Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9522,2,Mod(1,9522)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9522, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9522.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9522.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: | \(76.0335528047\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | 10.10.52900342088704.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 18x^{8} + 123x^{6} - 390x^{4} + 548x^{2} - 241 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 414) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(2.32333\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9522.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.24774 | 1.89964 | 0.949822 | − | 0.312790i | \(-0.101263\pi\) | ||||
0.949822 | + | 0.312790i | \(0.101263\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.296223 | −0.111962 | −0.0559808 | − | 0.998432i | \(-0.517829\pi\) | ||||
−0.0559808 | + | 0.998432i | \(0.517829\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.24774 | 1.34325 | ||||||||
\(11\) | 2.39725 | 0.722799 | 0.361400 | − | 0.932411i | \(-0.382299\pi\) | ||||
0.361400 | + | 0.932411i | \(0.382299\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.51372 | 0.697181 | 0.348590 | − | 0.937275i | \(-0.386660\pi\) | ||||
0.348590 | + | 0.937275i | \(0.386660\pi\) | |||||||
\(14\) | −0.296223 | −0.0791688 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.50912 | 1.09362 | 0.546811 | − | 0.837256i | \(-0.315842\pi\) | ||||
0.546811 | + | 0.837256i | \(0.315842\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.13579 | 0.260569 | 0.130285 | − | 0.991477i | \(-0.458411\pi\) | ||||
0.130285 | + | 0.991477i | \(0.458411\pi\) | |||||||
\(20\) | 4.24774 | 0.949822 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.39725 | 0.511096 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.0433 | 2.60865 | ||||||||
\(26\) | 2.51372 | 0.492981 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.296223 | −0.0559808 | ||||||||
\(29\) | 0.957087 | 0.177727 | 0.0888633 | − | 0.996044i | \(-0.471677\pi\) | ||||
0.0888633 | + | 0.996044i | \(0.471677\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.24911 | 1.48158 | 0.740792 | − | 0.671735i | \(-0.234451\pi\) | ||||
0.740792 | + | 0.671735i | \(0.234451\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.50912 | 0.773308 | ||||||||
\(35\) | −1.25827 | −0.212687 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.34724 | −1.37228 | −0.686139 | − | 0.727470i | \(-0.740696\pi\) | ||||
−0.686139 | + | 0.727470i | \(0.740696\pi\) | |||||||
\(38\) | 1.13579 | 0.184250 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.24774 | 0.671626 | ||||||||
\(41\) | 4.10669 | 0.641357 | 0.320678 | − | 0.947188i | \(-0.396089\pi\) | ||||
0.320678 | + | 0.947188i | \(0.396089\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.86276 | −0.589066 | −0.294533 | − | 0.955641i | \(-0.595164\pi\) | ||||
−0.294533 | + | 0.955641i | \(0.595164\pi\) | |||||||
\(44\) | 2.39725 | 0.361400 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.35841 | 0.489874 | 0.244937 | − | 0.969539i | \(-0.421233\pi\) | ||||
0.244937 | + | 0.969539i | \(0.421233\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.91225 | −0.987465 | ||||||||
\(50\) | 13.0433 | 1.84459 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.51372 | 0.348590 | ||||||||
\(53\) | −4.84637 | −0.665701 | −0.332850 | − | 0.942980i | \(-0.608010\pi\) | ||||
−0.332850 | + | 0.942980i | \(0.608010\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.1829 | 1.37306 | ||||||||
\(56\) | −0.296223 | −0.0395844 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.957087 | 0.125672 | ||||||||
\(59\) | −11.3103 | −1.47248 | −0.736240 | − | 0.676720i | \(-0.763401\pi\) | ||||
−0.736240 | + | 0.676720i | \(0.763401\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.76531 | 0.994246 | 0.497123 | − | 0.867680i | \(-0.334390\pi\) | ||||
0.497123 | + | 0.867680i | \(0.334390\pi\) | |||||||
\(62\) | 8.24911 | 1.04764 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.6776 | 1.32440 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.1030 | −1.72296 | −0.861478 | − | 0.507795i | \(-0.830461\pi\) | ||||
−0.861478 | + | 0.507795i | \(0.830461\pi\) | |||||||
\(68\) | 4.50912 | 0.546811 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.25827 | −0.150393 | ||||||||
\(71\) | −14.7692 | −1.75279 | −0.876393 | − | 0.481597i | \(-0.840057\pi\) | ||||
−0.876393 | + | 0.481597i | \(0.840057\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.1912 | −1.30983 | −0.654915 | − | 0.755703i | \(-0.727296\pi\) | ||||
−0.654915 | + | 0.755703i | \(0.727296\pi\) | |||||||
\(74\) | −8.34724 | −0.970347 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.13579 | 0.130285 | ||||||||
\(77\) | −0.710121 | −0.0809258 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0724 | 1.35826 | 0.679128 | − | 0.734020i | \(-0.262358\pi\) | ||||
0.679128 | + | 0.734020i | \(0.262358\pi\) | |||||||
\(80\) | 4.24774 | 0.474911 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.10669 | 0.453508 | ||||||||
\(83\) | 2.12541 | 0.233295 | 0.116647 | − | 0.993173i | \(-0.462785\pi\) | ||||
0.116647 | + | 0.993173i | \(0.462785\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.1536 | 2.07749 | ||||||||
\(86\) | −3.86276 | −0.416532 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.39725 | 0.255548 | ||||||||
\(89\) | −11.4844 | −1.21735 | −0.608673 | − | 0.793421i | \(-0.708298\pi\) | ||||
−0.608673 | + | 0.793421i | \(0.708298\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.744621 | −0.0780575 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.35841 | 0.346393 | ||||||||
\(95\) | 4.82455 | 0.494989 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.795359 | −0.0807565 | −0.0403782 | − | 0.999184i | \(-0.512856\pi\) | ||||
−0.0403782 | + | 0.999184i | \(0.512856\pi\) | |||||||
\(98\) | −6.91225 | −0.698243 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 13.0433 | 1.30433 | ||||||||
\(101\) | −9.35035 | −0.930395 | −0.465197 | − | 0.885207i | \(-0.654017\pi\) | ||||
−0.465197 | + | 0.885207i | \(0.654017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.90643 | 0.976109 | 0.488055 | − | 0.872813i | \(-0.337707\pi\) | ||||
0.488055 | + | 0.872813i | \(0.337707\pi\) | |||||||
\(104\) | 2.51372 | 0.246491 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.84637 | −0.470722 | ||||||||
\(107\) | −18.4893 | −1.78743 | −0.893714 | − | 0.448637i | \(-0.851910\pi\) | ||||
−0.893714 | + | 0.448637i | \(0.851910\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.4814 | 1.57863 | 0.789314 | − | 0.613990i | \(-0.210436\pi\) | ||||
0.789314 | + | 0.613990i | \(0.210436\pi\) | |||||||
\(110\) | 10.1829 | 0.970901 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.296223 | −0.0279904 | ||||||||
\(113\) | −4.27218 | −0.401893 | −0.200946 | − | 0.979602i | \(-0.564402\pi\) | ||||
−0.200946 | + | 0.979602i | \(0.564402\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.957087 | 0.0888633 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.3103 | −1.04120 | ||||||||
\(119\) | −1.33570 | −0.122444 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.25317 | −0.477561 | ||||||||
\(122\) | 7.76531 | 0.703038 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.24911 | 0.740792 | ||||||||
\(125\) | 34.1656 | 3.05586 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.5281 | −1.20042 | −0.600210 | − | 0.799842i | \(-0.704917\pi\) | ||||
−0.600210 | + | 0.799842i | \(0.704917\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.6776 | 0.936489 | ||||||||
\(131\) | −13.1098 | −1.14541 | −0.572706 | − | 0.819761i | \(-0.694106\pi\) | ||||
−0.572706 | + | 0.819761i | \(0.694106\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.336448 | −0.0291737 | ||||||||
\(134\) | −14.1030 | −1.21831 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.50912 | 0.386654 | ||||||||
\(137\) | 1.26947 | 0.108458 | 0.0542291 | − | 0.998529i | \(-0.482730\pi\) | ||||
0.0542291 | + | 0.998529i | \(0.482730\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.5662 | −1.32031 | −0.660155 | − | 0.751129i | \(-0.729509\pi\) | ||||
−0.660155 | + | 0.751129i | \(0.729509\pi\) | |||||||
\(140\) | −1.25827 | −0.106344 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.7692 | −1.23941 | ||||||||
\(143\) | 6.02603 | 0.503922 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.06545 | 0.337617 | ||||||||
\(146\) | −11.1912 | −0.926189 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.34724 | −0.686139 | ||||||||
\(149\) | 13.6820 | 1.12087 | 0.560435 | − | 0.828198i | \(-0.310634\pi\) | ||||
0.560435 | + | 0.828198i | \(0.310634\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.65087 | 0.622619 | 0.311309 | − | 0.950309i | \(-0.399232\pi\) | ||||
0.311309 | + | 0.950309i | \(0.399232\pi\) | |||||||
\(152\) | 1.13579 | 0.0921251 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.710121 | −0.0572232 | ||||||||
\(155\) | 35.0400 | 2.81448 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.27528 | 0.580631 | 0.290315 | − | 0.956931i | \(-0.406240\pi\) | ||||
0.290315 | + | 0.956931i | \(0.406240\pi\) | |||||||
\(158\) | 12.0724 | 0.960433 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.24774 | 0.335813 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.6142 | 1.37965 | 0.689824 | − | 0.723977i | \(-0.257688\pi\) | ||||
0.689824 | + | 0.723977i | \(0.257688\pi\) | |||||||
\(164\) | 4.10669 | 0.320678 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.12541 | 0.164964 | ||||||||
\(167\) | 12.8331 | 0.993054 | 0.496527 | − | 0.868021i | \(-0.334608\pi\) | ||||
0.496527 | + | 0.868021i | \(0.334608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.68121 | −0.513939 | ||||||||
\(170\) | 19.1536 | 1.46901 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.86276 | −0.294533 | ||||||||
\(173\) | −9.24925 | −0.703208 | −0.351604 | − | 0.936149i | \(-0.614364\pi\) | ||||
−0.351604 | + | 0.936149i | \(0.614364\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.86371 | −0.292069 | ||||||||
\(176\) | 2.39725 | 0.180700 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.4844 | −0.860793 | ||||||||
\(179\) | −18.9994 | −1.42008 | −0.710042 | − | 0.704160i | \(-0.751324\pi\) | ||||
−0.710042 | + | 0.704160i | \(0.751324\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.61367 | 0.194272 | 0.0971362 | − | 0.995271i | \(-0.469032\pi\) | ||||
0.0971362 | + | 0.995271i | \(0.469032\pi\) | |||||||
\(182\) | −0.744621 | −0.0551950 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −35.4569 | −2.60684 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.8095 | 0.790470 | ||||||||
\(188\) | 3.35841 | 0.244937 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.82455 | 0.350010 | ||||||||
\(191\) | 5.90298 | 0.427125 | 0.213562 | − | 0.976929i | \(-0.431493\pi\) | ||||
0.213562 | + | 0.976929i | \(0.431493\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.350668 | 0.0252416 | 0.0126208 | − | 0.999920i | \(-0.495983\pi\) | ||||
0.0126208 | + | 0.999920i | \(0.495983\pi\) | |||||||
\(194\) | −0.795359 | −0.0571035 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.91225 | −0.493732 | ||||||||
\(197\) | 18.8533 | 1.34324 | 0.671621 | − | 0.740895i | \(-0.265598\pi\) | ||||
0.671621 | + | 0.740895i | \(0.265598\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.3425 | −1.15849 | −0.579243 | − | 0.815155i | \(-0.696652\pi\) | ||||
−0.579243 | + | 0.815155i | \(0.696652\pi\) | |||||||
\(200\) | 13.0433 | 0.922297 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.35035 | −0.657888 | ||||||||
\(203\) | −0.283511 | −0.0198986 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.4441 | 1.21835 | ||||||||
\(206\) | 9.90643 | 0.690213 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.51372 | 0.174295 | ||||||||
\(209\) | 2.72279 | 0.188339 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8129 | 0.950918 | 0.475459 | − | 0.879738i | \(-0.342282\pi\) | ||||
0.475459 | + | 0.879738i | \(0.342282\pi\) | |||||||
\(212\) | −4.84637 | −0.332850 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.4893 | −1.26390 | ||||||||
\(215\) | −16.4080 | −1.11902 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.44357 | −0.165880 | ||||||||
\(218\) | 16.4814 | 1.11626 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.1829 | 0.686531 | ||||||||
\(221\) | 11.3347 | 0.762453 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.66413 | 0.245368 | 0.122684 | − | 0.992446i | \(-0.460850\pi\) | ||||
0.122684 | + | 0.992446i | \(0.460850\pi\) | |||||||
\(224\) | −0.296223 | −0.0197922 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.27218 | −0.284181 | ||||||||
\(227\) | 0.0570530 | 0.00378674 | 0.00189337 | − | 0.999998i | \(-0.499397\pi\) | ||||
0.00189337 | + | 0.999998i | \(0.499397\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.13532 | 0.405433 | 0.202717 | − | 0.979237i | \(-0.435023\pi\) | ||||
0.202717 | + | 0.979237i | \(0.435023\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.957087 | 0.0628358 | ||||||||
\(233\) | 20.3085 | 1.33045 | 0.665227 | − | 0.746641i | \(-0.268335\pi\) | ||||
0.665227 | + | 0.746641i | \(0.268335\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.2656 | 0.930586 | ||||||||
\(236\) | −11.3103 | −0.736240 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.33570 | −0.0865808 | ||||||||
\(239\) | −3.65555 | −0.236458 | −0.118229 | − | 0.992986i | \(-0.537722\pi\) | ||||
−0.118229 | + | 0.992986i | \(0.537722\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7513 | −0.756970 | −0.378485 | − | 0.925607i | \(-0.623555\pi\) | ||||
−0.378485 | + | 0.925607i | \(0.623555\pi\) | |||||||
\(242\) | −5.25317 | −0.337687 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.76531 | 0.497123 | ||||||||
\(245\) | −29.3614 | −1.87583 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.85507 | 0.181664 | ||||||||
\(248\) | 8.24911 | 0.523819 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 34.1656 | 2.16082 | ||||||||
\(251\) | −1.89694 | −0.119734 | −0.0598668 | − | 0.998206i | \(-0.519068\pi\) | ||||
−0.0598668 | + | 0.998206i | \(0.519068\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −13.5281 | −0.848826 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.43775 | 0.339198 | 0.169599 | − | 0.985513i | \(-0.445753\pi\) | ||||
0.169599 | + | 0.985513i | \(0.445753\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.47264 | 0.153642 | ||||||||
\(260\) | 10.6776 | 0.662198 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.1098 | −0.809928 | ||||||||
\(263\) | 23.1887 | 1.42988 | 0.714940 | − | 0.699186i | \(-0.246454\pi\) | ||||
0.714940 | + | 0.699186i | \(0.246454\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.5861 | −1.26460 | ||||||||
\(266\) | −0.336448 | −0.0206289 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −14.1030 | −0.861478 | ||||||||
\(269\) | 5.34716 | 0.326022 | 0.163011 | − | 0.986624i | \(-0.447879\pi\) | ||||
0.163011 | + | 0.986624i | \(0.447879\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0856 | −0.977128 | −0.488564 | − | 0.872528i | \(-0.662479\pi\) | ||||
−0.488564 | + | 0.872528i | \(0.662479\pi\) | |||||||
\(272\) | 4.50912 | 0.273406 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.26947 | 0.0766915 | ||||||||
\(275\) | 31.2680 | 1.88553 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.44954 | 0.207263 | 0.103631 | − | 0.994616i | \(-0.466954\pi\) | ||||
0.103631 | + | 0.994616i | \(0.466954\pi\) | |||||||
\(278\) | −15.5662 | −0.933600 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.25827 | −0.0751963 | ||||||||
\(281\) | −6.43983 | −0.384168 | −0.192084 | − | 0.981378i | \(-0.561525\pi\) | ||||
−0.192084 | + | 0.981378i | \(0.561525\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.6630 | 0.693292 | 0.346646 | − | 0.937996i | \(-0.387321\pi\) | ||||
0.346646 | + | 0.937996i | \(0.387321\pi\) | |||||||
\(284\) | −14.7692 | −0.876393 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.02603 | 0.356326 | ||||||||
\(287\) | −1.21649 | −0.0718073 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.33217 | 0.196010 | ||||||||
\(290\) | 4.06545 | 0.238732 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.1912 | −0.654915 | ||||||||
\(293\) | 5.15331 | 0.301059 | 0.150530 | − | 0.988605i | \(-0.451902\pi\) | ||||
0.150530 | + | 0.988605i | \(0.451902\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −48.0433 | −2.79719 | ||||||||
\(296\) | −8.34724 | −0.485174 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.6820 | 0.792575 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.14424 | 0.0659527 | ||||||||
\(302\) | 7.65087 | 0.440258 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.13579 | 0.0651423 | ||||||||
\(305\) | 32.9850 | 1.88871 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.5307 | −0.886382 | −0.443191 | − | 0.896427i | \(-0.646154\pi\) | ||||
−0.443191 | + | 0.896427i | \(0.646154\pi\) | |||||||
\(308\) | −0.710121 | −0.0404629 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 35.0400 | 1.99014 | ||||||||
\(311\) | 7.59667 | 0.430767 | 0.215384 | − | 0.976529i | \(-0.430900\pi\) | ||||
0.215384 | + | 0.976529i | \(0.430900\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.1607 | 1.47869 | 0.739344 | − | 0.673328i | \(-0.235136\pi\) | ||||
0.739344 | + | 0.673328i | \(0.235136\pi\) | |||||||
\(314\) | 7.27528 | 0.410568 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.0724 | 0.679128 | ||||||||
\(317\) | 24.2042 | 1.35944 | 0.679720 | − | 0.733471i | \(-0.262101\pi\) | ||||
0.679720 | + | 0.733471i | \(0.262101\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.29438 | 0.128461 | ||||||||
\(320\) | 4.24774 | 0.237456 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.12143 | 0.284964 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 32.7871 | 1.81870 | ||||||||
\(326\) | 17.6142 | 0.975559 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.10669 | 0.226754 | ||||||||
\(329\) | −0.994835 | −0.0548470 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.4228 | −1.72716 | −0.863578 | − | 0.504216i | \(-0.831782\pi\) | ||||
−0.863578 | + | 0.504216i | \(0.831782\pi\) | |||||||
\(332\) | 2.12541 | 0.116647 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.8331 | 0.702195 | ||||||||
\(335\) | −59.9058 | −3.27300 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.72615 | 0.311923 | 0.155962 | − | 0.987763i | \(-0.450152\pi\) | ||||
0.155962 | + | 0.987763i | \(0.450152\pi\) | |||||||
\(338\) | −6.68121 | −0.363410 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 19.1536 | 1.03875 | ||||||||
\(341\) | 19.7752 | 1.07089 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.12112 | 0.222520 | ||||||||
\(344\) | −3.86276 | −0.208266 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.24925 | −0.497243 | ||||||||
\(347\) | −19.6762 | −1.05628 | −0.528138 | − | 0.849159i | \(-0.677110\pi\) | ||||
−0.528138 | + | 0.849159i | \(0.677110\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.20578 | 0.118073 | 0.0590364 | − | 0.998256i | \(-0.481197\pi\) | ||||
0.0590364 | + | 0.998256i | \(0.481197\pi\) | |||||||
\(350\) | −3.86371 | −0.206524 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.39725 | 0.127774 | ||||||||
\(353\) | −11.8417 | −0.630269 | −0.315134 | − | 0.949047i | \(-0.602050\pi\) | ||||
−0.315134 | + | 0.949047i | \(0.602050\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −62.7358 | −3.32967 | ||||||||
\(356\) | −11.4844 | −0.608673 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.9994 | −1.00415 | ||||||||
\(359\) | −22.8264 | −1.20473 | −0.602367 | − | 0.798219i | \(-0.705776\pi\) | ||||
−0.602367 | + | 0.798219i | \(0.705776\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7100 | −0.932104 | ||||||||
\(362\) | 2.61367 | 0.137371 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.744621 | −0.0390287 | ||||||||
\(365\) | −47.5372 | −2.48821 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.0634 | −1.56930 | −0.784649 | − | 0.619941i | \(-0.787157\pi\) | ||||
−0.784649 | + | 0.619941i | \(0.787157\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −35.4569 | −1.84331 | ||||||||
\(371\) | 1.43561 | 0.0745329 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.5853 | 1.63543 | 0.817713 | − | 0.575625i | \(-0.195241\pi\) | ||||
0.817713 | + | 0.575625i | \(0.195241\pi\) | |||||||
\(374\) | 10.8095 | 0.558946 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.35841 | 0.173197 | ||||||||
\(377\) | 2.40585 | 0.123908 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.6283 | −1.31644 | −0.658218 | − | 0.752828i | \(-0.728689\pi\) | ||||
−0.658218 | + | 0.752828i | \(0.728689\pi\) | |||||||
\(380\) | 4.82455 | 0.247494 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.90298 | 0.302023 | ||||||||
\(383\) | −22.8494 | −1.16755 | −0.583774 | − | 0.811916i | \(-0.698425\pi\) | ||||
−0.583774 | + | 0.811916i | \(0.698425\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.01640 | −0.153730 | ||||||||
\(386\) | 0.350668 | 0.0178485 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.795359 | −0.0403782 | ||||||||
\(389\) | 16.2740 | 0.825124 | 0.412562 | − | 0.910930i | \(-0.364634\pi\) | ||||
0.412562 | + | 0.910930i | \(0.364634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −6.91225 | −0.349121 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.8533 | 0.949816 | ||||||||
\(395\) | 51.2806 | 2.58021 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.21827 | −0.261897 | −0.130949 | − | 0.991389i | \(-0.541802\pi\) | ||||
−0.130949 | + | 0.991389i | \(0.541802\pi\) | |||||||
\(398\) | −16.3425 | −0.819173 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.0433 | 0.652163 | ||||||||
\(401\) | 8.21417 | 0.410196 | 0.205098 | − | 0.978741i | \(-0.434249\pi\) | ||||
0.205098 | + | 0.978741i | \(0.434249\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.7360 | 1.03293 | ||||||||
\(404\) | −9.35035 | −0.465197 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.283511 | −0.0140704 | ||||||||
\(407\) | −20.0105 | −0.991882 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.9872 | −1.68056 | −0.840280 | − | 0.542153i | \(-0.817609\pi\) | ||||
−0.840280 | + | 0.542153i | \(0.817609\pi\) | |||||||
\(410\) | 17.4441 | 0.861504 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.90643 | 0.488055 | ||||||||
\(413\) | 3.35038 | 0.164861 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.02820 | 0.443177 | ||||||||
\(416\) | 2.51372 | 0.123245 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.72279 | 0.133176 | ||||||||
\(419\) | 22.8282 | 1.11523 | 0.557615 | − | 0.830100i | \(-0.311717\pi\) | ||||
0.557615 | + | 0.830100i | \(0.311717\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.6661 | 0.812256 | 0.406128 | − | 0.913816i | \(-0.366879\pi\) | ||||
0.406128 | + | 0.913816i | \(0.366879\pi\) | |||||||
\(422\) | 13.8129 | 0.672400 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.84637 | −0.235361 | ||||||||
\(425\) | 58.8136 | 2.85288 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.30026 | −0.111317 | ||||||||
\(428\) | −18.4893 | −0.893714 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −16.4080 | −0.791264 | ||||||||
\(431\) | 20.3455 | 0.980008 | 0.490004 | − | 0.871720i | \(-0.336995\pi\) | ||||
0.490004 | + | 0.871720i | \(0.336995\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.1178 | −1.39931 | −0.699655 | − | 0.714481i | \(-0.746663\pi\) | ||||
−0.699655 | + | 0.714481i | \(0.746663\pi\) | |||||||
\(434\) | −2.44357 | −0.117295 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.4814 | 0.789314 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.6105 | −0.935957 | −0.467979 | − | 0.883740i | \(-0.655018\pi\) | ||||
−0.467979 | + | 0.883740i | \(0.655018\pi\) | |||||||
\(440\) | 10.1829 | 0.485451 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.3347 | 0.539135 | ||||||||
\(443\) | −8.63954 | −0.410477 | −0.205238 | − | 0.978712i | \(-0.565797\pi\) | ||||
−0.205238 | + | 0.978712i | \(0.565797\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −48.7828 | −2.31252 | ||||||||
\(446\) | 3.66413 | 0.173502 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.296223 | −0.0139952 | ||||||||
\(449\) | 22.2983 | 1.05232 | 0.526161 | − | 0.850385i | \(-0.323631\pi\) | ||||
0.526161 | + | 0.850385i | \(0.323631\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.84477 | 0.463572 | ||||||||
\(452\) | −4.27218 | −0.200946 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.0570530 | 0.00267763 | ||||||||
\(455\) | −3.16295 | −0.148281 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.42721 | 0.160318 | 0.0801591 | − | 0.996782i | \(-0.474457\pi\) | ||||
0.0801591 | + | 0.996782i | \(0.474457\pi\) | |||||||
\(458\) | 6.13532 | 0.286685 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.9575 | −1.34869 | −0.674344 | − | 0.738418i | \(-0.735573\pi\) | ||||
−0.674344 | + | 0.738418i | \(0.735573\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.09325 | 0.422599 | 0.211299 | − | 0.977421i | \(-0.432230\pi\) | ||||
0.211299 | + | 0.977421i | \(0.432230\pi\) | |||||||
\(464\) | 0.957087 | 0.0444317 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.3085 | 0.940773 | ||||||||
\(467\) | 20.9454 | 0.969238 | 0.484619 | − | 0.874725i | \(-0.338958\pi\) | ||||
0.484619 | + | 0.874725i | \(0.338958\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.17763 | 0.192905 | ||||||||
\(470\) | 14.2656 | 0.658024 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.3103 | −0.520601 | ||||||||
\(473\) | −9.26002 | −0.425776 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.8145 | 0.679734 | ||||||||
\(476\) | −1.33570 | −0.0612219 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.65555 | −0.167201 | ||||||||
\(479\) | −9.92872 | −0.453655 | −0.226827 | − | 0.973935i | \(-0.572835\pi\) | ||||
−0.226827 | + | 0.973935i | \(0.572835\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.9826 | −0.956726 | ||||||||
\(482\) | −11.7513 | −0.535259 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.25317 | −0.238781 | ||||||||
\(485\) | −3.37848 | −0.153409 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.0194 | −0.680595 | −0.340298 | − | 0.940318i | \(-0.610528\pi\) | ||||
−0.340298 | + | 0.940318i | \(0.610528\pi\) | |||||||
\(488\) | 7.76531 | 0.351519 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −29.3614 | −1.32641 | ||||||||
\(491\) | 4.08834 | 0.184504 | 0.0922522 | − | 0.995736i | \(-0.470593\pi\) | ||||
0.0922522 | + | 0.995736i | \(0.470593\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.31562 | 0.194366 | ||||||||
\(494\) | 2.85507 | 0.128456 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.24911 | 0.370396 | ||||||||
\(497\) | 4.37498 | 0.196245 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.0954 | −0.675763 | −0.337881 | − | 0.941189i | \(-0.609710\pi\) | ||||
−0.337881 | + | 0.941189i | \(0.609710\pi\) | |||||||
\(500\) | 34.1656 | 1.52793 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.89694 | −0.0846644 | ||||||||
\(503\) | 33.3581 | 1.48736 | 0.743681 | − | 0.668534i | \(-0.233078\pi\) | ||||
0.743681 | + | 0.668534i | \(0.233078\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.7178 | −1.76742 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.5281 | −0.600210 | ||||||||
\(509\) | 33.1267 | 1.46832 | 0.734158 | − | 0.678979i | \(-0.237577\pi\) | ||||
0.734158 | + | 0.678979i | \(0.237577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.31508 | 0.146651 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.43775 | 0.239849 | ||||||||
\(515\) | 42.0799 | 1.85426 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.05095 | 0.354080 | ||||||||
\(518\) | 2.47264 | 0.108642 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.6776 | 0.468245 | ||||||||
\(521\) | 13.8143 | 0.605214 | 0.302607 | − | 0.953115i | \(-0.402143\pi\) | ||||
0.302607 | + | 0.953115i | \(0.402143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0204 | 0.700524 | 0.350262 | − | 0.936652i | \(-0.386093\pi\) | ||||
0.350262 | + | 0.936652i | \(0.386093\pi\) | |||||||
\(524\) | −13.1098 | −0.572706 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.1887 | 1.01108 | ||||||||
\(527\) | 37.1962 | 1.62029 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −20.5861 | −0.894204 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.336448 | −0.0145869 | ||||||||
\(533\) | 10.3231 | 0.447142 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −78.5377 | −3.39548 | ||||||||
\(536\) | −14.1030 | −0.609157 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.34716 | 0.230532 | ||||||||
\(539\) | −16.5704 | −0.713739 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.0153 | −0.516579 | −0.258289 | − | 0.966068i | \(-0.583159\pi\) | ||||
−0.258289 | + | 0.966068i | \(0.583159\pi\) | |||||||
\(542\) | −16.0856 | −0.690934 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.50912 | 0.193327 | ||||||||
\(545\) | 70.0084 | 2.99883 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.6869 | 1.26932 | 0.634661 | − | 0.772791i | \(-0.281140\pi\) | ||||
0.634661 | + | 0.772791i | \(0.281140\pi\) | |||||||
\(548\) | 1.26947 | 0.0542291 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 31.2680 | 1.33327 | ||||||||
\(551\) | 1.08705 | 0.0463101 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.57613 | −0.152073 | ||||||||
\(554\) | 3.44954 | 0.146557 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.5662 | −0.660155 | ||||||||
\(557\) | 30.1816 | 1.27883 | 0.639417 | − | 0.768860i | \(-0.279176\pi\) | ||||
0.639417 | + | 0.768860i | \(0.279176\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.70991 | −0.410685 | ||||||||
\(560\) | −1.25827 | −0.0531718 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.43983 | −0.271648 | ||||||||
\(563\) | 2.17257 | 0.0915630 | 0.0457815 | − | 0.998951i | \(-0.485422\pi\) | ||||
0.0457815 | + | 0.998951i | \(0.485422\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.1471 | −0.763454 | ||||||||
\(566\) | 11.6630 | 0.490231 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.7692 | −0.619703 | ||||||||
\(569\) | 2.10059 | 0.0880614 | 0.0440307 | − | 0.999030i | \(-0.485980\pi\) | ||||
0.0440307 | + | 0.999030i | \(0.485980\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.2711 | 1.39235 | 0.696177 | − | 0.717871i | \(-0.254883\pi\) | ||||
0.696177 | + | 0.717871i | \(0.254883\pi\) | |||||||
\(572\) | 6.02603 | 0.251961 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.21649 | −0.0507754 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.58875 | −0.149402 | −0.0747008 | − | 0.997206i | \(-0.523800\pi\) | ||||
−0.0747008 | + | 0.997206i | \(0.523800\pi\) | |||||||
\(578\) | 3.33217 | 0.138600 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.06545 | 0.168809 | ||||||||
\(581\) | −0.629596 | −0.0261200 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.6180 | −0.481168 | ||||||||
\(584\) | −11.1912 | −0.463095 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.15331 | 0.212881 | ||||||||
\(587\) | −37.5313 | −1.54908 | −0.774541 | − | 0.632524i | \(-0.782019\pi\) | ||||
−0.774541 | + | 0.632524i | \(0.782019\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.36929 | 0.386055 | ||||||||
\(590\) | −48.0433 | −1.97791 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.34724 | −0.343069 | ||||||||
\(593\) | 20.9062 | 0.858515 | 0.429258 | − | 0.903182i | \(-0.358775\pi\) | ||||
0.429258 | + | 0.903182i | \(0.358775\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.67371 | −0.232600 | ||||||||
\(596\) | 13.6820 | 0.560435 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.81949 | 0.115201 | 0.0576007 | − | 0.998340i | \(-0.481655\pi\) | ||||
0.0576007 | + | 0.998340i | \(0.481655\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.7258 | 1.21254 | 0.606269 | − | 0.795259i | \(-0.292665\pi\) | ||||
0.606269 | + | 0.795259i | \(0.292665\pi\) | |||||||
\(602\) | 1.14424 | 0.0466356 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.65087 | 0.311309 | ||||||||
\(605\) | −22.3141 | −0.907197 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.9379 | −0.931021 | −0.465511 | − | 0.885042i | \(-0.654129\pi\) | ||||
−0.465511 | + | 0.885042i | \(0.654129\pi\) | |||||||
\(608\) | 1.13579 | 0.0460625 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 32.9850 | 1.33552 | ||||||||
\(611\) | 8.44209 | 0.341531 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.7781 | −1.08156 | −0.540779 | − | 0.841164i | \(-0.681871\pi\) | ||||
−0.540779 | + | 0.841164i | \(0.681871\pi\) | |||||||
\(614\) | −15.5307 | −0.626766 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.710121 | −0.0286116 | ||||||||
\(617\) | −34.1884 | −1.37637 | −0.688187 | − | 0.725533i | \(-0.741593\pi\) | ||||
−0.688187 | + | 0.725533i | \(0.741593\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.18439 | 0.328958 | 0.164479 | − | 0.986381i | \(-0.447406\pi\) | ||||
0.164479 | + | 0.986381i | \(0.447406\pi\) | |||||||
\(620\) | 35.0400 | 1.40724 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.59667 | 0.304599 | ||||||||
\(623\) | 3.40194 | 0.136296 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 79.9102 | 3.19641 | ||||||||
\(626\) | 26.1607 | 1.04559 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.27528 | 0.290315 | ||||||||
\(629\) | −37.6387 | −1.50075 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.1546 | 1.47910 | 0.739550 | − | 0.673102i | \(-0.235038\pi\) | ||||
0.739550 | + | 0.673102i | \(0.235038\pi\) | |||||||
\(632\) | 12.0724 | 0.480216 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.2042 | 0.961270 | ||||||||
\(635\) | −57.4636 | −2.28037 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.3755 | −0.688441 | ||||||||
\(638\) | 2.29438 | 0.0908354 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.24774 | 0.167906 | ||||||||
\(641\) | 2.08457 | 0.0823357 | 0.0411679 | − | 0.999152i | \(-0.486892\pi\) | ||||
0.0411679 | + | 0.999152i | \(0.486892\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.7677 | 1.52885 | 0.764424 | − | 0.644713i | \(-0.223023\pi\) | ||||
0.764424 | + | 0.644713i | \(0.223023\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.12143 | 0.201500 | ||||||||
\(647\) | 7.60261 | 0.298889 | 0.149445 | − | 0.988770i | \(-0.452251\pi\) | ||||
0.149445 | + | 0.988770i | \(0.452251\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.1138 | −1.06431 | ||||||||
\(650\) | 32.7871 | 1.28602 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.6142 | 0.689824 | ||||||||
\(653\) | 9.86403 | 0.386009 | 0.193005 | − | 0.981198i | \(-0.438177\pi\) | ||||
0.193005 | + | 0.981198i | \(0.438177\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −55.6871 | −2.17587 | ||||||||
\(656\) | 4.10669 | 0.160339 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.994835 | −0.0387827 | ||||||||
\(659\) | −18.2003 | −0.708981 | −0.354491 | − | 0.935060i | \(-0.615346\pi\) | ||||
−0.354491 | + | 0.935060i | \(0.615346\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.1697 | −0.434451 | −0.217226 | − | 0.976121i | \(-0.569701\pi\) | ||||
−0.217226 | + | 0.976121i | \(0.569701\pi\) | |||||||
\(662\) | −31.4228 | −1.22128 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.12541 | 0.0824821 | ||||||||
\(665\) | −1.42914 | −0.0554197 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 12.8331 | 0.496527 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −59.9058 | −2.31436 | ||||||||
\(671\) | 18.6154 | 0.718640 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.7021 | 1.53040 | 0.765201 | − | 0.643792i | \(-0.222640\pi\) | ||||
0.765201 | + | 0.643792i | \(0.222640\pi\) | |||||||
\(674\) | 5.72615 | 0.220563 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.68121 | −0.256970 | ||||||||
\(677\) | −7.95806 | −0.305853 | −0.152926 | − | 0.988238i | \(-0.548870\pi\) | ||||
−0.152926 | + | 0.988238i | \(0.548870\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.235603 | 0.00904162 | ||||||||
\(680\) | 19.1536 | 0.734505 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19.7752 | 0.757232 | ||||||||
\(683\) | −17.4650 | −0.668280 | −0.334140 | − | 0.942523i | \(-0.608446\pi\) | ||||
−0.334140 | + | 0.942523i | \(0.608446\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.39237 | 0.206032 | ||||||||
\(686\) | 4.12112 | 0.157345 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.86276 | −0.147266 | ||||||||
\(689\) | −12.1824 | −0.464114 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.4115 | −0.548240 | −0.274120 | − | 0.961696i | \(-0.588386\pi\) | ||||
−0.274120 | + | 0.961696i | \(0.588386\pi\) | |||||||
\(692\) | −9.24925 | −0.351604 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.6762 | −0.746900 | ||||||||
\(695\) | −66.1212 | −2.50812 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.5175 | 0.701402 | ||||||||
\(698\) | 2.20578 | 0.0834901 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.86371 | −0.146034 | ||||||||
\(701\) | 27.1514 | 1.02550 | 0.512748 | − | 0.858539i | \(-0.328628\pi\) | ||||
0.512748 | + | 0.858539i | \(0.328628\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.48075 | −0.357573 | ||||||||
\(704\) | 2.39725 | 0.0903499 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.8417 | −0.445667 | ||||||||
\(707\) | 2.76978 | 0.104168 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.8838 | 0.558972 | 0.279486 | − | 0.960150i | \(-0.409836\pi\) | ||||
0.279486 | + | 0.960150i | \(0.409836\pi\) | |||||||
\(710\) | −62.7358 | −2.35443 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.4844 | −0.430397 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25.5970 | 0.957272 | ||||||||
\(716\) | −18.9994 | −0.710042 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.8264 | −0.851876 | ||||||||
\(719\) | 3.29160 | 0.122756 | 0.0613780 | − | 0.998115i | \(-0.480450\pi\) | ||||
0.0613780 | + | 0.998115i | \(0.480450\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.93451 | −0.109287 | ||||||||
\(722\) | −17.7100 | −0.659097 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.61367 | 0.0971362 | ||||||||
\(725\) | 12.4835 | 0.463627 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.1610 | −1.19279 | −0.596393 | − | 0.802693i | \(-0.703400\pi\) | ||||
−0.596393 | + | 0.802693i | \(0.703400\pi\) | |||||||
\(728\) | −0.744621 | −0.0275975 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −47.5372 | −1.75943 | ||||||||
\(731\) | −17.4177 | −0.644216 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −52.0402 | −1.92215 | −0.961074 | − | 0.276291i | \(-0.910895\pi\) | ||||
−0.961074 | + | 0.276291i | \(0.910895\pi\) | |||||||
\(734\) | −30.0634 | −1.10966 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −33.8085 | −1.24535 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.5749 | −0.609717 | −0.304859 | − | 0.952398i | \(-0.598609\pi\) | ||||
−0.304859 | + | 0.952398i | \(0.598609\pi\) | |||||||
\(740\) | −35.4569 | −1.30342 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.43561 | 0.0527027 | ||||||||
\(743\) | 9.13697 | 0.335203 | 0.167601 | − | 0.985855i | \(-0.446398\pi\) | ||||
0.167601 | + | 0.985855i | \(0.446398\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 58.1173 | 2.12925 | ||||||||
\(746\) | 31.5853 | 1.15642 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.8095 | 0.395235 | ||||||||
\(749\) | 5.47695 | 0.200123 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.0794 | −1.53550 | −0.767750 | − | 0.640750i | \(-0.778624\pi\) | ||||
−0.767750 | + | 0.640750i | \(0.778624\pi\) | |||||||
\(752\) | 3.35841 | 0.122468 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.40585 | 0.0876159 | ||||||||
\(755\) | 32.4989 | 1.18275 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.58553 | −0.275701 | −0.137850 | − | 0.990453i | \(-0.544019\pi\) | ||||
−0.137850 | + | 0.990453i | \(0.544019\pi\) | |||||||
\(758\) | −25.6283 | −0.930860 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.82455 | 0.175005 | ||||||||
\(761\) | −46.0739 | −1.67018 | −0.835089 | − | 0.550115i | \(-0.814584\pi\) | ||||
−0.835089 | + | 0.550115i | \(0.814584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.88215 | −0.176746 | ||||||||
\(764\) | 5.90298 | 0.213562 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.8494 | −0.825581 | ||||||||
\(767\) | −28.4310 | −1.02659 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.3780 | 0.446364 | 0.223182 | − | 0.974777i | \(-0.428356\pi\) | ||||
0.223182 | + | 0.974777i | \(0.428356\pi\) | |||||||
\(770\) | −3.01640 | −0.108704 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.350668 | 0.0126208 | ||||||||
\(773\) | 46.1635 | 1.66038 | 0.830192 | − | 0.557477i | \(-0.188231\pi\) | ||||
0.830192 | + | 0.557477i | \(0.188231\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 107.595 | 3.86493 | ||||||||
\(776\) | −0.795359 | −0.0285517 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.2740 | 0.583451 | ||||||||
\(779\) | 4.66435 | 0.167118 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.4056 | −1.26691 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.91225 | −0.246866 | ||||||||
\(785\) | 30.9035 | 1.10299 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.7894 | 0.455893 | 0.227946 | − | 0.973674i | \(-0.426799\pi\) | ||||
0.227946 | + | 0.973674i | \(0.426799\pi\) | |||||||
\(788\) | 18.8533 | 0.671621 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 51.2806 | 1.82448 | ||||||||
\(791\) | 1.26552 | 0.0449966 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.5198 | 0.693169 | ||||||||
\(794\) | −5.21827 | −0.185189 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.3425 | −0.579243 | ||||||||
\(797\) | 17.8798 | 0.633334 | 0.316667 | − | 0.948537i | \(-0.397436\pi\) | ||||
0.316667 | + | 0.948537i | \(0.397436\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.1435 | 0.535737 | ||||||||
\(800\) | 13.0433 | 0.461149 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.21417 | 0.290052 | ||||||||
\(803\) | −26.8281 | −0.946744 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.7360 | 0.730393 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.35035 | −0.328944 | ||||||||
\(809\) | 37.7595 | 1.32755 | 0.663776 | − | 0.747931i | \(-0.268953\pi\) | ||||
0.663776 | + | 0.747931i | \(0.268953\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.3002 | 0.747950 | 0.373975 | − | 0.927439i | \(-0.377995\pi\) | ||||
0.373975 | + | 0.927439i | \(0.377995\pi\) | |||||||
\(812\) | −0.283511 | −0.00994928 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.0105 | −0.701366 | ||||||||
\(815\) | 74.8204 | 2.62084 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.38730 | −0.153492 | ||||||||
\(818\) | −33.9872 | −1.18834 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.4441 | 0.609175 | ||||||||
\(821\) | 7.82220 | 0.272997 | 0.136498 | − | 0.990640i | \(-0.456415\pi\) | ||||
0.136498 | + | 0.990640i | \(0.456415\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.0399456 | 0.00139242 | 0.000696208 | − | 1.00000i | \(-0.499778\pi\) | ||||
0.000696208 | 1.00000i | \(0.499778\pi\) | ||||||||
\(824\) | 9.90643 | 0.345107 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.35038 | 0.116575 | ||||||||
\(827\) | 35.9303 | 1.24942 | 0.624710 | − | 0.780857i | \(-0.285217\pi\) | ||||
0.624710 | + | 0.780857i | \(0.285217\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.7357 | 0.407597 | 0.203799 | − | 0.979013i | \(-0.434671\pi\) | ||||
0.203799 | + | 0.979013i | \(0.434671\pi\) | |||||||
\(830\) | 9.02820 | 0.313373 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.51372 | 0.0871476 | ||||||||
\(833\) | −31.1682 | −1.07991 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54.5115 | 1.88645 | ||||||||
\(836\) | 2.72279 | 0.0941696 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.8282 | 0.788586 | ||||||||
\(839\) | −54.3029 | −1.87475 | −0.937373 | − | 0.348328i | \(-0.886749\pi\) | ||||
−0.937373 | + | 0.348328i | \(0.886749\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0840 | −0.968413 | ||||||||
\(842\) | 16.6661 | 0.574352 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.8129 | 0.475459 | ||||||||
\(845\) | −28.3800 | −0.976302 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.55611 | 0.0534685 | ||||||||
\(848\) | −4.84637 | −0.166425 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 58.8136 | 2.01729 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.1406 | 1.51135 | 0.755673 | − | 0.654949i | \(-0.227310\pi\) | ||||
0.755673 | + | 0.654949i | \(0.227310\pi\) | |||||||
\(854\) | −2.30026 | −0.0787132 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.4893 | −0.631951 | ||||||||
\(857\) | −25.1720 | −0.859860 | −0.429930 | − | 0.902862i | \(-0.641462\pi\) | ||||
−0.429930 | + | 0.902862i | \(0.641462\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.2254 | 0.587722 | 0.293861 | − | 0.955848i | \(-0.405060\pi\) | ||||
0.293861 | + | 0.955848i | \(0.405060\pi\) | |||||||
\(860\) | −16.4080 | −0.559508 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.3455 | 0.692971 | ||||||||
\(863\) | 37.7817 | 1.28610 | 0.643052 | − | 0.765823i | \(-0.277668\pi\) | ||||
0.643052 | + | 0.765823i | \(0.277668\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.2884 | −1.33585 | ||||||||
\(866\) | −29.1178 | −0.989462 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.44357 | −0.0829402 | ||||||||
\(869\) | 28.9407 | 0.981747 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.4510 | −1.20121 | ||||||||
\(872\) | 16.4814 | 0.558129 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.1206 | −0.342139 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −57.5016 | −1.94169 | −0.970845 | − | 0.239708i | \(-0.922948\pi\) | ||||
−0.970845 | + | 0.239708i | \(0.922948\pi\) | |||||||
\(878\) | −19.6105 | −0.661822 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.1829 | 0.343265 | ||||||||
\(881\) | 33.9249 | 1.14296 | 0.571479 | − | 0.820616i | \(-0.306370\pi\) | ||||
0.571479 | + | 0.820616i | \(0.306370\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.3770 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(884\) | 11.3347 | 0.381226 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.63954 | −0.290251 | ||||||||
\(887\) | −7.10730 | −0.238640 | −0.119320 | − | 0.992856i | \(-0.538071\pi\) | ||||
−0.119320 | + | 0.992856i | \(0.538071\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.00732 | 0.134401 | ||||||||
\(890\) | −48.7828 | −1.63520 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.66413 | 0.122684 | ||||||||
\(893\) | 3.81446 | 0.127646 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −80.7045 | −2.69765 | ||||||||
\(896\) | −0.296223 | −0.00989610 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.2983 | 0.744104 | ||||||||
\(899\) | 7.89511 | 0.263317 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.8529 | −0.728025 | ||||||||
\(902\) | 9.84477 | 0.327795 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.27218 | −0.142091 | ||||||||
\(905\) | 11.1022 | 0.369048 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.9535 | 0.961386 | 0.480693 | − | 0.876889i | \(-0.340385\pi\) | ||||
0.480693 | + | 0.876889i | \(0.340385\pi\) | |||||||
\(908\) | 0.0570530 | 0.00189337 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.16295 | −0.104851 | ||||||||
\(911\) | −3.10995 | −0.103037 | −0.0515186 | − | 0.998672i | \(-0.516406\pi\) | ||||
−0.0515186 | + | 0.998672i | \(0.516406\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.09516 | 0.168625 | ||||||||
\(914\) | 3.42721 | 0.113362 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.13532 | 0.202717 | ||||||||
\(917\) | 3.88343 | 0.128242 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.9768 | −0.494038 | −0.247019 | − | 0.969011i | \(-0.579451\pi\) | ||||
−0.247019 | + | 0.969011i | \(0.579451\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28.9575 | −0.953666 | ||||||||
\(923\) | −37.1257 | −1.22201 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −108.875 | −3.57979 | ||||||||
\(926\) | 9.09325 | 0.298823 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.957087 | 0.0314179 | ||||||||
\(929\) | 31.9251 | 1.04743 | 0.523715 | − | 0.851893i | \(-0.324546\pi\) | ||||
0.523715 | + | 0.851893i | \(0.324546\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.85090 | −0.257303 | ||||||||
\(932\) | 20.3085 | 0.665227 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.9454 | 0.685355 | ||||||||
\(935\) | 45.9159 | 1.50161 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.6312 | −0.706661 | −0.353330 | − | 0.935499i | \(-0.614951\pi\) | ||||
−0.353330 | + | 0.935499i | \(0.614951\pi\) | |||||||
\(938\) | 4.17763 | 0.136404 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 14.2656 | 0.465293 | ||||||||
\(941\) | 2.95773 | 0.0964193 | 0.0482097 | − | 0.998837i | \(-0.484648\pi\) | ||||
0.0482097 | + | 0.998837i | \(0.484648\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −11.3103 | −0.368120 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.26002 | −0.301069 | ||||||||
\(947\) | −1.61057 | −0.0523364 | −0.0261682 | − | 0.999658i | \(-0.508331\pi\) | ||||
−0.0261682 | + | 0.999658i | \(0.508331\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.1315 | −0.913188 | ||||||||
\(950\) | 14.8145 | 0.480644 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.33570 | −0.0432904 | ||||||||
\(953\) | −31.4202 | −1.01780 | −0.508899 | − | 0.860826i | \(-0.669947\pi\) | ||||
−0.508899 | + | 0.860826i | \(0.669947\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.0743 | 0.811385 | ||||||||
\(956\) | −3.65555 | −0.118229 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.92872 | −0.320782 | ||||||||
\(959\) | −0.376046 | −0.0121431 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.0478 | 1.19509 | ||||||||
\(962\) | −20.9826 | −0.676507 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.7513 | −0.378485 | ||||||||
\(965\) | 1.48955 | 0.0479502 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.2718 | 0.491108 | 0.245554 | − | 0.969383i | \(-0.421030\pi\) | ||||
0.245554 | + | 0.969383i | \(0.421030\pi\) | |||||||
\(968\) | −5.25317 | −0.168843 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.37848 | −0.108476 | ||||||||
\(971\) | −25.7653 | −0.826848 | −0.413424 | − | 0.910539i | \(-0.635667\pi\) | ||||
−0.413424 | + | 0.910539i | \(0.635667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.61107 | 0.147824 | ||||||||
\(974\) | −15.0194 | −0.481253 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.76531 | 0.248561 | ||||||||
\(977\) | 8.88263 | 0.284180 | 0.142090 | − | 0.989854i | \(-0.454618\pi\) | ||||
0.142090 | + | 0.989854i | \(0.454618\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.5311 | −0.879897 | ||||||||
\(980\) | −29.3614 | −0.937916 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.08834 | 0.130464 | ||||||||
\(983\) | 3.56769 | 0.113792 | 0.0568959 | − | 0.998380i | \(-0.481880\pi\) | ||||
0.0568959 | + | 0.998380i | \(0.481880\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 80.0838 | 2.55168 | ||||||||
\(986\) | 4.31562 | 0.137437 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.85507 | 0.0908319 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.467875 | 0.0148625 | 0.00743127 | − | 0.999972i | \(-0.497635\pi\) | ||||
0.00743127 | + | 0.999972i | \(0.497635\pi\) | |||||||
\(992\) | 8.24911 | 0.261909 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.37498 | 0.138766 | ||||||||
\(995\) | −69.4184 | −2.20071 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.2383 | 0.514273 | 0.257137 | − | 0.966375i | \(-0.417221\pi\) | ||||
0.257137 | + | 0.966375i | \(0.417221\pi\) | |||||||
\(998\) | −15.0954 | −0.477836 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9522.2.a.cj.1.10 | 10 | ||
3.2 | odd | 2 | 9522.2.a.cg.1.1 | 10 | |||
23.2 | even | 11 | 414.2.i.g.73.2 | ✓ | 20 | ||
23.12 | even | 11 | 414.2.i.g.397.2 | yes | 20 | ||
23.22 | odd | 2 | 9522.2.a.ci.1.1 | 10 | |||
69.2 | odd | 22 | 414.2.i.h.73.1 | yes | 20 | ||
69.35 | odd | 22 | 414.2.i.h.397.1 | yes | 20 | ||
69.68 | even | 2 | 9522.2.a.ch.1.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
414.2.i.g.73.2 | ✓ | 20 | 23.2 | even | 11 | ||
414.2.i.g.397.2 | yes | 20 | 23.12 | even | 11 | ||
414.2.i.h.73.1 | yes | 20 | 69.2 | odd | 22 | ||
414.2.i.h.397.1 | yes | 20 | 69.35 | odd | 22 | ||
9522.2.a.cg.1.1 | 10 | 3.2 | odd | 2 | |||
9522.2.a.ch.1.10 | 10 | 69.68 | even | 2 | |||
9522.2.a.ci.1.1 | 10 | 23.22 | odd | 2 | |||
9522.2.a.cj.1.10 | 10 | 1.1 | even | 1 | trivial |