Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, 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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 15x^{6} + 56x^{5} + 87x^{4} - 248x^{3} - 241x^{2} + 340x + 248 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.60188\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-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 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.60188 | 0.716384 | 0.358192 | − | 0.933648i | \(-0.383393\pi\) | ||||
0.358192 | + | 0.933648i | \(0.383393\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.96099 | −1.11915 | −0.559575 | − | 0.828780i | \(-0.689035\pi\) | ||||
−0.559575 | + | 0.828780i | \(0.689035\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.18049 | −1.86349 | −0.931743 | − | 0.363117i | \(-0.881712\pi\) | ||||
−0.931743 | + | 0.363117i | \(0.881712\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.15433 | 0.874852 | 0.437426 | − | 0.899254i | \(-0.355890\pi\) | ||||
0.437426 | + | 0.899254i | \(0.355890\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.39245 | −0.822790 | −0.411395 | − | 0.911457i | \(-0.634958\pi\) | ||||
−0.411395 | + | 0.911457i | \(0.634958\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.49250 | −0.936752 | −0.468376 | − | 0.883529i | \(-0.655161\pi\) | ||||
−0.468376 | + | 0.883529i | \(0.655161\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.43397 | −0.486794 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.60902 | −0.484484 | −0.242242 | − | 0.970216i | \(-0.577883\pi\) | ||||
−0.242242 | + | 0.970216i | \(0.577883\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.91390 | 0.343747 | 0.171873 | − | 0.985119i | \(-0.445018\pi\) | ||||
0.171873 | + | 0.985119i | \(0.445018\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.74316 | −0.801740 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.15697 | 0.354604 | 0.177302 | − | 0.984157i | \(-0.443263\pi\) | ||||
0.177302 | + | 0.984157i | \(0.443263\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.04381 | 0.631537 | 0.315768 | − | 0.948836i | \(-0.397738\pi\) | ||||
0.315768 | + | 0.948836i | \(0.397738\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.3442 | 1.57748 | 0.788742 | − | 0.614725i | \(-0.210733\pi\) | ||||
0.788742 | + | 0.614725i | \(0.210733\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.80565 | −0.716384 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.46005 | 1.37989 | 0.689945 | − | 0.723861i | \(-0.257635\pi\) | ||||
0.689945 | + | 0.723861i | \(0.257635\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.76746 | 0.252495 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.85330 | 0.941373 | 0.470686 | − | 0.882301i | \(-0.344006\pi\) | ||||
0.470686 | + | 0.882301i | \(0.344006\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.90041 | −1.33497 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.9794 | −1.55959 | −0.779795 | − | 0.626035i | \(-0.784677\pi\) | ||||
−0.779795 | + | 0.626035i | \(0.784677\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.13105 | −0.785000 | −0.392500 | − | 0.919752i | \(-0.628390\pi\) | ||||
−0.392500 | + | 0.919752i | \(0.628390\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.88297 | 1.11915 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.05286 | 0.626730 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.994333 | −0.121477 | −0.0607386 | − | 0.998154i | \(-0.519346\pi\) | ||||
−0.0607386 | + | 0.998154i | \(0.519346\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.98261 | 0.710005 | 0.355003 | − | 0.934865i | \(-0.384480\pi\) | ||||
0.355003 | + | 0.934865i | \(0.384480\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.489939 | 0.0573430 | 0.0286715 | − | 0.999589i | \(-0.490872\pi\) | ||||
0.0286715 | + | 0.999589i | \(0.490872\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18.3004 | 2.08552 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.53735 | −0.168746 | −0.0843730 | − | 0.996434i | \(-0.526889\pi\) | ||||
−0.0843730 | + | 0.996434i | \(0.526889\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.43431 | −0.589433 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.91571 | 1.05106 | 0.525532 | − | 0.850774i | \(-0.323866\pi\) | ||||
0.525532 | + | 0.850774i | \(0.323866\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.33993 | −0.979090 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.60188 | 0.164350 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.02985 | 0.409170 | 0.204585 | − | 0.978849i | \(-0.434416\pi\) | ||||
0.204585 | + | 0.978849i | \(0.434416\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.5415 | 1.86349 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.3528 | 1.52766 | 0.763832 | − | 0.645415i | \(-0.223316\pi\) | ||||
0.763832 | + | 0.645415i | \(0.223316\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.9671 | −1.57329 | −0.786645 | − | 0.617406i | \(-0.788184\pi\) | ||||
−0.786645 | + | 0.617406i | \(0.788184\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.0808 | 1.65126 | 0.825631 | − | 0.564211i | \(-0.190820\pi\) | ||||
0.825631 | + | 0.564211i | \(0.190820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.50364 | −0.144023 | −0.0720113 | − | 0.997404i | \(-0.522942\pi\) | ||||
−0.0720113 | + | 0.997404i | \(0.522942\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.82323 | 0.924092 | 0.462046 | − | 0.886856i | \(-0.347115\pi\) | ||||
0.462046 | + | 0.886856i | \(0.347115\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.19646 | −0.671074 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.46298 | −0.874852 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.0450 | 0.920825 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.1984 | 2.47258 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.9084 | −1.06512 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.1749 | −1.43529 | −0.717646 | − | 0.696408i | \(-0.754780\pi\) | ||||
−0.717646 | + | 0.696408i | \(0.754780\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.08734 | 0.0950013 | 0.0475007 | − | 0.998871i | \(-0.484874\pi\) | ||||
0.0475007 | + | 0.998871i | \(0.484874\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.96099 | −0.256750 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.95999 | −0.423760 | −0.211880 | − | 0.977296i | \(-0.567959\pi\) | ||||
−0.211880 | + | 0.977296i | \(0.567959\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.82121 | 0.493749 | 0.246874 | − | 0.969047i | \(-0.420596\pi\) | ||||
0.246874 | + | 0.969047i | \(0.420596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.4953 | −1.63028 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.17935 | −0.347076 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.6060 | 1.19657 | 0.598286 | − | 0.801283i | \(-0.295849\pi\) | ||||
0.598286 | + | 0.801283i | \(0.295849\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.7748 | −1.69063 | −0.845316 | − | 0.534266i | \(-0.820588\pi\) | ||||
−0.845316 | + | 0.534266i | \(0.820588\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.1774 | 0.822790 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.06584 | 0.246254 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.6648 | 1.80885 | 0.904426 | − | 0.426631i | \(-0.140300\pi\) | ||||
0.904426 | + | 0.426631i | \(0.140300\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.3023 | 1.04837 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.04190 | −0.316586 | −0.158293 | − | 0.987392i | \(-0.550599\pi\) | ||||
−0.158293 | + | 0.987392i | \(0.550599\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.3609 | 1.57558 | 0.787788 | − | 0.615946i | \(-0.211226\pi\) | ||||
0.787788 | + | 0.615946i | \(0.211226\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.05023 | −0.234633 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | −0.229416 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.4107 | 1.62783 | 0.813913 | − | 0.580986i | \(-0.197333\pi\) | ||||
0.813913 | + | 0.580986i | \(0.197333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.20697 | 0.544796 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.77997 | 0.432015 | 0.216008 | − | 0.976392i | \(-0.430696\pi\) | ||||
0.216008 | + | 0.976392i | \(0.430696\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.1791 | −1.05392 | −0.526960 | − | 0.849890i | \(-0.676668\pi\) | ||||
−0.526960 | + | 0.849890i | \(0.676668\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.45521 | 0.254032 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.9670 | 1.53326 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.21884 | −0.232907 | −0.116454 | − | 0.993196i | \(-0.537153\pi\) | ||||
−0.116454 | + | 0.993196i | \(0.537153\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.0991 | 1.66271 | 0.831354 | − | 0.555744i | \(-0.187566\pi\) | ||||
0.831354 | + | 0.555744i | \(0.187566\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.67837 | −0.475814 | −0.237907 | − | 0.971288i | \(-0.576461\pi\) | ||||
−0.237907 | + | 0.971288i | \(0.576461\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.68196 | −0.615448 | −0.307724 | − | 0.951476i | \(-0.599567\pi\) | ||||
−0.307724 | + | 0.951476i | \(0.599567\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.72529 | 0.542209 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.47771 | 0.452423 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.4775 | 0.936752 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.18049 | −0.427513 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.6971 | −0.942946 | −0.471473 | − | 0.881881i | \(-0.656277\pi\) | ||||
−0.471473 | + | 0.881881i | \(0.656277\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.5703 | 1.13008 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.66704 | −0.384704 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.7009 | −0.719820 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.5376 | −1.71012 | −0.855062 | − | 0.518525i | \(-0.826481\pi\) | ||||
−0.855062 | + | 0.518525i | \(0.826481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.30192 | 0.486794 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.3060 | 0.750405 | 0.375202 | − | 0.926943i | \(-0.377573\pi\) | ||||
0.375202 | + | 0.926943i | \(0.377573\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.7018 | 1.63234 | 0.816171 | − | 0.577811i | \(-0.196093\pi\) | ||||
0.816171 | + | 0.577811i | \(0.196093\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.2147 | −0.669186 | −0.334593 | − | 0.942363i | \(-0.608599\pi\) | ||||
−0.334593 | + | 0.942363i | \(0.608599\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.1539 | 0.988531 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.5094 | −0.679797 | −0.339899 | − | 0.940462i | \(-0.610393\pi\) | ||||
−0.339899 | + | 0.940462i | \(0.610393\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.15386 | −0.267573 | −0.133787 | − | 0.991010i | \(-0.542714\pi\) | ||||
−0.133787 | + | 0.991010i | \(0.542714\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.83127 | 0.180883 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.15433 | 0.200705 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.5040 | 1.04172 | 0.520862 | − | 0.853641i | \(-0.325611\pi\) | ||||
0.520862 | + | 0.853641i | \(0.325611\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.7659 | 1.74562 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.8772 | 0.803260 | 0.401630 | − | 0.915802i | \(-0.368444\pi\) | ||||
0.401630 | + | 0.915802i | \(0.368444\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.38677 | −0.396854 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.82707 | 0.484484 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.4959 | −1.32549 | −0.662747 | − | 0.748844i | \(-0.730609\pi\) | ||||
−0.662747 | + | 0.748844i | \(0.730609\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.9782 | 0.674384 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.95294 | −0.301986 | −0.150993 | − | 0.988535i | \(-0.548247\pi\) | ||||
−0.150993 | + | 0.988535i | \(0.548247\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.4688 | −1.00041 | −0.500203 | − | 0.865908i | \(-0.666741\pi\) | ||||
−0.500203 | + | 0.865908i | \(0.666741\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.0431 | 0.907135 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.6690 | 1.12171 | 0.560855 | − | 0.827914i | \(-0.310473\pi\) | ||||
0.560855 | + | 0.827914i | \(0.310473\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.74170 | −0.343747 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.3257 | −1.68977 | −0.844886 | − | 0.534946i | \(-0.820332\pi\) | ||||
−0.844886 | + | 0.534946i | \(0.820332\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.93603 | −0.531192 | −0.265596 | − | 0.964084i | \(-0.585569\pi\) | ||||
−0.265596 | + | 0.964084i | \(0.585569\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.9737 | −0.706784 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.49128 | −0.323016 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.61796 | −0.269784 | −0.134892 | − | 0.990860i | \(-0.543069\pi\) | ||||
−0.134892 | + | 0.990860i | \(0.543069\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.1896 | −1.11726 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.1708 | −0.819520 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.6292 | −1.76544 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.82122 | −0.562361 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.7797 | −1.24303 | −0.621516 | − | 0.783401i | \(-0.713483\pi\) | ||||
−0.621516 | + | 0.783401i | \(0.713483\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.3867 | −0.759089 | −0.379544 | − | 0.925173i | \(-0.623919\pi\) | ||||
−0.379544 | + | 0.925173i | \(0.623919\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.8251 | 1.51625 | 0.758123 | − | 0.652111i | \(-0.226116\pi\) | ||||
0.758123 | + | 0.652111i | \(0.226116\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.2295 | 0.801740 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.190107 | −0.0106775 | −0.00533873 | − | 0.999986i | \(-0.501699\pi\) | ||||
−0.00533873 | + | 0.999986i | \(0.501699\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.1250 | 0.902829 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.39245 | −0.188761 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.67754 | −0.425873 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.0111 | −1.54430 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.71372 | 0.423984 | 0.211992 | − | 0.977271i | \(-0.432005\pi\) | ||||
0.211992 | + | 0.977271i | \(0.432005\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.47091 | −0.354604 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.59281 | −0.0870242 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.6809 | −1.56235 | −0.781173 | − | 0.624314i | \(-0.785379\pi\) | ||||
−0.781173 | + | 0.624314i | \(0.785379\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.8288 | −0.640567 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4935 | 0.836570 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.6441 | 1.26928 | 0.634640 | − | 0.772808i | \(-0.281149\pi\) | ||||
0.634640 | + | 0.772808i | \(0.281149\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.0960 | −0.915128 | −0.457564 | − | 0.889177i | \(-0.651278\pi\) | ||||
−0.457564 | + | 0.889177i | \(0.651278\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.50478 | −0.292990 | −0.146495 | − | 0.989211i | \(-0.546799\pi\) | ||||
−0.146495 | + | 0.989211i | \(0.546799\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.58344 | 0.508636 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.27449 | −0.489489 | −0.244745 | − | 0.969588i | \(-0.578704\pi\) | ||||
−0.244745 | + | 0.969588i | \(0.578704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.784825 | 0.0410796 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.4748 | 1.79957 | 0.899784 | − | 0.436335i | \(-0.143724\pi\) | ||||
0.899784 | + | 0.436335i | \(0.143724\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.1314 | −0.631537 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.2925 | −1.05354 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −36.8435 | −1.90768 | −0.953841 | − | 0.300313i | \(-0.902909\pi\) | ||||
−0.953841 | + | 0.300313i | \(0.902909\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.22971 | −0.423852 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8052 | 0.965956 | 0.482978 | − | 0.875632i | \(-0.339555\pi\) | ||||
0.482978 | + | 0.875632i | \(0.339555\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.9132 | 1.01752 | 0.508759 | − | 0.860909i | \(-0.330104\pi\) | ||||
0.508759 | + | 0.860909i | \(0.330104\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 29.3150 | 1.49403 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −31.0327 | −1.57748 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.5507 | 1.70109 | 0.850543 | − | 0.525905i | \(-0.176273\pi\) | ||||
0.850543 | + | 0.525905i | \(0.176273\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.2406 | 0.770750 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.60188 | 0.0805995 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.9649 | 0.901632 | 0.450816 | − | 0.892617i | \(-0.351133\pi\) | ||||
0.450816 | + | 0.892617i | \(0.351133\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.13847 | −0.456354 | −0.228177 | − | 0.973620i | \(-0.573276\pi\) | ||||
−0.228177 | + | 0.973620i | \(0.573276\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.03706 | 0.300727 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.4169 | 0.716384 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.3311 | −0.660799 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.9748 | 1.72939 | 0.864696 | − | 0.502296i | \(-0.167511\pi\) | ||||
0.864696 | + | 0.502296i | \(0.167511\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 35.4710 | 1.74541 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.46265 | −0.120887 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.1087 | −1.51976 | −0.759881 | − | 0.650063i | \(-0.774743\pi\) | ||||
−0.759881 | + | 0.650063i | \(0.774743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.1940 | 0.789248 | 0.394624 | − | 0.918843i | \(-0.370875\pi\) | ||||
0.394624 | + | 0.918843i | \(0.370875\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.3802 | −1.37989 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.25713 | 0.400530 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.1540 | 0.878532 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.36886 | −0.114104 | −0.0570520 | − | 0.998371i | \(-0.518170\pi\) | ||||
−0.0570520 | + | 0.998371i | \(0.518170\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.65098 | −0.0793411 | −0.0396706 | − | 0.999213i | \(-0.512631\pi\) | ||||
−0.0396706 | + | 0.999213i | \(0.512631\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.49250 | −0.214906 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.1570 | −1.15295 | −0.576475 | − | 0.817115i | \(-0.695572\pi\) | ||||
−0.576475 | + | 0.817115i | \(0.695572\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.30239 | −0.252495 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.1895 | 1.48186 | 0.740929 | − | 0.671583i | \(-0.234385\pi\) | ||||
0.740929 | + | 0.671583i | \(0.234385\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.8838 | 0.752965 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.8012 | 1.64237 | 0.821185 | − | 0.570661i | \(-0.193313\pi\) | ||||
0.821185 | + | 0.570661i | \(0.193313\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.9927 | −1.17686 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.9615 | −0.701404 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.81118 | 0.0847235 | 0.0423617 | − | 0.999102i | \(-0.486512\pi\) | ||||
0.0423617 | + | 0.999102i | \(0.486512\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.01490 | −0.326716 | −0.163358 | − | 0.986567i | \(-0.552233\pi\) | ||||
−0.163358 | + | 0.986567i | \(0.552233\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.2063 | −0.939064 | −0.469532 | − | 0.882915i | \(-0.655577\pi\) | ||||
−0.469532 | + | 0.882915i | \(0.655577\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.5724 | −0.581782 | −0.290891 | − | 0.956756i | \(-0.593952\pi\) | ||||
−0.290891 | + | 0.956756i | \(0.593952\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.94421 | 0.135951 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −63.9325 | −2.93962 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.43397 | −0.111678 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.5599 | −0.941373 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.8020 | 0.904775 | 0.452387 | − | 0.891822i | \(-0.350572\pi\) | ||||
0.452387 | + | 0.891822i | \(0.350572\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.80378 | 0.310226 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.45535 | 0.293122 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.38065 | 0.107878 | 0.0539388 | − | 0.998544i | \(-0.482822\pi\) | ||||
0.0539388 | + | 0.998544i | \(0.482822\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.1657 | 1.00032 | 0.500162 | − | 0.865932i | \(-0.333274\pi\) | ||||
0.500162 | + | 0.865932i | \(0.333274\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.85098 | 0.398628 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 29.7012 | 1.33497 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.7144 | −0.794602 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.279456 | −0.0125102 | −0.00625509 | − | 0.999980i | \(-0.501991\pi\) | ||||
−0.00625509 | + | 0.999980i | \(0.501991\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0134 | −0.535652 | −0.267826 | − | 0.963467i | \(-0.586305\pi\) | ||||
−0.267826 | + | 0.963467i | \(0.586305\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.5934 | 1.09439 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.7225 | 1.40608 | 0.703039 | − | 0.711152i | \(-0.251826\pi\) | ||||
0.703039 | + | 0.711152i | \(0.251826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.45070 | −0.0641754 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.5775 | −1.12708 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −58.4677 | −2.57141 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.57824 | −0.419630 | −0.209815 | − | 0.977741i | \(-0.567286\pi\) | ||||
−0.209815 | + | 0.977741i | \(0.567286\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.1221 | 1.05479 | 0.527393 | − | 0.849622i | \(-0.323170\pi\) | ||||
0.527393 | + | 0.849622i | \(0.323170\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.49281 | −0.282831 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.81741 | −0.122496 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 35.9383 | 1.55959 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.7555 | 0.552501 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.3614 | 1.18294 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.9238 | −0.470521 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.4239 | −0.448157 | −0.224079 | − | 0.974571i | \(-0.571937\pi\) | ||||
−0.224079 | + | 0.974571i | \(0.571937\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.40865 | −0.103175 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.44329 | 0.403766 | 0.201883 | − | 0.979410i | \(-0.435294\pi\) | ||||
0.201883 | + | 0.979410i | \(0.435294\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.3931 | 0.785000 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.60902 | −0.111148 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.96099 | −0.125914 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.95386 | 0.421759 | 0.210879 | − | 0.977512i | \(-0.432367\pi\) | ||||
0.210879 | + | 0.977512i | \(0.432367\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.6291 | 1.38006 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.38192 | 0.226821 | 0.113410 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.7357 | 0.662004 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −26.6489 | −1.11915 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.26481 | −0.220712 | −0.110356 | − | 0.993892i | \(-0.535199\pi\) | ||||
−0.110356 | + | 0.993892i | \(0.535199\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.7075 | −1.49431 | −0.747157 | − | 0.664648i | \(-0.768582\pi\) | ||||
−0.747157 | + | 0.664648i | \(0.768582\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.9346 | 0.456006 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.9138 | 0.829024 | 0.414512 | − | 0.910044i | \(-0.363952\pi\) | ||||
0.414512 | + | 0.910044i | \(0.363952\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.55207 | 0.188852 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −42.3567 | −1.75424 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.1586 | −0.626730 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.0599 | 0.951783 | 0.475892 | − | 0.879504i | \(-0.342125\pi\) | ||||
0.475892 | + | 0.879504i | \(0.342125\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.91390 | 0.0788609 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.6058 | 1.58535 | 0.792676 | − | 0.609643i | \(-0.208687\pi\) | ||||
0.792676 | + | 0.609643i | \(0.208687\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.0909 | 0.659664 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.97002 | 0.243928 | 0.121964 | − | 0.992534i | \(-0.461081\pi\) | ||||
0.121964 | + | 0.992534i | \(0.461081\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.49599 | −0.142604 | −0.0713022 | − | 0.997455i | \(-0.522715\pi\) | ||||
−0.0713022 | + | 0.997455i | \(0.522715\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.98300 | 0.121477 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 43.5687 | 1.77132 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.8392 | 1.25173 | 0.625863 | − | 0.779933i | \(-0.284747\pi\) | ||||
0.625863 | + | 0.779933i | \(0.284747\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.8401 | 1.20720 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.13623 | 0.207450 | 0.103725 | − | 0.994606i | \(-0.466924\pi\) | ||||
0.103725 | + | 0.994606i | \(0.466924\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.8690 | −0.518085 | −0.259042 | − | 0.965866i | \(-0.583407\pi\) | ||||
−0.259042 | + | 0.965866i | \(0.583407\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.3048 | 1.45921 | 0.729606 | − | 0.683868i | \(-0.239704\pi\) | ||||
0.729606 | + | 0.683868i | \(0.239704\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.3603 | −1.17630 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.90592 | −0.276237 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.31741 | −0.291764 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.57355 | 0.102451 | 0.0512256 | − | 0.998687i | \(-0.483687\pi\) | ||||
0.0512256 | + | 0.998687i | \(0.483687\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.9103 | −1.02822 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.57515 | 0.220896 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.9478 | −0.710005 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.4874 | 1.28317 | 0.641587 | − | 0.767050i | \(-0.278276\pi\) | ||||
0.641587 | + | 0.767050i | \(0.278276\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.9261 | 1.49566 | 0.747831 | − | 0.663890i | \(-0.231096\pi\) | ||||
0.747831 | + | 0.663890i | \(0.231096\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.57368 | 0.297752 | 0.148876 | − | 0.988856i | \(-0.452434\pi\) | ||||
0.148876 | + | 0.988856i | \(0.452434\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 74.0387 | 2.90627 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.1701 | −0.867583 | −0.433792 | − | 0.901013i | \(-0.642825\pi\) | ||||
−0.433792 | + | 0.901013i | \(0.642825\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.74179 | 0.0680574 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.46982 | −0.0573430 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.9592 | 0.933319 | 0.466659 | − | 0.884437i | \(-0.345457\pi\) | ||||
0.466659 | + | 0.884437i | \(0.345457\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.5426 | −1.49913 | −0.749566 | − | 0.661929i | \(-0.769738\pi\) | ||||
−0.749566 | + | 0.661929i | \(0.769738\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.74316 | −0.183932 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.7210 | 0.453841 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.8929 | 1.46284 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.9549 | −1.54015 | −0.770075 | − | 0.637954i | \(-0.779781\pi\) | ||||
−0.770075 | + | 0.637954i | \(0.779781\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.5706 | 0.867457 | 0.433729 | − | 0.901044i | \(-0.357198\pi\) | ||||
0.433729 | + | 0.901044i | \(0.357198\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.9324 | −0.457922 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.4357 | 1.04980 | 0.524900 | − | 0.851164i | \(-0.324103\pi\) | ||||
0.524900 | + | 0.851164i | \(0.324103\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.94532 | −0.303575 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.6175 | 0.823562 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.5742 | 0.782681 | 0.391340 | − | 0.920246i | \(-0.372012\pi\) | ||||
0.391340 | + | 0.920246i | \(0.372012\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −54.9011 | −2.08552 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.32490 | 0.353714 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.7184 | −0.519622 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.0856 | 0.796394 | 0.398197 | − | 0.917300i | \(-0.369636\pi\) | ||||
0.398197 | + | 0.917300i | \(0.369636\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.15697 | 0.0813517 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −45.4596 | −1.70968 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.69713 | 0.213960 | 0.106980 | − | 0.994261i | \(-0.465882\pi\) | ||||
0.106980 | + | 0.994261i | \(0.465882\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.00000 | −0.112509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.59820 | −0.322005 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.2291 | −1.16790 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.56754 | 0.0957531 | 0.0478766 | − | 0.998853i | \(-0.484755\pi\) | ||||
0.0478766 | + | 0.998853i | \(0.484755\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 47.2786 | 1.76075 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.35029 | 0.235844 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.2307 | 0.861580 | 0.430790 | − | 0.902452i | \(-0.358235\pi\) | ||||
0.430790 | + | 0.902452i | \(0.358235\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.0924 | −1.29794 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.138669 | 0.00512185 | 0.00256093 | − | 0.999997i | \(-0.499185\pi\) | ||||
0.00256093 | + | 0.999997i | \(0.499185\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.14546 | 0.226371 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.4978 | −1.60009 | −0.800046 | − | 0.599939i | \(-0.795191\pi\) | ||||
−0.800046 | + | 0.599939i | \(0.795191\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.8136 | 0.836951 | 0.418475 | − | 0.908228i | \(-0.362565\pi\) | ||||
0.418475 | + | 0.908228i | \(0.362565\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.3971 | 0.857205 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.61205 | 0.168746 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −50.5760 | −1.84801 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.8560 | 0.432633 | 0.216316 | − | 0.976323i | \(-0.430596\pi\) | ||||
0.216316 | + | 0.976323i | \(0.430596\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33.2789 | −1.21114 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.7204 | −1.48001 | −0.740005 | − | 0.672602i | \(-0.765177\pi\) | ||||
−0.740005 | + | 0.672602i | \(0.765177\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.1068 | 1.63512 | 0.817561 | − | 0.575843i | \(-0.195326\pi\) | ||||
0.817561 | + | 0.575843i | \(0.195326\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.45226 | 0.161183 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.3029 | 0.589433 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.7870 | −1.36441 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.3550 | 0.697961 | 0.348980 | − | 0.937130i | \(-0.386528\pi\) | ||||
0.348980 | + | 0.937130i | \(0.386528\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.8207 | −0.928707 | −0.464353 | − | 0.885650i | \(-0.653713\pi\) | ||||
−0.464353 | + | 0.885650i | \(0.653713\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.65838 | −0.167334 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.04381 | 0.144884 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.9754 | −1.32309 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.3064 | 1.29583 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.39178 | −0.156550 | −0.0782751 | − | 0.996932i | \(-0.524941\pi\) | ||||
−0.0782751 | + | 0.996932i | \(0.524941\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.0865 | −1.03420 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.3393 | −0.686759 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.64624 | 0.200000 | 0.100000 | − | 0.994987i | \(-0.468116\pi\) | ||||
0.100000 | + | 0.994987i | \(0.468116\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.0928 | −1.13536 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29.7471 | −1.05106 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.02806 | −0.106858 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.3087 | 0.751032 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.4943 | −0.650227 | −0.325113 | − | 0.945675i | \(-0.605402\pi\) | ||||
−0.325113 | + | 0.945675i | \(0.605402\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.0901 | 0.600115 | 0.300057 | − | 0.953921i | \(-0.402994\pi\) | ||||
0.300057 | + | 0.953921i | \(0.402994\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.47464 | −0.226797 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.3442 | 0.361899 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28.0198 | 0.979090 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.8760 | 0.972880 | 0.486440 | − | 0.873714i | \(-0.338295\pi\) | ||||
0.486440 | + | 0.873714i | \(0.338295\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.7731 | 0.584673 | 0.292337 | − | 0.956315i | \(-0.405567\pi\) | ||||
0.292337 | + | 0.956315i | \(0.405567\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.0722 | −1.46300 | −0.731498 | − | 0.681844i | \(-0.761178\pi\) | ||||
−0.731498 | + | 0.681844i | \(0.761178\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.6729 | 0.544344 | 0.272172 | − | 0.962249i | \(-0.412258\pi\) | ||||
0.272172 | + | 0.962249i | \(0.412258\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.99603 | −0.207750 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.6158 | 1.12872 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.7289 | 0.370401 | 0.185201 | − | 0.982701i | \(-0.440707\pi\) | ||||
0.185201 | + | 0.982701i | \(0.440707\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.1930 | −0.765276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.88612 | −0.168088 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −80.5343 | −2.76719 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.69020 | −0.332176 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.4097 | 1.21241 | 0.606203 | − | 0.795310i | \(-0.292692\pi\) | ||||
0.606203 | + | 0.795310i | \(0.292692\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.80565 | −0.164350 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.963968 | 0.0329285 | 0.0164643 | − | 0.999864i | \(-0.494759\pi\) | ||||
0.0164643 | + | 0.999864i | \(0.494759\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.6832 | 1.72929 | 0.864645 | − | 0.502384i | \(-0.167544\pi\) | ||||
0.864645 | + | 0.502384i | \(0.167544\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.8580 | −1.45890 | −0.729452 | − | 0.684032i | \(-0.760225\pi\) | ||||
−0.729452 | + | 0.684032i | \(0.760225\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.2975 | 1.16615 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.18049 | −0.209659 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.13645 | −0.106275 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.0896 | −0.409170 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 35.2605 | 1.19202 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.7853 | −0.600569 | −0.300284 | − | 0.953850i | \(-0.597082\pi\) | ||||
−0.300284 | + | 0.953850i | \(0.597082\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.1540 | −1.62235 | −0.811176 | − | 0.584803i | \(-0.801172\pi\) | ||||
−0.811176 | + | 0.584803i | \(0.801172\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.1943 | −1.21804 | −0.609018 | − | 0.793156i | \(-0.708436\pi\) | ||||
−0.609018 | + | 0.793156i | \(0.708436\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.4004 | 1.25578 | 0.627891 | − | 0.778301i | \(-0.283918\pi\) | ||||
0.627891 | + | 0.778301i | \(0.283918\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 47.8938 | 1.60631 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −55.6244 | −1.86349 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.46005 | 0.316569 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.25883 | 0.309489 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.99341 | −0.166540 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.2495 | −0.774552 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.7132 | −0.755011 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.2635 | −0.838862 | −0.419431 | − | 0.907787i | \(-0.637770\pi\) | ||||
−0.419431 | + | 0.907787i | \(0.637770\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −46.0585 | −1.52766 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.9132 | −0.825410 | −0.412705 | − | 0.910865i | \(-0.635416\pi\) | ||||
−0.412705 | + | 0.910865i | \(0.635416\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.50156 | 0.314456 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.21960 | −0.106321 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.8721 | 0.622533 | 0.311267 | − | 0.950323i | \(-0.399247\pi\) | ||||
0.311267 | + | 0.950323i | \(0.399247\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.8711 | 0.621150 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.25001 | −0.172619 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 47.9014 | 1.57329 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.65253 | −0.0542177 | −0.0271088 | − | 0.999632i | \(-0.508630\pi\) | ||||
−0.0271088 | + | 0.999632i | \(0.508630\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.76746 | 0.0579263 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33.5867 | 1.09840 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.2763 | 0.368381 | 0.184190 | − | 0.982891i | \(-0.441034\pi\) | ||||
0.184190 | + | 0.982891i | \(0.441034\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.9473 | −1.23705 | −0.618523 | − | 0.785767i | \(-0.712269\pi\) | ||||
−0.618523 | + | 0.785767i | \(0.712269\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.1668 | −0.591593 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.7654 | −1.19472 | −0.597358 | − | 0.801975i | \(-0.703783\pi\) | ||||
−0.597358 | + | 0.801975i | \(0.703783\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.54543 | 0.0501667 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.8155 | −1.16018 | −0.580088 | − | 0.814554i | \(-0.696982\pi\) | ||||
−0.580088 | + | 0.814554i | \(0.696982\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.15620 | −0.166851 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.6865 | 0.474251 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.3370 | −0.881838 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −51.2423 | −1.65126 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.0020 | 1.19114 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.6691 | −1.40431 | −0.702153 | − | 0.712026i | \(-0.747778\pi\) | ||||
−0.702153 | + | 0.712026i | \(0.747778\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.5533 | 1.33351 | 0.666755 | − | 0.745277i | \(-0.267683\pi\) | ||||
0.666755 | + | 0.745277i | \(0.267683\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.2366 | −0.552579 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.44477 | 0.142201 | 0.0711004 | − | 0.997469i | \(-0.477349\pi\) | ||||
0.0711004 | + | 0.997469i | \(0.477349\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −61.2839 | −1.95864 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.51092 | 0.144023 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.5915 | −1.07140 | −0.535701 | − | 0.844408i | \(-0.679953\pi\) | ||||
−0.535701 | + | 0.844408i | \(0.679953\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.6980 | −0.340866 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −46.4716 | −1.47771 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.7079 | 1.26136 | 0.630682 | − | 0.776042i | \(-0.282775\pi\) | ||||
0.630682 | + | 0.776042i | \(0.282775\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.9075 | −0.440897 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.8133 | 1.03921 | 0.519604 | − | 0.854407i | \(-0.326080\pi\) | ||||
0.519604 | + | 0.854407i | \(0.326080\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 6004.2.a.d.1.5 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.d.1.5 | ✓ | 8 | 1.1 | even | 1 | trivial |