Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2008,2,Mod(1,2008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2008 = 2^{3} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2008.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: | \(16.0339607259\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 2008.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.21536 | −1.27904 | −0.639520 | − | 0.768774i | \(-0.720867\pi\) | ||||
−0.639520 | + | 0.768774i | \(0.720867\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.09704 | 1.38504 | 0.692519 | − | 0.721400i | \(-0.256501\pi\) | ||||
0.692519 | + | 0.721400i | \(0.256501\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.67984 | −1.76881 | −0.884407 | − | 0.466716i | \(-0.845437\pi\) | ||||
−0.884407 | + | 0.466716i | \(0.845437\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.90784 | 0.635946 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.76411 | −1.43643 | −0.718217 | − | 0.695819i | \(-0.755041\pi\) | ||||
−0.718217 | + | 0.695819i | \(0.755041\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.18229 | −1.15996 | −0.579980 | − | 0.814631i | \(-0.696940\pi\) | ||||
−0.579980 | + | 0.814631i | \(0.696940\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.86107 | −1.77152 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.76575 | −0.670792 | −0.335396 | − | 0.942077i | \(-0.608870\pi\) | ||||
−0.335396 | + | 0.942077i | \(0.608870\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.43902 | −1.01838 | −0.509190 | − | 0.860654i | \(-0.670055\pi\) | ||||
−0.509190 | + | 0.860654i | \(0.670055\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.3676 | 2.26239 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.88455 | 1.85256 | 0.926279 | − | 0.376840i | \(-0.122989\pi\) | ||||
0.926279 | + | 0.376840i | \(0.122989\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.59165 | 0.918331 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.41954 | 0.465640 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.14992 | 0.399231 | 0.199615 | − | 0.979874i | \(-0.436031\pi\) | ||||
0.199615 | + | 0.979874i | \(0.436031\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.46623 | 1.34098 | 0.670488 | − | 0.741921i | \(-0.266085\pi\) | ||||
0.670488 | + | 0.741921i | \(0.266085\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.5542 | 1.83726 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −14.4937 | −2.44988 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.30620 | 1.52993 | 0.764965 | − | 0.644072i | \(-0.222756\pi\) | ||||
0.764965 | + | 0.644072i | \(0.222756\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.26530 | 1.48364 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.39778 | −1.31151 | −0.655756 | − | 0.754973i | \(-0.727650\pi\) | ||||
−0.655756 | + | 0.754973i | \(0.727650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.77980 | −0.576413 | −0.288207 | − | 0.957568i | \(-0.593059\pi\) | ||||
−0.288207 | + | 0.957568i | \(0.593059\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.90865 | 0.880809 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.41612 | −0.498293 | −0.249146 | − | 0.968466i | \(-0.580150\pi\) | ||||
−0.249146 | + | 0.968466i | \(0.580150\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.9009 | 2.12870 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.12714 | 0.857971 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.5655 | 1.58865 | 0.794323 | − | 0.607496i | \(-0.207826\pi\) | ||||
0.794323 | + | 0.607496i | \(0.207826\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.7546 | −1.98952 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.83404 | 1.30255 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.620556 | 0.0807895 | 0.0403947 | − | 0.999184i | \(-0.487138\pi\) | ||||
0.0403947 | + | 0.999184i | \(0.487138\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.0665 | −1.41692 | −0.708460 | − | 0.705751i | \(-0.750610\pi\) | ||||
−0.708460 | + | 0.705751i | \(0.750610\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.92838 | −1.12487 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.9527 | −1.60659 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.88032 | 0.474056 | 0.237028 | − | 0.971503i | \(-0.423827\pi\) | ||||
0.237028 | + | 0.971503i | \(0.423827\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −19.6825 | −2.36950 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.36865 | 0.637142 | 0.318571 | − | 0.947899i | \(-0.396797\pi\) | ||||
0.318571 | + | 0.947899i | \(0.396797\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.41033 | 0.165066 | 0.0825331 | − | 0.996588i | \(-0.473699\pi\) | ||||
0.0825331 | + | 0.996588i | \(0.473699\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.1722 | −1.17458 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22.2953 | 2.54078 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.15937 | 0.692983 | 0.346492 | − | 0.938053i | \(-0.387373\pi\) | ||||
0.346492 | + | 0.938053i | \(0.387373\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0837 | −1.23152 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.20676 | 0.461752 | 0.230876 | − | 0.972983i | \(-0.425841\pi\) | ||||
0.230876 | + | 0.972983i | \(0.425841\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.56563 | −0.929073 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.76286 | −0.510632 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.8333 | −1.78433 | −0.892164 | − | 0.451712i | \(-0.850814\pi\) | ||||
−0.892164 | + | 0.451712i | \(0.850814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.5725 | 2.05175 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.5404 | −1.71516 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.7478 | −1.41050 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.25212 | 0.939411 | 0.469705 | − | 0.882823i | \(-0.344360\pi\) | ||||
0.469705 | + | 0.882823i | \(0.344360\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.08915 | −0.913494 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.90761 | 0.388821 | 0.194411 | − | 0.980920i | \(-0.437721\pi\) | ||||
0.194411 | + | 0.980920i | \(0.437721\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.244985 | −0.0241391 | −0.0120695 | − | 0.999927i | \(-0.503842\pi\) | ||||
−0.0120695 | + | 0.999927i | \(0.503842\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 32.1087 | 3.13349 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.64689 | 0.255884 | 0.127942 | − | 0.991782i | \(-0.459163\pi\) | ||||
0.127942 | + | 0.991782i | \(0.459163\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.7928 | 1.89581 | 0.947905 | − | 0.318554i | \(-0.103197\pi\) | ||||
0.947905 | + | 0.318554i | \(0.103197\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.6166 | −1.95684 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.57936 | 0.807079 | 0.403539 | − | 0.914962i | \(-0.367780\pi\) | ||||
0.403539 | + | 0.914962i | \(0.367780\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 27.5158 | 2.56586 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.97914 | −0.737671 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.9433 | 1.18651 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.6968 | 1.06334 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.6041 | 1.67748 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.26466 | −0.113115 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.05904 | −0.182710 | −0.0913552 | − | 0.995818i | \(-0.529120\pi\) | ||||
−0.0913552 | + | 0.995818i | \(0.529120\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.37362 | 0.737256 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.45887 | −0.739055 | −0.369527 | − | 0.929220i | \(-0.620480\pi\) | ||||
−0.369527 | + | 0.929220i | \(0.620480\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.7739 | 1.80133 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.49341 | 0.644930 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.8914 | −1.01595 | −0.507977 | − | 0.861370i | \(-0.669607\pi\) | ||||
−0.507977 | + | 0.861370i | \(0.669607\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.0936 | 1.44986 | 0.724932 | − | 0.688821i | \(-0.241871\pi\) | ||||
0.724932 | + | 0.688821i | \(0.241871\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.56796 | 0.637337 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.9249 | 1.66621 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.65840 | 0.552950 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −33.0110 | −2.72270 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.0639 | −1.15216 | −0.576079 | − | 0.817394i | \(-0.695418\pi\) | ||||
−0.576079 | + | 0.817394i | \(0.695418\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.7621 | 1.44546 | 0.722731 | − | 0.691129i | \(-0.242887\pi\) | ||||
0.722731 | + | 0.691129i | \(0.242887\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.27659 | −0.426587 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.1232 | 1.85730 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.5184 | −1.63755 | −0.818774 | − | 0.574116i | \(-0.805346\pi\) | ||||
−0.818774 | + | 0.574116i | \(0.805346\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −25.6218 | −2.03194 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −41.5783 | −3.27683 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.63658 | −0.676469 | −0.338235 | − | 0.941062i | \(-0.609830\pi\) | ||||
−0.338235 | + | 0.941062i | \(0.609830\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 32.6869 | 2.54467 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.3671 | 1.65344 | 0.826719 | − | 0.562615i | \(-0.190205\pi\) | ||||
0.826719 | + | 0.562615i | \(0.190205\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.49159 | 0.345507 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.46892 | −0.647635 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.23508 | 0.702130 | 0.351065 | − | 0.936351i | \(-0.385820\pi\) | ||||
0.351065 | + | 0.936351i | \(0.385820\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.4882 | −1.62436 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.37476 | −0.103333 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.4876 | −1.53131 | −0.765657 | − | 0.643249i | \(-0.777586\pi\) | ||||
−0.765657 | + | 0.643249i | \(0.777586\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.31659 | −0.618167 | −0.309084 | − | 0.951035i | \(-0.600022\pi\) | ||||
−0.309084 | + | 0.951035i | \(0.600022\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.5163 | 1.81230 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 28.8217 | 2.11901 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.1763 | 0.963548 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.3231 | −0.823631 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.9096 | −1.07882 | −0.539411 | − | 0.842043i | \(-0.681353\pi\) | ||||
−0.539411 | + | 0.842043i | \(0.681353\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.6297 | 1.84486 | 0.922432 | − | 0.386159i | \(-0.126198\pi\) | ||||
0.922432 | + | 0.386159i | \(0.126198\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 28.6950 | 2.05489 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.72377 | 0.407802 | 0.203901 | − | 0.978992i | \(-0.434638\pi\) | ||||
0.203901 | + | 0.978992i | \(0.434638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.6418 | 0.896154 | 0.448077 | − | 0.893995i | \(-0.352109\pi\) | ||||
0.448077 | + | 0.893995i | \(0.352109\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.59631 | −0.606337 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.0613 | −0.706165 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26.0082 | −1.81649 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.9503 | 1.17813 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.1480 | 1.46284 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.1293 | −1.11039 | −0.555194 | − | 0.831721i | \(-0.687356\pi\) | ||||
−0.555194 | + | 0.831721i | \(0.687356\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.8935 | −0.814930 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.7062 | −0.798355 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −34.9408 | −2.37194 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.12439 | −0.211126 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.5672 | 0.778092 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.9175 | 0.798053 | 0.399026 | − | 0.916939i | \(-0.369348\pi\) | ||||
0.399026 | + | 0.916939i | \(0.369348\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.76013 | 0.584009 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.85776 | −0.388793 | −0.194397 | − | 0.980923i | \(-0.562275\pi\) | ||||
−0.194397 | + | 0.980923i | \(0.562275\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.73938 | 0.313187 | 0.156594 | − | 0.987663i | \(-0.449949\pi\) | ||||
0.156594 | + | 0.987663i | \(0.449949\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −49.3922 | −3.24977 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.31495 | 0.217169 | 0.108585 | − | 0.994087i | \(-0.465368\pi\) | ||||
0.108585 | + | 0.994087i | \(0.465368\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.5799 | −0.690155 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.6452 | −0.886354 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.512422 | −0.0331458 | −0.0165729 | − | 0.999863i | \(-0.505276\pi\) | ||||
−0.0165729 | + | 0.999863i | \(0.505276\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.4997 | −0.934011 | −0.467005 | − | 0.884254i | \(-0.654667\pi\) | ||||
−0.467005 | + | 0.884254i | \(0.654667\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.2957 | 1.10952 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 46.1488 | 2.94834 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.5653 | 1.18128 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.31951 | −0.590600 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −42.3270 | −2.66108 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.9760 | 1.18832 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.3085 | 1.76584 | 0.882918 | − | 0.469527i | \(-0.155576\pi\) | ||||
0.882918 | + | 0.469527i | \(0.155576\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −43.5515 | −2.70616 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.10170 | 0.253889 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.7409 | 0.970625 | 0.485312 | − | 0.874341i | \(-0.338706\pi\) | ||||
0.485312 | + | 0.874341i | \(0.338706\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35.8189 | 2.20033 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 37.2919 | 2.28223 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.435839 | 0.0265736 | 0.0132868 | − | 0.999912i | \(-0.495771\pi\) | ||||
0.0132868 | + | 0.999912i | \(0.495771\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.6737 | 1.13434 | 0.567172 | − | 0.823599i | \(-0.308037\pi\) | ||||
0.567172 | + | 0.823599i | \(0.308037\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −43.3602 | −2.62428 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.8752 | −1.31912 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.9307 | 1.25761 | 0.628803 | − | 0.777564i | \(-0.283545\pi\) | ||||
0.628803 | + | 0.777564i | \(0.283545\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.2444 | 0.852787 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.1763 | 1.68086 | 0.840428 | − | 0.541924i | \(-0.182304\pi\) | ||||
0.840428 | + | 0.541924i | \(0.182304\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.7841 | −1.41382 | −0.706910 | − | 0.707303i | \(-0.749912\pi\) | ||||
−0.706910 | + | 0.707303i | \(0.749912\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 30.4564 | 1.80408 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 39.3003 | 2.31982 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.35064 | −0.550038 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.4968 | −1.20154 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.0129 | −0.935482 | −0.467741 | − | 0.883866i | \(-0.654932\pi\) | ||||
−0.467741 | + | 0.883866i | \(0.654932\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.92189 | 0.111897 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.5270 | −0.668862 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −37.1578 | −2.14889 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.6888 | 1.01957 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.65677 | −0.497319 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −34.2734 | −1.96249 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.39255 | −0.0794772 | −0.0397386 | − | 0.999210i | \(-0.512653\pi\) | ||||
−0.0397386 | + | 0.999210i | \(0.512653\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.542731 | 0.0308749 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.9348 | 1.69745 | 0.848724 | − | 0.528836i | \(-0.177371\pi\) | ||||
0.848724 | + | 0.528836i | \(0.177371\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.51730 | −0.142286 | −0.0711432 | − | 0.997466i | \(-0.522665\pi\) | ||||
−0.0711432 | + | 0.997466i | \(0.522665\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −27.6515 | −1.55799 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.00168 | 0.112425 | 0.0562127 | − | 0.998419i | \(-0.482098\pi\) | ||||
0.0562127 | + | 0.998419i | \(0.482098\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.2425 | −0.573468 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.86382 | −0.327286 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.2772 | 0.683121 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.2036 | −1.06523 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −43.8483 | −2.42482 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.9869 | 0.881388 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.32431 | −0.237686 | −0.118843 | − | 0.992913i | \(-0.537918\pi\) | ||||
−0.118843 | + | 0.992913i | \(0.537918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.7547 | 0.972952 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0175 | 0.656586 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.56938 | 0.412330 | 0.206165 | − | 0.978517i | \(-0.433902\pi\) | ||||
0.206165 | + | 0.978517i | \(0.433902\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.0064 | −1.03229 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −35.5700 | −1.92622 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −36.9751 | −1.99647 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −60.9575 | −3.28184 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.7995 | 1.17026 | 0.585128 | − | 0.810941i | \(-0.301044\pi\) | ||||
0.585128 | + | 0.810941i | \(0.301044\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.6011 | 0.835109 | 0.417554 | − | 0.908652i | \(-0.362887\pi\) | ||||
0.417554 | + | 0.908652i | \(0.362887\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.1192 | −0.540124 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.89144 | 0.420019 | 0.210010 | − | 0.977699i | \(-0.432650\pi\) | ||||
0.210010 | + | 0.977699i | \(0.432650\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.6269 | 0.882466 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −28.6740 | −1.51759 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.07626 | 0.162359 | 0.0811794 | − | 0.996700i | \(-0.474131\pi\) | ||||
0.0811794 | + | 0.996700i | \(0.474131\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.704867 | 0.0370982 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −25.9126 | −1.36006 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.36784 | 0.228623 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.13202 | 0.476688 | 0.238344 | − | 0.971181i | \(-0.423395\pi\) | ||||
0.238344 | + | 0.971181i | \(0.423395\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.0216 | −0.834050 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −54.1248 | −2.81002 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.0955 | −0.678060 | −0.339030 | − | 0.940776i | \(-0.610099\pi\) | ||||
−0.339030 | + | 0.940776i | \(0.610099\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.80169 | 0.144679 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.99161 | −0.463092 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.1576 | −1.54909 | −0.774547 | − | 0.632517i | \(-0.782022\pi\) | ||||
−0.774547 | + | 0.632517i | \(0.782022\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.56153 | 0.233694 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.8329 | −0.604635 | −0.302317 | − | 0.953207i | \(-0.597760\pi\) | ||||
−0.302317 | + | 0.953207i | \(0.597760\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 69.0494 | 3.51908 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.21123 | −0.366568 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.7765 | −0.799901 | −0.399951 | − | 0.916537i | \(-0.630973\pi\) | ||||
−0.399951 | + | 0.916537i | \(0.630973\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.5724 | −1.24268 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.7395 | 0.945281 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.0758 | 0.959808 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.2207 | 1.01485 | 0.507424 | − | 0.861697i | \(-0.330598\pi\) | ||||
0.507424 | + | 0.861697i | \(0.330598\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −46.0217 | −2.30397 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.28020 | 0.463431 | 0.231716 | − | 0.972784i | \(-0.425566\pi\) | ||||
0.231716 | + | 0.972784i | \(0.425566\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31.2260 | −1.55548 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −34.3266 | −1.70570 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −44.3358 | −2.19764 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.6673 | 0.675804 | 0.337902 | − | 0.941181i | \(-0.390283\pi\) | ||||
0.337902 | + | 0.941181i | \(0.390283\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.3439 | 1.29945 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.90410 | −0.142902 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.0285 | 0.639544 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −37.8686 | −1.85443 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.3777 | 0.506982 | 0.253491 | − | 0.967338i | \(-0.418421\pi\) | ||||
0.253491 | + | 0.967338i | \(0.418421\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.2237 | 0.693222 | 0.346611 | − | 0.938009i | \(-0.387332\pi\) | ||||
0.346611 | + | 0.938009i | \(0.387332\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.51741 | −0.316887 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.6994 | −0.616009 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 51.7895 | 2.50627 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −44.1409 | −2.13114 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.0895 | −0.485994 | −0.242997 | − | 0.970027i | \(-0.578131\pi\) | ||||
−0.242997 | + | 0.970027i | \(0.578131\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.51477 | −0.120852 | −0.0604261 | − | 0.998173i | \(-0.519246\pi\) | ||||
−0.0604261 | + | 0.998173i | \(0.519246\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.7508 | −0.707245 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −39.4387 | −1.88661 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.73881 | −0.321626 | −0.160813 | − | 0.986985i | \(-0.551412\pi\) | ||||
−0.160813 | + | 0.986985i | \(0.551412\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 28.4285 | 1.35374 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.9799 | 0.664204 | 0.332102 | − | 0.943243i | \(-0.392242\pi\) | ||||
0.332102 | + | 0.943243i | \(0.392242\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −52.1334 | −2.47136 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 31.1566 | 1.47366 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.6552 | 0.502850 | 0.251425 | − | 0.967877i | \(-0.419101\pi\) | ||||
0.251425 | + | 0.967877i | \(0.419101\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.0079 | 1.88390 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −39.3496 | −1.84881 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 60.6168 | 2.84176 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.7899 | −1.58062 | −0.790312 | − | 0.612704i | \(-0.790082\pi\) | ||||
−0.790312 | + | 0.612704i | \(0.790082\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.69183 | −0.312348 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.1644 | 0.473406 | 0.236703 | − | 0.971582i | \(-0.423933\pi\) | ||||
0.236703 | + | 0.971582i | \(0.423933\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.8546 | −0.783299 | −0.391650 | − | 0.920114i | \(-0.628095\pi\) | ||||
−0.391650 | + | 0.920114i | \(0.628095\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −51.2263 | −2.37556 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.51332 | −0.301401 | −0.150700 | − | 0.988579i | \(-0.548153\pi\) | ||||
−0.150700 | + | 0.988579i | \(0.548153\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.1593 | −0.838517 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 45.4558 | 2.09449 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.0074 | 0.827980 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.3824 | −0.935210 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.0651 | 1.01029 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.9557 | −0.500579 | −0.250290 | − | 0.968171i | \(-0.580526\pi\) | ||||
−0.250290 | + | 0.968171i | \(0.580526\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.9213 | −1.77466 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 92.1111 | 4.19120 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.6542 | 1.30112 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.58900 | −0.343891 | −0.171945 | − | 0.985106i | \(-0.555005\pi\) | ||||
−0.171945 | + | 0.985106i | \(0.555005\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.1332 | 0.865232 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.97891 | −0.0893070 | −0.0446535 | − | 0.999003i | \(-0.514218\pi\) | ||||
−0.0446535 | + | 0.999003i | \(0.514218\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.94614 | −0.267801 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −28.1495 | −1.26522 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.1244 | −1.12699 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.0373 | −1.07606 | −0.538029 | − | 0.842926i | \(-0.680831\pi\) | ||||
−0.538029 | + | 0.842926i | \(0.680831\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −47.3360 | −2.11482 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.9120 | −1.64582 | −0.822912 | − | 0.568169i | \(-0.807652\pi\) | ||||
−0.822912 | + | 0.568169i | \(0.807652\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1020 | 0.538533 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.95050 | −0.441917 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.19623 | 0.0530218 | 0.0265109 | − | 0.999649i | \(-0.491560\pi\) | ||||
0.0265109 | + | 0.999649i | \(0.491560\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.60010 | −0.291971 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.7404 | −0.474199 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.758728 | −0.0334335 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.2748 | 0.715765 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.4591 | −0.898053 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.0169 | −1.84080 | −0.920398 | − | 0.390984i | \(-0.872135\pi\) | ||||
−0.920398 | + | 0.390984i | \(0.872135\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.1386 | 1.53650 | 0.768252 | − | 0.640148i | \(-0.221127\pi\) | ||||
0.768252 | + | 0.640148i | \(0.221127\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 47.6042 | 2.07762 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.6497 | −0.899516 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 55.9353 | 2.43197 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.18392 | 0.0513777 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.1220 | 1.52130 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.19751 | 0.354409 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 45.3875 | 1.95861 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −70.9897 | −3.05774 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.9408 | 0.642357 | 0.321179 | − | 0.947019i | \(-0.395921\pi\) | ||||
0.321179 | + | 0.947019i | \(0.395921\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.4243 | 0.790661 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 61.2992 | 2.62577 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.19872 | −0.265038 | −0.132519 | − | 0.991180i | \(-0.542307\pi\) | ||||
−0.132519 | + | 0.991180i | \(0.542307\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.1131 | −0.901085 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.54354 | −0.406569 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.8249 | −1.22576 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −63.8505 | −2.71030 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.9864 | 0.634993 | 0.317496 | − | 0.948259i | \(-0.397158\pi\) | ||||
0.317496 | + | 0.948259i | \(0.397158\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.8082 | 0.668616 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29.1904 | −1.23242 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.1225 | 1.10093 | 0.550466 | − | 0.834858i | \(-0.314450\pi\) | ||||
0.550466 | + | 0.834858i | \(0.314450\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.5706 | 1.11783 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 51.8698 | 2.17833 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.5984 | 1.19891 | 0.599453 | − | 0.800410i | \(-0.295385\pi\) | ||||
0.599453 | + | 0.800410i | \(0.295385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.3749 | −1.06191 | −0.530953 | − | 0.847402i | \(-0.678166\pi\) | ||||
−0.530953 | + | 0.847402i | \(0.678166\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.0302 | 1.37986 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 40.7948 | 1.70126 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.4355 | 1.14216 | 0.571078 | − | 0.820896i | \(-0.306525\pi\) | ||||
0.571078 | + | 0.820896i | \(0.306525\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −56.7791 | −2.35966 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.6870 | −0.816753 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −55.0994 | −2.28198 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −24.7117 | −1.02170 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.4349 | 1.09109 | 0.545543 | − | 0.838083i | \(-0.316324\pi\) | ||||
0.545543 | + | 0.838083i | \(0.316324\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.1427 | −1.36562 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.6802 | −0.521595 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.22666 | −0.378893 | −0.189447 | − | 0.981891i | \(-0.560669\pi\) | ||||
−0.189447 | + | 0.981891i | \(0.560669\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 40.0858 | 1.64336 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.0062 | −1.14622 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 47.6451 | 1.94673 | 0.973363 | − | 0.229268i | \(-0.0736332\pi\) | ||||
0.973363 | + | 0.229268i | \(0.0736332\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.7911 | −0.766506 | −0.383253 | − | 0.923643i | \(-0.625196\pi\) | ||||
−0.383253 | + | 0.923643i | \(0.625196\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.40301 | 0.301474 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 36.2253 | 1.47277 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.16527 | 0.372007 | 0.186003 | − | 0.982549i | \(-0.440446\pi\) | ||||
0.186003 | + | 0.982549i | \(0.440446\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.2894 | 0.903214 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.2872 | 0.578000 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.2067 | 0.412243 | 0.206122 | − | 0.978526i | \(-0.433916\pi\) | ||||
0.206122 | + | 0.978526i | \(0.433916\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 57.6177 | 2.32337 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.3435 | 1.86572 | 0.932860 | − | 0.360240i | \(-0.117305\pi\) | ||||
0.932860 | + | 0.360240i | \(0.117305\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.6308 | −0.829221 | −0.414610 | − | 0.909999i | \(-0.636082\pi\) | ||||
−0.414610 | + | 0.909999i | \(0.636082\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.4965 | 0.862625 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 78.7773 | 3.15614 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.8750 | −1.07500 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −46.8504 | −1.87103 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.7386 | −1.02626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.503235 | 0.0200335 | 0.0100167 | − | 0.999950i | \(-0.496812\pi\) | ||||
0.0100167 | + | 0.999950i | \(0.496812\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 35.7323 | 1.42023 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.37693 | −0.253061 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −62.3201 | −2.46921 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.2425 | 0.405187 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.3295 | 1.47443 | 0.737214 | − | 0.675659i | \(-0.236141\pi\) | ||||
0.737214 | + | 0.675659i | \(0.236141\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.106240 | 0.00418969 | 0.00209485 | − | 0.999998i | \(-0.499333\pi\) | ||||
0.00209485 | + | 0.999998i | \(0.499333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.9334 | 1.02113 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.1931 | 0.636616 | 0.318308 | − | 0.947987i | \(-0.396885\pi\) | ||||
0.318308 | + | 0.947987i | \(0.396885\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.95640 | −0.116049 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 77.4066 | 3.03380 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.0952 | −0.668989 | −0.334494 | − | 0.942398i | \(-0.608565\pi\) | ||||
−0.334494 | + | 0.942398i | \(0.608565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.1975 | −1.02362 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.69067 | 0.104973 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.4895 | −0.564431 | −0.282216 | − | 0.959351i | \(-0.591069\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591069\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.1919 | 0.396418 | 0.198209 | − | 0.980160i | \(-0.436487\pi\) | ||||
0.198209 | + | 0.980160i | \(0.436487\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −25.6255 | −0.995211 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 64.3376 | 2.49490 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.1011 | 0.739598 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26.4015 | −1.02074 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 52.7221 | 2.03531 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.0132 | 1.46530 | 0.732651 | − | 0.680604i | \(-0.238283\pi\) | ||||
0.732651 | + | 0.680604i | \(0.238283\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.1097 | 0.427612 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.3781 | −1.62872 | −0.814361 | − | 0.580358i | \(-0.802913\pi\) | ||||
−0.814361 | + | 0.580358i | \(0.802913\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −43.2985 | −1.66164 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.9771 | 0.497282 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.7923 | 1.40782 | 0.703908 | − | 0.710291i | \(-0.251437\pi\) | ||||
0.703908 | + | 0.710291i | \(0.251437\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.8283 | −1.40714 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.4995 | −0.400579 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −48.3704 | −1.84277 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.24309 | −0.0472893 | −0.0236446 | − | 0.999720i | \(-0.507527\pi\) | ||||
−0.0236446 | + | 0.999720i | \(0.507527\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 42.5358 | 1.61580 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 52.9397 | 2.00812 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.2261 | 0.879752 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.34382 | −0.277769 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.7481 | 0.519257 | 0.259629 | − | 0.965709i | \(-0.416400\pi\) | ||||
0.259629 | + | 0.965709i | \(0.416400\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −41.3104 | −1.55805 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.4383 | 0.882736 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.2870 | −0.687753 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.7096 | 1.52888 | 0.764441 | − | 0.644694i | \(-0.223015\pi\) | ||||
0.764441 | + | 0.644694i | \(0.223015\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.7511 | 0.440700 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 66.3341 | 2.48423 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 61.7083 | 2.30776 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.13520 | 0.0423948 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.7959 | 0.812851 | 0.406425 | − | 0.913684i | \(-0.366775\pi\) | ||||
0.406425 | + | 0.913684i | \(0.366775\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.14649 | 0.0426975 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.1222 | 1.19464 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.87170 | 0.366626 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.6383 | 1.65554 | 0.827772 | − | 0.561064i | \(-0.189608\pi\) | ||||
0.827772 | + | 0.561064i | \(0.189608\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.06536 | −0.187606 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.4540 | 0.386654 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.1455 | −0.891836 | −0.445918 | − | 0.895074i | \(-0.647123\pi\) | ||||
−0.445918 | + | 0.895074i | \(0.647123\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −102.236 | −3.77104 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.4863 | −0.680950 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.696924 | 0.0256368 | 0.0128184 | − | 0.999918i | \(-0.495920\pi\) | ||||
0.0128184 | + | 0.999918i | \(0.495920\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −41.1288 | −1.51091 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.1443 | 0.408846 | 0.204423 | − | 0.978883i | \(-0.434468\pi\) | ||||
0.204423 | + | 0.978883i | \(0.434468\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −43.5564 | −1.59578 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.02581 | 0.293649 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.3870 | −0.452612 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.8606 | −0.907174 | −0.453587 | − | 0.891212i | \(-0.649856\pi\) | ||||
−0.453587 | + | 0.891212i | \(0.649856\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.21536 | 0.0807323 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 55.0100 | 2.00202 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.6288 | −0.422657 | −0.211329 | − | 0.977415i | \(-0.567779\pi\) | ||||
−0.211329 | + | 0.977415i | \(0.567779\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 93.7697 | 3.40362 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.1632 | 1.05717 | 0.528583 | − | 0.848881i | \(-0.322723\pi\) | ||||
0.528583 | + | 0.848881i | \(0.322723\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −92.6273 | −3.35333 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.3418 | −0.590840 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.59535 | −0.0937126 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.3770 | −0.879056 | −0.439528 | − | 0.898229i | \(-0.644854\pi\) | ||||
−0.439528 | + | 0.898229i | \(0.644854\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −62.7136 | −2.25858 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −41.2500 | −1.48366 | −0.741830 | − | 0.670588i | \(-0.766042\pi\) | ||||
−0.741830 | + | 0.670588i | \(0.766042\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.2824 | 1.23146 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 96.4825 | 3.46129 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37.2779 | 1.33562 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.5769 | −0.915212 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.20182 | 0.185898 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −63.5464 | −2.26807 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.65386 | −0.0589537 | −0.0294769 | − | 0.999565i | \(-0.509384\pi\) | ||||
−0.0294769 | + | 0.999565i | \(0.509384\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −34.8718 | −1.24147 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −40.1501 | −1.42757 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.2834 | 1.64357 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −79.3518 | −2.81432 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.53175 | 0.0896793 | 0.0448396 | − | 0.998994i | \(-0.485722\pi\) | ||||
0.0448396 | + | 0.998994i | \(0.485722\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.44813 | 0.334251 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.1152 | −1.13474 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.71895 | −0.237107 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −128.770 | −4.53853 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.965542 | −0.0339887 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.3444 | 0.504323 | 0.252161 | − | 0.967685i | \(-0.418859\pi\) | ||||
0.252161 | + | 0.967685i | \(0.418859\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.5339 | −0.896618 | −0.448309 | − | 0.893879i | \(-0.647974\pi\) | ||||
−0.448309 | + | 0.893879i | \(0.647974\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −41.3690 | −1.45087 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26.7478 | −0.936935 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.7786 | 0.587008 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 37.3411 | 1.30480 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.58307 | −0.125050 | −0.0625249 | − | 0.998043i | \(-0.519915\pi\) | ||||
−0.0625249 | + | 0.998043i | \(0.519915\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.1716 | −0.842568 | −0.421284 | − | 0.906929i | \(-0.638420\pi\) | ||||
−0.421284 | + | 0.906929i | \(0.638420\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 48.4614 | 1.68721 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.63507 | −0.161177 | −0.0805885 | − | 0.996747i | \(-0.525680\pi\) | ||||
−0.0805885 | + | 0.996747i | \(0.525680\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.8954 | −1.66348 | −0.831738 | − | 0.555169i | \(-0.812654\pi\) | ||||
−0.831738 | + | 0.555169i | \(0.812654\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −46.3692 | −1.60853 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −41.2122 | −1.42792 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 66.1749 | 2.29008 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.0648 | 0.624412 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.6951 | 1.12876 | 0.564380 | − | 0.825515i | \(-0.309115\pi\) | ||||
0.564380 | + | 0.825515i | \(0.309115\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.3778 | −0.840615 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −62.4207 | −2.14988 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.9106 | 0.478540 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −54.7390 | −1.88085 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 52.6905 | 1.80833 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 82.6814 | 2.83428 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.10625 | 0.140595 | 0.0702977 | − | 0.997526i | \(-0.477605\pi\) | ||||
0.0702977 | + | 0.997526i | \(0.477605\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −26.2286 | −0.896999 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.0056 | 0.478424 | 0.239212 | − | 0.970967i | \(-0.423111\pi\) | ||||
0.239212 | + | 0.970967i | \(0.423111\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.1442 | −0.584954 | −0.292477 | − | 0.956273i | \(-0.594480\pi\) | ||||
−0.292477 | + | 0.956273i | \(0.594480\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −87.0644 | −2.96715 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −57.5292 | −1.95832 | −0.979158 | − | 0.203098i | \(-0.934899\pi\) | ||||
−0.979158 | + | 0.203098i | \(0.934899\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.6014 | 0.972477 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.7151 | 0.703521 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.3439 | −0.995425 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.2286 | −0.549886 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.6515 | 0.597414 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.91843 | 0.200079 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.5128 | 1.57063 | 0.785313 | − | 0.619099i | \(-0.212502\pi\) | ||||
0.785313 | + | 0.619099i | \(0.212502\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 35.4743 | 1.19652 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.0699 | −0.372954 | −0.186477 | − | 0.982459i | \(-0.559707\pi\) | ||||
−0.186477 | + | 0.982459i | \(0.559707\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.152523 | 0.00513280 | 0.00256640 | − | 0.999997i | \(-0.499183\pi\) | ||||
0.00256640 | + | 0.999997i | \(0.499183\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.25768 | −0.143120 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.69157 | 0.325411 | 0.162706 | − | 0.986675i | \(-0.447978\pi\) | ||||
0.162706 | + | 0.986675i | \(0.447978\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.63599 | 0.323181 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 52.8038 | 1.76900 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.1642 | 0.507452 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −63.4509 | −2.12093 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 82.3181 | 2.74852 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.0518 | 0.535358 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.9873 | −1.06565 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −39.1872 | −1.30407 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.7568 | −0.856185 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.2135 | −0.737587 | −0.368793 | − | 0.929511i | \(-0.620229\pi\) | ||||
−0.368793 | + | 0.929511i | \(0.620229\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.45508 | 0.247269 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.3519 | −1.03873 | −0.519367 | − | 0.854551i | \(-0.673832\pi\) | ||||
−0.519367 | + | 0.854551i | \(0.673832\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.0415 | −0.663276 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 75.9281 | 2.51010 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 39.5862 | 1.30725 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.1544 | 1.25860 | 0.629299 | − | 0.777163i | \(-0.283342\pi\) | ||||
0.629299 | + | 0.777163i | \(0.283342\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.08501 | 0.101655 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.4533 | −0.739059 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.7308 | 1.40498 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.467391 | −0.0153511 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.3278 | −0.338843 | −0.169421 | − | 0.985544i | \(-0.554190\pi\) | ||||
−0.169421 | + | 0.985544i | \(0.554190\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −66.1455 | −2.16783 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −66.3165 | −2.17111 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 40.8076 | 1.33455 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.05077 | 0.263007 | 0.131504 | − | 0.991316i | \(-0.458020\pi\) | ||||
0.131504 | + | 0.991316i | \(0.458020\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.57674 | 0.181990 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.8005 | 0.938870 | 0.469435 | − | 0.882967i | \(-0.344458\pi\) | ||||
0.469435 | + | 0.882967i | \(0.344458\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −74.6105 | −2.42965 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −35.0680 | −1.14076 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.4582 | 0.632305 | 0.316152 | − | 0.948708i | \(-0.397609\pi\) | ||||
0.316152 | + | 0.948708i | \(0.397609\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.89840 | −0.191470 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.43444 | −0.143797 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.9075 | −1.58427 | −0.792135 | − | 0.610346i | \(-0.791031\pi\) | ||||
−0.792135 | + | 0.610346i | \(0.791031\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −46.1757 | −1.49421 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.6908 | 0.733490 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 55.6501 | 1.79704 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.7446 | 0.798214 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.04983 | 0.162728 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 79.3761 | 2.55521 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.7258 | 1.43828 | 0.719142 | − | 0.694863i | \(-0.244535\pi\) | ||||
0.719142 | + | 0.694863i | \(0.244535\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −27.1985 | −0.873740 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.73713 | −0.0878386 | −0.0439193 | − | 0.999035i | \(-0.513984\pi\) | ||||
−0.0439193 | + | 0.999035i | \(0.513984\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −79.9955 | −2.56454 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 42.5431 | 1.36247 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.8910 | −0.476404 | −0.238202 | − | 0.971216i | \(-0.576558\pi\) | ||||
−0.238202 | + | 0.971216i | \(0.576558\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 80.1958 | 2.56307 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.7615 | 1.20563 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.3312 | −0.903626 | −0.451813 | − | 0.892113i | \(-0.649223\pi\) | ||||
−0.451813 | + | 0.892113i | \(0.649223\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.7267 | 0.564821 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −35.4169 | −1.12733 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.5818 | −1.06784 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.3125 | 0.645248 | 0.322624 | − | 0.946527i | \(-0.395435\pi\) | ||||
0.322624 | + | 0.946527i | \(0.395435\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.57992 | 0.304010 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.1522 | 1.24121 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.2802 | 0.768961 | 0.384480 | − | 0.923133i | \(-0.374381\pi\) | ||||
0.384480 | + | 0.923133i | \(0.374381\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.5167 | 0.712397 |
(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 | 2008.2.a.d.1.5 | ✓ | 23 | |
4.3 | odd | 2 | 4016.2.a.m.1.19 | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.d.1.5 | ✓ | 23 | 1.1 | even | 1 | trivial | |
4016.2.a.m.1.19 | 23 | 4.3 | odd | 2 |