Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3584,2,Mod(1,3584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3584, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3584.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3584 = 2^{9} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3584.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: | \(28.6183840844\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 19x^{8} + 44x^{7} + 86x^{6} - 236x^{5} - 58x^{4} + 368x^{3} - 194x^{2} - 12x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-3.66546\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3584.1 |
$q$-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 | ||||||||
\(3\) | −0.460386 | −0.265804 | −0.132902 | − | 0.991129i | \(-0.542430\pi\) | ||||
−0.132902 | + | 0.991129i | \(0.542430\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.55819 | 0.696842 | 0.348421 | − | 0.937338i | \(-0.386718\pi\) | ||||
0.348421 | + | 0.937338i | \(0.386718\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.78804 | −0.929348 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.69782 | 1.71796 | 0.858979 | − | 0.512011i | \(-0.171099\pi\) | ||||
0.858979 | + | 0.512011i | \(0.171099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.801102 | 0.222186 | 0.111093 | − | 0.993810i | \(-0.464565\pi\) | ||||
0.111093 | + | 0.993810i | \(0.464565\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.717367 | −0.185223 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.85469 | 1.17744 | 0.588718 | − | 0.808339i | \(-0.299633\pi\) | ||||
0.588718 | + | 0.808339i | \(0.299633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.04590 | −0.928192 | −0.464096 | − | 0.885785i | \(-0.653621\pi\) | ||||
−0.464096 | + | 0.885785i | \(0.653621\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.460386 | −0.100465 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.34057 | −1.11359 | −0.556793 | − | 0.830652i | \(-0.687968\pi\) | ||||
−0.556793 | + | 0.830652i | \(0.687968\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.57206 | −0.514412 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.66474 | 0.512829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.47347 | 1.57348 | 0.786742 | − | 0.617282i | \(-0.211766\pi\) | ||||
0.786742 | + | 0.617282i | \(0.211766\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.9126 | 1.95997 | 0.979983 | − | 0.199083i | \(-0.0637963\pi\) | ||||
0.979983 | + | 0.199083i | \(0.0637963\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.62320 | −0.456640 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.55819 | 0.263381 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.26476 | −1.19432 | −0.597159 | − | 0.802123i | \(-0.703704\pi\) | ||||
−0.597159 | + | 0.802123i | \(0.703704\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.368817 | −0.0590579 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.6105 | 1.81325 | 0.906624 | − | 0.421939i | \(-0.138650\pi\) | ||||
0.906624 | + | 0.421939i | \(0.138650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.90654 | −1.05324 | −0.526618 | − | 0.850102i | \(-0.676540\pi\) | ||||
−0.526618 | + | 0.850102i | \(0.676540\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.34429 | −0.647608 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.07068 | −0.739634 | −0.369817 | − | 0.929105i | \(-0.620580\pi\) | ||||
−0.369817 | + | 0.929105i | \(0.620580\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.23503 | −0.312967 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.2227 | 1.67891 | 0.839457 | − | 0.543427i | \(-0.182873\pi\) | ||||
0.839457 | + | 0.543427i | \(0.182873\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.87826 | 1.19714 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.86268 | 0.246717 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.61096 | 0.209729 | 0.104864 | − | 0.994487i | \(-0.466559\pi\) | ||||
0.104864 | + | 0.994487i | \(0.466559\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.21504 | −0.923791 | −0.461896 | − | 0.886934i | \(-0.652831\pi\) | ||||
−0.461896 | + | 0.886934i | \(0.652831\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.78804 | −0.351261 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.24827 | 0.154828 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.44702 | −1.15414 | −0.577069 | − | 0.816696i | \(-0.695803\pi\) | ||||
−0.577069 | + | 0.816696i | \(0.695803\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.45872 | 0.295996 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.51816 | −0.180172 | −0.0900859 | − | 0.995934i | \(-0.528714\pi\) | ||||
−0.0900859 | + | 0.995934i | \(0.528714\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.21599 | 0.493444 | 0.246722 | − | 0.969086i | \(-0.420647\pi\) | ||||
0.246722 | + | 0.969086i | \(0.420647\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.18414 | 0.136733 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.69782 | 0.649327 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.48184 | 0.279229 | 0.139615 | − | 0.990206i | \(-0.455414\pi\) | ||||
0.139615 | + | 0.990206i | \(0.455414\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.13732 | 0.793036 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.11724 | −0.671454 | −0.335727 | − | 0.941959i | \(-0.608982\pi\) | ||||
−0.335727 | + | 0.941959i | \(0.608982\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.56451 | 0.820486 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.90107 | −0.418239 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0579 | 1.06614 | 0.533069 | − | 0.846072i | \(-0.321038\pi\) | ||||
0.533069 | + | 0.846072i | \(0.321038\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.801102 | 0.0839783 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.02402 | −0.520967 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.30426 | −0.646803 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0236 | 1.22081 | 0.610404 | − | 0.792090i | \(-0.291007\pi\) | ||||
0.610404 | + | 0.792090i | \(0.291007\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −15.8858 | −1.59658 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.7744 | −1.86812 | −0.934060 | − | 0.357117i | \(-0.883760\pi\) | ||||
−0.934060 | + | 0.357117i | \(0.883760\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.2148 | −1.59769 | −0.798846 | − | 0.601536i | \(-0.794556\pi\) | ||||
−0.798846 | + | 0.601536i | \(0.794556\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.717367 | −0.0700079 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.75247 | 0.942807 | 0.471403 | − | 0.881918i | \(-0.343748\pi\) | ||||
0.471403 | + | 0.881918i | \(0.343748\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.59214 | 0.727195 | 0.363597 | − | 0.931556i | \(-0.381548\pi\) | ||||
0.363597 | + | 0.931556i | \(0.381548\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.34460 | 0.317455 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.2814 | 1.24941 | 0.624706 | − | 0.780860i | \(-0.285219\pi\) | ||||
0.624706 | + | 0.780860i | \(0.285219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.32159 | −0.775992 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.23351 | −0.206488 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.85469 | 0.445029 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.4651 | 1.95138 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.34530 | −0.481969 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7987 | −1.05531 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9167 | −1.14617 | −0.573084 | − | 0.819497i | \(-0.694253\pi\) | ||||
−0.573084 | + | 0.819497i | \(0.694253\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.17968 | 0.279955 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3527 | 1.16663 | 0.583315 | − | 0.812246i | \(-0.301755\pi\) | ||||
0.583315 | + | 0.812246i | \(0.301755\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.04590 | −0.350824 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.15215 | 0.357361 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.3601 | 1.14143 | 0.570715 | − | 0.821148i | \(-0.306666\pi\) | ||||
0.570715 | + | 0.821148i | \(0.306666\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.68524 | 0.821492 | 0.410746 | − | 0.911750i | \(-0.365268\pi\) | ||||
0.410746 | + | 0.911750i | \(0.365268\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.33447 | 0.196598 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.56454 | 0.381706 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.2032 | 1.09647 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.460386 | −0.0379720 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.299751 | 0.0245565 | 0.0122783 | − | 0.999925i | \(-0.496092\pi\) | ||||
0.0122783 | + | 0.999925i | \(0.496092\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.8803 | 1.12957 | 0.564783 | − | 0.825239i | \(-0.308960\pi\) | ||||
0.564783 | + | 0.825239i | \(0.308960\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.5351 | −1.09425 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.0039 | 1.36579 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.48629 | −0.757088 | −0.378544 | − | 0.925583i | \(-0.623575\pi\) | ||||
−0.378544 | + | 0.925583i | \(0.623575\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.62715 | −0.446262 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.34057 | −0.420896 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.66068 | −0.130074 | −0.0650371 | − | 0.997883i | \(-0.520717\pi\) | ||||
−0.0650371 | + | 0.997883i | \(0.520717\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.08743 | −0.318206 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.8959 | 1.46221 | 0.731105 | − | 0.682265i | \(-0.239005\pi\) | ||||
0.731105 | + | 0.682265i | \(0.239005\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3582 | −0.950633 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.2801 | 0.862614 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.61641 | −0.350979 | −0.175490 | − | 0.984481i | \(-0.556151\pi\) | ||||
−0.175490 | + | 0.984481i | \(0.556151\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.57206 | −0.194429 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.741663 | −0.0557468 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.79017 | 0.283290 | 0.141645 | − | 0.989918i | \(-0.454761\pi\) | ||||
0.141645 | + | 0.989918i | \(0.454761\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.6282 | 1.38462 | 0.692311 | − | 0.721599i | \(-0.256593\pi\) | ||||
0.692311 | + | 0.721599i | \(0.256593\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.32171 | 0.245548 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.3198 | −0.832251 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.6612 | 2.02278 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.66474 | 0.193831 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.89496 | 0.354187 | 0.177093 | − | 0.984194i | \(-0.443331\pi\) | ||||
0.177093 | + | 0.984194i | \(0.443331\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.7517 | 0.773927 | 0.386963 | − | 0.922095i | \(-0.373524\pi\) | ||||
0.386963 | + | 0.922095i | \(0.373524\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.574685 | −0.0411540 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.28829 | −0.305528 | −0.152764 | − | 0.988263i | \(-0.548817\pi\) | ||||
−0.152764 | + | 0.988263i | \(0.548817\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0177 | −0.710134 | −0.355067 | − | 0.934841i | \(-0.615542\pi\) | ||||
−0.355067 | + | 0.934841i | \(0.615542\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.34928 | 0.306775 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.47347 | 0.594721 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.0912 | 1.26355 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.8897 | 1.03491 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.0528 | −1.59459 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.51264 | 0.104134 | 0.0520671 | − | 0.998644i | \(-0.483419\pi\) | ||||
0.0520671 | + | 0.998644i | \(0.483419\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.698938 | 0.0478904 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.7617 | −0.733939 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.9126 | 0.740797 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.94098 | −0.131159 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.88910 | 0.261609 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.86743 | −0.258983 | −0.129491 | − | 0.991581i | \(-0.541334\pi\) | ||||
−0.129491 | + | 0.991581i | \(0.541334\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.17101 | 0.478068 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.0174 | −1.06311 | −0.531557 | − | 0.847023i | \(-0.678393\pi\) | ||||
−0.531557 | + | 0.847023i | \(0.678393\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.04044 | 0.0687544 | 0.0343772 | − | 0.999409i | \(-0.489055\pi\) | ||||
0.0343772 | + | 0.999409i | \(0.489055\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.62320 | −0.172594 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.65072 | −0.108142 | −0.0540711 | − | 0.998537i | \(-0.517220\pi\) | ||||
−0.0540711 | + | 0.998537i | \(0.517220\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.90105 | −0.515408 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.14261 | −0.0742204 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.5102 | −1.19732 | −0.598662 | − | 0.801002i | \(-0.704301\pi\) | ||||
−0.598662 | + | 0.801002i | \(0.704301\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.31491 | 0.277948 | 0.138974 | − | 0.990296i | \(-0.455620\pi\) | ||||
0.138974 | + | 0.990296i | \(0.455620\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.2801 | −0.723621 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.55819 | 0.0995488 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.24118 | −0.206231 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.81629 | 0.178475 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.95879 | 0.502354 | 0.251177 | − | 0.967941i | \(-0.419182\pi\) | ||||
0.251177 | + | 0.967941i | \(0.419182\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.4296 | −1.91309 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.48260 | −0.218089 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.44352 | 0.339558 | 0.169779 | − | 0.985482i | \(-0.445695\pi\) | ||||
0.169779 | + | 0.985482i | \(0.445695\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.26476 | −0.451410 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −23.6244 | −1.46231 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.91382 | 0.426324 | 0.213162 | − | 0.977017i | \(-0.431624\pi\) | ||||
0.213162 | + | 0.977017i | \(0.431624\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.0452 | 1.16994 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.63054 | −0.283384 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.61641 | 0.281468 | 0.140734 | − | 0.990047i | \(-0.455054\pi\) | ||||
0.140734 | + | 0.990047i | \(0.455054\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.13257 | −0.251035 | −0.125518 | − | 0.992091i | \(-0.540059\pi\) | ||||
−0.125518 | + | 0.992091i | \(0.540059\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.368817 | −0.0223218 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.6551 | −0.883737 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.74830 | −0.585719 | −0.292859 | − | 0.956156i | \(-0.594607\pi\) | ||||
−0.292859 | + | 0.956156i | \(0.594607\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −30.4249 | −1.82149 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.5478 | 0.987161 | 0.493581 | − | 0.869700i | \(-0.335688\pi\) | ||||
0.493581 | + | 0.869700i | \(0.335688\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.4101 | −1.27270 | −0.636350 | − | 0.771401i | \(-0.719556\pi\) | ||||
−0.636350 | + | 0.771401i | \(0.719556\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.90239 | 0.171923 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.6105 | 0.685344 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.56803 | 0.386355 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.53549 | −0.324496 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.09788 | −0.531504 | −0.265752 | − | 0.964041i | \(-0.585620\pi\) | ||||
−0.265752 | + | 0.964041i | \(0.585620\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.51017 | 0.146148 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.1832 | 0.881018 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.27834 | −0.247423 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.90654 | −0.398086 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.64346 | 0.496554 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.2424 | −0.643736 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0068 | 1.02770 | 0.513852 | − | 0.857879i | \(-0.328218\pi\) | ||||
0.513852 | + | 0.857879i | \(0.328218\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.46507 | 0.424673 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34.6644 | 1.96564 | 0.982820 | − | 0.184567i | \(-0.0590884\pi\) | ||||
0.982820 | + | 0.184567i | \(0.0590884\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.9134 | 0.616859 | 0.308430 | − | 0.951247i | \(-0.400197\pi\) | ||||
0.308430 | + | 0.951247i | \(0.400197\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.34429 | −0.244773 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.2997 | 1.36481 | 0.682405 | − | 0.730974i | \(-0.260934\pi\) | ||||
0.682405 | + | 0.730974i | \(0.260934\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 48.2803 | 2.70318 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.48990 | −0.250602 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.6416 | −1.09289 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.06048 | −0.114295 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.49532 | −0.193291 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.07068 | −0.279555 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.9808 | 0.823420 | 0.411710 | − | 0.911315i | \(-0.364932\pi\) | ||||
0.411710 | + | 0.911315i | \(0.364932\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.2545 | 1.10994 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.7202 | −0.804251 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.3178 | 0.888885 | 0.444442 | − | 0.895807i | \(-0.353402\pi\) | ||||
0.444442 | + | 0.895807i | \(0.353402\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.11460 | −0.332099 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 62.1782 | 3.36714 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.83115 | 0.206262 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.4158 | 1.09598 | 0.547990 | − | 0.836485i | \(-0.315393\pi\) | ||||
0.547990 | + | 0.836485i | \(0.315393\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.958684 | 0.0513172 | 0.0256586 | − | 0.999671i | \(-0.491832\pi\) | ||||
0.0256586 | + | 0.999671i | \(0.491832\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.13473 | 0.113943 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.08835 | 0.483724 | 0.241862 | − | 0.970311i | \(-0.422242\pi\) | ||||
0.241862 | + | 0.970311i | \(0.422242\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.36557 | −0.125551 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.23503 | −0.118291 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.6180 | 0.771507 | 0.385754 | − | 0.922602i | \(-0.373941\pi\) | ||||
0.385754 | + | 0.922602i | \(0.373941\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.63072 | −0.138459 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.88226 | −0.518684 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.56929 | 0.343852 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.43473 | −0.492489 | −0.246245 | − | 0.969208i | \(-0.579197\pi\) | ||||
−0.246245 | + | 0.969208i | \(0.579197\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −32.3705 | −1.68514 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.2227 | 0.634570 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.04020 | 0.468084 | 0.234042 | − | 0.972227i | \(-0.424805\pi\) | ||||
0.234042 | + | 0.972227i | \(0.424805\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.43195 | 0.280505 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.78812 | 0.349606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.9672 | −1.33384 | −0.666921 | − | 0.745128i | \(-0.732388\pi\) | ||||
−0.666921 | + | 0.745128i | \(0.732388\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.94665 | 0.304656 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.05912 | −0.309607 | −0.154803 | − | 0.987945i | \(-0.549474\pi\) | ||||
−0.154803 | + | 0.987945i | \(0.549474\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.87826 | 0.452478 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 19.2557 | 0.978824 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.4354 | −1.69524 | −0.847620 | − | 0.530604i | \(-0.821965\pi\) | ||||
−0.847620 | + | 0.530604i | \(0.821965\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.9268 | −1.31117 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.14740 | −0.310095 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.86717 | 0.194579 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.85496 | −0.494606 | −0.247303 | − | 0.968938i | \(-0.579544\pi\) | ||||
−0.247303 | + | 0.968938i | \(0.579544\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.86268 | 0.0932504 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.22278 | 0.360688 | 0.180344 | − | 0.983604i | \(-0.442279\pi\) | ||||
0.180344 | + | 0.983604i | \(0.442279\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.74213 | 0.435476 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.1213 | 0.552620 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −41.3933 | −2.05179 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.4416 | 0.615197 | 0.307598 | − | 0.951516i | \(-0.400475\pi\) | ||||
0.307598 | + | 0.951516i | \(0.400475\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.15081 | −0.303397 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.61096 | 0.0792700 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.53179 | −0.467897 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.45896 | −0.218356 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.27840 | 0.257867 | 0.128933 | − | 0.991653i | \(-0.458845\pi\) | ||||
0.128933 | + | 0.991653i | \(0.458845\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.74830 | −0.475103 | −0.237552 | − | 0.971375i | \(-0.576345\pi\) | ||||
−0.237552 | + | 0.971375i | \(0.576345\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.1373 | 0.687378 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.4866 | −0.605687 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.21504 | −0.349160 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.10145 | −0.101459 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.170962 | −0.00823495 | −0.00411747 | − | 0.999992i | \(-0.501311\pi\) | ||||
−0.00411747 | + | 0.999992i | \(0.501311\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.8097 | 1.04811 | 0.524055 | − | 0.851685i | \(-0.324419\pi\) | ||||
0.524055 | + | 0.851685i | \(0.324419\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.07859 | −0.291446 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.6074 | 1.03362 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.0646 | −0.480355 | −0.240178 | − | 0.970729i | \(-0.577206\pi\) | ||||
−0.240178 | + | 0.970729i | \(0.577206\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.78804 | −0.132764 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.26719 | −0.0602059 | −0.0301030 | − | 0.999547i | \(-0.509584\pi\) | ||||
−0.0301030 | + | 0.999547i | \(0.509584\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.6721 | 0.742930 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.138001 | −0.00652723 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.9899 | −0.565840 | −0.282920 | − | 0.959144i | \(-0.591303\pi\) | ||||
−0.282920 | + | 0.959144i | \(0.591303\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 66.1543 | 3.11508 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.39032 | −0.300244 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.24827 | 0.0585196 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.2451 | −0.479247 | −0.239624 | − | 0.970866i | \(-0.577024\pi\) | ||||
−0.239624 | + | 0.970866i | \(0.577024\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.9365 | 0.603823 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.6741 | −1.10261 | −0.551307 | − | 0.834302i | \(-0.685871\pi\) | ||||
−0.551307 | + | 0.834302i | \(0.685871\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.2464 | 0.615612 | 0.307806 | − | 0.951449i | \(-0.400405\pi\) | ||||
0.307806 | + | 0.951449i | \(0.400405\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.82836 | −0.363032 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.95855 | −0.136905 | −0.0684526 | − | 0.997654i | \(-0.521806\pi\) | ||||
−0.0684526 | + | 0.997654i | \(0.521806\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.44702 | −0.436223 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.36736 | 0.201237 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −39.3522 | −1.80942 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.4063 | 0.477473 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −34.0774 | −1.56029 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.7626 | −1.31420 | −0.657099 | − | 0.753804i | \(-0.728217\pi\) | ||||
−0.657099 | + | 0.753804i | \(0.728217\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.81981 | −0.265361 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.45872 | 0.111876 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.7349 | 0.850710 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.6260 | −0.481512 | −0.240756 | − | 0.970586i | \(-0.577395\pi\) | ||||
−0.240756 | + | 0.970586i | \(0.577395\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.764553 | 0.0345743 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.7765 | −0.666854 | −0.333427 | − | 0.942776i | \(-0.608205\pi\) | ||||
−0.333427 | + | 0.942776i | \(0.608205\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.1361 | 1.85268 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −24.7530 | −1.11256 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.51816 | −0.0680986 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.7038 | 0.926829 | 0.463414 | − | 0.886142i | \(-0.346624\pi\) | ||||
0.463414 | + | 0.886142i | \(0.346624\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.69943 | −0.388662 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.28256 | 0.101774 | 0.0508871 | − | 0.998704i | \(-0.483795\pi\) | ||||
0.0508871 | + | 0.998704i | \(0.483795\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.2539 | −1.30178 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.68956 | 0.252682 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.2009 | −1.51593 | −0.757963 | − | 0.652297i | \(-0.773806\pi\) | ||||
−0.757963 | + | 0.652297i | \(0.773806\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.21599 | 0.186504 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.7813 | −0.476004 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.2657 | −1.11334 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.8918 | −1.27066 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.12533 | 0.0932918 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.5003 | −1.55529 | −0.777647 | − | 0.628701i | \(-0.783587\pi\) | ||||
−0.777647 | + | 0.628701i | \(0.783587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.1836 | −0.751388 | −0.375694 | − | 0.926744i | \(-0.622596\pi\) | ||||
−0.375694 | + | 0.926744i | \(0.622596\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.18414 | 0.0516802 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 52.9774 | 2.30773 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.52165 | 0.240072 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.49142 | −0.194911 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.30116 | 0.402878 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.1962 | 0.656987 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.74494 | −0.0752998 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.69782 | 0.245422 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.89210 | 0.124341 | 0.0621705 | − | 0.998066i | \(-0.480198\pi\) | ||||
0.0621705 | + | 0.998066i | \(0.480198\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.57616 | −0.368038 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.8300 | 0.506740 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.8601 | 1.36224 | 0.681119 | − | 0.732172i | \(-0.261493\pi\) | ||||
0.681119 | + | 0.732172i | \(0.261493\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.1158 | 0.858524 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.2828 | −1.46050 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.48184 | 0.105539 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.21150 | 0.221216 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.9735 | 0.549704 | 0.274852 | − | 0.961487i | \(-0.411371\pi\) | ||||
0.274852 | + | 0.961487i | \(0.411371\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.53284 | −0.234014 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.7348 | −0.537665 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −44.3192 | −1.86783 | −0.933916 | − | 0.357493i | \(-0.883632\pi\) | ||||
−0.933916 | + | 0.357493i | \(0.883632\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.6949 | 0.870643 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.13732 | 0.299739 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.3003 | −1.43794 | −0.718972 | − | 0.695039i | \(-0.755387\pi\) | ||||
−0.718972 | + | 0.695039i | \(0.755387\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.9170 | −1.33569 | −0.667843 | − | 0.744302i | \(-0.732782\pi\) | ||||
−0.667843 | + | 0.744302i | \(0.732782\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.25357 | −0.0941443 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.7363 | 0.572841 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.11936 | −0.379644 | −0.189822 | − | 0.981819i | \(-0.560791\pi\) | ||||
−0.189822 | + | 0.981819i | \(0.560791\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.94995 | −0.205713 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.11724 | −0.253786 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 69.6426 | 2.88430 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.48022 | −0.143889 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.1574 | −0.790711 | −0.395355 | − | 0.918528i | \(-0.629379\pi\) | ||||
−0.395355 | + | 0.918528i | \(0.629379\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −44.1514 | −1.81922 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.97427 | 0.0812107 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.4877 | −0.430680 | −0.215340 | − | 0.976539i | \(-0.569086\pi\) | ||||
−0.215340 | + | 0.976539i | \(0.569086\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.56451 | 0.310115 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.61200 | 0.188757 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.2087 | −0.539692 | −0.269846 | − | 0.962903i | \(-0.586973\pi\) | ||||
−0.269846 | + | 0.962903i | \(0.586973\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.130554 | −0.00532540 | −0.00266270 | − | 0.999996i | \(-0.500848\pi\) | ||||
−0.00266270 | + | 0.999996i | \(0.500848\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.3387 | 1.07260 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.4467 | 1.35980 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.3130 | −1.71743 | −0.858716 | − | 0.512452i | \(-0.828737\pi\) | ||||
−0.858716 | + | 0.512452i | \(0.828737\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.90107 | −0.158079 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.06213 | −0.164336 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.8036 | −0.517134 | −0.258567 | − | 0.965993i | \(-0.583250\pi\) | ||||
−0.258567 | + | 0.965993i | \(0.583250\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.32896 | −0.335856 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.74659 | 0.392383 | 0.196191 | − | 0.980566i | \(-0.437143\pi\) | ||||
0.196191 | + | 0.980566i | \(0.437143\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.51608 | 0.101130 | 0.0505649 | − | 0.998721i | \(-0.483898\pi\) | ||||
0.0505649 | + | 0.998721i | \(0.483898\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.2312 | −0.571079 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.0579 | 0.402963 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.52422 | −0.220969 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.6132 | 0.423850 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −35.2682 | −1.40623 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.25431 | 0.129552 | 0.0647760 | − | 0.997900i | \(-0.479367\pi\) | ||||
0.0647760 | + | 0.997900i | \(0.479367\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.696398 | −0.0276793 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.1265 | −0.798697 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.801102 | 0.0317408 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.23268 | 0.167442 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.61844 | −0.182417 | −0.0912087 | − | 0.995832i | \(-0.529073\pi\) | ||||
−0.0912087 | + | 0.995832i | \(0.529073\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.0982 | −1.42358 | −0.711788 | − | 0.702394i | \(-0.752114\pi\) | ||||
−0.711788 | + | 0.702394i | \(0.752114\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.95452 | 0.195084 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.8076 | 0.778716 | 0.389358 | − | 0.921086i | \(-0.372697\pi\) | ||||
0.389358 | + | 0.921086i | \(0.372697\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.17895 | 0.360305 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.02402 | −0.196907 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.94237 | 0.154277 | 0.0771385 | − | 0.997020i | \(-0.475422\pi\) | ||||
0.0771385 | + | 0.997020i | \(0.475422\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.8060 | 0.812956 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.7544 | −0.458581 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.9519 | 0.894079 | 0.447040 | − | 0.894514i | \(-0.352478\pi\) | ||||
0.447040 | + | 0.894514i | \(0.352478\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.9033 | −1.20200 | −0.601000 | − | 0.799249i | \(-0.705231\pi\) | ||||
−0.601000 | + | 0.799249i | \(0.705231\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.79049 | −0.0695369 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.30426 | −0.244469 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −45.2531 | −1.75221 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.78051 | 0.0688387 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.1100 | −1.58703 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.2803 | −1.24432 | −0.622158 | − | 0.782892i | \(-0.713744\pi\) | ||||
−0.622158 | + | 0.782892i | \(0.713744\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.85386 | −0.263805 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.7676 | 1.33623 | 0.668114 | − | 0.744059i | \(-0.267102\pi\) | ||||
0.668114 | + | 0.744059i | \(0.267102\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0236 | 0.461422 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.37420 | 0.282580 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.00766 | −0.268141 | −0.134070 | − | 0.990972i | \(-0.542805\pi\) | ||||
−0.134070 | + | 0.990972i | \(0.542805\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.8175 | 0.795396 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.479006 | −0.0182752 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.79161 | 0.373031 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.0950 | 1.18291 | 0.591454 | − | 0.806339i | \(-0.298554\pi\) | ||||
0.591454 | + | 0.806339i | \(0.298554\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.8858 | −0.603451 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.0914 | 0.572450 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 56.3652 | 2.13498 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.759969 | 0.0287447 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.0206 | 0.945016 | 0.472508 | − | 0.881327i | \(-0.343349\pi\) | ||||
0.472508 | + | 0.881327i | \(0.343349\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29.3925 | 1.10856 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.63754 | 0.136998 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.7744 | −0.706083 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.3014 | −0.649768 | −0.324884 | − | 0.945754i | \(-0.605325\pi\) | ||||
−0.324884 | + | 0.945754i | \(0.605325\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.91949 | −0.259501 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −58.2796 | −2.18259 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.11239 | 0.265988 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.52183 | 0.318254 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.8103 | −0.776095 | −0.388047 | − | 0.921639i | \(-0.626850\pi\) | ||||
−0.388047 | + | 0.921639i | \(0.626850\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.2148 | −0.603871 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.98653 | −0.0738797 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.7943 | −0.809419 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.2308 | −0.527790 | −0.263895 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263895 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.2187 | −0.600694 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −33.5291 | −1.24012 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.8888 | −1.73188 | −0.865939 | − | 0.500149i | \(-0.833279\pi\) | ||||
−0.865939 | + | 0.500149i | \(0.833279\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.717367 | −0.0264605 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −53.8274 | −1.98276 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.4989 | 1.23228 | 0.616138 | − | 0.787638i | \(-0.288696\pi\) | ||||
0.616138 | + | 0.787638i | \(0.288696\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.49219 | 0.0548171 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.6341 | −1.71084 | −0.855420 | − | 0.517936i | \(-0.826701\pi\) | ||||
−0.855420 | + | 0.517936i | \(0.826701\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.467067 | 0.0171120 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.0551 | 0.624015 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.75247 | 0.356347 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.1941 | −1.39372 | −0.696861 | − | 0.717207i | \(-0.745420\pi\) | ||||
−0.696861 | + | 0.717207i | \(0.745420\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.66412 | −0.133528 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.6281 | 0.787129 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.4810 | 1.61669 | 0.808345 | − | 0.588709i | \(-0.200363\pi\) | ||||
0.808345 | + | 0.588709i | \(0.200363\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.0094 | 0.508508 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.8684 | −1.44523 | −0.722614 | − | 0.691251i | \(-0.757060\pi\) | ||||
−0.722614 | + | 0.691251i | \(0.757060\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.59214 | 0.274854 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −21.0902 | −0.762517 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.29054 | 0.0465988 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.0582 | −1.37241 | −0.686206 | − | 0.727407i | \(-0.740725\pi\) | ||||
−0.686206 | + | 0.727407i | \(0.740725\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.50612 | −0.0902559 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.5593 | −1.38688 | −0.693441 | − | 0.720514i | \(-0.743906\pi\) | ||||
−0.693441 | + | 0.720514i | \(0.743906\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.0679 | −1.00823 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.34460 | 0.119987 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −46.9747 | −1.68304 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.65017 | −0.309528 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.5796 | 0.806928 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.7814 | −0.527571 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.8098 | −0.991313 | −0.495656 | − | 0.868519i | \(-0.665072\pi\) | ||||
−0.495656 | + | 0.868519i | \(0.665072\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.18303 | −0.113319 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.2814 | 0.472234 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.77998 | −0.205253 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.76815 | −0.310974 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.1683 | −0.856084 | −0.428042 | − | 0.903759i | \(-0.640796\pi\) | ||||
−0.428042 | + | 0.903759i | \(0.640796\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.6166 | −0.870872 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −28.0420 | −0.990814 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.0219 | 0.847715 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.32159 | −0.293298 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.12533 | −0.0748153 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.4025 | −0.365731 | −0.182865 | − | 0.983138i | \(-0.558537\pi\) | ||||
−0.182865 | + | 0.983138i | \(0.558537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.0878 | −0.810722 | −0.405361 | − | 0.914157i | \(-0.632854\pi\) | ||||
−0.405361 | + | 0.914157i | \(0.632854\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.90258 | 0.0667263 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.58764 | −0.0906411 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.9431 | 0.977606 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.23351 | −0.0780451 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.4927 | −1.09910 | −0.549551 | − | 0.835460i | \(-0.685201\pi\) | ||||
−0.549551 | + | 0.835460i | \(0.685201\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.8088 | 0.551059 | 0.275530 | − | 0.961293i | \(-0.411147\pi\) | ||||
0.275530 | + | 0.961293i | \(0.411147\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.74702 | 0.234901 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.2711 | −0.635348 | −0.317674 | − | 0.948200i | \(-0.602902\pi\) | ||||
−0.317674 | + | 0.948200i | \(0.602902\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.26253 | −0.148044 | −0.0740219 | − | 0.997257i | \(-0.523583\pi\) | ||||
−0.0740219 | + | 0.997257i | \(0.523583\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.48798 | 0.155686 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.85469 | 0.168205 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.4434 | 1.01893 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29.0793 | 1.00513 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.7742 | 1.23506 | 0.617531 | − | 0.786547i | \(-0.288133\pi\) | ||||
0.617531 | + | 0.786547i | \(0.288133\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7998 | 1.47585 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.61840 | −0.262392 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.2564 | −0.662441 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.4651 | 0.737551 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.85693 | 0.338289 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.7979 | 1.32998 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.7771 | 0.677154 | 0.338577 | − | 0.940939i | \(-0.390054\pi\) | ||||
0.338577 | + | 0.940939i | \(0.390054\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17.5765 | 0.601105 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.4409 | −0.629927 | −0.314964 | − | 0.949104i | \(-0.601992\pi\) | ||||
−0.314964 | + | 0.949104i | \(0.601992\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.5239 | −1.24618 | −0.623089 | − | 0.782151i | \(-0.714123\pi\) | ||||
−0.623089 | + | 0.782151i | \(0.714123\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.34530 | −0.182167 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.5455 | 1.38018 | 0.690092 | − | 0.723722i | \(-0.257570\pi\) | ||||
0.690092 | + | 0.723722i | \(0.257570\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.19322 | −0.244577 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.02383 | −0.102695 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.1411 | 0.479704 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.56803 | −0.256433 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −33.5222 | −1.13456 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.7987 | −0.398868 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.4834 | 1.46833 | 0.734165 | − | 0.678971i | \(-0.237574\pi\) | ||||
0.734165 | + | 0.678971i | \(0.237574\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.18854 | 0.141276 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.9941 | 0.370401 | 0.185201 | − | 0.982701i | \(-0.440706\pi\) | ||||
0.185201 | + | 0.982701i | \(0.440706\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.3203 | 1.25593 | 0.627964 | − | 0.778242i | \(-0.283889\pi\) | ||||
0.627964 | + | 0.778242i | \(0.283889\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.15565 | −0.0388467 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.10169 | 0.171298 | 0.0856490 | − | 0.996325i | \(-0.472704\pi\) | ||||
0.0856490 | + | 0.996325i | \(0.472704\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.9167 | −0.433211 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 40.6672 | 1.36240 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.5154 | 0.686523 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.90578 | 0.197408 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.96969 | 0.0657660 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 92.4678 | 3.08398 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 59.3373 | 1.97681 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.17968 | 0.105813 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29.0262 | 0.964862 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −54.0312 | −1.79408 | −0.897038 | − | 0.441954i | \(-0.854285\pi\) | ||||
−0.897038 | + | 0.441954i | \(0.854285\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 52.3438 | 1.73613 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.23276 | −0.0408431 | −0.0204216 | − | 0.999791i | \(-0.506501\pi\) | ||||
−0.0204216 | + | 0.999791i | \(0.506501\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.8549 | −1.15353 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.17583 | 0.171108 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.3527 | 0.440945 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.2708 | −0.833606 | −0.416803 | − | 0.908997i | \(-0.636850\pi\) | ||||
−0.416803 | + | 0.908997i | \(0.636850\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.29010 | −0.273168 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.21620 | −0.0400316 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.6854 | 0.614372 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 45.2076 | 1.48481 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.3081 | 1.65055 | 0.825277 | − | 0.564728i | \(-0.191019\pi\) | ||||
0.825277 | + | 0.564728i | \(0.191019\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.04590 | −0.132599 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.9590 | −0.522475 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 43.1012 | 1.40956 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.6694 | −1.09993 | −0.549965 | − | 0.835188i | \(-0.685359\pi\) | ||||
−0.549965 | + | 0.835188i | \(0.685359\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.02436 | −0.163964 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.2749 | −1.11733 | −0.558666 | − | 0.829393i | \(-0.688686\pi\) | ||||
−0.558666 | + | 0.829393i | \(0.688686\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −62.0064 | −2.01921 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.15215 | 0.135070 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.1716 | −1.72784 | −0.863922 | − | 0.503626i | \(-0.831999\pi\) | ||||
−0.863922 | + | 0.503626i | \(0.831999\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.37744 | 0.109636 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.1873 | −0.362772 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.3378 | −1.04752 | −0.523761 | − | 0.851865i | \(-0.675472\pi\) | ||||
−0.523761 | + | 0.851865i | \(0.675472\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.62725 | 0.246812 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −22.2276 | −0.718517 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.3601 | 0.431420 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 88.0854 | 2.84146 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −27.1903 | −0.876196 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.7532 | 0.539304 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.2841 | 0.748765 | 0.374383 | − | 0.927274i | \(-0.377855\pi\) | ||||
0.374383 | + | 0.927274i | \(0.377855\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.04272 | 0.290494 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.3114 | 0.651824 | 0.325912 | − | 0.945400i | \(-0.394329\pi\) | ||||
0.325912 | + | 0.945400i | \(0.394329\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.68524 | 0.310495 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.948618 | 0.0303801 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.54568 | −0.0814434 | −0.0407217 | − | 0.999171i | \(-0.512966\pi\) | ||||
−0.0407217 | + | 0.999171i | \(0.512966\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 57.3083 | 1.83158 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.1672 | −0.675817 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.0045 | −1.18026 | −0.590130 | − | 0.807309i | \(-0.700923\pi\) | ||||
−0.590130 | + | 0.807309i | \(0.700923\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.68195 | −0.212905 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.33447 | 0.0743070 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 36.8848 | 1.17287 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.5737 | 0.653545 | 0.326772 | − | 0.945103i | \(-0.394039\pi\) | ||||
0.326772 | + | 0.945103i | \(0.394039\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.89697 | −0.218869 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.6094 | −0.494851 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.2391 | −1.14770 | −0.573851 | − | 0.818960i | \(-0.694551\pi\) | ||||
−0.573851 | + | 0.818960i | \(0.694551\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19.3587 | −0.612481 |
(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 | 3584.2.a.p.1.5 | yes | 10 | |
4.3 | odd | 2 | 3584.2.a.o.1.6 | yes | 10 | ||
8.3 | odd | 2 | 3584.2.a.o.1.5 | ✓ | 10 | ||
8.5 | even | 2 | inner | 3584.2.a.p.1.6 | yes | 10 | |
16.3 | odd | 4 | 3584.2.b.h.1793.6 | 10 | |||
16.5 | even | 4 | 3584.2.b.g.1793.6 | 10 | |||
16.11 | odd | 4 | 3584.2.b.h.1793.5 | 10 | |||
16.13 | even | 4 | 3584.2.b.g.1793.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3584.2.a.o.1.5 | ✓ | 10 | 8.3 | odd | 2 | ||
3584.2.a.o.1.6 | yes | 10 | 4.3 | odd | 2 | ||
3584.2.a.p.1.5 | yes | 10 | 1.1 | even | 1 | trivial | |
3584.2.a.p.1.6 | yes | 10 | 8.5 | even | 2 | inner | |
3584.2.b.g.1793.5 | 10 | 16.13 | even | 4 | |||
3584.2.b.g.1793.6 | 10 | 16.5 | even | 4 | |||
3584.2.b.h.1793.5 | 10 | 16.11 | odd | 4 | |||
3584.2.b.h.1793.6 | 10 | 16.3 | odd | 4 |