Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(249,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.bh (of order \(6\), degree \(2\), 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: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 15x^{14} + 170x^{12} - 789x^{10} + 2754x^{8} - 960x^{6} + 269x^{4} - 18x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 249.8 | ||
Root | \(2.00531 + 1.15777i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.249 |
Dual form | 1400.2.bh.j.849.8 |
$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 2.87134 | + | 1.65777i | 1.65777 | + | 0.957112i | 0.973743 | + | 0.227652i | \(0.0731049\pi\) |
0.684024 | + | 0.729460i | \(0.260228\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.49733 | − | 0.873699i | 0.943901 | − | 0.330227i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.99638 | + | 6.92193i | 1.33213 | + | 2.30731i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.12268 | − | 3.67659i | 0.640012 | − | 1.10853i | −0.345418 | − | 0.938449i | \(-0.612263\pi\) |
0.985430 | − | 0.170084i | \(-0.0544039\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.10909i | 1.41701i | 0.705708 | + | 0.708503i | \(0.250629\pi\) | ||||
−0.705708 | + | 0.708503i | \(0.749371\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.765278 | − | 0.441833i | −0.185607 | − | 0.107160i | 0.404317 | − | 0.914619i | \(-0.367509\pi\) |
−0.589924 | + | 0.807458i | \(0.700842\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.27048 | − | 5.66463i | −0.750299 | − | 1.29956i | −0.947678 | − | 0.319229i | \(-0.896576\pi\) |
0.197379 | − | 0.980327i | \(-0.436757\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.61906 | + | 1.63130i | 1.88083 | + | 0.355980i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.62065 | − | 2.66773i | 0.963472 | − | 0.556261i | 0.0662322 | − | 0.997804i | \(-0.478902\pi\) |
0.897240 | + | 0.441543i | \(0.145569\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.5536i | 3.18575i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.54096 | −0.843234 | −0.421617 | − | 0.906774i | \(-0.638537\pi\) | ||||
−0.421617 | + | 0.906774i | \(0.638537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.338612 | + | 0.586493i | −0.0608165 | + | 0.105337i | −0.894831 | − | 0.446406i | \(-0.852704\pi\) |
0.834014 | + | 0.551743i | \(0.186037\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.1898 | − | 7.03781i | 2.12198 | − | 1.22513i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.31807 | + | 0.760988i | −0.216689 | + | 0.125106i | −0.604416 | − | 0.796669i | \(-0.706594\pi\) |
0.387727 | + | 0.921774i | \(0.373260\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.46968 | + | 14.6699i | −1.35623 | + | 2.34907i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.92666 | −0.925589 | −0.462795 | − | 0.886466i | \(-0.653153\pi\) | ||||
−0.462795 | + | 0.886466i | \(0.653153\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.49796i | − | 0.838431i | −0.907887 | − | 0.419215i | \(-0.862305\pi\) | ||
0.907887 | − | 0.419215i | \(-0.137695\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.29546 | + | 3.63469i | −0.918288 | + | 0.530174i | −0.883088 | − | 0.469207i | \(-0.844540\pi\) |
−0.0351992 | + | 0.999380i | \(0.511207\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.47330 | − | 4.36383i | 0.781900 | − | 0.623404i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.46491 | − | 2.53730i | −0.205129 | − | 0.355293i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.22407 | − | 1.28407i | −0.305499 | − | 0.176380i | 0.339411 | − | 0.940638i | \(-0.389772\pi\) |
−0.644911 | + | 0.764258i | \(0.723105\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 21.6868i | − | 2.87248i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.97330 | + | 6.88196i | −0.517279 | + | 0.895954i | 0.482519 | + | 0.875885i | \(0.339722\pi\) |
−0.999799 | + | 0.0200689i | \(0.993611\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.50997 | + | 7.81149i | 0.577442 | + | 1.00016i | 0.995772 | + | 0.0918637i | \(0.0292824\pi\) |
−0.418329 | + | 0.908295i | \(0.637384\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 16.0280 | + | 13.7947i | 2.01933 | + | 1.73797i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.63614 | + | 1.52198i | 0.322056 | + | 0.185939i | 0.652308 | − | 0.757954i | \(-0.273801\pi\) |
−0.330253 | + | 0.943892i | \(0.607134\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.6899 | 2.12962 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.39840 | 0.640672 | 0.320336 | − | 0.947304i | \(-0.396204\pi\) | ||||
0.320336 | + | 0.947304i | \(0.396204\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.34256 | − | 1.92983i | −0.391216 | − | 0.225869i | 0.291471 | − | 0.956580i | \(-0.405855\pi\) |
−0.682687 | + | 0.730711i | \(0.739189\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.08879 | − | 11.0362i | 0.238040 | − | 1.25770i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.352201 | + | 0.610030i | 0.0396257 | + | 0.0686337i | 0.885158 | − | 0.465290i | \(-0.154050\pi\) |
−0.845532 | + | 0.533924i | \(0.820717\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −15.4529 | + | 26.7653i | −1.71699 | + | 2.97392i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.8135i | − | 1.18693i | −0.804858 | − | 0.593467i | \(-0.797759\pi\) | ||
0.804858 | − | 0.593467i | \(-0.202241\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.0386 | − | 7.52784i | −1.39789 | − | 0.807070i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.20282 | − | 7.27950i | −0.445498 | − | 0.771625i | 0.552589 | − | 0.833454i | \(-0.313640\pi\) |
−0.998087 | + | 0.0618287i | \(0.980307\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.46381 | + | 12.7591i | 0.467934 | + | 1.33751i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.94454 | + | 1.12268i | −0.201639 | + | 0.116416i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 0.614293i | − | 0.0623720i | −0.999514 | − | 0.0311860i | \(-0.990072\pi\) | ||
0.999514 | − | 0.0311860i | \(-0.00992842\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 33.9321 | 3.41031 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.82550 | + | 4.89391i | −0.281148 | + | 0.486962i | −0.971668 | − | 0.236351i | \(-0.924048\pi\) |
0.690520 | + | 0.723313i | \(0.257382\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.02802 | + | 1.17088i | −0.199827 | + | 0.115370i | −0.596575 | − | 0.802558i | \(-0.703472\pi\) |
0.396748 | + | 0.917928i | \(0.370139\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.859752 | + | 0.496378i | −0.0831154 | + | 0.0479867i | −0.540982 | − | 0.841034i | \(-0.681947\pi\) |
0.457866 | + | 0.889021i | \(0.348614\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.06928 | + | 15.7084i | −0.868679 | + | 1.50460i | −0.00533214 | + | 0.999986i | \(0.501697\pi\) |
−0.863347 | + | 0.504611i | \(0.831636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.04616 | −0.478960 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.22638i | − | 0.585728i | −0.956154 | − | 0.292864i | \(-0.905392\pi\) | ||
0.956154 | − | 0.292864i | \(-0.0946084\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −35.3648 | + | 20.4179i | −3.26947 | + | 1.88763i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.29718 | − | 0.434780i | −0.210582 | − | 0.0398562i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.51153 | − | 6.08215i | −0.319230 | − | 0.552923i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.0174 | − | 9.82502i | −1.53441 | − | 0.885892i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.62382i | 0.144091i | 0.997401 | + | 0.0720454i | \(0.0229527\pi\) | ||||
−0.997401 | + | 0.0720454i | \(0.977047\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.11433 | − | 15.7865i | 0.802472 | − | 1.38992i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.14103 | − | 5.44043i | −0.274433 | − | 0.475332i | 0.695559 | − | 0.718469i | \(-0.255157\pi\) |
−0.969992 | + | 0.243137i | \(0.921824\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.1166 | − | 11.2890i | −1.13736 | − | 0.978884i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.5124 | + | 8.95609i | 1.32531 | + | 0.765170i | 0.984571 | − | 0.174986i | \(-0.0559881\pi\) |
0.340743 | + | 0.940157i | \(0.389321\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −23.0023 | −1.95103 | −0.975514 | − | 0.219936i | \(-0.929415\pi\) | ||||
−0.975514 | + | 0.219936i | \(0.929415\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.1018 | −2.02974 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.7840 | + | 10.8450i | 1.57080 | + | 0.906901i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 22.9499 | − | 3.45656i | 1.89287 | − | 0.285093i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.20030 | − | 9.00719i | −0.426025 | − | 0.737898i | 0.570490 | − | 0.821304i | \(-0.306753\pi\) |
−0.996516 | + | 0.0834067i | \(0.973420\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.5860 | + | 18.3355i | −0.861477 | + | 1.49212i | 0.00902561 | + | 0.999959i | \(0.497127\pi\) |
−0.870503 | + | 0.492163i | \(0.836206\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 7.06293i | − | 0.571004i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.77296 | + | 3.91037i | 0.540541 | + | 0.312081i | 0.745298 | − | 0.666731i | \(-0.232307\pi\) |
−0.204757 | + | 0.978813i | \(0.565641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.25737 | − | 7.37397i | −0.337631 | − | 0.584794i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.20848 | − | 10.6993i | 0.725730 | − | 0.843220i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.2960 | − | 11.1406i | 1.51138 | − | 0.872596i | 0.511468 | − | 0.859302i | \(-0.329102\pi\) |
0.999912 | − | 0.0132936i | \(-0.00423160\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 23.8180i | − | 1.84309i | −0.388270 | − | 0.921546i | \(-0.626927\pi\) | ||
0.388270 | − | 0.921546i | \(-0.373073\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.1028 | −1.00791 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 26.1401 | − | 45.2760i | 1.99899 | − | 3.46235i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.31546 | + | 3.64624i | −0.480156 | + | 0.277218i | −0.720481 | − | 0.693474i | \(-0.756079\pi\) |
0.240326 | + | 0.970692i | \(0.422746\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −22.8173 | + | 13.1736i | −1.71506 | + | 0.990189i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.92258 | − | 15.4544i | 0.666905 | − | 1.15511i | −0.311860 | − | 0.950128i | \(-0.600952\pi\) |
0.978765 | − | 0.204985i | \(-0.0657147\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.62478 | −0.715404 | −0.357702 | − | 0.933836i | \(-0.616440\pi\) | ||||
−0.357702 | + | 0.933836i | \(0.616440\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29.9059i | 2.21071i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.24888 | + | 1.87574i | −0.237581 | + | 0.137168i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.4629 | + | 41.3399i | 1.05202 | + | 3.00703i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.71818 | + | 15.1003i | 0.630825 | + | 1.09262i | 0.987383 | + | 0.158348i | \(0.0506169\pi\) |
−0.356558 | + | 0.934273i | \(0.616050\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.26213 | − | 1.30604i | −0.162832 | − | 0.0940110i | 0.416370 | − | 0.909195i | \(-0.363302\pi\) |
−0.579201 | + | 0.815184i | \(0.696636\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.4853i | − | 1.31703i | −0.752569 | − | 0.658513i | \(-0.771186\pi\) | ||
0.752569 | − | 0.658513i | \(-0.228814\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.7637 | + | 18.6433i | −0.763019 | + | 1.32159i | 0.178268 | + | 0.983982i | \(0.442951\pi\) |
−0.941287 | + | 0.337606i | \(0.890383\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.04616 | + | 8.74020i | 0.355929 | + | 0.616486i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.3403 | + | 3.96743i | −0.795930 | + | 0.278459i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 36.9317 | + | 21.3225i | 2.56693 | + | 1.48202i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.7687 | −1.92080 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.3200 | 1.26120 | 0.630601 | − | 0.776107i | \(-0.282808\pi\) | ||||
0.630601 | + | 0.776107i | \(0.282808\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.5006 | + | 8.94928i | 1.06208 | + | 0.613195i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.333207 | + | 1.76051i | −0.0226195 | + | 0.119511i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.39840 | − | 11.0824i | −0.432364 | − | 0.748876i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.25737 | − | 3.90987i | 0.151847 | − | 0.263006i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.61429i | 0.175066i | 0.996162 | + | 0.0875330i | \(0.0278983\pi\) | ||||
−0.996162 | + | 0.0875330i | \(0.972102\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.21695 | − | 3.01201i | −0.346261 | − | 0.199914i | 0.316776 | − | 0.948500i | \(-0.397400\pi\) |
−0.663037 | + | 0.748586i | \(0.730733\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.52150 | − | 13.0276i | −0.497035 | − | 0.860889i | 0.502960 | − | 0.864310i | \(-0.332244\pi\) |
−0.999994 | + | 0.00342076i | \(0.998911\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24.2931 | − | 28.2260i | 1.59837 | − | 1.85713i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.47332 | + | 0.850620i | −0.0965202 | + | 0.0557260i | −0.547483 | − | 0.836817i | \(-0.684414\pi\) |
0.450963 | + | 0.892543i | \(0.351081\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.33547i | 0.151705i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.8208 | 1.67021 | 0.835105 | − | 0.550091i | \(-0.185407\pi\) | ||||
0.835105 | + | 0.550091i | \(0.185407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.54254 | − | 9.59996i | 0.357026 | − | 0.618387i | −0.630436 | − | 0.776241i | \(-0.717124\pi\) |
0.987463 | + | 0.157853i | \(0.0504574\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −45.7335 | + | 26.4043i | −2.93381 | + | 1.69383i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.9411 | − | 16.7092i | 1.84148 | − | 1.06318i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.9262 | − | 31.0492i | 1.13603 | − | 1.96766i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.96558 | 0.439663 | 0.219832 | − | 0.975538i | \(-0.429449\pi\) | ||||
0.219832 | + | 0.975538i | \(0.429449\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 22.6510i | − | 1.42405i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.62359 | − | 1.51473i | 0.163655 | − | 0.0944864i | −0.415935 | − | 0.909394i | \(-0.636546\pi\) |
0.579591 | + | 0.814908i | \(0.303212\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.62678 | + | 3.05203i | −0.163220 | + | 0.189644i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.1474 | − | 31.4322i | −1.12329 | − | 1.94560i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.35461 | + | 3.66884i | 0.391842 | + | 0.226230i | 0.682958 | − | 0.730458i | \(-0.260693\pi\) |
−0.291116 | + | 0.956688i | \(0.594027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 27.8692i | − | 1.70557i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.70711 | − | 13.3491i | 0.469911 | − | 0.813909i | −0.529497 | − | 0.848312i | \(-0.677619\pi\) |
0.999408 | + | 0.0344024i | \(0.0109528\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.30467 | − | 5.72385i | −0.200744 | − | 0.347699i | 0.748024 | − | 0.663671i | \(-0.231003\pi\) |
−0.948768 | + | 0.315972i | \(0.897669\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.33447 | + | 44.0355i | −0.504425 | + | 2.66515i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.31660 | + | 5.37894i | 0.559780 | + | 0.323189i | 0.753057 | − | 0.657955i | \(-0.228578\pi\) |
−0.193277 | + | 0.981144i | \(0.561912\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.41289 | −0.324061 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.3033 | 1.50947 | 0.754735 | − | 0.656030i | \(-0.227765\pi\) | ||||
0.754735 | + | 0.656030i | \(0.227765\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.49493 | − | 3.17250i | −0.326640 | − | 0.188585i | 0.327709 | − | 0.944779i | \(-0.393724\pi\) |
−0.654348 | + | 0.756193i | \(0.727057\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.8008 | + | 5.17812i | −0.873665 | + | 0.305655i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.10957 | − | 14.0462i | −0.477033 | − | 0.826246i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.01835 | − | 1.76384i | 0.0596969 | − | 0.103398i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 20.3589i | − | 1.18938i | −0.803954 | − | 0.594691i | \(-0.797274\pi\) | ||
0.803954 | − | 0.594691i | \(-0.202726\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 60.8609 | + | 35.1381i | 3.53151 | + | 2.03892i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.6297 | + | 23.6073i | 0.788225 | + | 1.36525i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.80356 | − | 13.7302i | −0.276873 | − | 0.791396i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.2259 | + | 9.36804i | −0.932154 | + | 0.538180i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.5695i | 1.68762i | 0.536643 | + | 0.843809i | \(0.319692\pi\) | ||||
−0.536643 | + | 0.843809i | \(0.680308\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.76417 | −0.441688 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.24153 | − | 10.8106i | 0.353925 | − | 0.613016i | −0.633009 | − | 0.774145i | \(-0.718180\pi\) |
0.986933 | + | 0.161129i | \(0.0515136\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.912273 | + | 0.526701i | −0.0515647 | + | 0.0297709i | −0.525561 | − | 0.850756i | \(-0.676144\pi\) |
0.473996 | + | 0.880527i | \(0.342811\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.26840 | + | 1.30966i | −0.127406 | + | 0.0735581i | −0.562349 | − | 0.826900i | \(-0.690102\pi\) |
0.434942 | + | 0.900458i | \(0.356769\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.63899 | + | 16.6952i | −0.539680 | + | 0.934753i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.29152 | −0.183715 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.78002i | 0.321609i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −52.0819 | + | 30.0695i | −2.88013 | + | 1.66285i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.5462 | + | 14.5773i | −0.691695 | + | 0.803675i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.63693 | − | 16.6917i | −0.529694 | − | 0.917457i | −0.999400 | − | 0.0346338i | \(-0.988974\pi\) |
0.469706 | − | 0.882823i | \(-0.344360\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.5350 | − | 6.08239i | −0.577315 | − | 0.333313i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.2979i | 0.560961i | 0.959860 | + | 0.280481i | \(0.0904939\pi\) | ||||
−0.959860 | + | 0.280481i | \(0.909506\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.3219 | − | 17.8780i | 0.560607 | − | 0.971001i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.43753 | + | 2.48987i | 0.0778465 | + | 0.134834i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.85595 | − | 15.6799i | 0.532171 | − | 0.846637i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.5848 | − | 10.1526i | −0.943999 | − | 0.545018i | −0.0527875 | − | 0.998606i | \(-0.516811\pi\) |
−0.891212 | + | 0.453588i | \(0.850144\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.62249 | 0.140379 | 0.0701893 | − | 0.997534i | \(-0.477640\pi\) | ||||
0.0701893 | + | 0.997534i | \(0.477640\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −84.5741 | −4.51423 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.55629 | + | 4.36263i | 0.402181 | + | 0.232199i | 0.687425 | − | 0.726256i | \(-0.258741\pi\) |
−0.285244 | + | 0.958455i | \(0.592075\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.87521 | − | 5.05659i | −0.310949 | − | 0.267623i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.02470 | − | 10.4351i | −0.317971 | − | 0.550743i | 0.662093 | − | 0.749421i | \(-0.269668\pi\) |
−0.980065 | + | 0.198679i | \(0.936335\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.8921 | + | 20.5976i | −0.625898 | + | 1.08409i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 23.2852i | − | 1.22216i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.01833 | − | 1.74263i | −0.157556 | − | 0.0909648i | 0.419149 | − | 0.907917i | \(-0.362328\pi\) |
−0.576705 | + | 0.816953i | \(0.695662\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.6852 | − | 41.0240i | −1.23300 | − | 2.13562i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.67612 | − | 1.26357i | −0.346607 | − | 0.0656012i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.5362 | + | 18.7848i | −1.68466 | + | 0.972639i | −0.726171 | + | 0.687515i | \(0.758702\pi\) |
−0.958490 | + | 0.285125i | \(0.907965\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 23.2002i | − | 1.19487i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.48935 | 0.127869 | 0.0639347 | − | 0.997954i | \(-0.479635\pi\) | ||||
0.0639347 | + | 0.997954i | \(0.479635\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.69192 | + | 4.66254i | −0.137911 | + | 0.238869i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.5981 | − | 10.7376i | 0.950320 | − | 0.548668i | 0.0571398 | − | 0.998366i | \(-0.481802\pi\) |
0.893180 | + | 0.449699i | \(0.148469\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 38.0565 | − | 21.9719i | 1.93452 | − | 1.11690i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.67880 | − | 9.83598i | 0.287927 | − | 0.498704i | −0.685388 | − | 0.728178i | \(-0.740367\pi\) |
0.973315 | + | 0.229474i | \(0.0737007\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.71477 | −0.238436 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 20.8284i | − | 1.05065i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.5675 | − | 12.4520i | 1.08244 | − | 0.624948i | 0.150888 | − | 0.988551i | \(-0.451787\pi\) |
0.931554 | + | 0.363603i | \(0.118453\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.9477 | − | 54.1589i | −0.948572 | − | 2.71134i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.68494 | − | 8.11456i | −0.233955 | − | 0.405222i | 0.725014 | − | 0.688735i | \(-0.241833\pi\) |
−0.958968 | + | 0.283513i | \(0.908500\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.99645 | − | 1.73000i | −0.149264 | − | 0.0861774i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.46133i | 0.320276i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.50724 | + | 11.2709i | −0.321762 | + | 0.557309i | −0.980852 | − | 0.194756i | \(-0.937609\pi\) |
0.659089 | + | 0.752065i | \(0.270942\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.6942 | + | 51.4319i | 1.46471 | + | 2.53695i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.90987 | + | 20.6580i | −0.192392 | + | 1.01651i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −66.0473 | − | 38.1324i | −3.23435 | − | 1.86735i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.76954 | −0.477273 | −0.238637 | − | 0.971109i | \(-0.576700\pi\) | ||||
−0.238637 | + | 0.971109i | \(0.576700\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.5881 | −1.05214 | −0.526069 | − | 0.850442i | \(-0.676335\pi\) | ||||
−0.526069 | + | 0.850442i | \(0.676335\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −50.3181 | − | 29.0512i | −2.44655 | − | 1.41252i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.0878 | + | 15.5675i | 0.875328 | + | 0.753364i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 35.9568 | + | 62.2790i | 1.73601 | + | 3.00686i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.99844 | + | 15.5857i | −0.433439 | + | 0.750739i | −0.997167 | − | 0.0752218i | \(-0.976034\pi\) |
0.563727 | + | 0.825961i | \(0.309367\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.2236i | 1.16411i | 0.813148 | + | 0.582057i | \(0.197752\pi\) | ||||
−0.813148 | + | 0.582057i | \(0.802248\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −30.2235 | − | 17.4495i | −1.44578 | − | 0.834724i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.507449 | − | 0.878928i | −0.0242192 | − | 0.0419490i | 0.853662 | − | 0.520828i | \(-0.174377\pi\) |
−0.877881 | + | 0.478879i | \(0.841043\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 52.0795 | + | 20.4463i | 2.47998 | + | 0.973633i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.1326 | + | 7.00476i | −0.576438 | + | 0.332806i | −0.759716 | − | 0.650255i | \(-0.774662\pi\) |
0.183279 | + | 0.983061i | \(0.441329\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 34.4835i | − | 1.63102i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.76134 | 0.460666 | 0.230333 | − | 0.973112i | \(-0.426018\pi\) | ||||
0.230333 | + | 0.973112i | \(0.426018\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.5804 | + | 21.7899i | −0.592388 | + | 1.02605i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −60.7920 | + | 35.0983i | −2.85626 | + | 1.64906i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.2826 | − | 12.8649i | 1.04234 | − | 0.601794i | 0.121844 | − | 0.992549i | \(-0.461119\pi\) |
0.920495 | + | 0.390755i | \(0.127786\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.31395 | − | 12.6681i | 0.341386 | − | 0.591298i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.3115 | 1.17888 | 0.589438 | − | 0.807814i | \(-0.299349\pi\) | ||||
0.589438 | + | 0.807814i | \(0.299349\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 35.8484i | − | 1.66602i | −0.553261 | − | 0.833008i | \(-0.686617\pi\) | ||
0.553261 | − | 0.833008i | \(-0.313383\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.16733 | + | 1.82866i | −0.146567 | + | 0.0846204i | −0.571490 | − | 0.820609i | \(-0.693634\pi\) |
0.424923 | + | 0.905229i | \(0.360301\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.91305 | + | 1.49768i | 0.365391 | + | 0.0691564i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.9650 | + | 22.4560i | 0.597393 | + | 1.03472i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.2137 | − | 11.6704i | −0.929428 | − | 0.536606i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 20.5265i | − | 0.939842i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.935505 | − | 1.62034i | 0.0427443 | − | 0.0740353i | −0.843862 | − | 0.536561i | \(-0.819723\pi\) |
0.886606 | + | 0.462525i | \(0.153057\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.88795 | − | 6.73413i | −0.177275 | − | 0.307050i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 44.1775 | − | 15.4557i | 2.01015 | − | 0.703257i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.12552 | − | 4.69127i | −0.368203 | − | 0.212582i | 0.304470 | − | 0.952522i | \(-0.401521\pi\) |
−0.672673 | + | 0.739940i | \(0.734854\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 73.8738 | 3.34069 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.6545 | −1.74445 | −0.872227 | − | 0.489100i | \(-0.837325\pi\) | ||||
−0.872227 | + | 0.489100i | \(0.837325\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.47509 | + | 2.00635i | 0.156510 | + | 0.0903613i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.4816 | − | 4.71658i | 0.604731 | − | 0.211567i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.05298 | + | 3.55587i | 0.0919040 | + | 0.159182i | 0.908312 | − | 0.418293i | \(-0.137371\pi\) |
−0.816408 | + | 0.577475i | \(0.804038\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 39.4847 | − | 68.3894i | 1.76404 | − | 3.05541i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.6922i | 1.19015i | 0.803672 | + | 0.595073i | \(0.202877\pi\) | ||||
−0.803672 | + | 0.595073i | \(0.797123\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −37.6225 | − | 21.7214i | −1.67088 | − | 0.964680i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.40469 | − | 11.0932i | −0.283883 | − | 0.491699i | 0.688455 | − | 0.725279i | \(-0.258289\pi\) |
−0.972338 | + | 0.233580i | \(0.924956\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0335 | − | 1.89902i | −0.443858 | − | 0.0840077i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 93.7704 | − | 54.1383i | 4.14006 | − | 2.39027i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.8611i | 1.35727i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.1784 | −1.06131 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.9106 | + | 20.6297i | −0.521811 | + | 0.903803i | 0.477867 | + | 0.878432i | \(0.341410\pi\) |
−0.999678 | + | 0.0253710i | \(0.991923\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.0580 | − | 6.38433i | 0.483532 | − | 0.279167i | −0.238355 | − | 0.971178i | \(-0.576608\pi\) |
0.721887 | + | 0.692011i | \(0.243275\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.518264 | − | 0.299220i | 0.0225759 | − | 0.0130342i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.73360 | − | 4.73474i | 0.118852 | − | 0.205858i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −63.5152 | −2.75633 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 30.2799i | − | 1.31157i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 51.2395 | − | 29.5831i | 2.21115 | − | 1.27661i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.42594 | − | 29.3861i | −0.190639 | − | 1.26575i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.84180 | + | 15.3144i | 0.380138 | + | 0.658419i | 0.991082 | − | 0.133255i | \(-0.0425430\pi\) |
−0.610943 | + | 0.791674i | \(0.709210\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −27.6360 | − | 15.9556i | −1.18597 | − | 0.684722i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.0580i | 1.02864i | 0.857597 | + | 0.514322i | \(0.171956\pi\) | ||||
−0.857597 | + | 0.514322i | \(0.828044\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −36.0471 | + | 62.4354i | −1.53845 | + | 2.66468i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.8511 | + | 25.7229i | 0.632678 | + | 1.09583i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.41254 | + | 1.21573i | 0.0600675 | + | 0.0516980i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.21103 | − | 2.43124i | −0.178427 | − | 0.103015i | 0.408126 | − | 0.912925i | \(-0.366182\pi\) |
−0.586553 | + | 0.809911i | \(0.699516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.0896 | 1.18806 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.4382 | −0.525139 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.59960 | + | 5.54233i | 0.404575 | + | 0.233581i | 0.688456 | − | 0.725278i | \(-0.258289\pi\) |
−0.283881 | + | 0.958859i | \(0.591622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.2063 | + | 80.3429i | −0.638603 | + | 3.37409i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.47854 | − | 14.6853i | −0.355439 | − | 0.615638i | 0.631754 | − | 0.775169i | \(-0.282335\pi\) |
−0.987193 | + | 0.159531i | \(0.949002\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.1725 | + | 17.6193i | −0.425706 | + | 0.737344i | −0.996486 | − | 0.0837588i | \(-0.973307\pi\) |
0.570780 | + | 0.821103i | \(0.306641\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 57.8108i | 2.41508i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.1689 | + | 20.8821i | 1.50573 | + | 0.869335i | 0.999978 | + | 0.00665740i | \(0.00211913\pi\) |
0.505754 | + | 0.862678i | \(0.331214\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.33023 | − | 7.50017i | −0.179958 | − | 0.311696i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.44774 | − | 27.0048i | −0.391958 | − | 1.12035i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.44197 | + | 5.45132i | −0.391046 | + | 0.225771i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.6858i | 1.59674i | 0.602170 | + | 0.798368i | \(0.294303\pi\) | ||||
−0.602170 | + | 0.798368i | \(0.705697\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.42969 | 0.182522 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.6444 | − | 53.0776i | 1.26054 | − | 2.18332i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.1049 | − | 9.29817i | 0.661349 | − | 0.381830i | −0.131442 | − | 0.991324i | \(-0.541961\pi\) |
0.792791 | + | 0.609494i | \(0.208627\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −61.8125 | + | 35.6874i | −2.52982 | + | 1.46059i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.0269 | + | 19.0991i | −0.450547 | + | 0.780369i | −0.998420 | − | 0.0561917i | \(-0.982104\pi\) |
0.547873 | + | 0.836561i | \(0.315438\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.6533 | −0.842465 | −0.421233 | − | 0.906953i | \(-0.638402\pi\) | ||||
−0.421233 | + | 0.906953i | \(0.638402\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.3296i | 0.990776i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.9329 | − | 12.0856i | 0.849638 | − | 0.490539i | −0.0108905 | − | 0.999941i | \(-0.503467\pi\) |
0.860529 | + | 0.509402i | \(0.170133\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −39.1388 | − | 7.40768i | −1.58598 | − | 0.300174i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.5699 | − | 32.1641i | −0.751259 | − | 1.30122i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.7302 | + | 22.9383i | 1.60469 | + | 0.926467i | 0.990532 | + | 0.137283i | \(0.0438369\pi\) |
0.614156 | + | 0.789184i | \(0.289496\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.8072i | 1.03896i | 0.854483 | + | 0.519479i | \(0.173874\pi\) | ||||
−0.854483 | + | 0.519479i | \(0.826126\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.5216 | + | 37.2764i | −0.865024 | + | 1.49827i | 0.00199877 | + | 0.999998i | \(0.499364\pi\) |
−0.867023 | + | 0.498268i | \(0.833970\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 44.1607 | + | 76.4886i | 1.77211 | + | 3.06938i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.8559 | − | 14.5073i | −0.675318 | − | 0.581223i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −79.7332 | − | 46.0340i | −3.18424 | − | 1.83842i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.34492 | 0.0536254 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.8872 | 0.831508 | 0.415754 | − | 0.909477i | \(-0.363518\pi\) | ||||
0.415754 | + | 0.909477i | \(0.363518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 52.6029 | + | 30.3703i | 2.09078 | + | 1.20711i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.2952 | + | 27.9636i | 0.883368 | + | 1.10796i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.5740 | + | 37.3673i | 0.853456 | + | 1.47823i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.9466 | − | 27.6203i | 0.629853 | − | 1.09094i | −0.357727 | − | 0.933826i | \(-0.616448\pi\) |
0.987581 | − | 0.157112i | \(-0.0502184\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.850088i | 0.0335242i | 0.999860 | + | 0.0167621i | \(0.00533579\pi\) | ||||
−0.999860 | + | 0.0167621i | \(0.994664\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.7557 | + | 17.1795i | 1.16982 | + | 0.675395i | 0.953637 | − | 0.300959i | \(-0.0973066\pi\) |
0.216181 | + | 0.976353i | \(0.430640\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.8681 | + | 29.2164i | 0.662130 | + | 1.14684i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.87526 | + | 4.50264i | −0.151884 | + | 0.176472i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.0945 | + | 11.0242i | −0.747226 | + | 0.431411i | −0.824691 | − | 0.565584i | \(-0.808651\pi\) |
0.0774647 | + | 0.996995i | \(0.475317\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 30.8492i | − | 1.20354i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.9046 | 0.658508 | 0.329254 | − | 0.944241i | \(-0.393203\pi\) | ||||
0.329254 | + | 0.944241i | \(0.393203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.44864 | + | 12.9014i | −0.289718 | + | 0.501807i | −0.973742 | − | 0.227652i | \(-0.926895\pi\) |
0.684024 | + | 0.729460i | \(0.260228\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.9633 | − | 7.48437i | 0.503453 | − | 0.290669i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.9822 | + | 12.1141i | −0.812433 | + | 0.469058i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.33389 | + | 7.50651i | −0.167558 | + | 0.290218i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.2928 | 1.47828 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 26.1490i | − | 1.00797i | −0.863713 | − | 0.503984i | \(-0.831867\pi\) | ||
0.863713 | − | 0.503984i | \(-0.168133\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.0943 | + | 16.2202i | −1.07975 | + | 0.623394i | −0.930829 | − | 0.365455i | \(-0.880914\pi\) |
−0.148922 | + | 0.988849i | \(0.547580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.536707 | − | 1.53409i | −0.0205969 | − | 0.0588730i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.98641 | − | 17.2970i | −0.382680 | − | 0.662821i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.3251 | + | 22.1270i | 1.46647 | + | 0.846667i | 0.999297 | − | 0.0374987i | \(-0.0119390\pi\) |
0.467174 | + | 0.884166i | \(0.345272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 49.8755i | − | 1.90287i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.56041 | − | 11.3630i | 0.249932 | − | 0.432895i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.1793 | + | 33.2196i | 0.729616 | + | 1.26373i | 0.957046 | + | 0.289937i | \(0.0936344\pi\) |
−0.227430 | + | 0.973794i | \(0.573032\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 84.7396 | − | 29.6465i | 3.21899 | − | 1.12618i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.53554 | + | 2.61860i | 0.171796 | + | 0.0991864i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.64052 | −0.213344 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.0696 | 0.493633 | 0.246817 | − | 0.969062i | \(-0.420615\pi\) | ||||
0.246817 | + | 0.969062i | \(0.420615\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.62143 | + | 4.97759i | 0.325164 | + | 0.187733i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.78040 | + | 14.6903i | −0.104568 | + | 0.552487i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.97959 | − | 8.62490i | −0.187012 | − | 0.323915i | 0.757240 | − | 0.653136i | \(-0.226547\pi\) |
−0.944253 | + | 0.329221i | \(0.893214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.81506 | + | 4.87582i | −0.105573 | + | 0.182858i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.61331i | 0.135319i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 74.1402 | + | 42.8049i | 2.76882 | + | 1.59858i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.7298 | + | 41.1012i | 0.884971 | + | 1.53281i | 0.845747 | + | 0.533584i | \(0.179155\pi\) |
0.0392240 | + | 0.999230i | \(0.487511\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.04164 | + | 4.69595i | −0.150518 | + | 0.174886i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31.8290 | − | 18.3765i | 1.18373 | − | 0.683428i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.84829i | − | 0.142725i | −0.997450 | − | 0.0713626i | \(-0.977265\pi\) | ||
0.997450 | − | 0.0713626i | \(-0.0227348\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −82.3708 | −3.05077 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.42918 | + | 4.20747i | −0.0898465 | + | 0.155619i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.82391 | + | 1.63038i | −0.104303 | + | 0.0602196i | −0.551244 | − | 0.834344i | \(-0.685847\pi\) |
0.446941 | + | 0.894563i | \(0.352513\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.1914 | − | 6.46133i | 0.412239 | − | 0.238006i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.50067 | + | 16.4556i | −0.349488 | + | 0.605330i | −0.986159 | − | 0.165805i | \(-0.946978\pi\) |
0.636671 | + | 0.771136i | \(0.280311\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 110.800 | 4.07032 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.02310i | 0.147593i | 0.997273 | + | 0.0737965i | \(0.0235115\pi\) | ||||
−0.997273 | + | 0.0737965i | \(0.976488\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 74.8502 | − | 43.2148i | 2.73863 | − | 1.58115i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.71340 | + | 1.99078i | −0.0626062 | + | 0.0727417i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.345395 | + | 0.598242i | 0.0126037 | + | 0.0218302i | 0.872258 | − | 0.489045i | \(-0.162655\pi\) |
−0.859655 | + | 0.510875i | \(0.829321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.0005 | + | 11.5473i | 0.728859 | + | 0.420807i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.5723i | 0.856751i | 0.903601 | + | 0.428375i | \(0.140914\pi\) | ||||
−0.903601 | + | 0.428375i | \(0.859086\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 37.5500 | − | 65.0385i | 1.36298 | − | 2.36075i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.86169 | − | 4.95659i | −0.103736 | − | 0.179676i | 0.809485 | − | 0.587141i | \(-0.199746\pi\) |
−0.913221 | + | 0.407464i | \(0.866413\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.92450 | + | 47.1530i | −0.323089 | + | 1.70705i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.1605 | − | 20.2999i | −1.26957 | − | 0.732988i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.8252 | 1.25583 | 0.627915 | − | 0.778282i | \(-0.283909\pi\) | ||||
0.627915 | + | 0.778282i | \(0.283909\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.0443 | 0.361736 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.63093 | − | 3.25102i | −0.202531 | − | 0.116931i | 0.395305 | − | 0.918550i | \(-0.370639\pi\) |
−0.597835 | + | 0.801619i | \(0.703972\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.6019 | + | 4.40883i | −0.452091 | + | 0.158166i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.3830 | + | 33.5724i | 0.694469 | + | 1.20286i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4591 | − | 19.8477i | 0.410038 | − | 0.710206i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 75.1694i | − | 2.68633i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.2834 | − | 12.8653i | −0.794317 | − | 0.458599i | 0.0471634 | − | 0.998887i | \(-0.484982\pi\) |
−0.841480 | + | 0.540288i | \(0.818315\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.1642 | + | 21.0689i | 0.433055 | + | 0.750074i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.43998 | − | 15.5493i | −0.193423 | − | 0.552870i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.9096 | + | 23.0418i | −1.41723 | + | 0.818239i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 44.8212i | − | 1.58765i | −0.608147 | − | 0.793825i | \(-0.708087\pi\) | ||
0.608147 | − | 0.793825i | \(-0.291913\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.42370 | 0.227254 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 33.5921 | − | 58.1833i | 1.18692 | − | 2.05580i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.1903 | + | 8.19280i | −0.500766 | + | 0.289118i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 44.2594 | − | 25.5532i | 1.55800 | − | 0.899514i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.6919 | − | 21.9831i | 0.446225 | − | 0.772884i | −0.551912 | − | 0.833902i | \(-0.686102\pi\) |
0.998137 | + | 0.0610184i | \(0.0194348\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.86499 | −0.241062 | −0.120531 | − | 0.992710i | \(-0.538460\pi\) | ||||
−0.120531 | + | 0.992710i | \(0.538460\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 21.9135i | − | 0.768539i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.1439 | + | 17.9810i | −1.08959 | + | 0.629074i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −70.4784 | + | 81.8883i | −2.46271 | + | 2.86141i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.6253 | − | 27.0639i | −0.545328 | − | 0.944536i | −0.998586 | − | 0.0531570i | \(-0.983072\pi\) |
0.453258 | − | 0.891379i | \(-0.350262\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.7965 | − | 6.23335i | −0.376342 | − | 0.217281i | 0.299884 | − | 0.953976i | \(-0.403052\pi\) |
−0.676225 | + | 0.736695i | \(0.736385\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.0893i | 0.698572i | 0.937016 | + | 0.349286i | \(0.113576\pi\) | ||||
−0.937016 | + | 0.349286i | \(0.886424\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.1383 | + | 41.8088i | −0.838359 | + | 1.45208i | 0.0529061 | + | 0.998599i | \(0.483152\pi\) |
−0.891266 | + | 0.453482i | \(0.850182\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.8341 | + | 30.8895i | 0.618656 | + | 1.07154i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.11668 | + | 0.921255i | −0.211930 | + | 0.0319196i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.70860 | − | 5.60526i | −0.335578 | − | 0.193746i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 56.1020 | 1.93686 | 0.968429 | − | 0.249291i | \(-0.0801975\pi\) | ||||
0.968429 | + | 0.249291i | \(0.0801975\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.37972 | −0.288956 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 72.6544 | + | 41.9470i | 2.50235 | + | 1.44473i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.0834 | − | 12.1211i | −0.483912 | − | 0.416486i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.5185 | − | 18.2186i | −0.360995 | − | 0.625261i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.06022 | + | 7.03251i | −0.139183 | + | 0.241072i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 16.4092i | − | 0.561840i | −0.959731 | − | 0.280920i | \(-0.909360\pi\) | ||
0.959731 | − | 0.280920i | \(-0.0906395\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.87379 | − | 2.23653i | −0.132326 | − | 0.0763985i | 0.432376 | − | 0.901694i | \(-0.357675\pi\) |
−0.564702 | + | 0.825295i | \(0.691009\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.25579 | − | 12.5674i | −0.247564 | − | 0.428794i | 0.715285 | − | 0.698833i | \(-0.246297\pi\) |
−0.962849 | + | 0.270039i | \(0.912963\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −51.0823 | − | 9.66818i | −1.74088 | − | 0.329491i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.6317 | + | 7.29293i | −0.429989 | + | 0.248254i | −0.699342 | − | 0.714787i | \(-0.746524\pi\) |
0.269353 | + | 0.963042i | \(0.413190\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 53.7751i | − | 1.82630i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.99044 | 0.101444 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.77591 | + | 13.4683i | −0.263477 | + | 0.456355i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.25209 | − | 2.45495i | 0.143911 | − | 0.0830873i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.6133 | + | 18.8293i | −1.10127 | + | 0.635821i | −0.936555 | − | 0.350520i | \(-0.886005\pi\) |
−0.164718 | + | 0.986341i | \(0.552672\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 33.7504 | − | 58.4574i | 1.13837 | − | 1.97172i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.4007 | −1.49590 | −0.747949 | − | 0.663757i | \(-0.768961\pi\) | ||||
−0.747949 | + | 0.663757i | \(0.768961\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 51.7213i | − | 1.74056i | −0.492558 | − | 0.870279i | \(-0.663938\pi\) | ||
0.492558 | − | 0.870279i | \(-0.336062\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.423886 | + | 0.244731i | −0.0142327 | + | 0.00821725i | −0.507099 | − | 0.861888i | \(-0.669282\pi\) |
0.492867 | + | 0.870105i | \(0.335949\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.41873 | + | 4.05522i | 0.0475827 | + | 0.136008i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 65.6033 | + | 113.628i | 2.19779 | + | 3.80669i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41.1783 | + | 23.7743i | 1.37798 | + | 0.795578i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 90.3794i | 3.01768i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.53762 | − | 2.66324i | 0.0512826 | − | 0.0888240i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.13469 | + | 1.96534i | 0.0378019 | + | 0.0654748i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.96884 | − | 47.3872i | 0.298464 | − | 1.57695i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.6323 | + | 21.7270i | 1.24956 | + | 0.721435i | 0.971022 | − | 0.238990i | \(-0.0768164\pi\) |
0.278539 | + | 0.960425i | \(0.410150\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −45.1671 | −1.49810 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.77049 | −0.158054 | −0.0790268 | − | 0.996872i | \(-0.525181\pi\) | ||||
−0.0790268 | + | 0.996872i | \(0.525181\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.7568 | − | 22.9536i | −1.31576 | − | 0.759652i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.5975 | − | 10.8422i | −0.416006 | − | 0.358042i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.6175 | − | 35.7106i | −0.680109 | − | 1.17798i | −0.974947 | − | 0.222436i | \(-0.928599\pi\) |
0.294838 | − | 0.955547i | \(-0.404734\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −49.0193 | + | 84.9039i | −1.61524 | + | 2.79768i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.5809i | 0.907836i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.2095 | − | 9.35855i | −0.532389 | − | 0.307375i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.9461 | + | 27.6195i | 0.523175 | + | 0.906166i | 0.999636 | + | 0.0269705i | \(0.00858602\pi\) |
−0.476461 | + | 0.879196i | \(0.658081\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.6198 | − | 16.7324i | −1.39681 | − | 0.548383i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 35.8431 | − | 20.6940i | 1.17345 | − | 0.677491i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 23.2518i | − | 0.759602i | −0.925068 | − | 0.379801i | \(-0.875992\pi\) | ||
0.925068 | − | 0.379801i | \(-0.124008\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.49259 | −0.113976 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.3260 | + | 23.0812i | −0.434414 | + | 0.752427i | −0.997248 | − | 0.0741432i | \(-0.976378\pi\) |
0.562834 | + | 0.826570i | \(0.309711\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.3850 | + | 15.8108i | −0.891780 | + | 0.514869i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.51554 | + | 2.60705i | −0.146735 | + | 0.0847177i | −0.571570 | − | 0.820553i | \(-0.693666\pi\) |
0.424835 | + | 0.905271i | \(0.360332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.85965 | − | 17.0774i | 0.320058 | − | 0.554356i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.68447 | −0.281613 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.8674i | 1.22664i | 0.789833 | + | 0.613322i | \(0.210167\pi\) | ||||
−0.789833 | + | 0.613322i | \(0.789833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −55.3536 | + | 31.9584i | −1.78933 | + | 1.03307i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46.5645 | + | 8.81312i | 1.50365 | + | 0.284591i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.2707 | + | 26.4496i | 0.492603 | + | 0.853213i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.87179 | − | 3.96743i | −0.221440 | − | 0.127849i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.7266i | 0.570049i | 0.958520 | + | 0.285024i | \(0.0920017\pi\) | ||||
−0.958520 | + | 0.285024i | \(0.907998\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.58193 | + | 16.5964i | −0.307816 | + | 0.533153i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.38205 | − | 9.32198i | −0.172718 | − | 0.299157i | 0.766651 | − | 0.642064i | \(-0.221922\pi\) |
−0.939369 | + | 0.342907i | \(0.888588\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −57.4443 | + | 20.0971i | −1.84158 | + | 0.644283i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.2753 | − | 19.7888i | −1.09656 | − | 0.633101i | −0.161247 | − | 0.986914i | \(-0.551551\pi\) |
−0.935316 | + | 0.353813i | \(0.884885\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.6850 | −1.14050 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −144.977 | −4.62876 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.8261 | + | 15.4880i | 0.855618 | + | 0.493991i | 0.862543 | − | 0.505985i | \(-0.168871\pi\) |
−0.00692422 | + | 0.999976i | \(0.502204\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −60.1902 | + | 21.0578i | −1.91588 | + | 0.670276i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.6671 | − | 25.4041i | −0.466386 | − | 0.807805i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.5946 | − | 28.7427i | 0.527145 | − | 0.913042i | −0.472355 | − | 0.881409i | \(-0.656596\pi\) |
0.999500 | − | 0.0316332i | \(-0.0100708\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 63.9031i | − | 2.02790i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.65077 | − | 4.41717i | −0.242302 | − | 0.139893i | 0.373932 | − | 0.927456i | \(-0.378009\pi\) |
−0.616234 | + | 0.787563i | \(0.711343\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.5971 | − | 21.8189i | −0.398555 | − | 0.690318i |
(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 | 1400.2.bh.j.249.8 | 16 | ||
5.2 | odd | 4 | 1400.2.q.m.1201.4 | yes | 8 | ||
5.3 | odd | 4 | 1400.2.q.l.1201.1 | yes | 8 | ||
5.4 | even | 2 | inner | 1400.2.bh.j.249.1 | 16 | ||
7.2 | even | 3 | inner | 1400.2.bh.j.849.1 | 16 | ||
35.2 | odd | 12 | 1400.2.q.m.401.4 | yes | 8 | ||
35.3 | even | 12 | 9800.2.a.ck.1.1 | 4 | |||
35.9 | even | 6 | inner | 1400.2.bh.j.849.8 | 16 | ||
35.17 | even | 12 | 9800.2.a.cu.1.4 | 4 | |||
35.18 | odd | 12 | 9800.2.a.ct.1.4 | 4 | |||
35.23 | odd | 12 | 1400.2.q.l.401.1 | ✓ | 8 | ||
35.32 | odd | 12 | 9800.2.a.cj.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.q.l.401.1 | ✓ | 8 | 35.23 | odd | 12 | ||
1400.2.q.l.1201.1 | yes | 8 | 5.3 | odd | 4 | ||
1400.2.q.m.401.4 | yes | 8 | 35.2 | odd | 12 | ||
1400.2.q.m.1201.4 | yes | 8 | 5.2 | odd | 4 | ||
1400.2.bh.j.249.1 | 16 | 5.4 | even | 2 | inner | ||
1400.2.bh.j.249.8 | 16 | 1.1 | even | 1 | trivial | ||
1400.2.bh.j.849.1 | 16 | 7.2 | even | 3 | inner | ||
1400.2.bh.j.849.8 | 16 | 35.9 | even | 6 | inner | ||
9800.2.a.cj.1.1 | 4 | 35.32 | odd | 12 | |||
9800.2.a.ck.1.1 | 4 | 35.3 | even | 12 | |||
9800.2.a.ct.1.4 | 4 | 35.18 | odd | 12 | |||
9800.2.a.cu.1.4 | 4 | 35.17 | even | 12 |