Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(1,825)]
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, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.67513 | −1.89160 | −0.945802 | − | 0.324745i | \(-0.894721\pi\) | ||||
−0.945802 | + | 0.324745i | \(0.894721\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.15633 | 2.57816 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.67513 | −1.09212 | ||||||||
\(7\) | −2.80606 | −1.06059 | −0.530296 | − | 0.847812i | \(-0.677919\pi\) | ||||
−0.530296 | + | 0.847812i | \(0.677919\pi\) | |||||||
\(8\) | −8.44358 | −2.98526 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 5.15633 | 1.48850 | ||||||||
\(13\) | 5.11871 | 1.41968 | 0.709838 | − | 0.704365i | \(-0.248768\pi\) | ||||
0.709838 | + | 0.704365i | \(0.248768\pi\) | |||||||
\(14\) | 7.50659 | 2.00622 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.2750 | 3.06876 | ||||||||
\(17\) | −4.54420 | −1.10213 | −0.551065 | − | 0.834462i | \(-0.685778\pi\) | ||||
−0.551065 | + | 0.834462i | \(0.685778\pi\) | |||||||
\(18\) | −2.67513 | −0.630534 | ||||||||
\(19\) | −4.57452 | −1.04947 | −0.524733 | − | 0.851267i | \(-0.675835\pi\) | ||||
−0.524733 | + | 0.851267i | \(0.675835\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.80606 | −0.612333 | ||||||||
\(22\) | 2.67513 | 0.570340 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | −8.44358 | −1.72354 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −13.6932 | −2.68546 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −14.4690 | −2.73438 | ||||||||
\(29\) | −2.38787 | −0.443417 | −0.221708 | − | 0.975113i | \(-0.571163\pi\) | ||||
−0.221708 | + | 0.975113i | \(0.571163\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.962389 | −0.172850 | −0.0864250 | − | 0.996258i | \(-0.527544\pi\) | ||||
−0.0864250 | + | 0.996258i | \(0.527544\pi\) | |||||||
\(32\) | −15.9502 | −2.81962 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 12.1563 | 2.08479 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.15633 | 0.859388 | ||||||||
\(37\) | −1.61213 | −0.265032 | −0.132516 | − | 0.991181i | \(-0.542306\pi\) | ||||
−0.132516 | + | 0.991181i | \(0.542306\pi\) | |||||||
\(38\) | 12.2374 | 1.98517 | ||||||||
\(39\) | 5.11871 | 0.819650 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.38787 | −0.372923 | −0.186462 | − | 0.982462i | \(-0.559702\pi\) | ||||
−0.186462 | + | 0.982462i | \(0.559702\pi\) | |||||||
\(42\) | 7.50659 | 1.15829 | ||||||||
\(43\) | −2.80606 | −0.427921 | −0.213960 | − | 0.976842i | \(-0.568636\pi\) | ||||
−0.213960 | + | 0.976842i | \(0.568636\pi\) | |||||||
\(44\) | −5.15633 | −0.777345 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.7005 | 1.57771 | ||||||||
\(47\) | 4.31265 | 0.629065 | 0.314532 | − | 0.949247i | \(-0.398152\pi\) | ||||
0.314532 | + | 0.949247i | \(0.398152\pi\) | |||||||
\(48\) | 12.2750 | 1.77175 | ||||||||
\(49\) | 0.873992 | 0.124856 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.54420 | −0.636315 | ||||||||
\(52\) | 26.3938 | 3.66015 | ||||||||
\(53\) | 6.57452 | 0.903079 | 0.451540 | − | 0.892251i | \(-0.350875\pi\) | ||||
0.451540 | + | 0.892251i | \(0.350875\pi\) | |||||||
\(54\) | −2.67513 | −0.364039 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 23.6932 | 3.16614 | ||||||||
\(57\) | −4.57452 | −0.605909 | ||||||||
\(58\) | 6.38787 | 0.838769 | ||||||||
\(59\) | −13.2750 | −1.72826 | −0.864131 | − | 0.503266i | \(-0.832132\pi\) | ||||
−0.864131 | + | 0.503266i | \(0.832132\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.92478 | 1.01466 | 0.507332 | − | 0.861751i | \(-0.330632\pi\) | ||||
0.507332 | + | 0.861751i | \(0.330632\pi\) | |||||||
\(62\) | 2.57452 | 0.326964 | ||||||||
\(63\) | −2.80606 | −0.353531 | ||||||||
\(64\) | 18.1187 | 2.26484 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.67513 | 0.329286 | ||||||||
\(67\) | −10.7005 | −1.30728 | −0.653639 | − | 0.756807i | \(-0.726758\pi\) | ||||
−0.653639 | + | 0.756807i | \(0.726758\pi\) | |||||||
\(68\) | −23.4314 | −2.84147 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.35026 | −0.872316 | −0.436158 | − | 0.899870i | \(-0.643661\pi\) | ||||
−0.436158 | + | 0.899870i | \(0.643661\pi\) | |||||||
\(72\) | −8.44358 | −0.995086 | ||||||||
\(73\) | −6.41819 | −0.751192 | −0.375596 | − | 0.926783i | \(-0.622562\pi\) | ||||
−0.375596 | + | 0.926783i | \(0.622562\pi\) | |||||||
\(74\) | 4.31265 | 0.501335 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −23.5877 | −2.70569 | ||||||||
\(77\) | 2.80606 | 0.319781 | ||||||||
\(78\) | −13.6932 | −1.55045 | ||||||||
\(79\) | 1.35026 | 0.151916 | 0.0759582 | − | 0.997111i | \(-0.475798\pi\) | ||||
0.0759582 | + | 0.997111i | \(0.475798\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.38787 | 0.705423 | ||||||||
\(83\) | 0.806063 | 0.0884770 | 0.0442385 | − | 0.999021i | \(-0.485914\pi\) | ||||
0.0442385 | + | 0.999021i | \(0.485914\pi\) | |||||||
\(84\) | −14.4690 | −1.57869 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.50659 | 0.809456 | ||||||||
\(87\) | −2.38787 | −0.256007 | ||||||||
\(88\) | 8.44358 | 0.900089 | ||||||||
\(89\) | −2.96239 | −0.314013 | −0.157006 | − | 0.987598i | \(-0.550184\pi\) | ||||
−0.157006 | + | 0.987598i | \(0.550184\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.3634 | −1.50570 | ||||||||
\(92\) | −20.6253 | −2.15034 | ||||||||
\(93\) | −0.962389 | −0.0997950 | ||||||||
\(94\) | −11.5369 | −1.18994 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −15.9502 | −1.62791 | ||||||||
\(97\) | 9.92478 | 1.00771 | 0.503854 | − | 0.863789i | \(-0.331915\pi\) | ||||
0.503854 | + | 0.863789i | \(0.331915\pi\) | |||||||
\(98\) | −2.33804 | −0.236178 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.6121 | −1.35446 | −0.677229 | − | 0.735773i | \(-0.736819\pi\) | ||||
−0.677229 | + | 0.735773i | \(0.736819\pi\) | |||||||
\(102\) | 12.1563 | 1.20366 | ||||||||
\(103\) | −16.3127 | −1.60733 | −0.803667 | − | 0.595080i | \(-0.797120\pi\) | ||||
−0.803667 | + | 0.595080i | \(0.797120\pi\) | |||||||
\(104\) | −43.2203 | −4.23810 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.5877 | −1.70827 | ||||||||
\(107\) | 9.43136 | 0.911764 | 0.455882 | − | 0.890040i | \(-0.349324\pi\) | ||||
0.455882 | + | 0.890040i | \(0.349324\pi\) | |||||||
\(108\) | 5.15633 | 0.496168 | ||||||||
\(109\) | −15.4010 | −1.47515 | −0.737576 | − | 0.675264i | \(-0.764030\pi\) | ||||
−0.737576 | + | 0.675264i | \(0.764030\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.61213 | −0.153016 | ||||||||
\(112\) | −34.4445 | −3.25470 | ||||||||
\(113\) | 13.7381 | 1.29238 | 0.646188 | − | 0.763179i | \(-0.276362\pi\) | ||||
0.646188 | + | 0.763179i | \(0.276362\pi\) | |||||||
\(114\) | 12.2374 | 1.14614 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.3127 | −1.14320 | ||||||||
\(117\) | 5.11871 | 0.473225 | ||||||||
\(118\) | 35.5125 | 3.26919 | ||||||||
\(119\) | 12.7513 | 1.16891 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −21.1998 | −1.91934 | ||||||||
\(123\) | −2.38787 | −0.215307 | ||||||||
\(124\) | −4.96239 | −0.445636 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.50659 | 0.668740 | ||||||||
\(127\) | −12.4182 | −1.10194 | −0.550968 | − | 0.834526i | \(-0.685741\pi\) | ||||
−0.550968 | + | 0.834526i | \(0.685741\pi\) | |||||||
\(128\) | −16.5696 | −1.46456 | ||||||||
\(129\) | −2.80606 | −0.247060 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.92478 | 0.517650 | 0.258825 | − | 0.965924i | \(-0.416665\pi\) | ||||
0.258825 | + | 0.965924i | \(0.416665\pi\) | |||||||
\(132\) | −5.15633 | −0.448800 | ||||||||
\(133\) | 12.8364 | 1.11306 | ||||||||
\(134\) | 28.6253 | 2.47285 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 38.3693 | 3.29014 | ||||||||
\(137\) | −9.79877 | −0.837165 | −0.418583 | − | 0.908179i | \(-0.637473\pi\) | ||||
−0.418583 | + | 0.908179i | \(0.637473\pi\) | |||||||
\(138\) | 10.7005 | 0.910889 | ||||||||
\(139\) | −2.12601 | −0.180326 | −0.0901628 | − | 0.995927i | \(-0.528739\pi\) | ||||
−0.0901628 | + | 0.995927i | \(0.528739\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.31265 | 0.363191 | ||||||||
\(142\) | 19.6629 | 1.65007 | ||||||||
\(143\) | −5.11871 | −0.428048 | ||||||||
\(144\) | 12.2750 | 1.02292 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 17.1695 | 1.42096 | ||||||||
\(147\) | 0.873992 | 0.0720856 | ||||||||
\(148\) | −8.31265 | −0.683296 | ||||||||
\(149\) | 8.31265 | 0.680999 | 0.340499 | − | 0.940245i | \(-0.389404\pi\) | ||||
0.340499 | + | 0.940245i | \(0.389404\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2750 | −1.24307 | −0.621533 | − | 0.783388i | \(-0.713490\pi\) | ||||
−0.621533 | + | 0.783388i | \(0.713490\pi\) | |||||||
\(152\) | 38.6253 | 3.13293 | ||||||||
\(153\) | −4.54420 | −0.367377 | ||||||||
\(154\) | −7.50659 | −0.604898 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 26.3938 | 2.11319 | ||||||||
\(157\) | −7.01317 | −0.559712 | −0.279856 | − | 0.960042i | \(-0.590287\pi\) | ||||
−0.279856 | + | 0.960042i | \(0.590287\pi\) | |||||||
\(158\) | −3.61213 | −0.287365 | ||||||||
\(159\) | 6.57452 | 0.521393 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.2243 | 0.884595 | ||||||||
\(162\) | −2.67513 | −0.210178 | ||||||||
\(163\) | −6.76116 | −0.529575 | −0.264787 | − | 0.964307i | \(-0.585302\pi\) | ||||
−0.264787 | + | 0.964307i | \(0.585302\pi\) | |||||||
\(164\) | −12.3127 | −0.961456 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.15633 | −0.167363 | ||||||||
\(167\) | 11.8192 | 0.914600 | 0.457300 | − | 0.889312i | \(-0.348817\pi\) | ||||
0.457300 | + | 0.889312i | \(0.348817\pi\) | |||||||
\(168\) | 23.6932 | 1.82797 | ||||||||
\(169\) | 13.2012 | 1.01548 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.57452 | −0.349822 | ||||||||
\(172\) | −14.4690 | −1.10325 | ||||||||
\(173\) | −6.99271 | −0.531646 | −0.265823 | − | 0.964022i | \(-0.585644\pi\) | ||||
−0.265823 | + | 0.964022i | \(0.585644\pi\) | |||||||
\(174\) | 6.38787 | 0.484263 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.2750 | −0.925266 | ||||||||
\(177\) | −13.2750 | −0.997813 | ||||||||
\(178\) | 7.92478 | 0.593987 | ||||||||
\(179\) | −2.70052 | −0.201847 | −0.100923 | − | 0.994894i | \(-0.532180\pi\) | ||||
−0.100923 | + | 0.994894i | \(0.532180\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.1998 | −1.57577 | −0.787885 | − | 0.615822i | \(-0.788824\pi\) | ||||
−0.787885 | + | 0.615822i | \(0.788824\pi\) | |||||||
\(182\) | 38.4241 | 2.84818 | ||||||||
\(183\) | 7.92478 | 0.585816 | ||||||||
\(184\) | 33.7743 | 2.48988 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.57452 | 0.188773 | ||||||||
\(187\) | 4.54420 | 0.332305 | ||||||||
\(188\) | 22.2374 | 1.62183 | ||||||||
\(189\) | −2.80606 | −0.204111 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.1490 | 0.951430 | 0.475715 | − | 0.879599i | \(-0.342189\pi\) | ||||
0.475715 | + | 0.879599i | \(0.342189\pi\) | |||||||
\(192\) | 18.1187 | 1.30761 | ||||||||
\(193\) | −5.89446 | −0.424293 | −0.212146 | − | 0.977238i | \(-0.568045\pi\) | ||||
−0.212146 | + | 0.977238i | \(0.568045\pi\) | |||||||
\(194\) | −26.5501 | −1.90618 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.50659 | 0.321899 | ||||||||
\(197\) | −20.3938 | −1.45299 | −0.726497 | − | 0.687169i | \(-0.758853\pi\) | ||||
−0.726497 | + | 0.687169i | \(0.758853\pi\) | |||||||
\(198\) | 2.67513 | 0.190113 | ||||||||
\(199\) | 17.4010 | 1.23353 | 0.616764 | − | 0.787148i | \(-0.288443\pi\) | ||||
0.616764 | + | 0.787148i | \(0.288443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.7005 | −0.754757 | ||||||||
\(202\) | 36.4142 | 2.56210 | ||||||||
\(203\) | 6.70052 | 0.470285 | ||||||||
\(204\) | −23.4314 | −1.64052 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 43.6385 | 3.04044 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 62.8324 | 4.35664 | ||||||||
\(209\) | 4.57452 | 0.316426 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.1260 | 1.24785 | 0.623923 | − | 0.781486i | \(-0.285538\pi\) | ||||
0.623923 | + | 0.781486i | \(0.285538\pi\) | |||||||
\(212\) | 33.9003 | 2.32828 | ||||||||
\(213\) | −7.35026 | −0.503632 | ||||||||
\(214\) | −25.2301 | −1.72470 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8.44358 | −0.574513 | ||||||||
\(217\) | 2.70052 | 0.183323 | ||||||||
\(218\) | 41.1998 | 2.79040 | ||||||||
\(219\) | −6.41819 | −0.433701 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.2605 | −1.56467 | ||||||||
\(222\) | 4.31265 | 0.289446 | ||||||||
\(223\) | −23.6385 | −1.58295 | −0.791475 | − | 0.611202i | \(-0.790686\pi\) | ||||
−0.791475 | + | 0.611202i | \(0.790686\pi\) | |||||||
\(224\) | 44.7572 | 2.99047 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −36.7513 | −2.44466 | ||||||||
\(227\) | 1.26916 | 0.0842371 | 0.0421185 | − | 0.999113i | \(-0.486589\pi\) | ||||
0.0421185 | + | 0.999113i | \(0.486589\pi\) | |||||||
\(228\) | −23.5877 | −1.56213 | ||||||||
\(229\) | 16.1768 | 1.06899 | 0.534496 | − | 0.845171i | \(-0.320501\pi\) | ||||
0.534496 | + | 0.845171i | \(0.320501\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.80606 | 0.184625 | ||||||||
\(232\) | 20.1622 | 1.32371 | ||||||||
\(233\) | 18.4690 | 1.20994 | 0.604971 | − | 0.796247i | \(-0.293185\pi\) | ||||
0.604971 | + | 0.796247i | \(0.293185\pi\) | |||||||
\(234\) | −13.6932 | −0.895154 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −68.4504 | −4.45574 | ||||||||
\(237\) | 1.35026 | 0.0877089 | ||||||||
\(238\) | −34.1114 | −2.21111 | ||||||||
\(239\) | 19.3258 | 1.25008 | 0.625042 | − | 0.780591i | \(-0.285082\pi\) | ||||
0.625042 | + | 0.780591i | \(0.285082\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.5501 | 1.83907 | 0.919536 | − | 0.393006i | \(-0.128565\pi\) | ||||
0.919536 | + | 0.393006i | \(0.128565\pi\) | |||||||
\(242\) | −2.67513 | −0.171964 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 40.8627 | 2.61597 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.38787 | 0.407276 | ||||||||
\(247\) | −23.4156 | −1.48990 | ||||||||
\(248\) | 8.12601 | 0.516002 | ||||||||
\(249\) | 0.806063 | 0.0510822 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.1998 | 1.46436 | 0.732180 | − | 0.681112i | \(-0.238503\pi\) | ||||
0.732180 | + | 0.681112i | \(0.238503\pi\) | |||||||
\(252\) | −14.4690 | −0.911460 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 33.2203 | 2.08443 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.08840 | 0.505525 | ||||||||
\(257\) | 10.8872 | 0.679123 | 0.339561 | − | 0.940584i | \(-0.389721\pi\) | ||||
0.339561 | + | 0.940584i | \(0.389721\pi\) | |||||||
\(258\) | 7.50659 | 0.467340 | ||||||||
\(259\) | 4.52373 | 0.281091 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.38787 | −0.147806 | ||||||||
\(262\) | −15.8496 | −0.979189 | ||||||||
\(263\) | −9.11871 | −0.562284 | −0.281142 | − | 0.959666i | \(-0.590713\pi\) | ||||
−0.281142 | + | 0.959666i | \(0.590713\pi\) | |||||||
\(264\) | 8.44358 | 0.519667 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −34.3390 | −2.10546 | ||||||||
\(267\) | −2.96239 | −0.181295 | ||||||||
\(268\) | −55.1754 | −3.37037 | ||||||||
\(269\) | −11.2995 | −0.688941 | −0.344471 | − | 0.938797i | \(-0.611942\pi\) | ||||
−0.344471 | + | 0.938797i | \(0.611942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.1998 | 1.53078 | 0.765390 | − | 0.643567i | \(-0.222546\pi\) | ||||
0.765390 | + | 0.643567i | \(0.222546\pi\) | |||||||
\(272\) | −55.7802 | −3.38217 | ||||||||
\(273\) | −14.3634 | −0.869315 | ||||||||
\(274\) | 26.2130 | 1.58358 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −20.6253 | −1.24150 | ||||||||
\(277\) | 2.41819 | 0.145295 | 0.0726475 | − | 0.997358i | \(-0.476855\pi\) | ||||
0.0726475 | + | 0.997358i | \(0.476855\pi\) | |||||||
\(278\) | 5.68735 | 0.341105 | ||||||||
\(279\) | −0.962389 | −0.0576167 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.4894 | 1.81885 | 0.909424 | − | 0.415870i | \(-0.136523\pi\) | ||||
0.909424 | + | 0.415870i | \(0.136523\pi\) | |||||||
\(282\) | −11.5369 | −0.687013 | ||||||||
\(283\) | −8.35756 | −0.496805 | −0.248403 | − | 0.968657i | \(-0.579906\pi\) | ||||
−0.248403 | + | 0.968657i | \(0.579906\pi\) | |||||||
\(284\) | −37.9003 | −2.24897 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.6932 | 0.809698 | ||||||||
\(287\) | 6.70052 | 0.395519 | ||||||||
\(288\) | −15.9502 | −0.939873 | ||||||||
\(289\) | 3.64974 | 0.214690 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.92478 | 0.581801 | ||||||||
\(292\) | −33.0943 | −1.93670 | ||||||||
\(293\) | 23.0943 | 1.34918 | 0.674591 | − | 0.738192i | \(-0.264320\pi\) | ||||
0.674591 | + | 0.738192i | \(0.264320\pi\) | |||||||
\(294\) | −2.33804 | −0.136357 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13.6121 | 0.791189 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −22.2374 | −1.28818 | ||||||||
\(299\) | −20.4749 | −1.18409 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.87399 | 0.453849 | ||||||||
\(302\) | 40.8627 | 2.35139 | ||||||||
\(303\) | −13.6121 | −0.781996 | ||||||||
\(304\) | −56.1524 | −3.22056 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 12.1563 | 0.694931 | ||||||||
\(307\) | −2.65562 | −0.151564 | −0.0757821 | − | 0.997124i | \(-0.524145\pi\) | ||||
−0.0757821 | + | 0.997124i | \(0.524145\pi\) | |||||||
\(308\) | 14.4690 | 0.824446 | ||||||||
\(309\) | −16.3127 | −0.927994 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.9756 | −0.905891 | −0.452946 | − | 0.891538i | \(-0.649627\pi\) | ||||
−0.452946 | + | 0.891538i | \(0.649627\pi\) | |||||||
\(312\) | −43.2203 | −2.44687 | ||||||||
\(313\) | 0.0606343 | 0.00342726 | 0.00171363 | − | 0.999999i | \(-0.499455\pi\) | ||||
0.00171363 | + | 0.999999i | \(0.499455\pi\) | |||||||
\(314\) | 18.7612 | 1.05875 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.96239 | 0.391665 | ||||||||
\(317\) | −3.81336 | −0.214180 | −0.107090 | − | 0.994249i | \(-0.534153\pi\) | ||||
−0.107090 | + | 0.994249i | \(0.534153\pi\) | |||||||
\(318\) | −17.5877 | −0.986269 | ||||||||
\(319\) | 2.38787 | 0.133695 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.43136 | 0.526407 | ||||||||
\(322\) | −30.0263 | −1.67330 | ||||||||
\(323\) | 20.7875 | 1.15665 | ||||||||
\(324\) | 5.15633 | 0.286463 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 18.0870 | 1.00175 | ||||||||
\(327\) | −15.4010 | −0.851680 | ||||||||
\(328\) | 20.1622 | 1.11327 | ||||||||
\(329\) | −12.1016 | −0.667181 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.2882 | 1.33500 | 0.667500 | − | 0.744609i | \(-0.267364\pi\) | ||||
0.667500 | + | 0.744609i | \(0.267364\pi\) | |||||||
\(332\) | 4.15633 | 0.228108 | ||||||||
\(333\) | −1.61213 | −0.0883440 | ||||||||
\(334\) | −31.6180 | −1.73006 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −34.4445 | −1.87910 | ||||||||
\(337\) | 22.5804 | 1.23003 | 0.615016 | − | 0.788514i | \(-0.289149\pi\) | ||||
0.615016 | + | 0.788514i | \(0.289149\pi\) | |||||||
\(338\) | −35.3150 | −1.92088 | ||||||||
\(339\) | 13.7381 | 0.746153 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.962389 | 0.0521163 | ||||||||
\(342\) | 12.2374 | 0.661724 | ||||||||
\(343\) | 17.1900 | 0.928171 | ||||||||
\(344\) | 23.6932 | 1.27745 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.7064 | 1.00566 | ||||||||
\(347\) | −20.1925 | −1.08399 | −0.541996 | − | 0.840381i | \(-0.682331\pi\) | ||||
−0.541996 | + | 0.840381i | \(0.682331\pi\) | |||||||
\(348\) | −12.3127 | −0.660027 | ||||||||
\(349\) | −27.2506 | −1.45869 | −0.729346 | − | 0.684145i | \(-0.760175\pi\) | ||||
−0.729346 | + | 0.684145i | \(0.760175\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.11871 | 0.273217 | ||||||||
\(352\) | 15.9502 | 0.850147 | ||||||||
\(353\) | −5.02302 | −0.267349 | −0.133674 | − | 0.991025i | \(-0.542678\pi\) | ||||
−0.133674 | + | 0.991025i | \(0.542678\pi\) | |||||||
\(354\) | 35.5125 | 1.88747 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −15.2750 | −0.809575 | ||||||||
\(357\) | 12.7513 | 0.674871 | ||||||||
\(358\) | 7.22425 | 0.381814 | ||||||||
\(359\) | −18.1768 | −0.959334 | −0.479667 | − | 0.877450i | \(-0.659243\pi\) | ||||
−0.479667 | + | 0.877450i | \(0.659243\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.92619 | 0.101379 | ||||||||
\(362\) | 56.7123 | 2.98073 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −74.0625 | −3.88193 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −21.1998 | −1.10813 | ||||||||
\(367\) | 8.56467 | 0.447072 | 0.223536 | − | 0.974696i | \(-0.428240\pi\) | ||||
0.223536 | + | 0.974696i | \(0.428240\pi\) | |||||||
\(368\) | −49.1002 | −2.55952 | ||||||||
\(369\) | −2.38787 | −0.124308 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.4485 | −0.957799 | ||||||||
\(372\) | −4.96239 | −0.257288 | ||||||||
\(373\) | −7.81924 | −0.404865 | −0.202432 | − | 0.979296i | \(-0.564885\pi\) | ||||
−0.202432 | + | 0.979296i | \(0.564885\pi\) | |||||||
\(374\) | −12.1563 | −0.628589 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −36.4142 | −1.87792 | ||||||||
\(377\) | −12.2228 | −0.629508 | ||||||||
\(378\) | 7.50659 | 0.386097 | ||||||||
\(379\) | 1.14903 | 0.0590218 | 0.0295109 | − | 0.999564i | \(-0.490605\pi\) | ||||
0.0295109 | + | 0.999564i | \(0.490605\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.4182 | −0.636203 | ||||||||
\(382\) | −35.1754 | −1.79973 | ||||||||
\(383\) | −34.0870 | −1.74176 | −0.870882 | − | 0.491493i | \(-0.836451\pi\) | ||||
−0.870882 | + | 0.491493i | \(0.836451\pi\) | |||||||
\(384\) | −16.5696 | −0.845563 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.7685 | 0.802593 | ||||||||
\(387\) | −2.80606 | −0.142640 | ||||||||
\(388\) | 51.1754 | 2.59804 | ||||||||
\(389\) | 23.7743 | 1.20541 | 0.602703 | − | 0.797965i | \(-0.294090\pi\) | ||||
0.602703 | + | 0.797965i | \(0.294090\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.1768 | 0.919240 | ||||||||
\(392\) | −7.37962 | −0.372727 | ||||||||
\(393\) | 5.92478 | 0.298865 | ||||||||
\(394\) | 54.5560 | 2.74849 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.15633 | −0.259115 | ||||||||
\(397\) | 4.15045 | 0.208305 | 0.104152 | − | 0.994561i | \(-0.466787\pi\) | ||||
0.104152 | + | 0.994561i | \(0.466787\pi\) | |||||||
\(398\) | −46.5501 | −2.33334 | ||||||||
\(399\) | 12.8364 | 0.642623 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.9149 | −1.69363 | −0.846815 | − | 0.531887i | \(-0.821483\pi\) | ||||
−0.846815 | + | 0.531887i | \(0.821483\pi\) | |||||||
\(402\) | 28.6253 | 1.42770 | ||||||||
\(403\) | −4.92619 | −0.245391 | ||||||||
\(404\) | −70.1886 | −3.49201 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.9248 | −0.889592 | ||||||||
\(407\) | 1.61213 | 0.0799102 | ||||||||
\(408\) | 38.3693 | 1.89956 | ||||||||
\(409\) | 8.55008 | 0.422774 | 0.211387 | − | 0.977402i | \(-0.432202\pi\) | ||||
0.211387 | + | 0.977402i | \(0.432202\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.79877 | −0.483338 | ||||||||
\(412\) | −84.1133 | −4.14397 | ||||||||
\(413\) | 37.2506 | 1.83298 | ||||||||
\(414\) | 10.7005 | 0.525902 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −81.6444 | −4.00294 | ||||||||
\(417\) | −2.12601 | −0.104111 | ||||||||
\(418\) | −12.2374 | −0.598552 | ||||||||
\(419\) | 13.2995 | 0.649722 | 0.324861 | − | 0.945762i | \(-0.394682\pi\) | ||||
0.324861 | + | 0.945762i | \(0.394682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.3014 | 1.62301 | 0.811505 | − | 0.584345i | \(-0.198649\pi\) | ||||
0.811505 | + | 0.584345i | \(0.198649\pi\) | |||||||
\(422\) | −48.4894 | −2.36043 | ||||||||
\(423\) | 4.31265 | 0.209688 | ||||||||
\(424\) | −55.5125 | −2.69592 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 19.6629 | 0.952671 | ||||||||
\(427\) | −22.2374 | −1.07614 | ||||||||
\(428\) | 48.6312 | 2.35068 | ||||||||
\(429\) | −5.11871 | −0.247134 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.07522 | 0.0999600 | 0.0499800 | − | 0.998750i | \(-0.484084\pi\) | ||||
0.0499800 | + | 0.998750i | \(0.484084\pi\) | |||||||
\(432\) | 12.2750 | 0.590583 | ||||||||
\(433\) | 37.4010 | 1.79738 | 0.898690 | − | 0.438585i | \(-0.144520\pi\) | ||||
0.898690 | + | 0.438585i | \(0.144520\pi\) | |||||||
\(434\) | −7.22425 | −0.346775 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −79.4128 | −3.80318 | ||||||||
\(437\) | 18.2981 | 0.875315 | ||||||||
\(438\) | 17.1695 | 0.820390 | ||||||||
\(439\) | −6.02444 | −0.287531 | −0.143765 | − | 0.989612i | \(-0.545921\pi\) | ||||
−0.143765 | + | 0.989612i | \(0.545921\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.873992 | 0.0416187 | ||||||||
\(442\) | 62.2247 | 2.95973 | ||||||||
\(443\) | 10.1359 | 0.481569 | 0.240785 | − | 0.970579i | \(-0.422595\pi\) | ||||
0.240785 | + | 0.970579i | \(0.422595\pi\) | |||||||
\(444\) | −8.31265 | −0.394501 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 63.2360 | 2.99431 | ||||||||
\(447\) | 8.31265 | 0.393175 | ||||||||
\(448\) | −50.8423 | −2.40207 | ||||||||
\(449\) | −11.4861 | −0.542063 | −0.271032 | − | 0.962570i | \(-0.587365\pi\) | ||||
−0.271032 | + | 0.962570i | \(0.587365\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.38787 | 0.112441 | ||||||||
\(452\) | 70.8383 | 3.33195 | ||||||||
\(453\) | −15.2750 | −0.717684 | ||||||||
\(454\) | −3.39517 | −0.159343 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 38.6253 | 1.80880 | ||||||||
\(457\) | 15.0435 | 0.703705 | 0.351852 | − | 0.936055i | \(-0.385552\pi\) | ||||
0.351852 | + | 0.936055i | \(0.385552\pi\) | |||||||
\(458\) | −43.2750 | −2.02211 | ||||||||
\(459\) | −4.54420 | −0.212105 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.2374 | −1.22200 | −0.610999 | − | 0.791631i | \(-0.709232\pi\) | ||||
−0.610999 | + | 0.791631i | \(0.709232\pi\) | |||||||
\(462\) | −7.50659 | −0.349238 | ||||||||
\(463\) | 5.46168 | 0.253826 | 0.126913 | − | 0.991914i | \(-0.459493\pi\) | ||||
0.126913 | + | 0.991914i | \(0.459493\pi\) | |||||||
\(464\) | −29.3112 | −1.36074 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −49.4069 | −2.28873 | ||||||||
\(467\) | 2.70052 | 0.124965 | 0.0624827 | − | 0.998046i | \(-0.480098\pi\) | ||||
0.0624827 | + | 0.998046i | \(0.480098\pi\) | |||||||
\(468\) | 26.3938 | 1.22005 | ||||||||
\(469\) | 30.0263 | 1.38649 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.01317 | −0.323150 | ||||||||
\(472\) | 112.089 | 5.15931 | ||||||||
\(473\) | 2.80606 | 0.129023 | ||||||||
\(474\) | −3.61213 | −0.165910 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 65.7499 | 3.01364 | ||||||||
\(477\) | 6.57452 | 0.301026 | ||||||||
\(478\) | −51.6991 | −2.36466 | ||||||||
\(479\) | 16.7757 | 0.766503 | 0.383252 | − | 0.923644i | \(-0.374804\pi\) | ||||
0.383252 | + | 0.923644i | \(0.374804\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.25202 | −0.376260 | ||||||||
\(482\) | −76.3752 | −3.47879 | ||||||||
\(483\) | 11.2243 | 0.510721 | ||||||||
\(484\) | 5.15633 | 0.234378 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.67513 | −0.121346 | ||||||||
\(487\) | 34.3996 | 1.55880 | 0.779398 | − | 0.626529i | \(-0.215525\pi\) | ||||
0.779398 | + | 0.626529i | \(0.215525\pi\) | |||||||
\(488\) | −66.9135 | −3.02903 | ||||||||
\(489\) | −6.76116 | −0.305750 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.9525 | 0.674799 | 0.337399 | − | 0.941362i | \(-0.390453\pi\) | ||||
0.337399 | + | 0.941362i | \(0.390453\pi\) | |||||||
\(492\) | −12.3127 | −0.555097 | ||||||||
\(493\) | 10.8510 | 0.488703 | ||||||||
\(494\) | 62.6399 | 2.81830 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.8134 | −0.530435 | ||||||||
\(497\) | 20.6253 | 0.925171 | ||||||||
\(498\) | −2.15633 | −0.0966272 | ||||||||
\(499\) | −2.85097 | −0.127627 | −0.0638135 | − | 0.997962i | \(-0.520326\pi\) | ||||
−0.0638135 | + | 0.997962i | \(0.520326\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.8192 | 0.528045 | ||||||||
\(502\) | −62.0625 | −2.76999 | ||||||||
\(503\) | −1.48024 | −0.0660006 | −0.0330003 | − | 0.999455i | \(-0.510506\pi\) | ||||
−0.0330003 | + | 0.999455i | \(0.510506\pi\) | |||||||
\(504\) | 23.6932 | 1.05538 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10.7005 | −0.475696 | ||||||||
\(507\) | 13.2012 | 0.586287 | ||||||||
\(508\) | −64.0322 | −2.84097 | ||||||||
\(509\) | −23.2995 | −1.03273 | −0.516366 | − | 0.856368i | \(-0.672715\pi\) | ||||
−0.516366 | + | 0.856368i | \(0.672715\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0098 | 0.796709 | ||||||||
\(512\) | 11.5017 | 0.508306 | ||||||||
\(513\) | −4.57452 | −0.201970 | ||||||||
\(514\) | −29.1246 | −1.28463 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −14.4690 | −0.636961 | ||||||||
\(517\) | −4.31265 | −0.189670 | ||||||||
\(518\) | −12.1016 | −0.531712 | ||||||||
\(519\) | −6.99271 | −0.306946 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.81194 | −0.298437 | −0.149218 | − | 0.988804i | \(-0.547676\pi\) | ||||
−0.149218 | + | 0.988804i | \(0.547676\pi\) | |||||||
\(522\) | 6.38787 | 0.279590 | ||||||||
\(523\) | 16.0567 | 0.702109 | 0.351054 | − | 0.936355i | \(-0.385823\pi\) | ||||
0.351054 | + | 0.936355i | \(0.385823\pi\) | |||||||
\(524\) | 30.5501 | 1.33459 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.3938 | 1.06362 | ||||||||
\(527\) | 4.37328 | 0.190503 | ||||||||
\(528\) | −12.2750 | −0.534203 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.2750 | −0.576088 | ||||||||
\(532\) | 66.1886 | 2.86964 | ||||||||
\(533\) | −12.2228 | −0.529430 | ||||||||
\(534\) | 7.92478 | 0.342939 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 90.3508 | 3.90256 | ||||||||
\(537\) | −2.70052 | −0.116536 | ||||||||
\(538\) | 30.2276 | 1.30320 | ||||||||
\(539\) | −0.873992 | −0.0376455 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.62530 | 0.284844 | 0.142422 | − | 0.989806i | \(-0.454511\pi\) | ||||
0.142422 | + | 0.989806i | \(0.454511\pi\) | |||||||
\(542\) | −67.4128 | −2.89563 | ||||||||
\(543\) | −21.1998 | −0.909771 | ||||||||
\(544\) | 72.4807 | 3.10759 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 38.4241 | 1.64440 | ||||||||
\(547\) | 5.75860 | 0.246220 | 0.123110 | − | 0.992393i | \(-0.460713\pi\) | ||||
0.123110 | + | 0.992393i | \(0.460713\pi\) | |||||||
\(548\) | −50.5256 | −2.15835 | ||||||||
\(549\) | 7.92478 | 0.338221 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.9234 | 0.465351 | ||||||||
\(552\) | 33.7743 | 1.43753 | ||||||||
\(553\) | −3.78892 | −0.161121 | ||||||||
\(554\) | −6.46898 | −0.274840 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.9624 | −0.464909 | ||||||||
\(557\) | −19.8700 | −0.841920 | −0.420960 | − | 0.907079i | \(-0.638307\pi\) | ||||
−0.420960 | + | 0.907079i | \(0.638307\pi\) | |||||||
\(558\) | 2.57452 | 0.108988 | ||||||||
\(559\) | −14.3634 | −0.607509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.54420 | 0.191856 | ||||||||
\(562\) | −81.5633 | −3.44054 | ||||||||
\(563\) | −5.83383 | −0.245866 | −0.122933 | − | 0.992415i | \(-0.539230\pi\) | ||||
−0.122933 | + | 0.992415i | \(0.539230\pi\) | |||||||
\(564\) | 22.2374 | 0.936365 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.3576 | 0.939758 | ||||||||
\(567\) | −2.80606 | −0.117844 | ||||||||
\(568\) | 62.0625 | 2.60409 | ||||||||
\(569\) | 46.7123 | 1.95828 | 0.979140 | − | 0.203185i | \(-0.0651293\pi\) | ||||
0.979140 | + | 0.203185i | \(0.0651293\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.4241 | −1.02212 | −0.511058 | − | 0.859546i | \(-0.670746\pi\) | ||||
−0.511058 | + | 0.859546i | \(0.670746\pi\) | |||||||
\(572\) | −26.3938 | −1.10358 | ||||||||
\(573\) | 13.1490 | 0.549309 | ||||||||
\(574\) | −17.9248 | −0.748166 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 18.1187 | 0.754946 | ||||||||
\(577\) | −16.5647 | −0.689596 | −0.344798 | − | 0.938677i | \(-0.612053\pi\) | ||||
−0.344798 | + | 0.938677i | \(0.612053\pi\) | |||||||
\(578\) | −9.76353 | −0.406109 | ||||||||
\(579\) | −5.89446 | −0.244965 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.26187 | −0.0938380 | ||||||||
\(582\) | −26.5501 | −1.10054 | ||||||||
\(583\) | −6.57452 | −0.272289 | ||||||||
\(584\) | 54.1925 | 2.24250 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −61.7802 | −2.55212 | ||||||||
\(587\) | −27.3258 | −1.12786 | −0.563929 | − | 0.825823i | \(-0.690711\pi\) | ||||
−0.563929 | + | 0.825823i | \(0.690711\pi\) | |||||||
\(588\) | 4.50659 | 0.185849 | ||||||||
\(589\) | 4.40246 | 0.181400 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.3938 | −0.838887 | ||||||||
\(592\) | −19.7889 | −0.813320 | ||||||||
\(593\) | 12.6048 | 0.517618 | 0.258809 | − | 0.965928i | \(-0.416670\pi\) | ||||
0.258809 | + | 0.965928i | \(0.416670\pi\) | |||||||
\(594\) | 2.67513 | 0.109762 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 42.8627 | 1.75573 | ||||||||
\(597\) | 17.4010 | 0.712177 | ||||||||
\(598\) | 54.7729 | 2.23983 | ||||||||
\(599\) | 10.5990 | 0.433061 | 0.216531 | − | 0.976276i | \(-0.430526\pi\) | ||||
0.216531 | + | 0.976276i | \(0.430526\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.4749 | −0.916768 | −0.458384 | − | 0.888754i | \(-0.651572\pi\) | ||||
−0.458384 | + | 0.888754i | \(0.651572\pi\) | |||||||
\(602\) | −21.0640 | −0.858503 | ||||||||
\(603\) | −10.7005 | −0.435759 | ||||||||
\(604\) | −78.7631 | −3.20482 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 36.4142 | 1.47923 | ||||||||
\(607\) | −33.5183 | −1.36047 | −0.680234 | − | 0.732995i | \(-0.738122\pi\) | ||||
−0.680234 | + | 0.732995i | \(0.738122\pi\) | |||||||
\(608\) | 72.9643 | 2.95909 | ||||||||
\(609\) | 6.70052 | 0.271519 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.0752 | 0.893068 | ||||||||
\(612\) | −23.4314 | −0.947157 | ||||||||
\(613\) | −11.5672 | −0.467196 | −0.233598 | − | 0.972333i | \(-0.575050\pi\) | ||||
−0.233598 | + | 0.972333i | \(0.575050\pi\) | |||||||
\(614\) | 7.10413 | 0.286699 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −23.6932 | −0.954627 | ||||||||
\(617\) | 33.3357 | 1.34204 | 0.671022 | − | 0.741438i | \(-0.265856\pi\) | ||||
0.671022 | + | 0.741438i | \(0.265856\pi\) | |||||||
\(618\) | 43.6385 | 1.75540 | ||||||||
\(619\) | 4.43866 | 0.178405 | 0.0892024 | − | 0.996014i | \(-0.471568\pi\) | ||||
0.0892024 | + | 0.996014i | \(0.471568\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 42.7367 | 1.71359 | ||||||||
\(623\) | 8.31265 | 0.333039 | ||||||||
\(624\) | 62.8324 | 2.51531 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.162205 | −0.00648301 | ||||||||
\(627\) | 4.57452 | 0.182689 | ||||||||
\(628\) | −36.1622 | −1.44303 | ||||||||
\(629\) | 7.32582 | 0.292100 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.8496 | −1.58639 | −0.793193 | − | 0.608971i | \(-0.791583\pi\) | ||||
−0.793193 | + | 0.608971i | \(0.791583\pi\) | |||||||
\(632\) | −11.4010 | −0.453509 | ||||||||
\(633\) | 18.1260 | 0.720444 | ||||||||
\(634\) | 10.2012 | 0.405143 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 33.9003 | 1.34424 | ||||||||
\(637\) | 4.47371 | 0.177255 | ||||||||
\(638\) | −6.38787 | −0.252898 | ||||||||
\(639\) | −7.35026 | −0.290772 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.88858 | −0.153590 | −0.0767948 | − | 0.997047i | \(-0.524469\pi\) | ||||
−0.0767948 | + | 0.997047i | \(0.524469\pi\) | |||||||
\(642\) | −25.2301 | −0.995754 | ||||||||
\(643\) | −40.9380 | −1.61444 | −0.807218 | − | 0.590254i | \(-0.799028\pi\) | ||||
−0.807218 | + | 0.590254i | \(0.799028\pi\) | |||||||
\(644\) | 57.8759 | 2.28063 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −55.6093 | −2.18792 | ||||||||
\(647\) | −1.76257 | −0.0692939 | −0.0346469 | − | 0.999400i | \(-0.511031\pi\) | ||||
−0.0346469 | + | 0.999400i | \(0.511031\pi\) | |||||||
\(648\) | −8.44358 | −0.331695 | ||||||||
\(649\) | 13.2750 | 0.521091 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.70052 | 0.105842 | ||||||||
\(652\) | −34.8627 | −1.36533 | ||||||||
\(653\) | 7.03761 | 0.275403 | 0.137702 | − | 0.990474i | \(-0.456029\pi\) | ||||
0.137702 | + | 0.990474i | \(0.456029\pi\) | |||||||
\(654\) | 41.1998 | 1.61104 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −29.3112 | −1.14441 | ||||||||
\(657\) | −6.41819 | −0.250397 | ||||||||
\(658\) | 32.3733 | 1.26204 | ||||||||
\(659\) | −12.6253 | −0.491812 | −0.245906 | − | 0.969294i | \(-0.579085\pi\) | ||||
−0.245906 | + | 0.969294i | \(0.579085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.2243 | 0.514364 | 0.257182 | − | 0.966363i | \(-0.417206\pi\) | ||||
0.257182 | + | 0.966363i | \(0.417206\pi\) | |||||||
\(662\) | −64.9741 | −2.52529 | ||||||||
\(663\) | −23.2605 | −0.903361 | ||||||||
\(664\) | −6.80606 | −0.264126 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.31265 | 0.167112 | ||||||||
\(667\) | 9.55149 | 0.369835 | ||||||||
\(668\) | 60.9438 | 2.35799 | ||||||||
\(669\) | −23.6385 | −0.913916 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.92478 | −0.305933 | ||||||||
\(672\) | 44.7572 | 1.72655 | ||||||||
\(673\) | −18.2677 | −0.704170 | −0.352085 | − | 0.935968i | \(-0.614527\pi\) | ||||
−0.352085 | + | 0.935968i | \(0.614527\pi\) | |||||||
\(674\) | −60.4055 | −2.32673 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 68.0698 | 2.61807 | ||||||||
\(677\) | 33.0191 | 1.26903 | 0.634513 | − | 0.772912i | \(-0.281201\pi\) | ||||
0.634513 | + | 0.772912i | \(0.281201\pi\) | |||||||
\(678\) | −36.7513 | −1.41143 | ||||||||
\(679\) | −27.8496 | −1.06877 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.26916 | 0.0486343 | ||||||||
\(682\) | −2.57452 | −0.0985833 | ||||||||
\(683\) | −30.8627 | −1.18093 | −0.590465 | − | 0.807063i | \(-0.701056\pi\) | ||||
−0.590465 | + | 0.807063i | \(0.701056\pi\) | |||||||
\(684\) | −23.5877 | −0.901898 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −45.9854 | −1.75573 | ||||||||
\(687\) | 16.1768 | 0.617183 | ||||||||
\(688\) | −34.4445 | −1.31319 | ||||||||
\(689\) | 33.6531 | 1.28208 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.6991 | 1.05372 | 0.526862 | − | 0.849951i | \(-0.323369\pi\) | ||||
0.526862 | + | 0.849951i | \(0.323369\pi\) | |||||||
\(692\) | −36.0567 | −1.37067 | ||||||||
\(693\) | 2.80606 | 0.106594 | ||||||||
\(694\) | 54.0176 | 2.05048 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 20.1622 | 0.764246 | ||||||||
\(697\) | 10.8510 | 0.411010 | ||||||||
\(698\) | 72.8989 | 2.75927 | ||||||||
\(699\) | 18.4690 | 0.698561 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.9643 | −1.47166 | −0.735831 | − | 0.677166i | \(-0.763208\pi\) | ||||
−0.735831 | + | 0.677166i | \(0.763208\pi\) | |||||||
\(702\) | −13.6932 | −0.516818 | ||||||||
\(703\) | 7.37470 | 0.278142 | ||||||||
\(704\) | −18.1187 | −0.682875 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.4372 | 0.505717 | ||||||||
\(707\) | 38.1965 | 1.43653 | ||||||||
\(708\) | −68.4504 | −2.57252 | ||||||||
\(709\) | −4.32250 | −0.162335 | −0.0811674 | − | 0.996700i | \(-0.525865\pi\) | ||||
−0.0811674 | + | 0.996700i | \(0.525865\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.35026 | 0.0506388 | ||||||||
\(712\) | 25.0132 | 0.937408 | ||||||||
\(713\) | 3.84955 | 0.144167 | ||||||||
\(714\) | −34.1114 | −1.27659 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13.9248 | −0.520393 | ||||||||
\(717\) | 19.3258 | 0.721736 | ||||||||
\(718\) | 48.6253 | 1.81468 | ||||||||
\(719\) | −38.3996 | −1.43206 | −0.716032 | − | 0.698067i | \(-0.754044\pi\) | ||||
−0.716032 | + | 0.698067i | \(0.754044\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45.7743 | 1.70473 | ||||||||
\(722\) | −5.15282 | −0.191768 | ||||||||
\(723\) | 28.5501 | 1.06179 | ||||||||
\(724\) | −109.313 | −4.06259 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.67513 | −0.0992834 | ||||||||
\(727\) | 21.6728 | 0.803798 | 0.401899 | − | 0.915684i | \(-0.368350\pi\) | ||||
0.401899 | + | 0.915684i | \(0.368350\pi\) | |||||||
\(728\) | 121.279 | 4.49489 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.7513 | 0.471624 | ||||||||
\(732\) | 40.8627 | 1.51033 | ||||||||
\(733\) | −25.0698 | −0.925976 | −0.462988 | − | 0.886365i | \(-0.653223\pi\) | ||||
−0.462988 | + | 0.886365i | \(0.653223\pi\) | |||||||
\(734\) | −22.9116 | −0.845683 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 63.8007 | 2.35172 | ||||||||
\(737\) | 10.7005 | 0.394159 | ||||||||
\(738\) | 6.38787 | 0.235141 | ||||||||
\(739\) | −18.9018 | −0.695312 | −0.347656 | − | 0.937622i | \(-0.613022\pi\) | ||||
−0.347656 | + | 0.937622i | \(0.613022\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.4156 | −0.860195 | ||||||||
\(742\) | 49.3522 | 1.81178 | ||||||||
\(743\) | −43.6688 | −1.60205 | −0.801026 | − | 0.598629i | \(-0.795712\pi\) | ||||
−0.801026 | + | 0.598629i | \(0.795712\pi\) | |||||||
\(744\) | 8.12601 | 0.297914 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20.9175 | 0.765843 | ||||||||
\(747\) | 0.806063 | 0.0294923 | ||||||||
\(748\) | 23.4314 | 0.856736 | ||||||||
\(749\) | −26.4650 | −0.967010 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.0541 | −1.71703 | −0.858514 | − | 0.512789i | \(-0.828612\pi\) | ||||
−0.858514 | + | 0.512789i | \(0.828612\pi\) | |||||||
\(752\) | 52.9380 | 1.93045 | ||||||||
\(753\) | 23.1998 | 0.845448 | ||||||||
\(754\) | 32.6977 | 1.19078 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −14.4690 | −0.526232 | ||||||||
\(757\) | 26.9116 | 0.978119 | 0.489059 | − | 0.872250i | \(-0.337340\pi\) | ||||
0.489059 | + | 0.872250i | \(0.337340\pi\) | |||||||
\(758\) | −3.07381 | −0.111646 | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.6859 | 0.604865 | 0.302432 | − | 0.953171i | \(-0.402201\pi\) | ||||
0.302432 | + | 0.953171i | \(0.402201\pi\) | |||||||
\(762\) | 33.2203 | 1.20344 | ||||||||
\(763\) | 43.2163 | 1.56454 | ||||||||
\(764\) | 67.8007 | 2.45294 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 91.1871 | 3.29473 | ||||||||
\(767\) | −67.9511 | −2.45357 | ||||||||
\(768\) | 8.08840 | 0.291865 | ||||||||
\(769\) | 23.2995 | 0.840201 | 0.420100 | − | 0.907478i | \(-0.361995\pi\) | ||||
0.420100 | + | 0.907478i | \(0.361995\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.8872 | 0.392092 | ||||||||
\(772\) | −30.3938 | −1.09390 | ||||||||
\(773\) | 1.63656 | 0.0588631 | 0.0294316 | − | 0.999567i | \(-0.490630\pi\) | ||||
0.0294316 | + | 0.999567i | \(0.490630\pi\) | |||||||
\(774\) | 7.50659 | 0.269819 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −83.8007 | −3.00827 | ||||||||
\(777\) | 4.52373 | 0.162288 | ||||||||
\(778\) | −63.5994 | −2.28015 | ||||||||
\(779\) | 10.9234 | 0.391370 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.35026 | 0.263013 | ||||||||
\(782\) | −48.6253 | −1.73884 | ||||||||
\(783\) | −2.38787 | −0.0853356 | ||||||||
\(784\) | 10.7283 | 0.383153 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −15.8496 | −0.565335 | ||||||||
\(787\) | 2.09095 | 0.0745344 | 0.0372672 | − | 0.999305i | \(-0.488135\pi\) | ||||
0.0372672 | + | 0.999305i | \(0.488135\pi\) | |||||||
\(788\) | −105.157 | −3.74606 | ||||||||
\(789\) | −9.11871 | −0.324635 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −38.5501 | −1.37068 | ||||||||
\(792\) | 8.44358 | 0.300030 | ||||||||
\(793\) | 40.5647 | 1.44049 | ||||||||
\(794\) | −11.1030 | −0.394030 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 89.7255 | 3.18023 | ||||||||
\(797\) | 26.8872 | 0.952392 | 0.476196 | − | 0.879339i | \(-0.342015\pi\) | ||||
0.476196 | + | 0.879339i | \(0.342015\pi\) | |||||||
\(798\) | −34.3390 | −1.21559 | ||||||||
\(799\) | −19.5975 | −0.693311 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.96239 | −0.104671 | ||||||||
\(802\) | 90.7269 | 3.20368 | ||||||||
\(803\) | 6.41819 | 0.226493 | ||||||||
\(804\) | −55.1754 | −1.94589 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.1782 | 0.464183 | ||||||||
\(807\) | −11.2995 | −0.397760 | ||||||||
\(808\) | 114.935 | 4.04340 | ||||||||
\(809\) | −45.4128 | −1.59663 | −0.798315 | − | 0.602241i | \(-0.794275\pi\) | ||||
−0.798315 | + | 0.602241i | \(0.794275\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.3488 | 1.20615 | 0.603076 | − | 0.797684i | \(-0.293942\pi\) | ||||
0.603076 | + | 0.797684i | \(0.293942\pi\) | |||||||
\(812\) | 34.5501 | 1.21247 | ||||||||
\(813\) | 25.1998 | 0.883796 | ||||||||
\(814\) | −4.31265 | −0.151158 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −55.7802 | −1.95270 | ||||||||
\(817\) | 12.8364 | 0.449088 | ||||||||
\(818\) | −22.8726 | −0.799721 | ||||||||
\(819\) | −14.3634 | −0.501899 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.7612 | 0.654769 | 0.327384 | − | 0.944891i | \(-0.393833\pi\) | ||||
0.327384 | + | 0.944891i | \(0.393833\pi\) | |||||||
\(822\) | 26.2130 | 0.914283 | ||||||||
\(823\) | 33.0592 | 1.15237 | 0.576186 | − | 0.817319i | \(-0.304540\pi\) | ||||
0.576186 | + | 0.817319i | \(0.304540\pi\) | |||||||
\(824\) | 137.737 | 4.79830 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −99.6502 | −3.46728 | ||||||||
\(827\) | 10.8813 | 0.378379 | 0.189190 | − | 0.981941i | \(-0.439414\pi\) | ||||
0.189190 | + | 0.981941i | \(0.439414\pi\) | |||||||
\(828\) | −20.6253 | −0.716779 | ||||||||
\(829\) | 42.7221 | 1.48380 | 0.741900 | − | 0.670510i | \(-0.233925\pi\) | ||||
0.741900 | + | 0.670510i | \(0.233925\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.41819 | 0.0838861 | ||||||||
\(832\) | 92.7445 | 3.21534 | ||||||||
\(833\) | −3.97159 | −0.137608 | ||||||||
\(834\) | 5.68735 | 0.196937 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 23.5877 | 0.815797 | ||||||||
\(837\) | −0.962389 | −0.0332650 | ||||||||
\(838\) | −35.5778 | −1.22902 | ||||||||
\(839\) | −21.1735 | −0.730989 | −0.365495 | − | 0.930813i | \(-0.619100\pi\) | ||||
−0.365495 | + | 0.930813i | \(0.619100\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.2981 | −0.803381 | ||||||||
\(842\) | −89.0856 | −3.07009 | ||||||||
\(843\) | 30.4894 | 1.05011 | ||||||||
\(844\) | 93.4636 | 3.21715 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.5369 | −0.396647 | ||||||||
\(847\) | −2.80606 | −0.0964175 | ||||||||
\(848\) | 80.7024 | 2.77133 | ||||||||
\(849\) | −8.35756 | −0.286831 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.44851 | 0.221052 | ||||||||
\(852\) | −37.9003 | −1.29844 | ||||||||
\(853\) | −54.4709 | −1.86505 | −0.932524 | − | 0.361109i | \(-0.882398\pi\) | ||||
−0.932524 | + | 0.361109i | \(0.882398\pi\) | |||||||
\(854\) | 59.4880 | 2.03564 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −79.6345 | −2.72185 | ||||||||
\(857\) | −38.5705 | −1.31754 | −0.658772 | − | 0.752342i | \(-0.728924\pi\) | ||||
−0.658772 | + | 0.752342i | \(0.728924\pi\) | |||||||
\(858\) | 13.6932 | 0.467479 | ||||||||
\(859\) | −18.5139 | −0.631685 | −0.315843 | − | 0.948812i | \(-0.602287\pi\) | ||||
−0.315843 | + | 0.948812i | \(0.602287\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.70052 | 0.228353 | ||||||||
\(862\) | −5.55149 | −0.189085 | ||||||||
\(863\) | −22.5383 | −0.767213 | −0.383607 | − | 0.923497i | \(-0.625318\pi\) | ||||
−0.383607 | + | 0.923497i | \(0.625318\pi\) | |||||||
\(864\) | −15.9502 | −0.542636 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −100.053 | −3.39993 | ||||||||
\(867\) | 3.64974 | 0.123952 | ||||||||
\(868\) | 13.9248 | 0.472638 | ||||||||
\(869\) | −1.35026 | −0.0458045 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −54.7729 | −1.85591 | ||||||||
\(872\) | 130.040 | 4.40371 | ||||||||
\(873\) | 9.92478 | 0.335903 | ||||||||
\(874\) | −48.9497 | −1.65575 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −33.0943 | −1.11815 | ||||||||
\(877\) | −18.9419 | −0.639623 | −0.319812 | − | 0.947481i | \(-0.603620\pi\) | ||||
−0.319812 | + | 0.947481i | \(0.603620\pi\) | |||||||
\(878\) | 16.1162 | 0.543894 | ||||||||
\(879\) | 23.0943 | 0.778951 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.0263 | −0.674705 | −0.337352 | − | 0.941378i | \(-0.609531\pi\) | ||||
−0.337352 | + | 0.941378i | \(0.609531\pi\) | |||||||
\(882\) | −2.33804 | −0.0787260 | ||||||||
\(883\) | −22.2981 | −0.750390 | −0.375195 | − | 0.926946i | \(-0.622424\pi\) | ||||
−0.375195 | + | 0.926946i | \(0.622424\pi\) | |||||||
\(884\) | −119.938 | −4.03397 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.1147 | −0.910938 | ||||||||
\(887\) | −3.10413 | −0.104226 | −0.0521132 | − | 0.998641i | \(-0.516596\pi\) | ||||
−0.0521132 | + | 0.998641i | \(0.516596\pi\) | |||||||
\(888\) | 13.6121 | 0.456793 | ||||||||
\(889\) | 34.8462 | 1.16871 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −121.888 | −4.08110 | ||||||||
\(893\) | −19.7283 | −0.660182 | ||||||||
\(894\) | −22.2374 | −0.743731 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 46.4953 | 1.55330 | ||||||||
\(897\) | −20.4749 | −0.683636 | ||||||||
\(898\) | 30.7269 | 1.02537 | ||||||||
\(899\) | 2.29806 | 0.0766447 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.8759 | −0.995311 | ||||||||
\(902\) | −6.38787 | −0.212693 | ||||||||
\(903\) | 7.87399 | 0.262030 | ||||||||
\(904\) | −115.999 | −3.85807 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 40.8627 | 1.35757 | ||||||||
\(907\) | −10.8627 | −0.360691 | −0.180345 | − | 0.983603i | \(-0.557722\pi\) | ||||
−0.180345 | + | 0.983603i | \(0.557722\pi\) | |||||||
\(908\) | 6.54420 | 0.217177 | ||||||||
\(909\) | −13.6121 | −0.451486 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.82321 | −0.192931 | −0.0964657 | − | 0.995336i | \(-0.530754\pi\) | ||||
−0.0964657 | + | 0.995336i | \(0.530754\pi\) | |||||||
\(912\) | −56.1524 | −1.85939 | ||||||||
\(913\) | −0.806063 | −0.0266768 | ||||||||
\(914\) | −40.2433 | −1.33113 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 83.4128 | 2.75604 | ||||||||
\(917\) | −16.6253 | −0.549016 | ||||||||
\(918\) | 12.1563 | 0.401219 | ||||||||
\(919\) | −31.2750 | −1.03167 | −0.515834 | − | 0.856688i | \(-0.672518\pi\) | ||||
−0.515834 | + | 0.856688i | \(0.672518\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.65562 | −0.0875056 | ||||||||
\(922\) | 70.1886 | 2.31154 | ||||||||
\(923\) | −37.6239 | −1.23841 | ||||||||
\(924\) | 14.4690 | 0.475994 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14.6107 | −0.480138 | ||||||||
\(927\) | −16.3127 | −0.535778 | ||||||||
\(928\) | 38.0870 | 1.25027 | ||||||||
\(929\) | −21.2243 | −0.696345 | −0.348173 | − | 0.937430i | \(-0.613198\pi\) | ||||
−0.348173 | + | 0.937430i | \(0.613198\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.99809 | −0.131032 | ||||||||
\(932\) | 95.2320 | 3.11943 | ||||||||
\(933\) | −15.9756 | −0.523016 | ||||||||
\(934\) | −7.22425 | −0.236385 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −43.2203 | −1.41270 | ||||||||
\(937\) | −16.4328 | −0.536835 | −0.268418 | − | 0.963303i | \(-0.586501\pi\) | ||||
−0.268418 | + | 0.963303i | \(0.586501\pi\) | |||||||
\(938\) | −80.3244 | −2.62268 | ||||||||
\(939\) | 0.0606343 | 0.00197873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.86414 | 0.191166 | 0.0955828 | − | 0.995421i | \(-0.469529\pi\) | ||||
0.0955828 | + | 0.995421i | \(0.469529\pi\) | |||||||
\(942\) | 18.7612 | 0.611272 | ||||||||
\(943\) | 9.55149 | 0.311039 | ||||||||
\(944\) | −162.952 | −5.30362 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.50659 | −0.244060 | ||||||||
\(947\) | 38.7415 | 1.25893 | 0.629464 | − | 0.777030i | \(-0.283274\pi\) | ||||
0.629464 | + | 0.777030i | \(0.283274\pi\) | |||||||
\(948\) | 6.96239 | 0.226128 | ||||||||
\(949\) | −32.8529 | −1.06645 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.81336 | −0.123657 | ||||||||
\(952\) | −107.667 | −3.48950 | ||||||||
\(953\) | 6.09569 | 0.197459 | 0.0987294 | − | 0.995114i | \(-0.468522\pi\) | ||||
0.0987294 | + | 0.995114i | \(0.468522\pi\) | |||||||
\(954\) | −17.5877 | −0.569422 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 99.6502 | 3.22292 | ||||||||
\(957\) | 2.38787 | 0.0771890 | ||||||||
\(958\) | −44.8773 | −1.44992 | ||||||||
\(959\) | 27.4960 | 0.887891 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0738 | −0.970123 | ||||||||
\(962\) | 22.0752 | 0.711734 | ||||||||
\(963\) | 9.43136 | 0.303921 | ||||||||
\(964\) | 147.213 | 4.74143 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −30.0263 | −0.966082 | ||||||||
\(967\) | −37.9697 | −1.22102 | −0.610511 | − | 0.792008i | \(-0.709036\pi\) | ||||
−0.610511 | + | 0.792008i | \(0.709036\pi\) | |||||||
\(968\) | −8.44358 | −0.271387 | ||||||||
\(969\) | 20.7875 | 0.667791 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −60.8773 | −1.95365 | −0.976823 | − | 0.214049i | \(-0.931335\pi\) | ||||
−0.976823 | + | 0.214049i | \(0.931335\pi\) | |||||||
\(972\) | 5.15633 | 0.165389 | ||||||||
\(973\) | 5.96571 | 0.191252 | ||||||||
\(974\) | −92.0235 | −2.94862 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 97.2769 | 3.11376 | ||||||||
\(977\) | −21.3963 | −0.684529 | −0.342264 | − | 0.939604i | \(-0.611194\pi\) | ||||
−0.342264 | + | 0.939604i | \(0.611194\pi\) | |||||||
\(978\) | 18.0870 | 0.578358 | ||||||||
\(979\) | 2.96239 | 0.0946784 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.4010 | −0.491718 | ||||||||
\(982\) | −40.0000 | −1.27645 | ||||||||
\(983\) | −18.8919 | −0.602558 | −0.301279 | − | 0.953536i | \(-0.597414\pi\) | ||||
−0.301279 | + | 0.953536i | \(0.597414\pi\) | |||||||
\(984\) | 20.1622 | 0.642748 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −29.0278 | −0.924432 | ||||||||
\(987\) | −12.1016 | −0.385197 | ||||||||
\(988\) | −120.739 | −3.84121 | ||||||||
\(989\) | 11.2243 | 0.356911 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.33567 | −0.0424291 | −0.0212145 | − | 0.999775i | \(-0.506753\pi\) | ||||
−0.0212145 | + | 0.999775i | \(0.506753\pi\) | |||||||
\(992\) | 15.3503 | 0.487371 | ||||||||
\(993\) | 24.2882 | 0.770763 | ||||||||
\(994\) | −55.1754 | −1.75006 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.15633 | 0.131698 | ||||||||
\(997\) | 48.9076 | 1.54892 | 0.774460 | − | 0.632623i | \(-0.218022\pi\) | ||||
0.774460 | + | 0.632623i | \(0.218022\pi\) | |||||||
\(998\) | 7.62672 | 0.241419 | ||||||||
\(999\) | −1.61213 | −0.0510054 |
(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.a.h.1.1 | 3 | ||
3.2 | odd | 2 | 2475.2.a.be.1.3 | 3 | |||
5.2 | odd | 4 | 165.2.c.a.34.1 | ✓ | 6 | ||
5.3 | odd | 4 | 165.2.c.a.34.6 | yes | 6 | ||
5.4 | even | 2 | 825.2.a.n.1.3 | 3 | |||
11.10 | odd | 2 | 9075.2.a.ck.1.3 | 3 | |||
15.2 | even | 4 | 495.2.c.d.199.6 | 6 | |||
15.8 | even | 4 | 495.2.c.d.199.1 | 6 | |||
15.14 | odd | 2 | 2475.2.a.y.1.1 | 3 | |||
20.3 | even | 4 | 2640.2.d.i.529.1 | 6 | |||
20.7 | even | 4 | 2640.2.d.i.529.4 | 6 | |||
55.32 | even | 4 | 1815.2.c.d.364.6 | 6 | |||
55.43 | even | 4 | 1815.2.c.d.364.1 | 6 | |||
55.54 | odd | 2 | 9075.2.a.cc.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.c.a.34.1 | ✓ | 6 | 5.2 | odd | 4 | ||
165.2.c.a.34.6 | yes | 6 | 5.3 | odd | 4 | ||
495.2.c.d.199.1 | 6 | 15.8 | even | 4 | |||
495.2.c.d.199.6 | 6 | 15.2 | even | 4 | |||
825.2.a.h.1.1 | 3 | 1.1 | even | 1 | trivial | ||
825.2.a.n.1.3 | 3 | 5.4 | even | 2 | |||
1815.2.c.d.364.1 | 6 | 55.43 | even | 4 | |||
1815.2.c.d.364.6 | 6 | 55.32 | even | 4 | |||
2475.2.a.y.1.1 | 3 | 15.14 | odd | 2 | |||
2475.2.a.be.1.3 | 3 | 3.2 | odd | 2 | |||
2640.2.d.i.529.1 | 6 | 20.3 | even | 4 | |||
2640.2.d.i.529.4 | 6 | 20.7 | even | 4 | |||
9075.2.a.cc.1.1 | 3 | 55.54 | odd | 2 | |||
9075.2.a.ck.1.3 | 3 | 11.10 | odd | 2 |