Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(113,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.f (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | 10.0.20322144469993472.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - x^{8} - 2x^{7} - 2x^{6} + 22x^{5} - 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.9 | ||
Root | \(-1.69134 + 0.373340i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.113 |
Dual form | 912.2.f.h.113.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.69134 | − | 0.373340i | 0.976493 | − | 0.215548i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.568907i | 0.254423i | 0.991876 | + | 0.127211i | \(0.0406027\pi\) | ||||
−0.991876 | + | 0.127211i | \(0.959397\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.718465 | −0.271554 | −0.135777 | − | 0.990739i | \(-0.543353\pi\) | ||||
−0.135777 | + | 0.990739i | \(0.543353\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.72123 | − | 1.26289i | 0.907078 | − | 0.420962i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.78814i | 1.44368i | 0.692061 | + | 0.721839i | \(0.256703\pi\) | ||||
−0.692061 | + | 0.721839i | \(0.743297\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.61037i | 1.27869i | 0.768922 | + | 0.639343i | \(0.220793\pi\) | ||||
−0.768922 | + | 0.639343i | \(0.779207\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.212396 | + | 0.962212i | 0.0548403 | + | 0.248442i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.10370i | 1.72290i | 0.507843 | + | 0.861450i | \(0.330443\pi\) | ||||
−0.507843 | + | 0.861450i | \(0.669557\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.62497 | + | 2.42067i | −0.831624 | + | 0.555339i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.21517 | + | 0.268232i | −0.265171 | + | 0.0585330i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.38946i | − | 1.33229i | −0.745820 | − | 0.666147i | \(-0.767942\pi\) | ||
0.745820 | − | 0.666147i | \(-0.232058\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.67635 | 0.935269 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.13104 | − | 3.15191i | 0.795018 | − | 0.606586i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.44247 | 1.01064 | 0.505321 | − | 0.862932i | \(-0.331374\pi\) | ||||
0.505321 | + | 0.862932i | \(0.331374\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.28147i | − | 1.30779i | −0.756585 | − | 0.653895i | \(-0.773134\pi\) | ||
0.756585 | − | 0.653895i | \(-0.226866\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.78760 | + | 8.09835i | 0.311182 | + | 1.40974i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 0.408739i | − | 0.0690896i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.99833i | − | 0.986119i | −0.869996 | − | 0.493059i | \(-0.835879\pi\) | ||
0.869996 | − | 0.493059i | \(-0.164121\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.72123 | + | 7.79768i | 0.275618 | + | 1.24863i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.82514 | 1.37826 | 0.689128 | − | 0.724640i | \(-0.257994\pi\) | ||||
0.689128 | + | 0.724640i | \(0.257994\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.08900 | −0.471068 | −0.235534 | − | 0.971866i | \(-0.575684\pi\) | ||||
−0.235534 | + | 0.971866i | \(0.575684\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.718465 | + | 1.54813i | 0.107102 | + | 0.230781i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.779123i | 0.113647i | 0.998384 | + | 0.0568234i | \(0.0180972\pi\) | ||||
−0.998384 | + | 0.0568234i | \(0.981903\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.48381 | −0.926258 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.65209 | + | 12.0147i | 0.371368 | + | 1.68240i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.86726 | 0.805930 | 0.402965 | − | 0.915215i | \(-0.367980\pi\) | ||||
0.402965 | + | 0.915215i | \(0.367980\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.72400 | −0.367305 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.22730 | + | 5.44750i | −0.692373 | + | 0.721540i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.45461 | 1.10070 | 0.550348 | − | 0.834935i | \(-0.314495\pi\) | ||||
0.550348 | + | 0.834935i | \(0.314495\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.4893 | −1.47106 | −0.735530 | − | 0.677492i | \(-0.763067\pi\) | ||||
−0.735530 | + | 0.677492i | \(0.763067\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.95511 | + | 0.907340i | −0.246321 | + | 0.114314i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.62287 | −0.325327 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.87380i | − | 0.473260i | −0.971600 | − | 0.236630i | \(-0.923957\pi\) | ||
0.971600 | − | 0.236630i | \(-0.0760430\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.38544 | − | 10.8067i | −0.287173 | − | 1.30098i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.30973 | −0.867505 | −0.433753 | − | 0.901032i | \(-0.642811\pi\) | ||||
−0.433753 | + | 0.901032i | \(0.642811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.20305 | −0.374889 | −0.187444 | − | 0.982275i | \(-0.560020\pi\) | ||||
−0.187444 | + | 0.982275i | \(0.560020\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.90927 | − | 1.74587i | 0.913284 | − | 0.201595i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.44011i | − | 0.392037i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.79886i | 0.202387i | 0.994867 | + | 0.101194i | \(0.0322662\pi\) | ||||
−0.994867 | + | 0.101194i | \(0.967734\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.81023 | − | 6.87322i | 0.645581 | − | 0.763691i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.28314i | 0.140843i | 0.997517 | + | 0.0704217i | \(0.0224345\pi\) | ||||
−0.997517 | + | 0.0704217i | \(0.977566\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.04134 | −0.438345 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.20504 | − | 2.03189i | 0.986884 | − | 0.217842i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.138279 | −0.0146576 | −0.00732878 | − | 0.999973i | \(-0.502333\pi\) | ||||
−0.00732878 | + | 0.999973i | \(0.502333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.31239i | − | 0.347232i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.71846 | − | 12.3154i | −0.281892 | − | 1.27705i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.37713 | − | 2.06227i | −0.141291 | − | 0.211584i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.25160i | − | 0.939358i | −0.882837 | − | 0.469679i | \(-0.844370\pi\) | ||
0.882837 | − | 0.469679i | \(-0.155630\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.04688 | + | 13.0296i | 0.607734 | + | 1.30953i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.9095i | 1.08553i | 0.839884 | + | 0.542766i | \(0.182623\pi\) | ||||
−0.839884 | + | 0.542766i | \(0.817377\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.8471i | 1.85706i | 0.371262 | + | 0.928528i | \(0.378925\pi\) | ||||
−0.371262 | + | 0.928528i | \(0.621075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.152599 | − | 0.691316i | −0.0148921 | − | 0.0674655i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.77088 | −0.461219 | −0.230609 | − | 0.973046i | \(-0.574072\pi\) | ||||
−0.230609 | + | 0.973046i | \(0.574072\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.7040i | − | 1.02525i | −0.858611 | − | 0.512627i | \(-0.828672\pi\) | ||
0.858611 | − | 0.512627i | \(-0.171328\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.23942 | − | 10.1452i | −0.212556 | − | 0.962938i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.508865 | −0.0478700 | −0.0239350 | − | 0.999714i | \(-0.507619\pi\) | ||||
−0.0239350 | + | 0.999714i | \(0.507619\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.63501 | 0.338966 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.82237 | + | 12.5459i | 0.538278 | + | 1.15987i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.10376i | − | 0.467861i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.9263 | −1.08421 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.9263 | − | 3.29478i | 1.34586 | − | 0.297080i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.50494i | 0.492376i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.4815i | − | 1.01882i | −0.860524 | − | 0.509410i | \(-0.829864\pi\) | ||
0.860524 | − | 0.509410i | \(-0.170136\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.22453 | + | 1.15325i | −0.459995 | + | 0.101538i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.92595i | 0.517753i | 0.965910 | + | 0.258876i | \(0.0833522\pi\) | ||||
−0.965910 | + | 0.258876i | \(0.916648\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.60441 | − | 1.73916i | 0.225831 | − | 0.150805i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.79314 | + | 2.35017i | 0.154329 | + | 0.202271i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 15.1420i | − | 1.29367i | −0.762632 | − | 0.646833i | \(-0.776093\pi\) | ||
0.762632 | − | 0.646833i | \(-0.223907\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.36975 | −0.455457 | −0.227728 | − | 0.973725i | \(-0.573130\pi\) | ||||
−0.227728 | + | 0.973725i | \(0.573130\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.290878 | + | 1.31776i | 0.0244963 | + | 0.110975i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.0751 | −1.84601 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.09626i | 0.257130i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.9663 | + | 2.42067i | −0.904485 | + | 0.199653i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2.63373i | − | 0.215764i | −0.994164 | − | 0.107882i | \(-0.965593\pi\) | ||
0.994164 | − | 0.107882i | \(-0.0344069\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.57038i | − | 0.534690i | −0.963601 | − | 0.267345i | \(-0.913854\pi\) | ||
0.963601 | − | 0.267345i | \(-0.0861463\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.97117 | + | 19.3308i | 0.725276 | + | 1.56280i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.14248 | 0.332732 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.9676 | 1.03493 | 0.517464 | − | 0.855705i | \(-0.326876\pi\) | ||||
0.517464 | + | 0.855705i | \(0.326876\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.92351 | − | 2.19048i | 0.786985 | − | 0.173717i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.59060i | 0.361790i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0938 | 1.26056 | 0.630280 | − | 0.776368i | \(-0.282940\pi\) | ||||
0.630280 | + | 0.776368i | \(0.282940\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.60721 | + | 1.01698i | −0.358670 | + | 0.0791718i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.0243 | −0.775702 | −0.387851 | − | 0.921722i | \(-0.626782\pi\) | ||||
−0.387851 | + | 0.921722i | \(0.626782\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.25547 | −0.635036 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.80735 | + | 11.1651i | −0.520571 | + | 0.853818i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.1714 | −1.15346 | −0.576732 | − | 0.816933i | \(-0.695672\pi\) | ||||
−0.576732 | + | 0.816933i | \(0.695672\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.35979 | −0.253976 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.2996 | − | 3.15644i | 1.07482 | − | 0.237253i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.7288 | 1.47460 | 0.737299 | − | 0.675567i | \(-0.236101\pi\) | ||||
0.737299 | + | 0.675567i | \(0.236101\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.4191i | 1.44341i | 0.692200 | + | 0.721705i | \(0.256641\pi\) | ||||
−0.692200 | + | 0.721705i | \(0.743359\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.4323 | + | 4.28943i | −1.43648 | + | 0.317084i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.41249 | 0.250891 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −34.0135 | −2.48731 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.96800 | + | 2.26454i | −0.215890 | + | 0.164721i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 15.8477i | − | 1.14670i | −0.819312 | − | 0.573348i | \(-0.805644\pi\) | ||
0.819312 | − | 0.573348i | \(-0.194356\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 8.50964i | − | 0.612537i | −0.951945 | − | 0.306269i | \(-0.900919\pi\) | ||
0.951945 | − | 0.306269i | \(-0.0990805\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.43615 | + | 0.979222i | −0.317679 | + | 0.0701235i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 14.0057i | − | 0.997867i | −0.866640 | − | 0.498933i | \(-0.833725\pi\) | ||
0.866640 | − | 0.498933i | \(-0.166275\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.6972 | 1.39629 | 0.698147 | − | 0.715954i | \(-0.254008\pi\) | ||||
0.698147 | + | 0.715954i | \(0.254008\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.44625 | − | 6.55190i | −0.102010 | − | 0.462136i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.91022 | −0.274444 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.02068i | 0.350660i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.06917 | − | 17.3872i | −0.560846 | − | 1.20850i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.5905 | − | 17.3568i | −0.801731 | − | 1.20060i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.30487i | 0.296359i | 0.988960 | + | 0.148180i | \(0.0473414\pi\) | ||||
−0.988960 | + | 0.148180i | \(0.952659\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.3632 | + | 2.72901i | −0.847113 | + | 0.186989i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.75735i | − | 0.119850i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.23148i | 0.355136i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.41744 | + | 1.19583i | −0.366077 | + | 0.0808066i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −32.7506 | −2.20305 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 20.8427i | − | 1.39573i | −0.716231 | − | 0.697864i | \(-0.754134\pi\) | ||
0.716231 | − | 0.697864i | \(-0.245866\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.7254 | − | 5.90570i | 0.848362 | − | 0.393713i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.88254 | 0.655927 | 0.327963 | − | 0.944690i | \(-0.393638\pi\) | ||||
0.327963 | + | 0.944690i | \(0.393638\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.8112 | 1.57349 | 0.786745 | − | 0.617279i | \(-0.211765\pi\) | ||||
0.786745 | + | 0.617279i | \(0.211765\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.28433 | − | 5.81838i | −0.0845028 | − | 0.382821i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.4784i | 0.751974i | 0.926625 | + | 0.375987i | \(0.122696\pi\) | ||||
−0.926625 | + | 0.375987i | \(0.877304\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.443248 | −0.0289143 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.671586 | + | 3.04247i | 0.0436242 | + | 0.197630i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.05755i | 0.133092i | 0.997783 | + | 0.0665459i | \(0.0211979\pi\) | ||||
−0.997783 | + | 0.0665459i | \(0.978802\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 29.2663i | − | 1.88521i | −0.333914 | − | 0.942604i | \(-0.608370\pi\) | ||
0.333914 | − | 0.942604i | \(-0.391630\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.26101 | − | 13.7941i | 0.465794 | − | 0.884893i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 3.68868i | − | 0.235661i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.1602 | − | 16.7124i | −0.710104 | − | 1.06339i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.479049 | + | 2.17023i | 0.0303585 | + | 0.137533i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 7.57035i | − | 0.477836i | −0.971040 | − | 0.238918i | \(-0.923207\pi\) | ||
0.971040 | − | 0.238918i | \(-0.0767927\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.5936 | 1.92340 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.83526 | + | 1.50879i | −0.428041 | + | 0.0944844i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.5825 | −1.03439 | −0.517195 | − | 0.855867i | \(-0.673024\pi\) | ||||
−0.517195 | + | 0.855867i | \(0.673024\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.30959i | 0.267785i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.8102 | − | 6.87322i | 0.916730 | − | 0.425442i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.76573i | 0.478855i | 0.970914 | + | 0.239428i | \(0.0769598\pi\) | ||||
−0.970914 | + | 0.239428i | \(0.923040\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.33792i | 0.205047i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.233877 | + | 0.0516252i | −0.0143130 | + | 0.00315941i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.5185 | 0.885212 | 0.442606 | − | 0.896716i | \(-0.354054\pi\) | ||||
0.442606 | + | 0.896716i | \(0.354054\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.8889 | −1.87637 | −0.938184 | − | 0.346137i | \(-0.887493\pi\) | ||||
−0.938184 | + | 0.346137i | \(0.887493\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.23665 | − | 5.60236i | −0.0748452 | − | 0.339070i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.3910i | 1.35023i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.1351 | −0.608959 | −0.304479 | − | 0.952519i | \(-0.598483\pi\) | ||||
−0.304479 | + | 0.952519i | \(0.598483\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.19567 | − | 19.8146i | −0.550531 | − | 1.18627i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.51541 | 0.567642 | 0.283821 | − | 0.958877i | \(-0.408398\pi\) | ||||
0.283821 | + | 0.958877i | \(0.408398\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.16093 | 0.485117 | 0.242559 | − | 0.970137i | \(-0.422013\pi\) | ||||
0.242559 | + | 0.970137i | \(0.422013\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.09912 | − | 2.97385i | −0.183576 | − | 0.176156i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.34055 | −0.374271 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −33.4625 | −1.96838 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.45399 | − | 15.6476i | −0.202477 | − | 0.917276i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.23864 | 0.189203 | 0.0946016 | − | 0.995515i | \(-0.469842\pi\) | ||||
0.0946016 | + | 0.995515i | \(0.469842\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.80988i | 0.280042i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.0918 | + | 19.7800i | 0.875715 | + | 1.14775i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.4577 | 1.70359 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.21934 | 0.127920 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.07294 | + | 18.4516i | 0.233984 | + | 1.06002i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 6.53637i | − | 0.374271i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 0.189980i | − | 0.0108427i | −0.999985 | − | 0.00542135i | \(-0.998274\pi\) | ||
0.999985 | − | 0.00542135i | \(-0.00172568\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.03636 | + | 31.8767i | 0.400285 | + | 1.81340i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.58052i | 0.316442i | 0.987404 | + | 0.158221i | \(0.0505759\pi\) | ||||
−0.987404 | + | 0.158221i | \(0.949424\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.9012 | −1.01184 | −0.505918 | − | 0.862581i | \(-0.668846\pi\) | ||||
−0.505918 | + | 0.862581i | \(0.668846\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.516192 | − | 1.11228i | −0.0290841 | − | 0.0626696i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.1633 | −1.24481 | −0.622407 | − | 0.782694i | \(-0.713845\pi\) | ||||
−0.622407 | + | 0.782694i | \(0.713845\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.0593i | 1.45904i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.06917 | + | 1.78116i | −0.450377 | + | 0.0994148i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.1957 | − | 25.7507i | −0.956793 | − | 1.43280i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.5597i | 1.19591i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.99622 | − | 18.1040i | −0.220992 | − | 1.00115i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 0.559773i | − | 0.0308613i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 25.9533i | − | 1.42652i | −0.700898 | − | 0.713262i | \(-0.747217\pi\) | ||
0.700898 | − | 0.713262i | \(-0.252783\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.57521 | − | 16.3229i | −0.415119 | − | 0.894487i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.20383 | 0.120408 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.0950i | 1.58491i | 0.609933 | + | 0.792453i | \(0.291196\pi\) | ||||
−0.609933 | + | 0.792453i | \(0.708804\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.860661 | + | 0.189980i | −0.0467447 | + | 0.0103183i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 34.8647 | 1.88803 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.68764 | 0.523083 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.14802 | − | 1.35709i | 0.330998 | − | 0.0730634i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.14187i | 0.329713i | 0.986318 | + | 0.164856i | \(0.0527161\pi\) | ||||
−0.986318 | + | 0.164856i | \(0.947284\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.91520 | −0.477220 | −0.238610 | − | 0.971116i | \(-0.576692\pi\) | ||||
−0.238610 | + | 0.971116i | \(0.576692\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.5315 | + | 19.0456i | 0.775632 | + | 1.01658i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 21.9955i | − | 1.17070i | −0.810780 | − | 0.585352i | \(-0.800957\pi\) | ||
0.810780 | − | 0.585352i | \(-0.199043\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 4.15855i | − | 0.220713i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.90544 | − | 8.63216i | −0.100846 | − | 0.456863i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.63327i | 0.244535i | 0.992497 | + | 0.122267i | \(0.0390165\pi\) | ||||
−0.992497 | + | 0.122267i | \(0.960983\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.28076 | − | 17.5497i | 0.383198 | − | 0.923666i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.1713 | + | 4.45256i | −1.05872 | + | 0.233699i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.82224i | − | 0.0953803i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.7087 | −1.02878 | −0.514392 | − | 0.857555i | \(-0.671983\pi\) | ||||
−0.514392 | + | 0.857555i | \(0.671983\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 24.0153 | − | 11.1452i | 1.25019 | − | 0.580194i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.21542 | −0.218854 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 13.5397i | − | 0.701057i | −0.936552 | − | 0.350529i | \(-0.886002\pi\) | ||
0.936552 | − | 0.350529i | \(-0.113998\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.05521 | + | 9.31070i | 0.106131 | + | 0.480802i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.0918i | 1.29229i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.4548i | 1.35889i | 0.733726 | + | 0.679445i | \(0.237780\pi\) | ||||
−0.733726 | + | 0.679445i | \(0.762220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.28651 | − | 19.4191i | −0.219605 | − | 0.994871i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.7319 | 1.26374 | 0.631871 | − | 0.775074i | \(-0.282287\pi\) | ||||
0.631871 | + | 0.775074i | \(0.282287\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.95710 | 0.0997431 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.40589 | + | 3.90106i | −0.427295 | + | 0.198302i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 2.52420i | − | 0.127982i | −0.997950 | − | 0.0639910i | \(-0.979617\pi\) | ||
0.997950 | − | 0.0639910i | \(-0.0203829\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 45.3888 | 2.29541 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.21240 | + | 10.0228i | 0.111601 | + | 0.505582i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.02338 | −0.0514919 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.4474 | 0.624719 | 0.312360 | − | 0.949964i | \(-0.398881\pi\) | ||||
0.312360 | + | 0.949964i | \(0.398881\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.75563 | − | 3.91384i | 0.188017 | − | 0.195937i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.1965 | −0.908691 | −0.454345 | − | 0.890826i | \(-0.650127\pi\) | ||||
−0.454345 | + | 0.890826i | \(0.650127\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.5702 | 1.67225 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.91022 | + | 3.30548i | 0.194300 | + | 0.164251i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.7208 | 1.42364 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 23.2016i | − | 1.14724i | −0.819120 | − | 0.573622i | \(-0.805538\pi\) | ||
0.819120 | − | 0.573622i | \(-0.194462\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.65310 | − | 25.6101i | −0.278847 | − | 1.26326i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.07434 | −0.298899 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.729989 | −0.0358337 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.08206 | + | 2.00474i | −0.444750 | + | 0.0981728i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.2544i | 1.47803i | 0.673692 | + | 0.739013i | \(0.264708\pi\) | ||||
−0.673692 | + | 0.739013i | \(0.735292\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.79979i | 0.428875i | 0.976738 | + | 0.214438i | \(0.0687919\pi\) | ||||
−0.976738 | + | 0.214438i | \(0.931208\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.983945 | + | 2.12018i | 0.0478410 | + | 0.103087i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 33.2193i | 1.61137i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.25469 | 0.399473 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −37.3364 | + | 8.24151i | −1.80262 | + | 0.397904i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.6900 | −0.659424 | −0.329712 | − | 0.944082i | \(-0.606952\pi\) | ||||
−0.329712 | + | 0.944082i | \(0.606952\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.50964i | − | 0.408947i | −0.978872 | − | 0.204474i | \(-0.934452\pi\) | ||
0.978872 | − | 0.204474i | \(-0.0655482\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.15596 | + | 5.23681i | 0.0554239 | + | 0.251086i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.4667 | + | 23.1616i | 0.739875 | + | 1.10797i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.21224i | 0.344221i | 0.985078 | + | 0.172111i | \(0.0550587\pi\) | ||||
−0.985078 | + | 0.172111i | \(0.944941\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.6440 | + | 8.18832i | −0.840189 | + | 0.389920i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.3326i | 1.77372i | 0.462034 | + | 0.886862i | \(0.347120\pi\) | ||||
−0.462034 | + | 0.886862i | \(0.652880\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 0.0786680i | − | 0.00372922i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.983278 | − | 4.45453i | −0.0465075 | − | 0.210692i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.67813 | −0.456739 | −0.228370 | − | 0.973574i | \(-0.573339\pi\) | ||||
−0.228370 | + | 0.973574i | \(0.573339\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.2560i | 1.98976i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.45298 | − | 11.1127i | −0.115251 | − | 0.522121i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.88444 | 0.0883438 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.99502 | 0.327213 | 0.163607 | − | 0.986526i | \(-0.447687\pi\) | ||||
0.163607 | + | 0.986526i | \(0.447687\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 22.3902 | + | 29.3456i | 1.04509 | + | 1.36974i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 38.3788i | − | 1.78748i | −0.448584 | − | 0.893741i | \(-0.648072\pi\) | ||
0.448584 | − | 0.893741i | \(-0.351928\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.3500 | 1.03869 | 0.519346 | − | 0.854564i | \(-0.326175\pi\) | ||||
0.519346 | + | 0.854564i | \(0.326175\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.00632 | − | 1.54655i | 0.324910 | − | 0.0717197i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.0209668i | 0.000970227i | 1.00000 | 0.000485113i | \(0.000154416\pi\) | |||||
−1.00000 | 0.000485113i | \(0.999846\pi\) | ||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.78319i | 0.128516i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.9326 | − | 4.84133i | 1.01060 | − | 0.223077i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 14.7906i | − | 0.680070i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.9516 | + | 11.3199i | −0.777792 | + | 0.519391i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.9662 | − | 7.40969i | 0.731042 | − | 0.339266i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.0140i | 1.69121i | 0.533807 | + | 0.845606i | \(0.320761\pi\) | ||||
−0.533807 | + | 0.845606i | \(0.679239\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.6545 | 1.26094 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.71386 | + | 7.76425i | 0.0779831 | + | 0.353286i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.26330 | 0.238994 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.9954i | 0.996709i | 0.866973 | + | 0.498354i | \(0.166062\pi\) | ||||
−0.866973 | + | 0.498354i | \(0.833938\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27.2200 | − | 6.00845i | 1.23093 | − | 0.271711i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 26.0141i | − | 1.17400i | −0.809588 | − | 0.586999i | \(-0.800309\pi\) | ||
0.809588 | − | 0.586999i | \(-0.199691\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.6616i | 1.74123i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.41265 | + | 3.44011i | −0.333174 | + | 0.154621i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.25178 | 0.235575 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.20204 | 0.277642 | 0.138821 | − | 0.990318i | \(-0.455669\pi\) | ||||
0.138821 | + | 0.990318i | \(0.455669\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.9544 | + | 3.74246i | −0.757468 | + | 0.167201i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 11.4208i | − | 0.509227i | −0.967043 | − | 0.254613i | \(-0.918052\pi\) | ||
0.967043 | − | 0.254613i | \(-0.0819482\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.20647 | −0.276184 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.9628 | + | 3.08210i | −0.620109 | + | 0.136881i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.235716 | 0.0104479 | 0.00522397 | − | 0.999986i | \(-0.498337\pi\) | ||||
0.00522397 | + | 0.999986i | \(0.498337\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.30128 | 0.101803 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.34514 | + | 21.4254i | −0.324296 | + | 0.945956i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.7222 | −0.472477 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.73055 | −0.164069 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.6600 | + | 5.66411i | −1.12635 | + | 0.248627i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.2131 | 1.71796 | 0.858978 | − | 0.512012i | \(-0.171100\pi\) | ||||
0.858978 | + | 0.512012i | \(0.171100\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.7721i | − | 0.733393i | −0.930341 | − | 0.366697i | \(-0.880489\pi\) | ||
0.930341 | − | 0.366697i | \(-0.119511\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.68253 | + | 1.25434i | −0.248006 | + | 0.0547441i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 51.7254 | 2.25319 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.8252 | −0.775008 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 23.0070 | − | 10.6772i | 0.998417 | − | 0.463352i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.6871i | 1.76235i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.71419i | − | 0.117345i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 33.3680 | − | 7.36554i | 1.43993 | − | 0.317846i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 31.0454i | − | 1.33722i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.978406 | −0.0420649 | −0.0210325 | − | 0.999779i | \(-0.506695\pi\) | ||||
−0.0210325 | + | 0.999779i | \(0.506695\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.24993 | + | 32.8442i | 0.311124 | + | 1.40948i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.08956 | 0.260848 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.8731i | − | 0.806956i | −0.914989 | − | 0.403478i | \(-0.867801\pi\) | ||
0.914989 | − | 0.403478i | \(-0.132199\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −31.2652 | + | 14.5097i | −1.33437 | + | 0.619261i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.7288 | + | 13.1744i | −0.840474 | + | 0.561248i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.29242i | − | 0.0549591i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.77166 | − | 1.27402i | 0.244993 | − | 0.0540791i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.53419i | 0.403977i | 0.979388 | + | 0.201988i | \(0.0647403\pi\) | ||||
−0.979388 | + | 0.201988i | \(0.935260\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 14.2414i | − | 0.602348i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −57.5282 | + | 12.6986i | −2.42884 | + | 0.536135i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.5947 | −0.488658 | −0.244329 | − | 0.969692i | \(-0.578568\pi\) | ||||
−0.244329 | + | 0.969692i | \(0.578568\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 0.289496i | − | 0.0121792i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.17445 | + | 4.93817i | −0.175310 | + | 0.207384i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 46.1820 | 1.93605 | 0.968026 | − | 0.250851i | \(-0.0807105\pi\) | ||||
0.968026 | + | 0.250851i | \(0.0807105\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.24993 | 0.303400 | 0.151700 | − | 0.988427i | \(-0.451525\pi\) | ||||
0.151700 | + | 0.988427i | \(0.451525\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.91657 | − | 26.8037i | −0.247168 | − | 1.11974i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 29.8793i | − | 1.24605i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.17967 | 0.257263 | 0.128632 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128632 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.17699 | − | 14.3927i | −0.132031 | − | 0.598138i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 0.921893i | − | 0.0382466i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.0933i | 1.16350i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.13744 | + | 3.31239i | −0.295097 | + | 0.136950i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 15.4820i | − | 0.639010i | −0.947585 | − | 0.319505i | \(-0.896483\pi\) | ||
0.947585 | − | 0.319505i | \(-0.103517\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.6260 | + | 26.3951i | 0.726267 | + | 1.08759i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.22890 | − | 23.6884i | −0.215088 | − | 0.974410i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 2.88034i | − | 0.118281i | −0.998250 | − | 0.0591406i | \(-0.981164\pi\) | ||
0.998250 | − | 0.0591406i | \(-0.0188360\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.90356 | 0.119034 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 33.3145 | − | 7.35374i | 1.36347 | − | 0.300969i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.66338 | −0.313117 | −0.156559 | − | 0.987669i | \(-0.550040\pi\) | ||||
−0.156559 | + | 0.987669i | \(0.550040\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 16.3265i | − | 0.665971i | −0.942932 | − | 0.332985i | \(-0.891944\pi\) | ||
0.942932 | − | 0.332985i | \(-0.108056\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.89218 | − | 10.5415i | −0.199225 | − | 0.429284i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 6.78494i | − | 0.275847i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 24.5202i | − | 0.995246i | −0.867394 | − | 0.497623i | \(-0.834206\pi\) | ||
0.867394 | − | 0.497623i | \(-0.165794\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.61350 | + | 1.45984i | −0.267992 | + | 0.0591558i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.59204 | −0.145319 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.07345 | 0.326084 | 0.163042 | − | 0.986619i | \(-0.447869\pi\) | ||||
0.163042 | + | 0.986619i | \(0.447869\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.87442 | + | 8.49166i | 0.0755840 | + | 0.342417i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.770572i | 0.0310220i | 0.999880 | + | 0.0155110i | \(0.00493751\pi\) | ||||
−0.999880 | + | 0.0155110i | \(0.995062\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.83275 | 0.355018 | 0.177509 | − | 0.984119i | \(-0.443196\pi\) | ||||
0.177509 | + | 0.984119i | \(0.443196\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.1390 | − | 26.3951i | −0.808151 | − | 1.05920i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.0993487 | 0.00398032 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.2499 | 0.809997 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −26.0834 | − | 25.0291i | −1.04167 | − | 0.999564i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.6103 | 1.69898 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.5460 | −0.499449 | −0.249724 | − | 0.968317i | \(-0.580340\pi\) | ||||
−0.249724 | + | 0.968317i | \(0.580340\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.60718 | + | 7.28098i | 0.0638797 | + | 0.289393i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.53191 | 0.259211 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 29.8927i | − | 1.18439i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.8915 | + | 9.23136i | −0.786895 | + | 0.365187i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.0121 | −1.06692 | −0.533458 | − | 0.845827i | \(-0.679108\pi\) | ||||
−0.533458 | + | 0.845827i | \(0.679108\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.8987 | −0.942473 | −0.471236 | − | 0.882007i | \(-0.656192\pi\) | ||||
−0.471236 | + | 0.882007i | \(0.656192\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.656090 | − | 2.97227i | −0.0258335 | − | 0.117033i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.16500i | 0.242371i | 0.992630 | + | 0.121186i | \(0.0386696\pi\) | ||||
−0.992630 | + | 0.121186i | \(0.961330\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.4818i | 1.58905i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.95312 | + | 8.84819i | 0.0765489 | + | 0.346788i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 20.7295i | − | 0.811208i | −0.914049 | − | 0.405604i | \(-0.867061\pi\) | ||
0.914049 | − | 0.405604i | \(-0.132939\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.37131 | −0.131728 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.71626 | + | 4.04509i | −0.340054 | + | 0.157814i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.5728 | −0.723494 | −0.361747 | − | 0.932276i | \(-0.617820\pi\) | ||||
−0.361747 | + | 0.932276i | \(0.617820\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 0.259282i | − | 0.0100849i | −0.999987 | − | 0.00504244i | \(-0.998395\pi\) | ||
0.999987 | − | 0.00504244i | \(-0.00160507\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −55.3923 | + | 12.2271i | −2.15126 | + | 0.474862i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.989421 | + | 1.48167i | 0.0383681 | + | 0.0574565i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 34.7744i | − | 1.34647i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.78140 | − | 35.2519i | −0.300846 | − | 1.36292i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 55.0126i | − | 2.12374i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.8663i | 0.650148i | 0.945689 | + | 0.325074i | \(0.105389\pi\) | ||||
−0.945689 | + | 0.325074i | \(0.894611\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.3181 | − | 14.7394i | 0.743556 | − | 0.567321i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −43.9992 | −1.69103 | −0.845513 | − | 0.533955i | \(-0.820705\pi\) | ||||
−0.845513 | + | 0.533955i | \(0.820705\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.64695i | 0.255086i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.7147 | − | 3.68955i | 0.640508 | − | 0.141384i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.9790 | −1.18538 | −0.592689 | − | 0.805432i | \(-0.701933\pi\) | ||||
−0.592689 | + | 0.805432i | \(0.701933\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.61436 | 0.329138 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 40.2728 | − | 8.88968i | 1.53650 | − | 0.339162i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.0502i | 1.03053i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.6698 | −0.862400 | −0.431200 | − | 0.902256i | \(-0.641910\pi\) | ||||
−0.431200 | + | 0.902256i | \(0.641910\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.34447 | − | 9.36134i | −0.165033 | − | 0.355608i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 3.05489i | − | 0.115879i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 62.6911i | 2.37460i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.28534 | + | 19.4138i | 0.162086 | + | 0.734297i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.35960i | 0.202429i | 0.994865 | + | 0.101215i | \(0.0322729\pi\) | ||||
−0.994865 | + | 0.101215i | \(0.967727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.5199 | + | 21.7437i | 0.547630 | + | 0.820080i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.749682 | + | 0.165482i | −0.0282347 | + | 0.00623243i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 7.83807i | − | 0.294781i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.53225 | −0.0575447 | −0.0287724 | − | 0.999586i | \(-0.509160\pi\) | ||||
−0.0287724 | + | 0.999586i | \(0.509160\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.27175 | + | 4.89511i | 0.0851975 | + | 0.183581i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −46.5247 | −1.74236 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 12.5587i | − | 0.469667i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.768165 | + | 3.48001i | 0.0286877 | + | 0.129963i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.8942i | 1.11486i | 0.830223 | + | 0.557432i | \(0.188213\pi\) | ||||
−0.830223 | + | 0.557432i | \(0.811787\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 13.5409i | − | 0.504291i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.9263 | − | 49.4991i | −0.406353 | − | 1.84089i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.4509 | 0.945221 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.6663 | −1.65658 | −0.828291 | − | 0.560298i | \(-0.810687\pi\) | ||||
−0.828291 | + | 0.560298i | \(0.810687\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.13090 | − | 26.0413i | 0.264107 | − | 0.964493i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 21.9433i | − | 0.811603i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.9257 | 0.662101 | 0.331051 | − | 0.943613i | \(-0.392597\pi\) | ||||
0.331051 | + | 0.943613i | \(0.392597\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.37713 | − | 6.23880i | −0.0507963 | − | 0.230122i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.5483 | 0.683236 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.0669 | 1.21639 | 0.608193 | − | 0.793789i | \(-0.291895\pi\) | ||||
0.608193 | + | 0.793789i | \(0.291895\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.1150 | − | 24.0998i | −0.922622 | − | 0.885328i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.63266 | −0.169956 | −0.0849778 | − | 0.996383i | \(-0.527082\pi\) | ||||
−0.0849778 | + | 0.996383i | \(0.527082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.49835 | 0.0548952 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.62047 | + | 3.49173i | 0.0592897 | + | 0.127756i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.42771 | 0.125246 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.7388i | 1.01220i | 0.862474 | + | 0.506101i | \(0.168914\pi\) | ||||
−0.862474 | + | 0.506101i | \(0.831086\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.82631 | − | 12.8040i | −0.102997 | − | 0.466604i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.73793 | 0.136037 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.3596 | 1.24882 | 0.624411 | − | 0.781096i | \(-0.285339\pi\) | ||||
0.624411 | + | 0.781096i | \(0.285339\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 51.7441 | − | 11.4218i | 1.87819 | − | 0.414586i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 5.53916i | − | 0.200795i | −0.994947 | − | 0.100397i | \(-0.967989\pi\) | ||
0.994947 | − | 0.100397i | \(-0.0320114\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.69043i | 0.278412i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.9974 | + | 5.10376i | −0.397613 | + | 0.184527i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 38.9788i | 1.40744i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.7969 | −0.605713 | −0.302857 | − | 0.953036i | \(-0.597940\pi\) | ||||
−0.302857 | + | 0.953036i | \(0.597940\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.0467 | + | 6.19093i | −1.01008 | + | 0.222961i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.3092 | −1.09015 | −0.545073 | − | 0.838389i | \(-0.683498\pi\) | ||||
−0.545073 | + | 0.838389i | \(0.683498\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 34.0507i | − | 1.22314i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.60894 | + | 7.28896i | 0.0577204 | + | 0.261490i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −31.9908 | + | 21.3627i | −1.14619 | + | 0.765399i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 35.0000i | − | 1.25240i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.4830 | − | 17.1542i | 0.803478 | − | 0.613040i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.37736i | 0.263309i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.2737i | 1.72077i | 0.509643 | + | 0.860386i | \(0.329778\pi\) | ||||
−0.509643 | + | 0.860386i | \(0.670222\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.89926 | + | 13.1345i | 0.103216 | + | 0.467599i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.365601 | 0.0129993 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 52.9701i | − | 1.88102i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.24618 | + | 5.64555i | 0.0441975 | + | 0.200227i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.8341 | 0.383763 | 0.191882 | − | 0.981418i | \(-0.438541\pi\) | ||||
0.191882 | + | 0.981418i | \(0.438541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.53466 | −0.195802 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.376290 | + | 0.174631i | −0.0132956 | + | 0.00617028i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 15.3367i | − | 0.541219i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.61162 | −0.0920476 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.5557 | − | 5.42036i | 0.864403 | − | 0.190806i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.1880i | 1.34262i | 0.741177 | + | 0.671310i | \(0.234268\pi\) | ||||
−0.741177 | + | 0.671310i | \(0.765732\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 16.0919i | − | 0.565063i | −0.959258 | − | 0.282531i | \(-0.908826\pi\) | ||
0.959258 | − | 0.282531i | \(-0.0911741\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −52.2435 | + | 11.5321i | −1.83226 | + | 0.404447i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.15584i | 0.320715i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.1975 | − | 7.47743i | 0.391751 | − | 0.261602i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.18317 | − | 9.01378i | −0.146172 | − | 0.314967i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.8593i | 0.727994i | 0.931400 | + | 0.363997i | \(0.118588\pi\) | ||||
−0.931400 | + | 0.363997i | \(0.881412\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.11462 | −0.178284 | −0.0891422 | − | 0.996019i | \(-0.528413\pi\) | ||||
−0.0891422 | + | 0.996019i | \(0.528413\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.35946 | + | 37.8707i | 0.291039 | + | 1.31849i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −53.1212 | −1.84721 | −0.923603 | − | 0.383350i | \(-0.874770\pi\) | ||||
−0.923603 | + | 0.383350i | \(0.874770\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.8202i | 0.757848i | 0.925428 | + | 0.378924i | \(0.123706\pi\) | ||||
−0.925428 | + | 0.378924i | \(0.876294\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.1419 | + | 3.78384i | −0.594644 | + | 0.131260i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 46.0590i | − | 1.59585i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 5.70288i | − | 0.197356i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.9506 | − | 30.0800i | −0.793287 | − | 1.03972i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.0659 | 1.17609 | 0.588043 | − | 0.808830i | \(-0.299899\pi\) | ||||
0.588043 | + | 0.808830i | \(0.299899\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.620465 | 0.0213954 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.0938 | − | 3.55248i | 0.554298 | − | 0.122354i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 4.69659i | − | 0.161568i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.56861 | 0.294421 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.8029 | − | 3.04680i | 0.473714 | − | 0.104566i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.3261 | −1.31380 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.6050 | 0.534304 | 0.267152 | − | 0.963654i | \(-0.413917\pi\) | ||||
0.267152 | + | 0.963654i | \(0.413917\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.35191 | − | 3.87275i | −0.217231 | − | 0.132445i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.5605 | −0.873128 | −0.436564 | − | 0.899673i | \(-0.643805\pi\) | ||||
−0.436564 | + | 0.899673i | \(0.643805\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.6287 | 1.31800 | 0.658998 | − | 0.752145i | \(-0.270981\pi\) | ||||
0.658998 | + | 0.752145i | \(0.270981\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.7240 | + | 2.36718i | −0.365473 | + | 0.0806734i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.2452 | 0.552994 | 0.276497 | − | 0.961015i | \(-0.410826\pi\) | ||||
0.276497 | + | 0.961015i | \(0.410826\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 8.63114i | − | 0.293467i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −56.5963 | + | 12.4929i | −1.92211 | + | 0.424281i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.61318 | −0.292182 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.8597 | 0.605151 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.6837 | − | 25.1758i | −0.395434 | − | 0.852071i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 3.95510i | − | 0.133707i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 19.8852i | − | 0.671475i | −0.941956 | − | 0.335737i | \(-0.891015\pi\) | ||
0.941956 | − | 0.335737i | \(-0.108985\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.47762 | − | 1.20911i | 0.184756 | − | 0.0407824i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 32.9959i | − | 1.11166i | −0.831296 | − | 0.555829i | \(-0.812401\pi\) | ||
0.831296 | − | 0.555829i | \(-0.187599\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.7441 | −0.630789 | −0.315394 | − | 0.948961i | \(-0.602137\pi\) | ||||
−0.315394 | + | 0.948961i | \(0.602137\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.79572 | + | 8.13513i | 0.0603625 | + | 0.273459i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.71898 | −0.192024 | −0.0960122 | − | 0.995380i | \(-0.530609\pi\) | ||||
−0.0960122 | + | 0.995380i | \(0.530609\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.24907i | 0.276665i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 32.9099 | + | 27.8202i | 1.10252 | + | 0.932012i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.88600 | − | 2.82430i | −0.0631125 | − | 0.0945115i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.2238i | 0.375171i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 49.8229 | − | 10.9978i | 1.66354 | − | 0.367204i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 39.6292i | − | 1.32171i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.6792i | 1.38854i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.75364 | − | 0.828567i | 0.124913 | − | 0.0275730i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.0477 | −0.367237 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 27.4189i | − | 0.910431i | −0.890381 | − | 0.455216i | \(-0.849562\pi\) | ||
0.890381 | − | 0.455216i | \(-0.150438\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.7774 | + | 29.6872i | 0.456969 | + | 0.984663i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.7522 | −1.21766 | −0.608828 | − | 0.793302i | \(-0.708360\pi\) | ||||
−0.608828 | + | 0.793302i | \(0.708360\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.14387 | −0.203332 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.44029 | − | 11.0552i | −0.0806734 | − | 0.365473i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 4.25759i | − | 0.140598i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.7497 | 1.57512 | 0.787558 | − | 0.616240i | \(-0.211345\pi\) | ||||
0.787558 | + | 0.616240i | \(0.211345\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.0709270 | − | 0.321319i | −0.00233712 | − | 0.0105878i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 33.7005i | − | 1.10927i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 28.0502i | − | 0.922286i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.8017 | + | 51.2873i | 0.781751 | + | 1.68449i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.9076i | 0.489104i | 0.969636 | + | 0.244552i | \(0.0786409\pi\) | ||||
−0.969636 | + | 0.244552i | \(0.921359\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.5036 | − | 15.6951i | 0.770299 | − | 0.514387i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.08343 | + | 9.43854i | 0.0682085 | + | 0.309004i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 19.3505i | − | 0.632829i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.4925 | −0.865473 | −0.432737 | − | 0.901520i | \(-0.642452\pi\) | ||||
−0.432737 | + | 0.901520i | \(0.642452\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.2770 | + | 6.68324i | −0.988052 | + | 0.218099i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.03967 | 0.262086 | 0.131043 | − | 0.991377i | \(-0.458167\pi\) | ||||
0.131043 | + | 0.991377i | \(0.458167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 56.3879i | − | 1.83624i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.28831 | − | 1.68852i | −0.0419087 | − | 0.0549274i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 41.6266i | − | 1.35268i | −0.736589 | − | 0.676341i | \(-0.763565\pi\) | ||
0.736589 | − | 0.676341i | \(-0.236435\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 14.7672i | − | 0.479365i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −37.4856 | + | 8.27445i | −1.21555 | + | 0.268317i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.5570 | 1.08702 | 0.543510 | − | 0.839403i | \(-0.317095\pi\) | ||||
0.543510 | + | 0.839403i | \(0.317095\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.01584 | 0.291746 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.72898 | + | 44.0750i | 0.314493 | + | 1.42474i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.8790i | 0.351300i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0198 | −0.710316 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.9827 | + | 6.02509i | −0.418361 | + | 0.194156i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.84119 | 0.155843 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.3041 | 0.878042 | 0.439021 | − | 0.898477i | \(-0.355325\pi\) | ||||
0.439021 | + | 0.898477i | \(0.355325\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −38.6974 | − | 37.1332i | −1.24314 | − | 1.19289i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.4588 | −0.399820 | −0.199910 | − | 0.979814i | \(-0.564065\pi\) | ||||
−0.199910 | + | 0.979814i | \(0.564065\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.85798 | 0.123681 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.04909 | + | 36.4646i | 0.257777 | + | 1.16780i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.7035 | −1.23824 | −0.619118 | − | 0.785298i | \(-0.712510\pi\) | ||||
−0.619118 | + | 0.785298i | \(0.712510\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 0.662100i | − | 0.0211608i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.5179 | − | 29.1280i | −0.431594 | − | 0.929986i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.8496 | 0.792579 | 0.396289 | − | 0.918126i | \(-0.370298\pi\) | ||||
0.396289 | + | 0.918126i | \(0.370298\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.96795 | 0.253880 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.208986 | − | 0.946764i | −0.00665208 | − | 0.0301358i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.7370i | 0.627601i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.3454i | 1.72634i | 0.504915 | + | 0.863169i | \(0.331524\pi\) | ||||
−0.504915 | + | 0.863169i | \(0.668476\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.68941 | − | 43.8958i | −0.307484 | − | 1.39299i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.2058i | 0.355249i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.5392 | −1.47391 | −0.736955 | − | 0.675941i | \(-0.763737\pi\) | ||||
−0.736955 | + | 0.675941i | \(0.763737\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.9062 | − | 24.7793i | −0.598166 | − | 0.783982i |
(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 | 912.2.f.h.113.9 | 10 | ||
3.2 | odd | 2 | 912.2.f.i.113.1 | 10 | |||
4.3 | odd | 2 | 456.2.f.b.113.2 | yes | 10 | ||
12.11 | even | 2 | 456.2.f.a.113.10 | yes | 10 | ||
19.18 | odd | 2 | 912.2.f.i.113.2 | 10 | |||
57.56 | even | 2 | inner | 912.2.f.h.113.10 | 10 | ||
76.75 | even | 2 | 456.2.f.a.113.9 | ✓ | 10 | ||
228.227 | odd | 2 | 456.2.f.b.113.1 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.f.a.113.9 | ✓ | 10 | 76.75 | even | 2 | ||
456.2.f.a.113.10 | yes | 10 | 12.11 | even | 2 | ||
456.2.f.b.113.1 | yes | 10 | 228.227 | odd | 2 | ||
456.2.f.b.113.2 | yes | 10 | 4.3 | odd | 2 | ||
912.2.f.h.113.9 | 10 | 1.1 | even | 1 | trivial | ||
912.2.f.h.113.10 | 10 | 57.56 | even | 2 | inner | ||
912.2.f.i.113.1 | 10 | 3.2 | odd | 2 | |||
912.2.f.i.113.2 | 10 | 19.18 | odd | 2 |