Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(37,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.cj (of order \(6\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.37 |
Dual form | 504.2.cj.b.109.1 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.866025 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | −1.37333 | − | 0.792893i | −0.614172 | − | 0.354593i | 0.160424 | − | 0.987048i | \(-0.448714\pi\) |
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.62132 | − | 2.09077i | 0.612801 | − | 0.790237i | ||||
\(8\) | − | 2.82843i | − | 1.00000i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.12132 | + | 1.94218i | 0.354593 | + | 0.614172i | ||||
\(11\) | −0.148586 | + | 0.0857864i | −0.0448005 | + | 0.0258656i | −0.522233 | − | 0.852803i | \(-0.674901\pi\) |
0.477432 | + | 0.878668i | \(0.341568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | −3.46410 | + | 1.41421i | −0.925820 | + | 0.377964i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(20\) | − | 3.17157i | − | 0.709185i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.242641 | 0.0517312 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.24264 | − | 2.15232i | −0.248528 | − | 0.430463i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.24264 | + | 0.717439i | 0.990766 | + | 0.135583i | ||||
\(29\) | − | 10.4142i | − | 1.93387i | −0.255021 | − | 0.966935i | \(-0.582082\pi\) | ||
0.255021 | − | 0.966935i | \(-0.417918\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.62132 | − | 8.00436i | −0.830014 | − | 1.43763i | −0.898027 | − | 0.439941i | \(-0.854999\pi\) |
0.0680129 | − | 0.997684i | \(-0.478334\pi\) | |||||||
\(32\) | 4.89898 | − | 2.82843i | 0.866025 | − | 0.500000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.88437 | + | 1.58579i | −0.656578 | + | 0.268047i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.24264 | + | 3.88437i | −0.354593 | + | 0.614172i | ||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | −0.297173 | − | 0.171573i | −0.0448005 | − | 0.0258656i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.74264 | − | 6.77962i | −0.248949 | − | 0.968517i | ||||
\(50\) | 3.51472i | 0.497056i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.72180 | − | 5.03553i | 1.19803 | − | 0.691684i | 0.237915 | − | 0.971286i | \(-0.423536\pi\) |
0.960116 | + | 0.279602i | \(0.0902025\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.272078 | 0.0366870 | ||||||||
\(56\) | −5.91359 | − | 4.58579i | −0.790237 | − | 0.612801i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.36396 | + | 12.7548i | −0.966935 | + | 1.67478i | ||||
\(59\) | −12.6932 | + | 7.32843i | −1.65251 | + | 0.954080i | −0.676481 | + | 0.736460i | \(0.736496\pi\) |
−0.976034 | + | 0.217620i | \(0.930171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(62\) | 13.0711i | 1.66003i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.87868 | + | 0.804479i | 0.702637 | + | 0.0961536i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | − | 12.1244i | −0.819288 | − | 1.41905i | −0.906208 | − | 0.422833i | \(-0.861036\pi\) |
0.0869195 | − | 0.996215i | \(-0.472298\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0615465 | + | 0.449747i | −0.00701388 | + | 0.0512535i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.86396 | − | 6.69258i | 0.434730 | − | 0.752974i | −0.562544 | − | 0.826767i | \(-0.690177\pi\) |
0.997274 | + | 0.0737937i | \(0.0235106\pi\) | |||||||
\(80\) | 5.49333 | − | 3.17157i | 0.614172 | − | 0.354593i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.8284i | 1.95692i | 0.206427 | + | 0.978462i | \(0.433816\pi\) | ||||
−0.206427 | + | 0.978462i | \(0.566184\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.242641 | + | 0.420266i | 0.0258656 | + | 0.0448005i | ||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.9706 | 1.62156 | 0.810782 | − | 0.585348i | \(-0.199042\pi\) | ||||
0.810782 | + | 0.585348i | \(0.199042\pi\) | |||||||
\(98\) | −2.65962 | + | 9.53553i | −0.268662 | + | 0.963234i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.48528 | − | 4.30463i | 0.248528 | − | 0.430463i | ||||
\(101\) | 17.1464 | − | 9.89949i | 1.70613 | − | 0.985037i | 0.766894 | − | 0.641774i | \(-0.221801\pi\) |
0.939239 | − | 0.343263i | \(-0.111532\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.00000 | + | 12.1244i | −0.689730 | + | 1.19465i | 0.282194 | + | 0.959357i | \(0.408938\pi\) |
−0.971925 | + | 0.235291i | \(0.924396\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.2426 | −1.38337 | ||||||||
\(107\) | 17.8894 | + | 10.3284i | 1.72943 | + | 0.998487i | 0.892211 | + | 0.451618i | \(0.149153\pi\) |
0.837218 | + | 0.546869i | \(0.184180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(110\) | −0.333226 | − | 0.192388i | −0.0317719 | − | 0.0183435i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.00000 | + | 9.79796i | 0.377964 | + | 0.925820i | ||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 18.0379 | − | 10.4142i | 1.67478 | − | 0.966935i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 20.7279 | 1.90816 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.48528 | + | 9.50079i | −0.498662 | + | 0.863708i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.24264 | − | 16.0087i | 0.830014 | − | 1.43763i | ||||
\(125\) | 11.8701i | 1.06169i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.75736 | 0.599619 | 0.299809 | − | 0.953999i | \(-0.403077\pi\) | ||||
0.299809 | + | 0.953999i | \(0.403077\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.866025 | + | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.19988 | − | 4.15685i | −0.629057 | − | 0.363186i | 0.151330 | − | 0.988483i | \(-0.451644\pi\) |
−0.780387 | + | 0.625297i | \(0.784978\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | −6.63103 | − | 5.14214i | −0.560424 | − | 0.434590i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.25736 | + | 14.3022i | −0.685736 | + | 1.18773i | ||||
\(146\) | 19.7990i | 1.63858i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.44949 | − | 1.41421i | −0.200670 | − | 0.115857i | 0.396298 | − | 0.918122i | \(-0.370295\pi\) |
−0.596968 | + | 0.802265i | \(0.703628\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.1066 | + | 19.2372i | 0.903842 | + | 1.56550i | 0.822464 | + | 0.568818i | \(0.192599\pi\) |
0.0813788 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.393398 | − | 0.507306i | 0.0317009 | − | 0.0408799i | ||||
\(155\) | 14.6569i | 1.17727i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(158\) | −9.46473 | + | 5.46447i | −0.752974 | + | 0.434730i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.97056 | −0.709185 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.6066 | − | 21.8353i | 0.978462 | − | 1.69475i | ||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.1464 | − | 9.89949i | −1.30362 | − | 0.752645i | −0.322596 | − | 0.946537i | \(-0.604555\pi\) |
−0.981023 | + | 0.193892i | \(0.937889\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.51472 | − | 0.891519i | −0.492466 | − | 0.0673925i | ||||
\(176\) | − | 0.686292i | − | 0.0517312i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.79796 | − | 5.65685i | 0.732334 | − | 0.422813i | −0.0869415 | − | 0.996213i | \(-0.527709\pi\) |
0.819275 | + | 0.573400i | \(0.194376\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.7426 | + | 18.6068i | 0.773272 | + | 1.33935i | 0.935760 | + | 0.352636i | \(0.114715\pi\) |
−0.162488 | + | 0.986710i | \(0.551952\pi\) | |||||||
\(194\) | −19.5599 | − | 11.2929i | −1.40432 | − | 0.810782i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.0000 | − | 9.79796i | 0.714286 | − | 0.699854i | ||||
\(197\) | − | 14.1421i | − | 1.00759i | −0.863825 | − | 0.503793i | \(-0.831938\pi\) | ||
0.863825 | − | 0.503793i | \(-0.168062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.00000 | − | 12.1244i | −0.496217 | − | 0.859473i | 0.503774 | − | 0.863836i | \(-0.331945\pi\) |
−0.999990 | + | 0.00436292i | \(0.998611\pi\) | |||||||
\(200\) | −6.08767 | + | 3.51472i | −0.430463 | + | 0.248528i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −28.0000 | −1.97007 | ||||||||
\(203\) | −21.7737 | − | 16.8848i | −1.52822 | − | 1.18508i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.1464 | − | 9.89949i | 1.19465 | − | 0.689730i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 17.4436 | + | 10.0711i | 1.19803 | + | 0.691684i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.6066 | − | 25.2994i | −0.998487 | − | 1.72943i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.2279 | − | 3.31552i | −1.64470 | − | 0.225072i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.272078 | + | 0.471253i | 0.0183435 | + | 0.0317719i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.272078 | −0.0182197 | −0.00910984 | − | 0.999959i | \(-0.502900\pi\) | ||||
−0.00910984 | + | 0.999959i | \(0.502900\pi\) | |||||||
\(224\) | 2.02922 | − | 14.8284i | 0.135583 | − | 0.990766i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.45322 | + | 2.57107i | −0.295571 | + | 0.170648i | −0.640451 | − | 0.767999i | \(-0.721253\pi\) |
0.344881 | + | 0.938647i | \(0.387919\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −29.4558 | −1.93387 | ||||||||
\(233\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −25.3864 | − | 14.6569i | −1.65251 | − | 0.954080i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2279 | + | 17.7153i | 0.658838 | + | 1.14114i | 0.980917 | + | 0.194429i | \(0.0622852\pi\) |
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 13.4361 | − | 7.75736i | 0.863708 | − | 0.498662i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.98229 | + | 10.6924i | −0.190531 | + | 0.683112i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −22.6398 | + | 13.0711i | −1.43763 | + | 0.830014i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.39340 | − | 14.5378i | 0.530845 | − | 0.919451i | ||||
\(251\) | − | 24.1716i | − | 1.52570i | −0.646578 | − | 0.762848i | \(-0.723800\pi\) | ||
0.646578 | − | 0.762848i | \(-0.276200\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8.27604 | − | 4.77817i | −0.519285 | − | 0.299809i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.87868 | + | 10.1822i | 0.363186 | + | 0.629057i | ||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.9706 | −0.981064 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.2664 | − | 12.2782i | 1.29664 | − | 0.748614i | 0.316815 | − | 0.948487i | \(-0.397387\pi\) |
0.979822 | + | 0.199874i | \(0.0640532\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.1066 | + | 27.8975i | −0.978406 | + | 1.69465i | −0.310204 | + | 0.950670i | \(0.600397\pi\) |
−0.668202 | + | 0.743980i | \(0.732936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.369279 | + | 0.213203i | 0.0222684 | + | 0.0128567i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.48528 | + | 10.9867i | 0.268047 | + | 0.656578i | ||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 20.2263 | − | 11.6777i | 1.18773 | − | 0.685736i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.0000 | − | 24.2487i | 0.819288 | − | 1.41905i | ||||
\(293\) | 34.0711i | 1.99045i | 0.0975919 | + | 0.995227i | \(0.468886\pi\) | ||||
−0.0975919 | + | 0.995227i | \(0.531114\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.2426 | 1.35324 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.00000 | + | 3.46410i | 0.115857 | + | 0.200670i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 31.4142i | − | 1.80768i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | −0.840532 | + | 0.343146i | −0.0478938 | + | 0.0195525i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.3640 | − | 17.9509i | 0.588633 | − | 1.01954i | ||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.7426 | + | 22.0709i | −0.720257 | + | 1.24752i | 0.240640 | + | 0.970614i | \(0.422643\pi\) |
−0.960897 | + | 0.276907i | \(0.910691\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.4558 | 0.869459 | ||||||||
\(317\) | −26.4626 | − | 15.2782i | −1.48629 | − | 0.858108i | −0.486408 | − | 0.873732i | \(-0.661693\pi\) |
−0.999878 | + | 0.0156238i | \(0.995027\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.893398 | + | 1.54741i | 0.0500207 | + | 0.0866384i | ||||
\(320\) | 10.9867 | + | 6.34315i | 0.614172 | + | 0.354593i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(332\) | −30.8797 | + | 17.8284i | −1.69475 | + | 0.978462i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 36.4558 | 1.98588 | 0.992938 | − | 0.118633i | \(-0.0378512\pi\) | ||||
0.992938 | + | 0.118633i | \(0.0378512\pi\) | |||||||
\(338\) | −15.9217 | − | 9.19239i | −0.866025 | − | 0.500000i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.37333 | + | 0.792893i | 0.0743701 | + | 0.0429376i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | − | 7.34847i | −0.917914 | − | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.0000 | + | 24.2487i | 0.752645 | + | 1.30362i | ||||
\(347\) | 24.4949 | − | 14.1421i | 1.31495 | − | 0.759190i | 0.332043 | − | 0.943264i | \(-0.392262\pi\) |
0.982912 | + | 0.184075i | \(0.0589288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 7.34847 | + | 5.69848i | 0.392792 | + | 0.304597i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.485281 | + | 0.840532i | −0.0258656 | + | 0.0448005i | ||||
\(353\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.0000 | −0.845626 | ||||||||
\(359\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.50000 | − | 16.4545i | −0.500000 | − | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.2010i | 1.16205i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.6213 | + | 20.1287i | 0.606628 | + | 1.05071i | 0.991792 | + | 0.127862i | \(0.0408116\pi\) |
−0.385164 | + | 0.922848i | \(0.625855\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.61269 | − | 26.3995i | 0.187561 | − | 1.37059i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.441125 | − | 0.568852i | 0.0224818 | − | 0.0289914i | ||||
\(386\) | − | 30.3848i | − | 1.54654i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.9706 | + | 27.6618i | 0.810782 | + | 1.40432i | ||||
\(389\) | −26.9444 | + | 15.5563i | −1.36613 | + | 0.788738i | −0.990432 | − | 0.138002i | \(-0.955932\pi\) |
−0.375703 | + | 0.926740i | \(0.622599\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −19.1757 | + | 4.92893i | −0.968517 | + | 0.248949i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.0000 | + | 17.3205i | −0.503793 | + | 0.872595i | ||||
\(395\) | −10.6130 | + | 6.12742i | −0.533998 | + | 0.308304i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(398\) | 19.7990i | 0.992434i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.94113 | 0.497056 | ||||||||
\(401\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 34.2929 | + | 19.7990i | 1.70613 | + | 0.985037i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14.7279 | + | 36.0759i | 0.730934 | + | 1.79042i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.4706 | − | 33.7240i | −0.962757 | − | 1.66754i | −0.715523 | − | 0.698589i | \(-0.753812\pi\) |
−0.247234 | − | 0.968956i | \(-0.579522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −28.0000 | −1.37946 | ||||||||
\(413\) | −5.25770 | + | 38.4203i | −0.258714 | + | 1.89054i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.1360 | − | 24.4843i | 0.693911 | − | 1.20189i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 39.5980i | − | 1.93449i | −0.253849 | − | 0.967244i | \(-0.581697\pi\) | ||
0.253849 | − | 0.967244i | \(-0.418303\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.2426 | − | 24.6690i | −0.691684 | − | 1.19803i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 41.3137i | 1.99697i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 27.3286 | + | 21.1924i | 1.31181 | + | 1.01727i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.10660 | − | 3.64874i | 0.100543 | − | 0.174145i | −0.811366 | − | 0.584539i | \(-0.801275\pi\) |
0.911908 | + | 0.410394i | \(0.134609\pi\) | |||||||
\(440\) | − | 0.769553i | − | 0.0366870i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.6301 | + | 20.5711i | 1.69284 | + | 0.977361i | 0.952209 | + | 0.305448i | \(0.0988061\pi\) |
0.740630 | + | 0.671913i | \(0.234527\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.333226 | + | 0.192388i | 0.0157787 | + | 0.00910984i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −12.9706 | + | 16.7262i | −0.612801 | + | 0.790237i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.27208 | 0.341296 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.9853 | − | 31.1514i | 0.841316 | − | 1.45720i | −0.0474665 | − | 0.998873i | \(-0.515115\pi\) |
0.888783 | − | 0.458329i | \(-0.151552\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.7990i | 0.922131i | 0.887366 | + | 0.461065i | \(0.152533\pi\) | ||||
−0.887366 | + | 0.461065i | \(0.847467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0000 | 1.20832 | 0.604161 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(464\) | 36.0759 | + | 20.8284i | 1.67478 | + | 0.966935i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.2929 | + | 19.7990i | 1.58688 | + | 0.916188i | 0.993816 | + | 0.111035i | \(0.0354167\pi\) |
0.593068 | + | 0.805153i | \(0.297917\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 20.7279 | + | 35.9018i | 0.954080 | + | 1.65251i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 28.9289i | − | 1.31768i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.9411 | −0.997324 | ||||||||
\(485\) | −21.9329 | − | 12.6630i | −0.995921 | − | 0.574995i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.5919 | − | 32.2021i | −0.842479 | − | 1.45922i | −0.887793 | − | 0.460243i | \(-0.847762\pi\) |
0.0453143 | − | 0.998973i | \(-0.485571\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.2132 | − | 10.9867i | 0.506561 | − | 0.496326i | ||||
\(491\) | − | 21.6863i | − | 0.978689i | −0.872091 | − | 0.489344i | \(-0.837236\pi\) | ||
0.872091 | − | 0.489344i | \(-0.162764\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.9706 | 1.66003 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | −20.5595 | + | 11.8701i | −0.919451 | + | 0.530845i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −17.0919 | + | 29.6040i | −0.762848 | + | 1.32129i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.3970 | −1.39715 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.75736 | + | 11.7041i | 0.299809 | + | 0.519285i | ||||
\(509\) | 34.9997 | + | 20.2071i | 1.55134 | + | 0.895664i | 0.998033 | + | 0.0626839i | \(0.0199660\pi\) |
0.553303 | + | 0.832980i | \(0.313367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.6985 | − | 5.02207i | −1.62345 | − | 0.222163i | ||||
\(512\) | 22.6274i | 1.00000i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.2266 | − | 11.1005i | 0.847227 | − | 0.489147i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(524\) | − | 16.6274i | − | 0.726372i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 19.5599 | + | 11.2929i | 0.849626 | + | 0.490532i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.3787 | − | 28.3687i | −0.708112 | − | 1.22649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −34.7279 | −1.49723 | ||||||||
\(539\) | 0.840532 | + | 0.857864i | 0.0362043 | + | 0.0369508i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(542\) | 39.4530 | − | 22.7782i | 1.69465 | − | 0.978406i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.301515 | − | 0.522240i | −0.0128567 | − | 0.0222684i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.72792 | − | 18.9295i | −0.328625 | − | 0.804963i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.6513 | + | 15.9645i | −1.17162 | + | 0.676436i | −0.954062 | − | 0.299611i | \(-0.903143\pi\) |
−0.217560 | + | 0.976047i | \(0.569810\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.27541 | − | 16.6274i | 0.0961536 | − | 0.702637i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.8263 | + | 23.5711i | −1.72062 | + | 0.993402i | −0.802970 | + | 0.596020i | \(0.796748\pi\) |
−0.917653 | + | 0.397382i | \(0.869919\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.22792 | − | 5.59093i | −0.134380 | − | 0.232753i | 0.790980 | − | 0.611842i | \(-0.209571\pi\) |
−0.925361 | + | 0.379088i | \(0.876238\pi\) | |||||||
\(578\) | −20.8207 | + | 12.0208i | −0.866025 | + | 0.500000i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −33.0294 | −1.37147 | ||||||||
\(581\) | 37.2751 | + | 28.9056i | 1.54643 | + | 1.19921i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.863961 | + | 1.49642i | −0.0357816 | + | 0.0619756i | ||||
\(584\) | −34.2929 | + | 19.7990i | −1.41905 | + | 0.819288i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.0919 | − | 41.7284i | 0.995227 | − | 1.72378i | ||||
\(587\) | − | 37.6274i | − | 1.55305i | −0.630087 | − | 0.776525i | \(-0.716981\pi\) | ||
0.630087 | − | 0.776525i | \(-0.283019\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −28.4663 | − | 16.4350i | −1.17194 | − | 0.676619i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 5.65685i | − | 0.231714i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.4264 | −1.77140 | −0.885700 | − | 0.464258i | \(-0.846321\pi\) | ||||
−0.885700 | + | 0.464258i | \(0.846321\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −22.2132 | + | 38.4744i | −0.903842 | + | 1.56550i | ||||
\(605\) | 15.0662 | − | 8.69848i | 0.612529 | − | 0.353644i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.5919 | − | 23.5418i | 0.551678 | − | 0.955533i | −0.446476 | − | 0.894795i | \(-0.647321\pi\) |
0.998154 | − | 0.0607380i | \(-0.0193454\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.27208 | + | 0.174080i | 0.0512535 | + | 0.00701388i | ||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(620\) | −25.3864 | + | 14.6569i | −1.01954 | + | 0.588633i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.19848 | − | 5.53994i | 0.127939 | − | 0.221598i | ||||
\(626\) | 31.2130 | − | 18.0208i | 1.24752 | − | 0.720257i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.7574 | −0.826337 | −0.413169 | − | 0.910654i | \(-0.635578\pi\) | ||||
−0.413169 | + | 0.910654i | \(0.635578\pi\) | |||||||
\(632\) | −18.9295 | − | 10.9289i | −0.752974 | − | 0.434730i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 21.6066 | + | 37.4237i | 0.858108 | + | 1.48629i | ||||
\(635\) | −9.28009 | − | 5.35786i | −0.368269 | − | 0.212620i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 2.52691i | − | 0.100041i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.97056 | − | 15.5375i | −0.354593 | − | 0.614172i | ||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.25736 | − | 2.17781i | 0.0493557 | − | 0.0854865i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.83028 | − | 4.52082i | −0.306423 | − | 0.176913i | 0.338902 | − | 0.940822i | \(-0.389945\pi\) |
−0.645325 | + | 0.763909i | \(0.723278\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.59188 | + | 11.4175i | 0.257566 | + | 0.446118i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.2548i | 1.76288i | 0.472298 | + | 0.881439i | \(0.343425\pi\) | ||||
−0.472298 | + | 0.881439i | \(0.656575\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 50.4264 | 1.95692 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.9411 | 1.96364 | 0.981818 | − | 0.189824i | \(-0.0607919\pi\) | ||||
0.981818 | + | 0.189824i | \(0.0607919\pi\) | |||||||
\(674\) | −44.6491 | − | 25.7782i | −1.71982 | − | 0.992938i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.0000 | + | 22.5167i | 0.500000 | + | 0.866025i | ||||
\(677\) | −37.7464 | − | 21.7929i | −1.45071 | − | 0.837569i | −0.452190 | − | 0.891922i | \(-0.649357\pi\) |
−0.998522 | + | 0.0543526i | \(0.982690\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.8934 | − | 33.3908i | 0.993697 | − | 1.28142i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.12132 | − | 1.94218i | −0.0429376 | − | 0.0743701i | ||||
\(683\) | −36.5217 | + | 21.0858i | −1.39746 | + | 0.806825i | −0.994126 | − | 0.108227i | \(-0.965483\pi\) |
−0.403336 | + | 0.915052i | \(0.632149\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.6245 | + | 21.0208i | 0.596547 | + | 0.802578i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(692\) | − | 39.5980i | − | 1.50529i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −40.0000 | −1.51838 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.97056 | − | 12.1753i | −0.187870 | − | 0.460185i | ||||
\(701\) | − | 51.3848i | − | 1.94078i | −0.241551 | − | 0.970388i | \(-0.577656\pi\) | ||
0.241551 | − | 0.970388i | \(-0.422344\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.18869 | − | 0.686292i | 0.0448005 | − | 0.0258656i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.10228 | − | 51.8995i | 0.267109 | − | 1.95188i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.5959 | + | 11.3137i | 0.732334 | + | 0.422813i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0000 | + | 34.2929i | 0.521387 | + | 1.27713i | ||||
\(722\) | 26.8701i | 1.00000i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.4147 | + | 12.9411i | −0.832461 | + | 0.480621i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.6690 | 1.69377 | 0.846886 | − | 0.531775i | \(-0.178475\pi\) | ||||
0.846886 | + | 0.531775i | \(0.178475\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15.6985 | − | 27.1906i | 0.581027 | − | 1.00637i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(734\) | − | 32.8701i | − | 1.21326i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23.0919 | + | 29.7781i | −0.847730 | + | 1.09319i | ||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.24264 | + | 3.88437i | 0.0821640 | + | 0.142312i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 50.5988 | − | 20.6569i | 1.84884 | − | 0.754785i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.8345 | + | 44.7467i | −0.942715 | + | 1.63283i | −0.182453 | + | 0.983215i | \(0.558404\pi\) |
−0.760263 | + | 0.649616i | \(0.774930\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 35.2254i | − | 1.28198i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.4264 | 1.06114 | 0.530572 | − | 0.847640i | \(-0.321977\pi\) | ||||
0.530572 | + | 0.847640i | \(0.321977\pi\) | |||||||
\(770\) | −0.942506 | + | 0.384776i | −0.0339655 | + | 0.0138664i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21.4853 | + | 37.2136i | −0.773272 | + | 1.33935i | ||||
\(773\) | 17.1464 | − | 9.89949i | 0.616714 | − | 0.356060i | −0.158874 | − | 0.987299i | \(-0.550787\pi\) |
0.775589 | + | 0.631239i | \(0.217453\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.4853 | + | 19.8931i | −0.412563 | + | 0.714581i | ||||
\(776\) | − | 45.1716i | − | 1.62156i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 44.0000 | 1.57748 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 26.9706 | + | 7.52255i | 0.963234 | + | 0.268662i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(788\) | 24.4949 | − | 14.1421i | 0.872595 | − | 0.503793i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 17.3310 | 0.616608 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.0000 | − | 24.2487i | 0.496217 | − | 0.859473i | ||||
\(797\) | − | 11.8701i | − | 0.420459i | −0.977652 | − | 0.210230i | \(-0.932579\pi\) | ||
0.977652 | − | 0.210230i | \(-0.0674211\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −12.1753 | − | 7.02944i | −0.430463 | − | 0.248528i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.08021 | + | 1.20101i | 0.0734090 | + | 0.0423827i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −28.0000 | − | 48.4974i | −0.985037 | − | 1.70613i | ||||
\(809\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 7.47156 | − | 54.5980i | 0.262200 | − | 1.91601i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 55.0711i | 1.92551i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.2033 | − | 25.5208i | −1.54271 | − | 0.890683i | −0.998667 | − | 0.0516239i | \(-0.983560\pi\) |
−0.544041 | − | 0.839059i | \(-0.683106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.0000 | + | 39.8372i | 0.801730 | + | 1.38864i | 0.918477 | + | 0.395475i | \(0.129420\pi\) |
−0.116747 | + | 0.993162i | \(0.537247\pi\) | |||||||
\(824\) | 34.2929 | + | 19.7990i | 1.19465 | + | 0.689730i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33.6066 | − | 43.3373i | 1.16932 | − | 1.50790i | ||||
\(827\) | 19.2843i | 0.670580i | 0.942115 | + | 0.335290i | \(0.108834\pi\) | ||||
−0.942115 | + | 0.335290i | \(0.891166\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(830\) | −34.6261 | + | 19.9914i | −1.20189 | + | 0.693911i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28.0000 | + | 48.4974i | −0.967244 | + | 1.67532i | ||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −79.4558 | −2.73986 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.8533 | − | 10.3076i | −0.614172 | − | 0.354593i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9706 | + | 26.8723i | 0.376953 | + | 0.923342i | ||||
\(848\) | 40.2843i | 1.38337i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.2132 | − | 50.5988i | 0.998487 | − | 1.72943i | ||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.6985 | + | 27.1906i | 0.533764 | + | 0.924507i | ||||
\(866\) | −17.1464 | − | 9.89949i | −0.582659 | − | 0.336399i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −18.4853 | − | 45.2795i | −0.627431 | − | 1.53689i | ||||
\(869\) | 1.32590i | 0.0449781i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.8176 | + | 19.2452i | 0.838987 | + | 0.650605i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(878\) | −5.16010 | + | 2.97918i | −0.174145 | + | 0.100543i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.544156 | + | 0.942506i | −0.0183435 | + | 0.0317719i | ||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.0919 | − | 50.3886i | −0.977361 | − | 1.69284i | ||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.9558 | − | 14.1281i | 0.367447 | − | 0.473841i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.272078 | − | 0.471253i | −0.00910984 | − | 0.0157787i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.9411 | −0.599706 | ||||||||
\(896\) | 27.7128 | − | 11.3137i | 0.925820 | − | 0.377964i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −83.3591 | + | 48.1274i | −2.78018 | + | 1.60514i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(908\) | −8.90644 | − | 5.14214i | −0.295571 | − | 0.170648i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.52944 | − | 2.64906i | −0.0506170 | − | 0.0876712i | ||||
\(914\) | −44.0548 | + | 25.4350i | −1.45720 | + | 0.841316i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.3643 | + | 8.31371i | −0.672490 | + | 0.274543i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.0000 | + | 43.3013i | −0.824674 | + | 1.42838i | 0.0774944 | + | 0.996993i | \(0.475308\pi\) |
−0.902168 | + | 0.431384i | \(0.858025\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.0000 | − | 24.2487i | 0.461065 | − | 0.798589i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −31.8434 | − | 18.3848i | −1.04644 | − | 0.604161i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −29.4558 | − | 51.0190i | −0.966935 | − | 1.67478i | ||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28.0000 | − | 48.4974i | −0.916188 | − | 1.58688i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.0294 | 0.392985 | 0.196492 | − | 0.980505i | \(-0.437045\pi\) | ||||
0.196492 | + | 0.980505i | \(0.437045\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49.3995 | − | 28.5208i | 1.61038 | − | 0.929752i | 0.621096 | − | 0.783735i | \(-0.286688\pi\) |
0.989282 | − | 0.146017i | \(-0.0466455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 58.6274i | − | 1.90816i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.9898 | + | 28.2843i | 1.59195 | + | 0.919115i | 0.992972 | + | 0.118354i | \(0.0377616\pi\) |
0.598983 | + | 0.800762i | \(0.295572\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.2132 | + | 47.1347i | −0.877845 | + | 1.52047i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.4558 | + | 35.4306i | −0.658838 | + | 1.14114i | ||||
\(965\) | − | 34.0711i | − | 1.09679i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.2426 | −1.13333 | −0.566663 | − | 0.823949i | \(-0.691766\pi\) | ||||
−0.566663 | + | 0.823949i | \(0.691766\pi\) | |||||||
\(968\) | 26.8723 | + | 15.5147i | 0.863708 | + | 0.498662i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17.9081 | + | 31.0178i | 0.574995 | + | 0.995921i | ||||
\(971\) | 24.3463 | + | 14.0563i | 0.781310 | + | 0.451090i | 0.836894 | − | 0.547364i | \(-0.184369\pi\) |
−0.0555842 | + | 0.998454i | \(0.517702\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 52.5858i | 1.68496i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −21.5020 | + | 5.52691i | −0.686858 | + | 0.176551i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.3345 | + | 26.5602i | −0.489344 | + | 0.847569i | ||||
\(983\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.2132 | + | 19.4218i | −0.357282 | + | 0.618831i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.1066 | − | 43.4859i | −0.797537 | − | 1.38138i | −0.921215 | − | 0.389053i | \(-0.872802\pi\) |
0.123678 | − | 0.992322i | \(-0.460531\pi\) | |||||||
\(992\) | −45.2795 | − | 26.1421i | −1.43763 | − | 0.830014i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.2010i | 0.703819i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(998\) | 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 | 504.2.cj.b.37.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 504.2.cj.b.37.4 | yes | 8 | |
4.3 | odd | 2 | 2016.2.cr.b.1297.2 | 8 | |||
7.4 | even | 3 | inner | 504.2.cj.b.109.4 | yes | 8 | |
8.3 | odd | 2 | 2016.2.cr.b.1297.3 | 8 | |||
8.5 | even | 2 | inner | 504.2.cj.b.37.4 | yes | 8 | |
12.11 | even | 2 | 2016.2.cr.b.1297.3 | 8 | |||
21.11 | odd | 6 | inner | 504.2.cj.b.109.1 | yes | 8 | |
24.5 | odd | 2 | CM | 504.2.cj.b.37.1 | ✓ | 8 | |
24.11 | even | 2 | 2016.2.cr.b.1297.2 | 8 | |||
28.11 | odd | 6 | 2016.2.cr.b.1873.3 | 8 | |||
56.11 | odd | 6 | 2016.2.cr.b.1873.2 | 8 | |||
56.53 | even | 6 | inner | 504.2.cj.b.109.1 | yes | 8 | |
84.11 | even | 6 | 2016.2.cr.b.1873.2 | 8 | |||
168.11 | even | 6 | 2016.2.cr.b.1873.3 | 8 | |||
168.53 | odd | 6 | inner | 504.2.cj.b.109.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.cj.b.37.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
504.2.cj.b.37.1 | ✓ | 8 | 24.5 | odd | 2 | CM | |
504.2.cj.b.37.4 | yes | 8 | 3.2 | odd | 2 | inner | |
504.2.cj.b.37.4 | yes | 8 | 8.5 | even | 2 | inner | |
504.2.cj.b.109.1 | yes | 8 | 21.11 | odd | 6 | inner | |
504.2.cj.b.109.1 | yes | 8 | 56.53 | even | 6 | inner | |
504.2.cj.b.109.4 | yes | 8 | 7.4 | even | 3 | inner | |
504.2.cj.b.109.4 | yes | 8 | 168.53 | odd | 6 | inner | |
2016.2.cr.b.1297.2 | 8 | 4.3 | odd | 2 | |||
2016.2.cr.b.1297.2 | 8 | 24.11 | even | 2 | |||
2016.2.cr.b.1297.3 | 8 | 8.3 | odd | 2 | |||
2016.2.cr.b.1297.3 | 8 | 12.11 | even | 2 | |||
2016.2.cr.b.1873.2 | 8 | 56.11 | odd | 6 | |||
2016.2.cr.b.1873.2 | 8 | 84.11 | even | 6 | |||
2016.2.cr.b.1873.3 | 8 | 28.11 | odd | 6 | |||
2016.2.cr.b.1873.3 | 8 | 168.11 | even | 6 |