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: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 49 x^{11} + 99 x^{10} + 901 x^{9} - 1879 x^{8} - 7582 x^{7} + 16968 x^{6} + \cdots + 12144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(4.20017\) 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 | ||||||||
\(5\) | 4.20017 | 1.87837 | 0.939186 | − | 0.343409i | \(-0.111582\pi\) | ||||
0.939186 | + | 0.343409i | \(0.111582\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.497670 | 0.188101 | 0.0940507 | − | 0.995567i | \(-0.470018\pi\) | ||||
0.0940507 | + | 0.995567i | \(0.470018\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.310660 | 0.0936674 | 0.0468337 | − | 0.998903i | \(-0.485087\pi\) | ||||
0.0468337 | + | 0.998903i | \(0.485087\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.223370 | −0.0619517 | −0.0309758 | − | 0.999520i | \(-0.509861\pi\) | ||||
−0.0309758 | + | 0.999520i | \(0.509861\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.20017 | −1.08448 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.33328 | 0.808438 | 0.404219 | − | 0.914662i | \(-0.367543\pi\) | ||||
0.404219 | + | 0.914662i | \(0.367543\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.261095 | 0.0598993 | 0.0299496 | − | 0.999551i | \(-0.490465\pi\) | ||||
0.0299496 | + | 0.999551i | \(0.490465\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.497670 | −0.108600 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.01998 | 1.88080 | 0.940398 | − | 0.340075i | \(-0.110452\pi\) | ||||
0.940398 | + | 0.340075i | \(0.110452\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.6414 | 2.52828 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.87692 | 0.719927 | 0.359963 | − | 0.932966i | \(-0.382789\pi\) | ||||
0.359963 | + | 0.932966i | \(0.382789\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.329778 | −0.0592299 | −0.0296150 | − | 0.999561i | \(-0.509428\pi\) | ||||
−0.0296150 | + | 0.999561i | \(0.509428\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.310660 | −0.0540789 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.09030 | 0.353325 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.490531 | −0.0806428 | −0.0403214 | − | 0.999187i | \(-0.512838\pi\) | ||||
−0.0403214 | + | 0.999187i | \(0.512838\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.223370 | 0.0357678 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.61488 | 1.50159 | 0.750796 | − | 0.660534i | \(-0.229670\pi\) | ||||
0.750796 | + | 0.660534i | \(0.229670\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.34275 | −0.357267 | −0.178633 | − | 0.983916i | \(-0.557168\pi\) | ||||
−0.178633 | + | 0.983916i | \(0.557168\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.20017 | 0.626124 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.94428 | −1.45052 | −0.725261 | − | 0.688474i | \(-0.758281\pi\) | ||||
−0.725261 | + | 0.688474i | \(0.758281\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.75232 | −0.964618 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.33328 | −0.466752 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.93441 | 0.403073 | 0.201536 | − | 0.979481i | \(-0.435407\pi\) | ||||
0.201536 | + | 0.979481i | \(0.435407\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.30482 | 0.175942 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.261095 | −0.0345829 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.69784 | −0.351228 | −0.175614 | − | 0.984459i | \(-0.556191\pi\) | ||||
−0.175614 | + | 0.984459i | \(0.556191\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.23520 | −0.158152 | −0.0790759 | − | 0.996869i | \(-0.525197\pi\) | ||||
−0.0790759 | + | 0.996869i | \(0.525197\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.497670 | 0.0627005 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.938191 | −0.116368 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.6982 | −1.42916 | −0.714582 | − | 0.699552i | \(-0.753383\pi\) | ||||
−0.714582 | + | 0.699552i | \(0.753383\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.01998 | −1.08588 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.61858 | 0.429446 | 0.214723 | − | 0.976675i | \(-0.431115\pi\) | ||||
0.214723 | + | 0.976675i | \(0.431115\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.33699 | −0.507607 | −0.253803 | − | 0.967256i | \(-0.581682\pi\) | ||||
−0.253803 | + | 0.967256i | \(0.581682\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.6414 | −1.45970 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.154606 | 0.0176190 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.59750 | 0.292241 | 0.146121 | − | 0.989267i | \(-0.453321\pi\) | ||||
0.146121 | + | 0.989267i | \(0.453321\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.06581 | −0.336517 | −0.168258 | − | 0.985743i | \(-0.553814\pi\) | ||||
−0.168258 | + | 0.985743i | \(0.553814\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.0003 | 1.51855 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.87692 | −0.415650 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.4181 | 1.52832 | 0.764158 | − | 0.645029i | \(-0.223155\pi\) | ||||
0.764158 | + | 0.645029i | \(0.223155\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.111164 | −0.0116532 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.329778 | 0.0341964 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.09664 | 0.112513 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.603712 | −0.0612977 | −0.0306489 | − | 0.999530i | \(-0.509757\pi\) | ||||
−0.0306489 | + | 0.999530i | \(0.509757\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.310660 | 0.0312225 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.25046 | −0.124425 | −0.0622126 | − | 0.998063i | \(-0.519816\pi\) | ||||
−0.0622126 | + | 0.998063i | \(0.519816\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.1837 | 1.49610 | 0.748049 | − | 0.663643i | \(-0.230991\pi\) | ||||
0.748049 | + | 0.663643i | \(0.230991\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.09030 | −0.203992 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.86387 | 0.663556 | 0.331778 | − | 0.943358i | \(-0.392352\pi\) | ||||
0.331778 | + | 0.943358i | \(0.392352\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.48328 | 0.620985 | 0.310493 | − | 0.950576i | \(-0.399506\pi\) | ||||
0.310493 | + | 0.950576i | \(0.399506\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.490531 | 0.0465592 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.94499 | −0.371113 | −0.185556 | − | 0.982634i | \(-0.559409\pi\) | ||||
−0.185556 | + | 0.982634i | \(0.559409\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 37.8854 | 3.53284 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.223370 | −0.0206506 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.65887 | 0.152068 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9035 | −0.991226 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.61488 | −0.866945 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 32.0952 | 2.87068 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.9104 | −1.41182 | −0.705911 | − | 0.708300i | \(-0.749462\pi\) | ||||
−0.705911 | + | 0.708300i | \(0.749462\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.34275 | 0.206268 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.83534 | −0.509836 | −0.254918 | − | 0.966963i | \(-0.582048\pi\) | ||||
−0.254918 | + | 0.966963i | \(0.582048\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.129939 | 0.0112671 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.20017 | −0.361493 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.0709 | 1.54390 | 0.771949 | − | 0.635684i | \(-0.219282\pi\) | ||||
0.771949 | + | 0.635684i | \(0.219282\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.08854 | −0.0923285 | −0.0461642 | − | 0.998934i | \(-0.514700\pi\) | ||||
−0.0461642 | + | 0.998934i | \(0.514700\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.94428 | 0.837459 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.0693920 | −0.00580285 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.2837 | 1.35229 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.75232 | 0.556922 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.57620 | −0.620667 | −0.310333 | − | 0.950628i | \(-0.600441\pi\) | ||||
−0.310333 | + | 0.950628i | \(0.600441\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.06300 | 0.493400 | 0.246700 | − | 0.969092i | \(-0.420654\pi\) | ||||
0.246700 | + | 0.969092i | \(0.420654\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.33328 | 0.269479 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.38512 | −0.111256 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.55015 | −0.522759 | −0.261379 | − | 0.965236i | \(-0.584177\pi\) | ||||
−0.261379 | + | 0.965236i | \(0.584177\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.93441 | −0.232714 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.48897 | 0.353781 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.61424 | 0.361415 | 0.180708 | − | 0.983537i | \(-0.442161\pi\) | ||||
0.180708 | + | 0.983537i | \(0.442161\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.30482 | −0.101580 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9501 | −0.996162 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.261095 | 0.0199664 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.3229 | −1.39306 | −0.696531 | − | 0.717526i | \(-0.745274\pi\) | ||||
−0.696531 | + | 0.717526i | \(0.745274\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.29125 | 0.475574 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.69784 | 0.202782 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.8576 | 1.18525 | 0.592625 | − | 0.805478i | \(-0.298092\pi\) | ||||
0.592625 | + | 0.805478i | \(0.298092\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.26382 | −0.465586 | −0.232793 | − | 0.972526i | \(-0.574786\pi\) | ||||
−0.232793 | + | 0.972526i | \(0.574786\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.23520 | 0.0913089 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.06031 | −0.151477 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.03551 | 0.0757243 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.497670 | −0.0362001 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.8669 | 0.858661 | 0.429331 | − | 0.903147i | \(-0.358750\pi\) | ||||
0.429331 | + | 0.903147i | \(0.358750\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.0978 | −0.870818 | −0.435409 | − | 0.900233i | \(-0.643396\pi\) | ||||
−0.435409 | + | 0.900233i | \(0.643396\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.938191 | 0.0671853 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.3800 | −1.16703 | −0.583513 | − | 0.812104i | \(-0.698322\pi\) | ||||
−0.583513 | + | 0.812104i | \(0.698322\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.9684 | −0.990190 | −0.495095 | − | 0.868839i | \(-0.664867\pi\) | ||||
−0.495095 | + | 0.868839i | \(0.664867\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.6982 | 0.825128 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.92943 | 0.135419 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 40.3841 | 2.82055 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.01998 | 0.626932 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0811117 | 0.00561061 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.16435 | 0.562057 | 0.281028 | − | 0.959699i | \(-0.409324\pi\) | ||||
0.281028 | + | 0.959699i | \(0.409324\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.61858 | −0.247941 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.83996 | −0.671080 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.164121 | −0.0111412 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.33699 | 0.293067 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.744554 | −0.0500841 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.9773 | −1.60564 | −0.802819 | − | 0.596222i | \(-0.796668\pi\) | ||||
−0.802819 | + | 0.596222i | \(0.796668\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.6414 | 0.842761 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.9052 | 1.32115 | 0.660576 | − | 0.750759i | \(-0.270312\pi\) | ||||
0.660576 | + | 0.750759i | \(0.270312\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.53054 | −0.299387 | −0.149693 | − | 0.988732i | \(-0.547829\pi\) | ||||
−0.149693 | + | 0.988732i | \(0.547829\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.154606 | −0.0101723 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.30087 | 0.347272 | 0.173636 | − | 0.984810i | \(-0.444448\pi\) | ||||
0.173636 | + | 0.984810i | \(0.444448\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −41.7676 | −2.72462 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.59750 | −0.168725 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.02390 | −0.454338 | −0.227169 | − | 0.973855i | \(-0.572947\pi\) | ||||
−0.227169 | + | 0.973855i | \(0.572947\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.34486 | −0.408708 | −0.204354 | − | 0.978897i | \(-0.565509\pi\) | ||||
−0.204354 | + | 0.978897i | \(0.565509\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −28.3609 | −1.81191 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0583208 | −0.00371086 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.06581 | 0.194288 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.3005 | 1.59695 | 0.798476 | − | 0.602026i | \(-0.205640\pi\) | ||||
0.798476 | + | 0.602026i | \(0.205640\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.80215 | 0.176169 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.0003 | −0.876734 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.70489 | −0.231105 | −0.115552 | − | 0.993301i | \(-0.536864\pi\) | ||||
−0.115552 | + | 0.993301i | \(0.536864\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.244122 | −0.0151690 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.87692 | 0.239976 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.5558 | 0.712563 | 0.356282 | − | 0.934379i | \(-0.384044\pi\) | ||||
0.356282 | + | 0.934379i | \(0.384044\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.3250 | 0.757120 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.4181 | −0.882374 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.8733 | −1.69946 | −0.849731 | − | 0.527216i | \(-0.823236\pi\) | ||||
−0.849731 | + | 0.527216i | \(0.823236\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.26815 | 0.198526 | 0.0992631 | − | 0.995061i | \(-0.468351\pi\) | ||||
0.0992631 | + | 0.995061i | \(0.468351\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.111164 | 0.00672798 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.92718 | 0.236818 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.68912 | −0.221658 | −0.110829 | − | 0.993840i | \(-0.535351\pi\) | ||||
−0.110829 | + | 0.993840i | \(0.535351\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.329778 | −0.0197433 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.1453 | −0.664874 | −0.332437 | − | 0.943126i | \(-0.607871\pi\) | ||||
−0.332437 | + | 0.943126i | \(0.607871\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.0956 | 1.49178 | 0.745890 | − | 0.666070i | \(-0.232025\pi\) | ||||
0.745890 | + | 0.666070i | \(0.232025\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.09664 | −0.0649595 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.78504 | 0.282452 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.88927 | −0.346428 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.603712 | 0.0353902 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.4221 | 1.60201 | 0.801007 | − | 0.598655i | \(-0.204298\pi\) | ||||
0.801007 | + | 0.598655i | \(0.204298\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.3314 | −0.659738 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.310660 | −0.0180263 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.01479 | −0.116518 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.16592 | −0.0672024 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.25046 | 0.0718370 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.18807 | −0.297068 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.7027 | −1.75229 | −0.876147 | − | 0.482044i | \(-0.839894\pi\) | ||||
−0.876147 | + | 0.482044i | \(0.839894\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.1837 | −0.863773 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.33888 | 0.0759212 | 0.0379606 | − | 0.999279i | \(-0.487914\pi\) | ||||
0.0379606 | + | 0.999279i | \(0.487914\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.5418 | 0.595856 | 0.297928 | − | 0.954588i | \(-0.403704\pi\) | ||||
0.297928 | + | 0.954588i | \(0.403704\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.09030 | 0.117775 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.08789 | −0.229599 | −0.114800 | − | 0.993389i | \(-0.536623\pi\) | ||||
−0.114800 | + | 0.993389i | \(0.536623\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.20440 | 0.0674337 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.86387 | −0.383104 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.870302 | 0.0484249 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.82371 | −0.156631 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.48328 | −0.358526 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.94897 | −0.272845 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.5164 | −1.01776 | −0.508878 | − | 0.860839i | \(-0.669939\pi\) | ||||
−0.508878 | + | 0.860839i | \(0.669939\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.490531 | −0.0268809 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −49.1344 | −2.68450 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.2998 | 0.996851 | 0.498425 | − | 0.866933i | \(-0.333912\pi\) | ||||
0.498425 | + | 0.866933i | \(0.333912\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.94499 | 0.214262 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.102449 | −0.00554791 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.84412 | −0.369548 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −37.8854 | −2.03968 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.00397972 | 0.000213642 0 | 0.000106821 | − | 1.00000i | \(-0.499966\pi\) | ||||
0.000106821 | 1.00000i | \(0.499966\pi\) | ||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.38445 | 0.395280 | 0.197640 | − | 0.980275i | \(-0.436672\pi\) | ||||
0.197640 | + | 0.980275i | \(0.436672\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.223370 | 0.0119226 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.3841 | 0.712362 | 0.356181 | − | 0.934417i | \(-0.384079\pi\) | ||||
0.356181 | + | 0.934417i | \(0.384079\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.1986 | 0.806659 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.65887 | −0.0877967 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.16101 | −0.272388 | −0.136194 | − | 0.990682i | \(-0.543487\pi\) | ||||
−0.136194 | + | 0.990682i | \(0.543487\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9318 | −0.996412 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.9035 | 0.572285 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.2161 | −0.953474 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.97797 | −0.155449 | −0.0777244 | − | 0.996975i | \(-0.524765\pi\) | ||||
−0.0777244 | + | 0.996975i | \(0.524765\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.61488 | 0.500531 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.46037 | 0.0758185 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.4777 | 1.78519 | 0.892595 | − | 0.450860i | \(-0.148883\pi\) | ||||
0.892595 | + | 0.450860i | \(0.148883\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −32.0952 | −1.65739 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.865988 | −0.0446007 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.8223 | 0.658639 | 0.329320 | − | 0.944218i | \(-0.393181\pi\) | ||||
0.329320 | + | 0.944218i | \(0.393181\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.9104 | 0.815116 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.6965 | 0.904246 | 0.452123 | − | 0.891955i | \(-0.350667\pi\) | ||||
0.452123 | + | 0.891955i | \(0.350667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.649371 | 0.0330950 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.34275 | −0.119089 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.00428 | −0.0509189 | −0.0254594 | − | 0.999676i | \(-0.508105\pi\) | ||||
−0.0254594 | + | 0.999676i | \(0.508105\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.0661 | 1.52051 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.83534 | 0.294354 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.9099 | 0.548937 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.25402 | 0.163315 | 0.0816573 | − | 0.996660i | \(-0.473979\pi\) | ||||
0.0816573 | + | 0.996660i | \(0.473979\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.129939 | −0.00650509 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.93586 | 0.396298 | 0.198149 | − | 0.980172i | \(-0.436507\pi\) | ||||
0.198149 | + | 0.980172i | \(0.436507\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0736626 | 0.00366939 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.20017 | 0.208708 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.152388 | −0.00755360 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.2683 | 0.804417 | 0.402208 | − | 0.915548i | \(-0.368243\pi\) | ||||
0.402208 | + | 0.915548i | \(0.368243\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.0709 | −0.891370 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.34263 | −0.0660666 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.8769 | −0.632104 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.08854 | 0.0533059 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.0257 | 0.489788 | 0.244894 | − | 0.969550i | \(-0.421247\pi\) | ||||
0.244894 | + | 0.969550i | \(0.421247\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.3083 | 1.62335 | 0.811673 | − | 0.584112i | \(-0.198557\pi\) | ||||
0.811673 | + | 0.584112i | \(0.198557\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.94428 | −0.483507 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 42.1373 | 2.04396 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.614724 | −0.0297486 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0693920 | 0.00335028 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.2930 | −1.41099 | −0.705496 | − | 0.708714i | \(-0.749276\pi\) | ||||
−0.705496 | + | 0.708714i | \(0.749276\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.8885 | −1.43635 | −0.718175 | − | 0.695862i | \(-0.755022\pi\) | ||||
−0.718175 | + | 0.695862i | \(0.755022\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.2837 | −0.780745 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.35507 | 0.112658 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.7837 | 0.610131 | 0.305065 | − | 0.952331i | \(-0.401322\pi\) | ||||
0.305065 | + | 0.952331i | \(0.401322\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.75232 | −0.321539 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.03002 | 0.0489375 | 0.0244688 | − | 0.999701i | \(-0.492211\pi\) | ||||
0.0244688 | + | 0.999701i | \(0.492211\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 60.5585 | 2.87075 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.57620 | 0.358342 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.9295 | 0.657374 | 0.328687 | − | 0.944439i | \(-0.393394\pi\) | ||||
0.328687 | + | 0.944439i | \(0.393394\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.98696 | 0.140650 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.06300 | −0.284865 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.466909 | −0.0218890 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.59714 | 0.448935 | 0.224468 | − | 0.974482i | \(-0.427936\pi\) | ||||
0.224468 | + | 0.974482i | \(0.427936\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.33328 | −0.155584 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.35477 | 0.249396 | 0.124698 | − | 0.992195i | \(-0.460204\pi\) | ||||
0.124698 | + | 0.992195i | \(0.460204\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.9012 | −0.831941 | −0.415970 | − | 0.909378i | \(-0.636558\pi\) | ||||
−0.415970 | + | 0.909378i | \(0.636558\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.38512 | 0.0642336 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.5496 | 1.13602 | 0.568010 | − | 0.823022i | \(-0.307714\pi\) | ||||
0.568010 | + | 0.823022i | \(0.307714\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.82184 | −0.268828 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.55015 | 0.301815 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.727799 | −0.0334642 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.30061 | 0.151442 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.93441 | 0.134358 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.06290 | 0.185639 | 0.0928194 | − | 0.995683i | \(-0.470412\pi\) | ||||
0.0928194 | + | 0.995683i | \(0.470412\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.109570 | 0.00499596 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.48897 | −0.204255 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.53569 | −0.115140 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.8338 | 0.717496 | 0.358748 | − | 0.933434i | \(-0.383204\pi\) | ||||
0.358748 | + | 0.933434i | \(0.383204\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.61424 | −0.208663 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.9595 | −0.584856 | −0.292428 | − | 0.956288i | \(-0.594463\pi\) | ||||
−0.292428 | + | 0.956288i | \(0.594463\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.9229 | 0.582016 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.30482 | 0.0586474 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.80086 | 0.0807794 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.9159 | −0.578194 | −0.289097 | − | 0.957300i | \(-0.593355\pi\) | ||||
−0.289097 | + | 0.957300i | \(0.593355\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.878522 | 0.0391713 | 0.0195857 | − | 0.999808i | \(-0.493765\pi\) | ||||
0.0195857 | + | 0.999808i | \(0.493765\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.25214 | −0.233717 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9501 | 0.575134 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.7414 | −0.697727 | −0.348864 | − | 0.937173i | \(-0.613432\pi\) | ||||
−0.348864 | + | 0.937173i | \(0.613432\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.15839 | −0.0954815 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.261095 | −0.0115276 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 63.7743 | 2.81023 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.08928 | −0.135867 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.3229 | 0.804285 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.29423 | 0.319566 | 0.159783 | − | 0.987152i | \(-0.448921\pi\) | ||||
0.159783 | + | 0.987152i | \(0.448921\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.5868 | 1.33747 | 0.668734 | − | 0.743501i | \(-0.266836\pi\) | ||||
0.668734 | + | 0.743501i | \(0.266836\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.29125 | −0.274573 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.09924 | −0.0478837 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 58.3601 | 2.53740 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.69784 | −0.117076 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.14768 | −0.0930262 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.8294 | 1.24640 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.8576 | −0.684305 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.09767 | −0.0903532 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.8053 | −0.636531 | −0.318265 | − | 0.948002i | \(-0.603100\pi\) | ||||
−0.318265 | + | 0.948002i | \(0.603100\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.26382 | 0.268806 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.2308 | 1.16644 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.2584 | −0.780673 | −0.390337 | − | 0.920672i | \(-0.627641\pi\) | ||||
−0.390337 | + | 0.920672i | \(0.627641\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.23520 | −0.0527172 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.01225 | 0.0431231 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.29269 | 0.0549710 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.06031 | 0.0874554 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −46.3035 | −1.96194 | −0.980972 | − | 0.194150i | \(-0.937805\pi\) | ||||
−0.980972 | + | 0.194150i | \(0.937805\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.523301 | 0.0221333 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.03551 | −0.0437194 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.0152 | −0.969975 | −0.484987 | − | 0.874521i | \(-0.661176\pi\) | ||||
−0.484987 | + | 0.874521i | \(0.661176\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.5696 | −0.697088 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.497670 | 0.0209002 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.9171 | −0.709203 | −0.354602 | − | 0.935017i | \(-0.615384\pi\) | ||||
−0.354602 | + | 0.935017i | \(0.615384\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.9472 | −0.834762 | −0.417381 | − | 0.908732i | \(-0.637052\pi\) | ||||
−0.417381 | + | 0.908732i | \(0.637052\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.8669 | −0.495748 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 114.025 | 4.75518 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.0310 | 1.54162 | 0.770811 | − | 0.637064i | \(-0.219851\pi\) | ||||
0.770811 | + | 0.637064i | \(0.219851\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.0978 | 0.502767 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.52576 | −0.0632993 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.911603 | 0.0377548 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.938191 | −0.0387894 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.8741 | −0.448821 | −0.224411 | − | 0.974495i | \(-0.572046\pi\) | ||||
−0.224411 | + | 0.974495i | \(0.572046\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0861035 | −0.00354783 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.3800 | 0.673783 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.4695 | 1.21017 | 0.605084 | − | 0.796162i | \(-0.293140\pi\) | ||||
0.605084 | + | 0.796162i | \(0.293140\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.96754 | 0.285641 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.9684 | 0.571687 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.1804 | 1.88688 | 0.943441 | − | 0.331542i | \(-0.107569\pi\) | ||||
0.943441 | + | 0.331542i | \(0.107569\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.9636 | −0.569587 | −0.284793 | − | 0.958589i | \(-0.591925\pi\) | ||||
−0.284793 | + | 0.958589i | \(0.591925\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.6982 | −0.476388 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −45.7965 | −1.86189 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.4257 | 0.991410 | 0.495705 | − | 0.868491i | \(-0.334910\pi\) | ||||
0.495705 | + | 0.868491i | \(0.334910\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.92943 | −0.0781844 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.22125 | 0.0898622 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.1745 | −1.09757 | −0.548785 | − | 0.835964i | \(-0.684909\pi\) | ||||
−0.548785 | + | 0.835964i | \(0.684909\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −40.3841 | −1.62845 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.1446 | −1.05254 | −0.526271 | − | 0.850317i | \(-0.676410\pi\) | ||||
−0.526271 | + | 0.850317i | \(0.676410\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.1844 | 0.972052 | 0.486026 | − | 0.873944i | \(-0.338446\pi\) | ||||
0.486026 | + | 0.873944i | \(0.338446\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.01998 | −0.361960 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.17545 | 0.287479 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 71.5982 | 2.86393 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0811117 | −0.00323929 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.63508 | −0.0651947 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.0814 | 0.520764 | 0.260382 | − | 0.965506i | \(-0.416152\pi\) | ||||
0.260382 | + | 0.965506i | \(0.416152\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.16435 | −0.324504 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −66.8265 | −2.65193 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.50827 | 0.0597597 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.61858 | 0.143149 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.8151 | −1.41461 | −0.707306 | − | 0.706908i | \(-0.750090\pi\) | ||||
−0.707306 | + | 0.706908i | \(0.750090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.5618 | −0.653133 | −0.326567 | − | 0.945174i | \(-0.605892\pi\) | ||||
−0.326567 | + | 0.945174i | \(0.605892\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.83996 | 0.387448 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.4892 | 1.47385 | 0.736927 | − | 0.675972i | \(-0.236276\pi\) | ||||
0.736927 | + | 0.675972i | \(0.236276\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.838109 | −0.0328987 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.164121 | 0.00643240 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.82610 | 0.227993 | 0.113996 | − | 0.993481i | \(-0.463635\pi\) | ||||
0.113996 | + | 0.993481i | \(0.463635\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.5094 | −0.957661 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.33699 | −0.169202 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.71072 | 0.339321 | 0.169661 | − | 0.985503i | \(-0.445733\pi\) | ||||
0.169661 | + | 0.985503i | \(0.445733\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.84867 | 0.149696 | 0.0748480 | − | 0.997195i | \(-0.476153\pi\) | ||||
0.0748480 | + | 0.997195i | \(0.476153\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.744554 | 0.0289161 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.545766 | 0.0211639 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.9698 | 1.35404 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.9773 | 0.927016 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.383728 | −0.0148137 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.8497 | 1.45900 | 0.729499 | − | 0.683982i | \(-0.239753\pi\) | ||||
0.729499 | + | 0.683982i | \(0.239753\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.6414 | −0.486568 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.2208 | −1.19991 | −0.599955 | − | 0.800033i | \(-0.704815\pi\) | ||||
−0.599955 | + | 0.800033i | \(0.704815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.300449 | −0.0115302 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.9052 | −0.762768 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.186306 | −0.00712880 | −0.00356440 | − | 0.999994i | \(-0.501135\pi\) | ||||
−0.00356440 | + | 0.999994i | \(0.501135\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 75.9007 | 2.90002 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.53054 | 0.172851 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.655459 | −0.0249710 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.85083 | −0.336702 | −0.168351 | − | 0.985727i | \(-0.553844\pi\) | ||||
−0.168351 | + | 0.985727i | \(0.553844\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.154606 | 0.00587299 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.57204 | −0.173427 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.0491 | 1.21394 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.30087 | −0.200497 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.7316 | −1.04741 | −0.523704 | − | 0.851900i | \(-0.675450\pi\) | ||||
−0.523704 | + | 0.851900i | \(0.675450\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.128075 | −0.00483045 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 41.7676 | 1.57306 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.622315 | −0.0234046 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.2925 | −1.62588 | −0.812941 | − | 0.582345i | \(-0.802135\pi\) | ||||
−0.812941 | + | 0.582345i | \(0.802135\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.59750 | 0.0974137 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.97460 | −0.111399 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.291458 | −0.0108999 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.02390 | 0.262312 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.05404 | −0.113896 | −0.0569482 | − | 0.998377i | \(-0.518137\pi\) | ||||
−0.0569482 | + | 0.998377i | \(0.518137\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.55649 | 0.281418 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.34486 | 0.235968 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 49.0098 | 1.82018 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.7202 | 0.990998 | 0.495499 | − | 0.868608i | \(-0.334985\pi\) | ||||
0.495499 | + | 0.868608i | \(0.334985\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.80905 | −0.288828 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.1754 | −1.52085 | −0.760424 | − | 0.649427i | \(-0.775009\pi\) | ||||
−0.760424 | + | 0.649427i | \(0.775009\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 28.3609 | 1.04611 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.63416 | −0.133866 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.4446 | −0.752067 | −0.376033 | − | 0.926606i | \(-0.622712\pi\) | ||||
−0.376033 | + | 0.926606i | \(0.622712\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0583208 | 0.00214247 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.6474 | −1.23440 | −0.617202 | − | 0.786805i | \(-0.711734\pi\) | ||||
−0.617202 | + | 0.786805i | \(0.711734\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31.8213 | −1.16584 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.06581 | −0.112172 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.41594 | 0.124816 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.6170 | 0.642853 | 0.321426 | − | 0.946935i | \(-0.395838\pi\) | ||||
0.321426 | + | 0.946935i | \(0.395838\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −25.3005 | −0.922001 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.4656 | 0.926789 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.9209 | −1.23288 | −0.616438 | − | 0.787404i | \(-0.711425\pi\) | ||||
−0.616438 | + | 0.787404i | \(0.711425\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.80215 | −0.101711 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.8074 | −0.645519 | −0.322760 | − | 0.946481i | \(-0.604611\pi\) | ||||
−0.322760 | + | 0.946481i | \(0.604611\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.22653 | 0.116808 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.0003 | 0.506183 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.602616 | 0.0217592 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.5232 | 1.38918 | 0.694592 | − | 0.719404i | \(-0.255585\pi\) | ||||
0.694592 | + | 0.719404i | \(0.255585\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.70489 | 0.133428 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.8426 | −1.46901 | −0.734504 | − | 0.678605i | \(-0.762585\pi\) | ||||
−0.734504 | + | 0.678605i | \(0.762585\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.16886 | −0.149750 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.244122 | 0.00875785 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.51040 | 0.0899443 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.12415 | 0.0402251 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.87692 | −0.138550 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −27.5117 | −0.981935 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.76921 | 0.312589 | 0.156294 | − | 0.987711i | \(-0.450045\pi\) | ||||
0.156294 | + | 0.987711i | \(0.450045\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.5558 | −0.411399 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.96330 | −0.0698069 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.275907 | 0.00979776 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.3250 | −0.437124 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.40598 | 0.262333 | 0.131167 | − | 0.991360i | \(-0.458128\pi\) | ||||
0.131167 | + | 0.991360i | \(0.458128\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.1470 | −1.17266 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.4181 | 0.509439 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.34733 | −0.0475462 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.8544 | 0.664532 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.8733 | 0.981185 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.6141 | 1.11149 | 0.555746 | − | 0.831352i | \(-0.312433\pi\) | ||||
0.555746 | + | 0.831352i | \(0.312433\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.7943 | 1.64317 | 0.821585 | − | 0.570086i | \(-0.193090\pi\) | ||||
0.821585 | + | 0.570086i | \(0.193090\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.26815 | −0.114619 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.3806 | 0.678872 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.611681 | −0.0214000 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.111164 | −0.00388440 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.5791 | −1.55582 | −0.777911 | − | 0.628374i | \(-0.783721\pi\) | ||||
−0.777911 | + | 0.628374i | \(0.783721\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.2960 | −0.951479 | −0.475739 | − | 0.879586i | \(-0.657819\pi\) | ||||
−0.475739 | + | 0.879586i | \(0.657819\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.92718 | −0.136727 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.4769 | −1.30320 | −0.651600 | − | 0.758562i | \(-0.725902\pi\) | ||||
−0.651600 | + | 0.758562i | \(0.725902\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.1688 | 0.631027 | 0.315514 | − | 0.948921i | \(-0.397823\pi\) | ||||
0.315514 | + | 0.948921i | \(0.397823\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.68912 | 0.127974 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.5074 | −0.779834 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.20017 | 0.145353 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.329778 | 0.0113988 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.6415 | 1.61024 | 0.805122 | − | 0.593109i | \(-0.202100\pi\) | ||||
0.805122 | + | 0.593109i | \(0.202100\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.9695 | −0.481705 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.1453 | 0.383865 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −54.3926 | −1.87116 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.42634 | −0.186451 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.0956 | −0.861279 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.42458 | −0.151673 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.9860 | 0.855504 | 0.427752 | − | 0.903896i | \(-0.359306\pi\) | ||||
0.427752 | + | 0.903896i | \(0.359306\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.09664 | 0.0375044 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.9695 | −0.545508 | −0.272754 | − | 0.962084i | \(-0.587935\pi\) | ||||
−0.272754 | + | 0.962084i | \(0.587935\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.7854 | −1.11862 | −0.559312 | − | 0.828957i | \(-0.688935\pi\) | ||||
−0.559312 | + | 0.828957i | \(0.688935\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.78504 | −0.163074 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.0578 | 0.444492 | 0.222246 | − | 0.974991i | \(-0.428661\pi\) | ||||
0.222246 | + | 0.974991i | \(0.428661\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −76.9592 | −2.61669 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.88927 | 0.200010 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.806937 | 0.0273735 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.61303 | 0.0885390 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.603712 | −0.0204326 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.9728 | 0.539980 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.8855 | 0.367578 | 0.183789 | − | 0.982966i | \(-0.441164\pi\) | ||||
0.183789 | + | 0.982966i | \(0.441164\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.4221 | −0.924923 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.00765 | 0.269785 | 0.134892 | − | 0.990860i | \(-0.456931\pi\) | ||||
0.134892 | + | 0.990860i | \(0.456931\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.54999 | −0.287730 | −0.143865 | − | 0.989597i | \(-0.545953\pi\) | ||||
−0.143865 | + | 0.989597i | \(0.545953\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.3314 | 0.380900 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.88800 | 0.197700 | 0.0988499 | − | 0.995102i | \(-0.468484\pi\) | ||||
0.0988499 | + | 0.995102i | \(0.468484\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.91814 | −0.265566 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.310660 | 0.0104075 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.59640 | −0.0868852 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 66.6045 | 2.22634 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.01479 | 0.0672720 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.27853 | −0.0426412 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.78121 | 0.325859 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.16592 | 0.0387993 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.3091 | −0.874544 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.9433 | 0.961048 | 0.480524 | − | 0.876982i | \(-0.340447\pi\) | ||||
0.480524 | + | 0.876982i | \(0.340447\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.25046 | −0.0414751 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.7063 | 1.05048 | 0.525239 | − | 0.850955i | \(-0.323976\pi\) | ||||
0.525239 | + | 0.850955i | \(0.323976\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.952424 | −0.0315206 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.18807 | 0.171512 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.90407 | −0.0959009 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.1347 | −1.55483 | −0.777415 | − | 0.628989i | \(-0.783469\pi\) | ||||
−0.777415 | + | 0.628989i | \(0.783469\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.7027 | 1.01169 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.808281 | −0.0266049 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.20100 | −0.203888 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.1837 | 0.498700 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.7815 | 0.878674 | 0.439337 | − | 0.898322i | \(-0.355213\pi\) | ||||
0.439337 | + | 0.898322i | \(0.355213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.76300 | −0.0577799 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.33888 | −0.0438331 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.34933 | 0.142238 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.24100 | −0.301890 | −0.150945 | − | 0.988542i | \(-0.548232\pi\) | ||||
−0.150945 | + | 0.988542i | \(0.548232\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.5418 | −0.344018 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.3552 | 1.25034 | 0.625172 | − | 0.780487i | \(-0.285029\pi\) | ||||
0.625172 | + | 0.780487i | \(0.285029\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 86.7261 | 2.82419 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.09030 | −0.0679973 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42.5887 | 1.38395 | 0.691973 | − | 0.721923i | \(-0.256742\pi\) | ||||
0.691973 | + | 0.721923i | \(0.256742\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.968753 | 0.0314471 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.08789 | 0.132559 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.5963 | −1.44462 | −0.722308 | − | 0.691572i | \(-0.756919\pi\) | ||||
−0.722308 | + | 0.691572i | \(0.756919\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 49.8431 | 1.61289 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.20440 | −0.0389328 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.99332 | 0.290410 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8912 | −0.996492 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.86387 | 0.221185 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −50.8128 | −1.63572 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.0774 | 0.742118 | 0.371059 | − | 0.928609i | \(-0.378995\pi\) | ||||
0.371059 | + | 0.928609i | \(0.378995\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.870302 | −0.0279581 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45.8648 | −1.47187 | −0.735936 | − | 0.677051i | \(-0.763257\pi\) | ||||
−0.735936 | + | 0.677051i | \(0.763257\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.541732 | −0.0173671 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.82371 | 0.0904311 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.0962 | 1.50674 | 0.753370 | − | 0.657597i | \(-0.228427\pi\) | ||||
0.753370 | + | 0.657597i | \(0.228427\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.47912 | 0.143153 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.48328 | 0.206995 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.6561 | 1.48810 | 0.744049 | − | 0.668125i | \(-0.232903\pi\) | ||||
0.744049 | + | 0.668125i | \(0.232903\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −68.7987 | −2.19211 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.94897 | 0.157527 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.1316 | −0.671946 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 59.1922 | 1.88030 | 0.940150 | − | 0.340760i | \(-0.110684\pi\) | ||||
0.940150 | + | 0.340760i | \(0.110684\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.5164 | 0.587601 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −58.6694 | −1.85995 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 58.9614 | 1.86733 | 0.933664 | − | 0.358150i | \(-0.116593\pi\) | ||||
0.933664 | + | 0.358150i | \(0.116593\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.490531 | 0.0155197 |
(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.bg.1.13 | 13 | ||
4.3 | odd | 2 | 4008.2.a.m.1.13 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.m.1.13 | ✓ | 13 | 4.3 | odd | 2 | ||
8016.2.a.bg.1.13 | 13 | 1.1 | even | 1 | trivial |