Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1537,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3072.1537");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 1536) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1537.1 | ||
Root | \(-1.14412 + 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1537 |
Dual form | 3072.2.d.g.1537.7 |
$q$-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 \(\left(\mathbb{Z}/3072\mathbb{Z}\right)^\times\).
\(n\) | \(1025\) | \(2047\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.16228i | − 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.74806 | 0.660706 | 0.330353 | − | 0.943857i | \(-0.392832\pi\) | ||||
0.330353 | + | 0.943857i | \(0.392832\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.47214i | 1.95142i | 0.219061 | + | 0.975711i | \(0.429701\pi\) | ||||
−0.219061 | + | 0.975711i | \(0.570299\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.41421i | − 0.392232i | −0.980581 | − | 0.196116i | \(-0.937167\pi\) | ||||
0.980581 | − | 0.196116i | \(-0.0628330\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.16228 | −0.816497 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.47214 | 0.599581 | 0.299791 | − | 0.954005i | \(-0.403083\pi\) | ||||
0.299791 | + | 0.954005i | \(0.403083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.47214i | 1.48481i | 0.669951 | + | 0.742405i | \(0.266315\pi\) | ||||
−0.669951 | + | 0.742405i | \(0.733685\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 1.74806i | − 0.381459i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.65685 | 1.17954 | 0.589768 | − | 0.807573i | \(-0.299219\pi\) | ||||
0.589768 | + | 0.807573i | \(0.299219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.99070i | 1.11245i | 0.831033 | + | 0.556223i | \(0.187750\pi\) | ||||
−0.831033 | + | 0.556223i | \(0.812250\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.90879 | 0.702039 | 0.351020 | − | 0.936368i | \(-0.385835\pi\) | ||||
0.351020 | + | 0.936368i | \(0.385835\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.47214 | 1.12665 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 5.52786i | − 0.934380i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5672i | 1.73724i | 0.495482 | + | 0.868618i | \(0.334991\pi\) | ||||
−0.495482 | + | 0.868618i | \(0.665009\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.41421 | −0.226455 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.47214 | 0.386083 | 0.193041 | − | 0.981191i | \(-0.438165\pi\) | ||||
0.193041 | + | 0.981191i | \(0.438165\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.52786i | 0.232997i | 0.993191 | + | 0.116499i | \(0.0371670\pi\) | ||||
−0.993191 | + | 0.116499i | \(0.962833\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.16228i | 0.471405i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.94427 | −0.563467 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 2.47214i | − 0.346168i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.6476i | 1.59992i | 0.600056 | + | 0.799958i | \(0.295145\pi\) | ||||
−0.600056 | + | 0.799958i | \(0.704855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 20.4667 | 2.75973 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.47214 | 0.857255 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.94427i | 1.16445i | 0.813029 | + | 0.582223i | \(0.197817\pi\) | ||||
−0.813029 | + | 0.582223i | \(0.802183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 2.08191i | − 0.266562i | −0.991078 | − | 0.133281i | \(-0.957449\pi\) | ||||
0.991078 | − | 0.133281i | \(-0.0425513\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.74806 | −0.220235 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.47214 | −0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 12.0000i | − 1.46603i | −0.680211 | − | 0.733017i | \(-0.738112\pi\) | ||||
0.680211 | − | 0.733017i | \(-0.261888\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 5.65685i | − 0.681005i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.15298 | −1.08626 | −0.543130 | − | 0.839649i | \(-0.682761\pi\) | ||||
−0.543130 | + | 0.839649i | \(0.682761\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.94427 | −0.344601 | −0.172300 | − | 0.985044i | \(-0.555120\pi\) | ||||
−0.172300 | + | 0.985044i | \(0.555120\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.00000i | 0.577350i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.3137i | 1.28932i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.40492 | 0.833118 | 0.416559 | − | 0.909109i | \(-0.363236\pi\) | ||||
0.416559 | + | 0.909109i | \(0.363236\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.47214i | 0.710409i | 0.934789 | + | 0.355205i | \(0.115589\pi\) | ||||
−0.934789 | + | 0.355205i | \(0.884411\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 7.81758i | − 0.847936i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.99070 | 0.642271 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 2.47214i | − 0.259150i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 3.90879i | − 0.405323i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20.4667 | 2.09984 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9443 | −1.31429 | −0.657146 | − | 0.753763i | \(-0.728236\pi\) | ||||
−0.657146 | + | 0.753763i | \(0.728236\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 6.47214i | − 0.650474i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 0.333851i | − 0.0332194i | −0.999862 | − | 0.0166097i | \(-0.994713\pi\) | ||||
0.999862 | − | 0.0166097i | \(-0.00528727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.74806 | −0.172242 | −0.0861209 | − | 0.996285i | \(-0.527447\pi\) | ||||
−0.0861209 | + | 0.996285i | \(0.527447\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.52786 | −0.539464 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 0.944272i | − 0.0912862i | −0.998958 | − | 0.0456431i | \(-0.985466\pi\) | ||||
0.998958 | − | 0.0456431i | \(-0.0145337\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 16.8918i | − 1.61794i | −0.587852 | − | 0.808968i | \(-0.700026\pi\) | ||||
0.587852 | − | 0.808968i | \(-0.299974\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.5672 | 1.00299 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 17.8885i | − 1.66812i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.41421i | 0.130744i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.32145 | 0.396147 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −30.8885 | −2.80805 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 2.47214i | − 0.222905i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9010 | 0.967311 | 0.483656 | − | 0.875258i | \(-0.339309\pi\) | ||||
0.483656 | + | 0.875258i | \(0.339309\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.52786 | 0.134521 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 16.9443i | − 1.48043i | −0.672371 | − | 0.740214i | \(-0.734724\pi\) | ||||
0.672371 | − | 0.740214i | \(-0.265276\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.3137i | 0.981023i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.16228 | 0.272166 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.47214 | −0.211209 | −0.105604 | − | 0.994408i | \(-0.533678\pi\) | ||||
−0.105604 | + | 0.994408i | \(0.533678\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.9443i | 1.43719i | 0.695427 | + | 0.718597i | \(0.255215\pi\) | ||||
−0.695427 | + | 0.718597i | \(0.744785\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.15298 | 0.765411 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.9443 | 1.57324 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.94427i | 0.325318i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 3.82998i | − 0.313764i | −0.987617 | − | 0.156882i | \(-0.949856\pi\) | ||||
0.987617 | − | 0.156882i | \(-0.0501442\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.0540 | −1.63197 | −0.815987 | − | 0.578070i | \(-0.803806\pi\) | ||||
−0.815987 | + | 0.578070i | \(0.803806\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.47214 | −0.199860 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 12.3607i | − 0.992834i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 13.3956i | − 1.06909i | −0.845141 | − | 0.534544i | \(-0.820484\pi\) | ||||
0.845141 | − | 0.534544i | \(-0.179516\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.6476 | 0.923712 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.88854 | 0.779326 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 14.4721i | − 1.13355i | −0.823874 | − | 0.566773i | \(-0.808192\pi\) | ||||
0.823874 | − | 0.566773i | \(-0.191808\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 20.4667i | − 1.59333i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.4667 | 1.58376 | 0.791880 | − | 0.610677i | \(-0.209102\pi\) | ||||
0.791880 | + | 0.610677i | \(0.209102\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000 | 0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 6.47214i | − 0.494937i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.48683i | 0.721271i | 0.932707 | + | 0.360635i | \(0.117440\pi\) | ||||
−0.932707 | + | 0.360635i | \(0.882560\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.74032 | −0.660706 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.94427 | 0.672293 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 12.0000i | − 0.896922i | −0.893802 | − | 0.448461i | \(-0.851972\pi\) | ||||
0.893802 | − | 0.448461i | \(-0.148028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 15.5563i | − 1.15629i | −0.815933 | − | 0.578147i | \(-0.803776\pi\) | ||||
0.815933 | − | 0.578147i | \(-0.196224\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.08191 | −0.153900 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 33.4164 | 2.45682 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.0000i | 1.17004i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.74806i | 0.127153i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.8098 | −1.07160 | −0.535801 | − | 0.844344i | \(-0.679990\pi\) | ||||
−0.535801 | + | 0.844344i | \(0.679990\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.94427 | 0.355896 | 0.177948 | − | 0.984040i | \(-0.443054\pi\) | ||||
0.177948 | + | 0.984040i | \(0.443054\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.47214i | 0.320256i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.32611i | 0.521964i | 0.965344 | + | 0.260982i | \(0.0840462\pi\) | ||||
−0.965344 | + | 0.260982i | \(0.915954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.24419 | −0.371751 | −0.185875 | − | 0.982573i | \(-0.559512\pi\) | ||||
−0.185875 | + | 0.982573i | \(0.559512\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.0000 | −0.846415 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.4721i | 0.735000i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 7.81758i | − 0.546003i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.65685 | −0.393179 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −41.8885 | −2.89749 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 7.05573i | − 0.485736i | −0.970059 | − | 0.242868i | \(-0.921912\pi\) | ||||
0.970059 | − | 0.242868i | \(-0.0780882\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.15298i | 0.627152i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.83153 | 0.329508 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.83282 | 0.463842 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.94427i | 0.198955i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 3.49613i | − 0.235175i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.90879 | 0.261752 | 0.130876 | − | 0.991399i | \(-0.458221\pi\) | ||||
0.130876 | + | 0.991399i | \(0.458221\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00000 | 0.333333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.4721i | 0.960549i | 0.877118 | + | 0.480275i | \(0.159463\pi\) | ||||
−0.877118 | + | 0.480275i | \(0.840537\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 14.0633i | − 0.929331i | −0.885486 | − | 0.464665i | \(-0.846175\pi\) | ||||
0.885486 | − | 0.464665i | \(-0.153825\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.3137 | 0.744387 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0000 | 0.655122 | 0.327561 | − | 0.944830i | \(-0.393773\pi\) | ||||
0.327561 | + | 0.944830i | \(0.393773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 7.40492i | − 0.481001i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.1235 | 1.68979 | 0.844896 | − | 0.534931i | \(-0.179662\pi\) | ||||
0.844896 | + | 0.534931i | \(0.179662\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.4729i | 0.796863i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.15298 | 0.582390 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.47214 | 0.410155 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.4164i | 0.720597i | 0.932837 | + | 0.360299i | \(0.117325\pi\) | ||||
−0.932837 | + | 0.360299i | \(0.882675\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.6119i | 2.30177i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.81758 | −0.489556 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.0000 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.4721i | 1.14780i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 5.99070i | − 0.370815i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.6491 | 0.779978 | 0.389989 | − | 0.920820i | \(-0.372479\pi\) | ||||
0.389989 | + | 0.920820i | \(0.372479\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 36.8328 | 2.26262 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 10.0000i | − 0.611990i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.32300i | 0.324549i | 0.986746 | + | 0.162275i | \(0.0518830\pi\) | ||||
−0.986746 | + | 0.162275i | \(0.948117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9010 | 0.662191 | 0.331096 | − | 0.943597i | \(-0.392582\pi\) | ||||
0.331096 | + | 0.943597i | \(0.392582\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.47214 | −0.149620 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 32.3607i | − 1.95142i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 18.3848i | − 1.10463i | −0.833634 | − | 0.552317i | \(-0.813744\pi\) | ||||
0.833634 | − | 0.552317i | \(-0.186256\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.90879 | −0.234013 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.88854 | −0.231971 | −0.115986 | − | 0.993251i | \(-0.537003\pi\) | ||||
−0.115986 | + | 0.993251i | \(0.537003\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.8328i | 1.59505i | 0.603289 | + | 0.797523i | \(0.293857\pi\) | ||||
−0.603289 | + | 0.797523i | \(0.706143\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 20.4667i | − 1.21234i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.32145 | 0.255087 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8885 | −0.640503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.9443i | 0.758807i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.9613i | 1.34141i | 0.741723 | + | 0.670706i | \(0.234009\pi\) | ||||
−0.741723 | + | 0.670706i | \(0.765991\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.2843 | 1.64677 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.47214 | −0.375551 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 8.00000i | − 0.462652i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.67080i | 0.153943i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.333851 | −0.0191792 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.58359 | −0.376975 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.88854i | 0.336077i | 0.985780 | + | 0.168038i | \(0.0537433\pi\) | ||||
−0.985780 | + | 0.168038i | \(0.946257\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.74806i | 0.0994439i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.6414 | 1.11376 | 0.556880 | − | 0.830593i | \(-0.311998\pi\) | ||||
0.556880 | + | 0.830593i | \(0.311998\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.9443 | −1.18384 | −0.591920 | − | 0.805997i | \(-0.701630\pi\) | ||||
−0.591920 | + | 0.805997i | \(0.701630\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.52786i | 0.311460i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.3044i | 0.971913i | 0.873983 | + | 0.485956i | \(0.161529\pi\) | ||||
−0.873983 | + | 0.485956i | \(0.838471\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −38.7727 | −2.17085 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.944272 | −0.0527041 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.0000i | 0.890264i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.07107i | 0.392232i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.8918 | −0.934116 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 16.9443i | − 0.931341i | −0.884958 | − | 0.465671i | \(-0.845813\pi\) | ||||
0.884958 | − | 0.465671i | \(-0.154187\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 10.5672i | − 0.579079i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −37.9473 | −2.07328 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.9443 | 0.814066 | 0.407033 | − | 0.913413i | \(-0.366563\pi\) | ||||
0.407033 | + | 0.913413i | \(0.366563\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.00000i | 0.108625i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.2982i | 1.36998i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.1313 | −1.03299 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.8885 | −0.963087 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.4721i | 1.20637i | 0.797602 | + | 0.603184i | \(0.206101\pi\) | ||||
−0.797602 | + | 0.603184i | \(0.793899\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 9.23179i | − 0.494167i | −0.968994 | − | 0.247083i | \(-0.920528\pi\) | ||||
0.968994 | − | 0.247083i | \(-0.0794721\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.41421 | 0.0754851 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.8885 | −0.632763 | −0.316382 | − | 0.948632i | \(-0.602468\pi\) | ||||
−0.316382 | + | 0.948632i | \(0.602468\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.9443i | 1.53620i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 4.32145i | − 0.228715i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.4744 | 0.711153 | 0.355577 | − | 0.934647i | \(-0.384284\pi\) | ||||
0.355577 | + | 0.934647i | \(0.384284\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.8885 | −1.20466 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 30.8885i | 1.62123i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.31061i | 0.487339i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.8933 | 0.934023 | 0.467011 | − | 0.884251i | \(-0.345331\pi\) | ||||
0.467011 | + | 0.884251i | \(0.345331\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.47214 | −0.128694 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.3607i | 1.05707i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 21.8809i | − 1.13295i | −0.824079 | − | 0.566475i | \(-0.808307\pi\) | ||||
0.824079 | − | 0.566475i | \(-0.191693\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.47214 | 0.436337 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 27.4164i | − 1.40829i | −0.710058 | − | 0.704143i | \(-0.751331\pi\) | ||||
0.710058 | − | 0.704143i | \(-0.248669\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 10.9010i | − 0.558478i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.1313 | −0.977563 | −0.488782 | − | 0.872406i | \(-0.662559\pi\) | ||||
−0.488782 | + | 0.872406i | \(0.662559\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 35.7771 | 1.82337 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.52786i | − 0.0776657i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 33.4497i | − 1.69596i | −0.530024 | − | 0.847982i | \(-0.677817\pi\) | ||||
0.530024 | − | 0.847982i | \(-0.322183\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.9845 | 0.707227 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.9443 | −0.854725 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 23.4164i | − 1.17821i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 9.07417i | − 0.455420i | −0.973729 | − | 0.227710i | \(-0.926876\pi\) | ||||
0.973729 | − | 0.227710i | \(-0.0731238\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.3137 | 0.566394 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.5279 | 0.675549 | 0.337775 | − | 0.941227i | \(-0.390326\pi\) | ||||
0.337775 | + | 0.941227i | \(0.390326\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 5.52786i | − 0.275363i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 3.16228i | − 0.157135i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −68.3923 | −3.39008 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.9443 | 0.640053 | 0.320027 | − | 0.947409i | \(-0.396308\pi\) | ||||
0.320027 | + | 0.947409i | \(0.396308\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.47214i | 0.121941i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.6352i | 0.769356i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.4667 | 1.00467 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.9443 | 0.829765 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.52786i | 0.0746410i | 0.999303 | + | 0.0373205i | \(0.0118823\pi\) | ||||
−0.999303 | + | 0.0373205i | \(0.988118\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 7.07107i | − 0.344623i | −0.985043 | − | 0.172311i | \(-0.944876\pi\) | ||||
0.985043 | − | 0.172311i | \(-0.0551235\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.3607 | −0.599581 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3.63932i | − 0.176119i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 9.15298i | − 0.441910i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.3060 | −0.881767 | −0.440884 | − | 0.897564i | \(-0.645335\pi\) | ||||
−0.440884 | + | 0.897564i | \(0.645335\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.0000 | 1.15337 | 0.576683 | − | 0.816968i | \(-0.304347\pi\) | ||||
0.576683 | + | 0.816968i | \(0.304347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 18.9443i | − 0.908308i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 36.6119i | 1.75139i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.06952 | 0.289682 | 0.144841 | − | 0.989455i | \(-0.453733\pi\) | ||||
0.144841 | + | 0.989455i | \(0.453733\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.94427 | 0.187822 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 11.4164i | − 0.542410i | −0.962522 | − | 0.271205i | \(-0.912578\pi\) | ||||
0.962522 | − | 0.271205i | \(-0.0874221\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 31.6228i | − 1.49906i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.82998 | −0.181152 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.4164 | −1.10509 | −0.552544 | − | 0.833484i | \(-0.686343\pi\) | ||||
−0.552544 | + | 0.833484i | \(0.686343\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.0000i | 0.753411i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.0540i | 0.942220i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.81758 | −0.366494 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.05573 | −0.142941 | −0.0714705 | − | 0.997443i | \(-0.522769\pi\) | ||||
−0.0714705 | + | 0.997443i | \(0.522769\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.47214i | 0.115389i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.81913i | 0.410748i | 0.978684 | + | 0.205374i | \(0.0658411\pi\) | ||||
−0.978684 | + | 0.205374i | \(0.934159\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.40492 | −0.344136 | −0.172068 | − | 0.985085i | \(-0.555045\pi\) | ||||
−0.172068 | + | 0.985085i | \(0.555045\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.3607 | −0.573213 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.58359i | 0.212103i | 0.994361 | + | 0.106052i | \(0.0338209\pi\) | ||||
−0.994361 | + | 0.106052i | \(0.966179\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 20.9768i | − 0.968617i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.3956 | −0.617238 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.88854 | −0.454676 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 32.3607i | − 1.48481i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 11.6476i | − 0.533305i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.49613 | 0.159742 | 0.0798711 | − | 0.996805i | \(-0.474549\pi\) | ||||
0.0798711 | + | 0.996805i | \(0.474549\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.9443 | 0.681400 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 9.88854i | − 0.449944i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 40.9334i | 1.85869i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.5579 | 0.750310 | 0.375155 | − | 0.926962i | \(-0.377589\pi\) | ||||
0.375155 | + | 0.926962i | \(0.377589\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.4721 | −0.654453 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.8885i | 0.987816i | 0.869514 | + | 0.493908i | \(0.164432\pi\) | ||||
−0.869514 | + | 0.493908i | \(0.835568\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.8098i | 0.667001i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −20.4667 | −0.919909 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.0000 | −0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.9443i | 1.11666i | 0.829619 | + | 0.558329i | \(0.188557\pi\) | ||||
−0.829619 | + | 0.558329i | \(0.811443\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 20.4667i | − 0.914384i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.83153 | −0.215427 | −0.107714 | − | 0.994182i | \(-0.534353\pi\) | ||||
−0.107714 | + | 0.994182i | \(0.534353\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.05573 | −0.0469793 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 11.0000i | − 0.488527i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 39.9318i | − 1.76995i | −0.465641 | − | 0.884974i | \(-0.654176\pi\) | ||||
0.465641 | − | 0.884974i | \(-0.345824\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.14678 | −0.227680 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.47214 | −0.285752 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.52786i | 0.243587i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.48683 | 0.416426 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.3607 | 1.24250 | 0.621252 | − | 0.783611i | \(-0.286624\pi\) | ||||
0.621252 | + | 0.783611i | \(0.286624\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 16.3607i | − 0.715403i | −0.933836 | − | 0.357701i | \(-0.883561\pi\) | ||||
0.933836 | − | 0.357701i | \(-0.116439\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.74032i | 0.381459i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.66306 | 0.420930 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00000 | 0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 8.94427i | − 0.388148i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3.49613i | − 0.151434i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.98605 | −0.129098 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0000 | −0.517838 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 25.5279i | − 1.09956i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.7124i | 1.14846i | 0.818695 | + | 0.574229i | \(0.194698\pi\) | ||||
−0.818695 | + | 0.574229i | \(0.805302\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.5563 | −0.667587 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −53.4164 | −2.28811 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 32.3607i | − 1.38364i | −0.722069 | − | 0.691821i | \(-0.756809\pi\) | ||||
0.722069 | − | 0.691821i | \(-0.243191\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.08191i | 0.0888540i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.7727 | −1.65177 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.9443 | 0.550446 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 33.4164i | − 1.41845i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 15.8114i | − 0.669950i | −0.942227 | − | 0.334975i | \(-0.891272\pi\) | ||||
0.942227 | − | 0.334975i | \(-0.108728\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.16073 | 0.0913890 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.0000 | 0.675521 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.52786i | − 0.0643918i | −0.999482 | − | 0.0321959i | \(-0.989750\pi\) | ||||
0.999482 | − | 0.0321959i | \(-0.0102500\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.32456i | 0.266076i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.74806 | 0.0734118 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.41641 | −0.310912 | −0.155456 | − | 0.987843i | \(-0.549685\pi\) | ||||
−0.155456 | + | 0.987843i | \(0.549685\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 8.94427i | − 0.374306i | −0.982331 | − | 0.187153i | \(-0.940074\pi\) | ||||
0.982331 | − | 0.187153i | \(-0.0599260\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.8098i | 0.618690i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.2843 | −1.17954 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.9443 | 1.12170 | 0.560852 | − | 0.827916i | \(-0.310474\pi\) | ||||
0.560852 | + | 0.827916i | \(0.310474\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 4.94427i | − 0.205477i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.3137i | 0.469372i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −75.3846 | −3.12211 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.47214 | 0.184900 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 32.9443i | − 1.35976i | −0.733325 | − | 0.679878i | \(-0.762033\pi\) | ||||
0.733325 | − | 0.679878i | \(-0.237967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.2982i | 1.04240i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.32611 | 0.301356 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.88854 | 0.323944 | 0.161972 | − | 0.986795i | \(-0.448215\pi\) | ||||
0.161972 | + | 0.986795i | \(0.448215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 13.6656i | − 0.560236i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.24419i | 0.214631i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.65685 | −0.231133 | −0.115566 | − | 0.993300i | \(-0.536868\pi\) | ||||
−0.115566 | + | 0.993300i | \(0.536868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.94427 | 0.283263 | 0.141631 | − | 0.989919i | \(-0.454765\pi\) | ||||
0.141631 | + | 0.989919i | \(0.454765\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.0000i | 0.488678i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 97.6782i | 3.97118i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.8422 | 1.82009 | 0.910044 | − | 0.414512i | \(-0.136048\pi\) | ||||
0.910044 | + | 0.414512i | \(0.136048\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.4721 | 0.424352 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 10.5672i | − 0.426805i | −0.976964 | − | 0.213403i | \(-0.931545\pi\) | ||||
0.976964 | − | 0.213403i | \(-0.0684546\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.81758 | −0.315235 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.8885 | 0.639649 | 0.319824 | − | 0.947477i | \(-0.396376\pi\) | ||||
0.319824 | + | 0.947477i | \(0.396376\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 5.88854i | − 0.236681i | −0.992973 | − | 0.118340i | \(-0.962243\pi\) | ||||
0.992973 | − | 0.118340i | \(-0.0377574\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.65685i | 0.227002i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.4806 | 0.700347 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 41.8885i | 1.67287i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.1235i | 1.04161i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.0463 | −1.07670 | −0.538348 | − | 0.842723i | \(-0.680951\pi\) | ||||
−0.538348 | + | 0.842723i | \(0.680951\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.05573 | −0.280440 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 34.4721i | − 1.36798i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.57804i | 0.221010i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.15298 | 0.362086 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.58359 | 0.339032 | 0.169516 | − | 0.985527i | \(-0.445780\pi\) | ||||
0.169516 | + | 0.985527i | \(0.445780\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.36068i | 0.329713i | 0.986318 | + | 0.164857i | \(0.0527161\pi\) | ||||
−0.986318 | + | 0.164857i | \(0.947284\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 4.83153i | − 0.190241i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.2688 | −1.66176 | −0.830879 | − | 0.556454i | \(-0.812162\pi\) | ||||
−0.830879 | + | 0.556454i | \(0.812162\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −57.8885 | −2.27232 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 6.83282i | − 0.267799i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.4388i | 1.50423i | 0.659034 | + | 0.752113i | \(0.270965\pi\) | ||||
−0.659034 | + | 0.752113i | \(0.729035\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −53.5825 | −2.09364 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.94427 | 0.114867 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.00000i | 0.155818i | 0.996960 | + | 0.0779089i | \(0.0248243\pi\) | ||||
−0.996960 | + | 0.0779089i | \(0.975176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.1869i | 1.56309i | 0.623850 | + | 0.781544i | \(0.285568\pi\) | ||||
−0.623850 | + | 0.781544i | \(0.714432\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.49613 | −0.135778 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 35.7771 | 1.38738 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.8885i | 1.31217i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 3.90879i | − 0.151123i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.4744 | 0.520175 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.8885 | −0.689553 | −0.344776 | − | 0.938685i | \(-0.612045\pi\) | ||||
−0.344776 | + | 0.938685i | \(0.612045\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 5.00000i | − 0.192450i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.491473i | 0.0188889i | 0.999955 | + | 0.00944443i | \(0.00300630\pi\) | ||||
−0.999955 | + | 0.00944443i | \(0.996994\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.6274 | −0.868361 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.4721 | 0.554573 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.41641i | 0.130725i | 0.997862 | + | 0.0653626i | \(0.0208204\pi\) | ||||
−0.997862 | + | 0.0653626i | \(0.979180\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.81758i | 0.298694i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.0633 | −0.536549 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.4721 | 0.627538 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.5279i | 0.971126i | 0.874202 | + | 0.485563i | \(0.161385\pi\) | ||||
−0.874202 | + | 0.485563i | \(0.838615\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 11.3137i | − 0.429772i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 53.5825 | 2.03250 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.11146 | 0.231488 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 10.0000i | − 0.378235i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 35.6104i | − 1.34499i | −0.740104 | − | 0.672493i | \(-0.765224\pi\) | ||||
0.740104 | − | 0.672493i | \(-0.234776\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −68.3923 | −2.57947 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 0.583592i | − 0.0219482i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 33.8623i | − 1.27173i | −0.771802 | − | 0.635863i | \(-0.780644\pi\) | ||||
0.771802 | − | 0.635863i | \(-0.219356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.40492 | −0.277706 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.1115 | 0.828081 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 28.9443i | − 1.08245i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 26.1235i | − 0.975602i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.8021 | 0.813081 | 0.406540 | − | 0.913633i | \(-0.366735\pi\) | ||||
0.406540 | + | 0.913633i | \(0.366735\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.05573 | −0.113801 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 29.9535i | − 1.11245i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.0540 | 0.743763 | 0.371881 | − | 0.928280i | \(-0.378713\pi\) | ||||
0.371881 | + | 0.928280i | \(0.378713\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.77709i | 0.139701i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 31.0339i | − 1.14626i | −0.819463 | − | 0.573131i | \(-0.805728\pi\) | ||||
0.819463 | − | 0.573131i | \(-0.194272\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.4729 | 0.460069 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 77.6656 | 2.86085 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.9443i | 1.21187i | 0.795512 | + | 0.605937i | \(0.207202\pi\) | ||||
−0.795512 | + | 0.605937i | \(0.792798\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 9.15298i | − 0.336243i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.16073 | −0.0792694 | −0.0396347 | − | 0.999214i | \(-0.512619\pi\) | ||||
−0.0396347 | + | 0.999214i | \(0.512619\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.1115 | −0.443729 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 6.47214i | − 0.236803i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1.65065i | − 0.0603134i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.40492 | −0.270209 | −0.135105 | − | 0.990831i | \(-0.543137\pi\) | ||||
−0.135105 | + | 0.990831i | \(0.543137\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.4164 | 0.416037 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 63.4164i | 2.30796i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.0633i | 0.511140i | 0.966791 | + | 0.255570i | \(0.0822632\pi\) | ||||
−0.966791 | + | 0.255570i | \(0.917737\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 36.6119 | 1.32893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.41641 | 0.268845 | 0.134422 | − | 0.990924i | \(-0.457082\pi\) | ||||
0.134422 | + | 0.990924i | \(0.457082\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 29.5279i | − 1.06898i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.81758i | 0.282645i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.6491 | 0.456733 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.8328 | −1.11186 | −0.555930 | − | 0.831229i | \(-0.687638\pi\) | ||||
−0.555930 | + | 0.831229i | \(0.687638\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.0000i | 0.504198i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.65841i | 0.239486i | 0.992805 | + | 0.119743i | \(0.0382071\pi\) | ||||
−0.992805 | + | 0.119743i | \(0.961793\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.5440 | −0.702039 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.4721 | 0.662684 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.0000i | 0.573259i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 59.2393i | − 2.11975i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.99070 | −0.214090 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42.3607 | −1.51192 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.4721i | 0.515876i | 0.966161 | + | 0.257938i | \(0.0830430\pi\) | ||||
−0.966161 | + | 0.257938i | \(0.916957\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 12.6491i | − 0.450320i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.49613 | −0.124308 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.94427 | −0.104554 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 36.8328i | − 1.30633i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 5.16538i | − 0.182967i | −0.995807 | − | 0.0914836i | \(-0.970839\pi\) | ||||
0.995807 | − | 0.0914836i | \(-0.0291609\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.0000 | −0.353333 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 19.0557i | − 0.672462i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 31.2703i | − 1.10213i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.32300 | 0.187379 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.4164 | 0.823277 | 0.411639 | − | 0.911347i | \(-0.364957\pi\) | ||||
0.411639 | + | 0.911347i | \(0.364957\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.3050i | 1.02904i | 0.857480 | + | 0.514518i | \(0.172029\pi\) | ||||
−0.857480 | + | 0.514518i | \(0.827971\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 10.9010i | − 0.382316i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −45.7649 | −1.60307 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.88854 | −0.345956 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.47214i | 0.0863834i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 50.2626i | − 1.75418i | −0.480329 | − | 0.877088i | \(-0.659483\pi\) | ||||
0.480329 | − | 0.877088i | \(-0.340517\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.74806 | −0.0609337 | −0.0304668 | − | 0.999536i | \(-0.509699\pi\) | ||||
−0.0304668 | + | 0.999536i | \(0.509699\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −32.3607 | −1.12665 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.1115i | 0.629797i | 0.949125 | + | 0.314899i | \(0.101970\pi\) | ||||
−0.949125 | + | 0.314899i | \(0.898030\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 5.57804i | − 0.193733i | −0.995297 | − | 0.0968667i | \(-0.969118\pi\) | ||||
0.995297 | − | 0.0968667i | \(-0.0308821\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.3848 | −0.637761 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.75078 | −0.337844 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 64.7214i | − 2.23978i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.90879i | 0.135108i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.48218 | −0.223790 | −0.111895 | − | 0.993720i | \(-0.535692\pi\) | ||||
−0.111895 | + | 0.993720i | \(0.535692\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.88854 | −0.237536 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.88854i | 0.133929i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 34.7851i | − 1.19664i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −53.9952 | −1.85530 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.8328 | 0.920900 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 59.7771i | 2.04913i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.3662i | 1.03972i | 0.854252 | + | 0.519859i | \(0.174016\pi\) | ||||
−0.854252 | + | 0.519859i | \(0.825984\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.4667 | −0.699946 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −55.4164 | −1.89299 | −0.946494 | − | 0.322721i | \(-0.895403\pi\) | ||||
−0.946494 | + | 0.322721i | \(0.895403\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 54.4721i | − 1.85857i | −0.369369 | − | 0.929283i | \(-0.620426\pi\) | ||||
0.369369 | − | 0.929283i | \(-0.379574\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 4.32145i | − 0.147275i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.7943 | 0.980171 | 0.490086 | − | 0.871674i | \(-0.336966\pi\) | ||||
0.490086 | + | 0.871674i | \(0.336966\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.0000 | 1.02003 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.8885i | 0.369794i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 47.9256i | 1.62577i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.9706 | −0.575026 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.9443 | 0.438097 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 27.3801i | − 0.924561i | −0.886734 | − | 0.462281i | \(-0.847031\pi\) | ||||
0.886734 | − | 0.462281i | \(-0.152969\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.9613 | 0.774464 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.88854 | −0.265772 | −0.132886 | − | 0.991131i | \(-0.542424\pi\) | ||||
−0.132886 | + | 0.991131i | \(0.542424\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 9.52786i | − 0.320638i | −0.987065 | − | 0.160319i | \(-0.948748\pi\) | ||||
0.987065 | − | 0.160319i | \(-0.0512523\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 28.2843i | − 0.950765i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.32766 | −0.279615 | −0.139808 | − | 0.990179i | \(-0.544648\pi\) | ||||
−0.139808 | + | 0.990179i | \(0.544648\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.0557 | 0.639109 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.47214i | 0.216825i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37.9473 | −1.26844 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.00000 | −0.267112 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.4164i | 0.780981i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.7943i | 0.959279i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.67080 | 0.0888788 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −49.1935 | −1.63525 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.1935i | 1.56703i | 0.621370 | + | 0.783517i | \(0.286576\pi\) | ||||
−0.621370 | + | 0.783517i | \(0.713424\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.333851i | 0.0110731i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.8098 | −0.490672 | −0.245336 | − | 0.969438i | \(-0.578898\pi\) | ||||
−0.245336 | + | 0.969438i | \(0.578898\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.8885 | −1.38631 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.58359i | 0.217647i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 29.6197i | − 0.978128i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.57339 | 0.0848882 | 0.0424441 | − | 0.999099i | \(-0.486486\pi\) | ||||
0.0424441 | + | 0.999099i | \(0.486486\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.88854 | 0.194034 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.9443i | 0.426066i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 52.8360i | − 1.73724i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.74806 | 0.0574140 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.47214 | −0.0811081 | −0.0405541 | − | 0.999177i | \(-0.512912\pi\) | ||||
−0.0405541 | + | 0.999177i | \(0.512912\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 25.5279i | − 0.836642i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 19.6414i | − 0.643029i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 50.5964 | 1.65468 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.9443i | 0.683490i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.4465i | 1.02513i | 0.858649 | + | 0.512564i | \(0.171304\pi\) | ||||
−0.858649 | + | 0.512564i | \(0.828696\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.9845 | 0.455398 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.52786 | 0.179821 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 23.7771i | − 0.772652i | −0.922362 | − | 0.386326i | \(-0.873744\pi\) | ||||
0.922362 | − | 0.386326i | \(-0.126256\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.16383i | 0.135164i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.3044 | 0.561134 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.4721 | 0.598371 | 0.299186 | − | 0.954195i | \(-0.403285\pi\) | ||||
0.299186 | + | 0.954195i | \(0.403285\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 46.8328i | 1.51547i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 38.7727i | 1.25334i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.32145 | −0.139547 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.7214 | −0.507141 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.944272i | 0.0304287i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 15.6352i | − 0.503314i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.3600 | 1.23357 | 0.616787 | − | 0.787130i | \(-0.288434\pi\) | ||||
0.616787 | + | 0.787130i | \(0.288434\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.0000 | 0.513994 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.3607i | 0.781771i | 0.920439 | + | 0.390886i | \(0.127831\pi\) | ||||
−0.920439 | + | 0.390886i | \(0.872169\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.6197i | 0.949563i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.07107 | 0.226455 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.4164 | 1.26104 | 0.630521 | − | 0.776172i | \(-0.282841\pi\) | ||||
0.630521 | + | 0.776172i | \(0.282841\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 64.7214i | 2.06850i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.8918i | 0.539312i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.98605 | −0.0952402 | −0.0476201 | − | 0.998866i | \(-0.515164\pi\) | ||||
−0.0476201 | + | 0.998866i | \(0.515164\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.1672 | 0.738168 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.64290i | 0.274828i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.3972 | −0.457341 | −0.228671 | − | 0.973504i | \(-0.573438\pi\) | ||||
−0.228671 | + | 0.973504i | \(0.573438\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.9443 | −0.537710 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.5836i | 0.525735i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 41.6799i | − 1.32002i | −0.751259 | − | 0.660008i | \(-0.770553\pi\) | ||||
0.751259 | − | 0.660008i | \(-0.229447\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.5672 | −0.334331 |
(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 | 3072.2.d.g.1537.1 | 8 | ||
4.3 | odd | 2 | inner | 3072.2.d.g.1537.6 | 8 | ||
8.3 | odd | 2 | inner | 3072.2.d.g.1537.4 | 8 | ||
8.5 | even | 2 | inner | 3072.2.d.g.1537.7 | 8 | ||
16.3 | odd | 4 | 3072.2.a.k.1.1 | 4 | |||
16.5 | even | 4 | 3072.2.a.k.1.4 | 4 | |||
16.11 | odd | 4 | 3072.2.a.q.1.3 | 4 | |||
16.13 | even | 4 | 3072.2.a.q.1.2 | 4 | |||
32.3 | odd | 8 | 1536.2.j.g.385.2 | ✓ | 8 | ||
32.5 | even | 8 | 1536.2.j.g.1153.4 | yes | 8 | ||
32.11 | odd | 8 | 1536.2.j.h.1153.3 | yes | 8 | ||
32.13 | even | 8 | 1536.2.j.h.385.1 | yes | 8 | ||
32.19 | odd | 8 | 1536.2.j.h.385.3 | yes | 8 | ||
32.21 | even | 8 | 1536.2.j.h.1153.1 | yes | 8 | ||
32.27 | odd | 8 | 1536.2.j.g.1153.2 | yes | 8 | ||
32.29 | even | 8 | 1536.2.j.g.385.4 | yes | 8 | ||
48.5 | odd | 4 | 9216.2.a.bj.1.2 | 4 | |||
48.11 | even | 4 | 9216.2.a.bd.1.1 | 4 | |||
48.29 | odd | 4 | 9216.2.a.bd.1.4 | 4 | |||
48.35 | even | 4 | 9216.2.a.bj.1.3 | 4 | |||
96.5 | odd | 8 | 4608.2.k.bf.1153.2 | 8 | |||
96.11 | even | 8 | 4608.2.k.bg.1153.3 | 8 | |||
96.29 | odd | 8 | 4608.2.k.bf.3457.1 | 8 | |||
96.35 | even | 8 | 4608.2.k.bf.3457.2 | 8 | |||
96.53 | odd | 8 | 4608.2.k.bg.1153.4 | 8 | |||
96.59 | even | 8 | 4608.2.k.bf.1153.1 | 8 | |||
96.77 | odd | 8 | 4608.2.k.bg.3457.3 | 8 | |||
96.83 | even | 8 | 4608.2.k.bg.3457.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.j.g.385.2 | ✓ | 8 | 32.3 | odd | 8 | ||
1536.2.j.g.385.4 | yes | 8 | 32.29 | even | 8 | ||
1536.2.j.g.1153.2 | yes | 8 | 32.27 | odd | 8 | ||
1536.2.j.g.1153.4 | yes | 8 | 32.5 | even | 8 | ||
1536.2.j.h.385.1 | yes | 8 | 32.13 | even | 8 | ||
1536.2.j.h.385.3 | yes | 8 | 32.19 | odd | 8 | ||
1536.2.j.h.1153.1 | yes | 8 | 32.21 | even | 8 | ||
1536.2.j.h.1153.3 | yes | 8 | 32.11 | odd | 8 | ||
3072.2.a.k.1.1 | 4 | 16.3 | odd | 4 | |||
3072.2.a.k.1.4 | 4 | 16.5 | even | 4 | |||
3072.2.a.q.1.2 | 4 | 16.13 | even | 4 | |||
3072.2.a.q.1.3 | 4 | 16.11 | odd | 4 | |||
3072.2.d.g.1537.1 | 8 | 1.1 | even | 1 | trivial | ||
3072.2.d.g.1537.4 | 8 | 8.3 | odd | 2 | inner | ||
3072.2.d.g.1537.6 | 8 | 4.3 | odd | 2 | inner | ||
3072.2.d.g.1537.7 | 8 | 8.5 | even | 2 | inner | ||
4608.2.k.bf.1153.1 | 8 | 96.59 | even | 8 | |||
4608.2.k.bf.1153.2 | 8 | 96.5 | odd | 8 | |||
4608.2.k.bf.3457.1 | 8 | 96.29 | odd | 8 | |||
4608.2.k.bf.3457.2 | 8 | 96.35 | even | 8 | |||
4608.2.k.bg.1153.3 | 8 | 96.11 | even | 8 | |||
4608.2.k.bg.1153.4 | 8 | 96.53 | odd | 8 | |||
4608.2.k.bg.3457.3 | 8 | 96.77 | odd | 8 | |||
4608.2.k.bg.3457.4 | 8 | 96.83 | even | 8 | |||
9216.2.a.bd.1.1 | 4 | 48.11 | even | 4 | |||
9216.2.a.bd.1.4 | 4 | 48.29 | odd | 4 | |||
9216.2.a.bj.1.2 | 4 | 48.5 | odd | 4 | |||
9216.2.a.bj.1.3 | 4 | 48.35 | even | 4 |