Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 33 x^{9} + 22 x^{8} + 417 x^{7} - 151 x^{6} - 2470 x^{5} + 272 x^{4} + 6584 x^{3} + 292 x^{2} - 5687 x + 242 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-2.34947\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.34947 | 1.49793 | 0.748965 | − | 0.662610i | \(-0.230551\pi\) | ||||
0.748965 | + | 0.662610i | \(0.230551\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.54581 | −1.34019 | −0.670094 | − | 0.742276i | \(-0.733746\pi\) | ||||
−0.670094 | + | 0.742276i | \(0.733746\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.22121 | 1.57425 | 0.787127 | − | 0.616791i | \(-0.211567\pi\) | ||||
0.787127 | + | 0.616791i | \(0.211567\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.27416 | 1.46279 | 0.731394 | − | 0.681955i | \(-0.238870\pi\) | ||||
0.731394 | + | 0.681955i | \(0.238870\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.34947 | 0.864830 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.86903 | 1.66598 | 0.832992 | − | 0.553285i | \(-0.186626\pi\) | ||||
0.832992 | + | 0.553285i | \(0.186626\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.25090 | −1.20464 | −0.602320 | − | 0.798255i | \(-0.705757\pi\) | ||||
−0.602320 | + | 0.798255i | \(0.705757\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.54581 | −0.773758 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.32838 | −0.485500 | −0.242750 | − | 0.970089i | \(-0.578050\pi\) | ||||
−0.242750 | + | 0.970089i | \(0.578050\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.21896 | 1.24379 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.922527 | −0.171309 | −0.0856545 | − | 0.996325i | \(-0.527298\pi\) | ||||
−0.0856545 | + | 0.996325i | \(0.527298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.9921 | 1.97425 | 0.987123 | − | 0.159963i | \(-0.0511375\pi\) | ||||
0.987123 | + | 0.159963i | \(0.0511375\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.22121 | 0.908896 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.8766 | −2.00751 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.2033 | −1.67742 | −0.838708 | − | 0.544581i | \(-0.816689\pi\) | ||||
−0.838708 | + | 0.544581i | \(0.816689\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.27416 | 0.844541 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.58506 | 0.403719 | 0.201859 | − | 0.979415i | \(-0.435302\pi\) | ||||
0.201859 | + | 0.979415i | \(0.435302\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.38272 | −0.668359 | −0.334179 | − | 0.942509i | \(-0.608459\pi\) | ||||
−0.334179 | + | 0.942509i | \(0.608459\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.34947 | 0.499310 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.30219 | −0.919270 | −0.459635 | − | 0.888108i | \(-0.652020\pi\) | ||||
−0.459635 | + | 0.888108i | \(0.652020\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.57274 | 0.796106 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.86903 | 0.961857 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.7064 | 1.47064 | 0.735319 | − | 0.677721i | \(-0.237032\pi\) | ||||
0.735319 | + | 0.677721i | \(0.237032\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.4883 | 2.35812 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.25090 | −0.695499 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.3875 | −1.35234 | −0.676169 | − | 0.736747i | \(-0.736361\pi\) | ||||
−0.676169 | + | 0.736747i | \(0.736361\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.7958 | 1.38226 | 0.691129 | − | 0.722732i | \(-0.257114\pi\) | ||||
0.691129 | + | 0.722732i | \(0.257114\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.54581 | −0.446730 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.6657 | 2.19115 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.19936 | 1.00171 | 0.500856 | − | 0.865531i | \(-0.333019\pi\) | ||||
0.500856 | + | 0.865531i | \(0.333019\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.32838 | −0.280304 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.27323 | 0.388460 | 0.194230 | − | 0.980956i | \(-0.437779\pi\) | ||||
0.194230 | + | 0.980956i | \(0.437779\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.70252 | −1.13559 | −0.567797 | − | 0.823169i | \(-0.692204\pi\) | ||||
−0.567797 | + | 0.823169i | \(0.692204\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.21896 | 0.718104 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.5134 | −2.10980 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.2308 | 1.60109 | 0.800543 | − | 0.599275i | \(-0.204544\pi\) | ||||
0.800543 | + | 0.599275i | \(0.204544\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.2173 | 1.34103 | 0.670513 | − | 0.741898i | \(-0.266074\pi\) | ||||
0.670513 | + | 0.741898i | \(0.266074\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 23.0076 | 2.49553 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.922527 | −0.0989053 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.83867 | 0.194899 | 0.0974494 | − | 0.995240i | \(-0.468932\pi\) | ||||
0.0974494 | + | 0.995240i | \(0.468932\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.7011 | −1.96041 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.9921 | 1.13983 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −17.5878 | −1.80447 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0691 | −1.02237 | −0.511183 | − | 0.859472i | \(-0.670792\pi\) | ||||
−0.511183 | + | 0.859472i | \(0.670792\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.22121 | 0.524752 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.62392 | 0.360593 | 0.180297 | − | 0.983612i | \(-0.442294\pi\) | ||||
0.180297 | + | 0.983612i | \(0.442294\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.34478 | −0.132505 | −0.0662527 | − | 0.997803i | \(-0.521104\pi\) | ||||
−0.0662527 | + | 0.997803i | \(0.521104\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.8766 | −1.15904 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.14056 | −0.496957 | −0.248479 | − | 0.968637i | \(-0.579931\pi\) | ||||
−0.248479 | + | 0.968637i | \(0.579931\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.05520 | −0.771549 | −0.385774 | − | 0.922593i | \(-0.626066\pi\) | ||||
−0.385774 | + | 0.922593i | \(0.626066\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.2033 | −0.968457 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0162 | −1.69482 | −0.847412 | − | 0.530936i | \(-0.821841\pi\) | ||||
−0.847412 | + | 0.530936i | \(0.821841\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.79884 | −0.727245 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.27416 | 0.487596 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.3563 | −2.23273 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.2611 | 1.47828 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.58506 | 0.233087 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.08289 | 0.365185 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.40394 | 0.568258 | 0.284129 | − | 0.958786i | \(-0.408296\pi\) | ||||
0.284129 | + | 0.958786i | \(0.408296\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.38272 | −0.385877 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.2197 | −1.50449 | −0.752246 | − | 0.658882i | \(-0.771030\pi\) | ||||
−0.752246 | + | 0.658882i | \(0.771030\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.6187 | 1.61445 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.34947 | 0.288277 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.8321 | −1.43806 | −0.719032 | − | 0.694977i | \(-0.755415\pi\) | ||||
−0.719032 | + | 0.694977i | \(0.755415\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.08472 | 0.770556 | 0.385278 | − | 0.922801i | \(-0.374106\pi\) | ||||
0.385278 | + | 0.922801i | \(0.374106\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.30219 | −0.530741 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 27.5375 | 2.30280 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.08998 | −0.256609 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.57274 | 0.459632 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.5718 | −0.866077 | −0.433038 | − | 0.901376i | \(-0.642559\pi\) | ||||
−0.433038 | + | 0.901376i | \(0.642559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.42466 | −0.766968 | −0.383484 | − | 0.923548i | \(-0.625276\pi\) | ||||
−0.383484 | + | 0.923548i | \(0.625276\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.86903 | 0.555328 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 36.8179 | 2.95728 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.0413 | −0.881195 | −0.440597 | − | 0.897705i | \(-0.645233\pi\) | ||||
−0.440597 | + | 0.897705i | \(0.645233\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.7064 | 0.849073 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.25598 | 0.650662 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.204447 | −0.0160135 | −0.00800676 | − | 0.999968i | \(-0.502549\pi\) | ||||
−0.00800676 | + | 0.999968i | \(0.502549\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 17.4883 | 1.36146 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.8168 | 1.13975 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.25090 | −0.401547 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.27958 | −0.401399 | −0.200700 | − | 0.979653i | \(-0.564322\pi\) | ||||
−0.200700 | + | 0.979653i | \(0.564322\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −22.0512 | −1.66692 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.3875 | −0.780773 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.1223 | −1.42926 | −0.714632 | − | 0.699501i | \(-0.753406\pi\) | ||||
−0.714632 | + | 0.699501i | \(0.753406\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.5626 | 1.82572 | 0.912861 | − | 0.408270i | \(-0.133868\pi\) | ||||
0.912861 | + | 0.408270i | \(0.133868\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.7958 | 0.798046 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −34.1758 | −2.51265 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 35.8647 | 2.62268 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.54581 | −0.257919 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.5678 | −0.837016 | −0.418508 | − | 0.908213i | \(-0.637447\pi\) | ||||
−0.418508 | + | 0.908213i | \(0.637447\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.06662 | −0.292722 | −0.146361 | − | 0.989231i | \(-0.546756\pi\) | ||||
−0.146361 | + | 0.989231i | \(0.546756\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.6657 | 1.26506 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.7058 | 1.76021 | 0.880106 | − | 0.474777i | \(-0.157471\pi\) | ||||
0.880106 | + | 0.474777i | \(0.157471\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.95811 | 0.493247 | 0.246624 | − | 0.969111i | \(-0.420679\pi\) | ||||
0.246624 | + | 0.969111i | \(0.420679\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.19936 | 0.578338 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.27110 | 0.229586 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.65859 | 0.604742 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.32838 | −0.161833 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.4161 | −1.89641 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0883 | 0.832196 | 0.416098 | − | 0.909320i | \(-0.363397\pi\) | ||||
0.416098 | + | 0.909320i | \(0.363397\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.27323 | 0.224278 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.6798 | −1.00115 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −38.9760 | −2.64586 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.70252 | −0.655635 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 36.2284 | 2.43698 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.74178 | −0.451463 | −0.225732 | − | 0.974190i | \(-0.572477\pi\) | ||||
−0.225732 | + | 0.974190i | \(0.572477\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.21896 | 0.414598 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.6461 | 1.10484 | 0.552419 | − | 0.833566i | \(-0.313705\pi\) | ||||
0.552419 | + | 0.833566i | \(0.313705\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.34626 | 0.287209 | 0.143604 | − | 0.989635i | \(-0.454131\pi\) | ||||
0.143604 | + | 0.989635i | \(0.454131\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.5134 | −1.21809 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.4375 | 1.01135 | 0.505674 | − | 0.862725i | \(-0.331244\pi\) | ||||
0.505674 | + | 0.862725i | \(0.331244\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.1090 | −1.37700 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.2308 | 0.924388 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.91114 | −0.252990 | −0.126495 | − | 0.991967i | \(-0.540373\pi\) | ||||
−0.126495 | + | 0.991967i | \(0.540373\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.89534 | 0.508584 | 0.254292 | − | 0.967128i | \(-0.418158\pi\) | ||||
0.254292 | + | 0.967128i | \(0.418158\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.6657 | 1.19251 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −27.6941 | −1.76213 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.2173 | 0.774241 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.57349 | 0.604273 | 0.302137 | − | 0.953265i | \(-0.402300\pi\) | ||||
0.302137 | + | 0.953265i | \(0.402300\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.1570 | −0.764301 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 23.0076 | 1.44079 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.3318 | −1.39302 | −0.696511 | − | 0.717546i | \(-0.745265\pi\) | ||||
−0.696511 | + | 0.717546i | \(0.745265\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.1790 | 2.24805 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.922527 | −0.0571030 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.8026 | −1.22108 | −0.610539 | − | 0.791986i | \(-0.709047\pi\) | ||||
−0.610539 | + | 0.791986i | \(0.709047\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35.8608 | 2.20291 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.83867 | 0.112525 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.4173 | 0.818068 | 0.409034 | − | 0.912519i | \(-0.365866\pi\) | ||||
0.409034 | + | 0.912519i | \(0.365866\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.1007 | 1.52476 | 0.762379 | − | 0.647130i | \(-0.224031\pi\) | ||||
0.762379 | + | 0.647130i | \(0.224031\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.7011 | −1.13184 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 32.4705 | 1.95805 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.87307 | −0.232710 | −0.116355 | − | 0.993208i | \(-0.537121\pi\) | ||||
−0.116355 | + | 0.993208i | \(0.537121\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.9921 | 0.658082 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.69139 | −0.220210 | −0.110105 | − | 0.993920i | \(-0.535119\pi\) | ||||
−0.110105 | + | 0.993920i | \(0.535119\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.75352 | −0.460899 | −0.230449 | − | 0.973084i | \(-0.574020\pi\) | ||||
−0.230449 | + | 0.973084i | \(0.574020\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.5878 | −1.04181 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.16613 | −0.541059 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.1836 | 1.77550 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.0691 | −0.590263 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.01242 | −0.0591460 | −0.0295730 | − | 0.999563i | \(-0.509415\pi\) | ||||
−0.0295730 | + | 0.999563i | \(0.509415\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −34.7927 | −2.02571 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.22121 | 0.302965 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.2802 | −0.710184 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.5403 | 0.895727 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.62392 | 0.208189 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 36.1601 | 2.07052 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.9773 | −1.48260 | −0.741301 | − | 0.671173i | \(-0.765791\pi\) | ||||
−0.741301 | + | 0.671173i | \(0.765791\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.34478 | −0.0765020 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.2568 | 0.581608 | 0.290804 | − | 0.956783i | \(-0.406077\pi\) | ||||
0.290804 | + | 0.956783i | \(0.406077\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.2574 | 0.749351 | 0.374675 | − | 0.927156i | \(-0.377754\pi\) | ||||
0.374675 | + | 0.927156i | \(0.377754\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.8766 | −0.669169 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.0416 | 1.18181 | 0.590907 | − | 0.806739i | \(-0.298770\pi\) | ||||
0.590907 | + | 0.806739i | \(0.298770\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.81671 | −0.269684 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.14056 | −0.286918 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −36.0686 | −2.00691 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 32.7998 | 1.81941 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.05520 | −0.445454 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.3464 | 1.23199 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.4570 | −0.629735 | −0.314868 | − | 0.949136i | \(-0.601960\pi\) | ||||
−0.314868 | + | 0.949136i | \(0.601960\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.2033 | −0.559139 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.4635 | 1.50049 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.81048 | −0.262044 | −0.131022 | − | 0.991379i | \(-0.541826\pi\) | ||||
−0.131022 | + | 0.991379i | \(0.541826\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.0162 | −0.978507 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 57.3923 | 3.10797 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.06078 | 0.273256 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.79884 | −0.419875 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.5296 | −0.565258 | −0.282629 | − | 0.959229i | \(-0.591207\pi\) | ||||
−0.282629 | + | 0.959229i | \(0.591207\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.11284 | −0.434271 | −0.217135 | − | 0.976142i | \(-0.569671\pi\) | ||||
−0.217135 | + | 0.976142i | \(0.569671\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.27416 | 0.281514 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.7942 | 0.893867 | 0.446933 | − | 0.894567i | \(-0.352516\pi\) | ||||
0.446933 | + | 0.894567i | \(0.352516\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.9636 | 0.581886 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −24.3563 | −1.28907 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.05875 | −0.266991 | −0.133495 | − | 0.991049i | \(-0.542620\pi\) | ||||
−0.133495 | + | 0.991049i | \(0.542620\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.57200 | 0.451158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.2611 | 0.853484 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.4983 | −1.70104 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.3665 | −0.958723 | −0.479362 | − | 0.877617i | \(-0.659132\pi\) | ||||
−0.479362 | + | 0.877617i | \(0.659132\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.58506 | 0.134573 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −37.9628 | −1.97093 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.5025 | −0.647355 | −0.323678 | − | 0.946167i | \(-0.604919\pi\) | ||||
−0.323678 | + | 0.946167i | \(0.604919\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.08289 | 0.210839 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.86555 | −0.250589 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.8449 | 1.07073 | 0.535365 | − | 0.844621i | \(-0.320174\pi\) | ||||
0.535365 | + | 0.844621i | \(0.320174\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.40394 | 0.328084 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.4740 | 1.60825 | 0.804123 | − | 0.594463i | \(-0.202635\pi\) | ||||
0.804123 | + | 0.594463i | \(0.202635\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −62.0101 | −3.16033 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.38272 | −0.222786 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.57981 | 0.435014 | 0.217507 | − | 0.976059i | \(-0.430208\pi\) | ||||
0.217507 | + | 0.976059i | \(0.430208\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.9937 | −0.808836 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.2197 | −0.868619 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 47.6656 | 2.39831 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.3543 | 1.02155 | 0.510776 | − | 0.859714i | \(-0.329358\pi\) | ||||
0.510776 | + | 0.859714i | \(0.329358\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.6187 | 0.932100 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.1277 | 0.805378 | 0.402689 | − | 0.915337i | \(-0.368076\pi\) | ||||
0.402689 | + | 0.915337i | \(0.368076\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 57.9743 | 2.88790 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.34947 | 0.166437 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −53.2737 | −2.64068 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.1245 | −0.896199 | −0.448099 | − | 0.893984i | \(-0.647899\pi\) | ||||
−0.448099 | + | 0.893984i | \(0.647899\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.8321 | −0.830267 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.8321 | 1.81239 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 40.9216 | 2.00876 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.08472 | 0.444881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.7981 | 1.16261 | 0.581307 | − | 0.813684i | \(-0.302541\pi\) | ||||
0.581307 | + | 0.813684i | \(0.302541\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.4408 | −0.703800 | −0.351900 | − | 0.936038i | \(-0.614464\pi\) | ||||
−0.351900 | + | 0.936038i | \(0.614464\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.30219 | −0.306423 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 42.7183 | 2.07214 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −38.2797 | −1.85249 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.5375 | 1.32952 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.8595 | 0.619420 | 0.309710 | − | 0.950831i | \(-0.399768\pi\) | ||||
0.309710 | + | 0.950831i | \(0.399768\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.3060 | 0.783618 | 0.391809 | − | 0.920047i | \(-0.371849\pi\) | ||||
0.391809 | + | 0.920047i | \(0.371849\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.08998 | −0.148153 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.2261 | 0.584853 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.2780 | −0.490544 | −0.245272 | − | 0.969454i | \(-0.578877\pi\) | ||||
−0.245272 | + | 0.969454i | \(0.578877\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.57274 | 0.265369 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.8390 | 1.56023 | 0.780113 | − | 0.625638i | \(-0.215161\pi\) | ||||
0.780113 | + | 0.625638i | \(0.215161\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.15858 | 0.291945 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.5718 | −0.500030 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.3707 | 1.76363 | 0.881817 | − | 0.471592i | \(-0.156321\pi\) | ||||
0.881817 | + | 0.471592i | \(0.156321\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.4972 | 0.635556 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.42466 | −0.442809 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −62.6390 | −2.93656 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.2479 | 1.50849 | 0.754246 | − | 0.656592i | \(-0.228003\pi\) | ||||
0.754246 | + | 0.656592i | \(0.228003\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.86903 | 0.320619 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.8346 | −1.29639 | −0.648193 | − | 0.761476i | \(-0.724475\pi\) | ||||
−0.648193 | + | 0.761476i | \(0.724475\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.04994 | −0.281164 | −0.140582 | − | 0.990069i | \(-0.544897\pi\) | ||||
−0.140582 | + | 0.990069i | \(0.544897\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 36.8179 | 1.70739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.8938 | −0.828028 | −0.414014 | − | 0.910271i | \(-0.635874\pi\) | ||||
−0.414014 | + | 0.910271i | \(0.635874\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.0733 | −1.34248 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.0413 | −0.508758 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.8831 | −1.05217 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −32.6552 | −1.49832 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.7064 | 0.490213 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.3503 | 0.655683 | 0.327841 | − | 0.944733i | \(-0.393679\pi\) | ||||
0.327841 | + | 0.944733i | \(0.393679\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −53.8140 | −2.45371 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.25598 | 0.375660 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −33.7263 | −1.53143 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.1796 | 0.733170 | 0.366585 | − | 0.930385i | \(-0.380527\pi\) | ||||
0.366585 | + | 0.930385i | \(0.380527\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.204447 | −0.00924541 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.6911 | −1.52046 | −0.760228 | − | 0.649656i | \(-0.774913\pi\) | ||||
−0.760228 | + | 0.649656i | \(0.774913\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.33687 | −0.285398 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.4883 | 0.786041 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.6062 | −0.520610 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.5927 | 1.10092 | 0.550461 | − | 0.834861i | \(-0.314452\pi\) | ||||
0.550461 | + | 0.834861i | \(0.314452\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.11857 | −0.361989 | −0.180995 | − | 0.983484i | \(-0.557932\pi\) | ||||
−0.180995 | + | 0.983484i | \(0.557932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1382 | 0.540143 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.8168 | 0.658035 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.74908 | 0.254823 | 0.127412 | − | 0.991850i | \(-0.459333\pi\) | ||||
0.127412 | + | 0.991850i | \(0.459333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.4032 | 1.52191 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.25090 | −0.231833 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.50431 | −0.198484 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.9051 | −1.44716 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.27958 | −0.231748 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.3615 | −1.41778 | −0.708891 | − | 0.705318i | \(-0.750804\pi\) | ||||
−0.708891 | + | 0.705318i | \(0.750804\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.4106 | −1.59213 | −0.796063 | − | 0.605214i | \(-0.793088\pi\) | ||||
−0.796063 | + | 0.605214i | \(0.793088\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.0512 | −0.962395 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 75.5053 | 3.28906 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5787 | −0.764289 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.3875 | −0.450779 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.6340 | 0.590555 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.2182 | −0.744407 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.1223 | −0.825186 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.0965 | 1.25327 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.8083 | −0.765637 | −0.382818 | − | 0.923824i | \(-0.625047\pi\) | ||||
−0.382818 | + | 0.923824i | \(0.625047\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.5626 | 1.05408 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.9807 | −1.15573 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.2379 | 0.480500 | 0.240250 | − | 0.970711i | \(-0.422771\pi\) | ||||
0.240250 | + | 0.970711i | \(0.422771\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.7958 | 0.460752 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.84410 | 0.206366 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −50.4595 | −2.14576 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −34.1758 | −1.45068 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.44916 | −0.273260 | −0.136630 | − | 0.990622i | \(-0.543627\pi\) | ||||
−0.136630 | + | 0.990622i | \(0.543627\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.1152 | −0.977668 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35.8647 | 1.51421 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.4201 | −0.565590 | −0.282795 | − | 0.959180i | \(-0.591262\pi\) | ||||
−0.282795 | + | 0.959180i | \(0.591262\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −60.3449 | −2.53873 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.54581 | −0.148910 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.4681 | −0.564613 | −0.282306 | − | 0.959324i | \(-0.591099\pi\) | ||||
−0.282306 | + | 0.959324i | \(0.591099\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.5925 | −0.819919 | −0.409959 | − | 0.912104i | \(-0.634457\pi\) | ||||
−0.409959 | + | 0.912104i | \(0.634457\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.5678 | −0.483251 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.4801 | −0.603862 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.3611 | −0.889274 | −0.444637 | − | 0.895711i | \(-0.646667\pi\) | ||||
−0.444637 | + | 0.895711i | \(0.646667\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.06662 | −0.169003 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −43.3203 | −1.79723 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 55.9004 | 2.31516 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.6657 | 0.730385 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.4585 | 1.17461 | 0.587305 | − | 0.809366i | \(-0.300189\pi\) | ||||
0.587305 | + | 0.809366i | \(0.300189\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −57.7187 | −2.37826 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.7058 | 1.01626 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.7257 | −0.604711 | −0.302355 | − | 0.953195i | \(-0.597773\pi\) | ||||
−0.302355 | + | 0.953195i | \(0.597773\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −81.5806 | −3.34448 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.95811 | 0.284777 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.5093 | −1.00142 | −0.500712 | − | 0.865614i | \(-0.666928\pi\) | ||||
−0.500712 | + | 0.865614i | \(0.666928\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.6537 | −1.41355 | −0.706777 | − | 0.707436i | \(-0.749852\pi\) | ||||
−0.706777 | + | 0.707436i | \(0.749852\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.19936 | 0.333904 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 54.4659 | 2.21436 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.43186 | 0.382827 | 0.191414 | − | 0.981509i | \(-0.438693\pi\) | ||||
0.191414 | + | 0.981509i | \(0.438693\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.27110 | 0.132552 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.2388 | −1.34470 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.6729 | 1.48121 | 0.740603 | − | 0.671943i | \(-0.234540\pi\) | ||||
0.740603 | + | 0.671943i | \(0.234540\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.65859 | 0.349148 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.27551 | −0.333159 | −0.166580 | − | 0.986028i | \(-0.553272\pi\) | ||||
−0.166580 | + | 0.986028i | \(0.553272\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.8480 | −1.07911 | −0.539556 | − | 0.841950i | \(-0.681408\pi\) | ||||
−0.539556 | + | 0.841950i | \(0.681408\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.32838 | −0.0934346 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.51957 | −0.261201 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.4193 | −0.696772 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −27.4161 | −1.09489 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −70.0870 | −2.79455 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.42971 | 0.335581 | 0.167791 | − | 0.985823i | \(-0.446337\pi\) | ||||
0.167791 | + | 0.985823i | \(0.446337\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.0883 | 0.480468 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.4498 | 0.851210 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.3915 | 1.16453 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.27323 | 0.129487 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.5628 | 1.72063 | 0.860313 | − | 0.509766i | \(-0.170268\pi\) | ||||
0.860313 | + | 0.509766i | \(0.170268\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.3839 | 0.409500 | 0.204750 | − | 0.978814i | \(-0.434362\pi\) | ||||
0.204750 | + | 0.978814i | \(0.434362\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.6798 | −0.578017 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.4049 | −0.527003 | −0.263501 | − | 0.964659i | \(-0.584877\pi\) | ||||
−0.263501 | + | 0.964659i | \(0.584877\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −54.2354 | −2.12892 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38.9760 | −1.52759 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.6733 | 0.965539 | 0.482770 | − | 0.875747i | \(-0.339631\pi\) | ||||
0.482770 | + | 0.875747i | \(0.339631\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −57.6769 | −2.25362 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.70252 | −0.378531 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.9385 | −1.32206 | −0.661028 | − | 0.750362i | \(-0.729879\pi\) | ||||
−0.661028 | + | 0.750362i | \(0.729879\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.3567 | −0.791783 | −0.395891 | − | 0.918297i | \(-0.629564\pi\) | ||||
−0.395891 | + | 0.918297i | \(0.629564\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 36.2284 | 1.40699 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 62.3628 | 2.41833 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.14799 | 0.0831706 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.74178 | −0.260652 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 56.3670 | 2.17602 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.5647 | −0.908352 | −0.454176 | − | 0.890912i | \(-0.650066\pi\) | ||||
−0.454176 | + | 0.890912i | \(0.650066\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.21896 | 0.239368 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.6458 | 0.793482 | 0.396741 | − | 0.917931i | \(-0.370141\pi\) | ||||
0.396741 | + | 0.917931i | \(0.370141\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 35.7032 | 1.37016 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.6461 | 0.637879 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.2872 | 0.584950 | 0.292475 | − | 0.956273i | \(-0.405521\pi\) | ||||
0.292475 | + | 0.956273i | \(0.405521\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −56.3787 | −2.15412 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.34626 | 0.165820 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 56.4673 | 2.15123 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.05755 | −0.0402310 | −0.0201155 | − | 0.999798i | \(-0.506403\pi\) | ||||
−0.0201155 | + | 0.999798i | \(0.506403\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.5134 | −0.703266 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30.4290 | 1.15424 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.7569 | 0.672589 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.4375 | 0.583902 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.2205 | −1.02810 | −0.514051 | − | 0.857759i | \(-0.671856\pi\) | ||||
−0.514051 | + | 0.857759i | \(0.671856\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 53.5767 | 2.02068 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21.1090 | −0.795012 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.8497 | −0.483263 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.84618 | 0.144446 | 0.0722231 | − | 0.997388i | \(-0.476991\pi\) | ||||
0.0722231 | + | 0.997388i | \(0.476991\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.2308 | 0.533695 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.5938 | −0.958497 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 92.2361 | 3.44943 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.91114 | −0.146064 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.7863 | −1.18543 | −0.592715 | − | 0.805412i | \(-0.701944\pi\) | ||||
−0.592715 | + | 0.805412i | \(0.701944\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.76834 | 0.177582 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.89534 | 0.293631 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.73716 | −0.213073 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.8047 | −0.437813 | −0.218907 | − | 0.975746i | \(-0.570249\pi\) | ||||
−0.218907 | + | 0.975746i | \(0.570249\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.1050 | −1.11348 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.2574 | −0.563546 | −0.281773 | − | 0.959481i | \(-0.590923\pi\) | ||||
−0.281773 | + | 0.959481i | \(0.590923\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.6657 | 0.688496 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42.8106 | 1.57695 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.0262 | 1.43560 | 0.717802 | − | 0.696248i | \(-0.245148\pi\) | ||||
0.717802 | + | 0.696248i | \(0.245148\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27.6941 | −1.01737 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.20570 | 0.337724 | 0.168862 | − | 0.985640i | \(-0.445991\pi\) | ||||
0.168862 | + | 0.985640i | \(0.445991\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35.4100 | −1.29732 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.2173 | 0.447008 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.2274 | 0.666016 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.3585 | 1.39972 | 0.699861 | − | 0.714279i | \(-0.253245\pi\) | ||||
0.699861 | + | 0.714279i | \(0.253245\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.57349 | 0.348877 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.5676 | −1.14886 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.1329 | 1.34962 | 0.674810 | − | 0.737992i | \(-0.264226\pi\) | ||||
0.674810 | + | 0.737992i | \(0.264226\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.1570 | −0.441269 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.9072 | −0.939137 | −0.469568 | − | 0.882896i | \(-0.655590\pi\) | ||||
−0.469568 | + | 0.882896i | \(0.655590\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.5622 | 1.03402 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 23.0076 | 0.831843 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −54.7854 | −1.97818 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.98095 | −0.179618 | −0.0898089 | − | 0.995959i | \(-0.528626\pi\) | ||||
−0.0898089 | + | 0.995959i | \(0.528626\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.3318 | −0.804262 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.71962 | 0.133785 | 0.0668927 | − | 0.997760i | \(-0.478691\pi\) | ||||
0.0668927 | + | 0.997760i | \(0.478691\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 68.3597 | 2.45555 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 36.1790 | 1.29791 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.5739 | −0.486336 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.0902 | 0.611536 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.922527 | −0.0329684 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.9827 | −1.31997 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.36356 | 0.0486056 | 0.0243028 | − | 0.999705i | \(-0.492263\pi\) | ||||
0.0243028 | + | 0.999705i | \(0.492263\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.8026 | −0.704990 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 63.8821 | 2.27138 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 56.9386 | 2.02195 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 35.8608 | 1.27185 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.5615 | −1.25965 | −0.629826 | − | 0.776736i | \(-0.716874\pi\) | ||||
−0.629826 | + | 0.776736i | \(0.716874\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.2900 | −1.53149 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.83867 | 0.0649663 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −50.6589 | −1.78771 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27.6532 | 0.974646 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.4173 | 0.472312 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.8127 | −0.977842 | −0.488921 | − | 0.872328i | \(-0.662609\pi\) | ||||
−0.488921 | + | 0.872328i | \(0.662609\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.8403 | 1.92570 | 0.962851 | − | 0.270033i | \(-0.0870348\pi\) | ||||
0.962851 | + | 0.270033i | \(0.0870348\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.1007 | 0.880320 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.684789 | −0.0239871 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.0133 | 0.805132 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.7011 | −0.653471 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.8424 | −0.727404 | −0.363702 | − | 0.931515i | \(-0.618487\pi\) | ||||
−0.363702 | + | 0.931515i | \(0.618487\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.4050 | −0.502125 | −0.251063 | − | 0.967971i | \(-0.580780\pi\) | ||||
−0.251063 | + | 0.967971i | \(0.580780\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 32.4705 | 1.13048 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.2464 | 0.634490 | 0.317245 | − | 0.948344i | \(-0.397242\pi\) | ||||
0.317245 | + | 0.948344i | \(0.397242\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.2942 | −0.635385 | −0.317693 | − | 0.948194i | \(-0.602908\pi\) | ||||
−0.317693 | + | 0.948194i | \(0.602908\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.87307 | −0.134355 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 38.2793 | 1.32630 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.34947 | −0.115913 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.9921 | 0.379944 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.08068 | 0.0373092 | 0.0186546 | − | 0.999826i | \(-0.494062\pi\) | ||||
0.0186546 | + | 0.999826i | \(0.494062\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1489 | −0.970653 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.69139 | −0.127138 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 49.6283 | 1.70727 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −57.6585 | −1.98117 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.75352 | −0.266100 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.7572 | 0.814386 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.1917 | −0.862546 | −0.431273 | − | 0.902221i | \(-0.641935\pi\) | ||||
−0.431273 | + | 0.902221i | \(0.641935\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.5878 | −0.601489 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.0093 | −1.36669 | −0.683345 | − | 0.730095i | \(-0.739476\pi\) | ||||
−0.683345 | + | 0.730095i | \(0.739476\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 55.1265 | 1.88089 | 0.940445 | − | 0.339945i | \(-0.110409\pi\) | ||||
0.940445 | + | 0.339945i | \(0.110409\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.16613 | −0.312381 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.1875 | 1.36800 | 0.684000 | − | 0.729482i | \(-0.260239\pi\) | ||||
0.684000 | + | 0.729482i | \(0.260239\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.6838 | −0.601268 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 30.1836 | 1.02509 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 74.3019 | 2.52052 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.2447 | 1.46529 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.0691 | −0.340789 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.4771 | −0.489416 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.9315 | 0.909412 | 0.454706 | − | 0.890642i | \(-0.349744\pi\) | ||||
0.454706 | + | 0.890642i | \(0.349744\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.01242 | −0.0341480 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.4956 | 1.46540 | 0.732701 | − | 0.680550i | \(-0.238259\pi\) | ||||
0.732701 | + | 0.680550i | \(0.238259\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.9488 | −1.84917 | −0.924587 | − | 0.380970i | \(-0.875590\pi\) | ||||
−0.924587 | + | 0.380970i | \(0.875590\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −34.7927 | −1.16954 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.4217 | 1.52511 | 0.762556 | − | 0.646923i | \(-0.223944\pi\) | ||||
0.762556 | + | 0.646923i | \(0.223944\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.7071 | −0.761572 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.22121 | 0.174917 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.0922 | 1.10739 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −64.0495 | −2.14094 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.2802 | −0.410025 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.1405 | −0.338206 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 73.5426 | 2.45006 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.5403 | 0.517148 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 82.2717 | 2.73480 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.43231 | −0.113968 | −0.0569840 | − | 0.998375i | \(-0.518148\pi\) | ||||
−0.0569840 | + | 0.998375i | \(0.518148\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.62392 | 0.120198 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.2715 | 0.539098 | 0.269549 | − | 0.962987i | \(-0.413125\pi\) | ||||
0.269549 | + | 0.962987i | \(0.413125\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 63.7892 | 2.11112 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 36.1601 | 1.19542 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 61.0577 | 2.01630 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.6271 | −1.57107 | −0.785537 | − | 0.618815i | \(-0.787613\pi\) | ||||
−0.785537 | + | 0.618815i | \(0.787613\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.9773 | −0.855980 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.2635 | 0.568236 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −63.4541 | −2.08636 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.34478 | −0.0441685 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.6196 | 0.348417 | 0.174208 | − | 0.984709i | \(-0.444263\pi\) | ||||
0.174208 | + | 0.984709i | \(0.444263\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.2619 | −0.959021 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.2568 | 0.335792 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 120.128 | 3.92860 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.3052 | −1.05537 | −0.527683 | − | 0.849441i | \(-0.676939\pi\) | ||||
−0.527683 | + | 0.849441i | \(0.676939\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.2574 | 0.432638 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.9102 | −1.13804 | −0.569020 | − | 0.822324i | \(-0.692677\pi\) | ||||
−0.569020 | + | 0.822324i | \(0.692677\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.01900 | −0.196006 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.8766 | −0.386345 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.60729 | −0.0522299 | −0.0261149 | − | 0.999659i | \(-0.508314\pi\) | ||||
−0.0261149 | + | 0.999659i | \(0.508314\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −51.1726 | −1.66113 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.0416 | 0.682321 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.1682 | −0.556133 | −0.278067 | − | 0.960562i | \(-0.589694\pi\) | ||||
−0.278067 | + | 0.960562i | \(0.589694\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.7460 | −1.25379 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.81671 | −0.155702 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 59.6834 | 1.92728 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 89.8271 | 2.89765 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.14056 | −0.165652 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.6210 | −0.438476 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.4971 | 0.626984 | 0.313492 | − | 0.949591i | \(-0.398501\pi\) | ||||
0.313492 | + | 0.949591i | \(0.398501\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36.0686 | −1.15869 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.8748 | 0.669903 | 0.334952 | − | 0.942235i | \(-0.391280\pi\) | ||||
0.334952 | + | 0.942235i | \(0.391280\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.2126 | −1.03269 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 32.7998 | 1.05043 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52.7385 | −1.68725 | −0.843627 | − | 0.536930i | \(-0.819584\pi\) | ||||
−0.843627 | + | 0.536930i | \(0.819584\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.60009 | 0.306820 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.05520 | −0.257183 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.3260 | 0.552613 | 0.276307 | − | 0.961070i | \(-0.410890\pi\) | ||||
0.276307 | + | 0.961070i | \(0.410890\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 82.7512 | 2.63667 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.3464 | 0.711293 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.2046 | 0.324488 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.9567 | −1.49163 | −0.745814 | − | 0.666154i | \(-0.767939\pi\) | ||||
−0.745814 | + | 0.666154i | \(0.767939\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.4570 | −0.363578 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.3060 | 0.738850 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.3277 | −0.992159 | −0.496080 | − | 0.868277i | \(-0.665228\pi\) | ||||
−0.496080 | + | 0.868277i | \(0.665228\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.2033 | −0.322819 |
(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 | 8016.2.a.be.1.9 | 11 | ||
4.3 | odd | 2 | 4008.2.a.k.1.9 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.k.1.9 | ✓ | 11 | 4.3 | odd | 2 | ||
8016.2.a.be.1.9 | 11 | 1.1 | even | 1 | trivial |