Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [170,2,Mod(21,170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(170, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("170.21");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 170 = 2 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 170.h (of order \(4\), 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: | \(1.35745683436\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 21.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 170.21 |
Dual form | 170.2.h.a.81.2 |
$q$-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 \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).
\(n\) | \(71\) | \(137\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.70711 | − | 1.70711i | 0.985599 | − | 0.985599i | −0.0142992 | − | 0.999898i | \(-0.504552\pi\) |
0.999898 | + | 0.0142992i | \(0.00455173\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | 1.70711 | + | 1.70711i | 0.696923 | + | 0.696923i | ||||
\(7\) | −0.414214 | − | 0.414214i | −0.156558 | − | 0.156558i | 0.624482 | − | 0.781040i | \(-0.285310\pi\) |
−0.781040 | + | 0.624482i | \(0.785310\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | − | 2.82843i | − | 0.942809i | ||||||
\(10\) | 0.707107 | + | 0.707107i | 0.223607 | + | 0.223607i | ||||
\(11\) | 1.00000 | + | 1.00000i | 0.301511 | + | 0.301511i | 0.841605 | − | 0.540094i | \(-0.181611\pi\) |
−0.540094 | + | 0.841605i | \(0.681611\pi\) | |||||||
\(12\) | −1.70711 | + | 1.70711i | −0.492799 | + | 0.492799i | ||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0.414214 | − | 0.414214i | 0.110703 | − | 0.110703i | ||||
\(15\) | − | 2.41421i | − | 0.623347i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.12132 | + | 0.121320i | −0.999567 | + | 0.0294245i | ||||
\(18\) | 2.82843 | 0.666667 | ||||||||
\(19\) | 2.41421i | 0.553859i | 0.960890 | + | 0.276929i | \(0.0893168\pi\) | ||||
−0.960890 | + | 0.276929i | \(0.910683\pi\) | |||||||
\(20\) | −0.707107 | + | 0.707107i | −0.158114 | + | 0.158114i | ||||
\(21\) | −1.41421 | −0.308607 | ||||||||
\(22\) | −1.00000 | + | 1.00000i | −0.213201 | + | 0.213201i | ||||
\(23\) | 2.24264 | + | 2.24264i | 0.467623 | + | 0.467623i | 0.901144 | − | 0.433521i | \(-0.142729\pi\) |
−0.433521 | + | 0.901144i | \(0.642729\pi\) | |||||||
\(24\) | −1.70711 | − | 1.70711i | −0.348462 | − | 0.348462i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 1.00000i | 0.196116i | ||||||||
\(27\) | 0.292893 | + | 0.292893i | 0.0563673 | + | 0.0563673i | ||||
\(28\) | 0.414214 | + | 0.414214i | 0.0782790 | + | 0.0782790i | ||||
\(29\) | −6.94975 | + | 6.94975i | −1.29054 | + | 1.29054i | −0.356080 | + | 0.934455i | \(0.615887\pi\) |
−0.934455 | + | 0.356080i | \(0.884113\pi\) | |||||||
\(30\) | 2.41421 | 0.440773 | ||||||||
\(31\) | −3.70711 | + | 3.70711i | −0.665816 | + | 0.665816i | −0.956745 | − | 0.290929i | \(-0.906036\pi\) |
0.290929 | + | 0.956745i | \(0.406036\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 3.41421 | 0.594338 | ||||||||
\(34\) | −0.121320 | − | 4.12132i | −0.0208063 | − | 0.706801i | ||||
\(35\) | −0.585786 | −0.0990160 | ||||||||
\(36\) | 2.82843i | 0.471405i | ||||||||
\(37\) | 1.58579 | − | 1.58579i | 0.260702 | − | 0.260702i | −0.564637 | − | 0.825339i | \(-0.690984\pi\) |
0.825339 | + | 0.564637i | \(0.190984\pi\) | |||||||
\(38\) | −2.41421 | −0.391637 | ||||||||
\(39\) | 1.70711 | − | 1.70711i | 0.273356 | − | 0.273356i | ||||
\(40\) | −0.707107 | − | 0.707107i | −0.111803 | − | 0.111803i | ||||
\(41\) | −6.65685 | − | 6.65685i | −1.03963 | − | 1.03963i | −0.999182 | − | 0.0404442i | \(-0.987123\pi\) |
−0.0404442 | − | 0.999182i | \(-0.512877\pi\) | |||||||
\(42\) | − | 1.41421i | − | 0.218218i | ||||||
\(43\) | − | 10.2426i | − | 1.56199i | −0.624538 | − | 0.780994i | \(-0.714713\pi\) | ||
0.624538 | − | 0.780994i | \(-0.285287\pi\) | |||||||
\(44\) | −1.00000 | − | 1.00000i | −0.150756 | − | 0.150756i | ||||
\(45\) | −2.00000 | − | 2.00000i | −0.298142 | − | 0.298142i | ||||
\(46\) | −2.24264 | + | 2.24264i | −0.330659 | + | 0.330659i | ||||
\(47\) | 3.24264 | 0.472988 | 0.236494 | − | 0.971633i | \(-0.424002\pi\) | ||||
0.236494 | + | 0.971633i | \(0.424002\pi\) | |||||||
\(48\) | 1.70711 | − | 1.70711i | 0.246400 | − | 0.246400i | ||||
\(49\) | − | 6.65685i | − | 0.950979i | ||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −6.82843 | + | 7.24264i | −0.956171 | + | 1.01417i | ||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 3.48528i | 0.478740i | 0.970928 | + | 0.239370i | \(0.0769409\pi\) | ||||
−0.970928 | + | 0.239370i | \(0.923059\pi\) | |||||||
\(54\) | −0.292893 | + | 0.292893i | −0.0398577 | + | 0.0398577i | ||||
\(55\) | 1.41421 | 0.190693 | ||||||||
\(56\) | −0.414214 | + | 0.414214i | −0.0553516 | + | 0.0553516i | ||||
\(57\) | 4.12132 | + | 4.12132i | 0.545882 | + | 0.545882i | ||||
\(58\) | −6.94975 | − | 6.94975i | −0.912547 | − | 0.912547i | ||||
\(59\) | 10.8995i | 1.41899i | 0.704709 | + | 0.709497i | \(0.251078\pi\) | ||||
−0.704709 | + | 0.709497i | \(0.748922\pi\) | |||||||
\(60\) | 2.41421i | 0.311674i | ||||||||
\(61\) | −5.77817 | − | 5.77817i | −0.739819 | − | 0.739819i | 0.232723 | − | 0.972543i | \(-0.425236\pi\) |
−0.972543 | + | 0.232723i | \(0.925236\pi\) | |||||||
\(62\) | −3.70711 | − | 3.70711i | −0.470803 | − | 0.470803i | ||||
\(63\) | −1.17157 | + | 1.17157i | −0.147604 | + | 0.147604i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.707107 | − | 0.707107i | 0.0877058 | − | 0.0877058i | ||||
\(66\) | 3.41421i | 0.420261i | ||||||||
\(67\) | 8.82843 | 1.07856 | 0.539282 | − | 0.842125i | \(-0.318696\pi\) | ||||
0.539282 | + | 0.842125i | \(0.318696\pi\) | |||||||
\(68\) | 4.12132 | − | 0.121320i | 0.499784 | − | 0.0147123i | ||||
\(69\) | 7.65685 | 0.921777 | ||||||||
\(70\) | − | 0.585786i | − | 0.0700149i | ||||||
\(71\) | −8.29289 | + | 8.29289i | −0.984185 | + | 0.984185i | −0.999877 | − | 0.0156915i | \(-0.995005\pi\) |
0.0156915 | + | 0.999877i | \(0.495005\pi\) | |||||||
\(72\) | −2.82843 | −0.333333 | ||||||||
\(73\) | 5.53553 | − | 5.53553i | 0.647885 | − | 0.647885i | −0.304596 | − | 0.952482i | \(-0.598522\pi\) |
0.952482 | + | 0.304596i | \(0.0985215\pi\) | |||||||
\(74\) | 1.58579 | + | 1.58579i | 0.184344 | + | 0.184344i | ||||
\(75\) | −1.70711 | − | 1.70711i | −0.197120 | − | 0.197120i | ||||
\(76\) | − | 2.41421i | − | 0.276929i | ||||||
\(77\) | − | 0.828427i | − | 0.0944080i | ||||||
\(78\) | 1.70711 | + | 1.70711i | 0.193292 | + | 0.193292i | ||||
\(79\) | 8.24264 | + | 8.24264i | 0.927370 | + | 0.927370i | 0.997535 | − | 0.0701658i | \(-0.0223528\pi\) |
−0.0701658 | + | 0.997535i | \(0.522353\pi\) | |||||||
\(80\) | 0.707107 | − | 0.707107i | 0.0790569 | − | 0.0790569i | ||||
\(81\) | 9.48528 | 1.05392 | ||||||||
\(82\) | 6.65685 | − | 6.65685i | 0.735127 | − | 0.735127i | ||||
\(83\) | − | 9.89949i | − | 1.08661i | −0.839535 | − | 0.543305i | \(-0.817173\pi\) | ||
0.839535 | − | 0.543305i | \(-0.182827\pi\) | |||||||
\(84\) | 1.41421 | 0.154303 | ||||||||
\(85\) | −2.82843 | + | 3.00000i | −0.306786 | + | 0.325396i | ||||
\(86\) | 10.2426 | 1.10449 | ||||||||
\(87\) | 23.7279i | 2.54390i | ||||||||
\(88\) | 1.00000 | − | 1.00000i | 0.106600 | − | 0.106600i | ||||
\(89\) | 14.6569 | 1.55362 | 0.776812 | − | 0.629733i | \(-0.216836\pi\) | ||||
0.776812 | + | 0.629733i | \(0.216836\pi\) | |||||||
\(90\) | 2.00000 | − | 2.00000i | 0.210819 | − | 0.210819i | ||||
\(91\) | −0.414214 | − | 0.414214i | −0.0434214 | − | 0.0434214i | ||||
\(92\) | −2.24264 | − | 2.24264i | −0.233811 | − | 0.233811i | ||||
\(93\) | 12.6569i | 1.31245i | ||||||||
\(94\) | 3.24264i | 0.334453i | ||||||||
\(95\) | 1.70711 | + | 1.70711i | 0.175145 | + | 0.175145i | ||||
\(96\) | 1.70711 | + | 1.70711i | 0.174231 | + | 0.174231i | ||||
\(97\) | 10.1213 | − | 10.1213i | 1.02766 | − | 1.02766i | 0.0280581 | − | 0.999606i | \(-0.491068\pi\) |
0.999606 | − | 0.0280581i | \(-0.00893234\pi\) | |||||||
\(98\) | 6.65685 | 0.672444 | ||||||||
\(99\) | 2.82843 | − | 2.82843i | 0.284268 | − | 0.284268i | ||||
\(100\) | 1.00000i | 0.100000i | ||||||||
\(101\) | −4.34315 | −0.432159 | −0.216080 | − | 0.976376i | \(-0.569327\pi\) | ||||
−0.216080 | + | 0.976376i | \(0.569327\pi\) | |||||||
\(102\) | −7.24264 | − | 6.82843i | −0.717128 | − | 0.676115i | ||||
\(103\) | −2.34315 | −0.230877 | −0.115439 | − | 0.993315i | \(-0.536827\pi\) | ||||
−0.115439 | + | 0.993315i | \(0.536827\pi\) | |||||||
\(104\) | − | 1.00000i | − | 0.0980581i | ||||||
\(105\) | −1.00000 | + | 1.00000i | −0.0975900 | + | 0.0975900i | ||||
\(106\) | −3.48528 | −0.338520 | ||||||||
\(107\) | −8.82843 | + | 8.82843i | −0.853476 | + | 0.853476i | −0.990560 | − | 0.137083i | \(-0.956227\pi\) |
0.137083 | + | 0.990560i | \(0.456227\pi\) | |||||||
\(108\) | −0.292893 | − | 0.292893i | −0.0281837 | − | 0.0281837i | ||||
\(109\) | −8.36396 | − | 8.36396i | −0.801122 | − | 0.801122i | 0.182149 | − | 0.983271i | \(-0.441695\pi\) |
−0.983271 | + | 0.182149i | \(0.941695\pi\) | |||||||
\(110\) | 1.41421i | 0.134840i | ||||||||
\(111\) | − | 5.41421i | − | 0.513894i | ||||||
\(112\) | −0.414214 | − | 0.414214i | −0.0391395 | − | 0.0391395i | ||||
\(113\) | 2.46447 | + | 2.46447i | 0.231837 | + | 0.231837i | 0.813459 | − | 0.581622i | \(-0.197582\pi\) |
−0.581622 | + | 0.813459i | \(0.697582\pi\) | |||||||
\(114\) | −4.12132 | + | 4.12132i | −0.385997 | + | 0.385997i | ||||
\(115\) | 3.17157 | 0.295751 | ||||||||
\(116\) | 6.94975 | − | 6.94975i | 0.645268 | − | 0.645268i | ||||
\(117\) | − | 2.82843i | − | 0.261488i | ||||||
\(118\) | −10.8995 | −1.00338 | ||||||||
\(119\) | 1.75736 | + | 1.65685i | 0.161097 | + | 0.151884i | ||||
\(120\) | −2.41421 | −0.220387 | ||||||||
\(121\) | − | 9.00000i | − | 0.818182i | ||||||
\(122\) | 5.77817 | − | 5.77817i | 0.523131 | − | 0.523131i | ||||
\(123\) | −22.7279 | −2.04931 | ||||||||
\(124\) | 3.70711 | − | 3.70711i | 0.332908 | − | 0.332908i | ||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | −1.17157 | − | 1.17157i | −0.104372 | − | 0.104372i | ||||
\(127\) | 7.72792i | 0.685742i | 0.939382 | + | 0.342871i | \(0.111399\pi\) | ||||
−0.939382 | + | 0.342871i | \(0.888601\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −17.4853 | − | 17.4853i | −1.53949 | − | 1.53949i | ||||
\(130\) | 0.707107 | + | 0.707107i | 0.0620174 | + | 0.0620174i | ||||
\(131\) | 14.0711 | − | 14.0711i | 1.22939 | − | 1.22939i | 0.265202 | − | 0.964193i | \(-0.414561\pi\) |
0.964193 | − | 0.265202i | \(-0.0854387\pi\) | |||||||
\(132\) | −3.41421 | −0.297169 | ||||||||
\(133\) | 1.00000 | − | 1.00000i | 0.0867110 | − | 0.0867110i | ||||
\(134\) | 8.82843i | 0.762660i | ||||||||
\(135\) | 0.414214 | 0.0356498 | ||||||||
\(136\) | 0.121320 | + | 4.12132i | 0.0104031 | + | 0.353400i | ||||
\(137\) | −16.7279 | −1.42916 | −0.714581 | − | 0.699552i | \(-0.753383\pi\) | ||||
−0.714581 | + | 0.699552i | \(0.753383\pi\) | |||||||
\(138\) | 7.65685i | 0.651795i | ||||||||
\(139\) | −0.656854 | + | 0.656854i | −0.0557137 | + | 0.0557137i | −0.734415 | − | 0.678701i | \(-0.762543\pi\) |
0.678701 | + | 0.734415i | \(0.262543\pi\) | |||||||
\(140\) | 0.585786 | 0.0495080 | ||||||||
\(141\) | 5.53553 | − | 5.53553i | 0.466176 | − | 0.466176i | ||||
\(142\) | −8.29289 | − | 8.29289i | −0.695924 | − | 0.695924i | ||||
\(143\) | 1.00000 | + | 1.00000i | 0.0836242 | + | 0.0836242i | ||||
\(144\) | − | 2.82843i | − | 0.235702i | ||||||
\(145\) | 9.82843i | 0.816206i | ||||||||
\(146\) | 5.53553 | + | 5.53553i | 0.458124 | + | 0.458124i | ||||
\(147\) | −11.3640 | − | 11.3640i | −0.937284 | − | 0.937284i | ||||
\(148\) | −1.58579 | + | 1.58579i | −0.130351 | + | 0.130351i | ||||
\(149\) | −1.75736 | −0.143968 | −0.0719842 | − | 0.997406i | \(-0.522933\pi\) | ||||
−0.0719842 | + | 0.997406i | \(0.522933\pi\) | |||||||
\(150\) | 1.70711 | − | 1.70711i | 0.139385 | − | 0.139385i | ||||
\(151\) | − | 4.82843i | − | 0.392932i | −0.980511 | − | 0.196466i | \(-0.937053\pi\) | ||
0.980511 | − | 0.196466i | \(-0.0629465\pi\) | |||||||
\(152\) | 2.41421 | 0.195819 | ||||||||
\(153\) | 0.343146 | + | 11.6569i | 0.0277417 | + | 0.942401i | ||||
\(154\) | 0.828427 | 0.0667566 | ||||||||
\(155\) | 5.24264i | 0.421099i | ||||||||
\(156\) | −1.70711 | + | 1.70711i | −0.136678 | + | 0.136678i | ||||
\(157\) | 2.82843 | 0.225733 | 0.112867 | − | 0.993610i | \(-0.463997\pi\) | ||||
0.112867 | + | 0.993610i | \(0.463997\pi\) | |||||||
\(158\) | −8.24264 | + | 8.24264i | −0.655749 | + | 0.655749i | ||||
\(159\) | 5.94975 | + | 5.94975i | 0.471846 | + | 0.471846i | ||||
\(160\) | 0.707107 | + | 0.707107i | 0.0559017 | + | 0.0559017i | ||||
\(161\) | − | 1.85786i | − | 0.146420i | ||||||
\(162\) | 9.48528i | 0.745234i | ||||||||
\(163\) | 0.343146 | + | 0.343146i | 0.0268772 | + | 0.0268772i | 0.720418 | − | 0.693540i | \(-0.243950\pi\) |
−0.693540 | + | 0.720418i | \(0.743950\pi\) | |||||||
\(164\) | 6.65685 | + | 6.65685i | 0.519813 | + | 0.519813i | ||||
\(165\) | 2.41421 | − | 2.41421i | 0.187946 | − | 0.187946i | ||||
\(166\) | 9.89949 | 0.768350 | ||||||||
\(167\) | 10.7279 | − | 10.7279i | 0.830152 | − | 0.830152i | −0.157386 | − | 0.987537i | \(-0.550307\pi\) |
0.987537 | + | 0.157386i | \(0.0503066\pi\) | |||||||
\(168\) | 1.41421i | 0.109109i | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | −3.00000 | − | 2.82843i | −0.230089 | − | 0.216930i | ||||
\(171\) | 6.82843 | 0.522183 | ||||||||
\(172\) | 10.2426i | 0.780994i | ||||||||
\(173\) | 0.928932 | − | 0.928932i | 0.0706254 | − | 0.0706254i | −0.670912 | − | 0.741537i | \(-0.734097\pi\) |
0.741537 | + | 0.670912i | \(0.234097\pi\) | |||||||
\(174\) | −23.7279 | −1.79881 | ||||||||
\(175\) | −0.414214 | + | 0.414214i | −0.0313116 | + | 0.0313116i | ||||
\(176\) | 1.00000 | + | 1.00000i | 0.0753778 | + | 0.0753778i | ||||
\(177\) | 18.6066 | + | 18.6066i | 1.39856 | + | 1.39856i | ||||
\(178\) | 14.6569i | 1.09858i | ||||||||
\(179\) | − | 6.82843i | − | 0.510381i | −0.966891 | − | 0.255190i | \(-0.917862\pi\) | ||
0.966891 | − | 0.255190i | \(-0.0821381\pi\) | |||||||
\(180\) | 2.00000 | + | 2.00000i | 0.149071 | + | 0.149071i | ||||
\(181\) | 6.82843 | + | 6.82843i | 0.507553 | + | 0.507553i | 0.913775 | − | 0.406222i | \(-0.133154\pi\) |
−0.406222 | + | 0.913775i | \(0.633154\pi\) | |||||||
\(182\) | 0.414214 | − | 0.414214i | 0.0307036 | − | 0.0307036i | ||||
\(183\) | −19.7279 | −1.45833 | ||||||||
\(184\) | 2.24264 | − | 2.24264i | 0.165330 | − | 0.165330i | ||||
\(185\) | − | 2.24264i | − | 0.164882i | ||||||
\(186\) | −12.6569 | −0.928046 | ||||||||
\(187\) | −4.24264 | − | 4.00000i | −0.310253 | − | 0.292509i | ||||
\(188\) | −3.24264 | −0.236494 | ||||||||
\(189\) | − | 0.242641i | − | 0.0176495i | ||||||
\(190\) | −1.70711 | + | 1.70711i | −0.123847 | + | 0.123847i | ||||
\(191\) | 0.242641 | 0.0175569 | 0.00877843 | − | 0.999961i | \(-0.497206\pi\) | ||||
0.00877843 | + | 0.999961i | \(0.497206\pi\) | |||||||
\(192\) | −1.70711 | + | 1.70711i | −0.123200 | + | 0.123200i | ||||
\(193\) | 2.82843 | + | 2.82843i | 0.203595 | + | 0.203595i | 0.801538 | − | 0.597944i | \(-0.204015\pi\) |
−0.597944 | + | 0.801538i | \(0.704015\pi\) | |||||||
\(194\) | 10.1213 | + | 10.1213i | 0.726668 | + | 0.726668i | ||||
\(195\) | − | 2.41421i | − | 0.172885i | ||||||
\(196\) | 6.65685i | 0.475490i | ||||||||
\(197\) | −18.0711 | − | 18.0711i | −1.28751 | − | 1.28751i | −0.936295 | − | 0.351216i | \(-0.885768\pi\) |
−0.351216 | − | 0.936295i | \(-0.614232\pi\) | |||||||
\(198\) | 2.82843 | + | 2.82843i | 0.201008 | + | 0.201008i | ||||
\(199\) | −8.05025 | + | 8.05025i | −0.570667 | + | 0.570667i | −0.932315 | − | 0.361648i | \(-0.882214\pi\) |
0.361648 | + | 0.932315i | \(0.382214\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 15.0711 | − | 15.0711i | 1.06303 | − | 1.06303i | ||||
\(202\) | − | 4.34315i | − | 0.305583i | ||||||
\(203\) | 5.75736 | 0.404087 | ||||||||
\(204\) | 6.82843 | − | 7.24264i | 0.478086 | − | 0.507086i | ||||
\(205\) | −9.41421 | −0.657517 | ||||||||
\(206\) | − | 2.34315i | − | 0.163255i | ||||||
\(207\) | 6.34315 | − | 6.34315i | 0.440879 | − | 0.440879i | ||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −2.41421 | + | 2.41421i | −0.166995 | + | 0.166995i | ||||
\(210\) | −1.00000 | − | 1.00000i | −0.0690066 | − | 0.0690066i | ||||
\(211\) | 3.41421 | + | 3.41421i | 0.235044 | + | 0.235044i | 0.814794 | − | 0.579750i | \(-0.196850\pi\) |
−0.579750 | + | 0.814794i | \(0.696850\pi\) | |||||||
\(212\) | − | 3.48528i | − | 0.239370i | ||||||
\(213\) | 28.3137i | 1.94002i | ||||||||
\(214\) | −8.82843 | − | 8.82843i | −0.603499 | − | 0.603499i | ||||
\(215\) | −7.24264 | − | 7.24264i | −0.493944 | − | 0.493944i | ||||
\(216\) | 0.292893 | − | 0.292893i | 0.0199289 | − | 0.0199289i | ||||
\(217\) | 3.07107 | 0.208478 | ||||||||
\(218\) | 8.36396 | − | 8.36396i | 0.566479 | − | 0.566479i | ||||
\(219\) | − | 18.8995i | − | 1.27711i | ||||||
\(220\) | −1.41421 | −0.0953463 | ||||||||
\(221\) | −4.12132 | + | 0.121320i | −0.277230 | + | 0.00816089i | ||||
\(222\) | 5.41421 | 0.363378 | ||||||||
\(223\) | − | 25.3848i | − | 1.69989i | −0.526871 | − | 0.849945i | \(-0.676635\pi\) | ||
0.526871 | − | 0.849945i | \(-0.323365\pi\) | |||||||
\(224\) | 0.414214 | − | 0.414214i | 0.0276758 | − | 0.0276758i | ||||
\(225\) | −2.82843 | −0.188562 | ||||||||
\(226\) | −2.46447 | + | 2.46447i | −0.163934 | + | 0.163934i | ||||
\(227\) | −14.5355 | − | 14.5355i | −0.964757 | − | 0.964757i | 0.0346425 | − | 0.999400i | \(-0.488971\pi\) |
−0.999400 | + | 0.0346425i | \(0.988971\pi\) | |||||||
\(228\) | −4.12132 | − | 4.12132i | −0.272941 | − | 0.272941i | ||||
\(229\) | 16.2426i | 1.07334i | 0.843791 | + | 0.536672i | \(0.180319\pi\) | ||||
−0.843791 | + | 0.536672i | \(0.819681\pi\) | |||||||
\(230\) | 3.17157i | 0.209127i | ||||||||
\(231\) | −1.41421 | − | 1.41421i | −0.0930484 | − | 0.0930484i | ||||
\(232\) | 6.94975 | + | 6.94975i | 0.456273 | + | 0.456273i | ||||
\(233\) | −8.36396 | + | 8.36396i | −0.547941 | + | 0.547941i | −0.925845 | − | 0.377904i | \(-0.876645\pi\) |
0.377904 | + | 0.925845i | \(0.376645\pi\) | |||||||
\(234\) | 2.82843 | 0.184900 | ||||||||
\(235\) | 2.29289 | − | 2.29289i | 0.149572 | − | 0.149572i | ||||
\(236\) | − | 10.8995i | − | 0.709497i | ||||||
\(237\) | 28.1421 | 1.82803 | ||||||||
\(238\) | −1.65685 | + | 1.75736i | −0.107398 | + | 0.113913i | ||||
\(239\) | 27.4142 | 1.77328 | 0.886639 | − | 0.462462i | \(-0.153034\pi\) | ||||
0.886639 | + | 0.462462i | \(0.153034\pi\) | |||||||
\(240\) | − | 2.41421i | − | 0.155837i | ||||||
\(241\) | −19.8284 | + | 19.8284i | −1.27726 | + | 1.27726i | −0.335067 | + | 0.942194i | \(0.608759\pi\) |
−0.942194 | + | 0.335067i | \(0.891241\pi\) | |||||||
\(242\) | 9.00000 | 0.578542 | ||||||||
\(243\) | 15.3137 | − | 15.3137i | 0.982375 | − | 0.982375i | ||||
\(244\) | 5.77817 | + | 5.77817i | 0.369910 | + | 0.369910i | ||||
\(245\) | −4.70711 | − | 4.70711i | −0.300726 | − | 0.300726i | ||||
\(246\) | − | 22.7279i | − | 1.44908i | ||||||
\(247\) | 2.41421i | 0.153613i | ||||||||
\(248\) | 3.70711 | + | 3.70711i | 0.235402 | + | 0.235402i | ||||
\(249\) | −16.8995 | − | 16.8995i | −1.07096 | − | 1.07096i | ||||
\(250\) | 0.707107 | − | 0.707107i | 0.0447214 | − | 0.0447214i | ||||
\(251\) | −2.14214 | −0.135210 | −0.0676052 | − | 0.997712i | \(-0.521536\pi\) | ||||
−0.0676052 | + | 0.997712i | \(0.521536\pi\) | |||||||
\(252\) | 1.17157 | − | 1.17157i | 0.0738022 | − | 0.0738022i | ||||
\(253\) | 4.48528i | 0.281987i | ||||||||
\(254\) | −7.72792 | −0.484893 | ||||||||
\(255\) | 0.292893 | + | 9.94975i | 0.0183417 | + | 0.623077i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.5858i | 1.40886i | 0.709772 | + | 0.704431i | \(0.248798\pi\) | ||||
−0.709772 | + | 0.704431i | \(0.751202\pi\) | |||||||
\(258\) | 17.4853 | − | 17.4853i | 1.08859 | − | 1.08859i | ||||
\(259\) | −1.31371 | −0.0816299 | ||||||||
\(260\) | −0.707107 | + | 0.707107i | −0.0438529 | + | 0.0438529i | ||||
\(261\) | 19.6569 | + | 19.6569i | 1.21673 | + | 1.21673i | ||||
\(262\) | 14.0711 | + | 14.0711i | 0.869313 | + | 0.869313i | ||||
\(263\) | 29.7279i | 1.83310i | 0.399918 | + | 0.916551i | \(0.369039\pi\) | ||||
−0.399918 | + | 0.916551i | \(0.630961\pi\) | |||||||
\(264\) | − | 3.41421i | − | 0.210130i | ||||||
\(265\) | 2.46447 | + | 2.46447i | 0.151391 | + | 0.151391i | ||||
\(266\) | 1.00000 | + | 1.00000i | 0.0613139 | + | 0.0613139i | ||||
\(267\) | 25.0208 | − | 25.0208i | 1.53125 | − | 1.53125i | ||||
\(268\) | −8.82843 | −0.539282 | ||||||||
\(269\) | −2.46447 | + | 2.46447i | −0.150261 | + | 0.150261i | −0.778235 | − | 0.627974i | \(-0.783885\pi\) |
0.627974 | + | 0.778235i | \(0.283885\pi\) | |||||||
\(270\) | 0.414214i | 0.0252082i | ||||||||
\(271\) | −6.34315 | −0.385319 | −0.192659 | − | 0.981266i | \(-0.561711\pi\) | ||||
−0.192659 | + | 0.981266i | \(0.561711\pi\) | |||||||
\(272\) | −4.12132 | + | 0.121320i | −0.249892 | + | 0.00735613i | ||||
\(273\) | −1.41421 | −0.0855921 | ||||||||
\(274\) | − | 16.7279i | − | 1.01057i | ||||||
\(275\) | 1.00000 | − | 1.00000i | 0.0603023 | − | 0.0603023i | ||||
\(276\) | −7.65685 | −0.460888 | ||||||||
\(277\) | 5.89949 | − | 5.89949i | 0.354466 | − | 0.354466i | −0.507302 | − | 0.861768i | \(-0.669357\pi\) |
0.861768 | + | 0.507302i | \(0.169357\pi\) | |||||||
\(278\) | −0.656854 | − | 0.656854i | −0.0393955 | − | 0.0393955i | ||||
\(279\) | 10.4853 | + | 10.4853i | 0.627737 | + | 0.627737i | ||||
\(280\) | 0.585786i | 0.0350074i | ||||||||
\(281\) | 1.48528i | 0.0886045i | 0.999018 | + | 0.0443022i | \(0.0141065\pi\) | ||||
−0.999018 | + | 0.0443022i | \(0.985894\pi\) | |||||||
\(282\) | 5.53553 | + | 5.53553i | 0.329636 | + | 0.329636i | ||||
\(283\) | 6.77817 | + | 6.77817i | 0.402921 | + | 0.402921i | 0.879261 | − | 0.476340i | \(-0.158037\pi\) |
−0.476340 | + | 0.879261i | \(0.658037\pi\) | |||||||
\(284\) | 8.29289 | − | 8.29289i | 0.492093 | − | 0.492093i | ||||
\(285\) | 5.82843 | 0.345246 | ||||||||
\(286\) | −1.00000 | + | 1.00000i | −0.0591312 | + | 0.0591312i | ||||
\(287\) | 5.51472i | 0.325524i | ||||||||
\(288\) | 2.82843 | 0.166667 | ||||||||
\(289\) | 16.9706 | − | 1.00000i | 0.998268 | − | 0.0588235i | ||||
\(290\) | −9.82843 | −0.577145 | ||||||||
\(291\) | − | 34.5563i | − | 2.02573i | ||||||
\(292\) | −5.53553 | + | 5.53553i | −0.323943 | + | 0.323943i | ||||
\(293\) | 5.48528 | 0.320454 | 0.160227 | − | 0.987080i | \(-0.448777\pi\) | ||||
0.160227 | + | 0.987080i | \(0.448777\pi\) | |||||||
\(294\) | 11.3640 | − | 11.3640i | 0.662760 | − | 0.662760i | ||||
\(295\) | 7.70711 | + | 7.70711i | 0.448725 | + | 0.448725i | ||||
\(296\) | −1.58579 | − | 1.58579i | −0.0921720 | − | 0.0921720i | ||||
\(297\) | 0.585786i | 0.0339908i | ||||||||
\(298\) | − | 1.75736i | − | 0.101801i | ||||||
\(299\) | 2.24264 | + | 2.24264i | 0.129695 | + | 0.129695i | ||||
\(300\) | 1.70711 | + | 1.70711i | 0.0985599 | + | 0.0985599i | ||||
\(301\) | −4.24264 | + | 4.24264i | −0.244542 | + | 0.244542i | ||||
\(302\) | 4.82843 | 0.277845 | ||||||||
\(303\) | −7.41421 | + | 7.41421i | −0.425935 | + | 0.425935i | ||||
\(304\) | 2.41421i | 0.138465i | ||||||||
\(305\) | −8.17157 | −0.467903 | ||||||||
\(306\) | −11.6569 | + | 0.343146i | −0.666378 | + | 0.0196163i | ||||
\(307\) | 9.89949 | 0.564994 | 0.282497 | − | 0.959268i | \(-0.408837\pi\) | ||||
0.282497 | + | 0.959268i | \(0.408837\pi\) | |||||||
\(308\) | 0.828427i | 0.0472040i | ||||||||
\(309\) | −4.00000 | + | 4.00000i | −0.227552 | + | 0.227552i | ||||
\(310\) | −5.24264 | −0.297762 | ||||||||
\(311\) | −2.58579 | + | 2.58579i | −0.146626 | + | 0.146626i | −0.776609 | − | 0.629983i | \(-0.783062\pi\) |
0.629983 | + | 0.776609i | \(0.283062\pi\) | |||||||
\(312\) | −1.70711 | − | 1.70711i | −0.0966459 | − | 0.0966459i | ||||
\(313\) | 6.48528 | + | 6.48528i | 0.366570 | + | 0.366570i | 0.866225 | − | 0.499655i | \(-0.166540\pi\) |
−0.499655 | + | 0.866225i | \(0.666540\pi\) | |||||||
\(314\) | 2.82843i | 0.159617i | ||||||||
\(315\) | 1.65685i | 0.0933532i | ||||||||
\(316\) | −8.24264 | − | 8.24264i | −0.463685 | − | 0.463685i | ||||
\(317\) | −24.4853 | − | 24.4853i | −1.37523 | − | 1.37523i | −0.852495 | − | 0.522735i | \(-0.824912\pi\) |
−0.522735 | − | 0.852495i | \(-0.675088\pi\) | |||||||
\(318\) | −5.94975 | + | 5.94975i | −0.333645 | + | 0.333645i | ||||
\(319\) | −13.8995 | −0.778222 | ||||||||
\(320\) | −0.707107 | + | 0.707107i | −0.0395285 | + | 0.0395285i | ||||
\(321\) | 30.1421i | 1.68237i | ||||||||
\(322\) | 1.85786 | 0.103535 | ||||||||
\(323\) | −0.292893 | − | 9.94975i | −0.0162970 | − | 0.553619i | ||||
\(324\) | −9.48528 | −0.526960 | ||||||||
\(325\) | − | 1.00000i | − | 0.0554700i | ||||||
\(326\) | −0.343146 | + | 0.343146i | −0.0190051 | + | 0.0190051i | ||||
\(327\) | −28.5563 | −1.57917 | ||||||||
\(328\) | −6.65685 | + | 6.65685i | −0.367563 | + | 0.367563i | ||||
\(329\) | −1.34315 | − | 1.34315i | −0.0740500 | − | 0.0740500i | ||||
\(330\) | 2.41421 | + | 2.41421i | 0.132898 | + | 0.132898i | ||||
\(331\) | 8.55635i | 0.470299i | 0.971959 | + | 0.235150i | \(0.0755581\pi\) | ||||
−0.971959 | + | 0.235150i | \(0.924442\pi\) | |||||||
\(332\) | 9.89949i | 0.543305i | ||||||||
\(333\) | −4.48528 | − | 4.48528i | −0.245792 | − | 0.245792i | ||||
\(334\) | 10.7279 | + | 10.7279i | 0.587006 | + | 0.587006i | ||||
\(335\) | 6.24264 | − | 6.24264i | 0.341072 | − | 0.341072i | ||||
\(336\) | −1.41421 | −0.0771517 | ||||||||
\(337\) | −21.4350 | + | 21.4350i | −1.16764 | + | 1.16764i | −0.184879 | + | 0.982761i | \(0.559189\pi\) |
−0.982761 | + | 0.184879i | \(0.940811\pi\) | |||||||
\(338\) | − | 12.0000i | − | 0.652714i | ||||||
\(339\) | 8.41421 | 0.456997 | ||||||||
\(340\) | 2.82843 | − | 3.00000i | 0.153393 | − | 0.162698i | ||||
\(341\) | −7.41421 | −0.401502 | ||||||||
\(342\) | 6.82843i | 0.369239i | ||||||||
\(343\) | −5.65685 | + | 5.65685i | −0.305441 | + | 0.305441i | ||||
\(344\) | −10.2426 | −0.552246 | ||||||||
\(345\) | 5.41421 | − | 5.41421i | 0.291491 | − | 0.291491i | ||||
\(346\) | 0.928932 | + | 0.928932i | 0.0499397 | + | 0.0499397i | ||||
\(347\) | −10.4350 | − | 10.4350i | −0.560182 | − | 0.560182i | 0.369177 | − | 0.929359i | \(-0.379640\pi\) |
−0.929359 | + | 0.369177i | \(0.879640\pi\) | |||||||
\(348\) | − | 23.7279i | − | 1.27195i | ||||||
\(349\) | − | 8.97056i | − | 0.480183i | −0.970750 | − | 0.240092i | \(-0.922823\pi\) | ||
0.970750 | − | 0.240092i | \(-0.0771775\pi\) | |||||||
\(350\) | −0.414214 | − | 0.414214i | −0.0221406 | − | 0.0221406i | ||||
\(351\) | 0.292893 | + | 0.292893i | 0.0156335 | + | 0.0156335i | ||||
\(352\) | −1.00000 | + | 1.00000i | −0.0533002 | + | 0.0533002i | ||||
\(353\) | 5.31371 | 0.282820 | 0.141410 | − | 0.989951i | \(-0.454836\pi\) | ||||
0.141410 | + | 0.989951i | \(0.454836\pi\) | |||||||
\(354\) | −18.6066 | + | 18.6066i | −0.988930 | + | 0.988930i | ||||
\(355\) | 11.7279i | 0.622453i | ||||||||
\(356\) | −14.6569 | −0.776812 | ||||||||
\(357\) | 5.82843 | − | 0.171573i | 0.308473 | − | 0.00908060i | ||||
\(358\) | 6.82843 | 0.360894 | ||||||||
\(359\) | 12.3848i | 0.653643i | 0.945086 | + | 0.326822i | \(0.105978\pi\) | ||||
−0.945086 | + | 0.326822i | \(0.894022\pi\) | |||||||
\(360\) | −2.00000 | + | 2.00000i | −0.105409 | + | 0.105409i | ||||
\(361\) | 13.1716 | 0.693241 | ||||||||
\(362\) | −6.82843 | + | 6.82843i | −0.358894 | + | 0.358894i | ||||
\(363\) | −15.3640 | − | 15.3640i | −0.806399 | − | 0.806399i | ||||
\(364\) | 0.414214 | + | 0.414214i | 0.0217107 | + | 0.0217107i | ||||
\(365\) | − | 7.82843i | − | 0.409759i | ||||||
\(366\) | − | 19.7279i | − | 1.03120i | ||||||
\(367\) | 5.55635 | + | 5.55635i | 0.290039 | + | 0.290039i | 0.837096 | − | 0.547057i | \(-0.184252\pi\) |
−0.547057 | + | 0.837096i | \(0.684252\pi\) | |||||||
\(368\) | 2.24264 | + | 2.24264i | 0.116906 | + | 0.116906i | ||||
\(369\) | −18.8284 | + | 18.8284i | −0.980169 | + | 0.980169i | ||||
\(370\) | 2.24264 | 0.116589 | ||||||||
\(371\) | 1.44365 | − | 1.44365i | 0.0749506 | − | 0.0749506i | ||||
\(372\) | − | 12.6569i | − | 0.656227i | ||||||
\(373\) | 24.2843 | 1.25739 | 0.628696 | − | 0.777651i | \(-0.283589\pi\) | ||||
0.628696 | + | 0.777651i | \(0.283589\pi\) | |||||||
\(374\) | 4.00000 | − | 4.24264i | 0.206835 | − | 0.219382i | ||||
\(375\) | −2.41421 | −0.124669 | ||||||||
\(376\) | − | 3.24264i | − | 0.167226i | ||||||
\(377\) | −6.94975 | + | 6.94975i | −0.357930 | + | 0.357930i | ||||
\(378\) | 0.242641 | 0.0124801 | ||||||||
\(379\) | −4.00000 | + | 4.00000i | −0.205466 | + | 0.205466i | −0.802337 | − | 0.596871i | \(-0.796410\pi\) |
0.596871 | + | 0.802337i | \(0.296410\pi\) | |||||||
\(380\) | −1.70711 | − | 1.70711i | −0.0875727 | − | 0.0875727i | ||||
\(381\) | 13.1924 | + | 13.1924i | 0.675867 | + | 0.675867i | ||||
\(382\) | 0.242641i | 0.0124146i | ||||||||
\(383\) | − | 22.2132i | − | 1.13504i | −0.823359 | − | 0.567521i | \(-0.807903\pi\) | ||
0.823359 | − | 0.567521i | \(-0.192097\pi\) | |||||||
\(384\) | −1.70711 | − | 1.70711i | −0.0871154 | − | 0.0871154i | ||||
\(385\) | −0.585786 | − | 0.585786i | −0.0298544 | − | 0.0298544i | ||||
\(386\) | −2.82843 | + | 2.82843i | −0.143963 | + | 0.143963i | ||||
\(387\) | −28.9706 | −1.47266 | ||||||||
\(388\) | −10.1213 | + | 10.1213i | −0.513832 | + | 0.513832i | ||||
\(389\) | 10.6274i | 0.538831i | 0.963024 | + | 0.269416i | \(0.0868306\pi\) | ||||
−0.963024 | + | 0.269416i | \(0.913169\pi\) | |||||||
\(390\) | 2.41421 | 0.122248 | ||||||||
\(391\) | −9.51472 | − | 8.97056i | −0.481180 | − | 0.453661i | ||||
\(392\) | −6.65685 | −0.336222 | ||||||||
\(393\) | − | 48.0416i | − | 2.42338i | ||||||
\(394\) | 18.0711 | − | 18.0711i | 0.910407 | − | 0.910407i | ||||
\(395\) | 11.6569 | 0.586520 | ||||||||
\(396\) | −2.82843 | + | 2.82843i | −0.142134 | + | 0.142134i | ||||
\(397\) | −16.4853 | − | 16.4853i | −0.827373 | − | 0.827373i | 0.159780 | − | 0.987153i | \(-0.448921\pi\) |
−0.987153 | + | 0.159780i | \(0.948921\pi\) | |||||||
\(398\) | −8.05025 | − | 8.05025i | −0.403523 | − | 0.403523i | ||||
\(399\) | − | 3.41421i | − | 0.170924i | ||||||
\(400\) | − | 1.00000i | − | 0.0500000i | ||||||
\(401\) | 14.8284 | + | 14.8284i | 0.740496 | + | 0.740496i | 0.972674 | − | 0.232177i | \(-0.0745849\pi\) |
−0.232177 | + | 0.972674i | \(0.574585\pi\) | |||||||
\(402\) | 15.0711 | + | 15.0711i | 0.751677 | + | 0.751677i | ||||
\(403\) | −3.70711 | + | 3.70711i | −0.184664 | + | 0.184664i | ||||
\(404\) | 4.34315 | 0.216080 | ||||||||
\(405\) | 6.70711 | − | 6.70711i | 0.333279 | − | 0.333279i | ||||
\(406\) | 5.75736i | 0.285733i | ||||||||
\(407\) | 3.17157 | 0.157209 | ||||||||
\(408\) | 7.24264 | + | 6.82843i | 0.358564 | + | 0.338058i | ||||
\(409\) | 11.4853 | 0.567911 | 0.283955 | − | 0.958838i | \(-0.408353\pi\) | ||||
0.283955 | + | 0.958838i | \(0.408353\pi\) | |||||||
\(410\) | − | 9.41421i | − | 0.464935i | ||||||
\(411\) | −28.5563 | + | 28.5563i | −1.40858 | + | 1.40858i | ||||
\(412\) | 2.34315 | 0.115439 | ||||||||
\(413\) | 4.51472 | − | 4.51472i | 0.222155 | − | 0.222155i | ||||
\(414\) | 6.34315 | + | 6.34315i | 0.311749 | + | 0.311749i | ||||
\(415\) | −7.00000 | − | 7.00000i | −0.343616 | − | 0.343616i | ||||
\(416\) | 1.00000i | 0.0490290i | ||||||||
\(417\) | 2.24264i | 0.109823i | ||||||||
\(418\) | −2.41421 | − | 2.41421i | −0.118083 | − | 0.118083i | ||||
\(419\) | 9.75736 | + | 9.75736i | 0.476678 | + | 0.476678i | 0.904068 | − | 0.427389i | \(-0.140567\pi\) |
−0.427389 | + | 0.904068i | \(0.640567\pi\) | |||||||
\(420\) | 1.00000 | − | 1.00000i | 0.0487950 | − | 0.0487950i | ||||
\(421\) | 22.9289 | 1.11749 | 0.558744 | − | 0.829340i | \(-0.311283\pi\) | ||||
0.558744 | + | 0.829340i | \(0.311283\pi\) | |||||||
\(422\) | −3.41421 | + | 3.41421i | −0.166201 | + | 0.166201i | ||||
\(423\) | − | 9.17157i | − | 0.445937i | ||||||
\(424\) | 3.48528 | 0.169260 | ||||||||
\(425\) | 0.121320 | + | 4.12132i | 0.00588490 | + | 0.199913i | ||||
\(426\) | −28.3137 | −1.37180 | ||||||||
\(427\) | 4.78680i | 0.231649i | ||||||||
\(428\) | 8.82843 | − | 8.82843i | 0.426738 | − | 0.426738i | ||||
\(429\) | 3.41421 | 0.164840 | ||||||||
\(430\) | 7.24264 | − | 7.24264i | 0.349271 | − | 0.349271i | ||||
\(431\) | 16.0000 | + | 16.0000i | 0.770693 | + | 0.770693i | 0.978228 | − | 0.207535i | \(-0.0665440\pi\) |
−0.207535 | + | 0.978228i | \(0.566544\pi\) | |||||||
\(432\) | 0.292893 | + | 0.292893i | 0.0140918 | + | 0.0140918i | ||||
\(433\) | 0.928932i | 0.0446416i | 0.999751 | + | 0.0223208i | \(0.00710553\pi\) | ||||
−0.999751 | + | 0.0223208i | \(0.992894\pi\) | |||||||
\(434\) | 3.07107i | 0.147416i | ||||||||
\(435\) | 16.7782 | + | 16.7782i | 0.804452 | + | 0.804452i | ||||
\(436\) | 8.36396 | + | 8.36396i | 0.400561 | + | 0.400561i | ||||
\(437\) | −5.41421 | + | 5.41421i | −0.258997 | + | 0.258997i | ||||
\(438\) | 18.8995 | 0.903053 | ||||||||
\(439\) | −22.6274 | + | 22.6274i | −1.07995 | + | 1.07995i | −0.0834344 | + | 0.996513i | \(0.526589\pi\) |
−0.996513 | + | 0.0834344i | \(0.973411\pi\) | |||||||
\(440\) | − | 1.41421i | − | 0.0674200i | ||||||
\(441\) | −18.8284 | −0.896592 | ||||||||
\(442\) | −0.121320 | − | 4.12132i | −0.00577062 | − | 0.196031i | ||||
\(443\) | −20.0000 | −0.950229 | −0.475114 | − | 0.879924i | \(-0.657593\pi\) | ||||
−0.475114 | + | 0.879924i | \(0.657593\pi\) | |||||||
\(444\) | 5.41421i | 0.256947i | ||||||||
\(445\) | 10.3640 | − | 10.3640i | 0.491299 | − | 0.491299i | ||||
\(446\) | 25.3848 | 1.20200 | ||||||||
\(447\) | −3.00000 | + | 3.00000i | −0.141895 | + | 0.141895i | ||||
\(448\) | 0.414214 | + | 0.414214i | 0.0195698 | + | 0.0195698i | ||||
\(449\) | −29.3848 | − | 29.3848i | −1.38675 | − | 1.38675i | −0.832045 | − | 0.554709i | \(-0.812830\pi\) |
−0.554709 | − | 0.832045i | \(-0.687170\pi\) | |||||||
\(450\) | − | 2.82843i | − | 0.133333i | ||||||
\(451\) | − | 13.3137i | − | 0.626918i | ||||||
\(452\) | −2.46447 | − | 2.46447i | −0.115919 | − | 0.115919i | ||||
\(453\) | −8.24264 | − | 8.24264i | −0.387273 | − | 0.387273i | ||||
\(454\) | 14.5355 | − | 14.5355i | 0.682186 | − | 0.682186i | ||||
\(455\) | −0.585786 | −0.0274621 | ||||||||
\(456\) | 4.12132 | − | 4.12132i | 0.192999 | − | 0.192999i | ||||
\(457\) | 27.5563i | 1.28903i | 0.764591 | + | 0.644516i | \(0.222941\pi\) | ||||
−0.764591 | + | 0.644516i | \(0.777059\pi\) | |||||||
\(458\) | −16.2426 | −0.758969 | ||||||||
\(459\) | −1.24264 | − | 1.17157i | −0.0580015 | − | 0.0546843i | ||||
\(460\) | −3.17157 | −0.147875 | ||||||||
\(461\) | 6.97056i | 0.324651i | 0.986737 | + | 0.162326i | \(0.0518995\pi\) | ||||
−0.986737 | + | 0.162326i | \(0.948100\pi\) | |||||||
\(462\) | 1.41421 | − | 1.41421i | 0.0657952 | − | 0.0657952i | ||||
\(463\) | −1.10051 | −0.0511448 | −0.0255724 | − | 0.999673i | \(-0.508141\pi\) | ||||
−0.0255724 | + | 0.999673i | \(0.508141\pi\) | |||||||
\(464\) | −6.94975 | + | 6.94975i | −0.322634 | + | 0.322634i | ||||
\(465\) | 8.94975 | + | 8.94975i | 0.415035 | + | 0.415035i | ||||
\(466\) | −8.36396 | − | 8.36396i | −0.387453 | − | 0.387453i | ||||
\(467\) | − | 25.2132i | − | 1.16673i | −0.812211 | − | 0.583364i | \(-0.801736\pi\) | ||
0.812211 | − | 0.583364i | \(-0.198264\pi\) | |||||||
\(468\) | 2.82843i | 0.130744i | ||||||||
\(469\) | −3.65685 | − | 3.65685i | −0.168858 | − | 0.168858i | ||||
\(470\) | 2.29289 | + | 2.29289i | 0.105763 | + | 0.105763i | ||||
\(471\) | 4.82843 | − | 4.82843i | 0.222482 | − | 0.222482i | ||||
\(472\) | 10.8995 | 0.501690 | ||||||||
\(473\) | 10.2426 | − | 10.2426i | 0.470957 | − | 0.470957i | ||||
\(474\) | 28.1421i | 1.29261i | ||||||||
\(475\) | 2.41421 | 0.110772 | ||||||||
\(476\) | −1.75736 | − | 1.65685i | −0.0805484 | − | 0.0759418i | ||||
\(477\) | 9.85786 | 0.451361 | ||||||||
\(478\) | 27.4142i | 1.25390i | ||||||||
\(479\) | 19.0208 | − | 19.0208i | 0.869083 | − | 0.869083i | −0.123288 | − | 0.992371i | \(-0.539344\pi\) |
0.992371 | + | 0.123288i | \(0.0393438\pi\) | |||||||
\(480\) | 2.41421 | 0.110193 | ||||||||
\(481\) | 1.58579 | − | 1.58579i | 0.0723056 | − | 0.0723056i | ||||
\(482\) | −19.8284 | − | 19.8284i | −0.903160 | − | 0.903160i | ||||
\(483\) | −3.17157 | − | 3.17157i | −0.144312 | − | 0.144312i | ||||
\(484\) | 9.00000i | 0.409091i | ||||||||
\(485\) | − | 14.3137i | − | 0.649952i | ||||||
\(486\) | 15.3137 | + | 15.3137i | 0.694644 | + | 0.694644i | ||||
\(487\) | 14.4142 | + | 14.4142i | 0.653170 | + | 0.653170i | 0.953755 | − | 0.300585i | \(-0.0971818\pi\) |
−0.300585 | + | 0.953755i | \(0.597182\pi\) | |||||||
\(488\) | −5.77817 | + | 5.77817i | −0.261566 | + | 0.261566i | ||||
\(489\) | 1.17157 | 0.0529804 | ||||||||
\(490\) | 4.70711 | − | 4.70711i | 0.212645 | − | 0.212645i | ||||
\(491\) | 8.27208i | 0.373314i | 0.982425 | + | 0.186657i | \(0.0597652\pi\) | ||||
−0.982425 | + | 0.186657i | \(0.940235\pi\) | |||||||
\(492\) | 22.7279 | 1.02465 | ||||||||
\(493\) | 27.7990 | − | 29.4853i | 1.25200 | − | 1.32795i | ||||
\(494\) | −2.41421 | −0.108621 | ||||||||
\(495\) | − | 4.00000i | − | 0.179787i | ||||||
\(496\) | −3.70711 | + | 3.70711i | −0.166454 | + | 0.166454i | ||||
\(497\) | 6.87006 | 0.308164 | ||||||||
\(498\) | 16.8995 | − | 16.8995i | 0.757284 | − | 0.757284i | ||||
\(499\) | −19.2426 | − | 19.2426i | −0.861419 | − | 0.861419i | 0.130084 | − | 0.991503i | \(-0.458475\pi\) |
−0.991503 | + | 0.130084i | \(0.958475\pi\) | |||||||
\(500\) | 0.707107 | + | 0.707107i | 0.0316228 | + | 0.0316228i | ||||
\(501\) | − | 36.6274i | − | 1.63639i | ||||||
\(502\) | − | 2.14214i | − | 0.0956082i | ||||||
\(503\) | 26.1421 | + | 26.1421i | 1.16562 | + | 1.16562i | 0.983225 | + | 0.182395i | \(0.0583849\pi\) |
0.182395 | + | 0.983225i | \(0.441615\pi\) | |||||||
\(504\) | 1.17157 | + | 1.17157i | 0.0521860 | + | 0.0521860i | ||||
\(505\) | −3.07107 | + | 3.07107i | −0.136661 | + | 0.136661i | ||||
\(506\) | −4.48528 | −0.199395 | ||||||||
\(507\) | −20.4853 | + | 20.4853i | −0.909783 | + | 0.909783i | ||||
\(508\) | − | 7.72792i | − | 0.342871i | ||||||
\(509\) | 32.0000 | 1.41838 | 0.709188 | − | 0.705020i | \(-0.249062\pi\) | ||||
0.709188 | + | 0.705020i | \(0.249062\pi\) | |||||||
\(510\) | −9.94975 | + | 0.292893i | −0.440582 | + | 0.0129695i | ||||
\(511\) | −4.58579 | −0.202863 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −0.707107 | + | 0.707107i | −0.0312195 | + | 0.0312195i | ||||
\(514\) | −22.5858 | −0.996216 | ||||||||
\(515\) | −1.65685 | + | 1.65685i | −0.0730097 | + | 0.0730097i | ||||
\(516\) | 17.4853 | + | 17.4853i | 0.769747 | + | 0.769747i | ||||
\(517\) | 3.24264 | + | 3.24264i | 0.142611 | + | 0.142611i | ||||
\(518\) | − | 1.31371i | − | 0.0577210i | ||||||
\(519\) | − | 3.17157i | − | 0.139217i | ||||||
\(520\) | −0.707107 | − | 0.707107i | −0.0310087 | − | 0.0310087i | ||||
\(521\) | 4.68629 | + | 4.68629i | 0.205310 | + | 0.205310i | 0.802271 | − | 0.596960i | \(-0.203625\pi\) |
−0.596960 | + | 0.802271i | \(0.703625\pi\) | |||||||
\(522\) | −19.6569 | + | 19.6569i | −0.860357 | + | 0.860357i | ||||
\(523\) | 4.82843 | 0.211132 | 0.105566 | − | 0.994412i | \(-0.466335\pi\) | ||||
0.105566 | + | 0.994412i | \(0.466335\pi\) | |||||||
\(524\) | −14.0711 | + | 14.0711i | −0.614697 | + | 0.614697i | ||||
\(525\) | 1.41421i | 0.0617213i | ||||||||
\(526\) | −29.7279 | −1.29620 | ||||||||
\(527\) | 14.8284 | − | 15.7279i | 0.645936 | − | 0.685119i | ||||
\(528\) | 3.41421 | 0.148585 | ||||||||
\(529\) | − | 12.9411i | − | 0.562658i | ||||||
\(530\) | −2.46447 | + | 2.46447i | −0.107050 | + | 0.107050i | ||||
\(531\) | 30.8284 | 1.33784 | ||||||||
\(532\) | −1.00000 | + | 1.00000i | −0.0433555 | + | 0.0433555i | ||||
\(533\) | −6.65685 | − | 6.65685i | −0.288340 | − | 0.288340i | ||||
\(534\) | 25.0208 | + | 25.0208i | 1.08276 | + | 1.08276i | ||||
\(535\) | 12.4853i | 0.539786i | ||||||||
\(536\) | − | 8.82843i | − | 0.381330i | ||||||
\(537\) | −11.6569 | − | 11.6569i | −0.503030 | − | 0.503030i | ||||
\(538\) | −2.46447 | − | 2.46447i | −0.106251 | − | 0.106251i | ||||
\(539\) | 6.65685 | − | 6.65685i | 0.286731 | − | 0.286731i | ||||
\(540\) | −0.414214 | −0.0178249 | ||||||||
\(541\) | −11.3137 | + | 11.3137i | −0.486414 | + | 0.486414i | −0.907173 | − | 0.420758i | \(-0.861764\pi\) |
0.420758 | + | 0.907173i | \(0.361764\pi\) | |||||||
\(542\) | − | 6.34315i | − | 0.272461i | ||||||
\(543\) | 23.3137 | 1.00049 | ||||||||
\(544\) | −0.121320 | − | 4.12132i | −0.00520157 | − | 0.176700i | ||||
\(545\) | −11.8284 | −0.506674 | ||||||||
\(546\) | − | 1.41421i | − | 0.0605228i | ||||||
\(547\) | 11.4645 | − | 11.4645i | 0.490185 | − | 0.490185i | −0.418179 | − | 0.908364i | \(-0.637332\pi\) |
0.908364 | + | 0.418179i | \(0.137332\pi\) | |||||||
\(548\) | 16.7279 | 0.714581 | ||||||||
\(549\) | −16.3431 | + | 16.3431i | −0.697508 | + | 0.697508i | ||||
\(550\) | 1.00000 | + | 1.00000i | 0.0426401 | + | 0.0426401i | ||||
\(551\) | −16.7782 | − | 16.7782i | −0.714774 | − | 0.714774i | ||||
\(552\) | − | 7.65685i | − | 0.325897i | ||||||
\(553\) | − | 6.82843i | − | 0.290374i | ||||||
\(554\) | 5.89949 | + | 5.89949i | 0.250646 | + | 0.250646i | ||||
\(555\) | −3.82843 | − | 3.82843i | −0.162508 | − | 0.162508i | ||||
\(556\) | 0.656854 | − | 0.656854i | 0.0278568 | − | 0.0278568i | ||||
\(557\) | 7.82843 | 0.331701 | 0.165851 | − | 0.986151i | \(-0.446963\pi\) | ||||
0.165851 | + | 0.986151i | \(0.446963\pi\) | |||||||
\(558\) | −10.4853 | + | 10.4853i | −0.443877 | + | 0.443877i | ||||
\(559\) | − | 10.2426i | − | 0.433218i | ||||||
\(560\) | −0.585786 | −0.0247540 | ||||||||
\(561\) | −14.0711 | + | 0.414214i | −0.594081 | + | 0.0174881i | ||||
\(562\) | −1.48528 | −0.0626528 | ||||||||
\(563\) | 32.1421i | 1.35463i | 0.735693 | + | 0.677315i | \(0.236856\pi\) | ||||
−0.735693 | + | 0.677315i | \(0.763144\pi\) | |||||||
\(564\) | −5.53553 | + | 5.53553i | −0.233088 | + | 0.233088i | ||||
\(565\) | 3.48528 | 0.146627 | ||||||||
\(566\) | −6.77817 | + | 6.77817i | −0.284908 | + | 0.284908i | ||||
\(567\) | −3.92893 | − | 3.92893i | −0.165000 | − | 0.165000i | ||||
\(568\) | 8.29289 | + | 8.29289i | 0.347962 | + | 0.347962i | ||||
\(569\) | − | 25.9706i | − | 1.08874i | −0.838844 | − | 0.544371i | \(-0.816768\pi\) | ||
0.838844 | − | 0.544371i | \(-0.183232\pi\) | |||||||
\(570\) | 5.82843i | 0.244126i | ||||||||
\(571\) | 23.0416 | + | 23.0416i | 0.964262 | + | 0.964262i | 0.999383 | − | 0.0351208i | \(-0.0111816\pi\) |
−0.0351208 | + | 0.999383i | \(0.511182\pi\) | |||||||
\(572\) | −1.00000 | − | 1.00000i | −0.0418121 | − | 0.0418121i | ||||
\(573\) | 0.414214 | − | 0.414214i | 0.0173040 | − | 0.0173040i | ||||
\(574\) | −5.51472 | −0.230180 | ||||||||
\(575\) | 2.24264 | − | 2.24264i | 0.0935246 | − | 0.0935246i | ||||
\(576\) | 2.82843i | 0.117851i | ||||||||
\(577\) | 18.3431 | 0.763635 | 0.381818 | − | 0.924238i | \(-0.375298\pi\) | ||||
0.381818 | + | 0.924238i | \(0.375298\pi\) | |||||||
\(578\) | 1.00000 | + | 16.9706i | 0.0415945 | + | 0.705882i | ||||
\(579\) | 9.65685 | 0.401325 | ||||||||
\(580\) | − | 9.82843i | − | 0.408103i | ||||||
\(581\) | −4.10051 | + | 4.10051i | −0.170118 | + | 0.170118i | ||||
\(582\) | 34.5563 | 1.43241 | ||||||||
\(583\) | −3.48528 | + | 3.48528i | −0.144346 | + | 0.144346i | ||||
\(584\) | −5.53553 | − | 5.53553i | −0.229062 | − | 0.229062i | ||||
\(585\) | −2.00000 | − | 2.00000i | −0.0826898 | − | 0.0826898i | ||||
\(586\) | 5.48528i | 0.226595i | ||||||||
\(587\) | 3.17157i | 0.130905i | 0.997856 | + | 0.0654524i | \(0.0208491\pi\) | ||||
−0.997856 | + | 0.0654524i | \(0.979151\pi\) | |||||||
\(588\) | 11.3640 | + | 11.3640i | 0.468642 | + | 0.468642i | ||||
\(589\) | −8.94975 | − | 8.94975i | −0.368768 | − | 0.368768i | ||||
\(590\) | −7.70711 | + | 7.70711i | −0.317297 | + | 0.317297i | ||||
\(591\) | −61.6985 | −2.53794 | ||||||||
\(592\) | 1.58579 | − | 1.58579i | 0.0651754 | − | 0.0651754i | ||||
\(593\) | 14.2843i | 0.586585i | 0.956023 | + | 0.293292i | \(0.0947509\pi\) | ||||
−0.956023 | + | 0.293292i | \(0.905249\pi\) | |||||||
\(594\) | −0.585786 | −0.0240351 | ||||||||
\(595\) | 2.41421 | − | 0.0710678i | 0.0989731 | − | 0.00291350i | ||||
\(596\) | 1.75736 | 0.0719842 | ||||||||
\(597\) | 27.4853i | 1.12490i | ||||||||
\(598\) | −2.24264 | + | 2.24264i | −0.0917084 | + | 0.0917084i | ||||
\(599\) | 42.7696 | 1.74752 | 0.873758 | − | 0.486360i | \(-0.161676\pi\) | ||||
0.873758 | + | 0.486360i | \(0.161676\pi\) | |||||||
\(600\) | −1.70711 | + | 1.70711i | −0.0696923 | + | 0.0696923i | ||||
\(601\) | 13.1716 | + | 13.1716i | 0.537280 | + | 0.537280i | 0.922729 | − | 0.385449i | \(-0.125954\pi\) |
−0.385449 | + | 0.922729i | \(0.625954\pi\) | |||||||
\(602\) | −4.24264 | − | 4.24264i | −0.172917 | − | 0.172917i | ||||
\(603\) | − | 24.9706i | − | 1.01688i | ||||||
\(604\) | 4.82843i | 0.196466i | ||||||||
\(605\) | −6.36396 | − | 6.36396i | −0.258732 | − | 0.258732i | ||||
\(606\) | −7.41421 | − | 7.41421i | −0.301182 | − | 0.301182i | ||||
\(607\) | −4.07107 | + | 4.07107i | −0.165240 | + | 0.165240i | −0.784883 | − | 0.619644i | \(-0.787277\pi\) |
0.619644 | + | 0.784883i | \(0.287277\pi\) | |||||||
\(608\) | −2.41421 | −0.0979093 | ||||||||
\(609\) | 9.82843 | − | 9.82843i | 0.398268 | − | 0.398268i | ||||
\(610\) | − | 8.17157i | − | 0.330857i | ||||||
\(611\) | 3.24264 | 0.131183 | ||||||||
\(612\) | −0.343146 | − | 11.6569i | −0.0138708 | − | 0.471200i | ||||
\(613\) | −23.2843 | −0.940443 | −0.470221 | − | 0.882548i | \(-0.655826\pi\) | ||||
−0.470221 | + | 0.882548i | \(0.655826\pi\) | |||||||
\(614\) | 9.89949i | 0.399511i | ||||||||
\(615\) | −16.0711 | + | 16.0711i | −0.648048 | + | 0.648048i | ||||
\(616\) | −0.828427 | −0.0333783 | ||||||||
\(617\) | 0.564971 | − | 0.564971i | 0.0227449 | − | 0.0227449i | −0.695643 | − | 0.718388i | \(-0.744880\pi\) |
0.718388 | + | 0.695643i | \(0.244880\pi\) | |||||||
\(618\) | −4.00000 | − | 4.00000i | −0.160904 | − | 0.160904i | ||||
\(619\) | −10.2426 | − | 10.2426i | −0.411686 | − | 0.411686i | 0.470639 | − | 0.882326i | \(-0.344023\pi\) |
−0.882326 | + | 0.470639i | \(0.844023\pi\) | |||||||
\(620\) | − | 5.24264i | − | 0.210550i | ||||||
\(621\) | 1.31371i | 0.0527173i | ||||||||
\(622\) | −2.58579 | − | 2.58579i | −0.103681 | − | 0.103681i | ||||
\(623\) | −6.07107 | − | 6.07107i | −0.243232 | − | 0.243232i | ||||
\(624\) | 1.70711 | − | 1.70711i | 0.0683390 | − | 0.0683390i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | −6.48528 | + | 6.48528i | −0.259204 | + | 0.259204i | ||||
\(627\) | 8.24264i | 0.329179i | ||||||||
\(628\) | −2.82843 | −0.112867 | ||||||||
\(629\) | −6.34315 | + | 6.72792i | −0.252918 | + | 0.268260i | ||||
\(630\) | −1.65685 | −0.0660107 | ||||||||
\(631\) | − | 49.6569i | − | 1.97681i | −0.151847 | − | 0.988404i | \(-0.548522\pi\) | ||
0.151847 | − | 0.988404i | \(-0.451478\pi\) | |||||||
\(632\) | 8.24264 | − | 8.24264i | 0.327875 | − | 0.327875i | ||||
\(633\) | 11.6569 | 0.463318 | ||||||||
\(634\) | 24.4853 | − | 24.4853i | 0.972435 | − | 0.972435i | ||||
\(635\) | 5.46447 | + | 5.46447i | 0.216851 | + | 0.216851i | ||||
\(636\) | −5.94975 | − | 5.94975i | −0.235923 | − | 0.235923i | ||||
\(637\) | − | 6.65685i | − | 0.263754i | ||||||
\(638\) | − | 13.8995i | − | 0.550286i | ||||||
\(639\) | 23.4558 | + | 23.4558i | 0.927899 | + | 0.927899i | ||||
\(640\) | −0.707107 | − | 0.707107i | −0.0279508 | − | 0.0279508i | ||||
\(641\) | −11.0711 | + | 11.0711i | −0.437281 | + | 0.437281i | −0.891096 | − | 0.453815i | \(-0.850063\pi\) |
0.453815 | + | 0.891096i | \(0.350063\pi\) | |||||||
\(642\) | −30.1421 | −1.18962 | ||||||||
\(643\) | −18.3848 | + | 18.3848i | −0.725025 | + | 0.725025i | −0.969624 | − | 0.244599i | \(-0.921344\pi\) |
0.244599 | + | 0.969624i | \(0.421344\pi\) | |||||||
\(644\) | 1.85786i | 0.0732101i | ||||||||
\(645\) | −24.7279 | −0.973661 | ||||||||
\(646\) | 9.94975 | − | 0.292893i | 0.391468 | − | 0.0115237i | ||||
\(647\) | 48.2132 | 1.89546 | 0.947728 | − | 0.319078i | \(-0.103373\pi\) | ||||
0.947728 | + | 0.319078i | \(0.103373\pi\) | |||||||
\(648\) | − | 9.48528i | − | 0.372617i | ||||||
\(649\) | −10.8995 | + | 10.8995i | −0.427843 | + | 0.427843i | ||||
\(650\) | 1.00000 | 0.0392232 | ||||||||
\(651\) | 5.24264 | − | 5.24264i | 0.205475 | − | 0.205475i | ||||
\(652\) | −0.343146 | − | 0.343146i | −0.0134386 | − | 0.0134386i | ||||
\(653\) | 6.51472 | + | 6.51472i | 0.254941 | + | 0.254941i | 0.822993 | − | 0.568052i | \(-0.192303\pi\) |
−0.568052 | + | 0.822993i | \(0.692303\pi\) | |||||||
\(654\) | − | 28.5563i | − | 1.11664i | ||||||
\(655\) | − | 19.8995i | − | 0.777538i | ||||||
\(656\) | −6.65685 | − | 6.65685i | −0.259906 | − | 0.259906i | ||||
\(657\) | −15.6569 | − | 15.6569i | −0.610832 | − | 0.610832i | ||||
\(658\) | 1.34315 | − | 1.34315i | 0.0523613 | − | 0.0523613i | ||||
\(659\) | −10.7574 | −0.419047 | −0.209524 | − | 0.977804i | \(-0.567191\pi\) | ||||
−0.209524 | + | 0.977804i | \(0.567191\pi\) | |||||||
\(660\) | −2.41421 | + | 2.41421i | −0.0939731 | + | 0.0939731i | ||||
\(661\) | 11.3137i | 0.440052i | 0.975494 | + | 0.220026i | \(0.0706143\pi\) | ||||
−0.975494 | + | 0.220026i | \(0.929386\pi\) | |||||||
\(662\) | −8.55635 | −0.332552 | ||||||||
\(663\) | −6.82843 | + | 7.24264i | −0.265194 | + | 0.281281i | ||||
\(664\) | −9.89949 | −0.384175 | ||||||||
\(665\) | − | 1.41421i | − | 0.0548408i | ||||||
\(666\) | 4.48528 | − | 4.48528i | 0.173801 | − | 0.173801i | ||||
\(667\) | −31.1716 | −1.20697 | ||||||||
\(668\) | −10.7279 | + | 10.7279i | −0.415076 | + | 0.415076i | ||||
\(669\) | −43.3345 | − | 43.3345i | −1.67541 | − | 1.67541i | ||||
\(670\) | 6.24264 | + | 6.24264i | 0.241174 | + | 0.241174i | ||||
\(671\) | − | 11.5563i | − | 0.446128i | ||||||
\(672\) | − | 1.41421i | − | 0.0545545i | ||||||
\(673\) | −8.46447 | − | 8.46447i | −0.326281 | − | 0.326281i | 0.524889 | − | 0.851170i | \(-0.324107\pi\) |
−0.851170 | + | 0.524889i | \(0.824107\pi\) | |||||||
\(674\) | −21.4350 | − | 21.4350i | −0.825646 | − | 0.825646i | ||||
\(675\) | 0.292893 | − | 0.292893i | 0.0112735 | − | 0.0112735i | ||||
\(676\) | 12.0000 | 0.461538 | ||||||||
\(677\) | −31.8284 | + | 31.8284i | −1.22327 | + | 1.22327i | −0.256802 | + | 0.966464i | \(0.582669\pi\) |
−0.966464 | + | 0.256802i | \(0.917331\pi\) | |||||||
\(678\) | 8.41421i | 0.323146i | ||||||||
\(679\) | −8.38478 | −0.321778 | ||||||||
\(680\) | 3.00000 | + | 2.82843i | 0.115045 | + | 0.108465i | ||||
\(681\) | −49.6274 | −1.90173 | ||||||||
\(682\) | − | 7.41421i | − | 0.283905i | ||||||
\(683\) | 8.19239 | − | 8.19239i | 0.313473 | − | 0.313473i | −0.532780 | − | 0.846253i | \(-0.678853\pi\) |
0.846253 | + | 0.532780i | \(0.178853\pi\) | |||||||
\(684\) | −6.82843 | −0.261091 | ||||||||
\(685\) | −11.8284 | + | 11.8284i | −0.451941 | + | 0.451941i | ||||
\(686\) | −5.65685 | − | 5.65685i | −0.215980 | − | 0.215980i | ||||
\(687\) | 27.7279 | + | 27.7279i | 1.05789 | + | 1.05789i | ||||
\(688\) | − | 10.2426i | − | 0.390497i | ||||||
\(689\) | 3.48528i | 0.132779i | ||||||||
\(690\) | 5.41421 | + | 5.41421i | 0.206116 | + | 0.206116i | ||||
\(691\) | −23.8284 | − | 23.8284i | −0.906476 | − | 0.906476i | 0.0895098 | − | 0.995986i | \(-0.471470\pi\) |
−0.995986 | + | 0.0895098i | \(0.971470\pi\) | |||||||
\(692\) | −0.928932 | + | 0.928932i | −0.0353127 | + | 0.0353127i | ||||
\(693\) | −2.34315 | −0.0890087 | ||||||||
\(694\) | 10.4350 | − | 10.4350i | 0.396108 | − | 0.396108i | ||||
\(695\) | 0.928932i | 0.0352364i | ||||||||
\(696\) | 23.7279 | 0.899405 | ||||||||
\(697\) | 28.2426 | + | 26.6274i | 1.06977 | + | 1.00859i | ||||
\(698\) | 8.97056 | 0.339541 | ||||||||
\(699\) | 28.5563i | 1.08010i | ||||||||
\(700\) | 0.414214 | − | 0.414214i | 0.0156558 | − | 0.0156558i | ||||
\(701\) | 8.97056 | 0.338813 | 0.169407 | − | 0.985546i | \(-0.445815\pi\) | ||||
0.169407 | + | 0.985546i | \(0.445815\pi\) | |||||||
\(702\) | −0.292893 | + | 0.292893i | −0.0110545 | + | 0.0110545i | ||||
\(703\) | 3.82843 | + | 3.82843i | 0.144392 | + | 0.144392i | ||||
\(704\) | −1.00000 | − | 1.00000i | −0.0376889 | − | 0.0376889i | ||||
\(705\) | − | 7.82843i | − | 0.294836i | ||||||
\(706\) | 5.31371i | 0.199984i | ||||||||
\(707\) | 1.79899 | + | 1.79899i | 0.0676580 | + | 0.0676580i | ||||
\(708\) | −18.6066 | − | 18.6066i | −0.699279 | − | 0.699279i | ||||
\(709\) | −16.5061 | + | 16.5061i | −0.619899 | + | 0.619899i | −0.945506 | − | 0.325606i | \(-0.894432\pi\) |
0.325606 | + | 0.945506i | \(0.394432\pi\) | |||||||
\(710\) | −11.7279 | −0.440141 | ||||||||
\(711\) | 23.3137 | − | 23.3137i | 0.874332 | − | 0.874332i | ||||
\(712\) | − | 14.6569i | − | 0.549289i | ||||||
\(713\) | −16.6274 | −0.622702 | ||||||||
\(714\) | 0.171573 | + | 5.82843i | 0.00642095 | + | 0.218123i | ||||
\(715\) | 1.41421 | 0.0528886 | ||||||||
\(716\) | 6.82843i | 0.255190i | ||||||||
\(717\) | 46.7990 | − | 46.7990i | 1.74774 | − | 1.74774i | ||||
\(718\) | −12.3848 | −0.462196 | ||||||||
\(719\) | −36.6777 | + | 36.6777i | −1.36785 | + | 1.36785i | −0.504343 | + | 0.863504i | \(0.668265\pi\) |
−0.863504 | + | 0.504343i | \(0.831735\pi\) | |||||||
\(720\) | −2.00000 | − | 2.00000i | −0.0745356 | − | 0.0745356i | ||||
\(721\) | 0.970563 | + | 0.970563i | 0.0361456 | + | 0.0361456i | ||||
\(722\) | 13.1716i | 0.490195i | ||||||||
\(723\) | 67.6985i | 2.51773i | ||||||||
\(724\) | −6.82843 | − | 6.82843i | −0.253776 | − | 0.253776i | ||||
\(725\) | 6.94975 | + | 6.94975i | 0.258107 | + | 0.258107i | ||||
\(726\) | 15.3640 | − | 15.3640i | 0.570210 | − | 0.570210i | ||||
\(727\) | −22.2132 | −0.823842 | −0.411921 | − | 0.911220i | \(-0.635142\pi\) | ||||
−0.411921 | + | 0.911220i | \(0.635142\pi\) | |||||||
\(728\) | −0.414214 | + | 0.414214i | −0.0153518 | + | 0.0153518i | ||||
\(729\) | − | 23.8284i | − | 0.882534i | ||||||
\(730\) | 7.82843 | 0.289743 | ||||||||
\(731\) | 1.24264 | + | 42.2132i | 0.0459607 | + | 1.56131i | ||||
\(732\) | 19.7279 | 0.729165 | ||||||||
\(733\) | 10.8284i | 0.399957i | 0.979800 | + | 0.199979i | \(0.0640872\pi\) | ||||
−0.979800 | + | 0.199979i | \(0.935913\pi\) | |||||||
\(734\) | −5.55635 | + | 5.55635i | −0.205089 | + | 0.205089i | ||||
\(735\) | −16.0711 | −0.592790 | ||||||||
\(736\) | −2.24264 | + | 2.24264i | −0.0826648 | + | 0.0826648i | ||||
\(737\) | 8.82843 | + | 8.82843i | 0.325199 | + | 0.325199i | ||||
\(738\) | −18.8284 | − | 18.8284i | −0.693084 | − | 0.693084i | ||||
\(739\) | − | 5.87006i | − | 0.215934i | −0.994155 | − | 0.107967i | \(-0.965566\pi\) | ||
0.994155 | − | 0.107967i | \(-0.0344340\pi\) | |||||||
\(740\) | 2.24264i | 0.0824411i | ||||||||
\(741\) | 4.12132 | + | 4.12132i | 0.151400 | + | 0.151400i | ||||
\(742\) | 1.44365 | + | 1.44365i | 0.0529981 | + | 0.0529981i | ||||
\(743\) | 4.55635 | − | 4.55635i | 0.167156 | − | 0.167156i | −0.618572 | − | 0.785728i | \(-0.712288\pi\) |
0.785728 | + | 0.618572i | \(0.212288\pi\) | |||||||
\(744\) | 12.6569 | 0.464023 | ||||||||
\(745\) | −1.24264 | + | 1.24264i | −0.0455268 | + | 0.0455268i | ||||
\(746\) | 24.2843i | 0.889110i | ||||||||
\(747\) | −28.0000 | −1.02447 | ||||||||
\(748\) | 4.24264 | + | 4.00000i | 0.155126 | + | 0.146254i | ||||
\(749\) | 7.31371 | 0.267237 | ||||||||
\(750\) | − | 2.41421i | − | 0.0881546i | ||||||
\(751\) | −2.15076 | + | 2.15076i | −0.0784823 | + | 0.0784823i | −0.745258 | − | 0.666776i | \(-0.767674\pi\) |
0.666776 | + | 0.745258i | \(0.267674\pi\) | |||||||
\(752\) | 3.24264 | 0.118247 | ||||||||
\(753\) | −3.65685 | + | 3.65685i | −0.133263 | + | 0.133263i | ||||
\(754\) | −6.94975 | − | 6.94975i | −0.253095 | − | 0.253095i | ||||
\(755\) | −3.41421 | − | 3.41421i | −0.124256 | − | 0.124256i | ||||
\(756\) | 0.242641i | 0.00882476i | ||||||||
\(757\) | − | 39.8284i | − | 1.44759i | −0.690016 | − | 0.723794i | \(-0.742396\pi\) | ||
0.690016 | − | 0.723794i | \(-0.257604\pi\) | |||||||
\(758\) | −4.00000 | − | 4.00000i | −0.145287 | − | 0.145287i | ||||
\(759\) | 7.65685 | + | 7.65685i | 0.277926 | + | 0.277926i | ||||
\(760\) | 1.70711 | − | 1.70711i | 0.0619233 | − | 0.0619233i | ||||
\(761\) | 43.1127 | 1.56283 | 0.781417 | − | 0.624009i | \(-0.214497\pi\) | ||||
0.781417 | + | 0.624009i | \(0.214497\pi\) | |||||||
\(762\) | −13.1924 | + | 13.1924i | −0.477910 | + | 0.477910i | ||||
\(763\) | 6.92893i | 0.250844i | ||||||||
\(764\) | −0.242641 | −0.00877843 | ||||||||
\(765\) | 8.48528 | + | 8.00000i | 0.306786 | + | 0.289241i | ||||
\(766\) | 22.2132 | 0.802596 | ||||||||
\(767\) | 10.8995i | 0.393558i | ||||||||
\(768\) | 1.70711 | − | 1.70711i | 0.0615999 | − | 0.0615999i | ||||
\(769\) | 23.1421 | 0.834527 | 0.417263 | − | 0.908786i | \(-0.362989\pi\) | ||||
0.417263 | + | 0.908786i | \(0.362989\pi\) | |||||||
\(770\) | 0.585786 | − | 0.585786i | 0.0211103 | − | 0.0211103i | ||||
\(771\) | 38.5563 | + | 38.5563i | 1.38857 | + | 1.38857i | ||||
\(772\) | −2.82843 | − | 2.82843i | −0.101797 | − | 0.101797i | ||||
\(773\) | 23.5147i | 0.845766i | 0.906184 | + | 0.422883i | \(0.138982\pi\) | ||||
−0.906184 | + | 0.422883i | \(0.861018\pi\) | |||||||
\(774\) | − | 28.9706i | − | 1.04133i | ||||||
\(775\) | 3.70711 | + | 3.70711i | 0.133163 | + | 0.133163i | ||||
\(776\) | −10.1213 | − | 10.1213i | −0.363334 | − | 0.363334i | ||||
\(777\) | −2.24264 | + | 2.24264i | −0.0804543 | + | 0.0804543i | ||||
\(778\) | −10.6274 | −0.381011 | ||||||||
\(779\) | 16.0711 | − | 16.0711i | 0.575806 | − | 0.575806i | ||||
\(780\) | 2.41421i | 0.0864427i | ||||||||
\(781\) | −16.5858 | −0.593486 | ||||||||
\(782\) | 8.97056 | − | 9.51472i | 0.320787 | − | 0.340246i | ||||
\(783\) | −4.07107 | −0.145488 | ||||||||
\(784\) | − | 6.65685i | − | 0.237745i | ||||||
\(785\) | 2.00000 | − | 2.00000i | 0.0713831 | − | 0.0713831i | ||||
\(786\) | 48.0416 | 1.71359 | ||||||||
\(787\) | −0.393398 | + | 0.393398i | −0.0140231 | + | 0.0140231i | −0.714084 | − | 0.700060i | \(-0.753156\pi\) |
0.700060 | + | 0.714084i | \(0.253156\pi\) | |||||||
\(788\) | 18.0711 | + | 18.0711i | 0.643755 | + | 0.643755i | ||||
\(789\) | 50.7487 | + | 50.7487i | 1.80670 | + | 1.80670i | ||||
\(790\) | 11.6569i | 0.414732i | ||||||||
\(791\) | − | 2.04163i | − | 0.0725920i | ||||||
\(792\) | −2.82843 | − | 2.82843i | −0.100504 | − | 0.100504i | ||||
\(793\) | −5.77817 | − | 5.77817i | −0.205189 | − | 0.205189i | ||||
\(794\) | 16.4853 | − | 16.4853i | 0.585041 | − | 0.585041i | ||||
\(795\) | 8.41421 | 0.298421 | ||||||||
\(796\) | 8.05025 | − | 8.05025i | 0.285334 | − | 0.285334i | ||||
\(797\) | − | 26.6274i | − | 0.943192i | −0.881815 | − | 0.471596i | \(-0.843678\pi\) | ||
0.881815 | − | 0.471596i | \(-0.156322\pi\) | |||||||
\(798\) | 3.41421 | 0.120862 | ||||||||
\(799\) | −13.3640 | + | 0.393398i | −0.472783 | + | 0.0139174i | ||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | − | 41.4558i | − | 1.46477i | ||||||
\(802\) | −14.8284 | + | 14.8284i | −0.523610 | + | 0.523610i | ||||
\(803\) | 11.0711 | 0.390689 | ||||||||
\(804\) | −15.0711 | + | 15.0711i | −0.531516 | + | 0.531516i | ||||
\(805\) | −1.31371 | − | 1.31371i | −0.0463021 | − | 0.0463021i | ||||
\(806\) | −3.70711 | − | 3.70711i | −0.130577 | − | 0.130577i | ||||
\(807\) | 8.41421i | 0.296194i | ||||||||
\(808\) | 4.34315i | 0.152791i | ||||||||
\(809\) | 25.8284 | + | 25.8284i | 0.908079 | + | 0.908079i | 0.996117 | − | 0.0880380i | \(-0.0280597\pi\) |
−0.0880380 | + | 0.996117i | \(0.528060\pi\) | |||||||
\(810\) | 6.70711 | + | 6.70711i | 0.235664 | + | 0.235664i | ||||
\(811\) | 36.0711 | − | 36.0711i | 1.26663 | − | 1.26663i | 0.318807 | − | 0.947820i | \(-0.396718\pi\) |
0.947820 | − | 0.318807i | \(-0.103282\pi\) | |||||||
\(812\) | −5.75736 | −0.202044 | ||||||||
\(813\) | −10.8284 | + | 10.8284i | −0.379770 | + | 0.379770i | ||||
\(814\) | 3.17157i | 0.111164i | ||||||||
\(815\) | 0.485281 | 0.0169987 | ||||||||
\(816\) | −6.82843 | + | 7.24264i | −0.239043 | + | 0.253543i | ||||
\(817\) | 24.7279 | 0.865120 | ||||||||
\(818\) | 11.4853i | 0.401573i | ||||||||
\(819\) | −1.17157 | + | 1.17157i | −0.0409381 | + | 0.0409381i | ||||
\(820\) | 9.41421 | 0.328759 | ||||||||
\(821\) | −3.92031 | + | 3.92031i | −0.136820 | + | 0.136820i | −0.772200 | − | 0.635380i | \(-0.780844\pi\) |
0.635380 | + | 0.772200i | \(0.280844\pi\) | |||||||
\(822\) | −28.5563 | − | 28.5563i | −0.996017 | − | 0.996017i | ||||
\(823\) | 8.58579 | + | 8.58579i | 0.299282 | + | 0.299282i | 0.840732 | − | 0.541451i | \(-0.182125\pi\) |
−0.541451 | + | 0.840732i | \(0.682125\pi\) | |||||||
\(824\) | 2.34315i | 0.0816274i | ||||||||
\(825\) | − | 3.41421i | − | 0.118868i | ||||||
\(826\) | 4.51472 | + | 4.51472i | 0.157087 | + | 0.157087i | ||||
\(827\) | 10.1421 | + | 10.1421i | 0.352677 | + | 0.352677i | 0.861105 | − | 0.508428i | \(-0.169773\pi\) |
−0.508428 | + | 0.861105i | \(0.669773\pi\) | |||||||
\(828\) | −6.34315 | + | 6.34315i | −0.220440 | + | 0.220440i | ||||
\(829\) | −11.3137 | −0.392941 | −0.196471 | − | 0.980510i | \(-0.562948\pi\) | ||||
−0.196471 | + | 0.980510i | \(0.562948\pi\) | |||||||
\(830\) | 7.00000 | − | 7.00000i | 0.242974 | − | 0.242974i | ||||
\(831\) | − | 20.1421i | − | 0.698723i | ||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 0.807612 | + | 27.4350i | 0.0279821 | + | 0.950567i | ||||
\(834\) | −2.24264 | −0.0776563 | ||||||||
\(835\) | − | 15.1716i | − | 0.525034i | ||||||
\(836\) | 2.41421 | − | 2.41421i | 0.0834973 | − | 0.0834973i | ||||
\(837\) | −2.17157 | −0.0750605 | ||||||||
\(838\) | −9.75736 | + | 9.75736i | −0.337062 | + | 0.337062i | ||||
\(839\) | −8.87868 | − | 8.87868i | −0.306526 | − | 0.306526i | 0.537034 | − | 0.843560i | \(-0.319545\pi\) |
−0.843560 | + | 0.537034i | \(0.819545\pi\) | |||||||
\(840\) | 1.00000 | + | 1.00000i | 0.0345033 | + | 0.0345033i | ||||
\(841\) | − | 67.5980i | − | 2.33096i | ||||||
\(842\) | 22.9289i | 0.790183i | ||||||||
\(843\) | 2.53553 | + | 2.53553i | 0.0873284 | + | 0.0873284i | ||||
\(844\) | −3.41421 | − | 3.41421i | −0.117522 | − | 0.117522i | ||||
\(845\) | −8.48528 | + | 8.48528i | −0.291903 | + | 0.291903i | ||||
\(846\) | 9.17157 | 0.315325 | ||||||||
\(847\) | −3.72792 | + | 3.72792i | −0.128093 | + | 0.128093i | ||||
\(848\) | 3.48528i | 0.119685i | ||||||||
\(849\) | 23.1421 | 0.794236 | ||||||||
\(850\) | −4.12132 | + | 0.121320i | −0.141360 | + | 0.00416125i | ||||
\(851\) | 7.11270 | 0.243820 | ||||||||
\(852\) | − | 28.3137i | − | 0.970012i | ||||||
\(853\) | −0.514719 | + | 0.514719i | −0.0176236 | + | 0.0176236i | −0.715864 | − | 0.698240i | \(-0.753967\pi\) |
0.698240 | + | 0.715864i | \(0.253967\pi\) | |||||||
\(854\) | −4.78680 | −0.163801 | ||||||||
\(855\) | 4.82843 | − | 4.82843i | 0.165129 | − | 0.165129i | ||||
\(856\) | 8.82843 | + | 8.82843i | 0.301749 | + | 0.301749i | ||||
\(857\) | −15.4350 | − | 15.4350i | −0.527251 | − | 0.527251i | 0.392501 | − | 0.919752i | \(-0.371610\pi\) |
−0.919752 | + | 0.392501i | \(0.871610\pi\) | |||||||
\(858\) | 3.41421i | 0.116559i | ||||||||
\(859\) | 47.8701i | 1.63331i | 0.577129 | + | 0.816653i | \(0.304173\pi\) | ||||
−0.577129 | + | 0.816653i | \(0.695827\pi\) | |||||||
\(860\) | 7.24264 | + | 7.24264i | 0.246972 | + | 0.246972i | ||||
\(861\) | 9.41421 | + | 9.41421i | 0.320836 | + | 0.320836i | ||||
\(862\) | −16.0000 | + | 16.0000i | −0.544962 | + | 0.544962i | ||||
\(863\) | −1.45584 | −0.0495575 | −0.0247788 | − | 0.999693i | \(-0.507888\pi\) | ||||
−0.0247788 | + | 0.999693i | \(0.507888\pi\) | |||||||
\(864\) | −0.292893 | + | 0.292893i | −0.00996443 | + | 0.00996443i | ||||
\(865\) | − | 1.31371i | − | 0.0446674i | ||||||
\(866\) | −0.928932 | −0.0315664 | ||||||||
\(867\) | 27.2635 | − | 30.6777i | 0.925916 | − | 1.04187i | ||||
\(868\) | −3.07107 | −0.104239 | ||||||||
\(869\) | 16.4853i | 0.559225i | ||||||||
\(870\) | −16.7782 | + | 16.7782i | −0.568833 | + | 0.568833i | ||||
\(871\) | 8.82843 | 0.299140 | ||||||||
\(872\) | −8.36396 | + | 8.36396i | −0.283239 | + | 0.283239i | ||||
\(873\) | −28.6274 | − | 28.6274i | −0.968891 | − | 0.968891i | ||||
\(874\) | −5.41421 | − | 5.41421i | −0.183139 | − | 0.183139i | ||||
\(875\) | 0.585786i | 0.0198032i | ||||||||
\(876\) | 18.8995i | 0.638555i | ||||||||
\(877\) | −34.2132 | − | 34.2132i | −1.15530 | − | 1.15530i | −0.985475 | − | 0.169823i | \(-0.945680\pi\) |
−0.169823 | − | 0.985475i | \(-0.554320\pi\) | |||||||
\(878\) | −22.6274 | − | 22.6274i | −0.763638 | − | 0.763638i | ||||
\(879\) | 9.36396 | − | 9.36396i | 0.315839 | − | 0.315839i | ||||
\(880\) | 1.41421 | 0.0476731 | ||||||||
\(881\) | 28.0416 | − | 28.0416i | 0.944747 | − | 0.944747i | −0.0538049 | − | 0.998551i | \(-0.517135\pi\) |
0.998551 | + | 0.0538049i | \(0.0171349\pi\) | |||||||
\(882\) | − | 18.8284i | − | 0.633986i | ||||||
\(883\) | −55.4975 | −1.86764 | −0.933819 | − | 0.357745i | \(-0.883546\pi\) | ||||
−0.933819 | + | 0.357745i | \(0.883546\pi\) | |||||||
\(884\) | 4.12132 | − | 0.121320i | 0.138615 | − | 0.00408044i | ||||
\(885\) | 26.3137 | 0.884526 | ||||||||
\(886\) | − | 20.0000i | − | 0.671913i | ||||||
\(887\) | 36.8995 | − | 36.8995i | 1.23896 | − | 1.23896i | 0.278539 | − | 0.960425i | \(-0.410150\pi\) |
0.960425 | − | 0.278539i | \(-0.0898501\pi\) | |||||||
\(888\) | −5.41421 | −0.181689 | ||||||||
\(889\) | 3.20101 | − | 3.20101i | 0.107358 | − | 0.107358i | ||||
\(890\) | 10.3640 | + | 10.3640i | 0.347401 | + | 0.347401i | ||||
\(891\) | 9.48528 | + | 9.48528i | 0.317769 | + | 0.317769i | ||||
\(892\) | 25.3848i | 0.849945i | ||||||||
\(893\) | 7.82843i | 0.261968i | ||||||||
\(894\) | −3.00000 | − | 3.00000i | −0.100335 | − | 0.100335i | ||||
\(895\) | −4.82843 | − | 4.82843i | −0.161397 | − | 0.161397i | ||||
\(896\) | −0.414214 | + | 0.414214i | −0.0138379 | + | 0.0138379i | ||||
\(897\) | 7.65685 | 0.255655 | ||||||||
\(898\) | 29.3848 | − | 29.3848i | 0.980583 | − | 0.980583i | ||||
\(899\) | − | 51.5269i | − | 1.71852i | ||||||
\(900\) | 2.82843 | 0.0942809 | ||||||||
\(901\) | −0.422836 | − | 14.3640i | −0.0140867 | − | 0.478533i | ||||
\(902\) | 13.3137 | 0.443298 | ||||||||
\(903\) | 14.4853i | 0.482040i | ||||||||
\(904\) | 2.46447 | − | 2.46447i | 0.0819669 | − | 0.0819669i | ||||
\(905\) | 9.65685 | 0.321005 | ||||||||
\(906\) | 8.24264 | − | 8.24264i | 0.273843 | − | 0.273843i | ||||
\(907\) | 2.97918 | + | 2.97918i | 0.0989222 | + | 0.0989222i | 0.754836 | − | 0.655914i | \(-0.227716\pi\) |
−0.655914 | + | 0.754836i | \(0.727716\pi\) | |||||||
\(908\) | 14.5355 | + | 14.5355i | 0.482379 | + | 0.482379i | ||||
\(909\) | 12.2843i | 0.407444i | ||||||||
\(910\) | − | 0.585786i | − | 0.0194186i | ||||||
\(911\) | −3.31371 | − | 3.31371i | −0.109788 | − | 0.109788i | 0.650079 | − | 0.759867i | \(-0.274736\pi\) |
−0.759867 | + | 0.650079i | \(0.774736\pi\) | |||||||
\(912\) | 4.12132 | + | 4.12132i | 0.136471 | + | 0.136471i | ||||
\(913\) | 9.89949 | − | 9.89949i | 0.327625 | − | 0.327625i | ||||
\(914\) | −27.5563 | −0.911483 | ||||||||
\(915\) | −13.9497 | + | 13.9497i | −0.461164 | + | 0.461164i | ||||
\(916\) | − | 16.2426i | − | 0.536672i | ||||||
\(917\) | −11.6569 | −0.384943 | ||||||||
\(918\) | 1.17157 | − | 1.24264i | 0.0386677 | − | 0.0410133i | ||||
\(919\) | −43.0122 | −1.41884 | −0.709421 | − | 0.704785i | \(-0.751043\pi\) | ||||
−0.709421 | + | 0.704785i | \(0.751043\pi\) | |||||||
\(920\) | − | 3.17157i | − | 0.104564i | ||||||
\(921\) | 16.8995 | − | 16.8995i | 0.556857 | − | 0.556857i | ||||
\(922\) | −6.97056 | −0.229563 | ||||||||
\(923\) | −8.29289 | + | 8.29289i | −0.272964 | + | 0.272964i | ||||
\(924\) | 1.41421 | + | 1.41421i | 0.0465242 | + | 0.0465242i | ||||
\(925\) | −1.58579 | − | 1.58579i | −0.0521403 | − | 0.0521403i | ||||
\(926\) | − | 1.10051i | − | 0.0361648i | ||||||
\(927\) | 6.62742i | 0.217673i | ||||||||
\(928\) | −6.94975 | − | 6.94975i | −0.228137 | − | 0.228137i | ||||
\(929\) | 13.4853 | + | 13.4853i | 0.442438 | + | 0.442438i | 0.892831 | − | 0.450393i | \(-0.148716\pi\) |
−0.450393 | + | 0.892831i | \(0.648716\pi\) | |||||||
\(930\) | −8.94975 | + | 8.94975i | −0.293474 | + | 0.293474i | ||||
\(931\) | 16.0711 | 0.526708 | ||||||||
\(932\) | 8.36396 | − | 8.36396i | 0.273971 | − | 0.273971i | ||||
\(933\) | 8.82843i | 0.289030i | ||||||||
\(934\) | 25.2132 | 0.825001 | ||||||||
\(935\) | −5.82843 | + | 0.171573i | −0.190610 | + | 0.00561103i | ||||
\(936\) | −2.82843 | −0.0924500 | ||||||||
\(937\) | − | 45.8406i | − | 1.49755i | −0.662826 | − | 0.748774i | \(-0.730643\pi\) | ||
0.662826 | − | 0.748774i | \(-0.269357\pi\) | |||||||
\(938\) | 3.65685 | − | 3.65685i | 0.119401 | − | 0.119401i | ||||
\(939\) | 22.1421 | 0.722581 | ||||||||
\(940\) | −2.29289 | + | 2.29289i | −0.0747859 | + | 0.0747859i | ||||
\(941\) | −38.4056 | − | 38.4056i | −1.25199 | − | 1.25199i | −0.954828 | − | 0.297158i | \(-0.903961\pi\) |
−0.297158 | − | 0.954828i | \(-0.596039\pi\) | |||||||
\(942\) | 4.82843 | + | 4.82843i | 0.157319 | + | 0.157319i | ||||
\(943\) | − | 29.8579i | − | 0.972306i | ||||||
\(944\) | 10.8995i | 0.354748i | ||||||||
\(945\) | −0.171573 | − | 0.171573i | −0.00558127 | − | 0.00558127i | ||||
\(946\) | 10.2426 | + | 10.2426i | 0.333017 | + | 0.333017i | ||||
\(947\) | −14.7782 | + | 14.7782i | −0.480226 | + | 0.480226i | −0.905204 | − | 0.424978i | \(-0.860282\pi\) |
0.424978 | + | 0.905204i | \(0.360282\pi\) | |||||||
\(948\) | −28.1421 | −0.914014 | ||||||||
\(949\) | 5.53553 | − | 5.53553i | 0.179691 | − | 0.179691i | ||||
\(950\) | 2.41421i | 0.0783274i | ||||||||
\(951\) | −83.5980 | −2.71085 | ||||||||
\(952\) | 1.65685 | − | 1.75736i | 0.0536990 | − | 0.0569563i | ||||
\(953\) | −20.5858 | −0.666839 | −0.333420 | − | 0.942779i | \(-0.608203\pi\) | ||||
−0.333420 | + | 0.942779i | \(0.608203\pi\) | |||||||
\(954\) | 9.85786i | 0.319160i | ||||||||
\(955\) | 0.171573 | − | 0.171573i | 0.00555197 | − | 0.00555197i | ||||
\(956\) | −27.4142 | −0.886639 | ||||||||
\(957\) | −23.7279 | + | 23.7279i | −0.767015 | + | 0.767015i | ||||
\(958\) | 19.0208 | + | 19.0208i | 0.614535 | + | 0.614535i | ||||
\(959\) | 6.92893 | + | 6.92893i | 0.223747 | + | 0.223747i | ||||
\(960\) | 2.41421i | 0.0779184i | ||||||||
\(961\) | 3.51472i | 0.113378i | ||||||||
\(962\) | 1.58579 | + | 1.58579i | 0.0511278 | + | 0.0511278i | ||||
\(963\) | 24.9706 | + | 24.9706i | 0.804665 | + | 0.804665i | ||||
\(964\) | 19.8284 | − | 19.8284i | 0.638631 | − | 0.638631i | ||||
\(965\) | 4.00000 | 0.128765 | ||||||||
\(966\) | 3.17157 | − | 3.17157i | 0.102044 | − | 0.102044i | ||||
\(967\) | 33.5980i | 1.08044i | 0.841524 | + | 0.540219i | \(0.181659\pi\) | ||||
−0.841524 | + | 0.540219i | \(0.818341\pi\) | |||||||
\(968\) | −9.00000 | −0.289271 | ||||||||
\(969\) | −17.4853 | − | 16.4853i | −0.561708 | − | 0.529584i | ||||
\(970\) | 14.3137 | 0.459585 | ||||||||
\(971\) | 22.0122i | 0.706405i | 0.935547 | + | 0.353202i | \(0.114907\pi\) | ||||
−0.935547 | + | 0.353202i | \(0.885093\pi\) | |||||||
\(972\) | −15.3137 | + | 15.3137i | −0.491187 | + | 0.491187i | ||||
\(973\) | 0.544156 | 0.0174448 | ||||||||
\(974\) | −14.4142 | + | 14.4142i | −0.461861 | + | 0.461861i | ||||
\(975\) | −1.70711 | − | 1.70711i | −0.0546712 | − | 0.0546712i | ||||
\(976\) | −5.77817 | − | 5.77817i | −0.184955 | − | 0.184955i | ||||
\(977\) | 34.2426i | 1.09552i | 0.836636 | + | 0.547760i | \(0.184519\pi\) | ||||
−0.836636 | + | 0.547760i | \(0.815481\pi\) | |||||||
\(978\) | 1.17157i | 0.0374628i | ||||||||
\(979\) | 14.6569 | + | 14.6569i | 0.468435 | + | 0.468435i | ||||
\(980\) | 4.70711 | + | 4.70711i | 0.150363 | + | 0.150363i | ||||
\(981\) | −23.6569 | + | 23.6569i | −0.755305 | + | 0.755305i | ||||
\(982\) | −8.27208 | −0.263973 | ||||||||
\(983\) | −8.07107 | + | 8.07107i | −0.257427 | + | 0.257427i | −0.824007 | − | 0.566580i | \(-0.808266\pi\) |
0.566580 | + | 0.824007i | \(0.308266\pi\) | |||||||
\(984\) | 22.7279i | 0.724540i | ||||||||
\(985\) | −25.5563 | −0.814293 | ||||||||
\(986\) | 29.4853 | + | 27.7990i | 0.939003 | + | 0.885300i | ||||
\(987\) | −4.58579 | −0.145967 | ||||||||
\(988\) | − | 2.41421i | − | 0.0768064i | ||||||
\(989\) | 22.9706 | − | 22.9706i | 0.730421 | − | 0.730421i | ||||
\(990\) | 4.00000 | 0.127128 | ||||||||
\(991\) | 22.0919 | − | 22.0919i | 0.701772 | − | 0.701772i | −0.263019 | − | 0.964791i | \(-0.584718\pi\) |
0.964791 | + | 0.263019i | \(0.0847182\pi\) | |||||||
\(992\) | −3.70711 | − | 3.70711i | −0.117701 | − | 0.117701i | ||||
\(993\) | 14.6066 | + | 14.6066i | 0.463526 | + | 0.463526i | ||||
\(994\) | 6.87006i | 0.217905i | ||||||||
\(995\) | 11.3848i | 0.360922i | ||||||||
\(996\) | 16.8995 | + | 16.8995i | 0.535481 | + | 0.535481i | ||||
\(997\) | 33.2843 | + | 33.2843i | 1.05412 | + | 1.05412i | 0.998449 | + | 0.0556745i | \(0.0177309\pi\) |
0.0556745 | + | 0.998449i | \(0.482269\pi\) | |||||||
\(998\) | 19.2426 | − | 19.2426i | 0.609115 | − | 0.609115i | ||||
\(999\) | 0.928932 | 0.0293901 |
(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 | 170.2.h.a.21.2 | ✓ | 4 | |
3.2 | odd | 2 | 1530.2.q.c.361.1 | 4 | |||
4.3 | odd | 2 | 1360.2.bt.a.1041.1 | 4 | |||
5.2 | odd | 4 | 850.2.g.e.599.1 | 4 | |||
5.3 | odd | 4 | 850.2.g.h.599.2 | 4 | |||
5.4 | even | 2 | 850.2.h.g.701.1 | 4 | |||
17.2 | even | 8 | 2890.2.b.j.2311.1 | 4 | |||
17.8 | even | 8 | 2890.2.a.t.1.1 | 2 | |||
17.9 | even | 8 | 2890.2.a.v.1.2 | 2 | |||
17.13 | even | 4 | inner | 170.2.h.a.81.2 | yes | 4 | |
17.15 | even | 8 | 2890.2.b.j.2311.4 | 4 | |||
51.47 | odd | 4 | 1530.2.q.c.1441.1 | 4 | |||
68.47 | odd | 4 | 1360.2.bt.a.81.1 | 4 | |||
85.13 | odd | 4 | 850.2.g.e.149.1 | 4 | |||
85.47 | odd | 4 | 850.2.g.h.149.2 | 4 | |||
85.64 | even | 4 | 850.2.h.g.251.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
170.2.h.a.21.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
170.2.h.a.81.2 | yes | 4 | 17.13 | even | 4 | inner | |
850.2.g.e.149.1 | 4 | 85.13 | odd | 4 | |||
850.2.g.e.599.1 | 4 | 5.2 | odd | 4 | |||
850.2.g.h.149.2 | 4 | 85.47 | odd | 4 | |||
850.2.g.h.599.2 | 4 | 5.3 | odd | 4 | |||
850.2.h.g.251.1 | 4 | 85.64 | even | 4 | |||
850.2.h.g.701.1 | 4 | 5.4 | even | 2 | |||
1360.2.bt.a.81.1 | 4 | 68.47 | odd | 4 | |||
1360.2.bt.a.1041.1 | 4 | 4.3 | odd | 2 | |||
1530.2.q.c.361.1 | 4 | 3.2 | odd | 2 | |||
1530.2.q.c.1441.1 | 4 | 51.47 | odd | 4 | |||
2890.2.a.t.1.1 | 2 | 17.8 | even | 8 | |||
2890.2.a.v.1.2 | 2 | 17.9 | even | 8 | |||
2890.2.b.j.2311.1 | 4 | 17.2 | even | 8 | |||
2890.2.b.j.2311.4 | 4 | 17.15 | even | 8 |