Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(793,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.k (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: | \(11.0672657201\) |
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: | no (minimal twist has level 462) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 793.2 | ||
Root | \(1.32288 - 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.793 |
Dual form | 1386.2.k.r.991.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.32288 | − | 2.29129i | 0.591608 | − | 1.02470i | −0.402408 | − | 0.915460i | \(-0.631827\pi\) |
0.994016 | − | 0.109235i | \(-0.0348400\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.32288 | + | 2.29129i | −0.500000 | + | 0.866025i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.32288 | + | 2.29129i | 0.418330 | + | 0.724569i | ||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −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 | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −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 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −1.32288 | + | 2.29129i | −0.275839 | + | 0.477767i | −0.970346 | − | 0.241719i | \(-0.922289\pi\) |
0.694508 | + | 0.719485i | \(0.255622\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 1.73205i | −0.200000 | − | 0.346410i | ||||
\(26\) | 2.00000 | − | 3.46410i | 0.392232 | − | 0.679366i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.64575 | 0.500000 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 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 | 0 | ||||||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | 3.50000 | + | 6.06218i | 0.591608 | + | 1.02470i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −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 | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.32288 | − | 2.29129i | 0.209165 | − | 0.362284i | ||||
\(41\) | −9.00000 | −1.40556 | −0.702782 | − | 0.711405i | \(-0.748059\pi\) | ||||
−0.702782 | + | 0.711405i | \(0.748059\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 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 | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.32288 | − | 2.29129i | −0.195047 | − | 0.337832i | ||||
\(47\) | −1.96863 | + | 3.40976i | −0.287154 | + | 0.497365i | −0.973129 | − | 0.230260i | \(-0.926042\pi\) |
0.685975 | + | 0.727625i | \(0.259376\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.50000 | − | 6.06218i | −0.500000 | − | 0.866025i | ||||
\(50\) | 2.00000 | 0.282843 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | + | 3.46410i | 0.277350 | + | 0.480384i | ||||
\(53\) | 2.00000 | + | 3.46410i | 0.274721 | + | 0.475831i | 0.970065 | − | 0.242846i | \(-0.0780811\pi\) |
−0.695344 | + | 0.718677i | \(0.744748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.64575 | 0.356753 | ||||||||
\(56\) | −1.32288 | + | 2.29129i | −0.176777 | + | 0.306186i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.00000 | − | 1.73205i | 0.131306 | − | 0.227429i | ||||
\(59\) | 3.29150 | + | 5.70105i | 0.428517 | + | 0.742213i | 0.996742 | − | 0.0806601i | \(-0.0257028\pi\) |
−0.568225 | + | 0.822874i | \(0.692369\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −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 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.29150 | + | 9.16515i | −0.656330 | + | 1.13680i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −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 | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.00000 | −0.836660 | ||||||||
\(71\) | 2.70850 | 0.321440 | 0.160720 | − | 0.987000i | \(-0.448618\pi\) | ||||
0.160720 | + | 0.987000i | \(0.448618\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 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 | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.29150 | 0.606977 | ||||||||
\(77\) | −2.64575 | −0.301511 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −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 | 0 | ||||||||
\(82\) | 4.50000 | − | 7.79423i | 0.496942 | − | 0.860729i | ||||
\(83\) | −15.5830 | −1.71046 | −0.855229 | − | 0.518251i | \(-0.826583\pi\) | ||||
−0.855229 | + | 0.518251i | \(0.826583\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.93725 | −0.860916 | ||||||||
\(86\) | −4.64575 | + | 8.04668i | −0.500964 | + | 0.867696i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | 1.35425 | − | 2.34563i | 0.143550 | − | 0.248636i | −0.785281 | − | 0.619140i | \(-0.787482\pi\) |
0.928831 | + | 0.370504i | \(0.120815\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.29150 | − | 9.16515i | 0.554700 | − | 0.960769i | ||||
\(92\) | 2.64575 | 0.275839 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.96863 | − | 3.40976i | −0.203048 | − | 0.351690i | ||||
\(95\) | 7.00000 | + | 12.1244i | 0.718185 | + | 1.24393i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.5830 | −1.17608 | −0.588038 | − | 0.808833i | \(-0.700099\pi\) | ||||
−0.588038 | + | 0.808833i | \(0.700099\pi\) | |||||||
\(98\) | 7.00000 | 0.707107 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | + | 1.73205i | −0.100000 | + | 0.173205i | ||||
\(101\) | 3.64575 | + | 6.31463i | 0.362766 | + | 0.628329i | 0.988415 | − | 0.151776i | \(-0.0484992\pi\) |
−0.625649 | + | 0.780105i | \(0.715166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 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 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | 4.50000 | − | 7.79423i | 0.435031 | − | 0.753497i | −0.562267 | − | 0.826956i | \(-0.690071\pi\) |
0.997298 | + | 0.0734594i | \(0.0234039\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 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 | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.32288 | − | 2.29129i | −0.125000 | − | 0.216506i | ||||
\(113\) | −12.5830 | −1.18371 | −0.591855 | − | 0.806045i | \(-0.701604\pi\) | ||||
−0.591855 | + | 0.806045i | \(0.701604\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.50000 | + | 6.06218i | 0.326377 | + | 0.565301i | ||||
\(116\) | 1.00000 | + | 1.73205i | 0.0928477 | + | 0.160817i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.58301 | −0.606015 | ||||||||
\(119\) | 7.93725 | 0.727607 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −5.96863 | − | 10.3380i | −0.540374 | − | 0.935955i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | 7.93725 | 0.709930 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 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 | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.29150 | − | 9.16515i | −0.464095 | − | 0.803837i | ||||
\(131\) | −9.29150 | + | 16.0934i | −0.811802 | + | 1.40608i | 0.0997990 | + | 0.995008i | \(0.468180\pi\) |
−0.911601 | + | 0.411075i | \(0.865153\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.00000 | − | 12.1244i | −0.606977 | − | 1.05131i | ||||
\(134\) | 7.58301 | 0.655072 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.50000 | − | 2.59808i | −0.128624 | − | 0.222783i | ||||
\(137\) | −6.64575 | − | 11.5108i | −0.567785 | − | 0.983432i | −0.996785 | − | 0.0801276i | \(-0.974467\pi\) |
0.429000 | − | 0.903305i | \(-0.358866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −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 | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.35425 | + | 2.34563i | −0.113646 | + | 0.196841i | ||||
\(143\) | −2.00000 | − | 3.46410i | −0.167248 | − | 0.289683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.64575 | + | 4.58258i | −0.219718 | + | 0.380562i | ||||
\(146\) | −15.2915 | −1.26553 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.29150 | 0.106161 | ||||||||
\(149\) | 9.93725 | − | 17.2118i | 0.814092 | − | 1.41005i | −0.0958868 | − | 0.995392i | \(-0.530569\pi\) |
0.909978 | − | 0.414656i | \(-0.136098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −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 | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.32288 | − | 2.29129i | 0.106600 | − | 0.184637i | ||||
\(155\) | 10.5830 | 0.850047 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 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 | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.64575 | −0.209165 | ||||||||
\(161\) | −3.50000 | − | 6.06218i | −0.275839 | − | 0.477767i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 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 | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.79150 | − | 13.4953i | 0.604738 | − | 1.04744i | ||||
\(167\) | −8.70850 | −0.673884 | −0.336942 | − | 0.941525i | \(-0.609393\pi\) | ||||
−0.336942 | + | 0.941525i | \(0.609393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 3.96863 | − | 6.87386i | 0.304380 | − | 0.527201i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.64575 | − | 8.04668i | −0.354235 | − | 0.613553i | ||||
\(173\) | 2.00000 | − | 3.46410i | 0.152057 | − | 0.263371i | −0.779926 | − | 0.625871i | \(-0.784744\pi\) |
0.931984 | + | 0.362500i | \(0.118077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.29150 | 0.400000 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.35425 | + | 2.34563i | 0.101505 | + | 0.175812i | ||||
\(179\) | 2.35425 | + | 4.07768i | 0.175965 | + | 0.304780i | 0.940495 | − | 0.339808i | \(-0.110362\pi\) |
−0.764530 | + | 0.644588i | \(0.777029\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −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 | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.32288 | + | 2.29129i | −0.0975237 | + | 0.168916i | ||||
\(185\) | 1.70850 | + | 2.95920i | 0.125611 | + | 0.217565i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.50000 | − | 2.59808i | 0.109691 | − | 0.189990i | ||||
\(188\) | 3.93725 | 0.287154 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.0000 | −1.01567 | ||||||||
\(191\) | 3.35425 | − | 5.80973i | 0.242705 | − | 0.420377i | −0.718779 | − | 0.695239i | \(-0.755299\pi\) |
0.961484 | + | 0.274861i | \(0.0886320\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 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 | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.50000 | + | 6.06218i | −0.250000 | + | 0.433013i | ||||
\(197\) | −21.8745 | −1.55849 | −0.779247 | − | 0.626717i | \(-0.784398\pi\) | ||||
−0.779247 | + | 0.626717i | \(0.784398\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 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 | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.29150 | −0.513028 | ||||||||
\(203\) | 2.64575 | − | 4.58258i | 0.185695 | − | 0.321634i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.9059 | + | 20.6216i | −0.831543 | + | 1.44027i | ||||
\(206\) | 5.00000 | + | 8.66025i | 0.348367 | + | 0.603388i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000 | − | 3.46410i | 0.138675 | − | 0.240192i | ||||
\(209\) | −5.29150 | −0.366021 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 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 | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.50000 | + | 7.79423i | 0.307614 | + | 0.532803i | ||||
\(215\) | 12.2915 | − | 21.2895i | 0.838274 | − | 1.45193i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.5830 | −0.718421 | ||||||||
\(218\) | −3.93725 | −0.266664 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.32288 | − | 2.29129i | −0.0891883 | − | 0.154479i | ||||
\(221\) | 6.00000 | + | 10.3923i | 0.403604 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.4575 | 1.90566 | 0.952828 | − | 0.303511i | \(-0.0981588\pi\) | ||||
0.952828 | + | 0.303511i | \(0.0981588\pi\) | |||||||
\(224\) | 2.64575 | 0.176777 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.29150 | − | 10.8972i | 0.418505 | − | 0.724871i | ||||
\(227\) | 1.20850 | + | 2.09318i | 0.0802108 | + | 0.138929i | 0.903340 | − | 0.428924i | \(-0.141107\pi\) |
−0.823130 | + | 0.567854i | \(0.807774\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −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 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | 10.0830 | − | 17.4643i | 0.660560 | − | 1.14412i | −0.319909 | − | 0.947448i | \(-0.603652\pi\) |
0.980469 | − | 0.196675i | \(-0.0630143\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.20850 | + | 9.02138i | 0.339765 | + | 0.588490i | ||||
\(236\) | 3.29150 | − | 5.70105i | 0.214259 | − | 0.371107i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.96863 | + | 6.87386i | −0.257248 | + | 0.445566i | ||||
\(239\) | −2.70850 | −0.175198 | −0.0875991 | − | 0.996156i | \(-0.527919\pi\) | ||||
−0.0875991 | + | 0.996156i | \(0.527919\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 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 | 0 | ||||||||
\(244\) | 11.9373 | 0.764204 | ||||||||
\(245\) | −18.5203 | −1.18322 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.5830 | − | 18.3303i | 0.673380 | − | 1.16633i | ||||
\(248\) | 2.00000 | + | 3.46410i | 0.127000 | + | 0.219971i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.96863 | + | 6.87386i | −0.250998 | + | 0.434741i | ||||
\(251\) | −23.2915 | −1.47015 | −0.735073 | − | 0.677988i | \(-0.762852\pi\) | ||||
−0.735073 | + | 0.677988i | \(0.762852\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.64575 | −0.166337 | ||||||||
\(254\) | −1.32288 | + | 2.29129i | −0.0830046 | + | 0.143768i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 4.64575 | − | 8.04668i | 0.289794 | − | 0.501938i | −0.683966 | − | 0.729513i | \(-0.739747\pi\) |
0.973760 | + | 0.227576i | \(0.0730799\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.70850 | − | 2.95920i | −0.106161 | − | 0.183876i | ||||
\(260\) | 10.5830 | 0.656330 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.29150 | − | 16.0934i | −0.574031 | − | 0.994251i | ||||
\(263\) | 10.9373 | + | 18.9439i | 0.674420 | + | 1.16813i | 0.976638 | + | 0.214891i | \(0.0689396\pi\) |
−0.302218 | + | 0.953239i | \(0.597727\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.5830 | 0.650109 | ||||||||
\(266\) | 14.0000 | 0.858395 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.79150 | + | 6.56708i | −0.231603 | + | 0.401148i | ||||
\(269\) | −5.32288 | − | 9.21949i | −0.324541 | − | 0.562122i | 0.656878 | − | 0.753997i | \(-0.271877\pi\) |
−0.981419 | + | 0.191875i | \(0.938543\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −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 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.2915 | 0.802969 | ||||||||
\(275\) | 1.00000 | − | 1.73205i | 0.0603023 | − | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 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 | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.50000 | + | 6.06218i | 0.209165 | + | 0.362284i | ||||
\(281\) | 3.00000 | 0.178965 | 0.0894825 | − | 0.995988i | \(-0.471479\pi\) | ||||
0.0894825 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −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 | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 11.9059 | − | 20.6216i | 0.702782 | − | 1.21725i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | −2.64575 | − | 4.58258i | −0.155364 | − | 0.269098i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.64575 | − | 13.2428i | 0.447434 | − | 0.774978i | ||||
\(293\) | 14.5830 | 0.851948 | 0.425974 | − | 0.904735i | \(-0.359931\pi\) | ||||
0.425974 | + | 0.904735i | \(0.359931\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.4170 | 1.01406 | ||||||||
\(296\) | −0.645751 | + | 1.11847i | −0.0375335 | + | 0.0650100i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.93725 | + | 17.2118i | 0.575650 | + | 0.997054i | ||||
\(299\) | 5.29150 | − | 9.16515i | 0.306015 | − | 0.530034i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.2915 | + | 21.2895i | −0.708470 | + | 1.22711i | ||||
\(302\) | 22.6458 | 1.30312 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.64575 | − | 4.58258i | −0.151744 | − | 0.262829i | ||||
\(305\) | 15.7915 | + | 27.3517i | 0.904219 | + | 1.56615i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −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 | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.29150 | + | 9.16515i | −0.300537 | + | 0.520546i | ||||
\(311\) | 11.2601 | + | 19.5031i | 0.638503 | + | 1.10592i | 0.985761 | + | 0.168151i | \(0.0537795\pi\) |
−0.347258 | + | 0.937770i | \(0.612887\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 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 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.6458 | 0.598870 | ||||||||
\(317\) | 4.61438 | − | 7.99234i | 0.259169 | − | 0.448894i | −0.706850 | − | 0.707363i | \(-0.749885\pi\) |
0.966020 | + | 0.258469i | \(0.0832179\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.00000 | − | 1.73205i | −0.0559893 | − | 0.0969762i | ||||
\(320\) | 1.32288 | − | 2.29129i | 0.0739510 | − | 0.128087i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.00000 | 0.390095 | ||||||||
\(323\) | 15.8745 | 0.883281 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | + | 6.92820i | 0.221880 | + | 0.384308i | ||||
\(326\) | 2.79150 | + | 4.83502i | 0.154607 | + | 0.267787i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.00000 | −0.496942 | ||||||||
\(329\) | −5.20850 | − | 9.02138i | −0.287154 | − | 0.497365i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −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 | 0 | ||||||||
\(334\) | 4.35425 | − | 7.54178i | 0.238254 | − | 0.412668i | ||||
\(335\) | −20.0627 | −1.09614 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 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 | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.96863 | + | 6.87386i | 0.215229 | + | 0.372788i | ||||
\(341\) | −2.00000 | + | 3.46410i | −0.108306 | + | 0.187592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203 | 1.00000 | ||||||||
\(344\) | 9.29150 | 0.500964 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.00000 | + | 3.46410i | 0.107521 | + | 0.186231i | ||||
\(347\) | 14.7915 | + | 25.6196i | 0.794049 | + | 1.37533i | 0.923441 | + | 0.383740i | \(0.125364\pi\) |
−0.129392 | + | 0.991594i | \(0.541302\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −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 | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | −11.6458 | − | 20.1710i | −0.619841 | − | 1.07360i | −0.989514 | − | 0.144434i | \(-0.953864\pi\) |
0.369674 | − | 0.929162i | \(-0.379469\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.58301 | − | 6.20595i | 0.190166 | − | 0.329377i | ||||
\(356\) | −2.70850 | −0.143550 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.70850 | −0.248852 | ||||||||
\(359\) | 10.2915 | − | 17.8254i | 0.543165 | − | 0.940789i | −0.455555 | − | 0.890208i | \(-0.650559\pi\) |
0.998720 | − | 0.0505814i | \(-0.0161074\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.50000 | − | 7.79423i | −0.236842 | − | 0.410223i | ||||
\(362\) | 2.64575 | − | 4.58258i | 0.139058 | − | 0.240855i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.5830 | −0.554700 | ||||||||
\(365\) | 40.4575 | 2.11764 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −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 | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.41699 | −0.177641 | ||||||||
\(371\) | −10.5830 | −0.549442 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 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 | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.96863 | + | 3.40976i | −0.101524 | + | 0.175845i | ||||
\(377\) | 8.00000 | 0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −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 | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.35425 | + | 5.80973i | 0.171618 | + | 0.297252i | ||||
\(383\) | 9.35425 | − | 16.2020i | 0.477980 | − | 0.827885i | −0.521702 | − | 0.853128i | \(-0.674703\pi\) |
0.999681 | + | 0.0252428i | \(0.00803588\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.50000 | + | 6.06218i | −0.178377 | + | 0.308957i | ||||
\(386\) | −15.8745 | −0.807991 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.79150 | + | 10.0312i | 0.294019 | + | 0.509256i | ||||
\(389\) | 15.9686 | + | 27.6585i | 0.809642 | + | 1.40234i | 0.913112 | + | 0.407708i | \(0.133672\pi\) |
−0.103471 | + | 0.994632i | \(0.532995\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.93725 | 0.401404 | ||||||||
\(392\) | −3.50000 | − | 6.06218i | −0.176777 | − | 0.306186i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.9373 | − | 18.9439i | 0.551011 | − | 0.954379i | ||||
\(395\) | 14.0830 | + | 24.3925i | 0.708593 | + | 1.22732i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −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 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.00000 | 0.100000 | ||||||||
\(401\) | −17.9373 | + | 31.0682i | −0.895744 | + | 1.55147i | −0.0628623 | + | 0.998022i | \(0.520023\pi\) |
−0.832881 | + | 0.553451i | \(0.813310\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | − | 13.8564i | −0.398508 | − | 0.690237i | ||||
\(404\) | 3.64575 | − | 6.31463i | 0.181383 | − | 0.314164i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.64575 | + | 4.58258i | 0.131306 | + | 0.227429i | ||||
\(407\) | −1.29150 | −0.0640174 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −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 | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.0000 | −0.492665 | ||||||||
\(413\) | −17.4170 | −0.857034 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.6144 | + | 35.7052i | −1.01192 | + | 1.75270i | ||||
\(416\) | 2.00000 | + | 3.46410i | 0.0980581 | + | 0.169842i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.64575 | − | 4.58258i | 0.129408 | − | 0.224141i | ||||
\(419\) | 9.87451 | 0.482401 | 0.241201 | − | 0.970475i | \(-0.422459\pi\) | ||||
0.241201 | + | 0.970475i | \(0.422459\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 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 | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.00000 | + | 3.46410i | 0.0971286 | + | 0.168232i | ||||
\(425\) | −3.00000 | + | 5.19615i | −0.145521 | + | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.7915 | − | 27.3517i | −0.764204 | − | 1.32364i | ||||
\(428\) | −9.00000 | −0.435031 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.2915 | + | 21.2895i | 0.592749 | + | 1.02667i | ||||
\(431\) | −8.64575 | − | 14.9749i | −0.416451 | − | 0.721315i | 0.579128 | − | 0.815236i | \(-0.303393\pi\) |
−0.995580 | + | 0.0939217i | \(0.970060\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 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 | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.96863 | − | 3.40976i | 0.0942801 | − | 0.163298i | ||||
\(437\) | −7.00000 | − | 12.1244i | −0.334855 | − | 0.579987i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | −15.5830 | + | 26.9906i | −0.740371 | + | 1.28236i | 0.211956 | + | 0.977279i | \(0.432017\pi\) |
−0.952326 | + | 0.305081i | \(0.901317\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.58301 | − | 6.20595i | −0.169851 | − | 0.294190i | ||||
\(446\) | −14.2288 | + | 24.6449i | −0.673751 | + | 1.16697i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.32288 | + | 2.29129i | −0.0625000 | + | 0.108253i | ||||
\(449\) | −30.4575 | −1.43738 | −0.718689 | − | 0.695331i | \(-0.755258\pi\) | ||||
−0.718689 | + | 0.695331i | \(0.755258\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.50000 | − | 7.79423i | −0.211897 | − | 0.367016i | ||||
\(452\) | 6.29150 | + | 10.8972i | 0.295927 | + | 0.512561i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.41699 | −0.113435 | ||||||||
\(455\) | −14.0000 | − | 24.2487i | −0.656330 | − | 1.13680i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 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 | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.50000 | − | 6.06218i | 0.163188 | − | 0.282650i | ||||
\(461\) | 24.5830 | 1.14494 | 0.572472 | − | 0.819924i | \(-0.305984\pi\) | ||||
0.572472 | + | 0.819924i | \(0.305984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 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 | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.0830 | + | 17.4643i | 0.467086 | + | 0.809017i | ||||
\(467\) | 4.00000 | − | 6.92820i | 0.185098 | − | 0.320599i | −0.758512 | − | 0.651660i | \(-0.774073\pi\) |
0.943610 | + | 0.331061i | \(0.107406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.0627 | 0.926412 | ||||||||
\(470\) | −10.4170 | −0.480500 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.29150 | + | 5.70105i | 0.151504 | + | 0.262412i | ||||
\(473\) | 4.64575 | + | 8.04668i | 0.213612 | + | 0.369987i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.5830 | 0.485582 | ||||||||
\(476\) | −3.96863 | − | 6.87386i | −0.181902 | − | 0.315063i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.35425 | − | 2.34563i | 0.0619419 | − | 0.107287i | ||||
\(479\) | −16.9373 | − | 29.3362i | −0.773883 | − | 1.34040i | −0.935420 | − | 0.353538i | \(-0.884979\pi\) |
0.161537 | − | 0.986867i | \(-0.448355\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.58301 | − | 4.47390i | 0.117775 | − | 0.203992i | ||||
\(482\) | −27.1660 | −1.23738 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −15.3229 | + | 26.5400i | −0.695776 | + | 1.20512i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −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 | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.26013 | − | 16.0390i | 0.418330 | − | 0.724569i | ||||
\(491\) | 1.00000 | 0.0451294 | 0.0225647 | − | 0.999745i | \(-0.492817\pi\) | ||||
0.0225647 | + | 0.999745i | \(0.492817\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.00000 | + | 5.19615i | 0.135113 | + | 0.234023i | ||||
\(494\) | 10.5830 | + | 18.3303i | 0.476152 | + | 0.824719i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −3.58301 | + | 6.20595i | −0.160720 | + | 0.278375i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 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 | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.6458 | − | 20.1710i | 0.519775 | − | 0.900277i | ||||
\(503\) | 1.29150 | 0.0575853 | 0.0287926 | − | 0.999585i | \(-0.490834\pi\) | ||||
0.0287926 | + | 0.999585i | \(0.490834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.2915 | 0.858461 | ||||||||
\(506\) | 1.32288 | − | 2.29129i | 0.0588090 | − | 0.101860i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.32288 | − | 2.29129i | −0.0586931 | − | 0.101659i | ||||
\(509\) | 12.5830 | − | 21.7944i | 0.557732 | − | 0.966020i | −0.439953 | − | 0.898021i | \(-0.645005\pi\) |
0.997685 | − | 0.0679994i | \(-0.0216616\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.4575 | −1.78974 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.64575 | + | 8.04668i | 0.204915 | + | 0.354924i | ||||
\(515\) | −13.2288 | − | 22.9129i | −0.582929 | − | 1.00966i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.93725 | −0.173160 | ||||||||
\(518\) | 3.41699 | 0.150134 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.29150 | + | 9.16515i | −0.232048 | + | 0.401918i | ||||
\(521\) | 21.0000 | + | 36.3731i | 0.920027 | + | 1.59353i | 0.799370 | + | 0.600839i | \(0.205167\pi\) |
0.120656 | + | 0.992694i | \(0.461500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −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 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.8745 | −0.953774 | ||||||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.00000 | + | 13.8564i | 0.347826 | + | 0.602452i | ||||
\(530\) | −5.29150 | + | 9.16515i | −0.229848 | + | 0.398109i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.00000 | + | 12.1244i | −0.303488 | + | 0.525657i | ||||
\(533\) | 36.0000 | 1.55933 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.9059 | − | 20.6216i | −0.514736 | − | 0.891549i | ||||
\(536\) | −3.79150 | − | 6.56708i | −0.163768 | − | 0.283654i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.6458 | 0.458971 | ||||||||
\(539\) | 3.50000 | − | 6.06218i | 0.150756 | − | 0.261116i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.50000 | + | 2.59808i | −0.0643120 | + | 0.111392i | ||||
\(545\) | 10.4170 | 0.446215 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 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 | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.00000 | + | 1.73205i | 0.0426401 | + | 0.0738549i | ||||
\(551\) | 5.29150 | − | 9.16515i | 0.225426 | − | 0.390449i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.0830 | − | 24.3925i | −0.598870 | − | 1.03727i | ||||
\(554\) | −17.1660 | −0.729314 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.29150 | + | 10.8972i | 0.266819 | + | 0.462144i | ||||
\(557\) | −9.64575 | − | 16.7069i | −0.408704 | − | 0.707895i | 0.586041 | − | 0.810281i | \(-0.300686\pi\) |
−0.994745 | + | 0.102386i | \(0.967352\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.1660 | −1.57195 | ||||||||
\(560\) | −7.00000 | −0.295804 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.50000 | + | 2.59808i | −0.0632737 | + | 0.109593i | ||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.6458 | + | 28.8313i | −0.700292 | + | 1.21294i | ||||
\(566\) | 30.4575 | 1.28022 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.70850 | 0.113646 | ||||||||
\(569\) | −7.58301 | + | 13.1342i | −0.317896 | + | 0.550612i | −0.980049 | − | 0.198757i | \(-0.936310\pi\) |
0.662153 | + | 0.749369i | \(0.269643\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 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 | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.9059 | + | 20.6216i | 0.496942 | + | 0.860729i | ||||
\(575\) | 5.29150 | 0.220671 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −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 | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.29150 | 0.219718 | ||||||||
\(581\) | 20.6144 | − | 35.7052i | 0.855229 | − | 1.48130i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.00000 | + | 3.46410i | −0.0828315 | + | 0.143468i | ||||
\(584\) | 7.64575 | + | 13.2428i | 0.316383 | + | 0.547992i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.29150 | + | 12.6293i | −0.301209 | + | 0.521710i | ||||
\(587\) | −9.87451 | −0.407565 | −0.203782 | − | 0.979016i | \(-0.565323\pi\) | ||||
−0.203782 | + | 0.979016i | \(0.565323\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.1660 | −0.872130 | ||||||||
\(590\) | −8.70850 | + | 15.0836i | −0.358523 | + | 0.620980i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.645751 | − | 1.11847i | −0.0265402 | − | 0.0459690i | ||||
\(593\) | −12.8745 | + | 22.2993i | −0.528693 | + | 0.915723i | 0.470748 | + | 0.882268i | \(0.343984\pi\) |
−0.999440 | + | 0.0334546i | \(0.989349\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.5000 | − | 18.1865i | 0.430458 | − | 0.745575i | ||||
\(596\) | −19.8745 | −0.814092 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.29150 | + | 9.16515i | 0.216386 | + | 0.374791i | ||||
\(599\) | 14.6771 | + | 25.4215i | 0.599691 | + | 1.03870i | 0.992866 | + | 0.119232i | \(0.0380432\pi\) |
−0.393175 | + | 0.919463i | \(0.628623\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −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 | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.3229 | + | 19.6118i | −0.460721 | + | 0.797993i | ||||
\(605\) | 1.32288 | + | 2.29129i | 0.0537825 | + | 0.0931541i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 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 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −31.5830 | −1.27876 | ||||||||
\(611\) | 7.87451 | − | 13.6390i | 0.318568 | − | 0.551777i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −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 | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.64575 | −0.106600 | ||||||||
\(617\) | 14.7085 | 0.592142 | 0.296071 | − | 0.955166i | \(-0.404324\pi\) | ||||
0.296071 | + | 0.955166i | \(0.404324\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 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 | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.5203 | −0.902980 | ||||||||
\(623\) | 3.58301 | + | 6.20595i | 0.143550 | + | 0.248636i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5000 | − | 26.8468i | 0.620000 | − | 1.07387i | ||||
\(626\) | 10.2915 | + | 17.8254i | 0.411331 | + | 0.712446i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.354249 | − | 0.613577i | 0.0141361 | − | 0.0244844i | ||||
\(629\) | 3.87451 | 0.154487 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.61438 | + | 7.99234i | 0.183260 | + | 0.317416i | ||||
\(635\) | 3.50000 | − | 6.06218i | 0.138893 | − | 0.240570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.0000 | + | 24.2487i | 0.554700 | + | 0.960769i | ||||
\(638\) | 2.00000 | 0.0791808 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.32288 | + | 2.29129i | 0.0522913 | + | 0.0905711i | ||||
\(641\) | −13.2915 | − | 23.0216i | −0.524983 | − | 0.909297i | −0.999577 | − | 0.0290920i | \(-0.990738\pi\) |
0.474594 | − | 0.880205i | \(-0.342595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −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 | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.93725 | + | 13.7477i | −0.312287 | + | 0.540897i | ||||
\(647\) | −13.1974 | − | 22.8585i | −0.518843 | − | 0.898662i | −0.999760 | − | 0.0218961i | \(-0.993030\pi\) |
0.480918 | − | 0.876766i | \(-0.340304\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.29150 | + | 5.70105i | −0.129203 | + | 0.223786i | ||||
\(650\) | −8.00000 | −0.313786 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.58301 | −0.218647 | ||||||||
\(653\) | −22.5516 | + | 39.0606i | −0.882514 | + | 1.52856i | −0.0339763 | + | 0.999423i | \(0.510817\pi\) |
−0.848537 | + | 0.529136i | \(0.822516\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.5830 | + | 42.5790i | 0.960537 | + | 1.66370i | ||||
\(656\) | 4.50000 | − | 7.79423i | 0.175695 | − | 0.304314i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.4170 | 0.406097 | ||||||||
\(659\) | 24.1660 | 0.941374 | 0.470687 | − | 0.882300i | \(-0.344006\pi\) | ||||
0.470687 | + | 0.882300i | \(0.344006\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −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 | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.5830 | −0.604738 | ||||||||
\(665\) | −37.0405 | −1.43637 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.64575 | − | 4.58258i | 0.102444 | − | 0.177438i | ||||
\(668\) | 4.35425 | + | 7.54178i | 0.168471 | + | 0.291800i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.0314 | − | 17.3748i | 0.387546 | − | 0.671249i | ||||
\(671\) | −11.9373 | −0.460833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −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 | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.50000 | − | 2.59808i | −0.0576923 | − | 0.0999260i | ||||
\(677\) | −4.06275 | + | 7.03688i | −0.156144 | + | 0.270449i | −0.933475 | − | 0.358642i | \(-0.883240\pi\) |
0.777331 | + | 0.629092i | \(0.216573\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.3229 | − | 26.5400i | 0.588038 | − | 1.01851i | ||||
\(680\) | −7.93725 | −0.304380 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.00000 | − | 3.46410i | −0.0765840 | − | 0.132647i | ||||
\(683\) | −8.58301 | − | 14.8662i | −0.328420 | − | 0.568839i | 0.653779 | − | 0.756686i | \(-0.273183\pi\) |
−0.982198 | + | 0.187846i | \(0.939849\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −35.1660 | −1.34362 | ||||||||
\(686\) | −9.26013 | + | 16.0390i | −0.353553 | + | 0.612372i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.64575 | + | 8.04668i | −0.177118 | + | 0.306777i | ||||
\(689\) | −8.00000 | − | 13.8564i | −0.304776 | − | 0.527887i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.5830 | −1.12296 | ||||||||
\(695\) | −16.6458 | + | 28.8313i | −0.631409 | + | 1.09363i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.5000 | + | 23.3827i | 0.511349 | + | 0.885682i | ||||
\(698\) | 6.61438 | − | 11.4564i | 0.250358 | − | 0.433633i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.64575 | − | 4.58258i | −0.100000 | − | 0.173205i | ||||
\(701\) | −42.4575 | −1.60360 | −0.801799 | − | 0.597594i | \(-0.796124\pi\) | ||||
−0.801799 | + | 0.597594i | \(0.796124\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.41699 | − | 5.91841i | −0.128874 | − | 0.223217i | ||||
\(704\) | 0.500000 | + | 0.866025i | 0.0188445 | + | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.2915 | 0.876587 | ||||||||
\(707\) | −19.2915 | −0.725532 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −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 | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.35425 | − | 2.34563i | 0.0507526 | − | 0.0879061i | ||||
\(713\) | −10.5830 | −0.396337 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.5830 | −0.395782 | ||||||||
\(716\) | 2.35425 | − | 4.07768i | 0.0879824 | − | 0.152390i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.2915 | + | 17.8254i | 0.384075 | + | 0.665238i | ||||
\(719\) | −14.0314 | + | 24.3031i | −0.523282 | + | 0.906351i | 0.476351 | + | 0.879255i | \(0.341959\pi\) |
−0.999633 | + | 0.0270956i | \(0.991374\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.2288 | + | 22.9129i | 0.492665 | + | 0.853320i | ||||
\(722\) | 9.00000 | 0.334945 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.64575 | + | 4.58258i | 0.0983286 | + | 0.170310i | ||||
\(725\) | 2.00000 | + | 3.46410i | 0.0742781 | + | 0.128654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −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 | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −20.2288 | + | 35.0372i | −0.748700 | + | 1.29679i | ||||
\(731\) | −13.9373 | − | 24.1400i | −0.515488 | − | 0.892851i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −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 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.64575 | 0.0975237 | ||||||||
\(737\) | 3.79150 | − | 6.56708i | 0.139662 | − | 0.241901i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 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 | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.29150 | − | 9.16515i | 0.194257 | − | 0.336463i | ||||
\(743\) | 18.7085 | 0.686348 | 0.343174 | − | 0.939272i | \(-0.388498\pi\) | ||||
0.343174 | + | 0.939272i | \(0.388498\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.2915 | − | 45.5382i | −0.963246 | − | 1.66839i | ||||
\(746\) | 7.90588 | + | 13.6934i | 0.289455 | + | 0.501351i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.00000 | −0.109691 | ||||||||
\(749\) | 11.9059 | + | 20.6216i | 0.435031 | + | 0.753497i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 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 | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.00000 | + | 6.92820i | −0.145671 | + | 0.252310i | ||||
\(755\) | −59.9150 | −2.18053 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −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 | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.00000 | + | 12.1244i | 0.253917 | + | 0.439797i | ||||
\(761\) | 23.7915 | − | 41.2081i | 0.862441 | − | 1.49379i | −0.00712426 | − | 0.999975i | \(-0.502268\pi\) |
0.869566 | − | 0.493818i | \(-0.164399\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.4170 | −0.377121 | ||||||||
\(764\) | −6.70850 | −0.242705 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.35425 | + | 16.2020i | 0.337983 | + | 0.585403i | ||||
\(767\) | −13.1660 | − | 22.8042i | −0.475397 | − | 0.823412i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −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 | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.93725 | − | 13.7477i | 0.285668 | − | 0.494792i | ||||
\(773\) | −4.03137 | − | 6.98254i | −0.144998 | − | 0.251145i | 0.784374 | − | 0.620288i | \(-0.212984\pi\) |
−0.929372 | + | 0.369144i | \(0.879651\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000 | − | 6.92820i | 0.143684 | − | 0.248868i | ||||
\(776\) | −11.5830 | −0.415806 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.9373 | −1.14501 | ||||||||
\(779\) | 23.8118 | − | 41.2432i | 0.853145 | − | 1.47769i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.35425 | + | 2.34563i | 0.0484588 | + | 0.0839332i | ||||
\(782\) | −3.96863 | + | 6.87386i | −0.141918 | + | 0.245809i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.00000 | 0.250000 | ||||||||
\(785\) | 1.87451 | 0.0669041 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −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 | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −28.1660 | −1.00210 | ||||||||
\(791\) | 16.6458 | − | 28.8313i | 0.591855 | − | 1.02512i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.8745 | − | 41.3519i | 0.847809 | − | 1.46845i | ||||
\(794\) | −3.00000 | − | 5.19615i | −0.106466 | − | 0.184405i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.58301 | − | 16.5983i | 0.339661 | − | 0.588309i | ||||
\(797\) | −45.1033 | −1.59764 | −0.798820 | − | 0.601570i | \(-0.794542\pi\) | ||||
−0.798820 | + | 0.601570i | \(0.794542\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.8118 | 0.417870 | ||||||||
\(800\) | −1.00000 | + | 1.73205i | −0.0353553 | + | 0.0612372i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17.9373 | − | 31.0682i | −0.633386 | − | 1.09706i | ||||
\(803\) | −7.64575 | + | 13.2428i | −0.269813 | + | 0.467329i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.5203 | −0.652753 | ||||||||
\(806\) | 16.0000 | 0.563576 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.64575 | + | 6.31463i | 0.128257 | + | 0.222148i | ||||
\(809\) | 22.6660 | + | 39.2587i | 0.796894 | + | 1.38026i | 0.921629 | + | 0.388072i | \(0.126859\pi\) |
−0.124735 | + | 0.992190i | \(0.539808\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.5830 | 0.582308 | 0.291154 | − | 0.956676i | \(-0.405961\pi\) | ||||
0.291154 | + | 0.956676i | \(0.405961\pi\) | |||||||
\(812\) | −5.29150 | −0.185695 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.645751 | − | 1.11847i | 0.0226336 | − | 0.0392025i | ||||
\(815\) | −7.38562 | − | 12.7923i | −0.258707 | − | 0.448094i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.5830 | + | 42.5790i | −0.860050 | + | 1.48965i | ||||
\(818\) | 35.8745 | 1.25432 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.8118 | 0.831543 | ||||||||
\(821\) | −15.1660 | + | 26.2683i | −0.529297 | + | 0.916770i | 0.470119 | + | 0.882603i | \(0.344211\pi\) |
−0.999416 | + | 0.0341668i | \(0.989122\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 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 | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.70850 | − | 15.0836i | 0.303007 | − | 0.524824i | ||||
\(827\) | −35.3320 | −1.22861 | −0.614307 | − | 0.789067i | \(-0.710565\pi\) | ||||
−0.614307 | + | 0.789067i | \(0.710565\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −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 | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.00000 | −0.138675 | ||||||||
\(833\) | −10.5000 | + | 18.1865i | −0.363803 | + | 0.630126i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.5203 | + | 19.9537i | −0.398675 | + | 0.690525i | ||||
\(836\) | 2.64575 | + | 4.58258i | 0.0915052 | + | 0.158492i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.93725 | + | 8.55157i | −0.170555 | + | 0.295409i | ||||
\(839\) | 37.1033 | 1.28095 | 0.640473 | − | 0.767980i | \(-0.278738\pi\) | ||||
0.640473 | + | 0.767980i | \(0.278738\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | −3.06275 | + | 5.30483i | −0.105549 | + | 0.182817i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.6458 | − | 18.4390i | −0.366442 | − | 0.634696i | ||||
\(845\) | 3.96863 | − | 6.87386i | 0.136525 | − | 0.236468i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.32288 | − | 2.29129i | −0.0454545 | − | 0.0787296i | ||||
\(848\) | −4.00000 | −0.137361 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.00000 | − | 5.19615i | −0.102899 | − | 0.178227i | ||||
\(851\) | −1.70850 | − | 2.95920i | −0.0585665 | − | 0.101440i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.5203 | 0.497164 | 0.248582 | − | 0.968611i | \(-0.420035\pi\) | ||||
0.248582 | + | 0.968611i | \(0.420035\pi\) | |||||||
\(854\) | 31.5830 | 1.08075 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.50000 | − | 7.79423i | 0.153807 | − | 0.266401i | ||||
\(857\) | 4.91699 | + | 8.51648i | 0.167961 | + | 0.290918i | 0.937703 | − | 0.347438i | \(-0.112948\pi\) |
−0.769742 | + | 0.638356i | \(0.779615\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −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 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.2915 | 0.588951 | ||||||||
\(863\) | −16.5516 | + | 28.6683i | −0.563424 | + | 0.975879i | 0.433770 | + | 0.901024i | \(0.357183\pi\) |
−0.997194 | + | 0.0748557i | \(0.976150\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.29150 | − | 9.16515i | −0.179916 | − | 0.311624i | ||||
\(866\) | −0.791503 | + | 1.37092i | −0.0268964 | + | 0.0465859i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.29150 | + | 9.16515i | 0.179605 | + | 0.311086i | ||||
\(869\) | −10.6458 | −0.361132 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.1660 | + | 26.2683i | 0.513881 | + | 0.890067i | ||||
\(872\) | 1.96863 | + | 3.40976i | 0.0666661 | + | 0.115469i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14.0000 | 0.473557 | ||||||||
\(875\) | −10.5000 | + | 18.1865i | −0.354965 | + | 0.614817i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −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 | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.32288 | + | 2.29129i | −0.0445941 | + | 0.0772393i | ||||
\(881\) | −23.1660 | −0.780483 | −0.390241 | − | 0.920713i | \(-0.627608\pi\) | ||||
−0.390241 | + | 0.920713i | \(0.627608\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −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 | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.5830 | − | 26.9906i | −0.523521 | − | 0.906765i | ||||
\(887\) | −15.5203 | + | 26.8819i | −0.521119 | + | 0.902605i | 0.478579 | + | 0.878044i | \(0.341152\pi\) |
−0.999698 | + | 0.0245606i | \(0.992181\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.50000 | + | 6.06218i | −0.117386 | + | 0.203319i | ||||
\(890\) | 7.16601 | 0.240205 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.2288 | − | 24.6449i | −0.476414 | − | 0.825173i | ||||
\(893\) | −10.4170 | − | 18.0428i | −0.348591 | − | 0.603778i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.4575 | 0.416409 | ||||||||
\(896\) | −1.32288 | − | 2.29129i | −0.0441942 | − | 0.0765466i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.2288 | − | 26.3770i | 0.508190 | − | 0.880211i | ||||
\(899\) | −4.00000 | − | 6.92820i | −0.133407 | − | 0.231069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.00000 | − | 10.3923i | 0.199889 | − | 0.346218i | ||||
\(902\) | 9.00000 | 0.299667 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.5830 | −0.418505 | ||||||||
\(905\) | −7.00000 | + | 12.1244i | −0.232688 | + | 0.403027i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 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 | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 28.0000 | 0.928191 | ||||||||
\(911\) | 18.3948 | 0.609446 | 0.304723 | − | 0.952441i | \(-0.401436\pi\) | ||||
0.304723 | + | 0.952441i | \(0.401436\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.79150 | − | 13.4953i | −0.257861 | − | 0.446629i | ||||
\(914\) | 20.2915 | + | 35.1459i | 0.671183 | + | 1.16252i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.70850 | 0.221655 | ||||||||
\(917\) | −24.5830 | − | 42.5790i | −0.811802 | − | 1.40608i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −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 | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.2915 | + | 21.2895i | −0.404799 | + | 0.701133i | ||||
\(923\) | −10.8340 | −0.356605 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.58301 | 0.0849287 | ||||||||
\(926\) | −19.5203 | + | 33.8101i | −0.641476 | + | 1.11107i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.00000 | + | 1.73205i | 0.0328266 | + | 0.0568574i | ||||
\(929\) | −17.2288 | + | 29.8411i | −0.565257 | + | 0.979054i | 0.431769 | + | 0.901984i | \(0.357890\pi\) |
−0.997026 | + | 0.0770697i | \(0.975444\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.0405 | 1.21395 | ||||||||
\(932\) | −20.1660 | −0.660560 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.00000 | + | 6.92820i | 0.130884 | + | 0.226698i | ||||
\(935\) | −3.96863 | − | 6.87386i | −0.129788 | − | 0.224799i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 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 | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.20850 | − | 9.02138i | 0.169882 | − | 0.294245i | ||||
\(941\) | 1.70850 | + | 2.95920i | 0.0556954 | + | 0.0964673i | 0.892529 | − | 0.450990i | \(-0.148929\pi\) |
−0.836833 | + | 0.547458i | \(0.815596\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.9059 | − | 20.6216i | 0.387709 | − | 0.671531i | ||||
\(944\) | −6.58301 | −0.214259 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.29150 | −0.302093 | ||||||||
\(947\) | −7.70850 | + | 13.3515i | −0.250493 | + | 0.433866i | −0.963662 | − | 0.267126i | \(-0.913926\pi\) |
0.713169 | + | 0.700992i | \(0.247259\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.5830 | − | 52.9713i | −0.992766 | − | 1.71952i | ||||
\(950\) | −5.29150 | + | 9.16515i | −0.171679 | + | 0.297357i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.93725 | 0.257248 | ||||||||
\(953\) | −26.7490 | −0.866486 | −0.433243 | − | 0.901277i | \(-0.642631\pi\) | ||||
−0.433243 | + | 0.901277i | \(0.642631\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.87451 | − | 15.3711i | −0.287172 | − | 0.497397i | ||||
\(956\) | 1.35425 | + | 2.34563i | 0.0437995 | + | 0.0758630i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.8745 | 1.09444 | ||||||||
\(959\) | 35.1660 | 1.13557 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 2.58301 | + | 4.47390i | 0.0832794 | + | 0.144244i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.5830 | − | 23.5265i | 0.437479 | − | 0.757736i | ||||
\(965\) | 42.0000 | 1.35203 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 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 | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15.3229 | − | 26.5400i | −0.491988 | − | 0.852148i | ||||
\(971\) | 3.00000 | − | 5.19615i | 0.0962746 | − | 0.166752i | −0.813865 | − | 0.581054i | \(-0.802641\pi\) |
0.910140 | + | 0.414301i | \(0.135974\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.6458 | − | 28.8313i | 0.533638 | − | 0.924289i | ||||
\(974\) | 21.8745 | 0.700904 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.96863 | − | 10.3380i | −0.191051 | − | 0.330910i | ||||
\(977\) | 6.58301 | + | 11.4021i | 0.210609 | + | 0.364785i | 0.951905 | − | 0.306392i | \(-0.0991220\pi\) |
−0.741296 | + | 0.671178i | \(0.765789\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.70850 | 0.0865640 | ||||||||
\(980\) | 9.26013 | + | 16.0390i | 0.295804 | + | 0.512348i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.500000 | + | 0.866025i | −0.0159556 | + | 0.0276360i | ||||
\(983\) | 21.2601 | + | 36.8236i | 0.678093 | + | 1.17449i | 0.975555 | + | 0.219757i | \(0.0705266\pi\) |
−0.297462 | + | 0.954734i | \(0.596140\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.9373 | + | 50.1208i | −0.922018 | + | 1.59698i | ||||
\(986\) | −6.00000 | −0.191079 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.1660 | −0.673380 | ||||||||
\(989\) | −12.2915 | + | 21.2895i | −0.390847 | + | 0.676967i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.58301 | − | 6.20595i | −0.113646 | − | 0.196841i | ||||
\(995\) | 50.7085 | 1.60757 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −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 | 0 |
(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 | 1386.2.k.r.793.2 | 4 | ||
3.2 | odd | 2 | 462.2.i.e.331.1 | yes | 4 | ||
7.2 | even | 3 | 9702.2.a.db.1.1 | 2 | |||
7.4 | even | 3 | inner | 1386.2.k.r.991.2 | 4 | ||
7.5 | odd | 6 | 9702.2.a.dm.1.2 | 2 | |||
21.2 | odd | 6 | 3234.2.a.w.1.2 | 2 | |||
21.5 | even | 6 | 3234.2.a.ba.1.1 | 2 | |||
21.11 | odd | 6 | 462.2.i.e.67.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.e.67.1 | ✓ | 4 | 21.11 | odd | 6 | ||
462.2.i.e.331.1 | yes | 4 | 3.2 | odd | 2 | ||
1386.2.k.r.793.2 | 4 | 1.1 | even | 1 | trivial | ||
1386.2.k.r.991.2 | 4 | 7.4 | even | 3 | inner | ||
3234.2.a.w.1.2 | 2 | 21.2 | odd | 6 | |||
3234.2.a.ba.1.1 | 2 | 21.5 | even | 6 | |||
9702.2.a.db.1.1 | 2 | 7.2 | even | 3 | |||
9702.2.a.dm.1.2 | 2 | 7.5 | odd | 6 |