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 | 1.8 | ||
Root | \(-2.17907\) 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 | ||||||||
\(5\) | 3.17907 | 1.42172 | 0.710862 | − | 0.703331i | \(-0.248305\pi\) | ||||
0.710862 | + | 0.703331i | \(0.248305\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.651548 | −0.246262 | −0.123131 | − | 0.992390i | \(-0.539294\pi\) | ||||
−0.123131 | + | 0.992390i | \(0.539294\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.35582 | −0.710307 | −0.355153 | − | 0.934808i | \(-0.615571\pi\) | ||||
−0.355153 | + | 0.934808i | \(0.615571\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.77932 | 1.60289 | 0.801447 | − | 0.598065i | \(-0.204064\pi\) | ||||
0.801447 | + | 0.598065i | \(0.204064\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.17907 | 0.820833 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.736701 | −0.178676 | −0.0893381 | − | 0.996001i | \(-0.528475\pi\) | ||||
−0.0893381 | + | 0.996001i | \(0.528475\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.04977 | 0.699666 | 0.349833 | − | 0.936812i | \(-0.386238\pi\) | ||||
0.349833 | + | 0.936812i | \(0.386238\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.651548 | −0.142180 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.45399 | 0.303177 | 0.151588 | − | 0.988444i | \(-0.451561\pi\) | ||||
0.151588 | + | 0.988444i | \(0.451561\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.10651 | 1.02130 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.59579 | 0.667721 | 0.333860 | − | 0.942623i | \(-0.391649\pi\) | ||||
0.333860 | + | 0.942623i | \(0.391649\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.65723 | −1.01607 | −0.508034 | − | 0.861337i | \(-0.669628\pi\) | ||||
−0.508034 | + | 0.861337i | \(0.669628\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.35582 | −0.410096 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.07132 | −0.350117 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.15702 | 1.17661 | 0.588304 | − | 0.808640i | \(-0.299796\pi\) | ||||
0.588304 | + | 0.808640i | \(0.299796\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.77932 | 0.925432 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.85120 | 1.38232 | 0.691162 | − | 0.722700i | \(-0.257099\pi\) | ||||
0.691162 | + | 0.722700i | \(0.257099\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.96597 | 0.757304 | 0.378652 | − | 0.925539i | \(-0.376388\pi\) | ||||
0.378652 | + | 0.925539i | \(0.376388\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.17907 | 0.473908 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.18019 | −0.463878 | −0.231939 | − | 0.972730i | \(-0.574507\pi\) | ||||
−0.231939 | + | 0.972730i | \(0.574507\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.57548 | −0.939355 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.736701 | −0.103159 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.50138 | 0.206230 | 0.103115 | − | 0.994669i | \(-0.467119\pi\) | ||||
0.103115 | + | 0.994669i | \(0.467119\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.48933 | −1.00986 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.04977 | 0.403952 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.09356 | −0.402747 | −0.201373 | − | 0.979515i | \(-0.564540\pi\) | ||||
−0.201373 | + | 0.979515i | \(0.564540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.8291 | −1.77063 | −0.885317 | − | 0.464988i | \(-0.846059\pi\) | ||||
−0.885317 | + | 0.464988i | \(0.846059\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.651548 | −0.0820874 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.3729 | 2.27888 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.06273 | 0.740680 | 0.370340 | − | 0.928896i | \(-0.379241\pi\) | ||||
0.370340 | + | 0.928896i | \(0.379241\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.45399 | 0.175039 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.79383 | 0.806279 | 0.403139 | − | 0.915139i | \(-0.367919\pi\) | ||||
0.403139 | + | 0.915139i | \(0.367919\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00965 | −0.118171 | −0.0590855 | − | 0.998253i | \(-0.518818\pi\) | ||||
−0.0590855 | + | 0.998253i | \(0.518818\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.10651 | 0.589649 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.53493 | 0.174922 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.3793 | −1.50529 | −0.752646 | − | 0.658425i | \(-0.771223\pi\) | ||||
−0.752646 | + | 0.658425i | \(0.771223\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.30393 | 0.911475 | 0.455737 | − | 0.890114i | \(-0.349376\pi\) | ||||
0.455737 | + | 0.890114i | \(0.349376\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.34203 | −0.254028 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.59579 | 0.385509 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.5653 | −1.22592 | −0.612962 | − | 0.790113i | \(-0.710022\pi\) | ||||
−0.612962 | + | 0.790113i | \(0.710022\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.76551 | −0.394732 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.65723 | −0.586628 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.69545 | 0.994732 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.62123 | 0.976888 | 0.488444 | − | 0.872595i | \(-0.337565\pi\) | ||||
0.488444 | + | 0.872595i | \(0.337565\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.35582 | −0.236769 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.374583 | −0.0372724 | −0.0186362 | − | 0.999826i | \(-0.505932\pi\) | ||||
−0.0186362 | + | 0.999826i | \(0.505932\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0604 | −0.991282 | −0.495641 | − | 0.868527i | \(-0.665067\pi\) | ||||
−0.495641 | + | 0.868527i | \(0.665067\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.07132 | −0.202140 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.8116 | 1.43189 | 0.715944 | − | 0.698158i | \(-0.245997\pi\) | ||||
0.715944 | + | 0.698158i | \(0.245997\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.4949 | 1.48414 | 0.742070 | − | 0.670323i | \(-0.233844\pi\) | ||||
0.742070 | + | 0.670323i | \(0.233844\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.15702 | 0.679315 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.98184 | 0.186436 | 0.0932178 | − | 0.995646i | \(-0.470285\pi\) | ||||
0.0932178 | + | 0.995646i | \(0.470285\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.62233 | 0.431034 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.77932 | 0.534298 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.479996 | 0.0440012 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.45011 | −0.495464 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.85120 | 0.798086 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.338597 | 0.0302851 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.57114 | −0.405623 | −0.202812 | − | 0.979218i | \(-0.565008\pi\) | ||||
−0.202812 | + | 0.979218i | \(0.565008\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.96597 | 0.437230 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.46187 | 0.739317 | 0.369658 | − | 0.929168i | \(-0.379475\pi\) | ||||
0.369658 | + | 0.929168i | \(0.379475\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.98707 | −0.172301 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.17907 | 0.273611 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.15273 | −0.781970 | −0.390985 | − | 0.920397i | \(-0.627866\pi\) | ||||
−0.390985 | + | 0.920397i | \(0.627866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.94667 | 0.419571 | 0.209786 | − | 0.977747i | \(-0.432723\pi\) | ||||
0.209786 | + | 0.977747i | \(0.432723\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.18019 | −0.267820 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.6150 | −1.13855 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.4313 | 0.949315 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.57548 | −0.542337 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.47425 | −0.776161 | −0.388080 | − | 0.921626i | \(-0.626862\pi\) | ||||
−0.388080 | + | 0.921626i | \(0.626862\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.22991 | 0.425604 | 0.212802 | − | 0.977095i | \(-0.431741\pi\) | ||||
0.212802 | + | 0.977095i | \(0.431741\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.736701 | −0.0595587 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.9848 | −1.44457 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.0547 | 1.28131 | 0.640654 | − | 0.767830i | \(-0.278663\pi\) | ||||
0.640654 | + | 0.767830i | \(0.278663\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.50138 | 0.119067 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.947342 | −0.0746610 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.3004 | 1.74670 | 0.873351 | − | 0.487091i | \(-0.161942\pi\) | ||||
0.873351 | + | 0.487091i | \(0.161942\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.48933 | −0.583043 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.4005 | 1.56927 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.04977 | 0.233222 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.5505 | 1.33434 | 0.667171 | − | 0.744904i | \(-0.267505\pi\) | ||||
0.667171 | + | 0.744904i | \(0.267505\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.32714 | −0.251508 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.09356 | −0.232526 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.4005 | −1.59955 | −0.799773 | − | 0.600303i | \(-0.795047\pi\) | ||||
−0.799773 | + | 0.600303i | \(0.795047\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4205 | −0.774550 | −0.387275 | − | 0.921964i | \(-0.626584\pi\) | ||||
−0.387275 | + | 0.921964i | \(0.626584\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.8291 | −1.02228 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.7527 | 1.67281 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.73554 | 0.126915 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.651548 | −0.0473932 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3798 | −0.751059 | −0.375529 | − | 0.926810i | \(-0.622539\pi\) | ||||
−0.375529 | + | 0.926810i | \(0.622539\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.9382 | −1.43518 | −0.717591 | − | 0.696465i | \(-0.754755\pi\) | ||||
−0.717591 | + | 0.696465i | \(0.754755\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18.3729 | 1.31571 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.5273 | 1.53375 | 0.766877 | − | 0.641794i | \(-0.221810\pi\) | ||||
0.766877 | + | 0.641794i | \(0.221810\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.57836 | −0.111887 | −0.0559435 | − | 0.998434i | \(-0.517817\pi\) | ||||
−0.0559435 | + | 0.998434i | \(0.517817\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.06273 | 0.427632 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.34283 | −0.164434 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.1386 | 1.96529 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.45399 | 0.101059 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.18472 | −0.496977 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.1516 | −1.11192 | −0.555960 | − | 0.831209i | \(-0.687649\pi\) | ||||
−0.555960 | + | 0.831209i | \(0.687649\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.79383 | 0.465505 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.7872 | 1.07668 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.68596 | 0.250219 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.00965 | −0.0682260 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.25763 | −0.286399 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.9061 | 1.06515 | 0.532577 | − | 0.846382i | \(-0.321224\pi\) | ||||
0.532577 | + | 0.846382i | \(0.321224\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.10651 | 0.340434 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.5938 | −1.69872 | −0.849359 | − | 0.527816i | \(-0.823011\pi\) | ||||
−0.849359 | + | 0.527816i | \(0.823011\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.79809 | −0.250985 | −0.125492 | − | 0.992095i | \(-0.540051\pi\) | ||||
−0.125492 | + | 0.992095i | \(0.540051\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.53493 | 0.100991 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.9836 | 0.785070 | 0.392535 | − | 0.919737i | \(-0.371598\pi\) | ||||
0.392535 | + | 0.919737i | \(0.371598\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1101 | −0.659507 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.3793 | −0.869081 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.97611 | −0.321878 | −0.160939 | − | 0.986964i | \(-0.551452\pi\) | ||||
−0.160939 | + | 0.986964i | \(0.551452\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.08605 | 0.327621 | 0.163811 | − | 0.986492i | \(-0.447621\pi\) | ||||
0.163811 | + | 0.986492i | \(0.447621\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −20.9039 | −1.33550 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.6256 | 1.12149 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.30393 | 0.526240 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.9778 | 1.45034 | 0.725172 | − | 0.688568i | \(-0.241760\pi\) | ||||
0.725172 | + | 0.688568i | \(0.241760\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.42533 | −0.215349 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.34203 | −0.146663 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.54328 | 0.345781 | 0.172890 | − | 0.984941i | \(-0.444689\pi\) | ||||
0.172890 | + | 0.984941i | \(0.444689\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.66315 | −0.289754 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.59579 | 0.222574 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.0070 | −0.617060 | −0.308530 | − | 0.951215i | \(-0.599837\pi\) | ||||
−0.308530 | + | 0.951215i | \(0.599837\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.77298 | 0.293202 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.5653 | −0.707787 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.4920 | 1.73719 | 0.868594 | − | 0.495525i | \(-0.165024\pi\) | ||||
0.868594 | + | 0.495525i | \(0.165024\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.31835 | 0.201575 | 0.100788 | − | 0.994908i | \(-0.467864\pi\) | ||||
0.100788 | + | 0.994908i | \(0.467864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.76551 | −0.227899 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.0300 | −0.725437 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.48347 | −0.209301 | −0.104651 | − | 0.994509i | \(-0.533372\pi\) | ||||
−0.104651 | + | 0.994509i | \(0.533372\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.65723 | −0.338690 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.76222 | 0.224435 | 0.112218 | − | 0.993684i | \(-0.464205\pi\) | ||||
0.112218 | + | 0.993684i | \(0.464205\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.4873 | 0.980066 | 0.490033 | − | 0.871704i | \(-0.336985\pi\) | ||||
0.490033 | + | 0.871704i | \(0.336985\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.69545 | 0.574309 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.76698 | −0.340414 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4573 | −0.968075 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.62123 | 0.564006 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.965119 | 0.0563828 | 0.0281914 | − | 0.999603i | \(-0.491025\pi\) | ||||
0.0281914 | + | 0.999603i | \(0.491025\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.83465 | −0.572595 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.35582 | −0.136699 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.40305 | 0.485961 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.23557 | −0.186495 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.374583 | −0.0215192 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −43.9637 | −2.51735 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.8989 | 0.622030 | 0.311015 | − | 0.950405i | \(-0.399331\pi\) | ||||
0.311015 | + | 0.950405i | \(0.399331\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.0604 | −0.572317 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.2877 | 1.32052 | 0.660262 | − | 0.751035i | \(-0.270445\pi\) | ||||
0.660262 | + | 0.751035i | \(0.270445\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.2329 | 1.48277 | 0.741386 | − | 0.671078i | \(-0.234169\pi\) | ||||
0.741386 | + | 0.671078i | \(0.234169\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.07132 | −0.116706 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.5938 | 1.54982 | 0.774911 | − | 0.632070i | \(-0.217795\pi\) | ||||
0.774911 | + | 0.632070i | \(0.217795\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.47103 | −0.474287 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.8116 | 0.826701 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.24677 | −0.125014 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29.5121 | 1.63704 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.4949 | 0.856868 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.07205 | 0.114236 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.6057 | −0.637905 | −0.318952 | − | 0.947771i | \(-0.603331\pi\) | ||||
−0.318952 | + | 0.947771i | \(0.603331\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.15702 | 0.392202 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.2739 | 1.05304 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.4885 | −0.789241 | −0.394620 | − | 0.918844i | \(-0.629124\pi\) | ||||
−0.394620 | + | 0.918844i | \(0.629124\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.98184 | 0.107639 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.3274 | 0.721721 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.84508 | 0.477590 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.62233 | 0.248858 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.21580 | −0.494730 | −0.247365 | − | 0.968922i | \(-0.579565\pi\) | ||||
−0.247365 | + | 0.968922i | \(0.579565\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.40211 | −0.182111 | −0.0910555 | − | 0.995846i | \(-0.529024\pi\) | ||||
−0.0910555 | + | 0.995846i | \(0.529024\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.77932 | 0.308477 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.0856 | −0.856151 | −0.428075 | − | 0.903743i | \(-0.640808\pi\) | ||||
−0.428075 | + | 0.903743i | \(0.640808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.5981 | 1.14631 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.479996 | 0.0254041 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.0982 | −1.37741 | −0.688704 | − | 0.725042i | \(-0.741820\pi\) | ||||
−0.688704 | + | 0.725042i | \(0.741820\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.69889 | −0.510468 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.45011 | −0.286056 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.20976 | −0.168007 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.5886 | 0.604918 | 0.302459 | − | 0.953162i | \(-0.402192\pi\) | ||||
0.302459 | + | 0.953162i | \(0.402192\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.85120 | 0.460775 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.978219 | −0.0507866 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.42795 | −0.384605 | −0.192302 | − | 0.981336i | \(-0.561595\pi\) | ||||
−0.192302 | + | 0.981336i | \(0.561595\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.338597 | 0.0174851 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.7812 | 1.07029 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.6468 | 0.700991 | 0.350495 | − | 0.936564i | \(-0.386013\pi\) | ||||
0.350495 | + | 0.936564i | \(0.386013\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.57114 | −0.234187 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.5127 | −1.66132 | −0.830661 | − | 0.556779i | \(-0.812037\pi\) | ||||
−0.830661 | + | 0.556779i | \(0.812037\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.87966 | 0.248690 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.96597 | 0.252435 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.12806 | 0.361407 | 0.180703 | − | 0.983538i | \(-0.442163\pi\) | ||||
0.180703 | + | 0.983538i | \(0.442163\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.07115 | −0.0541705 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.46187 | 0.426845 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −42.5339 | −2.14011 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.1636 | −0.761041 | −0.380520 | − | 0.924773i | \(-0.624255\pi\) | ||||
−0.380520 | + | 0.924773i | \(0.624255\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.98707 | −0.0994781 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.19754 | 0.209615 | 0.104808 | − | 0.994493i | \(-0.466577\pi\) | ||||
0.104808 | + | 0.994493i | \(0.466577\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.6950 | −1.62865 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.17907 | 0.157969 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.8607 | −0.835752 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.9137 | −0.539648 | −0.269824 | − | 0.962910i | \(-0.586966\pi\) | ||||
−0.269824 | + | 0.962910i | \(0.586966\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.15273 | −0.451471 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.01560 | 0.0991813 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.3988 | 1.29587 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.94667 | 0.242240 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.7174 | −0.767843 | −0.383921 | − | 0.923366i | \(-0.625427\pi\) | ||||
−0.383921 | + | 0.923366i | \(0.625427\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.26688 | −0.305429 | −0.152714 | − | 0.988270i | \(-0.548801\pi\) | ||||
−0.152714 | + | 0.988270i | \(0.548801\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.18019 | −0.154626 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.76197 | −0.182482 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.01033 | 0.436040 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.6150 | −0.657341 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.93255 | 0.189424 | 0.0947122 | − | 0.995505i | \(-0.469807\pi\) | ||||
0.0947122 | + | 0.995505i | \(0.469807\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.01897 | 0.0489686 | 0.0244843 | − | 0.999700i | \(-0.492206\pi\) | ||||
0.0244843 | + | 0.999700i | \(0.492206\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.4313 | 0.548088 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.43433 | 0.212123 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.3685 | −1.54487 | −0.772433 | − | 0.635097i | \(-0.780960\pi\) | ||||
−0.772433 | + | 0.635097i | \(0.780960\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.57548 | −0.313118 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.1882 | 0.864149 | 0.432075 | − | 0.901838i | \(-0.357782\pi\) | ||||
0.432075 | + | 0.901838i | \(0.357782\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −36.7671 | −1.74293 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.47425 | −0.448117 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.8478 | −0.842288 | −0.421144 | − | 0.906994i | \(-0.638371\pi\) | ||||
−0.421144 | + | 0.906994i | \(0.638371\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.8518 | −0.981875 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.22991 | 0.245723 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.9708 | −0.561201 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.7658 | −1.53272 | −0.766359 | − | 0.642413i | \(-0.777934\pi\) | ||||
−0.766359 | + | 0.642413i | \(0.777934\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.736701 | −0.0343863 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.0329 | 1.39877 | 0.699386 | − | 0.714744i | \(-0.253457\pi\) | ||||
0.699386 | + | 0.714744i | \(0.253457\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.2896 | −1.87242 | −0.936208 | − | 0.351445i | \(-0.885690\pi\) | ||||
−0.936208 | + | 0.351445i | \(0.885690\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.9848 | −0.834023 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.79685 | −0.175697 | −0.0878485 | − | 0.996134i | \(-0.527999\pi\) | ||||
−0.0878485 | + | 0.996134i | \(0.527999\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.95016 | −0.182401 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.0547 | 0.739763 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.6989 | −0.537918 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.5737 | 0.714570 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.50138 | 0.0687433 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.1667 | −1.14989 | −0.574947 | − | 0.818190i | \(-0.694977\pi\) | ||||
−0.574947 | + | 0.818190i | \(0.694977\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 41.3627 | 1.88598 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.947342 | −0.0431056 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30.5866 | 1.38887 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.54863 | −0.387375 | −0.193688 | − | 0.981063i | \(-0.562045\pi\) | ||||
−0.193688 | + | 0.981063i | \(0.562045\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.3004 | 1.00846 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.8474 | 1.16648 | 0.583238 | − | 0.812301i | \(-0.301785\pi\) | ||||
0.583238 | + | 0.812301i | \(0.301785\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.64902 | −0.119306 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.48933 | −0.336620 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.42651 | −0.198556 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.1286 | −0.945847 | −0.472923 | − | 0.881104i | \(-0.656801\pi\) | ||||
−0.472923 | + | 0.881104i | \(0.656801\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.82587 | −0.348938 | −0.174469 | − | 0.984663i | \(-0.555821\pi\) | ||||
−0.174469 | + | 0.984663i | \(0.555821\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.19083 | −0.0529911 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.4005 | 0.906020 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.7245 | −1.00725 | −0.503623 | − | 0.863923i | \(-0.668000\pi\) | ||||
−0.503623 | + | 0.863923i | \(0.668000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.657838 | 0.0291010 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.04977 | 0.134651 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −31.9828 | −1.40933 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.49195 | 0.329496 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.5505 | 0.770383 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.1453 | −0.488286 | −0.244143 | − | 0.969739i | \(-0.578507\pi\) | ||||
−0.244143 | + | 0.969739i | \(0.578507\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.3399 | 1.15176 | 0.575881 | − | 0.817534i | \(-0.304659\pi\) | ||||
0.575881 | + | 0.817534i | \(0.304659\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.32714 | −0.145208 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.16769 | 0.181547 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.8859 | −0.908084 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.09356 | −0.134249 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 51.1539 | 2.21572 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 47.0870 | 2.03575 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.4005 | −0.923498 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.4907 | 0.667230 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.6396 | 1.14532 | 0.572662 | − | 0.819791i | \(-0.305911\pi\) | ||||
0.572662 | + | 0.819791i | \(0.305911\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.4205 | −0.447187 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 49.2593 | 2.11004 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.96240 | −0.126663 | −0.0633315 | − | 0.997993i | \(-0.520173\pi\) | ||||
−0.0633315 | + | 0.997993i | \(0.520173\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.8291 | −0.590211 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.9663 | 0.467182 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.71728 | 0.370696 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22.7527 | 0.965798 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.2995 | 1.24146 | 0.620730 | − | 0.784024i | \(-0.286836\pi\) | ||||
0.620730 | + | 0.784024i | \(0.286836\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.6999 | 1.21388 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.73554 | 0.0732744 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.57725 | 0.403633 | 0.201816 | − | 0.979423i | \(-0.435316\pi\) | ||||
0.201816 | + | 0.979423i | \(0.435316\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.30041 | 0.265060 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.651548 | −0.0273625 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.4227 | −0.436944 | −0.218472 | − | 0.975843i | \(-0.570107\pi\) | ||||
−0.218472 | + | 0.975843i | \(0.570107\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.2919 | 0.598097 | 0.299048 | − | 0.954238i | \(-0.403331\pi\) | ||||
0.299048 | + | 0.954238i | \(0.403331\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.3798 | −0.433624 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.42479 | 0.309635 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.12593 | −0.0885038 | −0.0442519 | − | 0.999020i | \(-0.514090\pi\) | ||||
−0.0442519 | + | 0.999020i | \(0.514090\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.9382 | −0.828603 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.41041 | −0.224462 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.53697 | −0.146486 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.3729 | 0.759625 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.4771 | −1.25792 | −0.628962 | − | 0.777436i | \(-0.716520\pi\) | ||||
−0.628962 | + | 0.777436i | \(0.716520\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.2533 | −0.710909 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.5273 | 0.885513 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −40.2084 | −1.65116 | −0.825580 | − | 0.564285i | \(-0.809152\pi\) | ||||
−0.825580 | + | 0.564285i | \(0.809152\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.52594 | 0.0625576 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.57836 | −0.0645980 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.845760 | −0.0345568 | −0.0172784 | − | 0.999851i | \(-0.505500\pi\) | ||||
−0.0172784 | + | 0.999851i | \(0.505500\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.0722 | −1.22667 | −0.613335 | − | 0.789823i | \(-0.710172\pi\) | ||||
−0.613335 | + | 0.789823i | \(0.710172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.06273 | 0.246893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.3263 | −0.704414 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.9582 | 1.29714 | 0.648572 | − | 0.761153i | \(-0.275366\pi\) | ||||
0.648572 | + | 0.761153i | \(0.275366\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.34283 | −0.0949362 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.3793 | −0.743548 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.1244 | 0.610868 | 0.305434 | − | 0.952213i | \(-0.401198\pi\) | ||||
0.305434 | + | 0.952213i | \(0.401198\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 28.1386 | 1.13466 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.5830 | −0.627350 | −0.313675 | − | 0.949530i | \(-0.601560\pi\) | ||||
−0.313675 | + | 0.949530i | \(0.601560\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.89579 | −0.357552 | −0.178776 | − | 0.983890i | \(-0.557214\pi\) | ||||
−0.178776 | + | 0.983890i | \(0.557214\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.45399 | 0.0583464 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.53538 | 0.301898 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.4561 | −0.978245 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.18472 | −0.286930 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.27259 | −0.210232 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.4222 | 1.68880 | 0.844400 | − | 0.535713i | \(-0.179957\pi\) | ||||
0.844400 | + | 0.535713i | \(0.179957\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.1516 | −0.641967 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.5320 | −0.576684 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −38.0018 | −1.50569 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.79383 | 0.268760 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.9454 | 1.38026 | 0.690130 | − | 0.723685i | \(-0.257553\pi\) | ||||
0.690130 | + | 0.723685i | \(0.257553\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.2870 | −0.721170 | −0.360585 | − | 0.932726i | \(-0.617423\pi\) | ||||
−0.360585 | + | 0.932726i | \(0.617423\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.7872 | 0.621620 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.9514 | 1.13820 | 0.569099 | − | 0.822269i | \(-0.307292\pi\) | ||||
0.569099 | + | 0.822269i | \(0.307292\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.28787 | 0.286074 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.68596 | 0.144464 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.68083 | −0.300574 | −0.150287 | − | 0.988642i | \(-0.548020\pi\) | ||||
−0.150287 | + | 0.988642i | \(0.548020\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.9009 | 1.05111 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.00965 | −0.0393903 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.8279 | 0.655523 | 0.327761 | − | 0.944761i | \(-0.393706\pi\) | ||||
0.327761 | + | 0.944761i | \(0.393706\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.2589 | −1.33252 | −0.666258 | − | 0.745721i | \(-0.732105\pi\) | ||||
−0.666258 | + | 0.745721i | \(0.732105\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.25763 | −0.165353 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.31706 | −0.244965 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.22822 | 0.202438 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.9061 | 0.614967 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.5789 | 1.25769 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.98223 | −0.153504 | −0.0767519 | − | 0.997050i | \(-0.524455\pi\) | ||||
−0.0767519 | + | 0.997050i | \(0.524455\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.10651 | 0.196550 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.2722 | 0.894424 | 0.447212 | − | 0.894428i | \(-0.352417\pi\) | ||||
0.447212 | + | 0.894428i | \(0.352417\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.26870 | −0.240570 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.5938 | −0.980755 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.0489 | −0.537564 | −0.268782 | − | 0.963201i | \(-0.586621\pi\) | ||||
−0.268782 | + | 0.963201i | \(0.586621\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.0972 | −1.11175 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.79809 | −0.144906 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.67693 | 0.330565 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.46717 | −0.207981 | −0.103990 | − | 0.994578i | \(-0.533161\pi\) | ||||
−0.103990 | + | 0.994578i | \(0.533161\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.53493 | 0.0583072 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.7258 | 0.596515 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.52069 | −0.246989 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.9836 | 0.453261 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.62817 | 0.0614952 | 0.0307476 | − | 0.999527i | \(-0.490211\pi\) | ||||
0.0307476 | + | 0.999527i | \(0.490211\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.8273 | 0.823232 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.1101 | −0.380767 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.244059 | 0.00917878 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −49.5471 | −1.86078 | −0.930390 | − | 0.366572i | \(-0.880531\pi\) | ||||
−0.930390 | + | 0.366572i | \(0.880531\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.3793 | −0.501764 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.22554 | −0.308049 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −43.2832 | −1.61870 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.97611 | −0.185836 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.8137 | 1.67127 | 0.835635 | − | 0.549286i | \(-0.185100\pi\) | ||||
0.835635 | + | 0.549286i | \(0.185100\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.55485 | 0.244115 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.08605 | 0.189152 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.3619 | 0.681944 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.63373 | −0.171856 | −0.0859278 | − | 0.996301i | \(-0.527385\pi\) | ||||
−0.0859278 | + | 0.996301i | \(0.527385\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.65844 | −0.135312 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.5214 | −0.684103 | −0.342052 | − | 0.939681i | \(-0.611122\pi\) | ||||
−0.342052 | + | 0.939681i | \(0.611122\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20.9039 | −0.771054 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.2827 | −0.526110 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.8273 | −0.471860 | −0.235930 | − | 0.971770i | \(-0.575814\pi\) | ||||
−0.235930 | + | 0.971770i | \(0.575814\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.6256 | 0.647493 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.8237 | 0.543827 | 0.271914 | − | 0.962322i | \(-0.412344\pi\) | ||||
0.271914 | + | 0.962322i | \(0.412344\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.1193 | −1.10349 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.30393 | 0.303825 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.65045 | −0.352620 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.09316 | −0.222343 | −0.111171 | − | 0.993801i | \(-0.535460\pi\) | ||||
−0.111171 | + | 0.993801i | \(0.535460\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.9778 | 0.837356 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.6263 | 0.605092 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.7244 | 0.644203 | 0.322101 | − | 0.946705i | \(-0.395611\pi\) | ||||
0.322101 | + | 0.946705i | \(0.395611\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.42533 | −0.124332 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.5542 | −1.03509 | −0.517544 | − | 0.855657i | \(-0.673153\pi\) | ||||
−0.517544 | + | 0.855657i | \(0.673153\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0957 | −0.365487 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.34203 | −0.0846762 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.8787 | −0.645561 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.8197 | −1.25563 | −0.627815 | − | 0.778362i | \(-0.716051\pi\) | ||||
−0.627815 | + | 0.778362i | \(0.716051\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.54328 | 0.199637 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.10623 | −0.0397883 | −0.0198941 | − | 0.999802i | \(-0.506333\pi\) | ||||
−0.0198941 | + | 0.999802i | \(0.506333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.8887 | −1.03771 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.66315 | −0.167289 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.9941 | 0.967165 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0050 | −0.572705 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.59579 | 0.128503 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 51.0392 | 1.82167 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.4837 | 0.765812 | 0.382906 | − | 0.923787i | \(-0.374923\pi\) | ||||
0.382906 | + | 0.923787i | \(0.374923\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.0070 | −0.356260 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.29126 | −0.0459120 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −79.9228 | −2.83814 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.77298 | 0.169280 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.3920 | −0.686900 | −0.343450 | − | 0.939171i | \(-0.611596\pi\) | ||||
−0.343450 | + | 0.939171i | \(0.611596\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.34285 | 0.0828840 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.5653 | −0.408641 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.37856 | 0.0839376 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.01167 | −0.106147 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.4920 | 1.00297 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.98259 | −0.0697041 | −0.0348520 | − | 0.999392i | \(-0.511096\pi\) | ||||
−0.0348520 | + | 0.999392i | \(0.511096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.12364 | 0.179915 | 0.0899577 | − | 0.995946i | \(-0.471327\pi\) | ||||
0.0899577 | + | 0.995946i | \(0.471327\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.31835 | 0.116379 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 70.8946 | 2.48333 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.1451 | 0.529860 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.76551 | −0.131577 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.0449 | 0.525072 | 0.262536 | − | 0.964922i | \(-0.415441\pi\) | ||||
0.262536 | + | 0.964922i | \(0.415441\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.86337 | −0.308958 | −0.154479 | − | 0.987996i | \(-0.549370\pi\) | ||||
−0.154479 | + | 0.987996i | \(0.549370\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.0300 | −0.418832 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.1782 | 0.527797 | 0.263898 | − | 0.964551i | \(-0.414992\pi\) | ||||
0.263898 | + | 0.964551i | \(0.414992\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.1528 | −0.665205 | −0.332602 | − | 0.943067i | \(-0.607927\pi\) | ||||
−0.332602 | + | 0.943067i | \(0.607927\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.48347 | −0.120840 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.84417 | 0.167840 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.17907 | −0.110016 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.65723 | −0.195543 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.8741 | 1.41113 | 0.705565 | − | 0.708645i | \(-0.250693\pi\) | ||||
0.705565 | + | 0.708645i | \(0.250693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.0703 | −0.554149 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.76222 | 0.129578 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 64.8548 | 2.23107 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.55101 | 0.122014 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.4873 | 0.565841 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.4062 | 0.356720 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.0999 | 0.380052 | 0.190026 | − | 0.981779i | \(-0.439143\pi\) | ||||
0.190026 | + | 0.981779i | \(0.439143\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.69545 | 0.331577 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.658909 | −0.0225079 | −0.0112539 | − | 0.999937i | \(-0.503582\pi\) | ||||
−0.0112539 | + | 0.999937i | \(0.503582\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.9062 | −0.713310 | −0.356655 | − | 0.934236i | \(-0.616083\pi\) | ||||
−0.356655 | + | 0.934236i | \(0.616083\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.76698 | −0.196538 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.9133 | 1.56291 | 0.781453 | − | 0.623964i | \(-0.214479\pi\) | ||||
0.781453 | + | 0.623964i | \(0.214479\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 55.7945 | 1.89707 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.4573 | −0.558918 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.5193 | 1.06922 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.0384 | 1.18723 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.62123 | 0.325629 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.220612 | −0.00745806 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1757 | 0.782587 | 0.391293 | − | 0.920266i | \(-0.372028\pi\) | ||||
0.391293 | + | 0.920266i | \(0.372028\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.965119 | 0.0325526 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.5672 | 1.13091 | 0.565454 | − | 0.824780i | \(-0.308701\pi\) | ||||
0.565454 | + | 0.824780i | \(0.308701\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.5629 | 0.759301 | 0.379651 | − | 0.925130i | \(-0.376044\pi\) | ||||
0.379651 | + | 0.925130i | \(0.376044\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.83465 | −0.330588 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.5003 | 0.621181 | 0.310590 | − | 0.950544i | \(-0.399473\pi\) | ||||
0.310590 | + | 0.950544i | \(0.399473\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.97832 | 0.0998896 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.35582 | −0.0789230 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.69885 | −0.324560 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −68.0336 | −2.27411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.40305 | 0.280570 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.3422 | −0.678450 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.10606 | −0.0368484 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.23557 | −0.107673 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.1276 | −1.10120 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.1224 | 1.09981 | 0.549905 | − | 0.835227i | \(-0.314664\pi\) | ||||
0.549905 | + | 0.835227i | \(0.314664\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.374583 | −0.0124241 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.6212 | 1.64402 | 0.822012 | − | 0.569470i | \(-0.192851\pi\) | ||||
0.822012 | + | 0.569470i | \(0.192851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.5626 | −0.647427 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −43.9637 | −1.45340 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.51332 | −0.182066 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.74469 | −0.255474 | −0.127737 | − | 0.991808i | \(-0.540771\pi\) | ||||
−0.127737 | + | 0.991808i | \(0.540771\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.8989 | 0.359129 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.2637 | 1.29238 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.5474 | 1.20167 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.0604 | −0.330427 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.7929 | −0.944663 | −0.472332 | − | 0.881421i | \(-0.656587\pi\) | ||||
−0.472332 | + | 0.881421i | \(0.656587\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.0537 | −0.657235 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.2877 | 0.762405 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.51740 | 0.180438 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.6507 | 0.543953 | 0.271977 | − | 0.962304i | \(-0.412323\pi\) | ||||
0.271977 | + | 0.962304i | \(0.412323\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.2329 | 0.856079 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.4130 | 1.18703 | 0.593515 | − | 0.804823i | \(-0.297740\pi\) | ||||
0.593515 | + | 0.804823i | \(0.297740\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.8695 | 0.419089 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.07132 | −0.0673800 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.7734 | −1.12998 | −0.564992 | − | 0.825097i | \(-0.691121\pi\) | ||||
−0.564992 | + | 0.825097i | \(0.691121\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.83511 | −0.189416 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.5938 | 0.894790 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.4050 | −1.08209 | −0.541046 | − | 0.840993i | \(-0.681972\pi\) | ||||
−0.541046 | + | 0.840993i | \(0.681972\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.9983 | −1.06780 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.47103 | −0.273830 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.96344 | 0.192570 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00428 | 0.0323962 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.8116 | 0.477296 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −63.3850 | −2.04043 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.8553 | 1.31382 | 0.656910 | − | 0.753969i | \(-0.271863\pi\) | ||||
0.656910 | + | 0.753969i | \(0.271863\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.24677 | −0.0721767 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.6557 | 1.04797 | 0.523986 | − | 0.851727i | \(-0.324444\pi\) | ||||
0.523986 | + | 0.851727i | \(0.324444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.22300 | −0.103325 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 29.5121 | 0.945145 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.0370 | 0.832996 | 0.416498 | − | 0.909137i | \(-0.363257\pi\) | ||||
0.416498 | + | 0.909137i | \(0.363257\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.2459 | 0.870782 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.4949 | 0.494713 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50.8084 | −1.62054 | −0.810269 | − | 0.586059i | \(-0.800679\pi\) | ||||
−0.810269 | + | 0.586059i | \(0.800679\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 68.4368 | 2.18058 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.07205 | 0.0659540 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.22045 | 0.229597 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.1305 | 0.448871 | 0.224436 | − | 0.974489i | \(-0.427946\pi\) | ||||
0.224436 | + | 0.974489i | \(0.427946\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.6057 | −0.368295 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.01772 | −0.159073 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.7523 | −1.60734 | −0.803671 | − | 0.595074i | \(-0.797123\pi\) | ||||
−0.803671 | + | 0.595074i | \(0.797123\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.15702 | 0.226438 |
(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.1.8 | 11 | ||
4.3 | odd | 2 | 4008.2.a.k.1.8 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.k.1.8 | ✓ | 11 | 4.3 | odd | 2 | ||
8016.2.a.be.1.8 | 11 | 1.1 | even | 1 | trivial |