | |||||||
\(992\) | − 37.4558i | − 1.18922i | ||||||||
\(993\) | 3.85786i | 0.122426i | ||||||||
\(994\) | −2.17157 | −0.0688781 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −22.8284 | −0.723346 | ||||||||
\(997\) | − 47.2548i | − 1.49658i | −0.663374 | − | 0.748288i | \(-0.730876\pi\) | ||||
0.663374 | − | 0.748288i | \(-0.269124\pi\) | |||||||
\(998\) | 16.9117i | 0.535330i | ||||||||
\(999\) | 5.82843 | 0.184403 |
(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 | 825.2.c.d.199.2 | 4 | ||
3.2 | odd | 2 | 2475.2.c.o.199.3 | 4 | |||
5.2 | odd | 4 | 825.2.a.d.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 825.2.a.f.1.1 | yes | 2 | ||
5.4 | even | 2 | inner | 825.2.c.d.199.3 | 4 | ||
15.2 | even | 4 | 2475.2.a.w.1.1 | 2 | |||
15.8 | even | 4 | 2475.2.a.l.1.2 | 2 | |||
15.14 | odd | 2 | 2475.2.c.o.199.2 | 4 | |||
55.32 | even | 4 | 9075.2.a.ca.1.1 | 2 | |||
55.43 | even | 4 | 9075.2.a.w.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.a.d.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
825.2.a.f.1.1 | yes | 2 | 5.3 | odd | 4 | ||
825.2.c.d.199.2 | 4 | 1.1 | even | 1 | trivial | ||
825.2.c.d.199.3 | 4 | 5.4 | even | 2 | inner | ||
2475.2.a.l.1.2 | 2 | 15.8 | even | 4 | |||
2475.2.a.w.1.1 | 2 | 15.2 | even | 4 | |||
2475.2.c.o.199.2 | 4 | 15.14 | odd | 2 | |||
2475.2.c.o.199.3 | 4 | 3.2 | odd | 2 | |||
9075.2.a.w.1.2 | 2 | 55.43 | even | 4 | |||
9075.2.a.ca.1.1 | 2 | 55.32 | even | 4 |