Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [250,2,Mod(49,250)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(250, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("250.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 250 = 2 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 250.e (of order \(10\), 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: | \(1.99626005053\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 50) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(0.917186 - 1.66637i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 250.199 |
Dual form | 250.2.e.c.49.1 |
$q$-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 \(\left(\mathbb{Z}/250\mathbb{Z}\right)^\times\).
\(n\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.587785 | − | 0.809017i | −0.415627 | − | 0.572061i | ||||
\(3\) | −1.63079 | − | 0.529876i | −0.941538 | − | 0.305924i | −0.202265 | − | 0.979331i | \(-0.564830\pi\) |
−0.739272 | + | 0.673407i | \(0.764830\pi\) | |||||||
\(4\) | −0.309017 | + | 0.951057i | −0.154508 | + | 0.475528i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.529876 | + | 1.63079i | 0.216321 | + | 0.665768i | ||||
\(7\) | − | 2.77447i | − | 1.04865i | −0.851518 | − | 0.524325i | \(-0.824318\pi\) | ||
0.851518 | − | 0.524325i | \(-0.175682\pi\) | |||||||
\(8\) | 0.951057 | − | 0.309017i | 0.336249 | − | 0.109254i | ||||
\(9\) | −0.0483405 | − | 0.0351215i | −0.0161135 | − | 0.0117072i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.24459 | + | 1.63079i | −0.676770 | + | 0.491702i | −0.872284 | − | 0.488999i | \(-0.837362\pi\) |
0.195515 | + | 0.980701i | \(0.437362\pi\) | |||||||
\(12\) | 1.00788 | − | 1.38723i | 0.290951 | − | 0.400460i | ||||
\(13\) | −3.33732 | + | 4.59343i | −0.925606 | + | 1.27399i | 0.0359433 | + | 0.999354i | \(0.488556\pi\) |
−0.961549 | + | 0.274633i | \(0.911444\pi\) | |||||||
\(14\) | −2.24459 | + | 1.63079i | −0.599892 | + | 0.435847i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −4.90406 | + | 1.59343i | −1.18941 | + | 0.386462i | −0.835854 | − | 0.548951i | \(-0.815027\pi\) |
−0.353555 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(18\) | 0.0597522i | 0.0140837i | ||||||||
\(19\) | −0.436451 | − | 1.34326i | −0.100129 | − | 0.308164i | 0.888428 | − | 0.459017i | \(-0.151798\pi\) |
−0.988556 | + | 0.150852i | \(0.951798\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.47012 | + | 4.52458i | −0.320807 | + | 0.987343i | ||||
\(22\) | 2.63868 | + | 0.857358i | 0.562567 | + | 0.182789i | ||||
\(23\) | −0.384978 | − | 0.529876i | −0.0802734 | − | 0.110487i | 0.766992 | − | 0.641657i | \(-0.221753\pi\) |
−0.847265 | + | 0.531170i | \(0.821753\pi\) | |||||||
\(24\) | −1.71472 | −0.350015 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.67779 | 1.11351 | ||||||||
\(27\) | 3.08388 | + | 4.24459i | 0.593492 | + | 0.816872i | ||||
\(28\) | 2.63868 | + | 0.857358i | 0.498663 | + | 0.162025i | ||||
\(29\) | −1.26594 | + | 3.89618i | −0.235080 | + | 0.723502i | 0.762031 | + | 0.647541i | \(0.224202\pi\) |
−0.997111 | + | 0.0759609i | \(0.975798\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.20239 | − | 6.77827i | −0.395562 | − | 1.21741i | −0.928523 | − | 0.371274i | \(-0.878921\pi\) |
0.532961 | − | 0.846140i | \(-0.321079\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 4.52458 | − | 1.47012i | 0.787628 | − | 0.255916i | ||||
\(34\) | 4.17164 | + | 3.03088i | 0.715431 | + | 0.519791i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0483405 | − | 0.0351215i | 0.00805676 | − | 0.00585358i | ||||
\(37\) | −0.615684 | + | 0.847416i | −0.101218 | + | 0.139314i | −0.856622 | − | 0.515945i | \(-0.827441\pi\) |
0.755404 | + | 0.655260i | \(0.227441\pi\) | |||||||
\(38\) | −0.830178 | + | 1.14264i | −0.134673 | + | 0.185361i | ||||
\(39\) | 7.87642 | − | 5.72255i | 1.26124 | − | 0.916342i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.36789 | − | 5.35309i | −1.15067 | − | 0.836012i | −0.162101 | − | 0.986774i | \(-0.551827\pi\) |
−0.988570 | + | 0.150762i | \(0.951827\pi\) | |||||||
\(42\) | 4.52458 | − | 1.47012i | 0.698157 | − | 0.226845i | ||||
\(43\) | − | 9.24660i | − | 1.41009i | −0.709161 | − | 0.705047i | \(-0.750926\pi\) | ||
0.709161 | − | 0.705047i | \(-0.249074\pi\) | |||||||
\(44\) | −0.857358 | − | 2.63868i | −0.129252 | − | 0.397795i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.202395 | + | 0.622907i | −0.0298415 | + | 0.0918426i | ||||
\(47\) | −2.63868 | − | 0.857358i | −0.384890 | − | 0.125058i | 0.110179 | − | 0.993912i | \(-0.464857\pi\) |
−0.495070 | + | 0.868853i | \(0.664857\pi\) | |||||||
\(48\) | 1.00788 | + | 1.38723i | 0.145476 | + | 0.200230i | ||||
\(49\) | −0.697669 | −0.0996670 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.84181 | 1.23810 | ||||||||
\(52\) | −3.33732 | − | 4.59343i | −0.462803 | − | 0.636994i | ||||
\(53\) | 0.500362 | + | 0.162577i | 0.0687299 | + | 0.0223317i | 0.343180 | − | 0.939270i | \(-0.388496\pi\) |
−0.274450 | + | 0.961601i | \(0.588496\pi\) | |||||||
\(54\) | 1.62129 | − | 4.98982i | 0.220630 | − | 0.679028i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.857358 | − | 2.63868i | −0.114569 | − | 0.352608i | ||||
\(57\) | 2.42184i | 0.320780i | ||||||||
\(58\) | 3.89618 | − | 1.26594i | 0.511593 | − | 0.166227i | ||||
\(59\) | −3.05975 | − | 2.22304i | −0.398346 | − | 0.289415i | 0.370521 | − | 0.928824i | \(-0.379179\pi\) |
−0.768867 | + | 0.639409i | \(0.779179\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.76365 | − | 6.36716i | 1.12207 | − | 0.815232i | 0.137549 | − | 0.990495i | \(-0.456078\pi\) |
0.984522 | + | 0.175263i | \(0.0560776\pi\) | |||||||
\(62\) | −4.18920 | + | 5.76594i | −0.532029 | + | 0.732276i | ||||
\(63\) | −0.0974433 | + | 0.134119i | −0.0122767 | + | 0.0168974i | ||||
\(64\) | 0.809017 | − | 0.587785i | 0.101127 | − | 0.0734732i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.84883 | − | 2.79634i | −0.473759 | − | 0.344206i | ||||
\(67\) | 4.11180 | − | 1.33600i | 0.502336 | − | 0.163219i | −0.0468778 | − | 0.998901i | \(-0.514927\pi\) |
0.549214 | + | 0.835682i | \(0.314927\pi\) | |||||||
\(68\) | − | 5.15643i | − | 0.625309i | ||||||
\(69\) | 0.347049 | + | 1.06811i | 0.0417798 | + | 0.128585i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.09343 | + | 12.5983i | −0.485800 | + | 1.49514i | 0.345018 | + | 0.938596i | \(0.387873\pi\) |
−0.830819 | + | 0.556543i | \(0.812127\pi\) | |||||||
\(72\) | −0.0568277 | − | 0.0184644i | −0.00669721 | − | 0.00217606i | ||||
\(73\) | 2.47648 | + | 3.40859i | 0.289850 | + | 0.398945i | 0.928966 | − | 0.370166i | \(-0.120699\pi\) |
−0.639115 | + | 0.769111i | \(0.720699\pi\) | |||||||
\(74\) | 1.04746 | 0.121765 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.41238 | 0.162012 | ||||||||
\(77\) | 4.52458 | + | 6.22754i | 0.515623 | + | 0.709695i | ||||
\(78\) | −9.25928 | − | 3.00852i | −1.04841 | − | 0.340648i | ||||
\(79\) | 3.05975 | − | 9.41695i | 0.344249 | − | 1.05949i | −0.617736 | − | 0.786386i | \(-0.711950\pi\) |
0.961985 | − | 0.273104i | \(-0.0880502\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.72466 | − | 8.38563i | −0.302740 | − | 0.931737i | ||||
\(82\) | 9.10722i | 1.00572i | ||||||||
\(83\) | 4.44717 | − | 1.44497i | 0.488141 | − | 0.158606i | −0.0545976 | − | 0.998508i | \(-0.517388\pi\) |
0.542738 | + | 0.839902i | \(0.317388\pi\) | |||||||
\(84\) | −3.84883 | − | 2.79634i | −0.419942 | − | 0.305106i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.48066 | + | 5.43502i | −0.806660 | + | 0.586073i | ||||
\(87\) | 4.12898 | − | 5.68305i | 0.442673 | − | 0.609287i | ||||
\(88\) | −1.63079 | + | 2.24459i | −0.173843 | + | 0.239274i | ||||
\(89\) | −7.43002 | + | 5.39823i | −0.787581 | + | 0.572211i | −0.907245 | − | 0.420603i | \(-0.861818\pi\) |
0.119664 | + | 0.992814i | \(0.461818\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.7443 | + | 9.25928i | 1.33597 | + | 0.970637i | ||||
\(92\) | 0.622907 | − | 0.202395i | 0.0649425 | − | 0.0211011i | ||||
\(93\) | 12.2209i | 1.26725i | ||||||||
\(94\) | 0.857358 | + | 2.63868i | 0.0884297 | + | 0.272159i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.529876 | − | 1.63079i | 0.0540803 | − | 0.166442i | ||||
\(97\) | −0.0857567 | − | 0.0278640i | −0.00870727 | − | 0.00282917i | 0.304660 | − | 0.952461i | \(-0.401457\pi\) |
−0.313367 | + | 0.949632i | \(0.601457\pi\) | |||||||
\(98\) | 0.410079 | + | 0.564426i | 0.0414243 | + | 0.0570156i | ||||
\(99\) | 0.165781 | 0.0166616 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.90632 | −0.786709 | −0.393354 | − | 0.919387i | \(-0.628685\pi\) | ||||
−0.393354 | + | 0.919387i | \(0.628685\pi\) | |||||||
\(102\) | −5.19709 | − | 7.15318i | −0.514588 | − | 0.708270i | ||||
\(103\) | −7.45079 | − | 2.42091i | −0.734148 | − | 0.238539i | −0.0820014 | − | 0.996632i | \(-0.526131\pi\) |
−0.652146 | + | 0.758093i | \(0.726131\pi\) | |||||||
\(104\) | −1.75453 | + | 5.39990i | −0.172046 | + | 0.529503i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.162577 | − | 0.500362i | −0.0157909 | − | 0.0485994i | ||||
\(107\) | − | 10.2220i | − | 0.988194i | −0.869407 | − | 0.494097i | \(-0.835499\pi\) | ||
0.869407 | − | 0.494097i | \(-0.164501\pi\) | |||||||
\(108\) | −4.98982 | + | 1.62129i | −0.480145 | + | 0.156009i | ||||
\(109\) | 3.16400 | + | 2.29878i | 0.303056 | + | 0.220183i | 0.728911 | − | 0.684608i | \(-0.240027\pi\) |
−0.425855 | + | 0.904791i | \(0.640027\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.45308 | − | 1.05572i | 0.137920 | − | 0.100205i | ||||
\(112\) | −1.63079 | + | 2.24459i | −0.154095 | + | 0.212094i | ||||
\(113\) | 3.74740 | − | 5.15785i | 0.352526 | − | 0.485210i | −0.595522 | − | 0.803339i | \(-0.703055\pi\) |
0.948047 | + | 0.318129i | \(0.103055\pi\) | |||||||
\(114\) | 1.95931 | − | 1.42352i | 0.183506 | − | 0.133325i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.31428 | − | 2.40797i | −0.307724 | − | 0.223574i | ||||
\(117\) | 0.322656 | − | 0.104837i | 0.0298295 | − | 0.00969220i | ||||
\(118\) | 3.78206i | 0.348167i | ||||||||
\(119\) | 4.42091 | + | 13.6062i | 0.405264 | + | 1.24727i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.02048 | + | 3.14070i | −0.0927706 | + | 0.285519i | ||||
\(122\) | −10.3023 | − | 3.34742i | −0.932725 | − | 0.303061i | ||||
\(123\) | 9.17902 | + | 12.6338i | 0.827644 | + | 1.13915i | ||||
\(124\) | 7.12710 | 0.640032 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.165781 | 0.0147689 | ||||||||
\(127\) | −5.61272 | − | 7.72525i | −0.498049 | − | 0.685505i | 0.483798 | − | 0.875179i | \(-0.339257\pi\) |
−0.981847 | + | 0.189674i | \(0.939257\pi\) | |||||||
\(128\) | −0.951057 | − | 0.309017i | −0.0840623 | − | 0.0273135i | ||||
\(129\) | −4.89955 | + | 15.0793i | −0.431382 | + | 1.32766i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.73026 | + | 5.32519i | 0.151173 | + | 0.465264i | 0.997753 | − | 0.0669981i | \(-0.0213421\pi\) |
−0.846580 | + | 0.532262i | \(0.821342\pi\) | |||||||
\(132\) | 4.75742i | 0.414080i | ||||||||
\(133\) | −3.72682 | + | 1.21092i | −0.323156 | + | 0.105000i | ||||
\(134\) | −3.49771 | − | 2.54123i | −0.302156 | − | 0.219529i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.17164 | + | 3.03088i | −0.357715 | + | 0.259895i | ||||
\(137\) | 4.69296 | − | 6.45931i | 0.400947 | − | 0.551856i | −0.560035 | − | 0.828469i | \(-0.689212\pi\) |
0.960981 | + | 0.276613i | \(0.0892122\pi\) | |||||||
\(138\) | 0.660127 | − | 0.908587i | 0.0561937 | − | 0.0773440i | ||||
\(139\) | −17.8699 | + | 12.9832i | −1.51571 | + | 1.10122i | −0.552140 | + | 0.833751i | \(0.686189\pi\) |
−0.963565 | + | 0.267473i | \(0.913811\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.84883 | + | 2.79634i | 0.324130 | + | 0.235494i | ||||
\(142\) | 12.5983 | − | 4.09343i | 1.05722 | − | 0.343513i | ||||
\(143\) | − | 15.7528i | − | 1.31732i | ||||||
\(144\) | 0.0184644 | + | 0.0568277i | 0.00153870 | + | 0.00473564i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.30196 | − | 4.00703i | 0.107751 | − | 0.331624i | ||||
\(147\) | 1.13775 | + | 0.369678i | 0.0938402 | + | 0.0304905i | ||||
\(148\) | −0.615684 | − | 0.847416i | −0.0506089 | − | 0.0696572i | ||||
\(149\) | −4.18401 | −0.342768 | −0.171384 | − | 0.985204i | \(-0.554824\pi\) | ||||
−0.171384 | + | 0.985204i | \(0.554824\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.331561 | −0.0269821 | −0.0134910 | − | 0.999909i | \(-0.504294\pi\) | ||||
−0.0134910 | + | 0.999909i | \(0.504294\pi\) | |||||||
\(152\) | −0.830178 | − | 1.14264i | −0.0673364 | − | 0.0926805i | ||||
\(153\) | 0.293028 | + | 0.0952107i | 0.0236899 | + | 0.00769733i | ||||
\(154\) | 2.37871 | − | 7.32092i | 0.191682 | − | 0.589936i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00852 | + | 9.25928i | 0.240875 | + | 0.741336i | ||||
\(157\) | 3.60750i | 0.287910i | 0.989584 | + | 0.143955i | \(0.0459820\pi\) | ||||
−0.989584 | + | 0.143955i | \(0.954018\pi\) | |||||||
\(158\) | −9.41695 | + | 3.05975i | −0.749172 | + | 0.243421i | ||||
\(159\) | −0.729839 | − | 0.530259i | −0.0578800 | − | 0.0420523i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.47012 | + | 1.06811i | −0.115862 | + | 0.0841787i | ||||
\(162\) | −5.18260 | + | 7.13324i | −0.407184 | + | 0.560440i | ||||
\(163\) | −2.99409 | + | 4.12101i | −0.234515 | + | 0.322782i | −0.910013 | − | 0.414580i | \(-0.863929\pi\) |
0.675498 | + | 0.737362i | \(0.263929\pi\) | |||||||
\(164\) | 7.36789 | − | 5.35309i | 0.575336 | − | 0.418006i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.78299 | − | 2.74850i | −0.293617 | − | 0.213325i | ||||
\(167\) | −19.8418 | + | 6.44699i | −1.53540 | + | 0.498883i | −0.950104 | − | 0.311934i | \(-0.899023\pi\) |
−0.585300 | + | 0.810817i | \(0.699023\pi\) | |||||||
\(168\) | 4.75742i | 0.367043i | ||||||||
\(169\) | −5.94464 | − | 18.2957i | −0.457280 | − | 1.40736i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0260789 | + | 0.0802625i | −0.00199430 | + | 0.00613783i | ||||
\(172\) | 8.79404 | + | 2.85736i | 0.670539 | + | 0.217871i | ||||
\(173\) | −7.04620 | − | 9.69826i | −0.535713 | − | 0.737345i | 0.452275 | − | 0.891879i | \(-0.350613\pi\) |
−0.987988 | + | 0.154533i | \(0.950613\pi\) | |||||||
\(174\) | −7.02464 | −0.532537 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.77447 | 0.209133 | ||||||||
\(177\) | 3.81188 | + | 5.24660i | 0.286518 | + | 0.394359i | ||||
\(178\) | 8.73452 | + | 2.83802i | 0.654680 | + | 0.212718i | ||||
\(179\) | 2.63942 | − | 8.12330i | 0.197279 | − | 0.607164i | −0.802663 | − | 0.596433i | \(-0.796584\pi\) |
0.999942 | − | 0.0107309i | \(-0.00341581\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.41912 | + | 7.44529i | 0.179812 | + | 0.553404i | 0.999820 | − | 0.0189471i | \(-0.00603140\pi\) |
−0.820009 | + | 0.572351i | \(0.806031\pi\) | |||||||
\(182\) | − | 15.7528i | − | 1.16768i | ||||||
\(183\) | −17.6655 | + | 5.73987i | −1.30587 | + | 0.424303i | ||||
\(184\) | −0.529876 | − | 0.384978i | −0.0390630 | − | 0.0283809i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.88695 | − | 7.18329i | 0.724946 | − | 0.526704i | ||||
\(187\) | 8.40906 | − | 11.5741i | 0.614932 | − | 0.846381i | ||||
\(188\) | 1.63079 | − | 2.24459i | 0.118938 | − | 0.163704i | ||||
\(189\) | 11.7765 | − | 8.55611i | 0.856613 | − | 0.622366i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.72324 | − | 1.97855i | −0.197047 | − | 0.143163i | 0.484887 | − | 0.874577i | \(-0.338861\pi\) |
−0.681934 | + | 0.731414i | \(0.738861\pi\) | |||||||
\(192\) | −1.63079 | + | 0.529876i | −0.117692 | + | 0.0382405i | ||||
\(193\) | 15.4211i | 1.11004i | 0.831839 | + | 0.555018i | \(0.187288\pi\) | ||||
−0.831839 | + | 0.555018i | \(0.812712\pi\) | |||||||
\(194\) | 0.0278640 | + | 0.0857567i | 0.00200052 | + | 0.00615697i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.215591 | − | 0.663522i | 0.0153994 | − | 0.0473945i | ||||
\(197\) | 8.37394 | + | 2.72086i | 0.596619 | + | 0.193853i | 0.591732 | − | 0.806135i | \(-0.298444\pi\) |
0.00488692 | + | 0.999988i | \(0.498444\pi\) | |||||||
\(198\) | −0.0974433 | − | 0.134119i | −0.00692500 | − | 0.00953144i | ||||
\(199\) | 17.6222 | 1.24920 | 0.624601 | − | 0.780944i | \(-0.285262\pi\) | ||||
0.624601 | + | 0.780944i | \(0.285262\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.41340 | −0.522901 | ||||||||
\(202\) | 4.64722 | + | 6.39635i | 0.326977 | + | 0.450046i | ||||
\(203\) | 10.8098 | + | 3.51232i | 0.758700 | + | 0.246517i | ||||
\(204\) | −2.73227 | + | 8.40906i | −0.191297 | + | 0.588752i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.42091 | + | 7.45079i | 0.168673 | + | 0.519121i | ||||
\(207\) | 0.0391355i | 0.00272010i | ||||||||
\(208\) | 5.39990 | − | 1.75453i | 0.374415 | − | 0.121655i | ||||
\(209\) | 3.17022 | + | 2.30330i | 0.219289 | + | 0.159323i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.93617 | + | 3.58634i | −0.339820 | + | 0.246894i | −0.744586 | − | 0.667527i | \(-0.767353\pi\) |
0.404766 | + | 0.914420i | \(0.367353\pi\) | |||||||
\(212\) | −0.309240 | + | 0.425633i | −0.0212387 | + | 0.0292326i | ||||
\(213\) | 13.3510 | − | 18.3761i | 0.914798 | − | 1.25911i | ||||
\(214\) | −8.26974 | + | 6.00832i | −0.565308 | + | 0.410720i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.24459 | + | 3.08388i | 0.288808 | + | 0.209831i | ||||
\(217\) | −18.8061 | + | 6.11047i | −1.27664 | + | 0.414806i | ||||
\(218\) | − | 3.91091i | − | 0.264880i | ||||||
\(219\) | −2.23250 | − | 6.87092i | −0.150858 | − | 0.464294i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.04713 | − | 27.8442i | 0.608576 | − | 1.87300i | ||||
\(222\) | −1.70820 | − | 0.555026i | −0.114647 | − | 0.0372509i | ||||
\(223\) | −2.95578 | − | 4.06828i | −0.197933 | − | 0.272432i | 0.698500 | − | 0.715610i | \(-0.253851\pi\) |
−0.896434 | + | 0.443178i | \(0.853851\pi\) | |||||||
\(224\) | 2.77447 | 0.185377 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.37545 | −0.424089 | ||||||||
\(227\) | 10.4851 | + | 14.4314i | 0.695918 | + | 0.957848i | 0.999986 | + | 0.00519840i | \(0.00165471\pi\) |
−0.304069 | + | 0.952650i | \(0.598345\pi\) | |||||||
\(228\) | −2.30330 | − | 0.748388i | −0.152540 | − | 0.0495632i | ||||
\(229\) | 6.66137 | − | 20.5016i | 0.440195 | − | 1.35478i | −0.447472 | − | 0.894298i | \(-0.647676\pi\) |
0.887668 | − | 0.460485i | \(-0.152324\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.07881 | − | 12.5533i | −0.268366 | − | 0.825946i | ||||
\(232\) | 4.09668i | 0.268960i | ||||||||
\(233\) | 13.9867 | − | 4.54454i | 0.916297 | − | 0.297723i | 0.187350 | − | 0.982293i | \(-0.440010\pi\) |
0.728947 | + | 0.684570i | \(0.240010\pi\) | |||||||
\(234\) | −0.274467 | − | 0.199412i | −0.0179425 | − | 0.0130360i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.05975 | − | 2.22304i | 0.199173 | − | 0.144708i | ||||
\(237\) | −9.97963 | + | 13.7358i | −0.648247 | + | 0.892235i | ||||
\(238\) | 8.40906 | − | 11.5741i | 0.545079 | − | 0.750236i | ||||
\(239\) | 5.61478 | − | 4.07938i | 0.363190 | − | 0.263873i | −0.391192 | − | 0.920309i | \(-0.627937\pi\) |
0.754381 | + | 0.656436i | \(0.227937\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.67787 | − | 1.94559i | −0.172497 | − | 0.125326i | 0.498187 | − | 0.867070i | \(-0.333999\pi\) |
−0.670684 | + | 0.741743i | \(0.733999\pi\) | |||||||
\(242\) | 3.14070 | − | 1.02048i | 0.201892 | − | 0.0655987i | ||||
\(243\) | − | 0.620870i | − | 0.0398288i | ||||||
\(244\) | 3.34742 | + | 10.3023i | 0.214296 | + | 0.659536i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.82570 | − | 14.8520i | 0.307675 | − | 0.946927i | ||||
\(247\) | 7.62672 | + | 2.47807i | 0.485277 | + | 0.157676i | ||||
\(248\) | −4.18920 | − | 5.76594i | −0.266015 | − | 0.366138i | ||||
\(249\) | −8.01806 | −0.508124 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.46454 | −0.597397 | −0.298698 | − | 0.954348i | \(-0.596552\pi\) | ||||
−0.298698 | + | 0.954348i | \(0.596552\pi\) | |||||||
\(252\) | −0.0974433 | − | 0.134119i | −0.00613835 | − | 0.00844872i | ||||
\(253\) | 1.72823 | + | 0.561537i | 0.108653 | + | 0.0353036i | ||||
\(254\) | −2.95078 | + | 9.08158i | −0.185149 | + | 0.569829i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | − | 7.07963i | − | 0.441615i | −0.975317 | − | 0.220808i | \(-0.929131\pi\) | ||
0.975317 | − | 0.220808i | \(-0.0708693\pi\) | |||||||
\(258\) | 15.0793 | − | 4.89955i | 0.938795 | − | 0.305033i | ||||
\(259\) | 2.35113 | + | 1.70820i | 0.146092 | + | 0.106142i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.198036 | − | 0.143881i | 0.0122581 | − | 0.00890604i | ||||
\(262\) | 3.29115 | − | 4.52988i | 0.203328 | − | 0.279857i | ||||
\(263\) | −0.842563 | + | 1.15969i | −0.0519547 | + | 0.0715095i | −0.834204 | − | 0.551456i | \(-0.814072\pi\) |
0.782249 | + | 0.622966i | \(0.214072\pi\) | |||||||
\(264\) | 3.84883 | − | 2.79634i | 0.236879 | − | 0.172103i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.17022 | + | 2.30330i | 0.194379 | + | 0.141225i | ||||
\(267\) | 14.9772 | − | 4.86639i | 0.916590 | − | 0.297818i | ||||
\(268\) | 4.32340i | 0.264094i | ||||||||
\(269\) | 4.41368 | + | 13.5839i | 0.269107 | + | 0.828226i | 0.990719 | + | 0.135928i | \(0.0434015\pi\) |
−0.721612 | + | 0.692298i | \(0.756598\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.51325 | − | 29.2788i | 0.577889 | − | 1.77856i | −0.0482363 | − | 0.998836i | \(-0.515360\pi\) |
0.626125 | − | 0.779723i | \(-0.284640\pi\) | |||||||
\(272\) | 4.90406 | + | 1.59343i | 0.297352 | + | 0.0966156i | ||||
\(273\) | −15.8770 | − | 21.8529i | −0.960922 | − | 1.32260i | ||||
\(274\) | −7.98414 | −0.482340 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.12307 | −0.0676012 | ||||||||
\(277\) | −1.87485 | − | 2.58051i | −0.112649 | − | 0.155048i | 0.748970 | − | 0.662604i | \(-0.230549\pi\) |
−0.861619 | + | 0.507556i | \(0.830549\pi\) | |||||||
\(278\) | 21.0073 | + | 6.82570i | 1.25994 | + | 0.409378i | ||||
\(279\) | −0.131598 | + | 0.405017i | −0.00787856 | + | 0.0242477i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.30053 | + | 19.3910i | 0.375858 | + | 1.15677i | 0.942898 | + | 0.333081i | \(0.108088\pi\) |
−0.567040 | + | 0.823690i | \(0.691912\pi\) | |||||||
\(282\) | − | 4.75742i | − | 0.283300i | ||||||
\(283\) | −12.6461 | + | 4.10897i | −0.751733 | + | 0.244253i | −0.659727 | − | 0.751506i | \(-0.729328\pi\) |
−0.0920063 | + | 0.995758i | \(0.529328\pi\) | |||||||
\(284\) | −10.7167 | − | 7.78616i | −0.635921 | − | 0.462023i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.7443 | + | 9.25928i | −0.753587 | + | 0.547513i | ||||
\(287\) | −14.8520 | + | 20.4420i | −0.876684 | + | 1.20665i | ||||
\(288\) | 0.0351215 | − | 0.0483405i | 0.00206955 | − | 0.00284849i | ||||
\(289\) | 7.75751 | − | 5.63616i | 0.456324 | − | 0.331539i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.125087 | + | 0.0908809i | 0.00733272 | + | 0.00532753i | ||||
\(292\) | −4.00703 | + | 1.30196i | −0.234494 | + | 0.0761917i | ||||
\(293\) | 26.0420i | 1.52139i | 0.649108 | + | 0.760696i | \(0.275142\pi\) | ||||
−0.649108 | + | 0.760696i | \(0.724858\pi\) | |||||||
\(294\) | −0.369678 | − | 1.13775i | −0.0215601 | − | 0.0663550i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.323684 | + | 0.996198i | −0.0188138 | + | 0.0579028i | ||||
\(297\) | −13.8441 | − | 4.49821i | −0.803315 | − | 0.261013i | ||||
\(298\) | 2.45930 | + | 3.38494i | 0.142464 | + | 0.196084i | ||||
\(299\) | 3.71874 | 0.215060 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.6544 | −1.47869 | ||||||||
\(302\) | 0.194887 | + | 0.268239i | 0.0112145 | + | 0.0154354i | ||||
\(303\) | 12.8936 | + | 4.18937i | 0.740716 | + | 0.240673i | ||||
\(304\) | −0.436451 | + | 1.34326i | −0.0250322 | + | 0.0770411i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.0952107 | − | 0.293028i | −0.00544283 | − | 0.0167513i | ||||
\(307\) | 25.1000i | 1.43253i | 0.697826 | + | 0.716267i | \(0.254151\pi\) | ||||
−0.697826 | + | 0.716267i | \(0.745849\pi\) | |||||||
\(308\) | −7.32092 | + | 2.37871i | −0.417148 | + | 0.135540i | ||||
\(309\) | 10.8679 | + | 7.89599i | 0.618253 | + | 0.449187i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.585185 | + | 0.425162i | −0.0331828 | + | 0.0241087i | −0.604253 | − | 0.796792i | \(-0.706528\pi\) |
0.571070 | + | 0.820901i | \(0.306528\pi\) | |||||||
\(312\) | 5.72255 | − | 7.87642i | 0.323976 | − | 0.445914i | ||||
\(313\) | −12.7057 | + | 17.4879i | −0.718170 | + | 0.988477i | 0.281412 | + | 0.959587i | \(0.409197\pi\) |
−0.999583 | + | 0.0288898i | \(0.990803\pi\) | |||||||
\(314\) | 2.91853 | − | 2.12043i | 0.164702 | − | 0.119663i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.01054 | + | 5.81999i | 0.450628 | + | 0.327400i | ||||
\(317\) | 17.9119 | − | 5.81992i | 1.00603 | − | 0.326879i | 0.240758 | − | 0.970585i | \(-0.422604\pi\) |
0.765273 | + | 0.643706i | \(0.222604\pi\) | |||||||
\(318\) | 0.902131i | 0.0505890i | ||||||||
\(319\) | −3.51232 | − | 10.8098i | −0.196652 | − | 0.605233i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.41637 | + | 16.6699i | −0.302312 | + | 0.930422i | ||||
\(322\) | 1.72823 | + | 0.561537i | 0.0963107 | + | 0.0312933i | ||||
\(323\) | 4.28076 | + | 5.89196i | 0.238188 | + | 0.327837i | ||||
\(324\) | 8.81717 | 0.489843 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.09385 | 0.282122 | ||||||||
\(327\) | −3.94175 | − | 5.42535i | −0.217979 | − | 0.300023i | ||||
\(328\) | −8.66148 | − | 2.81428i | −0.478250 | − | 0.155393i | ||||
\(329\) | −2.37871 | + | 7.32092i | −0.131143 | + | 0.403615i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.21494 | + | 16.0499i | 0.286639 | + | 0.882185i | 0.985903 | + | 0.167320i | \(0.0535115\pi\) |
−0.699263 | + | 0.714864i | \(0.746489\pi\) | |||||||
\(332\) | 4.67603i | 0.256631i | ||||||||
\(333\) | 0.0595250 | − | 0.0193408i | 0.00326195 | − | 0.00105987i | ||||
\(334\) | 16.8784 | + | 12.2629i | 0.923546 | + | 0.670996i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.84883 | − | 2.79634i | 0.209971 | − | 0.152553i | ||||
\(337\) | 11.3749 | − | 15.6562i | 0.619628 | − | 0.852845i | −0.377698 | − | 0.925929i | \(-0.623284\pi\) |
0.997326 | + | 0.0730841i | \(0.0232841\pi\) | |||||||
\(338\) | −11.3074 | + | 15.5633i | −0.615040 | + | 0.846530i | ||||
\(339\) | −8.84425 | + | 6.42572i | −0.480353 | + | 0.348997i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.9974 | + | 11.6228i | 0.866309 | + | 0.629410i | ||||
\(342\) | 0.0802625 | − | 0.0260789i | 0.00434010 | − | 0.00141018i | ||||
\(343\) | − | 17.4856i | − | 0.944134i | ||||||
\(344\) | −2.85736 | − | 8.79404i | −0.154058 | − | 0.474143i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.70441 | + | 11.4010i | −0.199150 | + | 0.612921i | ||||
\(347\) | −8.59630 | − | 2.79311i | −0.461473 | − | 0.149942i | 0.0690480 | − | 0.997613i | \(-0.478004\pi\) |
−0.530521 | + | 0.847672i | \(0.678004\pi\) | |||||||
\(348\) | 4.12898 | + | 5.68305i | 0.221337 | + | 0.304644i | ||||
\(349\) | −36.7305 | −1.96614 | −0.983068 | − | 0.183240i | \(-0.941342\pi\) | ||||
−0.983068 | + | 0.183240i | \(0.941342\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −29.7891 | −1.59002 | ||||||||
\(352\) | −1.63079 | − | 2.24459i | −0.0869214 | − | 0.119637i | ||||
\(353\) | −17.4744 | − | 5.67779i | −0.930070 | − | 0.302198i | −0.195479 | − | 0.980708i | \(-0.562626\pi\) |
−0.734591 | + | 0.678510i | \(0.762626\pi\) | |||||||
\(354\) | 2.00402 | − | 6.16775i | 0.106513 | − | 0.327812i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.83802 | − | 8.73452i | −0.150415 | − | 0.462928i | ||||
\(357\) | − | 24.5313i | − | 1.29834i | ||||||
\(358\) | −8.12330 | + | 2.63942i | −0.429330 | + | 0.139498i | ||||
\(359\) | −19.7609 | − | 14.3572i | −1.04294 | − | 0.757742i | −0.0720846 | − | 0.997399i | \(-0.522965\pi\) |
−0.970858 | + | 0.239657i | \(0.922965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.7575 | − | 9.99539i | 0.724078 | − | 0.526073i | ||||
\(362\) | 4.60144 | − | 6.33334i | 0.241846 | − | 0.332873i | ||||
\(363\) | 3.32837 | − | 4.58111i | 0.174694 | − | 0.240446i | ||||
\(364\) | −12.7443 | + | 9.25928i | −0.667983 | + | 0.485318i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 15.0272 | + | 10.9179i | 0.785482 | + | 0.570686i | ||||
\(367\) | −13.8117 | + | 4.48768i | −0.720963 | + | 0.234255i | −0.646441 | − | 0.762964i | \(-0.723743\pi\) |
−0.0745221 | + | 0.997219i | \(0.523743\pi\) | |||||||
\(368\) | 0.654963i | 0.0341423i | ||||||||
\(369\) | 0.168160 | + | 0.517542i | 0.00875404 | + | 0.0269422i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.451065 | − | 1.38824i | 0.0234182 | − | 0.0720737i | ||||
\(372\) | −11.6228 | − | 3.77648i | −0.602615 | − | 0.195801i | ||||
\(373\) | −13.6888 | − | 18.8410i | −0.708778 | − | 0.975549i | −0.999823 | − | 0.0188399i | \(-0.994003\pi\) |
0.291044 | − | 0.956710i | \(-0.405997\pi\) | |||||||
\(374\) | −14.3064 | −0.739764 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.77447 | −0.143082 | ||||||||
\(377\) | −13.6719 | − | 18.8178i | −0.704140 | − | 0.969166i | ||||
\(378\) | −13.8441 | − | 4.49821i | −0.712063 | − | 0.231363i | ||||
\(379\) | −8.84332 | + | 27.2169i | −0.454251 | + | 1.39804i | 0.417762 | + | 0.908556i | \(0.362815\pi\) |
−0.872013 | + | 0.489483i | \(0.837185\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.05975 | + | 15.5723i | 0.259219 | + | 0.797794i | ||||
\(382\) | 3.36611i | 0.172225i | ||||||||
\(383\) | −15.8025 | + | 5.13454i | −0.807469 | + | 0.262363i | −0.683526 | − | 0.729927i | \(-0.739554\pi\) |
−0.123944 | + | 0.992289i | \(0.539554\pi\) | |||||||
\(384\) | 1.38723 | + | 1.00788i | 0.0707920 | + | 0.0514334i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.4759 | − | 9.06430i | 0.635008 | − | 0.461361i | ||||
\(387\) | −0.324754 | + | 0.446986i | −0.0165082 | + | 0.0227216i | ||||
\(388\) | 0.0530006 | − | 0.0729490i | 0.00269070 | − | 0.00370343i | ||||
\(389\) | 21.3392 | − | 15.5039i | 1.08194 | − | 0.786077i | 0.103922 | − | 0.994585i | \(-0.466861\pi\) |
0.978021 | + | 0.208508i | \(0.0668609\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.73227 | + | 1.98511i | 0.138177 | + | 0.100391i | ||||
\(392\) | −0.663522 | + | 0.215591i | −0.0335129 | + | 0.0108890i | ||||
\(393\) | − | 9.60109i | − | 0.484311i | ||||||
\(394\) | −2.72086 | − | 8.37394i | −0.137075 | − | 0.421873i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.0512290 | + | 0.157667i | −0.00257435 | + | 0.00792305i | ||||
\(397\) | −17.0321 | − | 5.53406i | −0.854816 | − | 0.277747i | −0.151354 | − | 0.988480i | \(-0.548363\pi\) |
−0.703462 | + | 0.710733i | \(0.748363\pi\) | |||||||
\(398\) | −10.3580 | − | 14.2566i | −0.519202 | − | 0.714620i | ||||
\(399\) | 6.71930 | 0.336386 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.0164 | 1.59882 | 0.799411 | − | 0.600785i | \(-0.205145\pi\) | ||||
0.799411 | + | 0.600785i | \(0.205145\pi\) | |||||||
\(402\) | 4.35749 | + | 5.99757i | 0.217332 | + | 0.299132i | ||||
\(403\) | 38.4856 | + | 12.5047i | 1.91710 | + | 0.622905i | ||||
\(404\) | 2.44319 | − | 7.51936i | 0.121553 | − | 0.374102i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.51232 | − | 10.8098i | −0.174314 | − | 0.536482i | ||||
\(407\) | − | 2.90615i | − | 0.144053i | ||||||
\(408\) | 8.40906 | − | 2.73227i | 0.416311 | − | 0.135268i | ||||
\(409\) | 14.5901 | + | 10.6003i | 0.721435 | + | 0.524153i | 0.886842 | − | 0.462072i | \(-0.152894\pi\) |
−0.165407 | + | 0.986225i | \(0.552894\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.0759 | + | 8.04709i | −0.546332 | + | 0.396934i | ||||
\(412\) | 4.60484 | − | 6.33802i | 0.226864 | − | 0.312252i | ||||
\(413\) | −6.16775 | + | 8.48918i | −0.303495 | + | 0.417725i | ||||
\(414\) | 0.0316613 | − | 0.0230033i | 0.00155607 | − | 0.00113055i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.59343 | − | 3.33732i | −0.225211 | − | 0.163626i | ||||
\(417\) | 36.0216 | − | 11.7041i | 1.76398 | − | 0.573153i | ||||
\(418\) | − | 3.91861i | − | 0.191666i | ||||||
\(419\) | 6.03511 | + | 18.5742i | 0.294834 | + | 0.907407i | 0.983277 | + | 0.182116i | \(0.0582947\pi\) |
−0.688443 | + | 0.725291i | \(0.741705\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.04242 | + | 18.5967i | −0.294490 | + | 0.906346i | 0.688903 | + | 0.724854i | \(0.258093\pi\) |
−0.983392 | + | 0.181492i | \(0.941907\pi\) | |||||||
\(422\) | 5.80281 | + | 1.88545i | 0.282477 | + | 0.0917822i | ||||
\(423\) | 0.0974433 | + | 0.134119i | 0.00473786 | + | 0.00652110i | ||||
\(424\) | 0.526111 | 0.0255502 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −22.7142 | −1.10050 | ||||||||
\(427\) | −17.6655 | − | 24.3145i | −0.854893 | − | 1.17666i | ||||
\(428\) | 9.72166 | + | 3.15876i | 0.469914 | + | 0.152684i | ||||
\(429\) | −8.34705 | + | 25.6896i | −0.402999 | + | 1.24030i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.55002 | − | 20.1589i | −0.315503 | − | 0.971019i | −0.975547 | − | 0.219792i | \(-0.929462\pi\) |
0.660044 | − | 0.751227i | \(-0.270538\pi\) | |||||||
\(432\) | − | 5.24660i | − | 0.252427i | ||||||
\(433\) | 8.13122 | − | 2.64199i | 0.390761 | − | 0.126966i | −0.107045 | − | 0.994254i | \(-0.534139\pi\) |
0.497807 | + | 0.867288i | \(0.334139\pi\) | |||||||
\(434\) | 15.9974 | + | 11.6228i | 0.767901 | + | 0.557913i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.16400 | + | 2.29878i | −0.151528 | + | 0.110091i | ||||
\(437\) | −0.543736 | + | 0.748388i | −0.0260104 | + | 0.0358003i | ||||
\(438\) | −4.24646 | + | 5.84475i | −0.202904 | + | 0.279273i | ||||
\(439\) | −22.7102 | + | 16.4999i | −1.08390 | + | 0.787499i | −0.978359 | − | 0.206916i | \(-0.933657\pi\) |
−0.105541 | + | 0.994415i | \(0.533657\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0337257 | + | 0.0245031i | 0.00160598 | + | 0.00116682i | ||||
\(442\) | −27.8442 | + | 9.04713i | −1.32441 | + | 0.430328i | ||||
\(443\) | 33.0546i | 1.57047i | 0.619197 | + | 0.785236i | \(0.287458\pi\) | ||||
−0.619197 | + | 0.785236i | \(0.712542\pi\) | |||||||
\(444\) | 0.555026 | + | 1.70820i | 0.0263404 | + | 0.0810673i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.55394 | + | 4.78254i | −0.0735813 | + | 0.226460i | ||||
\(447\) | 6.82325 | + | 2.21701i | 0.322729 | + | 0.104861i | ||||
\(448\) | −1.63079 | − | 2.24459i | −0.0770476 | − | 0.106047i | ||||
\(449\) | 37.1628 | 1.75382 | 0.876911 | − | 0.480652i | \(-0.159600\pi\) | ||||
0.876911 | + | 0.480652i | \(0.159600\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.2677 | 1.18981 | ||||||||
\(452\) | 3.74740 | + | 5.15785i | 0.176263 | + | 0.242605i | ||||
\(453\) | 0.540707 | + | 0.175686i | 0.0254046 | + | 0.00825446i | ||||
\(454\) | 5.51232 | − | 16.9652i | 0.258706 | − | 0.796215i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.748388 | + | 2.30330i | 0.0350465 | + | 0.107862i | ||||
\(457\) | 29.3139i | 1.37125i | 0.727956 | + | 0.685624i | \(0.240471\pi\) | ||||
−0.727956 | + | 0.685624i | \(0.759529\pi\) | |||||||
\(458\) | −20.5016 | + | 6.66137i | −0.957976 | + | 0.311265i | ||||
\(459\) | −21.8870 | − | 15.9018i | −1.02160 | − | 0.742233i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.20624 | + | 5.23564i | −0.335628 | + | 0.243848i | −0.742815 | − | 0.669497i | \(-0.766510\pi\) |
0.407187 | + | 0.913345i | \(0.366510\pi\) | |||||||
\(462\) | −7.75836 | + | 10.6785i | −0.360952 | + | 0.496807i | ||||
\(463\) | 10.7430 | − | 14.7865i | 0.499271 | − | 0.687187i | −0.482793 | − | 0.875734i | \(-0.660378\pi\) |
0.982064 | + | 0.188547i | \(0.0603778\pi\) | |||||||
\(464\) | 3.31428 | − | 2.40797i | 0.153862 | − | 0.111787i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.8978 | − | 8.64424i | −0.551154 | − | 0.400436i | ||||
\(467\) | 34.8886 | − | 11.3360i | 1.61445 | − | 0.524568i | 0.643829 | − | 0.765169i | \(-0.277345\pi\) |
0.970624 | + | 0.240601i | \(0.0773446\pi\) | |||||||
\(468\) | 0.339260i | 0.0156823i | ||||||||
\(469\) | −3.70670 | − | 11.4081i | −0.171160 | − | 0.526775i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.91153 | − | 5.88308i | 0.0880785 | − | 0.271078i | ||||
\(472\) | −3.59695 | − | 1.16872i | −0.165563 | − | 0.0537948i | ||||
\(473\) | 15.0793 | + | 20.7548i | 0.693346 | + | 0.954309i | ||||
\(474\) | 16.9784 | 0.779842 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.3064 | −0.655731 | ||||||||
\(477\) | −0.0184778 | − | 0.0254325i | −0.000846040 | − | 0.00116447i | ||||
\(478\) | −6.60057 | − | 2.14465i | −0.301903 | − | 0.0980942i | ||||
\(479\) | 3.89046 | − | 11.9736i | 0.177760 | − | 0.547088i | −0.821989 | − | 0.569503i | \(-0.807136\pi\) |
0.999749 | + | 0.0224155i | \(0.00713568\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.83781 | − | 5.65620i | −0.0837969 | − | 0.257900i | ||||
\(482\) | 3.31003i | 0.150768i | ||||||||
\(483\) | 2.96343 | − | 0.962877i | 0.134841 | − | 0.0438124i | ||||
\(484\) | −2.67164 | − | 1.94106i | −0.121438 | − | 0.0882301i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.502294 | + | 0.364938i | −0.0227845 | + | 0.0165539i | ||||
\(487\) | −10.7715 | + | 14.8257i | −0.488103 | + | 0.671816i | −0.980037 | − | 0.198816i | \(-0.936290\pi\) |
0.491934 | + | 0.870633i | \(0.336290\pi\) | |||||||
\(488\) | 6.36716 | − | 8.76365i | 0.288228 | − | 0.396712i | ||||
\(489\) | 7.06635 | − | 5.13401i | 0.319552 | − | 0.232168i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.5595 | − | 12.7577i | −0.792448 | − | 0.575747i | 0.116241 | − | 0.993221i | \(-0.462915\pi\) |
−0.908689 | + | 0.417474i | \(0.862915\pi\) | |||||||
\(492\) | −14.8520 | + | 4.82570i | −0.669578 | + | 0.217559i | ||||
\(493\) | − | 21.1243i | − | 0.951389i | ||||||
\(494\) | −2.47807 | − | 7.62672i | −0.111494 | − | 0.343143i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.20239 | + | 6.77827i | −0.0988904 | + | 0.304353i | ||||
\(497\) | 34.9535 | + | 11.3571i | 1.56788 | + | 0.509434i | ||||
\(498\) | 4.71290 | + | 6.48675i | 0.211190 | + | 0.290678i | ||||
\(499\) | −15.8391 | −0.709055 | −0.354527 | − | 0.935046i | \(-0.615358\pi\) | ||||
−0.354527 | + | 0.935046i | \(0.615358\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 35.7739 | 1.59826 | ||||||||
\(502\) | 5.56312 | + | 7.65697i | 0.248294 | + | 0.341748i | ||||
\(503\) | −26.2044 | − | 8.51433i | −1.16840 | − | 0.379635i | −0.340353 | − | 0.940298i | \(-0.610547\pi\) |
−0.828044 | + | 0.560662i | \(0.810547\pi\) | |||||||
\(504\) | −0.0512290 | + | 0.157667i | −0.00228192 | + | 0.00702303i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.561537 | − | 1.72823i | −0.0249634 | − | 0.0768294i | ||||
\(507\) | 32.9864i | 1.46498i | ||||||||
\(508\) | 9.08158 | − | 2.95078i | 0.402930 | − | 0.130920i | ||||
\(509\) | −22.3386 | − | 16.2300i | −0.990142 | − | 0.719380i | −0.0301894 | − | 0.999544i | \(-0.509611\pi\) |
−0.959952 | + | 0.280164i | \(0.909611\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.45701 | − | 6.87092i | 0.418354 | − | 0.303952i | ||||
\(512\) | 0.587785 | − | 0.809017i | 0.0259767 | − | 0.0357538i | ||||
\(513\) | 4.35562 | − | 5.99499i | 0.192305 | − | 0.264685i | ||||
\(514\) | −5.72754 | + | 4.16130i | −0.252631 | + | 0.183547i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −12.8272 | − | 9.31951i | −0.564686 | − | 0.410268i | ||||
\(517\) | 7.32092 | − | 2.37871i | 0.321974 | − | 0.104616i | ||||
\(518\) | − | 2.90615i | − | 0.127689i | ||||||
\(519\) | 6.35200 | + | 19.5495i | 0.278822 | + | 0.858126i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.28084 | − | 16.2527i | 0.231358 | − | 0.712046i | −0.766226 | − | 0.642571i | \(-0.777868\pi\) |
0.997584 | − | 0.0694747i | \(-0.0221323\pi\) | |||||||
\(522\) | −0.232805 | − | 0.0756429i | −0.0101896 | − | 0.00331080i | ||||
\(523\) | 21.3456 | + | 29.3796i | 0.933376 | + | 1.28468i | 0.958528 | + | 0.284999i | \(0.0919932\pi\) |
−0.0251516 | + | 0.999684i | \(0.508007\pi\) | |||||||
\(524\) | −5.59923 | −0.244604 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.43345 | 0.0625016 | ||||||||
\(527\) | 21.6013 | + | 29.7317i | 0.940970 | + | 1.29513i | ||||
\(528\) | −4.52458 | − | 1.47012i | −0.196907 | − | 0.0639789i | ||||
\(529\) | 6.97483 | − | 21.4663i | 0.303253 | − | 0.933318i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.0698337 | + | 0.214926i | 0.00303052 | + | 0.00932699i | ||||
\(532\) | − | 3.91861i | − | 0.169893i | ||||||
\(533\) | 49.1780 | − | 15.9789i | 2.13014 | − | 0.692123i | ||||
\(534\) | −12.7404 | − | 9.25642i | −0.551330 | − | 0.400565i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.49771 | − | 2.54123i | 0.151078 | − | 0.109764i | ||||
\(537\) | −8.60868 | + | 11.8488i | −0.371492 | + | 0.511315i | ||||
\(538\) | 8.39532 | − | 11.5552i | 0.361948 | − | 0.498178i | ||||
\(539\) | 1.56598 | − | 1.13775i | 0.0674516 | − | 0.0490064i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.1742 | − | 14.6574i | −0.867355 | − | 0.630170i | 0.0625209 | − | 0.998044i | \(-0.480086\pi\) |
−0.929876 | + | 0.367873i | \(0.880086\pi\) | |||||||
\(542\) | −29.2788 | + | 9.51325i | −1.25763 | + | 0.408629i | ||||
\(543\) | − | 13.4235i | − | 0.576060i | ||||||
\(544\) | −1.59343 | − | 4.90406i | −0.0683176 | − | 0.210260i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.34705 | + | 25.6896i | −0.357221 | + | 1.09941i | ||||
\(547\) | 6.34546 | + | 2.06176i | 0.271312 | + | 0.0881547i | 0.441513 | − | 0.897255i | \(-0.354442\pi\) |
−0.170201 | + | 0.985409i | \(0.554442\pi\) | |||||||
\(548\) | 4.69296 | + | 6.45931i | 0.200473 | + | 0.275928i | ||||
\(549\) | −0.647264 | −0.0276245 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.78609 | 0.246496 | ||||||||
\(552\) | 0.660127 | + | 0.908587i | 0.0280969 | + | 0.0386720i | ||||
\(553\) | −26.1270 | − | 8.48918i | −1.11103 | − | 0.360997i | ||||
\(554\) | −0.985668 | + | 3.03357i | −0.0418770 | + | 0.128884i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.82570 | − | 21.0073i | −0.289474 | − | 0.890909i | ||||
\(557\) | − | 20.4328i | − | 0.865765i | −0.901450 | − | 0.432882i | \(-0.857497\pi\) | ||
0.901450 | − | 0.432882i | \(-0.142503\pi\) | |||||||
\(558\) | 0.405017 | − | 0.131598i | 0.0171457 | − | 0.00557098i | ||||
\(559\) | 42.4736 | + | 30.8589i | 1.79644 | + | 1.30519i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.8463 | + | 14.4192i | −0.837910 | + | 0.608777i | ||||
\(562\) | 11.9843 | − | 16.4950i | 0.505528 | − | 0.695799i | ||||
\(563\) | 0.354320 | − | 0.487680i | 0.0149328 | − | 0.0205532i | −0.801485 | − | 0.598014i | \(-0.795957\pi\) |
0.816418 | + | 0.577461i | \(0.195957\pi\) | |||||||
\(564\) | −3.84883 | + | 2.79634i | −0.162065 | + | 0.117747i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.7574 | + | 7.81572i | 0.452168 | + | 0.328519i | ||||
\(567\) | −23.2657 | + | 7.55947i | −0.977066 | + | 0.317468i | ||||
\(568\) | 13.2466i | 0.555815i | ||||||||
\(569\) | −10.4688 | − | 32.2195i | −0.438873 | − | 1.35071i | −0.889065 | − | 0.457781i | \(-0.848644\pi\) |
0.450192 | − | 0.892932i | \(-0.351356\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.92521 | + | 5.92520i | −0.0805677 | + | 0.247962i | −0.983225 | − | 0.182399i | \(-0.941614\pi\) |
0.902657 | + | 0.430361i | \(0.141614\pi\) | |||||||
\(572\) | 14.9818 | + | 4.86789i | 0.626422 | + | 0.203537i | ||||
\(573\) | 3.39265 | + | 4.66958i | 0.141730 | + | 0.195074i | ||||
\(574\) | 25.2677 | 1.05465 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.0597522 | −0.00248967 | ||||||||
\(577\) | −2.22244 | − | 3.05893i | −0.0925214 | − | 0.127345i | 0.760247 | − | 0.649634i | \(-0.225078\pi\) |
−0.852768 | + | 0.522290i | \(0.825078\pi\) | |||||||
\(578\) | −9.11949 | − | 2.96310i | −0.379321 | − | 0.123249i | ||||
\(579\) | 8.17127 | − | 25.1486i | 0.339587 | − | 1.04514i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.00903 | − | 12.3385i | −0.166323 | − | 0.511889i | ||||
\(582\) | − | 0.154616i | − | 0.00640903i | ||||||
\(583\) | −1.38824 | + | 0.451065i | −0.0574949 | + | 0.0186812i | ||||
\(584\) | 3.40859 | + | 2.47648i | 0.141048 | + | 0.102478i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.0684 | − | 15.3071i | 0.870330 | − | 0.632332i | ||||
\(587\) | 9.61184 | − | 13.2296i | 0.396723 | − | 0.546042i | −0.563195 | − | 0.826324i | \(-0.690428\pi\) |
0.959918 | + | 0.280282i | \(0.0904279\pi\) | |||||||
\(588\) | −0.703169 | + | 0.967829i | −0.0289982 | + | 0.0399126i | ||||
\(589\) | −8.14373 | + | 5.91676i | −0.335556 | + | 0.243796i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.2144 | − | 8.87430i | −0.502435 | − | 0.365040i | ||||
\(592\) | 0.996198 | − | 0.323684i | 0.0409435 | − | 0.0133033i | ||||
\(593\) | − | 9.53314i | − | 0.391479i | −0.980656 | − | 0.195740i | \(-0.937289\pi\) | ||
0.980656 | − | 0.195740i | \(-0.0627107\pi\) | |||||||
\(594\) | 4.49821 | + | 13.8441i | 0.184564 | + | 0.568030i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.29293 | − | 3.97923i | 0.0529605 | − | 0.162996i | ||||
\(597\) | −28.7381 | − | 9.33756i | −1.17617 | − | 0.382161i | ||||
\(598\) | −2.18582 | − | 3.00852i | −0.0893848 | − | 0.123028i | ||||
\(599\) | 16.0682 | 0.656528 | 0.328264 | − | 0.944586i | \(-0.393536\pi\) | ||||
0.328264 | + | 0.944586i | \(0.393536\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0380 | 0.613413 | 0.306707 | − | 0.951804i | \(-0.400773\pi\) | ||||
0.306707 | + | 0.951804i | \(0.400773\pi\) | |||||||
\(602\) | 15.0793 | + | 20.7548i | 0.614585 | + | 0.845904i | ||||
\(603\) | −0.245689 | − | 0.0798292i | −0.0100052 | − | 0.00325090i | ||||
\(604\) | 0.102458 | − | 0.315333i | 0.00416896 | − | 0.0128307i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.18937 | − | 12.8936i | −0.170182 | − | 0.523765i | ||||
\(607\) | − | 44.8348i | − | 1.81979i | −0.414840 | − | 0.909894i | \(-0.636163\pi\) | ||
0.414840 | − | 0.909894i | \(-0.363837\pi\) | |||||||
\(608\) | 1.34326 | − | 0.436451i | 0.0544763 | − | 0.0177004i | ||||
\(609\) | −15.7674 | − | 11.4557i | −0.638929 | − | 0.464209i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.7443 | − | 9.25928i | 0.515580 | − | 0.374590i | ||||
\(612\) | −0.181101 | + | 0.249265i | −0.00732059 | + | 0.0100759i | ||||
\(613\) | 9.13937 | − | 12.5793i | 0.369136 | − | 0.508072i | −0.583530 | − | 0.812092i | \(-0.698329\pi\) |
0.952666 | + | 0.304020i | \(0.0983289\pi\) | |||||||
\(614\) | 20.3064 | − | 14.7534i | 0.819498 | − | 0.595400i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.22754 | + | 4.52458i | 0.250915 | + | 0.182300i | ||||
\(617\) | −16.7380 | + | 5.43852i | −0.673848 | + | 0.218946i | −0.625900 | − | 0.779903i | \(-0.715268\pi\) |
−0.0479478 | + | 0.998850i | \(0.515268\pi\) | |||||||
\(618\) | − | 13.4335i | − | 0.540373i | ||||||
\(619\) | 11.5229 | + | 35.4637i | 0.463143 | + | 1.42541i | 0.861303 | + | 0.508091i | \(0.169649\pi\) |
−0.398161 | + | 0.917316i | \(0.630351\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.06188 | − | 3.26814i | 0.0426120 | − | 0.131146i | ||||
\(622\) | 0.687926 | + | 0.223521i | 0.0275833 | + | 0.00896236i | ||||
\(623\) | 14.9772 | + | 20.6144i | 0.600049 | + | 0.825897i | ||||
\(624\) | −9.73579 | −0.389743 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.6163 | 0.863960 | ||||||||
\(627\) | −3.94951 | − | 5.43603i | −0.157728 | − | 0.217094i | ||||
\(628\) | −3.43094 | − | 1.11478i | −0.136909 | − | 0.0444845i | ||||
\(629\) | 1.66906 | − | 5.13683i | 0.0665496 | − | 0.204819i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.64380 | + | 8.13677i | 0.105248 | + | 0.323920i | 0.989789 | − | 0.142543i | \(-0.0455280\pi\) |
−0.884541 | + | 0.466463i | \(0.845528\pi\) | |||||||
\(632\) | − | 9.90157i | − | 0.393863i | ||||||
\(633\) | 9.95017 | − | 3.23301i | 0.395484 | − | 0.128500i | ||||
\(634\) | −15.2367 | − | 11.0701i | −0.605129 | − | 0.439652i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.729839 | − | 0.530259i | 0.0289400 | − | 0.0210261i | ||||
\(637\) | 2.32834 | − | 3.20469i | 0.0922523 | − | 0.126974i | ||||
\(638\) | −6.68083 | + | 9.19537i | −0.264497 | + | 0.364048i | ||||
\(639\) | 0.640348 | − | 0.465240i | 0.0253318 | − | 0.0184046i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.4582 | + | 13.4107i | 0.729055 | + | 0.529690i | 0.889264 | − | 0.457394i | \(-0.151217\pi\) |
−0.160209 | + | 0.987083i | \(0.551217\pi\) | |||||||
\(642\) | 16.6699 | − | 5.41637i | 0.657908 | − | 0.213767i | ||||
\(643\) | − | 34.7745i | − | 1.37137i | −0.727898 | − | 0.685686i | \(-0.759503\pi\) | ||
0.727898 | − | 0.685686i | \(-0.240497\pi\) | |||||||
\(644\) | −0.561537 | − | 1.72823i | −0.0221277 | − | 0.0681020i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.25053 | − | 6.92641i | 0.0885459 | − | 0.272516i | ||||
\(647\) | −15.6526 | − | 5.08583i | −0.615366 | − | 0.199945i | −0.0152844 | − | 0.999883i | \(-0.504865\pi\) |
−0.600082 | + | 0.799939i | \(0.704865\pi\) | |||||||
\(648\) | −5.18260 | − | 7.13324i | −0.203592 | − | 0.280220i | ||||
\(649\) | 10.4932 | 0.411894 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33.9066 | 1.32890 | ||||||||
\(652\) | −2.99409 | − | 4.12101i | −0.117257 | − | 0.161391i | ||||
\(653\) | −28.7306 | − | 9.33515i | −1.12432 | − | 0.365313i | −0.312903 | − | 0.949785i | \(-0.601301\pi\) |
−0.811414 | + | 0.584473i | \(0.801301\pi\) | |||||||
\(654\) | −2.07230 | + | 6.37788i | −0.0810333 | + | 0.249395i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.81428 | + | 8.66148i | 0.109879 | + | 0.338174i | ||||
\(657\) | − | 0.251751i | − | 0.00982173i | ||||||
\(658\) | 7.32092 | − | 2.37871i | 0.285399 | − | 0.0927318i | ||||
\(659\) | −23.0523 | − | 16.7485i | −0.897991 | − | 0.652428i | 0.0399585 | − | 0.999201i | \(-0.487277\pi\) |
−0.937949 | + | 0.346773i | \(0.887277\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.0448 | + | 29.8208i | −1.59646 | + | 1.15990i | −0.702562 | + | 0.711622i | \(0.747961\pi\) |
−0.893897 | + | 0.448273i | \(0.852039\pi\) | |||||||
\(662\) | 9.91941 | − | 13.6529i | 0.385529 | − | 0.530635i | ||||
\(663\) | −29.5080 | + | 40.6142i | −1.14599 | + | 1.57733i | ||||
\(664\) | 3.78299 | − | 2.74850i | 0.146809 | − | 0.106663i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.0506350 | − | 0.0367885i | −0.00196207 | − | 0.00142552i | ||||
\(667\) | 2.55185 | − | 0.829146i | 0.0988080 | − | 0.0321047i | ||||
\(668\) | − | 20.8629i | − | 0.807209i | ||||||
\(669\) | 2.66457 | + | 8.20070i | 0.103018 | + | 0.317057i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.28730 | + | 28.5834i | −0.358532 | + | 1.10345i | ||||
\(672\) | −4.52458 | − | 1.47012i | −0.174539 | − | 0.0567113i | ||||
\(673\) | −12.0171 | − | 16.5401i | −0.463224 | − | 0.637573i | 0.511949 | − | 0.859016i | \(-0.328923\pi\) |
−0.975173 | + | 0.221442i | \(0.928923\pi\) | |||||||
\(674\) | −19.3521 | −0.745414 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.2373 | 0.739894 | ||||||||
\(677\) | −5.01592 | − | 6.90383i | −0.192778 | − | 0.265336i | 0.701676 | − | 0.712496i | \(-0.252435\pi\) |
−0.894454 | + | 0.447160i | \(0.852435\pi\) | |||||||
\(678\) | 10.3970 | + | 3.37820i | 0.399296 | + | 0.129739i | ||||
\(679\) | −0.0773079 | + | 0.237929i | −0.00296680 | + | 0.00913088i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.45206 | − | 29.0904i | −0.362204 | − | 1.11475i | ||||
\(682\) | − | 19.7739i | − | 0.757182i | ||||||
\(683\) | −46.1913 | + | 15.0085i | −1.76746 | + | 0.574283i | −0.997929 | − | 0.0643246i | \(-0.979511\pi\) |
−0.769532 | + | 0.638608i | \(0.779511\pi\) | |||||||
\(684\) | −0.0682754 | − | 0.0496050i | −0.00261058 | − | 0.00189669i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −14.1462 | + | 10.2778i | −0.540103 | + | 0.392408i | ||||
\(687\) | −21.7266 | + | 29.9041i | −0.828921 | + | 1.14091i | ||||
\(688\) | −5.43502 | + | 7.48066i | −0.207208 | + | 0.285197i | ||||
\(689\) | −2.41665 | + | 1.75580i | −0.0920671 | + | 0.0668907i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.2501 | − | 26.3373i | −1.37902 | − | 1.00192i | −0.996971 | − | 0.0777740i | \(-0.975219\pi\) |
−0.382048 | − | 0.924142i | \(-0.624781\pi\) | |||||||
\(692\) | 11.4010 | − | 3.70441i | 0.433401 | − | 0.140820i | ||||
\(693\) | − | 0.459953i | − | 0.0174722i | ||||||
\(694\) | 2.79311 | + | 8.59630i | 0.106025 | + | 0.326311i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.17073 | − | 6.68083i | 0.0822814 | − | 0.253236i | ||||
\(697\) | 44.6623 | + | 14.5117i | 1.69171 | + | 0.549669i | ||||
\(698\) | 21.5896 | + | 29.7156i | 0.817179 | + | 1.12475i | ||||
\(699\) | −25.2174 | −0.953809 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.21913 | 0.0838152 | 0.0419076 | − | 0.999121i | \(-0.486656\pi\) | ||||
0.0419076 | + | 0.999121i | \(0.486656\pi\) | |||||||
\(702\) | 17.5096 | + | 24.0999i | 0.660857 | + | 0.909591i | ||||
\(703\) | 1.40701 | + | 0.457166i | 0.0530665 | + | 0.0172424i | ||||
\(704\) | −0.857358 | + | 2.63868i | −0.0323129 | + | 0.0994488i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.67779 | + | 17.4744i | 0.213686 | + | 0.657659i | ||||
\(707\) | 21.9358i | 0.824982i | ||||||||
\(708\) | −6.16775 | + | 2.00402i | −0.231798 | + | 0.0753158i | ||||
\(709\) | 27.7968 | + | 20.1955i | 1.04393 | + | 0.758459i | 0.971049 | − | 0.238882i | \(-0.0767808\pi\) |
0.0728805 | + | 0.997341i | \(0.476781\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.478647 | + | 0.347757i | −0.0179507 | + | 0.0130419i | ||||
\(712\) | −5.39823 | + | 7.43002i | −0.202307 | + | 0.278452i | ||||
\(713\) | −2.74377 | + | 3.77648i | −0.102755 | + | 0.141430i | ||||
\(714\) | −19.8463 | + | 14.4192i | −0.742728 | + | 0.539623i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.91009 | + | 5.02047i | 0.258242 | + | 0.187624i | ||||
\(717\) | −11.3181 | + | 3.67747i | −0.422682 | + | 0.137338i | ||||
\(718\) | 24.4259i | 0.911565i | ||||||||
\(719\) | −3.70511 | − | 11.4032i | −0.138177 | − | 0.425266i | 0.857893 | − | 0.513828i | \(-0.171773\pi\) |
−0.996071 | + | 0.0885618i | \(0.971773\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.71673 | + | 20.6720i | −0.250144 | + | 0.769864i | ||||
\(722\) | −16.1729 | − | 5.25489i | −0.601892 | − | 0.195567i | ||||
\(723\) | 3.33613 | + | 4.59179i | 0.124072 | + | 0.170770i | ||||
\(724\) | −7.82844 | −0.290942 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.66256 | −0.210157 | ||||||||
\(727\) | −24.7944 | − | 34.1265i | −0.919573 | − | 1.26568i | −0.963790 | − | 0.266661i | \(-0.914080\pi\) |
0.0442177 | − | 0.999022i | \(-0.485920\pi\) | |||||||
\(728\) | 14.9818 | + | 4.86789i | 0.555264 | + | 0.180416i | ||||
\(729\) | −8.50295 | + | 26.1694i | −0.314924 | + | 0.969237i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.7338 | + | 45.3459i | 0.544948 | + | 1.67718i | ||||
\(732\) | − | 18.5746i | − | 0.686537i | ||||||
\(733\) | −0.306605 | + | 0.0996219i | −0.0113247 | + | 0.00367962i | −0.314674 | − | 0.949200i | \(-0.601895\pi\) |
0.303349 | + | 0.952879i | \(0.401895\pi\) | |||||||
\(734\) | 11.7489 | + | 8.53607i | 0.433660 | + | 0.315072i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.529876 | − | 0.384978i | 0.0195315 | − | 0.0141905i | ||||
\(737\) | −7.05056 | + | 9.70427i | −0.259711 | + | 0.357461i | ||||
\(738\) | 0.319859 | − | 0.440248i | 0.0117742 | − | 0.0162057i | ||||
\(739\) | −4.44942 | + | 3.23269i | −0.163674 | + | 0.118916i | −0.666607 | − | 0.745409i | \(-0.732254\pi\) |
0.502933 | + | 0.864325i | \(0.332254\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.1245 | − | 8.08244i | −0.408670 | − | 0.296916i | ||||
\(742\) | −1.38824 | + | 0.451065i | −0.0509638 | + | 0.0165591i | ||||
\(743\) | 6.03812i | 0.221517i | 0.993847 | + | 0.110759i | \(0.0353280\pi\) | ||||
−0.993847 | + | 0.110759i | \(0.964672\pi\) | |||||||
\(744\) | 3.77648 | + | 11.6228i | 0.138452 | + | 0.426113i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.19662 | + | 22.1489i | −0.263487 | + | 0.810929i | ||||
\(747\) | −0.265728 | − | 0.0863404i | −0.00972249 | − | 0.00315903i | ||||
\(748\) | 8.40906 | + | 11.5741i | 0.307466 | + | 0.423190i | ||||
\(749\) | −28.3605 | −1.03627 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.5719 | −0.495244 | −0.247622 | − | 0.968857i | \(-0.579649\pi\) | ||||
−0.247622 | + | 0.968857i | \(0.579649\pi\) | |||||||
\(752\) | 1.63079 | + | 2.24459i | 0.0594688 | + | 0.0818518i | ||||
\(753\) | 15.4347 | + | 5.01503i | 0.562471 | + | 0.182758i | ||||
\(754\) | −7.18776 | + | 22.1216i | −0.261763 | + | 0.805623i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.49821 | + | 13.8441i | 0.163598 | + | 0.503504i | ||||
\(757\) | 33.0661i | 1.20181i | 0.799321 | + | 0.600904i | \(0.205193\pi\) | ||||
−0.799321 | + | 0.600904i | \(0.794807\pi\) | |||||||
\(758\) | 27.2169 | − | 8.84332i | 0.988563 | − | 0.321204i | ||||
\(759\) | −2.52084 | − | 1.83150i | −0.0915008 | − | 0.0664792i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.19767 | + | 3.04978i | −0.152165 | + | 0.110555i | −0.661263 | − | 0.750154i | \(-0.729979\pi\) |
0.509098 | + | 0.860709i | \(0.329979\pi\) | |||||||
\(762\) | 9.62422 | − | 13.2466i | 0.348649 | − | 0.479874i | ||||
\(763\) | 6.37788 | − | 8.77840i | 0.230895 | − | 0.317799i | ||||
\(764\) | 2.72324 | − | 1.97855i | 0.0985233 | − | 0.0715814i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.4424 | + | 9.76647i | 0.485694 | + | 0.352877i | ||||
\(767\) | 20.4227 | − | 6.63575i | 0.737422 | − | 0.239603i | ||||
\(768\) | − | 1.71472i | − | 0.0618745i | ||||||
\(769\) | −10.2191 | − | 31.4512i | −0.368511 | − | 1.13416i | −0.947753 | − | 0.319005i | \(-0.896651\pi\) |
0.579242 | − | 0.815156i | \(-0.303349\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.75133 | + | 11.5454i | −0.135101 | + | 0.415798i | ||||
\(772\) | −14.6663 | − | 4.76538i | −0.527853 | − | 0.171510i | ||||
\(773\) | −0.664758 | − | 0.914961i | −0.0239097 | − | 0.0329088i | 0.796895 | − | 0.604118i | \(-0.206474\pi\) |
−0.820804 | + | 0.571209i | \(0.806474\pi\) | |||||||
\(774\) | 0.552505 | 0.0198594 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.0901699 | −0.00323691 | ||||||||
\(777\) | −2.92907 | − | 4.03152i | −0.105080 | − | 0.144630i | ||||
\(778\) | −25.0858 | − | 8.15086i | −0.899369 | − | 0.292223i | ||||
\(779\) | −3.97485 | + | 12.2333i | −0.142414 | + | 0.438305i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.3571 | − | 34.9535i | −0.406388 | − | 1.25073i | ||||
\(782\) | − | 3.37727i | − | 0.120771i | ||||||
\(783\) | −20.4417 | + | 6.64191i | −0.730526 | + | 0.237362i | ||||
\(784\) | 0.564426 | + | 0.410079i | 0.0201581 | + | 0.0146457i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.76745 | + | 5.64338i | −0.277056 | + | 0.201293i | ||||
\(787\) | 9.26408 | − | 12.7509i | 0.330229 | − | 0.454521i | −0.611327 | − | 0.791378i | \(-0.709364\pi\) |
0.941556 | + | 0.336857i | \(0.109364\pi\) | |||||||
\(788\) | −5.17538 | + | 7.12330i | −0.184365 | + | 0.253757i | ||||
\(789\) | 1.98854 | − | 1.44476i | 0.0707938 | − | 0.0514347i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.3103 | − | 10.3970i | −0.508815 | − | 0.369676i | ||||
\(792\) | 0.157667 | − | 0.0512290i | 0.00560244 | − | 0.00182034i | ||||
\(793\) | 61.5044i | 2.18409i | ||||||||
\(794\) | 5.53406 | + | 17.0321i | 0.196396 | + | 0.604446i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.44555 | + | 16.7597i | −0.193012 | + | 0.594031i | ||||
\(797\) | −22.0071 | − | 7.15055i | −0.779532 | − | 0.253285i | −0.107892 | − | 0.994163i | \(-0.534410\pi\) |
−0.671640 | + | 0.740877i | \(0.734410\pi\) | |||||||
\(798\) | −3.94951 | − | 5.43603i | −0.139811 | − | 0.192433i | ||||
\(799\) | 14.3064 | 0.506122 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.548765 | 0.0193897 | ||||||||
\(802\) | −18.8188 | − | 25.9018i | −0.664513 | − | 0.914624i | ||||
\(803\) | −11.1174 | − | 3.61226i | −0.392324 | − | 0.127474i | ||||
\(804\) | 2.29087 | − | 7.05056i | 0.0807927 | − | 0.248654i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.5047 | − | 38.4856i | −0.440460 | − | 1.35560i | ||||
\(807\) | − | 24.4912i | − | 0.862132i | ||||||
\(808\) | −7.51936 | + | 2.44319i | −0.264530 | + | 0.0859511i | ||||
\(809\) | 27.1345 | + | 19.7143i | 0.953997 | + | 0.693119i | 0.951749 | − | 0.306878i | \(-0.0992844\pi\) |
0.00224811 | + | 0.999997i | \(0.499284\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.67796 | − | 7.03145i | 0.339839 | − | 0.246907i | −0.404755 | − | 0.914425i | \(-0.632643\pi\) |
0.744594 | + | 0.667518i | \(0.232643\pi\) | |||||||
\(812\) | −6.68083 | + | 9.19537i | −0.234451 | + | 0.322694i | ||||
\(813\) | −31.0282 | + | 42.7067i | −1.08821 | + | 1.49779i | ||||
\(814\) | −2.35113 | + | 1.70820i | −0.0824070 | + | 0.0598722i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7.15318 | − | 5.19709i | −0.250411 | − | 0.181934i | ||||
\(817\) | −12.4206 | + | 4.03569i | −0.434540 | + | 0.141191i | ||||
\(818\) | − | 18.0344i | − | 0.630557i | ||||||
\(819\) | −0.290867 | − | 0.895198i | −0.0101637 | − | 0.0312807i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.30466 | + | 10.1707i | −0.115333 | + | 0.354960i | −0.992016 | − | 0.126109i | \(-0.959751\pi\) |
0.876683 | + | 0.481068i | \(0.159751\pi\) | |||||||
\(822\) | 13.0205 | + | 4.23061i | 0.454141 | + | 0.147559i | ||||
\(823\) | −7.06581 | − | 9.72525i | −0.246299 | − | 0.339001i | 0.667912 | − | 0.744240i | \(-0.267188\pi\) |
−0.914211 | + | 0.405239i | \(0.867188\pi\) | |||||||
\(824\) | −7.83422 | −0.272918 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.4932 | 0.365105 | ||||||||
\(827\) | 2.43328 | + | 3.34912i | 0.0846133 | + | 0.116460i | 0.849225 | − | 0.528031i | \(-0.177069\pi\) |
−0.764612 | + | 0.644491i | \(0.777069\pi\) | |||||||
\(828\) | −0.0372200 | − | 0.0120935i | −0.00129349 | − | 0.000420279i | ||||
\(829\) | 6.28859 | − | 19.3543i | 0.218412 | − | 0.672203i | −0.780482 | − | 0.625178i | \(-0.785026\pi\) |
0.998894 | − | 0.0470242i | \(-0.0149738\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.69014 | + | 5.20171i | 0.0586303 | + | 0.180445i | ||||
\(832\) | 5.67779i | 0.196842i | ||||||||
\(833\) | 3.42141 | − | 1.11168i | 0.118545 | − | 0.0385175i | ||||
\(834\) | −30.6418 | − | 22.2626i | −1.06104 | − | 0.770890i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.17022 | + | 2.30330i | −0.109644 | + | 0.0796614i | ||||
\(837\) | 21.9791 | − | 30.2516i | 0.759708 | − | 1.04565i | ||||
\(838\) | 11.4795 | − | 15.8001i | 0.396552 | − | 0.545806i | ||||
\(839\) | 2.53639 | − | 1.84279i | 0.0875658 | − | 0.0636203i | −0.543141 | − | 0.839642i | \(-0.682765\pi\) |
0.630707 | + | 0.776021i | \(0.282765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.88393 | + | 7.18109i | 0.340825 | + | 0.247624i | ||||
\(842\) | 18.5967 | − | 6.04242i | 0.640883 | − | 0.208236i | ||||
\(843\) | − | 34.9612i | − | 1.20413i | ||||||
\(844\) | −1.88545 | − | 5.80281i | −0.0648998 | − | 0.199741i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.0512290 | − | 0.157667i | 0.00176129 | − | 0.00542069i | ||||
\(847\) | 8.71378 | + | 2.83128i | 0.299409 | + | 0.0972839i | ||||
\(848\) | −0.309240 | − | 0.425633i | −0.0106194 | − | 0.0146163i | ||||
\(849\) | 22.8004 | 0.782508 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.686050 | 0.0235175 | ||||||||
\(852\) | 13.3510 | + | 18.3761i | 0.457399 | + | 0.629556i | ||||
\(853\) | −22.2044 | − | 7.21464i | −0.760263 | − | 0.247025i | −0.0968717 | − | 0.995297i | \(-0.530884\pi\) |
−0.663392 | + | 0.748272i | \(0.730884\pi\) | |||||||
\(854\) | −9.28730 | + | 28.5834i | −0.317805 | + | 0.978102i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.15876 | − | 9.72166i | −0.107964 | − | 0.332280i | ||||
\(857\) | 15.3036i | 0.522762i | 0.965236 | + | 0.261381i | \(0.0841779\pi\) | ||||
−0.965236 | + | 0.261381i | \(0.915822\pi\) | |||||||
\(858\) | 25.6896 | − | 8.34705i | 0.877028 | − | 0.284964i | ||||
\(859\) | −2.39576 | − | 1.74062i | −0.0817422 | − | 0.0593892i | 0.546164 | − | 0.837679i | \(-0.316088\pi\) |
−0.627906 | + | 0.778289i | \(0.716088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.0522 | − | 25.4669i | 1.19457 | − | 0.867909i | ||||
\(862\) | −12.4589 | + | 17.1482i | −0.424351 | + | 0.584069i | ||||
\(863\) | 22.2312 | − | 30.5987i | 0.756760 | − | 1.04159i | −0.240717 | − | 0.970595i | \(-0.577382\pi\) |
0.997477 | − | 0.0709954i | \(-0.0226176\pi\) | |||||||
\(864\) | −4.24459 | + | 3.08388i | −0.144404 | + | 0.104916i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.91683 | − | 5.02537i | −0.235043 | − | 0.170769i | ||||
\(867\) | −15.6373 | + | 5.08088i | −0.531072 | + | 0.172556i | ||||
\(868\) | − | 19.7739i | − | 0.671170i | ||||||
\(869\) | 8.48918 | + | 26.1270i | 0.287976 | + | 0.886298i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.58555 | + | 23.3459i | −0.257027 | + | 0.791046i | ||||
\(872\) | 3.71950 | + | 1.20854i | 0.125958 | + | 0.0409263i | ||||
\(873\) | 0.00316690 | + | 0.00435886i | 0.000107183 | + | 0.000147525i | ||||
\(874\) | 0.925059 | 0.0312906 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.22451 | 0.244094 | ||||||||
\(877\) | 9.17007 | + | 12.6215i | 0.309651 | + | 0.426198i | 0.935272 | − | 0.353929i | \(-0.115154\pi\) |
−0.625621 | + | 0.780127i | \(0.715154\pi\) | |||||||
\(878\) | 26.6975 | + | 8.67453i | 0.900996 | + | 0.292751i | ||||
\(879\) | 13.7991 | − | 42.4691i | 0.465430 | − | 1.43245i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.359812 | + | 1.10739i | 0.0121224 | + | 0.0373089i | 0.956935 | − | 0.290303i | \(-0.0937561\pi\) |
−0.944812 | + | 0.327612i | \(0.893756\pi\) | |||||||
\(882\) | − | 0.0416872i | − | 0.00140368i | ||||||
\(883\) | 46.4925 | − | 15.1063i | 1.56460 | − | 0.508368i | 0.606566 | − | 0.795033i | \(-0.292547\pi\) |
0.958031 | + | 0.286665i | \(0.0925466\pi\) | |||||||
\(884\) | 23.6857 | + | 17.2087i | 0.796636 | + | 0.578790i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 26.7417 | − | 19.4290i | 0.898406 | − | 0.652730i | ||||
\(887\) | 5.07195 | − | 6.98094i | 0.170299 | − | 0.234397i | −0.715333 | − | 0.698783i | \(-0.753725\pi\) |
0.885633 | + | 0.464386i | \(0.153725\pi\) | |||||||
\(888\) | 1.05572 | − | 1.45308i | 0.0354277 | − | 0.0487621i | ||||
\(889\) | −21.4335 | + | 15.5723i | −0.718855 | + | 0.522279i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.7909 | + | 14.3790i | 0.663022 | + | 0.481713i | ||||
\(892\) | 4.78254 | − | 1.55394i | 0.160131 | − | 0.0520299i | ||||
\(893\) | 3.91861i | 0.131131i | ||||||||
\(894\) | −2.21701 | − | 6.82325i | −0.0741479 | − | 0.228204i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.857358 | + | 2.63868i | −0.0286423 | + | 0.0881520i | ||||
\(897\) | −6.06449 | − | 1.97047i | −0.202487 | − | 0.0657921i | ||||
\(898\) | −21.8438 | − | 30.0654i | −0.728936 | − | 1.00329i | ||||
\(899\) | 29.1975 | 0.973790 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.71286 | −0.0903784 | ||||||||
\(902\) | −14.8520 | − | 20.4420i | −0.494516 | − | 0.680643i | ||||
\(903\) | 41.8370 | + | 13.5937i | 1.39225 | + | 0.452368i | ||||
\(904\) | 1.97012 | − | 6.06342i | 0.0655253 | − | 0.201666i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.175686 | − | 0.540707i | −0.00583679 | − | 0.0179638i | ||||
\(907\) | 29.5085i | 0.979815i | 0.871774 | + | 0.489907i | \(0.162969\pi\) | ||||
−0.871774 | + | 0.489907i | \(0.837031\pi\) | |||||||
\(908\) | −16.9652 | + | 5.51232i | −0.563009 | + | 0.182933i | ||||
\(909\) | 0.382196 | + | 0.277682i | 0.0126766 | + | 0.00921012i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.0734 | − | 22.5761i | 1.02951 | − | 0.747981i | 0.0612971 | − | 0.998120i | \(-0.480476\pi\) |
0.968210 | + | 0.250139i | \(0.0804763\pi\) | |||||||
\(912\) | 1.42352 | − | 1.95931i | 0.0471374 | − | 0.0648791i | ||||
\(913\) | −7.62563 | + | 10.4958i | −0.252372 | + | 0.347360i | ||||
\(914\) | 23.7155 | − | 17.2303i | 0.784438 | − | 0.569928i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.4397 | + | 12.6707i | 0.576223 | + | 0.418651i | ||||
\(917\) | 14.7746 | − | 4.80055i | 0.487899 | − | 0.158528i | ||||
\(918\) | 27.0538i | 0.892907i | ||||||||
\(919\) | −12.8831 | − | 39.6500i | −0.424974 | − | 1.30793i | −0.903020 | − | 0.429600i | \(-0.858655\pi\) |
0.478046 | − | 0.878335i | \(-0.341345\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.2999 | − | 40.9329i | 0.438247 | − | 1.34879i | ||||
\(922\) | 8.47145 | + | 2.75254i | 0.278992 | + | 0.0906501i | ||||
\(923\) | −44.2081 | − | 60.8473i | −1.45513 | − | 2.00281i | ||||
\(924\) | 13.1993 | 0.434225 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.2771 | −0.600624 | ||||||||
\(927\) | 0.275149 | + | 0.378710i | 0.00903709 | + | 0.0124385i | ||||
\(928\) | −3.89618 | − | 1.26594i | −0.127898 | − | 0.0415567i | ||||
\(929\) | −8.68484 | + | 26.7292i | −0.284940 | + | 0.876956i | 0.701476 | + | 0.712693i | \(0.252525\pi\) |
−0.986417 | + | 0.164263i | \(0.947475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.304498 | + | 0.937148i | 0.00997952 | + | 0.0307138i | ||||
\(932\) | 14.7065i | 0.481726i | ||||||||
\(933\) | 1.17960 | − | 0.383274i | 0.0386183 | − | 0.0125478i | ||||
\(934\) | −29.6780 | − | 21.5624i | −0.971095 | − | 0.705542i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.274467 | − | 0.199412i | 0.00897124 | − | 0.00651799i | ||||
\(937\) | −7.56796 | + | 10.4164i | −0.247234 | + | 0.340289i | −0.914540 | − | 0.404495i | \(-0.867447\pi\) |
0.667306 | + | 0.744784i | \(0.267447\pi\) | |||||||
\(938\) | −7.05056 | + | 9.70427i | −0.230209 | + | 0.316856i | ||||
\(939\) | 29.9868 | − | 21.7867i | 0.978583 | − | 0.710982i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.21234 | − | 5.96661i | −0.267714 | − | 0.194506i | 0.445827 | − | 0.895119i | \(-0.352910\pi\) |
−0.713541 | + | 0.700613i | \(0.752910\pi\) | |||||||
\(942\) | −5.88308 | + | 1.91153i | −0.191681 | + | 0.0622809i | ||||
\(943\) | 5.96489i | 0.194243i | ||||||||
\(944\) | 1.16872 | + | 3.59695i | 0.0380386 | + | 0.117071i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.92764 | − | 24.3988i | 0.257750 | − | 0.793273i | ||||
\(947\) | −54.5669 | − | 17.7298i | −1.77318 | − | 0.576143i | −0.774760 | − | 0.632255i | \(-0.782129\pi\) |
−0.998424 | + | 0.0561124i | \(0.982129\pi\) | |||||||
\(948\) | −9.97963 | − | 13.7358i | −0.324123 | − | 0.446118i | ||||
\(949\) | −23.9219 | −0.776538 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.2944 | −1.04722 | ||||||||
\(952\) | 8.40906 | + | 11.5741i | 0.272539 | + | 0.375118i | ||||
\(953\) | −4.91947 | − | 1.59843i | −0.159357 | − | 0.0517784i | 0.228252 | − | 0.973602i | \(-0.426699\pi\) |
−0.387609 | + | 0.921824i | \(0.626699\pi\) | |||||||
\(954\) | −0.00971435 | + | 0.0298977i | −0.000314514 | + | 0.000967974i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.14465 | + | 6.60057i | 0.0693631 | + | 0.213478i | ||||
\(957\) | 19.4896i | 0.630010i | ||||||||
\(958\) | −11.9736 | + | 3.89046i | −0.386849 | + | 0.125695i | ||||
\(959\) | −17.9211 | − | 13.0205i | −0.578704 | − | 0.420453i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.0149 | + | 11.6355i | −0.516611 | + | 0.375340i | ||||
\(962\) | −3.49572 | + | 4.81145i | −0.112707 | + | 0.155127i | ||||
\(963\) | −0.359010 | + | 0.494135i | −0.0115689 | + | 0.0159233i | ||||
\(964\) | 2.67787 | − | 1.94559i | 0.0862484 | − | 0.0626631i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.52084 | − | 1.83150i | −0.0811068 | − | 0.0589275i | ||||
\(967\) | 39.3718 | − | 12.7927i | 1.26611 | − | 0.411384i | 0.402443 | − | 0.915445i | \(-0.368161\pi\) |
0.863668 | + | 0.504061i | \(0.168161\pi\) | |||||||
\(968\) | 3.30233i | 0.106141i | ||||||||
\(969\) | −3.85901 | − | 11.8768i | −0.123969 | − | 0.381539i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.3139 | − | 40.9761i | 0.427265 | − | 1.31499i | −0.473544 | − | 0.880770i | \(-0.657025\pi\) |
0.900809 | − | 0.434216i | \(-0.142975\pi\) | |||||||
\(972\) | 0.590483 | + | 0.191859i | 0.0189397 | + | 0.00615389i | ||||
\(973\) | 36.0216 | + | 49.5795i | 1.15480 | + | 1.58944i | ||||
\(974\) | 18.3256 | 0.587189 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.8325 | −0.346739 | ||||||||
\(977\) | −23.7826 | − | 32.7340i | −0.760874 | − | 1.04725i | −0.997141 | − | 0.0755652i | \(-0.975924\pi\) |
0.236267 | − | 0.971688i | \(-0.424076\pi\) | |||||||
\(978\) | −8.30700 | − | 2.69911i | −0.265628 | − | 0.0863079i | ||||
\(979\) | 7.87398 | − | 24.2336i | 0.251654 | − | 0.774510i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.0722128 | − | 0.222248i | −0.00230558 | − | 0.00709584i | ||||
\(982\) | 21.7047i | 0.692625i | ||||||||
\(983\) | 38.4023 | − | 12.4777i | 1.22484 | − | 0.397976i | 0.376000 | − | 0.926620i | \(-0.377299\pi\) |
0.848844 | + | 0.528644i | \(0.177299\pi\) | |||||||
\(984\) | 12.6338 | + | 9.17902i | 0.402752 | + | 0.292616i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −17.0899 | + | 12.4165i | −0.544253 | + | 0.395423i | ||||
\(987\) | 7.75836 | − | 10.6785i | 0.246951 | − | 0.339899i | ||||
\(988\) | −4.71358 | + | 6.48768i | −0.149959 | + | 0.206401i | ||||
\(989\) | −4.89955 | + | 3.55973i | −0.155797 | + | 0.113193i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.0391 | + | 34.1759i | 1.49424 | + | 1.08563i | 0.972604 | + | 0.232467i | \(0.0746798\pi\) |
0.521641 | + | 0.853165i | \(0.325320\pi\) | |||||||
\(992\) | 6.77827 | − | 2.20239i | 0.215210 | − | 0.0699261i | ||||
\(993\) | − | 28.9374i | − | 0.918300i | ||||||
\(994\) | −11.3571 | − | 34.9535i | −0.360225 | − | 1.10866i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.47772 | − | 7.62563i | 0.0785095 | − | 0.241627i | ||||
\(997\) | 37.3735 | + | 12.1434i | 1.18363 | + | 0.384585i | 0.833714 | − | 0.552197i | \(-0.186210\pi\) |
0.349916 | + | 0.936781i | \(0.386210\pi\) | |||||||
\(998\) | 9.30998 | + | 12.8141i | 0.294702 | + | 0.405623i | ||||
\(999\) | −5.49563 | −0.173874 |
(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 | 250.2.e.c.199.1 | 16 | ||
5.2 | odd | 4 | 250.2.d.d.51.1 | 8 | |||
5.3 | odd | 4 | 50.2.d.b.11.2 | ✓ | 8 | ||
5.4 | even | 2 | inner | 250.2.e.c.199.4 | 16 | ||
15.8 | even | 4 | 450.2.h.e.361.1 | 8 | |||
20.3 | even | 4 | 400.2.u.d.161.1 | 8 | |||
25.3 | odd | 20 | 1250.2.a.l.1.3 | 4 | |||
25.4 | even | 10 | 1250.2.b.e.1249.3 | 8 | |||
25.9 | even | 10 | inner | 250.2.e.c.49.1 | 16 | ||
25.12 | odd | 20 | 250.2.d.d.201.1 | 8 | |||
25.13 | odd | 20 | 50.2.d.b.41.2 | yes | 8 | ||
25.16 | even | 5 | inner | 250.2.e.c.49.4 | 16 | ||
25.21 | even | 5 | 1250.2.b.e.1249.6 | 8 | |||
25.22 | odd | 20 | 1250.2.a.f.1.2 | 4 | |||
75.38 | even | 20 | 450.2.h.e.91.1 | 8 | |||
100.3 | even | 20 | 10000.2.a.t.1.2 | 4 | |||
100.47 | even | 20 | 10000.2.a.x.1.3 | 4 | |||
100.63 | even | 20 | 400.2.u.d.241.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.2.d.b.11.2 | ✓ | 8 | 5.3 | odd | 4 | ||
50.2.d.b.41.2 | yes | 8 | 25.13 | odd | 20 | ||
250.2.d.d.51.1 | 8 | 5.2 | odd | 4 | |||
250.2.d.d.201.1 | 8 | 25.12 | odd | 20 | |||
250.2.e.c.49.1 | 16 | 25.9 | even | 10 | inner | ||
250.2.e.c.49.4 | 16 | 25.16 | even | 5 | inner | ||
250.2.e.c.199.1 | 16 | 1.1 | even | 1 | trivial | ||
250.2.e.c.199.4 | 16 | 5.4 | even | 2 | inner | ||
400.2.u.d.161.1 | 8 | 20.3 | even | 4 | |||
400.2.u.d.241.1 | 8 | 100.63 | even | 20 | |||
450.2.h.e.91.1 | 8 | 75.38 | even | 20 | |||
450.2.h.e.361.1 | 8 | 15.8 | even | 4 | |||
1250.2.a.f.1.2 | 4 | 25.22 | odd | 20 | |||
1250.2.a.l.1.3 | 4 | 25.3 | odd | 20 | |||
1250.2.b.e.1249.3 | 8 | 25.4 | even | 10 | |||
1250.2.b.e.1249.6 | 8 | 25.21 | even | 5 | |||
10000.2.a.t.1.2 | 4 | 100.3 | even | 20 | |||
10000.2.a.x.1.3 | 4 | 100.47 | even | 20 |