Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3456,2,Mod(1153,3456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3456, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3456.1153");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3456 = 2^{7} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3456.i (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: | \(27.5962989386\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.8528759163648.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 1152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1153.4 | ||
Root | \(1.72806 + 0.117480i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3456.1153 |
Dual form | 3456.2.i.f.2305.4 |
$q$-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 \(\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times\).
\(n\) | \(2053\) | \(2431\) | \(2945\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | 0.705463 | + | 1.22190i | 0.315493 | + | 0.546449i | 0.979542 | − | 0.201239i | \(-0.0644969\pi\) |
−0.664049 | + | 0.747689i | \(0.731164\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.17123 | − | 2.02864i | 0.442685 | − | 0.766753i | −0.555203 | − | 0.831715i | \(-0.687359\pi\) |
0.997888 | + | 0.0649620i | \(0.0206926\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.30116 | − | 2.25368i | 0.392315 | − | 0.679510i | −0.600439 | − | 0.799670i | \(-0.705008\pi\) |
0.992754 | + | 0.120161i | \(0.0383409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.26229 | − | 2.18635i | −0.350096 | − | 0.606385i | 0.636170 | − | 0.771549i | \(-0.280518\pi\) |
−0.986266 | + | 0.165164i | \(0.947185\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.94479 | −1.19929 | −0.599644 | − | 0.800267i | \(-0.704691\pi\) | ||||
−0.599644 | + | 0.800267i | \(0.704691\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00929 | −0.231546 | −0.115773 | − | 0.993276i | \(-0.536935\pi\) | ||||
−0.115773 | + | 0.993276i | \(0.536935\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.50663 | + | 2.60955i | 0.314153 | + | 0.544129i | 0.979257 | − | 0.202622i | \(-0.0649461\pi\) |
−0.665104 | + | 0.746751i | \(0.731613\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.50464 | − | 2.60612i | 0.300929 | − | 0.521224i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0708926 | + | 0.122790i | −0.0131644 | + | 0.0228015i | −0.872533 | − | 0.488556i | \(-0.837524\pi\) |
0.859368 | + | 0.511357i | \(0.170857\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.77135 | − | 8.26422i | −0.856960 | − | 1.48430i | −0.874815 | − | 0.484458i | \(-0.839017\pi\) |
0.0178546 | − | 0.999841i | \(-0.494316\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.30505 | 0.558656 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.00324 | −1.48012 | −0.740062 | − | 0.672539i | \(-0.765204\pi\) | ||||
−0.740062 | + | 0.672539i | \(0.765204\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.33084 | − | 7.50123i | −0.676364 | − | 1.17150i | −0.976068 | − | 0.217464i | \(-0.930222\pi\) |
0.299705 | − | 0.954032i | \(-0.403112\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.15717 | + | 5.46838i | −0.481464 | + | 0.833920i | −0.999774 | − | 0.0212731i | \(-0.993228\pi\) |
0.518310 | + | 0.855193i | \(0.326561\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.24898 | − | 5.62740i | 0.473912 | − | 0.820840i | −0.525642 | − | 0.850706i | \(-0.676175\pi\) |
0.999554 | + | 0.0298661i | \(0.00950808\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.756418 | + | 1.31015i | 0.108060 | + | 0.187165i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.02590 | −0.827721 | −0.413861 | − | 0.910340i | \(-0.635820\pi\) | ||||
−0.413861 | + | 0.910340i | \(0.635820\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.67169 | 0.495090 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.64142 | + | 9.77123i | 0.734451 | + | 1.27211i | 0.954964 | + | 0.296722i | \(0.0958935\pi\) |
−0.220513 | + | 0.975384i | \(0.570773\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.45856 | − | 5.99040i | 0.442823 | − | 0.766992i | −0.555075 | − | 0.831801i | \(-0.687310\pi\) |
0.997898 | + | 0.0648083i | \(0.0206436\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.78100 | − | 3.08478i | 0.220906 | − | 0.382620i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.154962 | + | 0.268402i | 0.0189316 | + | 0.0327905i | 0.875336 | − | 0.483515i | \(-0.160640\pi\) |
−0.856404 | + | 0.516306i | \(0.827307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.24940 | −0.979023 | −0.489512 | − | 0.871997i | \(-0.662825\pi\) | ||||
−0.489512 | + | 0.871997i | \(0.662825\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.78931 | −0.794628 | −0.397314 | − | 0.917683i | \(-0.630058\pi\) | ||||
−0.397314 | + | 0.917683i | \(0.630058\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.04793 | − | 5.27917i | −0.347344 | − | 0.601618i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.99530 | + | 8.65211i | −0.562015 | + | 0.973438i | 0.435306 | + | 0.900283i | \(0.356640\pi\) |
−0.997321 | + | 0.0731553i | \(0.976693\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.47041 | + | 6.01093i | −0.380928 | + | 0.659786i | −0.991195 | − | 0.132410i | \(-0.957729\pi\) |
0.610268 | + | 0.792195i | \(0.291062\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.48837 | − | 6.04203i | −0.378367 | − | 0.655351i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.8969 | −1.68507 | −0.842535 | − | 0.538642i | \(-0.818938\pi\) | ||||
−0.842535 | + | 0.538642i | \(0.818938\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.91375 | −0.619930 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.712014 | − | 1.23325i | −0.0730511 | − | 0.126528i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.44449 | − | 12.8942i | 0.755874 | − | 1.30921i | −0.189065 | − | 0.981965i | \(-0.560546\pi\) |
0.944939 | − | 0.327247i | \(-0.106121\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.823082 | + | 1.42562i | −0.0818997 | + | 0.141855i | −0.904066 | − | 0.427393i | \(-0.859432\pi\) |
0.822166 | + | 0.569248i | \(0.192765\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.40783 | − | 11.0987i | −0.631382 | − | 1.09359i | −0.987269 | − | 0.159057i | \(-0.949155\pi\) |
0.355887 | − | 0.934529i | \(-0.384179\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.6556 | 1.32014 | 0.660070 | − | 0.751204i | \(-0.270527\pi\) | ||||
0.660070 | + | 0.751204i | \(0.270527\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.9953 | 1.24473 | 0.622363 | − | 0.782729i | \(-0.286173\pi\) | ||||
0.622363 | + | 0.782729i | \(0.286173\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.75804 | + | 6.50912i | 0.353527 | + | 0.612326i | 0.986865 | − | 0.161549i | \(-0.0516491\pi\) |
−0.633338 | + | 0.773875i | \(0.718316\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.12574 | + | 3.68189i | −0.198226 | + | 0.343338i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.79151 | + | 10.0312i | −0.530907 | + | 0.919558i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.11395 | + | 3.66148i | 0.192178 | + | 0.332861i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3005 | 1.01075 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.09832 | −0.186196 | −0.0930981 | − | 0.995657i | \(-0.529677\pi\) | ||||
−0.0930981 | + | 0.995657i | \(0.529677\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00428 | + | 6.93562i | 0.349856 | + | 0.605968i | 0.986224 | − | 0.165418i | \(-0.0528973\pi\) |
−0.636368 | + | 0.771386i | \(0.719564\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.18211 | + | 2.04748i | −0.102502 | + | 0.177539i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.17445 | + | 2.03420i | −0.100340 | + | 0.173793i | −0.911825 | − | 0.410580i | \(-0.865326\pi\) |
0.811485 | + | 0.584373i | \(0.198660\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.62654 | + | 9.74546i | 0.477237 | + | 0.826599i | 0.999660 | − | 0.0260876i | \(-0.00830490\pi\) |
−0.522422 | + | 0.852687i | \(0.674972\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.56978 | −0.549392 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.200049 | −0.0166131 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.9924 | − | 20.7715i | −0.982458 | − | 1.70167i | −0.652729 | − | 0.757591i | \(-0.726376\pi\) |
−0.329729 | − | 0.944076i | \(-0.606957\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.56507 | − | 11.3710i | 0.534258 | − | 0.925362i | −0.464941 | − | 0.885342i | \(-0.653924\pi\) |
0.999199 | − | 0.0400204i | \(-0.0127423\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.73203 | − | 11.6602i | 0.540729 | − | 0.936571i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.6217 | − | 20.1293i | −0.927511 | − | 1.60650i | −0.787473 | − | 0.616350i | \(-0.788611\pi\) |
−0.140038 | − | 0.990146i | \(-0.544722\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.05845 | 0.556284 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.5825 | 1.76879 | 0.884397 | − | 0.466735i | \(-0.154570\pi\) | ||||
0.884397 | + | 0.466735i | \(0.154570\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.4260 | − | 21.5224i | −0.961549 | − | 1.66545i | −0.718614 | − | 0.695409i | \(-0.755223\pi\) |
−0.242935 | − | 0.970043i | \(-0.578110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.31325 | − | 5.73871i | 0.254865 | − | 0.441439i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.98389 | + | 6.90030i | −0.302890 | + | 0.524620i | −0.976789 | − | 0.214203i | \(-0.931285\pi\) |
0.673900 | + | 0.738823i | \(0.264618\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.52458 | − | 6.10475i | −0.266433 | − | 0.461476i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.70760 | 0.277119 | 0.138560 | − | 0.990354i | \(-0.455753\pi\) | ||||
0.138560 | + | 0.990354i | \(0.455753\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0683 | 0.971362 | 0.485681 | − | 0.874136i | \(-0.338572\pi\) | ||||
0.485681 | + | 0.874136i | \(0.338572\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.35146 | − | 11.0010i | −0.466968 | − | 0.808813i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.43398 | + | 11.1440i | −0.470499 | + | 0.814928i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.157984 | − | 0.273636i | 0.0114313 | − | 0.0197996i | −0.860253 | − | 0.509867i | \(-0.829695\pi\) |
0.871684 | + | 0.490068i | \(0.163028\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0237 | − | 17.3616i | −0.721522 | − | 1.24971i | −0.960390 | − | 0.278661i | \(-0.910109\pi\) |
0.238867 | − | 0.971052i | \(-0.423224\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.5586 | −1.67848 | −0.839240 | − | 0.543761i | \(-0.817000\pi\) | ||||
−0.839240 | + | 0.543761i | \(0.817000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.249396 | −0.0176792 | −0.00883960 | − | 0.999961i | \(-0.502814\pi\) | ||||
−0.00883960 | + | 0.999961i | \(0.502814\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.166064 | + | 0.287631i | 0.0116554 | + | 0.0201877i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.11050 | − | 10.5837i | 0.426776 | − | 0.739197i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.31325 | + | 2.27461i | −0.0908391 | + | 0.157338i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.17490 | + | 2.03499i | 0.0808834 | + | 0.140094i | 0.903630 | − | 0.428315i | \(-0.140893\pi\) |
−0.822746 | + | 0.568409i | \(0.807559\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.90907 | −0.607593 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.3535 | −1.51745 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.24177 | + | 10.8111i | 0.419867 | + | 0.727230i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.71439 | − | 8.16556i | 0.315699 | − | 0.546806i | −0.663887 | − | 0.747833i | \(-0.731094\pi\) |
0.979586 | + | 0.201027i | \(0.0644277\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.0231851 | + | 0.0401577i | −0.00153885 | + | 0.00266536i | −0.866794 | − | 0.498667i | \(-0.833823\pi\) |
0.865255 | + | 0.501332i | \(0.167156\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.03468 | − | 6.98827i | −0.266619 | − | 0.461798i | 0.701367 | − | 0.712800i | \(-0.252573\pi\) |
−0.967987 | + | 0.251002i | \(0.919240\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.99336 | −0.261614 | −0.130807 | − | 0.991408i | \(-0.541757\pi\) | ||||
−0.130807 | + | 0.991408i | \(0.541757\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.16814 | 0.598063 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.84910 | − | 3.20273i | −0.119608 | − | 0.207167i | 0.800004 | − | 0.599994i | \(-0.204830\pi\) |
−0.919612 | + | 0.392827i | \(0.871497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0879 | − | 22.6689i | 0.843066 | − | 1.46023i | −0.0442246 | − | 0.999022i | \(-0.514082\pi\) |
0.887290 | − | 0.461211i | \(-0.152585\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.06725 | + | 1.84853i | −0.0681841 | + | 0.118098i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.27401 | + | 2.20665i | 0.0810635 | + | 0.140406i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.7393 | −1.24593 | −0.622967 | − | 0.782248i | \(-0.714073\pi\) | ||||
−0.622967 | + | 0.782248i | \(0.714073\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.84146 | 0.492988 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.53591 | + | 6.12438i | 0.220564 | + | 0.382028i | 0.954979 | − | 0.296672i | \(-0.0958769\pi\) |
−0.734415 | + | 0.678700i | \(0.762544\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.5449 | + | 18.2643i | −0.655229 | + | 1.13489i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.03211 | − | 6.98383i | 0.248631 | − | 0.430641i | −0.714515 | − | 0.699620i | \(-0.753353\pi\) |
0.963146 | + | 0.268979i | \(0.0866861\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.25105 | − | 7.36304i | −0.261140 | − | 0.452308i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.76619 | −0.534484 | −0.267242 | − | 0.963629i | \(-0.586112\pi\) | ||||
−0.267242 | + | 0.963629i | \(0.586112\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.7606 | 1.68634 | 0.843168 | − | 0.537650i | \(-0.180688\pi\) | ||||
0.843168 | + | 0.537650i | \(0.180688\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.91557 | − | 6.78197i | −0.236118 | − | 0.408968i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.7727 | + | 23.8551i | −0.827524 | + | 1.43331i | 0.0724506 | + | 0.997372i | \(0.476918\pi\) |
−0.899975 | + | 0.435942i | \(0.856415\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.24109 | + | 5.61373i | −0.193347 | + | 0.334887i | −0.946357 | − | 0.323122i | \(-0.895268\pi\) |
0.753010 | + | 0.658009i | \(0.228601\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.32863 | − | 5.76536i | −0.197866 | − | 0.342715i | 0.749970 | − | 0.661472i | \(-0.230068\pi\) |
−0.947836 | + | 0.318757i | \(0.896735\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.2897 | −1.19766 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.45099 | 0.438293 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.61375 | − | 4.52714i | −0.152697 | − | 0.264479i | 0.779521 | − | 0.626376i | \(-0.215462\pi\) |
−0.932218 | + | 0.361897i | \(0.882129\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.95963 | + | 13.7865i | −0.463428 | + | 0.802681i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.80360 | − | 6.58802i | 0.219968 | − | 0.380995i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.39557 | + | 12.8095i | 0.426274 | + | 0.738328i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.75955 | 0.558830 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.8311 | 0.903531 | 0.451765 | − | 0.892137i | \(-0.350794\pi\) | ||||
0.451765 | + | 0.892137i | \(0.350794\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.40298 | − | 2.43003i | −0.0795557 | − | 0.137794i | 0.823503 | − | 0.567312i | \(-0.192017\pi\) |
−0.903058 | + | 0.429518i | \(0.858683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.35704 | + | 12.7428i | −0.415845 | + | 0.720264i | −0.995517 | − | 0.0945858i | \(-0.969847\pi\) |
0.579672 | + | 0.814850i | \(0.303181\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.668345 | − | 1.15761i | 0.0375380 | − | 0.0650178i | −0.846646 | − | 0.532156i | \(-0.821382\pi\) |
0.884184 | + | 0.467139i | \(0.154715\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.184486 | + | 0.319538i | 0.0103292 | + | 0.0178907i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.99071 | 0.277691 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.59719 | −0.421416 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.61063 | − | 13.1820i | −0.419588 | − | 0.726747i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.69612 | − | 4.66981i | 0.148192 | − | 0.256676i | −0.782367 | − | 0.622817i | \(-0.785988\pi\) |
0.930559 | + | 0.366141i | \(0.119321\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.218640 | + | 0.378695i | −0.0119456 | + | 0.0206903i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.8198 | + | 20.4725i | 0.643866 | + | 1.11521i | 0.984562 | + | 0.175035i | \(0.0560039\pi\) |
−0.340696 | + | 0.940173i | \(0.610663\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.8332 | −1.34479 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9411 | 1.07672 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.649676 | + | 1.12527i | 0.0348764 | + | 0.0604077i | 0.882937 | − | 0.469492i | \(-0.155563\pi\) |
−0.848060 | + | 0.529900i | \(0.822230\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.27720 | + | 10.8724i | −0.336011 | + | 0.581988i | −0.983678 | − | 0.179935i | \(-0.942411\pi\) |
0.647668 | + | 0.761923i | \(0.275745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.71760 | − | 13.3673i | 0.410766 | − | 0.711468i | −0.584207 | − | 0.811604i | \(-0.698595\pi\) |
0.994974 | + | 0.100136i | \(0.0319278\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.81965 | − | 10.0799i | −0.308875 | − | 0.534987i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.8687 | 1.52363 | 0.761817 | − | 0.647792i | \(-0.224308\pi\) | ||||
0.761817 | + | 0.647792i | \(0.224308\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9813 | −0.946386 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.78961 | − | 8.29584i | −0.250699 | − | 0.434224i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.959507 | + | 1.66192i | −0.0500859 | + | 0.0867513i | −0.889981 | − | 0.455997i | \(-0.849283\pi\) |
0.839896 | + | 0.542748i | \(0.182616\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.05775 | + | 12.2244i | −0.366420 | + | 0.634658i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.71108 | − | 8.15984i | −0.243931 | − | 0.422500i | 0.717900 | − | 0.696147i | \(-0.245104\pi\) |
−0.961830 | + | 0.273646i | \(0.911770\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.357948 | 0.0184353 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.1191 | 0.827984 | 0.413992 | − | 0.910281i | \(-0.364134\pi\) | ||||
0.413992 | + | 0.910281i | \(0.364134\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.35380 | + | 7.54100i | 0.222469 | + | 0.385327i | 0.955557 | − | 0.294806i | \(-0.0952552\pi\) |
−0.733088 | + | 0.680133i | \(0.761922\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.30041 | − | 7.44853i | 0.219169 | − | 0.379612i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.1015 | − | 17.4963i | 0.512167 | − | 0.887099i | −0.487734 | − | 0.872993i | \(-0.662176\pi\) |
0.999900 | − | 0.0141065i | \(-0.00449040\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.44995 | − | 12.9037i | −0.376760 | − | 0.652568i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.0960 | −0.709246 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.3319 | 1.77326 | 0.886628 | − | 0.462483i | \(-0.153041\pi\) | ||||
0.886628 | + | 0.462483i | \(0.153041\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.03813 | − | 8.72630i | −0.251592 | − | 0.435771i | 0.712372 | − | 0.701802i | \(-0.247621\pi\) |
−0.963964 | + | 0.266031i | \(0.914288\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0457 | + | 20.8637i | −0.600037 | + | 1.03930i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.7147 | + | 20.2904i | −0.580675 | + | 1.00576i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.08466 | + | 3.61073i | 0.103080 | + | 0.178539i | 0.912952 | − | 0.408067i | \(-0.133797\pi\) |
−0.809872 | + | 0.586606i | \(0.800464\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.4297 | 1.30052 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.79300 | −0.480719 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.13944 | − | 14.0979i | −0.397638 | − | 0.688729i | 0.595796 | − | 0.803136i | \(-0.296837\pi\) |
−0.993434 | + | 0.114407i | \(0.963503\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.90585 | + | 11.9613i | −0.336570 | + | 0.582957i | −0.983785 | − | 0.179351i | \(-0.942600\pi\) |
0.647215 | + | 0.762308i | \(0.275934\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.44015 | + | 12.8867i | −0.360900 | + | 0.625098i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.10157 | − | 14.0323i | −0.392063 | − | 0.679072i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.2716 | −0.639268 | −0.319634 | − | 0.947541i | \(-0.603560\pi\) | ||||
−0.319634 | + | 0.947541i | \(0.603560\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.32495 | −0.207844 | −0.103922 | − | 0.994585i | \(-0.533139\pi\) | ||||
−0.103922 | + | 0.994585i | \(0.533139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.52062 | − | 2.63379i | −0.0727410 | − | 0.125991i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.69938 | + | 16.7998i | −0.462926 | + | 0.801812i | −0.999105 | − | 0.0422926i | \(-0.986534\pi\) |
0.536179 | + | 0.844104i | \(0.319867\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.1280 | + | 26.2025i | −0.718754 | + | 1.24492i | 0.242740 | + | 0.970091i | \(0.421954\pi\) |
−0.961494 | + | 0.274827i | \(0.911380\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.2147 | − | 19.4244i | −0.531627 | − | 0.920806i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.49691 | 0.400994 | 0.200497 | − | 0.979694i | \(-0.435744\pi\) | ||||
0.200497 | + | 0.979694i | \(0.435744\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.5405 | −1.06139 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.17194 | − | 7.22601i | −0.195583 | − | 0.338760i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.8223 | + | 27.4050i | −0.740136 | + | 1.28195i | 0.212297 | + | 0.977205i | \(0.431906\pi\) |
−0.952433 | + | 0.304748i | \(0.901428\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.62685 | − | 16.6742i | 0.448367 | − | 0.776594i | −0.549913 | − | 0.835222i | \(-0.685339\pi\) |
0.998280 | + | 0.0586276i | \(0.0186725\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.46981 | − | 12.9381i | −0.347151 | − | 0.601284i | 0.638591 | − | 0.769546i | \(-0.279518\pi\) |
−0.985742 | + | 0.168263i | \(0.946184\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 39.9590 | 1.84908 | 0.924540 | − | 0.381084i | \(-0.124449\pi\) | ||||
0.924540 | + | 0.381084i | \(0.124449\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.725987 | 0.0335230 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.21598 | + | 14.2305i | 0.377771 | + | 0.654319i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.51862 | + | 2.63032i | −0.0696789 | + | 0.120687i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.1993 | − | 28.0581i | 0.740167 | − | 1.28201i | −0.212252 | − | 0.977215i | \(-0.568080\pi\) |
0.952419 | − | 0.304792i | \(-0.0985869\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.3647 | + | 19.6843i | 0.518186 | + | 0.897525i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.0073 | 0.953891 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.8763 | −1.26320 | −0.631598 | − | 0.775296i | \(-0.717601\pi\) | ||||
−0.631598 | + | 0.775296i | \(0.717601\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.12126 | + | 14.0664i | 0.366507 | + | 0.634809i | 0.989017 | − | 0.147803i | \(-0.0472202\pi\) |
−0.622510 | + | 0.782612i | \(0.713887\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.350549 | − | 0.607170i | 0.0157880 | − | 0.0273455i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.66198 | + | 16.7350i | −0.433399 | + | 0.750669i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.1826 | − | 31.4932i | −0.813966 | − | 1.40983i | −0.910068 | − | 0.414459i | \(-0.863971\pi\) |
0.0961021 | − | 0.995371i | \(-0.469362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 43.2509 | 1.92846 | 0.964231 | − | 0.265063i | \(-0.0853929\pi\) | ||||
0.964231 | + | 0.265063i | \(0.0853929\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.32262 | −0.103355 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.2885 | + | 36.8728i | 0.943597 | + | 1.63436i | 0.758536 | + | 0.651632i | \(0.225915\pi\) |
0.185062 | + | 0.982727i | \(0.440751\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.95187 | + | 13.7730i | −0.351770 | + | 0.609284i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.04098 | − | 15.6594i | 0.398393 | − | 0.690037i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.45489 | − | 14.6443i | −0.371846 | − | 0.644056i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.0544 | −0.922408 | −0.461204 | − | 0.887294i | \(-0.652582\pi\) | ||||
−0.461204 | + | 0.887294i | \(0.652582\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.0092 | 0.918667 | 0.459333 | − | 0.888264i | \(-0.348088\pi\) | ||||
0.459333 | + | 0.888264i | \(0.348088\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.5934 | + | 40.8649i | 1.02774 | + | 1.78010i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.96016 | − | 12.0554i | 0.302616 | − | 0.524146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.9336 | + | 18.9375i | −0.473585 | + | 0.820273i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.63355 | + | 16.6858i | 0.416495 | + | 0.721390i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.93689 | 0.169574 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.3375 | −0.530429 | −0.265215 | − | 0.964189i | \(-0.585443\pi\) | ||||
−0.265215 | + | 0.964189i | \(0.585443\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.16772 | + | 15.8790i | 0.392702 | + | 0.680179i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.461070 | − | 0.798596i | 0.0197139 | − | 0.0341455i | −0.856000 | − | 0.516976i | \(-0.827058\pi\) |
0.875714 | + | 0.482830i | \(0.160391\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0715510 | − | 0.123930i | 0.00304817 | − | 0.00527959i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.7013 | + | 20.2673i | 0.497591 | + | 0.861853i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.1352 | −0.810786 | −0.405393 | − | 0.914142i | \(-0.632865\pi\) | ||||
−0.405393 | + | 0.914142i | \(0.632865\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.9411 | 0.674235 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.9309 | − | 29.3252i | −0.713552 | − | 1.23591i | −0.963515 | − | 0.267653i | \(-0.913752\pi\) |
0.249963 | − | 0.968255i | \(-0.419581\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.30232 | + | 9.18388i | −0.223070 | + | 0.386369i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.1745 | − | 24.5509i | 0.594225 | − | 1.02923i | −0.399431 | − | 0.916763i | \(-0.630792\pi\) |
0.993656 | − | 0.112465i | \(-0.0358745\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.9901 | − | 20.7674i | −0.501769 | − | 0.869089i | −0.999998 | − | 0.00204345i | \(-0.999350\pi\) |
0.498229 | − | 0.867045i | \(-0.333984\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.06773 | 0.378151 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.2508 | 0.426746 | 0.213373 | − | 0.976971i | \(-0.431555\pi\) | ||||
0.213373 | + | 0.976971i | \(0.431555\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.12934 | + | 14.0804i | 0.337262 | + | 0.584155i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.84068 | + | 13.5805i | −0.324728 | + | 0.562445i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.15393 | − | 3.73071i | 0.0889021 | − | 0.153983i | −0.818145 | − | 0.575012i | \(-0.804998\pi\) |
0.907047 | + | 0.421029i | \(0.138331\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.81566 | + | 8.34097i | 0.198426 | + | 0.343684i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.4046 | 1.12537 | 0.562686 | − | 0.826670i | \(-0.309768\pi\) | ||||
0.562686 | + | 0.826670i | \(0.309768\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.3428 | −0.669990 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.5711 | + | 23.5058i | 0.554500 | + | 0.960423i | 0.997942 | + | 0.0641195i | \(0.0204239\pi\) |
−0.443442 | + | 0.896303i | \(0.646243\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.7512 | − | 20.3537i | 0.479341 | − | 0.830244i | −0.520378 | − | 0.853936i | \(-0.674209\pi\) |
0.999719 | + | 0.0236923i | \(0.00754221\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.98263 | + | 5.16607i | −0.121261 | + | 0.210031i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.69717 | − | 4.67164i | −0.109475 | − | 0.189616i | 0.806083 | − | 0.591803i | \(-0.201584\pi\) |
−0.915558 | + | 0.402187i | \(0.868250\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.4046 | −0.663660 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.92486 | 0.239303 | 0.119651 | − | 0.992816i | \(-0.461822\pi\) | ||||
0.119651 | + | 0.992816i | \(0.461822\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.12456 | + | 10.6081i | 0.246566 | + | 0.427064i | 0.962571 | − | 0.271031i | \(-0.0873646\pi\) |
−0.716005 | + | 0.698095i | \(0.754031\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.656697 | + | 1.13743i | −0.0263949 | + | 0.0457173i | −0.878921 | − | 0.476967i | \(-0.841736\pi\) |
0.852526 | + | 0.522684i | \(0.175069\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.6190 | + | 32.2491i | −0.745955 | + | 1.29203i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.448881 | + | 0.777485i | 0.0179553 | + | 0.0310994i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 44.5192 | 1.77510 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.7173 | 1.14322 | 0.571608 | − | 0.820527i | \(-0.306320\pi\) | ||||
0.571608 | + | 0.820527i | \(0.306320\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.48029 | − | 2.56394i | −0.0587435 | − | 0.101747i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.90964 | − | 3.30759i | 0.0756626 | − | 0.131052i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.67893 | + | 16.7644i | −0.382295 | + | 0.662154i | −0.991390 | − | 0.130943i | \(-0.958199\pi\) |
0.609095 | + | 0.793097i | \(0.291533\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.415416 | + | 0.719521i | 0.0163824 | + | 0.0283751i | 0.874100 | − | 0.485745i | \(-0.161452\pi\) |
−0.857718 | + | 0.514120i | \(0.828118\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.1290 | 0.398211 | 0.199106 | − | 0.979978i | \(-0.436196\pi\) | ||||
0.199106 | + | 0.979978i | \(0.436196\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.3616 | 1.15254 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.0565 | + | 36.4709i | 0.824004 | + | 1.42722i | 0.902678 | + | 0.430317i | \(0.141598\pi\) |
−0.0786734 | + | 0.996900i | \(0.525068\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.64975 | + | 9.78565i | −0.220754 | + | 0.382357i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.0094 | + | 22.5329i | −0.506774 | + | 0.877759i | 0.493195 | + | 0.869919i | \(0.335829\pi\) |
−0.999969 | + | 0.00784021i | \(0.997504\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.6544 | + | 25.3822i | 0.569990 | + | 0.987252i | 0.996566 | + | 0.0828004i | \(0.0263864\pi\) |
−0.426576 | + | 0.904452i | \(0.640280\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.33574 | −0.129355 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.427235 | −0.0165426 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.00029 | − | 15.5890i | −0.347453 | − | 0.601805i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.72976 | + | 13.3883i | −0.297960 | + | 0.516082i | −0.975669 | − | 0.219248i | \(-0.929640\pi\) |
0.677709 | + | 0.735330i | \(0.262973\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.02467 | + | 5.23889i | −0.116248 | + | 0.201347i | −0.918278 | − | 0.395937i | \(-0.870420\pi\) |
0.802030 | + | 0.597284i | \(0.203753\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.4385 | − | 30.2044i | −0.669228 | − | 1.15914i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.1518 | −0.962406 | −0.481203 | − | 0.876609i | \(-0.659800\pi\) | ||||
−0.481203 | + | 0.876609i | \(0.659800\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.31411 | −0.126626 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.60644 | + | 13.1747i | 0.289782 | + | 0.501918i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.8943 | − | 37.9221i | 0.832899 | − | 1.44262i | −0.0628298 | − | 0.998024i | \(-0.520013\pi\) |
0.895729 | − | 0.444600i | \(-0.146654\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.93864 | + | 13.7501i | −0.301130 | + | 0.521572i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.4151 | + | 37.0921i | 0.811155 | + | 1.40496i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.4594 | 1.41482 | 0.707412 | − | 0.706802i | \(-0.249863\pi\) | ||||
0.707412 | + | 0.706802i | \(0.249863\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.08685 | 0.342717 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.92804 | + | 3.33947i | 0.0725116 | + | 0.125594i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.4907 | + | 28.5627i | −0.619321 | + | 1.07269i | 0.370289 | + | 0.928916i | \(0.379259\pi\) |
−0.989610 | + | 0.143778i | \(0.954075\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.3773 | − | 24.9022i | 0.538433 | − | 0.932594i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.63474 | − | 8.02760i | −0.173329 | − | 0.300215i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.0397 | 0.449006 | 0.224503 | − | 0.974473i | \(-0.427924\pi\) | ||||
0.224503 | + | 0.974473i | \(0.427924\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.0203 | −1.11801 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.213336 | + | 0.369509i | 0.00792311 | + | 0.0137232i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.6359 | + | 27.0822i | −0.579905 | + | 1.00443i | 0.415585 | + | 0.909555i | \(0.363577\pi\) |
−0.995490 | + | 0.0948705i | \(0.969756\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.6116 | − | 27.0400i | 0.577414 | − | 1.00011i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.40335 | + | 4.16273i | 0.0887699 | + | 0.153754i | 0.906991 | − | 0.421149i | \(-0.138373\pi\) |
−0.818222 | + | 0.574903i | \(0.805040\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.806522 | 0.0297086 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.79606 | −0.286783 | −0.143391 | − | 0.989666i | \(-0.545801\pi\) | ||||
−0.143391 | + | 0.989666i | \(0.545801\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.5475 | − | 40.7855i | −0.863875 | − | 1.49628i | −0.868160 | − | 0.496285i | \(-0.834697\pi\) |
0.00428429 | − | 0.999991i | \(-0.498636\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.9204 | − | 29.3071i | 0.619917 | − | 1.07373i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.9940 | − | 27.7023i | 0.584406 | − | 1.01222i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.25631 | + | 10.8362i | 0.228296 | + | 0.395420i | 0.957303 | − | 0.289086i | \(-0.0933513\pi\) |
−0.729007 | + | 0.684506i | \(0.760018\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.5257 | 0.674218 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.0507 | −0.474337 | −0.237168 | − | 0.971469i | \(-0.576219\pi\) | ||||
−0.237168 | + | 0.971469i | \(0.576219\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.5379 | − | 19.9842i | −0.418249 | − | 0.724428i | 0.577515 | − | 0.816380i | \(-0.304023\pi\) |
−0.995763 | + | 0.0919523i | \(0.970689\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.2206 | − | 26.3628i | 0.551021 | − | 0.954397i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.2422 | − | 24.6683i | 0.514257 | − | 0.890720i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.7111 | + | 28.9444i | 0.602617 | + | 1.04376i | 0.992423 | + | 0.122866i | \(0.0392085\pi\) |
−0.389807 | + | 0.920897i | \(0.627458\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.28916 | −0.334108 | −0.167054 | − | 0.985948i | \(-0.553425\pi\) | ||||
−0.167054 | + | 0.985948i | \(0.553425\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.7167 | −1.03154 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.37106 | + | 7.57089i | 0.156609 | + | 0.271255i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.7338 | + | 18.5915i | −0.384086 | + | 0.665256i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.3973 | − | 28.4010i | 0.585246 | − | 1.01368i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.77105 | + | 8.26370i | 0.170070 | + | 0.294569i | 0.938444 | − | 0.345431i | \(-0.112267\pi\) |
−0.768374 | + | 0.640001i | \(0.778934\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.6062 | 0.626004 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.4628 | −0.620123 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.3400 | − | 19.6415i | −0.401685 | − | 0.695738i | 0.592245 | − | 0.805758i | \(-0.298242\pi\) |
−0.993929 | + | 0.110020i | \(0.964909\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.0655 | + | 27.8263i | −0.568358 | + | 0.984424i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.83399 | + | 15.3009i | −0.311745 | + | 0.539958i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.97948 | + | 8.62471i | 0.175503 | + | 0.303981i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.1636 | 1.13081 | 0.565405 | − | 0.824813i | \(-0.308720\pi\) | ||||
0.565405 | + | 0.824813i | \(0.308720\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.49576 | 0.122753 | 0.0613764 | − | 0.998115i | \(-0.480451\pi\) | ||||
0.0613764 | + | 0.998115i | \(0.480451\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.9311 | + | 27.5935i | 0.558042 | + | 0.966557i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.18649 | − | 5.51916i | 0.111481 | − | 0.193091i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.6693 | + | 21.9438i | −0.442160 | + | 0.765844i | −0.997850 | − | 0.0655463i | \(-0.979121\pi\) |
0.555690 | + | 0.831390i | \(0.312454\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.8599 | + | 43.0585i | 0.866560 | + | 1.50093i | 0.865490 | + | 0.500926i | \(0.167007\pi\) |
0.00107015 | + | 0.999999i | \(0.499659\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.4868 | −1.51218 | −0.756092 | − | 0.654466i | \(-0.772894\pi\) | ||||
−0.756092 | + | 0.654466i | \(0.772894\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.62272 | 0.0563594 | 0.0281797 | − | 0.999603i | \(-0.491029\pi\) | ||||
0.0281797 | + | 0.999603i | \(0.491029\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.74033 | − | 6.47844i | −0.129595 | − | 0.224465i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.5321 | − | 30.3665i | 0.606724 | − | 1.05088i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.9586 | − | 36.3014i | 0.723573 | − | 1.25326i | −0.235986 | − | 0.971756i | \(-0.575832\pi\) |
0.959559 | − | 0.281508i | \(-0.0908348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4899 | + | 25.0973i | 0.499653 | + | 0.865425i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.34949 | 0.321632 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.90375 | 0.340297 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.5645 | − | 23.4944i | −0.464986 | − | 0.805379i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.30061 | + | 5.71683i | −0.113011 | + | 0.195741i | −0.916983 | − | 0.398927i | \(-0.869383\pi\) |
0.803972 | + | 0.594667i | \(0.202716\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.0909 | + | 20.9421i | −0.413018 | + | 0.715368i | −0.995218 | − | 0.0976773i | \(-0.968859\pi\) |
0.582200 | + | 0.813046i | \(0.302192\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.44631 | − | 16.3615i | −0.322304 | − | 0.558247i | 0.658659 | − | 0.752442i | \(-0.271124\pi\) |
−0.980963 | + | 0.194195i | \(0.937791\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.37925 | −0.183112 | −0.0915559 | − | 0.995800i | \(-0.529184\pi\) | ||||
−0.0915559 | + | 0.995800i | \(0.529184\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.2420 | −0.382238 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.9994 | + | 22.5156i | 0.440974 | + | 0.763789i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.391214 | − | 0.677602i | 0.0132558 | − | 0.0229597i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.2356 | − | 22.9247i | 0.447443 | − | 0.774995i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.00289 | − | 5.20115i | −0.101400 | − | 0.175630i | 0.810862 | − | 0.585238i | \(-0.198999\pi\) |
−0.912262 | + | 0.409608i | \(0.865666\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.3457 | 0.954991 | 0.477496 | − | 0.878634i | \(-0.341545\pi\) | ||||
0.477496 | + | 0.878634i | \(0.341545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.1360 | 0.408409 | 0.204204 | − | 0.978928i | \(-0.434539\pi\) | ||||
0.204204 | + | 0.978928i | \(0.434539\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.9032 | + | 39.6696i | 0.769015 | + | 1.33197i | 0.938097 | + | 0.346372i | \(0.112586\pi\) |
−0.169082 | + | 0.985602i | \(0.554080\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.45763 | + | 4.25674i | −0.0824263 | + | 0.142766i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.27915 | + | 5.67965i | −0.109733 | + | 0.190062i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.61558 | + | 4.53031i | 0.0874290 | + | 0.151432i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.35301 | 0.0451256 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.7968 | 0.992677 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.21923 | + | 15.9682i | 0.306458 | + | 0.530800i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.9721 | + | 19.0043i | −0.364324 | + | 0.631028i | −0.988667 | − | 0.150122i | \(-0.952033\pi\) |
0.624343 | + | 0.781150i | \(0.285367\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.2789 | − | 21.2676i | 0.406817 | − | 0.704628i | −0.587714 | − | 0.809069i | \(-0.699972\pi\) |
0.994531 | + | 0.104441i | \(0.0333053\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.03114 | + | 15.6424i | 0.298887 | + | 0.517688i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.7598 | 0.619504 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.9172 | 1.58064 | 0.790322 | − | 0.612692i | \(-0.209913\pi\) | ||||
0.790322 | + | 0.612692i | \(0.209913\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.4131 | + | 18.0361i | 0.342752 | + | 0.593665i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.5467 | + | 23.4635i | −0.445412 | + | 0.771476i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.5376 | + | 26.9120i | −0.509773 | + | 0.882953i | 0.490163 | + | 0.871631i | \(0.336937\pi\) |
−0.999936 | + | 0.0113223i | \(0.996396\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.763443 | − | 1.32232i | −0.0250208 | − | 0.0433373i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.1557 | −0.593756 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.1142 | −1.11446 | −0.557232 | − | 0.830357i | \(-0.688137\pi\) | ||||
−0.557232 | + | 0.830357i | \(0.688137\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.3292 | − | 26.5509i | −0.499716 | − | 0.865534i | 0.500284 | − | 0.865861i | \(-0.333229\pi\) |
−1.00000 | 0.000327806i | \(0.999896\pi\) | ||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.0499 | − | 22.6031i | 0.424963 | − | 0.736058i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.01450 | + | 12.1495i | −0.227941 | + | 0.394805i | −0.957198 | − | 0.289435i | \(-0.906533\pi\) |
0.729257 | + | 0.684240i | \(0.239866\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.57008 | + | 14.8438i | 0.278197 | + | 0.481850i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.9957 | 0.680117 | 0.340059 | − | 0.940404i | \(-0.389553\pi\) | ||||
0.340059 | + | 0.940404i | \(0.389553\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.445808 | 0.0144260 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.75110 | + | 4.76505i | 0.0888378 | + | 0.153872i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0316 | + | 52.0162i | −0.968761 | + | 1.67794i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.1427 | − | 24.4959i | 0.455270 | − | 0.788551i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.5923 | − | 30.4708i | −0.565731 | − | 0.979875i | −0.996981 | − | 0.0776429i | \(-0.975261\pi\) |
0.431250 | − | 0.902233i | \(-0.358073\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.7300 | −1.37127 | −0.685635 | − | 0.727945i | \(-0.740475\pi\) | ||||
−0.685635 | + | 0.727945i | \(0.740475\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.3600 | 0.845063 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.84824 | − | 3.20125i | −0.0591305 | − | 0.102417i | 0.834945 | − | 0.550334i | \(-0.185499\pi\) |
−0.894075 | + | 0.447917i | \(0.852166\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.6845 | + | 35.8265i | −0.661078 | + | 1.14502i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.7711 | + | 39.4407i | −0.726285 | + | 1.25796i | 0.232158 | + | 0.972678i | \(0.425421\pi\) |
−0.958443 | + | 0.285284i | \(0.907912\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.6197 | − | 28.7862i | −0.529548 | − | 0.917205i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.0267 | −0.605013 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.1458 | −0.639951 | −0.319976 | − | 0.947426i | \(-0.603675\pi\) | ||||
−0.319976 | + | 0.947426i | \(0.603675\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.175940 | − | 0.304736i | −0.00557766 | − | 0.00966079i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.3577 | − | 30.0645i | 0.549725 | − | 0.952152i | −0.448568 | − | 0.893749i | \(-0.648066\pi\) |
0.998293 | − | 0.0584029i | \(-0.0186008\pi\) | |||||||
\(998\) | 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 | 3456.2.i.f.1153.4 | 10 | ||
3.2 | odd | 2 | 1152.2.i.g.385.4 | yes | 10 | ||
4.3 | odd | 2 | 3456.2.i.g.1153.4 | 10 | |||
8.3 | odd | 2 | 3456.2.i.h.1153.2 | 10 | |||
8.5 | even | 2 | 3456.2.i.e.1153.2 | 10 | |||
9.4 | even | 3 | inner | 3456.2.i.f.2305.4 | 10 | ||
9.5 | odd | 6 | 1152.2.i.g.769.4 | yes | 10 | ||
12.11 | even | 2 | 1152.2.i.f.385.2 | yes | 10 | ||
24.5 | odd | 2 | 1152.2.i.e.385.2 | ✓ | 10 | ||
24.11 | even | 2 | 1152.2.i.h.385.4 | yes | 10 | ||
36.23 | even | 6 | 1152.2.i.f.769.2 | yes | 10 | ||
36.31 | odd | 6 | 3456.2.i.g.2305.4 | 10 | |||
72.5 | odd | 6 | 1152.2.i.e.769.2 | yes | 10 | ||
72.13 | even | 6 | 3456.2.i.e.2305.2 | 10 | |||
72.59 | even | 6 | 1152.2.i.h.769.4 | yes | 10 | ||
72.67 | odd | 6 | 3456.2.i.h.2305.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.i.e.385.2 | ✓ | 10 | 24.5 | odd | 2 | ||
1152.2.i.e.769.2 | yes | 10 | 72.5 | odd | 6 | ||
1152.2.i.f.385.2 | yes | 10 | 12.11 | even | 2 | ||
1152.2.i.f.769.2 | yes | 10 | 36.23 | even | 6 | ||
1152.2.i.g.385.4 | yes | 10 | 3.2 | odd | 2 | ||
1152.2.i.g.769.4 | yes | 10 | 9.5 | odd | 6 | ||
1152.2.i.h.385.4 | yes | 10 | 24.11 | even | 2 | ||
1152.2.i.h.769.4 | yes | 10 | 72.59 | even | 6 | ||
3456.2.i.e.1153.2 | 10 | 8.5 | even | 2 | |||
3456.2.i.e.2305.2 | 10 | 72.13 | even | 6 | |||
3456.2.i.f.1153.4 | 10 | 1.1 | even | 1 | trivial | ||
3456.2.i.f.2305.4 | 10 | 9.4 | even | 3 | inner | ||
3456.2.i.g.1153.4 | 10 | 4.3 | odd | 2 | |||
3456.2.i.g.2305.4 | 10 | 36.31 | odd | 6 | |||
3456.2.i.h.1153.2 | 10 | 8.3 | odd | 2 | |||
3456.2.i.h.2305.2 | 10 | 72.67 | odd | 6 |