Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(143,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.w (of order \(8\), degree \(4\), 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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 143.8 | ||
Character | \(\chi\) | \(=\) | 1152.143 |
Dual form | 1152.2.w.a.1007.8 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.39555 | − | 3.36915i | 0.624108 | − | 1.50673i | −0.222731 | − | 0.974880i | \(-0.571497\pi\) |
0.846839 | − | 0.531850i | \(-0.178503\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.05755 | − | 1.05755i | 0.399715 | − | 0.399715i | −0.478417 | − | 0.878133i | \(-0.658789\pi\) |
0.878133 | + | 0.478417i | \(0.158789\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50977 | − | 3.64490i | 0.455211 | − | 1.09898i | −0.515102 | − | 0.857129i | \(-0.672246\pi\) |
0.970314 | − | 0.241849i | \(-0.0777539\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.23818 | + | 0.927086i | −0.620761 | + | 0.257127i | −0.670822 | − | 0.741619i | \(-0.734058\pi\) |
0.0500610 | + | 0.998746i | \(0.484058\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.49610 | 1.81807 | 0.909036 | − | 0.416717i | \(-0.136820\pi\) | ||||
0.909036 | + | 0.416717i | \(0.136820\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.818262 | − | 1.97546i | −0.187722 | − | 0.453201i | 0.801798 | − | 0.597595i | \(-0.203877\pi\) |
−0.989520 | + | 0.144393i | \(0.953877\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.80392 | + | 5.80392i | −1.21020 | + | 1.21020i | −0.239241 | + | 0.970960i | \(0.576898\pi\) |
−0.970960 | + | 0.239241i | \(0.923102\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.86809 | − | 5.86809i | −1.17362 | − | 1.17362i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.326633 | + | 0.135296i | −0.0606542 | + | 0.0251238i | −0.412804 | − | 0.910820i | \(-0.635451\pi\) |
0.352150 | + | 0.935944i | \(0.385451\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.71021i | − | 0.307163i | −0.988136 | − | 0.153582i | \(-0.950919\pi\) | ||
0.988136 | − | 0.153582i | \(-0.0490808\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.08718 | − | 5.03889i | −0.352797 | − | 0.851728i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.387384 | + | 0.160460i | 0.0636856 | + | 0.0263794i | 0.414299 | − | 0.910141i | \(-0.364027\pi\) |
−0.350613 | + | 0.936520i | \(0.614027\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50401 | + | 1.50401i | 0.234887 | + | 0.234887i | 0.814729 | − | 0.579842i | \(-0.196886\pi\) |
−0.579842 | + | 0.814729i | \(0.696886\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.40227 | − | 3.06612i | −1.12884 | − | 0.467579i | −0.261450 | − | 0.965217i | \(-0.584201\pi\) |
−0.867385 | + | 0.497638i | \(0.834201\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.27404i | − | 1.06103i | −0.847676 | − | 0.530514i | \(-0.821999\pi\) | ||
0.847676 | − | 0.530514i | \(-0.178001\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.76319i | 0.680455i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.94866 | − | 1.63559i | −0.542390 | − | 0.224665i | 0.0946303 | − | 0.995512i | \(-0.469833\pi\) |
−0.637020 | + | 0.770847i | \(0.719833\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.1733 | − | 10.1733i | −1.37176 | − | 1.37176i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.7979 | + | 5.30105i | 1.66614 | + | 0.690138i | 0.998521 | − | 0.0543646i | \(-0.0173133\pi\) |
0.667619 | + | 0.744503i | \(0.267313\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.579943 | − | 1.40011i | −0.0742542 | − | 0.179265i | 0.882394 | − | 0.470511i | \(-0.155930\pi\) |
−0.956648 | + | 0.291245i | \(0.905930\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.83457i | 1.09579i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.96385 | − | 3.29874i | 0.972940 | − | 0.403005i | 0.161134 | − | 0.986933i | \(-0.448485\pi\) |
0.811806 | + | 0.583928i | \(0.198485\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.75505 | + | 4.75505i | 0.564320 | + | 0.564320i | 0.930532 | − | 0.366211i | \(-0.119345\pi\) |
−0.366211 | + | 0.930532i | \(0.619345\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.99854 | + | 7.99854i | −0.936158 | + | 0.936158i | −0.998081 | − | 0.0619229i | \(-0.980277\pi\) |
0.0619229 | + | 0.998081i | \(0.480277\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.25800 | − | 5.45130i | −0.257323 | − | 0.621233i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.3967 | −1.61975 | −0.809877 | − | 0.586600i | \(-0.800466\pi\) | ||||
−0.809877 | + | 0.586600i | \(0.800466\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.35250 | − | 0.560224i | 0.148456 | − | 0.0614926i | −0.307218 | − | 0.951639i | \(-0.599398\pi\) |
0.455674 | + | 0.890147i | \(0.349398\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.4612 | − | 25.2555i | 1.13467 | − | 2.73934i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.75638 | − | 4.75638i | 0.504176 | − | 0.504176i | −0.408557 | − | 0.912733i | \(-0.633968\pi\) |
0.912733 | + | 0.408557i | \(0.133968\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.38655 | + | 3.34742i | −0.145350 | + | 0.350905i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.79754 | −0.800011 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.28856 | −0.130834 | −0.0654168 | − | 0.997858i | \(-0.520838\pi\) | ||||
−0.0654168 | + | 0.997858i | \(0.520838\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.56084 | − | 11.0109i | 0.453821 | − | 1.09562i | −0.517037 | − | 0.855963i | \(-0.672965\pi\) |
0.970858 | − | 0.239657i | \(-0.0770351\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.69287 | − | 8.69287i | 0.856533 | − | 0.856533i | −0.134394 | − | 0.990928i | \(-0.542909\pi\) |
0.990928 | + | 0.134394i | \(0.0429089\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.21290 | − | 14.9993i | 0.600624 | − | 1.45003i | −0.272316 | − | 0.962208i | \(-0.587790\pi\) |
0.872940 | − | 0.487827i | \(-0.162210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.20531 | − | 0.499254i | 0.115447 | − | 0.0478198i | −0.324212 | − | 0.945984i | \(-0.605099\pi\) |
0.439659 | + | 0.898165i | \(0.355099\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.83947 | −0.455259 | −0.227630 | − | 0.973748i | \(-0.573098\pi\) | ||||
−0.227630 | + | 0.973748i | \(0.573098\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.4546 | + | 27.6539i | 1.06815 | + | 2.57874i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.92748 | − | 7.92748i | 0.726711 | − | 0.726711i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.22771 | − | 3.22771i | −0.293428 | − | 0.293428i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1139 | + | 4.60353i | −0.994059 | + | 0.411753i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.85060i | 0.164214i | 0.996624 | + | 0.0821069i | \(0.0261649\pi\) | ||||
−0.996624 | + | 0.0821069i | \(0.973835\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.44102 | + | 5.89314i | 0.213273 | + | 0.514886i | 0.993922 | − | 0.110083i | \(-0.0351116\pi\) |
−0.780650 | + | 0.624969i | \(0.785112\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.95449 | − | 1.22379i | −0.256187 | − | 0.106116i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.65921 | − | 2.65921i | −0.227192 | − | 0.227192i | 0.584327 | − | 0.811519i | \(-0.301359\pi\) |
−0.811519 | + | 0.584327i | \(0.801359\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7567 | + | 4.86980i | 0.997193 | + | 0.413051i | 0.820767 | − | 0.571263i | \(-0.193546\pi\) |
0.176426 | + | 0.984314i | \(0.443546\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.55763i | 0.799250i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.28929i | 0.107070i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.23656 | + | 3.41170i | 0.674765 | + | 0.279497i | 0.693637 | − | 0.720325i | \(-0.256007\pi\) |
−0.0188714 | + | 0.999822i | \(0.506007\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.9992 | + | 11.9992i | 0.976478 | + | 0.976478i | 0.999730 | − | 0.0232512i | \(-0.00740175\pi\) |
−0.0232512 | + | 0.999730i | \(0.507402\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.76197 | − | 2.38669i | −0.462812 | − | 0.191703i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.47915 | + | 13.2278i | 0.437284 | + | 1.05570i | 0.976883 | + | 0.213775i | \(0.0685759\pi\) |
−0.539599 | + | 0.841922i | \(0.681424\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.2758i | 0.967471i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.3137 | + | 4.27206i | −0.807828 | + | 0.334614i | −0.748087 | − | 0.663600i | \(-0.769028\pi\) |
−0.0597412 | + | 0.998214i | \(0.519028\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.27058 | + | 6.27058i | 0.485232 | + | 0.485232i | 0.906798 | − | 0.421566i | \(-0.138519\pi\) |
−0.421566 | + | 0.906798i | \(0.638519\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.04241 | + | 5.04241i | −0.387878 | + | 0.387878i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.58864 | − | 23.1490i | −0.729011 | − | 1.75999i | −0.645866 | − | 0.763451i | \(-0.723504\pi\) |
−0.0831448 | − | 0.996537i | \(-0.526496\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.4116 | −0.938226 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.32195 | − | 2.61864i | 0.472524 | − | 0.195726i | −0.133697 | − | 0.991022i | \(-0.542685\pi\) |
0.606221 | + | 0.795296i | \(0.292685\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.02155 | + | 2.46625i | −0.0759314 | + | 0.183315i | −0.957287 | − | 0.289138i | \(-0.906631\pi\) |
0.881356 | + | 0.472453i | \(0.156631\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.08123 | − | 1.08123i | 0.0794934 | − | 0.0794934i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.3174 | − | 27.3225i | 0.827607 | − | 1.99802i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.7890 | −1.50424 | −0.752121 | − | 0.659025i | \(-0.770969\pi\) | ||||
−0.752121 | + | 0.659025i | \(0.770969\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.9444 | 1.07572 | 0.537861 | − | 0.843034i | \(-0.319233\pi\) | ||||
0.537861 | + | 0.843034i | \(0.319233\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.50419 | + | 22.9451i | −0.677145 | + | 1.63477i | 0.0920460 | + | 0.995755i | \(0.470659\pi\) |
−0.769191 | + | 0.639019i | \(0.779341\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.24926 | − | 1.24926i | 0.0885579 | − | 0.0885579i | −0.661440 | − | 0.749998i | \(-0.730054\pi\) |
0.749998 | + | 0.661440i | \(0.230054\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.202348 | + | 0.488512i | −0.0142021 | + | 0.0342868i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.16615 | − | 2.96832i | 0.500506 | − | 0.207316i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.43573 | −0.583512 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.04903 | + | 9.77521i | 0.278746 | + | 0.672953i | 0.999801 | − | 0.0199244i | \(-0.00634254\pi\) |
−0.721055 | + | 0.692878i | \(0.756343\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.6604 | + | 20.6604i | −1.40903 | + | 1.40903i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.80863 | − | 1.80863i | −0.122778 | − | 0.122778i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.7777 | + | 6.94954i | −1.12859 | + | 0.467476i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.2531i | 1.28928i | 0.764485 | + | 0.644641i | \(0.222993\pi\) | ||||
−0.764485 | + | 0.644641i | \(0.777007\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.98915 | + | 14.4591i | 0.397514 | + | 0.959684i | 0.988254 | + | 0.152822i | \(0.0488361\pi\) |
−0.590740 | + | 0.806862i | \(0.701164\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.93338 | − | 3.28612i | −0.524253 | − | 0.217153i | 0.104831 | − | 0.994490i | \(-0.466570\pi\) |
−0.629084 | + | 0.777337i | \(0.716570\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.2337 | + | 12.2337i | 0.801455 | + | 0.801455i | 0.983323 | − | 0.181868i | \(-0.0582145\pi\) |
−0.181868 | + | 0.983323i | \(0.558214\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.5073 | − | 10.1513i | −1.59868 | − | 0.662196i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3650i | 0.670459i | 0.942137 | + | 0.335229i | \(0.108814\pi\) | ||||
−0.942137 | + | 0.335229i | \(0.891186\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 14.1048i | − | 0.908572i | −0.890856 | − | 0.454286i | \(-0.849894\pi\) | ||
0.890856 | − | 0.454286i | \(-0.150106\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.0479 | + | 6.64726i | 1.02526 | + | 0.424678i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.66284 | + | 3.66284i | 0.233061 | + | 0.233061i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.92406 | − | 2.03961i | −0.310804 | − | 0.128739i | 0.221829 | − | 0.975086i | \(-0.428797\pi\) |
−0.532633 | + | 0.846346i | \(0.678797\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.3921 | + | 29.9172i | 0.779087 | + | 1.88088i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.2370i | 1.26235i | 0.775640 | + | 0.631175i | \(0.217427\pi\) | ||||
−0.775640 | + | 0.631175i | \(0.782573\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.579371 | − | 0.239983i | 0.0360004 | − | 0.0149118i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.63751 | − | 3.63751i | −0.224299 | − | 0.224299i | 0.586007 | − | 0.810306i | \(-0.300699\pi\) |
−0.810306 | + | 0.586007i | \(0.800699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.0211 | + | 11.0211i | −0.677019 | + | 0.677019i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.92241 | − | 7.05531i | −0.178182 | − | 0.430170i | 0.809403 | − | 0.587254i | \(-0.199791\pi\) |
−0.987585 | + | 0.157083i | \(0.949791\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.63925 | 0.464052 | 0.232026 | − | 0.972710i | \(-0.425465\pi\) | ||||
0.232026 | + | 0.972710i | \(0.425465\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −30.2480 | + | 12.5291i | −1.82402 | + | 0.755535i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.85371 | + | 16.5463i | −0.411799 | + | 0.994172i | 0.572855 | + | 0.819657i | \(0.305836\pi\) |
−0.984655 | + | 0.174515i | \(0.944164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.5776 | − | 13.5776i | 0.809969 | − | 0.809969i | −0.174660 | − | 0.984629i | \(-0.555883\pi\) |
0.984629 | + | 0.174660i | \(0.0558826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.17080 | + | 17.3118i | −0.426260 | + | 1.02908i | 0.554204 | + | 0.832381i | \(0.313023\pi\) |
−0.980463 | + | 0.196701i | \(0.936977\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.18112 | 0.187776 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 39.1916 | 2.30539 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.11909 | − | 2.70172i | 0.0653780 | − | 0.157836i | −0.887814 | − | 0.460203i | \(-0.847777\pi\) |
0.953192 | + | 0.302367i | \(0.0977767\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 35.7201 | − | 35.7201i | 2.07970 | − | 2.07970i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.60951 | − | 18.3710i | 0.440069 | − | 1.06242i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.0708 | + | 4.58568i | −0.638111 | + | 0.264314i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.52651 | −0.316447 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.597072 | − | 1.44146i | −0.0340767 | − | 0.0822684i | 0.905925 | − | 0.423438i | \(-0.139177\pi\) |
−0.940002 | + | 0.341170i | \(0.889177\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.3415 | − | 16.3415i | 0.926640 | − | 0.926640i | −0.0708472 | − | 0.997487i | \(-0.522570\pi\) |
0.997487 | + | 0.0708472i | \(0.0225703\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0100 | + | 11.0100i | 0.622320 | + | 0.622320i | 0.946124 | − | 0.323804i | \(-0.104962\pi\) |
−0.323804 | + | 0.946124i | \(0.604962\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.87945 | − | 2.84956i | 0.386388 | − | 0.160047i | −0.181029 | − | 0.983478i | \(-0.557943\pi\) |
0.567417 | + | 0.823430i | \(0.307943\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.39481i | 0.0780943i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.13378 | − | 14.8082i | −0.341292 | − | 0.823953i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.5741 | + | 7.69364i | 1.03030 | + | 0.426766i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.69264 | − | 7.69264i | −0.424109 | − | 0.424109i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.18235 | − | 1.31817i | −0.174918 | − | 0.0724533i | 0.293506 | − | 0.955957i | \(-0.405178\pi\) |
−0.468424 | + | 0.883504i | \(0.655178\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 31.4350i | − | 1.71748i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.5837i | 1.82942i | 0.404110 | + | 0.914710i | \(0.367581\pi\) | ||||
−0.404110 | + | 0.914710i | \(0.632419\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.23355 | − | 2.58202i | −0.337566 | − | 0.139824i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.4401 | + | 12.4401i | 0.671704 | + | 0.671704i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.5727 | − | 4.37938i | −0.567575 | − | 0.235097i | 0.0803952 | − | 0.996763i | \(-0.474382\pi\) |
−0.647970 | + | 0.761666i | \(0.724382\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.93540 | − | 4.67246i | −0.103599 | − | 0.250111i | 0.863577 | − | 0.504217i | \(-0.168219\pi\) |
−0.967176 | + | 0.254106i | \(0.918219\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 11.8710i | − | 0.631829i | −0.948788 | − | 0.315915i | \(-0.897689\pi\) | ||
0.948788 | − | 0.315915i | \(-0.102311\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.6564 | − | 9.38458i | 1.20248 | − | 0.498082i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.19895 | + | 7.19895i | 0.379946 | + | 0.379946i | 0.871083 | − | 0.491137i | \(-0.163418\pi\) |
−0.491137 | + | 0.871083i | \(0.663418\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.2021 | − | 10.2021i | 0.536955 | − | 0.536955i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.7859 | + | 38.1106i | 0.826274 | + | 1.99480i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.49636 | −0.286908 | −0.143454 | − | 0.989657i | \(-0.545821\pi\) | ||||
−0.143454 | + | 0.989657i | \(0.545821\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.90560 | + | 2.44618i | −0.306603 | + | 0.126999i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.45992 | − | 22.8383i | 0.489816 | − | 1.18252i | −0.464996 | − | 0.885313i | \(-0.653944\pi\) |
0.954813 | − | 0.297208i | \(-0.0960556\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.605634 | − | 0.605634i | 0.0311917 | − | 0.0311917i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.26808 | − | 12.7183i | 0.270603 | − | 0.653293i | −0.728906 | − | 0.684613i | \(-0.759971\pi\) |
0.999509 | + | 0.0313200i | \(0.00997110\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.651517 | 0.0332910 | 0.0166455 | − | 0.999861i | \(-0.494701\pi\) | ||||
0.0166455 | + | 0.999861i | \(0.494701\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.5174 | −1.09663 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.58251 | − | 15.8916i | 0.333747 | − | 0.805736i | −0.664542 | − | 0.747251i | \(-0.731373\pi\) |
0.998288 | − | 0.0584844i | \(-0.0186268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −43.5068 | + | 43.5068i | −2.20023 | + | 2.20023i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.0913 | + | 48.5046i | −1.01090 | + | 2.44053i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.5792 | + | 9.76681i | −1.18340 | + | 0.490182i | −0.885602 | − | 0.464446i | \(-0.846254\pi\) |
−0.297802 | + | 0.954628i | \(0.596254\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.64431 | 0.281864 | 0.140932 | − | 0.990019i | \(-0.454990\pi\) | ||||
0.140932 | + | 0.990019i | \(0.454990\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.58552 | + | 3.82777i | 0.0789802 | + | 0.190675i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.16972 | − | 1.16972i | 0.0579808 | − | 0.0579808i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.4062 | − | 15.4062i | −0.761790 | − | 0.761790i | 0.214856 | − | 0.976646i | \(-0.431072\pi\) |
−0.976646 | + | 0.214856i | \(0.931072\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.1405 | − | 7.92824i | 0.941840 | − | 0.390123i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 5.33860i | − | 0.262061i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.62264 | + | 23.2311i | 0.470097 | + | 1.13491i | 0.964120 | + | 0.265466i | \(0.0855257\pi\) |
−0.494024 | + | 0.869449i | \(0.664474\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00854 | − | 0.831963i | −0.0978901 | − | 0.0405474i | 0.333201 | − | 0.942856i | \(-0.391871\pi\) |
−0.431091 | + | 0.902308i | \(0.641871\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −43.9878 | − | 43.9878i | −2.13372 | − | 2.13372i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.09400 | − | 0.867362i | −0.101336 | − | 0.0419746i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 16.8804i | − | 0.813100i | −0.913628 | − | 0.406550i | \(-0.866732\pi\) | ||
0.913628 | − | 0.406550i | \(-0.133268\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.162457i | 0.00780716i | 0.999992 | + | 0.00390358i | \(0.00124255\pi\) | ||||
−0.999992 | + | 0.00390358i | \(0.998757\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.2145 | + | 6.71628i | 0.775646 | + | 0.321283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.853136 | + | 0.853136i | 0.0407180 | + | 0.0407180i | 0.727173 | − | 0.686455i | \(-0.240834\pi\) |
−0.686455 | + | 0.727173i | \(0.740834\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.2491 | + | 9.21590i | 1.05709 | + | 0.437860i | 0.842417 | − | 0.538826i | \(-0.181132\pi\) |
0.214672 | + | 0.976686i | \(0.431132\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.38721 | − | 22.6627i | −0.444996 | − | 1.07432i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 23.1544i | − | 1.09272i | −0.837549 | − | 0.546362i | \(-0.816012\pi\) | ||
0.837549 | − | 0.546362i | \(-0.183988\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.75266 | − | 3.21126i | 0.365059 | − | 0.151212i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.34298 | + | 9.34298i | 0.438006 | + | 0.438006i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.2233 | − | 15.2233i | 0.712114 | − | 0.712114i | −0.254863 | − | 0.966977i | \(-0.582030\pi\) |
0.966977 | + | 0.254863i | \(0.0820304\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.2190 | + | 29.4992i | 0.569093 | + | 1.37391i | 0.902320 | + | 0.431066i | \(0.141862\pi\) |
−0.333227 | + | 0.942847i | \(0.608138\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.577924 | −0.0268584 | −0.0134292 | − | 0.999910i | \(-0.504275\pi\) | ||||
−0.0134292 | + | 0.999910i | \(0.504275\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.0132 | + | 10.3608i | −1.15747 | + | 0.479441i | −0.877033 | − | 0.480431i | \(-0.840480\pi\) |
−0.280440 | + | 0.959872i | \(0.590480\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.93358 | − | 11.9107i | 0.227812 | − | 0.549986i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.3514 | + | 22.3514i | −1.02772 | + | 1.02772i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.79053 | + | 16.3938i | −0.311571 | + | 0.752199i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.6865 | 0.945188 | 0.472594 | − | 0.881280i | \(-0.343318\pi\) | ||||
0.472594 | + | 0.881280i | \(0.343318\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.01580 | −0.0463164 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.79825 | + | 4.34136i | −0.0816543 | + | 0.197131i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.8979 | − | 17.8979i | 0.811031 | − | 0.811031i | −0.173757 | − | 0.984788i | \(-0.555591\pi\) |
0.984788 | + | 0.173757i | \(0.0555909\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.919341 | + | 2.21949i | −0.0414893 | + | 0.100164i | −0.943266 | − | 0.332039i | \(-0.892264\pi\) |
0.901776 | + | 0.432203i | \(0.142264\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.44848 | + | 1.01419i | −0.110274 | + | 0.0456769i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.0574 | 0.451135 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.65228 | − | 20.8884i | −0.387329 | − | 0.935095i | −0.990504 | − | 0.137486i | \(-0.956098\pi\) |
0.603175 | − | 0.797609i | \(-0.293902\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.91458 | − | 9.91458i | 0.442069 | − | 0.442069i | −0.450638 | − | 0.892707i | \(-0.648803\pi\) |
0.892707 | + | 0.450638i | \(0.148803\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.7323 | − | 30.7323i | −1.36757 | − | 1.36757i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.70757 | + | 3.60679i | −0.385956 | + | 0.159868i | −0.567220 | − | 0.823566i | \(-0.691981\pi\) |
0.181264 | + | 0.983434i | \(0.441981\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.9177i | 0.748393i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.1563 | − | 41.4189i | −0.755995 | − | 1.82513i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.5131 | − | 10.9821i | −1.16605 | − | 0.482992i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.843541 | − | 0.843541i | −0.0369562 | − | 0.0369562i | 0.688387 | − | 0.725343i | \(-0.258319\pi\) |
−0.725343 | + | 0.688387i | \(0.758319\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.0207812 | − | 0.00860784i | −0.000908697 | − | 0.000376395i | 0.382229 | − | 0.924068i | \(-0.375157\pi\) |
−0.383138 | + | 0.923691i | \(0.625157\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 12.8199i | − | 0.558445i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 44.3710i | − | 1.92917i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.76060 | − | 1.97190i | −0.206204 | − | 0.0854126i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −41.8644 | − | 41.8644i | −1.80996 | − | 1.80996i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.3613 | + | 7.19130i | 0.747805 | + | 0.309751i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.78856 | + | 4.31796i | 0.0768961 | + | 0.185644i | 0.957653 | − | 0.287925i | \(-0.0929655\pi\) |
−0.880757 | + | 0.473569i | \(0.842965\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4.75759i | − | 0.203793i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.9790 | + | 11.1751i | −1.15354 | + | 0.477811i | −0.875718 | − | 0.482823i | \(-0.839612\pi\) |
−0.277819 | + | 0.960633i | \(0.589612\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.534543 | + | 0.534543i | 0.0227723 | + | 0.0227723i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.2252 | + | 15.2252i | −0.647440 | + | 0.647440i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.15147 | + | 5.19412i | 0.0911609 | + | 0.220082i | 0.962883 | − | 0.269918i | \(-0.0869967\pi\) |
−0.871722 | + | 0.490000i | \(0.836997\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.4102 | 0.820964 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.9450 | − | 6.60465i | 0.672003 | − | 0.278353i | −0.0204766 | − | 0.999790i | \(-0.506518\pi\) |
0.692479 | + | 0.721438i | \(0.256518\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.75372 | + | 16.3049i | −0.284131 | + | 0.685953i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.67703 | − | 1.67703i | 0.0703046 | − | 0.0703046i | −0.671080 | − | 0.741385i | \(-0.734169\pi\) |
0.741385 | + | 0.671080i | \(0.234169\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.41843 | − | 5.83861i | 0.101208 | − | 0.244338i | −0.865162 | − | 0.501492i | \(-0.832785\pi\) |
0.966371 | + | 0.257154i | \(0.0827847\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 68.1158 | 2.84063 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.8983 | 0.453703 | 0.226851 | − | 0.973929i | \(-0.427157\pi\) | ||||
0.226851 | + | 0.973929i | \(0.427157\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.837869 | − | 2.02280i | 0.0347607 | − | 0.0839197i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.9231 | + | 11.9231i | −0.493804 | + | 0.493804i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0840 | − | 29.1734i | 0.498760 | − | 1.20411i | −0.451392 | − | 0.892326i | \(-0.649072\pi\) |
0.950152 | − | 0.311788i | \(-0.100928\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.37846 | + | 1.39940i | −0.139207 | + | 0.0576614i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.8516 | −1.06160 | −0.530800 | − | 0.847497i | \(-0.678108\pi\) | ||||
−0.530800 | + | 0.847497i | \(0.678108\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.6457 | − | 37.7721i | −0.641411 | − | 1.54850i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.76404 | + | 7.76404i | −0.317230 | + | 0.317230i | −0.847702 | − | 0.530472i | \(-0.822015\pi\) |
0.530472 | + | 0.847702i | \(0.322015\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.7695 | + | 27.7695i | 1.13274 | + | 1.13274i | 0.989720 | + | 0.143020i | \(0.0456812\pi\) |
0.143020 | + | 0.989720i | \(0.454319\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.3790 | + | 6.37021i | −0.625247 | + | 0.258986i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.83755i | 0.277527i | 0.990326 | + | 0.138764i | \(0.0443129\pi\) | ||||
−0.990326 | + | 0.138764i | \(0.955687\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.74366 | + | 16.2806i | 0.272819 | + | 0.658644i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.88592 | + | 0.781173i | 0.0761716 | + | 0.0315513i | 0.420444 | − | 0.907319i | \(-0.361874\pi\) |
−0.344272 | + | 0.938870i | \(0.611874\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.5582 | + | 16.5582i | 0.666610 | + | 0.666610i | 0.956930 | − | 0.290320i | \(-0.0937617\pi\) |
−0.290320 | + | 0.956930i | \(0.593762\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.0627 | − | 14.1093i | −1.36910 | − | 0.567099i | −0.427554 | − | 0.903990i | \(-0.640625\pi\) |
−0.941544 | + | 0.336891i | \(0.890625\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 10.0602i | − | 0.403053i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.37526i | 0.0950104i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.90387 | + | 1.20282i | 0.115785 | + | 0.0479597i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.8332 | + | 18.8332i | 0.749737 | + | 0.749737i | 0.974430 | − | 0.224693i | \(-0.0721379\pi\) |
−0.224693 | + | 0.974430i | \(0.572138\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.23494 | + | 2.58260i | 0.247426 | + | 0.102487i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.41589 | − | 10.6609i | −0.174964 | − | 0.422400i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 34.0636i | − | 1.34543i | −0.739900 | − | 0.672716i | \(-0.765127\pi\) | ||
0.739900 | − | 0.672716i | \(-0.234873\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.14924 | + | 3.37552i | −0.321374 | + | 0.133118i | −0.537538 | − | 0.843239i | \(-0.680646\pi\) |
0.216164 | + | 0.976357i | \(0.430646\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.9458 | − | 15.9458i | −0.626894 | − | 0.626894i | 0.320391 | − | 0.947285i | \(-0.396186\pi\) |
−0.947285 | + | 0.320391i | \(0.896186\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.6436 | − | 38.6436i | 1.51689 | − | 1.51689i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.3560 | − | 25.0017i | −0.405263 | − | 0.978391i | −0.986367 | − | 0.164562i | \(-0.947379\pi\) |
0.581104 | − | 0.813829i | \(-0.302621\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.2614 | 0.908900 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.976716 | − | 0.404569i | 0.0380475 | − | 0.0157598i | −0.363579 | − | 0.931564i | \(-0.618445\pi\) |
0.401626 | + | 0.915804i | \(0.368445\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.6003 | + | 25.5914i | −0.412304 | + | 0.995389i | 0.572214 | + | 0.820104i | \(0.306085\pi\) |
−0.984518 | + | 0.175285i | \(0.943915\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.24627 | + | 8.24627i | −0.319777 | + | 0.319777i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.11051 | − | 2.68100i | 0.0429990 | − | 0.103809i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.97883 | −0.230810 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.3400 | −0.668409 | −0.334205 | − | 0.942501i | \(-0.608468\pi\) | ||||
−0.334205 | + | 0.942501i | \(0.608468\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.10411 | − | 2.66556i | 0.0424344 | − | 0.102446i | −0.901241 | − | 0.433318i | \(-0.857343\pi\) |
0.943676 | + | 0.330872i | \(0.107343\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.36271 | + | 1.36271i | −0.0522962 | + | 0.0522962i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.51934 | + | 22.9817i | −0.364247 | + | 0.879371i | 0.630422 | + | 0.776253i | \(0.282882\pi\) |
−0.994669 | + | 0.103118i | \(0.967118\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.6703 | + | 5.24823i | −0.484109 | + | 0.200525i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.3542 | 0.394462 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.56212 | − | 20.6708i | −0.325719 | − | 0.786354i | −0.998901 | − | 0.0468774i | \(-0.985073\pi\) |
0.673182 | − | 0.739477i | \(-0.264927\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.8142 | − | 32.8142i | 1.24471 | − | 1.24471i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.2742 | + | 11.2742i | 0.427041 | + | 0.427041i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.4517 | − | 16.7556i | 1.52784 | − | 0.632852i | 0.548695 | − | 0.836022i | \(-0.315125\pi\) |
0.979143 | + | 0.203171i | \(0.0651247\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.896560i | − | 0.0338144i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.82119 | − | 16.4678i | −0.256537 | − | 0.619335i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.2624 | − | 6.73611i | −0.610748 | − | 0.252980i | 0.0558005 | − | 0.998442i | \(-0.482229\pi\) |
−0.666548 | + | 0.745462i | \(0.732229\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.92594 | + | 9.92594i | 0.371730 | + | 0.371730i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.2011 | + | 13.3381i | 1.20425 | + | 0.498818i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.5642i | 0.878796i | 0.898292 | + | 0.439398i | \(0.144808\pi\) | ||||
−0.898292 | + | 0.439398i | \(0.855192\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 18.3862i | − | 0.684739i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.71064 | + | 1.12278i | 0.100671 | + | 0.0416991i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.5208 | + | 16.5208i | 0.612724 | + | 0.612724i | 0.943655 | − | 0.330931i | \(-0.107363\pi\) |
−0.330931 | + | 0.943655i | \(0.607363\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −55.4882 | − | 22.9840i | −2.05230 | − | 0.850092i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.74219 | − | 21.1055i | −0.322900 | − | 0.779550i | −0.999083 | − | 0.0428159i | \(-0.986367\pi\) |
0.676183 | − | 0.736734i | \(-0.263633\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 34.0077i | − | 1.25269i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.5366 | + | 17.2050i | −1.52795 | + | 0.632897i | −0.979165 | − | 0.203066i | \(-0.934909\pi\) |
−0.548785 | + | 0.835964i | \(0.684909\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.3232 | − | 19.3232i | −0.708900 | − | 0.708900i | 0.257404 | − | 0.966304i | \(-0.417133\pi\) |
−0.966304 | + | 0.257404i | \(0.917133\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.9890 | − | 22.9890i | 0.842253 | − | 0.842253i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.29200 | − | 22.4329i | −0.339522 | − | 0.819679i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.32371 | 0.340227 | 0.170114 | − | 0.985424i | \(-0.445587\pi\) | ||||
0.170114 | + | 0.985424i | \(0.445587\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 57.1724 | − | 23.6816i | 2.08072 | − | 0.861861i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.71720 | + | 23.4594i | −0.353178 | + | 0.852647i | 0.643046 | + | 0.765827i | \(0.277670\pi\) |
−0.996224 | + | 0.0868193i | \(0.972330\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.9092 | − | 21.9092i | 0.794207 | − | 0.794207i | −0.187968 | − | 0.982175i | \(-0.560190\pi\) |
0.982175 | + | 0.187968i | \(0.0601902\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.746683 | − | 1.80265i | 0.0270317 | − | 0.0652604i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −33.5585 | −1.21173 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.9106 | −0.429508 | −0.214754 | − | 0.976668i | \(-0.568895\pi\) | ||||
−0.214754 | + | 0.976668i | \(0.568895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.39696 | + | 8.20098i | −0.122180 | + | 0.294969i | −0.973122 | − | 0.230291i | \(-0.926032\pi\) |
0.850942 | + | 0.525260i | \(0.176032\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.0357 | + | 10.0357i | −0.360492 | + | 0.360492i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.74044 | − | 4.20178i | 0.0623576 | − | 0.150545i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.5107 | − | 10.1527i | 0.877061 | − | 0.363290i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 52.2130 | 1.86356 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.32430 | − | 15.2682i | −0.225437 | − | 0.544253i | 0.770175 | − | 0.637833i | \(-0.220169\pi\) |
−0.995612 | + | 0.0935798i | \(0.970169\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.11797 | + | 5.11797i | −0.181974 | + | 0.181974i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.59604 | + | 2.59604i | 0.0921881 | + | 0.0921881i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.4382 | − | 5.56628i | 0.476005 | − | 0.197168i | −0.131765 | − | 0.991281i | \(-0.542064\pi\) |
0.607770 | + | 0.794113i | \(0.292064\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 54.5269i | − | 1.92902i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.0779 | + | 41.2298i | 0.602667 | + | 1.45497i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 41.3591 | + | 17.1315i | 1.45772 | + | 0.603807i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.2173 | + | 17.2173i | 0.605330 | + | 0.605330i | 0.941722 | − | 0.336392i | \(-0.109207\pi\) |
−0.336392 | + | 0.941722i | \(0.609207\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.51193 | + | 3.11154i | 0.263779 | + | 0.109261i | 0.510654 | − | 0.859787i | \(-0.329403\pi\) |
−0.246874 | + | 0.969048i | \(0.579403\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40.7101i | 1.42601i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.1318i | 0.599365i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.2833 | − | 10.8869i | −0.917293 | − | 0.379955i | −0.126449 | − | 0.991973i | \(-0.540358\pi\) |
−0.790844 | + | 0.612018i | \(0.790358\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.913996 | + | 0.913996i | 0.0318599 | + | 0.0318599i | 0.722857 | − | 0.690997i | \(-0.242828\pi\) |
−0.690997 | + | 0.722857i | \(0.742828\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.8973 | − | 8.65593i | −0.726669 | − | 0.300996i | −0.0114866 | − | 0.999934i | \(-0.503656\pi\) |
−0.715182 | + | 0.698938i | \(0.753656\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.859841 | + | 2.07584i | 0.0298635 | + | 0.0720969i | 0.938108 | − | 0.346344i | \(-0.112577\pi\) |
−0.908244 | + | 0.418440i | \(0.862577\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.7054i | 1.23712i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.8774 | − | 12.3756i | 1.03395 | − | 0.428277i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.5340 | + | 29.5340i | 1.01963 | + | 1.01963i | 0.999803 | + | 0.0198249i | \(0.00631087\pi\) |
0.0198249 | + | 0.999803i | \(0.493689\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.4177 | + | 20.4177i | −0.704059 | + | 0.704059i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.95171 | + | 24.0256i | 0.342349 | + | 0.826504i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.82690 | −0.234575 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.17964 | + | 1.31705i | −0.108997 | + | 0.0451479i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.7113 | + | 33.1021i | −0.469467 | + | 1.13339i | 0.494930 | + | 0.868933i | \(0.335194\pi\) |
−0.964397 | + | 0.264460i | \(0.914806\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.6839 | − | 10.6839i | 0.364955 | − | 0.364955i | −0.500679 | − | 0.865633i | \(-0.666916\pi\) |
0.865633 | + | 0.500679i | \(0.166916\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.9567 | − | 38.5229i | 0.544435 | − | 1.31438i | −0.377130 | − | 0.926160i | \(-0.623089\pi\) |
0.921566 | − | 0.388223i | \(-0.126911\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −53.2679 | −1.81326 | −0.906630 | − | 0.421927i | \(-0.861354\pi\) | ||||
−0.906630 | + | 0.421927i | \(0.861354\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −91.3740 | −3.10681 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.7356 | + | 52.4744i | −0.737330 | + | 1.78007i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.7664 | + | 14.7664i | −0.500339 | + | 0.500339i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.88503 | + | 16.6219i | −0.232757 | + | 0.561924i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.8915 | − | 14.4525i | 1.17820 | − | 0.488027i | 0.294306 | − | 0.955711i | \(-0.404911\pi\) |
0.883896 | + | 0.467684i | \(0.154911\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.2340 | −1.65874 | −0.829368 | − | 0.558703i | \(-0.811299\pi\) | ||||
−0.829368 | + | 0.558703i | \(0.811299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.3303 | + | 37.0107i | 0.515907 | + | 1.24551i | 0.940398 | + | 0.340077i | \(0.110453\pi\) |
−0.424491 | + | 0.905432i | \(0.639547\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.81816 | − | 9.81816i | 0.329661 | − | 0.329661i | −0.522796 | − | 0.852458i | \(-0.675111\pi\) |
0.852458 | + | 0.522796i | \(0.175111\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.95709 | + | 1.95709i | 0.0656388 | + | 0.0656388i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.3696 | + | 5.95207i | −0.480859 | + | 0.199178i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 24.9540i | − | 0.834121i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.231385 | + | 0.558612i | 0.00771712 | + | 0.0186308i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.5995 | − | 12.2605i | −0.986104 | − | 0.408457i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.88353 | + | 6.88353i | 0.228816 | + | 0.228816i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.54772 | + | 1.46951i | 0.117800 | + | 0.0487944i | 0.440805 | − | 0.897603i | \(-0.354693\pi\) |
−0.323005 | + | 0.946397i | \(0.604693\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.8756i | 1.81811i | 0.416678 | + | 0.909054i | \(0.363194\pi\) | ||||
−0.416678 | + | 0.909054i | \(0.636806\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 5.77553i | − | 0.191142i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.81377 | + | 3.65078i | 0.291056 | + | 0.120559i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.01238 | − | 1.01238i | −0.0333953 | − | 0.0333953i | 0.690212 | − | 0.723607i | \(-0.257517\pi\) |
−0.723607 | + | 0.690212i | \(0.757517\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.0510 | − | 6.23433i | −0.495410 | − | 0.205206i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.33161 | − | 3.21480i | −0.0437831 | − | 0.105702i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.1188i | 1.41468i | 0.706873 | + | 0.707341i | \(0.250105\pi\) | ||||
−0.706873 | + | 0.707341i | \(0.749895\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.40948 | − | 3.89754i | 0.308383 | − | 0.127737i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −76.2598 | − | 76.2598i | −2.49396 | − | 2.49396i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.1126 | + | 38.1126i | −1.24508 | + | 1.24508i | −0.287218 | + | 0.957865i | \(0.592730\pi\) |
−0.957865 | + | 0.287218i | \(0.907270\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.30761 | + | 15.2279i | 0.205622 | + | 0.496416i | 0.992725 | − | 0.120406i | \(-0.0384198\pi\) |
−0.787103 | + | 0.616822i | \(0.788420\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.4583 | −0.568521 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.4534 | + | 5.15836i | −0.404681 | + | 0.167624i | −0.575733 | − | 0.817638i | \(-0.695283\pi\) |
0.171052 | + | 0.985262i | \(0.445283\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.4869 | − | 25.3175i | 0.340418 | − | 0.821842i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.0665 | + | 23.0665i | −0.747197 | + | 0.747197i | −0.973952 | − | 0.226755i | \(-0.927188\pi\) |
0.226755 | + | 0.973952i | \(0.427188\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.0121 | + | 70.0414i | −0.938809 | + | 2.26649i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.62448 | −0.181624 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0752 | 0.905651 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.8556 | − | 50.3499i | 0.671366 | − | 1.62082i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.28781 | + | 5.28781i | −0.170045 | + | 0.170045i | −0.786999 | − | 0.616954i | \(-0.788366\pi\) |
0.616954 | + | 0.786999i | \(0.288366\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.8434 | + | 35.8352i | −0.476348 | + | 1.15001i | 0.484962 | + | 0.874535i | \(0.338833\pi\) |
−0.961310 | + | 0.275470i | \(0.911167\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.5833 | − | 7.28326i | 0.563696 | − | 0.233491i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.4029 | −1.51655 | −0.758277 | − | 0.651932i | \(-0.773959\pi\) | ||||
−0.758277 | + | 0.651932i | \(0.773959\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.1555 | − | 24.5176i | −0.324571 | − | 0.783584i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.5390 | + | 25.5390i | −0.814567 | + | 0.814567i | −0.985315 | − | 0.170748i | \(-0.945382\pi\) |
0.170748 | + | 0.985315i | \(0.445382\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 64.0421 | + | 64.0421i | 2.04055 | + | 2.04055i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 60.7577 | − | 25.1667i | 1.93198 | − | 0.800253i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 6.52875i | − | 0.207392i | −0.994609 | − | 0.103696i | \(-0.966933\pi\) | ||
0.994609 | − | 0.103696i | \(-0.0330670\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.46555 | − | 5.95236i | −0.0781631 | − | 0.188702i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0113 | + | 4.56102i | 0.348731 | + | 0.144449i | 0.550172 | − | 0.835052i | \(-0.314562\pi\) |
−0.201441 | + | 0.979501i | \(0.564562\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1152.2.w.a.143.8 | 32 | ||
3.2 | odd | 2 | 1152.2.w.b.143.1 | 32 | |||
4.3 | odd | 2 | 288.2.w.b.251.7 | yes | 32 | ||
12.11 | even | 2 | 288.2.w.a.251.2 | yes | 32 | ||
32.13 | even | 8 | 288.2.w.a.179.2 | ✓ | 32 | ||
32.19 | odd | 8 | 1152.2.w.b.1007.1 | 32 | |||
96.77 | odd | 8 | 288.2.w.b.179.7 | yes | 32 | ||
96.83 | even | 8 | inner | 1152.2.w.a.1007.8 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.w.a.179.2 | ✓ | 32 | 32.13 | even | 8 | ||
288.2.w.a.251.2 | yes | 32 | 12.11 | even | 2 | ||
288.2.w.b.179.7 | yes | 32 | 96.77 | odd | 8 | ||
288.2.w.b.251.7 | yes | 32 | 4.3 | odd | 2 | ||
1152.2.w.a.143.8 | 32 | 1.1 | even | 1 | trivial | ||
1152.2.w.a.1007.8 | 32 | 96.83 | even | 8 | inner | ||
1152.2.w.b.143.1 | 32 | 3.2 | odd | 2 | |||
1152.2.w.b.1007.1 | 32 | 32.19 | odd | 8 |