Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [104,2,Mod(53,104)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(104, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("104.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 104 = 2^{3} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 104.b (of order \(2\), degree \(1\), 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: | \(0.830444181021\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 53.3 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 104.53 |
Dual form | 104.2.b.b.53.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/104\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(53\) | \(79\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | − | 0.366025i | 0.965926 | − | 0.258819i | ||||
\(3\) | − | 2.00000i | − | 1.15470i | −0.816497 | − | 0.577350i | \(-0.804087\pi\) | ||
0.816497 | − | 0.577350i | \(-0.195913\pi\) | |||||||
\(4\) | 1.73205 | − | 1.00000i | 0.866025 | − | 0.500000i | ||||
\(5\) | 3.46410i | 1.54919i | 0.632456 | + | 0.774597i | \(0.282047\pi\) | ||||
−0.632456 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(6\) | −0.732051 | − | 2.73205i | −0.298858 | − | 1.11536i | ||||
\(7\) | −4.73205 | −1.78855 | −0.894274 | − | 0.447521i | \(-0.852307\pi\) | ||||
−0.894274 | + | 0.447521i | \(0.852307\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.26795 | + | 4.73205i | 0.400961 | + | 1.49641i | ||||
\(11\) | 1.26795i | 0.382301i | 0.981561 | + | 0.191151i | \(0.0612219\pi\) | ||||
−0.981561 | + | 0.191151i | \(0.938778\pi\) | |||||||
\(12\) | −2.00000 | − | 3.46410i | −0.577350 | − | 1.00000i | ||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | −6.46410 | + | 1.73205i | −1.72760 | + | 0.462910i | ||||
\(15\) | 6.92820 | 1.78885 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | −1.46410 | −0.355097 | −0.177548 | − | 0.984112i | \(-0.556817\pi\) | ||||
−0.177548 | + | 0.984112i | \(0.556817\pi\) | |||||||
\(18\) | −1.36603 | + | 0.366025i | −0.321975 | + | 0.0862730i | ||||
\(19\) | 2.73205i | 0.626775i | 0.949625 | + | 0.313388i | \(0.101464\pi\) | ||||
−0.949625 | + | 0.313388i | \(0.898536\pi\) | |||||||
\(20\) | 3.46410 | + | 6.00000i | 0.774597 | + | 1.34164i | ||||
\(21\) | 9.46410i | 2.06524i | ||||||||
\(22\) | 0.464102 | + | 1.73205i | 0.0989468 | + | 0.369274i | ||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | −4.00000 | − | 4.00000i | −0.816497 | − | 0.816497i | ||||
\(25\) | −7.00000 | −1.40000 | ||||||||
\(26\) | −0.366025 | − | 1.36603i | −0.0717835 | − | 0.267900i | ||||
\(27\) | − | 4.00000i | − | 0.769800i | ||||||
\(28\) | −8.19615 | + | 4.73205i | −1.54893 | + | 0.894274i | ||||
\(29\) | − | 2.00000i | − | 0.371391i | −0.982607 | − | 0.185695i | \(-0.940546\pi\) | ||
0.982607 | − | 0.185695i | \(-0.0594537\pi\) | |||||||
\(30\) | 9.46410 | − | 2.53590i | 1.72790 | − | 0.462990i | ||||
\(31\) | −3.26795 | −0.586941 | −0.293471 | − | 0.955968i | \(-0.594810\pi\) | ||||
−0.293471 | + | 0.955968i | \(0.594810\pi\) | |||||||
\(32\) | 1.46410 | − | 5.46410i | 0.258819 | − | 0.965926i | ||||
\(33\) | 2.53590 | 0.441443 | ||||||||
\(34\) | −2.00000 | + | 0.535898i | −0.342997 | + | 0.0919058i | ||||
\(35\) | − | 16.3923i | − | 2.77081i | ||||||
\(36\) | −1.73205 | + | 1.00000i | −0.288675 | + | 0.166667i | ||||
\(37\) | − | 4.92820i | − | 0.810192i | −0.914274 | − | 0.405096i | \(-0.867238\pi\) | ||
0.914274 | − | 0.405096i | \(-0.132762\pi\) | |||||||
\(38\) | 1.00000 | + | 3.73205i | 0.162221 | + | 0.605419i | ||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 6.92820 | + | 6.92820i | 1.09545 | + | 1.09545i | ||||
\(41\) | −4.92820 | −0.769656 | −0.384828 | − | 0.922988i | \(-0.625739\pi\) | ||||
−0.384828 | + | 0.922988i | \(0.625739\pi\) | |||||||
\(42\) | 3.46410 | + | 12.9282i | 0.534522 | + | 1.99487i | ||||
\(43\) | 7.46410i | 1.13826i | 0.822246 | + | 0.569132i | \(0.192721\pi\) | ||||
−0.822246 | + | 0.569132i | \(0.807279\pi\) | |||||||
\(44\) | 1.26795 | + | 2.19615i | 0.191151 | + | 0.331082i | ||||
\(45\) | − | 3.46410i | − | 0.516398i | ||||||
\(46\) | 5.46410 | − | 1.46410i | 0.805638 | − | 0.215870i | ||||
\(47\) | 3.26795 | 0.476679 | 0.238340 | − | 0.971182i | \(-0.423397\pi\) | ||||
0.238340 | + | 0.971182i | \(0.423397\pi\) | |||||||
\(48\) | −6.92820 | − | 4.00000i | −1.00000 | − | 0.577350i | ||||
\(49\) | 15.3923 | 2.19890 | ||||||||
\(50\) | −9.56218 | + | 2.56218i | −1.35230 | + | 0.362347i | ||||
\(51\) | 2.92820i | 0.410030i | ||||||||
\(52\) | −1.00000 | − | 1.73205i | −0.138675 | − | 0.240192i | ||||
\(53\) | − | 10.9282i | − | 1.50110i | −0.660811 | − | 0.750552i | \(-0.729788\pi\) | ||
0.660811 | − | 0.750552i | \(-0.270212\pi\) | |||||||
\(54\) | −1.46410 | − | 5.46410i | −0.199239 | − | 0.743570i | ||||
\(55\) | −4.39230 | −0.592258 | ||||||||
\(56\) | −9.46410 | + | 9.46410i | −1.26469 | + | 1.26469i | ||||
\(57\) | 5.46410 | 0.723738 | ||||||||
\(58\) | −0.732051 | − | 2.73205i | −0.0961230 | − | 0.358736i | ||||
\(59\) | − | 0.196152i | − | 0.0255369i | −0.999918 | − | 0.0127684i | \(-0.995936\pi\) | ||
0.999918 | − | 0.0127684i | \(-0.00406443\pi\) | |||||||
\(60\) | 12.0000 | − | 6.92820i | 1.54919 | − | 0.894427i | ||||
\(61\) | 10.9282i | 1.39921i | 0.714528 | + | 0.699607i | \(0.246641\pi\) | ||||
−0.714528 | + | 0.699607i | \(0.753359\pi\) | |||||||
\(62\) | −4.46410 | + | 1.19615i | −0.566941 | + | 0.151912i | ||||
\(63\) | 4.73205 | 0.596182 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 3.46410 | 0.429669 | ||||||||
\(66\) | 3.46410 | − | 0.928203i | 0.426401 | − | 0.114254i | ||||
\(67\) | 2.73205i | 0.333773i | 0.985976 | + | 0.166887i | \(0.0533714\pi\) | ||||
−0.985976 | + | 0.166887i | \(0.946629\pi\) | |||||||
\(68\) | −2.53590 | + | 1.46410i | −0.307523 | + | 0.177548i | ||||
\(69\) | − | 8.00000i | − | 0.963087i | ||||||
\(70\) | −6.00000 | − | 22.3923i | −0.717137 | − | 2.67639i | ||||
\(71\) | 2.19615 | 0.260635 | 0.130318 | − | 0.991472i | \(-0.458400\pi\) | ||||
0.130318 | + | 0.991472i | \(0.458400\pi\) | |||||||
\(72\) | −2.00000 | + | 2.00000i | −0.235702 | + | 0.235702i | ||||
\(73\) | −0.535898 | −0.0627222 | −0.0313611 | − | 0.999508i | \(-0.509984\pi\) | ||||
−0.0313611 | + | 0.999508i | \(0.509984\pi\) | |||||||
\(74\) | −1.80385 | − | 6.73205i | −0.209693 | − | 0.782585i | ||||
\(75\) | 14.0000i | 1.61658i | ||||||||
\(76\) | 2.73205 | + | 4.73205i | 0.313388 | + | 0.542803i | ||||
\(77\) | − | 6.00000i | − | 0.683763i | ||||||
\(78\) | −2.73205 | + | 0.732051i | −0.309344 | + | 0.0828884i | ||||
\(79\) | −1.46410 | −0.164724 | −0.0823622 | − | 0.996602i | \(-0.526246\pi\) | ||||
−0.0823622 | + | 0.996602i | \(0.526246\pi\) | |||||||
\(80\) | 12.0000 | + | 6.92820i | 1.34164 | + | 0.774597i | ||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | −6.73205 | + | 1.80385i | −0.743431 | + | 0.199202i | ||||
\(83\) | − | 6.73205i | − | 0.738939i | −0.929243 | − | 0.369469i | \(-0.879539\pi\) | ||
0.929243 | − | 0.369469i | \(-0.120461\pi\) | |||||||
\(84\) | 9.46410 | + | 16.3923i | 1.03262 | + | 1.78855i | ||||
\(85\) | − | 5.07180i | − | 0.550114i | ||||||
\(86\) | 2.73205 | + | 10.1962i | 0.294605 | + | 1.09948i | ||||
\(87\) | −4.00000 | −0.428845 | ||||||||
\(88\) | 2.53590 | + | 2.53590i | 0.270328 | + | 0.270328i | ||||
\(89\) | 17.3205 | 1.83597 | 0.917985 | − | 0.396615i | \(-0.129815\pi\) | ||||
0.917985 | + | 0.396615i | \(0.129815\pi\) | |||||||
\(90\) | −1.26795 | − | 4.73205i | −0.133654 | − | 0.498802i | ||||
\(91\) | 4.73205i | 0.496054i | ||||||||
\(92\) | 6.92820 | − | 4.00000i | 0.722315 | − | 0.417029i | ||||
\(93\) | 6.53590i | 0.677741i | ||||||||
\(94\) | 4.46410 | − | 1.19615i | 0.460437 | − | 0.123374i | ||||
\(95\) | −9.46410 | −0.970996 | ||||||||
\(96\) | −10.9282 | − | 2.92820i | −1.11536 | − | 0.298858i | ||||
\(97\) | −14.3923 | −1.46132 | −0.730659 | − | 0.682743i | \(-0.760787\pi\) | ||||
−0.730659 | + | 0.682743i | \(0.760787\pi\) | |||||||
\(98\) | 21.0263 | − | 5.63397i | 2.12397 | − | 0.569117i | ||||
\(99\) | − | 1.26795i | − | 0.127434i | ||||||
\(100\) | −12.1244 | + | 7.00000i | −1.21244 | + | 0.700000i | ||||
\(101\) | 12.0000i | 1.19404i | 0.802225 | + | 0.597022i | \(0.203650\pi\) | ||||
−0.802225 | + | 0.597022i | \(0.796350\pi\) | |||||||
\(102\) | 1.07180 | + | 4.00000i | 0.106124 | + | 0.396059i | ||||
\(103\) | −6.92820 | −0.682656 | −0.341328 | − | 0.939944i | \(-0.610877\pi\) | ||||
−0.341328 | + | 0.939944i | \(0.610877\pi\) | |||||||
\(104\) | −2.00000 | − | 2.00000i | −0.196116 | − | 0.196116i | ||||
\(105\) | −32.7846 | −3.19945 | ||||||||
\(106\) | −4.00000 | − | 14.9282i | −0.388514 | − | 1.44996i | ||||
\(107\) | 8.92820i | 0.863122i | 0.902084 | + | 0.431561i | \(0.142037\pi\) | ||||
−0.902084 | + | 0.431561i | \(0.857963\pi\) | |||||||
\(108\) | −4.00000 | − | 6.92820i | −0.384900 | − | 0.666667i | ||||
\(109\) | 2.00000i | 0.191565i | 0.995402 | + | 0.0957826i | \(0.0305354\pi\) | ||||
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | −6.00000 | + | 1.60770i | −0.572078 | + | 0.153288i | ||||
\(111\) | −9.85641 | −0.935529 | ||||||||
\(112\) | −9.46410 | + | 16.3923i | −0.894274 | + | 1.54893i | ||||
\(113\) | 9.46410 | 0.890308 | 0.445154 | − | 0.895454i | \(-0.353149\pi\) | ||||
0.445154 | + | 0.895454i | \(0.353149\pi\) | |||||||
\(114\) | 7.46410 | − | 2.00000i | 0.699077 | − | 0.187317i | ||||
\(115\) | 13.8564i | 1.29212i | ||||||||
\(116\) | −2.00000 | − | 3.46410i | −0.185695 | − | 0.321634i | ||||
\(117\) | 1.00000i | 0.0924500i | ||||||||
\(118\) | −0.0717968 | − | 0.267949i | −0.00660943 | − | 0.0246667i | ||||
\(119\) | 6.92820 | 0.635107 | ||||||||
\(120\) | 13.8564 | − | 13.8564i | 1.26491 | − | 1.26491i | ||||
\(121\) | 9.39230 | 0.853846 | ||||||||
\(122\) | 4.00000 | + | 14.9282i | 0.362143 | + | 1.35154i | ||||
\(123\) | 9.85641i | 0.888722i | ||||||||
\(124\) | −5.66025 | + | 3.26795i | −0.508306 | + | 0.293471i | ||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 6.46410 | − | 1.73205i | 0.575868 | − | 0.154303i | ||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | −2.92820 | − | 10.9282i | −0.258819 | − | 0.965926i | ||||
\(129\) | 14.9282 | 1.31436 | ||||||||
\(130\) | 4.73205 | − | 1.26795i | 0.415028 | − | 0.111207i | ||||
\(131\) | 7.85641i | 0.686417i | 0.939259 | + | 0.343209i | \(0.111514\pi\) | ||||
−0.939259 | + | 0.343209i | \(0.888486\pi\) | |||||||
\(132\) | 4.39230 | − | 2.53590i | 0.382301 | − | 0.220722i | ||||
\(133\) | − | 12.9282i | − | 1.12102i | ||||||
\(134\) | 1.00000 | + | 3.73205i | 0.0863868 | + | 0.322400i | ||||
\(135\) | 13.8564 | 1.19257 | ||||||||
\(136\) | −2.92820 | + | 2.92820i | −0.251091 | + | 0.251091i | ||||
\(137\) | −0.928203 | −0.0793018 | −0.0396509 | − | 0.999214i | \(-0.512625\pi\) | ||||
−0.0396509 | + | 0.999214i | \(0.512625\pi\) | |||||||
\(138\) | −2.92820 | − | 10.9282i | −0.249265 | − | 0.930270i | ||||
\(139\) | 10.0000i | 0.848189i | 0.905618 | + | 0.424094i | \(0.139408\pi\) | ||||
−0.905618 | + | 0.424094i | \(0.860592\pi\) | |||||||
\(140\) | −16.3923 | − | 28.3923i | −1.38540 | − | 2.39959i | ||||
\(141\) | − | 6.53590i | − | 0.550422i | ||||||
\(142\) | 3.00000 | − | 0.803848i | 0.251754 | − | 0.0674574i | ||||
\(143\) | 1.26795 | 0.106031 | ||||||||
\(144\) | −2.00000 | + | 3.46410i | −0.166667 | + | 0.288675i | ||||
\(145\) | 6.92820 | 0.575356 | ||||||||
\(146\) | −0.732051 | + | 0.196152i | −0.0605850 | + | 0.0162337i | ||||
\(147\) | − | 30.7846i | − | 2.53907i | ||||||
\(148\) | −4.92820 | − | 8.53590i | −0.405096 | − | 0.701647i | ||||
\(149\) | − | 0.928203i | − | 0.0760414i | −0.999277 | − | 0.0380207i | \(-0.987895\pi\) | ||
0.999277 | − | 0.0380207i | \(-0.0121053\pi\) | |||||||
\(150\) | 5.12436 | + | 19.1244i | 0.418402 | + | 1.56150i | ||||
\(151\) | 17.1244 | 1.39356 | 0.696780 | − | 0.717285i | \(-0.254615\pi\) | ||||
0.696780 | + | 0.717285i | \(0.254615\pi\) | |||||||
\(152\) | 5.46410 | + | 5.46410i | 0.443197 | + | 0.443197i | ||||
\(153\) | 1.46410 | 0.118366 | ||||||||
\(154\) | −2.19615 | − | 8.19615i | −0.176971 | − | 0.660465i | ||||
\(155\) | − | 11.3205i | − | 0.909285i | ||||||
\(156\) | −3.46410 | + | 2.00000i | −0.277350 | + | 0.160128i | ||||
\(157\) | 3.07180i | 0.245156i | 0.992459 | + | 0.122578i | \(0.0391162\pi\) | ||||
−0.992459 | + | 0.122578i | \(0.960884\pi\) | |||||||
\(158\) | −2.00000 | + | 0.535898i | −0.159111 | + | 0.0426338i | ||||
\(159\) | −21.8564 | −1.73333 | ||||||||
\(160\) | 18.9282 | + | 5.07180i | 1.49641 | + | 0.400961i | ||||
\(161\) | −18.9282 | −1.49175 | ||||||||
\(162\) | −15.0263 | + | 4.02628i | −1.18058 | + | 0.316334i | ||||
\(163\) | − | 13.2679i | − | 1.03923i | −0.854402 | − | 0.519613i | \(-0.826076\pi\) | ||
0.854402 | − | 0.519613i | \(-0.173924\pi\) | |||||||
\(164\) | −8.53590 | + | 4.92820i | −0.666542 | + | 0.384828i | ||||
\(165\) | 8.78461i | 0.683881i | ||||||||
\(166\) | −2.46410 | − | 9.19615i | −0.191251 | − | 0.713760i | ||||
\(167\) | 11.6603 | 0.902298 | 0.451149 | − | 0.892449i | \(-0.351014\pi\) | ||||
0.451149 | + | 0.892449i | \(0.351014\pi\) | |||||||
\(168\) | 18.9282 | + | 18.9282i | 1.46034 | + | 1.46034i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | −1.85641 | − | 6.92820i | −0.142380 | − | 0.531369i | ||||
\(171\) | − | 2.73205i | − | 0.208925i | ||||||
\(172\) | 7.46410 | + | 12.9282i | 0.569132 | + | 0.985766i | ||||
\(173\) | 6.92820i | 0.526742i | 0.964695 | + | 0.263371i | \(0.0848343\pi\) | ||||
−0.964695 | + | 0.263371i | \(0.915166\pi\) | |||||||
\(174\) | −5.46410 | + | 1.46410i | −0.414232 | + | 0.110993i | ||||
\(175\) | 33.1244 | 2.50397 | ||||||||
\(176\) | 4.39230 | + | 2.53590i | 0.331082 | + | 0.191151i | ||||
\(177\) | −0.392305 | −0.0294874 | ||||||||
\(178\) | 23.6603 | − | 6.33975i | 1.77341 | − | 0.475184i | ||||
\(179\) | − | 10.3923i | − | 0.776757i | −0.921500 | − | 0.388379i | \(-0.873035\pi\) | ||
0.921500 | − | 0.388379i | \(-0.126965\pi\) | |||||||
\(180\) | −3.46410 | − | 6.00000i | −0.258199 | − | 0.447214i | ||||
\(181\) | − | 4.92820i | − | 0.366310i | −0.983084 | − | 0.183155i | \(-0.941369\pi\) | ||
0.983084 | − | 0.183155i | \(-0.0586311\pi\) | |||||||
\(182\) | 1.73205 | + | 6.46410i | 0.128388 | + | 0.479151i | ||||
\(183\) | 21.8564 | 1.61567 | ||||||||
\(184\) | 8.00000 | − | 8.00000i | 0.589768 | − | 0.589768i | ||||
\(185\) | 17.0718 | 1.25514 | ||||||||
\(186\) | 2.39230 | + | 8.92820i | 0.175412 | + | 0.654648i | ||||
\(187\) | − | 1.85641i | − | 0.135754i | ||||||
\(188\) | 5.66025 | − | 3.26795i | 0.412816 | − | 0.238340i | ||||
\(189\) | 18.9282i | 1.37682i | ||||||||
\(190\) | −12.9282 | + | 3.46410i | −0.937910 | + | 0.251312i | ||||
\(191\) | −21.4641 | −1.55309 | −0.776544 | − | 0.630063i | \(-0.783029\pi\) | ||||
−0.776544 | + | 0.630063i | \(0.783029\pi\) | |||||||
\(192\) | −16.0000 | −1.15470 | ||||||||
\(193\) | −22.3923 | −1.61183 | −0.805917 | − | 0.592029i | \(-0.798327\pi\) | ||||
−0.805917 | + | 0.592029i | \(0.798327\pi\) | |||||||
\(194\) | −19.6603 | + | 5.26795i | −1.41152 | + | 0.378217i | ||||
\(195\) | − | 6.92820i | − | 0.496139i | ||||||
\(196\) | 26.6603 | − | 15.3923i | 1.90430 | − | 1.09945i | ||||
\(197\) | 16.9282i | 1.20608i | 0.797709 | + | 0.603042i | \(0.206045\pi\) | ||||
−0.797709 | + | 0.603042i | \(0.793955\pi\) | |||||||
\(198\) | −0.464102 | − | 1.73205i | −0.0329823 | − | 0.123091i | ||||
\(199\) | −24.7846 | −1.75693 | −0.878467 | − | 0.477803i | \(-0.841433\pi\) | ||||
−0.878467 | + | 0.477803i | \(0.841433\pi\) | |||||||
\(200\) | −14.0000 | + | 14.0000i | −0.989949 | + | 0.989949i | ||||
\(201\) | 5.46410 | 0.385408 | ||||||||
\(202\) | 4.39230 | + | 16.3923i | 0.309041 | + | 1.15336i | ||||
\(203\) | 9.46410i | 0.664250i | ||||||||
\(204\) | 2.92820 | + | 5.07180i | 0.205015 | + | 0.355097i | ||||
\(205\) | − | 17.0718i | − | 1.19235i | ||||||
\(206\) | −9.46410 | + | 2.53590i | −0.659395 | + | 0.176684i | ||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | −3.46410 | − | 2.00000i | −0.240192 | − | 0.138675i | ||||
\(209\) | −3.46410 | −0.239617 | ||||||||
\(210\) | −44.7846 | + | 12.0000i | −3.09043 | + | 0.828079i | ||||
\(211\) | − | 19.8564i | − | 1.36697i | −0.729964 | − | 0.683486i | \(-0.760463\pi\) | ||
0.729964 | − | 0.683486i | \(-0.239537\pi\) | |||||||
\(212\) | −10.9282 | − | 18.9282i | −0.750552 | − | 1.29999i | ||||
\(213\) | − | 4.39230i | − | 0.300956i | ||||||
\(214\) | 3.26795 | + | 12.1962i | 0.223392 | + | 0.833712i | ||||
\(215\) | −25.8564 | −1.76339 | ||||||||
\(216\) | −8.00000 | − | 8.00000i | −0.544331 | − | 0.544331i | ||||
\(217\) | 15.4641 | 1.04977 | ||||||||
\(218\) | 0.732051 | + | 2.73205i | 0.0495807 | + | 0.185038i | ||||
\(219\) | 1.07180i | 0.0724253i | ||||||||
\(220\) | −7.60770 | + | 4.39230i | −0.512911 | + | 0.296129i | ||||
\(221\) | 1.46410i | 0.0984861i | ||||||||
\(222\) | −13.4641 | + | 3.60770i | −0.903651 | + | 0.242133i | ||||
\(223\) | 10.1962 | 0.682785 | 0.341392 | − | 0.939921i | \(-0.389101\pi\) | ||||
0.341392 | + | 0.939921i | \(0.389101\pi\) | |||||||
\(224\) | −6.92820 | + | 25.8564i | −0.462910 | + | 1.72760i | ||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 12.9282 | − | 3.46410i | 0.859971 | − | 0.230429i | ||||
\(227\) | − | 27.1244i | − | 1.80031i | −0.435573 | − | 0.900153i | \(-0.643454\pi\) | ||
0.435573 | − | 0.900153i | \(-0.356546\pi\) | |||||||
\(228\) | 9.46410 | − | 5.46410i | 0.626775 | − | 0.361869i | ||||
\(229\) | − | 29.3205i | − | 1.93755i | −0.247934 | − | 0.968777i | \(-0.579752\pi\) | ||
0.247934 | − | 0.968777i | \(-0.420248\pi\) | |||||||
\(230\) | 5.07180 | + | 18.9282i | 0.334424 | + | 1.24809i | ||||
\(231\) | −12.0000 | −0.789542 | ||||||||
\(232\) | −4.00000 | − | 4.00000i | −0.262613 | − | 0.262613i | ||||
\(233\) | 3.07180 | 0.201240 | 0.100620 | − | 0.994925i | \(-0.467917\pi\) | ||||
0.100620 | + | 0.994925i | \(0.467917\pi\) | |||||||
\(234\) | 0.366025 | + | 1.36603i | 0.0239278 | + | 0.0892999i | ||||
\(235\) | 11.3205i | 0.738469i | ||||||||
\(236\) | −0.196152 | − | 0.339746i | −0.0127684 | − | 0.0221156i | ||||
\(237\) | 2.92820i | 0.190207i | ||||||||
\(238\) | 9.46410 | − | 2.53590i | 0.613467 | − | 0.164378i | ||||
\(239\) | 15.2679 | 0.987602 | 0.493801 | − | 0.869575i | \(-0.335607\pi\) | ||||
0.493801 | + | 0.869575i | \(0.335607\pi\) | |||||||
\(240\) | 13.8564 | − | 24.0000i | 0.894427 | − | 1.54919i | ||||
\(241\) | −9.60770 | −0.618886 | −0.309443 | − | 0.950918i | \(-0.600143\pi\) | ||||
−0.309443 | + | 0.950918i | \(0.600143\pi\) | |||||||
\(242\) | 12.8301 | − | 3.43782i | 0.824752 | − | 0.220992i | ||||
\(243\) | 10.0000i | 0.641500i | ||||||||
\(244\) | 10.9282 | + | 18.9282i | 0.699607 | + | 1.21175i | ||||
\(245\) | 53.3205i | 3.40652i | ||||||||
\(246\) | 3.60770 | + | 13.4641i | 0.230018 | + | 0.858440i | ||||
\(247\) | 2.73205 | 0.173836 | ||||||||
\(248\) | −6.53590 | + | 6.53590i | −0.415030 | + | 0.415030i | ||||
\(249\) | −13.4641 | −0.853253 | ||||||||
\(250\) | −2.53590 | − | 9.46410i | −0.160384 | − | 0.598562i | ||||
\(251\) | 14.3923i | 0.908434i | 0.890891 | + | 0.454217i | \(0.150081\pi\) | ||||
−0.890891 | + | 0.454217i | \(0.849919\pi\) | |||||||
\(252\) | 8.19615 | − | 4.73205i | 0.516309 | − | 0.298091i | ||||
\(253\) | 5.07180i | 0.318861i | ||||||||
\(254\) | −5.46410 | + | 1.46410i | −0.342848 | + | 0.0918659i | ||||
\(255\) | −10.1436 | −0.635216 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 3.85641 | 0.240556 | 0.120278 | − | 0.992740i | \(-0.461621\pi\) | ||||
0.120278 | + | 0.992740i | \(0.461621\pi\) | |||||||
\(258\) | 20.3923 | − | 5.46410i | 1.26957 | − | 0.340180i | ||||
\(259\) | 23.3205i | 1.44907i | ||||||||
\(260\) | 6.00000 | − | 3.46410i | 0.372104 | − | 0.214834i | ||||
\(261\) | 2.00000i | 0.123797i | ||||||||
\(262\) | 2.87564 | + | 10.7321i | 0.177658 | + | 0.663028i | ||||
\(263\) | 7.32051 | 0.451402 | 0.225701 | − | 0.974197i | \(-0.427533\pi\) | ||||
0.225701 | + | 0.974197i | \(0.427533\pi\) | |||||||
\(264\) | 5.07180 | − | 5.07180i | 0.312148 | − | 0.312148i | ||||
\(265\) | 37.8564 | 2.32550 | ||||||||
\(266\) | −4.73205 | − | 17.6603i | −0.290141 | − | 1.08282i | ||||
\(267\) | − | 34.6410i | − | 2.12000i | ||||||
\(268\) | 2.73205 | + | 4.73205i | 0.166887 | + | 0.289056i | ||||
\(269\) | − | 19.8564i | − | 1.21067i | −0.795972 | − | 0.605333i | \(-0.793040\pi\) | ||
0.795972 | − | 0.605333i | \(-0.206960\pi\) | |||||||
\(270\) | 18.9282 | − | 5.07180i | 1.15193 | − | 0.308660i | ||||
\(271\) | −9.80385 | −0.595541 | −0.297771 | − | 0.954637i | \(-0.596243\pi\) | ||||
−0.297771 | + | 0.954637i | \(0.596243\pi\) | |||||||
\(272\) | −2.92820 | + | 5.07180i | −0.177548 | + | 0.307523i | ||||
\(273\) | 9.46410 | 0.572793 | ||||||||
\(274\) | −1.26795 | + | 0.339746i | −0.0765996 | + | 0.0205248i | ||||
\(275\) | − | 8.87564i | − | 0.535221i | ||||||
\(276\) | −8.00000 | − | 13.8564i | −0.481543 | − | 0.834058i | ||||
\(277\) | 25.8564i | 1.55356i | 0.629771 | + | 0.776780i | \(0.283149\pi\) | ||||
−0.629771 | + | 0.776780i | \(0.716851\pi\) | |||||||
\(278\) | 3.66025 | + | 13.6603i | 0.219527 | + | 0.819288i | ||||
\(279\) | 3.26795 | 0.195647 | ||||||||
\(280\) | −32.7846 | − | 32.7846i | −1.95926 | − | 1.95926i | ||||
\(281\) | −25.3205 | −1.51049 | −0.755247 | − | 0.655440i | \(-0.772483\pi\) | ||||
−0.755247 | + | 0.655440i | \(0.772483\pi\) | |||||||
\(282\) | −2.39230 | − | 8.92820i | −0.142460 | − | 0.531667i | ||||
\(283\) | − | 12.5359i | − | 0.745182i | −0.927996 | − | 0.372591i | \(-0.878469\pi\) | ||
0.927996 | − | 0.372591i | \(-0.121531\pi\) | |||||||
\(284\) | 3.80385 | − | 2.19615i | 0.225717 | − | 0.130318i | ||||
\(285\) | 18.9282i | 1.12121i | ||||||||
\(286\) | 1.73205 | − | 0.464102i | 0.102418 | − | 0.0274429i | ||||
\(287\) | 23.3205 | 1.37657 | ||||||||
\(288\) | −1.46410 | + | 5.46410i | −0.0862730 | + | 0.321975i | ||||
\(289\) | −14.8564 | −0.873906 | ||||||||
\(290\) | 9.46410 | − | 2.53590i | 0.555751 | − | 0.148913i | ||||
\(291\) | 28.7846i | 1.68738i | ||||||||
\(292\) | −0.928203 | + | 0.535898i | −0.0543190 | + | 0.0313611i | ||||
\(293\) | − | 19.0718i | − | 1.11419i | −0.830450 | − | 0.557093i | \(-0.811917\pi\) | ||
0.830450 | − | 0.557093i | \(-0.188083\pi\) | |||||||
\(294\) | −11.2679 | − | 42.0526i | −0.657160 | − | 2.45256i | ||||
\(295\) | 0.679492 | 0.0395615 | ||||||||
\(296\) | −9.85641 | − | 9.85641i | −0.572892 | − | 0.572892i | ||||
\(297\) | 5.07180 | 0.294295 | ||||||||
\(298\) | −0.339746 | − | 1.26795i | −0.0196810 | − | 0.0734503i | ||||
\(299\) | − | 4.00000i | − | 0.231326i | ||||||
\(300\) | 14.0000 | + | 24.2487i | 0.808290 | + | 1.40000i | ||||
\(301\) | − | 35.3205i | − | 2.03584i | ||||||
\(302\) | 23.3923 | − | 6.26795i | 1.34608 | − | 0.360680i | ||||
\(303\) | 24.0000 | 1.37876 | ||||||||
\(304\) | 9.46410 | + | 5.46410i | 0.542803 | + | 0.313388i | ||||
\(305\) | −37.8564 | −2.16765 | ||||||||
\(306\) | 2.00000 | − | 0.535898i | 0.114332 | − | 0.0306353i | ||||
\(307\) | 2.73205i | 0.155926i | 0.996956 | + | 0.0779632i | \(0.0248417\pi\) | ||||
−0.996956 | + | 0.0779632i | \(0.975158\pi\) | |||||||
\(308\) | −6.00000 | − | 10.3923i | −0.341882 | − | 0.592157i | ||||
\(309\) | 13.8564i | 0.788263i | ||||||||
\(310\) | −4.14359 | − | 15.4641i | −0.235340 | − | 0.878302i | ||||
\(311\) | 14.9282 | 0.846501 | 0.423250 | − | 0.906013i | \(-0.360889\pi\) | ||||
0.423250 | + | 0.906013i | \(0.360889\pi\) | |||||||
\(312\) | −4.00000 | + | 4.00000i | −0.226455 | + | 0.226455i | ||||
\(313\) | −20.3923 | −1.15264 | −0.576321 | − | 0.817224i | \(-0.695512\pi\) | ||||
−0.576321 | + | 0.817224i | \(0.695512\pi\) | |||||||
\(314\) | 1.12436 | + | 4.19615i | 0.0634511 | + | 0.236803i | ||||
\(315\) | 16.3923i | 0.923602i | ||||||||
\(316\) | −2.53590 | + | 1.46410i | −0.142655 | + | 0.0823622i | ||||
\(317\) | 3.46410i | 0.194563i | 0.995257 | + | 0.0972817i | \(0.0310148\pi\) | ||||
−0.995257 | + | 0.0972817i | \(0.968985\pi\) | |||||||
\(318\) | −29.8564 | + | 8.00000i | −1.67426 | + | 0.448618i | ||||
\(319\) | 2.53590 | 0.141983 | ||||||||
\(320\) | 27.7128 | 1.54919 | ||||||||
\(321\) | 17.8564 | 0.996647 | ||||||||
\(322\) | −25.8564 | + | 6.92820i | −1.44092 | + | 0.386094i | ||||
\(323\) | − | 4.00000i | − | 0.222566i | ||||||
\(324\) | −19.0526 | + | 11.0000i | −1.05848 | + | 0.611111i | ||||
\(325\) | 7.00000i | 0.388290i | ||||||||
\(326\) | −4.85641 | − | 18.1244i | −0.268971 | − | 1.00382i | ||||
\(327\) | 4.00000 | 0.221201 | ||||||||
\(328\) | −9.85641 | + | 9.85641i | −0.544229 | + | 0.544229i | ||||
\(329\) | −15.4641 | −0.852564 | ||||||||
\(330\) | 3.21539 | + | 12.0000i | 0.177001 | + | 0.660578i | ||||
\(331\) | 27.5167i | 1.51245i | 0.654310 | + | 0.756226i | \(0.272959\pi\) | ||||
−0.654310 | + | 0.756226i | \(0.727041\pi\) | |||||||
\(332\) | −6.73205 | − | 11.6603i | −0.369469 | − | 0.639940i | ||||
\(333\) | 4.92820i | 0.270064i | ||||||||
\(334\) | 15.9282 | − | 4.26795i | 0.871553 | − | 0.233532i | ||||
\(335\) | −9.46410 | −0.517079 | ||||||||
\(336\) | 32.7846 | + | 18.9282i | 1.78855 | + | 1.03262i | ||||
\(337\) | −5.46410 | −0.297649 | −0.148824 | − | 0.988864i | \(-0.547549\pi\) | ||||
−0.148824 | + | 0.988864i | \(0.547549\pi\) | |||||||
\(338\) | −1.36603 | + | 0.366025i | −0.0743020 | + | 0.0199092i | ||||
\(339\) | − | 18.9282i | − | 1.02804i | ||||||
\(340\) | −5.07180 | − | 8.78461i | −0.275057 | − | 0.476412i | ||||
\(341\) | − | 4.14359i | − | 0.224388i | ||||||
\(342\) | −1.00000 | − | 3.73205i | −0.0540738 | − | 0.201806i | ||||
\(343\) | −39.7128 | −2.14429 | ||||||||
\(344\) | 14.9282 | + | 14.9282i | 0.804875 | + | 0.804875i | ||||
\(345\) | 27.7128 | 1.49201 | ||||||||
\(346\) | 2.53590 | + | 9.46410i | 0.136331 | + | 0.508793i | ||||
\(347\) | 20.9282i | 1.12348i | 0.827312 | + | 0.561742i | \(0.189869\pi\) | ||||
−0.827312 | + | 0.561742i | \(0.810131\pi\) | |||||||
\(348\) | −6.92820 | + | 4.00000i | −0.371391 | + | 0.214423i | ||||
\(349\) | − | 30.3923i | − | 1.62686i | −0.581661 | − | 0.813431i | \(-0.697597\pi\) | ||
0.581661 | − | 0.813431i | \(-0.302403\pi\) | |||||||
\(350\) | 45.2487 | − | 12.1244i | 2.41865 | − | 0.648074i | ||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | 6.92820 | + | 1.85641i | 0.369274 | + | 0.0989468i | ||||
\(353\) | −24.9282 | −1.32679 | −0.663397 | − | 0.748267i | \(-0.730886\pi\) | ||||
−0.663397 | + | 0.748267i | \(0.730886\pi\) | |||||||
\(354\) | −0.535898 | + | 0.143594i | −0.0284827 | + | 0.00763191i | ||||
\(355\) | 7.60770i | 0.403775i | ||||||||
\(356\) | 30.0000 | − | 17.3205i | 1.59000 | − | 0.917985i | ||||
\(357\) | − | 13.8564i | − | 0.733359i | ||||||
\(358\) | −3.80385 | − | 14.1962i | −0.201040 | − | 0.750290i | ||||
\(359\) | −13.5167 | −0.713382 | −0.356691 | − | 0.934222i | \(-0.616095\pi\) | ||||
−0.356691 | + | 0.934222i | \(0.616095\pi\) | |||||||
\(360\) | −6.92820 | − | 6.92820i | −0.365148 | − | 0.365148i | ||||
\(361\) | 11.5359 | 0.607153 | ||||||||
\(362\) | −1.80385 | − | 6.73205i | −0.0948081 | − | 0.353829i | ||||
\(363\) | − | 18.7846i | − | 0.985936i | ||||||
\(364\) | 4.73205 | + | 8.19615i | 0.248027 | + | 0.429595i | ||||
\(365\) | − | 1.85641i | − | 0.0971688i | ||||||
\(366\) | 29.8564 | − | 8.00000i | 1.56062 | − | 0.418167i | ||||
\(367\) | 26.2487 | 1.37017 | 0.685086 | − | 0.728462i | \(-0.259765\pi\) | ||||
0.685086 | + | 0.728462i | \(0.259765\pi\) | |||||||
\(368\) | 8.00000 | − | 13.8564i | 0.417029 | − | 0.722315i | ||||
\(369\) | 4.92820 | 0.256552 | ||||||||
\(370\) | 23.3205 | − | 6.24871i | 1.21238 | − | 0.324855i | ||||
\(371\) | 51.7128i | 2.68480i | ||||||||
\(372\) | 6.53590 | + | 11.3205i | 0.338871 | + | 0.586941i | ||||
\(373\) | − | 26.7846i | − | 1.38685i | −0.720527 | − | 0.693427i | \(-0.756100\pi\) | ||
0.720527 | − | 0.693427i | \(-0.243900\pi\) | |||||||
\(374\) | −0.679492 | − | 2.53590i | −0.0351357 | − | 0.131128i | ||||
\(375\) | −13.8564 | −0.715542 | ||||||||
\(376\) | 6.53590 | − | 6.53590i | 0.337063 | − | 0.337063i | ||||
\(377\) | −2.00000 | −0.103005 | ||||||||
\(378\) | 6.92820 | + | 25.8564i | 0.356348 | + | 1.32991i | ||||
\(379\) | 16.5885i | 0.852092i | 0.904702 | + | 0.426046i | \(0.140094\pi\) | ||||
−0.904702 | + | 0.426046i | \(0.859906\pi\) | |||||||
\(380\) | −16.3923 | + | 9.46410i | −0.840907 | + | 0.485498i | ||||
\(381\) | 8.00000i | 0.409852i | ||||||||
\(382\) | −29.3205 | + | 7.85641i | −1.50017 | + | 0.401969i | ||||
\(383\) | −27.6603 | −1.41337 | −0.706686 | − | 0.707527i | \(-0.749811\pi\) | ||||
−0.706686 | + | 0.707527i | \(0.749811\pi\) | |||||||
\(384\) | −21.8564 | + | 5.85641i | −1.11536 | + | 0.298858i | ||||
\(385\) | 20.7846 | 1.05928 | ||||||||
\(386\) | −30.5885 | + | 8.19615i | −1.55691 | + | 0.417173i | ||||
\(387\) | − | 7.46410i | − | 0.379422i | ||||||
\(388\) | −24.9282 | + | 14.3923i | −1.26554 | + | 0.730659i | ||||
\(389\) | − | 2.00000i | − | 0.101404i | −0.998714 | − | 0.0507020i | \(-0.983854\pi\) | ||
0.998714 | − | 0.0507020i | \(-0.0161459\pi\) | |||||||
\(390\) | −2.53590 | − | 9.46410i | −0.128410 | − | 0.479233i | ||||
\(391\) | −5.85641 | −0.296171 | ||||||||
\(392\) | 30.7846 | − | 30.7846i | 1.55486 | − | 1.55486i | ||||
\(393\) | 15.7128 | 0.792607 | ||||||||
\(394\) | 6.19615 | + | 23.1244i | 0.312158 | + | 1.16499i | ||||
\(395\) | − | 5.07180i | − | 0.255190i | ||||||
\(396\) | −1.26795 | − | 2.19615i | −0.0637168 | − | 0.110361i | ||||
\(397\) | 11.4641i | 0.575367i | 0.957726 | + | 0.287683i | \(0.0928851\pi\) | ||||
−0.957726 | + | 0.287683i | \(0.907115\pi\) | |||||||
\(398\) | −33.8564 | + | 9.07180i | −1.69707 | + | 0.454728i | ||||
\(399\) | −25.8564 | −1.29444 | ||||||||
\(400\) | −14.0000 | + | 24.2487i | −0.700000 | + | 1.21244i | ||||
\(401\) | 11.4641 | 0.572490 | 0.286245 | − | 0.958156i | \(-0.407593\pi\) | ||||
0.286245 | + | 0.958156i | \(0.407593\pi\) | |||||||
\(402\) | 7.46410 | − | 2.00000i | 0.372276 | − | 0.0997509i | ||||
\(403\) | 3.26795i | 0.162788i | ||||||||
\(404\) | 12.0000 | + | 20.7846i | 0.597022 | + | 1.03407i | ||||
\(405\) | − | 38.1051i | − | 1.89346i | ||||||
\(406\) | 3.46410 | + | 12.9282i | 0.171920 | + | 0.641616i | ||||
\(407\) | 6.24871 | 0.309737 | ||||||||
\(408\) | 5.85641 | + | 5.85641i | 0.289935 | + | 0.289935i | ||||
\(409\) | −0.928203 | −0.0458967 | −0.0229483 | − | 0.999737i | \(-0.507305\pi\) | ||||
−0.0229483 | + | 0.999737i | \(0.507305\pi\) | |||||||
\(410\) | −6.24871 | − | 23.3205i | −0.308602 | − | 1.15172i | ||||
\(411\) | 1.85641i | 0.0915698i | ||||||||
\(412\) | −12.0000 | + | 6.92820i | −0.591198 | + | 0.341328i | ||||
\(413\) | 0.928203i | 0.0456739i | ||||||||
\(414\) | −5.46410 | + | 1.46410i | −0.268546 | + | 0.0719567i | ||||
\(415\) | 23.3205 | 1.14476 | ||||||||
\(416\) | −5.46410 | − | 1.46410i | −0.267900 | − | 0.0717835i | ||||
\(417\) | 20.0000 | 0.979404 | ||||||||
\(418\) | −4.73205 | + | 1.26795i | −0.231452 | + | 0.0620174i | ||||
\(419\) | − | 10.7846i | − | 0.526863i | −0.964678 | − | 0.263431i | \(-0.915146\pi\) | ||
0.964678 | − | 0.263431i | \(-0.0848542\pi\) | |||||||
\(420\) | −56.7846 | + | 32.7846i | −2.77081 | + | 1.59973i | ||||
\(421\) | 24.2487i | 1.18181i | 0.806741 | + | 0.590905i | \(0.201229\pi\) | ||||
−0.806741 | + | 0.590905i | \(0.798771\pi\) | |||||||
\(422\) | −7.26795 | − | 27.1244i | −0.353798 | − | 1.32039i | ||||
\(423\) | −3.26795 | −0.158893 | ||||||||
\(424\) | −21.8564 | − | 21.8564i | −1.06144 | − | 1.06144i | ||||
\(425\) | 10.2487 | 0.497136 | ||||||||
\(426\) | −1.60770 | − | 6.00000i | −0.0778931 | − | 0.290701i | ||||
\(427\) | − | 51.7128i | − | 2.50256i | ||||||
\(428\) | 8.92820 | + | 15.4641i | 0.431561 | + | 0.747486i | ||||
\(429\) | − | 2.53590i | − | 0.122434i | ||||||
\(430\) | −35.3205 | + | 9.46410i | −1.70331 | + | 0.456400i | ||||
\(431\) | 14.8756 | 0.716535 | 0.358267 | − | 0.933619i | \(-0.383368\pi\) | ||||
0.358267 | + | 0.933619i | \(0.383368\pi\) | |||||||
\(432\) | −13.8564 | − | 8.00000i | −0.666667 | − | 0.384900i | ||||
\(433\) | 34.7846 | 1.67164 | 0.835821 | − | 0.549002i | \(-0.184992\pi\) | ||||
0.835821 | + | 0.549002i | \(0.184992\pi\) | |||||||
\(434\) | 21.1244 | − | 5.66025i | 1.01400 | − | 0.271701i | ||||
\(435\) | − | 13.8564i | − | 0.664364i | ||||||
\(436\) | 2.00000 | + | 3.46410i | 0.0957826 | + | 0.165900i | ||||
\(437\) | 10.9282i | 0.522767i | ||||||||
\(438\) | 0.392305 | + | 1.46410i | 0.0187451 | + | 0.0699575i | ||||
\(439\) | −10.9282 | −0.521575 | −0.260787 | − | 0.965396i | \(-0.583982\pi\) | ||||
−0.260787 | + | 0.965396i | \(0.583982\pi\) | |||||||
\(440\) | −8.78461 | + | 8.78461i | −0.418790 | + | 0.418790i | ||||
\(441\) | −15.3923 | −0.732967 | ||||||||
\(442\) | 0.535898 | + | 2.00000i | 0.0254901 | + | 0.0951303i | ||||
\(443\) | 30.0000i | 1.42534i | 0.701498 | + | 0.712672i | \(0.252515\pi\) | ||||
−0.701498 | + | 0.712672i | \(0.747485\pi\) | |||||||
\(444\) | −17.0718 | + | 9.85641i | −0.810192 | + | 0.467764i | ||||
\(445\) | 60.0000i | 2.84427i | ||||||||
\(446\) | 13.9282 | − | 3.73205i | 0.659520 | − | 0.176718i | ||||
\(447\) | −1.85641 | −0.0878050 | ||||||||
\(448\) | 37.8564i | 1.78855i | ||||||||
\(449\) | 38.3923 | 1.81184 | 0.905922 | − | 0.423444i | \(-0.139179\pi\) | ||||
0.905922 | + | 0.423444i | \(0.139179\pi\) | |||||||
\(450\) | 9.56218 | − | 2.56218i | 0.450765 | − | 0.120782i | ||||
\(451\) | − | 6.24871i | − | 0.294240i | ||||||
\(452\) | 16.3923 | − | 9.46410i | 0.771029 | − | 0.445154i | ||||
\(453\) | − | 34.2487i | − | 1.60914i | ||||||
\(454\) | −9.92820 | − | 37.0526i | −0.465954 | − | 1.73896i | ||||
\(455\) | −16.3923 | −0.768483 | ||||||||
\(456\) | 10.9282 | − | 10.9282i | 0.511760 | − | 0.511760i | ||||
\(457\) | −14.0000 | −0.654892 | −0.327446 | − | 0.944870i | \(-0.606188\pi\) | ||||
−0.327446 | + | 0.944870i | \(0.606188\pi\) | |||||||
\(458\) | −10.7321 | − | 40.0526i | −0.501476 | − | 1.87153i | ||||
\(459\) | 5.85641i | 0.273354i | ||||||||
\(460\) | 13.8564 | + | 24.0000i | 0.646058 | + | 1.11901i | ||||
\(461\) | − | 7.07180i | − | 0.329366i | −0.986347 | − | 0.164683i | \(-0.947340\pi\) | ||
0.986347 | − | 0.164683i | \(-0.0526602\pi\) | |||||||
\(462\) | −16.3923 | + | 4.39230i | −0.762639 | + | 0.204349i | ||||
\(463\) | −15.6603 | −0.727794 | −0.363897 | − | 0.931439i | \(-0.618554\pi\) | ||||
−0.363897 | + | 0.931439i | \(0.618554\pi\) | |||||||
\(464\) | −6.92820 | − | 4.00000i | −0.321634 | − | 0.185695i | ||||
\(465\) | −22.6410 | −1.04995 | ||||||||
\(466\) | 4.19615 | − | 1.12436i | 0.194383 | − | 0.0520848i | ||||
\(467\) | 12.2487i | 0.566803i | 0.959001 | + | 0.283401i | \(0.0914629\pi\) | ||||
−0.959001 | + | 0.283401i | \(0.908537\pi\) | |||||||
\(468\) | 1.00000 | + | 1.73205i | 0.0462250 | + | 0.0800641i | ||||
\(469\) | − | 12.9282i | − | 0.596969i | ||||||
\(470\) | 4.14359 | + | 15.4641i | 0.191130 | + | 0.713306i | ||||
\(471\) | 6.14359 | 0.283082 | ||||||||
\(472\) | −0.392305 | − | 0.392305i | −0.0180573 | − | 0.0180573i | ||||
\(473\) | −9.46410 | −0.435160 | ||||||||
\(474\) | 1.07180 | + | 4.00000i | 0.0492293 | + | 0.183726i | ||||
\(475\) | − | 19.1244i | − | 0.877486i | ||||||
\(476\) | 12.0000 | − | 6.92820i | 0.550019 | − | 0.317554i | ||||
\(477\) | 10.9282i | 0.500368i | ||||||||
\(478\) | 20.8564 | − | 5.58846i | 0.953950 | − | 0.255610i | ||||
\(479\) | 24.7321 | 1.13004 | 0.565018 | − | 0.825078i | \(-0.308869\pi\) | ||||
0.565018 | + | 0.825078i | \(0.308869\pi\) | |||||||
\(480\) | 10.1436 | − | 37.8564i | 0.462990 | − | 1.72790i | ||||
\(481\) | −4.92820 | −0.224707 | ||||||||
\(482\) | −13.1244 | + | 3.51666i | −0.597798 | + | 0.160179i | ||||
\(483\) | 37.8564i | 1.72253i | ||||||||
\(484\) | 16.2679 | − | 9.39230i | 0.739452 | − | 0.426923i | ||||
\(485\) | − | 49.8564i | − | 2.26386i | ||||||
\(486\) | 3.66025 | + | 13.6603i | 0.166032 | + | 0.619642i | ||||
\(487\) | 16.4449 | 0.745188 | 0.372594 | − | 0.927994i | \(-0.378468\pi\) | ||||
0.372594 | + | 0.927994i | \(0.378468\pi\) | |||||||
\(488\) | 21.8564 | + | 21.8564i | 0.989393 | + | 0.989393i | ||||
\(489\) | −26.5359 | −1.19999 | ||||||||
\(490\) | 19.5167 | + | 72.8372i | 0.881673 | + | 3.29045i | ||||
\(491\) | − | 24.2487i | − | 1.09433i | −0.837025 | − | 0.547165i | \(-0.815707\pi\) | ||
0.837025 | − | 0.547165i | \(-0.184293\pi\) | |||||||
\(492\) | 9.85641 | + | 17.0718i | 0.444361 | + | 0.769656i | ||||
\(493\) | 2.92820i | 0.131880i | ||||||||
\(494\) | 3.73205 | − | 1.00000i | 0.167913 | − | 0.0449921i | ||||
\(495\) | 4.39230 | 0.197419 | ||||||||
\(496\) | −6.53590 | + | 11.3205i | −0.293471 | + | 0.508306i | ||||
\(497\) | −10.3923 | −0.466159 | ||||||||
\(498\) | −18.3923 | + | 4.92820i | −0.824179 | + | 0.220838i | ||||
\(499\) | 10.7321i | 0.480433i | 0.970719 | + | 0.240216i | \(0.0772184\pi\) | ||||
−0.970719 | + | 0.240216i | \(0.922782\pi\) | |||||||
\(500\) | −6.92820 | − | 12.0000i | −0.309839 | − | 0.536656i | ||||
\(501\) | − | 23.3205i | − | 1.04188i | ||||||
\(502\) | 5.26795 | + | 19.6603i | 0.235120 | + | 0.877480i | ||||
\(503\) | 37.4641 | 1.67044 | 0.835221 | − | 0.549915i | \(-0.185340\pi\) | ||||
0.835221 | + | 0.549915i | \(0.185340\pi\) | |||||||
\(504\) | 9.46410 | − | 9.46410i | 0.421565 | − | 0.421565i | ||||
\(505\) | −41.5692 | −1.84981 | ||||||||
\(506\) | 1.85641 | + | 6.92820i | 0.0825273 | + | 0.307996i | ||||
\(507\) | 2.00000i | 0.0888231i | ||||||||
\(508\) | −6.92820 | + | 4.00000i | −0.307389 | + | 0.177471i | ||||
\(509\) | 6.39230i | 0.283334i | 0.989914 | + | 0.141667i | \(0.0452462\pi\) | ||||
−0.989914 | + | 0.141667i | \(0.954754\pi\) | |||||||
\(510\) | −13.8564 | + | 3.71281i | −0.613572 | + | 0.164406i | ||||
\(511\) | 2.53590 | 0.112182 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | 10.9282 | 0.482492 | ||||||||
\(514\) | 5.26795 | − | 1.41154i | 0.232359 | − | 0.0622605i | ||||
\(515\) | − | 24.0000i | − | 1.05757i | ||||||
\(516\) | 25.8564 | − | 14.9282i | 1.13826 | − | 0.657178i | ||||
\(517\) | 4.14359i | 0.182235i | ||||||||
\(518\) | 8.53590 | + | 31.8564i | 0.375046 | + | 1.39969i | ||||
\(519\) | 13.8564 | 0.608229 | ||||||||
\(520\) | 6.92820 | − | 6.92820i | 0.303822 | − | 0.303822i | ||||
\(521\) | 37.1769 | 1.62875 | 0.814375 | − | 0.580339i | \(-0.197080\pi\) | ||||
0.814375 | + | 0.580339i | \(0.197080\pi\) | |||||||
\(522\) | 0.732051 | + | 2.73205i | 0.0320410 | + | 0.119579i | ||||
\(523\) | − | 14.0000i | − | 0.612177i | −0.952003 | − | 0.306089i | \(-0.900980\pi\) | ||
0.952003 | − | 0.306089i | \(-0.0990204\pi\) | |||||||
\(524\) | 7.85641 | + | 13.6077i | 0.343209 | + | 0.594455i | ||||
\(525\) | − | 66.2487i | − | 2.89133i | ||||||
\(526\) | 10.0000 | − | 2.67949i | 0.436021 | − | 0.116831i | ||||
\(527\) | 4.78461 | 0.208421 | ||||||||
\(528\) | 5.07180 | − | 8.78461i | 0.220722 | − | 0.382301i | ||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 51.7128 | − | 13.8564i | 2.24626 | − | 0.601884i | ||||
\(531\) | 0.196152i | 0.00851229i | ||||||||
\(532\) | −12.9282 | − | 22.3923i | −0.560509 | − | 0.970830i | ||||
\(533\) | 4.92820i | 0.213464i | ||||||||
\(534\) | −12.6795 | − | 47.3205i | −0.548695 | − | 2.04776i | ||||
\(535\) | −30.9282 | −1.33714 | ||||||||
\(536\) | 5.46410 | + | 5.46410i | 0.236013 | + | 0.236013i | ||||
\(537\) | −20.7846 | −0.896922 | ||||||||
\(538\) | −7.26795 | − | 27.1244i | −0.313344 | − | 1.16941i | ||||
\(539\) | 19.5167i | 0.840642i | ||||||||
\(540\) | 24.0000 | − | 13.8564i | 1.03280 | − | 0.596285i | ||||
\(541\) | 16.9282i | 0.727800i | 0.931438 | + | 0.363900i | \(0.118555\pi\) | ||||
−0.931438 | + | 0.363900i | \(0.881445\pi\) | |||||||
\(542\) | −13.3923 | + | 3.58846i | −0.575249 | + | 0.154137i | ||||
\(543\) | −9.85641 | −0.422979 | ||||||||
\(544\) | −2.14359 | + | 8.00000i | −0.0919058 | + | 0.342997i | ||||
\(545\) | −6.92820 | −0.296772 | ||||||||
\(546\) | 12.9282 | − | 3.46410i | 0.553276 | − | 0.148250i | ||||
\(547\) | − | 15.8564i | − | 0.677971i | −0.940792 | − | 0.338985i | \(-0.889916\pi\) | ||
0.940792 | − | 0.338985i | \(-0.110084\pi\) | |||||||
\(548\) | −1.60770 | + | 0.928203i | −0.0686773 | + | 0.0396509i | ||||
\(549\) | − | 10.9282i | − | 0.466404i | ||||||
\(550\) | −3.24871 | − | 12.1244i | −0.138526 | − | 0.516984i | ||||
\(551\) | 5.46410 | 0.232779 | ||||||||
\(552\) | −16.0000 | − | 16.0000i | −0.681005 | − | 0.681005i | ||||
\(553\) | 6.92820 | 0.294617 | ||||||||
\(554\) | 9.46410 | + | 35.3205i | 0.402091 | + | 1.50062i | ||||
\(555\) | − | 34.1436i | − | 1.44931i | ||||||
\(556\) | 10.0000 | + | 17.3205i | 0.424094 | + | 0.734553i | ||||
\(557\) | 6.78461i | 0.287473i | 0.989616 | + | 0.143737i | \(0.0459118\pi\) | ||||
−0.989616 | + | 0.143737i | \(0.954088\pi\) | |||||||
\(558\) | 4.46410 | − | 1.19615i | 0.188980 | − | 0.0506372i | ||||
\(559\) | 7.46410 | 0.315698 | ||||||||
\(560\) | −56.7846 | − | 32.7846i | −2.39959 | − | 1.38540i | ||||
\(561\) | −3.71281 | −0.156755 | ||||||||
\(562\) | −34.5885 | + | 9.26795i | −1.45903 | + | 0.390945i | ||||
\(563\) | 0.535898i | 0.0225854i | 0.999936 | + | 0.0112927i | \(0.00359466\pi\) | ||||
−0.999936 | + | 0.0112927i | \(0.996405\pi\) | |||||||
\(564\) | −6.53590 | − | 11.3205i | −0.275211 | − | 0.476679i | ||||
\(565\) | 32.7846i | 1.37926i | ||||||||
\(566\) | −4.58846 | − | 17.1244i | −0.192867 | − | 0.719790i | ||||
\(567\) | 52.0526 | 2.18600 | ||||||||
\(568\) | 4.39230 | − | 4.39230i | 0.184297 | − | 0.184297i | ||||
\(569\) | −14.0000 | −0.586911 | −0.293455 | − | 0.955973i | \(-0.594805\pi\) | ||||
−0.293455 | + | 0.955973i | \(0.594805\pi\) | |||||||
\(570\) | 6.92820 | + | 25.8564i | 0.290191 | + | 1.08301i | ||||
\(571\) | − | 37.3205i | − | 1.56181i | −0.624647 | − | 0.780907i | \(-0.714757\pi\) | ||
0.624647 | − | 0.780907i | \(-0.285243\pi\) | |||||||
\(572\) | 2.19615 | − | 1.26795i | 0.0918257 | − | 0.0530156i | ||||
\(573\) | 42.9282i | 1.79335i | ||||||||
\(574\) | 31.8564 | − | 8.53590i | 1.32966 | − | 0.356282i | ||||
\(575\) | −28.0000 | −1.16768 | ||||||||
\(576\) | 8.00000i | 0.333333i | ||||||||
\(577\) | −20.9282 | −0.871253 | −0.435626 | − | 0.900128i | \(-0.643473\pi\) | ||||
−0.435626 | + | 0.900128i | \(0.643473\pi\) | |||||||
\(578\) | −20.2942 | + | 5.43782i | −0.844129 | + | 0.226184i | ||||
\(579\) | 44.7846i | 1.86118i | ||||||||
\(580\) | 12.0000 | − | 6.92820i | 0.498273 | − | 0.287678i | ||||
\(581\) | 31.8564i | 1.32163i | ||||||||
\(582\) | 10.5359 | + | 39.3205i | 0.436727 | + | 1.62989i | ||||
\(583\) | 13.8564 | 0.573874 | ||||||||
\(584\) | −1.07180 | + | 1.07180i | −0.0443513 | + | 0.0443513i | ||||
\(585\) | −3.46410 | −0.143223 | ||||||||
\(586\) | −6.98076 | − | 26.0526i | −0.288373 | − | 1.07622i | ||||
\(587\) | 21.6603i | 0.894014i | 0.894530 | + | 0.447007i | \(0.147510\pi\) | ||||
−0.894530 | + | 0.447007i | \(0.852490\pi\) | |||||||
\(588\) | −30.7846 | − | 53.3205i | −1.26954 | − | 2.19890i | ||||
\(589\) | − | 8.92820i | − | 0.367880i | ||||||
\(590\) | 0.928203 | − | 0.248711i | 0.0382135 | − | 0.0102393i | ||||
\(591\) | 33.8564 | 1.39267 | ||||||||
\(592\) | −17.0718 | − | 9.85641i | −0.701647 | − | 0.405096i | ||||
\(593\) | 19.8564 | 0.815405 | 0.407702 | − | 0.913115i | \(-0.366330\pi\) | ||||
0.407702 | + | 0.913115i | \(0.366330\pi\) | |||||||
\(594\) | 6.92820 | − | 1.85641i | 0.284268 | − | 0.0761693i | ||||
\(595\) | 24.0000i | 0.983904i | ||||||||
\(596\) | −0.928203 | − | 1.60770i | −0.0380207 | − | 0.0658538i | ||||
\(597\) | 49.5692i | 2.02873i | ||||||||
\(598\) | −1.46410 | − | 5.46410i | −0.0598716 | − | 0.223444i | ||||
\(599\) | 17.1769 | 0.701830 | 0.350915 | − | 0.936407i | \(-0.385871\pi\) | ||||
0.350915 | + | 0.936407i | \(0.385871\pi\) | |||||||
\(600\) | 28.0000 | + | 28.0000i | 1.14310 | + | 1.14310i | ||||
\(601\) | 16.3923 | 0.668656 | 0.334328 | − | 0.942457i | \(-0.391491\pi\) | ||||
0.334328 | + | 0.942457i | \(0.391491\pi\) | |||||||
\(602\) | −12.9282 | − | 48.2487i | −0.526914 | − | 1.96647i | ||||
\(603\) | − | 2.73205i | − | 0.111258i | ||||||
\(604\) | 29.6603 | − | 17.1244i | 1.20686 | − | 0.696780i | ||||
\(605\) | 32.5359i | 1.32277i | ||||||||
\(606\) | 32.7846 | − | 8.78461i | 1.33178 | − | 0.356850i | ||||
\(607\) | −27.3205 | −1.10891 | −0.554453 | − | 0.832215i | \(-0.687072\pi\) | ||||
−0.554453 | + | 0.832215i | \(0.687072\pi\) | |||||||
\(608\) | 14.9282 | + | 4.00000i | 0.605419 | + | 0.162221i | ||||
\(609\) | 18.9282 | 0.767010 | ||||||||
\(610\) | −51.7128 | + | 13.8564i | −2.09379 | + | 0.561029i | ||||
\(611\) | − | 3.26795i | − | 0.132207i | ||||||
\(612\) | 2.53590 | − | 1.46410i | 0.102508 | − | 0.0591828i | ||||
\(613\) | 44.6410i | 1.80303i | 0.432744 | + | 0.901517i | \(0.357545\pi\) | ||||
−0.432744 | + | 0.901517i | \(0.642455\pi\) | |||||||
\(614\) | 1.00000 | + | 3.73205i | 0.0403567 | + | 0.150613i | ||||
\(615\) | −34.1436 | −1.37680 | ||||||||
\(616\) | −12.0000 | − | 12.0000i | −0.483494 | − | 0.483494i | ||||
\(617\) | 6.67949 | 0.268906 | 0.134453 | − | 0.990920i | \(-0.457072\pi\) | ||||
0.134453 | + | 0.990920i | \(0.457072\pi\) | |||||||
\(618\) | 5.07180 | + | 18.9282i | 0.204018 | + | 0.761404i | ||||
\(619\) | − | 12.5885i | − | 0.505973i | −0.967470 | − | 0.252986i | \(-0.918587\pi\) | ||
0.967470 | − | 0.252986i | \(-0.0814128\pi\) | |||||||
\(620\) | −11.3205 | − | 19.6077i | −0.454643 | − | 0.787464i | ||||
\(621\) | − | 16.0000i | − | 0.642058i | ||||||
\(622\) | 20.3923 | − | 5.46410i | 0.817657 | − | 0.219091i | ||||
\(623\) | −81.9615 | −3.28372 | ||||||||
\(624\) | −4.00000 | + | 6.92820i | −0.160128 | + | 0.277350i | ||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −27.8564 | + | 7.46410i | −1.11337 | + | 0.298325i | ||||
\(627\) | 6.92820i | 0.276686i | ||||||||
\(628\) | 3.07180 | + | 5.32051i | 0.122578 | + | 0.212311i | ||||
\(629\) | 7.21539i | 0.287696i | ||||||||
\(630\) | 6.00000 | + | 22.3923i | 0.239046 | + | 0.892131i | ||||
\(631\) | −3.94744 | −0.157145 | −0.0785726 | − | 0.996908i | \(-0.525036\pi\) | ||||
−0.0785726 | + | 0.996908i | \(0.525036\pi\) | |||||||
\(632\) | −2.92820 | + | 2.92820i | −0.116478 | + | 0.116478i | ||||
\(633\) | −39.7128 | −1.57844 | ||||||||
\(634\) | 1.26795 | + | 4.73205i | 0.0503567 | + | 0.187934i | ||||
\(635\) | − | 13.8564i | − | 0.549875i | ||||||
\(636\) | −37.8564 | + | 21.8564i | −1.50110 | + | 0.866663i | ||||
\(637\) | − | 15.3923i | − | 0.609865i | ||||||
\(638\) | 3.46410 | − | 0.928203i | 0.137145 | − | 0.0367479i | ||||
\(639\) | −2.19615 | −0.0868784 | ||||||||
\(640\) | 37.8564 | − | 10.1436i | 1.49641 | − | 0.400961i | ||||
\(641\) | 26.2487 | 1.03676 | 0.518381 | − | 0.855150i | \(-0.326535\pi\) | ||||
0.518381 | + | 0.855150i | \(0.326535\pi\) | |||||||
\(642\) | 24.3923 | − | 6.53590i | 0.962687 | − | 0.257951i | ||||
\(643\) | 9.26795i | 0.365492i | 0.983160 | + | 0.182746i | \(0.0584986\pi\) | ||||
−0.983160 | + | 0.182746i | \(0.941501\pi\) | |||||||
\(644\) | −32.7846 | + | 18.9282i | −1.29189 | + | 0.745876i | ||||
\(645\) | 51.7128i | 2.03619i | ||||||||
\(646\) | −1.46410 | − | 5.46410i | −0.0576043 | − | 0.214982i | ||||
\(647\) | 10.1436 | 0.398786 | 0.199393 | − | 0.979920i | \(-0.436103\pi\) | ||||
0.199393 | + | 0.979920i | \(0.436103\pi\) | |||||||
\(648\) | −22.0000 | + | 22.0000i | −0.864242 | + | 0.864242i | ||||
\(649\) | 0.248711 | 0.00976277 | ||||||||
\(650\) | 2.56218 | + | 9.56218i | 0.100497 | + | 0.375059i | ||||
\(651\) | − | 30.9282i | − | 1.21217i | ||||||
\(652\) | −13.2679 | − | 22.9808i | −0.519613 | − | 0.899996i | ||||
\(653\) | 16.9282i | 0.662452i | 0.943551 | + | 0.331226i | \(0.107462\pi\) | ||||
−0.943551 | + | 0.331226i | \(0.892538\pi\) | |||||||
\(654\) | 5.46410 | − | 1.46410i | 0.213663 | − | 0.0572509i | ||||
\(655\) | −27.2154 | −1.06339 | ||||||||
\(656\) | −9.85641 | + | 17.0718i | −0.384828 | + | 0.666542i | ||||
\(657\) | 0.535898 | 0.0209074 | ||||||||
\(658\) | −21.1244 | + | 5.66025i | −0.823513 | + | 0.220660i | ||||
\(659\) | − | 14.0000i | − | 0.545363i | −0.962104 | − | 0.272681i | \(-0.912090\pi\) | ||
0.962104 | − | 0.272681i | \(-0.0879105\pi\) | |||||||
\(660\) | 8.78461 | + | 15.2154i | 0.341940 | + | 0.592258i | ||||
\(661\) | 17.3205i | 0.673690i | 0.941560 | + | 0.336845i | \(0.109360\pi\) | ||||
−0.941560 | + | 0.336845i | \(0.890640\pi\) | |||||||
\(662\) | 10.0718 | + | 37.5885i | 0.391451 | + | 1.46092i | ||||
\(663\) | 2.92820 | 0.113722 | ||||||||
\(664\) | −13.4641 | − | 13.4641i | −0.522508 | − | 0.522508i | ||||
\(665\) | 44.7846 | 1.73667 | ||||||||
\(666\) | 1.80385 | + | 6.73205i | 0.0698977 | + | 0.260862i | ||||
\(667\) | − | 8.00000i | − | 0.309761i | ||||||
\(668\) | 20.1962 | − | 11.6603i | 0.781413 | − | 0.451149i | ||||
\(669\) | − | 20.3923i | − | 0.788412i | ||||||
\(670\) | −12.9282 | + | 3.46410i | −0.499460 | + | 0.133830i | ||||
\(671\) | −13.8564 | −0.534921 | ||||||||
\(672\) | 51.7128 | + | 13.8564i | 1.99487 | + | 0.534522i | ||||
\(673\) | −29.1769 | −1.12469 | −0.562344 | − | 0.826904i | \(-0.690100\pi\) | ||||
−0.562344 | + | 0.826904i | \(0.690100\pi\) | |||||||
\(674\) | −7.46410 | + | 2.00000i | −0.287506 | + | 0.0770371i | ||||
\(675\) | 28.0000i | 1.07772i | ||||||||
\(676\) | −1.73205 | + | 1.00000i | −0.0666173 | + | 0.0384615i | ||||
\(677\) | − | 34.9282i | − | 1.34240i | −0.741276 | − | 0.671200i | \(-0.765779\pi\) | ||
0.741276 | − | 0.671200i | \(-0.234221\pi\) | |||||||
\(678\) | −6.92820 | − | 25.8564i | −0.266076 | − | 0.993009i | ||||
\(679\) | 68.1051 | 2.61363 | ||||||||
\(680\) | −10.1436 | − | 10.1436i | −0.388989 | − | 0.388989i | ||||
\(681\) | −54.2487 | −2.07882 | ||||||||
\(682\) | −1.51666 | − | 5.66025i | −0.0580759 | − | 0.216742i | ||||
\(683\) | 28.1962i | 1.07890i | 0.842019 | + | 0.539448i | \(0.181367\pi\) | ||||
−0.842019 | + | 0.539448i | \(0.818633\pi\) | |||||||
\(684\) | −2.73205 | − | 4.73205i | −0.104463 | − | 0.180934i | ||||
\(685\) | − | 3.21539i | − | 0.122854i | ||||||
\(686\) | −54.2487 | + | 14.5359i | −2.07123 | + | 0.554983i | ||||
\(687\) | −58.6410 | −2.23729 | ||||||||
\(688\) | 25.8564 | + | 14.9282i | 0.985766 | + | 0.569132i | ||||
\(689\) | −10.9282 | −0.416331 | ||||||||
\(690\) | 37.8564 | − | 10.1436i | 1.44117 | − | 0.386160i | ||||
\(691\) | − | 46.8372i | − | 1.78177i | −0.454229 | − | 0.890885i | \(-0.650085\pi\) | ||
0.454229 | − | 0.890885i | \(-0.349915\pi\) | |||||||
\(692\) | 6.92820 | + | 12.0000i | 0.263371 | + | 0.456172i | ||||
\(693\) | 6.00000i | 0.227921i | ||||||||
\(694\) | 7.66025 | + | 28.5885i | 0.290779 | + | 1.08520i | ||||
\(695\) | −34.6410 | −1.31401 | ||||||||
\(696\) | −8.00000 | + | 8.00000i | −0.303239 | + | 0.303239i | ||||
\(697\) | 7.21539 | 0.273302 | ||||||||
\(698\) | −11.1244 | − | 41.5167i | −0.421063 | − | 1.57143i | ||||
\(699\) | − | 6.14359i | − | 0.232372i | ||||||
\(700\) | 57.3731 | − | 33.1244i | 2.16850 | − | 1.25198i | ||||
\(701\) | − | 28.6410i | − | 1.08176i | −0.841101 | − | 0.540878i | \(-0.818092\pi\) | ||
0.841101 | − | 0.540878i | \(-0.181908\pi\) | |||||||
\(702\) | −5.46410 | + | 1.46410i | −0.206229 | + | 0.0552590i | ||||
\(703\) | 13.4641 | 0.507808 | ||||||||
\(704\) | 10.1436 | 0.382301 | ||||||||
\(705\) | 22.6410 | 0.852710 | ||||||||
\(706\) | −34.0526 | + | 9.12436i | −1.28158 | + | 0.343400i | ||||
\(707\) | − | 56.7846i | − | 2.13561i | ||||||
\(708\) | −0.679492 | + | 0.392305i | −0.0255369 | + | 0.0147437i | ||||
\(709\) | 5.32051i | 0.199816i | 0.994997 | + | 0.0999079i | \(0.0318548\pi\) | ||||
−0.994997 | + | 0.0999079i | \(0.968145\pi\) | |||||||
\(710\) | 2.78461 | + | 10.3923i | 0.104505 | + | 0.390016i | ||||
\(711\) | 1.46410 | 0.0549081 | ||||||||
\(712\) | 34.6410 | − | 34.6410i | 1.29823 | − | 1.29823i | ||||
\(713\) | −13.0718 | −0.489543 | ||||||||
\(714\) | −5.07180 | − | 18.9282i | −0.189807 | − | 0.708370i | ||||
\(715\) | 4.39230i | 0.164263i | ||||||||
\(716\) | −10.3923 | − | 18.0000i | −0.388379 | − | 0.672692i | ||||
\(717\) | − | 30.5359i | − | 1.14038i | ||||||
\(718\) | −18.4641 | + | 4.94744i | −0.689074 | + | 0.184637i | ||||
\(719\) | 17.0718 | 0.636671 | 0.318335 | − | 0.947978i | \(-0.396876\pi\) | ||||
0.318335 | + | 0.947978i | \(0.396876\pi\) | |||||||
\(720\) | −12.0000 | − | 6.92820i | −0.447214 | − | 0.258199i | ||||
\(721\) | 32.7846 | 1.22096 | ||||||||
\(722\) | 15.7583 | − | 4.22243i | 0.586464 | − | 0.157143i | ||||
\(723\) | 19.2154i | 0.714628i | ||||||||
\(724\) | −4.92820 | − | 8.53590i | −0.183155 | − | 0.317234i | ||||
\(725\) | 14.0000i | 0.519947i | ||||||||
\(726\) | −6.87564 | − | 25.6603i | −0.255179 | − | 0.952341i | ||||
\(727\) | −9.07180 | −0.336454 | −0.168227 | − | 0.985748i | \(-0.553804\pi\) | ||||
−0.168227 | + | 0.985748i | \(0.553804\pi\) | |||||||
\(728\) | 9.46410 | + | 9.46410i | 0.350763 | + | 0.350763i | ||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | −0.679492 | − | 2.53590i | −0.0251491 | − | 0.0938578i | ||||
\(731\) | − | 10.9282i | − | 0.404194i | ||||||
\(732\) | 37.8564 | − | 21.8564i | 1.39921 | − | 0.807836i | ||||
\(733\) | − | 2.67949i | − | 0.0989693i | −0.998775 | − | 0.0494846i | \(-0.984242\pi\) | ||
0.998775 | − | 0.0494846i | \(-0.0157579\pi\) | |||||||
\(734\) | 35.8564 | − | 9.60770i | 1.32348 | − | 0.354626i | ||||
\(735\) | 106.641 | 3.93351 | ||||||||
\(736\) | 5.85641 | − | 21.8564i | 0.215870 | − | 0.805638i | ||||
\(737\) | −3.46410 | −0.127602 | ||||||||
\(738\) | 6.73205 | − | 1.80385i | 0.247810 | − | 0.0664005i | ||||
\(739\) | 53.7654i | 1.97779i | 0.148612 | + | 0.988896i | \(0.452519\pi\) | ||||
−0.148612 | + | 0.988896i | \(0.547481\pi\) | |||||||
\(740\) | 29.5692 | − | 17.0718i | 1.08699 | − | 0.627572i | ||||
\(741\) | − | 5.46410i | − | 0.200729i | ||||||
\(742\) | 18.9282 | + | 70.6410i | 0.694876 | + | 2.59331i | ||||
\(743\) | −21.8038 | −0.799906 | −0.399953 | − | 0.916536i | \(-0.630973\pi\) | ||||
−0.399953 | + | 0.916536i | \(0.630973\pi\) | |||||||
\(744\) | 13.0718 | + | 13.0718i | 0.479235 | + | 0.479235i | ||||
\(745\) | 3.21539 | 0.117803 | ||||||||
\(746\) | −9.80385 | − | 36.5885i | −0.358944 | − | 1.33960i | ||||
\(747\) | 6.73205i | 0.246313i | ||||||||
\(748\) | −1.85641 | − | 3.21539i | −0.0678769 | − | 0.117566i | ||||
\(749\) | − | 42.2487i | − | 1.54373i | ||||||
\(750\) | −18.9282 | + | 5.07180i | −0.691160 | + | 0.185196i | ||||
\(751\) | 14.9282 | 0.544738 | 0.272369 | − | 0.962193i | \(-0.412193\pi\) | ||||
0.272369 | + | 0.962193i | \(0.412193\pi\) | |||||||
\(752\) | 6.53590 | − | 11.3205i | 0.238340 | − | 0.412816i | ||||
\(753\) | 28.7846 | 1.04897 | ||||||||
\(754\) | −2.73205 | + | 0.732051i | −0.0994954 | + | 0.0266597i | ||||
\(755\) | 59.3205i | 2.15889i | ||||||||
\(756\) | 18.9282 | + | 32.7846i | 0.688412 | + | 1.19236i | ||||
\(757\) | 0.784610i | 0.0285171i | 0.999898 | + | 0.0142586i | \(0.00453880\pi\) | ||||
−0.999898 | + | 0.0142586i | \(0.995461\pi\) | |||||||
\(758\) | 6.07180 | + | 22.6603i | 0.220538 | + | 0.823057i | ||||
\(759\) | 10.1436 | 0.368189 | ||||||||
\(760\) | −18.9282 | + | 18.9282i | −0.686598 | + | 0.686598i | ||||
\(761\) | −22.7846 | −0.825941 | −0.412971 | − | 0.910744i | \(-0.635509\pi\) | ||||
−0.412971 | + | 0.910744i | \(0.635509\pi\) | |||||||
\(762\) | 2.92820 | + | 10.9282i | 0.106078 | + | 0.395887i | ||||
\(763\) | − | 9.46410i | − | 0.342623i | ||||||
\(764\) | −37.1769 | + | 21.4641i | −1.34501 | + | 0.776544i | ||||
\(765\) | 5.07180i | 0.183371i | ||||||||
\(766\) | −37.7846 | + | 10.1244i | −1.36521 | + | 0.365808i | ||||
\(767\) | −0.196152 | −0.00708265 | ||||||||
\(768\) | −27.7128 | + | 16.0000i | −1.00000 | + | 0.577350i | ||||
\(769\) | 24.5359 | 0.884787 | 0.442394 | − | 0.896821i | \(-0.354129\pi\) | ||||
0.442394 | + | 0.896821i | \(0.354129\pi\) | |||||||
\(770\) | 28.3923 | − | 7.60770i | 1.02319 | − | 0.274162i | ||||
\(771\) | − | 7.71281i | − | 0.277770i | ||||||
\(772\) | −38.7846 | + | 22.3923i | −1.39589 | + | 0.805917i | ||||
\(773\) | − | 20.5359i | − | 0.738625i | −0.929305 | − | 0.369312i |