Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(505,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.505");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.r (of order \(3\), degree \(2\), not 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.508277025.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 505.4 | ||
Root | \(-0.734668 - 0.348716i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.505 |
Dual form | 1512.2.r.d.1009.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.21814 | + | 2.10988i | 0.544768 | + | 0.943566i | 0.998621 | + | 0.0524895i | \(0.0167156\pi\) |
−0.453853 | + | 0.891076i | \(0.649951\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.379477 | − | 0.657274i | 0.114417 | − | 0.198176i | −0.803130 | − | 0.595804i | \(-0.796833\pi\) |
0.917546 | + | 0.397629i | \(0.130167\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.11414 | − | 1.92976i | −0.309008 | − | 0.535218i | 0.669138 | − | 0.743139i | \(-0.266664\pi\) |
−0.978146 | + | 0.207921i | \(0.933330\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.04904 | 1.70964 | 0.854822 | − | 0.518922i | \(-0.173666\pi\) | ||||
0.854822 | + | 0.518922i | \(0.173666\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.37172 | −0.314694 | −0.157347 | − | 0.987543i | \(-0.550294\pi\) | ||||
−0.157347 | + | 0.987543i | \(0.550294\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.51814 | + | 6.09360i | 0.733583 | + | 1.27060i | 0.955342 | + | 0.295502i | \(0.0954870\pi\) |
−0.221759 | + | 0.975102i | \(0.571180\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.467722 | + | 0.810117i | −0.0935443 | + | 0.162023i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.418134 | − | 0.724229i | 0.0776455 | − | 0.134486i | −0.824588 | − | 0.565733i | \(-0.808593\pi\) |
0.902234 | + | 0.431248i | \(0.141926\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.265332 | + | 0.459569i | 0.0476551 | + | 0.0825411i | 0.888869 | − | 0.458161i | \(-0.151492\pi\) |
−0.841214 | + | 0.540702i | \(0.818158\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.43628 | −0.411806 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.53066 | 0.744837 | 0.372418 | − | 0.928065i | \(-0.378529\pi\) | ||||
0.372418 | + | 0.928065i | \(0.378529\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.42852 | + | 7.67042i | 0.691618 | + | 1.19792i | 0.971307 | + | 0.237828i | \(0.0764353\pi\) |
−0.279689 | + | 0.960091i | \(0.590231\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.70161 | + | 6.41137i | −0.564490 | + | 0.977725i | 0.432607 | + | 0.901583i | \(0.357594\pi\) |
−0.997097 | + | 0.0761428i | \(0.975740\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.39762 | + | 5.88485i | −0.495594 | + | 0.858394i | −0.999987 | − | 0.00508036i | \(-0.998383\pi\) |
0.504393 | + | 0.863474i | \(0.331716\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.607978 | 0.0835122 | 0.0417561 | − | 0.999128i | \(-0.486705\pi\) | ||||
0.0417561 | + | 0.999128i | \(0.486705\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.84902 | 0.249322 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.581866 | − | 1.00782i | −0.0757525 | − | 0.131207i | 0.825661 | − | 0.564167i | \(-0.190803\pi\) |
−0.901413 | + | 0.432960i | \(0.857469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.85680 | + | 10.1443i | −0.749887 | + | 1.29884i | 0.197990 | + | 0.980204i | \(0.436559\pi\) |
−0.947876 | + | 0.318638i | \(0.896775\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.71436 | − | 4.70142i | 0.336676 | − | 0.583139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.152801 | + | 0.264659i | 0.0186676 | + | 0.0323333i | 0.875208 | − | 0.483746i | \(-0.160724\pi\) |
−0.856541 | + | 0.516080i | \(0.827391\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.6192 | −1.49763 | −0.748813 | − | 0.662781i | \(-0.769376\pi\) | ||||
−0.748813 | + | 0.662781i | \(0.769376\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.1499 | −1.18795 | −0.593977 | − | 0.804482i | \(-0.702443\pi\) | ||||
−0.593977 | + | 0.804482i | \(0.702443\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.379477 | + | 0.657274i | 0.0432455 | + | 0.0749033i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.62453 | + | 13.2061i | −0.857827 | + | 1.48580i | 0.0161711 | + | 0.999869i | \(0.494852\pi\) |
−0.873998 | + | 0.485930i | \(0.838481\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.18909 | − | 14.1839i | 0.898869 | − | 1.55689i | 0.0699272 | − | 0.997552i | \(-0.477723\pi\) |
0.828942 | − | 0.559335i | \(-0.188943\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.58671 | + | 14.8726i | 0.931359 | + | 1.61316i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.63151 | 1.02094 | 0.510469 | − | 0.859896i | \(-0.329472\pi\) | ||||
0.510469 | + | 0.859896i | \(0.329472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.22829 | 0.233588 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.67094 | − | 2.89416i | −0.171435 | − | 0.296935i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.46718 | − | 9.46943i | 0.555108 | − | 0.961474i | −0.442788 | − | 0.896627i | \(-0.646010\pi\) |
0.997895 | − | 0.0648479i | \(-0.0206562\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.750417 | − | 1.29976i | 0.0746693 | − | 0.129331i | −0.826273 | − | 0.563270i | \(-0.809543\pi\) |
0.900942 | + | 0.433939i | \(0.142877\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.13229 | − | 8.88938i | −0.505699 | − | 0.875897i | −0.999978 | − | 0.00659356i | \(-0.997901\pi\) |
0.494279 | − | 0.869303i | \(-0.335432\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.84428 | 0.758335 | 0.379168 | − | 0.925328i | \(-0.376210\pi\) | ||||
0.379168 | + | 0.925328i | \(0.376210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.1754 | 1.16619 | 0.583096 | − | 0.812403i | \(-0.301841\pi\) | ||||
0.583096 | + | 0.812403i | \(0.301841\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.98586 | + | 3.43962i | 0.186814 | + | 0.323572i | 0.944186 | − | 0.329412i | \(-0.106850\pi\) |
−0.757372 | + | 0.652984i | \(0.773517\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.57117 | + | 14.8457i | −0.799266 | + | 1.38437i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.52452 | + | 6.10465i | −0.323092 | + | 0.559612i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.21199 | + | 9.02744i | 0.473818 | + | 0.820676i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.90238 | 0.885696 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.7579 | 1.39828 | 0.699142 | − | 0.714983i | \(-0.253565\pi\) | ||||
0.699142 | + | 0.714983i | \(0.253565\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.93789 | − | 10.2847i | −0.518796 | − | 0.898581i | −0.999761 | − | 0.0218413i | \(-0.993047\pi\) |
0.480966 | − | 0.876739i | \(-0.340286\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.685860 | − | 1.18794i | 0.0594716 | − | 0.103008i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.1869 | + | 17.6443i | −0.870328 | + | 1.50745i | −0.00867008 | + | 0.999962i | \(0.502760\pi\) |
−0.861658 | + | 0.507490i | \(0.830574\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.13489 | + | 5.42979i | 0.265898 | + | 0.460549i | 0.967799 | − | 0.251726i | \(-0.0809982\pi\) |
−0.701900 | + | 0.712275i | \(0.747665\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.69117 | −0.141423 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.03738 | 0.169195 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.45679 | − | 4.25529i | −0.201268 | − | 0.348607i | 0.747669 | − | 0.664071i | \(-0.231173\pi\) |
−0.948937 | + | 0.315465i | \(0.897840\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.80878 | − | 4.86494i | 0.228575 | − | 0.395903i | −0.728811 | − | 0.684715i | \(-0.759927\pi\) |
0.957386 | + | 0.288811i | \(0.0932601\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.646423 | + | 1.11964i | −0.0519220 | + | 0.0899315i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.3174 | − | 17.8702i | −0.823416 | − | 1.42620i | −0.903124 | − | 0.429379i | \(-0.858732\pi\) |
0.0797087 | − | 0.996818i | \(-0.474601\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.03629 | −0.554537 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.95096 | 0.387789 | 0.193895 | − | 0.981022i | \(-0.437888\pi\) | ||||
0.193895 | + | 0.981022i | \(0.437888\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.485864 | − | 0.841542i | −0.0375973 | − | 0.0651205i | 0.846614 | − | 0.532207i | \(-0.178637\pi\) |
−0.884212 | + | 0.467086i | \(0.845304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.01736 | − | 6.95828i | 0.309028 | − | 0.535252i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.90960 | + | 15.4319i | −0.677384 | + | 1.17326i | 0.298382 | + | 0.954447i | \(0.403553\pi\) |
−0.975766 | + | 0.218817i | \(0.929780\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.467722 | − | 0.810117i | −0.0353564 | − | 0.0612391i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.6065 | 0.792764 | 0.396382 | − | 0.918086i | \(-0.370266\pi\) | ||||
0.396382 | + | 0.918086i | \(0.370266\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.7360 | 1.83862 | 0.919308 | − | 0.393539i | \(-0.128749\pi\) | ||||
0.919308 | + | 0.393539i | \(0.128749\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.51898 | + | 9.55915i | 0.405763 | + | 0.702802i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.67495 | − | 4.63315i | 0.195612 | − | 0.338810i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.25120 | − | 16.0235i | 0.669393 | − | 1.15942i | −0.308681 | − | 0.951166i | \(-0.599888\pi\) |
0.978074 | − | 0.208257i | \(-0.0667791\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.24505 | − | 14.2808i | −0.593492 | − | 1.02796i | −0.993758 | − | 0.111559i | \(-0.964416\pi\) |
0.400266 | − | 0.916399i | \(-0.368918\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.68164 | 0.618541 | 0.309271 | − | 0.950974i | \(-0.399915\pi\) | ||||
0.309271 | + | 0.950974i | \(0.399915\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.2352 | −1.36355 | −0.681774 | − | 0.731563i | \(-0.738791\pi\) | ||||
−0.681774 | + | 0.731563i | \(0.738791\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.418134 | + | 0.724229i | 0.0293472 | + | 0.0508309i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.7891 | + | 18.6873i | −0.753543 | + | 1.30518i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.520536 | + | 0.901595i | −0.0360063 | + | 0.0623647i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3584 | − | 19.6734i | −0.781946 | − | 1.35437i | −0.930807 | − | 0.365512i | \(-0.880894\pi\) |
0.148861 | − | 0.988858i | \(-0.452439\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.0363 | −1.23006 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.530665 | −0.0360239 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.85365 | − | 13.6029i | −0.528294 | − | 0.915032i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.76320 | + | 13.4462i | −0.519862 | + | 0.900427i | 0.479871 | + | 0.877339i | \(0.340683\pi\) |
−0.999733 | + | 0.0230886i | \(0.992650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.13468 | − | 1.96533i | 0.0753114 | − | 0.130443i | −0.825910 | − | 0.563802i | \(-0.809338\pi\) |
0.901222 | + | 0.433358i | \(0.142672\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.61037 | − | 7.98540i | −0.304662 | − | 0.527690i | 0.672524 | − | 0.740075i | \(-0.265210\pi\) |
−0.977186 | + | 0.212385i | \(0.931877\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.0842 | 1.57781 | 0.788905 | − | 0.614515i | \(-0.210648\pi\) | ||||
0.788905 | + | 0.614515i | \(0.210648\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.5551 | −1.07993 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.50000 | + | 4.33013i | 0.161712 | + | 0.280093i | 0.935483 | − | 0.353373i | \(-0.114965\pi\) |
−0.773771 | + | 0.633465i | \(0.781632\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.61761 | − | 14.9261i | 0.555109 | − | 0.961477i | −0.442786 | − | 0.896627i | \(-0.646010\pi\) |
0.997895 | − | 0.0648494i | \(-0.0206567\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.21814 | − | 2.10988i | 0.0778240 | − | 0.134795i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.52829 | + | 2.64708i | 0.0972430 | + | 0.168430i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.2725 | −0.963994 | −0.481997 | − | 0.876173i | \(-0.660088\pi\) | ||||
−0.481997 | + | 0.876173i | \(0.660088\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.34022 | 0.335737 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.79524 | − | 10.0377i | −0.361497 | − | 0.626131i | 0.626710 | − | 0.779252i | \(-0.284401\pi\) |
−0.988207 | + | 0.153121i | \(0.951068\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.26533 | + | 3.92367i | −0.140761 | + | 0.243805i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.05602 | + | 7.02523i | −0.250105 | + | 0.433194i | −0.963554 | − | 0.267512i | \(-0.913798\pi\) |
0.713450 | + | 0.700707i | \(0.247132\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.740601 | + | 1.28276i | 0.0454948 | + | 0.0787992i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.4598 | −0.698717 | −0.349358 | − | 0.936989i | \(-0.613600\pi\) | ||||
−0.349358 | + | 0.936989i | \(0.613600\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.30404 | −0.200706 | −0.100353 | − | 0.994952i | \(-0.531997\pi\) | ||||
−0.100353 | + | 0.994952i | \(0.531997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.354979 | + | 0.614842i | 0.0214061 | + | 0.0370764i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.12453 | − | 8.87595i | 0.307903 | − | 0.533304i | −0.670000 | − | 0.742361i | \(-0.733706\pi\) |
0.977903 | + | 0.209057i | \(0.0670394\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.861334 | + | 1.49188i | −0.0513829 | + | 0.0889978i | −0.890573 | − | 0.454841i | \(-0.849696\pi\) |
0.839190 | + | 0.543838i | \(0.183030\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.0752 | − | 20.9148i | −0.717795 | − | 1.24326i | −0.961872 | − | 0.273501i | \(-0.911818\pi\) |
0.244077 | − | 0.969756i | \(-0.421515\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.85704 | −0.522814 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.6890 | 1.92288 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.46533 | − | 12.9303i | −0.436129 | − | 0.755398i | 0.561258 | − | 0.827641i | \(-0.310318\pi\) |
−0.997387 | + | 0.0722432i | \(0.976984\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.41759 | − | 2.45533i | 0.0825351 | − | 0.142955i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.83944 | − | 13.5783i | 0.453367 | − | 0.785254i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.70161 | − | 6.41137i | −0.213357 | − | 0.369545i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −28.5376 | −1.63406 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.9563 | −1.02482 | −0.512411 | − | 0.858741i | \(-0.671247\pi\) | ||||
−0.512411 | + | 0.858741i | \(0.671247\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.8931 | + | 18.8673i | 0.617689 | + | 1.06987i | 0.989906 | + | 0.141723i | \(0.0452643\pi\) |
−0.372217 | + | 0.928146i | \(0.621402\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.0624 | + | 19.1606i | −0.625284 | + | 1.08302i | 0.363202 | + | 0.931710i | \(0.381683\pi\) |
−0.988486 | + | 0.151313i | \(0.951650\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.86480 | − | 4.96197i | 0.160903 | − | 0.278692i | −0.774290 | − | 0.632831i | \(-0.781893\pi\) |
0.935193 | + | 0.354139i | \(0.115226\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.317344 | − | 0.549657i | −0.0177679 | − | 0.0307749i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.66931 | −0.538015 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.08444 | 0.115624 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.39762 | − | 5.88485i | −0.187317 | − | 0.324442i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.8178 | − | 27.3973i | 0.869427 | − | 1.50589i | 0.00684339 | − | 0.999977i | \(-0.497822\pi\) |
0.862583 | − | 0.505915i | \(-0.168845\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.372266 | + | 0.644784i | −0.0203391 | + | 0.0352283i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.7771 | − | 20.3985i | −0.641539 | − | 1.11118i | −0.985089 | − | 0.172044i | \(-0.944963\pi\) |
0.343550 | − | 0.939134i | \(-0.388371\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.402751 | 0.0218102 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.81359 | − | 16.9976i | −0.526821 | − | 0.912481i | −0.999512 | − | 0.0312526i | \(-0.990050\pi\) |
0.472690 | − | 0.881229i | \(-0.343283\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0363 | − | 22.5795i | 0.697816 | − | 1.20865i | −0.271406 | − | 0.962465i | \(-0.587488\pi\) |
0.969222 | − | 0.246188i | \(-0.0791782\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.30878 | − | 5.73097i | 0.176108 | − | 0.305029i | −0.764436 | − | 0.644700i | \(-0.776982\pi\) |
0.940544 | + | 0.339671i | \(0.110316\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.3720 | − | 26.6250i | −0.815859 | − | 1.41311i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.0527 | 1.21668 | 0.608338 | − | 0.793678i | \(-0.291836\pi\) | ||||
0.608338 | + | 0.793678i | \(0.291836\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1184 | −0.900968 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.3640 | − | 21.4150i | −0.647159 | − | 1.12091i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.08931 | + | 7.08289i | −0.213460 | + | 0.369724i | −0.952795 | − | 0.303614i | \(-0.901807\pi\) |
0.739335 | + | 0.673338i | \(0.235140\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.303989 | + | 0.526524i | −0.0157823 | + | 0.0273358i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.75341 | − | 13.4293i | −0.401456 | − | 0.695343i | 0.592446 | − | 0.805610i | \(-0.298163\pi\) |
−0.993902 | + | 0.110268i | \(0.964829\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.86345 | −0.0959723 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.5814 | 0.954461 | 0.477231 | − | 0.878778i | \(-0.341641\pi\) | ||||
0.477231 | + | 0.878778i | \(0.341641\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.30959 | + | 14.3926i | 0.424600 | + | 0.735429i | 0.996383 | − | 0.0849761i | \(-0.0270814\pi\) |
−0.571783 | + | 0.820405i | \(0.693748\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.924512 | + | 1.60130i | −0.0471175 | + | 0.0816099i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.9112 | + | 22.3629i | −0.654624 | + | 1.13384i | 0.327364 | + | 0.944898i | \(0.393840\pi\) |
−0.981988 | + | 0.188944i | \(0.939494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.7995 | + | 42.9541i | 1.25417 | + | 2.17228i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −37.1509 | −1.86927 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.729016 | −0.0365883 | −0.0182941 | − | 0.999833i | \(-0.505824\pi\) | ||||
−0.0182941 | + | 0.999833i | \(0.505824\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.67094 | − | 15.0185i | −0.433006 | − | 0.749989i | 0.564124 | − | 0.825690i | \(-0.309214\pi\) |
−0.997131 | + | 0.0757010i | \(0.975881\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.591238 | − | 1.02405i | 0.0294516 | − | 0.0510117i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.71928 | − | 2.97789i | 0.0852218 | − | 0.147608i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.82351 | + | 3.15841i | 0.0901668 | + | 0.156174i | 0.907581 | − | 0.419877i | \(-0.137927\pi\) |
−0.817414 | + | 0.576050i | \(0.804593\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.16373 | 0.0572635 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 39.9018 | 1.95870 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.117685 | + | 0.203836i | 0.00574927 | + | 0.00995803i | 0.868886 | − | 0.495013i | \(-0.164837\pi\) |
−0.863136 | + | 0.504971i | \(0.831503\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.8985 | + | 18.8767i | −0.531158 | + | 0.919993i | 0.468181 | + | 0.883633i | \(0.344910\pi\) |
−0.999339 | + | 0.0363601i | \(0.988424\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.29699 | + | 5.71055i | −0.159927 | + | 0.277002i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.85680 | − | 10.1443i | −0.283431 | − | 0.490916i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.28806 | 0.206549 | 0.103274 | − | 0.994653i | \(-0.467068\pi\) | ||||
0.103274 | + | 0.994653i | \(0.467068\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.9263 | −0.669257 | −0.334628 | − | 0.942350i | \(-0.608611\pi\) | ||||
−0.334628 | + | 0.942350i | \(0.608611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.82591 | − | 8.35871i | −0.230854 | − | 0.399851i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.9397 | − | 27.6084i | 0.760762 | − | 1.31768i | −0.181696 | − | 0.983355i | \(-0.558159\pi\) |
0.942458 | − | 0.334324i | \(-0.108508\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.56216 | − | 4.43780i | 0.121732 | − | 0.210846i | −0.798719 | − | 0.601705i | \(-0.794488\pi\) |
0.920451 | + | 0.390858i | \(0.127822\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.7325 | + | 20.3213i | 0.556174 | + | 0.963322i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.9914 | 1.60415 | 0.802077 | − | 0.597221i | \(-0.203728\pi\) | ||||
0.802077 | + | 0.597221i | \(0.203728\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.72209 | 0.316531 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.71436 | + | 4.70142i | 0.127251 | + | 0.220406i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.78826 | + | 4.82941i | −0.130429 | + | 0.225910i | −0.923842 | − | 0.382774i | \(-0.874969\pi\) |
0.793413 | + | 0.608684i | \(0.208302\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.24904 | − | 2.16340i | 0.0581734 | − | 0.100759i | −0.835472 | − | 0.549533i | \(-0.814806\pi\) |
0.893646 | + | 0.448774i | \(0.148139\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.77517 | + | 8.27084i | 0.221921 | + | 0.384378i | 0.955391 | − | 0.295343i | \(-0.0954340\pi\) |
−0.733470 | + | 0.679722i | \(0.762101\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.2128 | −0.842787 | −0.421393 | − | 0.906878i | \(-0.638459\pi\) | ||||
−0.421393 | + | 0.906878i | \(0.638459\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.305602 | −0.0141114 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.80935 | + | 4.86594i | 0.129174 | + | 0.223736i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.641583 | − | 1.11125i | 0.0294378 | − | 0.0509878i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.87648 | + | 4.98222i | −0.131430 | + | 0.227643i | −0.924228 | − | 0.381841i | \(-0.875290\pi\) |
0.792798 | + | 0.609484i | \(0.208623\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.04782 | − | 8.74308i | −0.230161 | − | 0.398650i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.6391 | 1.20962 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.8918 | 1.08264 | 0.541321 | − | 0.840816i | \(-0.317925\pi\) | ||||
0.541321 | + | 0.840816i | \(0.317925\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.31437 | + | 12.6689i | 0.330093 | + | 0.571738i | 0.982530 | − | 0.186105i | \(-0.0595865\pi\) |
−0.652437 | + | 0.757843i | \(0.726253\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.94744 | − | 5.10512i | 0.132746 | − | 0.229923i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.30961 | − | 10.9286i | 0.283025 | − | 0.490213i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.9579 | + | 20.7117i | 0.535308 | + | 0.927181i | 0.999148 | + | 0.0412621i | \(0.0131379\pi\) |
−0.463840 | + | 0.885919i | \(0.653529\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.57496 | −0.337751 | −0.168875 | − | 0.985637i | \(-0.554014\pi\) | ||||
−0.168875 | + | 0.985637i | \(0.554014\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.65645 | 0.162710 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.50078 | − | 6.06353i | −0.155169 | − | 0.268761i | 0.777951 | − | 0.628325i | \(-0.216259\pi\) |
−0.933121 | + | 0.359563i | \(0.882926\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.07494 | − | 8.79006i | 0.224502 | − | 0.388849i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.5037 | − | 21.6570i | 0.550978 | − | 0.954321i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.57864 | + | 4.46633i | 0.113408 | + | 0.196429i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.4564 | −1.86005 | −0.930025 | − | 0.367497i | \(-0.880215\pi\) | ||||
−0.930025 | + | 0.367497i | \(0.880215\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.6096 | −0.813743 | −0.406871 | − | 0.913485i | \(-0.633380\pi\) | ||||
−0.406871 | + | 0.913485i | \(0.633380\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.87034 | + | 3.23952i | 0.0814733 | + | 0.141116i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.2547 | + | 22.9577i | −0.576289 | + | 0.998163i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.86802 | − | 17.0919i | 0.427431 | − | 0.740333i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.55542 | + | 16.5505i | 0.413117 | + | 0.715539i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.758955 | −0.0326905 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.694443 | −0.0298564 | −0.0149282 | − | 0.999889i | \(-0.504752\pi\) | ||||
−0.0149282 | + | 0.999889i | \(0.504752\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.8313 | + | 25.6886i | 0.635304 | + | 1.10038i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.77655 | + | 15.2014i | −0.375258 | + | 0.649966i | −0.990366 | − | 0.138477i | \(-0.955779\pi\) |
0.615107 | + | 0.788443i | \(0.289113\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.573562 | + | 0.993439i | −0.0244346 | + | 0.0423219i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.62453 | − | 13.2061i | −0.324228 | − | 0.561579i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.2666 | −0.604495 | −0.302248 | − | 0.953229i | \(-0.597737\pi\) | ||||
−0.302248 | + | 0.953229i | \(0.597737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.4965 | 0.697728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.8742 | − | 29.2270i | −0.711162 | − | 1.23177i | −0.964421 | − | 0.264371i | \(-0.914836\pi\) |
0.253259 | − | 0.967399i | \(-0.418498\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.83811 | + | 8.37986i | −0.203541 | + | 0.352543i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.9867 | − | 34.6180i | 0.837886 | − | 1.45126i | −0.0537729 | − | 0.998553i | \(-0.517125\pi\) |
0.891659 | − | 0.452708i | \(-0.149542\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.2266 | − | 35.0335i | −0.846457 | − | 1.46611i | −0.884350 | − | 0.466824i | \(-0.845398\pi\) |
0.0378934 | − | 0.999282i | \(-0.487935\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.58204 | −0.274490 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.6758 | −1.31868 | −0.659340 | − | 0.751845i | \(-0.729164\pi\) | ||||
−0.659340 | + | 0.751845i | \(0.729164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.18909 | + | 14.1839i | 0.339741 | + | 0.588448i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.230714 | − | 0.399608i | 0.00955519 | − | 0.0165501i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.65220 | − | 13.2540i | 0.315840 | − | 0.547051i | −0.663776 | − | 0.747932i | \(-0.731047\pi\) |
0.979616 | + | 0.200881i | \(0.0643803\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.363962 | − | 0.630400i | −0.0149968 | − | 0.0259752i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.2583 | −1.61214 | −0.806072 | − | 0.591817i | \(-0.798411\pi\) | ||||
−0.806072 | + | 0.591817i | \(0.798411\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.1734 | −0.704041 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.77972 | + | 15.2069i | 0.358730 | + | 0.621338i | 0.987749 | − | 0.156052i | \(-0.0498766\pi\) |
−0.629019 | + | 0.777390i | \(0.716543\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.12937 | + | 15.8125i | −0.372395 | + | 0.645007i | −0.989933 | − | 0.141534i | \(-0.954797\pi\) |
0.617539 | + | 0.786541i | \(0.288130\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.6979 | + | 21.9933i | −0.516241 | + | 0.894156i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.71415 | + | 6.43310i | 0.150753 | + | 0.261112i | 0.931504 | − | 0.363730i | \(-0.118497\pi\) |
−0.780752 | + | 0.624842i | \(0.785164\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.1418 | 0.612570 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.8772 | −1.61062 | −0.805312 | − | 0.592851i | \(-0.798002\pi\) | ||||
−0.805312 | + | 0.592851i | \(0.798002\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.187473 | + | 0.324713i | 0.00754739 | + | 0.0130725i | 0.869774 | − | 0.493450i | \(-0.164264\pi\) |
−0.862227 | + | 0.506522i | \(0.830931\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.95166 | − | 12.0406i | 0.279411 | − | 0.483954i | −0.691828 | − | 0.722063i | \(-0.743194\pi\) |
0.971238 | + | 0.238109i | \(0.0765275\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.81575 | + | 8.34113i | −0.192939 | + | 0.334180i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.4011 | + | 24.9434i | 0.576043 | + | 0.997736i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.9368 | 1.27341 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.6049 | 1.13874 | 0.569372 | − | 0.822080i | \(-0.307187\pi\) | ||||
0.569372 | + | 0.822080i | \(0.307187\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.1953 | + | 33.2472i | 0.761740 | + | 1.31937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.11414 | + | 1.92976i | −0.0441440 | + | 0.0764597i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.9011 | + | 18.8812i | −0.430566 | + | 0.745762i | −0.996922 | − | 0.0783986i | \(-0.975019\pi\) |
0.566356 | + | 0.824161i | \(0.308353\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.9205 | + | 36.2354i | 0.825025 | + | 1.42899i | 0.901900 | + | 0.431945i | \(0.142172\pi\) |
−0.0768751 | + | 0.997041i | \(0.524494\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.2614 | −0.678615 | −0.339308 | − | 0.940675i | \(-0.610193\pi\) | ||||
−0.339308 | + | 0.940675i | \(0.610193\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.883220 | −0.0346694 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.237661 | + | 0.411641i | 0.00930039 | + | 0.0161087i | 0.870638 | − | 0.491924i | \(-0.163706\pi\) |
−0.861338 | + | 0.508033i | \(0.830373\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.4663 | − | 25.0564i | 0.565247 | − | 0.979036i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.2344 | − | 31.5828i | 0.710310 | − | 1.23029i | −0.254431 | − | 0.967091i | \(-0.581888\pi\) |
0.964741 | − | 0.263201i | \(-0.0847784\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.04982 | − | 8.74655i | −0.196415 | − | 0.340201i | 0.750948 | − | 0.660361i | \(-0.229597\pi\) |
−0.947364 | + | 0.320160i | \(0.896263\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.34189 | 0.129593 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.88422 | 0.227838 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.44505 | + | 7.69905i | 0.171599 | + | 0.297218i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.51044 | − | 16.4726i | 0.366600 | − | 0.634971i | −0.622431 | − | 0.782675i | \(-0.713855\pi\) |
0.989032 | + | 0.147704i | \(0.0471883\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.6374 | + | 39.2091i | −0.870024 | + | 1.50693i | −0.00805435 | + | 0.999968i | \(0.502564\pi\) |
−0.861970 | + | 0.506959i | \(0.830770\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.46718 | + | 9.46943i | 0.209811 | + | 0.363403i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 45.5318 | 1.74222 | 0.871112 | − | 0.491084i | \(-0.163399\pi\) | ||||
0.871112 | + | 0.491084i | \(0.163399\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −49.6363 | −1.89651 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.677375 | − | 1.17325i | −0.0258059 | − | 0.0446972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.09446 | − | 14.0200i | 0.307928 | − | 0.533347i | −0.669981 | − | 0.742378i | \(-0.733698\pi\) |
0.977909 | + | 0.209031i | \(0.0670311\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.63746 | + | 13.2285i | −0.289706 | + | 0.501785i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.2168 | + | 54.0691i | 1.18242 | + | 2.04801i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.61120 | 0.0986238 | 0.0493119 | − | 0.998783i | \(-0.484297\pi\) | ||||
0.0493119 | + | 0.998783i | \(0.484297\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.21480 | −0.234396 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.750417 | + | 1.29976i | 0.0282223 | + | 0.0488825i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.1702 | + | 40.1319i | −0.870175 | + | 1.50719i | −0.00835896 | + | 0.999965i | \(0.502661\pi\) |
−0.861816 | + | 0.507222i | \(0.830673\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.86696 | + | 3.23366i | −0.0699180 | + | 0.121102i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.06008 | − | 3.56816i | −0.0770426 | − | 0.133442i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 46.2069 | 1.72323 | 0.861614 | − | 0.507564i | \(-0.169454\pi\) | ||||
0.861614 | + | 0.507564i | \(0.169454\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.2646 | 0.382273 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.391140 | + | 0.677475i | 0.0145266 | + | 0.0251608i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.72988 | − | 16.8526i | 0.360861 | − | 0.625030i | −0.627242 | − | 0.778825i | \(-0.715816\pi\) |
0.988103 | + | 0.153795i | \(0.0491494\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.0928 | + | 45.1940i | −0.965077 | + | 1.67156i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.68617 | − | 13.3128i | −0.283895 | − | 0.491721i | 0.688445 | − | 0.725288i | \(-0.258293\pi\) |
−0.972341 | + | 0.233567i | \(0.924960\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.231938 | 0.00854356 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.4962 | −1.19539 | −0.597696 | − | 0.801723i | \(-0.703917\pi\) | ||||
−0.597696 | + | 0.801723i | \(0.703917\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.8664 | + | 36.1417i | 0.765514 | + | 1.32591i | 0.939974 | + | 0.341245i | \(0.110849\pi\) |
−0.174460 | + | 0.984664i | \(0.555818\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.98542 | − | 10.3671i | 0.219289 | − | 0.379819i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.92214 | + | 6.79335i | −0.143312 | + | 0.248224i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.02452 | − | 8.70273i | −0.183347 | − | 0.317567i | 0.759671 | − | 0.650308i | \(-0.225360\pi\) |
−0.943018 | + | 0.332741i | \(0.892027\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.6859 | 0.498081 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.7989 | −1.15575 | −0.577876 | − | 0.816125i | \(-0.696118\pi\) | ||||
−0.577876 | + | 0.816125i | \(0.696118\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.4352 | − | 47.5192i | −0.994526 | − | 1.72257i | −0.587751 | − | 0.809042i | \(-0.699987\pi\) |
−0.406775 | − | 0.913528i | \(-0.633347\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.08770 | + | 10.5442i | −0.220389 | + | 0.381726i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.29657 | + | 2.24572i | −0.0468163 | + | 0.0810882i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.39041 | + | 9.33646i | 0.194383 | + | 0.336681i | 0.946698 | − | 0.322122i | \(-0.104396\pi\) |
−0.752315 | + | 0.658804i | \(0.771063\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.4885 | 1.70804 | 0.854022 | − | 0.520237i | \(-0.174156\pi\) | ||||
0.854022 | + | 0.520237i | \(0.174156\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.496407 | −0.0178315 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.07469 | − | 10.5217i | −0.217648 | − | 0.376978i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.78871 | + | 8.29428i | −0.171353 | + | 0.296793i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.1360 | − | 43.5368i | 0.897141 | − | 1.55389i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.0563 | + | 20.8820i | 0.429759 | + | 0.744364i | 0.996852 | − | 0.0792896i | \(-0.0252652\pi\) |
−0.567093 | + | 0.823654i | \(0.691932\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.97173 | −0.141218 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.1013 | 0.926885 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.54620 | − | 13.0704i | −0.267300 | − | 0.462978i | 0.700863 | − | 0.713295i | \(-0.252798\pi\) |
−0.968164 | + | 0.250318i | \(0.919465\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.9500 | + | 41.4826i | −0.847289 | + | 1.46755i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.85165 | + | 6.67125i | −0.135922 | + | 0.235423i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.57117 | − | 14.8457i | −0.302094 | − | 0.523242i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.1104 | −0.707043 | −0.353522 | − | 0.935426i | \(-0.615016\pi\) | ||||
−0.353522 | + | 0.935426i | \(0.615016\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.9770 | −1.43890 | −0.719448 | − | 0.694546i | \(-0.755605\pi\) | ||||
−0.719448 | + | 0.694546i | \(0.755605\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.03095 | + | 10.4459i | 0.211255 | + | 0.365904i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.07757 | − | 8.79461i | 0.177642 | − | 0.307684i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.9427 | + | 20.6854i | −0.416803 | + | 0.721925i | −0.995616 | − | 0.0935360i | \(-0.970183\pi\) |
0.578813 | + | 0.815461i | \(0.303516\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.9451 | − | 25.8857i | −0.520954 | − | 0.902319i | −0.999703 | − | 0.0243673i | \(-0.992243\pi\) |
0.478749 | − | 0.877952i | \(-0.341090\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.7265 | 1.55529 | 0.777647 | − | 0.628702i | \(-0.216413\pi\) | ||||
0.777647 | + | 0.628702i | \(0.216413\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.8943 | 1.28139 | 0.640695 | − | 0.767795i | \(-0.278646\pi\) | ||||
0.640695 | + | 0.767795i | \(0.278646\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.52452 | − | 6.10465i | −0.122117 | − | 0.211514i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.18370 | − | 2.05023i | 0.0409636 | − | 0.0709511i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.918446 | − | 1.59080i | 0.0317083 | − | 0.0549204i | −0.849736 | − | 0.527209i | \(-0.823239\pi\) |
0.881444 | + | 0.472288i | \(0.156572\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.1503 | + | 24.5091i | 0.487942 | + | 0.845141i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.5748 | 0.673394 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.4240 | −0.358172 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.9395 | + | 27.6081i | 0.546400 | + | 0.946392i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.0385 | − | 45.1000i | 0.891542 | − | 1.54420i | 0.0535152 | − | 0.998567i | \(-0.482957\pi\) |
0.838027 | − | 0.545629i | \(-0.183709\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.46663 | + | 16.3967i | −0.323374 | + | 0.560100i | −0.981182 | − | 0.193086i | \(-0.938150\pi\) |
0.657808 | + | 0.753186i | \(0.271484\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00700 | + | 6.94033i | 0.136717 | + | 0.236801i | 0.926252 | − | 0.376905i | \(-0.123012\pi\) |
−0.789535 | + | 0.613706i | \(0.789678\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.8647 | 0.812364 | 0.406182 | − | 0.913792i | \(-0.366860\pi\) | ||||
0.406182 | + | 0.913792i | \(0.366860\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43.4125 | −1.47607 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.78667 | + | 10.0228i | 0.196299 | + | 0.340001i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.340485 | − | 0.589738i | 0.0115369 | − | 0.0199825i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.95119 | + | 8.57572i | −0.167381 | + | 0.289912i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.0238 | + | 29.4861i | 0.574853 | + | 0.995674i | 0.996058 | + | 0.0887086i | \(0.0282740\pi\) |
−0.421205 | + | 0.906965i | \(0.638393\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.8018 | 1.30727 | 0.653633 | − | 0.756812i | \(-0.273244\pi\) | ||||
0.653633 | + | 0.756812i | \(0.273244\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.0944 | −1.41659 | −0.708294 | − | 0.705917i | \(-0.750535\pi\) | ||||
−0.708294 | + | 0.705917i | \(0.750535\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.1168 | + | 20.9869i | 0.406841 | + | 0.704670i | 0.994534 | − | 0.104414i | \(-0.0332968\pi\) |
−0.587692 | + | 0.809084i | \(0.699964\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.87893 | + | 13.6467i | −0.264251 | + | 0.457696i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.66058 | − | 8.07236i | 0.155960 | − | 0.270131i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.9201 | + | 22.3783i | 0.431873 | + | 0.748025i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.443778 | 0.0148008 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.28566 | 0.142776 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.1319 | + | 52.1900i | 1.00162 | + | 1.73485i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.9424 | − | 22.4170i | 0.429747 | − | 0.744343i | −0.567104 | − | 0.823646i | \(-0.691936\pi\) |
0.996851 | + | 0.0793031i | \(0.0252695\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.9571 | + | 38.0308i | −0.727471 | + | 1.26002i | 0.230478 | + | 0.973078i | \(0.425971\pi\) |
−0.957949 | + | 0.286939i | \(0.907362\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.21514 | − | 10.7649i | −0.205691 | − | 0.356268i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.8758 | 0.392173 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.4335 | 1.36677 | 0.683383 | − | 0.730060i | \(-0.260508\pi\) | ||||
0.683383 | + | 0.730060i | \(0.260508\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.0596 | + | 24.3520i | 0.462779 | + | 0.801556i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.11909 | + | 3.67037i | −0.0696752 | + | 0.120681i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.56911 | + | 2.71778i | −0.0514808 | + | 0.0891674i | −0.890617 | − | 0.454753i | \(-0.849727\pi\) |
0.839137 | + | 0.543921i | \(0.183061\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.685860 | + | 1.18794i | 0.0224781 | + | 0.0389333i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.0338 | 0.426252 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.2810 | 0.335866 | 0.167933 | − | 0.985798i | \(-0.446291\pi\) | ||||
0.167933 | + | 0.985798i | \(0.446291\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.23844 | − | 12.5373i | −0.235966 | − | 0.408706i | 0.723587 | − | 0.690234i | \(-0.242492\pi\) |
−0.959553 | + | 0.281528i | \(0.909159\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.1603 | + | 53.9713i | −1.01472 | + | 1.75755i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.8714 | − | 25.7580i | 0.483256 | − | 0.837024i | −0.516559 | − | 0.856251i | \(-0.672787\pi\) |
0.999815 | + | 0.0192278i | \(0.00612078\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.3084 | + | 19.5868i | 0.367088 | + | 0.635814i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.4869 | −0.631242 | −0.315621 | − | 0.948885i | \(-0.602213\pi\) | ||||
−0.315621 | + | 0.948885i | \(0.602213\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.0769 | 1.45866 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.1869 | − | 17.6443i | −0.328953 | − | 0.569763i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3592 | − | 26.6029i | 0.495458 | − | 0.858158i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.0872 | − | 34.7921i | 0.646631 | − | 1.12000i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.94942 | + | 12.0368i | 0.223478 | + | 0.387076i | 0.955862 | − | 0.293817i | \(-0.0949255\pi\) |
−0.732384 | + | 0.680892i | \(0.761592\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.2406 | −0.617460 | −0.308730 | − | 0.951150i | \(-0.599904\pi\) | ||||
−0.308730 | + | 0.951150i | \(0.599904\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.26978 | −0.201000 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.44479 | + | 4.23450i | 0.0782158 | + | 0.135474i | 0.902480 | − | 0.430731i | \(-0.141744\pi\) |
−0.824264 | + | 0.566205i | \(0.808411\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.65494 | − | 6.33054i | 0.116812 | − | 0.202325i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.9670 | + | 25.9236i | −0.477373 | + | 0.826834i | −0.999664 | − | 0.0259332i | \(-0.991744\pi\) |
0.522291 | + | 0.852768i | \(0.325078\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.5754 | + | 18.3172i | 0.336962 | + | 0.583634i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −52.0912 | −1.65640 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.36157 | −0.297380 | −0.148690 | − | 0.988884i | \(-0.547506\pi\) | ||||
−0.148690 | + | 0.988884i | \(0.547506\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.4311 | − | 40.5839i | −0.742817 | − | 1.28660i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.8210 | − | 41.2592i | 0.754420 | − | 1.30669i | −0.191242 | − | 0.981543i | \(-0.561252\pi\) |
0.945662 | − | 0.325151i | \(-0.105415\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1512.2.r.d.505.4 | 8 | ||
3.2 | odd | 2 | 504.2.r.d.169.3 | ✓ | 8 | ||
4.3 | odd | 2 | 3024.2.r.l.2017.4 | 8 | |||
9.2 | odd | 6 | 4536.2.a.x.1.4 | 4 | |||
9.4 | even | 3 | inner | 1512.2.r.d.1009.4 | 8 | ||
9.5 | odd | 6 | 504.2.r.d.337.3 | yes | 8 | ||
9.7 | even | 3 | 4536.2.a.ba.1.1 | 4 | |||
12.11 | even | 2 | 1008.2.r.m.673.2 | 8 | |||
36.7 | odd | 6 | 9072.2.a.cl.1.1 | 4 | |||
36.11 | even | 6 | 9072.2.a.ce.1.4 | 4 | |||
36.23 | even | 6 | 1008.2.r.m.337.2 | 8 | |||
36.31 | odd | 6 | 3024.2.r.l.1009.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.d.169.3 | ✓ | 8 | 3.2 | odd | 2 | ||
504.2.r.d.337.3 | yes | 8 | 9.5 | odd | 6 | ||
1008.2.r.m.337.2 | 8 | 36.23 | even | 6 | |||
1008.2.r.m.673.2 | 8 | 12.11 | even | 2 | |||
1512.2.r.d.505.4 | 8 | 1.1 | even | 1 | trivial | ||
1512.2.r.d.1009.4 | 8 | 9.4 | even | 3 | inner | ||
3024.2.r.l.1009.4 | 8 | 36.31 | odd | 6 | |||
3024.2.r.l.2017.4 | 8 | 4.3 | odd | 2 | |||
4536.2.a.x.1.4 | 4 | 9.2 | odd | 6 | |||
4536.2.a.ba.1.1 | 4 | 9.7 | even | 3 | |||
9072.2.a.ce.1.4 | 4 | 36.11 | even | 6 | |||
9072.2.a.cl.1.1 | 4 | 36.7 | odd | 6 |