Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(257,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.r (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.79102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.257 |
Dual form | 600.2.r.b.593.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | −1.00000 | − | 1.41421i | −0.577350 | − | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.41421 | + | 2.41421i | 0.912487 | + | 0.912487i | 0.996467 | − | 0.0839804i | \(-0.0267633\pi\) |
−0.0839804 | + | 0.996467i | \(0.526763\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.828427i | 0.249780i | 0.992171 | + | 0.124890i | \(0.0398578\pi\) | ||||
−0.992171 | + | 0.124890i | \(0.960142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.82843 | + | 3.82843i | −1.06181 | + | 1.06181i | −0.0638555 | + | 0.997959i | \(0.520340\pi\) |
−0.997959 | + | 0.0638555i | \(0.979660\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.82843 | + | 1.82843i | −0.443459 | + | 0.443459i | −0.893173 | − | 0.449714i | \(-0.851526\pi\) |
0.449714 | + | 0.893173i | \(0.351526\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.828427i | − | 0.190054i | −0.995475 | − | 0.0950271i | \(-0.969706\pi\) | ||
0.995475 | − | 0.0950271i | \(-0.0302938\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | − | 5.82843i | 0.218218 | − | 1.27187i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.41421 | + | 4.41421i | 0.920427 | + | 0.920427i | 0.997059 | − | 0.0766323i | \(-0.0244167\pi\) |
−0.0766323 | + | 0.997059i | \(0.524417\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | − | 1.41421i | 0.962250 | − | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.65685 | −0.679061 | −0.339530 | − | 0.940595i | \(-0.610268\pi\) | ||||
−0.339530 | + | 0.940595i | \(0.610268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685 | 1.01600 | 0.508001 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508001 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.17157 | − | 0.828427i | 0.203945 | − | 0.144211i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.82843 | + | 5.82843i | 0.958188 | + | 0.958188i | 0.999160 | − | 0.0409727i | \(-0.0130457\pi\) |
−0.0409727 | + | 0.999160i | \(0.513046\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.24264 | + | 1.58579i | 1.48001 | + | 0.253929i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.65685i | 0.883452i | 0.897150 | + | 0.441726i | \(0.145634\pi\) | ||||
−0.897150 | + | 0.441726i | \(0.854366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.414214 | − | 0.414214i | 0.0631670 | − | 0.0631670i | −0.674818 | − | 0.737985i | \(-0.735778\pi\) |
0.737985 | + | 0.674818i | \(0.235778\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.58579 | − | 3.58579i | 0.523041 | − | 0.523041i | −0.395448 | − | 0.918488i | \(-0.629411\pi\) |
0.918488 | + | 0.395448i | \(0.129411\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.65685i | 0.665265i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.41421 | + | 0.757359i | 0.618114 | + | 0.106052i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.00000 | − | 3.00000i | −0.412082 | − | 0.412082i | 0.470381 | − | 0.882463i | \(-0.344116\pi\) |
−0.882463 | + | 0.470381i | \(0.844116\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.17157 | + | 0.828427i | −0.155179 | + | 0.109728i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.343146 | 0.0439353 | 0.0219677 | − | 0.999759i | \(-0.493007\pi\) | ||||
0.0219677 | + | 0.999759i | \(0.493007\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.24264 | + | 4.41421i | −1.16446 | + | 0.556139i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.0711 | − | 10.0711i | −1.23038 | − | 1.23038i | −0.963819 | − | 0.266558i | \(-0.914114\pi\) |
−0.266558 | − | 0.963819i | \(-0.585886\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.82843 | − | 10.6569i | 0.220117 | − | 1.28293i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.4853i | 1.24437i | 0.782869 | + | 0.622187i | \(0.213756\pi\) | ||||
−0.782869 | + | 0.622187i | \(0.786244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.65685 | − | 4.65685i | 0.545044 | − | 0.545044i | −0.379960 | − | 0.925003i | \(-0.624062\pi\) |
0.925003 | + | 0.379960i | \(0.124062\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00000 | + | 2.00000i | −0.227921 | + | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.828427i | 0.0932053i | 0.998914 | + | 0.0466027i | \(0.0148395\pi\) | ||||
−0.998914 | + | 0.0466027i | \(0.985161\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.24264 | + | 3.24264i | 0.355926 | + | 0.355926i | 0.862309 | − | 0.506383i | \(-0.169018\pi\) |
−0.506383 | + | 0.862309i | \(0.669018\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.65685 | + | 5.17157i | 0.392056 | + | 0.554451i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.6569 | −1.65962 | −0.829812 | − | 0.558044i | \(-0.811552\pi\) | ||||
−0.829812 | + | 0.558044i | \(0.811552\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.4853 | −1.93778 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.65685 | − | 8.00000i | −0.586588 | − | 0.829561i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | − | 1.00000i | −0.101535 | − | 0.101535i | 0.654515 | − | 0.756049i | \(-0.272873\pi\) |
−0.756049 | + | 0.654515i | \(0.772873\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.34315 | − | 0.828427i | −0.235495 | − | 0.0832601i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 9.65685i | − | 0.960893i | −0.877024 | − | 0.480446i | \(-0.840475\pi\) | ||
0.877024 | − | 0.480446i | \(-0.159525\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.58579 | − | 5.58579i | 0.550384 | − | 0.550384i | −0.376168 | − | 0.926552i | \(-0.622758\pi\) |
0.926552 | + | 0.376168i | \(0.122758\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.58579 | + | 9.58579i | −0.926693 | + | 0.926693i | −0.997491 | − | 0.0707977i | \(-0.977446\pi\) |
0.0707977 | + | 0.997491i | \(0.477446\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000i | 0.383131i | 0.981480 | + | 0.191565i | \(0.0613564\pi\) | ||||
−0.981480 | + | 0.191565i | \(0.938644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.41421 | − | 14.0711i | 0.229147 | − | 1.33557i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.48528 | + | 9.48528i | 0.892300 | + | 0.892300i | 0.994739 | − | 0.102439i | \(-0.0326647\pi\) |
−0.102439 | + | 0.994739i | \(0.532665\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.00000 | − | 14.6569i | −0.647150 | − | 1.35503i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.82843 | −0.809301 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3137 | 0.937610 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.00000 | − | 5.65685i | 0.721336 | − | 0.510061i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.58579 | − | 5.58579i | −0.495658 | − | 0.495658i | 0.414425 | − | 0.910083i | \(-0.363983\pi\) |
−0.910083 | + | 0.414425i | \(0.863983\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.00000 | − | 0.171573i | −0.0880451 | − | 0.0151061i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.82843i | 0.771343i | 0.922636 | + | 0.385672i | \(0.126030\pi\) | ||||
−0.922636 | + | 0.385672i | \(0.873970\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000 | − | 2.00000i | 0.173422 | − | 0.173422i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.82843 | + | 9.82843i | −0.839699 | + | 0.839699i | −0.988819 | − | 0.149120i | \(-0.952356\pi\) |
0.149120 | + | 0.988819i | \(0.452356\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8.82843i | − | 0.748817i | −0.927264 | − | 0.374409i | \(-0.877846\pi\) | ||
0.927264 | − | 0.374409i | \(-0.122154\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.65685 | − | 1.48528i | −0.729039 | − | 0.125083i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.17157 | − | 3.17157i | −0.265220 | − | 0.265220i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.58579 | − | 4.65685i | 0.543187 | − | 0.384091i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.3137 | 1.09070 | 0.545351 | − | 0.838208i | \(-0.316396\pi\) | ||||
0.545351 | + | 0.838208i | \(0.316396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.6569 | −1.11138 | −0.555690 | − | 0.831390i | \(-0.687546\pi\) | ||||
−0.555690 | + | 0.831390i | \(0.687546\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.34315 | − | 7.00000i | −0.270277 | − | 0.565916i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.48528 | − | 5.48528i | −0.437773 | − | 0.437773i | 0.453489 | − | 0.891262i | \(-0.350179\pi\) |
−0.891262 | + | 0.453489i | \(0.850179\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.24264 | + | 7.24264i | −0.0985478 | + | 0.574379i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 21.3137i | 1.67976i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.414214 | − | 0.414214i | 0.0324437 | − | 0.0324437i | −0.690699 | − | 0.723143i | \(-0.742697\pi\) |
0.723143 | + | 0.690699i | \(0.242697\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.24264 | − | 9.24264i | 0.715217 | − | 0.715217i | −0.252405 | − | 0.967622i | \(-0.581221\pi\) |
0.967622 | + | 0.252405i | \(0.0812214\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 16.3137i | − | 1.25490i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.34315 | + | 0.828427i | 0.179185 | + | 0.0633514i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.656854 | − | 0.656854i | −0.0499397 | − | 0.0499397i | 0.681696 | − | 0.731636i | \(-0.261243\pi\) |
−0.731636 | + | 0.681696i | \(0.761243\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | − | 5.65685i | −0.300658 | − | 0.425195i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.31371 | −0.394965 | −0.197482 | − | 0.980306i | \(-0.563277\pi\) | ||||
−0.197482 | + | 0.980306i | \(0.563277\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.343146 | − | 0.485281i | −0.0253661 | − | 0.0358730i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.51472 | − | 1.51472i | −0.110767 | − | 0.110767i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.4853 | + | 8.65685i | 1.12639 | + | 0.629693i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.14214i | − | 0.299714i | −0.988708 | − | 0.149857i | \(-0.952119\pi\) | ||
0.988708 | − | 0.149857i | \(-0.0478814\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.6569 | + | 14.6569i | −1.05502 | + | 1.05502i | −0.0566281 | + | 0.998395i | \(0.518035\pi\) |
−0.998395 | + | 0.0566281i | \(0.981965\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.6569 | − | 14.6569i | 1.04426 | − | 1.04426i | 0.0452834 | − | 0.998974i | \(-0.485581\pi\) |
0.998974 | − | 0.0452834i | \(-0.0144191\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 18.4853i | − | 1.31039i | −0.755461 | − | 0.655193i | \(-0.772587\pi\) | ||
0.755461 | − | 0.655193i | \(-0.227413\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.17157 | + | 24.3137i | −0.294240 | + | 1.71496i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.82843 | − | 8.82843i | −0.619634 | − | 0.619634i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.8995 | + | 8.07107i | −1.17460 | + | 0.560978i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.686292 | 0.0474718 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.9706 | 1.44367 | 0.721837 | − | 0.692064i | \(-0.243298\pi\) | ||||
0.721837 | + | 0.692064i | \(0.243298\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.8284 | − | 10.4853i | 1.01603 | − | 0.718440i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.6569 | + | 13.6569i | 0.927088 | + | 0.927088i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.2426 | − | 1.92893i | −0.759707 | − | 0.130345i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 14.0000i | − | 0.941742i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.58579 | − | 5.58579i | 0.374052 | − | 0.374052i | −0.494899 | − | 0.868951i | \(-0.664795\pi\) |
0.868951 | + | 0.494899i | \(0.164795\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.89949 | + | 4.89949i | −0.325191 | + | 0.325191i | −0.850754 | − | 0.525563i | \(-0.823855\pi\) |
0.525563 | + | 0.850754i | \(0.323855\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.3431i | 0.947822i | 0.880573 | + | 0.473911i | \(0.157158\pi\) | ||||
−0.880573 | + | 0.473911i | \(0.842842\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.82843 | + | 0.828427i | 0.317687 | + | 0.0545065i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.8284 | + | 11.8284i | 0.774906 | + | 0.774906i | 0.978960 | − | 0.204054i | \(-0.0654117\pi\) |
−0.204054 | + | 0.978960i | \(0.565412\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.17157 | − | 0.828427i | 0.0761018 | − | 0.0538121i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.343146 | −0.0221040 | −0.0110520 | − | 0.999939i | \(-0.503518\pi\) | ||||
−0.0110520 | + | 0.999939i | \(0.503518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | + | 15.5563i | −0.0641500 | + | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.17157 | + | 3.17157i | 0.201802 | + | 0.201802i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.34315 | − | 7.82843i | 0.0851184 | − | 0.496106i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 26.4853i | − | 1.67174i | −0.548930 | − | 0.835868i | \(-0.684965\pi\) | ||
0.548930 | − | 0.835868i | \(-0.315035\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.65685 | + | 3.65685i | −0.229904 | + | 0.229904i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.48528 | − | 9.48528i | 0.591676 | − | 0.591676i | −0.346408 | − | 0.938084i | \(-0.612599\pi\) |
0.938084 | + | 0.346408i | \(0.112599\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.1421i | 1.74867i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.65685 | − | 10.3431i | 0.226354 | − | 0.640225i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.89949 | − | 6.89949i | −0.425441 | − | 0.425441i | 0.461631 | − | 0.887072i | \(-0.347264\pi\) |
−0.887072 | + | 0.461631i | \(0.847264\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.6569 | + | 22.1421i | 0.958184 | + | 1.35508i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.6274 | 1.01379 | 0.506896 | − | 0.862007i | \(-0.330793\pi\) | ||||
0.506896 | + | 0.862007i | \(0.330793\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.3431 | 0.628301 | 0.314151 | − | 0.949373i | \(-0.398280\pi\) | ||||
0.314151 | + | 0.949373i | \(0.398280\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18.4853 | + | 26.1421i | 1.11878 | + | 1.58219i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.17157 | + | 8.17157i | 0.490982 | + | 0.490982i | 0.908616 | − | 0.417633i | \(-0.137140\pi\) |
−0.417633 | + | 0.908616i | \(0.637140\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.65685 | + | 16.0000i | −0.338667 | + | 0.957895i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.65685i | − | 0.337460i | −0.985662 | − | 0.168730i | \(-0.946033\pi\) | ||
0.985662 | − | 0.168730i | \(-0.0539665\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.24264 | + | 5.24264i | −0.311643 | + | 0.311643i | −0.845546 | − | 0.533903i | \(-0.820725\pi\) |
0.533903 | + | 0.845546i | \(0.320725\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.6569 | + | 13.6569i | −0.806139 | + | 0.806139i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.3137i | 0.606689i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.414214 | + | 2.41421i | −0.0242816 | + | 0.141524i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.6569 | − | 16.6569i | −0.973104 | − | 0.973104i | 0.0265438 | − | 0.999648i | \(-0.491550\pi\) |
−0.999648 | + | 0.0265438i | \(0.991550\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.17157 | + | 4.14214i | 0.0679816 | + | 0.240351i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −33.7990 | −1.95465 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | 0.115278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.6569 | + | 9.65685i | −0.784566 | + | 0.554772i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.89949 | + | 6.89949i | 0.393775 | + | 0.393775i | 0.876031 | − | 0.482256i | \(-0.160182\pi\) |
−0.482256 | + | 0.876031i | \(0.660182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.4853 | − | 2.31371i | −0.767151 | − | 0.131622i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5.51472i | − | 0.312711i | −0.987701 | − | 0.156356i | \(-0.950025\pi\) | ||
0.987701 | − | 0.156356i | \(-0.0499746\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.31371 | − | 2.31371i | 0.130779 | − | 0.130779i | −0.638688 | − | 0.769466i | \(-0.720522\pi\) |
0.769466 | + | 0.638688i | \(0.220522\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.65685 | + | 4.65685i | −0.261555 | + | 0.261555i | −0.825686 | − | 0.564131i | \(-0.809211\pi\) |
0.564131 | + | 0.825686i | \(0.309211\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.02944i | − | 0.169616i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.1421 | + | 3.97056i | 1.29167 | + | 0.221615i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.51472 | + | 1.51472i | 0.0842812 | + | 0.0842812i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.65685 | − | 4.00000i | 0.312825 | − | 0.221201i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.3137 | 0.954536 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.65685 | −0.530789 | −0.265394 | − | 0.964140i | \(-0.585502\pi\) | ||||
−0.265394 | + | 0.964140i | \(0.585502\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22.3137 | + | 10.6569i | −1.22278 | + | 0.583992i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | − | 1.00000i | −0.0544735 | − | 0.0544735i | 0.679345 | − | 0.733819i | \(-0.262264\pi\) |
−0.733819 | + | 0.679345i | \(0.762264\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.92893 | − | 22.8995i | 0.213390 | − | 1.24373i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.68629i | 0.253777i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.65685 | − | 5.65685i | 0.305441 | − | 0.305441i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0711 | − | 12.0711i | 0.648009 | − | 0.648009i | −0.304503 | − | 0.952511i | \(-0.598490\pi\) |
0.952511 | + | 0.304503i | \(0.0984902\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9.65685i | − | 0.516920i | −0.966022 | − | 0.258460i | \(-0.916785\pi\) | ||
0.966022 | − | 0.258460i | \(-0.0832149\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.7279 | + | 24.5563i | −0.732742 | + | 1.31072i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.4853 | − | 15.4853i | −0.824198 | − | 0.824198i | 0.162509 | − | 0.986707i | \(-0.448041\pi\) |
−0.986707 | + | 0.162509i | \(0.948041\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.82843 | + | 12.4853i | 0.467250 | + | 0.660791i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35.3137 | 1.86379 | 0.931893 | − | 0.362733i | \(-0.118156\pi\) | ||||
0.931893 | + | 0.362733i | \(0.118156\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.3137 | 0.963879 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.3137 | − | 14.5858i | −0.541329 | − | 0.765555i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.75736 | + | 4.75736i | 0.248332 | + | 0.248332i | 0.820286 | − | 0.571954i | \(-0.193814\pi\) |
−0.571954 | + | 0.820286i | \(0.693814\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.0000 | − | 5.65685i | −0.832927 | − | 0.294484i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 14.4853i | − | 0.752038i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.514719 | + | 0.514719i | −0.0266511 | + | 0.0266511i | −0.720307 | − | 0.693656i | \(-0.755999\pi\) |
0.693656 | + | 0.720307i | \(0.255999\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.0000 | − | 14.0000i | 0.721037 | − | 0.721037i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.7990i | 1.53067i | 0.643631 | + | 0.765336i | \(0.277427\pi\) | ||||
−0.643631 | + | 0.765336i | \(0.722573\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.31371 | + | 13.4853i | −0.118535 | + | 0.690872i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.4142 | + | 12.4142i | 0.634337 | + | 0.634337i | 0.949153 | − | 0.314816i | \(-0.101943\pi\) |
−0.314816 | + | 0.949153i | \(0.601943\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.757359 | + | 1.58579i | 0.0384987 | + | 0.0806101i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.68629 | 0.339008 | 0.169504 | − | 0.985529i | \(-0.445783\pi\) | ||||
0.169504 | + | 0.985529i | \(0.445783\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.1421 | −0.816343 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.4853 | − | 8.82843i | 0.629799 | − | 0.445335i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.82843 | − | 7.82843i | −0.392897 | − | 0.392897i | 0.482821 | − | 0.875719i | \(-0.339612\pi\) |
−0.875719 | + | 0.482821i | \(0.839612\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.82843 | − | 0.828427i | −0.241724 | − | 0.0414732i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.0000i | 0.799002i | 0.916733 | + | 0.399501i | \(0.130817\pi\) | ||||
−0.916733 | + | 0.399501i | \(0.869183\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.6569 | + | 21.6569i | −1.07880 | + | 1.07880i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.82843 | + | 4.82843i | −0.239336 | + | 0.239336i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.6569i | 1.07086i | 0.844579 | + | 0.535431i | \(0.179851\pi\) | ||||
−0.844579 | + | 0.535431i | \(0.820149\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.7279 | + | 4.07107i | 1.17041 | + | 0.200811i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.65685 | + | 9.65685i | 0.475183 | + | 0.475183i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.4853 | + | 8.82843i | −0.611407 | + | 0.432330i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.9411 | 1.46272 | 0.731360 | − | 0.681992i | \(-0.238886\pi\) | ||||
0.731360 | + | 0.681992i | \(0.238886\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.9706 | 1.50941 | 0.754706 | − | 0.656063i | \(-0.227779\pi\) | ||||
0.754706 | + | 0.656063i | \(0.227779\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.55635 | + | 13.7279i | 0.318781 | + | 0.667474i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.828427 | + | 0.828427i | 0.0400904 | + | 0.0400904i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.31371 | + | 7.65685i | −0.0634264 | + | 0.369676i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 20.1421i | − | 0.970213i | −0.874455 | − | 0.485106i | \(-0.838781\pi\) | ||
0.874455 | − | 0.485106i | \(-0.161219\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.0000 | − | 15.0000i | 0.720854 | − | 0.720854i | −0.247925 | − | 0.968779i | \(-0.579749\pi\) |
0.968779 | + | 0.247925i | \(0.0797487\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.65685 | − | 3.65685i | 0.174931 | − | 0.174931i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13.7990i | − | 0.658590i | −0.944227 | − | 0.329295i | \(-0.893189\pi\) | ||
0.944227 | − | 0.329295i | \(-0.106811\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.1716 | − | 4.65685i | −0.627218 | − | 0.221755i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.0710678 | − | 0.0710678i | −0.00337653 | − | 0.00337653i | 0.705416 | − | 0.708793i | \(-0.250760\pi\) |
−0.708793 | + | 0.705416i | \(0.750760\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.3137 | − | 18.8284i | −0.629717 | − | 0.890554i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.31371 | 0.0619977 | 0.0309989 | − | 0.999519i | \(-0.490131\pi\) | ||||
0.0309989 | + | 0.999519i | \(0.490131\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.68629 | −0.220669 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.6569 | + | 19.3137i | 0.641655 | + | 0.907437i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | − | 1.00000i | −0.0467780 | − | 0.0467780i | 0.683331 | − | 0.730109i | \(-0.260531\pi\) |
−0.730109 | + | 0.683331i | \(0.760531\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.55635 | + | 11.7279i | −0.306024 | + | 0.547413i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 28.9706i | − | 1.34929i | −0.738141 | − | 0.674647i | \(-0.764296\pi\) | ||
0.738141 | − | 0.674647i | \(-0.235704\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.5858 | − | 21.5858i | 1.00318 | − | 1.00318i | 0.00318163 | − | 0.999995i | \(-0.498987\pi\) |
0.999995 | − | 0.00318163i | \(-0.00101275\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.3848 | − | 23.3848i | 1.08212 | − | 1.08212i | 0.0858066 | − | 0.996312i | \(-0.472653\pi\) |
0.996312 | − | 0.0858066i | \(-0.0273467\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 48.6274i | − | 2.24541i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.27208 | + | 13.2426i | −0.104692 | + | 0.610189i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.343146 | + | 0.343146i | 0.0157779 | + | 0.0157779i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.4853 | − | 5.48528i | 0.525875 | − | 0.251154i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.6274 | −1.03387 | −0.516937 | − | 0.856024i | \(-0.672928\pi\) | ||||
−0.516937 | + | 0.856024i | \(0.672928\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −44.6274 | −2.03484 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 30.1421 | − | 21.3137i | 1.37151 | − | 0.969807i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.5563 | − | 14.5563i | −0.659611 | − | 0.659611i | 0.295677 | − | 0.955288i | \(-0.404455\pi\) |
−0.955288 | + | 0.295677i | \(0.904455\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.00000 | − | 0.171573i | −0.0452216 | − | 0.00775879i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.5147i | 0.970946i | 0.874252 | + | 0.485473i | \(0.161353\pi\) | ||||
−0.874252 | + | 0.485473i | \(0.838647\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.68629 | − | 6.68629i | 0.301135 | − | 0.301135i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.3137 | + | 25.3137i | −1.13548 | + | 1.13548i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 34.7696i | − | 1.55650i | −0.627955 | − | 0.778249i | \(-0.716108\pi\) | ||
0.627955 | − | 0.778249i | \(-0.283892\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.3137 | − | 3.82843i | −0.996903 | − | 0.171042i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.92893 | − | 5.92893i | −0.264358 | − | 0.264358i | 0.562464 | − | 0.826822i | \(-0.309854\pi\) |
−0.826822 | + | 0.562464i | \(0.809854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.0711 | + | 16.3137i | −1.02462 | + | 0.724517i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.65685 | −0.162087 | −0.0810436 | − | 0.996711i | \(-0.525825\pi\) | ||||
−0.0810436 | + | 0.996711i | \(0.525825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.4853 | 0.994690 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.17157 | − | 4.14214i | −0.0517262 | − | 0.182880i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.97056 | + | 2.97056i | 0.130645 | + | 0.130645i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.272078 | + | 1.58579i | −0.0119429 | + | 0.0696083i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 24.0000i | − | 1.05146i | −0.850652 | − | 0.525730i | \(-0.823792\pi\) | ||
0.850652 | − | 0.525730i | \(-0.176208\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.8995 | + | 26.8995i | −1.17623 | + | 1.17623i | −0.195536 | + | 0.980696i | \(0.562645\pi\) |
−0.980696 | + | 0.195536i | \(0.937355\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.3431 | + | 10.3431i | −0.450555 | + | 0.450555i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.9706i | 0.694372i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | + | 11.3137i | −0.173585 | + | 0.490973i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.6569 | − | 21.6569i | −0.938062 | − | 0.938062i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0000 | − | 16.9706i | −0.517838 | − | 0.732334i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.85786 | −0.166170 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.3137 | −1.26029 | −0.630147 | − | 0.776476i | \(-0.717006\pi\) | ||||
−0.630147 | + | 0.776476i | \(0.717006\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.31371 | + | 7.51472i | 0.228033 | + | 0.322487i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.7279 | − | 15.7279i | −0.672477 | − | 0.672477i | 0.285809 | − | 0.958287i | \(-0.407738\pi\) |
−0.958287 | + | 0.285809i | \(0.907738\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.343146 | + | 0.970563i | −0.0146451 | + | 0.0414226i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.02944i | 0.129058i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.00000 | + | 2.00000i | −0.0850487 | + | 0.0850487i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.6274 | − | 15.6274i | 0.662155 | − | 0.662155i | −0.293733 | − | 0.955888i | \(-0.594898\pi\) |
0.955888 | + | 0.293733i | \(0.0948976\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.17157i | 0.134143i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.627417 | + | 3.65685i | −0.0264896 | + | 0.154393i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.44365 | − | 1.44365i | −0.0608426 | − | 0.0608426i | 0.676031 | − | 0.736873i | \(-0.263699\pi\) |
−0.736873 | + | 0.676031i | \(0.763699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.24264 | − | 30.5563i | −0.136178 | − | 1.28325i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −45.3137 | −1.89965 | −0.949825 | − | 0.312783i | \(-0.898739\pi\) | ||||
−0.949825 | + | 0.312783i | \(0.898739\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.97056 | −0.208012 | −0.104006 | − | 0.994577i | \(-0.533166\pi\) | ||||
−0.104006 | + | 0.994577i | \(0.533166\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.85786 | + | 4.14214i | −0.244716 | + | 0.173040i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.6569 | − | 14.6569i | −0.610173 | − | 0.610173i | 0.332818 | − | 0.942991i | \(-0.392000\pi\) |
−0.942991 | + | 0.332818i | \(0.892000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 35.3848 | + | 6.07107i | 1.47054 | + | 0.252305i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.6569i | 0.649556i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.48528 | − | 2.48528i | 0.102930 | − | 0.102930i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.5563 | + | 10.5563i | −0.435707 | + | 0.435707i | −0.890564 | − | 0.454857i | \(-0.849690\pi\) |
0.454857 | + | 0.890564i | \(0.349690\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.68629i | − | 0.193095i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.3848 | − | 6.07107i | −1.45554 | − | 0.249730i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.4853 | − | 15.4853i | −0.635904 | − | 0.635904i | 0.313638 | − | 0.949543i | \(-0.398452\pi\) |
−0.949543 | + | 0.313638i | \(0.898452\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.1421 | + | 18.4853i | −1.06993 | + | 0.756552i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.9411 | 1.71367 | 0.856834 | − | 0.515592i | \(-0.172428\pi\) | ||||
0.856834 | + | 0.515592i | \(0.172428\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.9706 | −0.610662 | −0.305331 | − | 0.952246i | \(-0.598767\pi\) | ||||
−0.305331 | + | 0.952246i | \(0.598767\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 38.5563 | − | 18.4142i | 1.57014 | − | 0.749885i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.0416 | + | 33.0416i | 1.34112 | + | 1.34112i | 0.894948 | + | 0.446170i | \(0.147212\pi\) |
0.446170 | + | 0.894948i | \(0.352788\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.65685 | + | 21.3137i | −0.148183 | + | 0.863675i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.4558i | 1.11074i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.48528 | + | 9.48528i | −0.383107 | + | 0.383107i | −0.872220 | − | 0.489113i | \(-0.837320\pi\) |
0.489113 | + | 0.872220i | \(0.337320\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.1716 | + | 12.1716i | −0.490009 | + | 0.490009i | −0.908309 | − | 0.418300i | \(-0.862626\pi\) |
0.418300 | + | 0.908309i | \(0.362626\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 20.1421i | − | 0.809581i | −0.914410 | − | 0.404790i | \(-0.867344\pi\) | ||
0.914410 | − | 0.404790i | \(-0.132656\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.3137 | + | 15.8284i | 1.13619 | + | 0.635173i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −37.7990 | − | 37.7990i | −1.51438 | − | 1.51438i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.686292 | − | 0.970563i | −0.0274078 | − | 0.0387605i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.3137 | −0.849833 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.5980 | 1.25790 | 0.628948 | − | 0.777447i | \(-0.283486\pi\) | ||||
0.628948 | + | 0.777447i | \(0.283486\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.9706 | − | 29.6569i | −0.833505 | − | 1.17875i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.8284 | − | 17.8284i | −0.706388 | − | 0.706388i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.6569 | − | 10.4853i | −1.17321 | − | 0.414791i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 20.2843i | − | 0.801181i | −0.916257 | − | 0.400590i | \(-0.868805\pi\) | ||
0.916257 | − | 0.400590i | \(-0.131195\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.6985 | − | 28.6985i | 1.13176 | − | 1.13176i | 0.141873 | − | 0.989885i | \(-0.454688\pi\) |
0.989885 | − | 0.141873i | \(-0.0453124\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.2132 | − | 26.2132i | 1.03055 | − | 1.03055i | 0.0310289 | − | 0.999518i | \(-0.490122\pi\) |
0.999518 | − | 0.0310289i | \(-0.00987838\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.31371i | 0.130074i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.65685 | − | 32.9706i | 0.221710 | − | 1.29222i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.6569 | + | 26.6569i | 1.04316 | + | 1.04316i | 0.999025 | + | 0.0441379i | \(0.0140541\pi\) |
0.0441379 | + | 0.999025i | \(0.485946\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.51472 | + | 17.8284i | 0.332191 | + | 0.695553i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.6274 | −0.413985 | −0.206993 | − | 0.978342i | \(-0.566368\pi\) | ||||
−0.206993 | + | 0.978342i | \(0.566368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.65685 | −0.297817 | −0.148909 | − | 0.988851i | \(-0.547576\pi\) | ||||
−0.148909 | + | 0.988851i | \(0.547576\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.7990 | + | 14.0000i | −0.768929 | + | 0.543715i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.1421 | − | 16.1421i | −0.625026 | − | 0.625026i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.4853 | − | 2.31371i | −0.521371 | − | 0.0894531i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.284271i | 0.0109742i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.68629 | − | 3.68629i | 0.142096 | − | 0.142096i | −0.632480 | − | 0.774576i | \(-0.717963\pi\) |
0.774576 | + | 0.632480i | \(0.217963\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.2843 | + | 35.2843i | −1.35608 | + | 1.35608i | −0.477397 | + | 0.878688i | \(0.658420\pi\) |
−0.878688 | + | 0.477397i | \(0.841580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4.82843i | − | 0.185298i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.8284 | + | 2.02944i | 0.453266 | + | 0.0777682i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.5563 | + | 22.5563i | 0.863095 | + | 0.863095i | 0.991696 | − | 0.128602i | \(-0.0410488\pi\) |
−0.128602 | + | 0.991696i | \(0.541049\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.2843 | − | 14.3431i | 0.773893 | − | 0.547225i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.9706 | 0.875109 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.6569 | −1.28037 | −0.640184 | − | 0.768222i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768222i | \(0.721142\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.65685 | − | 7.65685i | −0.138912 | − | 0.290860i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.3431 | − | 10.3431i | −0.391775 | − | 0.391775i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.89949 | − | 28.5563i | 0.185316 | − | 1.08010i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.00000i | − | 0.151078i | −0.997143 | − | 0.0755390i | \(-0.975932\pi\) | ||
0.997143 | − | 0.0755390i | \(-0.0240677\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.82843 | − | 4.82843i | 0.182108 | − | 0.182108i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.3137 | − | 23.3137i | 0.876802 | − | 0.876802i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.2843i | 1.21246i | 0.795289 | + | 0.606231i | \(0.207319\pi\) | ||||
−0.795289 | + | 0.606231i | \(0.792681\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.34315 | − | 0.828427i | −0.0878748 | − | 0.0310684i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.9706 | + | 24.9706i | 0.935155 | + | 0.935155i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.0000 | + | 22.6274i | 0.597531 | + | 0.845036i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.0000 | 0.596699 | 0.298350 | − | 0.954457i | \(-0.403564\pi\) | ||||
0.298350 | + | 0.954457i | \(0.403564\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.9706 | 1.00444 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.343146 | + | 0.485281i | 0.0127617 | + | 0.0180478i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.7574 | + | 12.7574i | 0.473144 | + | 0.473144i | 0.902931 | − | 0.429786i | \(-0.141411\pi\) |
−0.429786 | + | 0.902931i | \(0.641411\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.51472i | 0.0560239i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.14214 | − | 5.14214i | 0.189929 | − | 0.189929i | −0.605736 | − | 0.795665i | \(-0.707121\pi\) |
0.795665 | + | 0.605736i | \(0.207121\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.34315 | − | 8.34315i | 0.307324 | − | 0.307324i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.1716i | 1.73523i | 0.497233 | + | 0.867617i | \(0.334350\pi\) | ||||
−0.497233 | + | 0.867617i | \(0.665650\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.31371 | − | 7.65685i | 0.0482603 | − | 0.281282i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.3848 | + | 37.3848i | 1.37151 | + | 1.37151i | 0.858202 | + | 0.513313i | \(0.171582\pi\) |
0.513313 | + | 0.858202i | \(0.328418\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.4142 | + | 5.92893i | −0.454212 | + | 0.216928i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46.2843 | −1.69119 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.2843 | −0.448259 | −0.224130 | − | 0.974559i | \(-0.571954\pi\) | ||||
−0.224130 | + | 0.974559i | \(0.571954\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −37.4558 | + | 26.4853i | −1.36497 | + | 0.965177i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.4558 | − | 14.4558i | −0.525407 | − | 0.525407i | 0.393793 | − | 0.919199i | \(-0.371163\pi\) |
−0.919199 | + | 0.393793i | \(0.871163\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.82843 | + | 1.51472i | 0.320452 | + | 0.0549808i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 12.6863i | − | 0.459878i | −0.973205 | − | 0.229939i | \(-0.926147\pi\) | ||
0.973205 | − | 0.229939i | \(-0.0738526\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.65685 | + | 9.65685i | −0.349602 | + | 0.349602i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.3137 | + | 15.3137i | −0.552946 | + | 0.552946i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 49.9411i | − | 1.80092i | −0.434936 | − | 0.900462i | \(-0.643229\pi\) | ||
0.434936 | − | 0.900462i | \(-0.356771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.8995 | − | 3.92893i | −0.824705 | − | 0.141497i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.6569 | + | 10.6569i | 0.383300 | + | 0.383300i | 0.872290 | − | 0.488989i | \(-0.162634\pi\) |
−0.488989 | + | 0.872290i | \(0.662634\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 39.7990 | − | 28.1421i | 1.42778 | − | 1.00959i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.68629 | 0.167904 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.68629 | −0.310820 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.2843 | + | 5.17157i | −0.653427 | + | 0.184817i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.5858 | + | 27.5858i | 0.983327 | + | 0.983327i | 0.999863 | − | 0.0165362i | \(-0.00526387\pi\) |
−0.0165362 | + | 0.999863i | \(0.505264\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.85786 | + | 16.6569i | −0.101743 | + | 0.593000i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 45.7990i | 1.62842i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.31371 | + | 1.31371i | −0.0466512 | + | 0.0466512i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.65685 | + | 4.65685i | −0.164954 | + | 0.164954i | −0.784757 | − | 0.619803i | \(-0.787212\pi\) |
0.619803 | + | 0.784757i | \(0.287212\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.1127i | 0.463894i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.6569 | − | 44.2843i | 0.553208 | − | 1.56471i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.85786 | + | 3.85786i | 0.136141 | + | 0.136141i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.6274 | − | 23.5147i | −0.585313 | − | 0.827757i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.3431 | 1.13712 | 0.568562 | − | 0.822640i | \(-0.307500\pi\) | ||||
0.568562 | + | 0.822640i | \(0.307500\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.6569 | 1.18185 | 0.590926 | − | 0.806726i | \(-0.298763\pi\) | ||||
0.590926 | + | 0.806726i | \(0.298763\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.3431 | − | 14.6274i | −0.362750 | − | 0.513006i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.343146 | − | 0.343146i | −0.0120052 | − | 0.0120052i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.4853 | − | 52.2843i | 0.645928 | − | 1.82696i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.9411i | 1.32415i | 0.749436 | + | 0.662077i | \(0.230325\pi\) | ||||
−0.749436 | + | 0.662077i | \(0.769675\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.72792 | + | 5.72792i | −0.199663 | + | 0.199663i | −0.799855 | − | 0.600193i | \(-0.795091\pi\) |
0.600193 | + | 0.799855i | \(0.295091\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.5269 | + | 27.5269i | −0.957205 | + | 0.957205i | −0.999121 | − | 0.0419166i | \(-0.986654\pi\) |
0.0419166 | + | 0.999121i | \(0.486654\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.3137i | 0.531867i | 0.963991 | + | 0.265934i | \(0.0856802\pi\) | ||||
−0.963991 | + | 0.265934i | \(0.914320\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.38478 | − | 19.7279i | 0.117417 | − | 0.684354i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.51472 | − | 8.51472i | −0.295018 | − | 0.295018i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 28.2843 | − | 8.00000i | 0.977647 | − | 0.276520i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.6863 | 0.437979 | 0.218990 | − | 0.975727i | \(-0.429724\pi\) | ||||
0.218990 | + | 0.975727i | \(0.429724\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6274 | −0.538876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.00000 | + | 5.65685i | −0.275535 | + | 0.194832i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.8995 | + | 24.8995i | 0.855557 | + | 0.855557i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.6569 | + | 2.17157i | 0.434382 | + | 0.0745282i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51.4558i | 1.76388i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.4558 | − | 24.4558i | 0.837352 | − | 0.837352i | −0.151158 | − | 0.988510i | \(-0.548300\pi\) |
0.988510 | + | 0.151158i | \(0.0483001\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.4853 | − | 33.4853i | 1.14384 | − | 1.14384i | 0.156093 | − | 0.987742i | \(-0.450110\pi\) |
0.987742 | − | 0.156093i | \(-0.0498900\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 52.4264i | 1.78877i | 0.447302 | + | 0.894383i | \(0.352385\pi\) | ||||
−0.447302 | + | 0.894383i | \(0.647615\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 32.9706 | + | 5.65685i | 1.12363 | + | 0.192785i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.58579 | − | 3.58579i | −0.122062 | − | 0.122062i | 0.643437 | − | 0.765499i | \(-0.277508\pi\) |
−0.765499 | + | 0.643437i | \(0.777508\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.5858 | − | 10.3137i | 0.495359 | − | 0.350272i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.686292 | −0.0232808 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 77.1127 | 2.61286 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.82843 | − | 1.82843i | 0.129573 | − | 0.0618829i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.4558 | + | 12.4558i | 0.420604 | + | 0.420604i | 0.885412 | − | 0.464808i | \(-0.153877\pi\) |
−0.464808 | + | 0.885412i | \(0.653877\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.89949 | + | 40.2132i | −0.232714 | + | 1.35636i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.97056i | 0.302226i | 0.988516 | + | 0.151113i | \(0.0482857\pi\) | ||||
−0.988516 | + | 0.151113i | \(0.951714\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.5858 | + | 31.5858i | −1.06295 | + | 1.06295i | −0.0650653 | + | 0.997881i | \(0.520726\pi\) |
−0.997881 | + | 0.0650653i | \(0.979274\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.72792 | + | 7.72792i | −0.259478 | + | 0.259478i | −0.824842 | − | 0.565364i | \(-0.808736\pi\) |
0.565364 | + | 0.824842i | \(0.308736\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 26.9706i | − | 0.904564i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.68629 | − | 5.79899i | 0.156997 | − | 0.194273i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.97056 | − | 2.97056i | −0.0994061 | − | 0.0994061i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.7990 | + | 47.7990i | 1.12852 | + | 1.59596i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.6863 | −0.689926 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.9706 | 0.365482 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.00000 | − | 2.82843i | −0.0665558 | − | 0.0941242i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.4142 | − | 28.4142i | −0.943478 | − | 0.943478i | 0.0550075 | − | 0.998486i | \(-0.482482\pi\) |
−0.998486 | + | 0.0550075i | \(0.982482\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27.3137 | + | 9.65685i | 0.905939 | + | 0.320298i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 40.8284i | − | 1.35271i | −0.736578 | − | 0.676353i | \(-0.763559\pi\) | ||
0.736578 | − | 0.676353i | \(-0.236441\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.68629 | + | 2.68629i | −0.0889033 | + | 0.0889033i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.3137 | + | 21.3137i | −0.703841 | + | 0.703841i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.82843i | 0.291223i | 0.989342 | + | 0.145611i | \(0.0465149\pi\) | ||||
−0.989342 | + | 0.145611i | \(0.953485\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.85786 | − | 16.6569i | 0.0941698 | − | 0.548862i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40.1421 | − | 40.1421i | −1.32129 | − | 1.32129i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.2132 | + | 21.3848i | 0.335446 | + | 0.702368i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.9411 | −0.391776 | −0.195888 | − | 0.980626i | \(-0.562759\pi\) | ||||
−0.195888 | + | 0.980626i | \(0.562759\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.85786 | 0.126436 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.79899 | + | 5.51472i | −0.255327 | + | 0.180544i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.0000 | + | 31.0000i | 1.01273 | + | 1.01273i | 0.999918 | + | 0.0128079i | \(0.00407699\pi\) |
0.0128079 | + | 0.999918i | \(0.495923\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.58579 | − | 0.958369i | −0.182285 | − | 0.0312752i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.5980i | 1.42125i | 0.703569 | + | 0.710627i | \(0.251589\pi\) | ||||
−0.703569 | + | 0.710627i | \(0.748411\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.9706 | + | 24.9706i | −0.813153 | + | 0.813153i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.72792 | − | 1.72792i | 0.0561499 | − | 0.0561499i | −0.678474 | − | 0.734624i | \(-0.737359\pi\) |
0.734624 | + | 0.678474i | \(0.237359\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.6569i | 1.15747i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.2426 | + | 1.92893i | 0.364568 | + | 0.0625499i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.4853 | − | 15.4853i | −0.501617 | − | 0.501617i | 0.410323 | − | 0.911940i | \(-0.365416\pi\) |
−0.911940 | + | 0.410323i | \(0.865416\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.28427 | + | 3.02944i | −0.138491 | + | 0.0979278i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −47.4558 | −1.53243 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.5269 | − | 36.6985i | −0.564797 | − | 1.18259i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.4142 | + | 18.4142i | 0.592161 | + | 0.592161i | 0.938215 | − | 0.346054i | \(-0.112478\pi\) |
−0.346054 | + | 0.938215i | \(0.612478\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.627417 | − | 3.65685i | 0.0201555 | − | 0.117475i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 42.4853i | − | 1.36342i | −0.731624 | − | 0.681709i | \(-0.761237\pi\) | ||
0.731624 | − | 0.681709i | \(-0.238763\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.3137 | − | 21.3137i | 0.683286 | − | 0.683286i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.1421 | − | 23.1421i | 0.740383 | − | 0.740383i | −0.232269 | − | 0.972652i | \(-0.574615\pi\) |
0.972652 | + | 0.232269i | \(0.0746150\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 12.9706i | − | 0.414541i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.3137 | − | 4.00000i | −0.361219 | − | 0.127710i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.6985 | + | 32.6985i | 1.04292 | + | 1.04292i | 0.999037 | + | 0.0438830i | \(0.0139729\pi\) |
0.0438830 | + | 0.999037i | \(0.486027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.3137 | − | 24.4853i | −0.551101 | − | 0.779375i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.65685 | 0.116281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.9706 | −1.55560 | −0.777801 | − | 0.628511i | \(-0.783665\pi\) | ||||
−0.777801 | + | 0.628511i | \(0.783665\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.65685 | + | 13.6569i | 0.306451 | + | 0.433387i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.7990 | + | 30.7990i | 0.975414 | + | 0.975414i | 0.999705 | − | 0.0242911i | \(-0.00773287\pi\) |
−0.0242911 | + | 0.999705i | \(0.507733\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 37.3848 | + | 20.8995i | 1.18280 | + | 0.661231i |
(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 | 600.2.r.b.257.1 | 4 | ||
3.2 | odd | 2 | 600.2.r.c.257.2 | 4 | |||
4.3 | odd | 2 | 1200.2.v.j.257.2 | 4 | |||
5.2 | odd | 4 | 120.2.r.b.113.1 | yes | 4 | ||
5.3 | odd | 4 | 600.2.r.c.593.2 | 4 | |||
5.4 | even | 2 | 120.2.r.c.17.2 | yes | 4 | ||
12.11 | even | 2 | 1200.2.v.d.257.1 | 4 | |||
15.2 | even | 4 | 120.2.r.c.113.1 | yes | 4 | ||
15.8 | even | 4 | inner | 600.2.r.b.593.2 | 4 | ||
15.14 | odd | 2 | 120.2.r.b.17.1 | ✓ | 4 | ||
20.3 | even | 4 | 1200.2.v.d.593.1 | 4 | |||
20.7 | even | 4 | 240.2.v.c.113.2 | 4 | |||
20.19 | odd | 2 | 240.2.v.a.17.1 | 4 | |||
40.19 | odd | 2 | 960.2.v.i.257.2 | 4 | |||
40.27 | even | 4 | 960.2.v.g.833.1 | 4 | |||
40.29 | even | 2 | 960.2.v.a.257.1 | 4 | |||
40.37 | odd | 4 | 960.2.v.f.833.2 | 4 | |||
60.23 | odd | 4 | 1200.2.v.j.593.1 | 4 | |||
60.47 | odd | 4 | 240.2.v.a.113.2 | 4 | |||
60.59 | even | 2 | 240.2.v.c.17.2 | 4 | |||
120.29 | odd | 2 | 960.2.v.f.257.2 | 4 | |||
120.59 | even | 2 | 960.2.v.g.257.1 | 4 | |||
120.77 | even | 4 | 960.2.v.a.833.2 | 4 | |||
120.107 | odd | 4 | 960.2.v.i.833.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.2.r.b.17.1 | ✓ | 4 | 15.14 | odd | 2 | ||
120.2.r.b.113.1 | yes | 4 | 5.2 | odd | 4 | ||
120.2.r.c.17.2 | yes | 4 | 5.4 | even | 2 | ||
120.2.r.c.113.1 | yes | 4 | 15.2 | even | 4 | ||
240.2.v.a.17.1 | 4 | 20.19 | odd | 2 | |||
240.2.v.a.113.2 | 4 | 60.47 | odd | 4 | |||
240.2.v.c.17.2 | 4 | 60.59 | even | 2 | |||
240.2.v.c.113.2 | 4 | 20.7 | even | 4 | |||
600.2.r.b.257.1 | 4 | 1.1 | even | 1 | trivial | ||
600.2.r.b.593.2 | 4 | 15.8 | even | 4 | inner | ||
600.2.r.c.257.2 | 4 | 3.2 | odd | 2 | |||
600.2.r.c.593.2 | 4 | 5.3 | odd | 4 | |||
960.2.v.a.257.1 | 4 | 40.29 | even | 2 | |||
960.2.v.a.833.2 | 4 | 120.77 | even | 4 | |||
960.2.v.f.257.2 | 4 | 120.29 | odd | 2 | |||
960.2.v.f.833.2 | 4 | 40.37 | odd | 4 | |||
960.2.v.g.257.1 | 4 | 120.59 | even | 2 | |||
960.2.v.g.833.1 | 4 | 40.27 | even | 4 | |||
960.2.v.i.257.2 | 4 | 40.19 | odd | 2 | |||
960.2.v.i.833.1 | 4 | 120.107 | odd | 4 | |||
1200.2.v.d.257.1 | 4 | 12.11 | even | 2 | |||
1200.2.v.d.593.1 | 4 | 20.3 | even | 4 | |||
1200.2.v.j.257.2 | 4 | 4.3 | odd | 2 | |||
1200.2.v.j.593.1 | 4 | 60.23 | odd | 4 |