Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(49,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.y (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.17284886784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.70006 + 1.70006i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.49 |
Dual form | 1950.2.y.k.199.1 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.866025 | − | 0.500000i | −0.353553 | − | 0.204124i | ||||
\(7\) | −2.32233 | + | 4.02239i | −0.877758 | + | 1.52032i | −0.0239629 | + | 0.999713i | \(0.507628\pi\) |
−0.853795 | + | 0.520609i | \(0.825705\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.81062 | − | 2.20006i | 1.14895 | − | 0.663344i | 0.200316 | − | 0.979731i | \(-0.435803\pi\) |
0.948630 | + | 0.316387i | \(0.102470\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 1.32233 | + | 3.35432i | 0.366748 | + | 0.930320i | ||||
\(14\) | −4.64466 | −1.24134 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.46410 | + | 2.00000i | 0.840168 | + | 0.485071i | 0.857321 | − | 0.514782i | \(-0.172127\pi\) |
−0.0171533 | + | 0.999853i | \(0.505460\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 6.96699 | + | 4.02239i | 1.59834 | + | 0.922800i | 0.991808 | + | 0.127739i | \(0.0407720\pi\) |
0.606529 | + | 0.795061i | \(0.292561\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 4.64466i | − | 1.01355i | ||||||
\(22\) | 3.81062 | + | 2.20006i | 0.812427 | + | 0.469055i | ||||
\(23\) | −0.845746 | + | 0.488292i | −0.176350 | + | 0.101816i | −0.585577 | − | 0.810617i | \(-0.699132\pi\) |
0.409226 | + | 0.912433i | \(0.365799\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.24376 | + | 2.82233i | −0.440037 | + | 0.553504i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −2.32233 | − | 4.02239i | −0.438879 | − | 0.760161i | ||||
\(29\) | −2.15637 | − | 3.73494i | −0.400427 | − | 0.693561i | 0.593350 | − | 0.804945i | \(-0.297805\pi\) |
−0.993777 | + | 0.111384i | \(0.964472\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.44069i | 1.15678i | 0.815760 | + | 0.578391i | \(0.196319\pi\) | ||||
−0.815760 | + | 0.578391i | \(0.803681\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −2.20006 | + | 3.81062i | −0.382982 | + | 0.663344i | ||||
\(34\) | 4.00000i | 0.685994i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 1.89801 | + | 3.28745i | 0.312031 | + | 0.540454i | 0.978802 | − | 0.204809i | \(-0.0656573\pi\) |
−0.666771 | + | 0.745263i | \(0.732324\pi\) | |||||||
\(38\) | 8.04479i | 1.30504i | ||||||||
\(39\) | −2.82233 | − | 2.24376i | −0.451934 | − | 0.359289i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.31274 | + | 3.64466i | −0.985884 | + | 0.569200i | −0.904041 | − | 0.427445i | \(-0.859414\pi\) |
−0.0818424 | + | 0.996645i | \(0.526080\pi\) | |||||||
\(42\) | 4.02239 | − | 2.32233i | 0.620669 | − | 0.358343i | ||||
\(43\) | −0.620469 | − | 0.358228i | −0.0946207 | − | 0.0546293i | 0.451943 | − | 0.892047i | \(-0.350731\pi\) |
−0.546564 | + | 0.837418i | \(0.684064\pi\) | |||||||
\(44\) | 4.40013i | 0.663344i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.845746 | − | 0.488292i | −0.124698 | − | 0.0719947i | ||||
\(47\) | −9.75342 | −1.42268 | −0.711341 | − | 0.702847i | \(-0.751912\pi\) | ||||
−0.711341 | + | 0.702847i | \(0.751912\pi\) | |||||||
\(48\) | 0.866025 | + | 0.500000i | 0.125000 | + | 0.0721688i | ||||
\(49\) | −7.28643 | − | 12.6205i | −1.04092 | − | 1.80292i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | −3.56609 | − | 0.531987i | −0.494528 | − | 0.0737734i | ||||
\(53\) | − | 13.5089i | − | 1.85559i | −0.373092 | − | 0.927794i | \(-0.621703\pi\) | ||
0.373092 | − | 0.927794i | \(-0.378297\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.32233 | − | 4.02239i | 0.310334 | − | 0.537515i | ||||
\(57\) | −8.04479 | −1.06556 | ||||||||
\(58\) | 2.15637 | − | 3.73494i | 0.283145 | − | 0.490421i | ||||
\(59\) | 1.88842 | + | 1.09028i | 0.245851 | + | 0.141942i | 0.617863 | − | 0.786286i | \(-0.287999\pi\) |
−0.372012 | + | 0.928228i | \(0.621332\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.73205 | + | 6.46410i | −0.477840 | + | 0.827643i | −0.999677 | − | 0.0254017i | \(-0.991914\pi\) |
0.521837 | + | 0.853045i | \(0.325247\pi\) | |||||||
\(62\) | −5.57780 | + | 3.22034i | −0.708381 | + | 0.408984i | ||||
\(63\) | 2.32233 | + | 4.02239i | 0.292586 | + | 0.506774i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.40013 | −0.541618 | ||||||||
\(67\) | −0.912609 | − | 1.58068i | −0.111493 | − | 0.193111i | 0.804879 | − | 0.593438i | \(-0.202230\pi\) |
−0.916372 | + | 0.400327i | \(0.868897\pi\) | |||||||
\(68\) | −3.46410 | + | 2.00000i | −0.420084 | + | 0.242536i | ||||
\(69\) | 0.488292 | − | 0.845746i | 0.0587834 | − | 0.101816i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.88764 | − | 3.97658i | −0.817413 | − | 0.471934i | 0.0321105 | − | 0.999484i | \(-0.489777\pi\) |
−0.849524 | + | 0.527551i | \(0.823110\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −4.36112 | −0.510430 | −0.255215 | − | 0.966884i | \(-0.582146\pi\) | ||||
−0.255215 | + | 0.966884i | \(0.582146\pi\) | |||||||
\(74\) | −1.89801 | + | 3.28745i | −0.220640 | + | 0.382159i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.96699 | + | 4.02239i | −0.799168 | + | 0.461400i | ||||
\(77\) | 20.4371i | 2.32902i | ||||||||
\(78\) | 0.531987 | − | 3.56609i | 0.0602357 | − | 0.403780i | ||||
\(79\) | 14.9340 | 1.68020 | 0.840102 | − | 0.542429i | \(-0.182495\pi\) | ||||
0.840102 | + | 0.542429i | \(0.182495\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −6.31274 | − | 3.64466i | −0.697125 | − | 0.402485i | ||||
\(83\) | 3.51093 | 0.385375 | 0.192688 | − | 0.981260i | \(-0.438280\pi\) | ||||
0.192688 | + | 0.981260i | \(0.438280\pi\) | |||||||
\(84\) | 4.02239 | + | 2.32233i | 0.438879 | + | 0.253387i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 0.716456i | − | 0.0772575i | ||||||
\(87\) | 3.73494 | + | 2.15637i | 0.400427 | + | 0.231187i | ||||
\(88\) | −3.81062 | + | 2.20006i | −0.406214 | + | 0.234528i | ||||
\(89\) | −7.07780 | + | 4.08637i | −0.750245 | + | 0.433154i | −0.825782 | − | 0.563989i | \(-0.809266\pi\) |
0.0755374 | + | 0.997143i | \(0.475933\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.5633 | − | 2.47090i | −1.73630 | − | 0.259021i | ||||
\(92\) | − | 0.976584i | − | 0.101816i | ||||||
\(93\) | −3.22034 | − | 5.57780i | −0.333934 | − | 0.578391i | ||||
\(94\) | −4.87671 | − | 8.44671i | −0.502994 | − | 0.871212i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −6.91261 | + | 11.9730i | −0.701869 | + | 1.21567i | 0.265941 | + | 0.963989i | \(0.414318\pi\) |
−0.967810 | + | 0.251683i | \(0.919016\pi\) | |||||||
\(98\) | 7.28643 | − | 12.6205i | 0.736041 | − | 1.27486i | ||||
\(99\) | − | 4.40013i | − | 0.442229i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.40013 | − | 5.88919i | −0.338325 | − | 0.585997i | 0.645793 | − | 0.763513i | \(-0.276527\pi\) |
−0.984118 | + | 0.177516i | \(0.943194\pi\) | |||||||
\(102\) | −2.00000 | − | 3.46410i | −0.198030 | − | 0.342997i | ||||
\(103\) | 5.29137i | 0.521374i | 0.965423 | + | 0.260687i | \(0.0839490\pi\) | ||||
−0.965423 | + | 0.260687i | \(0.916051\pi\) | |||||||
\(104\) | −1.32233 | − | 3.35432i | −0.129665 | − | 0.328918i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.6990 | − | 6.75444i | 1.13631 | − | 0.656050i | ||||
\(107\) | 14.6603 | − | 8.46410i | 1.41726 | − | 0.818256i | 0.421203 | − | 0.906966i | \(-0.361608\pi\) |
0.996057 | + | 0.0887109i | \(0.0282747\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | − | 12.8003i | − | 1.22604i | −0.790067 | − | 0.613021i | \(-0.789954\pi\) | ||
0.790067 | − | 0.613021i | \(-0.210046\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.28745 | − | 1.89801i | −0.312031 | − | 0.180151i | ||||
\(112\) | 4.64466 | 0.438879 | ||||||||
\(113\) | 11.3156 | + | 6.53308i | 1.06448 | + | 0.614580i | 0.926669 | − | 0.375878i | \(-0.122659\pi\) |
0.137815 | + | 0.990458i | \(0.455992\pi\) | |||||||
\(114\) | −4.02239 | − | 6.96699i | −0.376732 | − | 0.652518i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.31274 | 0.400427 | ||||||||
\(117\) | 3.56609 | + | 0.531987i | 0.329685 | + | 0.0491823i | ||||
\(118\) | 2.18056i | 0.200737i | ||||||||
\(119\) | −16.0896 | + | 9.28932i | −1.47493 | + | 0.851550i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.18056 | − | 7.24094i | 0.380051 | − | 0.658267i | ||||
\(122\) | −7.46410 | −0.675768 | ||||||||
\(123\) | 3.64466 | − | 6.31274i | 0.328628 | − | 0.569200i | ||||
\(124\) | −5.57780 | − | 3.22034i | −0.500901 | − | 0.289195i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.32233 | + | 4.02239i | −0.206890 | + | 0.358343i | ||||
\(127\) | −10.5825 | + | 6.10978i | −0.939041 | + | 0.542156i | −0.889660 | − | 0.456624i | \(-0.849058\pi\) |
−0.0493816 | + | 0.998780i | \(0.515725\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0.716456 | 0.0630805 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.378757 | −0.0330921 | −0.0165461 | − | 0.999863i | \(-0.505267\pi\) | ||||
−0.0165461 | + | 0.999863i | \(0.505267\pi\) | |||||||
\(132\) | −2.20006 | − | 3.81062i | −0.191491 | − | 0.331672i | ||||
\(133\) | −32.3593 | + | 18.6826i | −2.80591 | + | 1.61999i | ||||
\(134\) | 0.912609 | − | 1.58068i | 0.0788374 | − | 0.136550i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.46410 | − | 2.00000i | −0.297044 | − | 0.171499i | ||||
\(137\) | 0.626177 | − | 1.08457i | 0.0534979 | − | 0.0926612i | −0.838036 | − | 0.545615i | \(-0.816296\pi\) |
0.891534 | + | 0.452953i | \(0.149630\pi\) | |||||||
\(138\) | 0.976584 | 0.0831323 | ||||||||
\(139\) | 1.67767 | − | 2.90581i | 0.142298 | − | 0.246468i | −0.786064 | − | 0.618146i | \(-0.787884\pi\) |
0.928362 | + | 0.371678i | \(0.121217\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.44671 | − | 4.87671i | 0.711341 | − | 0.410693i | ||||
\(142\) | − | 7.95317i | − | 0.667415i | ||||||
\(143\) | 12.4186 | + | 9.87282i | 1.03850 | + | 0.825607i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.18056 | − | 3.77684i | −0.180464 | − | 0.312573i | ||||
\(147\) | 12.6205 | + | 7.28643i | 1.04092 | + | 0.600975i | ||||
\(148\) | −3.79603 | −0.312031 | ||||||||
\(149\) | 4.00077 | + | 2.30985i | 0.327756 | + | 0.189230i | 0.654844 | − | 0.755764i | \(-0.272734\pi\) |
−0.327088 | + | 0.944994i | \(0.606067\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2425i | 0.914901i | 0.889235 | + | 0.457450i | \(0.151237\pi\) | ||||
−0.889235 | + | 0.457450i | \(0.848763\pi\) | |||||||
\(152\) | −6.96699 | − | 4.02239i | −0.565097 | − | 0.326259i | ||||
\(153\) | 3.46410 | − | 2.00000i | 0.280056 | − | 0.161690i | ||||
\(154\) | −17.6990 | + | 10.2185i | −1.42623 | + | 0.823434i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.35432 | − | 1.32233i | 0.268560 | − | 0.105871i | ||||
\(157\) | − | 1.50311i | − | 0.119961i | −0.998200 | − | 0.0599807i | \(-0.980896\pi\) | ||
0.998200 | − | 0.0599807i | \(-0.0191039\pi\) | |||||||
\(158\) | 7.46699 | + | 12.9332i | 0.594042 | + | 1.02891i | ||||
\(159\) | 6.75444 | + | 11.6990i | 0.535662 | + | 0.927794i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.53590i | − | 0.357479i | ||||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | −0.0881650 | + | 0.152706i | −0.00690561 | + | 0.0119609i | −0.869458 | − | 0.494008i | \(-0.835531\pi\) |
0.862552 | + | 0.505969i | \(0.168865\pi\) | |||||||
\(164\) | − | 7.28932i | − | 0.569200i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.75547 | + | 3.04056i | 0.136251 | + | 0.235993i | ||||
\(167\) | 4.34081 | + | 7.51851i | 0.335902 | + | 0.581800i | 0.983658 | − | 0.180049i | \(-0.0576255\pi\) |
−0.647756 | + | 0.761848i | \(0.724292\pi\) | |||||||
\(168\) | 4.64466i | 0.358343i | ||||||||
\(169\) | −9.50289 | + | 8.87103i | −0.730991 | + | 0.682387i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.96699 | − | 4.02239i | 0.532779 | − | 0.307600i | ||||
\(172\) | 0.620469 | − | 0.358228i | 0.0473103 | − | 0.0273146i | ||||
\(173\) | −1.54190 | − | 0.890216i | −0.117228 | − | 0.0676818i | 0.440239 | − | 0.897880i | \(-0.354894\pi\) |
−0.557468 | + | 0.830199i | \(0.688227\pi\) | |||||||
\(174\) | 4.31274i | 0.326948i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.81062 | − | 2.20006i | −0.287236 | − | 0.165836i | ||||
\(177\) | −2.18056 | −0.163901 | ||||||||
\(178\) | −7.07780 | − | 4.08637i | −0.530503 | − | 0.306286i | ||||
\(179\) | 8.70786 | + | 15.0825i | 0.650856 | + | 1.12732i | 0.982916 | + | 0.184057i | \(0.0589232\pi\) |
−0.332059 | + | 0.943258i | \(0.607743\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.3611 | −0.770136 | −0.385068 | − | 0.922888i | \(-0.625822\pi\) | ||||
−0.385068 | + | 0.922888i | \(0.625822\pi\) | |||||||
\(182\) | −6.14177 | − | 15.5797i | −0.455258 | − | 1.15484i | ||||
\(183\) | − | 7.46410i | − | 0.551762i | ||||||
\(184\) | 0.845746 | − | 0.488292i | 0.0623492 | − | 0.0359973i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.22034 | − | 5.57780i | 0.236127 | − | 0.408984i | ||||
\(187\) | 17.6005 | 1.28708 | ||||||||
\(188\) | 4.87671 | − | 8.44671i | 0.355671 | − | 0.616040i | ||||
\(189\) | −4.02239 | − | 2.32233i | −0.292586 | − | 0.168925i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.448507 | − | 0.776837i | 0.0324528 | − | 0.0562100i | −0.849343 | − | 0.527842i | \(-0.823001\pi\) |
0.881796 | + | 0.471632i | \(0.156335\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −10.1322 | − | 17.5494i | −0.729330 | − | 1.26324i | −0.957167 | − | 0.289537i | \(-0.906499\pi\) |
0.227837 | − | 0.973699i | \(-0.426835\pi\) | |||||||
\(194\) | −13.8252 | −0.992593 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.5729 | 1.04092 | ||||||||
\(197\) | 4.59028 | + | 7.95060i | 0.327044 | + | 0.566457i | 0.981924 | − | 0.189276i | \(-0.0606142\pi\) |
−0.654880 | + | 0.755733i | \(0.727281\pi\) | |||||||
\(198\) | 3.81062 | − | 2.20006i | 0.270809 | − | 0.156352i | ||||
\(199\) | 8.10876 | − | 14.0448i | 0.574815 | − | 0.995609i | −0.421247 | − | 0.906946i | \(-0.638407\pi\) |
0.996062 | − | 0.0886625i | \(-0.0282593\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.58068 | + | 0.912609i | 0.111493 | + | 0.0643705i | ||||
\(202\) | 3.40013 | − | 5.88919i | 0.239232 | − | 0.414362i | ||||
\(203\) | 20.0312 | 1.40591 | ||||||||
\(204\) | 2.00000 | − | 3.46410i | 0.140028 | − | 0.242536i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.58246 | + | 2.64568i | −0.319275 | + | 0.184333i | ||||
\(207\) | 0.976584i | 0.0678773i | ||||||||
\(208\) | 2.24376 | − | 2.82233i | 0.155577 | − | 0.195693i | ||||
\(209\) | 35.3981 | 2.44854 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.809848 | + | 1.40270i | 0.0557522 | + | 0.0965657i | 0.892555 | − | 0.450939i | \(-0.148911\pi\) |
−0.836802 | + | 0.547505i | \(0.815578\pi\) | |||||||
\(212\) | 11.6990 | + | 6.75444i | 0.803493 | + | 0.463897i | ||||
\(213\) | 7.95317 | 0.544942 | ||||||||
\(214\) | 14.6603 | + | 8.46410i | 1.00215 | + | 0.578594i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −25.9070 | − | 14.9574i | −1.75868 | − | 1.01537i | ||||
\(218\) | 11.0853 | − | 6.40013i | 0.750794 | − | 0.433471i | ||||
\(219\) | 3.77684 | − | 2.18056i | 0.255215 | − | 0.147348i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.12795 | + | 14.2644i | −0.143141 | + | 0.959524i | ||||
\(222\) | − | 3.79603i | − | 0.254773i | ||||||
\(223\) | −1.11836 | − | 1.93705i | −0.0748906 | − | 0.129714i | 0.826148 | − | 0.563453i | \(-0.190527\pi\) |
−0.901039 | + | 0.433739i | \(0.857194\pi\) | |||||||
\(224\) | 2.32233 | + | 4.02239i | 0.155167 | + | 0.268757i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.0662i | 0.869148i | ||||||||
\(227\) | 7.66025 | − | 13.2679i | 0.508429 | − | 0.880625i | −0.491523 | − | 0.870864i | \(-0.663560\pi\) |
0.999952 | − | 0.00976038i | \(-0.00310687\pi\) | |||||||
\(228\) | 4.02239 | − | 6.96699i | 0.266389 | − | 0.461400i | ||||
\(229\) | 10.1279i | 0.669274i | 0.942347 | + | 0.334637i | \(0.108614\pi\) | ||||
−0.942347 | + | 0.334637i | \(0.891386\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.2185 | − | 17.6990i | −0.672331 | − | 1.16451i | ||||
\(232\) | 2.15637 | + | 3.73494i | 0.141572 | + | 0.245211i | ||||
\(233\) | − | 20.7519i | − | 1.35950i | −0.733444 | − | 0.679750i | \(-0.762088\pi\) | ||
0.733444 | − | 0.679750i | \(-0.237912\pi\) | |||||||
\(234\) | 1.32233 | + | 3.35432i | 0.0864434 | + | 0.219279i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.88842 | + | 1.09028i | −0.122926 | + | 0.0709711i | ||||
\(237\) | −12.9332 | + | 7.46699i | −0.840102 | + | 0.485033i | ||||
\(238\) | −16.0896 | − | 9.28932i | −1.04293 | − | 0.602137i | ||||
\(239\) | 24.3539i | 1.57532i | 0.616107 | + | 0.787662i | \(0.288709\pi\) | ||||
−0.616107 | + | 0.787662i | \(0.711291\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.2066 | − | 9.93423i | −1.10837 | − | 0.639920i | −0.169966 | − | 0.985450i | \(-0.554366\pi\) |
−0.938408 | + | 0.345530i | \(0.887699\pi\) | |||||||
\(242\) | 8.36112 | 0.537473 | ||||||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | −3.73205 | − | 6.46410i | −0.238920 | − | 0.413822i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.28932 | 0.464750 | ||||||||
\(247\) | −4.27973 | + | 28.6884i | −0.272312 | + | 1.82540i | ||||
\(248\) | − | 6.44069i | − | 0.408984i | ||||||
\(249\) | −3.04056 | + | 1.75547i | −0.192688 | + | 0.111248i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.78566 | − | 11.7531i | 0.428307 | − | 0.741849i | −0.568416 | − | 0.822741i | \(-0.692444\pi\) |
0.996723 | + | 0.0808920i | \(0.0257769\pi\) | |||||||
\(252\) | −4.64466 | −0.292586 | ||||||||
\(253\) | −2.14855 | + | 3.72139i | −0.135078 | + | 0.233962i | ||||
\(254\) | −10.5825 | − | 6.10978i | −0.664002 | − | 0.383362i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −0.573569 | + | 0.331150i | −0.0357783 | + | 0.0206566i | −0.517782 | − | 0.855512i | \(-0.673242\pi\) |
0.482004 | + | 0.876169i | \(0.339909\pi\) | |||||||
\(258\) | 0.358228 | + | 0.620469i | 0.0223023 | + | 0.0386287i | ||||
\(259\) | −17.6312 | −1.09555 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.31274 | −0.266952 | ||||||||
\(262\) | −0.189378 | − | 0.328013i | −0.0116998 | − | 0.0202647i | ||||
\(263\) | −26.6301 | + | 15.3749i | −1.64208 | + | 0.948058i | −0.661993 | + | 0.749510i | \(0.730289\pi\) |
−0.980091 | + | 0.198548i | \(0.936377\pi\) | |||||||
\(264\) | 2.20006 | − | 3.81062i | 0.135405 | − | 0.234528i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −32.3593 | − | 18.6826i | −1.98408 | − | 1.14551i | ||||
\(267\) | 4.08637 | − | 7.07780i | 0.250082 | − | 0.433154i | ||||
\(268\) | 1.82522 | 0.111493 | ||||||||
\(269\) | −1.87205 | + | 3.24249i | −0.114141 | + | 0.197698i | −0.917436 | − | 0.397883i | \(-0.869745\pi\) |
0.803295 | + | 0.595581i | \(0.203078\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.0419 | − | 13.8806i | 1.46044 | − | 0.843186i | 0.461410 | − | 0.887187i | \(-0.347344\pi\) |
0.999031 | + | 0.0440009i | \(0.0140104\pi\) | |||||||
\(272\) | − | 4.00000i | − | 0.242536i | ||||||
\(273\) | 15.5797 | − | 6.14177i | 0.942924 | − | 0.371717i | ||||
\(274\) | 1.25235 | 0.0756575 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.488292 | + | 0.845746i | 0.0293917 | + | 0.0509079i | ||||
\(277\) | 10.3855 | + | 5.99609i | 0.624006 | + | 0.360270i | 0.778427 | − | 0.627735i | \(-0.216018\pi\) |
−0.154421 | + | 0.988005i | \(0.549351\pi\) | |||||||
\(278\) | 3.35534 | 0.201240 | ||||||||
\(279\) | 5.57780 | + | 3.22034i | 0.333934 | + | 0.192797i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.63888i | 0.217078i | 0.994092 | + | 0.108539i | \(0.0346172\pi\) | ||||
−0.994092 | + | 0.108539i | \(0.965383\pi\) | |||||||
\(282\) | 8.44671 | + | 4.87671i | 0.502994 | + | 0.290404i | ||||
\(283\) | 4.19538 | − | 2.42220i | 0.249389 | − | 0.143985i | −0.370095 | − | 0.928994i | \(-0.620675\pi\) |
0.619485 | + | 0.785009i | \(0.287342\pi\) | |||||||
\(284\) | 6.88764 | − | 3.97658i | 0.408707 | − | 0.235967i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.34081 | + | 15.6912i | −0.138415 | + | 0.927843i | ||||
\(287\) | − | 33.8564i | − | 1.99848i | ||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −0.500000 | − | 0.866025i | −0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 13.8252i | − | 0.810449i | ||||||
\(292\) | 2.18056 | − | 3.77684i | 0.127608 | − | 0.221023i | ||||
\(293\) | 1.85041 | − | 3.20500i | 0.108102 | − | 0.187238i | −0.806899 | − | 0.590689i | \(-0.798856\pi\) |
0.915001 | + | 0.403451i | \(0.132189\pi\) | |||||||
\(294\) | 14.5729i | 0.849907i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.89801 | − | 3.28745i | −0.110320 | − | 0.191079i | ||||
\(297\) | 2.20006 | + | 3.81062i | 0.127661 | + | 0.221115i | ||||
\(298\) | 4.61970i | 0.267612i | ||||||||
\(299\) | −2.75624 | − | 2.19122i | −0.159398 | − | 0.126721i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.88187 | − | 1.66385i | 0.166108 | − | 0.0959026i | ||||
\(302\) | −9.73628 | + | 5.62124i | −0.560260 | + | 0.323466i | ||||
\(303\) | 5.88919 | + | 3.40013i | 0.338325 | + | 0.195332i | ||||
\(304\) | − | 8.04479i | − | 0.461400i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.46410 | + | 2.00000i | 0.198030 | + | 0.114332i | ||||
\(307\) | 7.11454 | 0.406048 | 0.203024 | − | 0.979174i | \(-0.434923\pi\) | ||||
0.203024 | + | 0.979174i | \(0.434923\pi\) | |||||||
\(308\) | −17.6990 | − | 10.2185i | −1.00850 | − | 0.582256i | ||||
\(309\) | −2.64568 | − | 4.58246i | −0.150508 | − | 0.260687i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.9148 | −1.12926 | −0.564632 | − | 0.825343i | \(-0.690982\pi\) | ||||
−0.564632 | + | 0.825343i | \(0.690982\pi\) | |||||||
\(312\) | 2.82233 | + | 2.24376i | 0.159783 | + | 0.127028i | ||||
\(313\) | − | 6.13950i | − | 0.347025i | −0.984832 | − | 0.173513i | \(-0.944488\pi\) | ||
0.984832 | − | 0.173513i | \(-0.0555117\pi\) | |||||||
\(314\) | 1.30173 | − | 0.751556i | 0.0734611 | − | 0.0424128i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.46699 | + | 12.9332i | −0.420051 | + | 0.727550i | ||||
\(317\) | −7.85286 | −0.441061 | −0.220530 | − | 0.975380i | \(-0.570779\pi\) | ||||
−0.220530 | + | 0.975380i | \(0.570779\pi\) | |||||||
\(318\) | −6.75444 | + | 11.6990i | −0.378770 | + | 0.656050i | ||||
\(319\) | −16.4342 | − | 9.48829i | −0.920139 | − | 0.531242i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.46410 | + | 14.6603i | −0.472420 | + | 0.818256i | ||||
\(322\) | 3.92820 | − | 2.26795i | 0.218910 | − | 0.126388i | ||||
\(323\) | 16.0896 | + | 27.8680i | 0.895248 | + | 1.55061i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.176330 | −0.00976601 | ||||||||
\(327\) | 6.40013 | + | 11.0853i | 0.353928 | + | 0.613021i | ||||
\(328\) | 6.31274 | − | 3.64466i | 0.348563 | − | 0.201243i | ||||
\(329\) | 22.6507 | − | 39.2321i | 1.24877 | − | 2.16294i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.7093 | + | 15.9980i | 1.52304 | + | 0.879327i | 0.999629 | + | 0.0272463i | \(0.00867385\pi\) |
0.523410 | + | 0.852081i | \(0.324659\pi\) | |||||||
\(332\) | −1.75547 | + | 3.04056i | −0.0963438 | + | 0.166872i | ||||
\(333\) | 3.79603 | 0.208021 | ||||||||
\(334\) | −4.34081 | + | 7.51851i | −0.237519 | + | 0.411394i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.02239 | + | 2.32233i | −0.219440 | + | 0.126693i | ||||
\(337\) | − | 35.6432i | − | 1.94161i | −0.239867 | − | 0.970806i | \(-0.577104\pi\) | ||
0.239867 | − | 0.970806i | \(-0.422896\pi\) | |||||||
\(338\) | −12.4340 | − | 3.79423i | −0.676319 | − | 0.206379i | ||||
\(339\) | −13.0662 | −0.709656 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.1699 | + | 24.5430i | 0.767344 | + | 1.32908i | ||||
\(342\) | 6.96699 | + | 4.02239i | 0.376732 | + | 0.217506i | ||||
\(343\) | 35.1734 | 1.89918 | ||||||||
\(344\) | 0.620469 | + | 0.358228i | 0.0334535 | + | 0.0193144i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 1.78043i | − | 0.0957166i | ||||||
\(347\) | 5.97299 | + | 3.44851i | 0.320647 | + | 0.185126i | 0.651681 | − | 0.758493i | \(-0.274064\pi\) |
−0.331034 | + | 0.943619i | \(0.607397\pi\) | |||||||
\(348\) | −3.73494 | + | 2.15637i | −0.200214 | + | 0.115593i | ||||
\(349\) | −16.7321 | + | 9.66025i | −0.895646 | + | 0.517102i | −0.875785 | − | 0.482701i | \(-0.839656\pi\) |
−0.0198610 | + | 0.999803i | \(0.506322\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.35432 | + | 1.32233i | −0.179040 | + | 0.0705807i | ||||
\(352\) | − | 4.40013i | − | 0.234528i | ||||||
\(353\) | 13.7086 | + | 23.7441i | 0.729637 | + | 1.26377i | 0.957037 | + | 0.289967i | \(0.0936443\pi\) |
−0.227400 | + | 0.973802i | \(0.573022\pi\) | |||||||
\(354\) | −1.09028 | − | 1.88842i | −0.0579477 | − | 0.100368i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 8.17274i | − | 0.433154i | ||||||
\(357\) | 9.28932 | − | 16.0896i | 0.491643 | − | 0.851550i | ||||
\(358\) | −8.70786 | + | 15.0825i | −0.460225 | + | 0.797133i | ||||
\(359\) | − | 14.3611i | − | 0.757951i | −0.925407 | − | 0.378975i | \(-0.876277\pi\) | ||
0.925407 | − | 0.378975i | \(-0.123723\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.8593 | + | 39.5935i | 1.20312 | + | 2.08387i | ||||
\(362\) | −5.18056 | − | 8.97299i | −0.272284 | − | 0.471610i | ||||
\(363\) | 8.36112i | 0.438845i | ||||||||
\(364\) | 10.4215 | − | 13.1088i | 0.546235 | − | 0.687086i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.46410 | − | 3.73205i | 0.337884 | − | 0.195077i | ||||
\(367\) | −11.9298 | + | 6.88764i | −0.622728 | + | 0.359532i | −0.777930 | − | 0.628351i | \(-0.783730\pi\) |
0.155202 | + | 0.987883i | \(0.450397\pi\) | |||||||
\(368\) | 0.845746 | + | 0.488292i | 0.0440876 | + | 0.0254540i | ||||
\(369\) | 7.28932i | 0.379467i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 54.3381 | + | 31.3721i | 2.82109 | + | 1.62876i | ||||
\(372\) | 6.44069 | 0.333934 | ||||||||
\(373\) | −28.9795 | − | 16.7313i | −1.50050 | − | 0.866316i | −1.00000 | 0.000581860i | \(-0.999815\pi\) | |
−0.500504 | − | 0.865734i | \(-0.666852\pi\) | |||||||
\(374\) | 8.80025 | + | 15.2425i | 0.455050 | + | 0.788170i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.75342 | 0.502994 | ||||||||
\(377\) | 9.67674 | − | 12.1720i | 0.498377 | − | 0.626888i | ||||
\(378\) | − | 4.64466i | − | 0.238896i | ||||||
\(379\) | 28.9052 | − | 16.6884i | 1.48476 | − | 0.857227i | 0.484910 | − | 0.874564i | \(-0.338852\pi\) |
0.999850 | + | 0.0173371i | \(0.00551884\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.10978 | − | 10.5825i | 0.313014 | − | 0.542156i | ||||
\(382\) | 0.897014 | 0.0458952 | ||||||||
\(383\) | 3.66519 | − | 6.34829i | 0.187282 | − | 0.324383i | −0.757061 | − | 0.653344i | \(-0.773365\pi\) |
0.944343 | + | 0.328962i | \(0.106699\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.1322 | − | 17.5494i | 0.515714 | − | 0.893243i | ||||
\(387\) | −0.620469 | + | 0.358228i | −0.0315402 | + | 0.0182098i | ||||
\(388\) | −6.91261 | − | 11.9730i | −0.350935 | − | 0.607836i | ||||
\(389\) | 32.6198 | 1.65389 | 0.826946 | − | 0.562282i | \(-0.190076\pi\) | ||||
0.826946 | + | 0.562282i | \(0.190076\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.90633 | −0.197552 | ||||||||
\(392\) | 7.28643 | + | 12.6205i | 0.368020 | + | 0.637430i | ||||
\(393\) | 0.328013 | − | 0.189378i | 0.0165461 | − | 0.00955288i | ||||
\(394\) | −4.59028 | + | 7.95060i | −0.231255 | + | 0.400545i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.81062 | + | 2.20006i | 0.191491 | + | 0.110557i | ||||
\(397\) | −7.23416 | + | 12.5299i | −0.363072 | + | 0.628860i | −0.988465 | − | 0.151451i | \(-0.951606\pi\) |
0.625392 | + | 0.780310i | \(0.284939\pi\) | |||||||
\(398\) | 16.2175 | 0.812911 | ||||||||
\(399\) | 18.6826 | − | 32.3593i | 0.935302 | − | 1.61999i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.31096 | + | 3.64364i | −0.315154 | + | 0.181955i | −0.649231 | − | 0.760592i | \(-0.724909\pi\) |
0.334076 | + | 0.942546i | \(0.391576\pi\) | |||||||
\(402\) | 1.82522i | 0.0910336i | ||||||||
\(403\) | −21.6041 | + | 8.51671i | −1.07618 | + | 0.424248i | ||||
\(404\) | 6.80025 | 0.338325 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.0156 | + | 17.3475i | 0.497066 | + | 0.860943i | ||||
\(407\) | 14.4652 | + | 8.35150i | 0.717014 | + | 0.413968i | ||||
\(408\) | 4.00000 | 0.198030 | ||||||||
\(409\) | 21.2840 | + | 12.2883i | 1.05242 | + | 0.607617i | 0.923327 | − | 0.384015i | \(-0.125459\pi\) |
0.129097 | + | 0.991632i | \(0.458792\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.25235i | 0.0617741i | ||||||||
\(412\) | −4.58246 | − | 2.64568i | −0.225761 | − | 0.130343i | ||||
\(413\) | −8.77106 | + | 5.06397i | −0.431596 | + | 0.249182i | ||||
\(414\) | −0.845746 | + | 0.488292i | −0.0415662 | + | 0.0239982i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.56609 | + | 0.531987i | 0.174842 | + | 0.0260828i | ||||
\(417\) | 3.35534i | 0.164312i | ||||||||
\(418\) | 17.6990 | + | 30.6556i | 0.865688 | + | 1.49942i | ||||
\(419\) | 7.77684 | + | 13.4699i | 0.379923 | + | 0.658047i | 0.991051 | − | 0.133486i | \(-0.0426170\pi\) |
−0.611127 | + | 0.791532i | \(0.709284\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 22.3143i | − | 1.08753i | −0.839237 | − | 0.543766i | \(-0.816998\pi\) | ||
0.839237 | − | 0.543766i | \(-0.183002\pi\) | |||||||
\(422\) | −0.809848 | + | 1.40270i | −0.0394228 | + | 0.0682822i | ||||
\(423\) | −4.87671 | + | 8.44671i | −0.237114 | + | 0.410693i | ||||
\(424\) | 13.5089i | 0.656050i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.97658 | + | 6.88764i | 0.192666 | + | 0.333707i | ||||
\(427\) | −17.3341 | − | 30.0236i | −0.838856 | − | 1.45294i | ||||
\(428\) | 16.9282i | 0.818256i | ||||||||
\(429\) | −15.6912 | − | 2.34081i | −0.757580 | − | 0.113015i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.0135 | − | 12.1322i | 1.01219 | − | 0.584386i | 0.100356 | − | 0.994952i | \(-0.468002\pi\) |
0.911831 | + | 0.410565i | \(0.134669\pi\) | |||||||
\(432\) | 0.866025 | − | 0.500000i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | 20.0042 | + | 11.5494i | 0.961342 | + | 0.555031i | 0.896586 | − | 0.442870i | \(-0.146040\pi\) |
0.0647561 | + | 0.997901i | \(0.479373\pi\) | |||||||
\(434\) | − | 29.9148i | − | 1.43596i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.0853 | + | 6.40013i | 0.530892 | + | 0.306510i | ||||
\(437\) | −7.85641 | −0.375823 | ||||||||
\(438\) | 3.77684 | + | 2.18056i | 0.180464 | + | 0.104191i | ||||
\(439\) | 19.9980 | + | 34.6375i | 0.954450 | + | 1.65316i | 0.735621 | + | 0.677393i | \(0.236890\pi\) |
0.218829 | + | 0.975763i | \(0.429776\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.5729 | −0.693946 | ||||||||
\(442\) | −13.4173 | + | 5.28932i | −0.638194 | + | 0.251587i | ||||
\(443\) | 15.6036i | 0.741350i | 0.928763 | + | 0.370675i | \(0.120874\pi\) | ||||
−0.928763 | + | 0.370675i | \(0.879126\pi\) | |||||||
\(444\) | 3.28745 | − | 1.89801i | 0.156016 | − | 0.0900757i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.11836 | − | 1.93705i | 0.0529557 | − | 0.0917219i | ||||
\(447\) | −4.61970 | −0.218504 | ||||||||
\(448\) | −2.32233 | + | 4.02239i | −0.109720 | + | 0.190040i | ||||
\(449\) | −23.3863 | − | 13.5021i | −1.10367 | − | 0.637203i | −0.166486 | − | 0.986044i | \(-0.553242\pi\) |
−0.937182 | + | 0.348841i | \(0.886575\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.0370 | + | 27.7768i | −0.755151 | + | 1.30796i | ||||
\(452\) | −11.3156 | + | 6.53308i | −0.532242 | + | 0.307290i | ||||
\(453\) | −5.62124 | − | 9.73628i | −0.264109 | − | 0.457450i | ||||
\(454\) | 15.3205 | 0.719027 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.04479 | 0.376732 | ||||||||
\(457\) | 8.89342 | + | 15.4039i | 0.416017 | + | 0.720562i | 0.995535 | − | 0.0943975i | \(-0.0300925\pi\) |
−0.579518 | + | 0.814959i | \(0.696759\pi\) | |||||||
\(458\) | −8.77106 | + | 5.06397i | −0.409845 | + | 0.236624i | ||||
\(459\) | −2.00000 | + | 3.46410i | −0.0933520 | + | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.6205 | + | 12.4826i | 1.00697 | + | 0.581372i | 0.910302 | − | 0.413945i | \(-0.135849\pi\) |
0.0966638 | + | 0.995317i | \(0.469183\pi\) | |||||||
\(462\) | 10.2185 | − | 17.6990i | 0.475410 | − | 0.823434i | ||||
\(463\) | 15.6389 | 0.726801 | 0.363400 | − | 0.931633i | \(-0.381616\pi\) | ||||
0.363400 | + | 0.931633i | \(0.381616\pi\) | |||||||
\(464\) | −2.15637 | + | 3.73494i | −0.100107 | + | 0.173390i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.9716 | − | 10.3759i | 0.832521 | − | 0.480656i | ||||
\(467\) | − | 2.43914i | − | 0.112870i | −0.998406 | − | 0.0564349i | \(-0.982027\pi\) | ||
0.998406 | − | 0.0564349i | \(-0.0179733\pi\) | |||||||
\(468\) | −2.24376 | + | 2.82233i | −0.103718 | + | 0.130462i | ||||
\(469\) | 8.47751 | 0.391455 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.751556 | + | 1.30173i | 0.0346299 | + | 0.0599807i | ||||
\(472\) | −1.88842 | − | 1.09028i | −0.0869215 | − | 0.0501842i | ||||
\(473\) | −3.15250 | −0.144952 | ||||||||
\(474\) | −12.9332 | − | 7.46699i | −0.594042 | − | 0.342970i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 18.5786i | − | 0.851550i | ||||||
\(477\) | −11.6990 | − | 6.75444i | −0.535662 | − | 0.309265i | ||||
\(478\) | −21.0911 | + | 12.1770i | −0.964685 | + | 0.556961i | ||||
\(479\) | −12.2857 | + | 7.09317i | −0.561349 | + | 0.324095i | −0.753687 | − | 0.657234i | \(-0.771726\pi\) |
0.192338 | + | 0.981329i | \(0.438393\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.51737 | + | 10.7136i | −0.388358 | + | 0.488500i | ||||
\(482\) | − | 19.8685i | − | 0.904983i | ||||||
\(483\) | 2.26795 | + | 3.92820i | 0.103195 | + | 0.178739i | ||||
\(484\) | 4.18056 | + | 7.24094i | 0.190025 | + | 0.329134i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | −2.88164 | + | 4.99115i | −0.130580 | + | 0.226171i | −0.923900 | − | 0.382633i | \(-0.875017\pi\) |
0.793320 | + | 0.608804i | \(0.208351\pi\) | |||||||
\(488\) | 3.73205 | − | 6.46410i | 0.168942 | − | 0.292616i | ||||
\(489\) | − | 0.176330i | − | 0.00797392i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.537671 | − | 0.931273i | −0.0242647 | − | 0.0420278i | 0.853638 | − | 0.520867i | \(-0.174391\pi\) |
−0.877903 | + | 0.478839i | \(0.841058\pi\) | |||||||
\(492\) | 3.64466 | + | 6.31274i | 0.164314 | + | 0.284600i | ||||
\(493\) | − | 17.2509i | − | 0.776943i | ||||||
\(494\) | −26.9848 | + | 10.6379i | −1.21410 | + | 0.478620i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.57780 | − | 3.22034i | 0.250450 | − | 0.144598i | ||||
\(497\) | 31.9908 | − | 18.4699i | 1.43498 | − | 0.828487i | ||||
\(498\) | −3.04056 | − | 1.75547i | −0.136251 | − | 0.0786644i | ||||
\(499\) | − | 14.7534i | − | 0.660454i | −0.943902 | − | 0.330227i | \(-0.892875\pi\) | ||
0.943902 | − | 0.330227i | \(-0.107125\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.51851 | − | 4.34081i | −0.335902 | − | 0.193933i | ||||
\(502\) | 13.5713 | 0.605717 | ||||||||
\(503\) | −23.0898 | − | 13.3309i | −1.02952 | − | 0.594395i | −0.112675 | − | 0.993632i | \(-0.535942\pi\) |
−0.916848 | + | 0.399236i | \(0.869275\pi\) | |||||||
\(504\) | −2.32233 | − | 4.02239i | −0.103445 | − | 0.179172i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.29709 | −0.191029 | ||||||||
\(507\) | 3.79423 | − | 12.4340i | 0.168508 | − | 0.552212i | ||||
\(508\) | − | 12.2196i | − | 0.542156i | ||||||
\(509\) | −12.2807 | + | 7.09028i | −0.544333 | + | 0.314271i | −0.746833 | − | 0.665011i | \(-0.768427\pi\) |
0.202500 | + | 0.979282i | \(0.435093\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.1279 | − | 17.5421i | 0.448034 | − | 0.776018i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.02239 | + | 6.96699i | −0.177593 | + | 0.307600i | ||||
\(514\) | −0.573569 | − | 0.331150i | −0.0252990 | − | 0.0146064i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.358228 | + | 0.620469i | −0.0157701 | + | 0.0273146i | ||||
\(517\) | −37.1666 | + | 21.4581i | −1.63459 | + | 0.943728i | ||||
\(518\) | −8.81562 | − | 15.2691i | −0.387336 | − | 0.670886i | ||||
\(519\) | 1.78043 | 0.0781523 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.7476 | 1.04040 | 0.520202 | − | 0.854043i | \(-0.325857\pi\) | ||||
0.520202 | + | 0.854043i | \(0.325857\pi\) | |||||||
\(522\) | −2.15637 | − | 3.73494i | −0.0943817 | − | 0.163474i | ||||
\(523\) | −11.9950 | + | 6.92532i | −0.524505 | + | 0.302823i | −0.738776 | − | 0.673951i | \(-0.764596\pi\) |
0.214271 | + | 0.976774i | \(0.431262\pi\) | |||||||
\(524\) | 0.189378 | − | 0.328013i | 0.00827303 | − | 0.0143293i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.6301 | − | 15.3749i | −1.16113 | − | 0.670378i | ||||
\(527\) | −12.8814 | + | 22.3112i | −0.561121 | + | 0.971891i | ||||
\(528\) | 4.40013 | 0.191491 | ||||||||
\(529\) | −11.0231 | + | 19.0926i | −0.479267 | + | 0.830115i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.88842 | − | 1.09028i | 0.0819504 | − | 0.0473141i | ||||
\(532\) | − | 37.3653i | − | 1.61999i | ||||||
\(533\) | −20.5729 | − | 16.3555i | −0.891110 | − | 0.708434i | ||||
\(534\) | 8.17274 | 0.353669 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.912609 | + | 1.58068i | 0.0394187 | + | 0.0682752i | ||||
\(537\) | −15.0825 | − | 8.70786i | −0.650856 | − | 0.375772i | ||||
\(538\) | −3.74410 | −0.161420 | ||||||||
\(539\) | −55.5317 | − | 32.0612i | −2.39192 | − | 1.38097i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.8898i | 0.640164i | 0.947390 | + | 0.320082i | \(0.103710\pi\) | ||||
−0.947390 | + | 0.320082i | \(0.896290\pi\) | |||||||
\(542\) | 24.0419 | + | 13.8806i | 1.03269 | + | 0.596223i | ||||
\(543\) | 8.97299 | − | 5.18056i | 0.385068 | − | 0.222319i | ||||
\(544\) | 3.46410 | − | 2.00000i | 0.148522 | − | 0.0857493i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 13.1088 | + | 10.4215i | 0.561003 | + | 0.445999i | ||||
\(547\) | − | 22.2019i | − | 0.949284i | −0.880179 | − | 0.474642i | \(-0.842578\pi\) | ||
0.880179 | − | 0.474642i | \(-0.157422\pi\) | |||||||
\(548\) | 0.626177 | + | 1.08457i | 0.0267490 | + | 0.0463306i | ||||
\(549\) | 3.73205 | + | 6.46410i | 0.159280 | + | 0.275881i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 34.6950i | − | 1.47806i | ||||||
\(552\) | −0.488292 | + | 0.845746i | −0.0207831 | + | 0.0359973i | ||||
\(553\) | −34.6816 | + | 60.0703i | −1.47481 | + | 2.55445i | ||||
\(554\) | 11.9922i | 0.509499i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.67767 | + | 2.90581i | 0.0711491 | + | 0.123234i | ||||
\(557\) | 0.949847 | + | 1.64518i | 0.0402463 | + | 0.0697087i | 0.885447 | − | 0.464741i | \(-0.153852\pi\) |
−0.845201 | + | 0.534449i | \(0.820519\pi\) | |||||||
\(558\) | 6.44069i | 0.272656i | ||||||||
\(559\) | 0.381146 | − | 2.55495i | 0.0161207 | − | 0.108063i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.2425 | + | 8.80025i | −0.643538 | + | 0.371547i | ||||
\(562\) | −3.15137 | + | 1.81944i | −0.132932 | + | 0.0767485i | ||||
\(563\) | 1.48956 | + | 0.860000i | 0.0627777 | + | 0.0362447i | 0.531060 | − | 0.847334i | \(-0.321794\pi\) |
−0.468283 | + | 0.883579i | \(0.655127\pi\) | |||||||
\(564\) | 9.75342i | 0.410693i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.19538 | + | 2.42220i | 0.176345 | + | 0.101813i | ||||
\(567\) | 4.64466 | 0.195057 | ||||||||
\(568\) | 6.88764 | + | 3.97658i | 0.288999 | + | 0.166854i | ||||
\(569\) | 0.300960 | + | 0.521278i | 0.0126169 | + | 0.0218531i | 0.872265 | − | 0.489034i | \(-0.162650\pi\) |
−0.859648 | + | 0.510887i | \(0.829317\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.9808 | 0.501381 | 0.250691 | − | 0.968067i | \(-0.419342\pi\) | ||||
0.250691 | + | 0.968067i | \(0.419342\pi\) | |||||||
\(572\) | −14.7594 | + | 5.81842i | −0.617122 | + | 0.243280i | ||||
\(573\) | 0.897014i | 0.0374733i | ||||||||
\(574\) | 29.3205 | − | 16.9282i | 1.22381 | − | 0.706570i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 43.0293 | 1.79133 | 0.895667 | − | 0.444725i | \(-0.146699\pi\) | ||||
0.895667 | + | 0.444725i | \(0.146699\pi\) | |||||||
\(578\) | 0.500000 | − | 0.866025i | 0.0207973 | − | 0.0360219i | ||||
\(579\) | 17.5494 | + | 10.1322i | 0.729330 | + | 0.421079i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.15355 | + | 14.1224i | −0.338266 | + | 0.585894i | ||||
\(582\) | 11.9730 | − | 6.91261i | 0.496296 | − | 0.286537i | ||||
\(583\) | −29.7204 | − | 51.4773i | −1.23089 | − | 2.13197i | ||||
\(584\) | 4.36112 | 0.180464 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.70081 | 0.152879 | ||||||||
\(587\) | −8.95740 | − | 15.5147i | −0.369711 | − | 0.640359i | 0.619809 | − | 0.784753i | \(-0.287210\pi\) |
−0.989520 | + | 0.144394i | \(0.953877\pi\) | |||||||
\(588\) | −12.6205 | + | 7.28643i | −0.520459 | + | 0.300487i | ||||
\(589\) | −25.9070 | + | 44.8722i | −1.06748 | + | 1.84893i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.95060 | − | 4.59028i | −0.327044 | − | 0.188819i | ||||
\(592\) | 1.89801 | − | 3.28745i | 0.0780078 | − | 0.135114i | ||||
\(593\) | 0.669624 | 0.0274981 | 0.0137491 | − | 0.999905i | \(-0.495623\pi\) | ||||
0.0137491 | + | 0.999905i | \(0.495623\pi\) | |||||||
\(594\) | −2.20006 | + | 3.81062i | −0.0902697 | + | 0.156352i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.00077 | + | 2.30985i | −0.163878 | + | 0.0946151i | ||||
\(597\) | 16.2175i | 0.663739i | ||||||||
\(598\) | 0.519530 | − | 3.48258i | 0.0212452 | − | 0.142413i | ||||
\(599\) | −1.29241 | −0.0528066 | −0.0264033 | − | 0.999651i | \(-0.508405\pi\) | ||||
−0.0264033 | + | 0.999651i | \(0.508405\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.73671 | + | 9.93627i | 0.234005 | + | 0.405309i | 0.958983 | − | 0.283463i | \(-0.0914834\pi\) |
−0.724978 | + | 0.688772i | \(0.758150\pi\) | |||||||
\(602\) | 2.88187 | + | 1.66385i | 0.117456 | + | 0.0678134i | ||||
\(603\) | −1.82522 | −0.0743286 | ||||||||
\(604\) | −9.73628 | − | 5.62124i | −0.396164 | − | 0.228725i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.80025i | 0.276241i | ||||||||
\(607\) | 20.9010 | + | 12.0672i | 0.848344 | + | 0.489792i | 0.860092 | − | 0.510139i | \(-0.170406\pi\) |
−0.0117477 | + | 0.999931i | \(0.503739\pi\) | |||||||
\(608\) | 6.96699 | − | 4.02239i | 0.282549 | − | 0.163130i | ||||
\(609\) | −17.3475 | + | 10.0156i | −0.702957 | + | 0.405852i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.8972 | − | 32.7161i | −0.521766 | − | 1.32355i | ||||
\(612\) | 4.00000i | 0.161690i | ||||||||
\(613\) | −14.4751 | − | 25.0716i | −0.584644 | − | 1.01263i | −0.994920 | − | 0.100671i | \(-0.967901\pi\) |
0.410276 | − | 0.911961i | \(-0.365432\pi\) | |||||||
\(614\) | 3.55727 | + | 6.16137i | 0.143560 | + | 0.248653i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 20.4371i | − | 0.823434i | ||||||
\(617\) | 0.420655 | − | 0.728597i | 0.0169349 | − | 0.0293322i | −0.857434 | − | 0.514594i | \(-0.827943\pi\) |
0.874369 | + | 0.485262i | \(0.161276\pi\) | |||||||
\(618\) | 2.64568 | − | 4.58246i | 0.106425 | − | 0.184333i | ||||
\(619\) | 6.25076i | 0.251239i | 0.992078 | + | 0.125620i | \(0.0400919\pi\) | ||||
−0.992078 | + | 0.125620i | \(0.959908\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.488292 | − | 0.845746i | −0.0195945 | − | 0.0339386i | ||||
\(622\) | −9.95740 | − | 17.2467i | −0.399255 | − | 0.691530i | ||||
\(623\) | − | 37.9596i | − | 1.52082i | ||||||
\(624\) | −0.531987 | + | 3.56609i | −0.0212965 | + | 0.142758i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.31696 | − | 3.06975i | 0.212509 | − | 0.122692i | ||||
\(627\) | −30.6556 | + | 17.6990i | −1.22427 | + | 0.706832i | ||||
\(628\) | 1.30173 | + | 0.751556i | 0.0519448 | + | 0.0299904i | ||||
\(629\) | 15.1841i | 0.605430i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.61970 | + | 1.51248i | 0.104288 | + | 0.0602110i | 0.551237 | − | 0.834349i | \(-0.314156\pi\) |
−0.446949 | + | 0.894560i | \(0.647489\pi\) | |||||||
\(632\) | −14.9340 | −0.594042 | ||||||||
\(633\) | −1.40270 | − | 0.809848i | −0.0557522 | − | 0.0321886i | ||||
\(634\) | −3.92643 | − | 6.80078i | −0.155938 | − | 0.270093i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.5089 | −0.535662 | ||||||||
\(637\) | 32.6980 | − | 41.1294i | 1.29554 | − | 1.62961i | ||||
\(638\) | − | 18.9766i | − | 0.751290i | ||||||
\(639\) | −6.88764 | + | 3.97658i | −0.272471 | + | 0.157311i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.386305 | − | 0.669099i | 0.0152581 | − | 0.0264278i | −0.858296 | − | 0.513156i | \(-0.828476\pi\) |
0.873554 | + | 0.486728i | \(0.161810\pi\) | |||||||
\(642\) | −16.9282 | −0.668103 | ||||||||
\(643\) | 9.68726 | − | 16.7788i | 0.382028 | − | 0.661693i | −0.609324 | − | 0.792922i | \(-0.708559\pi\) |
0.991352 | + | 0.131229i | \(0.0418923\pi\) | |||||||
\(644\) | 3.92820 | + | 2.26795i | 0.154793 | + | 0.0893697i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.0896 | + | 27.8680i | −0.633036 | + | 1.09645i | ||||
\(647\) | 23.5477 | − | 13.5953i | 0.925755 | − | 0.534485i | 0.0402882 | − | 0.999188i | \(-0.487172\pi\) |
0.885466 | + | 0.464703i | \(0.153839\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 9.59473 | 0.376626 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.9148 | 1.17245 | ||||||||
\(652\) | −0.0881650 | − | 0.152706i | −0.00345281 | − | 0.00598044i | ||||
\(653\) | −13.6797 | + | 7.89799i | −0.535329 | + | 0.309072i | −0.743184 | − | 0.669088i | \(-0.766685\pi\) |
0.207855 | + | 0.978160i | \(0.433352\pi\) | |||||||
\(654\) | −6.40013 | + | 11.0853i | −0.250265 | + | 0.433471i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.31274 | + | 3.64466i | 0.246471 | + | 0.142300i | ||||
\(657\) | −2.18056 | + | 3.77684i | −0.0850717 | + | 0.147348i | ||||
\(658\) | 45.3013 | 1.76603 | ||||||||
\(659\) | 15.2381 | − | 26.3932i | 0.593593 | − | 1.02813i | −0.400151 | − | 0.916449i | \(-0.631042\pi\) |
0.993744 | − | 0.111684i | \(-0.0356243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.1514 | + | 13.9438i | −0.939379 | + | 0.542351i | −0.889766 | − | 0.456418i | \(-0.849132\pi\) |
−0.0496136 | + | 0.998768i | \(0.515799\pi\) | |||||||
\(662\) | 31.9959i | 1.24356i | ||||||||
\(663\) | −5.28932 | − | 13.4173i | −0.205420 | − | 0.521084i | ||||
\(664\) | −3.51093 | −0.136251 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.89801 | + | 3.28745i | 0.0735465 | + | 0.127386i | ||||
\(667\) | 3.64748 | + | 2.10587i | 0.141231 | + | 0.0815397i | ||||
\(668\) | −8.68162 | −0.335902 | ||||||||
\(669\) | 1.93705 | + | 1.11836i | 0.0748906 | + | 0.0432381i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.8430i | 1.26789i | ||||||||
\(672\) | −4.02239 | − | 2.32233i | −0.155167 | − | 0.0895858i | ||||
\(673\) | −0.847086 | + | 0.489066i | −0.0326528 | + | 0.0188521i | −0.516238 | − | 0.856445i | \(-0.672668\pi\) |
0.483585 | + | 0.875298i | \(0.339334\pi\) | |||||||
\(674\) | 30.8680 | − | 17.8216i | 1.18899 | − | 0.686463i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.93109 | − | 12.6653i | −0.112734 | − | 0.487125i | ||||
\(677\) | − | 19.1926i | − | 0.737630i | −0.929503 | − | 0.368815i | \(-0.879764\pi\) | ||
0.929503 | − | 0.368815i | \(-0.120236\pi\) | |||||||
\(678\) | −6.53308 | − | 11.3156i | −0.250901 | − | 0.434574i | ||||
\(679\) | −32.1067 | − | 55.6105i | −1.23214 | − | 2.13413i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.3205i | 0.587083i | ||||||||
\(682\) | −14.1699 | + | 24.5430i | −0.542594 | + | 0.939801i | ||||
\(683\) | −0.755467 | + | 1.30851i | −0.0289071 | + | 0.0500687i | −0.880117 | − | 0.474757i | \(-0.842536\pi\) |
0.851210 | + | 0.524825i | \(0.175869\pi\) | |||||||
\(684\) | 8.04479i | 0.307600i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.5867 | + | 30.4610i | 0.671463 | + | 1.16301i | ||||
\(687\) | −5.06397 | − | 8.77106i | −0.193203 | − | 0.334637i | ||||
\(688\) | 0.716456i | 0.0273146i | ||||||||
\(689\) | 45.3131 | − | 17.8632i | 1.72629 | − | 0.680534i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.6798 | − | 16.5583i | 1.09103 | − | 0.629907i | 0.157180 | − | 0.987570i | \(-0.449760\pi\) |
0.933851 | + | 0.357663i | \(0.116426\pi\) | |||||||
\(692\) | 1.54190 | − | 0.890216i | 0.0586142 | − | 0.0338409i | ||||
\(693\) | 17.6990 | + | 10.2185i | 0.672331 | + | 0.388170i | ||||
\(694\) | 6.89701i | 0.261807i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.73494 | − | 2.15637i | −0.141572 | − | 0.0817369i | ||||
\(697\) | −29.1573 | −1.10441 | ||||||||
\(698\) | −16.7321 | − | 9.66025i | −0.633317 | − | 0.365646i | ||||
\(699\) | 10.3759 | + | 17.9716i | 0.392454 | + | 0.679750i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.8695 | 1.05262 | 0.526308 | − | 0.850294i | \(-0.323576\pi\) | ||||
0.526308 | + | 0.850294i | \(0.323576\pi\) | |||||||
\(702\) | −2.82233 | − | 2.24376i | −0.106522 | − | 0.0846852i | ||||
\(703\) | 30.5382i | 1.15177i | ||||||||
\(704\) | 3.81062 | − | 2.20006i | 0.143618 | − | 0.0829180i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.7086 | + | 23.7441i | −0.515931 | + | 0.893619i | ||||
\(707\) | 31.5849 | 1.18787 | ||||||||
\(708\) | 1.09028 | − | 1.88842i | 0.0409752 | − | 0.0709711i | ||||
\(709\) | 9.57491 | + | 5.52808i | 0.359593 | + | 0.207611i | 0.668902 | − | 0.743350i | \(-0.266764\pi\) |
−0.309309 | + | 0.950962i | \(0.600098\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.46699 | − | 12.9332i | 0.280034 | − | 0.485033i | ||||
\(712\) | 7.07780 | − | 4.08637i | 0.265252 | − | 0.153143i | ||||
\(713\) | −3.14493 | − | 5.44719i | −0.117779 | − | 0.203999i | ||||
\(714\) | 18.5786 | 0.695288 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.4157 | −0.650856 | ||||||||
\(717\) | −12.1770 | − | 21.0911i | −0.454757 | − | 0.787662i | ||||
\(718\) | 12.4371 | − | 7.18056i | 0.464148 | − | 0.267976i | ||||
\(719\) | −5.85641 | + | 10.1436i | −0.218407 | + | 0.378292i | −0.954321 | − | 0.298783i | \(-0.903419\pi\) |
0.735914 | + | 0.677075i | \(0.236753\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.2840 | − | 12.2883i | −0.792656 | − | 0.457640i | ||||
\(722\) | −22.8593 | + | 39.5935i | −0.850735 | + | 1.47352i | ||||
\(723\) | 19.8685 | 0.738916 | ||||||||
\(724\) | 5.18056 | − | 8.97299i | 0.192534 | − | 0.333479i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.24094 | + | 4.18056i | −0.268736 | + | 0.155155i | ||||
\(727\) | − | 19.4152i | − | 0.720071i | −0.932939 | − | 0.360035i | \(-0.882765\pi\) | ||
0.932939 | − | 0.360035i | \(-0.117235\pi\) | |||||||
\(728\) | 16.5633 | + | 2.47090i | 0.613876 | + | 0.0915777i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.43291 | − | 2.48188i | −0.0529982 | − | 0.0917956i | ||||
\(732\) | 6.46410 | + | 3.73205i | 0.238920 | + | 0.137941i | ||||
\(733\) | 11.9340 | 0.440792 | 0.220396 | − | 0.975411i | \(-0.429265\pi\) | ||||
0.220396 | + | 0.975411i | \(0.429265\pi\) | |||||||
\(734\) | −11.9298 | − | 6.88764i | −0.440335 | − | 0.254228i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.976584i | 0.0359973i | ||||||||
\(737\) | −6.95521 | − | 4.01559i | −0.256199 | − | 0.147916i | ||||
\(738\) | −6.31274 | + | 3.64466i | −0.232375 | + | 0.134162i | ||||
\(739\) | −17.2017 | + | 9.93141i | −0.632775 | + | 0.365333i | −0.781826 | − | 0.623497i | \(-0.785711\pi\) |
0.149051 | + | 0.988830i | \(0.452378\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.6379 | − | 26.9848i | −0.390792 | − | 0.991310i | ||||
\(742\) | 62.7442i | 2.30341i | ||||||||
\(743\) | −8.24383 | − | 14.2787i | −0.302437 | − | 0.523836i | 0.674251 | − | 0.738503i | \(-0.264467\pi\) |
−0.976687 | + | 0.214667i | \(0.931133\pi\) | |||||||
\(744\) | 3.22034 | + | 5.57780i | 0.118063 | + | 0.204492i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 33.4627i | − | 1.22516i | ||||||
\(747\) | 1.75547 | − | 3.04056i | 0.0642292 | − | 0.111248i | ||||
\(748\) | −8.80025 | + | 15.2425i | −0.321769 | + | 0.557320i | ||||
\(749\) | 78.6257i | 2.87292i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.3312 | − | 40.4109i | −0.851368 | − | 1.47461i | −0.879974 | − | 0.475022i | \(-0.842440\pi\) |
0.0286056 | − | 0.999591i | \(-0.490893\pi\) | |||||||
\(752\) | 4.87671 | + | 8.44671i | 0.177835 | + | 0.308020i | ||||
\(753\) | 13.5713i | 0.494566i | ||||||||
\(754\) | 15.3796 | + | 2.29432i | 0.560092 | + | 0.0835542i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.02239 | − | 2.32233i | 0.146293 | − | 0.0844623i | ||||
\(757\) | 2.28282 | − | 1.31799i | 0.0829705 | − | 0.0479030i | −0.457941 | − | 0.888983i | \(-0.651413\pi\) |
0.540911 | + | 0.841080i | \(0.318079\pi\) | |||||||
\(758\) | 28.9052 | + | 16.6884i | 1.04988 | + | 0.606151i | ||||
\(759\) | − | 4.29709i | − | 0.155975i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.0693410 | + | 0.0400340i | 0.00251361 | + | 0.00145123i | 0.501256 | − | 0.865299i | \(-0.332871\pi\) |
−0.498743 | + | 0.866750i | \(0.666205\pi\) | |||||||
\(762\) | 12.2196 | 0.442668 | ||||||||
\(763\) | 51.4877 | + | 29.7264i | 1.86398 | + | 1.07617i | ||||
\(764\) | 0.448507 | + | 0.776837i | 0.0162264 | + | 0.0281050i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.33038 | 0.264857 | ||||||||
\(767\) | −1.16003 | + | 7.77606i | −0.0418862 | + | 0.280777i | ||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −4.92177 | + | 2.84159i | −0.177484 | + | 0.102470i | −0.586110 | − | 0.810232i | \(-0.699341\pi\) |
0.408626 | + | 0.912702i | \(0.366008\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.331150 | − | 0.573569i | 0.0119261 | − | 0.0206566i | ||||
\(772\) | 20.2644 | 0.729330 | ||||||||
\(773\) | −3.79425 | + | 6.57184i | −0.136470 | + | 0.236373i | −0.926158 | − | 0.377136i | \(-0.876909\pi\) |
0.789688 | + | 0.613508i | \(0.210242\pi\) | |||||||
\(774\) | −0.620469 | − | 0.358228i | −0.0223023 | − | 0.0128762i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.91261 | − | 11.9730i | 0.248148 | − | 0.429805i | ||||
\(777\) | 15.2691 | − | 8.81562i | 0.547776 | − | 0.316259i | ||||
\(778\) | 16.3099 | + | 28.2496i | 0.584739 | + | 1.01280i | ||||
\(779\) | −58.6410 | −2.10103 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.9949 | −1.25222 | ||||||||
\(782\) | −1.95317 | − | 3.38298i | −0.0698451 | − | 0.120975i | ||||
\(783\) | 3.73494 | − | 2.15637i | 0.133476 | − | 0.0770623i | ||||
\(784\) | −7.28643 | + | 12.6205i | −0.260230 | + | 0.450731i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.328013 | + | 0.189378i | 0.0116998 | + | 0.00675490i | ||||
\(787\) | 2.36811 | − | 4.10169i | 0.0844142 | − | 0.146210i | −0.820727 | − | 0.571320i | \(-0.806431\pi\) |
0.905141 | + | 0.425111i | \(0.139765\pi\) | |||||||
\(788\) | −9.18056 | −0.327044 | ||||||||
\(789\) | 15.3749 | − | 26.6301i | 0.547361 | − | 0.948058i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −52.5572 | + | 30.3439i | −1.86872 | + | 1.07891i | ||||
\(792\) | 4.40013i | 0.156352i | ||||||||
\(793\) | −26.6176 | − | 3.97081i | −0.945220 | − | 0.141008i | ||||
\(794\) | −14.4683 | −0.513462 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.10876 | + | 14.0448i | 0.287407 | + | 0.497804i | ||||
\(797\) | −35.5621 | − | 20.5318i | −1.25968 | − | 0.727274i | −0.286664 | − | 0.958031i | \(-0.592546\pi\) |
−0.973011 | + | 0.230757i | \(0.925880\pi\) | |||||||
\(798\) | 37.3653 | 1.32272 | ||||||||
\(799\) | −33.7868 | − | 19.5068i | −1.19529 | − | 0.690102i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.17274i | 0.288769i | ||||||||
\(802\) | −6.31096 | − | 3.64364i | −0.222848 | − | 0.128661i | ||||
\(803\) | −16.6186 | + | 9.59473i | −0.586456 | + | 0.338591i | ||||
\(804\) | −1.58068 | + | 0.912609i | −0.0557465 | + | 0.0321852i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −18.1777 | − | 14.4513i | −0.640284 | − | 0.509027i | ||||
\(807\) | − | 3.74410i | − | 0.131799i | ||||||
\(808\) | 3.40013 | + | 5.88919i | 0.119616 | + | 0.207181i | ||||
\(809\) | −13.8003 | − | 23.9027i | −0.485191 | − | 0.840376i | 0.514664 | − | 0.857392i | \(-0.327917\pi\) |
−0.999855 | + | 0.0170163i | \(0.994583\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.6930i | 0.375482i | 0.982219 | + | 0.187741i | \(0.0601165\pi\) | ||||
−0.982219 | + | 0.187741i | \(0.939883\pi\) | |||||||
\(812\) | −10.0156 | + | 17.3475i | −0.351478 | + | 0.608779i | ||||
\(813\) | −13.8806 | + | 24.0419i | −0.486814 | + | 0.843186i | ||||
\(814\) | 16.7030i | 0.585440i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.00000 | + | 3.46410i | 0.0700140 | + | 0.121268i | ||||
\(817\) | −2.88187 | − | 4.99154i | −0.100824 | − | 0.174632i | ||||
\(818\) | 24.5766i | 0.859300i | ||||||||
\(819\) | −10.4215 | + | 13.1088i | −0.364157 | + | 0.458057i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.2105 | − | 8.78177i | 0.530849 | − | 0.306486i | −0.210513 | − | 0.977591i | \(-0.567513\pi\) |
0.741362 | + | 0.671105i | \(0.234180\pi\) | |||||||
\(822\) | −1.08457 | + | 0.626177i | −0.0378288 | + | 0.0218404i | ||||
\(823\) | 33.5264 | + | 19.3565i | 1.16866 | + | 0.674725i | 0.953364 | − | 0.301824i | \(-0.0975955\pi\) |
0.215295 | + | 0.976549i | \(0.430929\pi\) | |||||||
\(824\) | − | 5.29137i | − | 0.184333i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.77106 | − | 5.06397i | −0.305184 | − | 0.176198i | ||||
\(827\) | −28.4703 | −0.990010 | −0.495005 | − | 0.868890i | \(-0.664834\pi\) | ||||
−0.495005 | + | 0.868890i | \(0.664834\pi\) | |||||||
\(828\) | −0.845746 | − | 0.488292i | −0.0293917 | − | 0.0169693i | ||||
\(829\) | −4.14354 | − | 7.17683i | −0.143911 | − | 0.249262i | 0.785055 | − | 0.619426i | \(-0.212635\pi\) |
−0.928966 | + | 0.370165i | \(0.879301\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.9922 | −0.416004 | ||||||||
\(832\) | 1.32233 | + | 3.35432i | 0.0458435 | + | 0.116290i | ||||
\(833\) | − | 58.2915i | − | 2.01968i | ||||||
\(834\) | −2.90581 | + | 1.67767i | −0.100620 | + | 0.0580930i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −17.6990 | + | 30.6556i | −0.612134 | + | 1.06025i | ||||
\(837\) | −6.44069 | −0.222623 | ||||||||
\(838\) | −7.77684 | + | 13.4699i | −0.268646 | + | 0.465309i | ||||
\(839\) | 36.8606 | + | 21.2815i | 1.27257 | + | 0.734719i | 0.975471 | − | 0.220128i | \(-0.0706474\pi\) |
0.297099 | + | 0.954847i | \(0.403981\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.20016 | − | 9.00693i | 0.179316 | − | 0.310584i | ||||
\(842\) | 19.3247 | − | 11.1571i | 0.665974 | − | 0.384500i | ||||
\(843\) | −1.81944 | − | 3.15137i | −0.0626649 | − | 0.108539i | ||||
\(844\) | −1.61970 | −0.0557522 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.75342 | −0.335330 | ||||||||
\(847\) | 19.4173 | + | 33.6317i | 0.667185 | + | 1.15560i | ||||
\(848\) | −11.6990 | + | 6.75444i | −0.401747 | + | 0.231949i | ||||
\(849\) | −2.42220 | + | 4.19538i | −0.0831298 | + | 0.143985i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.21047 | − | 1.85357i | −0.110054 | − | 0.0635395i | ||||
\(852\) | −3.97658 | + | 6.88764i | −0.136236 | + | 0.235967i | ||||
\(853\) | 28.1380 | 0.963425 | 0.481713 | − | 0.876329i | \(-0.340015\pi\) | ||||
0.481713 | + | 0.876329i | \(0.340015\pi\) | |||||||
\(854\) | 17.3341 | − | 30.0236i | 0.593161 | − | 1.02738i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.6603 | + | 8.46410i | −0.501077 | + | 0.289297i | ||||
\(857\) | − | 10.3355i | − | 0.353053i | −0.984296 | − | 0.176526i | \(-0.943514\pi\) | ||
0.984296 | − | 0.176526i | \(-0.0564861\pi\) | |||||||
\(858\) | −5.81842 | − | 14.7594i | −0.198638 | − | 0.503878i | ||||
\(859\) | −0.380304 | −0.0129758 | −0.00648791 | − | 0.999979i | \(-0.502065\pi\) | ||||
−0.00648791 | + | 0.999979i | \(0.502065\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.9282 | + | 29.3205i | 0.576912 | + | 0.999240i | ||||
\(862\) | 21.0135 | + | 12.1322i | 0.715724 | + | 0.413224i | ||||
\(863\) | 47.1484 | 1.60495 | 0.802475 | − | 0.596685i | \(-0.203516\pi\) | ||||
0.802475 | + | 0.596685i | \(0.203516\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 23.0989i | 0.784932i | ||||||||
\(867\) | 0.866025 | + | 0.500000i | 0.0294118 | + | 0.0169809i | ||||
\(868\) | 25.9070 | − | 14.9574i | 0.879340 | − | 0.507687i | ||||
\(869\) | 56.9077 | − | 32.8557i | 1.93046 | − | 1.11455i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.09535 | − | 5.15137i | 0.138766 | − | 0.174547i | ||||
\(872\) | 12.8003i | 0.433471i | ||||||||
\(873\) | 6.91261 | + | 11.9730i | 0.233956 | + | 0.405224i | ||||
\(874\) | −3.92820 | − | 6.80385i | −0.132873 | − | 0.230144i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.36112i | 0.147348i | ||||||||
\(877\) | −20.0206 | + | 34.6767i | −0.676047 | + | 1.17095i | 0.300114 | + | 0.953903i | \(0.402975\pi\) |
−0.976162 | + | 0.217045i | \(0.930358\pi\) | |||||||
\(878\) | −19.9980 | + | 34.6375i | −0.674898 | + | 1.16896i | ||||
\(879\) | 3.70081i | 0.124825i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.72246 | − | 13.3757i | −0.260176 | − | 0.450638i | 0.706112 | − | 0.708100i | \(-0.250447\pi\) |
−0.966289 | + | 0.257461i | \(0.917114\pi\) | |||||||
\(882\) | −7.28643 | − | 12.6205i | −0.245347 | − | 0.424953i | ||||
\(883\) | 6.02142i | 0.202637i | 0.994854 | + | 0.101318i | \(0.0323061\pi\) | ||||
−0.994854 | + | 0.101318i | \(0.967694\pi\) | |||||||
\(884\) | −11.2893 | − | 8.97504i | −0.379701 | − | 0.301863i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.5131 | + | 7.80180i | −0.453982 | + | 0.262107i | ||||
\(887\) | −42.5548 | + | 24.5690i | −1.42885 | + | 0.824947i | −0.997030 | − | 0.0770129i | \(-0.975462\pi\) |
−0.431820 | + | 0.901960i | \(0.642128\pi\) | |||||||
\(888\) | 3.28745 | + | 1.89801i | 0.110320 | + | 0.0636931i | ||||
\(889\) | − | 56.7557i | − | 1.90353i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.81062 | − | 2.20006i | −0.127661 | − | 0.0737049i | ||||
\(892\) | 2.23671 | 0.0748906 | ||||||||
\(893\) | −67.9520 | − | 39.2321i | −2.27393 | − | 1.31285i | ||||
\(894\) | −2.30985 | − | 4.00077i | −0.0772529 | − | 0.133806i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.64466 | −0.155167 | ||||||||
\(897\) | 3.48258 | + | 0.519530i | 0.116280 | + | 0.0173466i | ||||
\(898\) | − | 27.0042i | − | 0.901141i | ||||||
\(899\) | 24.0556 | − | 13.8885i | 0.802298 | − | 0.463207i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.0178 | − | 46.7962i | 0.900093 | − | 1.55901i | ||||
\(902\) | −32.0739 | −1.06795 | ||||||||
\(903\) | −1.66385 | + | 2.88187i | −0.0553694 | + | 0.0959026i | ||||
\(904\) | −11.3156 | − | 6.53308i | −0.376352 | − | 0.217287i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.62124 | − | 9.73628i | 0.186753 | − | 0.323466i | ||||
\(907\) | −14.1741 | + | 8.18345i | −0.470645 | + | 0.271727i | −0.716510 | − | 0.697577i | \(-0.754261\pi\) |
0.245865 | + | 0.969304i | \(0.420928\pi\) | |||||||
\(908\) | 7.66025 | + | 13.2679i | 0.254214 | + | 0.440312i | ||||
\(909\) | −6.80025 | −0.225550 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.4819 | −0.347280 | −0.173640 | − | 0.984809i | \(-0.555553\pi\) | ||||
−0.173640 | + | 0.984809i | \(0.555553\pi\) | |||||||
\(912\) | 4.02239 | + | 6.96699i | 0.133195 | + | 0.230700i | ||||
\(913\) | 13.3788 | − | 7.72428i | 0.442775 | − | 0.255636i | ||||
\(914\) | −8.89342 | + | 15.4039i | −0.294168 | + | 0.509514i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.77106 | − | 5.06397i | −0.289804 | − | 0.167318i | ||||
\(917\) | 0.879598 | − | 1.52351i | 0.0290469 | − | 0.0503107i | ||||
\(918\) | −4.00000 | −0.132020 | ||||||||
\(919\) | 1.60565 | − | 2.78107i | 0.0529655 | − | 0.0917389i | −0.838327 | − | 0.545168i | \(-0.816466\pi\) |
0.891293 | + | 0.453429i | \(0.149799\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.16137 | + | 3.55727i | −0.203024 | + | 0.117216i | ||||
\(922\) | 24.9652i | 0.822184i | ||||||||
\(923\) | 4.23098 | − | 28.3617i | 0.139265 | − | 0.933537i | ||||
\(924\) | 20.4371 | 0.672331 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.81944 | + | 13.5437i | 0.256963 | + | 0.445073i | ||||
\(927\) | 4.58246 | + | 2.64568i | 0.150508 | + | 0.0868956i | ||||
\(928\) | −4.31274 | −0.141572 | ||||||||
\(929\) | −40.2518 | − | 23.2394i | −1.32062 | − | 0.762460i | −0.336792 | − | 0.941579i | \(-0.609342\pi\) |
−0.983827 | + | 0.179120i | \(0.942675\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 117.236i | − | 3.84224i | ||||||
\(932\) | 17.9716 | + | 10.3759i | 0.588681 | + | 0.339875i | ||||
\(933\) | 17.2467 | − | 9.95740i | 0.564632 | − | 0.325990i | ||||
\(934\) | 2.11236 | − | 1.21957i | 0.0691184 | − | 0.0399055i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.56609 | − | 0.531987i | −0.116561 | − | 0.0173886i | ||||
\(937\) | − | 27.7627i | − | 0.906969i | −0.891264 | − | 0.453485i | \(-0.850181\pi\) | ||
0.891264 | − | 0.453485i | \(-0.149819\pi\) | |||||||
\(938\) | 4.23876 | + | 7.34174i | 0.138400 | + | 0.239716i | ||||
\(939\) | 3.06975 | + | 5.31696i | 0.100178 | + | 0.173513i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 20.7962i | − | 0.677935i | −0.940798 | − | 0.338968i | \(-0.889922\pi\) | ||
0.940798 | − | 0.338968i | \(-0.110078\pi\) | |||||||
\(942\) | −0.751556 | + | 1.30173i | −0.0244870 | + | 0.0424128i | ||||
\(943\) | 3.55931 | − | 6.16491i | 0.115907 | − | 0.200757i | ||||
\(944\) | − | 2.18056i | − | 0.0709711i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.57625 | − | 2.73014i | −0.0512483 | − | 0.0887646i | ||||
\(947\) | 4.52962 | + | 7.84554i | 0.147193 | + | 0.254946i | 0.930189 | − | 0.367081i | \(-0.119643\pi\) |
−0.782996 | + | 0.622027i | \(0.786309\pi\) | |||||||
\(948\) | − | 14.9340i | − | 0.485033i | ||||||
\(949\) | −5.76683 | − | 14.6286i | −0.187199 | − | 0.474863i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.80078 | − | 3.92643i | 0.220530 | − | 0.127323i | ||||
\(952\) | 16.0896 | − | 9.28932i | 0.521466 | − | 0.301069i | ||||
\(953\) | 13.2296 | + | 7.63811i | 0.428549 | + | 0.247423i | 0.698728 | − | 0.715387i | \(-0.253750\pi\) |
−0.270180 | + | 0.962810i | \(0.587083\pi\) | |||||||
\(954\) | − | 13.5089i | − | 0.437366i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −21.0911 | − | 12.1770i | −0.682136 | − | 0.393831i | ||||
\(957\) | 18.9766 | 0.613426 | ||||||||
\(958\) | −12.2857 | − | 7.09317i | −0.396934 | − | 0.229170i | ||||
\(959\) | 2.90838 | + | 5.03746i | 0.0939165 | + | 0.162668i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.4824 | −0.338143 | ||||||||
\(962\) | −13.5370 | − | 2.01944i | −0.436449 | − | 0.0651093i | ||||
\(963\) | − | 16.9282i | − | 0.545504i | ||||||
\(964\) | 17.2066 | − | 9.93423i | 0.554187 | − | 0.319960i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.26795 | + | 3.92820i | −0.0729701 | + | 0.126388i | ||||
\(967\) | −46.3036 | −1.48902 | −0.744511 | − | 0.667610i | \(-0.767317\pi\) | ||||
−0.744511 | + | 0.667610i | \(0.767317\pi\) | |||||||
\(968\) | −4.18056 | + | 7.24094i | −0.134368 | + | 0.232733i | ||||
\(969\) | −27.8680 | − | 16.0896i | −0.895248 | − | 0.516872i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.98258 | + | 10.3621i | −0.191990 | + | 0.332537i | −0.945910 | − | 0.324430i | \(-0.894828\pi\) |
0.753919 | + | 0.656967i | \(0.228161\pi\) | |||||||
\(972\) | −0.866025 | + | 0.500000i | −0.0277778 | + | 0.0160375i | ||||
\(973\) | 7.79221 | + | 13.4965i | 0.249807 | + | 0.432678i | ||||
\(974\) | −5.76329 | −0.184668 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.46410 | 0.238920 | ||||||||
\(977\) | 0.882077 | + | 1.52780i | 0.0282201 | + | 0.0488787i | 0.879791 | − | 0.475362i | \(-0.157683\pi\) |
−0.851570 | + | 0.524240i | \(0.824349\pi\) | |||||||
\(978\) | 0.152706 | − | 0.0881650i | 0.00488301 | − | 0.00281921i | ||||
\(979\) | −17.9805 | + | 31.1432i | −0.574660 | + | 0.995341i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.0853 | − | 6.40013i | −0.353928 | − | 0.204340i | ||||
\(982\) | 0.537671 | − | 0.931273i | 0.0171578 | − | 0.0297181i | ||||
\(983\) | 54.2821 | 1.73133 | 0.865666 | − | 0.500623i | \(-0.166896\pi\) | ||||
0.865666 | + | 0.500623i | \(0.166896\pi\) | |||||||
\(984\) | −3.64466 | + | 6.31274i | −0.116188 | + | 0.201243i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 14.9398 | − | 8.62547i | 0.475779 | − | 0.274691i | ||||
\(987\) | 45.3013i | 1.44196i | ||||||||
\(988\) | −22.7050 | − | 18.0506i | −0.722344 | − | 0.574265i | ||||
\(989\) | 0.699680 | 0.0222485 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.73917 | + | 15.1367i | 0.277609 | + | 0.480833i | 0.970790 | − | 0.239931i | \(-0.0771248\pi\) |
−0.693181 | + | 0.720763i | \(0.743791\pi\) | |||||||
\(992\) | 5.57780 | + | 3.22034i | 0.177095 | + | 0.102246i | ||||
\(993\) | −31.9959 | −1.01536 | ||||||||
\(994\) | 31.9908 | + | 18.4699i | 1.01469 | + | 0.585829i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 3.51093i | − | 0.111248i | ||||||
\(997\) | 18.4389 | + | 10.6457i | 0.583965 | + | 0.337152i | 0.762707 | − | 0.646744i | \(-0.223870\pi\) |
−0.178743 | + | 0.983896i | \(0.557203\pi\) | |||||||
\(998\) | 12.7768 | − | 7.37671i | 0.404444 | − | 0.233506i | ||||
\(999\) | −3.28745 | + | 1.89801i | −0.104010 | + | 0.0600505i |
(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 | 1950.2.y.k.49.1 | 8 | ||
5.2 | odd | 4 | 1950.2.bc.g.751.1 | 8 | |||
5.3 | odd | 4 | 390.2.bb.c.361.4 | yes | 8 | ||
5.4 | even | 2 | 1950.2.y.j.49.4 | 8 | |||
13.4 | even | 6 | 1950.2.y.j.199.4 | 8 | |||
15.8 | even | 4 | 1170.2.bs.f.361.2 | 8 | |||
65.3 | odd | 12 | 5070.2.b.ba.1351.5 | 8 | |||
65.4 | even | 6 | inner | 1950.2.y.k.199.1 | 8 | ||
65.17 | odd | 12 | 1950.2.bc.g.901.1 | 8 | |||
65.23 | odd | 12 | 5070.2.b.ba.1351.4 | 8 | |||
65.28 | even | 12 | 5070.2.a.ca.1.4 | 4 | |||
65.43 | odd | 12 | 390.2.bb.c.121.4 | ✓ | 8 | ||
65.63 | even | 12 | 5070.2.a.bz.1.1 | 4 | |||
195.173 | even | 12 | 1170.2.bs.f.901.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.c.121.4 | ✓ | 8 | 65.43 | odd | 12 | ||
390.2.bb.c.361.4 | yes | 8 | 5.3 | odd | 4 | ||
1170.2.bs.f.361.2 | 8 | 15.8 | even | 4 | |||
1170.2.bs.f.901.2 | 8 | 195.173 | even | 12 | |||
1950.2.y.j.49.4 | 8 | 5.4 | even | 2 | |||
1950.2.y.j.199.4 | 8 | 13.4 | even | 6 | |||
1950.2.y.k.49.1 | 8 | 1.1 | even | 1 | trivial | ||
1950.2.y.k.199.1 | 8 | 65.4 | even | 6 | inner | ||
1950.2.bc.g.751.1 | 8 | 5.2 | odd | 4 | |||
1950.2.bc.g.901.1 | 8 | 65.17 | odd | 12 | |||
5070.2.a.bz.1.1 | 4 | 65.63 | even | 12 | |||
5070.2.a.ca.1.4 | 4 | 65.28 | even | 12 | |||
5070.2.b.ba.1351.4 | 8 | 65.23 | odd | 12 | |||
5070.2.b.ba.1351.5 | 8 | 65.3 | odd | 12 |