Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(865,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.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: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.310217769.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.4 | ||
Root | \(0.882007 - 1.52768i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.865 |
Dual form | 2268.2.i.l.2053.4 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | 1.25300 | − | 2.17026i | 0.560359 | − | 0.970570i | −0.437106 | − | 0.899410i | \(-0.643997\pi\) |
0.997465 | − | 0.0711601i | \(-0.0226701\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.71031 | − | 2.01862i | 0.646437 | − | 0.762967i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.542689 | + | 0.939965i | 0.163627 | + | 0.283410i | 0.936167 | − | 0.351556i | \(-0.114347\pi\) |
−0.772540 | + | 0.634966i | \(0.781014\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.457311 | − | 0.792086i | −0.126835 | − | 0.219685i | 0.795614 | − | 0.605804i | \(-0.207149\pi\) |
−0.922449 | + | 0.386119i | \(0.873815\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.39302 | − | 2.41278i | 0.337857 | − | 0.585186i | −0.646172 | − | 0.763192i | \(-0.723631\pi\) |
0.984029 | + | 0.178006i | \(0.0569645\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.667623 | + | 1.15636i | 0.153163 | + | 0.265286i | 0.932389 | − | 0.361457i | \(-0.117721\pi\) |
−0.779225 | + | 0.626744i | \(0.784387\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.06064 | − | 5.30119i | 0.638189 | − | 1.10537i | −0.347641 | − | 0.937628i | \(-0.613017\pi\) |
0.985830 | − | 0.167747i | \(-0.0536493\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.640021 | − | 1.10855i | −0.128004 | − | 0.221710i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.414622 | + | 0.718147i | −0.0769934 | + | 0.133357i | −0.901951 | − | 0.431838i | \(-0.857865\pi\) |
0.824958 | + | 0.565194i | \(0.191199\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.61529 | 0.469720 | 0.234860 | − | 0.972029i | \(-0.424537\pi\) | ||||
0.234860 | + | 0.972029i | \(0.424537\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.23791 | − | 6.24116i | −0.378276 | − | 1.05495i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.14602 | + | 5.44907i | 0.517203 | + | 0.895822i | 0.999800 | + | 0.0199794i | \(0.00636008\pi\) |
−0.482597 | + | 0.875842i | \(0.660307\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.817290 | − | 1.41559i | −0.127639 | − | 0.221078i | 0.795122 | − | 0.606449i | \(-0.207407\pi\) |
−0.922762 | + | 0.385371i | \(0.874073\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.795689 | − | 1.37817i | 0.121342 | − | 0.210170i | −0.798955 | − | 0.601390i | \(-0.794614\pi\) |
0.920297 | + | 0.391221i | \(0.127947\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.59138 | −0.961451 | −0.480726 | − | 0.876871i | \(-0.659627\pi\) | ||||
−0.480726 | + | 0.876871i | \(0.659627\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.14967 | − | 6.90495i | −0.164238 | − | 0.986421i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.95967 | − | 6.85835i | 0.543902 | − | 0.942066i | −0.454773 | − | 0.890607i | \(-0.650280\pi\) |
0.998675 | − | 0.0514588i | \(-0.0163871\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.71996 | 0.366759 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.07809 | 0.661111 | 0.330555 | − | 0.943787i | \(-0.392764\pi\) | ||||
0.330555 | + | 0.943787i | \(0.392764\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.6393 | −1.49026 | −0.745129 | − | 0.666920i | \(-0.767612\pi\) | ||||
−0.745129 | + | 0.666920i | \(0.767612\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.29204 | −0.284293 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.8954 | 1.94194 | 0.970968 | − | 0.239211i | \(-0.0768887\pi\) | ||||
0.970968 | + | 0.239211i | \(0.0768887\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.64658 | −1.14484 | −0.572419 | − | 0.819961i | \(-0.693995\pi\) | ||||
−0.572419 | + | 0.819961i | \(0.693995\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.03904 | + | 8.72788i | −0.589776 | + | 1.02152i | 0.404486 | + | 0.914544i | \(0.367450\pi\) |
−0.994262 | + | 0.106977i | \(0.965883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.82560 | + | 0.512149i | 0.322007 | + | 0.0583648i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.34725 | −1.05165 | −0.525824 | − | 0.850594i | \(-0.676243\pi\) | ||||
−0.525824 | + | 0.850594i | \(0.676243\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.09733 | − | 7.09679i | 0.449741 | − | 0.778974i | −0.548628 | − | 0.836066i | \(-0.684850\pi\) |
0.998369 | + | 0.0570928i | \(0.0181831\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.49091 | − | 6.04644i | −0.378643 | − | 0.655829i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.36829 | − | 11.0302i | −0.675037 | − | 1.16920i | −0.976458 | − | 0.215708i | \(-0.930794\pi\) |
0.301421 | − | 0.953491i | \(-0.402539\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.38107 | − | 0.431576i | −0.249604 | − | 0.0452415i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.34613 | 0.343305 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.46931 | + | 14.6693i | −0.859929 | + | 1.48944i | 0.0120677 | + | 0.999927i | \(0.496159\pi\) |
−0.871996 | + | 0.489513i | \(0.837175\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.56064 | − | 2.70312i | −0.155290 | − | 0.268970i | 0.777875 | − | 0.628420i | \(-0.216298\pi\) |
−0.933165 | + | 0.359449i | \(0.882965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.40867 | + | 4.17194i | −0.237333 | + | 0.411073i | −0.959948 | − | 0.280178i | \(-0.909607\pi\) |
0.722615 | + | 0.691251i | \(0.242940\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.12729 | − | 12.3448i | −0.689021 | − | 1.19342i | −0.972155 | − | 0.234339i | \(-0.924707\pi\) |
0.283134 | − | 0.959080i | \(-0.408626\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.94767 | + | 5.10551i | −0.282335 | + | 0.489019i | −0.971959 | − | 0.235149i | \(-0.924442\pi\) |
0.689624 | + | 0.724167i | \(0.257776\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.58173 | + | 7.93579i | 0.431013 | + | 0.746537i | 0.996961 | − | 0.0779045i | \(-0.0248229\pi\) |
−0.565948 | + | 0.824441i | \(0.691490\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.66998 | − | 13.2848i | −0.715229 | − | 1.23881i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.48800 | − | 6.93860i | −0.228074 | − | 0.636060i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.91098 | − | 8.50606i | 0.446453 | − | 0.773278i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.32222 | 0.833805 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.48671 | −0.486867 | −0.243433 | − | 0.969918i | \(-0.578274\pi\) | ||||
−0.243433 | + | 0.969918i | \(0.578274\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.8587 | − | 18.8078i | 0.948728 | − | 1.64325i | 0.200620 | − | 0.979669i | \(-0.435704\pi\) |
0.748109 | − | 0.663576i | \(-0.230962\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.47609 | + | 0.630053i | 0.301415 | + | 0.0546325i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.2012 | + | 17.6690i | 0.871550 | + | 1.50957i | 0.860393 | + | 0.509630i | \(0.170218\pi\) |
0.0111561 | + | 0.999938i | \(0.496449\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.41698 | + | 4.18633i | 0.205005 | + | 0.355080i | 0.950134 | − | 0.311840i | \(-0.100945\pi\) |
−0.745129 | + | 0.666920i | \(0.767612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.496355 | − | 0.859713i | 0.0415073 | − | 0.0718928i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.03904 | + | 1.79968i | 0.0862879 | + | 0.149455i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.90867 | − | 5.03796i | 0.238287 | − | 0.412726i | −0.721936 | − | 0.691960i | \(-0.756747\pi\) |
0.960223 | + | 0.279234i | \(0.0900806\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.30769 | + | 7.46114i | 0.350555 | + | 0.607179i | 0.986347 | − | 0.164682i | \(-0.0526596\pi\) |
−0.635792 | + | 0.771861i | \(0.719326\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.27696 | − | 5.67586i | 0.263212 | − | 0.455896i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.26187 | −0.659369 | −0.329685 | − | 0.944091i | \(-0.606942\pi\) | ||||
−0.329685 | + | 0.944091i | \(0.606942\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.46644 | − | 15.2450i | −0.430816 | − | 1.20147i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.02160 | + | 1.76946i | 0.0800179 | + | 0.138595i | 0.903257 | − | 0.429099i | \(-0.141169\pi\) |
−0.823239 | + | 0.567694i | \(0.807836\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.31965 | − | 14.4101i | −0.643794 | − | 1.11508i | −0.984579 | − | 0.174942i | \(-0.944026\pi\) |
0.340785 | − | 0.940141i | \(-0.389307\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.08173 | − | 10.5339i | 0.467826 | − | 0.810298i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.4685 | −1.55619 | −0.778097 | − | 0.628144i | \(-0.783815\pi\) | ||||
−0.778097 | + | 0.628144i | \(0.783815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.33238 | − | 0.604004i | −0.251904 | − | 0.0456584i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.624422 | − | 1.08153i | 0.0466715 | − | 0.0808374i | −0.841746 | − | 0.539874i | \(-0.818472\pi\) |
0.888417 | + | 0.459036i | \(0.151805\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.6153 | 1.08635 | 0.543173 | − | 0.839621i | \(-0.317223\pi\) | ||||
0.543173 | + | 0.839621i | \(0.317223\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.7679 | 1.15928 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.02391 | 0.221130 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.9495 | 1.29878 | 0.649390 | − | 0.760455i | \(-0.275024\pi\) | ||||
0.649390 | + | 0.760455i | \(0.275024\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.1812 | 1.66862 | 0.834310 | − | 0.551296i | \(-0.185866\pi\) | ||||
0.834310 | + | 0.551296i | \(0.185866\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.31134 | −0.449664 | −0.224832 | − | 0.974398i | \(-0.572183\pi\) | ||||
−0.224832 | + | 0.974398i | \(0.572183\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.82873 | − | 6.63156i | 0.271412 | − | 0.470099i | −0.697812 | − | 0.716281i | \(-0.745843\pi\) |
0.969224 | + | 0.246182i | \(0.0791762\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.740534 | + | 2.06522i | 0.0519753 | + | 0.144950i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.09626 | −0.286095 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.724623 | + | 1.25508i | −0.0501232 | + | 0.0868160i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.73740 | − | 4.74132i | −0.188450 | − | 0.326406i | 0.756283 | − | 0.654244i | \(-0.227013\pi\) |
−0.944734 | + | 0.327838i | \(0.893680\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.99400 | − | 3.45371i | −0.135990 | − | 0.235541i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.47296 | − | 5.27928i | 0.303644 | − | 0.358381i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.54818 | −0.171409 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.93807 | − | 6.82093i | 0.263712 | − | 0.456763i | −0.703513 | − | 0.710682i | \(-0.748386\pi\) |
0.967225 | + | 0.253919i | \(0.0817197\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.0913311 | + | 0.158190i | 0.00606186 | + | 0.0104994i | 0.869040 | − | 0.494741i | \(-0.164737\pi\) |
−0.862979 | + | 0.505241i | \(0.831404\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.32329 | + | 12.6843i | −0.483937 | + | 0.838203i | −0.999830 | − | 0.0184500i | \(-0.994127\pi\) |
0.515893 | + | 0.856653i | \(0.327460\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.4693 | + | 18.1334i | 0.685868 | + | 1.18796i | 0.973163 | + | 0.230116i | \(0.0739104\pi\) |
−0.287296 | + | 0.957842i | \(0.592756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.25900 | + | 14.3050i | −0.538758 | + | 0.933156i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.16398 | − | 14.1404i | −0.528084 | − | 0.914668i | −0.999464 | − | 0.0327379i | \(-0.989577\pi\) |
0.471380 | − | 0.881930i | \(-0.343756\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.152536 | + | 0.264200i | 0.00982571 | + | 0.0170186i | 0.870896 | − | 0.491467i | \(-0.163539\pi\) |
−0.861071 | + | 0.508485i | \(0.830206\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.4261 | − | 6.15682i | −1.04942 | − | 0.393345i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.610623 | − | 1.05763i | 0.0388530 | − | 0.0672954i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.2619 | 1.78387 | 0.891937 | − | 0.452160i | \(-0.149346\pi\) | ||||
0.891937 | + | 0.452160i | \(0.149346\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.64391 | 0.417699 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.1208 | + | 17.5297i | −0.631317 | + | 1.09347i | 0.355966 | + | 0.934499i | \(0.384152\pi\) |
−0.987283 | + | 0.158974i | \(0.949181\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.3803 | + | 2.96898i | 1.01782 | + | 0.184483i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.81078 | + | 11.7966i | 0.419970 | + | 0.727410i | 0.995936 | − | 0.0900638i | \(-0.0287071\pi\) |
−0.575966 | + | 0.817474i | \(0.695374\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.92293 | − | 17.1870i | −0.609561 | − | 1.05579i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.30169 | + | 2.25459i | −0.0793655 | + | 0.137465i | −0.902976 | − | 0.429690i | \(-0.858623\pi\) |
0.823611 | + | 0.567155i | \(0.191956\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.362288 | − | 0.627501i | −0.0220074 | − | 0.0381179i | 0.854812 | − | 0.518938i | \(-0.173672\pi\) |
−0.876819 | + | 0.480820i | \(0.840339\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.694665 | − | 1.20319i | 0.0418899 | − | 0.0725554i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.46331 | − | 12.9268i | −0.448427 | − | 0.776698i | 0.549857 | − | 0.835259i | \(-0.314682\pi\) |
−0.998284 | + | 0.0585606i | \(0.981349\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.67311 | + | 16.7543i | −0.577049 | + | 0.999479i | 0.418766 | + | 0.908094i | \(0.362463\pi\) |
−0.995816 | + | 0.0913849i | \(0.970871\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.38471 | 0.0823126 | 0.0411563 | − | 0.999153i | \(-0.486896\pi\) | ||||
0.0411563 | + | 0.999153i | \(0.486896\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.25536 | − | 0.771297i | −0.251186 | − | 0.0455282i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.61898 | + | 8.00031i | 0.271705 | + | 0.470606i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.61220 | + | 11.4527i | 0.386289 | + | 0.669072i | 0.991947 | − | 0.126653i | \(-0.0404234\pi\) |
−0.605658 | + | 0.795725i | \(0.707090\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.36285 | − | 11.0208i | 0.370459 | − | 0.641654i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.59867 | −0.323779 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.42114 | − | 3.96330i | −0.0819129 | − | 0.228441i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.5840 | + | 25.2603i | −0.835080 | + | 1.44640i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.3342 | 0.761024 | 0.380512 | − | 0.924776i | \(-0.375748\pi\) | ||||
0.380512 | + | 0.924776i | \(0.375748\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.2427 | −1.43138 | −0.715690 | − | 0.698418i | \(-0.753888\pi\) | ||||
−0.715690 | + | 0.698418i | \(0.753888\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.7933 | 0.723122 | 0.361561 | − | 0.932348i | \(-0.382244\pi\) | ||||
0.361561 | + | 0.932348i | \(0.382244\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.8028 | −0.775240 | −0.387620 | − | 0.921819i | \(-0.626703\pi\) | ||||
−0.387620 | + | 0.921819i | \(0.626703\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.900044 | −0.0503928 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.72005 | 0.206989 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.585378 | + | 1.01390i | −0.0324709 | + | 0.0562413i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.2733 | + | 13.3055i | −0.621518 | + | 0.733556i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.4951 | −0.686794 | −0.343397 | − | 0.939190i | \(-0.611578\pi\) | ||||
−0.343397 | + | 0.939190i | \(0.611578\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.9170 | − | 34.4972i | 1.08818 | − | 1.88478i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.56716 | + | 6.17850i | 0.194315 | + | 0.336564i | 0.946676 | − | 0.322187i | \(-0.104418\pi\) |
−0.752360 | + | 0.658752i | \(0.771085\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.41929 | + | 2.45828i | 0.0768587 | + | 0.133123i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.9048 | − | 9.48887i | −0.858776 | − | 0.512351i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.10200 | −0.273890 | −0.136945 | − | 0.990579i | \(-0.543728\pi\) | ||||
−0.136945 | + | 0.990579i | \(0.543728\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.7764 | + | 27.3256i | −0.844494 | + | 1.46271i | 0.0415664 | + | 0.999136i | \(0.486765\pi\) |
−0.886060 | + | 0.463570i | \(0.846568\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.52082 | + | 13.0265i | 0.400293 | + | 0.693328i | 0.993761 | − | 0.111530i | \(-0.0355750\pi\) |
−0.593468 | + | 0.804858i | \(0.702242\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0872 | + | 20.9356i | −0.641521 | + | 1.11115i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.49322 | + | 12.9786i | 0.395477 | + | 0.684987i | 0.993162 | − | 0.116745i | \(-0.0372459\pi\) |
−0.597685 | + | 0.801731i | \(0.703913\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.60856 | − | 14.9105i | 0.453082 | − | 0.784761i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.6279 | + | 21.8721i | 0.660972 | + | 1.14484i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.73006 | + | 15.1209i | 0.455706 | + | 0.789305i | 0.998728 | − | 0.0504126i | \(-0.0160536\pi\) |
−0.543023 | + | 0.839718i | \(0.682720\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.07214 | − | 19.7230i | −0.367167 | − | 1.02397i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.56716 | + | 9.64260i | −0.288257 | + | 0.499275i | −0.973394 | − | 0.229139i | \(-0.926409\pi\) |
0.685137 | + | 0.728414i | \(0.259742\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.758446 | 0.0390619 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.0958 | −1.54592 | −0.772959 | − | 0.634455i | \(-0.781224\pi\) | ||||
−0.772959 | + | 0.634455i | \(0.781224\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.07029 | + | 8.78200i | −0.259080 | + | 0.448739i | −0.965996 | − | 0.258558i | \(-0.916753\pi\) |
0.706916 | + | 0.707298i | \(0.250086\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.65198 | − | 5.49057i | 0.237087 | − | 0.279825i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.64367 | + | 14.9713i | 0.438251 | + | 0.759073i | 0.997555 | − | 0.0698895i | \(-0.0222647\pi\) |
−0.559303 | + | 0.828963i | \(0.688931\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.52709 | − | 14.7694i | −0.431233 | − | 0.746918i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.7121 | + | 20.2860i | −0.589300 | + | 1.02070i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.5666 | − | 21.7661i | −0.630702 | − | 1.09241i | −0.987408 | − | 0.158191i | \(-0.949434\pi\) |
0.356707 | − | 0.934216i | \(-0.383900\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.9956 | + | 20.7770i | −0.599031 | + | 1.03755i | 0.393934 | + | 0.919139i | \(0.371114\pi\) |
−0.992964 | + | 0.118413i | \(0.962219\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.19600 | − | 2.07153i | −0.0595770 | − | 0.103190i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.41462 | + | 5.91430i | −0.169257 | + | 0.293161i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.5898 | 1.56202 | 0.781008 | − | 0.624521i | \(-0.214706\pi\) | ||||
0.781008 | + | 0.624521i | \(0.214706\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.68511 | − | 10.2507i | 0.427367 | − | 0.504406i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.2679 | − | 17.7846i | −0.504032 | − | 0.873010i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.12729 | − | 7.14868i | −0.201631 | − | 0.349236i | 0.747423 | − | 0.664349i | \(-0.231291\pi\) |
−0.949054 | + | 0.315113i | \(0.897958\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.5557 | + | 26.9433i | −0.758139 | + | 1.31314i | 0.185660 | + | 0.982614i | \(0.440558\pi\) |
−0.943799 | + | 0.330521i | \(0.892775\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.56625 | −0.172989 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.9068 | + | 23.4953i | −0.963359 | + | 1.13702i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.0078 | + | 29.4585i | −0.819239 | + | 1.41896i | 0.0870045 | + | 0.996208i | \(0.472271\pi\) |
−0.906244 | + | 0.422756i | \(0.861063\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.46751 | −0.262752 | −0.131376 | − | 0.991333i | \(-0.541940\pi\) | ||||
−0.131376 | + | 0.991333i | \(0.541940\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.17343 | 0.390988 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.9303 | 1.09440 | 0.547202 | − | 0.837001i | \(-0.315693\pi\) | ||||
0.547202 | + | 0.837001i | \(0.315693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.5045 | 1.68687 | 0.843436 | − | 0.537230i | \(-0.180529\pi\) | ||||
0.843436 | + | 0.537230i | \(0.180529\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.9179 | −1.51305 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.82093 | −0.463478 | −0.231739 | − | 0.972778i | \(-0.574442\pi\) | ||||
−0.231739 | + | 0.972778i | \(0.574442\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.887068 | − | 1.53645i | 0.0417704 | − | 0.0723485i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.92011 | + | 4.62677i | −0.183778 | + | 0.216906i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0350 | 1.03075 | 0.515377 | − | 0.856964i | \(-0.327652\pi\) | ||||
0.515377 | + | 0.856964i | \(0.327652\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.1026 | − | 36.5507i | 0.982844 | − | 1.70234i | 0.331694 | − | 0.943387i | \(-0.392380\pi\) |
0.651150 | − | 0.758949i | \(-0.274287\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7637 | + | 30.7677i | 0.825550 | + | 1.42989i | 0.901498 | + | 0.432783i | \(0.142468\pi\) |
−0.0759485 | + | 0.997112i | \(0.524198\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.39015 | − | 9.33602i | −0.249427 | − | 0.432019i | 0.713940 | − | 0.700207i | \(-0.246909\pi\) |
−0.963367 | + | 0.268187i | \(0.913575\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.1861 | − | 32.0869i | 1.25534 | − | 1.48163i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.72725 | 0.0794189 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.854586 | − | 1.48019i | 0.0392111 | − | 0.0679156i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.4844 | + | 19.8916i | 0.524738 | + | 0.908873i | 0.999585 | + | 0.0288044i | \(0.00916998\pi\) |
−0.474847 | + | 0.880068i | \(0.657497\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.87742 | − | 4.98384i | 0.131199 | − | 0.227244i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.2241 | + | 36.7612i | 0.963737 | + | 1.66924i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.5432 | + | 25.1896i | −0.659018 | + | 1.14145i | 0.321853 | + | 0.946790i | \(0.395694\pi\) |
−0.980870 | + | 0.194662i | \(0.937639\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.81005 | − | 16.9915i | −0.442721 | − | 0.766816i | 0.555169 | − | 0.831738i | \(-0.312654\pi\) |
−0.997890 | + | 0.0649218i | \(0.979320\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.15516 | + | 2.00079i | 0.0520256 | + | 0.0901110i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.4987 | + | 19.4728i | −0.740066 | + | 0.873474i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.29805 | + | 2.24828i | −0.0581085 | + | 0.100647i | −0.893616 | − | 0.448832i | \(-0.851840\pi\) |
0.835508 | + | 0.549479i | \(0.185174\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.0865 | 1.60902 | 0.804509 | − | 0.593941i | \(-0.202429\pi\) | ||||
0.804509 | + | 0.593941i | \(0.202429\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.82196 | −0.348072 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.3826 | + | 30.1076i | −0.770472 | + | 1.33450i | 0.166832 | + | 0.985985i | \(0.446646\pi\) |
−0.937304 | + | 0.348512i | \(0.886687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.99995 | + | 25.0993i | 0.398134 | + | 1.11033i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.03613 | + | 10.4549i | 0.265984 | + | 0.460697i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.57707 | − | 6.19566i | −0.157319 | − | 0.272485i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.37609 | + | 11.0437i | −0.279341 | + | 0.483834i | −0.971221 | − | 0.238179i | \(-0.923449\pi\) |
0.691880 | + | 0.722013i | \(0.256783\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.0906 | − | 33.0659i | −0.834774 | − | 1.44587i | −0.894214 | − | 0.447639i | \(-0.852265\pi\) |
0.0594407 | − | 0.998232i | \(-0.481068\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.64315 | − | 6.31013i | 0.158698 | − | 0.274873i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.23509 | − | 12.5315i | −0.314569 | − | 0.544850i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.747512 | + | 1.29473i | −0.0323783 | + | 0.0560809i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35.7220 | −1.54440 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.86649 | − | 4.82788i | 0.252688 | − | 0.207952i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.26136 | + | 12.5770i | 0.312190 | + | 0.540729i | 0.978836 | − | 0.204645i | \(-0.0656041\pi\) |
−0.666646 | + | 0.745374i | \(0.732271\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.38685 | + | 12.7944i | 0.316418 | + | 0.548052i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.2907 | − | 23.0202i | 0.568270 | − | 0.984272i | −0.428468 | − | 0.903557i | \(-0.640946\pi\) |
0.996737 | − | 0.0807148i | \(-0.0257203\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.10725 | −0.0471703 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.9867 | + | 18.8686i | −0.679824 | + | 0.802373i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.3017 | + | 23.0392i | −0.563611 | + | 0.976202i | 0.433567 | + | 0.901121i | \(0.357255\pi\) |
−0.997177 | + | 0.0750809i | \(0.976078\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.45551 | −0.0615615 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.8220 | −1.08827 | −0.544133 | − | 0.838999i | \(-0.683141\pi\) | ||||
−0.544133 | + | 0.838999i | \(0.683141\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.9637 | 0.966088 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.7152 | 0.491129 | 0.245564 | − | 0.969380i | \(-0.421027\pi\) | ||||
0.245564 | + | 0.969380i | \(0.421027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.0973 | 0.422558 | 0.211279 | − | 0.977426i | \(-0.432237\pi\) | ||||
0.211279 | + | 0.977426i | \(0.432237\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.83551 | −0.326763 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.92842 | − | 8.53628i | 0.205173 | − | 0.355370i | −0.745015 | − | 0.667048i | \(-0.767558\pi\) |
0.950188 | + | 0.311678i | \(0.100891\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.31801 | − | 20.4087i | −0.303602 | − | 0.846695i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.59547 | 0.355988 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.2506 | − | 17.7546i | 0.423089 | − | 0.732812i | −0.573151 | − | 0.819450i | \(-0.694279\pi\) |
0.996240 | + | 0.0866378i | \(0.0276123\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.74603 | + | 3.02421i | 0.0719438 | + | 0.124610i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.94458 | + | 8.56427i | 0.203050 | + | 0.351692i | 0.949510 | − | 0.313738i | \(-0.101581\pi\) |
−0.746460 | + | 0.665430i | \(0.768248\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.1760 | − | 3.29446i | −0.745145 | − | 0.135060i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.34263 | 0.259153 | 0.129576 | − | 0.991569i | \(-0.458638\pi\) | ||||
0.129576 | + | 0.991569i | \(0.458638\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.74469 | + | 13.4142i | −0.315913 | + | 0.547177i | −0.979631 | − | 0.200806i | \(-0.935644\pi\) |
0.663719 | + | 0.747982i | \(0.268977\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.3069 | − | 21.3162i | −0.500347 | − | 0.866627i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.07942 | − | 1.86962i | 0.0438125 | − | 0.0758854i | −0.843288 | − | 0.537463i | \(-0.819383\pi\) |
0.887100 | + | 0.461577i | \(0.152716\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.01431 | + | 5.22094i | 0.121946 | + | 0.211217i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.944844 | − | 1.63652i | 0.0381619 | − | 0.0660983i | −0.846314 | − | 0.532685i | \(-0.821183\pi\) |
0.884476 | + | 0.466587i | \(0.154516\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.91093 | + | 13.7021i | 0.318482 | + | 0.551627i | 0.980172 | − | 0.198151i | \(-0.0634936\pi\) |
−0.661689 | + | 0.749778i | \(0.730160\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.87742 | + | 6.71589i | 0.155847 | + | 0.269935i | 0.933367 | − | 0.358923i | \(-0.116856\pi\) |
−0.777520 | + | 0.628858i | \(0.783523\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −33.1576 | − | 6.00992i | −1.32843 | − | 0.240782i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.8809 | − | 25.7744i | 0.595234 | − | 1.03098i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.5299 | 0.698963 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.7148 | 1.58102 | 0.790511 | − | 0.612448i | \(-0.209815\pi\) | ||||
0.790511 | + | 0.612448i | \(0.209815\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.87485 | + | 11.9076i | −0.272820 | + | 0.472538i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.94356 | + | 4.06834i | −0.195871 | + | 0.161194i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.4289 | + | 26.7237i | 0.609406 | + | 1.05552i | 0.991338 | + | 0.131332i | \(0.0419255\pi\) |
−0.381932 | + | 0.924190i | \(0.624741\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.93807 | − | 15.4812i | −0.352483 | − | 0.610518i | 0.634201 | − | 0.773168i | \(-0.281329\pi\) |
−0.986684 | + | 0.162650i | \(0.947996\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.3928 | + | 23.1969i | −0.526524 | + | 0.911966i | 0.472999 | + | 0.881063i | \(0.343172\pi\) |
−0.999522 | + | 0.0309026i | \(0.990162\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.75582 | + | 4.77322i | 0.108175 | + | 0.187365i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.2093 | + | 22.8792i | −0.516919 | + | 0.895331i | 0.482888 | + | 0.875682i | \(0.339588\pi\) |
−0.999807 | + | 0.0196482i | \(0.993745\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.2119 | − | 47.1324i | −1.06326 | − | 1.84161i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.3473 | + | 33.5105i | −0.753664 | + | 1.30538i | 0.192372 | + | 0.981322i | \(0.438382\pi\) |
−0.946036 | + | 0.324062i | \(0.894951\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.90004 | −0.307276 | −0.153638 | − | 0.988127i | \(-0.549099\pi\) | ||||
−0.153638 | + | 0.988127i | \(0.549099\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.72292 | − | 6.75457i | 0.221925 | − | 0.261931i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.53802 | + | 4.39599i | 0.0982727 | + | 0.170213i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.31651 | − | 10.9405i | −0.243846 | − | 0.422354i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.777686 | − | 1.34699i | 0.0299776 | − | 0.0519227i | −0.850647 | − | 0.525737i | \(-0.823790\pi\) |
0.880625 | + | 0.473814i | \(0.157123\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.1811 | −1.12152 | −0.560761 | − | 0.827978i | \(-0.689491\pi\) | ||||
−0.560761 | + | 0.827978i | \(0.689491\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.1266 | + | 42.1854i | 0.580504 | + | 1.61893i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.9993 | + | 31.1757i | −0.688723 | + | 1.19290i | 0.283528 | + | 0.958964i | \(0.408495\pi\) |
−0.972251 | + | 0.233939i | \(0.924838\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 51.1286 | 1.95352 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.24320 | −0.275944 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.8664 | 1.66876 | 0.834378 | − | 0.551193i | \(-0.185827\pi\) | ||||
0.834378 | + | 0.551193i | \(0.185827\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.1139 | 0.459507 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.55401 | −0.172495 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.5873 | 1.75958 | 0.879790 | − | 0.475363i | \(-0.157683\pi\) | ||||
0.879790 | + | 0.475363i | \(0.157683\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.20071 | + | 7.27585i | −0.158433 | + | 0.274414i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.12576 | − | 1.47282i | −0.305601 | − | 0.0553911i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.4805 | 0.694051 | 0.347026 | − | 0.937856i | \(-0.387192\pi\) | ||||
0.347026 | + | 0.937856i | \(0.387192\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.00447 | − | 13.8641i | 0.299770 | − | 0.519216i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.24387 | − | 2.15444i | −0.0465180 | − | 0.0805715i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.7978 | − | 34.2908i | −0.738333 | − | 1.27883i | −0.953246 | − | 0.302197i | \(-0.902280\pi\) |
0.214913 | − | 0.976633i | \(-0.431053\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.30199 | + | 11.9975i | 0.160214 | + | 0.446810i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.06147 | 0.0394219 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.9170 | − | 20.6409i | 0.441978 | − | 0.765528i | −0.555858 | − | 0.831277i | \(-0.687610\pi\) |
0.997836 | + | 0.0657487i | \(0.0209436\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.21683 | − | 3.83965i | −0.0819923 | − | 0.142015i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.02036 | − | 13.8917i | 0.296239 | − | 0.513101i | −0.679034 | − | 0.734107i | \(-0.737601\pi\) |
0.975272 | + | 0.221007i | \(0.0709343\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.62627 | + | 14.9411i | 0.317753 | + | 0.550364i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.74335 | − | 4.75163i | 0.100916 | − | 0.174792i | −0.811146 | − | 0.584843i | \(-0.801156\pi\) |
0.912062 | + | 0.410052i | \(0.134489\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.182662 | − | 0.316380i | −0.00670122 | − | 0.0116069i | 0.862655 | − | 0.505792i | \(-0.168800\pi\) |
−0.869357 | + | 0.494185i | \(0.835466\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.28913 | − | 12.6251i | −0.267053 | − | 0.462549i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −37.1094 | − | 6.72620i | −1.35595 | − | 0.245770i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.67855 | − | 9.83554i | 0.207213 | − | 0.358904i | −0.743622 | − | 0.668600i | \(-0.766894\pi\) |
0.950836 | + | 0.309696i | \(0.100227\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.5902 | 0.785746 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.4794 | −0.998757 | −0.499378 | − | 0.866384i | \(-0.666438\pi\) | ||||
−0.499378 | + | 0.866384i | \(0.666438\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.0210882 | − | 0.0365259i | 0.000764448 | − | 0.00132406i | −0.865643 | − | 0.500662i | \(-0.833090\pi\) |
0.866407 | + | 0.499338i | \(0.166423\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.26466 | + | 14.6822i | 0.190593 | + | 0.531532i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.32227 | − | 4.02228i | −0.0838522 | − | 0.145236i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.3233 | − | 23.0766i | −0.480450 | − | 0.832164i | 0.519298 | − | 0.854593i | \(-0.326193\pi\) |
−0.999748 | + | 0.0224290i | \(0.992860\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.6206 | − | 39.1800i | 0.813605 | − | 1.40921i | −0.0967202 | − | 0.995312i | \(-0.530835\pi\) |
0.910325 | − | 0.413894i | \(-0.135831\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.67384 | − | 2.89918i | −0.0601261 | − | 0.104141i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.09128 | − | 1.89016i | 0.0390993 | − | 0.0677219i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.23509 | − | 9.06745i | −0.187326 | − | 0.324459i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.3521 | + | 17.9304i | −0.369483 | + | 0.639964i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.2843 | 1.29340 | 0.646698 | − | 0.762746i | \(-0.276149\pi\) | ||||
0.646698 | + | 0.762746i | \(0.276149\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.8556 | + | 4.32390i | 0.848206 | + | 0.153740i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.32278 | + | 9.21932i | 0.189017 | + | 0.327388i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.35398 | − | 11.0054i | −0.225069 | − | 0.389832i | 0.731271 | − | 0.682087i | \(-0.238928\pi\) |
−0.956340 | + | 0.292256i | \(0.905594\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.18193 | + | 15.9036i | −0.324833 | + | 0.562628i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.9385 | −0.386012 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −39.9350 | − | 7.23835i | −1.40752 | − | 0.255118i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.6398 | + | 37.4812i | −0.760815 | + | 1.31777i | 0.181616 | + | 0.983370i | \(0.441867\pi\) |
−0.942431 | + | 0.334401i | \(0.891466\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.4941 | 0.544071 | 0.272036 | − | 0.962287i | \(-0.412303\pi\) | ||||
0.272036 | + | 0.962287i | \(0.412303\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.12026 | 0.179355 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.12488 | 0.0743402 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.7704 | 1.28330 | 0.641649 | − | 0.766999i | \(-0.278251\pi\) | ||||
0.641649 | + | 0.766999i | \(0.278251\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.13422 | 0.248683 | 0.124342 | − | 0.992239i | \(-0.460318\pi\) | ||||
0.124342 | + | 0.992239i | \(0.460318\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.7236 | −1.41610 | −0.708050 | − | 0.706162i | \(-0.750425\pi\) | ||||
−0.708050 | + | 0.706162i | \(0.750425\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.0794 | + | 26.1183i | −0.523730 | + | 0.907127i | 0.475888 | + | 0.879506i | \(0.342127\pi\) |
−0.999618 | + | 0.0276214i | \(0.991207\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.2617 | − | 6.84484i | −0.632729 | − | 0.237160i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41.6981 | −1.44302 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.37871 | − | 7.58415i | 0.151170 | − | 0.261834i | −0.780488 | − | 0.625171i | \(-0.785029\pi\) |
0.931658 | + | 0.363337i | \(0.118363\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.1562 | + | 24.5192i | 0.488144 | + | 0.845490i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.2408 | − | 26.3979i | −0.524301 | − | 0.908115i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.77122 | − | 24.4614i | −0.301383 | − | 0.840505i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.5154 | 1.32029 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.8129 | + | 39.5130i | −0.781098 | + | 1.35290i | 0.150205 | + | 0.988655i | \(0.452007\pi\) |
−0.931303 | + | 0.364246i | \(0.881327\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.3497 | + | 49.1030i | 0.968406 | + | 1.67733i | 0.700172 | + | 0.713974i | \(0.253107\pi\) |
0.268233 | + | 0.963354i | \(0.413560\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.29287 | − | 9.16752i | 0.180590 | − | 0.312792i | −0.761491 | − | 0.648175i | \(-0.775533\pi\) |
0.942082 | + | 0.335383i | \(0.108866\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.3124 | − | 35.1821i | −0.691442 | − | 1.19761i | −0.971365 | − | 0.237591i | \(-0.923642\pi\) |
0.279923 | − | 0.960022i | \(-0.409691\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.6471 | + | 44.4221i | −0.872027 | + | 1.51040i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.07265 | − | 8.78608i | −0.172078 | − | 0.298047i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.26916 | − | 12.5905i | −0.246306 | − | 0.426614i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.9439 | − | 18.8180i | 0.539002 | − | 0.636166i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.01744 | + | 10.4225i | −0.203195 | + | 0.351943i | −0.949556 | − | 0.313597i | \(-0.898466\pi\) |
0.746361 | + | 0.665541i | \(0.231799\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.07911 | 0.204811 | 0.102405 | − | 0.994743i | \(-0.467346\pi\) | ||||
0.102405 | + | 0.994743i | \(0.467346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.6345 | 0.391532 | 0.195766 | − | 0.980651i | \(-0.437281\pi\) | ||||
0.195766 | + | 0.980651i | \(0.437281\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.243915 | − | 0.422473i | 0.00818986 | − | 0.0141853i | −0.861901 | − | 0.507076i | \(-0.830726\pi\) |
0.870091 | + | 0.492891i | \(0.164060\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.38398 | + | 11.0756i | −0.314729 | + | 0.371463i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.40056 | − | 7.62199i | −0.147259 | − | 0.255060i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.56480 | − | 2.71032i | −0.0523056 | − | 0.0905959i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.08436 | + | 1.87816i | −0.0361653 | + | 0.0626402i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.0318 | − | 19.1076i | −0.367523 | − | 0.636568i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.3130 | − | 31.7190i | 0.608744 | − | 1.05437i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.02889 | + | 13.9064i | 0.266595 | + | 0.461756i | 0.967980 | − | 0.251027i | \(-0.0807681\pi\) |
−0.701385 | + | 0.712782i | \(0.747435\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.9439 | − | 34.5438i | 0.660769 | − | 1.14449i | −0.319645 | − | 0.947538i | \(-0.603563\pi\) |
0.980414 | − | 0.196949i | \(-0.0631032\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.89431 | 0.294359 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.3941 | − | 54.0868i | −0.640449 | − | 1.78610i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.47711 | − | 14.6828i | −0.279634 | − | 0.484340i | 0.691660 | − | 0.722224i | \(-0.256880\pi\) |
−0.971294 | + | 0.237883i | \(0.923546\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.41149 | + | 7.64092i | 0.145206 | + | 0.251504i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.02704 | − | 6.97504i | 0.132408 | − | 0.229338i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.7179 | −0.515688 | −0.257844 | − | 0.966187i | \(-0.583012\pi\) | ||||
−0.257844 | + | 0.966187i | \(0.583012\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.21704 | − | 5.93933i | 0.236529 | − | 0.194654i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.78896 | − | 6.56267i | 0.123912 | − | 0.214622i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.0501 | −0.687675 | −0.343838 | − | 0.939029i | \(-0.611727\pi\) | ||||
−0.343838 | + | 0.939029i | \(0.611727\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.3571 | 1.02221 | 0.511106 | − | 0.859518i | \(-0.329236\pi\) | ||||
0.511106 | + | 0.859518i | \(0.329236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.0057 | −0.325832 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.6365 | −0.508119 | −0.254059 | − | 0.967189i | \(-0.581766\pi\) | ||||
−0.254059 | + | 0.967189i | \(0.581766\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.21764 | 0.299217 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.7543 | −0.899051 | −0.449525 | − | 0.893268i | \(-0.648407\pi\) | ||||
−0.449525 | + | 0.893268i | \(0.648407\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.4907 | − | 38.9551i | 0.727783 | − | 1.26056i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53.1144 | + | 9.62715i | 1.71515 | + | 0.310877i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.1603 | −0.779363 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.0461 | − | 50.3093i | 0.935026 | − | 1.61951i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.6893 | + | 23.7105i | 0.440217 | + | 0.762479i | 0.997705 | − | 0.0677063i | \(-0.0215681\pi\) |
−0.557488 | + | 0.830185i | \(0.688235\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.88209 | − | 6.72398i | −0.124582 | − | 0.215783i | 0.796987 | − | 0.603996i | \(-0.206426\pi\) |
−0.921570 | + | 0.388213i | \(0.873092\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.5844 | + | 2.28096i | 0.403437 | + | 0.0731244i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.3134 | 0.585897 | 0.292948 | − | 0.956128i | \(-0.405364\pi\) | ||||
0.292948 | + | 0.956128i | \(0.405364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.91200 | − | 11.9719i | 0.220908 | − | 0.382625i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.09420 | + | 14.0196i | 0.258165 | + | 0.447155i | 0.965750 | − | 0.259473i | \(-0.0835489\pi\) |
−0.707585 | + | 0.706628i | \(0.750216\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.90811 | + | 13.6972i | −0.251973 | + | 0.436431i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.87065 | − | 8.43621i | −0.154878 | − | 0.268256i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.1897 | + | 33.2376i | −0.609582 | + | 1.05583i | 0.381727 | + | 0.924275i | \(0.375329\pi\) |
−0.991309 | + | 0.131552i | \(0.958004\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.59481 | − | 16.6187i | −0.304176 | − | 0.526848i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.5661 | + | 20.0331i | 0.366303 | + | 0.634456i | 0.988984 | − | 0.148020i | \(-0.0472900\pi\) |
−0.622681 | + | 0.782476i | \(0.713957\pi\) | |||||||
\(998\) | 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 | 2268.2.i.l.865.4 | 8 | ||
3.2 | odd | 2 | 2268.2.i.m.865.1 | 8 | |||
7.2 | even | 3 | 2268.2.l.m.541.1 | 8 | |||
9.2 | odd | 6 | 2268.2.k.d.1621.1 | yes | 8 | ||
9.4 | even | 3 | 2268.2.l.m.109.1 | 8 | |||
9.5 | odd | 6 | 2268.2.l.l.109.4 | 8 | |||
9.7 | even | 3 | 2268.2.k.c.1621.4 | yes | 8 | ||
21.2 | odd | 6 | 2268.2.l.l.541.4 | 8 | |||
63.2 | odd | 6 | 2268.2.k.d.1297.1 | yes | 8 | ||
63.16 | even | 3 | 2268.2.k.c.1297.4 | ✓ | 8 | ||
63.23 | odd | 6 | 2268.2.i.m.2053.1 | 8 | |||
63.58 | even | 3 | inner | 2268.2.i.l.2053.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2268.2.i.l.865.4 | 8 | 1.1 | even | 1 | trivial | ||
2268.2.i.l.2053.4 | 8 | 63.58 | even | 3 | inner | ||
2268.2.i.m.865.1 | 8 | 3.2 | odd | 2 | |||
2268.2.i.m.2053.1 | 8 | 63.23 | odd | 6 | |||
2268.2.k.c.1297.4 | ✓ | 8 | 63.16 | even | 3 | ||
2268.2.k.c.1621.4 | yes | 8 | 9.7 | even | 3 | ||
2268.2.k.d.1297.1 | yes | 8 | 63.2 | odd | 6 | ||
2268.2.k.d.1621.1 | yes | 8 | 9.2 | odd | 6 | ||
2268.2.l.l.109.4 | 8 | 9.5 | odd | 6 | |||
2268.2.l.l.541.4 | 8 | 21.2 | odd | 6 | |||
2268.2.l.m.109.1 | 8 | 9.4 | even | 3 | |||
2268.2.l.m.541.1 | 8 | 7.2 | even | 3 |