Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1064,2,Mod(305,1064)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1064, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1064.305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1064 = 2^{3} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1064.q (of order \(3\), degree \(2\), 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: | \(8.49608277506\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 305.2 | ||
Root | \(-1.19508 + 2.06994i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1064.305 |
Dual form | 1064.2.q.n.457.2 |
$q$-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 \(\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(799\) | \(913\) | \(1009\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.19508 | + | 2.06994i | −0.689981 | + | 1.19508i | 0.281863 | + | 0.959455i | \(0.409048\pi\) |
−0.971844 | + | 0.235627i | \(0.924286\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.62589 | − | 2.81613i | −0.727122 | − | 1.25941i | −0.958095 | − | 0.286452i | \(-0.907524\pi\) |
0.230973 | − | 0.972960i | \(-0.425809\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.05789 | + | 1.66286i | 0.777809 | + | 0.628501i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.35644 | − | 2.34943i | −0.452147 | − | 0.783142i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.201447 | − | 0.348916i | 0.0607385 | − | 0.105202i | −0.834057 | − | 0.551678i | \(-0.813988\pi\) |
0.894796 | + | 0.446476i | \(0.147321\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.63029 | −0.452160 | −0.226080 | − | 0.974109i | \(-0.572591\pi\) | ||||
−0.226080 | + | 0.974109i | \(0.572591\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.77230 | 2.00680 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.21778 | + | 3.84130i | −0.537890 | + | 0.931652i | 0.461128 | + | 0.887334i | \(0.347445\pi\) |
−0.999017 | + | 0.0443186i | \(0.985888\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | − | 0.866025i | −0.114708 | − | 0.198680i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.90137 | + | 2.27246i | −1.28778 | + | 0.495892i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.418614 | − | 0.725061i | −0.0872870 | − | 0.151186i | 0.819076 | − | 0.573684i | \(-0.194486\pi\) |
−0.906363 | + | 0.422499i | \(0.861153\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.78706 | + | 4.82733i | −0.557412 | + | 0.965466i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.686255 | −0.132070 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.33215 | −0.990156 | −0.495078 | − | 0.868849i | \(-0.664860\pi\) | ||||
−0.495078 | + | 0.868849i | \(0.664860\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.58020 | + | 2.73699i | −0.283813 | + | 0.491578i | −0.972321 | − | 0.233651i | \(-0.924933\pi\) |
0.688508 | + | 0.725229i | \(0.258266\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.481491 | + | 0.833966i | 0.0838168 | + | 0.145175i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.33692 | − | 8.49891i | 0.225980 | − | 1.43658i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.71311 | − | 9.89540i | −0.939230 | − | 1.62679i | −0.766912 | − | 0.641753i | \(-0.778208\pi\) |
−0.172318 | − | 0.985041i | \(-0.555126\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.94832 | − | 3.37460i | 0.311982 | − | 0.540368i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.93761 | 0.295483 | 0.147742 | − | 0.989026i | \(-0.452800\pi\) | ||||
0.147742 | + | 0.989026i | \(0.452800\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.41086 | + | 7.63983i | −0.657532 | + | 1.13888i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.32419 | − | 10.9538i | −0.922479 | − | 1.59778i | −0.795567 | − | 0.605866i | \(-0.792827\pi\) |
−0.126912 | − | 0.991914i | \(-0.540506\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.46981 | + | 6.84395i | 0.209973 | + | 0.977707i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.30085 | − | 9.18134i | −0.742267 | − | 1.28564i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.75320 | − | 9.96483i | 0.790263 | − | 1.36878i | −0.135541 | − | 0.990772i | \(-0.543277\pi\) |
0.925804 | − | 0.378004i | \(-0.123389\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.31012 | −0.176657 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.39016 | 0.316585 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.58481 | + | 4.47702i | −0.336514 | + | 0.582859i | −0.983774 | − | 0.179410i | \(-0.942581\pi\) |
0.647261 | + | 0.762269i | \(0.275914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0632036 | − | 0.109472i | −0.00809239 | − | 0.0140164i | 0.861951 | − | 0.506992i | \(-0.169243\pi\) |
−0.870043 | + | 0.492975i | \(0.835909\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.11535 | − | 7.09043i | 0.140521 | − | 0.893310i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.65067 | + | 4.59110i | 0.328775 | + | 0.569455i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.23638 | − | 2.14148i | 0.151048 | − | 0.261623i | −0.780565 | − | 0.625075i | \(-0.785069\pi\) |
0.931613 | + | 0.363452i | \(0.118402\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00111 | 0.240906 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.17338 | −0.257932 | −0.128966 | − | 0.991649i | \(-0.541166\pi\) | ||||
−0.128966 | + | 0.991649i | \(0.541166\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.25982 | + | 10.8423i | −0.732657 | + | 1.26900i | 0.223087 | + | 0.974798i | \(0.428387\pi\) |
−0.955744 | + | 0.294200i | \(0.904947\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.66153 | − | 11.5381i | −0.769207 | − | 1.33231i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.994752 | − | 0.383053i | 0.113363 | − | 0.0436529i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.20013 | + | 3.81073i | 0.247533 | + | 0.428740i | 0.962841 | − | 0.270069i | \(-0.0870467\pi\) |
−0.715307 | + | 0.698810i | \(0.753713\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.88946 | − | 8.46879i | 0.543273 | − | 0.940976i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.87386 | −0.205683 | −0.102841 | − | 0.994698i | \(-0.532793\pi\) | ||||
−0.102841 | + | 0.994698i | \(0.532793\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.4235 | 1.56445 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.37236 | − | 11.0372i | 0.683189 | − | 1.18332i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.29262 | − | 12.6312i | −0.773016 | − | 1.33890i | −0.935903 | − | 0.352259i | \(-0.885414\pi\) |
0.162886 | − | 0.986645i | \(-0.447920\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.35495 | − | 2.71093i | −0.351694 | − | 0.284183i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.77694 | − | 6.54186i | −0.391651 | − | 0.678359i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.62589 | + | 2.81613i | −0.166813 | + | 0.288929i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.50694 | −0.762215 | −0.381107 | − | 0.924531i | \(-0.624457\pi\) | ||||
−0.381107 | + | 0.924531i | \(0.624457\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.09300 | −0.109851 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.60230 | − | 2.77526i | 0.159435 | − | 0.276149i | −0.775230 | − | 0.631679i | \(-0.782366\pi\) |
0.934665 | + | 0.355530i | \(0.115700\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.91848 | − | 5.05495i | −0.287566 | − | 0.498079i | 0.685662 | − | 0.727920i | \(-0.259513\pi\) |
−0.973228 | + | 0.229841i | \(0.926179\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 15.9945 | + | 12.9242i | 1.56091 | + | 1.26128i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.67630 | − | 13.2957i | −0.742096 | − | 1.28535i | −0.951539 | − | 0.307527i | \(-0.900498\pi\) |
0.209443 | − | 0.977821i | \(-0.432835\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.96190 | + | 10.3263i | −0.571046 | + | 0.989081i | 0.425413 | + | 0.904999i | \(0.360129\pi\) |
−0.996459 | + | 0.0840813i | \(0.973204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 27.3106 | 2.59220 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.0112 | −1.78842 | −0.894210 | − | 0.447648i | \(-0.852262\pi\) | ||||
−0.894210 | + | 0.447648i | \(0.852262\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.36124 | + | 2.35774i | −0.126937 | + | 0.219861i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.21139 | + | 3.83023i | 0.204443 | + | 0.354105i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.9515 | + | 4.21712i | −1.00392 | + | 0.386583i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.41884 | + | 9.38570i | 0.492622 | + | 0.853246i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.39016 | − | 4.13989i | 0.215514 | − | 0.373281i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.86692 | 0.166982 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.16086 | 0.635424 | 0.317712 | − | 0.948187i | \(-0.397086\pi\) | ||||
0.317712 | + | 0.948187i | \(0.397086\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.31561 | + | 4.01075i | −0.203878 | + | 0.353127i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.980160 | + | 1.69769i | 0.0856370 | + | 0.148328i | 0.905662 | − | 0.423999i | \(-0.139374\pi\) |
−0.820026 | + | 0.572327i | \(0.806041\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.411132 | − | 2.61361i | 0.0356497 | − | 0.226629i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.11578 | + | 1.93258i | 0.0960308 | + | 0.166330i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.05386 | − | 13.9497i | 0.688088 | − | 1.19180i | −0.284368 | − | 0.958715i | \(-0.591784\pi\) |
0.972456 | − | 0.233088i | \(-0.0748830\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.58462 | −0.219224 | −0.109612 | − | 0.993974i | \(-0.534961\pi\) | ||||
−0.109612 | + | 0.993974i | \(0.534961\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 30.2317 | 2.54597 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.328416 | + | 0.568832i | −0.0274635 | + | 0.0475682i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.66951 | + | 15.0160i | 0.719964 | + | 1.24701i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.9231 | − | 5.13666i | −1.31332 | − | 0.423664i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.84038 | + | 8.38379i | 0.396540 | + | 0.686827i | 0.993296 | − | 0.115595i | \(-0.0368776\pi\) |
−0.596757 | + | 0.802422i | \(0.703544\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.95220 | + | 3.38131i | −0.158868 | + | 0.275167i | −0.934461 | − | 0.356066i | \(-0.884118\pi\) |
0.775593 | + | 0.631233i | \(0.217451\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.0331 | 0.972822 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.2770 | 0.825466 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.51743 | + | 13.0206i | −0.599956 | + | 1.03915i | 0.392871 | + | 0.919594i | \(0.371482\pi\) |
−0.992827 | + | 0.119561i | \(0.961851\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.7511 | + | 23.8176i | 1.09053 | + | 1.88886i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.344211 | − | 2.18819i | 0.0271277 | − | 0.172453i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.55353 | + | 14.8151i | 0.669964 | + | 1.16041i | 0.977914 | + | 0.209009i | \(0.0670238\pi\) |
−0.307950 | + | 0.951403i | \(0.599643\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.56570 | − | 2.71188i | 0.121890 | − | 0.211120i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.06642 | 0.701580 | 0.350790 | − | 0.936454i | \(-0.385913\pi\) | ||||
0.350790 | + | 0.936454i | \(0.385913\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.3422 | −0.795552 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.35644 | + | 2.34943i | −0.103730 | + | 0.179665i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.64278 | − | 9.77358i | −0.429013 | − | 0.743072i | 0.567773 | − | 0.823185i | \(-0.307805\pi\) |
−0.996786 | + | 0.0801135i | \(0.974472\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.7626 | + | 5.29962i | −1.04036 | + | 0.400614i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.17812 | − | 10.7008i | −0.464376 | − | 0.804323i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.7296 | + | 20.3162i | −0.876709 | + | 1.51850i | −0.0217770 | + | 0.999763i | \(0.506932\pi\) |
−0.854932 | + | 0.518741i | \(0.826401\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.24897 | −0.390153 | −0.195076 | − | 0.980788i | \(-0.562495\pi\) | ||||
−0.195076 | + | 0.980788i | \(0.562495\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.302134 | 0.0223344 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.5778 | + | 32.1777i | −1.36587 | + | 2.36575i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.893527 | + | 1.54763i | 0.0653412 | + | 0.113174i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.41224 | − | 1.14114i | −0.102725 | − | 0.0830060i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.71067 | + | 16.8194i | 0.702640 | + | 1.21701i | 0.967537 | + | 0.252731i | \(0.0813287\pi\) |
−0.264897 | + | 0.964277i | \(0.585338\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.94528 | − | 5.10137i | 0.212006 | − | 0.367205i | −0.740336 | − | 0.672237i | \(-0.765334\pi\) |
0.952342 | + | 0.305032i | \(0.0986671\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.6711 | −0.907394 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.994596 | 0.0708620 | 0.0354310 | − | 0.999372i | \(-0.488720\pi\) | ||||
0.0354310 | + | 0.999372i | \(0.488720\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.298176 | + | 0.516455i | −0.0211371 | + | 0.0366106i | −0.876400 | − | 0.481583i | \(-0.840062\pi\) |
0.855263 | + | 0.518194i | \(0.173395\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.95515 | + | 5.11848i | 0.208441 | + | 0.361030i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.9730 | − | 8.86661i | −0.770152 | − | 0.622314i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.25179 | + | 5.63226i | 0.227115 | + | 0.393374i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.13565 | + | 1.96701i | −0.0789332 | + | 0.136716i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.402893 | −0.0278687 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.2877 | 0.845921 | 0.422960 | − | 0.906148i | \(-0.360991\pi\) | ||||
0.422960 | + | 0.906148i | \(0.360991\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.59736 | − | 4.49876i | 0.177968 | − | 0.308250i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.15035 | − | 5.45657i | −0.214852 | − | 0.372135i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.80311 | + | 3.00477i | −0.529709 | + | 0.203977i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.9620 | − | 25.9149i | −1.01104 | − | 1.75117i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.61561 | − | 6.26242i | 0.243212 | − | 0.421256i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.41919 | −0.630755 | −0.315378 | − | 0.948966i | \(-0.602131\pi\) | ||||
−0.315378 | + | 0.948966i | \(0.602131\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.1219 | 1.00813 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.61222 | + | 6.25656i | −0.239752 | + | 0.415262i | −0.960643 | − | 0.277786i | \(-0.910399\pi\) |
0.720891 | + | 0.693048i | \(0.243733\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.77916 | − | 4.81365i | −0.183652 | − | 0.318095i | 0.759469 | − | 0.650543i | \(-0.225459\pi\) |
−0.943121 | + | 0.332448i | \(0.892125\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.395913 | + | 2.51686i | −0.0260491 | + | 0.165597i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.76784 | − | 9.99020i | −0.377864 | − | 0.654480i | 0.612887 | − | 0.790170i | \(-0.290008\pi\) |
−0.990751 | + | 0.135691i | \(0.956675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.5649 | + | 35.6195i | −1.34151 | + | 2.32356i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.5173 | −0.683173 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.9484 | 1.87252 | 0.936259 | − | 0.351309i | \(-0.114263\pi\) | ||||
0.936259 | + | 0.351309i | \(0.114263\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.1396 | + | 19.2944i | −0.717566 | + | 1.24286i | 0.244396 | + | 0.969676i | \(0.421410\pi\) |
−0.961962 | + | 0.273185i | \(0.911923\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.6572 | + | 18.4588i | 0.683661 | + | 1.18414i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.8837 | − | 15.2667i | 1.07866 | − | 0.975355i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.815143 | + | 1.41187i | 0.0518663 | + | 0.0898350i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.23942 | − | 3.87878i | 0.141917 | − | 0.245808i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.67790 | −0.421505 | −0.210753 | − | 0.977539i | \(-0.567591\pi\) | ||||
−0.210753 | + | 0.977539i | \(0.567591\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.337314 | −0.0212067 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.2372 | + | 29.8558i | −1.07944 | + | 1.86964i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.9189 | + | 24.1082i | 0.868236 | + | 1.50383i | 0.863798 | + | 0.503839i | \(0.168080\pi\) |
0.00443863 | + | 0.999990i | \(0.498587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.69769 | − | 29.8637i | 0.291900 | − | 1.85564i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.23275 | + | 12.5275i | 0.447696 | + | 0.775433i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.42613 | − | 2.47013i | 0.0879388 | − | 0.152315i | −0.818701 | − | 0.574220i | \(-0.805305\pi\) |
0.906640 | + | 0.421906i | \(0.138639\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.4164 | −2.29847 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 34.8611 | 2.13347 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.19250 | + | 7.26162i | −0.255621 | + | 0.442749i | −0.965064 | − | 0.262014i | \(-0.915613\pi\) |
0.709443 | + | 0.704763i | \(0.248947\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.12836 | + | 12.3467i | 0.433017 | + | 0.750008i | 0.997131 | − | 0.0756888i | \(-0.0241156\pi\) |
−0.564114 | + | 0.825697i | \(0.690782\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.62091 | − | 3.70476i | 0.582284 | − | 0.224222i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.12289 | + | 1.94490i | 0.0677127 | + | 0.117282i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.6694 | − | 21.9441i | 0.761233 | − | 1.31849i | −0.180983 | − | 0.983486i | \(-0.557928\pi\) |
0.942215 | − | 0.335008i | \(-0.108739\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.57381 | 0.513301 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.0107 | 1.13408 | 0.567041 | − | 0.823689i | \(-0.308088\pi\) | ||||
0.567041 | + | 0.823689i | \(0.308088\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.7665 | − | 20.3802i | 0.699447 | − | 1.21148i | −0.269211 | − | 0.963081i | \(-0.586763\pi\) |
0.968658 | − | 0.248397i | \(-0.0799038\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.88615 | − | 6.73101i | −0.230196 | − | 0.398711i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.11578 | − | 3.32571i | −0.242947 | − | 0.196311i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.33706 | − | 2.31586i | −0.0786507 | − | 0.136227i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.97141 | − | 15.5389i | 0.525913 | − | 0.910909i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.1260 | −0.649989 | −0.324995 | − | 0.945716i | \(-0.605362\pi\) | ||||
−0.324995 | + | 0.945716i | \(0.605362\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.8105 | 0.978746 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.138244 | + | 0.239445i | −0.00802171 | + | 0.0138940i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.682460 | + | 1.18206i | 0.0394677 | + | 0.0683600i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.98739 | + | 3.22198i | 0.229830 | + | 0.185712i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.82976 | + | 6.63333i | 0.220014 | + | 0.381075i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.205525 | + | 0.355979i | −0.0117683 | + | 0.0203833i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.8920 | 1.53481 | 0.767404 | − | 0.641164i | \(-0.221548\pi\) | ||||
0.767404 | + | 0.641164i | \(0.221548\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.9513 | 0.793660 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.5216 | − | 21.6881i | 0.710036 | − | 1.22982i | −0.254807 | − | 0.966992i | \(-0.582012\pi\) |
0.964843 | − | 0.262827i | \(-0.0846549\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.41896 | + | 11.1180i | 0.362821 | + | 0.628424i | 0.988424 | − | 0.151717i | \(-0.0484803\pi\) |
−0.625603 | + | 0.780142i | \(0.715147\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −21.7810 | + | 8.38730i | −1.22722 | + | 0.472571i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.24249 | + | 10.8123i | 0.350613 | + | 0.607280i | 0.986357 | − | 0.164620i | \(-0.0526399\pi\) |
−0.635744 | + | 0.771900i | \(0.719307\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.07414 | + | 1.86047i | −0.0601405 | + | 0.104166i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 36.6952 | 2.04813 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.43555 | 0.246801 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.54370 | − | 7.86992i | 0.252039 | − | 0.436545i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.2499 | − | 24.6816i | −0.788022 | − | 1.36489i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.20016 | − | 33.0580i | 0.286694 | − | 1.82255i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.11482 | − | 5.39502i | −0.171206 | − | 0.296537i | 0.767636 | − | 0.640886i | \(-0.221433\pi\) |
−0.938842 | + | 0.344349i | \(0.888100\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.4990 | + | 26.8451i | −0.849341 | + | 1.47110i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.04090 | −0.439321 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.0259 | −1.41772 | −0.708860 | − | 0.705349i | \(-0.750790\pi\) | ||||
−0.708860 | + | 0.705349i | \(0.750790\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.7199 | − | 39.3520i | 1.23398 | − | 2.13731i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.636653 | + | 1.10272i | 0.0344767 | + | 0.0597154i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.35581 | + | 16.5282i | −0.451171 | + | 0.892437i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.25359 | − | 5.63539i | −0.175168 | − | 0.303399i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.60355 | + | 7.97359i | −0.247132 | + | 0.428045i | −0.962729 | − | 0.270469i | \(-0.912821\pi\) |
0.715597 | + | 0.698513i | \(0.246155\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.8773 | −1.43871 | −0.719354 | − | 0.694643i | \(-0.755562\pi\) | ||||
−0.719354 | + | 0.694643i | \(0.755562\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.11879 | 0.0597166 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.3602 | − | 17.9443i | 0.551416 | − | 0.955080i | −0.446757 | − | 0.894655i | \(-0.647421\pi\) |
0.998173 | − | 0.0604245i | \(-0.0192454\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.53368 | + | 6.12051i | 0.187548 | + | 0.324843i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.35870 | − | 27.7087i | 0.230687 | − | 1.46650i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.3347 | + | 17.9001i | 0.545442 | + | 0.944733i | 0.998579 | + | 0.0532924i | \(0.0169715\pi\) |
−0.453137 | + | 0.891441i | \(0.649695\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.500000 | + | 0.866025i | −0.0263158 | + | 0.0455803i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −25.9038 | −1.35960 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 40.7112 | 2.13092 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.9463 | − | 29.3519i | 0.884590 | − | 1.53216i | 0.0384082 | − | 0.999262i | \(-0.487771\pi\) |
0.846182 | − | 0.532894i | \(-0.178895\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.71288 | + | 4.69885i | 0.141227 | + | 0.244612i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.4095 | − | 10.9398i | 1.47495 | − | 0.567964i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.5085 | − | 23.3974i | −0.699444 | − | 1.21147i | −0.968659 | − | 0.248393i | \(-0.920098\pi\) |
0.269215 | − | 0.963080i | \(-0.413236\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.23112 | + | 3.86441i | −0.115215 | + | 0.199557i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.69293 | 0.447709 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.8406 | −0.865041 | −0.432521 | − | 0.901624i | \(-0.642376\pi\) | ||||
−0.432521 | + | 0.901624i | \(0.642376\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.55782 | + | 14.8226i | −0.438430 | + | 0.759383i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.9859 | + | 29.4205i | 0.867940 | + | 1.50332i | 0.864098 | + | 0.503323i | \(0.167889\pi\) |
0.00384112 | + | 0.999993i | \(0.498777\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.69609 | − | 2.17855i | −0.137405 | − | 0.111029i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.62826 | − | 4.55228i | −0.133602 | − | 0.231405i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.84231 | − | 10.1192i | 0.296217 | − | 0.513062i | −0.679051 | − | 0.734092i | \(-0.737608\pi\) |
0.975267 | + | 0.221029i | \(0.0709416\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.71357 | 0.187803 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.68549 | −0.236351 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.15434 | − | 12.3917i | 0.359974 | − | 0.623493i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.00887 | + | 8.67562i | 0.251388 | + | 0.435417i | 0.963908 | − | 0.266235i | \(-0.0857796\pi\) |
−0.712520 | + | 0.701652i | \(0.752446\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.91869 | + | 3.97450i | 0.246243 | + | 0.198974i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.23488 | − | 9.06707i | −0.261417 | − | 0.452788i | 0.705202 | − | 0.709007i | \(-0.250857\pi\) |
−0.966619 | + | 0.256219i | \(0.917523\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.57618 | − | 4.46208i | 0.128329 | − | 0.222272i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −31.7989 | −1.58010 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.60355 | −0.228190 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0047 | − | 20.7927i | 0.593593 | − | 1.02813i | −0.400151 | − | 0.916449i | \(-0.631042\pi\) |
0.993744 | − | 0.111684i | \(-0.0356243\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.2501 | + | 33.3421i | 0.949535 | + | 1.64464i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.7639 | + | 4.91504i | −0.628071 | + | 0.241853i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.04670 | + | 5.27703i | 0.149556 | + | 0.259039i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.08883 | − | 5.35001i | 0.151261 | − | 0.261991i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.1723 | −0.741216 | −0.370608 | − | 0.928789i | \(-0.620851\pi\) | ||||
−0.370608 | + | 0.928789i | \(0.620851\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.77965 | 0.0867348 | 0.0433674 | − | 0.999059i | \(-0.486191\pi\) | ||||
0.0433674 | + | 0.999059i | \(0.486191\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.1568 | + | 29.7165i | −0.834192 | + | 1.44486i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.3622 | − | 21.4119i | −0.599652 | − | 1.03863i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0519701 | − | 0.330379i | 0.00251501 | − | 0.0159882i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.784967 | − | 1.35960i | −0.0378986 | − | 0.0656422i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.3674 | + | 28.3493i | −0.788392 | + | 1.36554i | 0.138559 | + | 0.990354i | \(0.455753\pi\) |
−0.926951 | + | 0.375181i | \(0.877580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.83058 | −0.232143 | −0.116071 | − | 0.993241i | \(-0.537030\pi\) | ||||
−0.116071 | + | 0.993241i | \(0.537030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −41.4431 | −1.98705 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.418614 | + | 0.725061i | −0.0200250 | + | 0.0346844i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.1797 | − | 24.5600i | −0.676762 | − | 1.17219i | −0.975950 | − | 0.217992i | \(-0.930049\pi\) |
0.299188 | − | 0.954194i | \(-0.403284\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.0856 | − | 12.7366i | 0.670745 | − | 0.606506i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.64006 | − | 16.6971i | −0.458013 | − | 0.793302i | 0.540843 | − | 0.841124i | \(-0.318105\pi\) |
−0.998856 | + | 0.0478218i | \(0.984772\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.7141 | + | 41.0739i | −1.12415 | + | 1.94709i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.1386 | −1.09442 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.0035 | −0.755254 | −0.377627 | − | 0.925958i | \(-0.623260\pi\) | ||||
−0.377627 | + | 0.925958i | \(0.623260\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.402893 | + | 0.697832i | −0.0189715 | + | 0.0328596i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.66608 | − | 8.08188i | −0.219231 | − | 0.379720i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.17955 | + | 13.8556i | −0.102179 | + | 0.649563i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.0173 | − | 20.8147i | −0.562148 | − | 0.973669i | −0.997309 | − | 0.0733158i | \(-0.976642\pi\) |
0.435161 | − | 0.900353i | \(-0.356691\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.52196 | − | 2.63611i | 0.0710390 | − | 0.123043i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.2907 | 1.27106 | 0.635528 | − | 0.772078i | \(-0.280782\pi\) | ||||
0.635528 | + | 0.772078i | \(0.280782\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.5689 | −1.18829 | −0.594143 | − | 0.804359i | \(-0.702509\pi\) | ||||
−0.594143 | + | 0.804359i | \(0.702509\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.2818 | + | 21.2727i | −0.569556 | + | 0.986499i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.85142 | + | 8.40291i | 0.224497 | + | 0.388840i | 0.956168 | − | 0.292817i | \(-0.0945927\pi\) |
−0.731671 | + | 0.681658i | \(0.761259\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.10530 | − | 2.35099i | 0.281917 | − | 0.108559i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.9679 | − | 31.1213i | −0.827916 | − | 1.43399i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.390326 | − | 0.676064i | 0.0179472 | − | 0.0310855i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.57412 | 0.255758 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −31.2155 | −1.42926 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.7515 | + | 23.8183i | −0.628323 | + | 1.08829i | 0.359565 | + | 0.933120i | \(0.382925\pi\) |
−0.987888 | + | 0.155167i | \(0.950408\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.31400 | + | 16.1323i | 0.424682 | + | 0.735571i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.11807 | + | 3.32756i | 0.187378 | + | 0.151409i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.2055 | + | 21.1405i | 0.554223 | + | 0.959942i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.38738 | + | 5.86711i | −0.153497 | + | 0.265864i | −0.932511 | − | 0.361142i | \(-0.882387\pi\) |
0.779014 | + | 0.627007i | \(0.215720\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −40.8887 | −1.84905 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.5603 | −1.87559 | −0.937796 | − | 0.347188i | \(-0.887137\pi\) | ||||
−0.937796 | + | 0.347188i | \(0.887137\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.8255 | − | 20.4824i | 0.532595 | − | 0.922481i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.77711 | + | 3.07804i | 0.0798750 | + | 0.138348i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.47256 | − | 3.61401i | −0.200622 | − | 0.162111i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.86140 | + | 13.6163i | 0.351924 | + | 0.609551i | 0.986587 | − | 0.163239i | \(-0.0521941\pi\) |
−0.634662 | + | 0.772790i | \(0.718861\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.8351 | + | 18.7670i | −0.484077 | + | 0.838446i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.0804 | 0.627813 | 0.313906 | − | 0.949454i | \(-0.398362\pi\) | ||||
0.313906 | + | 0.949454i | \(0.398362\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.4207 | −0.463714 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.3597 | − | 21.4077i | 0.548915 | − | 0.950749i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.7164 | − | 28.9536i | −0.740939 | − | 1.28334i | −0.952068 | − | 0.305886i | \(-0.901047\pi\) |
0.211129 | − | 0.977458i | \(-0.432286\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.9113 | + | 11.9031i | −1.36743 | + | 0.526563i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.343127 | + | 0.594314i | 0.0151494 | + | 0.0262396i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.49027 | + | 16.4376i | −0.418191 | + | 0.724328i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.09595 | −0.224120 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.9743 | 1.18404 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.4194 | − | 21.5111i | 0.544106 | − | 0.942419i | −0.454557 | − | 0.890718i | \(-0.650202\pi\) |
0.998663 | − | 0.0517012i | \(-0.0164644\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.31887 | + | 16.1407i | 0.407486 | + | 0.705786i | 0.994607 | − | 0.103713i | \(-0.0330723\pi\) |
−0.587122 | + | 0.809499i | \(0.699739\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.47754 | − | 34.8213i | 0.239060 | − | 1.51973i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.00907 | − | 12.1401i | −0.305320 | − | 0.528830i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1495 | − | 19.3115i | 0.484762 | − | 0.839632i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.0246 | 0.608615 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.26057 | 0.141231 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.9617 | + | 43.2349i | −1.07919 | + | 1.86921i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.0356 | − | 48.5590i | −1.20982 | − | 2.09548i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.68405 | + | 0.865851i | 0.115610 | + | 0.0372948i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.6806 | + | 21.9634i | 0.545181 | + | 0.944281i | 0.998596 | + | 0.0529813i | \(0.0168724\pi\) |
−0.453415 | + | 0.891300i | \(0.649794\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.27295 | − | 10.8651i | 0.269198 | − | 0.466265i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 38.7736 | 1.66088 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.1315 | 1.28833 | 0.644165 | − | 0.764886i | \(-0.277205\pi\) | ||||
0.644165 | + | 0.764886i | \(0.277205\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.171464 | + | 0.296984i | −0.00731791 | + | 0.0126750i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.66608 | + | 4.61778i | 0.113579 | + | 0.196724i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.80909 | + | 11.5005i | −0.0769301 | + | 0.489053i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −44.4041 | − | 76.9101i | −1.88485 | − | 3.26465i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.2661 | + | 29.9058i | −0.731589 | + | 1.26715i | 0.224614 | + | 0.974448i | \(0.427888\pi\) |
−0.956204 | + | 0.292702i | \(0.905446\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.15886 | −0.133606 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.27135 | −0.180337 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.96025 | − | 6.85935i | 0.166905 | − | 0.289087i | −0.770425 | − | 0.637530i | \(-0.779956\pi\) |
0.937330 | + | 0.348443i | \(0.113289\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.9101 | + | 53.5379i | 1.30040 | + | 2.25236i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.1443 | − | 9.29735i | 1.01397 | − | 0.390452i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.66672 | − | 6.35095i | −0.153717 | − | 0.266245i | 0.778874 | − | 0.627180i | \(-0.215791\pi\) |
−0.932591 | + | 0.360935i | \(0.882458\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.8922 | − | 20.5979i | 0.497673 | − | 0.861995i | −0.502323 | − | 0.864680i | \(-0.667521\pi\) |
0.999996 | + | 0.00268474i | \(0.000854579\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −46.4202 | −1.93923 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.66681 | 0.194619 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.898612 | + | 1.55644i | −0.0374097 | + | 0.0647955i | −0.884124 | − | 0.467252i | \(-0.845244\pi\) |
0.846714 | + | 0.532048i | \(0.178577\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.03970 | + | 12.1931i | 0.292560 | + | 0.506729i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.85620 | − | 3.11596i | −0.159982 | − | 0.129272i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.31793 | − | 4.01477i | −0.0959987 | − | 0.166275i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.19096 | − | 12.4551i | 0.297310 | − | 0.514955i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −40.2209 | −1.66009 | −0.830046 | − | 0.557695i | \(-0.811686\pi\) | ||||
−0.830046 | + | 0.557695i | \(0.811686\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.16041 | 0.130222 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.18862 | + | 2.05876i | −0.0488934 | + | 0.0846859i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.94620 | − | 8.56707i | −0.203116 | − | 0.351807i | 0.746415 | − | 0.665481i | \(-0.231774\pi\) |
−0.949531 | + | 0.313674i | \(0.898440\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 29.6819 | + | 23.9842i | 1.21684 | + | 0.983255i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.712689 | − | 1.23441i | −0.0291684 | − | 0.0505212i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.8152 | + | 22.1965i | −0.523613 | + | 0.906925i | 0.476009 | + | 0.879440i | \(0.342083\pi\) |
−0.999622 | + | 0.0274844i | \(0.991250\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.9887 | 1.30485 | 0.652423 | − | 0.757855i | \(-0.273753\pi\) | ||||
0.652423 | + | 0.757855i | \(0.273753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.70832 | −0.273184 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.6209 | − | 30.5203i | 0.716392 | − | 1.24083i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.7386 | + | 35.9202i | 0.841752 | + | 1.45796i | 0.888412 | + | 0.459047i | \(0.151809\pi\) |
−0.0466596 | + | 0.998911i | \(0.514858\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 31.4670 | − | 12.1171i | 1.27511 | − | 0.491010i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.3102 | + | 17.8579i | 0.417108 | + | 0.722452i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.66801 | + | 2.88908i | −0.0673703 | + | 0.116689i | −0.897743 | − | 0.440520i | \(-0.854794\pi\) |
0.830373 | + | 0.557208i | \(0.188128\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.5446 | −0.626819 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.45553 | 0.0585976 | 0.0292988 | − | 0.999571i | \(-0.490673\pi\) | ||||
0.0292988 | + | 0.999571i | \(0.490673\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.0016 | + | 34.6437i | −0.803931 | + | 1.39245i | 0.113079 | + | 0.993586i | \(0.463929\pi\) |
−0.917010 | + | 0.398863i | \(0.869405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.287276 | + | 0.497576i | 0.0115280 | + | 0.0199670i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.99647 | − | 38.1202i | 0.240243 | − | 1.52725i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.8999 | + | 18.8792i | 0.435996 | + | 0.755167i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.481491 | − | 0.833966i | 0.0192289 | − | 0.0333054i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 50.6816 | 2.02081 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.6609 | 1.18078 | 0.590390 | − | 0.807118i | \(-0.298974\pi\) | ||||
0.590390 | + | 0.807118i | \(0.298974\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.6848 | + | 25.4348i | −0.583669 | + | 1.01094i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.6428 | − | 20.1659i | −0.462030 | − | 0.800260i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.39621 | − | 11.1576i | −0.0949413 | − | 0.442080i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.94806 | + | 5.10618i | 0.116623 | + | 0.201998i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.9911 | − | 27.6975i | 0.631612 | − | 1.09398i | −0.355610 | − | 0.934634i | \(-0.615727\pi\) |
0.987222 | − | 0.159350i | \(-0.0509398\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.8251 | −0.781825 | −0.390912 | − | 0.920428i | \(-0.627840\pi\) | ||||
−0.390912 | + | 0.920428i | \(0.627840\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.0597 | 0.592976 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.43764 | − | 16.3465i | 0.371032 | − | 0.642646i | −0.618692 | − | 0.785633i | \(-0.712337\pi\) |
0.989725 | + | 0.142987i | \(0.0456706\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.04140 | + | 1.80376i | 0.0408786 | + | 0.0708039i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.10565 | − | 19.7429i | 0.121720 | − | 0.773787i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.04816 | + | 1.81547i | 0.0410178 | + | 0.0710449i | 0.885805 | − | 0.464057i | \(-0.153607\pi\) |
−0.844788 | + | 0.535102i | \(0.820273\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.18727 | − | 5.52052i | 0.124537 | − | 0.215704i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 33.9643 | 1.32507 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.1279 | −1.44630 | −0.723148 | − | 0.690693i | \(-0.757306\pi\) | ||||
−0.723148 | + | 0.690693i | \(0.757306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.4324 | − | 23.2656i | 0.522461 | − | 0.904929i | −0.477198 | − | 0.878796i | \(-0.658347\pi\) |
0.999658 | − | 0.0261328i | \(-0.00831928\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.64189 | + | 14.9682i | 0.335623 | + | 0.581317i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.02873 | + | 3.09165i | −0.311341 | + | 0.119889i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.23211 | + | 3.86613i | 0.0864278 | + | 0.149697i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.2567 | − | 19.4972i | 0.435209 | − | 0.753804i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0509286 | −0.00196608 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.79647 | 0.184890 | 0.0924452 | − | 0.995718i | \(-0.470532\pi\) | ||||
0.0924452 | + | 0.995718i | \(0.470532\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.91263 | − | 3.31278i | 0.0736173 | − | 0.127509i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.6597 | + | 39.2477i | 0.870882 | + | 1.50841i | 0.861086 | + | 0.508459i | \(0.169785\pi\) |
0.00979576 | + | 0.999952i | \(0.496882\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.4485 | − | 12.4830i | −0.592857 | − | 0.479053i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.63381 | − | 14.9542i | −0.330848 | − | 0.573046i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.82929 | + | 11.8287i | −0.261316 | + | 0.452612i | −0.966592 | − | 0.256321i | \(-0.917490\pi\) |
0.705276 | + | 0.708933i | \(0.250823\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −52.3789 | −2.00129 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.2853 | 0.506866 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.37936 | + | 16.2455i | −0.357325 | + | 0.618905i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.68144 | + | 8.10850i | 0.178090 | + | 0.308462i | 0.941226 | − | 0.337776i | \(-0.109675\pi\) |
−0.763136 | + | 0.646238i | \(0.776341\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.24928 | − | 1.81751i | −0.0854430 | − | 0.0690414i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.20231 | + | 7.27862i | 0.159403 | + | 0.276094i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.43555 | − | 7.68260i | 0.168009 | − | 0.290999i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.5722 | 1.04288 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.3095 | −0.616003 | −0.308001 | − | 0.951386i | \(-0.599660\pi\) | ||||
−0.308001 | + | 0.951386i | \(0.599660\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.71311 | + | 9.89540i | −0.215474 | + | 0.373212i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −49.1536 | − | 85.1365i | −1.85123 | − | 3.20643i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.91222 | − | 3.04679i | 0.297570 | − | 0.114586i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.6708 | − | 30.6068i | −0.663642 | − | 1.14946i | −0.979652 | − | 0.200705i | \(-0.935677\pi\) |
0.316010 | − | 0.948756i | \(-0.397657\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.96868 | − | 10.3381i | 0.223843 | − | 0.387708i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.64598 | 0.0990927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.13587 | 0.0798772 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −34.5958 | + | 59.9216i | −1.29200 | + | 2.23781i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.2748 | − | 28.1887i | −0.606946 | − | 1.05126i | −0.991741 | − | 0.128260i | \(-0.959061\pi\) |
0.384794 | − | 0.923002i | \(-0.374272\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.39976 | − | 15.2555i | 0.0893718 | − | 0.568146i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.6255 | − | 46.1167i | −0.990213 | − | 1.71510i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.8610 | − | 25.7401i | 0.551925 | − | 0.955962i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.5070 | −0.463859 | −0.231929 | − | 0.972733i | \(-0.574504\pi\) | ||||
−0.231929 | + | 0.972733i | \(0.574504\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.6083 | −0.800306 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.29719 | + | 7.44296i | −0.158937 | + | 0.275288i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.41623 | − | 14.5773i | −0.310861 | − | 0.538426i | 0.667688 | − | 0.744441i | \(-0.267284\pi\) |
−0.978549 | + | 0.206015i | \(0.933951\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.4238 | + | 53.1933i | 0.421374 | + | 1.96206i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.498130 | − | 0.862786i | −0.0183488 | − | 0.0317811i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.6385 | + | 40.9431i | −0.869556 | + | 1.50611i | −0.00710414 | + | 0.999975i | \(0.502261\pi\) |
−0.862451 | + | 0.506140i | \(0.831072\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.89665 | −0.143147 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.4769 | 1.08140 | 0.540701 | − | 0.841215i | \(-0.318159\pi\) | ||||
0.540701 | + | 0.841215i | \(0.318159\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.7399 | − | 27.2623i | 0.576665 | − | 0.998813i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.54178 | + | 4.40250i | 0.0929990 | + | 0.161079i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.31195 | − | 40.1258i | 0.230634 | − | 1.46616i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.0079 | − | 27.7266i | −0.584138 | − | 1.01176i | −0.994982 | − | 0.100052i | \(-0.968099\pi\) |
0.410844 | − | 0.911706i | \(-0.365234\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.98064 | − | 13.8229i | 0.290831 | − | 0.503733i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.6963 | 0.462065 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.8062 | −1.62851 | −0.814254 | − | 0.580509i | \(-0.802854\pi\) | ||||
−0.814254 | + | 0.580509i | \(0.802854\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.403117 | − | 0.698220i | 0.0146322 | − | 0.0253438i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.73474 | + | 15.1290i | 0.316634 | + | 0.548426i | 0.979783 | − | 0.200061i | \(-0.0641140\pi\) |
−0.663149 | + | 0.748487i | \(0.730781\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.4401 | + | 11.3366i | −1.06580 | + | 0.410413i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19.5646 | − | 33.8869i | −0.707360 | − | 1.22518i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.21398 | − | 7.29882i | 0.152158 | − | 0.263545i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.1746 | 0.655392 | 0.327696 | − | 0.944783i | \(-0.393728\pi\) | ||||
0.327696 | + | 0.944783i | \(0.393728\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −66.5368 | −2.39627 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.3940 | + | 23.1992i | −0.481750 | + | 0.834416i | −0.999781 | − | 0.0209465i | \(-0.993332\pi\) |
0.518030 | + | 0.855362i | \(0.326665\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.80824 | − | 15.2563i | −0.316401 | − | 0.548023i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 56.2021 | + | 45.4136i | 2.01624 | + | 1.62920i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.00000 | + | 1.73205i | 0.0358287 | + | 0.0620572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.437819 | + | 0.758325i | −0.0156664 | + | 0.0271350i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.65921 | 0.130770 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 48.8902 | 1.74496 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.0439 | + | 27.7889i | −0.571904 | + | 0.990567i | 0.424466 | + | 0.905444i | \(0.360462\pi\) |
−0.996370 | + | 0.0851233i | \(0.972872\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.40868 | + | 5.90401i | 0.121352 | + | 0.210188i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −39.1229 | − | 31.6129i | −1.39105 | − | 1.12402i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.103040 | + | 0.178470i | 0.00365905 | + | 0.00633767i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 44.7156 | − | 77.4497i | 1.58590 | − | 2.74686i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.2145 | −0.538925 | −0.269462 | − | 0.963011i | \(-0.586846\pi\) | ||||
−0.269462 | + | 0.963011i | \(0.586846\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 56.1026 | 1.98477 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.7840 | + | 34.2670i | −0.699035 | + | 1.21076i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.52204 | + | 4.36830i | 0.0890009 | + | 0.154154i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.72188 | + | 2.58842i | −0.236915 | + | 0.0912298i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.0208 | − | 17.3565i | −0.352747 | − | 0.610977i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.8710 | − | 22.2933i | 0.452521 | − | 0.783790i | −0.546021 | − | 0.837772i | \(-0.683858\pi\) |
0.998542 | + | 0.0539818i | \(0.0171913\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.6453 | 1.11122 | 0.555608 | − | 0.831444i | \(-0.312486\pi\) | ||||
0.555608 | + | 0.831444i | \(0.312486\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34.0759 | −1.19509 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.8143 | − | 48.1757i | 0.974291 | − | 1.68752i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.968807 | − | 1.67802i | −0.0338943 | − | 0.0587066i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.81835 | + | 11.5594i | −0.0635381 | + | 0.403919i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.5147 | + | 40.7287i | 0.820669 | + | 1.42144i | 0.905185 | + | 0.425018i | \(0.139732\pi\) |
−0.0845165 | + | 0.996422i | \(0.526935\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.15946 | + | 5.47234i | −0.110132 | + | 0.190754i | −0.915823 | − | 0.401582i | \(-0.868461\pi\) |
0.805691 | + | 0.592335i | \(0.201794\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.36777 | −0.186882 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.8959 | −1.63073 | −0.815364 | − | 0.578948i | \(-0.803463\pi\) | ||||
−0.815364 | + | 0.578948i | \(0.803463\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.18757 | − | 12.4492i | 0.249635 | − | 0.432380i | −0.713790 | − | 0.700360i | \(-0.753023\pi\) |
0.963424 | + | 0.267980i | \(0.0863561\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.2820 | + | 52.4500i | 1.05047 | + | 1.81947i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.5494 | − | 9.53236i | −1.02383 | − | 0.330277i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.7410 | − | 25.5322i | −0.510134 | − | 0.883579i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.08442 | − | 1.87827i | 0.0374831 | − | 0.0649226i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.5325 | 1.15767 | 0.578835 | − | 0.815445i | \(-0.303507\pi\) | ||||
0.578835 | + | 0.815445i | \(0.303507\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.568151 | −0.0195914 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.7193 | + | 39.3510i | −0.782495 | + | 1.35532i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.8153 | + | 29.1249i | 0.578463 | + | 1.00193i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.45572 | + | 28.3255i | −0.153100 | + | 0.973275i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.1239 | + | 48.7121i | 0.965211 | + | 1.67179i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.78318 | + | 8.28471i | −0.163965 | + | 0.283996i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.37139 | 0.115434 | 0.0577171 | − | 0.998333i | \(-0.481618\pi\) | ||||
0.0577171 | + | 0.998333i | \(0.481618\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.82172 | 0.301696 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.0314 | − | 32.9634i | 0.650101 | − | 1.12601i | −0.332998 | − | 0.942928i | \(-0.608060\pi\) |
0.983098 | − | 0.183080i | \(-0.0586066\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.3389 | + | 24.8357i | 0.489237 | + | 0.847384i | 0.999923 | − | 0.0123833i | \(-0.00394182\pi\) |
−0.510686 | + | 0.859767i | \(0.670608\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.8027 | − | 4.54492i | 0.402236 | − | 0.154891i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.9344 | − | 39.7236i | −0.780697 | − | 1.35221i | −0.931536 | − | 0.363649i | \(-0.881531\pi\) |
0.150839 | − | 0.988558i | \(-0.451802\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.3491 | + | 31.7816i | −0.623889 | + | 1.08061i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.39159 | 0.217070 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.77283 | 0.0601392 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.01565 | + | 3.49122i | −0.0682978 | + | 0.118295i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.1827 | + | 17.6370i | 0.344633 | + | 0.596922i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.84191 | + | 3.10442i | 0.129880 | + | 0.104948i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.00705 | + | 10.4045i | 0.202844 | + | 0.351335i | 0.949444 | − | 0.313938i | \(-0.101648\pi\) |
−0.746600 | + | 0.665273i | \(0.768315\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.2965 | − | 23.0302i | 0.448480 | − | 0.776790i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.35650 | 0.113083 | 0.0565417 | − | 0.998400i | \(-0.481993\pi\) | ||||
0.0565417 | + | 0.998400i | \(0.481993\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.45095 | 0.217092 | 0.108546 | − | 0.994091i | \(-0.465381\pi\) | ||||
0.108546 | + | 0.994091i | \(0.465381\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.0899 | + | 34.7968i | −0.675316 | + | 1.16968i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.1837 | − | 29.7630i | −0.576971 | − | 0.999344i | −0.995824 | − | 0.0912898i | \(-0.970901\pi\) |
0.418853 | − | 0.908054i | \(-0.362432\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.7363 | + | 11.9075i | 0.494238 | + | 0.399364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.96993 | − | 3.41202i | −0.0659951 | − | 0.114307i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.32419 | + | 10.9538i | −0.211631 | + | 0.366556i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 76.2841 | 2.54990 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.26238 | −0.108928 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.42588 | − | 14.5941i | 0.281019 | − | 0.486739i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.5186 | + | 44.1995i | 0.850148 | + | 1.47250i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.4346 | + | 4.40315i | −0.380519 | + | 0.146528i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.53426 | + | 14.7818i | 0.283689 | + | 0.491363i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.161426 | + | 0.279598i | −0.00536005 | + | 0.00928389i | −0.868693 | − | 0.495351i | \(-0.835039\pi\) |
0.863333 | + | 0.504635i | \(0.168373\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.69370 | −0.288352 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.3296 | 0.640419 | 0.320209 | − | 0.947347i | \(-0.396247\pi\) | ||||
0.320209 | + | 0.947347i | \(0.396247\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.377483 | + | 0.653820i | −0.0124929 | + | 0.0216383i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.491238 | − | 0.850848i | −0.0162398 | − | 0.0281282i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.805951 | + | 5.12352i | −0.0266148 | + | 0.169193i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.82201 | − | 10.0840i | −0.192050 | − | 0.332641i | 0.753879 | − | 0.657013i | \(-0.228180\pi\) |
−0.945930 | + | 0.324372i | \(0.894847\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.1382 | + | 55.6649i | −1.05899 | + | 1.83422i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.54322 | 0.116627 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 63.6912 | 2.09415 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.91749 | + | 13.7135i | −0.260044 | + | 0.450410i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.41199 | + | 9.37384i | 0.177562 | + | 0.307546i | 0.941045 | − | 0.338282i | \(-0.109846\pi\) |
−0.763483 | + | 0.645828i | \(0.776512\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.19213 | − | 4.69487i | 0.170165 | − | 0.153868i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29.9287 | + | 51.8381i | 0.979823 | + | 1.69710i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.90556 | − | 5.03258i | 0.0950220 | − | 0.164583i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.0113 | −0.588402 | −0.294201 | − | 0.955744i | \(-0.595054\pi\) | ||||
−0.294201 | + | 0.955744i | \(0.595054\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.6847 | −1.00136 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.67628 | − | 6.36751i | 0.119843 | − | 0.207575i | −0.799862 | − | 0.600184i | \(-0.795094\pi\) |
0.919705 | + | 0.392609i | \(0.128427\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.837228 | + | 1.45012i | 0.0272639 | + | 0.0472224i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.917464 | + | 5.83242i | −0.0298451 | + | 0.189729i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.65037 | − | 4.59057i | −0.0861253 | − | 0.149173i | 0.819745 | − | 0.572729i | \(-0.194115\pi\) |
−0.905870 | + | 0.423555i | \(0.860782\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.2053 | − | 17.6761i | 0.331278 | − | 0.573790i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.8411 | −0.967666 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46.1846 | −1.49607 | −0.748033 | − | 0.663661i | \(-0.769002\pi\) | ||||
−0.748033 | + | 0.663661i | \(0.769002\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.5770 | − | 54.6930i | 1.02181 | − | 1.76983i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.56738 | − | 4.44683i | −0.0829916 | − | 0.143746i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.7703 | − | 15.3145i | 1.28425 | − | 0.494531i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.5059 | + | 18.1968i | 0.338901 | + | 0.586993i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.8249 | + | 36.0698i | −0.671073 | + | 1.16233i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.1548 | −0.616616 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.76088 | 0.313889 | 0.156944 | − | 0.987607i | \(-0.449836\pi\) | ||||
0.156944 | + | 0.987607i | \(0.449836\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.30085 | + | 9.18134i | −0.170288 | + | 0.294947i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.6313 | − | 18.4139i | −0.341174 | − | 0.590930i | 0.643477 | − | 0.765465i | \(-0.277491\pi\) |
−0.984651 | + | 0.174535i | \(0.944158\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.31885 | − | 4.29785i | −0.170515 | − | 0.137783i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.8602 | + | 18.8104i | 0.347805 | + | 0.602415i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.944275 | − | 1.63553i | 0.0302100 | − | 0.0523253i | −0.850525 | − | 0.525934i | \(-0.823716\pi\) |
0.880735 | + | 0.473609i | \(0.157049\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.87630 | −0.187807 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32.3479 | 1.03279 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.9245 | + | 22.3858i | −0.412226 | + | 0.713997i | −0.995133 | − | 0.0985422i | \(-0.968582\pi\) |
0.582906 | + | 0.812539i | \(0.301915\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.61711 | − | 2.80091i | −0.0515253 | − | 0.0892444i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 62.2135 | + | 50.2710i | 1.98028 | + | 1.60014i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.811112 | − | 1.40489i | −0.0257919 | − | 0.0446728i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.49262 | − | 14.7097i | 0.269777 | − | 0.467267i | −0.699027 | − | 0.715095i | \(-0.746383\pi\) |
0.968804 | + | 0.247828i | \(0.0797167\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.8898 | 0.472515 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.93921 | 0.0614770 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.90432 | − | 10.2266i | 0.186992 | − | 0.323879i | −0.757254 | − | 0.653120i | \(-0.773460\pi\) |
0.944246 | + | 0.329241i | \(0.106793\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.92065 | + | 6.79077i | 0.124044 | + | 0.214850i |
(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 | 1064.2.q.n.305.2 | ✓ | 16 | |
7.2 | even | 3 | inner | 1064.2.q.n.457.2 | yes | 16 | |
7.3 | odd | 6 | 7448.2.a.br.1.2 | 8 | |||
7.4 | even | 3 | 7448.2.a.bq.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1064.2.q.n.305.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1064.2.q.n.457.2 | yes | 16 | 7.2 | even | 3 | inner | |
7448.2.a.bq.1.7 | 8 | 7.4 | even | 3 | |||
7448.2.a.br.1.2 | 8 | 7.3 | odd | 6 |