Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(109,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.d (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: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 3 x^{14} + 36 x^{13} - 78 x^{12} - 96 x^{11} + 1194 x^{10} + 1456 x^{9} + \cdots + 45658 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 109.11 | ||
Root | \(3.74844 - 1.37690i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.109 |
Dual form | 1080.2.d.g.109.10 |
$q$-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 \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).
\(n\) | \(217\) | \(271\) | \(541\) | \(1001\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.393855 | + | 1.35826i | 0.278498 | + | 0.960437i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.68976 | + | 1.06992i | −0.844878 | + | 0.534959i | ||||
\(5\) | −1.33104 | − | 1.79676i | −0.595259 | − | 0.803534i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.27541i | 1.61595i | 0.589216 | + | 0.807976i | \(0.299437\pi\) | ||||
−0.589216 | + | 0.807976i | \(0.700563\pi\) | |||||||
\(8\) | −2.11875 | − | 1.87374i | −0.749091 | − | 0.662467i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.91623 | − | 2.51556i | 0.605966 | − | 0.795491i | ||||
\(11\) | 0.381432i | 0.115006i | 0.998345 | + | 0.0575031i | \(0.0183139\pi\) | ||||
−0.998345 | + | 0.0575031i | \(0.981686\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.13006 | −0.868123 | −0.434061 | − | 0.900883i | \(-0.642920\pi\) | ||||
−0.434061 | + | 0.900883i | \(0.642920\pi\) | |||||||
\(14\) | −5.80712 | + | 1.68389i | −1.55202 | + | 0.450039i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.71055 | − | 3.61580i | 0.427638 | − | 0.903950i | ||||
\(17\) | 3.34970i | 0.812423i | 0.913779 | + | 0.406211i | \(0.133150\pi\) | ||||
−0.913779 | + | 0.406211i | \(0.866850\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.69099i | − | 0.846771i | −0.905950 | − | 0.423386i | \(-0.860842\pi\) | ||
0.905950 | − | 0.423386i | \(-0.139158\pi\) | |||||||
\(20\) | 4.17151 | + | 1.61198i | 0.932779 | + | 0.360449i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.518086 | + | 0.150229i | −0.110456 | + | 0.0320290i | ||||
\(23\) | − | 8.20607i | − | 1.71108i | −0.517734 | − | 0.855542i | \(-0.673224\pi\) | ||
0.517734 | − | 0.855542i | \(-0.326776\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.45667 | + | 4.78311i | −0.291334 | + | 0.956621i | ||||
\(26\) | −1.23279 | − | 4.25144i | −0.241770 | − | 0.833777i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.57433 | − | 7.22439i | −0.864468 | − | 1.36528i | ||||
\(29\) | − | 2.98635i | − | 0.554551i | −0.960790 | − | 0.277276i | \(-0.910569\pi\) | ||
0.960790 | − | 0.277276i | \(-0.0894315\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.30924 | −0.414751 | −0.207376 | − | 0.978261i | \(-0.566492\pi\) | ||||
−0.207376 | + | 0.978261i | \(0.566492\pi\) | |||||||
\(32\) | 5.58492 | + | 0.899275i | 0.987283 | + | 0.158971i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.54978 | + | 1.31930i | −0.780281 | + | 0.226258i | ||||
\(35\) | 7.68186 | − | 5.69073i | 1.29847 | − | 0.961909i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.5781 | −1.73903 | −0.869513 | − | 0.493911i | \(-0.835567\pi\) | ||||
−0.869513 | + | 0.493911i | \(0.835567\pi\) | |||||||
\(38\) | 5.01334 | − | 1.45372i | 0.813270 | − | 0.235824i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.546518 | + | 6.30090i | −0.0864121 | + | 0.996259i | ||||
\(41\) | −4.98243 | −0.778126 | −0.389063 | − | 0.921211i | \(-0.627201\pi\) | ||||
−0.389063 | + | 0.921211i | \(0.627201\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.59564 | −0.853327 | −0.426664 | − | 0.904410i | \(-0.640311\pi\) | ||||
−0.426664 | + | 0.904410i | \(0.640311\pi\) | |||||||
\(44\) | −0.408101 | − | 0.644528i | −0.0615236 | − | 0.0971662i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.1460 | − | 3.23200i | 1.64339 | − | 0.476533i | ||||
\(47\) | − | 5.88732i | − | 0.858753i | −0.903126 | − | 0.429377i | \(-0.858733\pi\) | ||
0.903126 | − | 0.429377i | \(-0.141267\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.2791 | −1.61130 | ||||||||
\(50\) | −7.07043 | − | 0.0946915i | −0.999910 | − | 0.0133914i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.28904 | − | 3.34891i | 0.733458 | − | 0.464410i | ||||
\(53\) | 4.40820 | 0.605513 | 0.302756 | − | 0.953068i | \(-0.402093\pi\) | ||||
0.302756 | + | 0.953068i | \(0.402093\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.685342 | − | 0.507701i | 0.0924114 | − | 0.0684584i | ||||
\(56\) | 8.01100 | − | 9.05851i | 1.07051 | − | 1.21049i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.05625 | − | 1.17619i | 0.532611 | − | 0.154441i | ||||
\(59\) | − | 5.51654i | − | 0.718192i | −0.933301 | − | 0.359096i | \(-0.883085\pi\) | ||
0.933301 | − | 0.359096i | \(-0.116915\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.32959i | − | 0.810421i | −0.914223 | − | 0.405210i | \(-0.867198\pi\) | ||
0.914223 | − | 0.405210i | \(-0.132802\pi\) | |||||||
\(62\) | −0.909505 | − | 3.13655i | −0.115507 | − | 0.398342i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.978197 | + | 7.93997i | 0.122275 | + | 0.992496i | ||||
\(65\) | 4.16623 | + | 5.62396i | 0.516757 | + | 0.697566i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.6504 | 1.54549 | 0.772747 | − | 0.634714i | \(-0.218882\pi\) | ||||
0.772747 | + | 0.634714i | \(0.218882\pi\) | |||||||
\(68\) | −3.58391 | − | 5.66018i | −0.434613 | − | 0.686398i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 10.7550 | + | 8.19267i | 1.28547 | + | 0.979211i | ||||
\(71\) | −15.7805 | −1.87280 | −0.936399 | − | 0.350937i | \(-0.885863\pi\) | ||||
−0.936399 | + | 0.350937i | \(0.885863\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.92303i | − | 0.225073i | −0.993648 | − | 0.112537i | \(-0.964102\pi\) | ||
0.993648 | − | 0.112537i | \(-0.0358976\pi\) | |||||||
\(74\) | −4.16623 | − | 14.3678i | −0.484315 | − | 1.67022i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.94906 | + | 6.23687i | 0.452988 | + | 0.715418i | ||||
\(77\) | −1.63078 | −0.185844 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.3371 | −1.38803 | −0.694014 | − | 0.719962i | \(-0.744159\pi\) | ||||
−0.694014 | + | 0.719962i | \(0.744159\pi\) | |||||||
\(80\) | −8.77353 | + | 1.73933i | −0.980910 | + | 0.194463i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.96236 | − | 6.76746i | −0.216706 | − | 0.747340i | ||||
\(83\) | −1.18214 | −0.129757 | −0.0648784 | − | 0.997893i | \(-0.520666\pi\) | ||||
−0.0648784 | + | 0.997893i | \(0.520666\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.01861 | − | 4.45859i | 0.652809 | − | 0.483602i | ||||
\(86\) | −2.20387 | − | 7.60035i | −0.237650 | − | 0.819567i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.714705 | − | 0.808160i | 0.0761878 | − | 0.0861501i | ||||
\(89\) | 11.8558 | 1.25671 | 0.628354 | − | 0.777927i | \(-0.283729\pi\) | ||||
0.628354 | + | 0.777927i | \(0.283729\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 13.3823i | − | 1.40284i | ||||||
\(92\) | 8.77982 | + | 13.8663i | 0.915359 | + | 1.44566i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.99652 | − | 2.31875i | 0.824778 | − | 0.239161i | ||||
\(95\) | −6.63181 | + | 4.91285i | −0.680410 | + | 0.504048i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.71322i | 0.783159i | 0.920144 | + | 0.391579i | \(0.128071\pi\) | ||||
−0.920144 | + | 0.391579i | \(0.871929\pi\) | |||||||
\(98\) | −4.44233 | − | 15.3200i | −0.448743 | − | 1.54755i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.65611 | − | 9.64080i | −0.265611 | − | 0.964080i | ||||
\(101\) | 13.6859i | 1.36180i | 0.732377 | + | 0.680900i | \(0.238411\pi\) | ||||
−0.732377 | + | 0.680900i | \(0.761589\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.2794i | 1.70259i | 0.524685 | + | 0.851297i | \(0.324183\pi\) | ||||
−0.524685 | + | 0.851297i | \(0.675817\pi\) | |||||||
\(104\) | 6.63181 | + | 5.86492i | 0.650303 | + | 0.575103i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.73619 | + | 5.98749i | 0.168634 | + | 0.581557i | ||||
\(107\) | −4.36922 | −0.422389 | −0.211194 | − | 0.977444i | \(-0.567735\pi\) | ||||
−0.211194 | + | 0.977444i | \(0.567735\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.6902i | 1.11972i | 0.828588 | + | 0.559858i | \(0.189145\pi\) | ||||
−0.828588 | + | 0.559858i | \(0.810855\pi\) | |||||||
\(110\) | 0.959517 | + | 0.730913i | 0.0914864 | + | 0.0696898i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 15.4590 | + | 7.31330i | 1.46074 | + | 0.691042i | ||||
\(113\) | − | 1.60764i | − | 0.151234i | −0.997137 | − | 0.0756172i | \(-0.975907\pi\) | ||
0.997137 | − | 0.0756172i | \(-0.0240927\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.7443 | + | 10.9226i | −1.37491 | + | 1.01854i | ||||
\(116\) | 3.19515 | + | 5.04620i | 0.296662 | + | 0.468528i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.49291 | − | 2.17272i | 0.689778 | − | 0.200015i | ||||
\(119\) | −14.3213 | −1.31284 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8545 | 0.986774 | ||||||||
\(122\) | 8.59724 | − | 2.49294i | 0.778358 | − | 0.225700i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.90205 | − | 2.47069i | 0.350414 | − | 0.221875i | ||||
\(125\) | 10.5330 | − | 3.74921i | 0.942097 | − | 0.335340i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.236674i | 0.0210014i | 0.999945 | + | 0.0105007i | \(0.00334255\pi\) | ||||
−0.999945 | + | 0.0105007i | \(0.996657\pi\) | |||||||
\(128\) | −10.3993 | + | 4.45585i | −0.919177 | + | 0.393845i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.99792 | + | 7.87386i | −0.526052 | + | 0.690583i | ||||
\(131\) | 8.02462i | 0.701114i | 0.936541 | + | 0.350557i | \(0.114008\pi\) | ||||
−0.936541 | + | 0.350557i | \(0.885992\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.7805 | 1.36834 | ||||||||
\(134\) | 4.98243 | + | 17.1826i | 0.430417 | + | 1.48435i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.27648 | − | 7.09718i | 0.538203 | − | 0.608579i | ||||
\(137\) | − | 4.48654i | − | 0.383311i | −0.981462 | − | 0.191656i | \(-0.938614\pi\) | ||
0.981462 | − | 0.191656i | \(-0.0613856\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.54603i | 0.470408i | 0.971946 | + | 0.235204i | \(0.0755758\pi\) | ||||
−0.971946 | + | 0.235204i | \(0.924424\pi\) | |||||||
\(140\) | −6.89186 | + | 17.8349i | −0.582469 | + | 1.50732i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.21523 | − | 21.4340i | −0.521570 | − | 1.79870i | ||||
\(143\) | − | 1.19391i | − | 0.0998395i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.36574 | + | 3.97495i | −0.445601 | + | 0.330101i | ||||
\(146\) | 2.61197 | − | 0.757394i | 0.216169 | − | 0.0626824i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.8744 | − | 11.3177i | 1.46926 | − | 0.930307i | ||||
\(149\) | 10.4259i | 0.854124i | 0.904222 | + | 0.427062i | \(0.140451\pi\) | ||||
−0.904222 | + | 0.427062i | \(0.859549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.2217 | 1.32010 | 0.660052 | − | 0.751220i | \(-0.270534\pi\) | ||||
0.660052 | + | 0.751220i | \(0.270534\pi\) | |||||||
\(152\) | −6.91596 | + | 7.82028i | −0.560958 | + | 0.634309i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.642291 | − | 2.21503i | −0.0517573 | − | 0.178492i | ||||
\(155\) | 3.07368 | + | 4.14914i | 0.246884 | + | 0.333267i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.3937 | −1.30836 | −0.654179 | − | 0.756339i | \(-0.726986\pi\) | ||||
−0.654179 | + | 0.756339i | \(0.726986\pi\) | |||||||
\(158\) | −4.85902 | − | 16.7570i | −0.386563 | − | 1.33311i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.81796 | − | 11.2317i | −0.459950 | − | 0.887945i | ||||
\(161\) | 35.0843 | 2.76503 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.5781 | −0.828539 | −0.414269 | − | 0.910154i | \(-0.635963\pi\) | ||||
−0.414269 | + | 0.910154i | \(0.635963\pi\) | |||||||
\(164\) | 8.41910 | − | 5.33080i | 0.657421 | − | 0.416265i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.465593 | − | 1.60566i | −0.0361370 | − | 0.124623i | ||||
\(167\) | − | 8.92917i | − | 0.690960i | −0.938426 | − | 0.345480i | \(-0.887716\pi\) | ||
0.938426 | − | 0.345480i | \(-0.112284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.20272 | −0.246363 | ||||||||
\(170\) | 8.42639 | + | 6.41881i | 0.646275 | + | 0.492300i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.45527 | − | 5.98688i | 0.720958 | − | 0.456495i | ||||
\(173\) | −23.8777 | −1.81539 | −0.907694 | − | 0.419633i | \(-0.862159\pi\) | ||||
−0.907694 | + | 0.419633i | \(0.862159\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.4497 | − | 6.22786i | −1.54585 | − | 0.470782i | ||||
\(176\) | 1.37918 | + | 0.652460i | 0.103960 | + | 0.0491810i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.66945 | + | 16.1032i | 0.349990 | + | 1.20699i | ||||
\(179\) | − | 5.40876i | − | 0.404270i | −0.979358 | − | 0.202135i | \(-0.935212\pi\) | ||
0.979358 | − | 0.202135i | \(-0.0647879\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.7143i | − | 1.39103i | −0.718514 | − | 0.695513i | \(-0.755177\pi\) | ||
0.718514 | − | 0.695513i | \(-0.244823\pi\) | |||||||
\(182\) | 18.1766 | − | 5.27068i | 1.34734 | − | 0.390689i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −15.3760 | + | 17.3866i | −1.13354 | + | 1.28176i | ||||
\(185\) | 14.0798 | + | 19.0062i | 1.03517 | + | 1.39737i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.27769 | −0.0934337 | ||||||||
\(188\) | 6.29895 | + | 9.94813i | 0.459398 | + | 0.725542i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.28492 | − | 7.07279i | −0.673599 | − | 0.513114i | ||||
\(191\) | −6.87333 | −0.497337 | −0.248668 | − | 0.968589i | \(-0.579993\pi\) | ||||
−0.248668 | + | 0.968589i | \(0.579993\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.0920i | 1.59021i | 0.606469 | + | 0.795107i | \(0.292586\pi\) | ||||
−0.606469 | + | 0.795107i | \(0.707414\pi\) | |||||||
\(194\) | −10.4766 | + | 3.03789i | −0.752175 | + | 0.218108i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 19.0589 | − | 12.0677i | 1.36135 | − | 0.861979i | ||||
\(197\) | −20.2935 | −1.44585 | −0.722924 | − | 0.690927i | \(-0.757202\pi\) | ||||
−0.722924 | + | 0.690927i | \(0.757202\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.9391 | 0.917232 | 0.458616 | − | 0.888635i | \(-0.348345\pi\) | ||||
0.458616 | + | 0.888635i | \(0.348345\pi\) | |||||||
\(200\) | 12.0486 | − | 7.40478i | 0.851966 | − | 0.523597i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.5891 | + | 5.39027i | −1.30792 | + | 0.379258i | ||||
\(203\) | 12.7679 | 0.896128 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.63181 | + | 8.95222i | 0.463186 | + | 0.625250i | ||||
\(206\) | −23.4700 | + | 6.80560i | −1.63523 | + | 0.474168i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.35413 | + | 11.3177i | −0.371242 | + | 0.784740i | ||||
\(209\) | 1.40786 | 0.0973840 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.3313i | 0.917762i | 0.888498 | + | 0.458881i | \(0.151750\pi\) | ||||
−0.888498 | + | 0.458881i | \(0.848250\pi\) | |||||||
\(212\) | −7.44878 | + | 4.71641i | −0.511584 | + | 0.323924i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.72084 | − | 5.93455i | −0.117634 | − | 0.405678i | ||||
\(215\) | 7.44802 | + | 10.0540i | 0.507950 | + | 0.685678i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9.87292i | − | 0.670217i | ||||||
\(218\) | −15.8783 | + | 4.60424i | −1.07542 | + | 0.311839i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.614861 | + | 1.59115i | −0.0414539 | + | 0.107275i | ||||
\(221\) | − | 10.4848i | − | 0.705282i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 17.2794i | − | 1.15712i | −0.815641 | − | 0.578558i | \(-0.803616\pi\) | ||
0.815641 | − | 0.578558i | \(-0.196384\pi\) | |||||||
\(224\) | −3.84477 | + | 23.8778i | −0.256889 | + | 1.59540i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.18360 | − | 0.633179i | 0.145251 | − | 0.0421184i | ||||
\(227\) | −19.0068 | −1.26153 | −0.630763 | − | 0.775975i | \(-0.717258\pi\) | ||||
−0.630763 | + | 0.775975i | \(0.717258\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.60897i | 0.304569i | 0.988337 | + | 0.152285i | \(0.0486630\pi\) | ||||
−0.988337 | + | 0.152285i | \(0.951337\pi\) | |||||||
\(230\) | −20.6429 | − | 15.7247i | −1.36115 | − | 1.03686i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.59564 | + | 6.32733i | −0.367372 | + | 0.415409i | ||||
\(233\) | 11.7746i | 0.771382i | 0.922628 | + | 0.385691i | \(0.126037\pi\) | ||||
−0.922628 | + | 0.385691i | \(0.873963\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.5781 | + | 7.83625i | −0.690038 | + | 0.511180i | ||||
\(236\) | 5.90225 | + | 9.32161i | 0.384203 | + | 0.606785i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.64054 | − | 19.4522i | −0.365622 | − | 1.26090i | ||||
\(239\) | −8.33246 | −0.538982 | −0.269491 | − | 0.963003i | \(-0.586855\pi\) | ||||
−0.269491 | + | 0.963003i | \(0.586855\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.69630 | −0.173684 | −0.0868420 | − | 0.996222i | \(-0.527678\pi\) | ||||
−0.0868420 | + | 0.996222i | \(0.527678\pi\) | |||||||
\(242\) | 4.27511 | + | 14.7433i | 0.274814 | + | 0.947734i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.77214 | + | 10.6955i | 0.433542 | + | 0.684707i | ||||
\(245\) | 15.0129 | + | 20.2658i | 0.959139 | + | 1.29473i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.5530i | 0.735101i | ||||||||
\(248\) | 4.89269 | + | 4.32691i | 0.310686 | + | 0.274759i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.24088 | + | 12.8299i | 0.584445 | + | 0.811433i | ||||
\(251\) | − | 30.2613i | − | 1.91008i | −0.296478 | − | 0.955040i | \(-0.595812\pi\) | ||
0.296478 | − | 0.955040i | \(-0.404188\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.13006 | 0.196785 | ||||||||
\(254\) | −0.321466 | + | 0.0932154i | −0.0201706 | + | 0.00584886i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.1480 | − | 12.3700i | −0.634252 | − | 0.773126i | ||||
\(257\) | 11.5438i | 0.720081i | 0.932937 | + | 0.360041i | \(0.117237\pi\) | ||||
−0.932937 | + | 0.360041i | \(0.882763\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 45.2256i | − | 2.81018i | ||||||
\(260\) | −13.0571 | − | 5.04559i | −0.809766 | − | 0.312914i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.8995 | + | 3.16054i | −0.673376 | + | 0.195259i | ||||
\(263\) | − | 13.6271i | − | 0.840285i | −0.907458 | − | 0.420142i | \(-0.861980\pi\) | ||
0.907458 | − | 0.420142i | \(-0.138020\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.86748 | − | 7.92046i | −0.360437 | − | 0.486550i | ||||
\(266\) | 6.21523 | + | 21.4340i | 0.381080 | + | 1.31421i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −21.3761 | + | 13.5349i | −1.30575 | + | 0.826776i | ||||
\(269\) | − | 7.49843i | − | 0.457187i | −0.973522 | − | 0.228594i | \(-0.926587\pi\) | ||
0.973522 | − | 0.228594i | \(-0.0734127\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00060 | −0.486002 | −0.243001 | − | 0.970026i | \(-0.578132\pi\) | ||||
−0.243001 | + | 0.970026i | \(0.578132\pi\) | |||||||
\(272\) | 12.1119 | + | 5.72984i | 0.734390 | + | 0.347423i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.09390 | − | 1.76705i | 0.368146 | − | 0.106751i | ||||
\(275\) | −1.82443 | − | 0.555622i | −0.110017 | − | 0.0335053i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.74327 | 0.224911 | 0.112456 | − | 0.993657i | \(-0.464128\pi\) | ||||
0.112456 | + | 0.993657i | \(0.464128\pi\) | |||||||
\(278\) | −7.53297 | + | 2.18433i | −0.451797 | + | 0.131008i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −26.9389 | − | 2.33659i | −1.60991 | − | 0.139638i | ||||
\(281\) | −3.52330 | −0.210182 | −0.105091 | − | 0.994463i | \(-0.533513\pi\) | ||||
−0.105091 | + | 0.994463i | \(0.533513\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.20885 | 0.369078 | 0.184539 | − | 0.982825i | \(-0.440921\pi\) | ||||
0.184539 | + | 0.982825i | \(0.440921\pi\) | |||||||
\(284\) | 26.6652 | − | 16.8838i | 1.58229 | − | 1.00187i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.62164 | − | 0.470226i | 0.0958895 | − | 0.0278051i | ||||
\(287\) | − | 21.3019i | − | 1.25741i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.77948 | 0.339969 | ||||||||
\(290\) | −7.51235 | − | 5.72254i | −0.441140 | − | 0.336039i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.05748 | + | 3.24944i | 0.120405 | + | 0.190159i | ||||
\(293\) | 18.6961 | 1.09224 | 0.546119 | − | 0.837707i | \(-0.316104\pi\) | ||||
0.546119 | + | 0.837707i | \(0.316104\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.91188 | + | 7.34273i | −0.577092 | + | 0.427510i | ||||
\(296\) | 22.4123 | + | 19.8206i | 1.30269 | + | 1.15205i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.1611 | + | 4.10630i | −0.820332 | + | 0.237872i | ||||
\(299\) | 25.6855i | 1.48543i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 23.9236i | − | 1.37894i | ||||||
\(302\) | 6.38901 | + | 22.0334i | 0.367646 | + | 1.26788i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −13.3459 | − | 6.31363i | −0.765439 | − | 0.362111i | ||||
\(305\) | −11.3727 | + | 8.42493i | −0.651201 | + | 0.482410i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.07234 | −0.118275 | −0.0591374 | − | 0.998250i | \(-0.518835\pi\) | ||||
−0.0591374 | + | 0.998250i | \(0.518835\pi\) | |||||||
\(308\) | 2.75562 | − | 1.74480i | 0.157016 | − | 0.0994192i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.42503 | + | 5.80903i | −0.251325 | + | 0.329931i | ||||
\(311\) | 25.7453 | 1.45988 | 0.729942 | − | 0.683509i | \(-0.239547\pi\) | ||||
0.729942 | + | 0.683509i | \(0.239547\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 13.6701i | − | 0.772677i | −0.922357 | − | 0.386339i | \(-0.873740\pi\) | ||
0.922357 | − | 0.386339i | \(-0.126260\pi\) | |||||||
\(314\) | −6.45674 | − | 22.2669i | −0.364375 | − | 1.25660i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.8466 | − | 13.1996i | 1.17271 | − | 0.742538i | ||||
\(317\) | −24.9535 | −1.40153 | −0.700764 | − | 0.713393i | \(-0.747158\pi\) | ||||
−0.700764 | + | 0.713393i | \(0.747158\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.13909 | 0.0637768 | ||||||||
\(320\) | 12.9642 | − | 12.3260i | 0.724720 | − | 0.689044i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.8181 | + | 47.6536i | 0.770054 | + | 2.65563i | ||||
\(323\) | 12.3637 | 0.687936 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.55947 | − | 14.9714i | 0.252914 | − | 0.830465i | ||||
\(326\) | −4.16623 | − | 14.3678i | −0.230746 | − | 0.795759i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.5565 | + | 9.33579i | 0.582887 | + | 0.515483i | ||||
\(329\) | 25.1707 | 1.38770 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 5.54603i | − | 0.304837i | −0.988316 | − | 0.152419i | \(-0.951294\pi\) | ||
0.988316 | − | 0.152419i | \(-0.0487062\pi\) | |||||||
\(332\) | 1.99753 | − | 1.26479i | 0.109629 | − | 0.0694146i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.1282 | − | 3.51680i | 0.663623 | − | 0.192431i | ||||
\(335\) | −16.8382 | − | 22.7297i | −0.919969 | − | 1.24186i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 13.9054i | − | 0.757476i | −0.925504 | − | 0.378738i | \(-0.876358\pi\) | ||
0.925504 | − | 0.378738i | \(-0.123642\pi\) | |||||||
\(338\) | −1.26141 | − | 4.35014i | −0.0686116 | − | 0.236616i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.39965 | + | 13.9733i | −0.292837 | + | 0.757811i | ||||
\(341\) | − | 0.880818i | − | 0.0476989i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.2948i | − | 0.987828i | ||||||
\(344\) | 11.8558 | + | 10.4848i | 0.639220 | + | 0.565301i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.40436 | − | 32.4322i | −0.505582 | − | 1.74357i | ||||
\(347\) | −6.48876 | −0.348335 | −0.174168 | − | 0.984716i | \(-0.555723\pi\) | ||||
−0.174168 | + | 0.984716i | \(0.555723\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.0107i | 1.60644i | 0.595684 | + | 0.803219i | \(0.296881\pi\) | ||||
−0.595684 | + | 0.803219i | \(0.703119\pi\) | |||||||
\(350\) | 0.404845 | − | 30.2290i | 0.0216399 | − | 1.61581i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.343013 | + | 2.13027i | −0.0182826 | + | 0.113544i | ||||
\(353\) | 26.2378i | 1.39650i | 0.715854 | + | 0.698250i | \(0.246037\pi\) | ||||
−0.715854 | + | 0.698250i | \(0.753963\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.0044 | + | 28.3537i | 1.11480 | + | 1.50486i | ||||
\(356\) | −20.0333 | + | 12.6847i | −1.06177 | + | 0.672287i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.34652 | − | 2.13027i | 0.388276 | − | 0.112588i | ||||
\(359\) | 8.50573 | 0.448915 | 0.224458 | − | 0.974484i | \(-0.427939\pi\) | ||||
0.224458 | + | 0.974484i | \(0.427939\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.37659 | 0.282978 | ||||||||
\(362\) | 25.4190 | − | 7.37074i | 1.33599 | − | 0.387398i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.3179 | + | 22.6128i | 0.750464 | + | 1.18523i | ||||
\(365\) | −3.45521 | + | 2.55962i | −0.180854 | + | 0.133977i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 6.86938i | − | 0.358579i | −0.983796 | − | 0.179289i | \(-0.942620\pi\) | ||
0.983796 | − | 0.179289i | \(-0.0573798\pi\) | |||||||
\(368\) | −29.6715 | − | 14.0369i | −1.54673 | − | 0.731724i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −20.2700 | + | 26.6098i | −1.05379 | + | 1.38338i | ||||
\(371\) | 18.8468i | 0.978479i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.1742 | −1.66592 | −0.832958 | − | 0.553337i | \(-0.813354\pi\) | ||||
−0.832958 | + | 0.553337i | \(0.813354\pi\) | |||||||
\(374\) | −0.503223 | − | 1.73543i | −0.0260211 | − | 0.0897371i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.0313 | + | 12.4737i | −0.568896 | + | 0.643284i | ||||
\(377\) | 9.34745i | 0.481418i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.2373i | 0.782688i | 0.920244 | + | 0.391344i | \(0.127990\pi\) | ||||
−0.920244 | + | 0.391344i | \(0.872010\pi\) | |||||||
\(380\) | 5.94980 | − | 15.3970i | 0.305218 | − | 0.789850i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.70710 | − | 9.33579i | −0.138507 | − | 0.477660i | ||||
\(383\) | 3.27016i | 0.167097i | 0.996504 | + | 0.0835486i | \(0.0266254\pi\) | ||||
−0.996504 | + | 0.0835486i | \(0.973375\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.17063 | + | 2.93011i | 0.110626 | + | 0.149332i | ||||
\(386\) | −30.0067 | + | 8.70104i | −1.52730 | + | 0.442871i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.25251 | − | 13.0335i | −0.418958 | − | 0.661674i | ||||
\(389\) | 29.1650i | 1.47872i | 0.673309 | + | 0.739361i | \(0.264872\pi\) | ||||
−0.673309 | + | 0.739361i | \(0.735128\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.4879 | 1.39012 | ||||||||
\(392\) | 23.8976 | + | 21.1341i | 1.20701 | + | 1.06743i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.99268 | − | 27.5638i | −0.402666 | − | 1.38865i | ||||
\(395\) | 16.4211 | + | 22.1667i | 0.826235 | + | 1.11533i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.9718 | 1.35367 | 0.676837 | − | 0.736133i | \(-0.263350\pi\) | ||||
0.676837 | + | 0.736133i | \(0.263350\pi\) | |||||||
\(398\) | 5.09615 | + | 17.5748i | 0.255447 | + | 0.880943i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.8030 | + | 13.4488i | 0.740152 | + | 0.672439i | ||||
\(401\) | −6.39030 | −0.319116 | −0.159558 | − | 0.987189i | \(-0.551007\pi\) | ||||
−0.159558 | + | 0.987189i | \(0.551007\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.22805 | 0.360055 | ||||||||
\(404\) | −14.6428 | − | 23.1259i | −0.728507 | − | 1.15055i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.02869 | + | 17.3421i | 0.249570 | + | 0.860674i | ||||
\(407\) | − | 4.03482i | − | 0.199999i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3411 | 0.709123 | 0.354562 | − | 0.935033i | \(-0.384630\pi\) | ||||
0.354562 | + | 0.935033i | \(0.384630\pi\) | |||||||
\(410\) | −9.54750 | + | 12.5336i | −0.471517 | + | 0.618992i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −18.4876 | − | 29.1980i | −0.910817 | − | 1.43848i | ||||
\(413\) | 23.5854 | 1.16056 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.57348 | + | 2.12402i | 0.0772389 | + | 0.104264i | ||||
\(416\) | −17.4811 | − | 2.81479i | −0.857083 | − | 0.138006i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.554495 | + | 1.91225i | 0.0271212 | + | 0.0935312i | ||||
\(419\) | − | 16.5213i | − | 0.807116i | −0.914954 | − | 0.403558i | \(-0.867773\pi\) | ||
0.914954 | − | 0.403558i | \(-0.132227\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.2560i | 1.71827i | 0.511747 | + | 0.859136i | \(0.328998\pi\) | ||||
−0.511747 | + | 0.859136i | \(0.671002\pi\) | |||||||
\(422\) | −18.1074 | + | 5.25059i | −0.881452 | + | 0.255595i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.33987 | − | 8.25982i | −0.453584 | − | 0.401132i | ||||
\(425\) | −16.0220 | − | 4.87942i | −0.777181 | − | 0.236687i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.0616 | 1.30960 | ||||||||
\(428\) | 7.38292 | − | 4.67471i | 0.356867 | − | 0.225961i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.7225 | + | 14.0762i | −0.517087 | + | 0.678814i | ||||
\(431\) | −13.8383 | −0.666568 | −0.333284 | − | 0.942826i | \(-0.608157\pi\) | ||||
−0.333284 | + | 0.942826i | \(0.608157\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.38265i | − | 0.162560i | −0.996691 | − | 0.0812799i | \(-0.974099\pi\) | ||
0.996691 | − | 0.0812799i | \(-0.0259008\pi\) | |||||||
\(434\) | 13.4100 | − | 3.88850i | 0.643702 | − | 0.186654i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.5075 | − | 19.7536i | −0.599003 | − | 0.946024i | ||||
\(437\) | −30.2885 | −1.44890 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.9454 | 1.19058 | 0.595289 | − | 0.803512i | \(-0.297038\pi\) | ||||
0.595289 | + | 0.803512i | \(0.297038\pi\) | |||||||
\(440\) | −2.40337 | − | 0.208460i | −0.114576 | − | 0.00993793i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.2411 | − | 4.12949i | 0.677379 | − | 0.196420i | ||||
\(443\) | −20.5705 | −0.977333 | −0.488667 | − | 0.872471i | \(-0.662517\pi\) | ||||
−0.488667 | + | 0.872471i | \(0.662517\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.7805 | − | 21.3019i | −0.748066 | − | 1.00981i | ||||
\(446\) | 23.4700 | − | 6.80560i | 1.11134 | − | 0.322254i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −33.9466 | + | 4.18219i | −1.60383 | + | 0.197590i | ||||
\(449\) | −30.1531 | −1.42301 | −0.711506 | − | 0.702680i | \(-0.751987\pi\) | ||||
−0.711506 | + | 0.702680i | \(0.751987\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.90046i | − | 0.0894893i | ||||||
\(452\) | 1.72005 | + | 2.71653i | 0.0809042 | + | 0.127775i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.48593 | − | 25.8162i | −0.351332 | − | 1.21162i | ||||
\(455\) | −24.0447 | + | 17.8123i | −1.12723 | + | 0.835055i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 11.8171i | − | 0.552779i | −0.961046 | − | 0.276389i | \(-0.910862\pi\) | ||
0.961046 | − | 0.276389i | \(-0.0891379\pi\) | |||||||
\(458\) | −6.26019 | + | 1.81527i | −0.292519 | + | 0.0848218i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13.2280 | − | 34.2317i | 0.616759 | − | 1.59606i | ||||
\(461\) | − | 19.6586i | − | 0.915593i | −0.889057 | − | 0.457797i | \(-0.848639\pi\) | ||
0.889057 | − | 0.457797i | \(-0.151361\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12.4557i | − | 0.578867i | −0.957198 | − | 0.289433i | \(-0.906533\pi\) | ||
0.957198 | − | 0.289433i | \(-0.0934668\pi\) | |||||||
\(464\) | −10.7980 | − | 5.10830i | −0.501287 | − | 0.237147i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.9930 | + | 4.63750i | −0.740864 | + | 0.214828i | ||||
\(467\) | −1.25941 | −0.0582787 | −0.0291394 | − | 0.999575i | \(-0.509277\pi\) | ||||
−0.0291394 | + | 0.999575i | \(0.509277\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 54.0857i | 2.49744i | ||||||||
\(470\) | −14.8099 | − | 11.2815i | −0.683130 | − | 0.520375i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.3366 | + | 11.6882i | −0.475779 | + | 0.537991i | ||||
\(473\) | − | 2.13436i | − | 0.0981380i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.6544 | + | 5.37656i | 0.810039 | + | 0.246694i | ||||
\(476\) | 24.1996 | − | 15.3227i | 1.10919 | − | 0.702313i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.28178 | − | 11.3177i | −0.150105 | − | 0.517658i | ||||
\(479\) | −7.44802 | −0.340309 | −0.170154 | − | 0.985417i | \(-0.554427\pi\) | ||||
−0.170154 | + | 0.985417i | \(0.554427\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.1100 | 1.50969 | ||||||||
\(482\) | −1.06195 | − | 3.66228i | −0.0483706 | − | 0.166812i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.3415 | + | 11.6134i | −0.833703 | + | 0.527883i | ||||
\(485\) | 13.8588 | − | 10.2666i | 0.629295 | − | 0.466182i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 14.9159i | − | 0.675903i | −0.941163 | − | 0.337952i | \(-0.890266\pi\) | ||
0.941163 | − | 0.337952i | \(-0.109734\pi\) | |||||||
\(488\) | −11.8600 | + | 13.4108i | −0.536877 | + | 0.607079i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21.6133 | + | 28.3733i | −0.976391 | + | 1.28177i | ||||
\(491\) | − | 27.3930i | − | 1.23623i | −0.786089 | − | 0.618113i | \(-0.787897\pi\) | ||
0.786089 | − | 0.618113i | \(-0.212103\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0034 | 0.450530 | ||||||||
\(494\) | −15.6920 | + | 4.55022i | −0.706018 | + | 0.204724i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.95007 | + | 8.34974i | −0.177363 | + | 0.374914i | ||||
\(497\) | − | 67.4679i | − | 3.02635i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 13.6320i | − | 0.610253i | −0.952312 | − | 0.305127i | \(-0.901301\pi\) | ||
0.952312 | − | 0.305127i | \(-0.0986988\pi\) | |||||||
\(500\) | −13.7868 | + | 17.6047i | −0.616564 | + | 0.787305i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 41.1029 | − | 11.9186i | 1.83451 | − | 0.531953i | ||||
\(503\) | 26.2664i | 1.17116i | 0.810615 | + | 0.585580i | \(0.199133\pi\) | ||||
−0.810615 | + | 0.585580i | \(0.800867\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.5903 | − | 18.2165i | 1.09425 | − | 0.810623i | ||||
\(506\) | 1.23279 | + | 4.25144i | 0.0548042 | + | 0.189000i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.253222 | − | 0.399922i | −0.0112349 | − | 0.0177437i | ||||
\(509\) | − | 7.43957i | − | 0.329753i | −0.986314 | − | 0.164876i | \(-0.947277\pi\) | ||
0.986314 | − | 0.164876i | \(-0.0527226\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.22171 | 0.363707 | ||||||||
\(512\) | 12.8049 | − | 18.6557i | 0.565901 | − | 0.824473i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.6795 | + | 4.54658i | −0.691593 | + | 0.200541i | ||||
\(515\) | 31.0469 | − | 22.9996i | 1.36809 | − | 1.01348i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.24561 | 0.0987620 | ||||||||
\(518\) | 61.4282 | − | 17.8123i | 2.69900 | − | 0.782629i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.71063 | − | 19.7222i | 0.0750163 | − | 0.864875i | ||||
\(521\) | 9.91360 | 0.434323 | 0.217161 | − | 0.976136i | \(-0.430320\pi\) | ||||
0.217161 | + | 0.976136i | \(0.430320\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.1386 | 1.14296 | 0.571480 | − | 0.820616i | \(-0.306369\pi\) | ||||
0.571480 | + | 0.820616i | \(0.306369\pi\) | |||||||
\(524\) | −8.58569 | − | 13.5596i | −0.375067 | − | 0.592356i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.5092 | − | 5.36712i | 0.807040 | − | 0.234017i | ||||
\(527\) | − | 7.73526i | − | 0.336953i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −44.3395 | −1.92781 | ||||||||
\(530\) | 8.44713 | − | 11.0891i | 0.366920 | − | 0.481680i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −26.6652 | + | 16.8838i | −1.15608 | + | 0.732006i | ||||
\(533\) | 15.5953 | 0.675508 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.81560 | + | 7.85043i | 0.251430 | + | 0.339404i | ||||
\(536\) | −26.8031 | − | 23.7036i | −1.15772 | − | 1.02384i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.1848 | − | 2.95330i | 0.439100 | − | 0.127326i | ||||
\(539\) | − | 4.30221i | − | 0.185309i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 28.1143i | − | 1.20873i | −0.796708 | − | 0.604364i | \(-0.793427\pi\) | ||
0.796708 | − | 0.604364i | \(-0.206573\pi\) | |||||||
\(542\) | −3.15108 | − | 10.8669i | −0.135350 | − | 0.466774i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.01231 | + | 18.7078i | −0.129152 | + | 0.802091i | ||||
\(545\) | 21.0044 | − | 15.5601i | 0.899731 | − | 0.666521i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.2144 | −1.50566 | −0.752830 | − | 0.658215i | \(-0.771312\pi\) | ||||
−0.752830 | + | 0.658215i | \(0.771312\pi\) | |||||||
\(548\) | 4.80023 | + | 7.58116i | 0.205056 | + | 0.323851i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.0361184 | − | 2.69689i | 0.00154009 | − | 0.114996i | ||||
\(551\) | −11.0226 | −0.469578 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 52.7459i | − | 2.24298i | ||||||
\(554\) | 1.47431 | + | 5.08434i | 0.0626373 | + | 0.216013i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.93380 | − | 9.37144i | −0.251649 | − | 0.397437i | ||||
\(557\) | 11.9112 | 0.504694 | 0.252347 | − | 0.967637i | \(-0.418798\pi\) | ||||
0.252347 | + | 0.967637i | \(0.418798\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.5147 | 0.740793 | ||||||||
\(560\) | −7.43633 | − | 37.5104i | −0.314242 | − | 1.58510i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.38767 | − | 4.78557i | −0.0585353 | − | 0.201867i | ||||
\(563\) | 25.8476 | 1.08934 | 0.544672 | − | 0.838649i | \(-0.316654\pi\) | ||||
0.544672 | + | 0.838649i | \(0.316654\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.88855 | + | 2.13984i | −0.121522 | + | 0.0900236i | ||||
\(566\) | 2.44539 | + | 8.43325i | 0.102787 | + | 0.354476i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 33.4349 | + | 29.5685i | 1.40290 | + | 1.24067i | ||||
\(569\) | 6.92460 | 0.290294 | 0.145147 | − | 0.989410i | \(-0.453634\pi\) | ||||
0.145147 | + | 0.989410i | \(0.453634\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.5498i | 1.44586i | 0.690919 | + | 0.722932i | \(0.257206\pi\) | ||||
−0.690919 | + | 0.722932i | \(0.742794\pi\) | |||||||
\(572\) | 1.27738 | + | 2.01741i | 0.0534100 | + | 0.0843522i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 28.9336 | − | 8.38988i | 1.20767 | − | 0.350187i | ||||
\(575\) | 39.2505 | + | 11.9535i | 1.63686 | + | 0.498497i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.5338i | 1.60418i | 0.597201 | + | 0.802092i | \(0.296280\pi\) | ||||
−0.597201 | + | 0.802092i | \(0.703720\pi\) | |||||||
\(578\) | 2.27628 | + | 7.85005i | 0.0946807 | + | 0.326519i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.81393 | − | 12.4576i | 0.199888 | − | 0.517274i | ||||
\(581\) | − | 5.05413i | − | 0.209681i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.68143i | 0.0696377i | ||||||||
\(584\) | −3.60325 | + | 4.07441i | −0.149104 | + | 0.168600i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.36356 | + | 25.3942i | 0.304186 | + | 1.04903i | ||||
\(587\) | −22.6932 | −0.936650 | −0.468325 | − | 0.883556i | \(-0.655142\pi\) | ||||
−0.468325 | + | 0.883556i | \(0.655142\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.52337i | 0.351199i | ||||||||
\(590\) | −13.8772 | − | 10.5710i | −0.571315 | − | 0.435200i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −18.0943 | + | 38.2482i | −0.743673 | + | 1.57199i | ||||
\(593\) | − | 1.74206i | − | 0.0715379i | −0.999360 | − | 0.0357689i | \(-0.988612\pi\) | ||
0.999360 | − | 0.0357689i | \(-0.0113880\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.0623 | + | 25.7320i | 0.781477 | + | 1.05491i | ||||
\(596\) | −11.1549 | − | 17.6173i | −0.456921 | − | 0.721631i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −34.8876 | + | 10.1164i | −1.42666 | + | 0.413689i | ||||
\(599\) | −17.4129 | −0.711471 | −0.355736 | − | 0.934587i | \(-0.615770\pi\) | ||||
−0.355736 | + | 0.934587i | \(0.615770\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.8993 | 1.83148 | 0.915740 | − | 0.401770i | \(-0.131605\pi\) | ||||
0.915740 | + | 0.401770i | \(0.131605\pi\) | |||||||
\(602\) | 32.4946 | − | 9.42245i | 1.32438 | − | 0.384030i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −27.4107 | + | 17.3559i | −1.11533 | + | 0.706202i | ||||
\(605\) | −14.4478 | − | 19.5029i | −0.587385 | − | 0.792906i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 28.0915i | − | 1.14020i | −0.821576 | − | 0.570099i | \(-0.806905\pi\) | ||
0.821576 | − | 0.570099i | \(-0.193095\pi\) | |||||||
\(608\) | 3.31922 | − | 20.6139i | 0.134612 | − | 0.836003i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.9225 | − | 12.1290i | −0.644682 | − | 0.491087i | ||||
\(611\) | 18.4277i | 0.745503i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.1913 | 0.452012 | 0.226006 | − | 0.974126i | \(-0.427433\pi\) | ||||
0.226006 | + | 0.974126i | \(0.427433\pi\) | |||||||
\(614\) | −0.816203 | − | 2.81479i | −0.0329393 | − | 0.113596i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.45521 | + | 3.05565i | 0.139214 | + | 0.123116i | ||||
\(617\) | − | 32.4154i | − | 1.30500i | −0.757791 | − | 0.652498i | \(-0.773721\pi\) | ||
0.757791 | − | 0.652498i | \(-0.226279\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 39.6795i | − | 1.59486i | −0.603415 | − | 0.797428i | \(-0.706194\pi\) | ||
0.603415 | − | 0.797428i | \(-0.293806\pi\) | |||||||
\(620\) | −9.63301 | − | 3.72244i | −0.386871 | − | 0.149497i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.1399 | + | 34.9690i | 0.406575 | + | 1.40213i | ||||
\(623\) | 50.6882i | 2.03078i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.7562 | − | 13.9348i | −0.830249 | − | 0.557393i | ||||
\(626\) | 18.5675 | − | 5.38402i | 0.742108 | − | 0.215189i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 27.7013 | − | 17.5399i | 1.10540 | − | 0.699918i | ||||
\(629\) | − | 35.4334i | − | 1.41282i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.0977 | −1.63607 | −0.818036 | − | 0.575167i | \(-0.804937\pi\) | ||||
−0.818036 | + | 0.575167i | \(0.804937\pi\) | |||||||
\(632\) | 26.1391 | + | 23.1164i | 1.03976 | + | 0.919523i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.82807 | − | 33.8934i | −0.390323 | − | 1.34608i | ||||
\(635\) | 0.425246 | − | 0.315023i | 0.0168754 | − | 0.0125013i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35.3042 | 1.39880 | ||||||||
\(638\) | 0.448637 | + | 1.54718i | 0.0177617 | + | 0.0612536i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 21.8479 | + | 12.7541i | 0.863616 | + | 0.504150i | ||||
\(641\) | −23.2285 | −0.917470 | −0.458735 | − | 0.888573i | \(-0.651697\pi\) | ||||
−0.458735 | + | 0.888573i | \(0.651697\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.7120 | 1.56609 | 0.783044 | − | 0.621967i | \(-0.213666\pi\) | ||||
0.783044 | + | 0.621967i | \(0.213666\pi\) | |||||||
\(644\) | −59.2838 | + | 37.5373i | −2.33611 | + | 1.47918i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.86952 | + | 16.7932i | 0.191589 | + | 0.660719i | ||||
\(647\) | − | 29.2392i | − | 1.14951i | −0.818326 | − | 0.574755i | \(-0.805097\pi\) | ||
0.818326 | − | 0.574755i | \(-0.194903\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.10419 | 0.0825966 | ||||||||
\(650\) | 22.1309 | + | 0.296390i | 0.868045 | + | 0.0116254i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.8744 | − | 11.3177i | 0.700014 | − | 0.443234i | ||||
\(653\) | 37.9006 | 1.48316 | 0.741582 | − | 0.670862i | \(-0.234076\pi\) | ||||
0.741582 | + | 0.670862i | \(0.234076\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.4183 | − | 10.6811i | 0.563369 | − | 0.417344i | ||||
\(656\) | −8.52271 | + | 18.0155i | −0.332756 | + | 0.703387i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.91360 | + | 34.1884i | 0.386472 | + | 1.33280i | ||||
\(659\) | − | 16.1193i | − | 0.627918i | −0.949437 | − | 0.313959i | \(-0.898345\pi\) | ||
0.949437 | − | 0.313959i | \(-0.101655\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 17.1112i | − | 0.665550i | −0.943006 | − | 0.332775i | \(-0.892015\pi\) | ||
0.943006 | − | 0.332775i | \(-0.107985\pi\) | |||||||
\(662\) | 7.53297 | − | 2.18433i | 0.292777 | − | 0.0848965i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.50466 | + | 2.21503i | 0.0971997 | + | 0.0859597i | ||||
\(665\) | −21.0044 | − | 28.3537i | −0.814517 | − | 1.09951i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.5062 | −0.948883 | ||||||||
\(668\) | 9.55348 | + | 15.0881i | 0.369635 | + | 0.583777i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.2411 | − | 31.8229i | 0.936517 | − | 1.22943i | ||||
\(671\) | 2.41431 | 0.0932034 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.6654i | 1.37480i | 0.726279 | + | 0.687400i | \(0.241248\pi\) | ||||
−0.726279 | + | 0.687400i | \(0.758752\pi\) | |||||||
\(674\) | 18.8872 | − | 5.47672i | 0.727507 | − | 0.210955i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.41182 | − | 3.42665i | 0.208147 | − | 0.131794i | ||||
\(677\) | 19.0953 | 0.733894 | 0.366947 | − | 0.930242i | \(-0.380403\pi\) | ||||
0.366947 | + | 0.930242i | \(0.380403\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.9771 | −1.26555 | ||||||||
\(680\) | −21.1061 | − | 1.83067i | −0.809384 | − | 0.0702032i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.19638 | − | 0.346915i | 0.0458118 | − | 0.0132840i | ||||
\(683\) | 12.7051 | 0.486148 | 0.243074 | − | 0.970008i | \(-0.421844\pi\) | ||||
0.243074 | + | 0.970008i | \(0.421844\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.06122 | + | 5.97176i | −0.308004 | + | 0.228169i | ||||
\(686\) | 24.8492 | − | 7.20552i | 0.948747 | − | 0.275108i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.57163 | + | 20.2327i | −0.364915 | + | 0.771366i | ||||
\(689\) | −13.7979 | −0.525659 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.25004i | 0.237763i | 0.992908 | + | 0.118881i | \(0.0379308\pi\) | ||||
−0.992908 | + | 0.118881i | \(0.962069\pi\) | |||||||
\(692\) | 40.3475 | − | 25.5472i | 1.53378 | − | 0.971158i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.55563 | − | 8.81345i | −0.0970106 | − | 0.334554i | ||||
\(695\) | 9.96487 | − | 7.38198i | 0.377989 | − | 0.280014i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 16.6897i | − | 0.632167i | ||||||
\(698\) | −40.7625 | + | 11.8199i | −1.54288 | + | 0.447389i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 41.2183 | − | 11.3560i | 1.55791 | − | 0.429215i | ||||
\(701\) | 18.8640i | 0.712484i | 0.934394 | + | 0.356242i | \(0.115942\pi\) | ||||
−0.934394 | + | 0.356242i | \(0.884058\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.0436i | 1.47256i | ||||||||
\(704\) | −3.02856 | + | 0.373116i | −0.114143 | + | 0.0140623i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −35.6379 | + | 10.3339i | −1.34125 | + | 0.388922i | ||||
\(707\) | −58.5128 | −2.20060 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.34976i | 0.0506914i | 0.999679 | + | 0.0253457i | \(0.00806865\pi\) | ||||
−0.999679 | + | 0.0253457i | \(0.991931\pi\) | |||||||
\(710\) | −30.2391 | + | 39.6968i | −1.13485 | + | 1.48979i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −25.1194 | − | 22.2146i | −0.941389 | − | 0.832528i | ||||
\(713\) | 18.9497i | 0.709674i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.14516 | + | 1.58914i | −0.0802244 | + | 0.0594303i | ||||
\(716\) | 5.78693 | + | 9.13949i | 0.216268 | + | 0.341559i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.35003 | + | 11.5530i | 0.125022 | + | 0.431155i | ||||
\(719\) | 31.5610 | 1.17703 | 0.588513 | − | 0.808488i | \(-0.299714\pi\) | ||||
0.588513 | + | 0.808488i | \(0.299714\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −73.8766 | −2.75131 | ||||||||
\(722\) | 2.11760 | + | 7.30282i | 0.0788088 | + | 0.271783i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.0228 | + | 31.6227i | 0.744142 | + | 1.17525i | ||||
\(725\) | 14.2840 | + | 4.35013i | 0.530495 | + | 0.161560i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 27.2812i | − | 1.01181i | −0.862591 | − | 0.505903i | \(-0.831159\pi\) | ||
0.862591 | − | 0.505903i | \(-0.168841\pi\) | |||||||
\(728\) | −25.0749 | + | 28.3537i | −0.929338 | + | 1.05086i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.83749 | − | 3.68496i | −0.179044 | − | 0.136387i | ||||
\(731\) | − | 18.7437i | − | 0.693263i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.613208 | −0.0226493 | −0.0113247 | − | 0.999936i | \(-0.503605\pi\) | ||||
−0.0113247 | + | 0.999936i | \(0.503605\pi\) | |||||||
\(734\) | 9.33042 | − | 2.70554i | 0.344392 | − | 0.0998634i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.37951 | − | 45.8302i | 0.272012 | − | 1.68932i | ||||
\(737\) | 4.82528i | 0.177741i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 34.0881i | − | 1.25395i | −0.779039 | − | 0.626975i | \(-0.784293\pi\) | ||
0.779039 | − | 0.626975i | \(-0.215707\pi\) | |||||||
\(740\) | −44.1266 | − | 17.0516i | −1.62213 | − | 0.626831i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −25.5990 | + | 7.42293i | −0.939767 | + | 0.272504i | ||||
\(743\) | − | 7.90870i | − | 0.290142i | −0.989421 | − | 0.145071i | \(-0.953659\pi\) | ||
0.989421 | − | 0.145071i | \(-0.0463411\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.7328 | − | 13.8773i | 0.686318 | − | 0.508425i | ||||
\(746\) | −12.6720 | − | 43.7010i | −0.463954 | − | 1.60001i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.15898 | − | 1.36702i | 0.0789401 | − | 0.0499832i | ||||
\(749\) | − | 18.6802i | − | 0.682559i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.5897 | 0.386422 | 0.193211 | − | 0.981157i | \(-0.438110\pi\) | ||||
0.193211 | + | 0.981157i | \(0.438110\pi\) | |||||||
\(752\) | −21.2874 | − | 10.0706i | −0.776270 | − | 0.367235i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.6963 | + | 3.68154i | −0.462372 | + | 0.134074i | ||||
\(755\) | −21.5917 | − | 29.1465i | −0.785804 | − | 1.06075i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.5802 | 1.18415 | 0.592073 | − | 0.805884i | \(-0.298310\pi\) | ||||
0.592073 | + | 0.805884i | \(0.298310\pi\) | |||||||
\(758\) | −20.6963 | + | 6.00130i | −0.751723 | + | 0.217977i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 23.2566 | + | 2.01719i | 0.843604 | + | 0.0731713i | ||||
\(761\) | −33.4519 | −1.21263 | −0.606314 | − | 0.795225i | \(-0.707353\pi\) | ||||
−0.606314 | + | 0.795225i | \(0.707353\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −49.9803 | −1.80941 | ||||||||
\(764\) | 11.6142 | − | 7.35390i | 0.420189 | − | 0.266055i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.44173 | + | 1.28797i | −0.160486 | + | 0.0465362i | ||||
\(767\) | 17.2671i | 0.623479i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.03867 | −0.181699 | −0.0908495 | − | 0.995865i | \(-0.528958\pi\) | ||||
−0.0908495 | + | 0.995865i | \(0.528958\pi\) | |||||||
\(770\) | −3.12495 | + | 4.10233i | −0.112615 | + | 0.147838i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −23.6366 | − | 37.3300i | −0.850700 | − | 1.34354i | ||||
\(773\) | −38.4946 | −1.38455 | −0.692277 | − | 0.721632i | \(-0.743392\pi\) | ||||
−0.692277 | + | 0.721632i | \(0.743392\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.36380 | − | 11.0453i | 0.120831 | − | 0.396760i | ||||
\(776\) | 14.4526 | − | 16.3424i | 0.518817 | − | 0.586657i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −39.6137 | + | 11.4868i | −1.42022 | + | 0.411821i | ||||
\(779\) | 18.3901i | 0.658894i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 6.01919i | − | 0.215383i | ||||||
\(782\) | 10.8263 | + | 37.3358i | 0.387146 | + | 1.33513i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −19.2935 | + | 40.7829i | −0.689052 | + | 1.45653i | ||||
\(785\) | 21.8206 | + | 29.4555i | 0.778812 | + | 1.05131i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.8000 | −1.27613 | −0.638066 | − | 0.769981i | \(-0.720265\pi\) | ||||
−0.638066 | + | 0.769981i | \(0.720265\pi\) | |||||||
\(788\) | 34.2910 | − | 21.7123i | 1.22157 | − | 0.773470i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −23.6407 | + | 31.0346i | −0.841097 | + | 1.10416i | ||||
\(791\) | 6.87333 | 0.244387 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.8120i | 0.703545i | ||||||||
\(794\) | 10.6230 | + | 36.6347i | 0.376995 | + | 1.30012i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21.8640 | + | 13.8438i | −0.774949 | + | 0.490682i | ||||
\(797\) | −13.4741 | −0.477278 | −0.238639 | − | 0.971108i | \(-0.576701\pi\) | ||||
−0.238639 | + | 0.971108i | \(0.576701\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.7208 | 0.697671 | ||||||||
\(800\) | −12.4367 | + | 25.4033i | −0.439704 | + | 0.898143i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.51685 | − | 8.67970i | −0.0888732 | − | 0.306491i | ||||
\(803\) | 0.733505 | 0.0258848 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −46.6985 | − | 63.0379i | −1.64591 | − | 2.22179i | ||||
\(806\) | 2.84681 | + | 9.81759i | 0.100274 | + | 0.345810i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 25.6439 | − | 28.9970i | 0.902148 | − | 1.02011i | ||||
\(809\) | −23.1772 | −0.814868 | −0.407434 | − | 0.913235i | \(-0.633576\pi\) | ||||
−0.407434 | + | 0.913235i | \(0.633576\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.64557i | 0.128013i | 0.997949 | + | 0.0640066i | \(0.0203879\pi\) | ||||
−0.997949 | + | 0.0640066i | \(0.979612\pi\) | |||||||
\(812\) | −21.5746 | + | 13.6606i | −0.757119 | + | 0.479392i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.48035 | − | 1.58914i | 0.192086 | − | 0.0556992i | ||||
\(815\) | 14.0798 | + | 19.0062i | 0.493195 | + | 0.665759i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.6535i | 0.722573i | ||||||||
\(818\) | 5.64833 | + | 19.4790i | 0.197489 | + | 0.681068i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.7843 | − | 8.03158i | −0.725819 | − | 0.280475i | ||||
\(821\) | 32.8395i | 1.14610i | 0.819519 | + | 0.573052i | \(0.194241\pi\) | ||||
−0.819519 | + | 0.573052i | \(0.805759\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 7.30498i | − | 0.254636i | −0.991862 | − | 0.127318i | \(-0.959363\pi\) | ||
0.991862 | − | 0.127318i | \(-0.0406368\pi\) | |||||||
\(824\) | 32.3772 | − | 36.6108i | 1.12791 | − | 1.27540i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.28925 | + | 32.0352i | 0.323214 | + | 1.11465i | ||||
\(827\) | −12.2507 | −0.425999 | −0.212999 | − | 0.977052i | \(-0.568323\pi\) | ||||
−0.212999 | + | 0.977052i | \(0.568323\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.1143i | 0.976450i | 0.872718 | + | 0.488225i | \(0.162356\pi\) | ||||
−0.872718 | + | 0.488225i | \(0.837644\pi\) | |||||||
\(830\) | −2.26526 | + | 2.97375i | −0.0786282 | + | 0.103220i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.06182 | − | 24.8526i | −0.106149 | − | 0.861608i | ||||
\(833\) | − | 37.7816i | − | 1.30906i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.0435 | + | 11.8851i | −0.555210 | + | 0.411300i | ||||
\(836\) | −2.37895 | + | 1.50630i | −0.0822776 | + | 0.0520964i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.4402 | − | 6.50699i | 0.775184 | − | 0.224780i | ||||
\(839\) | 51.8712 | 1.79079 | 0.895396 | − | 0.445271i | \(-0.146892\pi\) | ||||
0.895396 | + | 0.445271i | \(0.146892\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0817 | 0.692473 | ||||||||
\(842\) | −47.8869 | + | 13.8858i | −1.65029 | + | 0.478535i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14.2634 | − | 22.5266i | −0.490965 | − | 0.775397i | ||||
\(845\) | 4.26295 | + | 5.75451i | 0.146650 | + | 0.197961i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.4074i | 1.59458i | ||||||||
\(848\) | 7.54045 | − | 15.9392i | 0.258940 | − | 0.547353i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.317189 | − | 23.6839i | 0.0108795 | − | 0.812350i | ||||
\(851\) | 86.8044i | 2.97562i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.22642 | 0.0419917 | 0.0209958 | − | 0.999780i | \(-0.493316\pi\) | ||||
0.0209958 | + | 0.999780i | \(0.493316\pi\) | |||||||
\(854\) | 10.6583 | + | 36.7567i | 0.364721 | + | 1.25779i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.25729 | + | 8.18679i | 0.316407 | + | 0.279819i | ||||
\(857\) | − | 14.7535i | − | 0.503969i | −0.967731 | − | 0.251985i | \(-0.918917\pi\) | ||
0.967731 | − | 0.251985i | \(-0.0810832\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 34.8505i | − | 1.18909i | −0.804064 | − | 0.594543i | \(-0.797333\pi\) | ||
0.804064 | − | 0.594543i | \(-0.202667\pi\) | |||||||
\(860\) | −23.3423 | − | 9.02006i | −0.795966 | − | 0.307581i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.45029 | − | 18.7961i | −0.185638 | − | 0.640197i | ||||
\(863\) | 22.4673i | 0.764796i | 0.923998 | + | 0.382398i | \(0.124902\pi\) | ||||
−0.923998 | + | 0.382398i | \(0.875098\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.7821 | + | 42.9024i | 1.08063 | + | 1.45873i | ||||
\(866\) | 4.59453 | − | 1.33227i | 0.156128 | − | 0.0452725i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.5632 | + | 16.6828i | 0.358539 | + | 0.566252i | ||||
\(869\) | − | 4.70575i | − | 0.159632i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.5966 | −1.34168 | ||||||||
\(872\) | 21.9044 | − | 24.7686i | 0.741776 | − | 0.838770i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.9293 | − | 41.1398i | −0.403514 | − | 1.39157i | ||||
\(875\) | 16.0294 | + | 45.0327i | 0.541893 | + | 1.52238i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.8994 | −0.840794 | −0.420397 | − | 0.907340i | \(-0.638109\pi\) | ||||
−0.420397 | + | 0.907340i | \(0.638109\pi\) | |||||||
\(878\) | 9.82486 | + | 33.8824i | 0.331573 | + | 1.14347i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.663436 | − | 3.34651i | −0.0223644 | − | 0.112811i | ||||
\(881\) | −33.6251 | −1.13286 | −0.566430 | − | 0.824110i | \(-0.691676\pi\) | ||||
−0.566430 | + | 0.824110i | \(0.691676\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.4338 | −0.754959 | −0.377479 | − | 0.926018i | \(-0.623209\pi\) | ||||
−0.377479 | + | 0.926018i | \(0.623209\pi\) | |||||||
\(884\) | 11.2179 | + | 17.7167i | 0.377297 | + | 0.595878i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.10179 | − | 27.9401i | −0.272185 | − | 0.938667i | ||||
\(887\) | 15.8140i | 0.530982i | 0.964113 | + | 0.265491i | \(0.0855341\pi\) | ||||
−0.964113 | + | 0.265491i | \(0.914466\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.01188 | −0.0339373 | ||||||||
\(890\) | 22.7184 | − | 29.8239i | 0.761522 | − | 0.999700i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.4876 | + | 29.1980i | 0.619010 | + | 0.977622i | ||||
\(893\) | −21.7300 | −0.727168 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.71823 | + | 7.19927i | −0.324845 | + | 0.240645i | ||||
\(896\) | −19.0506 | − | 44.4612i | −0.636434 | − | 1.48534i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.8760 | − | 40.9558i | −0.396306 | − | 1.36671i | ||||
\(899\) | 6.89619i | 0.230001i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.7662i | 0.491932i | ||||||||
\(902\) | 2.58133 | − | 0.748507i | 0.0859488 | − | 0.0249226i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.01231 | + | 3.40619i | −0.100188 | + | 0.113288i | ||||
\(905\) | −33.6251 | + | 24.9095i | −1.11774 | + | 0.828020i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.9545 | −1.69192 | −0.845959 | − | 0.533248i | \(-0.820971\pi\) | ||||
−0.845959 | + | 0.533248i | \(0.820971\pi\) | |||||||
\(908\) | 32.1169 | − | 20.3357i | 1.06584 | − | 0.674865i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −33.6640 | − | 25.6435i | −1.11595 | − | 0.850075i | ||||
\(911\) | 56.3302 | 1.86630 | 0.933151 | − | 0.359484i | \(-0.117047\pi\) | ||||
0.933151 | + | 0.359484i | \(0.117047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 0.450907i | − | 0.0149228i | ||||||
\(914\) | 16.0507 | − | 4.65421i | 0.530909 | − | 0.153948i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.93122 | − | 7.78803i | −0.162932 | − | 0.257324i | ||||
\(917\) | −34.3085 | −1.13297 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.37513 | 0.144322 | 0.0721611 | − | 0.997393i | \(-0.477010\pi\) | ||||
0.0721611 | + | 0.997393i | \(0.477010\pi\) | |||||||
\(920\) | 51.7056 | + | 4.48476i | 1.70468 | + | 0.147858i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 26.7016 | − | 7.74265i | 0.879369 | − | 0.254991i | ||||
\(923\) | 49.3939 | 1.62582 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.4088 | − | 50.5961i | 0.506638 | − | 1.66359i | ||||
\(926\) | 16.9181 | − | 4.90575i | 0.555965 | − | 0.161213i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.68555 | − | 16.6785i | 0.0881575 | − | 0.547499i | ||||
\(929\) | −23.4870 | −0.770583 | −0.385291 | − | 0.922795i | \(-0.625899\pi\) | ||||
−0.385291 | + | 0.922795i | \(0.625899\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 41.6310i | 1.36440i | ||||||||
\(932\) | −12.5979 | − | 19.8963i | −0.412658 | − | 0.651724i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.496027 | − | 1.71062i | −0.0162305 | − | 0.0559730i | ||||
\(935\) | 1.70065 | + | 2.29569i | 0.0556172 | + | 0.0750771i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 32.7647i | − | 1.07038i | −0.844733 | − | 0.535189i | \(-0.820241\pi\) | ||
0.844733 | − | 0.535189i | \(-0.179759\pi\) | |||||||
\(938\) | −73.4625 | + | 21.3019i | −2.39864 | + | 0.695533i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.49023 | − | 24.5590i | 0.309537 | − | 0.801027i | ||||
\(941\) | 19.9859i | 0.651521i | 0.945452 | + | 0.325761i | \(0.105620\pi\) | ||||
−0.945452 | + | 0.325761i | \(0.894380\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.8862i | 1.33144i | ||||||||
\(944\) | −19.9467 | − | 9.43632i | −0.649210 | − | 0.307126i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.89902 | − | 0.840629i | 0.0942553 | − | 0.0273312i | ||||
\(947\) | 25.6951 | 0.834979 | 0.417490 | − | 0.908682i | \(-0.362910\pi\) | ||||
0.417490 | + | 0.908682i | \(0.362910\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.01919i | 0.195391i | ||||||||
\(950\) | −0.349505 | + | 26.0969i | −0.0113395 | + | 0.846695i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 30.3433 | + | 26.8345i | 0.983433 | + | 0.869710i | ||||
\(953\) | − | 18.9877i | − | 0.615073i | −0.951536 | − | 0.307536i | \(-0.900495\pi\) | ||
0.951536 | − | 0.307536i | \(-0.0995046\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.14867 | + | 12.3497i | 0.296044 | + | 0.399627i | ||||
\(956\) | 14.0798 | − | 8.91505i | 0.455374 | − | 0.288333i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.93344 | − | 10.1164i | −0.0947752 | − | 0.326845i | ||||
\(959\) | 19.1818 | 0.619412 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.6674 | −0.827982 | ||||||||
\(962\) | 13.0406 | + | 44.9721i | 0.420444 | + | 1.44996i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.55609 | − | 2.88482i | 0.146742 | − | 0.0929138i | ||||
\(965\) | 39.6939 | − | 29.4053i | 1.27779 | − | 0.946589i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.3552i | 0.751053i | 0.926812 | + | 0.375527i | \(0.122538\pi\) | ||||
−0.926812 | + | 0.375527i | \(0.877462\pi\) | |||||||
\(968\) | −22.9980 | − | 20.3385i | −0.739183 | − | 0.653705i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 19.4031 | + | 14.7803i | 0.622996 | + | 0.474567i | ||||
\(971\) | 24.6232i | 0.790195i | 0.918639 | + | 0.395097i | \(0.129289\pi\) | ||||
−0.918639 | + | 0.395097i | \(0.870711\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.7115 | −0.760157 | ||||||||
\(974\) | 20.2597 | − | 5.87470i | 0.649162 | − | 0.188238i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22.8865 | − | 10.8271i | −0.732580 | − | 0.346566i | ||||
\(977\) | 40.7010i | 1.30214i | 0.759017 | + | 0.651071i | \(0.225680\pi\) | ||||
−0.759017 | + | 0.651071i | \(0.774320\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.52217i | 0.144529i | ||||||||
\(980\) | −47.0509 | − | 18.1816i | −1.50298 | − | 0.580791i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 37.2068 | − | 10.7889i | 1.18732 | − | 0.344286i | ||||
\(983\) | − | 5.81942i | − | 0.185611i | −0.995684 | − | 0.0928053i | \(-0.970417\pi\) | ||
0.995684 | − | 0.0928053i | \(-0.0295834\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.0114 | + | 36.4624i | 0.860654 | + | 1.16179i | ||||
\(986\) | 3.93989 | + | 13.5872i | 0.125472 | + | 0.432706i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.3608 | − | 19.5218i | −0.393249 | − | 0.621071i | ||||
\(989\) | 45.9182i | 1.46011i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.08446 | −0.193279 | −0.0966396 | − | 0.995319i | \(-0.530809\pi\) | ||||
−0.0966396 | + | 0.995319i | \(0.530809\pi\) | |||||||
\(992\) | −12.8969 | − | 2.07664i | −0.409477 | − | 0.0659333i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 91.6392 | − | 26.5726i | 2.90662 | − | 0.842832i | ||||
\(995\) | −17.2225 | − | 23.2485i | −0.545990 | − | 0.737027i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.3958 | 1.21601 | 0.608003 | − | 0.793935i | \(-0.291971\pi\) | ||||
0.608003 | + | 0.793935i | \(0.291971\pi\) | |||||||
\(998\) | 18.5159 | − | 5.36904i | 0.586110 | − | 0.169954i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1080.2.d.g.109.11 | yes | 16 | |
3.2 | odd | 2 | 1080.2.d.h.109.6 | yes | 16 | ||
4.3 | odd | 2 | 4320.2.d.g.3889.5 | 16 | |||
5.4 | even | 2 | 1080.2.d.h.109.5 | yes | 16 | ||
8.3 | odd | 2 | 4320.2.d.h.3889.12 | 16 | |||
8.5 | even | 2 | 1080.2.d.h.109.8 | yes | 16 | ||
12.11 | even | 2 | 4320.2.d.h.3889.11 | 16 | |||
15.14 | odd | 2 | inner | 1080.2.d.g.109.12 | yes | 16 | |
20.19 | odd | 2 | 4320.2.d.h.3889.10 | 16 | |||
24.5 | odd | 2 | inner | 1080.2.d.g.109.9 | ✓ | 16 | |
24.11 | even | 2 | 4320.2.d.g.3889.6 | 16 | |||
40.19 | odd | 2 | 4320.2.d.g.3889.7 | 16 | |||
40.29 | even | 2 | inner | 1080.2.d.g.109.10 | yes | 16 | |
60.59 | even | 2 | 4320.2.d.g.3889.8 | 16 | |||
120.29 | odd | 2 | 1080.2.d.h.109.7 | yes | 16 | ||
120.59 | even | 2 | 4320.2.d.h.3889.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.2.d.g.109.9 | ✓ | 16 | 24.5 | odd | 2 | inner | |
1080.2.d.g.109.10 | yes | 16 | 40.29 | even | 2 | inner | |
1080.2.d.g.109.11 | yes | 16 | 1.1 | even | 1 | trivial | |
1080.2.d.g.109.12 | yes | 16 | 15.14 | odd | 2 | inner | |
1080.2.d.h.109.5 | yes | 16 | 5.4 | even | 2 | ||
1080.2.d.h.109.6 | yes | 16 | 3.2 | odd | 2 | ||
1080.2.d.h.109.7 | yes | 16 | 120.29 | odd | 2 | ||
1080.2.d.h.109.8 | yes | 16 | 8.5 | even | 2 | ||
4320.2.d.g.3889.5 | 16 | 4.3 | odd | 2 | |||
4320.2.d.g.3889.6 | 16 | 24.11 | even | 2 | |||
4320.2.d.g.3889.7 | 16 | 40.19 | odd | 2 | |||
4320.2.d.g.3889.8 | 16 | 60.59 | even | 2 | |||
4320.2.d.h.3889.9 | 16 | 120.59 | even | 2 | |||
4320.2.d.h.3889.10 | 16 | 20.19 | odd | 2 | |||
4320.2.d.h.3889.11 | 16 | 12.11 | even | 2 | |||
4320.2.d.h.3889.12 | 16 | 8.3 | odd | 2 |