Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [312,2,Mod(41,312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(312, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 6, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("312.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 312 = 2^{3} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 312.bp (of order \(12\), degree \(4\), 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: | \(2.49133254306\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 305.5 | ||
Character | \(\chi\) | \(=\) | 312.305 |
Dual form | 312.2.bp.a.89.5 |
$q$-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 \(\left(\mathbb{Z}/312\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(157\) | \(209\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.19941 | − | 1.24957i | −0.692477 | − | 0.721440i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.44076 | + | 1.44076i | 0.644328 | + | 0.644328i | 0.951616 | − | 0.307289i | \(-0.0994217\pi\) |
−0.307289 | + | 0.951616i | \(0.599422\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.918532 | − | 3.42801i | 0.347172 | − | 1.29567i | −0.542881 | − | 0.839809i | \(-0.682667\pi\) |
0.890054 | − | 0.455856i | \(-0.150667\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.122851 | + | 2.99748i | −0.0409503 | + | 0.999161i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0392149 | + | 0.146352i | 0.0118237 | + | 0.0441267i | 0.971586 | − | 0.236688i | \(-0.0760620\pi\) |
−0.959762 | + | 0.280815i | \(0.909395\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.92366 | − | 3.04952i | 0.533526 | − | 0.845784i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0722747 | − | 3.52839i | 0.0186612 | − | 0.911026i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.60706 | − | 2.78351i | −0.389770 | − | 0.675101i | 0.602648 | − | 0.798007i | \(-0.294112\pi\) |
−0.992418 | + | 0.122905i | \(0.960779\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.90607 | + | 0.510729i | 0.437282 | + | 0.117169i | 0.470742 | − | 0.882271i | \(-0.343986\pi\) |
−0.0334605 | + | 0.999440i | \(0.510653\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.38523 | + | 2.96380i | −1.17515 | + | 0.646755i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.19640 | − | 7.26837i | 0.875009 | − | 1.51556i | 0.0182561 | − | 0.999833i | \(-0.494189\pi\) |
0.856753 | − | 0.515727i | \(-0.172478\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 0.848416i | − | 0.169683i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.89291 | − | 3.44169i | 0.749192 | − | 0.662353i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0238088 | − | 0.0137460i | −0.00442119 | − | 0.00255258i | 0.497788 | − | 0.867299i | \(-0.334146\pi\) |
−0.502209 | + | 0.864746i | \(0.667479\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.54595 | + | 5.54595i | −0.996083 | + | 0.996083i | −0.999992 | − | 0.00390967i | \(-0.998756\pi\) |
0.00390967 | + | 0.999992i | \(0.498756\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.135842 | − | 0.224537i | 0.0236471 | − | 0.0390869i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.26232 | − | 3.61555i | 1.05853 | − | 0.611140i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.84429 | − | 1.03007i | 0.631997 | − | 0.169343i | 0.0714212 | − | 0.997446i | \(-0.477247\pi\) |
0.560576 | + | 0.828103i | \(0.310580\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.11783 | + | 1.25387i | −0.979637 | + | 0.200779i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.53382 | − | 0.678935i | 0.395716 | − | 0.106032i | −0.0554728 | − | 0.998460i | \(-0.517667\pi\) |
0.451189 | + | 0.892428i | \(0.351000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.90548 | + | 3.40953i | −0.900577 | + | 0.519948i | −0.877387 | − | 0.479783i | \(-0.840715\pi\) |
−0.0231896 | + | 0.999731i | \(0.507382\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.49566 | + | 4.14166i | −0.670173 | + | 0.617402i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.77303 | + | 4.77303i | −0.696218 | + | 0.696218i | −0.963593 | − | 0.267374i | \(-0.913844\pi\) |
0.267374 | + | 0.963593i | \(0.413844\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.84536 | − | 2.79747i | −0.692194 | − | 0.399638i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.55068 | + | 5.34670i | −0.217138 | + | 0.748688i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.3755i | 1.83726i | 0.395119 | + | 0.918630i | \(0.370703\pi\) | ||||
−0.395119 | + | 0.918630i | \(0.629297\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.154359 | + | 0.267357i | −0.0208137 | + | 0.0360504i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.64796 | − | 2.99434i | −0.218277 | − | 0.396610i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.09489 | + | 2.16902i | 1.05386 | + | 0.282382i | 0.743848 | − | 0.668349i | \(-0.232999\pi\) |
0.310017 | + | 0.950731i | \(0.399665\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.61697 | + | 11.4609i | 0.847216 | + | 1.46742i | 0.883683 | + | 0.468086i | \(0.155056\pi\) |
−0.0364673 | + | 0.999335i | \(0.511610\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.1626 | + | 3.17442i | 1.28036 | + | 0.399939i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.16515 | − | 1.62210i | 0.888728 | − | 0.201196i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.18370 | + | 4.41762i | 0.144612 | + | 0.539698i | 0.999772 | + | 0.0213353i | \(0.00679175\pi\) |
−0.855161 | + | 0.518363i | \(0.826542\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.1155 | + | 3.47404i | −1.69931 | + | 0.418225i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.29021 | − | 4.81512i | 0.153119 | − | 0.571449i | −0.846140 | − | 0.532961i | \(-0.821079\pi\) |
0.999259 | − | 0.0384882i | \(-0.0122542\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.22036 | + | 6.22036i | 0.728038 | + | 0.728038i | 0.970229 | − | 0.242191i | \(-0.0778660\pi\) |
−0.242191 | + | 0.970229i | \(0.577866\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.06016 | + | 1.01760i | −0.122416 | + | 0.117502i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.537715 | 0.0612784 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.3852 | −1.50596 | −0.752979 | − | 0.658045i | \(-0.771384\pi\) | ||||
−0.752979 | + | 0.658045i | \(0.771384\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.96982 | − | 0.736488i | −0.996646 | − | 0.0818320i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.94085 | + | 1.94085i | 0.213036 | + | 0.213036i | 0.805556 | − | 0.592520i | \(-0.201867\pi\) |
−0.592520 | + | 0.805556i | \(0.701867\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.69499 | − | 6.32577i | 0.183847 | − | 0.686126i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.0113798 | + | 0.0462379i | 0.00122005 | + | 0.00495722i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.87300 | − | 10.7222i | −0.304537 | − | 1.13655i | −0.933343 | − | 0.358987i | \(-0.883122\pi\) |
0.628805 | − | 0.777563i | \(-0.283544\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.68683 | − | 9.39538i | −0.910627 | − | 0.984904i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.5819 | + | 0.278209i | 1.40838 | + | 0.0288489i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.01035 | + | 3.48203i | 0.206257 | + | 0.357248i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.7357 | − | 4.75227i | −1.80079 | − | 0.482520i | −0.806687 | − | 0.590978i | \(-0.798742\pi\) |
−0.994101 | + | 0.108458i | \(0.965409\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.443505 | + | 0.0995664i | −0.0445739 | + | 0.0100068i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.226814 | + | 0.392853i | −0.0225688 | + | 0.0390903i | −0.877089 | − | 0.480327i | \(-0.840518\pi\) |
0.854520 | + | 0.519418i | \(0.173851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0525i | 0.990499i | 0.868751 | + | 0.495250i | \(0.164923\pi\) | ||||
−0.868751 | + | 0.495250i | \(0.835077\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.0290 | − | 3.48870i | −1.17391 | − | 0.340462i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.4165 | − | 6.59132i | −1.10368 | − | 0.637207i | −0.166492 | − | 0.986043i | \(-0.553244\pi\) |
−0.937184 | + | 0.348836i | \(0.886577\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.43289 | − | 4.43289i | 0.424594 | − | 0.424594i | −0.462188 | − | 0.886782i | \(-0.652936\pi\) |
0.886782 | + | 0.462188i | \(0.152936\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.89801 | − | 3.56823i | −0.559814 | − | 0.338681i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.33256 | − | 3.07875i | 0.501645 | − | 0.289625i | −0.227748 | − | 0.973720i | \(-0.573136\pi\) |
0.729393 | + | 0.684095i | \(0.239803\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.5180 | − | 4.42598i | 1.54031 | − | 0.412725i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.90455 | + | 6.14076i | 0.823226 | + | 0.567714i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.0180 | + | 2.95228i | −1.01002 | + | 0.270635i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.50640 | − | 5.48852i | 0.864218 | − | 0.498957i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.88746 | − | 2.35187i | −0.350520 | − | 0.212061i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.42617 | − | 8.42617i | 0.753659 | − | 0.753659i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.15516 | + | 4.70839i | 0.723654 | + | 0.417802i | 0.816096 | − | 0.577916i | \(-0.196134\pi\) |
−0.0924423 | + | 0.995718i | \(0.529467\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.3435 | + | 3.28990i | 0.998740 | + | 0.289659i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.8806i | 1.30012i | 0.759881 | + | 0.650062i | \(0.225257\pi\) | ||||
−0.759881 | + | 0.650062i | \(0.774743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.50157 | − | 6.06489i | 0.303624 | − | 0.525893i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.5674 | + | 0.650108i | 0.909498 | + | 0.0559524i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.69061 | − | 2.32864i | −0.742489 | − | 0.198949i | −0.132305 | − | 0.991209i | \(-0.542238\pi\) |
−0.610184 | + | 0.792260i | \(0.708905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.0458925 | − | 0.0794881i | −0.00389255 | − | 0.00674210i | 0.864073 | − | 0.503367i | \(-0.167906\pi\) |
−0.867965 | + | 0.496625i | \(0.834572\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.6890 | + | 0.239436i | 0.984395 | + | 0.0201641i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.521738 | + | 0.161944i | 0.0436299 | + | 0.0135424i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0144981 | − | 0.0541076i | −0.00120400 | − | 0.00449339i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.31592 | + | 9.40992i | 0.191014 | + | 0.776117i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.50013 | + | 13.0627i | −0.286742 | + | 1.07014i | 0.660815 | + | 0.750549i | \(0.270211\pi\) |
−0.947557 | + | 0.319587i | \(0.896456\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.24642 | + | 8.24642i | 0.671084 | + | 0.671084i | 0.957966 | − | 0.286882i | \(-0.0926187\pi\) |
−0.286882 | + | 0.957966i | \(0.592619\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.54097 | − | 4.47519i | 0.690496 | − | 0.361797i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.9808 | −1.28361 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.99636 | −0.478562 | −0.239281 | − | 0.970950i | \(-0.576912\pi\) | ||||
−0.239281 | + | 0.970950i | \(0.576912\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.7136 | − | 16.0426i | 1.32547 | − | 1.27226i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −21.0615 | − | 21.0615i | −1.65988 | − | 1.65988i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.72133 | − | 13.8882i | 0.291477 | − | 1.08781i | −0.652499 | − | 0.757790i | \(-0.726279\pi\) |
0.943975 | − | 0.330016i | \(-0.107054\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.519220 | − | 0.127788i | 0.0404213 | − | 0.00994826i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.36831 | + | 5.10660i | 0.105883 | + | 0.395161i | 0.998444 | − | 0.0557663i | \(-0.0177602\pi\) |
−0.892561 | + | 0.450927i | \(0.851094\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.59910 | − | 11.7324i | −0.430700 | − | 0.902495i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.76506 | + | 5.65066i | −0.134978 | + | 0.432117i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.05984 | + | 5.29979i | 0.232635 | + | 0.402936i | 0.958583 | − | 0.284814i | \(-0.0919319\pi\) |
−0.725948 | + | 0.687750i | \(0.758599\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.90838 | − | 0.779297i | −0.219853 | − | 0.0589093i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.99872 | − | 12.7167i | −0.526056 | − | 0.955843i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.1144 | + | 17.5187i | −0.755986 | + | 1.30941i | 0.188897 | + | 0.981997i | \(0.439509\pi\) |
−0.944883 | + | 0.327409i | \(0.893825\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.39016i | 0.326318i | 0.986600 | + | 0.163159i | \(0.0521683\pi\) | ||||
−0.986600 | + | 0.163159i | \(0.947832\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.38480 | − | 22.0147i | 0.471978 | − | 1.62737i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.02279 | + | 4.05461i | 0.516326 | + | 0.298101i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.344352 | − | 0.344352i | 0.0251815 | − | 0.0251815i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.22237 | − | 16.5062i | −0.598089 | − | 1.20065i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.3027 | − | 7.10298i | 0.890194 | − | 0.513954i | 0.0161878 | − | 0.999869i | \(-0.494847\pi\) |
0.874006 | + | 0.485915i | \(0.161514\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.1074 | − | 3.78006i | 1.01547 | − | 0.272095i | 0.287558 | − | 0.957763i | \(-0.407157\pi\) |
0.727914 | + | 0.685668i | \(0.240490\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.6208 | − | 7.00781i | −0.760575 | − | 0.501839i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.668505 | + | 0.179125i | −0.0476290 | + | 0.0127622i | −0.282555 | − | 0.959251i | \(-0.591182\pi\) |
0.234926 | + | 0.972013i | \(0.424515\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8158 | + | 7.97656i | −0.979377 | + | 0.565443i | −0.902082 | − | 0.431565i | \(-0.857962\pi\) |
−0.0772948 | + | 0.997008i | \(0.524628\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.10039 | − | 6.77764i | 0.289219 | − | 0.478058i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0689907 | + | 0.0689907i | −0.00484220 | + | 0.00484220i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.62881 | + | 2.67245i | 0.323290 | + | 0.186652i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21.2713 | + | 13.4716i | 1.47846 | + | 0.936338i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.298985i | 0.0206812i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.28525 | − | 5.69022i | 0.226166 | − | 0.391731i | −0.730503 | − | 0.682910i | \(-0.760714\pi\) |
0.956669 | + | 0.291179i | \(0.0940475\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.56431 | + | 4.16308i | −0.518298 | + | 0.285249i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.4207 | − | 3.59607i | −0.915284 | − | 0.245250i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.9174 | + | 24.1057i | 0.944777 | + | 1.63640i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.312040 | − | 15.2335i | 0.0210857 | − | 1.02938i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.5798 | − | 0.453757i | −0.778942 | − | 0.0305230i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.79575 | + | 6.70184i | 0.120252 | + | 0.448788i | 0.999626 | − | 0.0273441i | \(-0.00870497\pi\) |
−0.879374 | + | 0.476132i | \(0.842038\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.54311 | + | 0.104229i | 0.169541 | + | 0.00694859i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.00698 | − | 11.2222i | 0.199580 | − | 0.744843i | −0.791453 | − | 0.611230i | \(-0.790675\pi\) |
0.991033 | − | 0.133614i | \(-0.0426581\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.7056 | − | 18.7056i | −1.23610 | − | 1.23610i | −0.961580 | − | 0.274523i | \(-0.911480\pi\) |
−0.274523 | − | 0.961580i | \(-0.588520\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.644939 | − | 0.671913i | −0.0424339 | − | 0.0442086i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.96187 | 0.325063 | 0.162531 | − | 0.986703i | \(-0.448034\pi\) | ||||
0.162531 | + | 0.986703i | \(0.448034\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.7536 | −0.897186 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.0543 | + | 16.7258i | 1.04284 | + | 1.08646i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.8475 | + | 19.8475i | 1.28382 | + | 1.28382i | 0.938473 | + | 0.345352i | \(0.112240\pi\) |
0.345352 | + | 0.938473i | \(0.387760\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.59927 | − | 5.96857i | 0.103018 | − | 0.384469i | −0.895095 | − | 0.445876i | \(-0.852892\pi\) |
0.998113 | + | 0.0614071i | \(0.0195588\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.83816 | + | 12.0918i | 0.631118 | + | 0.775687i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.95052 | − | 11.0115i | −0.188502 | − | 0.703498i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.22409 | − | 4.83012i | 0.332401 | − | 0.307333i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.0973611 | − | 4.75309i | 0.00617001 | − | 0.301215i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.16622 | + | 3.75201i | 0.136731 | + | 0.236825i | 0.926257 | − | 0.376892i | \(-0.123007\pi\) |
−0.789526 | + | 0.613717i | \(0.789674\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.22830 | + | 0.329122i | 0.0772226 | + | 0.0206917i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.93747 | + | 5.46917i | −0.622309 | + | 0.342492i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.6302 | + | 18.4120i | −0.663093 | + | 1.14851i | 0.316706 | + | 0.948524i | \(0.397423\pi\) |
−0.979799 | + | 0.199986i | \(0.935910\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 14.1244i | − | 0.877648i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0441285 | − | 0.0696779i | 0.00273148 | − | 0.00431295i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.0017 | − | 8.66123i | −0.925044 | − | 0.534074i | −0.0398032 | − | 0.999208i | \(-0.512673\pi\) |
−0.885241 | + | 0.465133i | \(0.846006\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.2708 | + | 19.2708i | −1.18380 | + | 1.18380i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.95223 | + | 16.4503i | −0.609067 | + | 1.00674i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.3500 | + | 15.7905i | −1.66756 | + | 0.962766i | −0.698612 | + | 0.715500i | \(0.746199\pi\) |
−0.968948 | + | 0.247266i | \(0.920468\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.18818 | + | 2.19402i | −0.497397 | + | 0.133277i | −0.498792 | − | 0.866722i | \(-0.666223\pi\) |
0.00139487 | + | 0.999999i | \(0.499556\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.32116 | + | 22.1237i | −0.0799601 | + | 1.33899i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.124167 | − | 0.0332705i | 0.00748757 | − | 0.00200629i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.6692 | + | 9.62397i | −1.00156 | + | 0.578248i | −0.908708 | − | 0.417432i | \(-0.862930\pi\) |
−0.0928470 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.9426 | − | 17.3052i | −0.954457 | − | 1.03604i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.6481 | − | 16.6481i | 0.993141 | − | 0.993141i | −0.00683587 | − | 0.999977i | \(-0.502176\pi\) |
0.999977 | + | 0.00683587i | \(0.00217594\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.15184 | + | 4.70646i | 0.484576 | + | 0.279770i | 0.722322 | − | 0.691557i | \(-0.243075\pi\) |
−0.237745 | + | 0.971328i | \(0.576408\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.93981 | − | 6.68843i | 0.114905 | − | 0.396189i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 9.30958i | − | 0.549527i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.33470 | − | 5.77587i | 0.196159 | − | 0.339757i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.3340 | + | 27.8619i | 0.898896 | + | 1.63329i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.3285 | + | 6.78675i | 1.47971 | + | 0.396486i | 0.906248 | − | 0.422747i | \(-0.138934\pi\) |
0.573460 | + | 0.819234i | \(0.305601\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.53776 | + | 14.7878i | 0.497088 | + | 0.860981i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.656358 | + | 0.434770i | 0.0380857 | + | 0.0252279i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.0926 | − | 26.7788i | −0.814996 | − | 1.54866i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.26352 | + | 23.3758i | 0.361023 | + | 1.34736i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.762939 | − | 0.187770i | 0.0438297 | − | 0.0107871i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.97898 | + | 26.0459i | −0.399615 | + | 1.49138i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.7215 | − | 15.7215i | −0.897271 | − | 0.897271i | 0.0979227 | − | 0.995194i | \(-0.468780\pi\) |
−0.995194 | + | 0.0979227i | \(0.968780\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.5613 | − | 12.0570i | 0.714585 | − | 0.685898i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.34210 | −0.246218 | −0.123109 | − | 0.992393i | \(-0.539286\pi\) | ||||
−0.123109 | + | 0.992393i | \(0.539286\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.6341 | 1.05326 | 0.526630 | − | 0.850095i | \(-0.323455\pi\) | ||||
0.526630 | + | 0.850095i | \(0.323455\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.0682 | + | 19.2154i | 0.567281 | + | 1.08266i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.07889 | − | 9.07889i | −0.509921 | − | 0.509921i | 0.404581 | − | 0.914502i | \(-0.367417\pi\) |
−0.914502 | + | 0.404581i | \(0.867417\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.00107810 | − | 0.00402352i | 6.03619e−5 | − | 0.000225274i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.45671 | + | 22.1714i | 0.304564 | + | 1.23749i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.64155 | − | 6.12634i | −0.0913382 | − | 0.340879i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.58726 | − | 1.63206i | −0.143515 | − | 0.0905304i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.8560 | − | 0.222372i | −0.600340 | − | 0.0122972i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.9778 | + | 20.7462i | 0.660358 | + | 1.14377i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.3587 | + | 3.04354i | 0.624328 | + | 0.167288i | 0.557095 | − | 0.830449i | \(-0.311916\pi\) |
0.0672335 | + | 0.997737i | \(0.478583\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.61535 | + | 11.6497i | 0.143321 | + | 0.638401i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.65931 | + | 8.07016i | −0.254565 | + | 0.440920i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.7236i | 1.07441i | 0.843451 | + | 0.537206i | \(0.180520\pi\) | ||||
−0.843451 | + | 0.537206i | \(0.819480\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.2430 | − | 2.97073i | −0.556324 | − | 0.161348i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.02914 | − | 0.594177i | −0.0557313 | − | 0.0321765i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.52597 | − | 3.52597i | 0.190384 | − | 0.190384i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −25.3423 | − | 15.3318i | −1.36439 | − | 0.825438i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.5245 | − | 17.6233i | 1.63864 | − | 0.946071i | 0.657342 | − | 0.753593i | \(-0.271681\pi\) |
0.981301 | − | 0.192478i | \(-0.0616525\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.9572 | + | 6.15136i | −1.22887 | + | 0.329275i | −0.814139 | − | 0.580670i | \(-0.802791\pi\) |
−0.414730 | + | 0.909944i | \(0.636124\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.00686 | − | 18.4921i | −0.160494 | − | 0.987037i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.81588 | + | 2.09426i | −0.415997 | + | 0.111466i | −0.460746 | − | 0.887532i | \(-0.652418\pi\) |
0.0447484 | + | 0.998998i | \(0.485751\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.79631 | − | 5.07855i | 0.466860 | − | 0.269542i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.9042 | + | 10.2268i | 0.894665 | + | 0.541262i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.77619 | − | 9.77619i | 0.515968 | − | 0.515968i | −0.400381 | − | 0.916349i | \(-0.631122\pi\) |
0.916349 | + | 0.400381i | \(0.131122\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0822 | − | 7.55303i | −0.688539 | − | 0.397528i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.2603 | − | 5.29595i | −0.958418 | − | 0.277965i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.9241i | 0.938190i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.84234 | − | 11.8513i | 0.357167 | − | 0.618632i | −0.630319 | − | 0.776336i | \(-0.717076\pi\) |
0.987486 | + | 0.157704i | \(0.0504093\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.72382 | + | 7.67850i | 0.0897382 | + | 0.399727i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 45.8512 | + | 12.2858i | 2.38047 | + | 0.637846i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.97549 | − | 3.42164i | −0.102287 | − | 0.177166i | 0.810340 | − | 0.585960i | \(-0.199283\pi\) |
−0.912626 | + | 0.408794i | \(0.865949\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −20.6355 | − | 0.422692i | −1.06561 | − | 0.0218277i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.0877188 | + | 0.0461628i | −0.00451775 | + | 0.00237751i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.23059 | − | 15.7888i | −0.217311 | − | 0.811014i | −0.985340 | − | 0.170600i | \(-0.945429\pi\) |
0.768030 | − | 0.640414i | \(-0.221237\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.89789 | − | 15.8377i | −0.199695 | − | 0.811391i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.85081 | + | 21.8355i | −0.298963 | + | 1.11574i | 0.639057 | + | 0.769160i | \(0.279325\pi\) |
−0.938019 | + | 0.346584i | \(0.887342\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.774719 | + | 0.774719i | 0.0394834 | + | 0.0394834i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.49451 | − | 18.1204i | −0.482633 | − | 0.921114i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.80850 | −0.0916947 | −0.0458474 | − | 0.998948i | \(-0.514599\pi\) | ||||
−0.0458474 | + | 0.998948i | \(0.514599\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.9755 | −1.36421 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.5943 | − | 17.8479i | 0.937961 | − | 0.900306i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.2849 | − | 19.2849i | −0.970331 | − | 0.970331i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.04738 | + | 3.90888i | −0.0525665 | + | 0.196181i | −0.987216 | − | 0.159391i | \(-0.949047\pi\) |
0.934649 | + | 0.355572i | \(0.115714\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.7783 | + | 2.89881i | −0.589653 | + | 0.145122i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.540214 | − | 2.01611i | −0.0269770 | − | 0.100680i | 0.951125 | − | 0.308807i | \(-0.0999298\pi\) |
−0.978102 | + | 0.208128i | \(0.933263\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.24398 | + | 27.5810i | 0.311035 | + | 1.37391i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.8623 | − | 13.9845i | −0.589440 | − | 0.694894i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.301506 | + | 0.522224i | 0.0149451 | + | 0.0258857i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.15394 | − | 2.18484i | −0.403186 | − | 0.108033i | 0.0515263 | − | 0.998672i | \(-0.483591\pi\) |
−0.454713 | + | 0.890638i | \(0.650258\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.51377 | + | 13.6525i | 0.370627 | + | 0.673429i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.8708 | − | 25.7570i | 0.731746 | − | 1.26742i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.59259i | 0.274529i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.0442823 | + | 0.152684i | −0.00216851 | + | 0.00747699i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.585414 | + | 0.337989i | 0.0285993 | + | 0.0165118i | 0.514232 | − | 0.857651i | \(-0.328077\pi\) |
−0.485632 | + | 0.874163i | \(0.661411\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.17588 | − | 6.17588i | 0.300994 | − | 0.300994i | −0.540409 | − | 0.841403i | \(-0.681730\pi\) |
0.841403 | + | 0.540409i | \(0.181730\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.7207 | − | 14.8935i | −0.667124 | − | 0.724145i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.36158 | + | 1.36346i | −0.114553 | + | 0.0661374i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 45.3660 | − | 12.1558i | 2.19542 | − | 0.588260i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.423415 | − | 0.846185i | −0.0204427 | − | 0.0408542i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.78631 | − | 2.62223i | 0.471390 | − | 0.126309i | −0.0153006 | − | 0.999883i | \(-0.504871\pi\) |
0.486691 | + | 0.873574i | \(0.338204\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.0298 | + | 6.36809i | −0.530061 | + | 0.306031i | −0.741041 | − | 0.671460i | \(-0.765668\pi\) |
0.210980 | + | 0.977490i | \(0.432334\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0502222 | + | 0.0830134i | −0.00240797 | + | 0.00398019i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.7108 | − | 11.7108i | 0.560203 | − | 0.560203i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.07428 | + | 1.77494i | 0.146727 | + | 0.0847131i | 0.571566 | − | 0.820556i | \(-0.306336\pi\) |
−0.424839 | + | 0.905269i | \(0.639669\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.98063 | − | 14.1802i | 0.427649 | − | 0.675248i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 13.7327i | − | 0.652461i | −0.945290 | − | 0.326231i | \(-0.894221\pi\) | ||
0.945290 | − | 0.326231i | \(-0.105779\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.3088 | − | 19.5874i | 0.536088 | − | 0.928532i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.5208 | − | 11.2938i | 0.970601 | − | 0.534178i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.7370 | + | 3.41288i | 0.601098 | + | 0.161064i | 0.546520 | − | 0.837446i | \(-0.315952\pi\) |
0.0545774 | + | 0.998510i | \(0.482619\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.198727 | + | 0.344205i | 0.00935769 | + | 0.0162080i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.413675 | − | 20.1953i | 0.0194362 | − | 0.948857i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.02086 | − | 26.0521i | 0.0478586 | − | 1.22134i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.80678 | − | 17.9391i | −0.224852 | − | 0.839157i | −0.982464 | − | 0.186453i | \(-0.940301\pi\) |
0.757612 | − | 0.652705i | \(-0.226366\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.8361 | − | 5.30497i | −0.739168 | − | 0.247615i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.15902 | − | 4.32554i | 0.0539812 | − | 0.201460i | −0.933669 | − | 0.358138i | \(-0.883412\pi\) |
0.987650 | + | 0.156678i | \(0.0500784\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.53278 | + | 8.53278i | 0.396552 | + | 0.396552i | 0.877015 | − | 0.480463i | \(-0.159531\pi\) |
−0.480463 | + | 0.877015i | \(0.659531\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.1674 | + | 19.9691i | 0.888869 | + | 0.926045i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.69885 | −0.448809 | −0.224405 | − | 0.974496i | \(-0.572044\pi\) | ||||
−0.224405 | + | 0.974496i | \(0.572044\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.2309 | 0.749474 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.19207 | + | 7.49288i | 0.331393 | + | 0.345254i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.730573 | − | 0.730573i | −0.0335918 | − | 0.0335918i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.433311 | − | 1.61714i | 0.0198817 | − | 0.0741994i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −40.0927 | − | 1.64319i | −1.83572 | − | 0.0752364i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.64461 | + | 24.7980i | 0.303600 | + | 1.13305i | 0.934144 | + | 0.356897i | \(0.116165\pi\) |
−0.630544 | + | 0.776154i | \(0.717168\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.25386 | − | 13.7047i | 0.193959 | − | 0.624882i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.05653 | + | 51.5791i | −0.0480740 | + | 2.34693i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.7060 | − | 32.3998i | −0.849397 | − | 1.47120i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.4146 | − | 4.13033i | −0.698501 | − | 0.187163i | −0.107942 | − | 0.994157i | \(-0.534426\pi\) |
−0.590559 | + | 0.806994i | \(0.701093\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.8176 | + | 12.0075i | −0.986627 | + | 0.542998i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.38912 | + | 11.0663i | −0.288337 | + | 0.499414i | −0.973413 | − | 0.229057i | \(-0.926436\pi\) |
0.685076 | + | 0.728472i | \(0.259769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0883630i | 0.00397967i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.782436 | − | 0.495533i | −0.0351679 | − | 0.0222726i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.3212 | − | 8.84568i | −0.687248 | − | 0.396783i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.5255 | − | 26.5255i | 1.18744 | − | 1.18744i | 0.209671 | − | 0.977772i | \(-0.432761\pi\) |
0.977772 | − | 0.209671i | \(-0.0672393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.73990 | − | 7.83468i | 0.211763 | − | 0.350028i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.29946 | − | 1.90495i | 0.147116 | − | 0.0849374i | −0.424635 | − | 0.905365i | \(-0.639598\pi\) |
0.571751 | + | 0.820427i | \(0.306264\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.892792 | + | 0.239223i | −0.0397287 | + | 0.0106453i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.94491 | + | 21.0684i | −0.352846 | + | 0.935682i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.5368 | − | 10.0580i | 1.66379 | − | 0.445811i | 0.700364 | − | 0.713786i | \(-0.253021\pi\) |
0.963426 | + | 0.267975i | \(0.0863545\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.0370 | − | 15.6098i | 1.19605 | − | 0.690539i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.17793 | − | 4.57186i | 0.405215 | − | 0.201853i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.4832 | + | 14.4832i | −0.638206 | + | 0.638206i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.885716 | − | 0.511368i | −0.0389537 | − | 0.0224900i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.95248 | − | 10.1801i | 0.129599 | − | 0.446856i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.6988i | 1.82686i | 0.406996 | + | 0.913430i | \(0.366576\pi\) | ||||
−0.406996 | + | 0.913430i | \(0.633424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.1004 | + | 22.6906i | −0.572842 | + | 0.992192i | 0.423430 | + | 0.905929i | \(0.360826\pi\) |
−0.996272 | + | 0.0862632i | \(0.972507\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.51454 | + | 4.56892i | 0.109743 | + | 0.199404i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.3499 | + | 6.52455i | 1.06070 | + | 0.284214i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.7195 | − | 41.0833i | −1.03128 | − | 1.78623i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.49606 | + | 23.9978i | −0.325301 | + | 1.04142i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.80377 | − | 9.03297i | 0.121445 | − | 0.391261i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.95194 | − | 25.9450i | −0.300558 | − | 1.12170i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.0221 | − | 8.37333i | 1.46816 | − | 0.361336i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.219405 | − | 0.818830i | 0.00945043 | − | 0.0352695i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.9894 | + | 14.9894i | 0.644447 | + | 0.644447i | 0.951645 | − | 0.307199i | \(-0.0993916\pi\) |
−0.307199 | + | 0.951645i | \(0.599392\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.48581 | − | 5.26558i | 0.235419 | − | 0.225968i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.7735 | 0.547155 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.7046 | 1.01354 | 0.506768 | − | 0.862082i | \(-0.330840\pi\) | ||||
0.506768 | + | 0.862082i | \(0.330840\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −35.1668 | + | 18.4263i | −1.50088 | + | 0.786414i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0383608 | − | 0.0383608i | −0.00163422 | − | 0.00163422i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.2948 | + | 45.8847i | −0.522827 | + | 1.95122i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.35666 | − | 13.6386i | −0.142482 | − | 0.578926i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.2264 | − | 38.1653i | −0.433304 | − | 1.61711i | −0.745091 | − | 0.666962i | \(-0.767594\pi\) |
0.311787 | − | 0.950152i | \(-0.399072\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.962687 | + | 24.5676i | −0.0407173 | + | 1.03910i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.843309 | − | 0.0172741i | −0.0356045 | − | 0.000729315i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.48383 | + | 14.6944i | 0.357551 | + | 0.619296i | 0.987551 | − | 0.157299i | \(-0.0502785\pi\) |
−0.630000 | + | 0.776595i | \(0.716945\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.1187 | + | 3.24719i | 0.509837 | + | 0.136610i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.7637 | + | 30.0721i | −0.452035 | + | 1.26291i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.2347 | + | 26.3873i | −0.638674 | + | 1.10622i | 0.347051 | + | 0.937846i | \(0.387183\pi\) |
−0.985724 | + | 0.168369i | \(0.946150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 5.03996i | − | 0.210916i | −0.994424 | − | 0.105458i | \(-0.966369\pi\) | ||
0.994424 | − | 0.105458i | \(-0.0336309\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.6316 | − | 6.85376i | −0.987225 | − | 0.286320i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.16660 | − | 3.56029i | −0.257165 | − | 0.148474i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.8862 | − | 15.8862i | 0.661350 | − | 0.661350i | −0.294348 | − | 0.955698i | \(-0.595102\pi\) |
0.955698 | + | 0.294348i | \(0.0951024\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.6439 | − | 13.0943i | −0.899492 | − | 0.544182i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.43596 | − | 4.87051i | 0.349983 | − | 0.202063i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.95752 | + | 0.524516i | −0.0810723 | + | 0.0217233i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.98196 | + | 21.6767i | 0.164634 | + | 0.896221i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.06056 | + | 2.15982i | −0.332695 | + | 0.0891453i | −0.421300 | − | 0.906922i | \(-0.638426\pi\) |
0.0886047 | + | 0.996067i | \(0.471759\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.4034 | + | 7.73848i | −0.552279 | + | 0.318859i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.02564 | + | 0.620500i | 0.0421892 | + | 0.0255240i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.0266 | − | 30.0266i | 1.23305 | − | 1.23305i | 0.270257 | − | 0.962788i | \(-0.412891\pi\) |
0.962788 | − | 0.270257i | \(-0.0871086\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.1279 | − | 11.6208i | −0.825163 | − | 0.476408i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.5380 | + | 7.69669i | 1.08613 | + | 0.315004i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.0119i | 0.695088i | 0.937664 | + | 0.347544i | \(0.112984\pi\) | ||||
−0.937664 | + | 0.347544i | \(0.887016\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.8220 | + | 22.2084i | −0.523022 | + | 0.905901i | 0.476619 | + | 0.879110i | \(0.341862\pi\) |
−0.999641 | + | 0.0267907i | \(0.991471\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.3872 | + | 3.00541i | −0.545168 | + | 0.122390i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.6041 | + | 5.78880i | 0.878331 | + | 0.235348i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.99964 | − | 15.5878i | −0.365284 | − | 0.632691i | 0.623537 | − | 0.781793i | \(-0.285695\pi\) |
−0.988822 | + | 0.149103i | \(0.952362\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.168957 | + | 0.00346087i | 0.00684647 | + | 0.000140241i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.37377 | + | 23.7371i | 0.217400 | + | 0.960301i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.40516 | + | 23.9044i | 0.258702 | + | 0.965489i | 0.965993 | + | 0.258567i | \(0.0832502\pi\) |
−0.707292 | + | 0.706922i | \(0.750083\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.21242 | − | 8.98938i | −0.0892133 | − | 0.362487i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.32585 | − | 34.8045i | 0.375444 | − | 1.40118i | −0.477250 | − | 0.878768i | \(-0.658366\pi\) |
0.852694 | − | 0.522410i | \(-0.174967\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.29611 | − | 8.29611i | −0.333449 | − | 0.333449i | 0.520446 | − | 0.853895i | \(-0.325766\pi\) |
−0.853895 | + | 0.520446i | \(0.825766\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.67926 | − | 42.7378i | −0.348287 | − | 1.71501i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −39.3947 | −1.57831 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.0381 | 0.801524 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.373602 | − | 0.358604i | 0.0149202 | − | 0.0143213i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.04524 | − | 9.04524i | −0.360657 | − | 0.360657i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.40401 | − | 20.1680i | 0.215130 | − | 0.802877i | −0.770990 | − | 0.636847i | \(-0.780238\pi\) |
0.986121 | − | 0.166030i | \(-0.0530949\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.0507 | + | 2.71973i | −0.439225 | + | 0.108100i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.96598 | + | 18.5333i | 0.197069 | + | 0.735471i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.8517 | + | 9.39464i | −0.707311 | + | 0.372229i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.2747 | + | 4.45892i | 0.564700 | + | 0.176392i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.39416 | − | 9.34296i | −0.213056 | − | 0.369025i | 0.739613 | − | 0.673032i | \(-0.235008\pi\) |
−0.952670 | + | 0.304008i | \(0.901675\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.87352 | − | 2.37765i | −0.349937 | − | 0.0937655i | 0.0795687 | − | 0.996829i | \(-0.474646\pi\) |
−0.429506 | + | 0.903064i | \(0.641312\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.6033 | + | 21.0832i | 0.456881 | + | 0.830152i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.5642 | − | 21.7619i | 0.493951 | − | 0.855549i | −0.506024 | − | 0.862519i | \(-0.668885\pi\) |
0.999976 | + | 0.00697039i | \(0.00221876\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.26976i | 0.0498424i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.4291 | − | 46.3033i | 0.526329 | − | 1.81477i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.6456 | − | 7.30093i | −0.494860 | − | 0.285708i | 0.231728 | − | 0.972781i | \(-0.425562\pi\) |
−0.726588 | + | 0.687073i | \(0.758895\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.4394 | + | 21.4394i | −0.837706 | + | 0.837706i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.4096 | + | 17.8812i | −0.757240 | + | 0.697614i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.24365 | − | 5.33682i | 0.360081 | − | 0.207893i | −0.309035 | − | 0.951051i | \(-0.600006\pi\) |
0.669116 | + | 0.743158i | \(0.266673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.5548 | + | 10.5987i | −1.53850 | + | 0.412241i | −0.925782 | − | 0.378057i | \(-0.876592\pi\) |
−0.612723 | + | 0.790298i | \(0.709926\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.3219 | + | 15.0140i | 0.517379 | + | 0.583096i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.7830 | − | 3.69314i | 0.534481 | − | 0.143214i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.199823 | + | 0.115368i | −0.00773717 | + | 0.00446706i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.22058 | − | 10.2821i | 0.240502 | − | 0.397531i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.41784 | + | 1.41784i | −0.0547352 | + | 0.0547352i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.95408 | + | 1.70554i | 0.113871 | + | 0.0657437i | 0.555854 | − | 0.831280i | \(-0.312391\pi\) |
−0.441983 | + | 0.897024i | \(0.645725\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.91998 | − | 3.30281i | −0.112390 | − | 0.127125i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 9.33387i | − | 0.358730i | −0.983783 | − | 0.179365i | \(-0.942596\pi\) | ||
0.983783 | − | 0.179365i | \(-0.0574043\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.5816 | + | 56.4330i | −1.25037 | + | 2.16570i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.6295 | + | 9.70254i | −0.675564 | + | 0.371802i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.2277 | − | 5.42001i | −0.773993 | − | 0.207391i | −0.149858 | − | 0.988708i | \(-0.547882\pi\) |
−0.624135 | + | 0.781317i | \(0.714548\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.16608 | − | 15.8761i | −0.350218 | − | 0.606595i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.938354 | + | 45.8097i | −0.0358005 | + | 1.74775i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.7887 | + | 25.7298i | 1.55392 | + | 0.980226i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.861578 | − | 3.21545i | −0.0327760 | − | 0.122322i | 0.947600 | − | 0.319461i | \(-0.103502\pi\) |
−0.980376 | + | 0.197139i | \(0.936835\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0660589 | + | 1.61179i | −0.00250937 | + | 0.0612270i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0484033 | − | 0.180643i | 0.00183604 | − | 0.00685220i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.96184 | − | 5.96184i | −0.225821 | − | 0.225821i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.95130 | − | 6.20021i | −0.225099 | − | 0.234513i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.9388 | −0.450923 | −0.225462 | − | 0.974252i | \(-0.572389\pi\) | ||||
−0.225462 | + | 0.974252i | \(0.572389\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.85356 | 0.296203 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.4961 | + | 17.1861i | 0.621281 | + | 0.647265i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.13837 | + | 1.13837i | 0.0428127 | + | 0.0428127i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.31499 | + | 4.90761i | −0.0493855 | + | 0.184309i | −0.986212 | − | 0.165484i | \(-0.947081\pi\) |
0.936827 | + | 0.349793i | \(0.113748\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.64439 | − | 40.1221i | 0.0616695 | − | 1.50469i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.0370 | + | 63.5831i | 0.638042 | + | 2.38120i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.518377 | + | 0.985023i | 0.0193862 | + | 0.0368378i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.995633 | − | 48.6059i | 0.0371826 | − | 1.81522i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.78171 | + | 3.08602i | 0.0664468 | + | 0.115089i | 0.897335 | − | 0.441350i | \(-0.145500\pi\) |
−0.830888 | + | 0.556440i | \(0.812167\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.4599 | + | 9.23351i | 1.28336 | + | 0.343874i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.37632 | + | 5.16033i | −0.348709 | + | 0.191915i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0116624 | + | 0.0201998i | −0.000433129 | + | 0.000750202i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.2149i | 1.12061i | 0.828287 | + | 0.560304i | \(0.189316\pi\) | ||||
−0.828287 | + | 0.560304i | \(0.810684\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.30956 | − | 26.7964i | 0.122576 | − | 0.992459i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.9809 | + | 10.9587i | 0.702036 | + | 0.405321i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.27805 | + | 4.27805i | −0.158013 | + | 0.158013i | −0.781686 | − | 0.623672i | \(-0.785640\pi\) |
0.623672 | + | 0.781686i | \(0.285640\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.2208 | + | 16.8941i | −0.376998 | + | 0.623149i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.600109 | + | 0.346473i | −0.0221053 | + | 0.0127625i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.8637 | + | 6.12632i | −0.841056 | + | 0.225360i | −0.653531 | − | 0.756900i | \(-0.726713\pi\) |
−0.187525 | + | 0.982260i | \(0.560046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.3014 | − | 0.734600i | −0.451902 | − | 0.0269862i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.0215 | + | 12.0635i | −1.65168 | + | 0.442566i | −0.960082 | − | 0.279717i | \(-0.909759\pi\) |
−0.691597 | + | 0.722284i | \(0.743093\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.8630 | + | 13.7773i | −0.874274 | + | 0.504762i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.05609 | + | 5.57922i | −0.221581 | + | 0.204133i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −33.0815 | + | 33.0815i | −1.20877 | + | 1.20877i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.1177 | + | 22.0072i | 1.39093 | + | 0.803056i | 0.993419 | − | 0.114540i | \(-0.0365395\pi\) |
0.397514 | + | 0.917596i | \(0.369873\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.09022 | − | 7.20703i | 0.0761718 | − | 0.262639i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.7622i | 0.864796i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.5726 | − | 26.9726i | 0.565996 | − | 0.980334i | −0.430960 | − | 0.902371i | \(-0.641825\pi\) |
0.996956 | − | 0.0779632i | \(-0.0248417\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.06197 | − | 1.92960i | −0.0385471 | − | 0.0700400i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.3991 | − | 9.48515i | −1.28322 | − | 0.343836i | −0.448136 | − | 0.893966i | \(-0.647912\pi\) |
−0.835080 | + | 0.550129i | \(0.814578\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.1242 | − | 19.2677i | −0.402724 | − | 0.697538i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.7532 | + | 5.85782i | 0.678022 | + | 0.211790i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.1862 | − | 20.5131i | 0.801098 | − | 0.740683i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.493875 | − | 1.84317i | −0.0178096 | − | 0.0664663i | 0.956449 | − | 0.291899i | \(-0.0942871\pi\) |
−0.974259 | + | 0.225433i | \(0.927620\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.7570 | − | 8.80032i | 1.28776 | − | 0.316936i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.52425 | + | 28.0809i | −0.270629 | + | 1.01000i | 0.688086 | + | 0.725629i | \(0.258451\pi\) |
−0.958714 | + | 0.284371i | \(0.908215\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.70528 | + | 4.70528i | 0.169019 | + | 0.169019i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.6494 | + | 16.9409i | −0.633170 | + | 0.607751i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.17639 | 0.185463 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.755297 | 0.0270266 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.139995 | + | 0.0284305i | −0.00500303 | + | 0.00101602i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.63933 | − | 8.63933i | −0.308351 | − | 0.308351i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.8946 | + | 44.3912i | −0.423996 | + | 1.58237i | 0.342110 | + | 0.939660i | \(0.388858\pi\) |
−0.766106 | + | 0.642714i | \(0.777808\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.17030 | + | 29.1340i | 0.255270 | + | 1.03720i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.65587 | − | 21.1080i | −0.201099 | − | 0.750513i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 47.6790 | + | 1.86831i | 1.69313 | + | 0.0663457i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 47.1938 | + | 0.966707i | 1.67379 | + | 0.0342856i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.53756 | + | 7.85929i | 0.160729 | + | 0.278390i | 0.935130 | − | 0.354304i | \(-0.115282\pi\) |
−0.774402 | + | 0.632694i | \(0.781949\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.9564 | + | 5.61524i | 0.741383 | + | 0.198653i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.4925 | − | 7.29454i | 1.14807 | − | 0.257740i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.666430 | + | 1.15429i | −0.0235178 | + | 0.0407341i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 60.6892i | − | 2.13901i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 52.5352 | + | 15.2365i | 1.84933 | + | 0.536350i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −47.1684 | − | 27.2327i | −1.65835 | − | 0.957451i | −0.973475 | − | 0.228795i | \(-0.926522\pi\) |
−0.684879 | − | 0.728656i | \(-0.740145\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.2355 | + | 10.2355i | −0.359418 | + | 0.359418i | −0.863598 | − | 0.504180i | \(-0.831795\pi\) |
0.504180 | + | 0.863598i | \(0.331795\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.5625 | + | 7.60019i | 0.440587 | + | 0.266550i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.3711 | − | 14.6480i | 0.888710 | − | 0.513097i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.9976 | + | 3.48269i | −0.454728 | + | 0.121844i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 29.2297 | − | 24.8844i | 1.02137 | − | 0.869531i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.1061 | + | 10.2105i | −1.32991 | + | 0.356349i | −0.852683 | − | 0.522429i | \(-0.825026\pi\) |
−0.477230 | + | 0.878778i | \(0.658359\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.7150 | − | 13.6918i | 0.826652 | − | 0.477268i | −0.0260528 | − | 0.999661i | \(-0.508294\pi\) |
0.852705 | + | 0.522393i | \(0.174960\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.190501 | − | 0.115251i | −0.00663239 | − | 0.00401252i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.19558 | + | 4.19558i | −0.145895 | + | 0.145895i | −0.776281 | − | 0.630387i | \(-0.782896\pi\) |
0.630387 | + | 0.776281i | \(0.282896\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.55666 | − | 2.63079i | −0.158259 | − | 0.0913710i | 0.418779 | − | 0.908088i | \(-0.362458\pi\) |
−0.577038 | + | 0.816717i | \(0.695792\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32.0190 | + | 9.28629i | 1.11073 | + | 0.322138i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.9828i | 0.623068i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.38598 | + | 9.32880i | −0.186390 | + | 0.322836i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.50248 | + | 40.6774i | −0.0864983 | + | 1.40602i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.4794 | + | 2.80796i | 0.361790 | + | 0.0969414i | 0.435135 | − | 0.900365i | \(-0.356701\pi\) |
−0.0733447 | + | 0.997307i | \(0.523367\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4996 | − | 25.1141i | −0.499987 | − | 0.866003i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −40.7707 | − | 0.835138i | −1.40422 | − | 0.0287637i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.83667 | − | 24.9706i | 0.303991 | − | 0.859015i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.0828 | − | 37.6294i | −0.346448 | − | 1.29296i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.89630 | − | 15.8313i | −0.133721 | − | 0.543327i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.64519 | − | 32.2643i | 0.296353 | − | 1.10601i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.245921 | − | 0.245921i | −0.00842016 | − | 0.00842016i | 0.702884 | − | 0.711304i | \(-0.251895\pi\) |
−0.711304 | + | 0.702884i | \(0.751895\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.6843 | + | 5.59822i | −0.365395 | + | 0.191455i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38.9362 | −1.33004 | −0.665018 | − | 0.746827i | \(-0.731576\pi\) | ||||
−0.665018 | + | 0.746827i | \(0.731576\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.3610 | 0.626469 | 0.313234 | − | 0.949676i | \(-0.398587\pi\) | ||||
0.313234 | + | 0.949676i | \(0.398587\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.6330 | + | 11.1660i | −0.396451 | + | 0.380535i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.7327 | − | 19.7327i | −0.671710 | − | 0.671710i | 0.286400 | − | 0.958110i | \(-0.407541\pi\) |
−0.958110 | + | 0.286400i | \(0.907541\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.22724 | + | 12.0442i | −0.109729 | + | 0.409516i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.2170 | + | 2.76067i | −0.380949 | + | 0.0937572i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.524901 | − | 1.95896i | −0.0178060 | − | 0.0664530i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.7486 | + | 4.88827i | 0.533622 | + | 0.165633i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.4237 | − | 52.5787i | 0.555858 | − | 1.77952i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21.1453 | − | 36.6247i | −0.714841 | − | 1.23814i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.13636 | + | 1.10833i | 0.139675 | + | 0.0374258i | 0.327979 | − | 0.944685i | \(-0.393632\pi\) |
−0.188304 | + | 0.982111i | \(0.560299\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.8986 | − | 39.7898i | −0.738623 | − | 1.34208i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.4790 | + | 23.3463i | −0.454118 | + | 0.786556i | −0.998637 | − | 0.0521929i | \(-0.983379\pi\) |
0.544519 | + | 0.838749i | \(0.316712\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 34.0811i | − | 1.14692i | −0.819234 | − | 0.573460i | \(-0.805601\pi\) | ||
0.819234 | − | 0.573460i | \(-0.194399\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.23820 | − | 28.4052i | 0.276924 | − | 0.954829i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.2091 | − | 11.6677i | −0.678555 | − | 0.391764i | 0.120755 | − | 0.992682i | \(-0.461468\pi\) |
−0.799310 | + | 0.600918i | \(0.794802\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.6312 | − | 23.6312i | 0.792564 | − | 0.792564i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.243964 | − | 1.34163i | −0.00817309 | − | 0.0449463i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.5355 | + | 6.66000i | −0.386019 | + | 0.222868i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.8126 | + | 10.6678i | −1.33079 | + | 0.356584i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.5593 | + | 49.7284i | −0.552898 | + | 1.66038i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.208278 | − | 0.0558078i | 0.00694645 | − | 0.00186130i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.2308 | − | 21.4952i | 1.24034 | − | 0.716109i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.6972 | − | 35.8638i | 0.722037 | − | 1.19347i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.32517 | + | 6.32517i | −0.210256 | + | 0.210256i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.6995 | − | 18.8791i | −1.08577 | − | 0.626870i | −0.153323 | − | 0.988176i | \(-0.548997\pi\) |
−0.932447 | + | 0.361307i | \(0.882331\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.14971 | − | 0.728133i | −0.0381333 | − | 0.0241506i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.27053i | 0.274015i | 0.990570 | + | 0.137007i | \(0.0437484\pi\) | ||||
−0.990570 | + | 0.137007i | \(0.956252\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.207936 | + | 0.360156i | −0.00688169 | + | 0.0119194i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 40.9168 | − | 22.5189i | 1.35267 | − | 0.744452i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 51.0108 | + | 13.6683i | 1.68452 | + | 0.451367i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.64513 | − | 8.04561i | −0.153229 | − | 0.265400i | 0.779184 | − | 0.626795i | \(-0.215634\pi\) |
−0.932413 | + | 0.361395i | \(0.882301\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.788655 | + | 38.5015i | −0.0259871 | + | 1.26867i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.2019 | − | 13.1971i | −0.401629 | − | 0.434389i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.873931 | − | 3.26156i | −0.0287347 | − | 0.107239i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.1321 | − | 1.23496i | −0.989668 | − | 0.0405613i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.5588 | − | 46.8701i | 0.412041 | − | 1.53776i | −0.378648 | − | 0.925541i | \(-0.623611\pi\) |
0.790689 | − | 0.612218i | \(-0.209722\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.80683 | − | 7.80683i | −0.255859 | − | 0.255859i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.20794 | + | 5.42576i | 0.170500 | + | 0.177631i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.992257 | 0.0324503 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.0209 | 0.915405 | 0.457702 | − | 0.889106i | \(-0.348673\pi\) | ||||
0.457702 | + | 0.889106i | \(0.348673\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.3498 | − | 23.2846i | −0.729358 | − | 0.759863i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.59288 | − | 5.59288i | −0.182323 | − | 0.182323i | 0.610045 | − | 0.792367i | \(-0.291152\pi\) |
−0.792367 | + | 0.610045i | \(0.791152\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.69816 | − | 21.2658i | 0.185558 | − | 0.692511i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.9351 | − | 35.6280i | 0.388248 | − | 1.15898i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.77906 | − | 14.1036i | −0.122803 | − | 0.458307i | 0.876949 | − | 0.480583i | \(-0.159575\pi\) |
−0.999752 | + | 0.0222770i | \(0.992908\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.9349 | − | 7.00326i | 1.00419 | − | 0.227335i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.455435 | + | 22.2340i | −0.0147685 | + | 0.720986i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.0448 | + | 36.4507i | 0.681709 | + | 1.18076i | 0.974459 | + | 0.224566i | \(0.0720964\pi\) |
−0.292750 | + | 0.956189i | \(0.594570\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.9590 | + | 7.49158i | 0.904731 | + | 0.242422i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.00632075 | + | 0.00347867i | −0.000204321 | + | 0.000112449i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.9652 | + | 27.6526i | −0.515544 | + | 0.892948i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 30.5152i | − | 0.984361i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.1599 | − | 33.4110i | 0.681869 | − | 1.07666i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.7715 | + | 14.8792i | 0.829615 | + | 0.478979i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.40927 | + | 8.40927i | −0.270424 | + | 0.270424i | −0.829271 | − | 0.558847i | \(-0.811244\pi\) |
0.558847 | + | 0.829271i | \(0.311244\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.68641 | + | 9.39920i | −0.182674 | + | 0.301946i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.6595 | + | 25.7842i | −1.43319 | + | 0.827454i | −0.997363 | − | 0.0725748i | \(-0.976878\pi\) |
−0.435830 | + | 0.900029i | \(0.643545\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.314640 | + | 0.0843074i | −0.0100869 | + | 0.00270277i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.06380 | + | 5.19046i | 0.0340689 | + | 0.166228i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.2573 | + | 13.7343i | −1.63987 | + | 0.439401i | −0.956750 | − | 0.290910i | \(-0.906042\pi\) |
−0.683115 | + | 0.730311i | \(0.739375\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.45655 | − | 0.840938i | 0.0465515 | − | 0.0268765i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.7429 | + | 13.8321i | 0.406850 | + | 0.441625i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.5229 | − | 39.5229i | 1.26058 | − | 1.26058i | 0.309774 | − | 0.950810i | \(-0.399747\pi\) |
0.950810 | − | 0.309774i | \(-0.100253\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.22123 | − | 0.705079i | −0.0389117 | − | 0.0224657i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.5575 | − | 39.8502i | 0.367881 | − | 1.26845i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 57.2309i | 1.81984i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.81441 | − | 8.33881i | 0.152935 | − | 0.264891i | −0.779370 | − | 0.626564i | \(-0.784461\pi\) |
0.932305 | + | 0.361673i | \(0.117794\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.82052 | − | 17.8439i | −0.311645 | − | 0.566258i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31.3976 | − | 8.41296i | −0.995371 | − | 0.266709i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.1749 | + | 24.5517i | 0.448925 | + | 0.777561i | 0.998316 | − | 0.0580045i | \(-0.0184738\pi\) |
−0.549392 | + | 0.835565i | \(0.685140\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.4203 | − | 17.2408i | 0.361322 | − | 0.545476i |
(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 | 312.2.bp.a.305.5 | yes | 56 | |
3.2 | odd | 2 | inner | 312.2.bp.a.305.14 | yes | 56 | |
4.3 | odd | 2 | 624.2.cn.f.305.10 | 56 | |||
12.11 | even | 2 | 624.2.cn.f.305.1 | 56 | |||
13.11 | odd | 12 | inner | 312.2.bp.a.89.14 | yes | 56 | |
39.11 | even | 12 | inner | 312.2.bp.a.89.5 | ✓ | 56 | |
52.11 | even | 12 | 624.2.cn.f.401.1 | 56 | |||
156.11 | odd | 12 | 624.2.cn.f.401.10 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.bp.a.89.5 | ✓ | 56 | 39.11 | even | 12 | inner | |
312.2.bp.a.89.14 | yes | 56 | 13.11 | odd | 12 | inner | |
312.2.bp.a.305.5 | yes | 56 | 1.1 | even | 1 | trivial | |
312.2.bp.a.305.14 | yes | 56 | 3.2 | odd | 2 | inner | |
624.2.cn.f.305.1 | 56 | 12.11 | even | 2 | |||
624.2.cn.f.305.10 | 56 | 4.3 | odd | 2 | |||
624.2.cn.f.401.1 | 56 | 52.11 | even | 12 | |||
624.2.cn.f.401.10 | 56 | 156.11 | odd | 12 |