Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(121,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.bb (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.11416567883\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.4 | ||
Root | \(-1.70006 - 1.70006i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.361 |
Dual form | 390.2.bb.c.121.4 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | −0.866025 | − | 0.500000i | −0.353553 | − | 0.204124i | ||||
\(7\) | 4.02239 | + | 2.32233i | 1.52032 | + | 0.877758i | 0.999713 | + | 0.0239629i | \(0.00762835\pi\) |
0.520609 | + | 0.853795i | \(0.325705\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | 3.81062 | − | 2.20006i | 1.14895 | − | 0.663344i | 0.200316 | − | 0.979731i | \(-0.435803\pi\) |
0.948630 | + | 0.316387i | \(0.102470\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.35432 | + | 1.32233i | −0.930320 | + | 0.366748i | ||||
\(14\) | 4.64466 | 1.24134 | ||||||||
\(15\) | −0.866025 | + | 0.500000i | −0.223607 | + | 0.129099i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.00000 | − | 3.46410i | 0.485071 | − | 0.840168i | −0.514782 | − | 0.857321i | \(-0.672127\pi\) |
0.999853 | + | 0.0171533i | \(0.00546033\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −6.96699 | − | 4.02239i | −1.59834 | − | 0.922800i | −0.991808 | − | 0.127739i | \(-0.959228\pi\) |
−0.606529 | − | 0.795061i | \(-0.707439\pi\) | |||||||
\(20\) | −0.866025 | − | 0.500000i | −0.193649 | − | 0.111803i | ||||
\(21\) | − | 4.64466i | − | 1.01355i | ||||||
\(22\) | 2.20006 | − | 3.81062i | 0.469055 | − | 0.812427i | ||||
\(23\) | −0.488292 | − | 0.845746i | −0.101816 | − | 0.176350i | 0.810617 | − | 0.585577i | \(-0.199132\pi\) |
−0.912433 | + | 0.409226i | \(0.865799\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −2.24376 | + | 2.82233i | −0.440037 | + | 0.553504i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.02239 | − | 2.32233i | 0.760161 | − | 0.438879i | ||||
\(29\) | 2.15637 | + | 3.73494i | 0.400427 | + | 0.693561i | 0.993777 | − | 0.111384i | \(-0.0355283\pi\) |
−0.593350 | + | 0.804945i | \(0.702195\pi\) | |||||||
\(30\) | −0.500000 | + | 0.866025i | −0.0912871 | + | 0.158114i | ||||
\(31\) | 6.44069i | 1.15678i | 0.815760 | + | 0.578391i | \(0.196319\pi\) | ||||
−0.815760 | + | 0.578391i | \(0.803681\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −3.81062 | − | 2.20006i | −0.663344 | − | 0.382982i | ||||
\(34\) | − | 4.00000i | − | 0.685994i | ||||||
\(35\) | 2.32233 | − | 4.02239i | 0.392545 | − | 0.679909i | ||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 3.28745 | − | 1.89801i | 0.540454 | − | 0.312031i | −0.204809 | − | 0.978802i | \(-0.565657\pi\) |
0.745263 | + | 0.666771i | \(0.232324\pi\) | |||||||
\(38\) | −8.04479 | −1.30504 | ||||||||
\(39\) | 2.82233 | + | 2.24376i | 0.451934 | + | 0.359289i | ||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −6.31274 | + | 3.64466i | −0.985884 | + | 0.569200i | −0.904041 | − | 0.427445i | \(-0.859414\pi\) |
−0.0818424 | + | 0.996645i | \(0.526080\pi\) | |||||||
\(42\) | −2.32233 | − | 4.02239i | −0.358343 | − | 0.620669i | ||||
\(43\) | 0.358228 | − | 0.620469i | 0.0546293 | − | 0.0946207i | −0.837418 | − | 0.546564i | \(-0.815936\pi\) |
0.892047 | + | 0.451943i | \(0.149269\pi\) | |||||||
\(44\) | − | 4.40013i | − | 0.663344i | ||||||
\(45\) | 0.866025 | + | 0.500000i | 0.129099 | + | 0.0745356i | ||||
\(46\) | −0.845746 | − | 0.488292i | −0.124698 | − | 0.0719947i | ||||
\(47\) | 9.75342i | 1.42268i | 0.702847 | + | 0.711341i | \(0.251912\pi\) | ||||
−0.702847 | + | 0.711341i | \(0.748088\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | 7.28643 | + | 12.6205i | 1.04092 | + | 1.80292i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | −0.531987 | + | 3.56609i | −0.0737734 | + | 0.494528i | ||||
\(53\) | 13.5089 | 1.85559 | 0.927794 | − | 0.373092i | \(-0.121703\pi\) | ||||
0.927794 | + | 0.373092i | \(0.121703\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | −2.20006 | − | 3.81062i | −0.296656 | − | 0.513824i | ||||
\(56\) | 2.32233 | − | 4.02239i | 0.310334 | − | 0.537515i | ||||
\(57\) | 8.04479i | 1.06556i | ||||||||
\(58\) | 3.73494 | + | 2.15637i | 0.490421 | + | 0.283145i | ||||
\(59\) | −1.88842 | − | 1.09028i | −0.245851 | − | 0.141942i | 0.372012 | − | 0.928228i | \(-0.378668\pi\) |
−0.617863 | + | 0.786286i | \(0.712001\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | −3.73205 | + | 6.46410i | −0.477840 | + | 0.827643i | −0.999677 | − | 0.0254017i | \(-0.991914\pi\) |
0.521837 | + | 0.853045i | \(0.325247\pi\) | |||||||
\(62\) | 3.22034 | + | 5.57780i | 0.408984 | + | 0.708381i | ||||
\(63\) | −4.02239 | + | 2.32233i | −0.506774 | + | 0.292586i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.32233 | + | 3.35432i | 0.164015 | + | 0.416052i | ||||
\(66\) | −4.40013 | −0.541618 | ||||||||
\(67\) | −1.58068 | + | 0.912609i | −0.193111 | + | 0.111493i | −0.593438 | − | 0.804879i | \(-0.702230\pi\) |
0.400327 | + | 0.916372i | \(0.368897\pi\) | |||||||
\(68\) | −2.00000 | − | 3.46410i | −0.242536 | − | 0.420084i | ||||
\(69\) | −0.488292 | + | 0.845746i | −0.0587834 | + | 0.101816i | ||||
\(70\) | − | 4.64466i | − | 0.555143i | ||||||
\(71\) | −6.88764 | − | 3.97658i | −0.817413 | − | 0.471934i | 0.0321105 | − | 0.999484i | \(-0.489777\pi\) |
−0.849524 | + | 0.527551i | \(0.823110\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | − | 4.36112i | − | 0.510430i | −0.966884 | − | 0.255215i | \(-0.917854\pi\) | ||
0.966884 | − | 0.255215i | \(-0.0821463\pi\) | |||||||
\(74\) | 1.89801 | − | 3.28745i | 0.220640 | − | 0.382159i | ||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | −6.96699 | + | 4.02239i | −0.799168 | + | 0.461400i | ||||
\(77\) | 20.4371 | 2.32902 | ||||||||
\(78\) | 3.56609 | + | 0.531987i | 0.403780 | + | 0.0602357i | ||||
\(79\) | −14.9340 | −1.68020 | −0.840102 | − | 0.542429i | \(-0.817505\pi\) | ||||
−0.840102 | + | 0.542429i | \(0.817505\pi\) | |||||||
\(80\) | −0.866025 | + | 0.500000i | −0.0968246 | + | 0.0559017i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −3.64466 | + | 6.31274i | −0.402485 | + | 0.697125i | ||||
\(83\) | 3.51093i | 0.385375i | 0.981260 | + | 0.192688i | \(0.0617204\pi\) | ||||
−0.981260 | + | 0.192688i | \(0.938280\pi\) | |||||||
\(84\) | −4.02239 | − | 2.32233i | −0.438879 | − | 0.253387i | ||||
\(85\) | −3.46410 | − | 2.00000i | −0.375735 | − | 0.216930i | ||||
\(86\) | − | 0.716456i | − | 0.0772575i | ||||||
\(87\) | 2.15637 | − | 3.73494i | 0.231187 | − | 0.400427i | ||||
\(88\) | −2.20006 | − | 3.81062i | −0.234528 | − | 0.406214i | ||||
\(89\) | 7.07780 | − | 4.08637i | 0.750245 | − | 0.433154i | −0.0755374 | − | 0.997143i | \(-0.524067\pi\) |
0.825782 | + | 0.563989i | \(0.190734\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −16.5633 | − | 2.47090i | −1.73630 | − | 0.259021i | ||||
\(92\) | −0.976584 | −0.101816 | ||||||||
\(93\) | 5.57780 | − | 3.22034i | 0.578391 | − | 0.333934i | ||||
\(94\) | 4.87671 | + | 8.44671i | 0.502994 | + | 0.871212i | ||||
\(95\) | −4.02239 | + | 6.96699i | −0.412689 | + | 0.714798i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 11.9730 | + | 6.91261i | 1.21567 | + | 0.701869i | 0.963989 | − | 0.265941i | \(-0.0856825\pi\) |
0.251683 | + | 0.967810i | \(0.419016\pi\) | |||||||
\(98\) | 12.6205 | + | 7.28643i | 1.27486 | + | 0.736041i | ||||
\(99\) | 4.40013i | 0.442229i | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −3.40013 | − | 5.88919i | −0.338325 | − | 0.585997i | 0.645793 | − | 0.763513i | \(-0.276527\pi\) |
−0.984118 | + | 0.177516i | \(0.943194\pi\) | |||||||
\(102\) | −3.46410 | + | 2.00000i | −0.342997 | + | 0.198030i | ||||
\(103\) | −5.29137 | −0.521374 | −0.260687 | − | 0.965423i | \(-0.583949\pi\) | ||||
−0.260687 | + | 0.965423i | \(0.583949\pi\) | |||||||
\(104\) | 1.32233 | + | 3.35432i | 0.129665 | + | 0.328918i | ||||
\(105\) | −4.64466 | −0.453272 | ||||||||
\(106\) | 11.6990 | − | 6.75444i | 1.13631 | − | 0.656050i | ||||
\(107\) | −8.46410 | − | 14.6603i | −0.818256 | − | 1.41726i | −0.906966 | − | 0.421203i | \(-0.861608\pi\) |
0.0887109 | − | 0.996057i | \(-0.471725\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 12.8003i | 1.22604i | 0.790067 | + | 0.613021i | \(0.210046\pi\) | ||||
−0.790067 | + | 0.613021i | \(0.789954\pi\) | |||||||
\(110\) | −3.81062 | − | 2.20006i | −0.363329 | − | 0.209768i | ||||
\(111\) | −3.28745 | − | 1.89801i | −0.312031 | − | 0.180151i | ||||
\(112\) | − | 4.64466i | − | 0.438879i | ||||||
\(113\) | −6.53308 | + | 11.3156i | −0.614580 | + | 1.06448i | 0.375878 | + | 0.926669i | \(0.377341\pi\) |
−0.990458 | + | 0.137815i | \(0.955992\pi\) | |||||||
\(114\) | 4.02239 | + | 6.96699i | 0.376732 | + | 0.652518i | ||||
\(115\) | −0.845746 | + | 0.488292i | −0.0788662 | + | 0.0455334i | ||||
\(116\) | 4.31274 | 0.400427 | ||||||||
\(117\) | 0.531987 | − | 3.56609i | 0.0491823 | − | 0.329685i | ||||
\(118\) | −2.18056 | −0.200737 | ||||||||
\(119\) | 16.0896 | − | 9.28932i | 1.47493 | − | 0.851550i | ||||
\(120\) | 0.500000 | + | 0.866025i | 0.0456435 | + | 0.0790569i | ||||
\(121\) | 4.18056 | − | 7.24094i | 0.380051 | − | 0.658267i | ||||
\(122\) | 7.46410i | 0.675768i | ||||||||
\(123\) | 6.31274 | + | 3.64466i | 0.569200 | + | 0.328628i | ||||
\(124\) | 5.57780 | + | 3.22034i | 0.500901 | + | 0.289195i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −2.32233 | + | 4.02239i | −0.206890 | + | 0.358343i | ||||
\(127\) | 6.10978 | + | 10.5825i | 0.542156 | + | 0.939041i | 0.998780 | + | 0.0493816i | \(0.0157250\pi\) |
−0.456624 | + | 0.889660i | \(0.650942\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −0.716456 | −0.0630805 | ||||||||
\(130\) | 2.82233 | + | 2.24376i | 0.247535 | + | 0.196791i | ||||
\(131\) | −0.378757 | −0.0330921 | −0.0165461 | − | 0.999863i | \(-0.505267\pi\) | ||||
−0.0165461 | + | 0.999863i | \(0.505267\pi\) | |||||||
\(132\) | −3.81062 | + | 2.20006i | −0.331672 | + | 0.191491i | ||||
\(133\) | −18.6826 | − | 32.3593i | −1.61999 | − | 2.80591i | ||||
\(134\) | −0.912609 | + | 1.58068i | −0.0788374 | + | 0.136550i | ||||
\(135\) | − | 1.00000i | − | 0.0860663i | ||||||
\(136\) | −3.46410 | − | 2.00000i | −0.297044 | − | 0.171499i | ||||
\(137\) | −1.08457 | − | 0.626177i | −0.0926612 | − | 0.0534979i | 0.452953 | − | 0.891534i | \(-0.350370\pi\) |
−0.545615 | + | 0.838036i | \(0.683704\pi\) | |||||||
\(138\) | 0.976584i | 0.0831323i | ||||||||
\(139\) | −1.67767 | + | 2.90581i | −0.142298 | + | 0.246468i | −0.928362 | − | 0.371678i | \(-0.878783\pi\) |
0.786064 | + | 0.618146i | \(0.212116\pi\) | |||||||
\(140\) | −2.32233 | − | 4.02239i | −0.196273 | − | 0.339954i | ||||
\(141\) | 8.44671 | − | 4.87671i | 0.711341 | − | 0.410693i | ||||
\(142\) | −7.95317 | −0.667415 | ||||||||
\(143\) | −9.87282 | + | 12.4186i | −0.825607 | + | 1.03850i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.73494 | − | 2.15637i | 0.310170 | − | 0.179077i | ||||
\(146\) | −2.18056 | − | 3.77684i | −0.180464 | − | 0.312573i | ||||
\(147\) | 7.28643 | − | 12.6205i | 0.600975 | − | 1.04092i | ||||
\(148\) | − | 3.79603i | − | 0.312031i | ||||||
\(149\) | −4.00077 | − | 2.30985i | −0.327756 | − | 0.189230i | 0.327088 | − | 0.944994i | \(-0.393933\pi\) |
−0.654844 | + | 0.755764i | \(0.727266\pi\) | |||||||
\(150\) | 0.866025 | + | 0.500000i | 0.0707107 | + | 0.0408248i | ||||
\(151\) | 11.2425i | 0.914901i | 0.889235 | + | 0.457450i | \(0.151237\pi\) | ||||
−0.889235 | + | 0.457450i | \(0.848763\pi\) | |||||||
\(152\) | −4.02239 | + | 6.96699i | −0.326259 | + | 0.565097i | ||||
\(153\) | 2.00000 | + | 3.46410i | 0.161690 | + | 0.280056i | ||||
\(154\) | 17.6990 | − | 10.2185i | 1.42623 | − | 0.823434i | ||||
\(155\) | 6.44069 | 0.517328 | ||||||||
\(156\) | 3.35432 | − | 1.32233i | 0.268560 | − | 0.105871i | ||||
\(157\) | −1.50311 | −0.119961 | −0.0599807 | − | 0.998200i | \(-0.519104\pi\) | ||||
−0.0599807 | + | 0.998200i | \(0.519104\pi\) | |||||||
\(158\) | −12.9332 | + | 7.46699i | −1.02891 | + | 0.594042i | ||||
\(159\) | −6.75444 | − | 11.6990i | −0.535662 | − | 0.927794i | ||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | − | 4.53590i | − | 0.357479i | ||||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | −0.152706 | − | 0.0881650i | −0.0119609 | − | 0.00690561i | 0.494008 | − | 0.869458i | \(-0.335531\pi\) |
−0.505969 | + | 0.862552i | \(0.668865\pi\) | |||||||
\(164\) | 7.28932i | 0.569200i | ||||||||
\(165\) | −2.20006 | + | 3.81062i | −0.171275 | + | 0.296656i | ||||
\(166\) | 1.75547 | + | 3.04056i | 0.136251 | + | 0.235993i | ||||
\(167\) | 7.51851 | − | 4.34081i | 0.581800 | − | 0.335902i | −0.180049 | − | 0.983658i | \(-0.557626\pi\) |
0.761848 | + | 0.647756i | \(0.224292\pi\) | |||||||
\(168\) | −4.64466 | −0.358343 | ||||||||
\(169\) | 9.50289 | − | 8.87103i | 0.730991 | − | 0.682387i | ||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 6.96699 | − | 4.02239i | 0.532779 | − | 0.307600i | ||||
\(172\) | −0.358228 | − | 0.620469i | −0.0273146 | − | 0.0473103i | ||||
\(173\) | 0.890216 | − | 1.54190i | 0.0676818 | − | 0.117228i | −0.830199 | − | 0.557468i | \(-0.811773\pi\) |
0.897880 | + | 0.440239i | \(0.145106\pi\) | |||||||
\(174\) | − | 4.31274i | − | 0.326948i | ||||||
\(175\) | −4.02239 | − | 2.32233i | −0.304064 | − | 0.175552i | ||||
\(176\) | −3.81062 | − | 2.20006i | −0.287236 | − | 0.165836i | ||||
\(177\) | 2.18056i | 0.163901i | ||||||||
\(178\) | 4.08637 | − | 7.07780i | 0.306286 | − | 0.530503i | ||||
\(179\) | −8.70786 | − | 15.0825i | −0.650856 | − | 1.12732i | −0.982916 | − | 0.184057i | \(-0.941077\pi\) |
0.332059 | − | 0.943258i | \(-0.392257\pi\) | |||||||
\(180\) | 0.866025 | − | 0.500000i | 0.0645497 | − | 0.0372678i | ||||
\(181\) | −10.3611 | −0.770136 | −0.385068 | − | 0.922888i | \(-0.625822\pi\) | ||||
−0.385068 | + | 0.922888i | \(0.625822\pi\) | |||||||
\(182\) | −15.5797 | + | 6.14177i | −1.15484 | + | 0.455258i | ||||
\(183\) | 7.46410 | 0.551762 | ||||||||
\(184\) | −0.845746 | + | 0.488292i | −0.0623492 | + | 0.0359973i | ||||
\(185\) | −1.89801 | − | 3.28745i | −0.139545 | − | 0.241698i | ||||
\(186\) | 3.22034 | − | 5.57780i | 0.236127 | − | 0.408984i | ||||
\(187\) | − | 17.6005i | − | 1.28708i | ||||||
\(188\) | 8.44671 | + | 4.87671i | 0.616040 | + | 0.355671i | ||||
\(189\) | 4.02239 | + | 2.32233i | 0.292586 | + | 0.168925i | ||||
\(190\) | 8.04479i | 0.583630i | ||||||||
\(191\) | 0.448507 | − | 0.776837i | 0.0324528 | − | 0.0562100i | −0.849343 | − | 0.527842i | \(-0.823001\pi\) |
0.881796 | + | 0.471632i | \(0.156335\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 17.5494 | − | 10.1322i | 1.26324 | − | 0.729330i | 0.289537 | − | 0.957167i | \(-0.406499\pi\) |
0.973699 | + | 0.227837i | \(0.0731652\pi\) | |||||||
\(194\) | 13.8252 | 0.992593 | ||||||||
\(195\) | 2.24376 | − | 2.82233i | 0.160679 | − | 0.202111i | ||||
\(196\) | 14.5729 | 1.04092 | ||||||||
\(197\) | 7.95060 | − | 4.59028i | 0.566457 | − | 0.327044i | −0.189276 | − | 0.981924i | \(-0.560614\pi\) |
0.755733 | + | 0.654880i | \(0.227281\pi\) | |||||||
\(198\) | 2.20006 | + | 3.81062i | 0.156352 | + | 0.270809i | ||||
\(199\) | −8.10876 | + | 14.0448i | −0.574815 | + | 0.995609i | 0.421247 | + | 0.906946i | \(0.361593\pi\) |
−0.996062 | + | 0.0886625i | \(0.971741\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 1.58068 | + | 0.912609i | 0.111493 | + | 0.0643705i | ||||
\(202\) | −5.88919 | − | 3.40013i | −0.414362 | − | 0.239232i | ||||
\(203\) | 20.0312i | 1.40591i | ||||||||
\(204\) | −2.00000 | + | 3.46410i | −0.140028 | + | 0.242536i | ||||
\(205\) | 3.64466 | + | 6.31274i | 0.254554 | + | 0.440901i | ||||
\(206\) | −4.58246 | + | 2.64568i | −0.319275 | + | 0.184333i | ||||
\(207\) | 0.976584 | 0.0678773 | ||||||||
\(208\) | 2.82233 | + | 2.24376i | 0.195693 | + | 0.155577i | ||||
\(209\) | −35.3981 | −2.44854 | ||||||||
\(210\) | −4.02239 | + | 2.32233i | −0.277572 | + | 0.160256i | ||||
\(211\) | 0.809848 | + | 1.40270i | 0.0557522 | + | 0.0965657i | 0.892555 | − | 0.450939i | \(-0.148911\pi\) |
−0.836802 | + | 0.547505i | \(0.815578\pi\) | |||||||
\(212\) | 6.75444 | − | 11.6990i | 0.463897 | − | 0.803493i | ||||
\(213\) | 7.95317i | 0.544942i | ||||||||
\(214\) | −14.6603 | − | 8.46410i | −1.00215 | − | 0.578594i | ||||
\(215\) | −0.620469 | − | 0.358228i | −0.0423157 | − | 0.0244310i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −14.9574 | + | 25.9070i | −1.01537 | + | 1.75868i | ||||
\(218\) | 6.40013 | + | 11.0853i | 0.433471 | + | 0.750794i | ||||
\(219\) | −3.77684 | + | 2.18056i | −0.255215 | + | 0.147348i | ||||
\(220\) | −4.40013 | −0.296656 | ||||||||
\(221\) | −2.12795 | + | 14.2644i | −0.143141 | + | 0.959524i | ||||
\(222\) | −3.79603 | −0.254773 | ||||||||
\(223\) | 1.93705 | − | 1.11836i | 0.129714 | − | 0.0748906i | −0.433739 | − | 0.901039i | \(-0.642806\pi\) |
0.563453 | + | 0.826148i | \(0.309473\pi\) | |||||||
\(224\) | −2.32233 | − | 4.02239i | −0.155167 | − | 0.268757i | ||||
\(225\) | 0.500000 | − | 0.866025i | 0.0333333 | − | 0.0577350i | ||||
\(226\) | 13.0662i | 0.869148i | ||||||||
\(227\) | −13.2679 | − | 7.66025i | −0.880625 | − | 0.508429i | −0.00976038 | − | 0.999952i | \(-0.503107\pi\) |
−0.870864 | + | 0.491523i | \(0.836440\pi\) | |||||||
\(228\) | 6.96699 | + | 4.02239i | 0.461400 | + | 0.266389i | ||||
\(229\) | − | 10.1279i | − | 0.669274i | −0.942347 | − | 0.334637i | \(-0.891386\pi\) | ||
0.942347 | − | 0.334637i | \(-0.108614\pi\) | |||||||
\(230\) | −0.488292 | + | 0.845746i | −0.0321970 | + | 0.0557669i | ||||
\(231\) | −10.2185 | − | 17.6990i | −0.672331 | − | 1.16451i | ||||
\(232\) | 3.73494 | − | 2.15637i | 0.245211 | − | 0.141572i | ||||
\(233\) | 20.7519 | 1.35950 | 0.679750 | − | 0.733444i | \(-0.262088\pi\) | ||||
0.679750 | + | 0.733444i | \(0.262088\pi\) | |||||||
\(234\) | −1.32233 | − | 3.35432i | −0.0864434 | − | 0.219279i | ||||
\(235\) | 9.75342 | 0.636243 | ||||||||
\(236\) | −1.88842 | + | 1.09028i | −0.122926 | + | 0.0709711i | ||||
\(237\) | 7.46699 | + | 12.9332i | 0.485033 | + | 0.840102i | ||||
\(238\) | 9.28932 | − | 16.0896i | 0.602137 | − | 1.04293i | ||||
\(239\) | − | 24.3539i | − | 1.57532i | −0.616107 | − | 0.787662i | \(-0.711291\pi\) | ||
0.616107 | − | 0.787662i | \(-0.288709\pi\) | |||||||
\(240\) | 0.866025 | + | 0.500000i | 0.0559017 | + | 0.0322749i | ||||
\(241\) | −17.2066 | − | 9.93423i | −1.10837 | − | 0.639920i | −0.169966 | − | 0.985450i | \(-0.554366\pi\) |
−0.938408 | + | 0.345530i | \(0.887699\pi\) | |||||||
\(242\) | − | 8.36112i | − | 0.537473i | ||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 3.73205 | + | 6.46410i | 0.238920 | + | 0.413822i | ||||
\(245\) | 12.6205 | − | 7.28643i | 0.806292 | − | 0.465513i | ||||
\(246\) | 7.28932 | 0.464750 | ||||||||
\(247\) | 28.6884 | + | 4.27973i | 1.82540 | + | 0.272312i | ||||
\(248\) | 6.44069 | 0.408984 | ||||||||
\(249\) | 3.04056 | − | 1.75547i | 0.192688 | − | 0.111248i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | 6.78566 | − | 11.7531i | 0.428307 | − | 0.741849i | −0.568416 | − | 0.822741i | \(-0.692444\pi\) |
0.996723 | + | 0.0808920i | \(0.0257769\pi\) | |||||||
\(252\) | 4.64466i | 0.292586i | ||||||||
\(253\) | −3.72139 | − | 2.14855i | −0.233962 | − | 0.135078i | ||||
\(254\) | 10.5825 | + | 6.10978i | 0.664002 | + | 0.383362i | ||||
\(255\) | 4.00000i | 0.250490i | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 0.331150 | + | 0.573569i | 0.0206566 | + | 0.0357783i | 0.876169 | − | 0.482004i | \(-0.160091\pi\) |
−0.855512 | + | 0.517782i | \(0.826758\pi\) | |||||||
\(258\) | −0.620469 | + | 0.358228i | −0.0386287 | + | 0.0223023i | ||||
\(259\) | 17.6312 | 1.09555 | ||||||||
\(260\) | 3.56609 | + | 0.531987i | 0.221159 | + | 0.0329925i | ||||
\(261\) | −4.31274 | −0.266952 | ||||||||
\(262\) | −0.328013 | + | 0.189378i | −0.0202647 | + | 0.0116998i | ||||
\(263\) | −15.3749 | − | 26.6301i | −0.948058 | − | 1.64208i | −0.749510 | − | 0.661993i | \(-0.769711\pi\) |
−0.198548 | − | 0.980091i | \(-0.563623\pi\) | |||||||
\(264\) | −2.20006 | + | 3.81062i | −0.135405 | + | 0.234528i | ||||
\(265\) | − | 13.5089i | − | 0.829844i | ||||||
\(266\) | −32.3593 | − | 18.6826i | −1.98408 | − | 1.14551i | ||||
\(267\) | −7.07780 | − | 4.08637i | −0.433154 | − | 0.250082i | ||||
\(268\) | 1.82522i | 0.111493i | ||||||||
\(269\) | 1.87205 | − | 3.24249i | 0.114141 | − | 0.197698i | −0.803295 | − | 0.595581i | \(-0.796922\pi\) |
0.917436 | + | 0.397883i | \(0.130255\pi\) | |||||||
\(270\) | −0.500000 | − | 0.866025i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | 24.0419 | − | 13.8806i | 1.46044 | − | 0.843186i | 0.461410 | − | 0.887187i | \(-0.347344\pi\) |
0.999031 | + | 0.0440009i | \(0.0140104\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 6.14177 | + | 15.5797i | 0.371717 | + | 0.942924i | ||||
\(274\) | −1.25235 | −0.0756575 | ||||||||
\(275\) | −3.81062 | + | 2.20006i | −0.229789 | + | 0.132669i | ||||
\(276\) | 0.488292 | + | 0.845746i | 0.0293917 | + | 0.0509079i | ||||
\(277\) | 5.99609 | − | 10.3855i | 0.360270 | − | 0.624006i | −0.627735 | − | 0.778427i | \(-0.716018\pi\) |
0.988005 | + | 0.154421i | \(0.0493512\pi\) | |||||||
\(278\) | 3.35534i | 0.201240i | ||||||||
\(279\) | −5.57780 | − | 3.22034i | −0.333934 | − | 0.192797i | ||||
\(280\) | −4.02239 | − | 2.32233i | −0.240384 | − | 0.138786i | ||||
\(281\) | 3.63888i | 0.217078i | 0.994092 | + | 0.108539i | \(0.0346172\pi\) | ||||
−0.994092 | + | 0.108539i | \(0.965383\pi\) | |||||||
\(282\) | 4.87671 | − | 8.44671i | 0.290404 | − | 0.502994i | ||||
\(283\) | 2.42220 | + | 4.19538i | 0.143985 | + | 0.249389i | 0.928994 | − | 0.370095i | \(-0.120675\pi\) |
−0.785009 | + | 0.619485i | \(0.787342\pi\) | |||||||
\(284\) | −6.88764 | + | 3.97658i | −0.408707 | + | 0.235967i | ||||
\(285\) | 8.04479 | 0.476532 | ||||||||
\(286\) | −2.34081 | + | 15.6912i | −0.138415 | + | 0.927843i | ||||
\(287\) | −33.8564 | −1.99848 | ||||||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 2.15637 | − | 3.73494i | 0.126626 | − | 0.219323i | ||||
\(291\) | − | 13.8252i | − | 0.810449i | ||||||
\(292\) | −3.77684 | − | 2.18056i | −0.221023 | − | 0.127608i | ||||
\(293\) | 3.20500 | + | 1.85041i | 0.187238 | + | 0.108102i | 0.590689 | − | 0.806899i | \(-0.298856\pi\) |
−0.403451 | + | 0.915001i | \(0.632189\pi\) | |||||||
\(294\) | − | 14.5729i | − | 0.849907i | ||||||
\(295\) | −1.09028 | + | 1.88842i | −0.0634785 | + | 0.109948i | ||||
\(296\) | −1.89801 | − | 3.28745i | −0.110320 | − | 0.191079i | ||||
\(297\) | 3.81062 | − | 2.20006i | 0.221115 | − | 0.127661i | ||||
\(298\) | −4.61970 | −0.267612 | ||||||||
\(299\) | 2.75624 | + | 2.19122i | 0.159398 | + | 0.126721i | ||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 2.88187 | − | 1.66385i | 0.166108 | − | 0.0959026i | ||||
\(302\) | 5.62124 | + | 9.73628i | 0.323466 | + | 0.560260i | ||||
\(303\) | −3.40013 | + | 5.88919i | −0.195332 | + | 0.338325i | ||||
\(304\) | 8.04479i | 0.461400i | ||||||||
\(305\) | 6.46410 | + | 3.73205i | 0.370133 | + | 0.213697i | ||||
\(306\) | 3.46410 | + | 2.00000i | 0.198030 | + | 0.114332i | ||||
\(307\) | − | 7.11454i | − | 0.406048i | −0.979174 | − | 0.203024i | \(-0.934923\pi\) | ||
0.979174 | − | 0.203024i | \(-0.0650770\pi\) | |||||||
\(308\) | 10.2185 | − | 17.6990i | 0.582256 | − | 1.00850i | ||||
\(309\) | 2.64568 | + | 4.58246i | 0.150508 | + | 0.260687i | ||||
\(310\) | 5.57780 | − | 3.22034i | 0.316798 | − | 0.182903i | ||||
\(311\) | −19.9148 | −1.12926 | −0.564632 | − | 0.825343i | \(-0.690982\pi\) | ||||
−0.564632 | + | 0.825343i | \(0.690982\pi\) | |||||||
\(312\) | 2.24376 | − | 2.82233i | 0.127028 | − | 0.159783i | ||||
\(313\) | 6.13950 | 0.347025 | 0.173513 | − | 0.984832i | \(-0.444488\pi\) | ||||
0.173513 | + | 0.984832i | \(0.444488\pi\) | |||||||
\(314\) | −1.30173 | + | 0.751556i | −0.0734611 | + | 0.0424128i | ||||
\(315\) | 2.32233 | + | 4.02239i | 0.130848 | + | 0.226636i | ||||
\(316\) | −7.46699 | + | 12.9332i | −0.420051 | + | 0.727550i | ||||
\(317\) | 7.85286i | 0.441061i | 0.975380 | + | 0.220530i | \(0.0707788\pi\) | ||||
−0.975380 | + | 0.220530i | \(0.929221\pi\) | |||||||
\(318\) | −11.6990 | − | 6.75444i | −0.656050 | − | 0.378770i | ||||
\(319\) | 16.4342 | + | 9.48829i | 0.920139 | + | 0.531242i | ||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −8.46410 | + | 14.6603i | −0.472420 | + | 0.818256i | ||||
\(322\) | −2.26795 | − | 3.92820i | −0.126388 | − | 0.218910i | ||||
\(323\) | −27.8680 | + | 16.0896i | −1.55061 | + | 0.895248i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 3.35432 | − | 1.32233i | 0.186064 | − | 0.0733497i | ||||
\(326\) | −0.176330 | −0.00976601 | ||||||||
\(327\) | 11.0853 | − | 6.40013i | 0.613021 | − | 0.353928i | ||||
\(328\) | 3.64466 | + | 6.31274i | 0.201243 | + | 0.348563i | ||||
\(329\) | −22.6507 | + | 39.2321i | −1.24877 | + | 2.16294i | ||||
\(330\) | 4.40013i | 0.242219i | ||||||||
\(331\) | 27.7093 | + | 15.9980i | 1.52304 | + | 0.879327i | 0.999629 | + | 0.0272463i | \(0.00867385\pi\) |
0.523410 | + | 0.852081i | \(0.324659\pi\) | |||||||
\(332\) | 3.04056 | + | 1.75547i | 0.166872 | + | 0.0963438i | ||||
\(333\) | 3.79603i | 0.208021i | ||||||||
\(334\) | 4.34081 | − | 7.51851i | 0.237519 | − | 0.411394i | ||||
\(335\) | 0.912609 | + | 1.58068i | 0.0498611 | + | 0.0863620i | ||||
\(336\) | −4.02239 | + | 2.32233i | −0.219440 | + | 0.126693i | ||||
\(337\) | −35.6432 | −1.94161 | −0.970806 | − | 0.239867i | \(-0.922896\pi\) | ||||
−0.970806 | + | 0.239867i | \(0.922896\pi\) | |||||||
\(338\) | 3.79423 | − | 12.4340i | 0.206379 | − | 0.676319i | ||||
\(339\) | 13.0662 | 0.709656 | ||||||||
\(340\) | −3.46410 | + | 2.00000i | −0.187867 | + | 0.108465i | ||||
\(341\) | 14.1699 | + | 24.5430i | 0.767344 | + | 1.32908i | ||||
\(342\) | 4.02239 | − | 6.96699i | 0.217506 | − | 0.376732i | ||||
\(343\) | 35.1734i | 1.89918i | ||||||||
\(344\) | −0.620469 | − | 0.358228i | −0.0334535 | − | 0.0193144i | ||||
\(345\) | 0.845746 | + | 0.488292i | 0.0455334 | + | 0.0262887i | ||||
\(346\) | − | 1.78043i | − | 0.0957166i | ||||||
\(347\) | 3.44851 | − | 5.97299i | 0.185126 | − | 0.320647i | −0.758493 | − | 0.651681i | \(-0.774064\pi\) |
0.943619 | + | 0.331034i | \(0.107397\pi\) | |||||||
\(348\) | −2.15637 | − | 3.73494i | −0.115593 | − | 0.200214i | ||||
\(349\) | 16.7321 | − | 9.66025i | 0.895646 | − | 0.517102i | 0.0198610 | − | 0.999803i | \(-0.493678\pi\) |
0.875785 | + | 0.482701i | \(0.160344\pi\) | |||||||
\(350\) | −4.64466 | −0.248267 | ||||||||
\(351\) | −3.35432 | + | 1.32233i | −0.179040 | + | 0.0705807i | ||||
\(352\) | −4.40013 | −0.234528 | ||||||||
\(353\) | −23.7441 | + | 13.7086i | −1.26377 | + | 0.729637i | −0.973802 | − | 0.227400i | \(-0.926978\pi\) |
−0.289967 | + | 0.957037i | \(0.593644\pi\) | |||||||
\(354\) | 1.09028 | + | 1.88842i | 0.0579477 | + | 0.100368i | ||||
\(355\) | −3.97658 | + | 6.88764i | −0.211055 | + | 0.365558i | ||||
\(356\) | − | 8.17274i | − | 0.433154i | ||||||
\(357\) | −16.0896 | − | 9.28932i | −0.851550 | − | 0.491643i | ||||
\(358\) | −15.0825 | − | 8.70786i | −0.797133 | − | 0.460225i | ||||
\(359\) | 14.3611i | 0.757951i | 0.925407 | + | 0.378975i | \(0.123723\pi\) | ||||
−0.925407 | + | 0.378975i | \(0.876277\pi\) | |||||||
\(360\) | 0.500000 | − | 0.866025i | 0.0263523 | − | 0.0456435i | ||||
\(361\) | 22.8593 | + | 39.5935i | 1.20312 | + | 2.08387i | ||||
\(362\) | −8.97299 | + | 5.18056i | −0.471610 | + | 0.272284i | ||||
\(363\) | −8.36112 | −0.438845 | ||||||||
\(364\) | −10.4215 | + | 13.1088i | −0.546235 | + | 0.687086i | ||||
\(365\) | −4.36112 | −0.228271 | ||||||||
\(366\) | 6.46410 | − | 3.73205i | 0.337884 | − | 0.195077i | ||||
\(367\) | 6.88764 | + | 11.9298i | 0.359532 | + | 0.622728i | 0.987883 | − | 0.155202i | \(-0.0496030\pi\) |
−0.628351 | + | 0.777930i | \(0.716270\pi\) | |||||||
\(368\) | −0.488292 | + | 0.845746i | −0.0254540 | + | 0.0440876i | ||||
\(369\) | − | 7.28932i | − | 0.379467i | ||||||
\(370\) | −3.28745 | − | 1.89801i | −0.170907 | − | 0.0986730i | ||||
\(371\) | 54.3381 | + | 31.3721i | 2.82109 | + | 1.62876i | ||||
\(372\) | − | 6.44069i | − | 0.333934i | ||||||
\(373\) | 16.7313 | − | 28.9795i | 0.866316 | − | 1.50050i | 0.000581860 | − | 1.00000i | \(-0.499815\pi\) |
0.865734 | − | 0.500504i | \(-0.166852\pi\) | |||||||
\(374\) | −8.80025 | − | 15.2425i | −0.455050 | − | 0.788170i | ||||
\(375\) | 0.866025 | − | 0.500000i | 0.0447214 | − | 0.0258199i | ||||
\(376\) | 9.75342 | 0.502994 | ||||||||
\(377\) | −12.1720 | − | 9.67674i | −0.626888 | − | 0.498377i | ||||
\(378\) | 4.64466 | 0.238896 | ||||||||
\(379\) | −28.9052 | + | 16.6884i | −1.48476 | + | 0.857227i | −0.999850 | − | 0.0173371i | \(-0.994481\pi\) |
−0.484910 | + | 0.874564i | \(0.661148\pi\) | |||||||
\(380\) | 4.02239 | + | 6.96699i | 0.206344 | + | 0.357399i | ||||
\(381\) | 6.10978 | − | 10.5825i | 0.313014 | − | 0.542156i | ||||
\(382\) | − | 0.897014i | − | 0.0458952i | ||||||
\(383\) | 6.34829 | + | 3.66519i | 0.324383 | + | 0.187282i | 0.653344 | − | 0.757061i | \(-0.273365\pi\) |
−0.328962 | + | 0.944343i | \(0.606699\pi\) | |||||||
\(384\) | 0.866025 | + | 0.500000i | 0.0441942 | + | 0.0255155i | ||||
\(385\) | − | 20.4371i | − | 1.04157i | ||||||
\(386\) | 10.1322 | − | 17.5494i | 0.515714 | − | 0.893243i | ||||
\(387\) | 0.358228 | + | 0.620469i | 0.0182098 | + | 0.0315402i | ||||
\(388\) | 11.9730 | − | 6.91261i | 0.607836 | − | 0.350935i | ||||
\(389\) | −32.6198 | −1.65389 | −0.826946 | − | 0.562282i | \(-0.809924\pi\) | ||||
−0.826946 | + | 0.562282i | \(0.809924\pi\) | |||||||
\(390\) | 0.531987 | − | 3.56609i | 0.0269382 | − | 0.180576i | ||||
\(391\) | −3.90633 | −0.197552 | ||||||||
\(392\) | 12.6205 | − | 7.28643i | 0.637430 | − | 0.368020i | ||||
\(393\) | 0.189378 | + | 0.328013i | 0.00955288 | + | 0.0165461i | ||||
\(394\) | 4.59028 | − | 7.95060i | 0.231255 | − | 0.400545i | ||||
\(395\) | 14.9340i | 0.751410i | ||||||||
\(396\) | 3.81062 | + | 2.20006i | 0.191491 | + | 0.110557i | ||||
\(397\) | 12.5299 | + | 7.23416i | 0.628860 | + | 0.363072i | 0.780310 | − | 0.625392i | \(-0.215061\pi\) |
−0.151451 | + | 0.988465i | \(0.548394\pi\) | |||||||
\(398\) | 16.2175i | 0.812911i | ||||||||
\(399\) | −18.6826 | + | 32.3593i | −0.935302 | + | 1.61999i | ||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | −6.31096 | + | 3.64364i | −0.315154 | + | 0.181955i | −0.649231 | − | 0.760592i | \(-0.724909\pi\) |
0.334076 | + | 0.942546i | \(0.391576\pi\) | |||||||
\(402\) | 1.82522 | 0.0910336 | ||||||||
\(403\) | −8.51671 | − | 21.6041i | −0.424248 | − | 1.07618i | ||||
\(404\) | −6.80025 | −0.338325 | ||||||||
\(405\) | −0.866025 | + | 0.500000i | −0.0430331 | + | 0.0248452i | ||||
\(406\) | 10.0156 | + | 17.3475i | 0.497066 | + | 0.860943i | ||||
\(407\) | 8.35150 | − | 14.4652i | 0.413968 | − | 0.717014i | ||||
\(408\) | 4.00000i | 0.198030i | ||||||||
\(409\) | −21.2840 | − | 12.2883i | −1.05242 | − | 0.607617i | −0.129097 | − | 0.991632i | \(-0.541208\pi\) |
−0.923327 | + | 0.384015i | \(0.874541\pi\) | |||||||
\(410\) | 6.31274 | + | 3.64466i | 0.311764 | + | 0.179997i | ||||
\(411\) | 1.25235i | 0.0617741i | ||||||||
\(412\) | −2.64568 | + | 4.58246i | −0.130343 | + | 0.225761i | ||||
\(413\) | −5.06397 | − | 8.77106i | −0.249182 | − | 0.431596i | ||||
\(414\) | 0.845746 | − | 0.488292i | 0.0415662 | − | 0.0239982i | ||||
\(415\) | 3.51093 | 0.172345 | ||||||||
\(416\) | 3.56609 | + | 0.531987i | 0.174842 | + | 0.0260828i | ||||
\(417\) | 3.35534 | 0.164312 | ||||||||
\(418\) | −30.6556 | + | 17.6990i | −1.49942 | + | 0.865688i | ||||
\(419\) | −7.77684 | − | 13.4699i | −0.379923 | − | 0.658047i | 0.611127 | − | 0.791532i | \(-0.290716\pi\) |
−0.991051 | + | 0.133486i | \(0.957383\pi\) | |||||||
\(420\) | −2.32233 | + | 4.02239i | −0.113318 | + | 0.196273i | ||||
\(421\) | − | 22.3143i | − | 1.08753i | −0.839237 | − | 0.543766i | \(-0.816998\pi\) | ||
0.839237 | − | 0.543766i | \(-0.183002\pi\) | |||||||
\(422\) | 1.40270 | + | 0.809848i | 0.0682822 | + | 0.0394228i | ||||
\(423\) | −8.44671 | − | 4.87671i | −0.410693 | − | 0.237114i | ||||
\(424\) | − | 13.5089i | − | 0.656050i | ||||||
\(425\) | −2.00000 | + | 3.46410i | −0.0970143 | + | 0.168034i | ||||
\(426\) | 3.97658 | + | 6.88764i | 0.192666 | + | 0.333707i | ||||
\(427\) | −30.0236 | + | 17.3341i | −1.45294 | + | 0.838856i | ||||
\(428\) | −16.9282 | −0.818256 | ||||||||
\(429\) | 15.6912 | + | 2.34081i | 0.757580 | + | 0.113015i | ||||
\(430\) | −0.716456 | −0.0345506 | ||||||||
\(431\) | 21.0135 | − | 12.1322i | 1.01219 | − | 0.584386i | 0.100356 | − | 0.994952i | \(-0.468002\pi\) |
0.911831 | + | 0.410565i | \(0.134669\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −11.5494 | + | 20.0042i | −0.555031 | + | 0.961342i | 0.442870 | + | 0.896586i | \(0.353960\pi\) |
−0.997901 | + | 0.0647561i | \(0.979373\pi\) | |||||||
\(434\) | 29.9148i | 1.43596i | ||||||||
\(435\) | −3.73494 | − | 2.15637i | −0.179077 | − | 0.103390i | ||||
\(436\) | 11.0853 | + | 6.40013i | 0.530892 | + | 0.306510i | ||||
\(437\) | 7.85641i | 0.375823i | ||||||||
\(438\) | −2.18056 | + | 3.77684i | −0.104191 | + | 0.180464i | ||||
\(439\) | −19.9980 | − | 34.6375i | −0.954450 | − | 1.65316i | −0.735621 | − | 0.677393i | \(-0.763110\pi\) |
−0.218829 | − | 0.975763i | \(-0.570224\pi\) | |||||||
\(440\) | −3.81062 | + | 2.20006i | −0.181664 | + | 0.104884i | ||||
\(441\) | −14.5729 | −0.693946 | ||||||||
\(442\) | 5.28932 | + | 13.4173i | 0.251587 | + | 0.638194i | ||||
\(443\) | −15.6036 | −0.741350 | −0.370675 | − | 0.928763i | \(-0.620874\pi\) | ||||
−0.370675 | + | 0.928763i | \(0.620874\pi\) | |||||||
\(444\) | −3.28745 | + | 1.89801i | −0.156016 | + | 0.0900757i | ||||
\(445\) | −4.08637 | − | 7.07780i | −0.193712 | − | 0.335520i | ||||
\(446\) | 1.11836 | − | 1.93705i | 0.0529557 | − | 0.0917219i | ||||
\(447\) | 4.61970i | 0.218504i | ||||||||
\(448\) | −4.02239 | − | 2.32233i | −0.190040 | − | 0.109720i | ||||
\(449\) | 23.3863 | + | 13.5021i | 1.10367 | + | 0.637203i | 0.937182 | − | 0.348841i | \(-0.113425\pi\) |
0.166486 | + | 0.986044i | \(0.446758\pi\) | |||||||
\(450\) | − | 1.00000i | − | 0.0471405i | ||||||
\(451\) | −16.0370 | + | 27.7768i | −0.755151 | + | 1.30796i | ||||
\(452\) | 6.53308 | + | 11.3156i | 0.307290 | + | 0.532242i | ||||
\(453\) | 9.73628 | − | 5.62124i | 0.457450 | − | 0.264109i | ||||
\(454\) | −15.3205 | −0.719027 | ||||||||
\(455\) | −2.47090 | + | 16.5633i | −0.115838 | + | 0.776498i | ||||
\(456\) | 8.04479 | 0.376732 | ||||||||
\(457\) | 15.4039 | − | 8.89342i | 0.720562 | − | 0.416017i | −0.0943975 | − | 0.995535i | \(-0.530092\pi\) |
0.814959 | + | 0.579518i | \(0.196759\pi\) | |||||||
\(458\) | −5.06397 | − | 8.77106i | −0.236624 | − | 0.409845i | ||||
\(459\) | 2.00000 | − | 3.46410i | 0.0933520 | − | 0.161690i | ||||
\(460\) | 0.976584i | 0.0455334i | ||||||||
\(461\) | 21.6205 | + | 12.4826i | 1.00697 | + | 0.581372i | 0.910302 | − | 0.413945i | \(-0.135849\pi\) |
0.0966638 | + | 0.995317i | \(0.469183\pi\) | |||||||
\(462\) | −17.6990 | − | 10.2185i | −0.823434 | − | 0.475410i | ||||
\(463\) | 15.6389i | 0.726801i | 0.931633 | + | 0.363400i | \(0.118384\pi\) | ||||
−0.931633 | + | 0.363400i | \(0.881616\pi\) | |||||||
\(464\) | 2.15637 | − | 3.73494i | 0.100107 | − | 0.173390i | ||||
\(465\) | −3.22034 | − | 5.57780i | −0.149340 | − | 0.258664i | ||||
\(466\) | 17.9716 | − | 10.3759i | 0.832521 | − | 0.480656i | ||||
\(467\) | −2.43914 | −0.112870 | −0.0564349 | − | 0.998406i | \(-0.517973\pi\) | ||||
−0.0564349 | + | 0.998406i | \(0.517973\pi\) | |||||||
\(468\) | −2.82233 | − | 2.24376i | −0.130462 | − | 0.103718i | ||||
\(469\) | −8.47751 | −0.391455 | ||||||||
\(470\) | 8.44671 | − | 4.87671i | 0.389618 | − | 0.224946i | ||||
\(471\) | 0.751556 | + | 1.30173i | 0.0346299 | + | 0.0599807i | ||||
\(472\) | −1.09028 | + | 1.88842i | −0.0501842 | + | 0.0869215i | ||||
\(473\) | − | 3.15250i | − | 0.144952i | ||||||
\(474\) | 12.9332 | + | 7.46699i | 0.594042 | + | 0.342970i | ||||
\(475\) | 6.96699 | + | 4.02239i | 0.319667 | + | 0.184560i | ||||
\(476\) | − | 18.5786i | − | 0.851550i | ||||||
\(477\) | −6.75444 | + | 11.6990i | −0.309265 | + | 0.535662i | ||||
\(478\) | −12.1770 | − | 21.0911i | −0.556961 | − | 0.964685i | ||||
\(479\) | 12.2857 | − | 7.09317i | 0.561349 | − | 0.324095i | −0.192338 | − | 0.981329i | \(-0.561607\pi\) |
0.753687 | + | 0.657234i | \(0.228274\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −8.51737 | + | 10.7136i | −0.388358 | + | 0.488500i | ||||
\(482\) | −19.8685 | −0.904983 | ||||||||
\(483\) | −3.92820 | + | 2.26795i | −0.178739 | + | 0.103195i | ||||
\(484\) | −4.18056 | − | 7.24094i | −0.190025 | − | 0.329134i | ||||
\(485\) | 6.91261 | − | 11.9730i | 0.313885 | − | 0.543665i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 4.99115 | + | 2.88164i | 0.226171 | + | 0.130580i | 0.608804 | − | 0.793320i | \(-0.291649\pi\) |
−0.382633 | + | 0.923900i | \(0.624983\pi\) | |||||||
\(488\) | 6.46410 | + | 3.73205i | 0.292616 | + | 0.168942i | ||||
\(489\) | 0.176330i | 0.00797392i | ||||||||
\(490\) | 7.28643 | − | 12.6205i | 0.329167 | − | 0.570135i | ||||
\(491\) | −0.537671 | − | 0.931273i | −0.0242647 | − | 0.0420278i | 0.853638 | − | 0.520867i | \(-0.174391\pi\) |
−0.877903 | + | 0.478839i | \(0.841058\pi\) | |||||||
\(492\) | 6.31274 | − | 3.64466i | 0.284600 | − | 0.164314i | ||||
\(493\) | 17.2509 | 0.776943 | ||||||||
\(494\) | 26.9848 | − | 10.6379i | 1.21410 | − | 0.478620i | ||||
\(495\) | 4.40013 | 0.197771 | ||||||||
\(496\) | 5.57780 | − | 3.22034i | 0.250450 | − | 0.144598i | ||||
\(497\) | −18.4699 | − | 31.9908i | −0.828487 | − | 1.43498i | ||||
\(498\) | 1.75547 | − | 3.04056i | 0.0786644 | − | 0.136251i | ||||
\(499\) | 14.7534i | 0.660454i | 0.943902 | + | 0.330227i | \(0.107125\pi\) | ||||
−0.943902 | + | 0.330227i | \(0.892875\pi\) | |||||||
\(500\) | 0.866025 | + | 0.500000i | 0.0387298 | + | 0.0223607i | ||||
\(501\) | −7.51851 | − | 4.34081i | −0.335902 | − | 0.193933i | ||||
\(502\) | − | 13.5713i | − | 0.605717i | ||||||
\(503\) | 13.3309 | − | 23.0898i | 0.594395 | − | 1.02952i | −0.399236 | − | 0.916848i | \(-0.630725\pi\) |
0.993632 | − | 0.112675i | \(-0.0359419\pi\) | |||||||
\(504\) | 2.32233 | + | 4.02239i | 0.103445 | + | 0.179172i | ||||
\(505\) | −5.88919 | + | 3.40013i | −0.262066 | + | 0.151304i | ||||
\(506\) | −4.29709 | −0.191029 | ||||||||
\(507\) | −12.4340 | − | 3.79423i | −0.552212 | − | 0.168508i | ||||
\(508\) | 12.2196 | 0.542156 | ||||||||
\(509\) | 12.2807 | − | 7.09028i | 0.544333 | − | 0.314271i | −0.202500 | − | 0.979282i | \(-0.564907\pi\) |
0.746833 | + | 0.665011i | \(0.231573\pi\) | |||||||
\(510\) | 2.00000 | + | 3.46410i | 0.0885615 | + | 0.153393i | ||||
\(511\) | 10.1279 | − | 17.5421i | 0.448034 | − | 0.776018i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −6.96699 | − | 4.02239i | −0.307600 | − | 0.177593i | ||||
\(514\) | 0.573569 | + | 0.331150i | 0.0252990 | + | 0.0146064i | ||||
\(515\) | 5.29137i | 0.233165i | ||||||||
\(516\) | −0.358228 | + | 0.620469i | −0.0157701 | + | 0.0273146i | ||||
\(517\) | 21.4581 | + | 37.1666i | 0.943728 | + | 1.63459i | ||||
\(518\) | 15.2691 | − | 8.81562i | 0.670886 | − | 0.387336i | ||||
\(519\) | −1.78043 | −0.0781523 | ||||||||
\(520\) | 3.35432 | − | 1.32233i | 0.147097 | − | 0.0579880i | ||||
\(521\) | 23.7476 | 1.04040 | 0.520202 | − | 0.854043i | \(-0.325857\pi\) | ||||
0.520202 | + | 0.854043i | \(0.325857\pi\) | |||||||
\(522\) | −3.73494 | + | 2.15637i | −0.163474 | + | 0.0943817i | ||||
\(523\) | −6.92532 | − | 11.9950i | −0.302823 | − | 0.524505i | 0.673951 | − | 0.738776i | \(-0.264596\pi\) |
−0.976774 | + | 0.214271i | \(0.931262\pi\) | |||||||
\(524\) | −0.189378 | + | 0.328013i | −0.00827303 | + | 0.0143293i | ||||
\(525\) | 4.64466i | 0.202710i | ||||||||
\(526\) | −26.6301 | − | 15.3749i | −1.16113 | − | 0.670378i | ||||
\(527\) | 22.3112 | + | 12.8814i | 0.971891 | + | 0.561121i | ||||
\(528\) | 4.40013i | 0.191491i | ||||||||
\(529\) | 11.0231 | − | 19.0926i | 0.479267 | − | 0.830115i | ||||
\(530\) | −6.75444 | − | 11.6990i | −0.293394 | − | 0.508174i | ||||
\(531\) | 1.88842 | − | 1.09028i | 0.0819504 | − | 0.0473141i | ||||
\(532\) | −37.3653 | −1.61999 | ||||||||
\(533\) | 16.3555 | − | 20.5729i | 0.708434 | − | 0.891110i | ||||
\(534\) | −8.17274 | −0.353669 | ||||||||
\(535\) | −14.6603 | + | 8.46410i | −0.633818 | + | 0.365935i | ||||
\(536\) | 0.912609 | + | 1.58068i | 0.0394187 | + | 0.0682752i | ||||
\(537\) | −8.70786 | + | 15.0825i | −0.375772 | + | 0.650856i | ||||
\(538\) | − | 3.74410i | − | 0.161420i | ||||||
\(539\) | 55.5317 | + | 32.0612i | 2.39192 | + | 1.38097i | ||||
\(540\) | −0.866025 | − | 0.500000i | −0.0372678 | − | 0.0215166i | ||||
\(541\) | 14.8898i | 0.640164i | 0.947390 | + | 0.320082i | \(0.103710\pi\) | ||||
−0.947390 | + | 0.320082i | \(0.896290\pi\) | |||||||
\(542\) | 13.8806 | − | 24.0419i | 0.596223 | − | 1.03269i | ||||
\(543\) | 5.18056 | + | 8.97299i | 0.222319 | + | 0.385068i | ||||
\(544\) | −3.46410 | + | 2.00000i | −0.148522 | + | 0.0857493i | ||||
\(545\) | 12.8003 | 0.548303 | ||||||||
\(546\) | 13.1088 | + | 10.4215i | 0.561003 | + | 0.445999i | ||||
\(547\) | −22.2019 | −0.949284 | −0.474642 | − | 0.880179i | \(-0.657422\pi\) | ||||
−0.474642 | + | 0.880179i | \(0.657422\pi\) | |||||||
\(548\) | −1.08457 | + | 0.626177i | −0.0463306 | + | 0.0267490i | ||||
\(549\) | −3.73205 | − | 6.46410i | −0.159280 | − | 0.275881i | ||||
\(550\) | −2.20006 | + | 3.81062i | −0.0938110 | + | 0.162485i | ||||
\(551\) | − | 34.6950i | − | 1.47806i | ||||||
\(552\) | 0.845746 | + | 0.488292i | 0.0359973 | + | 0.0207831i | ||||
\(553\) | −60.0703 | − | 34.6816i | −2.55445 | − | 1.47481i | ||||
\(554\) | − | 11.9922i | − | 0.509499i | ||||||
\(555\) | −1.89801 | + | 3.28745i | −0.0805662 | + | 0.139545i | ||||
\(556\) | 1.67767 | + | 2.90581i | 0.0711491 | + | 0.123234i | ||||
\(557\) | 1.64518 | − | 0.949847i | 0.0697087 | − | 0.0402463i | −0.464741 | − | 0.885447i | \(-0.653852\pi\) |
0.534449 | + | 0.845201i | \(0.320519\pi\) | |||||||
\(558\) | −6.44069 | −0.272656 | ||||||||
\(559\) | −0.381146 | + | 2.55495i | −0.0161207 | + | 0.108063i | ||||
\(560\) | −4.64466 | −0.196273 | ||||||||
\(561\) | −15.2425 | + | 8.80025i | −0.643538 | + | 0.371547i | ||||
\(562\) | 1.81944 | + | 3.15137i | 0.0767485 | + | 0.132932i | ||||
\(563\) | −0.860000 | + | 1.48956i | −0.0362447 | + | 0.0627777i | −0.883579 | − | 0.468283i | \(-0.844873\pi\) |
0.847334 | + | 0.531060i | \(0.178206\pi\) | |||||||
\(564\) | − | 9.75342i | − | 0.410693i | ||||||
\(565\) | 11.3156 | + | 6.53308i | 0.476052 | + | 0.274849i | ||||
\(566\) | 4.19538 | + | 2.42220i | 0.176345 | + | 0.101813i | ||||
\(567\) | − | 4.64466i | − | 0.195057i | ||||||
\(568\) | −3.97658 | + | 6.88764i | −0.166854 | + | 0.288999i | ||||
\(569\) | −0.300960 | − | 0.521278i | −0.0126169 | − | 0.0218531i | 0.859648 | − | 0.510887i | \(-0.170683\pi\) |
−0.872265 | + | 0.489034i | \(0.837350\pi\) | |||||||
\(570\) | 6.96699 | − | 4.02239i | 0.291815 | − | 0.168480i | ||||
\(571\) | 11.9808 | 0.501381 | 0.250691 | − | 0.968067i | \(-0.419342\pi\) | ||||
0.250691 | + | 0.968067i | \(0.419342\pi\) | |||||||
\(572\) | 5.81842 | + | 14.7594i | 0.243280 | + | 0.617122i | ||||
\(573\) | −0.897014 | −0.0374733 | ||||||||
\(574\) | −29.3205 | + | 16.9282i | −1.22381 | + | 0.706570i | ||||
\(575\) | 0.488292 | + | 0.845746i | 0.0203632 | + | 0.0352701i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | − | 43.0293i | − | 1.79133i | −0.444725 | − | 0.895667i | \(-0.646699\pi\) | ||
0.444725 | − | 0.895667i | \(-0.353301\pi\) | |||||||
\(578\) | 0.866025 | + | 0.500000i | 0.0360219 | + | 0.0207973i | ||||
\(579\) | −17.5494 | − | 10.1322i | −0.729330 | − | 0.421079i | ||||
\(580\) | − | 4.31274i | − | 0.179077i | ||||||
\(581\) | −8.15355 | + | 14.1224i | −0.338266 | + | 0.585894i | ||||
\(582\) | −6.91261 | − | 11.9730i | −0.286537 | − | 0.496296i | ||||
\(583\) | 51.4773 | − | 29.7204i | 2.13197 | − | 1.23089i | ||||
\(584\) | −4.36112 | −0.180464 | ||||||||
\(585\) | −3.56609 | − | 0.531987i | −0.147440 | − | 0.0219950i | ||||
\(586\) | 3.70081 | 0.152879 | ||||||||
\(587\) | −15.5147 | + | 8.95740i | −0.640359 | + | 0.369711i | −0.784753 | − | 0.619809i | \(-0.787210\pi\) |
0.144394 | + | 0.989520i | \(0.453877\pi\) | |||||||
\(588\) | −7.28643 | − | 12.6205i | −0.300487 | − | 0.520459i | ||||
\(589\) | 25.9070 | − | 44.8722i | 1.06748 | − | 1.84893i | ||||
\(590\) | 2.18056i | 0.0897722i | ||||||||
\(591\) | −7.95060 | − | 4.59028i | −0.327044 | − | 0.188819i | ||||
\(592\) | −3.28745 | − | 1.89801i | −0.135114 | − | 0.0780078i | ||||
\(593\) | 0.669624i | 0.0274981i | 0.999905 | + | 0.0137491i | \(0.00437660\pi\) | ||||
−0.999905 | + | 0.0137491i | \(0.995623\pi\) | |||||||
\(594\) | 2.20006 | − | 3.81062i | 0.0902697 | − | 0.156352i | ||||
\(595\) | −9.28932 | − | 16.0896i | −0.380825 | − | 0.659608i | ||||
\(596\) | −4.00077 | + | 2.30985i | −0.163878 | + | 0.0946151i | ||||
\(597\) | 16.2175 | 0.663739 | ||||||||
\(598\) | 3.48258 | + | 0.519530i | 0.142413 | + | 0.0212452i | ||||
\(599\) | 1.29241 | 0.0528066 | 0.0264033 | − | 0.999651i | \(-0.491595\pi\) | ||||
0.0264033 | + | 0.999651i | \(0.491595\pi\) | |||||||
\(600\) | 0.866025 | − | 0.500000i | 0.0353553 | − | 0.0204124i | ||||
\(601\) | 5.73671 | + | 9.93627i | 0.234005 | + | 0.405309i | 0.958983 | − | 0.283463i | \(-0.0914834\pi\) |
−0.724978 | + | 0.688772i | \(0.758150\pi\) | |||||||
\(602\) | 1.66385 | − | 2.88187i | 0.0678134 | − | 0.117456i | ||||
\(603\) | − | 1.82522i | − | 0.0743286i | ||||||
\(604\) | 9.73628 | + | 5.62124i | 0.396164 | + | 0.228725i | ||||
\(605\) | −7.24094 | − | 4.18056i | −0.294386 | − | 0.169964i | ||||
\(606\) | 6.80025i | 0.276241i | ||||||||
\(607\) | 12.0672 | − | 20.9010i | 0.489792 | − | 0.848344i | −0.510139 | − | 0.860092i | \(-0.670406\pi\) |
0.999931 | + | 0.0117477i | \(0.00373949\pi\) | |||||||
\(608\) | 4.02239 | + | 6.96699i | 0.163130 | + | 0.282549i | ||||
\(609\) | 17.3475 | − | 10.0156i | 0.702957 | − | 0.405852i | ||||
\(610\) | 7.46410 | 0.302213 | ||||||||
\(611\) | −12.8972 | − | 32.7161i | −0.521766 | − | 1.32355i | ||||
\(612\) | 4.00000 | 0.161690 | ||||||||
\(613\) | 25.0716 | − | 14.4751i | 1.01263 | − | 0.584644i | 0.100671 | − | 0.994920i | \(-0.467901\pi\) |
0.911961 | + | 0.410276i | \(0.134568\pi\) | |||||||
\(614\) | −3.55727 | − | 6.16137i | −0.143560 | − | 0.248653i | ||||
\(615\) | 3.64466 | − | 6.31274i | 0.146967 | − | 0.254554i | ||||
\(616\) | − | 20.4371i | − | 0.823434i | ||||||
\(617\) | −0.728597 | − | 0.420655i | −0.0293322 | − | 0.0169349i | 0.485262 | − | 0.874369i | \(-0.338724\pi\) |
−0.514594 | + | 0.857434i | \(0.672057\pi\) | |||||||
\(618\) | 4.58246 | + | 2.64568i | 0.184333 | + | 0.106425i | ||||
\(619\) | − | 6.25076i | − | 0.251239i | −0.992078 | − | 0.125620i | \(-0.959908\pi\) | ||
0.992078 | − | 0.125620i | \(-0.0400919\pi\) | |||||||
\(620\) | 3.22034 | − | 5.57780i | 0.129332 | − | 0.224010i | ||||
\(621\) | −0.488292 | − | 0.845746i | −0.0195945 | − | 0.0339386i | ||||
\(622\) | −17.2467 | + | 9.95740i | −0.691530 | + | 0.399255i | ||||
\(623\) | 37.9596 | 1.52082 | ||||||||
\(624\) | 0.531987 | − | 3.56609i | 0.0212965 | − | 0.142758i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.31696 | − | 3.06975i | 0.212509 | − | 0.122692i | ||||
\(627\) | 17.6990 | + | 30.6556i | 0.706832 | + | 1.22427i | ||||
\(628\) | −0.751556 | + | 1.30173i | −0.0299904 | + | 0.0519448i | ||||
\(629\) | − | 15.1841i | − | 0.605430i | ||||||
\(630\) | 4.02239 | + | 2.32233i | 0.160256 | + | 0.0925238i | ||||
\(631\) | 2.61970 | + | 1.51248i | 0.104288 | + | 0.0602110i | 0.551237 | − | 0.834349i | \(-0.314156\pi\) |
−0.446949 | + | 0.894560i | \(0.647489\pi\) | |||||||
\(632\) | 14.9340i | 0.594042i | ||||||||
\(633\) | 0.809848 | − | 1.40270i | 0.0321886 | − | 0.0557522i | ||||
\(634\) | 3.92643 | + | 6.80078i | 0.155938 | + | 0.270093i | ||||
\(635\) | 10.5825 | − | 6.10978i | 0.419952 | − | 0.242459i | ||||
\(636\) | −13.5089 | −0.535662 | ||||||||
\(637\) | −41.1294 | − | 32.6980i | −1.62961 | − | 1.29554i | ||||
\(638\) | 18.9766 | 0.751290 | ||||||||
\(639\) | 6.88764 | − | 3.97658i | 0.272471 | − | 0.157311i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | 0.386305 | − | 0.669099i | 0.0152581 | − | 0.0264278i | −0.858296 | − | 0.513156i | \(-0.828476\pi\) |
0.873554 | + | 0.486728i | \(0.161810\pi\) | |||||||
\(642\) | 16.9282i | 0.668103i | ||||||||
\(643\) | 16.7788 | + | 9.68726i | 0.661693 | + | 0.382028i | 0.792922 | − | 0.609324i | \(-0.208559\pi\) |
−0.131229 | + | 0.991352i | \(0.541892\pi\) | |||||||
\(644\) | −3.92820 | − | 2.26795i | −0.154793 | − | 0.0893697i | ||||
\(645\) | 0.716456i | 0.0282104i | ||||||||
\(646\) | −16.0896 | + | 27.8680i | −0.633036 | + | 1.09645i | ||||
\(647\) | −13.5953 | − | 23.5477i | −0.534485 | − | 0.925755i | −0.999188 | − | 0.0402882i | \(-0.987172\pi\) |
0.464703 | − | 0.885466i | \(-0.346161\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | −9.59473 | −0.376626 | ||||||||
\(650\) | 2.24376 | − | 2.82233i | 0.0880075 | − | 0.110701i | ||||
\(651\) | 29.9148 | 1.17245 | ||||||||
\(652\) | −0.152706 | + | 0.0881650i | −0.00598044 | + | 0.00345281i | ||||
\(653\) | −7.89799 | − | 13.6797i | −0.309072 | − | 0.535329i | 0.669088 | − | 0.743184i | \(-0.266685\pi\) |
−0.978160 | + | 0.207855i | \(0.933352\pi\) | |||||||
\(654\) | 6.40013 | − | 11.0853i | 0.250265 | − | 0.433471i | ||||
\(655\) | 0.378757i | 0.0147993i | ||||||||
\(656\) | 6.31274 | + | 3.64466i | 0.246471 | + | 0.142300i | ||||
\(657\) | 3.77684 | + | 2.18056i | 0.147348 | + | 0.0850717i | ||||
\(658\) | 45.3013i | 1.76603i | ||||||||
\(659\) | −15.2381 | + | 26.3932i | −0.593593 | + | 1.02813i | 0.400151 | + | 0.916449i | \(0.368958\pi\) |
−0.993744 | + | 0.111684i | \(0.964376\pi\) | |||||||
\(660\) | 2.20006 | + | 3.81062i | 0.0856374 | + | 0.148328i | ||||
\(661\) | −24.1514 | + | 13.9438i | −0.939379 | + | 0.542351i | −0.889766 | − | 0.456418i | \(-0.849132\pi\) |
−0.0496136 | + | 0.998768i | \(0.515799\pi\) | |||||||
\(662\) | 31.9959 | 1.24356 | ||||||||
\(663\) | 13.4173 | − | 5.28932i | 0.521084 | − | 0.205420i | ||||
\(664\) | 3.51093 | 0.136251 | ||||||||
\(665\) | −32.3593 | + | 18.6826i | −1.25484 | + | 0.724482i | ||||
\(666\) | 1.89801 | + | 3.28745i | 0.0735465 | + | 0.127386i | ||||
\(667\) | 2.10587 | − | 3.64748i | 0.0815397 | − | 0.141231i | ||||
\(668\) | − | 8.68162i | − | 0.335902i | ||||||
\(669\) | −1.93705 | − | 1.11836i | −0.0748906 | − | 0.0432381i | ||||
\(670\) | 1.58068 | + | 0.912609i | 0.0610672 | + | 0.0352572i | ||||
\(671\) | 32.8430i | 1.26789i | ||||||||
\(672\) | −2.32233 | + | 4.02239i | −0.0895858 | + | 0.155167i | ||||
\(673\) | −0.489066 | − | 0.847086i | −0.0188521 | − | 0.0326528i | 0.856445 | − | 0.516238i | \(-0.172668\pi\) |
−0.875298 | + | 0.483585i | \(0.839334\pi\) | |||||||
\(674\) | −30.8680 | + | 17.8216i | −1.18899 | + | 0.686463i | ||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −2.93109 | − | 12.6653i | −0.112734 | − | 0.487125i | ||||
\(677\) | −19.1926 | −0.737630 | −0.368815 | − | 0.929503i | \(-0.620236\pi\) | ||||
−0.368815 | + | 0.929503i | \(0.620236\pi\) | |||||||
\(678\) | 11.3156 | − | 6.53308i | 0.434574 | − | 0.250901i | ||||
\(679\) | 32.1067 | + | 55.6105i | 1.23214 | + | 2.13413i | ||||
\(680\) | −2.00000 | + | 3.46410i | −0.0766965 | + | 0.132842i | ||||
\(681\) | 15.3205i | 0.587083i | ||||||||
\(682\) | 24.5430 | + | 14.1699i | 0.939801 | + | 0.542594i | ||||
\(683\) | −1.30851 | − | 0.755467i | −0.0500687 | − | 0.0289071i | 0.474757 | − | 0.880117i | \(-0.342536\pi\) |
−0.524825 | + | 0.851210i | \(0.675869\pi\) | |||||||
\(684\) | − | 8.04479i | − | 0.307600i | ||||||
\(685\) | −0.626177 | + | 1.08457i | −0.0239250 | + | 0.0414393i | ||||
\(686\) | 17.5867 | + | 30.4610i | 0.671463 | + | 1.16301i | ||||
\(687\) | −8.77106 | + | 5.06397i | −0.334637 | + | 0.193203i | ||||
\(688\) | −0.716456 | −0.0273146 | ||||||||
\(689\) | −45.3131 | + | 17.8632i | −1.72629 | + | 0.680534i | ||||
\(690\) | 0.976584 | 0.0371779 | ||||||||
\(691\) | 28.6798 | − | 16.5583i | 1.09103 | − | 0.629907i | 0.157180 | − | 0.987570i | \(-0.449760\pi\) |
0.933851 | + | 0.357663i | \(0.116426\pi\) | |||||||
\(692\) | −0.890216 | − | 1.54190i | −0.0338409 | − | 0.0586142i | ||||
\(693\) | −10.2185 | + | 17.6990i | −0.388170 | + | 0.672331i | ||||
\(694\) | − | 6.89701i | − | 0.261807i | ||||||
\(695\) | 2.90581 | + | 1.67767i | 0.110224 | + | 0.0636377i | ||||
\(696\) | −3.73494 | − | 2.15637i | −0.141572 | − | 0.0817369i | ||||
\(697\) | 29.1573i | 1.10441i | ||||||||
\(698\) | 9.66025 | − | 16.7321i | 0.365646 | − | 0.633317i | ||||
\(699\) | −10.3759 | − | 17.9716i | −0.392454 | − | 0.679750i | ||||
\(700\) | −4.02239 | + | 2.32233i | −0.152032 | + | 0.0877758i | ||||
\(701\) | 27.8695 | 1.05262 | 0.526308 | − | 0.850294i | \(-0.323576\pi\) | ||||
0.526308 | + | 0.850294i | \(0.323576\pi\) | |||||||
\(702\) | −2.24376 | + | 2.82233i | −0.0846852 | + | 0.106522i | ||||
\(703\) | −30.5382 | −1.15177 | ||||||||
\(704\) | −3.81062 | + | 2.20006i | −0.143618 | + | 0.0829180i | ||||
\(705\) | −4.87671 | − | 8.44671i | −0.183668 | − | 0.318122i | ||||
\(706\) | −13.7086 | + | 23.7441i | −0.515931 | + | 0.893619i | ||||
\(707\) | − | 31.5849i | − | 1.18787i | ||||||
\(708\) | 1.88842 | + | 1.09028i | 0.0709711 | + | 0.0409752i | ||||
\(709\) | −9.57491 | − | 5.52808i | −0.359593 | − | 0.207611i | 0.309309 | − | 0.950962i | \(-0.399902\pi\) |
−0.668902 | + | 0.743350i | \(0.733236\pi\) | |||||||
\(710\) | 7.95317i | 0.298477i | ||||||||
\(711\) | 7.46699 | − | 12.9332i | 0.280034 | − | 0.485033i | ||||
\(712\) | −4.08637 | − | 7.07780i | −0.153143 | − | 0.265252i | ||||
\(713\) | 5.44719 | − | 3.14493i | 0.203999 | − | 0.117779i | ||||
\(714\) | −18.5786 | −0.695288 | ||||||||
\(715\) | 12.4186 | + | 9.87282i | 0.464430 | + | 0.369223i | ||||
\(716\) | −17.4157 | −0.650856 | ||||||||
\(717\) | −21.0911 | + | 12.1770i | −0.787662 | + | 0.454757i | ||||
\(718\) | 7.18056 | + | 12.4371i | 0.267976 | + | 0.464148i | ||||
\(719\) | 5.85641 | − | 10.1436i | 0.218407 | − | 0.378292i | −0.735914 | − | 0.677075i | \(-0.763247\pi\) |
0.954321 | + | 0.298783i | \(0.0965806\pi\) | |||||||
\(720\) | − | 1.00000i | − | 0.0372678i | ||||||
\(721\) | −21.2840 | − | 12.2883i | −0.792656 | − | 0.457640i | ||||
\(722\) | 39.5935 | + | 22.8593i | 1.47352 | + | 0.850735i | ||||
\(723\) | 19.8685i | 0.738916i | ||||||||
\(724\) | −5.18056 | + | 8.97299i | −0.192534 | + | 0.333479i | ||||
\(725\) | −2.15637 | − | 3.73494i | −0.0800855 | − | 0.138712i | ||||
\(726\) | −7.24094 | + | 4.18056i | −0.268736 | + | 0.155155i | ||||
\(727\) | −19.4152 | −0.720071 | −0.360035 | − | 0.932939i | \(-0.617235\pi\) | ||||
−0.360035 | + | 0.932939i | \(0.617235\pi\) | |||||||
\(728\) | −2.47090 | + | 16.5633i | −0.0915777 | + | 0.613876i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −3.77684 | + | 2.18056i | −0.139787 | + | 0.0807061i | ||||
\(731\) | −1.43291 | − | 2.48188i | −0.0529982 | − | 0.0917956i | ||||
\(732\) | 3.73205 | − | 6.46410i | 0.137941 | − | 0.238920i | ||||
\(733\) | 11.9340i | 0.440792i | 0.975411 | + | 0.220396i | \(0.0707349\pi\) | ||||
−0.975411 | + | 0.220396i | \(0.929265\pi\) | |||||||
\(734\) | 11.9298 | + | 6.88764i | 0.440335 | + | 0.254228i | ||||
\(735\) | −12.6205 | − | 7.28643i | −0.465513 | − | 0.268764i | ||||
\(736\) | 0.976584i | 0.0359973i | ||||||||
\(737\) | −4.01559 | + | 6.95521i | −0.147916 | + | 0.256199i | ||||
\(738\) | −3.64466 | − | 6.31274i | −0.134162 | − | 0.232375i | ||||
\(739\) | 17.2017 | − | 9.93141i | 0.632775 | − | 0.365333i | −0.149051 | − | 0.988830i | \(-0.547622\pi\) |
0.781826 | + | 0.623497i | \(0.214289\pi\) | |||||||
\(740\) | −3.79603 | −0.139545 | ||||||||
\(741\) | −10.6379 | − | 26.9848i | −0.390792 | − | 0.991310i | ||||
\(742\) | 62.7442 | 2.30341 | ||||||||
\(743\) | 14.2787 | − | 8.24383i | 0.523836 | − | 0.302437i | −0.214667 | − | 0.976687i | \(-0.568867\pi\) |
0.738503 | + | 0.674251i | \(0.235533\pi\) | |||||||
\(744\) | −3.22034 | − | 5.57780i | −0.118063 | − | 0.204492i | ||||
\(745\) | −2.30985 | + | 4.00077i | −0.0846263 | + | 0.146577i | ||||
\(746\) | − | 33.4627i | − | 1.22516i | ||||||
\(747\) | −3.04056 | − | 1.75547i | −0.111248 | − | 0.0642292i | ||||
\(748\) | −15.2425 | − | 8.80025i | −0.557320 | − | 0.321769i | ||||
\(749\) | − | 78.6257i | − | 2.87292i | ||||||
\(750\) | 0.500000 | − | 0.866025i | 0.0182574 | − | 0.0316228i | ||||
\(751\) | −23.3312 | − | 40.4109i | −0.851368 | − | 1.47461i | −0.879974 | − | 0.475022i | \(-0.842440\pi\) |
0.0286056 | − | 0.999591i | \(-0.490893\pi\) | |||||||
\(752\) | 8.44671 | − | 4.87671i | 0.308020 | − | 0.177835i | ||||
\(753\) | −13.5713 | −0.494566 | ||||||||
\(754\) | −15.3796 | − | 2.29432i | −0.560092 | − | 0.0835542i | ||||
\(755\) | 11.2425 | 0.409156 | ||||||||
\(756\) | 4.02239 | − | 2.32233i | 0.146293 | − | 0.0844623i | ||||
\(757\) | −1.31799 | − | 2.28282i | −0.0479030 | − | 0.0829705i | 0.841080 | − | 0.540911i | \(-0.181921\pi\) |
−0.888983 | + | 0.457941i | \(0.848587\pi\) | |||||||
\(758\) | −16.6884 | + | 28.9052i | −0.606151 | + | 1.04988i | ||||
\(759\) | 4.29709i | 0.155975i | ||||||||
\(760\) | 6.96699 | + | 4.02239i | 0.252719 | + | 0.145908i | ||||
\(761\) | 0.0693410 | + | 0.0400340i | 0.00251361 | + | 0.00145123i | 0.501256 | − | 0.865299i | \(-0.332871\pi\) |
−0.498743 | + | 0.866750i | \(0.666205\pi\) | |||||||
\(762\) | − | 12.2196i | − | 0.442668i | ||||||
\(763\) | −29.7264 | + | 51.4877i | −1.07617 | + | 1.86398i | ||||
\(764\) | −0.448507 | − | 0.776837i | −0.0162264 | − | 0.0281050i | ||||
\(765\) | 3.46410 | − | 2.00000i | 0.125245 | − | 0.0723102i | ||||
\(766\) | 7.33038 | 0.264857 | ||||||||
\(767\) | 7.77606 | + | 1.16003i | 0.280777 | + | 0.0418862i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 4.92177 | − | 2.84159i | 0.177484 | − | 0.102470i | −0.408626 | − | 0.912702i | \(-0.633992\pi\) |
0.586110 | + | 0.810232i | \(0.300659\pi\) | |||||||
\(770\) | −10.2185 | − | 17.6990i | −0.368251 | − | 0.637829i | ||||
\(771\) | 0.331150 | − | 0.573569i | 0.0119261 | − | 0.0206566i | ||||
\(772\) | − | 20.2644i | − | 0.729330i | ||||||
\(773\) | −6.57184 | − | 3.79425i | −0.236373 | − | 0.136470i | 0.377136 | − | 0.926158i | \(-0.376909\pi\) |
−0.613508 | + | 0.789688i | \(0.710242\pi\) | |||||||
\(774\) | 0.620469 | + | 0.358228i | 0.0223023 | + | 0.0128762i | ||||
\(775\) | − | 6.44069i | − | 0.231356i | ||||||
\(776\) | 6.91261 | − | 11.9730i | 0.248148 | − | 0.429805i | ||||
\(777\) | −8.81562 | − | 15.2691i | −0.316259 | − | 0.547776i | ||||
\(778\) | −28.2496 | + | 16.3099i | −1.01280 | + | 0.584739i | ||||
\(779\) | 58.6410 | 2.10103 | ||||||||
\(780\) | −1.32233 | − | 3.35432i | −0.0473470 | − | 0.120104i | ||||
\(781\) | −34.9949 | −1.25222 | ||||||||
\(782\) | −3.38298 | + | 1.95317i | −0.120975 | + | 0.0698451i | ||||
\(783\) | 2.15637 | + | 3.73494i | 0.0770623 | + | 0.133476i | ||||
\(784\) | 7.28643 | − | 12.6205i | 0.260230 | − | 0.450731i | ||||
\(785\) | 1.50311i | 0.0536484i | ||||||||
\(786\) | 0.328013 | + | 0.189378i | 0.0116998 | + | 0.00675490i | ||||
\(787\) | −4.10169 | − | 2.36811i | −0.146210 | − | 0.0844142i | 0.425111 | − | 0.905141i | \(-0.360235\pi\) |
−0.571320 | + | 0.820727i | \(0.693569\pi\) | |||||||
\(788\) | − | 9.18056i | − | 0.327044i | ||||||
\(789\) | −15.3749 | + | 26.6301i | −0.547361 | + | 0.948058i | ||||
\(790\) | 7.46699 | + | 12.9332i | 0.265664 | + | 0.460143i | ||||
\(791\) | −52.5572 | + | 30.3439i | −1.86872 | + | 1.07891i | ||||
\(792\) | 4.40013 | 0.156352 | ||||||||
\(793\) | 3.97081 | − | 26.6176i | 0.141008 | − | 0.945220i | ||||
\(794\) | 14.4683 | 0.513462 | ||||||||
\(795\) | −11.6990 | + | 6.75444i | −0.414922 | + | 0.239555i | ||||
\(796\) | 8.10876 | + | 14.0448i | 0.287407 | + | 0.497804i | ||||
\(797\) | −20.5318 | + | 35.5621i | −0.727274 | + | 1.25968i | 0.230757 | + | 0.973011i | \(0.425880\pi\) |
−0.958031 | + | 0.286664i | \(0.907454\pi\) | |||||||
\(798\) | 37.3653i | 1.32272i | ||||||||
\(799\) | 33.7868 | + | 19.5068i | 1.19529 | + | 0.690102i | ||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | 8.17274i | 0.288769i | ||||||||
\(802\) | −3.64364 | + | 6.31096i | −0.128661 | + | 0.222848i | ||||
\(803\) | −9.59473 | − | 16.6186i | −0.338591 | − | 0.586456i | ||||
\(804\) | 1.58068 | − | 0.912609i | 0.0557465 | − | 0.0321852i | ||||
\(805\) | −4.53590 | −0.159869 | ||||||||
\(806\) | −18.1777 | − | 14.4513i | −0.640284 | − | 0.509027i | ||||
\(807\) | −3.74410 | −0.131799 | ||||||||
\(808\) | −5.88919 | + | 3.40013i | −0.207181 | + | 0.119616i | ||||
\(809\) | 13.8003 | + | 23.9027i | 0.485191 | + | 0.840376i | 0.999855 | − | 0.0170163i | \(-0.00541671\pi\) |
−0.514664 | + | 0.857392i | \(0.672083\pi\) | |||||||
\(810\) | −0.500000 | + | 0.866025i | −0.0175682 | + | 0.0304290i | ||||
\(811\) | 10.6930i | 0.375482i | 0.982219 | + | 0.187741i | \(0.0601165\pi\) | ||||
−0.982219 | + | 0.187741i | \(0.939883\pi\) | |||||||
\(812\) | 17.3475 | + | 10.0156i | 0.608779 | + | 0.351478i | ||||
\(813\) | −24.0419 | − | 13.8806i | −0.843186 | − | 0.486814i | ||||
\(814\) | − | 16.7030i | − | 0.585440i | ||||||
\(815\) | −0.0881650 | + | 0.152706i | −0.00308828 | + | 0.00534907i | ||||
\(816\) | 2.00000 | + | 3.46410i | 0.0700140 | + | 0.121268i | ||||
\(817\) | −4.99154 | + | 2.88187i | −0.174632 | + | 0.100824i | ||||
\(818\) | −24.5766 | −0.859300 | ||||||||
\(819\) | 10.4215 | − | 13.1088i | 0.364157 | − | 0.458057i | ||||
\(820\) | 7.28932 | 0.254554 | ||||||||
\(821\) | 15.2105 | − | 8.78177i | 0.530849 | − | 0.306486i | −0.210513 | − | 0.977591i | \(-0.567513\pi\) |
0.741362 | + | 0.671105i | \(0.234180\pi\) | |||||||
\(822\) | 0.626177 | + | 1.08457i | 0.0218404 | + | 0.0378288i | ||||
\(823\) | −19.3565 | + | 33.5264i | −0.674725 | + | 1.16866i | 0.301824 | + | 0.953364i | \(0.402404\pi\) |
−0.976549 | + | 0.215295i | \(0.930929\pi\) | |||||||
\(824\) | 5.29137i | 0.184333i | ||||||||
\(825\) | 3.81062 | + | 2.20006i | 0.132669 | + | 0.0765964i | ||||
\(826\) | −8.77106 | − | 5.06397i | −0.305184 | − | 0.176198i | ||||
\(827\) | 28.4703i | 0.990010i | 0.868890 | + | 0.495005i | \(0.164834\pi\) | ||||
−0.868890 | + | 0.495005i | \(0.835166\pi\) | |||||||
\(828\) | 0.488292 | − | 0.845746i | 0.0169693 | − | 0.0293917i | ||||
\(829\) | 4.14354 | + | 7.17683i | 0.143911 | + | 0.249262i | 0.928966 | − | 0.370165i | \(-0.120699\pi\) |
−0.785055 | + | 0.619426i | \(0.787365\pi\) | |||||||
\(830\) | 3.04056 | − | 1.75547i | 0.105539 | − | 0.0609332i | ||||
\(831\) | −11.9922 | −0.416004 | ||||||||
\(832\) | 3.35432 | − | 1.32233i | 0.116290 | − | 0.0458435i | ||||
\(833\) | 58.2915 | 2.01968 | ||||||||
\(834\) | 2.90581 | − | 1.67767i | 0.100620 | − | 0.0580930i | ||||
\(835\) | −4.34081 | − | 7.51851i | −0.150220 | − | 0.260189i | ||||
\(836\) | −17.6990 | + | 30.6556i | −0.612134 | + | 1.06025i | ||||
\(837\) | 6.44069i | 0.222623i | ||||||||
\(838\) | −13.4699 | − | 7.77684i | −0.465309 | − | 0.268646i | ||||
\(839\) | −36.8606 | − | 21.2815i | −1.27257 | − | 0.734719i | −0.297099 | − | 0.954847i | \(-0.596019\pi\) |
−0.975471 | + | 0.220128i | \(0.929353\pi\) | |||||||
\(840\) | 4.64466i | 0.160256i | ||||||||
\(841\) | 5.20016 | − | 9.00693i | 0.179316 | − | 0.310584i | ||||
\(842\) | −11.1571 | − | 19.3247i | −0.384500 | − | 0.665974i | ||||
\(843\) | 3.15137 | − | 1.81944i | 0.108539 | − | 0.0626649i | ||||
\(844\) | 1.61970 | 0.0557522 | ||||||||
\(845\) | −8.87103 | − | 9.50289i | −0.305173 | − | 0.326909i | ||||
\(846\) | −9.75342 | −0.335330 | ||||||||
\(847\) | 33.6317 | − | 19.4173i | 1.15560 | − | 0.667185i | ||||
\(848\) | −6.75444 | − | 11.6990i | −0.231949 | − | 0.401747i | ||||
\(849\) | 2.42220 | − | 4.19538i | 0.0831298 | − | 0.143985i | ||||
\(850\) | 4.00000i | 0.137199i | ||||||||
\(851\) | −3.21047 | − | 1.85357i | −0.110054 | − | 0.0635395i | ||||
\(852\) | 6.88764 | + | 3.97658i | 0.235967 | + | 0.136236i | ||||
\(853\) | 28.1380i | 0.963425i | 0.876329 | + | 0.481713i | \(0.159985\pi\) | ||||
−0.876329 | + | 0.481713i | \(0.840015\pi\) | |||||||
\(854\) | −17.3341 | + | 30.0236i | −0.593161 | + | 1.02738i | ||||
\(855\) | −4.02239 | − | 6.96699i | −0.137563 | − | 0.238266i | ||||
\(856\) | −14.6603 | + | 8.46410i | −0.501077 | + | 0.289297i | ||||
\(857\) | −10.3355 | −0.353053 | −0.176526 | − | 0.984296i | \(-0.556486\pi\) | ||||
−0.176526 | + | 0.984296i | \(0.556486\pi\) | |||||||
\(858\) | 14.7594 | − | 5.81842i | 0.503878 | − | 0.198638i | ||||
\(859\) | 0.380304 | 0.0129758 | 0.00648791 | − | 0.999979i | \(-0.497935\pi\) | ||||
0.00648791 | + | 0.999979i | \(0.497935\pi\) | |||||||
\(860\) | −0.620469 | + | 0.358228i | −0.0211578 | + | 0.0122155i | ||||
\(861\) | 16.9282 | + | 29.3205i | 0.576912 | + | 0.999240i | ||||
\(862\) | 12.1322 | − | 21.0135i | 0.413224 | − | 0.715724i | ||||
\(863\) | 47.1484i | 1.60495i | 0.596685 | + | 0.802475i | \(0.296484\pi\) | ||||
−0.596685 | + | 0.802475i | \(0.703516\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | −1.54190 | − | 0.890216i | −0.0524261 | − | 0.0302682i | ||||
\(866\) | 23.0989i | 0.784932i | ||||||||
\(867\) | 0.500000 | − | 0.866025i | 0.0169809 | − | 0.0294118i | ||||
\(868\) | 14.9574 | + | 25.9070i | 0.507687 | + | 0.879340i | ||||
\(869\) | −56.9077 | + | 32.8557i | −1.93046 | + | 1.11455i | ||||
\(870\) | −4.31274 | −0.146215 | ||||||||
\(871\) | 4.09535 | − | 5.15137i | 0.138766 | − | 0.174547i | ||||
\(872\) | 12.8003 | 0.433471 | ||||||||
\(873\) | −11.9730 | + | 6.91261i | −0.405224 | + | 0.233956i | ||||
\(874\) | 3.92820 | + | 6.80385i | 0.132873 | + | 0.230144i | ||||
\(875\) | −2.32233 | + | 4.02239i | −0.0785091 | + | 0.135982i | ||||
\(876\) | 4.36112i | 0.147348i | ||||||||
\(877\) | 34.6767 | + | 20.0206i | 1.17095 | + | 0.676047i | 0.953903 | − | 0.300114i | \(-0.0970247\pi\) |
0.217045 | + | 0.976162i | \(0.430358\pi\) | |||||||
\(878\) | −34.6375 | − | 19.9980i | −1.16896 | − | 0.674898i | ||||
\(879\) | − | 3.70081i | − | 0.124825i | ||||||
\(880\) | −2.20006 | + | 3.81062i | −0.0741641 | + | 0.128456i | ||||
\(881\) | −7.72246 | − | 13.3757i | −0.260176 | − | 0.450638i | 0.706112 | − | 0.708100i | \(-0.250447\pi\) |
−0.966289 | + | 0.257461i | \(0.917114\pi\) | |||||||
\(882\) | −12.6205 | + | 7.28643i | −0.424953 | + | 0.245347i | ||||
\(883\) | −6.02142 | −0.202637 | −0.101318 | − | 0.994854i | \(-0.532306\pi\) | ||||
−0.101318 | + | 0.994854i | \(0.532306\pi\) | |||||||
\(884\) | 11.2893 | + | 8.97504i | 0.379701 | + | 0.301863i | ||||
\(885\) | 2.18056 | 0.0732987 | ||||||||
\(886\) | −13.5131 | + | 7.80180i | −0.453982 | + | 0.262107i | ||||
\(887\) | 24.5690 | + | 42.5548i | 0.824947 | + | 1.42885i | 0.901960 | + | 0.431820i | \(0.142128\pi\) |
−0.0770129 | + | 0.997030i | \(0.524538\pi\) | |||||||
\(888\) | −1.89801 | + | 3.28745i | −0.0636931 | + | 0.110320i | ||||
\(889\) | 56.7557i | 1.90353i | ||||||||
\(890\) | −7.07780 | − | 4.08637i | −0.237248 | − | 0.136975i | ||||
\(891\) | −3.81062 | − | 2.20006i | −0.127661 | − | 0.0737049i | ||||
\(892\) | − | 2.23671i | − | 0.0748906i | ||||||
\(893\) | 39.2321 | − | 67.9520i | 1.31285 | − | 2.27393i | ||||
\(894\) | 2.30985 | + | 4.00077i | 0.0772529 | + | 0.133806i | ||||
\(895\) | −15.0825 | + | 8.70786i | −0.504151 | + | 0.291072i | ||||
\(896\) | −4.64466 | −0.155167 | ||||||||
\(897\) | 0.519530 | − | 3.48258i | 0.0173466 | − | 0.116280i | ||||
\(898\) | 27.0042 | 0.901141 | ||||||||
\(899\) | −24.0556 | + | 13.8885i | −0.802298 | + | 0.463207i | ||||
\(900\) | −0.500000 | − | 0.866025i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | 27.0178 | − | 46.7962i | 0.900093 | − | 1.55901i | ||||
\(902\) | 32.0739i | 1.06795i | ||||||||
\(903\) | −2.88187 | − | 1.66385i | −0.0959026 | − | 0.0553694i | ||||
\(904\) | 11.3156 | + | 6.53308i | 0.376352 | + | 0.217287i | ||||
\(905\) | 10.3611i | 0.344415i | ||||||||
\(906\) | 5.62124 | − | 9.73628i | 0.186753 | − | 0.323466i | ||||
\(907\) | 8.18345 | + | 14.1741i | 0.271727 | + | 0.470645i | 0.969304 | − | 0.245865i | \(-0.0790719\pi\) |
−0.697577 | + | 0.716510i | \(0.745739\pi\) | |||||||
\(908\) | −13.2679 | + | 7.66025i | −0.440312 | + | 0.254214i | ||||
\(909\) | 6.80025 | 0.225550 | ||||||||
\(910\) | 6.14177 | + | 15.5797i | 0.203598 | + | 0.516461i | ||||
\(911\) | −10.4819 | −0.347280 | −0.173640 | − | 0.984809i | \(-0.555553\pi\) | ||||
−0.173640 | + | 0.984809i | \(0.555553\pi\) | |||||||
\(912\) | 6.96699 | − | 4.02239i | 0.230700 | − | 0.133195i | ||||
\(913\) | 7.72428 | + | 13.3788i | 0.255636 | + | 0.442775i | ||||
\(914\) | 8.89342 | − | 15.4039i | 0.294168 | − | 0.509514i | ||||
\(915\) | − | 7.46410i | − | 0.246756i | ||||||
\(916\) | −8.77106 | − | 5.06397i | −0.289804 | − | 0.167318i | ||||
\(917\) | −1.52351 | − | 0.879598i | −0.0503107 | − | 0.0290469i | ||||
\(918\) | − | 4.00000i | − | 0.132020i | ||||||
\(919\) | −1.60565 | + | 2.78107i | −0.0529655 | + | 0.0917389i | −0.891293 | − | 0.453429i | \(-0.850201\pi\) |
0.838327 | + | 0.545168i | \(0.183534\pi\) | |||||||
\(920\) | 0.488292 | + | 0.845746i | 0.0160985 | + | 0.0278834i | ||||
\(921\) | −6.16137 | + | 3.55727i | −0.203024 | + | 0.117216i | ||||
\(922\) | 24.9652 | 0.822184 | ||||||||
\(923\) | 28.3617 | + | 4.23098i | 0.933537 | + | 0.139265i | ||||
\(924\) | −20.4371 | −0.672331 | ||||||||
\(925\) | −3.28745 | + | 1.89801i | −0.108091 | + | 0.0624063i | ||||
\(926\) | 7.81944 | + | 13.5437i | 0.256963 | + | 0.445073i | ||||
\(927\) | 2.64568 | − | 4.58246i | 0.0868956 | − | 0.150508i | ||||
\(928\) | − | 4.31274i | − | 0.141572i | ||||||
\(929\) | 40.2518 | + | 23.2394i | 1.32062 | + | 0.762460i | 0.983827 | − | 0.179120i | \(-0.0573249\pi\) |
0.336792 | + | 0.941579i | \(0.390658\pi\) | |||||||
\(930\) | −5.57780 | − | 3.22034i | −0.182903 | − | 0.105599i | ||||
\(931\) | − | 117.236i | − | 3.84224i | ||||||
\(932\) | 10.3759 | − | 17.9716i | 0.339875 | − | 0.588681i | ||||
\(933\) | 9.95740 | + | 17.2467i | 0.325990 | + | 0.564632i | ||||
\(934\) | −2.11236 | + | 1.21957i | −0.0691184 | + | 0.0399055i | ||||
\(935\) | −17.6005 | −0.575598 | ||||||||
\(936\) | −3.56609 | − | 0.531987i | −0.116561 | − | 0.0173886i | ||||
\(937\) | −27.7627 | −0.906969 | −0.453485 | − | 0.891264i | \(-0.649819\pi\) | ||||
−0.453485 | + | 0.891264i | \(0.649819\pi\) | |||||||
\(938\) | −7.34174 | + | 4.23876i | −0.239716 | + | 0.138400i | ||||
\(939\) | −3.06975 | − | 5.31696i | −0.100178 | − | 0.173513i | ||||
\(940\) | 4.87671 | − | 8.44671i | 0.159061 | − | 0.275501i | ||||
\(941\) | − | 20.7962i | − | 0.677935i | −0.940798 | − | 0.338968i | \(-0.889922\pi\) | ||
0.940798 | − | 0.338968i | \(-0.110078\pi\) | |||||||
\(942\) | 1.30173 | + | 0.751556i | 0.0424128 | + | 0.0244870i | ||||
\(943\) | 6.16491 | + | 3.55931i | 0.200757 | + | 0.115907i | ||||
\(944\) | 2.18056i | 0.0709711i | ||||||||
\(945\) | 2.32233 | − | 4.02239i | 0.0755454 | − | 0.130848i | ||||
\(946\) | −1.57625 | − | 2.73014i | −0.0512483 | − | 0.0887646i | ||||
\(947\) | 7.84554 | − | 4.52962i | 0.254946 | − | 0.147193i | −0.367081 | − | 0.930189i | \(-0.619643\pi\) |
0.622027 | + | 0.782996i | \(0.286309\pi\) | |||||||
\(948\) | 14.9340 | 0.485033 | ||||||||
\(949\) | 5.76683 | + | 14.6286i | 0.187199 | + | 0.474863i | ||||
\(950\) | 8.04479 | 0.261007 | ||||||||
\(951\) | 6.80078 | − | 3.92643i | 0.220530 | − | 0.127323i | ||||
\(952\) | −9.28932 | − | 16.0896i | −0.301069 | − | 0.521466i | ||||
\(953\) | −7.63811 | + | 13.2296i | −0.247423 | + | 0.428549i | −0.962810 | − | 0.270180i | \(-0.912917\pi\) |
0.715387 | + | 0.698728i | \(0.246250\pi\) | |||||||
\(954\) | 13.5089i | 0.437366i | ||||||||
\(955\) | −0.776837 | − | 0.448507i | −0.0251379 | − | 0.0145134i | ||||
\(956\) | −21.0911 | − | 12.1770i | −0.682136 | − | 0.393831i | ||||
\(957\) | − | 18.9766i | − | 0.613426i | ||||||
\(958\) | 7.09317 | − | 12.2857i | 0.229170 | − | 0.396934i | ||||
\(959\) | −2.90838 | − | 5.03746i | −0.0939165 | − | 0.162668i | ||||
\(960\) | 0.866025 | − | 0.500000i | 0.0279508 | − | 0.0161374i | ||||
\(961\) | −10.4824 | −0.338143 | ||||||||
\(962\) | −2.01944 | + | 13.5370i | −0.0651093 | + | 0.436449i | ||||
\(963\) | 16.9282 | 0.545504 | ||||||||
\(964\) | −17.2066 | + | 9.93423i | −0.554187 | + | 0.319960i | ||||
\(965\) | −10.1322 | − | 17.5494i | −0.326166 | − | 0.564937i | ||||
\(966\) | −2.26795 | + | 3.92820i | −0.0729701 | + | 0.126388i | ||||
\(967\) | 46.3036i | 1.48902i | 0.667610 | + | 0.744511i | \(0.267317\pi\) | ||||
−0.667610 | + | 0.744511i | \(0.732683\pi\) | |||||||
\(968\) | −7.24094 | − | 4.18056i | −0.232733 | − | 0.134368i | ||||
\(969\) | 27.8680 | + | 16.0896i | 0.895248 | + | 0.516872i | ||||
\(970\) | − | 13.8252i | − | 0.443901i | ||||||
\(971\) | −5.98258 | + | 10.3621i | −0.191990 | + | 0.332537i | −0.945910 | − | 0.324430i | \(-0.894828\pi\) |
0.753919 | + | 0.656967i | \(0.228161\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −13.4965 | + | 7.79221i | −0.432678 | + | 0.249807i | ||||
\(974\) | 5.76329 | 0.184668 | ||||||||
\(975\) | −2.82233 | − | 2.24376i | −0.0903869 | − | 0.0718578i | ||||
\(976\) | 7.46410 | 0.238920 | ||||||||
\(977\) | 1.52780 | − | 0.882077i | 0.0488787 | − | 0.0282201i | −0.475362 | − | 0.879791i | \(-0.657683\pi\) |
0.524240 | + | 0.851570i | \(0.324349\pi\) | |||||||
\(978\) | 0.0881650 | + | 0.152706i | 0.00281921 | + | 0.00488301i | ||||
\(979\) | 17.9805 | − | 31.1432i | 0.574660 | − | 0.995341i | ||||
\(980\) | − | 14.5729i | − | 0.465513i | ||||||
\(981\) | −11.0853 | − | 6.40013i | −0.353928 | − | 0.204340i | ||||
\(982\) | −0.931273 | − | 0.537671i | −0.0297181 | − | 0.0171578i | ||||
\(983\) | 54.2821i | 1.73133i | 0.500623 | + | 0.865666i | \(0.333104\pi\) | ||||
−0.500623 | + | 0.865666i | \(0.666896\pi\) | |||||||
\(984\) | 3.64466 | − | 6.31274i | 0.116188 | − | 0.201243i | ||||
\(985\) | −4.59028 | − | 7.95060i | −0.146258 | − | 0.253327i | ||||
\(986\) | 14.9398 | − | 8.62547i | 0.475779 | − | 0.274691i | ||||
\(987\) | 45.3013 | 1.44196 | ||||||||
\(988\) | 18.0506 | − | 22.7050i | 0.574265 | − | 0.722344i | ||||
\(989\) | −0.699680 | −0.0222485 | ||||||||
\(990\) | 3.81062 | − | 2.20006i | 0.121110 | − | 0.0699226i | ||||
\(991\) | 8.73917 | + | 15.1367i | 0.277609 | + | 0.480833i | 0.970790 | − | 0.239931i | \(-0.0771248\pi\) |
−0.693181 | + | 0.720763i | \(0.743791\pi\) | |||||||
\(992\) | 3.22034 | − | 5.57780i | 0.102246 | − | 0.177095i | ||||
\(993\) | − | 31.9959i | − | 1.01536i | ||||||
\(994\) | −31.9908 | − | 18.4699i | −1.01469 | − | 0.585829i | ||||
\(995\) | 14.0448 | + | 8.10876i | 0.445250 | + | 0.257065i | ||||
\(996\) | − | 3.51093i | − | 0.111248i | ||||||
\(997\) | 10.6457 | − | 18.4389i | 0.337152 | − | 0.583965i | −0.646744 | − | 0.762707i | \(-0.723870\pi\) |
0.983896 | + | 0.178743i | \(0.0572030\pi\) | |||||||
\(998\) | 7.37671 | + | 12.7768i | 0.233506 | + | 0.404444i | ||||
\(999\) | 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 | 390.2.bb.c.361.4 | yes | 8 | |
3.2 | odd | 2 | 1170.2.bs.f.361.2 | 8 | |||
5.2 | odd | 4 | 1950.2.y.k.49.1 | 8 | |||
5.3 | odd | 4 | 1950.2.y.j.49.4 | 8 | |||
5.4 | even | 2 | 1950.2.bc.g.751.1 | 8 | |||
13.2 | odd | 12 | 5070.2.a.ca.1.4 | 4 | |||
13.3 | even | 3 | 5070.2.b.ba.1351.5 | 8 | |||
13.4 | even | 6 | inner | 390.2.bb.c.121.4 | ✓ | 8 | |
13.10 | even | 6 | 5070.2.b.ba.1351.4 | 8 | |||
13.11 | odd | 12 | 5070.2.a.bz.1.1 | 4 | |||
39.17 | odd | 6 | 1170.2.bs.f.901.2 | 8 | |||
65.4 | even | 6 | 1950.2.bc.g.901.1 | 8 | |||
65.17 | odd | 12 | 1950.2.y.j.199.4 | 8 | |||
65.43 | odd | 12 | 1950.2.y.k.199.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.c.121.4 | ✓ | 8 | 13.4 | even | 6 | inner | |
390.2.bb.c.361.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1170.2.bs.f.361.2 | 8 | 3.2 | odd | 2 | |||
1170.2.bs.f.901.2 | 8 | 39.17 | odd | 6 | |||
1950.2.y.j.49.4 | 8 | 5.3 | odd | 4 | |||
1950.2.y.j.199.4 | 8 | 65.17 | odd | 12 | |||
1950.2.y.k.49.1 | 8 | 5.2 | odd | 4 | |||
1950.2.y.k.199.1 | 8 | 65.43 | odd | 12 | |||
1950.2.bc.g.751.1 | 8 | 5.4 | even | 2 | |||
1950.2.bc.g.901.1 | 8 | 65.4 | even | 6 | |||
5070.2.a.bz.1.1 | 4 | 13.11 | odd | 12 | |||
5070.2.a.ca.1.4 | 4 | 13.2 | odd | 12 | |||
5070.2.b.ba.1351.4 | 8 | 13.10 | even | 6 | |||
5070.2.b.ba.1351.5 | 8 | 13.3 | even | 3 |