Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(67,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 331.1 | ||
Root | \(1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.331 |
Dual form | 462.2.i.e.67.1 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.32288 | + | 2.29129i | −0.591608 | + | 1.02470i | 0.402408 | + | 0.915460i | \(0.368173\pi\) |
−0.994016 | + | 0.109235i | \(0.965160\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.32288 | + | 2.29129i | −0.500000 | + | 0.866025i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.32288 | + | 2.29129i | 0.418330 | + | 0.724569i | ||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 1.32288 | + | 2.29129i | 0.353553 | + | 0.612372i | ||||
\(15\) | −2.64575 | −0.683130 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.50000 | + | 2.59808i | 0.363803 | + | 0.630126i | 0.988583 | − | 0.150675i | \(-0.0481447\pi\) |
−0.624780 | + | 0.780801i | \(0.714811\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −2.64575 | + | 4.58258i | −0.606977 | + | 1.05131i | 0.384759 | + | 0.923017i | \(0.374285\pi\) |
−0.991736 | + | 0.128298i | \(0.959049\pi\) | |||||||
\(20\) | 2.64575 | 0.591608 | ||||||||
\(21\) | −2.64575 | −0.577350 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 1.32288 | − | 2.29129i | 0.275839 | − | 0.477767i | −0.694508 | − | 0.719485i | \(-0.744378\pi\) |
0.970346 | + | 0.241719i | \(0.0777111\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −1.00000 | − | 1.73205i | −0.200000 | − | 0.346410i | ||||
\(26\) | −2.00000 | + | 3.46410i | −0.392232 | + | 0.679366i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.64575 | 0.500000 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | −1.32288 | + | 2.29129i | −0.241523 | + | 0.418330i | ||||
\(31\) | 2.00000 | + | 3.46410i | 0.359211 | + | 0.622171i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0.500000 | − | 0.866025i | 0.0870388 | − | 0.150756i | ||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | −3.50000 | − | 6.06218i | −0.591608 | − | 1.02470i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.645751 | + | 1.11847i | −0.106161 | + | 0.183876i | −0.914212 | − | 0.405236i | \(-0.867189\pi\) |
0.808051 | + | 0.589112i | \(0.200523\pi\) | |||||||
\(38\) | 2.64575 | + | 4.58258i | 0.429198 | + | 0.743392i | ||||
\(39\) | −2.00000 | − | 3.46410i | −0.320256 | − | 0.554700i | ||||
\(40\) | 1.32288 | − | 2.29129i | 0.209165 | − | 0.362284i | ||||
\(41\) | 9.00000 | 1.40556 | 0.702782 | − | 0.711405i | \(-0.251941\pi\) | ||||
0.702782 | + | 0.711405i | \(0.251941\pi\) | |||||||
\(42\) | −1.32288 | + | 2.29129i | −0.204124 | + | 0.353553i | ||||
\(43\) | 9.29150 | 1.41694 | 0.708470 | − | 0.705740i | \(-0.249386\pi\) | ||||
0.708470 | + | 0.705740i | \(0.249386\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | −1.32288 | − | 2.29129i | −0.197203 | − | 0.341565i | ||||
\(46\) | −1.32288 | − | 2.29129i | −0.195047 | − | 0.337832i | ||||
\(47\) | 1.96863 | − | 3.40976i | 0.287154 | − | 0.497365i | −0.685975 | − | 0.727625i | \(-0.740624\pi\) |
0.973129 | + | 0.230260i | \(0.0739576\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −3.50000 | − | 6.06218i | −0.500000 | − | 0.866025i | ||||
\(50\) | −2.00000 | −0.282843 | ||||||||
\(51\) | −1.50000 | + | 2.59808i | −0.210042 | + | 0.363803i | ||||
\(52\) | 2.00000 | + | 3.46410i | 0.277350 | + | 0.480384i | ||||
\(53\) | −2.00000 | − | 3.46410i | −0.274721 | − | 0.475831i | 0.695344 | − | 0.718677i | \(-0.255252\pi\) |
−0.970065 | + | 0.242846i | \(0.921919\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 2.64575 | 0.356753 | ||||||||
\(56\) | 1.32288 | − | 2.29129i | 0.176777 | − | 0.306186i | ||||
\(57\) | −5.29150 | −0.700877 | ||||||||
\(58\) | 1.00000 | − | 1.73205i | 0.131306 | − | 0.227429i | ||||
\(59\) | −3.29150 | − | 5.70105i | −0.428517 | − | 0.742213i | 0.568225 | − | 0.822874i | \(-0.307631\pi\) |
−0.996742 | + | 0.0806601i | \(0.974297\pi\) | |||||||
\(60\) | 1.32288 | + | 2.29129i | 0.170783 | + | 0.295804i | ||||
\(61\) | −5.96863 | + | 10.3380i | −0.764204 | + | 1.32364i | 0.176462 | + | 0.984307i | \(0.443535\pi\) |
−0.940666 | + | 0.339333i | \(0.889799\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | −1.32288 | − | 2.29129i | −0.166667 | − | 0.288675i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.29150 | − | 9.16515i | 0.656330 | − | 1.13680i | ||||
\(66\) | −0.500000 | − | 0.866025i | −0.0615457 | − | 0.106600i | ||||
\(67\) | −3.79150 | − | 6.56708i | −0.463206 | − | 0.802296i | 0.535913 | − | 0.844273i | \(-0.319968\pi\) |
−0.999119 | + | 0.0419774i | \(0.986634\pi\) | |||||||
\(68\) | 1.50000 | − | 2.59808i | 0.181902 | − | 0.315063i | ||||
\(69\) | 2.64575 | 0.318511 | ||||||||
\(70\) | −7.00000 | −0.836660 | ||||||||
\(71\) | −2.70850 | −0.321440 | −0.160720 | − | 0.987000i | \(-0.551382\pi\) | ||||
−0.160720 | + | 0.987000i | \(0.551382\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 7.64575 | + | 13.2428i | 0.894868 | + | 1.54996i | 0.833969 | + | 0.551812i | \(0.186063\pi\) |
0.0608990 | + | 0.998144i | \(0.480603\pi\) | |||||||
\(74\) | 0.645751 | + | 1.11847i | 0.0750671 | + | 0.130020i | ||||
\(75\) | 1.00000 | − | 1.73205i | 0.115470 | − | 0.200000i | ||||
\(76\) | 5.29150 | 0.606977 | ||||||||
\(77\) | 2.64575 | 0.301511 | ||||||||
\(78\) | −4.00000 | −0.452911 | ||||||||
\(79\) | −5.32288 | + | 9.21949i | −0.598870 | + | 1.03727i | 0.394118 | + | 0.919060i | \(0.371050\pi\) |
−0.992988 | + | 0.118214i | \(0.962283\pi\) | |||||||
\(80\) | −1.32288 | − | 2.29129i | −0.147902 | − | 0.256174i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 4.50000 | − | 7.79423i | 0.496942 | − | 0.860729i | ||||
\(83\) | 15.5830 | 1.71046 | 0.855229 | − | 0.518251i | \(-0.173417\pi\) | ||||
0.855229 | + | 0.518251i | \(0.173417\pi\) | |||||||
\(84\) | 1.32288 | + | 2.29129i | 0.144338 | + | 0.250000i | ||||
\(85\) | −7.93725 | −0.860916 | ||||||||
\(86\) | 4.64575 | − | 8.04668i | 0.500964 | − | 0.867696i | ||||
\(87\) | 1.00000 | + | 1.73205i | 0.107211 | + | 0.185695i | ||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | −1.35425 | + | 2.34563i | −0.143550 | + | 0.248636i | −0.928831 | − | 0.370504i | \(-0.879185\pi\) |
0.785281 | + | 0.619140i | \(0.212518\pi\) | |||||||
\(90\) | −2.64575 | −0.278887 | ||||||||
\(91\) | 5.29150 | − | 9.16515i | 0.554700 | − | 0.960769i | ||||
\(92\) | −2.64575 | −0.275839 | ||||||||
\(93\) | −2.00000 | + | 3.46410i | −0.207390 | + | 0.359211i | ||||
\(94\) | −1.96863 | − | 3.40976i | −0.203048 | − | 0.351690i | ||||
\(95\) | −7.00000 | − | 12.1244i | −0.718185 | − | 1.24393i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −11.5830 | −1.17608 | −0.588038 | − | 0.808833i | \(-0.700099\pi\) | ||||
−0.588038 | + | 0.808833i | \(0.700099\pi\) | |||||||
\(98\) | −7.00000 | −0.707107 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −1.00000 | + | 1.73205i | −0.100000 | + | 0.173205i | ||||
\(101\) | −3.64575 | − | 6.31463i | −0.362766 | − | 0.628329i | 0.625649 | − | 0.780105i | \(-0.284834\pi\) |
−0.988415 | + | 0.151776i | \(0.951501\pi\) | |||||||
\(102\) | 1.50000 | + | 2.59808i | 0.148522 | + | 0.257248i | ||||
\(103\) | 5.00000 | − | 8.66025i | 0.492665 | − | 0.853320i | −0.507300 | − | 0.861770i | \(-0.669356\pi\) |
0.999964 | + | 0.00844953i | \(0.00268960\pi\) | |||||||
\(104\) | 4.00000 | 0.392232 | ||||||||
\(105\) | 3.50000 | − | 6.06218i | 0.341565 | − | 0.591608i | ||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | −4.50000 | + | 7.79423i | −0.435031 | + | 0.753497i | −0.997298 | − | 0.0734594i | \(-0.976596\pi\) |
0.562267 | + | 0.826956i | \(0.309929\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 1.96863 | + | 3.40976i | 0.188560 | + | 0.326596i | 0.944770 | − | 0.327733i | \(-0.106285\pi\) |
−0.756210 | + | 0.654329i | \(0.772951\pi\) | |||||||
\(110\) | 1.32288 | − | 2.29129i | 0.126131 | − | 0.218466i | ||||
\(111\) | −1.29150 | −0.122584 | ||||||||
\(112\) | −1.32288 | − | 2.29129i | −0.125000 | − | 0.216506i | ||||
\(113\) | 12.5830 | 1.18371 | 0.591855 | − | 0.806045i | \(-0.298396\pi\) | ||||
0.591855 | + | 0.806045i | \(0.298396\pi\) | |||||||
\(114\) | −2.64575 | + | 4.58258i | −0.247797 | + | 0.429198i | ||||
\(115\) | 3.50000 | + | 6.06218i | 0.326377 | + | 0.565301i | ||||
\(116\) | −1.00000 | − | 1.73205i | −0.0928477 | − | 0.160817i | ||||
\(117\) | 2.00000 | − | 3.46410i | 0.184900 | − | 0.320256i | ||||
\(118\) | −6.58301 | −0.606015 | ||||||||
\(119\) | −7.93725 | −0.727607 | ||||||||
\(120\) | 2.64575 | 0.241523 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 5.96863 | + | 10.3380i | 0.540374 | + | 0.935955i | ||||
\(123\) | 4.50000 | + | 7.79423i | 0.405751 | + | 0.702782i | ||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | −7.93725 | −0.709930 | ||||||||
\(126\) | −2.64575 | −0.235702 | ||||||||
\(127\) | 2.64575 | 0.234772 | 0.117386 | − | 0.993086i | \(-0.462548\pi\) | ||||
0.117386 | + | 0.993086i | \(0.462548\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 4.64575 | + | 8.04668i | 0.409036 | + | 0.708470i | ||||
\(130\) | −5.29150 | − | 9.16515i | −0.464095 | − | 0.803837i | ||||
\(131\) | 9.29150 | − | 16.0934i | 0.811802 | − | 1.40608i | −0.0997990 | − | 0.995008i | \(-0.531820\pi\) |
0.911601 | − | 0.411075i | \(-0.134847\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | −7.00000 | − | 12.1244i | −0.606977 | − | 1.05131i | ||||
\(134\) | −7.58301 | −0.655072 | ||||||||
\(135\) | 1.32288 | − | 2.29129i | 0.113855 | − | 0.197203i | ||||
\(136\) | −1.50000 | − | 2.59808i | −0.128624 | − | 0.222783i | ||||
\(137\) | 6.64575 | + | 11.5108i | 0.567785 | + | 0.983432i | 0.996785 | + | 0.0801276i | \(0.0255328\pi\) |
−0.429000 | + | 0.903305i | \(0.641134\pi\) | |||||||
\(138\) | 1.32288 | − | 2.29129i | 0.112611 | − | 0.195047i | ||||
\(139\) | −12.5830 | −1.06728 | −0.533638 | − | 0.845713i | \(-0.679176\pi\) | ||||
−0.533638 | + | 0.845713i | \(0.679176\pi\) | |||||||
\(140\) | −3.50000 | + | 6.06218i | −0.295804 | + | 0.512348i | ||||
\(141\) | 3.93725 | 0.331577 | ||||||||
\(142\) | −1.35425 | + | 2.34563i | −0.113646 | + | 0.196841i | ||||
\(143\) | 2.00000 | + | 3.46410i | 0.167248 | + | 0.289683i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −2.64575 | + | 4.58258i | −0.219718 | + | 0.380562i | ||||
\(146\) | 15.2915 | 1.26553 | ||||||||
\(147\) | 3.50000 | − | 6.06218i | 0.288675 | − | 0.500000i | ||||
\(148\) | 1.29150 | 0.106161 | ||||||||
\(149\) | −9.93725 | + | 17.2118i | −0.814092 | + | 1.41005i | 0.0958868 | + | 0.995392i | \(0.469431\pi\) |
−0.909978 | + | 0.414656i | \(0.863902\pi\) | |||||||
\(150\) | −1.00000 | − | 1.73205i | −0.0816497 | − | 0.141421i | ||||
\(151\) | −11.3229 | − | 19.6118i | −0.921443 | − | 1.59599i | −0.797185 | − | 0.603735i | \(-0.793678\pi\) |
−0.124258 | − | 0.992250i | \(-0.539655\pi\) | |||||||
\(152\) | 2.64575 | − | 4.58258i | 0.214599 | − | 0.371696i | ||||
\(153\) | −3.00000 | −0.242536 | ||||||||
\(154\) | 1.32288 | − | 2.29129i | 0.106600 | − | 0.184637i | ||||
\(155\) | −10.5830 | −0.850047 | ||||||||
\(156\) | −2.00000 | + | 3.46410i | −0.160128 | + | 0.277350i | ||||
\(157\) | 0.354249 | + | 0.613577i | 0.0282721 | + | 0.0489688i | 0.879815 | − | 0.475316i | \(-0.157666\pi\) |
−0.851543 | + | 0.524285i | \(0.824333\pi\) | |||||||
\(158\) | 5.32288 | + | 9.21949i | 0.423465 | + | 0.733463i | ||||
\(159\) | 2.00000 | − | 3.46410i | 0.158610 | − | 0.274721i | ||||
\(160\) | −2.64575 | −0.209165 | ||||||||
\(161\) | 3.50000 | + | 6.06218i | 0.275839 | + | 0.477767i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 2.79150 | − | 4.83502i | 0.218647 | − | 0.378708i | −0.735747 | − | 0.677256i | \(-0.763169\pi\) |
0.954395 | + | 0.298548i | \(0.0965022\pi\) | |||||||
\(164\) | −4.50000 | − | 7.79423i | −0.351391 | − | 0.608627i | ||||
\(165\) | 1.32288 | + | 2.29129i | 0.102986 | + | 0.178377i | ||||
\(166\) | 7.79150 | − | 13.4953i | 0.604738 | − | 1.04744i | ||||
\(167\) | 8.70850 | 0.673884 | 0.336942 | − | 0.941525i | \(-0.390607\pi\) | ||||
0.336942 | + | 0.941525i | \(0.390607\pi\) | |||||||
\(168\) | 2.64575 | 0.204124 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | −3.96863 | + | 6.87386i | −0.304380 | + | 0.527201i | ||||
\(171\) | −2.64575 | − | 4.58258i | −0.202326 | − | 0.350438i | ||||
\(172\) | −4.64575 | − | 8.04668i | −0.354235 | − | 0.613553i | ||||
\(173\) | −2.00000 | + | 3.46410i | −0.152057 | + | 0.263371i | −0.931984 | − | 0.362500i | \(-0.881923\pi\) |
0.779926 | + | 0.625871i | \(0.215256\pi\) | |||||||
\(174\) | 2.00000 | 0.151620 | ||||||||
\(175\) | 5.29150 | 0.400000 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 3.29150 | − | 5.70105i | 0.247404 | − | 0.428517i | ||||
\(178\) | 1.35425 | + | 2.34563i | 0.101505 | + | 0.175812i | ||||
\(179\) | −2.35425 | − | 4.07768i | −0.175965 | − | 0.304780i | 0.764530 | − | 0.644588i | \(-0.222971\pi\) |
−0.940495 | + | 0.339808i | \(0.889638\pi\) | |||||||
\(180\) | −1.32288 | + | 2.29129i | −0.0986013 | + | 0.170783i | ||||
\(181\) | −5.29150 | −0.393314 | −0.196657 | − | 0.980472i | \(-0.563009\pi\) | ||||
−0.196657 | + | 0.980472i | \(0.563009\pi\) | |||||||
\(182\) | −5.29150 | − | 9.16515i | −0.392232 | − | 0.679366i | ||||
\(183\) | −11.9373 | −0.882427 | ||||||||
\(184\) | −1.32288 | + | 2.29129i | −0.0975237 | + | 0.168916i | ||||
\(185\) | −1.70850 | − | 2.95920i | −0.125611 | − | 0.217565i | ||||
\(186\) | 2.00000 | + | 3.46410i | 0.146647 | + | 0.254000i | ||||
\(187\) | 1.50000 | − | 2.59808i | 0.109691 | − | 0.189990i | ||||
\(188\) | −3.93725 | −0.287154 | ||||||||
\(189\) | 1.32288 | − | 2.29129i | 0.0962250 | − | 0.166667i | ||||
\(190\) | −14.0000 | −1.01567 | ||||||||
\(191\) | −3.35425 | + | 5.80973i | −0.242705 | + | 0.420377i | −0.961484 | − | 0.274861i | \(-0.911368\pi\) |
0.718779 | + | 0.695239i | \(0.244701\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 7.93725 | + | 13.7477i | 0.571336 | + | 0.989583i | 0.996429 | + | 0.0844334i | \(0.0269080\pi\) |
−0.425093 | + | 0.905150i | \(0.639759\pi\) | |||||||
\(194\) | −5.79150 | + | 10.0312i | −0.415806 | + | 0.720197i | ||||
\(195\) | 10.5830 | 0.757865 | ||||||||
\(196\) | −3.50000 | + | 6.06218i | −0.250000 | + | 0.433013i | ||||
\(197\) | 21.8745 | 1.55849 | 0.779247 | − | 0.626717i | \(-0.215602\pi\) | ||||
0.779247 | + | 0.626717i | \(0.215602\pi\) | |||||||
\(198\) | 0.500000 | − | 0.866025i | 0.0355335 | − | 0.0615457i | ||||
\(199\) | 9.58301 | + | 16.5983i | 0.679321 | + | 1.17662i | 0.975186 | + | 0.221389i | \(0.0710590\pi\) |
−0.295864 | + | 0.955230i | \(0.595608\pi\) | |||||||
\(200\) | 1.00000 | + | 1.73205i | 0.0707107 | + | 0.122474i | ||||
\(201\) | 3.79150 | − | 6.56708i | 0.267432 | − | 0.463206i | ||||
\(202\) | −7.29150 | −0.513028 | ||||||||
\(203\) | −2.64575 | + | 4.58258i | −0.185695 | + | 0.321634i | ||||
\(204\) | 3.00000 | 0.210042 | ||||||||
\(205\) | −11.9059 | + | 20.6216i | −0.831543 | + | 1.44027i | ||||
\(206\) | −5.00000 | − | 8.66025i | −0.348367 | − | 0.603388i | ||||
\(207\) | 1.32288 | + | 2.29129i | 0.0919462 | + | 0.159256i | ||||
\(208\) | 2.00000 | − | 3.46410i | 0.138675 | − | 0.240192i | ||||
\(209\) | 5.29150 | 0.366021 | ||||||||
\(210\) | −3.50000 | − | 6.06218i | −0.241523 | − | 0.418330i | ||||
\(211\) | 21.2915 | 1.46577 | 0.732884 | − | 0.680354i | \(-0.238174\pi\) | ||||
0.732884 | + | 0.680354i | \(0.238174\pi\) | |||||||
\(212\) | −2.00000 | + | 3.46410i | −0.137361 | + | 0.237915i | ||||
\(213\) | −1.35425 | − | 2.34563i | −0.0927916 | − | 0.160720i | ||||
\(214\) | 4.50000 | + | 7.79423i | 0.307614 | + | 0.532803i | ||||
\(215\) | −12.2915 | + | 21.2895i | −0.838274 | + | 1.45193i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −10.5830 | −0.718421 | ||||||||
\(218\) | 3.93725 | 0.266664 | ||||||||
\(219\) | −7.64575 | + | 13.2428i | −0.516652 | + | 0.894868i | ||||
\(220\) | −1.32288 | − | 2.29129i | −0.0891883 | − | 0.154479i | ||||
\(221\) | −6.00000 | − | 10.3923i | −0.403604 | − | 0.699062i | ||||
\(222\) | −0.645751 | + | 1.11847i | −0.0433400 | + | 0.0750671i | ||||
\(223\) | 28.4575 | 1.90566 | 0.952828 | − | 0.303511i | \(-0.0981588\pi\) | ||||
0.952828 | + | 0.303511i | \(0.0981588\pi\) | |||||||
\(224\) | −2.64575 | −0.176777 | ||||||||
\(225\) | 2.00000 | 0.133333 | ||||||||
\(226\) | 6.29150 | − | 10.8972i | 0.418505 | − | 0.724871i | ||||
\(227\) | −1.20850 | − | 2.09318i | −0.0802108 | − | 0.138929i | 0.823130 | − | 0.567854i | \(-0.192226\pi\) |
−0.903340 | + | 0.428924i | \(0.858893\pi\) | |||||||
\(228\) | 2.64575 | + | 4.58258i | 0.175219 | + | 0.303488i | ||||
\(229\) | −3.35425 | + | 5.80973i | −0.221655 | + | 0.383918i | −0.955311 | − | 0.295604i | \(-0.904479\pi\) |
0.733656 | + | 0.679521i | \(0.237813\pi\) | |||||||
\(230\) | 7.00000 | 0.461566 | ||||||||
\(231\) | 1.32288 | + | 2.29129i | 0.0870388 | + | 0.150756i | ||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | −10.0830 | + | 17.4643i | −0.660560 | + | 1.14412i | 0.319909 | + | 0.947448i | \(0.396348\pi\) |
−0.980469 | + | 0.196675i | \(0.936986\pi\) | |||||||
\(234\) | −2.00000 | − | 3.46410i | −0.130744 | − | 0.226455i | ||||
\(235\) | 5.20850 | + | 9.02138i | 0.339765 | + | 0.588490i | ||||
\(236\) | −3.29150 | + | 5.70105i | −0.214259 | + | 0.371107i | ||||
\(237\) | −10.6458 | −0.691516 | ||||||||
\(238\) | −3.96863 | + | 6.87386i | −0.257248 | + | 0.445566i | ||||
\(239\) | 2.70850 | 0.175198 | 0.0875991 | − | 0.996156i | \(-0.472081\pi\) | ||||
0.0875991 | + | 0.996156i | \(0.472081\pi\) | |||||||
\(240\) | 1.32288 | − | 2.29129i | 0.0853913 | − | 0.147902i | ||||
\(241\) | 13.5830 | + | 23.5265i | 0.874958 | + | 1.51547i | 0.856807 | + | 0.515637i | \(0.172445\pi\) |
0.0181511 | + | 0.999835i | \(0.494222\pi\) | |||||||
\(242\) | 0.500000 | + | 0.866025i | 0.0321412 | + | 0.0556702i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 11.9373 | 0.764204 | ||||||||
\(245\) | 18.5203 | 1.18322 | ||||||||
\(246\) | 9.00000 | 0.573819 | ||||||||
\(247\) | 10.5830 | − | 18.3303i | 0.673380 | − | 1.16633i | ||||
\(248\) | −2.00000 | − | 3.46410i | −0.127000 | − | 0.219971i | ||||
\(249\) | 7.79150 | + | 13.4953i | 0.493766 | + | 0.855229i | ||||
\(250\) | −3.96863 | + | 6.87386i | −0.250998 | + | 0.434741i | ||||
\(251\) | 23.2915 | 1.47015 | 0.735073 | − | 0.677988i | \(-0.237148\pi\) | ||||
0.735073 | + | 0.677988i | \(0.237148\pi\) | |||||||
\(252\) | −1.32288 | + | 2.29129i | −0.0833333 | + | 0.144338i | ||||
\(253\) | −2.64575 | −0.166337 | ||||||||
\(254\) | 1.32288 | − | 2.29129i | 0.0830046 | − | 0.143768i | ||||
\(255\) | −3.96863 | − | 6.87386i | −0.248525 | − | 0.430458i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −4.64575 | + | 8.04668i | −0.289794 | + | 0.501938i | −0.973760 | − | 0.227576i | \(-0.926920\pi\) |
0.683966 | + | 0.729513i | \(0.260253\pi\) | |||||||
\(258\) | 9.29150 | 0.578464 | ||||||||
\(259\) | −1.70850 | − | 2.95920i | −0.106161 | − | 0.183876i | ||||
\(260\) | −10.5830 | −0.656330 | ||||||||
\(261\) | −1.00000 | + | 1.73205i | −0.0618984 | + | 0.107211i | ||||
\(262\) | −9.29150 | − | 16.0934i | −0.574031 | − | 0.994251i | ||||
\(263\) | −10.9373 | − | 18.9439i | −0.674420 | − | 1.16813i | −0.976638 | − | 0.214891i | \(-0.931060\pi\) |
0.302218 | − | 0.953239i | \(-0.402273\pi\) | |||||||
\(264\) | −0.500000 | + | 0.866025i | −0.0307729 | + | 0.0533002i | ||||
\(265\) | 10.5830 | 0.650109 | ||||||||
\(266\) | −14.0000 | −0.858395 | ||||||||
\(267\) | −2.70850 | −0.165757 | ||||||||
\(268\) | −3.79150 | + | 6.56708i | −0.231603 | + | 0.401148i | ||||
\(269\) | 5.32288 | + | 9.21949i | 0.324541 | + | 0.562122i | 0.981419 | − | 0.191875i | \(-0.0614567\pi\) |
−0.656878 | + | 0.753997i | \(0.728123\pi\) | |||||||
\(270\) | −1.32288 | − | 2.29129i | −0.0805076 | − | 0.139443i | ||||
\(271\) | −4.64575 | + | 8.04668i | −0.282209 | + | 0.488801i | −0.971929 | − | 0.235276i | \(-0.924401\pi\) |
0.689719 | + | 0.724077i | \(0.257734\pi\) | |||||||
\(272\) | −3.00000 | −0.181902 | ||||||||
\(273\) | 10.5830 | 0.640513 | ||||||||
\(274\) | 13.2915 | 0.802969 | ||||||||
\(275\) | −1.00000 | + | 1.73205i | −0.0603023 | + | 0.104447i | ||||
\(276\) | −1.32288 | − | 2.29129i | −0.0796278 | − | 0.137919i | ||||
\(277\) | 8.58301 | + | 14.8662i | 0.515703 | + | 0.893223i | 0.999834 | + | 0.0182280i | \(0.00580246\pi\) |
−0.484131 | + | 0.874995i | \(0.660864\pi\) | |||||||
\(278\) | −6.29150 | + | 10.8972i | −0.377339 | + | 0.653571i | ||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 3.50000 | + | 6.06218i | 0.209165 | + | 0.362284i | ||||
\(281\) | −3.00000 | −0.178965 | −0.0894825 | − | 0.995988i | \(-0.528521\pi\) | ||||
−0.0894825 | + | 0.995988i | \(0.528521\pi\) | |||||||
\(282\) | 1.96863 | − | 3.40976i | 0.117230 | − | 0.203048i | ||||
\(283\) | −15.2288 | − | 26.3770i | −0.905256 | − | 1.56795i | −0.820574 | − | 0.571541i | \(-0.806346\pi\) |
−0.0846819 | − | 0.996408i | \(-0.526987\pi\) | |||||||
\(284\) | 1.35425 | + | 2.34563i | 0.0803599 | + | 0.139187i | ||||
\(285\) | 7.00000 | − | 12.1244i | 0.414644 | − | 0.718185i | ||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | −11.9059 | + | 20.6216i | −0.702782 | + | 1.21725i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 2.64575 | + | 4.58258i | 0.155364 | + | 0.269098i | ||||
\(291\) | −5.79150 | − | 10.0312i | −0.339504 | − | 0.588038i | ||||
\(292\) | 7.64575 | − | 13.2428i | 0.447434 | − | 0.774978i | ||||
\(293\) | −14.5830 | −0.851948 | −0.425974 | − | 0.904735i | \(-0.640069\pi\) | ||||
−0.425974 | + | 0.904735i | \(0.640069\pi\) | |||||||
\(294\) | −3.50000 | − | 6.06218i | −0.204124 | − | 0.353553i | ||||
\(295\) | 17.4170 | 1.01406 | ||||||||
\(296\) | 0.645751 | − | 1.11847i | 0.0375335 | − | 0.0650100i | ||||
\(297\) | 0.500000 | + | 0.866025i | 0.0290129 | + | 0.0502519i | ||||
\(298\) | 9.93725 | + | 17.2118i | 0.575650 | + | 0.997054i | ||||
\(299\) | −5.29150 | + | 9.16515i | −0.306015 | + | 0.530034i | ||||
\(300\) | −2.00000 | −0.115470 | ||||||||
\(301\) | −12.2915 | + | 21.2895i | −0.708470 | + | 1.22711i | ||||
\(302\) | −22.6458 | −1.30312 | ||||||||
\(303\) | 3.64575 | − | 6.31463i | 0.209443 | − | 0.362766i | ||||
\(304\) | −2.64575 | − | 4.58258i | −0.151744 | − | 0.262829i | ||||
\(305\) | −15.7915 | − | 27.3517i | −0.904219 | − | 1.56615i | ||||
\(306\) | −1.50000 | + | 2.59808i | −0.0857493 | + | 0.148522i | ||||
\(307\) | −11.4170 | −0.651602 | −0.325801 | − | 0.945438i | \(-0.605634\pi\) | ||||
−0.325801 | + | 0.945438i | \(0.605634\pi\) | |||||||
\(308\) | −1.32288 | − | 2.29129i | −0.0753778 | − | 0.130558i | ||||
\(309\) | 10.0000 | 0.568880 | ||||||||
\(310\) | −5.29150 | + | 9.16515i | −0.300537 | + | 0.520546i | ||||
\(311\) | −11.2601 | − | 19.5031i | −0.638503 | − | 1.10592i | −0.985761 | − | 0.168151i | \(-0.946221\pi\) |
0.347258 | − | 0.937770i | \(-0.387113\pi\) | |||||||
\(312\) | 2.00000 | + | 3.46410i | 0.113228 | + | 0.196116i | ||||
\(313\) | 10.2915 | − | 17.8254i | 0.581710 | − | 1.00755i | −0.413567 | − | 0.910474i | \(-0.635717\pi\) |
0.995277 | − | 0.0970777i | \(-0.0309495\pi\) | |||||||
\(314\) | 0.708497 | 0.0399828 | ||||||||
\(315\) | 7.00000 | 0.394405 | ||||||||
\(316\) | 10.6458 | 0.598870 | ||||||||
\(317\) | −4.61438 | + | 7.99234i | −0.259169 | + | 0.448894i | −0.966020 | − | 0.258469i | \(-0.916782\pi\) |
0.706850 | + | 0.707363i | \(0.250115\pi\) | |||||||
\(318\) | −2.00000 | − | 3.46410i | −0.112154 | − | 0.194257i | ||||
\(319\) | −1.00000 | − | 1.73205i | −0.0559893 | − | 0.0969762i | ||||
\(320\) | −1.32288 | + | 2.29129i | −0.0739510 | + | 0.128087i | ||||
\(321\) | −9.00000 | −0.502331 | ||||||||
\(322\) | 7.00000 | 0.390095 | ||||||||
\(323\) | −15.8745 | −0.883281 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 4.00000 | + | 6.92820i | 0.221880 | + | 0.384308i | ||||
\(326\) | −2.79150 | − | 4.83502i | −0.154607 | − | 0.267787i | ||||
\(327\) | −1.96863 | + | 3.40976i | −0.108865 | + | 0.188560i | ||||
\(328\) | −9.00000 | −0.496942 | ||||||||
\(329\) | 5.20850 | + | 9.02138i | 0.287154 | + | 0.497365i | ||||
\(330\) | 2.64575 | 0.145644 | ||||||||
\(331\) | −6.50000 | + | 11.2583i | −0.357272 | + | 0.618814i | −0.987504 | − | 0.157593i | \(-0.949627\pi\) |
0.630232 | + | 0.776407i | \(0.282960\pi\) | |||||||
\(332\) | −7.79150 | − | 13.4953i | −0.427614 | − | 0.740650i | ||||
\(333\) | −0.645751 | − | 1.11847i | −0.0353870 | − | 0.0612920i | ||||
\(334\) | 4.35425 | − | 7.54178i | 0.238254 | − | 0.412668i | ||||
\(335\) | 20.0627 | 1.09614 | ||||||||
\(336\) | 1.32288 | − | 2.29129i | 0.0721688 | − | 0.125000i | ||||
\(337\) | 6.70850 | 0.365435 | 0.182718 | − | 0.983165i | \(-0.441511\pi\) | ||||
0.182718 | + | 0.983165i | \(0.441511\pi\) | |||||||
\(338\) | 1.50000 | − | 2.59808i | 0.0815892 | − | 0.141317i | ||||
\(339\) | 6.29150 | + | 10.8972i | 0.341708 | + | 0.591855i | ||||
\(340\) | 3.96863 | + | 6.87386i | 0.215229 | + | 0.372788i | ||||
\(341\) | 2.00000 | − | 3.46410i | 0.108306 | − | 0.187592i | ||||
\(342\) | −5.29150 | −0.286132 | ||||||||
\(343\) | 18.5203 | 1.00000 | ||||||||
\(344\) | −9.29150 | −0.500964 | ||||||||
\(345\) | −3.50000 | + | 6.06218i | −0.188434 | + | 0.326377i | ||||
\(346\) | 2.00000 | + | 3.46410i | 0.107521 | + | 0.186231i | ||||
\(347\) | −14.7915 | − | 25.6196i | −0.794049 | − | 1.37533i | −0.923441 | − | 0.383740i | \(-0.874636\pi\) |
0.129392 | − | 0.991594i | \(-0.458698\pi\) | |||||||
\(348\) | 1.00000 | − | 1.73205i | 0.0536056 | − | 0.0928477i | ||||
\(349\) | −13.2288 | −0.708119 | −0.354060 | − | 0.935223i | \(-0.615199\pi\) | ||||
−0.354060 | + | 0.935223i | \(0.615199\pi\) | |||||||
\(350\) | 2.64575 | − | 4.58258i | 0.141421 | − | 0.244949i | ||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | 11.6458 | + | 20.1710i | 0.619841 | + | 1.07360i | 0.989514 | + | 0.144434i | \(0.0461362\pi\) |
−0.369674 | + | 0.929162i | \(0.620531\pi\) | |||||||
\(354\) | −3.29150 | − | 5.70105i | −0.174941 | − | 0.303007i | ||||
\(355\) | 3.58301 | − | 6.20595i | 0.190166 | − | 0.329377i | ||||
\(356\) | 2.70850 | 0.143550 | ||||||||
\(357\) | −3.96863 | − | 6.87386i | −0.210042 | − | 0.363803i | ||||
\(358\) | −4.70850 | −0.248852 | ||||||||
\(359\) | −10.2915 | + | 17.8254i | −0.543165 | + | 0.940789i | 0.455555 | + | 0.890208i | \(0.349441\pi\) |
−0.998720 | + | 0.0505814i | \(0.983893\pi\) | |||||||
\(360\) | 1.32288 | + | 2.29129i | 0.0697217 | + | 0.120761i | ||||
\(361\) | −4.50000 | − | 7.79423i | −0.236842 | − | 0.410223i | ||||
\(362\) | −2.64575 | + | 4.58258i | −0.139058 | + | 0.240855i | ||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −10.5830 | −0.554700 | ||||||||
\(365\) | −40.4575 | −2.11764 | ||||||||
\(366\) | −5.96863 | + | 10.3380i | −0.311985 | + | 0.540374i | ||||
\(367\) | −5.35425 | − | 9.27383i | −0.279490 | − | 0.484090i | 0.691768 | − | 0.722119i | \(-0.256832\pi\) |
−0.971258 | + | 0.238029i | \(0.923499\pi\) | |||||||
\(368\) | 1.32288 | + | 2.29129i | 0.0689597 | + | 0.119442i | ||||
\(369\) | −4.50000 | + | 7.79423i | −0.234261 | + | 0.405751i | ||||
\(370\) | −3.41699 | −0.177641 | ||||||||
\(371\) | 10.5830 | 0.549442 | ||||||||
\(372\) | 4.00000 | 0.207390 | ||||||||
\(373\) | 7.90588 | − | 13.6934i | 0.409351 | − | 0.709017i | −0.585466 | − | 0.810697i | \(-0.699088\pi\) |
0.994817 | + | 0.101680i | \(0.0324218\pi\) | |||||||
\(374\) | −1.50000 | − | 2.59808i | −0.0775632 | − | 0.134343i | ||||
\(375\) | −3.96863 | − | 6.87386i | −0.204939 | − | 0.354965i | ||||
\(376\) | −1.96863 | + | 3.40976i | −0.101524 | + | 0.175845i | ||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | −1.32288 | − | 2.29129i | −0.0680414 | − | 0.117851i | ||||
\(379\) | −27.5830 | −1.41684 | −0.708422 | − | 0.705789i | \(-0.750593\pi\) | ||||
−0.708422 | + | 0.705789i | \(0.750593\pi\) | |||||||
\(380\) | −7.00000 | + | 12.1244i | −0.359092 | + | 0.621966i | ||||
\(381\) | 1.32288 | + | 2.29129i | 0.0677730 | + | 0.117386i | ||||
\(382\) | 3.35425 | + | 5.80973i | 0.171618 | + | 0.297252i | ||||
\(383\) | −9.35425 | + | 16.2020i | −0.477980 | + | 0.827885i | −0.999681 | − | 0.0252428i | \(-0.991964\pi\) |
0.521702 | + | 0.853128i | \(0.325297\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −3.50000 | + | 6.06218i | −0.178377 | + | 0.308957i | ||||
\(386\) | 15.8745 | 0.807991 | ||||||||
\(387\) | −4.64575 | + | 8.04668i | −0.236157 | + | 0.409036i | ||||
\(388\) | 5.79150 | + | 10.0312i | 0.294019 | + | 0.509256i | ||||
\(389\) | −15.9686 | − | 27.6585i | −0.809642 | − | 1.40234i | −0.913112 | − | 0.407708i | \(-0.866328\pi\) |
0.103471 | − | 0.994632i | \(-0.467005\pi\) | |||||||
\(390\) | 5.29150 | − | 9.16515i | 0.267946 | − | 0.464095i | ||||
\(391\) | 7.93725 | 0.401404 | ||||||||
\(392\) | 3.50000 | + | 6.06218i | 0.176777 | + | 0.306186i | ||||
\(393\) | 18.5830 | 0.937389 | ||||||||
\(394\) | 10.9373 | − | 18.9439i | 0.551011 | − | 0.954379i | ||||
\(395\) | −14.0830 | − | 24.3925i | −0.708593 | − | 1.22732i | ||||
\(396\) | −0.500000 | − | 0.866025i | −0.0251259 | − | 0.0435194i | ||||
\(397\) | −3.00000 | + | 5.19615i | −0.150566 | + | 0.260787i | −0.931436 | − | 0.363906i | \(-0.881443\pi\) |
0.780870 | + | 0.624694i | \(0.214776\pi\) | |||||||
\(398\) | 19.1660 | 0.960705 | ||||||||
\(399\) | 7.00000 | − | 12.1244i | 0.350438 | − | 0.606977i | ||||
\(400\) | 2.00000 | 0.100000 | ||||||||
\(401\) | 17.9373 | − | 31.0682i | 0.895744 | − | 1.55147i | 0.0628623 | − | 0.998022i | \(-0.479977\pi\) |
0.832881 | − | 0.553451i | \(-0.186690\pi\) | |||||||
\(402\) | −3.79150 | − | 6.56708i | −0.189103 | − | 0.327536i | ||||
\(403\) | −8.00000 | − | 13.8564i | −0.398508 | − | 0.690237i | ||||
\(404\) | −3.64575 | + | 6.31463i | −0.181383 | + | 0.314164i | ||||
\(405\) | 2.64575 | 0.131468 | ||||||||
\(406\) | 2.64575 | + | 4.58258i | 0.131306 | + | 0.227429i | ||||
\(407\) | 1.29150 | 0.0640174 | ||||||||
\(408\) | 1.50000 | − | 2.59808i | 0.0742611 | − | 0.128624i | ||||
\(409\) | −17.9373 | − | 31.0682i | −0.886940 | − | 1.53623i | −0.843474 | − | 0.537170i | \(-0.819493\pi\) |
−0.0434664 | − | 0.999055i | \(-0.513840\pi\) | |||||||
\(410\) | 11.9059 | + | 20.6216i | 0.587990 | + | 1.01843i | ||||
\(411\) | −6.64575 | + | 11.5108i | −0.327811 | + | 0.567785i | ||||
\(412\) | −10.0000 | −0.492665 | ||||||||
\(413\) | 17.4170 | 0.857034 | ||||||||
\(414\) | 2.64575 | 0.130032 | ||||||||
\(415\) | −20.6144 | + | 35.7052i | −1.01192 | + | 1.75270i | ||||
\(416\) | −2.00000 | − | 3.46410i | −0.0980581 | − | 0.169842i | ||||
\(417\) | −6.29150 | − | 10.8972i | −0.308096 | − | 0.533638i | ||||
\(418\) | 2.64575 | − | 4.58258i | 0.129408 | − | 0.224141i | ||||
\(419\) | −9.87451 | −0.482401 | −0.241201 | − | 0.970475i | \(-0.577541\pi\) | ||||
−0.241201 | + | 0.970475i | \(0.577541\pi\) | |||||||
\(420\) | −7.00000 | −0.341565 | ||||||||
\(421\) | 6.12549 | 0.298538 | 0.149269 | − | 0.988797i | \(-0.452308\pi\) | ||||
0.149269 | + | 0.988797i | \(0.452308\pi\) | |||||||
\(422\) | 10.6458 | − | 18.4390i | 0.518227 | − | 0.897596i | ||||
\(423\) | 1.96863 | + | 3.40976i | 0.0957179 | + | 0.165788i | ||||
\(424\) | 2.00000 | + | 3.46410i | 0.0971286 | + | 0.168232i | ||||
\(425\) | 3.00000 | − | 5.19615i | 0.145521 | − | 0.252050i | ||||
\(426\) | −2.70850 | −0.131227 | ||||||||
\(427\) | −15.7915 | − | 27.3517i | −0.764204 | − | 1.32364i | ||||
\(428\) | 9.00000 | 0.435031 | ||||||||
\(429\) | −2.00000 | + | 3.46410i | −0.0965609 | + | 0.167248i | ||||
\(430\) | 12.2915 | + | 21.2895i | 0.592749 | + | 1.02667i | ||||
\(431\) | 8.64575 | + | 14.9749i | 0.416451 | + | 0.721315i | 0.995580 | − | 0.0939217i | \(-0.0299403\pi\) |
−0.579128 | + | 0.815236i | \(0.696607\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 1.58301 | 0.0760744 | 0.0380372 | − | 0.999276i | \(-0.487889\pi\) | ||||
0.0380372 | + | 0.999276i | \(0.487889\pi\) | |||||||
\(434\) | −5.29150 | + | 9.16515i | −0.254000 | + | 0.439941i | ||||
\(435\) | −5.29150 | −0.253708 | ||||||||
\(436\) | 1.96863 | − | 3.40976i | 0.0942801 | − | 0.163298i | ||||
\(437\) | 7.00000 | + | 12.1244i | 0.334855 | + | 0.579987i | ||||
\(438\) | 7.64575 | + | 13.2428i | 0.365328 | + | 0.632767i | ||||
\(439\) | 4.67712 | − | 8.10102i | 0.223227 | − | 0.386640i | −0.732559 | − | 0.680703i | \(-0.761674\pi\) |
0.955786 | + | 0.294063i | \(0.0950076\pi\) | |||||||
\(440\) | −2.64575 | −0.126131 | ||||||||
\(441\) | 7.00000 | 0.333333 | ||||||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | 15.5830 | − | 26.9906i | 0.740371 | − | 1.28236i | −0.211956 | − | 0.977279i | \(-0.567983\pi\) |
0.952326 | − | 0.305081i | \(-0.0986835\pi\) | |||||||
\(444\) | 0.645751 | + | 1.11847i | 0.0306460 | + | 0.0530804i | ||||
\(445\) | −3.58301 | − | 6.20595i | −0.169851 | − | 0.294190i | ||||
\(446\) | 14.2288 | − | 24.6449i | 0.673751 | − | 1.16697i | ||||
\(447\) | −19.8745 | −0.940032 | ||||||||
\(448\) | −1.32288 | + | 2.29129i | −0.0625000 | + | 0.108253i | ||||
\(449\) | 30.4575 | 1.43738 | 0.718689 | − | 0.695331i | \(-0.244742\pi\) | ||||
0.718689 | + | 0.695331i | \(0.244742\pi\) | |||||||
\(450\) | 1.00000 | − | 1.73205i | 0.0471405 | − | 0.0816497i | ||||
\(451\) | −4.50000 | − | 7.79423i | −0.211897 | − | 0.367016i | ||||
\(452\) | −6.29150 | − | 10.8972i | −0.295927 | − | 0.512561i | ||||
\(453\) | 11.3229 | − | 19.6118i | 0.531995 | − | 0.921443i | ||||
\(454\) | −2.41699 | −0.113435 | ||||||||
\(455\) | 14.0000 | + | 24.2487i | 0.656330 | + | 1.13680i | ||||
\(456\) | 5.29150 | 0.247797 | ||||||||
\(457\) | 20.2915 | − | 35.1459i | 0.949196 | − | 1.64406i | 0.202074 | − | 0.979370i | \(-0.435232\pi\) |
0.747123 | − | 0.664686i | \(-0.231435\pi\) | |||||||
\(458\) | 3.35425 | + | 5.80973i | 0.156734 | + | 0.271471i | ||||
\(459\) | −1.50000 | − | 2.59808i | −0.0700140 | − | 0.121268i | ||||
\(460\) | 3.50000 | − | 6.06218i | 0.163188 | − | 0.282650i | ||||
\(461\) | −24.5830 | −1.14494 | −0.572472 | − | 0.819924i | \(-0.694016\pi\) | ||||
−0.572472 | + | 0.819924i | \(0.694016\pi\) | |||||||
\(462\) | 2.64575 | 0.123091 | ||||||||
\(463\) | 39.0405 | 1.81437 | 0.907183 | − | 0.420735i | \(-0.138228\pi\) | ||||
0.907183 | + | 0.420735i | \(0.138228\pi\) | |||||||
\(464\) | −1.00000 | + | 1.73205i | −0.0464238 | + | 0.0804084i | ||||
\(465\) | −5.29150 | − | 9.16515i | −0.245388 | − | 0.425024i | ||||
\(466\) | 10.0830 | + | 17.4643i | 0.467086 | + | 0.809017i | ||||
\(467\) | −4.00000 | + | 6.92820i | −0.185098 | + | 0.320599i | −0.943610 | − | 0.331061i | \(-0.892594\pi\) |
0.758512 | + | 0.651660i | \(0.225927\pi\) | |||||||
\(468\) | −4.00000 | −0.184900 | ||||||||
\(469\) | 20.0627 | 0.926412 | ||||||||
\(470\) | 10.4170 | 0.480500 | ||||||||
\(471\) | −0.354249 | + | 0.613577i | −0.0163229 | + | 0.0282721i | ||||
\(472\) | 3.29150 | + | 5.70105i | 0.151504 | + | 0.262412i | ||||
\(473\) | −4.64575 | − | 8.04668i | −0.213612 | − | 0.369987i | ||||
\(474\) | −5.32288 | + | 9.21949i | −0.244488 | + | 0.423465i | ||||
\(475\) | 10.5830 | 0.485582 | ||||||||
\(476\) | 3.96863 | + | 6.87386i | 0.181902 | + | 0.315063i | ||||
\(477\) | 4.00000 | 0.183147 | ||||||||
\(478\) | 1.35425 | − | 2.34563i | 0.0619419 | − | 0.107287i | ||||
\(479\) | 16.9373 | + | 29.3362i | 0.773883 | + | 1.34040i | 0.935420 | + | 0.353538i | \(0.115021\pi\) |
−0.161537 | + | 0.986867i | \(0.551645\pi\) | |||||||
\(480\) | −1.32288 | − | 2.29129i | −0.0603807 | − | 0.104583i | ||||
\(481\) | 2.58301 | − | 4.47390i | 0.117775 | − | 0.203992i | ||||
\(482\) | 27.1660 | 1.23738 | ||||||||
\(483\) | −3.50000 | + | 6.06218i | −0.159256 | + | 0.275839i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 15.3229 | − | 26.5400i | 0.695776 | − | 1.20512i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −10.9373 | − | 18.9439i | −0.495614 | − | 0.858429i | 0.504373 | − | 0.863486i | \(-0.331724\pi\) |
−0.999987 | + | 0.00505681i | \(0.998390\pi\) | |||||||
\(488\) | 5.96863 | − | 10.3380i | 0.270187 | − | 0.467978i | ||||
\(489\) | 5.58301 | 0.252472 | ||||||||
\(490\) | 9.26013 | − | 16.0390i | 0.418330 | − | 0.724569i | ||||
\(491\) | −1.00000 | −0.0451294 | −0.0225647 | − | 0.999745i | \(-0.507183\pi\) | ||||
−0.0225647 | + | 0.999745i | \(0.507183\pi\) | |||||||
\(492\) | 4.50000 | − | 7.79423i | 0.202876 | − | 0.351391i | ||||
\(493\) | 3.00000 | + | 5.19615i | 0.135113 | + | 0.234023i | ||||
\(494\) | −10.5830 | − | 18.3303i | −0.476152 | − | 0.824719i | ||||
\(495\) | −1.32288 | + | 2.29129i | −0.0594588 | + | 0.102986i | ||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 3.58301 | − | 6.20595i | 0.160720 | − | 0.278375i | ||||
\(498\) | 15.5830 | 0.698291 | ||||||||
\(499\) | 9.29150 | − | 16.0934i | 0.415945 | − | 0.720437i | −0.579582 | − | 0.814914i | \(-0.696784\pi\) |
0.995527 | + | 0.0944762i | \(0.0301176\pi\) | |||||||
\(500\) | 3.96863 | + | 6.87386i | 0.177482 | + | 0.307409i | ||||
\(501\) | 4.35425 | + | 7.54178i | 0.194533 | + | 0.336942i | ||||
\(502\) | 11.6458 | − | 20.1710i | 0.519775 | − | 0.900277i | ||||
\(503\) | −1.29150 | −0.0575853 | −0.0287926 | − | 0.999585i | \(-0.509166\pi\) | ||||
−0.0287926 | + | 0.999585i | \(0.509166\pi\) | |||||||
\(504\) | 1.32288 | + | 2.29129i | 0.0589256 | + | 0.102062i | ||||
\(505\) | 19.2915 | 0.858461 | ||||||||
\(506\) | −1.32288 | + | 2.29129i | −0.0588090 | + | 0.101860i | ||||
\(507\) | 1.50000 | + | 2.59808i | 0.0666173 | + | 0.115385i | ||||
\(508\) | −1.32288 | − | 2.29129i | −0.0586931 | − | 0.101659i | ||||
\(509\) | −12.5830 | + | 21.7944i | −0.557732 | + | 0.966020i | 0.439953 | + | 0.898021i | \(0.354995\pi\) |
−0.997685 | + | 0.0679994i | \(0.978338\pi\) | |||||||
\(510\) | −7.93725 | −0.351468 | ||||||||
\(511\) | −40.4575 | −1.78974 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.64575 | − | 4.58258i | 0.116813 | − | 0.202326i | ||||
\(514\) | 4.64575 | + | 8.04668i | 0.204915 | + | 0.354924i | ||||
\(515\) | 13.2288 | + | 22.9129i | 0.582929 | + | 1.00966i | ||||
\(516\) | 4.64575 | − | 8.04668i | 0.204518 | − | 0.354235i | ||||
\(517\) | −3.93725 | −0.173160 | ||||||||
\(518\) | −3.41699 | −0.150134 | ||||||||
\(519\) | −4.00000 | −0.175581 | ||||||||
\(520\) | −5.29150 | + | 9.16515i | −0.232048 | + | 0.401918i | ||||
\(521\) | −21.0000 | − | 36.3731i | −0.920027 | − | 1.59353i | −0.799370 | − | 0.600839i | \(-0.794833\pi\) |
−0.120656 | − | 0.992694i | \(-0.538500\pi\) | |||||||
\(522\) | 1.00000 | + | 1.73205i | 0.0437688 | + | 0.0758098i | ||||
\(523\) | −1.35425 | + | 2.34563i | −0.0592172 | + | 0.102567i | −0.894114 | − | 0.447839i | \(-0.852194\pi\) |
0.834897 | + | 0.550406i | \(0.185527\pi\) | |||||||
\(524\) | −18.5830 | −0.811802 | ||||||||
\(525\) | 2.64575 | + | 4.58258i | 0.115470 | + | 0.200000i | ||||
\(526\) | −21.8745 | −0.953774 | ||||||||
\(527\) | −6.00000 | + | 10.3923i | −0.261364 | + | 0.452696i | ||||
\(528\) | 0.500000 | + | 0.866025i | 0.0217597 | + | 0.0376889i | ||||
\(529\) | 8.00000 | + | 13.8564i | 0.347826 | + | 0.602452i | ||||
\(530\) | 5.29150 | − | 9.16515i | 0.229848 | − | 0.398109i | ||||
\(531\) | 6.58301 | 0.285678 | ||||||||
\(532\) | −7.00000 | + | 12.1244i | −0.303488 | + | 0.525657i | ||||
\(533\) | −36.0000 | −1.55933 | ||||||||
\(534\) | −1.35425 | + | 2.34563i | −0.0586041 | + | 0.101505i | ||||
\(535\) | −11.9059 | − | 20.6216i | −0.514736 | − | 0.891549i | ||||
\(536\) | 3.79150 | + | 6.56708i | 0.163768 | + | 0.283654i | ||||
\(537\) | 2.35425 | − | 4.07768i | 0.101593 | − | 0.175965i | ||||
\(538\) | 10.6458 | 0.458971 | ||||||||
\(539\) | −3.50000 | + | 6.06218i | −0.150756 | + | 0.261116i | ||||
\(540\) | −2.64575 | −0.113855 | ||||||||
\(541\) | −1.90588 | + | 3.30108i | −0.0819402 | + | 0.141925i | −0.904083 | − | 0.427356i | \(-0.859445\pi\) |
0.822143 | + | 0.569281i | \(0.192778\pi\) | |||||||
\(542\) | 4.64575 | + | 8.04668i | 0.199552 | + | 0.345634i | ||||
\(543\) | −2.64575 | − | 4.58258i | −0.113540 | − | 0.196657i | ||||
\(544\) | −1.50000 | + | 2.59808i | −0.0643120 | + | 0.111392i | ||||
\(545\) | −10.4170 | −0.446215 | ||||||||
\(546\) | 5.29150 | − | 9.16515i | 0.226455 | − | 0.392232i | ||||
\(547\) | 14.7085 | 0.628890 | 0.314445 | − | 0.949276i | \(-0.398182\pi\) | ||||
0.314445 | + | 0.949276i | \(0.398182\pi\) | |||||||
\(548\) | 6.64575 | − | 11.5108i | 0.283892 | − | 0.491716i | ||||
\(549\) | −5.96863 | − | 10.3380i | −0.254735 | − | 0.441214i | ||||
\(550\) | 1.00000 | + | 1.73205i | 0.0426401 | + | 0.0738549i | ||||
\(551\) | −5.29150 | + | 9.16515i | −0.225426 | + | 0.390449i | ||||
\(552\) | −2.64575 | −0.112611 | ||||||||
\(553\) | −14.0830 | − | 24.3925i | −0.598870 | − | 1.03727i | ||||
\(554\) | 17.1660 | 0.729314 | ||||||||
\(555\) | 1.70850 | − | 2.95920i | 0.0725217 | − | 0.125611i | ||||
\(556\) | 6.29150 | + | 10.8972i | 0.266819 | + | 0.462144i | ||||
\(557\) | 9.64575 | + | 16.7069i | 0.408704 | + | 0.707895i | 0.994745 | − | 0.102386i | \(-0.0326477\pi\) |
−0.586041 | + | 0.810281i | \(0.699314\pi\) | |||||||
\(558\) | −2.00000 | + | 3.46410i | −0.0846668 | + | 0.146647i | ||||
\(559\) | −37.1660 | −1.57195 | ||||||||
\(560\) | 7.00000 | 0.295804 | ||||||||
\(561\) | 3.00000 | 0.126660 | ||||||||
\(562\) | −1.50000 | + | 2.59808i | −0.0632737 | + | 0.109593i | ||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | −1.96863 | − | 3.40976i | −0.0828941 | − | 0.143577i | ||||
\(565\) | −16.6458 | + | 28.8313i | −0.700292 | + | 1.21294i | ||||
\(566\) | −30.4575 | −1.28022 | ||||||||
\(567\) | 2.64575 | 0.111111 | ||||||||
\(568\) | 2.70850 | 0.113646 | ||||||||
\(569\) | 7.58301 | − | 13.1342i | 0.317896 | − | 0.550612i | −0.662153 | − | 0.749369i | \(-0.730357\pi\) |
0.980049 | + | 0.198757i | \(0.0636903\pi\) | |||||||
\(570\) | −7.00000 | − | 12.1244i | −0.293198 | − | 0.507833i | ||||
\(571\) | 14.8745 | + | 25.7634i | 0.622479 | + | 1.07816i | 0.989023 | + | 0.147764i | \(0.0472076\pi\) |
−0.366544 | + | 0.930401i | \(0.619459\pi\) | |||||||
\(572\) | 2.00000 | − | 3.46410i | 0.0836242 | − | 0.144841i | ||||
\(573\) | −6.70850 | −0.280251 | ||||||||
\(574\) | 11.9059 | + | 20.6216i | 0.496942 | + | 0.860729i | ||||
\(575\) | −5.29150 | −0.220671 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −11.3745 | − | 19.7012i | −0.473527 | − | 0.820173i | 0.526014 | − | 0.850476i | \(-0.323686\pi\) |
−0.999541 | + | 0.0303033i | \(0.990353\pi\) | |||||||
\(578\) | −4.00000 | − | 6.92820i | −0.166378 | − | 0.288175i | ||||
\(579\) | −7.93725 | + | 13.7477i | −0.329861 | + | 0.571336i | ||||
\(580\) | 5.29150 | 0.219718 | ||||||||
\(581\) | −20.6144 | + | 35.7052i | −0.855229 | + | 1.48130i | ||||
\(582\) | −11.5830 | −0.480131 | ||||||||
\(583\) | −2.00000 | + | 3.46410i | −0.0828315 | + | 0.143468i | ||||
\(584\) | −7.64575 | − | 13.2428i | −0.316383 | − | 0.547992i | ||||
\(585\) | 5.29150 | + | 9.16515i | 0.218777 | + | 0.378932i | ||||
\(586\) | −7.29150 | + | 12.6293i | −0.301209 | + | 0.521710i | ||||
\(587\) | 9.87451 | 0.407565 | 0.203782 | − | 0.979016i | \(-0.434677\pi\) | ||||
0.203782 | + | 0.979016i | \(0.434677\pi\) | |||||||
\(588\) | −7.00000 | −0.288675 | ||||||||
\(589\) | −21.1660 | −0.872130 | ||||||||
\(590\) | 8.70850 | − | 15.0836i | 0.358523 | − | 0.620980i | ||||
\(591\) | 10.9373 | + | 18.9439i | 0.449899 | + | 0.779247i | ||||
\(592\) | −0.645751 | − | 1.11847i | −0.0265402 | − | 0.0459690i | ||||
\(593\) | 12.8745 | − | 22.2993i | 0.528693 | − | 0.915723i | −0.470748 | − | 0.882268i | \(-0.656016\pi\) |
0.999440 | − | 0.0334546i | \(-0.0106509\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 10.5000 | − | 18.1865i | 0.430458 | − | 0.745575i | ||||
\(596\) | 19.8745 | 0.814092 | ||||||||
\(597\) | −9.58301 | + | 16.5983i | −0.392206 | + | 0.679321i | ||||
\(598\) | 5.29150 | + | 9.16515i | 0.216386 | + | 0.374791i | ||||
\(599\) | −14.6771 | − | 25.4215i | −0.599691 | − | 1.03870i | −0.992866 | − | 0.119232i | \(-0.961957\pi\) |
0.393175 | − | 0.919463i | \(-0.371377\pi\) | |||||||
\(600\) | −1.00000 | + | 1.73205i | −0.0408248 | + | 0.0707107i | ||||
\(601\) | −38.5830 | −1.57383 | −0.786917 | − | 0.617059i | \(-0.788324\pi\) | ||||
−0.786917 | + | 0.617059i | \(0.788324\pi\) | |||||||
\(602\) | 12.2915 | + | 21.2895i | 0.500964 | + | 0.867696i | ||||
\(603\) | 7.58301 | 0.308804 | ||||||||
\(604\) | −11.3229 | + | 19.6118i | −0.460721 | + | 0.797993i | ||||
\(605\) | −1.32288 | − | 2.29129i | −0.0537825 | − | 0.0931541i | ||||
\(606\) | −3.64575 | − | 6.31463i | −0.148099 | − | 0.256514i | ||||
\(607\) | 6.55163 | − | 11.3478i | 0.265923 | − | 0.460591i | −0.701882 | − | 0.712293i | \(-0.747657\pi\) |
0.967805 | + | 0.251702i | \(0.0809901\pi\) | |||||||
\(608\) | −5.29150 | −0.214599 | ||||||||
\(609\) | −5.29150 | −0.214423 | ||||||||
\(610\) | −31.5830 | −1.27876 | ||||||||
\(611\) | −7.87451 | + | 13.6390i | −0.318568 | + | 0.551777i | ||||
\(612\) | 1.50000 | + | 2.59808i | 0.0606339 | + | 0.105021i | ||||
\(613\) | −3.90588 | − | 6.76518i | −0.157757 | − | 0.273243i | 0.776302 | − | 0.630361i | \(-0.217093\pi\) |
−0.934060 | + | 0.357117i | \(0.883760\pi\) | |||||||
\(614\) | −5.70850 | + | 9.88741i | −0.230376 | + | 0.399023i | ||||
\(615\) | −23.8118 | −0.960183 | ||||||||
\(616\) | −2.64575 | −0.106600 | ||||||||
\(617\) | −14.7085 | −0.592142 | −0.296071 | − | 0.955166i | \(-0.595676\pi\) | ||||
−0.296071 | + | 0.955166i | \(0.595676\pi\) | |||||||
\(618\) | 5.00000 | − | 8.66025i | 0.201129 | − | 0.348367i | ||||
\(619\) | 20.5000 | + | 35.5070i | 0.823965 | + | 1.42715i | 0.902708 | + | 0.430254i | \(0.141576\pi\) |
−0.0787435 | + | 0.996895i | \(0.525091\pi\) | |||||||
\(620\) | 5.29150 | + | 9.16515i | 0.212512 | + | 0.368081i | ||||
\(621\) | −1.32288 | + | 2.29129i | −0.0530852 | + | 0.0919462i | ||||
\(622\) | −22.5203 | −0.902980 | ||||||||
\(623\) | −3.58301 | − | 6.20595i | −0.143550 | − | 0.248636i | ||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 15.5000 | − | 26.8468i | 0.620000 | − | 1.07387i | ||||
\(626\) | −10.2915 | − | 17.8254i | −0.411331 | − | 0.712446i | ||||
\(627\) | 2.64575 | + | 4.58258i | 0.105661 | + | 0.183010i | ||||
\(628\) | 0.354249 | − | 0.613577i | 0.0141361 | − | 0.0244844i | ||||
\(629\) | −3.87451 | −0.154487 | ||||||||
\(630\) | 3.50000 | − | 6.06218i | 0.139443 | − | 0.241523i | ||||
\(631\) | 41.8745 | 1.66700 | 0.833499 | − | 0.552521i | \(-0.186334\pi\) | ||||
0.833499 | + | 0.552521i | \(0.186334\pi\) | |||||||
\(632\) | 5.32288 | − | 9.21949i | 0.211733 | − | 0.366732i | ||||
\(633\) | 10.6458 | + | 18.4390i | 0.423131 | + | 0.732884i | ||||
\(634\) | 4.61438 | + | 7.99234i | 0.183260 | + | 0.317416i | ||||
\(635\) | −3.50000 | + | 6.06218i | −0.138893 | + | 0.240570i | ||||
\(636\) | −4.00000 | −0.158610 | ||||||||
\(637\) | 14.0000 | + | 24.2487i | 0.554700 | + | 0.960769i | ||||
\(638\) | −2.00000 | −0.0791808 | ||||||||
\(639\) | 1.35425 | − | 2.34563i | 0.0535733 | − | 0.0927916i | ||||
\(640\) | 1.32288 | + | 2.29129i | 0.0522913 | + | 0.0905711i | ||||
\(641\) | 13.2915 | + | 23.0216i | 0.524983 | + | 0.909297i | 0.999577 | + | 0.0290920i | \(0.00926158\pi\) |
−0.474594 | + | 0.880205i | \(0.657405\pi\) | |||||||
\(642\) | −4.50000 | + | 7.79423i | −0.177601 | + | 0.307614i | ||||
\(643\) | −1.16601 | −0.0459830 | −0.0229915 | − | 0.999736i | \(-0.507319\pi\) | ||||
−0.0229915 | + | 0.999736i | \(0.507319\pi\) | |||||||
\(644\) | 3.50000 | − | 6.06218i | 0.137919 | − | 0.238883i | ||||
\(645\) | −24.5830 | −0.967955 | ||||||||
\(646\) | −7.93725 | + | 13.7477i | −0.312287 | + | 0.540897i | ||||
\(647\) | 13.1974 | + | 22.8585i | 0.518843 | + | 0.898662i | 0.999760 | + | 0.0218961i | \(0.00697029\pi\) |
−0.480918 | + | 0.876766i | \(0.659696\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −3.29150 | + | 5.70105i | −0.129203 | + | 0.223786i | ||||
\(650\) | 8.00000 | 0.313786 | ||||||||
\(651\) | −5.29150 | − | 9.16515i | −0.207390 | − | 0.359211i | ||||
\(652\) | −5.58301 | −0.218647 | ||||||||
\(653\) | 22.5516 | − | 39.0606i | 0.882514 | − | 1.52856i | 0.0339763 | − | 0.999423i | \(-0.489183\pi\) |
0.848537 | − | 0.529136i | \(-0.177484\pi\) | |||||||
\(654\) | 1.96863 | + | 3.40976i | 0.0769794 | + | 0.133332i | ||||
\(655\) | 24.5830 | + | 42.5790i | 0.960537 | + | 1.66370i | ||||
\(656\) | −4.50000 | + | 7.79423i | −0.175695 | + | 0.304314i | ||||
\(657\) | −15.2915 | −0.596578 | ||||||||
\(658\) | 10.4170 | 0.406097 | ||||||||
\(659\) | −24.1660 | −0.941374 | −0.470687 | − | 0.882300i | \(-0.655994\pi\) | ||||
−0.470687 | + | 0.882300i | \(0.655994\pi\) | |||||||
\(660\) | 1.32288 | − | 2.29129i | 0.0514929 | − | 0.0891883i | ||||
\(661\) | −10.3542 | − | 17.9341i | −0.402734 | − | 0.697555i | 0.591321 | − | 0.806436i | \(-0.298607\pi\) |
−0.994055 | + | 0.108881i | \(0.965273\pi\) | |||||||
\(662\) | 6.50000 | + | 11.2583i | 0.252630 | + | 0.437567i | ||||
\(663\) | 6.00000 | − | 10.3923i | 0.233021 | − | 0.403604i | ||||
\(664\) | −15.5830 | −0.604738 | ||||||||
\(665\) | 37.0405 | 1.43637 | ||||||||
\(666\) | −1.29150 | −0.0500447 | ||||||||
\(667\) | 2.64575 | − | 4.58258i | 0.102444 | − | 0.177438i | ||||
\(668\) | −4.35425 | − | 7.54178i | −0.168471 | − | 0.291800i | ||||
\(669\) | 14.2288 | + | 24.6449i | 0.550116 | + | 0.952828i | ||||
\(670\) | 10.0314 | − | 17.3748i | 0.387546 | − | 0.671249i | ||||
\(671\) | 11.9373 | 0.460833 | ||||||||
\(672\) | −1.32288 | − | 2.29129i | −0.0510310 | − | 0.0883883i | ||||
\(673\) | −19.4170 | −0.748470 | −0.374235 | − | 0.927334i | \(-0.622095\pi\) | ||||
−0.374235 | + | 0.927334i | \(0.622095\pi\) | |||||||
\(674\) | 3.35425 | − | 5.80973i | 0.129201 | − | 0.223782i | ||||
\(675\) | 1.00000 | + | 1.73205i | 0.0384900 | + | 0.0666667i | ||||
\(676\) | −1.50000 | − | 2.59808i | −0.0576923 | − | 0.0999260i | ||||
\(677\) | 4.06275 | − | 7.03688i | 0.156144 | − | 0.270449i | −0.777331 | − | 0.629092i | \(-0.783427\pi\) |
0.933475 | + | 0.358642i | \(0.116760\pi\) | |||||||
\(678\) | 12.5830 | 0.483247 | ||||||||
\(679\) | 15.3229 | − | 26.5400i | 0.588038 | − | 1.01851i | ||||
\(680\) | 7.93725 | 0.304380 | ||||||||
\(681\) | 1.20850 | − | 2.09318i | 0.0463097 | − | 0.0802108i | ||||
\(682\) | −2.00000 | − | 3.46410i | −0.0765840 | − | 0.132647i | ||||
\(683\) | 8.58301 | + | 14.8662i | 0.328420 | + | 0.568839i | 0.982198 | − | 0.187846i | \(-0.0601507\pi\) |
−0.653779 | + | 0.756686i | \(0.726817\pi\) | |||||||
\(684\) | −2.64575 | + | 4.58258i | −0.101163 | + | 0.175219i | ||||
\(685\) | −35.1660 | −1.34362 | ||||||||
\(686\) | 9.26013 | − | 16.0390i | 0.353553 | − | 0.612372i | ||||
\(687\) | −6.70850 | −0.255945 | ||||||||
\(688\) | −4.64575 | + | 8.04668i | −0.177118 | + | 0.306777i | ||||
\(689\) | 8.00000 | + | 13.8564i | 0.304776 | + | 0.527887i | ||||
\(690\) | 3.50000 | + | 6.06218i | 0.133243 | + | 0.230783i | ||||
\(691\) | −7.08301 | + | 12.2681i | −0.269450 | + | 0.466701i | −0.968720 | − | 0.248156i | \(-0.920175\pi\) |
0.699270 | + | 0.714858i | \(0.253509\pi\) | |||||||
\(692\) | 4.00000 | 0.152057 | ||||||||
\(693\) | −1.32288 | + | 2.29129i | −0.0502519 | + | 0.0870388i | ||||
\(694\) | −29.5830 | −1.12296 | ||||||||
\(695\) | 16.6458 | − | 28.8313i | 0.631409 | − | 1.09363i | ||||
\(696\) | −1.00000 | − | 1.73205i | −0.0379049 | − | 0.0656532i | ||||
\(697\) | 13.5000 | + | 23.3827i | 0.511349 | + | 0.885682i | ||||
\(698\) | −6.61438 | + | 11.4564i | −0.250358 | + | 0.433633i | ||||
\(699\) | −20.1660 | −0.762749 | ||||||||
\(700\) | −2.64575 | − | 4.58258i | −0.100000 | − | 0.173205i | ||||
\(701\) | 42.4575 | 1.60360 | 0.801799 | − | 0.597594i | \(-0.203876\pi\) | ||||
0.801799 | + | 0.597594i | \(0.203876\pi\) | |||||||
\(702\) | 2.00000 | − | 3.46410i | 0.0754851 | − | 0.130744i | ||||
\(703\) | −3.41699 | − | 5.91841i | −0.128874 | − | 0.223217i | ||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | −5.20850 | + | 9.02138i | −0.196163 | + | 0.339765i | ||||
\(706\) | 23.2915 | 0.876587 | ||||||||
\(707\) | 19.2915 | 0.725532 | ||||||||
\(708\) | −6.58301 | −0.247404 | ||||||||
\(709\) | −7.87451 | + | 13.6390i | −0.295733 | + | 0.512225i | −0.975155 | − | 0.221523i | \(-0.928897\pi\) |
0.679422 | + | 0.733748i | \(0.262231\pi\) | |||||||
\(710\) | −3.58301 | − | 6.20595i | −0.134468 | − | 0.232905i | ||||
\(711\) | −5.32288 | − | 9.21949i | −0.199623 | − | 0.345758i | ||||
\(712\) | 1.35425 | − | 2.34563i | 0.0507526 | − | 0.0879061i | ||||
\(713\) | 10.5830 | 0.396337 | ||||||||
\(714\) | −7.93725 | −0.297044 | ||||||||
\(715\) | −10.5830 | −0.395782 | ||||||||
\(716\) | −2.35425 | + | 4.07768i | −0.0879824 | + | 0.152390i | ||||
\(717\) | 1.35425 | + | 2.34563i | 0.0505753 | + | 0.0875991i | ||||
\(718\) | 10.2915 | + | 17.8254i | 0.384075 | + | 0.665238i | ||||
\(719\) | 14.0314 | − | 24.3031i | 0.523282 | − | 0.906351i | −0.476351 | − | 0.879255i | \(-0.658041\pi\) |
0.999633 | − | 0.0270956i | \(-0.00862586\pi\) | |||||||
\(720\) | 2.64575 | 0.0986013 | ||||||||
\(721\) | 13.2288 | + | 22.9129i | 0.492665 | + | 0.853320i | ||||
\(722\) | −9.00000 | −0.334945 | ||||||||
\(723\) | −13.5830 | + | 23.5265i | −0.505157 | + | 0.874958i | ||||
\(724\) | 2.64575 | + | 4.58258i | 0.0983286 | + | 0.170310i | ||||
\(725\) | −2.00000 | − | 3.46410i | −0.0742781 | − | 0.128654i | ||||
\(726\) | −0.500000 | + | 0.866025i | −0.0185567 | + | 0.0321412i | ||||
\(727\) | −2.00000 | −0.0741759 | −0.0370879 | − | 0.999312i | \(-0.511808\pi\) | ||||
−0.0370879 | + | 0.999312i | \(0.511808\pi\) | |||||||
\(728\) | −5.29150 | + | 9.16515i | −0.196116 | + | 0.339683i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −20.2288 | + | 35.0372i | −0.748700 | + | 1.29679i | ||||
\(731\) | 13.9373 | + | 24.1400i | 0.515488 | + | 0.892851i | ||||
\(732\) | 5.96863 | + | 10.3380i | 0.220607 | + | 0.382102i | ||||
\(733\) | −5.96863 | + | 10.3380i | −0.220456 | + | 0.381841i | −0.954947 | − | 0.296778i | \(-0.904088\pi\) |
0.734490 | + | 0.678619i | \(0.237421\pi\) | |||||||
\(734\) | −10.7085 | −0.395258 | ||||||||
\(735\) | 9.26013 | + | 16.0390i | 0.341565 | + | 0.591608i | ||||
\(736\) | 2.64575 | 0.0975237 | ||||||||
\(737\) | −3.79150 | + | 6.56708i | −0.139662 | + | 0.241901i | ||||
\(738\) | 4.50000 | + | 7.79423i | 0.165647 | + | 0.286910i | ||||
\(739\) | 12.2915 | + | 21.2895i | 0.452150 | + | 0.783147i | 0.998519 | − | 0.0543973i | \(-0.0173238\pi\) |
−0.546369 | + | 0.837544i | \(0.683990\pi\) | |||||||
\(740\) | −1.70850 | + | 2.95920i | −0.0628056 | + | 0.108783i | ||||
\(741\) | 21.1660 | 0.777553 | ||||||||
\(742\) | 5.29150 | − | 9.16515i | 0.194257 | − | 0.336463i | ||||
\(743\) | −18.7085 | −0.686348 | −0.343174 | − | 0.939272i | \(-0.611502\pi\) | ||||
−0.343174 | + | 0.939272i | \(0.611502\pi\) | |||||||
\(744\) | 2.00000 | − | 3.46410i | 0.0733236 | − | 0.127000i | ||||
\(745\) | −26.2915 | − | 45.5382i | −0.963246 | − | 1.66839i | ||||
\(746\) | −7.90588 | − | 13.6934i | −0.289455 | − | 0.501351i | ||||
\(747\) | −7.79150 | + | 13.4953i | −0.285076 | + | 0.493766i | ||||
\(748\) | −3.00000 | −0.109691 | ||||||||
\(749\) | −11.9059 | − | 20.6216i | −0.435031 | − | 0.753497i | ||||
\(750\) | −7.93725 | −0.289828 | ||||||||
\(751\) | 14.6458 | − | 25.3672i | 0.534431 | − | 0.925662i | −0.464760 | − | 0.885437i | \(-0.653859\pi\) |
0.999191 | − | 0.0402248i | \(-0.0128074\pi\) | |||||||
\(752\) | 1.96863 | + | 3.40976i | 0.0717884 | + | 0.124341i | ||||
\(753\) | 11.6458 | + | 20.1710i | 0.424395 | + | 0.735073i | ||||
\(754\) | −4.00000 | + | 6.92820i | −0.145671 | + | 0.252310i | ||||
\(755\) | 59.9150 | 2.18053 | ||||||||
\(756\) | −2.64575 | −0.0962250 | ||||||||
\(757\) | −32.5830 | −1.18425 | −0.592125 | − | 0.805846i | \(-0.701711\pi\) | ||||
−0.592125 | + | 0.805846i | \(0.701711\pi\) | |||||||
\(758\) | −13.7915 | + | 23.8876i | −0.500930 | + | 0.867636i | ||||
\(759\) | −1.32288 | − | 2.29129i | −0.0480173 | − | 0.0831685i | ||||
\(760\) | 7.00000 | + | 12.1244i | 0.253917 | + | 0.439797i | ||||
\(761\) | −23.7915 | + | 41.2081i | −0.862441 | + | 1.49379i | 0.00712426 | + | 0.999975i | \(0.497732\pi\) |
−0.869566 | + | 0.493818i | \(0.835601\pi\) | |||||||
\(762\) | 2.64575 | 0.0958455 | ||||||||
\(763\) | −10.4170 | −0.377121 | ||||||||
\(764\) | 6.70850 | 0.242705 | ||||||||
\(765\) | 3.96863 | − | 6.87386i | 0.143486 | − | 0.248525i | ||||
\(766\) | 9.35425 | + | 16.2020i | 0.337983 | + | 0.585403i | ||||
\(767\) | 13.1660 | + | 22.8042i | 0.475397 | + | 0.823412i | ||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | −30.7085 | −1.10738 | −0.553688 | − | 0.832724i | \(-0.686780\pi\) | ||||
−0.553688 | + | 0.832724i | \(0.686780\pi\) | |||||||
\(770\) | 3.50000 | + | 6.06218i | 0.126131 | + | 0.218466i | ||||
\(771\) | −9.29150 | −0.334625 | ||||||||
\(772\) | 7.93725 | − | 13.7477i | 0.285668 | − | 0.494792i | ||||
\(773\) | 4.03137 | + | 6.98254i | 0.144998 | + | 0.251145i | 0.929372 | − | 0.369144i | \(-0.120349\pi\) |
−0.784374 | + | 0.620288i | \(0.787016\pi\) | |||||||
\(774\) | 4.64575 | + | 8.04668i | 0.166988 | + | 0.289232i | ||||
\(775\) | 4.00000 | − | 6.92820i | 0.143684 | − | 0.248868i | ||||
\(776\) | 11.5830 | 0.415806 | ||||||||
\(777\) | 1.70850 | − | 2.95920i | 0.0612920 | − | 0.106161i | ||||
\(778\) | −31.9373 | −1.14501 | ||||||||
\(779\) | −23.8118 | + | 41.2432i | −0.853145 | + | 1.47769i | ||||
\(780\) | −5.29150 | − | 9.16515i | −0.189466 | − | 0.328165i | ||||
\(781\) | 1.35425 | + | 2.34563i | 0.0484588 | + | 0.0839332i | ||||
\(782\) | 3.96863 | − | 6.87386i | 0.141918 | − | 0.245809i | ||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 7.00000 | 0.250000 | ||||||||
\(785\) | −1.87451 | −0.0669041 | ||||||||
\(786\) | 9.29150 | − | 16.0934i | 0.331417 | − | 0.574031i | ||||
\(787\) | −4.64575 | − | 8.04668i | −0.165603 | − | 0.286833i | 0.771266 | − | 0.636513i | \(-0.219624\pi\) |
−0.936869 | + | 0.349680i | \(0.886290\pi\) | |||||||
\(788\) | −10.9373 | − | 18.9439i | −0.389624 | − | 0.674848i | ||||
\(789\) | 10.9373 | − | 18.9439i | 0.389377 | − | 0.674420i | ||||
\(790\) | −28.1660 | −1.00210 | ||||||||
\(791\) | −16.6458 | + | 28.8313i | −0.591855 | + | 1.02512i | ||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 23.8745 | − | 41.3519i | 0.847809 | − | 1.46845i | ||||
\(794\) | 3.00000 | + | 5.19615i | 0.106466 | + | 0.184405i | ||||
\(795\) | 5.29150 | + | 9.16515i | 0.187670 | + | 0.325054i | ||||
\(796\) | 9.58301 | − | 16.5983i | 0.339661 | − | 0.588309i | ||||
\(797\) | 45.1033 | 1.59764 | 0.798820 | − | 0.601570i | \(-0.205458\pi\) | ||||
0.798820 | + | 0.601570i | \(0.205458\pi\) | |||||||
\(798\) | −7.00000 | − | 12.1244i | −0.247797 | − | 0.429198i | ||||
\(799\) | 11.8118 | 0.417870 | ||||||||
\(800\) | 1.00000 | − | 1.73205i | 0.0353553 | − | 0.0612372i | ||||
\(801\) | −1.35425 | − | 2.34563i | −0.0478500 | − | 0.0828787i | ||||
\(802\) | −17.9373 | − | 31.0682i | −0.633386 | − | 1.09706i | ||||
\(803\) | 7.64575 | − | 13.2428i | 0.269813 | − | 0.467329i | ||||
\(804\) | −7.58301 | −0.267432 | ||||||||
\(805\) | −18.5203 | −0.652753 | ||||||||
\(806\) | −16.0000 | −0.563576 | ||||||||
\(807\) | −5.32288 | + | 9.21949i | −0.187374 | + | 0.324541i | ||||
\(808\) | 3.64575 | + | 6.31463i | 0.128257 | + | 0.222148i | ||||
\(809\) | −22.6660 | − | 39.2587i | −0.796894 | − | 1.38026i | −0.921629 | − | 0.388072i | \(-0.873141\pi\) |
0.124735 | − | 0.992190i | \(-0.460192\pi\) | |||||||
\(810\) | 1.32288 | − | 2.29129i | 0.0464811 | − | 0.0805076i | ||||
\(811\) | 16.5830 | 0.582308 | 0.291154 | − | 0.956676i | \(-0.405961\pi\) | ||||
0.291154 | + | 0.956676i | \(0.405961\pi\) | |||||||
\(812\) | 5.29150 | 0.185695 | ||||||||
\(813\) | −9.29150 | −0.325867 | ||||||||
\(814\) | 0.645751 | − | 1.11847i | 0.0226336 | − | 0.0392025i | ||||
\(815\) | 7.38562 | + | 12.7923i | 0.258707 | + | 0.448094i | ||||
\(816\) | −1.50000 | − | 2.59808i | −0.0525105 | − | 0.0909509i | ||||
\(817\) | −24.5830 | + | 42.5790i | −0.860050 | + | 1.48965i | ||||
\(818\) | −35.8745 | −1.25432 | ||||||||
\(819\) | 5.29150 | + | 9.16515i | 0.184900 | + | 0.320256i | ||||
\(820\) | 23.8118 | 0.831543 | ||||||||
\(821\) | 15.1660 | − | 26.2683i | 0.529297 | − | 0.916770i | −0.470119 | − | 0.882603i | \(-0.655789\pi\) |
0.999416 | − | 0.0341668i | \(-0.0108778\pi\) | |||||||
\(822\) | 6.64575 | + | 11.5108i | 0.231797 | + | 0.401485i | ||||
\(823\) | 6.06275 | + | 10.5010i | 0.211334 | + | 0.366041i | 0.952132 | − | 0.305686i | \(-0.0988859\pi\) |
−0.740798 | + | 0.671728i | \(0.765553\pi\) | |||||||
\(824\) | −5.00000 | + | 8.66025i | −0.174183 | + | 0.301694i | ||||
\(825\) | −2.00000 | −0.0696311 | ||||||||
\(826\) | 8.70850 | − | 15.0836i | 0.303007 | − | 0.524824i | ||||
\(827\) | 35.3320 | 1.22861 | 0.614307 | − | 0.789067i | \(-0.289435\pi\) | ||||
0.614307 | + | 0.789067i | \(0.289435\pi\) | |||||||
\(828\) | 1.32288 | − | 2.29129i | 0.0459731 | − | 0.0796278i | ||||
\(829\) | −9.93725 | − | 17.2118i | −0.345135 | − | 0.597792i | 0.640243 | − | 0.768172i | \(-0.278834\pi\) |
−0.985378 | + | 0.170381i | \(0.945500\pi\) | |||||||
\(830\) | 20.6144 | + | 35.7052i | 0.715536 | + | 1.23934i | ||||
\(831\) | −8.58301 | + | 14.8662i | −0.297741 | + | 0.515703i | ||||
\(832\) | −4.00000 | −0.138675 | ||||||||
\(833\) | 10.5000 | − | 18.1865i | 0.363803 | − | 0.630126i | ||||
\(834\) | −12.5830 | −0.435714 | ||||||||
\(835\) | −11.5203 | + | 19.9537i | −0.398675 | + | 0.690525i | ||||
\(836\) | −2.64575 | − | 4.58258i | −0.0915052 | − | 0.158492i | ||||
\(837\) | −2.00000 | − | 3.46410i | −0.0691301 | − | 0.119737i | ||||
\(838\) | −4.93725 | + | 8.55157i | −0.170555 | + | 0.295409i | ||||
\(839\) | −37.1033 | −1.28095 | −0.640473 | − | 0.767980i | \(-0.721262\pi\) | ||||
−0.640473 | + | 0.767980i | \(0.721262\pi\) | |||||||
\(840\) | −3.50000 | + | 6.06218i | −0.120761 | + | 0.209165i | ||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 3.06275 | − | 5.30483i | 0.105549 | − | 0.182817i | ||||
\(843\) | −1.50000 | − | 2.59808i | −0.0516627 | − | 0.0894825i | ||||
\(844\) | −10.6458 | − | 18.4390i | −0.366442 | − | 0.634696i | ||||
\(845\) | −3.96863 | + | 6.87386i | −0.136525 | + | 0.236468i | ||||
\(846\) | 3.93725 | 0.135366 | ||||||||
\(847\) | −1.32288 | − | 2.29129i | −0.0454545 | − | 0.0787296i | ||||
\(848\) | 4.00000 | 0.137361 | ||||||||
\(849\) | 15.2288 | − | 26.3770i | 0.522650 | − | 0.905256i | ||||
\(850\) | −3.00000 | − | 5.19615i | −0.102899 | − | 0.178227i | ||||
\(851\) | 1.70850 | + | 2.95920i | 0.0585665 | + | 0.101440i | ||||
\(852\) | −1.35425 | + | 2.34563i | −0.0463958 | + | 0.0803599i | ||||
\(853\) | 14.5203 | 0.497164 | 0.248582 | − | 0.968611i | \(-0.420035\pi\) | ||||
0.248582 | + | 0.968611i | \(0.420035\pi\) | |||||||
\(854\) | −31.5830 | −1.08075 | ||||||||
\(855\) | 14.0000 | 0.478790 | ||||||||
\(856\) | 4.50000 | − | 7.79423i | 0.153807 | − | 0.266401i | ||||
\(857\) | −4.91699 | − | 8.51648i | −0.167961 | − | 0.290918i | 0.769742 | − | 0.638356i | \(-0.220385\pi\) |
−0.937703 | + | 0.347438i | \(0.887052\pi\) | |||||||
\(858\) | 2.00000 | + | 3.46410i | 0.0682789 | + | 0.118262i | ||||
\(859\) | −24.3745 | + | 42.2179i | −0.831647 | + | 1.44046i | 0.0650836 | + | 0.997880i | \(0.479269\pi\) |
−0.896731 | + | 0.442576i | \(0.854065\pi\) | |||||||
\(860\) | 24.5830 | 0.838274 | ||||||||
\(861\) | −23.8118 | −0.811503 | ||||||||
\(862\) | 17.2915 | 0.588951 | ||||||||
\(863\) | 16.5516 | − | 28.6683i | 0.563424 | − | 0.975879i | −0.433770 | − | 0.901024i | \(-0.642817\pi\) |
0.997194 | − | 0.0748557i | \(-0.0238496\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −5.29150 | − | 9.16515i | −0.179916 | − | 0.311624i | ||||
\(866\) | 0.791503 | − | 1.37092i | 0.0268964 | − | 0.0465859i | ||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | 5.29150 | + | 9.16515i | 0.179605 | + | 0.311086i | ||||
\(869\) | 10.6458 | 0.361132 | ||||||||
\(870\) | −2.64575 | + | 4.58258i | −0.0896994 | + | 0.155364i | ||||
\(871\) | 15.1660 | + | 26.2683i | 0.513881 | + | 0.890067i | ||||
\(872\) | −1.96863 | − | 3.40976i | −0.0666661 | − | 0.115469i | ||||
\(873\) | 5.79150 | − | 10.0312i | 0.196013 | − | 0.339504i | ||||
\(874\) | 14.0000 | 0.473557 | ||||||||
\(875\) | 10.5000 | − | 18.1865i | 0.354965 | − | 0.614817i | ||||
\(876\) | 15.2915 | 0.516652 | ||||||||
\(877\) | −5.38562 | + | 9.32817i | −0.181860 | + | 0.314990i | −0.942514 | − | 0.334167i | \(-0.891545\pi\) |
0.760654 | + | 0.649157i | \(0.224878\pi\) | |||||||
\(878\) | −4.67712 | − | 8.10102i | −0.157845 | − | 0.273396i | ||||
\(879\) | −7.29150 | − | 12.6293i | −0.245936 | − | 0.425974i | ||||
\(880\) | −1.32288 | + | 2.29129i | −0.0445941 | + | 0.0772393i | ||||
\(881\) | 23.1660 | 0.780483 | 0.390241 | − | 0.920713i | \(-0.372392\pi\) | ||||
0.390241 | + | 0.920713i | \(0.372392\pi\) | |||||||
\(882\) | 3.50000 | − | 6.06218i | 0.117851 | − | 0.204124i | ||||
\(883\) | −34.4170 | −1.15822 | −0.579112 | − | 0.815248i | \(-0.696601\pi\) | ||||
−0.579112 | + | 0.815248i | \(0.696601\pi\) | |||||||
\(884\) | −6.00000 | + | 10.3923i | −0.201802 | + | 0.349531i | ||||
\(885\) | 8.70850 | + | 15.0836i | 0.292733 | + | 0.507028i | ||||
\(886\) | −15.5830 | − | 26.9906i | −0.523521 | − | 0.906765i | ||||
\(887\) | 15.5203 | − | 26.8819i | 0.521119 | − | 0.902605i | −0.478579 | − | 0.878044i | \(-0.658848\pi\) |
0.999698 | − | 0.0245606i | \(-0.00781868\pi\) | |||||||
\(888\) | 1.29150 | 0.0433400 | ||||||||
\(889\) | −3.50000 | + | 6.06218i | −0.117386 | + | 0.203319i | ||||
\(890\) | −7.16601 | −0.240205 | ||||||||
\(891\) | −0.500000 | + | 0.866025i | −0.0167506 | + | 0.0290129i | ||||
\(892\) | −14.2288 | − | 24.6449i | −0.476414 | − | 0.825173i | ||||
\(893\) | 10.4170 | + | 18.0428i | 0.348591 | + | 0.603778i | ||||
\(894\) | −9.93725 | + | 17.2118i | −0.332351 | + | 0.575650i | ||||
\(895\) | 12.4575 | 0.416409 | ||||||||
\(896\) | 1.32288 | + | 2.29129i | 0.0441942 | + | 0.0765466i | ||||
\(897\) | −10.5830 | −0.353356 | ||||||||
\(898\) | 15.2288 | − | 26.3770i | 0.508190 | − | 0.880211i | ||||
\(899\) | 4.00000 | + | 6.92820i | 0.133407 | + | 0.231069i | ||||
\(900\) | −1.00000 | − | 1.73205i | −0.0333333 | − | 0.0577350i | ||||
\(901\) | 6.00000 | − | 10.3923i | 0.199889 | − | 0.346218i | ||||
\(902\) | −9.00000 | −0.299667 | ||||||||
\(903\) | −24.5830 | −0.818071 | ||||||||
\(904\) | −12.5830 | −0.418505 | ||||||||
\(905\) | 7.00000 | − | 12.1244i | 0.232688 | − | 0.403027i | ||||
\(906\) | −11.3229 | − | 19.6118i | −0.376177 | − | 0.651558i | ||||
\(907\) | 7.91699 | + | 13.7126i | 0.262879 | + | 0.455321i | 0.967006 | − | 0.254754i | \(-0.0819945\pi\) |
−0.704126 | + | 0.710075i | \(0.748661\pi\) | |||||||
\(908\) | −1.20850 | + | 2.09318i | −0.0401054 | + | 0.0694646i | ||||
\(909\) | 7.29150 | 0.241844 | ||||||||
\(910\) | 28.0000 | 0.928191 | ||||||||
\(911\) | −18.3948 | −0.609446 | −0.304723 | − | 0.952441i | \(-0.598564\pi\) | ||||
−0.304723 | + | 0.952441i | \(0.598564\pi\) | |||||||
\(912\) | 2.64575 | − | 4.58258i | 0.0876096 | − | 0.151744i | ||||
\(913\) | −7.79150 | − | 13.4953i | −0.257861 | − | 0.446629i | ||||
\(914\) | −20.2915 | − | 35.1459i | −0.671183 | − | 1.16252i | ||||
\(915\) | 15.7915 | − | 27.3517i | 0.522051 | − | 0.904219i | ||||
\(916\) | 6.70850 | 0.221655 | ||||||||
\(917\) | 24.5830 | + | 42.5790i | 0.811802 | + | 1.40608i | ||||
\(918\) | −3.00000 | −0.0990148 | ||||||||
\(919\) | −4.67712 | + | 8.10102i | −0.154284 | + | 0.267228i | −0.932798 | − | 0.360399i | \(-0.882640\pi\) |
0.778514 | + | 0.627627i | \(0.215974\pi\) | |||||||
\(920\) | −3.50000 | − | 6.06218i | −0.115392 | − | 0.199864i | ||||
\(921\) | −5.70850 | − | 9.88741i | −0.188101 | − | 0.325801i | ||||
\(922\) | −12.2915 | + | 21.2895i | −0.404799 | + | 0.701133i | ||||
\(923\) | 10.8340 | 0.356605 | ||||||||
\(924\) | 1.32288 | − | 2.29129i | 0.0435194 | − | 0.0753778i | ||||
\(925\) | 2.58301 | 0.0849287 | ||||||||
\(926\) | 19.5203 | − | 33.8101i | 0.641476 | − | 1.11107i | ||||
\(927\) | 5.00000 | + | 8.66025i | 0.164222 | + | 0.284440i | ||||
\(928\) | 1.00000 | + | 1.73205i | 0.0328266 | + | 0.0568574i | ||||
\(929\) | 17.2288 | − | 29.8411i | 0.565257 | − | 0.979054i | −0.431769 | − | 0.901984i | \(-0.642110\pi\) |
0.997026 | − | 0.0770697i | \(-0.0245564\pi\) | |||||||
\(930\) | −10.5830 | −0.347030 | ||||||||
\(931\) | 37.0405 | 1.21395 | ||||||||
\(932\) | 20.1660 | 0.660560 | ||||||||
\(933\) | 11.2601 | − | 19.5031i | 0.368640 | − | 0.638503i | ||||
\(934\) | 4.00000 | + | 6.92820i | 0.130884 | + | 0.226698i | ||||
\(935\) | 3.96863 | + | 6.87386i | 0.129788 | + | 0.224799i | ||||
\(936\) | −2.00000 | + | 3.46410i | −0.0653720 | + | 0.113228i | ||||
\(937\) | 50.0000 | 1.63343 | 0.816714 | − | 0.577042i | \(-0.195793\pi\) | ||||
0.816714 | + | 0.577042i | \(0.195793\pi\) | |||||||
\(938\) | 10.0314 | − | 17.3748i | 0.327536 | − | 0.567309i | ||||
\(939\) | 20.5830 | 0.671701 | ||||||||
\(940\) | 5.20850 | − | 9.02138i | 0.169882 | − | 0.294245i | ||||
\(941\) | −1.70850 | − | 2.95920i | −0.0556954 | − | 0.0964673i | 0.836833 | − | 0.547458i | \(-0.184404\pi\) |
−0.892529 | + | 0.450990i | \(0.851071\pi\) | |||||||
\(942\) | 0.354249 | + | 0.613577i | 0.0115420 | + | 0.0199914i | ||||
\(943\) | 11.9059 | − | 20.6216i | 0.387709 | − | 0.671531i | ||||
\(944\) | 6.58301 | 0.214259 | ||||||||
\(945\) | 3.50000 | + | 6.06218i | 0.113855 | + | 0.197203i | ||||
\(946\) | −9.29150 | −0.302093 | ||||||||
\(947\) | 7.70850 | − | 13.3515i | 0.250493 | − | 0.433866i | −0.713169 | − | 0.700992i | \(-0.752741\pi\) |
0.963662 | + | 0.267126i | \(0.0860741\pi\) | |||||||
\(948\) | 5.32288 | + | 9.21949i | 0.172879 | + | 0.299435i | ||||
\(949\) | −30.5830 | − | 52.9713i | −0.992766 | − | 1.71952i | ||||
\(950\) | 5.29150 | − | 9.16515i | 0.171679 | − | 0.297357i | ||||
\(951\) | −9.22876 | −0.299263 | ||||||||
\(952\) | 7.93725 | 0.257248 | ||||||||
\(953\) | 26.7490 | 0.866486 | 0.433243 | − | 0.901277i | \(-0.357369\pi\) | ||||
0.433243 | + | 0.901277i | \(0.357369\pi\) | |||||||
\(954\) | 2.00000 | − | 3.46410i | 0.0647524 | − | 0.112154i | ||||
\(955\) | −8.87451 | − | 15.3711i | −0.287172 | − | 0.497397i | ||||
\(956\) | −1.35425 | − | 2.34563i | −0.0437995 | − | 0.0758630i | ||||
\(957\) | 1.00000 | − | 1.73205i | 0.0323254 | − | 0.0559893i | ||||
\(958\) | 33.8745 | 1.09444 | ||||||||
\(959\) | −35.1660 | −1.13557 | ||||||||
\(960\) | −2.64575 | −0.0853913 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | −2.58301 | − | 4.47390i | −0.0832794 | − | 0.144244i | ||||
\(963\) | −4.50000 | − | 7.79423i | −0.145010 | − | 0.251166i | ||||
\(964\) | 13.5830 | − | 23.5265i | 0.437479 | − | 0.757736i | ||||
\(965\) | −42.0000 | −1.35203 | ||||||||
\(966\) | 3.50000 | + | 6.06218i | 0.112611 | + | 0.195047i | ||||
\(967\) | 40.0627 | 1.28833 | 0.644166 | − | 0.764886i | \(-0.277205\pi\) | ||||
0.644166 | + | 0.764886i | \(0.277205\pi\) | |||||||
\(968\) | 0.500000 | − | 0.866025i | 0.0160706 | − | 0.0278351i | ||||
\(969\) | −7.93725 | − | 13.7477i | −0.254981 | − | 0.441641i | ||||
\(970\) | −15.3229 | − | 26.5400i | −0.491988 | − | 0.852148i | ||||
\(971\) | −3.00000 | + | 5.19615i | −0.0962746 | + | 0.166752i | −0.910140 | − | 0.414301i | \(-0.864026\pi\) |
0.813865 | + | 0.581054i | \(0.197359\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 16.6458 | − | 28.8313i | 0.533638 | − | 0.924289i | ||||
\(974\) | −21.8745 | −0.700904 | ||||||||
\(975\) | −4.00000 | + | 6.92820i | −0.128103 | + | 0.221880i | ||||
\(976\) | −5.96863 | − | 10.3380i | −0.191051 | − | 0.330910i | ||||
\(977\) | −6.58301 | − | 11.4021i | −0.210609 | − | 0.364785i | 0.741296 | − | 0.671178i | \(-0.234211\pi\) |
−0.951905 | + | 0.306392i | \(0.900878\pi\) | |||||||
\(978\) | 2.79150 | − | 4.83502i | 0.0892624 | − | 0.154607i | ||||
\(979\) | 2.70850 | 0.0865640 | ||||||||
\(980\) | −9.26013 | − | 16.0390i | −0.295804 | − | 0.512348i | ||||
\(981\) | −3.93725 | −0.125707 | ||||||||
\(982\) | −0.500000 | + | 0.866025i | −0.0159556 | + | 0.0276360i | ||||
\(983\) | −21.2601 | − | 36.8236i | −0.678093 | − | 1.17449i | −0.975555 | − | 0.219757i | \(-0.929473\pi\) |
0.297462 | − | 0.954734i | \(-0.403860\pi\) | |||||||
\(984\) | −4.50000 | − | 7.79423i | −0.143455 | − | 0.248471i | ||||
\(985\) | −28.9373 | + | 50.1208i | −0.922018 | + | 1.59698i | ||||
\(986\) | 6.00000 | 0.191079 | ||||||||
\(987\) | −5.20850 | + | 9.02138i | −0.165788 | + | 0.287154i | ||||
\(988\) | −21.1660 | −0.673380 | ||||||||
\(989\) | 12.2915 | − | 21.2895i | 0.390847 | − | 0.676967i | ||||
\(990\) | 1.32288 | + | 2.29129i | 0.0420437 | + | 0.0728219i | ||||
\(991\) | 21.9373 | + | 37.9964i | 0.696860 | + | 1.20700i | 0.969550 | + | 0.244895i | \(0.0787534\pi\) |
−0.272690 | + | 0.962102i | \(0.587913\pi\) | |||||||
\(992\) | −2.00000 | + | 3.46410i | −0.0635001 | + | 0.109985i | ||||
\(993\) | −13.0000 | −0.412543 | ||||||||
\(994\) | −3.58301 | − | 6.20595i | −0.113646 | − | 0.196841i | ||||
\(995\) | −50.7085 | −1.60757 | ||||||||
\(996\) | 7.79150 | − | 13.4953i | 0.246883 | − | 0.427614i | ||||
\(997\) | −3.41699 | − | 5.91841i | −0.108217 | − | 0.187438i | 0.806831 | − | 0.590783i | \(-0.201181\pi\) |
−0.915048 | + | 0.403345i | \(0.867848\pi\) | |||||||
\(998\) | −9.29150 | − | 16.0934i | −0.294117 | − | 0.509426i | ||||
\(999\) | 0.645751 | − | 1.11847i | 0.0204307 | − | 0.0353870i |
(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 | 462.2.i.e.331.1 | yes | 4 | |
3.2 | odd | 2 | 1386.2.k.r.793.2 | 4 | |||
7.2 | even | 3 | 3234.2.a.w.1.2 | 2 | |||
7.4 | even | 3 | inner | 462.2.i.e.67.1 | ✓ | 4 | |
7.5 | odd | 6 | 3234.2.a.ba.1.1 | 2 | |||
21.2 | odd | 6 | 9702.2.a.db.1.1 | 2 | |||
21.5 | even | 6 | 9702.2.a.dm.1.2 | 2 | |||
21.11 | odd | 6 | 1386.2.k.r.991.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.e.67.1 | ✓ | 4 | 7.4 | even | 3 | inner | |
462.2.i.e.331.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1386.2.k.r.793.2 | 4 | 3.2 | odd | 2 | |||
1386.2.k.r.991.2 | 4 | 21.11 | odd | 6 | |||
3234.2.a.w.1.2 | 2 | 7.2 | even | 3 | |||
3234.2.a.ba.1.1 | 2 | 7.5 | odd | 6 | |||
9702.2.a.db.1.1 | 2 | 21.2 | odd | 6 | |||
9702.2.a.dm.1.2 | 2 | 21.5 | even | 6 |