Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1250,2,Mod(1,1250)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1250, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1250.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1250 = 2 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1250.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: | \(9.98130025266\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 9x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 50) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.71472\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1250.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.71472 | 0.989991 | 0.494996 | − | 0.868895i | \(-0.335170\pi\) | ||||
0.494996 | + | 0.868895i | \(0.335170\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.71472 | 0.700029 | ||||||||
\(7\) | −2.77447 | −1.04865 | −0.524325 | − | 0.851518i | \(-0.675682\pi\) | ||||
−0.524325 | + | 0.851518i | \(0.675682\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.0597522 | −0.0199174 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.77447 | 0.836533 | 0.418267 | − | 0.908324i | \(-0.362638\pi\) | ||||
0.418267 | + | 0.908324i | \(0.362638\pi\) | |||||||
\(12\) | 1.71472 | 0.494996 | ||||||||
\(13\) | 5.67779 | 1.57473 | 0.787367 | − | 0.616484i | \(-0.211444\pi\) | ||||
0.787367 | + | 0.616484i | \(0.211444\pi\) | |||||||
\(14\) | −2.77447 | −0.741508 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.15643 | 1.25062 | 0.625309 | − | 0.780377i | \(-0.284973\pi\) | ||||
0.625309 | + | 0.780377i | \(0.284973\pi\) | |||||||
\(18\) | −0.0597522 | −0.0140837 | ||||||||
\(19\) | 1.41238 | 0.324023 | 0.162012 | − | 0.986789i | \(-0.448202\pi\) | ||||
0.162012 | + | 0.986789i | \(0.448202\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.75742 | −1.03815 | ||||||||
\(22\) | 2.77447 | 0.591518 | ||||||||
\(23\) | −0.654963 | −0.136569 | −0.0682846 | − | 0.997666i | \(-0.521753\pi\) | ||||
−0.0682846 | + | 0.997666i | \(0.521753\pi\) | |||||||
\(24\) | 1.71472 | 0.350015 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.67779 | 1.11351 | ||||||||
\(27\) | −5.24660 | −1.00971 | ||||||||
\(28\) | −2.77447 | −0.524325 | ||||||||
\(29\) | 4.09668 | 0.760735 | 0.380367 | − | 0.924836i | \(-0.375798\pi\) | ||||
0.380367 | + | 0.924836i | \(0.375798\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.12710 | −1.28006 | −0.640032 | − | 0.768348i | \(-0.721079\pi\) | ||||
−0.640032 | + | 0.768348i | \(0.721079\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.75742 | 0.828161 | ||||||||
\(34\) | 5.15643 | 0.884321 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0597522 | −0.00995870 | ||||||||
\(37\) | −1.04746 | −0.172202 | −0.0861010 | − | 0.996286i | \(-0.527441\pi\) | ||||
−0.0861010 | + | 0.996286i | \(0.527441\pi\) | |||||||
\(38\) | 1.41238 | 0.229119 | ||||||||
\(39\) | 9.73579 | 1.55897 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.10722 | 1.42231 | 0.711154 | − | 0.703036i | \(-0.248173\pi\) | ||||
0.711154 | + | 0.703036i | \(0.248173\pi\) | |||||||
\(42\) | −4.75742 | −0.734086 | ||||||||
\(43\) | 9.24660 | 1.41009 | 0.705047 | − | 0.709161i | \(-0.250926\pi\) | ||||
0.705047 | + | 0.709161i | \(0.250926\pi\) | |||||||
\(44\) | 2.77447 | 0.418267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.654963 | −0.0965690 | ||||||||
\(47\) | −2.77447 | −0.404698 | −0.202349 | − | 0.979314i | \(-0.564857\pi\) | ||||
−0.202349 | + | 0.979314i | \(0.564857\pi\) | |||||||
\(48\) | 1.71472 | 0.247498 | ||||||||
\(49\) | 0.697669 | 0.0996670 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.84181 | 1.23810 | ||||||||
\(52\) | 5.67779 | 0.787367 | ||||||||
\(53\) | −0.526111 | −0.0722669 | −0.0361335 | − | 0.999347i | \(-0.511504\pi\) | ||||
−0.0361335 | + | 0.999347i | \(0.511504\pi\) | |||||||
\(54\) | −5.24660 | −0.713972 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.77447 | −0.370754 | ||||||||
\(57\) | 2.42184 | 0.320780 | ||||||||
\(58\) | 4.09668 | 0.537921 | ||||||||
\(59\) | −3.78206 | −0.492382 | −0.246191 | − | 0.969221i | \(-0.579179\pi\) | ||||
−0.246191 | + | 0.969221i | \(0.579179\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8325 | −1.38696 | −0.693478 | − | 0.720478i | \(-0.743922\pi\) | ||||
−0.693478 | + | 0.720478i | \(0.743922\pi\) | |||||||
\(62\) | −7.12710 | −0.905142 | ||||||||
\(63\) | 0.165781 | 0.0208864 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.75742 | 0.585598 | ||||||||
\(67\) | −4.32340 | −0.528188 | −0.264094 | − | 0.964497i | \(-0.585073\pi\) | ||||
−0.264094 | + | 0.964497i | \(0.585073\pi\) | |||||||
\(68\) | 5.15643 | 0.625309 | ||||||||
\(69\) | −1.12307 | −0.135202 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.2466 | −1.57208 | −0.786041 | − | 0.618174i | \(-0.787873\pi\) | ||||
−0.786041 | + | 0.618174i | \(0.787873\pi\) | |||||||
\(72\) | −0.0597522 | −0.00704186 | ||||||||
\(73\) | 4.21324 | 0.493123 | 0.246561 | − | 0.969127i | \(-0.420699\pi\) | ||||
0.246561 | + | 0.969127i | \(0.420699\pi\) | |||||||
\(74\) | −1.04746 | −0.121765 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.41238 | 0.162012 | ||||||||
\(77\) | −7.69767 | −0.877231 | ||||||||
\(78\) | 9.73579 | 1.10236 | ||||||||
\(79\) | −9.90157 | −1.11401 | −0.557007 | − | 0.830508i | \(-0.688050\pi\) | ||||
−0.557007 | + | 0.830508i | \(0.688050\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.81717 | −0.979686 | ||||||||
\(82\) | 9.10722 | 1.00572 | ||||||||
\(83\) | 4.67603 | 0.513261 | 0.256631 | − | 0.966510i | \(-0.417388\pi\) | ||||
0.256631 | + | 0.966510i | \(0.417388\pi\) | |||||||
\(84\) | −4.75742 | −0.519077 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.24660 | 0.997087 | ||||||||
\(87\) | 7.02464 | 0.753121 | ||||||||
\(88\) | 2.77447 | 0.295759 | ||||||||
\(89\) | −9.18401 | −0.973504 | −0.486752 | − | 0.873540i | \(-0.661818\pi\) | ||||
−0.486752 | + | 0.873540i | \(0.661818\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.7528 | −1.65135 | ||||||||
\(92\) | −0.654963 | −0.0682846 | ||||||||
\(93\) | −12.2209 | −1.26725 | ||||||||
\(94\) | −2.77447 | −0.286164 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.71472 | 0.175007 | ||||||||
\(97\) | −0.0901699 | −0.00915537 | −0.00457769 | − | 0.999990i | \(-0.501457\pi\) | ||||
−0.00457769 | + | 0.999990i | \(0.501457\pi\) | |||||||
\(98\) | 0.697669 | 0.0704752 | ||||||||
\(99\) | −0.165781 | −0.0166616 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.90632 | −0.786709 | −0.393354 | − | 0.919387i | \(-0.628685\pi\) | ||||
−0.393354 | + | 0.919387i | \(0.628685\pi\) | |||||||
\(102\) | 8.84181 | 0.875470 | ||||||||
\(103\) | 7.83422 | 0.771929 | 0.385964 | − | 0.922514i | \(-0.373869\pi\) | ||||
0.385964 | + | 0.922514i | \(0.373869\pi\) | |||||||
\(104\) | 5.67779 | 0.556753 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.526111 | −0.0511004 | ||||||||
\(107\) | −10.2220 | −0.988194 | −0.494097 | − | 0.869407i | \(-0.664501\pi\) | ||||
−0.494097 | + | 0.869407i | \(0.664501\pi\) | |||||||
\(108\) | −5.24660 | −0.504855 | ||||||||
\(109\) | 3.91091 | 0.374598 | 0.187299 | − | 0.982303i | \(-0.440027\pi\) | ||||
0.187299 | + | 0.982303i | \(0.440027\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.79610 | −0.170479 | ||||||||
\(112\) | −2.77447 | −0.262163 | ||||||||
\(113\) | −6.37545 | −0.599752 | −0.299876 | − | 0.953978i | \(-0.596945\pi\) | ||||
−0.299876 | + | 0.953978i | \(0.596945\pi\) | |||||||
\(114\) | 2.42184 | 0.226826 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.09668 | 0.380367 | ||||||||
\(117\) | −0.339260 | −0.0313646 | ||||||||
\(118\) | −3.78206 | −0.348167 | ||||||||
\(119\) | −14.3064 | −1.31146 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.30233 | −0.300212 | ||||||||
\(122\) | −10.8325 | −0.980725 | ||||||||
\(123\) | 15.6163 | 1.40807 | ||||||||
\(124\) | −7.12710 | −0.640032 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.165781 | 0.0147689 | ||||||||
\(127\) | 9.54893 | 0.847331 | 0.423665 | − | 0.905819i | \(-0.360743\pi\) | ||||
0.423665 | + | 0.905819i | \(0.360743\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 15.8553 | 1.39598 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.59923 | 0.489207 | 0.244604 | − | 0.969623i | \(-0.421342\pi\) | ||||
0.244604 | + | 0.969623i | \(0.421342\pi\) | |||||||
\(132\) | 4.75742 | 0.414080 | ||||||||
\(133\) | −3.91861 | −0.339787 | ||||||||
\(134\) | −4.32340 | −0.373485 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.15643 | 0.442161 | ||||||||
\(137\) | 7.98414 | 0.682131 | 0.341066 | − | 0.940039i | \(-0.389212\pi\) | ||||
0.341066 | + | 0.940039i | \(0.389212\pi\) | |||||||
\(138\) | −1.12307 | −0.0956025 | ||||||||
\(139\) | −22.0884 | −1.87352 | −0.936758 | − | 0.349979i | \(-0.886189\pi\) | ||||
−0.936758 | + | 0.349979i | \(0.886189\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.75742 | −0.400647 | ||||||||
\(142\) | −13.2466 | −1.11163 | ||||||||
\(143\) | 15.7528 | 1.31732 | ||||||||
\(144\) | −0.0597522 | −0.00497935 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.21324 | 0.348691 | ||||||||
\(147\) | 1.19630 | 0.0986694 | ||||||||
\(148\) | −1.04746 | −0.0861010 | ||||||||
\(149\) | 4.18401 | 0.342768 | 0.171384 | − | 0.985204i | \(-0.445176\pi\) | ||||
0.171384 | + | 0.985204i | \(0.445176\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.331561 | −0.0269821 | −0.0134910 | − | 0.999909i | \(-0.504294\pi\) | ||||
−0.0134910 | + | 0.999909i | \(0.504294\pi\) | |||||||
\(152\) | 1.41238 | 0.114559 | ||||||||
\(153\) | −0.308108 | −0.0249091 | ||||||||
\(154\) | −7.69767 | −0.620296 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9.73579 | 0.779487 | ||||||||
\(157\) | 3.60750 | 0.287910 | 0.143955 | − | 0.989584i | \(-0.454018\pi\) | ||||
0.143955 | + | 0.989584i | \(0.454018\pi\) | |||||||
\(158\) | −9.90157 | −0.787726 | ||||||||
\(159\) | −0.902131 | −0.0715436 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.81717 | 0.143213 | ||||||||
\(162\) | −8.81717 | −0.692743 | ||||||||
\(163\) | 5.09385 | 0.398981 | 0.199490 | − | 0.979900i | \(-0.436071\pi\) | ||||
0.199490 | + | 0.979900i | \(0.436071\pi\) | |||||||
\(164\) | 9.10722 | 0.711154 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.67603 | 0.362931 | ||||||||
\(167\) | 20.8629 | 1.61442 | 0.807209 | − | 0.590265i | \(-0.200977\pi\) | ||||
0.807209 | + | 0.590265i | \(0.200977\pi\) | |||||||
\(168\) | −4.75742 | −0.367043 | ||||||||
\(169\) | 19.2373 | 1.47979 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0843930 | −0.00645370 | ||||||||
\(172\) | 9.24660 | 0.705047 | ||||||||
\(173\) | −11.9877 | −0.911409 | −0.455704 | − | 0.890131i | \(-0.650613\pi\) | ||||
−0.455704 | + | 0.890131i | \(0.650613\pi\) | |||||||
\(174\) | 7.02464 | 0.532537 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.77447 | 0.209133 | ||||||||
\(177\) | −6.48516 | −0.487454 | ||||||||
\(178\) | −9.18401 | −0.688371 | ||||||||
\(179\) | −8.54134 | −0.638410 | −0.319205 | − | 0.947686i | \(-0.603416\pi\) | ||||
−0.319205 | + | 0.947686i | \(0.603416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.82844 | 0.581884 | 0.290942 | − | 0.956741i | \(-0.406031\pi\) | ||||
0.290942 | + | 0.956741i | \(0.406031\pi\) | |||||||
\(182\) | −15.7528 | −1.16768 | ||||||||
\(183\) | −18.5746 | −1.37307 | ||||||||
\(184\) | −0.654963 | −0.0482845 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −12.2209 | −0.896083 | ||||||||
\(187\) | 14.3064 | 1.04618 | ||||||||
\(188\) | −2.77447 | −0.202349 | ||||||||
\(189\) | 14.5565 | 1.05883 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.36611 | 0.243563 | 0.121782 | − | 0.992557i | \(-0.461139\pi\) | ||||
0.121782 | + | 0.992557i | \(0.461139\pi\) | |||||||
\(192\) | 1.71472 | 0.123749 | ||||||||
\(193\) | −15.4211 | −1.11004 | −0.555018 | − | 0.831839i | \(-0.687288\pi\) | ||||
−0.555018 | + | 0.831839i | \(0.687288\pi\) | |||||||
\(194\) | −0.0901699 | −0.00647382 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.697669 | 0.0498335 | ||||||||
\(197\) | 8.80489 | 0.627322 | 0.313661 | − | 0.949535i | \(-0.398444\pi\) | ||||
0.313661 | + | 0.949535i | \(0.398444\pi\) | |||||||
\(198\) | −0.165781 | −0.0117815 | ||||||||
\(199\) | −17.6222 | −1.24920 | −0.624601 | − | 0.780944i | \(-0.714738\pi\) | ||||
−0.624601 | + | 0.780944i | \(0.714738\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.41340 | −0.522901 | ||||||||
\(202\) | −7.90632 | −0.556287 | ||||||||
\(203\) | −11.3661 | −0.797744 | ||||||||
\(204\) | 8.84181 | 0.619051 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.83422 | 0.545836 | ||||||||
\(207\) | 0.0391355 | 0.00272010 | ||||||||
\(208\) | 5.67779 | 0.393684 | ||||||||
\(209\) | 3.91861 | 0.271056 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.10144 | 0.420040 | 0.210020 | − | 0.977697i | \(-0.432647\pi\) | ||||
0.210020 | + | 0.977697i | \(0.432647\pi\) | |||||||
\(212\) | −0.526111 | −0.0361335 | ||||||||
\(213\) | −22.7142 | −1.55635 | ||||||||
\(214\) | −10.2220 | −0.698759 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.24660 | −0.356986 | ||||||||
\(217\) | 19.7739 | 1.34234 | ||||||||
\(218\) | 3.91091 | 0.264880 | ||||||||
\(219\) | 7.22451 | 0.488187 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.2771 | 1.96939 | ||||||||
\(222\) | −1.79610 | −0.120547 | ||||||||
\(223\) | −5.02866 | −0.336744 | −0.168372 | − | 0.985723i | \(-0.553851\pi\) | ||||
−0.168372 | + | 0.985723i | \(0.553851\pi\) | |||||||
\(224\) | −2.77447 | −0.185377 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.37545 | −0.424089 | ||||||||
\(227\) | −17.8382 | −1.18397 | −0.591983 | − | 0.805951i | \(-0.701655\pi\) | ||||
−0.591983 | + | 0.805951i | \(0.701655\pi\) | |||||||
\(228\) | 2.42184 | 0.160390 | ||||||||
\(229\) | −21.5566 | −1.42450 | −0.712251 | − | 0.701925i | \(-0.752324\pi\) | ||||
−0.712251 | + | 0.701925i | \(0.752324\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.1993 | −0.868451 | ||||||||
\(232\) | 4.09668 | 0.268960 | ||||||||
\(233\) | 14.7065 | 0.963452 | 0.481726 | − | 0.876322i | \(-0.340010\pi\) | ||||
0.481726 | + | 0.876322i | \(0.340010\pi\) | |||||||
\(234\) | −0.339260 | −0.0221781 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.78206 | −0.246191 | ||||||||
\(237\) | −16.9784 | −1.10286 | ||||||||
\(238\) | −14.3064 | −0.927343 | ||||||||
\(239\) | 6.94025 | 0.448927 | 0.224464 | − | 0.974482i | \(-0.427937\pi\) | ||||
0.224464 | + | 0.974482i | \(0.427937\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.31003 | 0.213218 | 0.106609 | − | 0.994301i | \(-0.466001\pi\) | ||||
0.106609 | + | 0.994301i | \(0.466001\pi\) | |||||||
\(242\) | −3.30233 | −0.212282 | ||||||||
\(243\) | 0.620870 | 0.0398288 | ||||||||
\(244\) | −10.8325 | −0.693478 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 15.6163 | 0.995658 | ||||||||
\(247\) | 8.01921 | 0.510250 | ||||||||
\(248\) | −7.12710 | −0.452571 | ||||||||
\(249\) | 8.01806 | 0.508124 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.46454 | −0.597397 | −0.298698 | − | 0.954348i | \(-0.596552\pi\) | ||||
−0.298698 | + | 0.954348i | \(0.596552\pi\) | |||||||
\(252\) | 0.165781 | 0.0104432 | ||||||||
\(253\) | −1.81717 | −0.114245 | ||||||||
\(254\) | 9.54893 | 0.599153 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.07963 | −0.441615 | −0.220808 | − | 0.975317i | \(-0.570869\pi\) | ||||
−0.220808 | + | 0.975317i | \(0.570869\pi\) | |||||||
\(258\) | 15.8553 | 0.987107 | ||||||||
\(259\) | 2.90615 | 0.180580 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.244786 | −0.0151519 | ||||||||
\(262\) | 5.59923 | 0.345922 | ||||||||
\(263\) | 1.43345 | 0.0883906 | 0.0441953 | − | 0.999023i | \(-0.485928\pi\) | ||||
0.0441953 | + | 0.999023i | \(0.485928\pi\) | |||||||
\(264\) | 4.75742 | 0.292799 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.91861 | −0.240266 | ||||||||
\(267\) | −15.7480 | −0.963760 | ||||||||
\(268\) | −4.32340 | −0.264094 | ||||||||
\(269\) | −14.2830 | −0.870848 | −0.435424 | − | 0.900226i | \(-0.643402\pi\) | ||||
−0.435424 | + | 0.900226i | \(0.643402\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.7855 | 1.87009 | 0.935044 | − | 0.354533i | \(-0.115360\pi\) | ||||
0.935044 | + | 0.354533i | \(0.115360\pi\) | |||||||
\(272\) | 5.15643 | 0.312655 | ||||||||
\(273\) | −27.0116 | −1.63482 | ||||||||
\(274\) | 7.98414 | 0.482340 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.12307 | −0.0676012 | ||||||||
\(277\) | 3.18969 | 0.191650 | 0.0958249 | − | 0.995398i | \(-0.469451\pi\) | ||||
0.0958249 | + | 0.995398i | \(0.469451\pi\) | |||||||
\(278\) | −22.0884 | −1.32478 | ||||||||
\(279\) | 0.425860 | 0.0254956 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.3889 | 1.21630 | 0.608151 | − | 0.793822i | \(-0.291912\pi\) | ||||
0.608151 | + | 0.793822i | \(0.291912\pi\) | |||||||
\(282\) | −4.75742 | −0.283300 | ||||||||
\(283\) | −13.2969 | −0.790419 | −0.395209 | − | 0.918591i | \(-0.629328\pi\) | ||||
−0.395209 | + | 0.918591i | \(0.629328\pi\) | |||||||
\(284\) | −13.2466 | −0.786041 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.7528 | 0.931484 | ||||||||
\(287\) | −25.2677 | −1.49150 | ||||||||
\(288\) | −0.0597522 | −0.00352093 | ||||||||
\(289\) | 9.58880 | 0.564047 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.154616 | −0.00906374 | ||||||||
\(292\) | 4.21324 | 0.246561 | ||||||||
\(293\) | −26.0420 | −1.52139 | −0.760696 | − | 0.649108i | \(-0.775142\pi\) | ||||
−0.760696 | + | 0.649108i | \(0.775142\pi\) | |||||||
\(294\) | 1.19630 | 0.0697698 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.04746 | −0.0608826 | ||||||||
\(297\) | −14.5565 | −0.844655 | ||||||||
\(298\) | 4.18401 | 0.242373 | ||||||||
\(299\) | −3.71874 | −0.215060 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.6544 | −1.47869 | ||||||||
\(302\) | −0.331561 | −0.0190792 | ||||||||
\(303\) | −13.5571 | −0.778835 | ||||||||
\(304\) | 1.41238 | 0.0810058 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.308108 | −0.0176134 | ||||||||
\(307\) | 25.1000 | 1.43253 | 0.716267 | − | 0.697826i | \(-0.245849\pi\) | ||||
0.716267 | + | 0.697826i | \(0.245849\pi\) | |||||||
\(308\) | −7.69767 | −0.438615 | ||||||||
\(309\) | 13.4335 | 0.764203 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.723328 | 0.0410162 | 0.0205081 | − | 0.999790i | \(-0.493472\pi\) | ||||
0.0205081 | + | 0.999790i | \(0.493472\pi\) | |||||||
\(312\) | 9.73579 | 0.551180 | ||||||||
\(313\) | 21.6163 | 1.22182 | 0.610912 | − | 0.791698i | \(-0.290803\pi\) | ||||
0.610912 | + | 0.791698i | \(0.290803\pi\) | |||||||
\(314\) | 3.60750 | 0.203583 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.90157 | −0.557007 | ||||||||
\(317\) | −18.8337 | −1.05780 | −0.528902 | − | 0.848683i | \(-0.677396\pi\) | ||||
−0.528902 | + | 0.848683i | \(0.677396\pi\) | |||||||
\(318\) | −0.902131 | −0.0505890 | ||||||||
\(319\) | 11.3661 | 0.636380 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.5278 | −0.978304 | ||||||||
\(322\) | 1.81717 | 0.101267 | ||||||||
\(323\) | 7.28286 | 0.405229 | ||||||||
\(324\) | −8.81717 | −0.489843 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.09385 | 0.282122 | ||||||||
\(327\) | 6.70610 | 0.370848 | ||||||||
\(328\) | 9.10722 | 0.502862 | ||||||||
\(329\) | 7.69767 | 0.424386 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.8759 | 0.927584 | 0.463792 | − | 0.885944i | \(-0.346489\pi\) | ||||
0.463792 | + | 0.885944i | \(0.346489\pi\) | |||||||
\(332\) | 4.67603 | 0.256631 | ||||||||
\(333\) | 0.0625883 | 0.00342982 | ||||||||
\(334\) | 20.8629 | 1.14157 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.75742 | −0.259539 | ||||||||
\(337\) | 19.3521 | 1.05417 | 0.527087 | − | 0.849811i | \(-0.323284\pi\) | ||||
0.527087 | + | 0.849811i | \(0.323284\pi\) | |||||||
\(338\) | 19.2373 | 1.04637 | ||||||||
\(339\) | −10.9321 | −0.593750 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.7739 | −1.07082 | ||||||||
\(342\) | −0.0843930 | −0.00456345 | ||||||||
\(343\) | 17.4856 | 0.944134 | ||||||||
\(344\) | 9.24660 | 0.498543 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.9877 | −0.644463 | ||||||||
\(347\) | −9.03868 | −0.485222 | −0.242611 | − | 0.970124i | \(-0.578004\pi\) | ||||
−0.242611 | + | 0.970124i | \(0.578004\pi\) | |||||||
\(348\) | 7.02464 | 0.376560 | ||||||||
\(349\) | 36.7305 | 1.96614 | 0.983068 | − | 0.183240i | \(-0.0586584\pi\) | ||||
0.983068 | + | 0.183240i | \(0.0586584\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −29.7891 | −1.59002 | ||||||||
\(352\) | 2.77447 | 0.147880 | ||||||||
\(353\) | 18.3737 | 0.977933 | 0.488967 | − | 0.872302i | \(-0.337374\pi\) | ||||
0.488967 | + | 0.872302i | \(0.337374\pi\) | |||||||
\(354\) | −6.48516 | −0.344682 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.18401 | −0.486752 | ||||||||
\(357\) | −24.5313 | −1.29834 | ||||||||
\(358\) | −8.54134 | −0.451424 | ||||||||
\(359\) | −24.4259 | −1.28915 | −0.644574 | − | 0.764542i | \(-0.722965\pi\) | ||||
−0.644574 | + | 0.764542i | \(0.722965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0052 | −0.895009 | ||||||||
\(362\) | 7.82844 | 0.411454 | ||||||||
\(363\) | −5.66256 | −0.297207 | ||||||||
\(364\) | −15.7528 | −0.825673 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −18.5746 | −0.970910 | ||||||||
\(367\) | 14.5224 | 0.758065 | 0.379032 | − | 0.925383i | \(-0.376257\pi\) | ||||
0.379032 | + | 0.925383i | \(0.376257\pi\) | |||||||
\(368\) | −0.654963 | −0.0341423 | ||||||||
\(369\) | −0.544176 | −0.0283287 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.45968 | 0.0757827 | ||||||||
\(372\) | −12.2209 | −0.633626 | ||||||||
\(373\) | −23.2887 | −1.20585 | −0.602923 | − | 0.797800i | \(-0.705997\pi\) | ||||
−0.602923 | + | 0.797800i | \(0.705997\pi\) | |||||||
\(374\) | 14.3064 | 0.739764 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.77447 | −0.143082 | ||||||||
\(377\) | 23.2601 | 1.19796 | ||||||||
\(378\) | 14.5565 | 0.748707 | ||||||||
\(379\) | 28.6176 | 1.46999 | 0.734993 | − | 0.678075i | \(-0.237185\pi\) | ||||
0.734993 | + | 0.678075i | \(0.237185\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.3737 | 0.838850 | ||||||||
\(382\) | 3.36611 | 0.172225 | ||||||||
\(383\) | −16.6157 | −0.849023 | −0.424512 | − | 0.905422i | \(-0.639554\pi\) | ||||
−0.424512 | + | 0.905422i | \(0.639554\pi\) | |||||||
\(384\) | 1.71472 | 0.0875037 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.4211 | −0.784913 | ||||||||
\(387\) | −0.552505 | −0.0280854 | ||||||||
\(388\) | −0.0901699 | −0.00457769 | ||||||||
\(389\) | 26.3767 | 1.33735 | 0.668677 | − | 0.743553i | \(-0.266861\pi\) | ||||
0.668677 | + | 0.743553i | \(0.266861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.37727 | −0.170796 | ||||||||
\(392\) | 0.697669 | 0.0352376 | ||||||||
\(393\) | 9.60109 | 0.484311 | ||||||||
\(394\) | 8.80489 | 0.443584 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.165781 | −0.00833078 | ||||||||
\(397\) | −17.9086 | −0.898807 | −0.449403 | − | 0.893329i | \(-0.648363\pi\) | ||||
−0.449403 | + | 0.893329i | \(0.648363\pi\) | |||||||
\(398\) | −17.6222 | −0.883319 | ||||||||
\(399\) | −6.71930 | −0.336386 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.0164 | 1.59882 | 0.799411 | − | 0.600785i | \(-0.205145\pi\) | ||||
0.799411 | + | 0.600785i | \(0.205145\pi\) | |||||||
\(402\) | −7.41340 | −0.369747 | ||||||||
\(403\) | −40.4661 | −2.01576 | ||||||||
\(404\) | −7.90632 | −0.393354 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.3661 | −0.564090 | ||||||||
\(407\) | −2.90615 | −0.144053 | ||||||||
\(408\) | 8.84181 | 0.437735 | ||||||||
\(409\) | 18.0344 | 0.891743 | 0.445871 | − | 0.895097i | \(-0.352894\pi\) | ||||
0.445871 | + | 0.895097i | \(0.352894\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.6905 | 0.675304 | ||||||||
\(412\) | 7.83422 | 0.385964 | ||||||||
\(413\) | 10.4932 | 0.516337 | ||||||||
\(414\) | 0.0391355 | 0.00192340 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.67779 | 0.278376 | ||||||||
\(417\) | −37.8753 | −1.85476 | ||||||||
\(418\) | 3.91861 | 0.191666 | ||||||||
\(419\) | −19.5300 | −0.954104 | −0.477052 | − | 0.878875i | \(-0.658295\pi\) | ||||
−0.477052 | + | 0.878875i | \(0.658295\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.5537 | −0.952989 | −0.476494 | − | 0.879178i | \(-0.658093\pi\) | ||||
−0.476494 | + | 0.879178i | \(0.658093\pi\) | |||||||
\(422\) | 6.10144 | 0.297013 | ||||||||
\(423\) | 0.165781 | 0.00806052 | ||||||||
\(424\) | −0.526111 | −0.0255502 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −22.7142 | −1.10050 | ||||||||
\(427\) | 30.0543 | 1.45443 | ||||||||
\(428\) | −10.2220 | −0.494097 | ||||||||
\(429\) | 27.0116 | 1.30413 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.1963 | −1.02099 | −0.510495 | − | 0.859881i | \(-0.670538\pi\) | ||||
−0.510495 | + | 0.859881i | \(0.670538\pi\) | |||||||
\(432\) | −5.24660 | −0.252427 | ||||||||
\(433\) | 8.54967 | 0.410871 | 0.205435 | − | 0.978671i | \(-0.434139\pi\) | ||||
0.205435 | + | 0.978671i | \(0.434139\pi\) | |||||||
\(434\) | 19.7739 | 0.949178 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.91091 | 0.187299 | ||||||||
\(437\) | −0.925059 | −0.0442516 | ||||||||
\(438\) | 7.22451 | 0.345201 | ||||||||
\(439\) | −28.0714 | −1.33977 | −0.669887 | − | 0.742463i | \(-0.733657\pi\) | ||||
−0.669887 | + | 0.742463i | \(0.733657\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0416872 | −0.00198511 | ||||||||
\(442\) | 29.2771 | 1.39257 | ||||||||
\(443\) | −33.0546 | −1.57047 | −0.785236 | − | 0.619197i | \(-0.787458\pi\) | ||||
−0.785236 | + | 0.619197i | \(0.787458\pi\) | |||||||
\(444\) | −1.79610 | −0.0852393 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.02866 | −0.238114 | ||||||||
\(447\) | 7.17439 | 0.339337 | ||||||||
\(448\) | −2.77447 | −0.131081 | ||||||||
\(449\) | −37.1628 | −1.75382 | −0.876911 | − | 0.480652i | \(-0.840400\pi\) | ||||
−0.876911 | + | 0.480652i | \(0.840400\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.2677 | 1.18981 | ||||||||
\(452\) | −6.37545 | −0.299876 | ||||||||
\(453\) | −0.568533 | −0.0267120 | ||||||||
\(454\) | −17.8382 | −0.837190 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.42184 | 0.113413 | ||||||||
\(457\) | 29.3139 | 1.37125 | 0.685624 | − | 0.727956i | \(-0.259529\pi\) | ||||
0.685624 | + | 0.727956i | \(0.259529\pi\) | |||||||
\(458\) | −21.5566 | −1.00728 | ||||||||
\(459\) | −27.0538 | −1.26276 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.90741 | 0.414859 | 0.207430 | − | 0.978250i | \(-0.433490\pi\) | ||||
0.207430 | + | 0.978250i | \(0.433490\pi\) | |||||||
\(462\) | −13.1993 | −0.614087 | ||||||||
\(463\) | −18.2771 | −0.849410 | −0.424705 | − | 0.905332i | \(-0.639622\pi\) | ||||
−0.424705 | + | 0.905332i | \(0.639622\pi\) | |||||||
\(464\) | 4.09668 | 0.190184 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.7065 | 0.681263 | ||||||||
\(467\) | −36.6841 | −1.69754 | −0.848768 | − | 0.528765i | \(-0.822655\pi\) | ||||
−0.848768 | + | 0.528765i | \(0.822655\pi\) | |||||||
\(468\) | −0.339260 | −0.0156823 | ||||||||
\(469\) | 11.9951 | 0.553884 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.18583 | 0.285028 | ||||||||
\(472\) | −3.78206 | −0.174084 | ||||||||
\(473\) | 25.6544 | 1.17959 | ||||||||
\(474\) | −16.9784 | −0.779842 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.3064 | −0.655731 | ||||||||
\(477\) | 0.0314363 | 0.00143937 | ||||||||
\(478\) | 6.94025 | 0.317440 | ||||||||
\(479\) | −12.5898 | −0.575242 | −0.287621 | − | 0.957744i | \(-0.592864\pi\) | ||||
−0.287621 | + | 0.957744i | \(0.592864\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.94728 | −0.271173 | ||||||||
\(482\) | 3.31003 | 0.150768 | ||||||||
\(483\) | 3.11593 | 0.141780 | ||||||||
\(484\) | −3.30233 | −0.150106 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.620870 | 0.0281632 | ||||||||
\(487\) | −18.3256 | −0.830411 | −0.415205 | − | 0.909728i | \(-0.636290\pi\) | ||||
−0.415205 | + | 0.909728i | \(0.636290\pi\) | |||||||
\(488\) | −10.8325 | −0.490363 | ||||||||
\(489\) | 8.73449 | 0.394987 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.7047 | 0.979519 | 0.489760 | − | 0.871857i | \(-0.337085\pi\) | ||||
0.489760 | + | 0.871857i | \(0.337085\pi\) | |||||||
\(492\) | 15.6163 | 0.704036 | ||||||||
\(493\) | 21.1243 | 0.951389 | ||||||||
\(494\) | 8.01921 | 0.360801 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.12710 | −0.320016 | ||||||||
\(497\) | 36.7523 | 1.64856 | ||||||||
\(498\) | 8.01806 | 0.359298 | ||||||||
\(499\) | 15.8391 | 0.709055 | 0.354527 | − | 0.935046i | \(-0.384642\pi\) | ||||
0.354527 | + | 0.935046i | \(0.384642\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 35.7739 | 1.59826 | ||||||||
\(502\) | −9.46454 | −0.422423 | ||||||||
\(503\) | 27.5530 | 1.22853 | 0.614263 | − | 0.789101i | \(-0.289453\pi\) | ||||
0.614263 | + | 0.789101i | \(0.289453\pi\) | |||||||
\(504\) | 0.165781 | 0.00738445 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.81717 | −0.0807832 | ||||||||
\(507\) | 32.9864 | 1.46498 | ||||||||
\(508\) | 9.54893 | 0.423665 | ||||||||
\(509\) | −27.6120 | −1.22388 | −0.611941 | − | 0.790903i | \(-0.709611\pi\) | ||||
−0.611941 | + | 0.790903i | \(0.709611\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.6895 | −0.517113 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −7.41022 | −0.327169 | ||||||||
\(514\) | −7.07963 | −0.312269 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 15.8553 | 0.697990 | ||||||||
\(517\) | −7.69767 | −0.338543 | ||||||||
\(518\) | 2.90615 | 0.127689 | ||||||||
\(519\) | −20.5555 | −0.902287 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.0892 | 0.748689 | 0.374345 | − | 0.927290i | \(-0.377868\pi\) | ||||
0.374345 | + | 0.927290i | \(0.377868\pi\) | |||||||
\(522\) | −0.244786 | −0.0107140 | ||||||||
\(523\) | 36.3152 | 1.58795 | 0.793977 | − | 0.607947i | \(-0.208007\pi\) | ||||
0.793977 | + | 0.607947i | \(0.208007\pi\) | |||||||
\(524\) | 5.59923 | 0.244604 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.43345 | 0.0625016 | ||||||||
\(527\) | −36.7504 | −1.60087 | ||||||||
\(528\) | 4.75742 | 0.207040 | ||||||||
\(529\) | −22.5710 | −0.981349 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.225987 | 0.00980698 | ||||||||
\(532\) | −3.91861 | −0.169893 | ||||||||
\(533\) | 51.7088 | 2.23976 | ||||||||
\(534\) | −15.7480 | −0.681481 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.32340 | −0.186743 | ||||||||
\(537\) | −14.6460 | −0.632020 | ||||||||
\(538\) | −14.2830 | −0.615782 | ||||||||
\(539\) | 1.93566 | 0.0833747 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.9366 | 1.07211 | 0.536055 | − | 0.844183i | \(-0.319914\pi\) | ||||
0.536055 | + | 0.844183i | \(0.319914\pi\) | |||||||
\(542\) | 30.7855 | 1.32235 | ||||||||
\(543\) | 13.4235 | 0.576060 | ||||||||
\(544\) | 5.15643 | 0.221080 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −27.0116 | −1.15599 | ||||||||
\(547\) | 6.67201 | 0.285275 | 0.142637 | − | 0.989775i | \(-0.454442\pi\) | ||||
0.142637 | + | 0.989775i | \(0.454442\pi\) | |||||||
\(548\) | 7.98414 | 0.341066 | ||||||||
\(549\) | 0.647264 | 0.0276245 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.78609 | 0.246496 | ||||||||
\(552\) | −1.12307 | −0.0478012 | ||||||||
\(553\) | 27.4716 | 1.16821 | ||||||||
\(554\) | 3.18969 | 0.135517 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22.0884 | −0.936758 | ||||||||
\(557\) | −20.4328 | −0.865765 | −0.432882 | − | 0.901450i | \(-0.642503\pi\) | ||||
−0.432882 | + | 0.901450i | \(0.642503\pi\) | |||||||
\(558\) | 0.425860 | 0.0180281 | ||||||||
\(559\) | 52.5002 | 2.22052 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.5313 | 1.03571 | ||||||||
\(562\) | 20.3889 | 0.860055 | ||||||||
\(563\) | −0.602805 | −0.0254052 | −0.0127026 | − | 0.999919i | \(-0.504043\pi\) | ||||
−0.0127026 | + | 0.999919i | \(0.504043\pi\) | |||||||
\(564\) | −4.75742 | −0.200324 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.2969 | −0.558911 | ||||||||
\(567\) | 24.4630 | 1.02735 | ||||||||
\(568\) | −13.2466 | −0.555815 | ||||||||
\(569\) | 33.8776 | 1.42022 | 0.710112 | − | 0.704089i | \(-0.248644\pi\) | ||||
0.710112 | + | 0.704089i | \(0.248644\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.23012 | −0.260722 | −0.130361 | − | 0.991467i | \(-0.541614\pi\) | ||||
−0.130361 | + | 0.991467i | \(0.541614\pi\) | |||||||
\(572\) | 15.7528 | 0.658659 | ||||||||
\(573\) | 5.77192 | 0.241125 | ||||||||
\(574\) | −25.2677 | −1.05465 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.0597522 | −0.00248967 | ||||||||
\(577\) | 3.78104 | 0.157407 | 0.0787034 | − | 0.996898i | \(-0.474922\pi\) | ||||
0.0787034 | + | 0.996898i | \(0.474922\pi\) | |||||||
\(578\) | 9.58880 | 0.398842 | ||||||||
\(579\) | −26.4428 | −1.09893 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.9735 | −0.538232 | ||||||||
\(582\) | −0.154616 | −0.00640903 | ||||||||
\(583\) | −1.45968 | −0.0604537 | ||||||||
\(584\) | 4.21324 | 0.174345 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.0420 | −1.07579 | ||||||||
\(587\) | 16.3526 | 0.674945 | 0.337473 | − | 0.941335i | \(-0.390428\pi\) | ||||
0.337473 | + | 0.941335i | \(0.390428\pi\) | |||||||
\(588\) | 1.19630 | 0.0493347 | ||||||||
\(589\) | −10.0662 | −0.414770 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.0979 | 0.621043 | ||||||||
\(592\) | −1.04746 | −0.0430505 | ||||||||
\(593\) | 9.53314 | 0.391479 | 0.195740 | − | 0.980656i | \(-0.437289\pi\) | ||||
0.195740 | + | 0.980656i | \(0.437289\pi\) | |||||||
\(594\) | −14.5565 | −0.597262 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.18401 | 0.171384 | ||||||||
\(597\) | −30.2170 | −1.23670 | ||||||||
\(598\) | −3.71874 | −0.152071 | ||||||||
\(599\) | −16.0682 | −0.656528 | −0.328264 | − | 0.944586i | \(-0.606464\pi\) | ||||
−0.328264 | + | 0.944586i | \(0.606464\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0380 | 0.613413 | 0.306707 | − | 0.951804i | \(-0.400773\pi\) | ||||
0.306707 | + | 0.951804i | \(0.400773\pi\) | |||||||
\(602\) | −25.6544 | −1.04560 | ||||||||
\(603\) | 0.258333 | 0.0105201 | ||||||||
\(604\) | −0.331561 | −0.0134910 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −13.5571 | −0.550719 | ||||||||
\(607\) | −44.8348 | −1.81979 | −0.909894 | − | 0.414840i | \(-0.863837\pi\) | ||||
−0.909894 | + | 0.414840i | \(0.863837\pi\) | |||||||
\(608\) | 1.41238 | 0.0572797 | ||||||||
\(609\) | −19.4896 | −0.789760 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.7528 | −0.637291 | ||||||||
\(612\) | −0.308108 | −0.0124545 | ||||||||
\(613\) | −15.5488 | −0.628011 | −0.314006 | − | 0.949421i | \(-0.601671\pi\) | ||||
−0.314006 | + | 0.949421i | \(0.601671\pi\) | |||||||
\(614\) | 25.1000 | 1.01296 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.69767 | −0.310148 | ||||||||
\(617\) | 17.5994 | 0.708525 | 0.354263 | − | 0.935146i | \(-0.384732\pi\) | ||||
0.354263 | + | 0.935146i | \(0.384732\pi\) | |||||||
\(618\) | 13.4335 | 0.540373 | ||||||||
\(619\) | −37.2887 | −1.49876 | −0.749381 | − | 0.662140i | \(-0.769649\pi\) | ||||
−0.749381 | + | 0.662140i | \(0.769649\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.43633 | 0.137895 | ||||||||
\(622\) | 0.723328 | 0.0290028 | ||||||||
\(623\) | 25.4807 | 1.02086 | ||||||||
\(624\) | 9.73579 | 0.389743 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.6163 | 0.863960 | ||||||||
\(627\) | 6.71930 | 0.268343 | ||||||||
\(628\) | 3.60750 | 0.143955 | ||||||||
\(629\) | −5.40118 | −0.215359 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.55551 | 0.340589 | 0.170295 | − | 0.985393i | \(-0.445528\pi\) | ||||
0.170295 | + | 0.985393i | \(0.445528\pi\) | |||||||
\(632\) | −9.90157 | −0.393863 | ||||||||
\(633\) | 10.4622 | 0.415836 | ||||||||
\(634\) | −18.8337 | −0.747980 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.902131 | −0.0357718 | ||||||||
\(637\) | 3.96121 | 0.156949 | ||||||||
\(638\) | 11.3661 | 0.449989 | ||||||||
\(639\) | 0.791514 | 0.0313118 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.8156 | −0.901162 | −0.450581 | − | 0.892736i | \(-0.648783\pi\) | ||||
−0.450581 | + | 0.892736i | \(0.648783\pi\) | |||||||
\(642\) | −17.5278 | −0.691765 | ||||||||
\(643\) | 34.7745 | 1.37137 | 0.685686 | − | 0.727898i | \(-0.259503\pi\) | ||||
0.685686 | + | 0.727898i | \(0.259503\pi\) | |||||||
\(644\) | 1.81717 | 0.0716067 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.28286 | 0.286540 | ||||||||
\(647\) | −16.4581 | −0.647034 | −0.323517 | − | 0.946222i | \(-0.604865\pi\) | ||||
−0.323517 | + | 0.946222i | \(0.604865\pi\) | |||||||
\(648\) | −8.81717 | −0.346371 | ||||||||
\(649\) | −10.4932 | −0.411894 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33.9066 | 1.32890 | ||||||||
\(652\) | 5.09385 | 0.199490 | ||||||||
\(653\) | 30.2092 | 1.18218 | 0.591088 | − | 0.806607i | \(-0.298699\pi\) | ||||
0.591088 | + | 0.806607i | \(0.298699\pi\) | |||||||
\(654\) | 6.70610 | 0.262229 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.10722 | 0.355577 | ||||||||
\(657\) | −0.251751 | −0.00982173 | ||||||||
\(658\) | 7.69767 | 0.300086 | ||||||||
\(659\) | −28.4942 | −1.10998 | −0.554989 | − | 0.831858i | \(-0.687277\pi\) | ||||
−0.554989 | + | 0.831858i | \(0.687277\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 50.7342 | 1.97333 | 0.986666 | − | 0.162759i | \(-0.0520393\pi\) | ||||
0.986666 | + | 0.162759i | \(0.0520393\pi\) | |||||||
\(662\) | 16.8759 | 0.655901 | ||||||||
\(663\) | 50.2019 | 1.94968 | ||||||||
\(664\) | 4.67603 | 0.181465 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.0625883 | 0.00242525 | ||||||||
\(667\) | −2.68317 | −0.103893 | ||||||||
\(668\) | 20.8629 | 0.807209 | ||||||||
\(669\) | −8.62273 | −0.333374 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.0543 | −1.16023 | ||||||||
\(672\) | −4.75742 | −0.183521 | ||||||||
\(673\) | −20.4447 | −0.788084 | −0.394042 | − | 0.919093i | \(-0.628923\pi\) | ||||
−0.394042 | + | 0.919093i | \(0.628923\pi\) | |||||||
\(674\) | 19.3521 | 0.745414 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.2373 | 0.739894 | ||||||||
\(677\) | 8.53360 | 0.327973 | 0.163986 | − | 0.986463i | \(-0.447565\pi\) | ||||
0.163986 | + | 0.986463i | \(0.447565\pi\) | |||||||
\(678\) | −10.9321 | −0.419844 | ||||||||
\(679\) | 0.250174 | 0.00960078 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.5875 | −1.17212 | ||||||||
\(682\) | −19.7739 | −0.757182 | ||||||||
\(683\) | −48.5684 | −1.85842 | −0.929210 | − | 0.369553i | \(-0.879511\pi\) | ||||
−0.929210 | + | 0.369553i | \(0.879511\pi\) | |||||||
\(684\) | −0.0843930 | −0.00322685 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.4856 | 0.667604 | ||||||||
\(687\) | −36.9635 | −1.41024 | ||||||||
\(688\) | 9.24660 | 0.352523 | ||||||||
\(689\) | −2.98715 | −0.113801 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.8076 | 1.70456 | 0.852281 | − | 0.523084i | \(-0.175219\pi\) | ||||
0.852281 | + | 0.523084i | \(0.175219\pi\) | |||||||
\(692\) | −11.9877 | −0.455704 | ||||||||
\(693\) | 0.459953 | 0.0174722 | ||||||||
\(694\) | −9.03868 | −0.343104 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.02464 | 0.266268 | ||||||||
\(697\) | 46.9608 | 1.77877 | ||||||||
\(698\) | 36.7305 | 1.39027 | ||||||||
\(699\) | 25.2174 | 0.953809 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.21913 | 0.0838152 | 0.0419076 | − | 0.999121i | \(-0.486656\pi\) | ||||
0.0419076 | + | 0.999121i | \(0.486656\pi\) | |||||||
\(702\) | −29.7891 | −1.12432 | ||||||||
\(703\) | −1.47942 | −0.0557974 | ||||||||
\(704\) | 2.77447 | 0.104567 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.3737 | 0.691503 | ||||||||
\(707\) | 21.9358 | 0.824982 | ||||||||
\(708\) | −6.48516 | −0.243727 | ||||||||
\(709\) | 34.3587 | 1.29037 | 0.645184 | − | 0.764027i | \(-0.276781\pi\) | ||||
0.645184 | + | 0.764027i | \(0.276781\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.591640 | 0.0221882 | ||||||||
\(712\) | −9.18401 | −0.344186 | ||||||||
\(713\) | 4.66799 | 0.174817 | ||||||||
\(714\) | −24.5313 | −0.918062 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.54134 | −0.319205 | ||||||||
\(717\) | 11.9005 | 0.444434 | ||||||||
\(718\) | −24.4259 | −0.911565 | ||||||||
\(719\) | 11.9900 | 0.447151 | 0.223575 | − | 0.974687i | \(-0.428227\pi\) | ||||
0.223575 | + | 0.974687i | \(0.428227\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.7358 | −0.809483 | ||||||||
\(722\) | −17.0052 | −0.632867 | ||||||||
\(723\) | 5.67576 | 0.211084 | ||||||||
\(724\) | 7.82844 | 0.290942 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.66256 | −0.210157 | ||||||||
\(727\) | 42.1827 | 1.56447 | 0.782235 | − | 0.622983i | \(-0.214080\pi\) | ||||
0.782235 | + | 0.622983i | \(0.214080\pi\) | |||||||
\(728\) | −15.7528 | −0.583839 | ||||||||
\(729\) | 27.5161 | 1.01912 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.6795 | 1.76349 | ||||||||
\(732\) | −18.5746 | −0.686537 | ||||||||
\(733\) | −0.322383 | −0.0119075 | −0.00595375 | − | 0.999982i | \(-0.501895\pi\) | ||||
−0.00595375 | + | 0.999982i | \(0.501895\pi\) | |||||||
\(734\) | 14.5224 | 0.536033 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.654963 | −0.0241423 | ||||||||
\(737\) | −11.9951 | −0.441847 | ||||||||
\(738\) | −0.544176 | −0.0200314 | ||||||||
\(739\) | −5.49978 | −0.202313 | −0.101156 | − | 0.994871i | \(-0.532254\pi\) | ||||
−0.101156 | + | 0.994871i | \(0.532254\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.7507 | 0.505143 | ||||||||
\(742\) | 1.45968 | 0.0535865 | ||||||||
\(743\) | −6.03812 | −0.221517 | −0.110759 | − | 0.993847i | \(-0.535328\pi\) | ||||
−0.110759 | + | 0.993847i | \(0.535328\pi\) | |||||||
\(744\) | −12.2209 | −0.448042 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −23.2887 | −0.852662 | ||||||||
\(747\) | −0.279403 | −0.0102228 | ||||||||
\(748\) | 14.3064 | 0.523092 | ||||||||
\(749\) | 28.3605 | 1.03627 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.5719 | −0.495244 | −0.247622 | − | 0.968857i | \(-0.579649\pi\) | ||||
−0.247622 | + | 0.968857i | \(0.579649\pi\) | |||||||
\(752\) | −2.77447 | −0.101174 | ||||||||
\(753\) | −16.2290 | −0.591417 | ||||||||
\(754\) | 23.2601 | 0.847082 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 14.5565 | 0.529416 | ||||||||
\(757\) | 33.0661 | 1.20181 | 0.600904 | − | 0.799321i | \(-0.294807\pi\) | ||||
0.600904 | + | 0.799321i | \(0.294807\pi\) | |||||||
\(758\) | 28.6176 | 1.03944 | ||||||||
\(759\) | −3.11593 | −0.113101 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.18860 | 0.188087 | 0.0940434 | − | 0.995568i | \(-0.470021\pi\) | ||||
0.0940434 | + | 0.995568i | \(0.470021\pi\) | |||||||
\(762\) | 16.3737 | 0.593157 | ||||||||
\(763\) | −10.8507 | −0.392822 | ||||||||
\(764\) | 3.36611 | 0.121782 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.6157 | −0.600350 | ||||||||
\(767\) | −21.4737 | −0.775372 | ||||||||
\(768\) | 1.71472 | 0.0618745 | ||||||||
\(769\) | 33.0698 | 1.19253 | 0.596264 | − | 0.802789i | \(-0.296651\pi\) | ||||
0.596264 | + | 0.802789i | \(0.296651\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.1396 | −0.437195 | ||||||||
\(772\) | −15.4211 | −0.555018 | ||||||||
\(773\) | −1.13095 | −0.0406776 | −0.0203388 | − | 0.999793i | \(-0.506474\pi\) | ||||
−0.0203388 | + | 0.999793i | \(0.506474\pi\) | |||||||
\(774\) | −0.552505 | −0.0198594 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.0901699 | −0.00323691 | ||||||||
\(777\) | 4.98323 | 0.178772 | ||||||||
\(778\) | 26.3767 | 0.945652 | ||||||||
\(779\) | 12.8629 | 0.460861 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.7523 | −1.31510 | ||||||||
\(782\) | −3.37727 | −0.120771 | ||||||||
\(783\) | −21.4937 | −0.768121 | ||||||||
\(784\) | 0.697669 | 0.0249167 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.60109 | 0.342460 | ||||||||
\(787\) | 15.7610 | 0.561819 | 0.280909 | − | 0.959734i | \(-0.409364\pi\) | ||||
0.280909 | + | 0.959734i | \(0.409364\pi\) | |||||||
\(788\) | 8.80489 | 0.313661 | ||||||||
\(789\) | 2.45797 | 0.0875059 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.6885 | 0.628930 | ||||||||
\(792\) | −0.165781 | −0.00589075 | ||||||||
\(793\) | −61.5044 | −2.18409 | ||||||||
\(794\) | −17.9086 | −0.635552 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −17.6222 | −0.624601 | ||||||||
\(797\) | −23.1397 | −0.819649 | −0.409824 | − | 0.912164i | \(-0.634410\pi\) | ||||
−0.409824 | + | 0.912164i | \(0.634410\pi\) | |||||||
\(798\) | −6.71930 | −0.237861 | ||||||||
\(799\) | −14.3064 | −0.506122 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.548765 | 0.0193897 | ||||||||
\(802\) | 32.0164 | 1.13054 | ||||||||
\(803\) | 11.6895 | 0.412514 | ||||||||
\(804\) | −7.41340 | −0.261451 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −40.4661 | −1.42536 | ||||||||
\(807\) | −24.4912 | −0.862132 | ||||||||
\(808\) | −7.90632 | −0.278144 | ||||||||
\(809\) | 33.5400 | 1.17921 | 0.589603 | − | 0.807694i | \(-0.299284\pi\) | ||||
0.589603 | + | 0.807694i | \(0.299284\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.9626 | −0.420064 | −0.210032 | − | 0.977695i | \(-0.567357\pi\) | ||||
−0.210032 | + | 0.977695i | \(0.567357\pi\) | |||||||
\(812\) | −11.3661 | −0.398872 | ||||||||
\(813\) | 52.7884 | 1.85137 | ||||||||
\(814\) | −2.90615 | −0.101861 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.84181 | 0.309525 | ||||||||
\(817\) | 13.0598 | 0.456903 | ||||||||
\(818\) | 18.0344 | 0.630557 | ||||||||
\(819\) | 0.941266 | 0.0328905 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.6941 | −0.373227 | −0.186613 | − | 0.982433i | \(-0.559751\pi\) | ||||
−0.186613 | + | 0.982433i | \(0.559751\pi\) | |||||||
\(822\) | 13.6905 | 0.477512 | ||||||||
\(823\) | −12.0211 | −0.419028 | −0.209514 | − | 0.977806i | \(-0.567188\pi\) | ||||
−0.209514 | + | 0.977806i | \(0.567188\pi\) | |||||||
\(824\) | 7.83422 | 0.272918 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.4932 | 0.365105 | ||||||||
\(827\) | −4.13974 | −0.143953 | −0.0719764 | − | 0.997406i | \(-0.522931\pi\) | ||||
−0.0719764 | + | 0.997406i | \(0.522931\pi\) | |||||||
\(828\) | 0.0391355 | 0.00136005 | ||||||||
\(829\) | −20.3503 | −0.706796 | −0.353398 | − | 0.935473i | \(-0.614974\pi\) | ||||
−0.353398 | + | 0.935473i | \(0.614974\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.46940 | 0.189732 | ||||||||
\(832\) | 5.67779 | 0.196842 | ||||||||
\(833\) | 3.59748 | 0.124645 | ||||||||
\(834\) | −37.8753 | −1.31152 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.91861 | 0.135528 | ||||||||
\(837\) | 37.3931 | 1.29249 | ||||||||
\(838\) | −19.5300 | −0.674654 | ||||||||
\(839\) | 3.13515 | 0.108237 | 0.0541186 | − | 0.998535i | \(-0.482765\pi\) | ||||
0.0541186 | + | 0.998535i | \(0.482765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.2172 | −0.421283 | ||||||||
\(842\) | −19.5537 | −0.673865 | ||||||||
\(843\) | 34.9612 | 1.20413 | ||||||||
\(844\) | 6.10144 | 0.210020 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.165781 | 0.00569965 | ||||||||
\(847\) | 9.16221 | 0.314817 | ||||||||
\(848\) | −0.526111 | −0.0180667 | ||||||||
\(849\) | −22.8004 | −0.782508 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.686050 | 0.0235175 | ||||||||
\(852\) | −22.7142 | −0.778174 | ||||||||
\(853\) | 23.3471 | 0.799388 | 0.399694 | − | 0.916649i | \(-0.369116\pi\) | ||||
0.399694 | + | 0.916649i | \(0.369116\pi\) | |||||||
\(854\) | 30.0543 | 1.02844 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.2220 | −0.349379 | ||||||||
\(857\) | 15.3036 | 0.522762 | 0.261381 | − | 0.965236i | \(-0.415822\pi\) | ||||
0.261381 | + | 0.965236i | \(0.415822\pi\) | |||||||
\(858\) | 27.0116 | 0.922161 | ||||||||
\(859\) | −2.96132 | −0.101039 | −0.0505194 | − | 0.998723i | \(-0.516088\pi\) | ||||
−0.0505194 | + | 0.998723i | \(0.516088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −43.3269 | −1.47658 | ||||||||
\(862\) | −21.1963 | −0.721949 | ||||||||
\(863\) | −37.8220 | −1.28748 | −0.643739 | − | 0.765246i | \(-0.722618\pi\) | ||||
−0.643739 | + | 0.765246i | \(0.722618\pi\) | |||||||
\(864\) | −5.24660 | −0.178493 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.54967 | 0.290530 | ||||||||
\(867\) | 16.4421 | 0.558402 | ||||||||
\(868\) | 19.7739 | 0.671170 | ||||||||
\(869\) | −27.4716 | −0.931909 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.5474 | −0.831755 | ||||||||
\(872\) | 3.91091 | 0.132440 | ||||||||
\(873\) | 0.00538785 | 0.000182351 0 | ||||||||
\(874\) | −0.925059 | −0.0312906 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.22451 | 0.244094 | ||||||||
\(877\) | −15.6011 | −0.526810 | −0.263405 | − | 0.964685i | \(-0.584846\pi\) | ||||
−0.263405 | + | 0.964685i | \(0.584846\pi\) | |||||||
\(878\) | −28.0714 | −0.947363 | ||||||||
\(879\) | −44.6547 | −1.50616 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.16438 | 0.0392289 | 0.0196144 | − | 0.999808i | \(-0.493756\pi\) | ||||
0.0196144 | + | 0.999808i | \(0.493756\pi\) | |||||||
\(882\) | −0.0416872 | −0.00140368 | ||||||||
\(883\) | 48.8851 | 1.64511 | 0.822557 | − | 0.568682i | \(-0.192547\pi\) | ||||
0.822557 | + | 0.568682i | \(0.192547\pi\) | |||||||
\(884\) | 29.2771 | 0.984696 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −33.0546 | −1.11049 | ||||||||
\(887\) | 8.62892 | 0.289731 | 0.144865 | − | 0.989451i | \(-0.453725\pi\) | ||||
0.144865 | + | 0.989451i | \(0.453725\pi\) | |||||||
\(888\) | −1.79610 | −0.0602733 | ||||||||
\(889\) | −26.4932 | −0.888554 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −24.4630 | −0.819540 | ||||||||
\(892\) | −5.02866 | −0.168372 | ||||||||
\(893\) | −3.91861 | −0.131131 | ||||||||
\(894\) | 7.17439 | 0.239948 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.77447 | −0.0926884 | ||||||||
\(897\) | −6.37658 | −0.212908 | ||||||||
\(898\) | −37.1628 | −1.24014 | ||||||||
\(899\) | −29.1975 | −0.973790 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.71286 | −0.0903784 | ||||||||
\(902\) | 25.2677 | 0.841322 | ||||||||
\(903\) | −43.9900 | −1.46389 | ||||||||
\(904\) | −6.37545 | −0.212044 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.568533 | −0.0188882 | ||||||||
\(907\) | 29.5085 | 0.979815 | 0.489907 | − | 0.871774i | \(-0.337031\pi\) | ||||
0.489907 | + | 0.871774i | \(0.337031\pi\) | |||||||
\(908\) | −17.8382 | −0.591983 | ||||||||
\(909\) | 0.472420 | 0.0156692 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.4088 | −1.27254 | −0.636270 | − | 0.771466i | \(-0.719524\pi\) | ||||
−0.636270 | + | 0.771466i | \(0.719524\pi\) | |||||||
\(912\) | 2.42184 | 0.0801950 | ||||||||
\(913\) | 12.9735 | 0.429360 | ||||||||
\(914\) | 29.3139 | 0.969619 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.5566 | −0.712251 | ||||||||
\(917\) | −15.5349 | −0.513007 | ||||||||
\(918\) | −27.0538 | −0.892907 | ||||||||
\(919\) | 41.6905 | 1.37524 | 0.687622 | − | 0.726069i | \(-0.258655\pi\) | ||||
0.687622 | + | 0.726069i | \(0.258655\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 43.0394 | 1.41820 | ||||||||
\(922\) | 8.90741 | 0.293350 | ||||||||
\(923\) | −75.2114 | −2.47561 | ||||||||
\(924\) | −13.1993 | −0.434225 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.2771 | −0.600624 | ||||||||
\(927\) | −0.468112 | −0.0153748 | ||||||||
\(928\) | 4.09668 | 0.134480 | ||||||||
\(929\) | 28.1047 | 0.922086 | 0.461043 | − | 0.887378i | \(-0.347475\pi\) | ||||
0.461043 | + | 0.887378i | \(0.347475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.985376 | 0.0322944 | ||||||||
\(932\) | 14.7065 | 0.481726 | ||||||||
\(933\) | 1.24030 | 0.0406056 | ||||||||
\(934\) | −36.6841 | −1.20034 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.339260 | −0.0110891 | ||||||||
\(937\) | −12.8754 | −0.420620 | −0.210310 | − | 0.977635i | \(-0.567447\pi\) | ||||
−0.210310 | + | 0.977635i | \(0.567447\pi\) | |||||||
\(938\) | 11.9951 | 0.391655 | ||||||||
\(939\) | 37.0658 | 1.20960 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.1510 | 0.330913 | 0.165457 | − | 0.986217i | \(-0.447090\pi\) | ||||
0.165457 | + | 0.986217i | \(0.447090\pi\) | |||||||
\(942\) | 6.18583 | 0.201545 | ||||||||
\(943\) | −5.96489 | −0.194243 | ||||||||
\(944\) | −3.78206 | −0.123096 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25.6544 | 0.834096 | ||||||||
\(947\) | −57.3750 | −1.86444 | −0.932218 | − | 0.361896i | \(-0.882129\pi\) | ||||
−0.932218 | + | 0.361896i | \(0.882129\pi\) | |||||||
\(948\) | −16.9784 | −0.551432 | ||||||||
\(949\) | 23.9219 | 0.776538 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.2944 | −1.04722 | ||||||||
\(952\) | −14.3064 | −0.463672 | ||||||||
\(953\) | 5.17264 | 0.167558 | 0.0837791 | − | 0.996484i | \(-0.473301\pi\) | ||||
0.0837791 | + | 0.996484i | \(0.473301\pi\) | |||||||
\(954\) | 0.0314363 | 0.00101779 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.94025 | 0.224464 | ||||||||
\(957\) | 19.4896 | 0.630010 | ||||||||
\(958\) | −12.5898 | −0.406757 | ||||||||
\(959\) | −22.1517 | −0.715317 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.7955 | 0.638566 | ||||||||
\(962\) | −5.94728 | −0.191748 | ||||||||
\(963\) | 0.610785 | 0.0196823 | ||||||||
\(964\) | 3.31003 | 0.106609 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.11593 | 0.100254 | ||||||||
\(967\) | −41.3979 | −1.33127 | −0.665634 | − | 0.746279i | \(-0.731839\pi\) | ||||
−0.665634 | + | 0.746279i | \(0.731839\pi\) | |||||||
\(968\) | −3.30233 | −0.106141 | ||||||||
\(969\) | 12.4880 | 0.401173 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.0848 | 1.38266 | 0.691329 | − | 0.722540i | \(-0.257025\pi\) | ||||
0.691329 | + | 0.722540i | \(0.257025\pi\) | |||||||
\(972\) | 0.620870 | 0.0199144 | ||||||||
\(973\) | 61.2836 | 1.96466 | ||||||||
\(974\) | −18.3256 | −0.587189 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.8325 | −0.346739 | ||||||||
\(977\) | 40.4614 | 1.29448 | 0.647238 | − | 0.762288i | \(-0.275924\pi\) | ||||
0.647238 | + | 0.762288i | \(0.275924\pi\) | |||||||
\(978\) | 8.73449 | 0.279298 | ||||||||
\(979\) | −25.4807 | −0.814368 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.233686 | −0.00746101 | ||||||||
\(982\) | 21.7047 | 0.692625 | ||||||||
\(983\) | 40.3786 | 1.28788 | 0.643938 | − | 0.765078i | \(-0.277299\pi\) | ||||
0.643938 | + | 0.765078i | \(0.277299\pi\) | |||||||
\(984\) | 15.6163 | 0.497829 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 21.1243 | 0.672734 | ||||||||
\(987\) | 13.1993 | 0.420139 | ||||||||
\(988\) | 8.01921 | 0.255125 | ||||||||
\(989\) | −6.05618 | −0.192575 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −58.1435 | −1.84699 | −0.923494 | − | 0.383613i | \(-0.874680\pi\) | ||||
−0.923494 | + | 0.383613i | \(0.874680\pi\) | |||||||
\(992\) | −7.12710 | −0.226286 | ||||||||
\(993\) | 28.9374 | 0.918300 | ||||||||
\(994\) | 36.7523 | 1.16571 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.01806 | 0.254062 | ||||||||
\(997\) | 39.2968 | 1.24454 | 0.622271 | − | 0.782802i | \(-0.286210\pi\) | ||||
0.622271 | + | 0.782802i | \(0.286210\pi\) | |||||||
\(998\) | 15.8391 | 0.501377 | ||||||||
\(999\) | 5.49563 | 0.173874 |
(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 | 1250.2.a.l.1.3 | 4 | ||
4.3 | odd | 2 | 10000.2.a.t.1.2 | 4 | |||
5.2 | odd | 4 | 1250.2.b.e.1249.6 | 8 | |||
5.3 | odd | 4 | 1250.2.b.e.1249.3 | 8 | |||
5.4 | even | 2 | 1250.2.a.f.1.2 | 4 | |||
20.19 | odd | 2 | 10000.2.a.x.1.3 | 4 | |||
25.3 | odd | 20 | 250.2.e.c.49.1 | 16 | |||
25.4 | even | 10 | 250.2.d.d.201.1 | 8 | |||
25.6 | even | 5 | 50.2.d.b.11.2 | ✓ | 8 | ||
25.8 | odd | 20 | 250.2.e.c.199.4 | 16 | |||
25.17 | odd | 20 | 250.2.e.c.199.1 | 16 | |||
25.19 | even | 10 | 250.2.d.d.51.1 | 8 | |||
25.21 | even | 5 | 50.2.d.b.41.2 | yes | 8 | ||
25.22 | odd | 20 | 250.2.e.c.49.4 | 16 | |||
75.56 | odd | 10 | 450.2.h.e.361.1 | 8 | |||
75.71 | odd | 10 | 450.2.h.e.91.1 | 8 | |||
100.31 | odd | 10 | 400.2.u.d.161.1 | 8 | |||
100.71 | odd | 10 | 400.2.u.d.241.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.2.d.b.11.2 | ✓ | 8 | 25.6 | even | 5 | ||
50.2.d.b.41.2 | yes | 8 | 25.21 | even | 5 | ||
250.2.d.d.51.1 | 8 | 25.19 | even | 10 | |||
250.2.d.d.201.1 | 8 | 25.4 | even | 10 | |||
250.2.e.c.49.1 | 16 | 25.3 | odd | 20 | |||
250.2.e.c.49.4 | 16 | 25.22 | odd | 20 | |||
250.2.e.c.199.1 | 16 | 25.17 | odd | 20 | |||
250.2.e.c.199.4 | 16 | 25.8 | odd | 20 | |||
400.2.u.d.161.1 | 8 | 100.31 | odd | 10 | |||
400.2.u.d.241.1 | 8 | 100.71 | odd | 10 | |||
450.2.h.e.91.1 | 8 | 75.71 | odd | 10 | |||
450.2.h.e.361.1 | 8 | 75.56 | odd | 10 | |||
1250.2.a.f.1.2 | 4 | 5.4 | even | 2 | |||
1250.2.a.l.1.3 | 4 | 1.1 | even | 1 | trivial | ||
1250.2.b.e.1249.3 | 8 | 5.3 | odd | 4 | |||
1250.2.b.e.1249.6 | 8 | 5.2 | odd | 4 | |||
10000.2.a.t.1.2 | 4 | 4.3 | odd | 2 | |||
10000.2.a.x.1.3 | 4 | 20.19 | odd | 2 |