Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3920,2,Mod(1,3920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3920, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3920.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3920.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: | \(31.3013575923\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 980) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3920.1 |
$q$-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 | ||||||||
\(3\) | −0.414214 | −0.239146 | −0.119573 | − | 0.992825i | \(-0.538153\pi\) | ||||
−0.119573 | + | 0.992825i | \(0.538153\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.82843 | 1.15431 | 0.577157 | − | 0.816633i | \(-0.304162\pi\) | ||||
0.577157 | + | 0.816633i | \(0.304162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.58579 | −0.994518 | −0.497259 | − | 0.867602i | \(-0.665660\pi\) | ||||
−0.497259 | + | 0.867602i | \(0.665660\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.414214 | −0.106949 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.41421 | −1.55568 | −0.777838 | − | 0.628465i | \(-0.783683\pi\) | ||||
−0.777838 | + | 0.628465i | \(0.783683\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.65685 | 0.838940 | 0.419470 | − | 0.907769i | \(-0.362216\pi\) | ||||
0.419470 | + | 0.907769i | \(0.362216\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.585786 | −0.122145 | −0.0610725 | − | 0.998133i | \(-0.519452\pi\) | ||||
−0.0610725 | + | 0.998133i | \(0.519452\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.41421 | 0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.65685 | 1.23615 | 0.618073 | − | 0.786120i | \(-0.287913\pi\) | ||||
0.618073 | + | 0.786120i | \(0.287913\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.58579 | 0.823632 | 0.411816 | − | 0.911267i | \(-0.364895\pi\) | ||||
0.411816 | + | 0.911267i | \(0.364895\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.58579 | −0.276050 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.41421 | −0.561293 | −0.280647 | − | 0.959811i | \(-0.590549\pi\) | ||||
−0.280647 | + | 0.959811i | \(0.590549\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.48528 | 0.237835 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.585786 | −0.0914845 | −0.0457422 | − | 0.998953i | \(-0.514565\pi\) | ||||
−0.0457422 | + | 0.998953i | \(0.514565\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.6569 | −1.77765 | −0.888827 | − | 0.458243i | \(-0.848479\pi\) | ||||
−0.888827 | + | 0.458243i | \(0.848479\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.82843 | −0.421637 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.89949 | −1.29812 | −0.649062 | − | 0.760735i | \(-0.724839\pi\) | ||||
−0.649062 | + | 0.760735i | \(0.724839\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.65685 | 0.372034 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.75736 | −0.516113 | −0.258056 | − | 0.966130i | \(-0.583082\pi\) | ||||
−0.258056 | + | 0.966130i | \(0.583082\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.82843 | 0.516225 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.51472 | −0.200629 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.41421 | 0.444493 | 0.222246 | − | 0.974991i | \(-0.428661\pi\) | ||||
0.222246 | + | 0.974991i | \(0.428661\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.17157 | −0.662152 | −0.331076 | − | 0.943604i | \(-0.607412\pi\) | ||||
−0.331076 | + | 0.943604i | \(0.607412\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.58579 | −0.444762 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.0711 | 1.35255 | 0.676273 | − | 0.736651i | \(-0.263594\pi\) | ||||
0.676273 | + | 0.736651i | \(0.263594\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.242641 | 0.0292105 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.48528 | −0.769661 | −0.384831 | − | 0.922987i | \(-0.625740\pi\) | ||||
−0.384831 | + | 0.922987i | \(0.625740\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.17157 | −0.605287 | −0.302643 | − | 0.953104i | \(-0.597869\pi\) | ||||
−0.302643 | + | 0.953104i | \(0.597869\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.414214 | −0.0478293 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.1421 | −1.47861 | −0.739303 | − | 0.673373i | \(-0.764845\pi\) | ||||
−0.739303 | + | 0.673373i | \(0.764845\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.41421 | −0.695719 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.75736 | −0.295620 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.9706 | −1.79888 | −0.899438 | − | 0.437048i | \(-0.856024\pi\) | ||||
−0.899438 | + | 0.437048i | \(0.856024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.89949 | −0.196968 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.65685 | 0.375185 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.7279 | −1.59693 | −0.798464 | − | 0.602042i | \(-0.794354\pi\) | ||||
−0.798464 | + | 0.602042i | \(0.794354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.8284 | −1.08830 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.82843 | 0.480446 | 0.240223 | − | 0.970718i | \(-0.422779\pi\) | ||||
0.240223 | + | 0.970718i | \(0.422779\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.58579 | 0.156252 | 0.0781261 | − | 0.996943i | \(-0.475106\pi\) | ||||
0.0781261 | + | 0.996943i | \(0.475106\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.8284 | 1.62687 | 0.813433 | − | 0.581659i | \(-0.197596\pi\) | ||||
0.813433 | + | 0.581659i | \(0.197596\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.00000 | 0.862044 | 0.431022 | − | 0.902342i | \(-0.358153\pi\) | ||||
0.431022 | + | 0.902342i | \(0.358153\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.41421 | 0.134231 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.07107 | −0.477046 | −0.238523 | − | 0.971137i | \(-0.576663\pi\) | ||||
−0.238523 | + | 0.971137i | \(0.576663\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.585786 | −0.0546249 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.1421 | 0.937641 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.65685 | 0.332441 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.242641 | 0.0218782 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.8995 | 1.94327 | 0.971633 | − | 0.236494i | \(-0.0759983\pi\) | ||||
0.971633 | + | 0.236494i | \(0.0759983\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.82843 | 0.425119 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.7574 | −1.02725 | −0.513623 | − | 0.858016i | \(-0.671697\pi\) | ||||
−0.513623 | + | 0.858016i | \(0.671697\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.41421 | 0.207782 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9706 | 1.10815 | 0.554075 | − | 0.832467i | \(-0.313072\pi\) | ||||
0.554075 | + | 0.832467i | \(0.313072\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.8995 | −1.17894 | −0.589470 | − | 0.807790i | \(-0.700663\pi\) | ||||
−0.589470 | + | 0.807790i | \(0.700663\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.68629 | 0.310442 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.7279 | −1.14799 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.65685 | 0.552822 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.51472 | 0.287937 | 0.143968 | − | 0.989582i | \(-0.454014\pi\) | ||||
0.143968 | + | 0.989582i | \(0.454014\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8284 | 0.962584 | 0.481292 | − | 0.876560i | \(-0.340168\pi\) | ||||
0.481292 | + | 0.876560i | \(0.340168\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.1421 | 1.46670 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.58579 | 0.368339 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.4853 | −0.836817 | −0.418408 | − | 0.908259i | \(-0.637412\pi\) | ||||
−0.418408 | + | 0.908259i | \(0.637412\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.55635 | 0.123427 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.5563 | −1.68842 | −0.844212 | − | 0.536010i | \(-0.819931\pi\) | ||||
−0.844212 | + | 0.536010i | \(0.819931\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.58579 | −0.123453 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.41421 | 0.186817 | 0.0934087 | − | 0.995628i | \(-0.470224\pi\) | ||||
0.0934087 | + | 0.995628i | \(0.470224\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.142136 | −0.0109335 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.3431 | −0.790960 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.5563 | −1.41081 | −0.705407 | − | 0.708803i | \(-0.749236\pi\) | ||||
−0.705407 | + | 0.708803i | \(0.749236\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.41421 | −0.106299 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.48528 | −0.484733 | −0.242366 | − | 0.970185i | \(-0.577924\pi\) | ||||
−0.242366 | + | 0.970185i | \(0.577924\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.75736 | −0.130623 | −0.0653117 | − | 0.997865i | \(-0.520804\pi\) | ||||
−0.0653117 | + | 0.997865i | \(0.520804\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.14214 | 0.158351 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.41421 | −0.251018 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.5563 | −1.79574 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.6569 | −1.20525 | −0.602624 | − | 0.798025i | \(-0.705878\pi\) | ||||
−0.602624 | + | 0.798025i | \(0.705878\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.65685 | 0.407189 | 0.203595 | − | 0.979055i | \(-0.434738\pi\) | ||||
0.203595 | + | 0.979055i | \(0.434738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.48528 | 0.106363 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −27.5563 | −1.96331 | −0.981654 | − | 0.190669i | \(-0.938934\pi\) | ||||
−0.981654 | + | 0.190669i | \(0.938934\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.7279 | −1.89469 | −0.947346 | − | 0.320212i | \(-0.896246\pi\) | ||||
−0.947346 | + | 0.320212i | \(0.896246\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.58579 | −0.323456 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.585786 | −0.0409131 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.65685 | 0.115159 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.0000 | 0.968400 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.3137 | 1.67382 | 0.836912 | − | 0.547337i | \(-0.184358\pi\) | ||||
0.836912 | + | 0.547337i | \(0.184358\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.68629 | 0.184062 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.6569 | −0.794991 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.14214 | 0.144752 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.0000 | 1.54715 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0711 | 1.61192 | 0.805959 | − | 0.591971i | \(-0.201650\pi\) | ||||
0.805959 | + | 0.591971i | \(0.201650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.82843 | −0.188562 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.72792 | 0.512920 | 0.256460 | − | 0.966555i | \(-0.417444\pi\) | ||||
0.256460 | + | 0.966555i | \(0.417444\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.8995 | −1.57932 | −0.789662 | − | 0.613543i | \(-0.789744\pi\) | ||||
−0.789662 | + | 0.613543i | \(0.789744\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.17157 | −0.600850 | −0.300425 | − | 0.953805i | \(-0.597128\pi\) | ||||
−0.300425 | + | 0.953805i | \(0.597128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.89949 | −0.580539 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.44365 | 0.353603 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.1716 | −0.916683 | −0.458341 | − | 0.888776i | \(-0.651556\pi\) | ||||
−0.458341 | + | 0.888776i | \(0.651556\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.55635 | 0.229085 | 0.114542 | − | 0.993418i | \(-0.463460\pi\) | ||||
0.114542 | + | 0.993418i | \(0.463460\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.3431 | −0.663513 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.1127 | −0.834341 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.31371 | 0.209998 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.0711 | −1.70871 | −0.854355 | − | 0.519689i | \(-0.826048\pi\) | ||||
−0.854355 | + | 0.519689i | \(0.826048\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.24264 | −0.140994 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.65685 | 0.166379 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.7990 | 1.60930 | 0.804648 | − | 0.593752i | \(-0.202354\pi\) | ||||
0.804648 | + | 0.593752i | \(0.202354\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.8284 | −1.16545 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.0000 | −0.616626 | −0.308313 | − | 0.951285i | \(-0.599764\pi\) | ||||
−0.308313 | + | 0.951285i | \(0.599764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.75736 | −0.230813 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.02944 | 0.430195 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.7279 | 1.01992 | 0.509960 | − | 0.860198i | \(-0.329660\pi\) | ||||
0.509960 | + | 0.860198i | \(0.329660\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.9706 | 1.75984 | 0.879918 | − | 0.475125i | \(-0.157597\pi\) | ||||
0.879918 | + | 0.475125i | \(0.157597\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.82843 | 0.230863 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.41421 | −0.445477 | −0.222738 | − | 0.974878i | \(-0.571500\pi\) | ||||
−0.222738 | + | 0.974878i | \(0.571500\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.9706 | −0.776527 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00000 | −0.0596550 | −0.0298275 | − | 0.999555i | \(-0.509496\pi\) | ||||
−0.0298275 | + | 0.999555i | \(0.509496\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.7574 | −1.11501 | −0.557505 | − | 0.830174i | \(-0.688241\pi\) | ||||
−0.557505 | + | 0.830174i | \(0.688241\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.51472 | −0.0897242 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.1421 | 1.42013 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.51472 | 0.381900 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.4142 | 0.842087 | 0.421044 | − | 0.907040i | \(-0.361664\pi\) | ||||
0.421044 | + | 0.907040i | \(0.361664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.41421 | 0.198783 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.24264 | 0.536312 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.10051 | 0.121475 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.00000 | −0.114897 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.17157 | −0.296123 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.58579 | 0.204652 | 0.102326 | − | 0.994751i | \(-0.467372\pi\) | ||||
0.102326 | + | 0.994751i | \(0.467372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.656854 | −0.0373671 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.97056 | 0.395264 | 0.197632 | − | 0.980276i | \(-0.436675\pi\) | ||||
0.197632 | + | 0.980276i | \(0.436675\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.5563 | −0.935820 | −0.467910 | − | 0.883776i | \(-0.654993\pi\) | ||||
−0.467910 | + | 0.883776i | \(0.654993\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.9706 | −0.840831 | −0.420415 | − | 0.907332i | \(-0.638116\pi\) | ||||
−0.420415 | + | 0.907332i | \(0.638116\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.4853 | 1.42690 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.97056 | −0.389059 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.4558 | −1.30512 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.58579 | −0.198904 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.72792 | −0.206155 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.82843 | −0.265394 | −0.132697 | − | 0.991157i | \(-0.542364\pi\) | ||||
−0.132697 | + | 0.991157i | \(0.542364\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.65685 | 0.529192 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.0711 | 0.604877 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.7279 | −1.02017 | −0.510087 | − | 0.860123i | \(-0.670387\pi\) | ||||
−0.510087 | + | 0.860123i | \(0.670387\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.10051 | 0.114084 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.5563 | 0.950730 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.242641 | 0.0130633 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.41421 | 0.398016 | 0.199008 | − | 0.979998i | \(-0.436228\pi\) | ||||
0.199008 | + | 0.979998i | \(0.436228\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.0000 | −0.963518 | −0.481759 | − | 0.876304i | \(-0.660002\pi\) | ||||
−0.481759 | + | 0.876304i | \(0.660002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.65685 | −0.462069 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.07107 | 0.110232 | 0.0551159 | − | 0.998480i | \(-0.482447\pi\) | ||||
0.0551159 | + | 0.998480i | \(0.482447\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.48528 | −0.344203 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.3137 | −0.597115 | −0.298557 | − | 0.954392i | \(-0.596505\pi\) | ||||
−0.298557 | + | 0.954392i | \(0.596505\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.62742 | −0.296180 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.51472 | −0.0795021 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.17157 | −0.270692 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.7279 | 1.02979 | 0.514895 | − | 0.857254i | \(-0.327831\pi\) | ||||
0.514895 | + | 0.857254i | \(0.327831\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.65685 | 0.0862524 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.4853 | 0.853576 | 0.426788 | − | 0.904352i | \(-0.359645\pi\) | ||||
0.426788 | + | 0.904352i | \(0.359645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.414214 | −0.0213899 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.8701 | −1.22937 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.0000 | −0.719132 | −0.359566 | − | 0.933120i | \(-0.617075\pi\) | ||||
−0.359566 | + | 0.933120i | \(0.617075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.07107 | −0.464725 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.51472 | −0.179594 | −0.0897969 | − | 0.995960i | \(-0.528622\pi\) | ||||
−0.0897969 | + | 0.995960i | \(0.528622\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 32.9706 | 1.67599 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.1421 | 0.666333 | 0.333166 | − | 0.942868i | \(-0.391883\pi\) | ||||
0.333166 | + | 0.942868i | \(0.391883\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.75736 | 0.190018 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.87006 | 0.245662 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.1421 | −0.661253 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.4142 | −0.723429 | −0.361714 | − | 0.932289i | \(-0.617808\pi\) | ||||
−0.361714 | + | 0.932289i | \(0.617808\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.514719 | 0.0257038 | 0.0128519 | − | 0.999917i | \(-0.495909\pi\) | ||||
0.0128519 | + | 0.999917i | \(0.495909\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.4437 | −0.819117 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.48528 | 0.371947 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.0711 | −0.647909 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.8284 | −1.62326 | −0.811631 | − | 0.584171i | \(-0.801420\pi\) | ||||
−0.811631 | + | 0.584171i | \(0.801420\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.37258 | −0.265010 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.75736 | 0.281939 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.55635 | −0.466858 | −0.233429 | − | 0.972374i | \(-0.574995\pi\) | ||||
−0.233429 | + | 0.972374i | \(0.574995\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.3137 | 0.990030 | 0.495015 | − | 0.868885i | \(-0.335163\pi\) | ||||
0.495015 | + | 0.868885i | \(0.335163\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 25.1716 | 1.22388 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.41421 | −0.311135 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.68629 | 0.274537 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.82843 | 0.473419 | 0.236709 | − | 0.971581i | \(-0.423931\pi\) | ||||
0.236709 | + | 0.971581i | \(0.423931\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.2843 | 1.07091 | 0.535457 | − | 0.844563i | \(-0.320139\pi\) | ||||
0.535457 | + | 0.844563i | \(0.320139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.75736 | −0.132205 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.14214 | −0.102472 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.2426 | 1.15704 | 0.578519 | − | 0.815669i | \(-0.303631\pi\) | ||||
0.578519 | + | 0.815669i | \(0.303631\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.4558 | 1.68456 | 0.842279 | − | 0.539042i | \(-0.181214\pi\) | ||||
0.842279 | + | 0.539042i | \(0.181214\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.9706 | −0.804482 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.45584 | −0.0688591 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.8284 | 1.12453 | 0.562267 | − | 0.826956i | \(-0.309930\pi\) | ||||
0.562267 | + | 0.826956i | \(0.309930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.24264 | −0.105602 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.89949 | −0.230198 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0711 | −0.704995 | −0.352497 | − | 0.935813i | \(-0.614667\pi\) | ||||
−0.352497 | + | 0.935813i | \(0.614667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.4853 | −0.722791 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.3431 | −1.04062 | −0.520312 | − | 0.853976i | \(-0.674184\pi\) | ||||
−0.520312 | + | 0.853976i | \(0.674184\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.4558 | 0.625346 | 0.312673 | − | 0.949861i | \(-0.398776\pi\) | ||||
0.312673 | + | 0.949861i | \(0.398776\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.89949 | −0.0880870 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.899495 | 0.0416237 | 0.0208118 | − | 0.999783i | \(-0.493375\pi\) | ||||
0.0208118 | + | 0.999783i | \(0.493375\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.34315 | 0.200122 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −44.6274 | −2.05197 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.65685 | 0.167788 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.6274 | 0.486596 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.41421 | 0.430146 | 0.215073 | − | 0.976598i | \(-0.431001\pi\) | ||||
0.215073 | + | 0.976598i | \(0.431001\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.2426 | 0.558216 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.7279 | −0.714168 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.41421 | 0.335970 | 0.167985 | − | 0.985790i | \(-0.446274\pi\) | ||||
0.167985 | + | 0.985790i | \(0.446274\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.92893 | 0.403780 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.2843 | −0.780028 | −0.390014 | − | 0.920809i | \(-0.627530\pi\) | ||||
−0.390014 | + | 0.920809i | \(0.627530\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −42.6985 | −1.92304 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.8284 | −0.486702 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.6274 | 0.610047 | 0.305023 | − | 0.952345i | \(-0.401336\pi\) | ||||
0.305023 | + | 0.952345i | \(0.401336\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.0416 | 1.74078 | 0.870390 | − | 0.492363i | \(-0.163867\pi\) | ||||
0.870390 | + | 0.492363i | \(0.163867\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.82843 | 0.214862 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.0588745 | 0.00261471 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.0711 | 1.55450 | 0.777249 | − | 0.629193i | \(-0.216615\pi\) | ||||
0.777249 | + | 0.629193i | \(0.216615\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.82843 | 0.389785 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.58579 | 0.0698781 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.0711 | −1.49844 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.68629 | 0.337391 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.68629 | −0.292932 | −0.146466 | − | 0.989216i | \(-0.546790\pi\) | ||||
−0.146466 | + | 0.989216i | \(0.546790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.85786 | 0.0812387 | 0.0406194 | − | 0.999175i | \(-0.487067\pi\) | ||||
0.0406194 | + | 0.999175i | \(0.487067\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.4142 | −1.28130 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6569 | −0.985081 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.65685 | −0.419072 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.10051 | 0.0909830 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.8284 | 0.727556 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.68629 | 0.115922 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.9706 | 0.686628 | 0.343314 | − | 0.939221i | \(-0.388450\pi\) | ||||
0.343314 | + | 0.939221i | \(0.388450\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.727922 | 0.0312381 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.00000 | 0.385518 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.51472 | −0.321306 | −0.160653 | − | 0.987011i | \(-0.551360\pi\) | ||||
−0.160653 | + | 0.987011i | \(0.551360\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.6274 | 0.624283 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.3431 | 1.03705 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.41421 | 0.0600300 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.79899 | −0.330454 | −0.165227 | − | 0.986256i | \(-0.552836\pi\) | ||||
−0.165227 | + | 0.986256i | \(0.552836\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41.7990 | 1.76791 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.1716 | 0.429444 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.6274 | −0.869342 | −0.434671 | − | 0.900589i | \(-0.643135\pi\) | ||||
−0.434671 | + | 0.900589i | \(0.643135\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.07107 | −0.213341 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.7990 | −1.33308 | −0.666542 | − | 0.745468i | \(-0.732226\pi\) | ||||
−0.666542 | + | 0.745468i | \(0.732226\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.82843 | −0.202063 | −0.101032 | − | 0.994883i | \(-0.532214\pi\) | ||||
−0.101032 | + | 0.994883i | \(0.532214\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.89949 | 0.288231 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.585786 | −0.0244290 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0711 | 0.585786 | 0.292893 | − | 0.956145i | \(-0.405382\pi\) | ||||
0.292893 | + | 0.956145i | \(0.405382\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.34315 | −0.0973778 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.3848 | −0.595757 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.1421 | 0.419326 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.8284 | −1.27243 | −0.636213 | − | 0.771514i | \(-0.719500\pi\) | ||||
−0.636213 | + | 0.771514i | \(0.719500\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.7696 | 0.690977 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.4142 | 0.469518 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.7279 | −0.727999 | −0.363999 | − | 0.931399i | \(-0.618589\pi\) | ||||
−0.363999 | + | 0.931399i | \(0.618589\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.0711 | 0.453109 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.7990 | 0.522953 | 0.261476 | − | 0.965210i | \(-0.415791\pi\) | ||||
0.261476 | + | 0.965210i | \(0.415791\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.6569 | −1.61764 | −0.808818 | − | 0.588058i | \(-0.799892\pi\) | ||||
−0.808818 | + | 0.588058i | \(0.799892\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −31.3137 | −1.27519 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.65685 | 0.148672 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.9289 | 0.565358 | 0.282679 | − | 0.959215i | \(-0.408777\pi\) | ||||
0.282679 | + | 0.959215i | \(0.408777\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.9117 | 1.29101 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.3137 | −1.66864 | −0.834322 | − | 0.551277i | \(-0.814141\pi\) | ||||
−0.834322 | + | 0.551277i | \(0.814141\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.242641 | 0.00978422 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.8701 | 1.64537 | 0.822683 | − | 0.568500i | \(-0.192476\pi\) | ||||
0.822683 | + | 0.568500i | \(0.192476\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.8701 | 0.436905 | 0.218452 | − | 0.975848i | \(-0.429899\pi\) | ||||
0.218452 | + | 0.975848i | \(0.429899\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.41421 | −0.0567504 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.79899 | −0.231589 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.8995 | 0.873190 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.4853 | 1.57188 | 0.785942 | − | 0.618300i | \(-0.212178\pi\) | ||||
0.785942 | + | 0.618300i | \(0.212178\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.0711 | −0.400289 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.8995 | 0.869055 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.3431 | 0.725644 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.3137 | 1.55280 | 0.776399 | − | 0.630242i | \(-0.217044\pi\) | ||||
0.776399 | + | 0.630242i | \(0.217044\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.21320 | 0.166153 | 0.0830763 | − | 0.996543i | \(-0.473525\pi\) | ||||
0.0830763 | + | 0.996543i | \(0.473525\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.82843 | 0.190119 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.1127 | 1.38042 | 0.690211 | − | 0.723608i | \(-0.257518\pi\) | ||||
0.690211 | + | 0.723608i | \(0.257518\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.0711 | 0.513084 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.6863 | −1.04432 | −0.522158 | − | 0.852849i | \(-0.674873\pi\) | ||||
−0.522158 | + | 0.852849i | \(0.674873\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.7574 | −0.459398 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.6274 | 0.570670 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.6569 | 0.804677 | 0.402338 | − | 0.915491i | \(-0.368198\pi\) | ||||
0.402338 | + | 0.915491i | \(0.368198\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.1421 | 1.32798 | 0.663988 | − | 0.747744i | \(-0.268863\pi\) | ||||
0.663988 | + | 0.747744i | \(0.268863\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.52691 | −0.369995 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.89949 | −0.150989 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.97056 | −0.385484 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.7990 | −0.764332 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.5147 | −1.06061 | −0.530307 | − | 0.847806i | \(-0.677923\pi\) | ||||
−0.530307 | + | 0.847806i | \(0.677923\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.41421 | 0.0929231 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.2721 | 0.394788 | 0.197394 | − | 0.980324i | \(-0.436752\pi\) | ||||
0.197394 | + | 0.980324i | \(0.436752\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.20101 | −0.122663 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.1127 | −1.34355 | −0.671775 | − | 0.740755i | \(-0.734468\pi\) | ||||
−0.671775 | + | 0.740755i | \(0.734468\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9706 | 0.495580 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.89949 | 0.377689 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.4731 | 0.513284 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.51472 | 0.133706 | 0.0668531 | − | 0.997763i | \(-0.478704\pi\) | ||||
0.0668531 | + | 0.997763i | \(0.478704\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.8995 | −0.527238 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.75736 | 0.142320 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.79899 | 0.143691 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.514719 | 0.0194407 | 0.00972033 | − | 0.999953i | \(-0.496906\pi\) | ||||
0.00972033 | + | 0.999953i | \(0.496906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.4853 | −0.470891 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.68629 | 0.138834 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.62742 | 0.136231 | 0.0681153 | − | 0.997677i | \(-0.478301\pi\) | ||||
0.0681153 | + | 0.997677i | \(0.478301\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37.1716 | 1.39404 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.68629 | −0.100602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.7279 | −0.513395 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.87006 | 0.219221 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.7574 | 0.587650 | 0.293825 | − | 0.955859i | \(-0.405072\pi\) | ||||
0.293825 | + | 0.955859i | \(0.405072\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.47309 | −0.0547847 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.65685 | 0.247229 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.0000 | −0.667583 | −0.333792 | − | 0.942647i | \(-0.608328\pi\) | ||||
−0.333792 | + | 0.942647i | \(0.608328\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 74.7696 | 2.76545 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.6985 | 1.13387 | 0.566937 | − | 0.823761i | \(-0.308128\pi\) | ||||
0.566937 | + | 0.823761i | \(0.308128\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42.3848 | 1.56126 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.6569 | −0.759875 | −0.379937 | − | 0.925012i | \(-0.624054\pi\) | ||||
−0.379937 | + | 0.925012i | \(0.624054\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.43146 | 0.199530 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.92893 | 0.327571 | 0.163785 | − | 0.986496i | \(-0.447630\pi\) | ||||
0.163785 | + | 0.986496i | \(0.447630\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.51472 | 0.128769 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.6274 | 0.827894 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.14214 | −0.0416771 | −0.0208386 | − | 0.999783i | \(-0.506634\pi\) | ||||
−0.0208386 | + | 0.999783i | \(0.506634\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.2132 | 0.408632 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.8284 | 0.430481 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.1716 | 1.35102 | 0.675512 | − | 0.737349i | \(-0.263923\pi\) | ||||
0.675512 | + | 0.737349i | \(0.263923\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.928932 | 0.0337181 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.8701 | 0.684039 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.1421 | 0.655930 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.2426 | −0.442056 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.1421 | −1.01483 | −0.507416 | − | 0.861701i | \(-0.669399\pi\) | ||||
−0.507416 | + | 0.861701i | \(0.669399\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.6863 | −0.384857 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 43.7279 | 1.57278 | 0.786392 | − | 0.617728i | \(-0.211947\pi\) | ||||
0.786392 | + | 0.617728i | \(0.211947\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.58579 | 0.164726 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.14214 | −0.0767500 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.8284 | −0.888431 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.0711 | 0.574333 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.4853 | −0.374236 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.7279 | −1.55873 | −0.779366 | − | 0.626569i | \(-0.784459\pi\) | ||||
−0.779366 | + | 0.626569i | \(0.784459\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.14214 | 0.147464 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.5442 | 0.658522 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.55635 | 0.0551980 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.3848 | 1.25339 | 0.626697 | − | 0.779263i | \(-0.284407\pi\) | ||||
0.626697 | + | 0.779263i | \(0.284407\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 57.0833 | 2.01946 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 48.0000 | 1.69600 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.7990 | −0.698691 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.92893 | −0.243910 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.02944 | 0.211984 | 0.105992 | − | 0.994367i | \(-0.466198\pi\) | ||||
0.105992 | + | 0.994367i | \(0.466198\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.5563 | −0.686716 | −0.343358 | − | 0.939205i | \(-0.611564\pi\) | ||||
−0.343358 | + | 0.939205i | \(0.611564\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0000 | −0.420858 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.5563 | −0.755086 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42.6274 | −1.49134 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.8284 | 1.66922 | 0.834612 | − | 0.550839i | \(-0.185692\pi\) | ||||
0.834612 | + | 0.550839i | \(0.185692\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.5269 | −1.27325 | −0.636624 | − | 0.771174i | \(-0.719670\pi\) | ||||
−0.636624 | + | 0.771174i | \(0.719670\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.58579 | −0.0552100 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.0416 | 0.349182 | 0.174591 | − | 0.984641i | \(-0.444140\pi\) | ||||
0.174591 | + | 0.984641i | \(0.444140\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.7279 | −0.789373 | −0.394687 | − | 0.918816i | \(-0.629147\pi\) | ||||
−0.394687 | + | 0.918816i | \(0.629147\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.07107 | 0.106534 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.41421 | 0.0835473 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.0711 | 0.382672 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.3848 | 0.772808 | 0.386404 | − | 0.922330i | \(-0.373717\pi\) | ||||
0.386404 | + | 0.922330i | \(0.373717\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.3137 | 0.528059 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.414214 | 0.0142663 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.142136 | −0.00488961 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.76955 | 0.266650 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.00000 | 0.0685591 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.2843 | 1.03691 | 0.518457 | − | 0.855104i | \(-0.326507\pi\) | ||||
0.518457 | + | 0.855104i | \(0.326507\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.3431 | −0.353728 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.8284 | 0.711486 | 0.355743 | − | 0.934584i | \(-0.384228\pi\) | ||||
0.355743 | + | 0.934584i | \(0.384228\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.4558 | −1.55093 | −0.775467 | − | 0.631388i | \(-0.782485\pi\) | ||||
−0.775467 | + | 0.631388i | \(0.782485\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.7574 | 0.672548 | 0.336274 | − | 0.941764i | \(-0.390833\pi\) | ||||
0.336274 | + | 0.941764i | \(0.390833\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.5563 | −0.630935 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.0000 | −0.339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −50.3137 | −1.70678 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.6985 | −1.34513 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 44.4853 | 1.50560 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.6863 | 0.360850 | 0.180425 | − | 0.983589i | \(-0.442253\pi\) | ||||
0.180425 | + | 0.983589i | \(0.442253\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.97056 | −0.201382 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 56.2843 | 1.89627 | 0.948133 | − | 0.317875i | \(-0.102969\pi\) | ||||
0.948133 | + | 0.317875i | \(0.102969\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.11270 | 0.239361 | 0.119681 | − | 0.992812i | \(-0.461813\pi\) | ||||
0.119681 | + | 0.992812i | \(0.461813\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.41421 | −0.0475383 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 57.5980 | 1.93395 | 0.966975 | − | 0.254870i | \(-0.0820325\pi\) | ||||
0.966975 | + | 0.254870i | \(0.0820325\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.6569 | 0.960041 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32.5442 | −1.08905 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.48528 | −0.216779 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.870058 | −0.0290504 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.5269 | 1.01813 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.1005 | 0.802904 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.75736 | −0.0584166 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.5269 | −0.747994 | −0.373997 | − | 0.927430i | \(-0.622013\pi\) | ||||
−0.373997 | + | 0.927430i | \(0.622013\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.6569 | −0.452969 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.5980 | 1.84204 | 0.921022 | − | 0.389511i | \(-0.127356\pi\) | ||||
0.921022 | + | 0.389511i | \(0.127356\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.6274 | −1.01362 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.14214 | 0.0708168 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.5147 | 0.610744 | 0.305372 | − | 0.952233i | \(-0.401219\pi\) | ||||
0.305372 | + | 0.952233i | \(0.401219\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.48528 | −0.0489417 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.2548 | 0.765442 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.41421 | −0.112259 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.48528 | −0.147316 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.2721 | 0.697914 | 0.348957 | − | 0.937139i | \(-0.386536\pi\) | ||||
0.348957 | + | 0.937139i | \(0.386536\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.88730 | −0.0945260 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −24.5563 | −0.803078 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.72792 | 0.252460 | 0.126230 | − | 0.992001i | \(-0.459712\pi\) | ||||
0.126230 | + | 0.992001i | \(0.459712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.85786 | 0.223798 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.00000 | 0.130396 | 0.0651981 | − | 0.997872i | \(-0.479232\pi\) | ||||
0.0651981 | + | 0.997872i | \(0.479232\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.343146 | 0.0111744 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.0416 | 1.04121 | 0.520607 | − | 0.853797i | \(-0.325706\pi\) | ||||
0.520607 | + | 0.853797i | \(0.325706\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.5442 | 0.601969 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.20101 | 0.201082 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.8701 | −1.25912 | −0.629562 | − | 0.776950i | \(-0.716766\pi\) | ||||
−0.629562 | + | 0.776950i | \(0.716766\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.6569 | −0.539003 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.5563 | −0.341238 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.97056 | −0.321631 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −47.5980 | −1.53382 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.65685 | 0.182101 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.45584 | 0.239764 | 0.119882 | − | 0.992788i | \(-0.461748\pi\) | ||||
0.119882 | + | 0.992788i | \(0.461748\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.71573 | 0.312114 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.5269 | −0.722923 | −0.361462 | − | 0.932387i | \(-0.617722\pi\) | ||||
−0.361462 | + | 0.932387i | \(0.617722\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.48528 | 0.0475671 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.14214 | −0.260490 | −0.130245 | − | 0.991482i | \(-0.541576\pi\) | ||||
−0.130245 | + | 0.991482i | \(0.541576\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −64.9706 | −2.07647 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.4558 | −0.812743 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.0122 | −1.33998 | −0.669990 | − | 0.742370i | \(-0.733702\pi\) | ||||
−0.669990 | + | 0.742370i | \(0.733702\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.5563 | −0.878018 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.82843 | 0.217131 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.3137 | −0.804116 | −0.402058 | − | 0.915614i | \(-0.631705\pi\) | ||||
−0.402058 | + | 0.915614i | \(0.631705\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.00000 | 0.0634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.7279 | −0.847332 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.8406 | 1.61014 | 0.805069 | − | 0.593181i | \(-0.202128\pi\) | ||||
0.805069 | + | 0.593181i | \(0.202128\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.24264 | −0.260786 |
(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 | 3920.2.a.bx.1.1 | 2 | ||
4.3 | odd | 2 | 980.2.a.j.1.2 | ✓ | 2 | ||
7.6 | odd | 2 | 3920.2.a.bo.1.2 | 2 | |||
12.11 | even | 2 | 8820.2.a.bg.1.2 | 2 | |||
20.3 | even | 4 | 4900.2.e.q.2549.3 | 4 | |||
20.7 | even | 4 | 4900.2.e.q.2549.2 | 4 | |||
20.19 | odd | 2 | 4900.2.a.z.1.1 | 2 | |||
28.3 | even | 6 | 980.2.i.k.961.2 | 4 | |||
28.11 | odd | 6 | 980.2.i.l.961.1 | 4 | |||
28.19 | even | 6 | 980.2.i.k.361.2 | 4 | |||
28.23 | odd | 6 | 980.2.i.l.361.1 | 4 | |||
28.27 | even | 2 | 980.2.a.k.1.1 | yes | 2 | ||
84.83 | odd | 2 | 8820.2.a.bl.1.2 | 2 | |||
140.27 | odd | 4 | 4900.2.e.r.2549.3 | 4 | |||
140.83 | odd | 4 | 4900.2.e.r.2549.2 | 4 | |||
140.139 | even | 2 | 4900.2.a.x.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
980.2.a.j.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
980.2.a.k.1.1 | yes | 2 | 28.27 | even | 2 | ||
980.2.i.k.361.2 | 4 | 28.19 | even | 6 | |||
980.2.i.k.961.2 | 4 | 28.3 | even | 6 | |||
980.2.i.l.361.1 | 4 | 28.23 | odd | 6 | |||
980.2.i.l.961.1 | 4 | 28.11 | odd | 6 | |||
3920.2.a.bo.1.2 | 2 | 7.6 | odd | 2 | |||
3920.2.a.bx.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4900.2.a.x.1.2 | 2 | 140.139 | even | 2 | |||
4900.2.a.z.1.1 | 2 | 20.19 | odd | 2 | |||
4900.2.e.q.2549.2 | 4 | 20.7 | even | 4 | |||
4900.2.e.q.2549.3 | 4 | 20.3 | even | 4 | |||
4900.2.e.r.2549.2 | 4 | 140.83 | odd | 4 | |||
4900.2.e.r.2549.3 | 4 | 140.27 | odd | 4 | |||
8820.2.a.bg.1.2 | 2 | 12.11 | even | 2 | |||
8820.2.a.bl.1.2 | 2 | 84.83 | odd | 2 |