Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1,3072)]
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, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3072.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.a (trivial) |
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: | yes |
Analytic conductor: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1536) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.28825\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.16228 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
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 | ||||||||
\(11\) | 6.47214 | 1.95142 | 0.975711 | − | 0.219061i | \(-0.0702993\pi\) | ||||
0.975711 | + | 0.219061i | \(0.0702993\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41421 | −0.392232 | −0.196116 | − | 0.980581i | \(-0.562833\pi\) | ||||
−0.196116 | + | 0.980581i | \(0.562833\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | −6.47214 | −1.48481 | −0.742405 | − | 0.669951i | \(-0.766315\pi\) | ||||
−0.742405 | + | 0.669951i | \(0.766315\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.74806 | 0.381459 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.99070 | 1.11245 | 0.556223 | − | 0.831033i | \(-0.312250\pi\) | ||||
0.556223 | + | 0.831033i | \(0.312250\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.90879 | −0.702039 | −0.351020 | − | 0.936368i | \(-0.614165\pi\) | ||||
−0.351020 | + | 0.936368i | \(0.614165\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.47214 | 1.12665 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.52786 | 0.934380 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.5672 | −1.73724 | −0.868618 | − | 0.495482i | \(-0.834991\pi\) | ||||
−0.868618 | + | 0.495482i | \(0.834991\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.41421 | −0.226455 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.47214 | −0.386083 | −0.193041 | − | 0.981191i | \(-0.561835\pi\) | ||||
−0.193041 | + | 0.981191i | \(0.561835\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.52786 | 0.232997 | 0.116499 | − | 0.993191i | \(-0.462833\pi\) | ||||
0.116499 | + | 0.993191i | \(0.462833\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.16228 | 0.471405 | ||||||||
\(46\) | 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 | ||||||||
\(51\) | 2.47214 | 0.346168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.6476 | −1.59992 | −0.799958 | − | 0.600056i | \(-0.795145\pi\) | ||||
−0.799958 | + | 0.600056i | \(0.795145\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 20.4667 | 2.75973 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.47214 | −0.857255 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.94427 | 1.16445 | 0.582223 | − | 0.813029i | \(-0.302183\pi\) | ||||
0.582223 | + | 0.813029i | \(0.302183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.08191 | −0.266562 | −0.133281 | − | 0.991078i | \(-0.542551\pi\) | ||||
−0.133281 | + | 0.991078i | \(0.542551\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.74806 | 0.220235 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.47214 | −0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.65685 | 0.681005 | ||||||||
\(70\) | 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 | \(-0.444880\pi\) | ||||
0.172300 | + | 0.985044i | \(0.444880\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.00000 | 0.577350 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.3137 | 1.28932 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.40492 | −0.833118 | −0.416559 | − | 0.909109i | \(-0.636764\pi\) | ||||
−0.416559 | + | 0.909109i | \(0.636764\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.47214 | −0.710409 | −0.355205 | − | 0.934789i | \(-0.615589\pi\) | ||||
−0.355205 | + | 0.934789i | \(0.615589\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.81758 | 0.847936 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.99070 | 0.642271 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.47214 | −0.259150 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.90879 | −0.405323 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 6.47214 | 0.650474 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.333851 | 0.0332194 | 0.0166097 | − | 0.999862i | \(-0.494713\pi\) | ||||
0.0166097 | + | 0.999862i | \(0.494713\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | −0.944272 | −0.0912862 | −0.0456431 | − | 0.998958i | \(-0.514534\pi\) | ||||
−0.0456431 | + | 0.998958i | \(0.514534\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.8918 | −1.61794 | −0.808968 | − | 0.587852i | \(-0.799974\pi\) | ||||
−0.808968 | + | 0.587852i | \(0.799974\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 17.8885 | 1.66812 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.41421 | −0.130744 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.32145 | 0.396147 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.8885 | 2.80805 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.47214 | −0.222905 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.9010 | −0.967311 | −0.483656 | − | 0.875258i | \(-0.660691\pi\) | ||||
−0.483656 | + | 0.875258i | \(0.660691\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.52786 | 0.134521 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.9443 | 1.48043 | 0.740214 | − | 0.672371i | \(-0.234724\pi\) | ||||
0.740214 | + | 0.672371i | \(0.234724\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.3137 | −0.981023 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.16228 | 0.272166 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.47214 | 0.211209 | 0.105604 | − | 0.994408i | \(-0.466322\pi\) | ||||
0.105604 | + | 0.994408i | \(0.466322\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.9443 | 1.43719 | 0.718597 | − | 0.695427i | \(-0.244785\pi\) | ||||
0.718597 | + | 0.695427i | \(0.244785\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.15298 | −0.765411 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.9443 | 1.57324 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.94427 | −0.325318 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.82998 | 0.313764 | 0.156882 | − | 0.987617i | \(-0.449856\pi\) | ||||
0.156882 | + | 0.987617i | \(0.449856\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | −12.3607 | −0.992834 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.3956 | −1.06909 | −0.534544 | − | 0.845141i | \(-0.679516\pi\) | ||||
−0.534544 | + | 0.845141i | \(0.679516\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.6476 | −0.923712 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.88854 | 0.779326 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.4721 | 1.13355 | 0.566773 | − | 0.823874i | \(-0.308192\pi\) | ||||
0.566773 | + | 0.823874i | \(0.308192\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 20.4667 | 1.59333 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | −6.47214 | −0.494937 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.48683 | 0.721271 | 0.360635 | − | 0.932707i | \(-0.382560\pi\) | ||||
0.360635 | + | 0.932707i | \(0.382560\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.74032 | 0.660706 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.94427 | 0.672293 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5563 | 1.15629 | 0.578147 | − | 0.815933i | \(-0.303776\pi\) | ||||
0.578147 | + | 0.815933i | \(0.303776\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.08191 | −0.153900 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −33.4164 | −2.45682 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.0000 | 1.17004 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.74806 | 0.127153 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.8098 | 1.07160 | 0.535801 | − | 0.844344i | \(-0.320010\pi\) | ||||
0.535801 | + | 0.844344i | \(0.320010\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.94427 | 0.355896 | 0.177948 | − | 0.984040i | \(-0.443054\pi\) | ||||
0.177948 | + | 0.984040i | \(0.443054\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.47214 | −0.320256 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.32611 | −0.521964 | −0.260982 | − | 0.965344i | \(-0.584046\pi\) | ||||
−0.260982 | + | 0.965344i | \(0.584046\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 10.4721 | 0.735000 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.81758 | −0.546003 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.65685 | 0.393179 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −41.8885 | −2.89749 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.05573 | 0.485736 | 0.242868 | − | 0.970059i | \(-0.421912\pi\) | ||||
0.242868 | + | 0.970059i | \(0.421912\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.15298 | −0.627152 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.83153 | 0.329508 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.83282 | −0.463842 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.94427 | 0.198955 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.49613 | −0.235175 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.90879 | −0.261752 | −0.130876 | − | 0.991399i | \(-0.541779\pi\) | ||||
−0.130876 | + | 0.991399i | \(0.541779\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00000 | 0.333333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.4721 | −0.960549 | −0.480275 | − | 0.877118i | \(-0.659463\pi\) | ||||
−0.480275 | + | 0.877118i | \(0.659463\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0633 | 0.929331 | 0.464665 | − | 0.885486i | \(-0.346175\pi\) | ||||
0.464665 | + | 0.885486i | \(0.346175\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.3137 | 0.744387 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.40492 | −0.481001 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.1235 | −1.68979 | −0.844896 | − | 0.534931i | \(-0.820338\pi\) | ||||
−0.844896 | + | 0.534931i | \(0.820338\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.4729 | −0.796863 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.15298 | 0.582390 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.47214 | −0.410155 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.4164 | 0.720597 | 0.360299 | − | 0.932837i | \(-0.382675\pi\) | ||||
0.360299 | + | 0.932837i | \(0.382675\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.6119 | 2.30177 | ||||||||
\(254\) | 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 | ||||||||
\(259\) | −18.4721 | −1.14780 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.99070 | 0.370815 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | −10.0000 | −0.611990 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.32300 | 0.324549 | 0.162275 | − | 0.986746i | \(-0.448117\pi\) | ||||
0.162275 | + | 0.986746i | \(0.448117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.9010 | −0.662191 | −0.331096 | − | 0.943597i | \(-0.607418\pi\) | ||||
−0.331096 | + | 0.943597i | \(0.607418\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.47214 | −0.149620 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 32.3607 | 1.95142 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.3848 | 1.10463 | 0.552317 | − | 0.833634i | \(-0.313744\pi\) | ||||
0.552317 | + | 0.833634i | \(0.313744\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.90879 | −0.234013 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.88854 | 0.231971 | 0.115986 | − | 0.993251i | \(-0.462997\pi\) | ||||
0.115986 | + | 0.993251i | \(0.462997\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.8328 | 1.59505 | 0.797523 | − | 0.603289i | \(-0.206143\pi\) | ||||
0.797523 | + | 0.603289i | \(0.206143\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −20.4667 | −1.21234 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.32145 | −0.255087 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8885 | −0.640503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.9443 | −0.758807 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.9613 | −1.34141 | −0.670706 | − | 0.741723i | \(-0.734009\pi\) | ||||
−0.670706 | + | 0.741723i | \(0.734009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.2843 | 1.64677 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.47214 | 0.375551 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.00000 | −0.462652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.67080 | 0.153943 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.333851 | 0.0191792 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.58359 | −0.376975 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.88854 | −0.336077 | −0.168038 | − | 0.985780i | \(-0.553743\pi\) | ||||
−0.168038 | + | 0.985780i | \(0.553743\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.74806 | −0.0994439 | ||||||||
\(310\) | 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 | \(-0.298370\pi\) | ||||
0.591920 | + | 0.805997i | \(0.298370\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.52786 | 0.311460 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.3044 | 0.971913 | 0.485956 | − | 0.873983i | \(-0.338471\pi\) | ||||
0.485956 | + | 0.873983i | \(0.338471\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 38.7727 | 2.17085 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.944272 | −0.0527041 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.0000 | −0.890264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.07107 | −0.392232 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.8918 | −0.934116 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.9443 | −0.931341 | −0.465671 | − | 0.884958i | \(-0.654187\pi\) | ||||
−0.465671 | + | 0.884958i | \(0.654187\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.5672 | −0.579079 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | −2.00000 | −0.108625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.2982 | −1.36998 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.1313 | −1.03299 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.8885 | 0.963087 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.4721 | 1.20637 | 0.603184 | − | 0.797602i | \(-0.293899\pi\) | ||||
0.603184 | + | 0.797602i | \(0.293899\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.23179 | −0.494167 | −0.247083 | − | 0.968994i | \(-0.579472\pi\) | ||||
−0.247083 | + | 0.968994i | \(0.579472\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | −28.9443 | −1.53620 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.32145 | 0.228715 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 30.8885 | 1.62123 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.31061 | 0.487339 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.8933 | −0.934023 | −0.467011 | − | 0.884251i | \(-0.654669\pi\) | ||||
−0.467011 | + | 0.884251i | \(0.654669\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.47214 | −0.128694 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.3607 | −1.05707 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.8809 | 1.13295 | 0.566475 | − | 0.824079i | \(-0.308307\pi\) | ||||
0.566475 | + | 0.824079i | \(0.308307\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.47214 | −0.436337 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.4164 | −1.40829 | −0.704143 | − | 0.710058i | \(-0.748669\pi\) | ||||
−0.704143 | + | 0.710058i | \(0.748669\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.9010 | −0.558478 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.1313 | 0.977563 | 0.488782 | − | 0.872406i | \(-0.337441\pi\) | ||||
0.488782 | + | 0.872406i | \(0.337441\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 35.7771 | 1.82337 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.52786 | 0.0776657 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.4497 | 1.69596 | 0.847982 | − | 0.530024i | \(-0.177817\pi\) | ||||
0.847982 | + | 0.530024i | \(0.177817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.9845 | 0.707227 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.9443 | 0.854725 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.4164 | −1.17821 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.07417 | −0.455420 | −0.227710 | − | 0.973729i | \(-0.573124\pi\) | ||||
−0.227710 | + | 0.973729i | \(0.573124\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 5.52786 | 0.275363 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.16228 | 0.157135 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −68.3923 | −3.39008 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.9443 | −0.640053 | −0.320027 | − | 0.947409i | \(-0.603692\pi\) | ||||
−0.320027 | + | 0.947409i | \(0.603692\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.47214 | 0.121941 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.6352 | 0.769356 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.4667 | −1.00467 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.9443 | 0.829765 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.52786 | −0.0746410 | −0.0373205 | − | 0.999303i | \(-0.511882\pi\) | ||||
−0.0373205 | + | 0.999303i | \(0.511882\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.07107 | 0.344623 | 0.172311 | − | 0.985043i | \(-0.444876\pi\) | ||||
0.172311 | + | 0.985043i | \(0.444876\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.3607 | 0.599581 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.63932 | −0.176119 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.15298 | −0.441910 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.3060 | 0.881767 | 0.440884 | − | 0.897564i | \(-0.354665\pi\) | ||||
0.440884 | + | 0.897564i | \(0.354665\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.0000 | 1.15337 | 0.576683 | − | 0.816968i | \(-0.304347\pi\) | ||||
0.576683 | + | 0.816968i | \(0.304347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.9443 | 0.908308 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −36.6119 | −1.75139 | ||||||||
\(438\) | 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 | ||||||||
\(443\) | −11.4164 | −0.542410 | −0.271205 | − | 0.962522i | \(-0.587422\pi\) | ||||
−0.271205 | + | 0.962522i | \(0.587422\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.6228 | −1.49906 | ||||||||
\(446\) | 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 | ||||||||
\(451\) | −16.0000 | −0.753411 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.0540 | −0.942220 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.81758 | −0.366494 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.05573 | 0.142941 | 0.0714705 | − | 0.997443i | \(-0.477231\pi\) | ||||
0.0714705 | + | 0.997443i | \(0.477231\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.47214 | 0.115389 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.81913 | 0.410748 | 0.205374 | − | 0.978684i | \(-0.434159\pi\) | ||||
0.205374 | + | 0.978684i | \(0.434159\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.40492 | 0.344136 | 0.172068 | − | 0.985085i | \(-0.444955\pi\) | ||||
0.172068 | + | 0.985085i | \(0.444955\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.3607 | −0.573213 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.58359 | −0.212103 | −0.106052 | − | 0.994361i | \(-0.533821\pi\) | ||||
−0.106052 | + | 0.994361i | \(0.533821\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.9768 | 0.968617 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.3956 | −0.617238 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.88854 | 0.454676 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −32.3607 | −1.48481 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.6476 | −0.533305 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.49613 | −0.159742 | −0.0798711 | − | 0.996805i | \(-0.525451\pi\) | ||||
−0.0798711 | + | 0.996805i | \(0.525451\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.9443 | 0.681400 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.88854 | 0.449944 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −40.9334 | −1.85869 | ||||||||
\(486\) | 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 | ||||||||
\(491\) | 21.8885 | 0.987816 | 0.493908 | − | 0.869514i | \(-0.335568\pi\) | ||||
0.493908 | + | 0.869514i | \(0.335568\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.8098 | 0.667001 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 20.4667 | 0.919909 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.0000 | −0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.9443 | −1.11666 | −0.558329 | − | 0.829619i | \(-0.688557\pi\) | ||||
−0.558329 | + | 0.829619i | \(0.688557\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.4667 | 0.914384 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | −11.0000 | −0.488527 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −39.9318 | −1.76995 | −0.884974 | − | 0.465641i | \(-0.845824\pi\) | ||||
−0.884974 | + | 0.465641i | \(0.845824\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.14678 | 0.227680 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.47214 | −0.285752 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.52786 | −0.243587 | ||||||||
\(516\) | 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 | \(-0.713376\pi\) | ||||
−0.621252 | + | 0.783611i | \(0.713376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.3607 | −0.715403 | −0.357701 | − | 0.933836i | \(-0.616439\pi\) | ||||
−0.357701 | + | 0.933836i | \(0.616439\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.74032 | 0.381459 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.66306 | −0.420930 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00000 | 0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.94427 | 0.388148 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.49613 | 0.151434 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.98605 | −0.129098 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.0000 | 0.517838 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.5279 | −1.09956 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.7124 | 1.14846 | 0.574229 | − | 0.818695i | \(-0.305302\pi\) | ||||
0.574229 | + | 0.818695i | \(0.305302\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.5563 | 0.667587 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −53.4164 | −2.28811 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.3607 | 1.38364 | 0.691821 | − | 0.722069i | \(-0.256809\pi\) | ||||
0.691821 | + | 0.722069i | \(0.256809\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.08191 | −0.0888540 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.7727 | −1.65177 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.9443 | −0.550446 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −33.4164 | −1.41845 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.8114 | −0.669950 | −0.334975 | − | 0.942227i | \(-0.608728\pi\) | ||||
−0.334975 | + | 0.942227i | \(0.608728\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.16073 | −0.0913890 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.0000 | 0.675521 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.52786 | 0.0643918 | 0.0321959 | − | 0.999482i | \(-0.489750\pi\) | ||||
0.0321959 | + | 0.999482i | \(0.489750\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.32456 | −0.266076 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.74806 | 0.0734118 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.41641 | 0.310912 | 0.155456 | − | 0.987843i | \(-0.450315\pi\) | ||||
0.155456 | + | 0.987843i | \(0.450315\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.94427 | −0.374306 | −0.187153 | − | 0.982331i | \(-0.559926\pi\) | ||||
−0.187153 | + | 0.982331i | \(0.559926\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.8098 | 0.618690 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 4.94427 | 0.205477 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.3137 | −0.469372 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −75.3846 | −3.12211 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.47214 | −0.184900 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.9443 | −1.35976 | −0.679878 | − | 0.733325i | \(-0.737967\pi\) | ||||
−0.679878 | + | 0.733325i | \(0.737967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.2982 | 1.04240 | ||||||||
\(590\) | 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 | ||||||||
\(595\) | 13.6656 | 0.560236 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.24419 | −0.214631 | ||||||||
\(598\) | 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 | \(-0.545235\pi\) | ||||
−0.141631 | + | 0.989919i | \(0.545235\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 97.6782 | 3.97118 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.8422 | −1.82009 | −0.910044 | − | 0.414512i | \(-0.863952\pi\) | ||||
−0.910044 | + | 0.414512i | \(0.863952\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.4721 | 0.424352 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.5672 | 0.426805 | 0.213403 | − | 0.976964i | \(-0.431545\pi\) | ||||
0.213403 | + | 0.976964i | \(0.431545\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.81758 | −0.315235 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.8885 | −0.639649 | −0.319824 | − | 0.947477i | \(-0.603624\pi\) | ||||
−0.319824 | + | 0.947477i | \(0.603624\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.88854 | −0.236681 | −0.118340 | − | 0.992973i | \(-0.537757\pi\) | ||||
−0.118340 | + | 0.992973i | \(0.537757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.65685 | 0.227002 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.4806 | −0.700347 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −41.8885 | −1.67287 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26.1235 | −1.04161 | ||||||||
\(630\) | 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 | ||||||||
\(635\) | −34.4721 | −1.36798 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.57804 | 0.221010 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | −8.36068 | −0.329713 | −0.164857 | − | 0.986318i | \(-0.552716\pi\) | ||||
−0.164857 | + | 0.986318i | \(0.552716\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.83153 | 0.190241 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | −6.83282 | −0.267799 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.4388 | 1.50423 | 0.752113 | − | 0.659034i | \(-0.229035\pi\) | ||||
0.752113 | + | 0.659034i | \(0.229035\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 53.5825 | 2.09364 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.94427 | 0.114867 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.1869 | −1.56309 | −0.781544 | − | 0.623850i | \(-0.785568\pi\) | ||||
−0.781544 | + | 0.623850i | \(0.785568\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.49613 | −0.135778 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −35.7771 | −1.38738 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.8885 | 1.31217 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.90879 | −0.151123 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 5.00000 | 0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.491473 | −0.0188889 | −0.00944443 | − | 0.999955i | \(-0.503006\pi\) | ||||
−0.00944443 | + | 0.999955i | \(0.503006\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.6274 | −0.868361 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.4721 | −0.554573 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.41641 | 0.130725 | 0.0653626 | − | 0.997862i | \(-0.479180\pi\) | ||||
0.0653626 | + | 0.997862i | \(0.479180\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.81758 | 0.298694 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.0633 | 0.536549 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.4721 | 0.627538 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.5279 | −0.971126 | −0.485563 | − | 0.874202i | \(-0.661385\pi\) | ||||
−0.485563 | + | 0.874202i | \(0.661385\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.3137 | 0.429772 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 53.5825 | 2.03250 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.11146 | −0.231488 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.0000 | −0.378235 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.6104 | −1.34499 | −0.672493 | − | 0.740104i | \(-0.734776\pi\) | ||||
−0.672493 | + | 0.740104i | \(0.734776\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 68.3923 | 2.57947 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.583592 | 0.0219482 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.8623 | 1.27173 | 0.635863 | − | 0.771802i | \(-0.280644\pi\) | ||||
0.635863 | + | 0.771802i | \(0.280644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.40492 | −0.277706 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.1115 | −0.828081 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.9443 | −1.08245 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.1235 | −0.975602 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.8021 | −0.813081 | −0.406540 | − | 0.913633i | \(-0.633265\pi\) | ||||
−0.406540 | + | 0.913633i | \(0.633265\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.05573 | −0.113801 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29.9535 | 1.11245 | ||||||||
\(726\) | 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 | ||||||||
\(731\) | 3.77709 | 0.139701 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.0339 | −1.14626 | −0.573131 | − | 0.819463i | \(-0.694272\pi\) | ||||
−0.573131 | + | 0.819463i | \(0.694272\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.4729 | −0.460069 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 77.6656 | 2.86085 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.9443 | −1.21187 | −0.605937 | − | 0.795512i | \(-0.707202\pi\) | ||||
−0.605937 | + | 0.795512i | \(0.707202\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.15298 | 0.336243 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | −6.47214 | −0.236803 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.65065 | −0.0603134 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.40492 | 0.270209 | 0.135105 | − | 0.990831i | \(-0.456863\pi\) | ||||
0.135105 | + | 0.990831i | \(0.456863\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.4164 | 0.416037 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −63.4164 | −2.30796 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0633 | −0.511140 | −0.255570 | − | 0.966791i | \(-0.582263\pi\) | ||||
−0.255570 | + | 0.966791i | \(0.582263\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 36.6119 | 1.32893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.41641 | −0.268845 | −0.134422 | − | 0.990924i | \(-0.542918\pi\) | ||||
−0.134422 | + | 0.990924i | \(0.542918\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.5279 | −1.06898 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.81758 | 0.282645 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.65841 | −0.239486 | −0.119743 | − | 0.992805i | \(-0.538207\pi\) | ||||
−0.119743 | + | 0.992805i | \(0.538207\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.5440 | −0.702039 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.4721 | −0.662684 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.0000 | 0.573259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −59.2393 | −2.11975 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.99070 | 0.214090 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42.3607 | −1.51192 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.4721 | −0.515876 | −0.257938 | − | 0.966161i | \(-0.583043\pi\) | ||||
−0.257938 | + | 0.966161i | \(0.583043\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.6491 | 0.450320 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.49613 | −0.124308 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.94427 | 0.104554 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −36.8328 | −1.30633 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.16538 | −0.182967 | −0.0914836 | − | 0.995807i | \(-0.529161\pi\) | ||||
−0.0914836 | + | 0.995807i | \(0.529161\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.0000 | −0.353333 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.0557 | 0.672462 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 31.2703 | 1.10213 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.32300 | 0.187379 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.4164 | −0.823277 | −0.411639 | − | 0.911347i | \(-0.635043\pi\) | ||||
−0.411639 | + | 0.911347i | \(0.635043\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.3050 | 1.02904 | 0.514518 | − | 0.857480i | \(-0.327971\pi\) | ||||
0.514518 | + | 0.857480i | \(0.327971\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.9010 | −0.382316 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 45.7649 | 1.60307 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.88854 | −0.345956 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.47214 | −0.0863834 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.2626 | 1.75418 | 0.877088 | − | 0.480329i | \(-0.159483\pi\) | ||||
0.877088 | + | 0.480329i | \(0.159483\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | 18.1115 | 0.629797 | 0.314899 | − | 0.949125i | \(-0.398030\pi\) | ||||
0.314899 | + | 0.949125i | \(0.398030\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.57804 | −0.193733 | −0.0968667 | − | 0.995297i | \(-0.530882\pi\) | ||||
−0.0968667 | + | 0.995297i | \(0.530882\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.3848 | 0.637761 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.75078 | −0.337844 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 64.7214 | 2.23978 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.90879 | −0.135108 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 3.88854 | 0.133929 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34.7851 | −1.19664 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 53.9952 | 1.85530 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.8328 | 0.920900 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −59.7771 | −2.04913 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.3662 | −1.03972 | −0.519859 | − | 0.854252i | \(-0.674016\pi\) | ||||
−0.519859 | + | 0.854252i | \(0.674016\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.4667 | −0.699946 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 55.4164 | 1.89299 | 0.946494 | − | 0.322721i | \(-0.104597\pi\) | ||||
0.946494 | + | 0.322721i | \(0.104597\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −54.4721 | −1.85857 | −0.929283 | − | 0.369369i | \(-0.879574\pi\) | ||||
−0.929283 | + | 0.369369i | \(0.879574\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.32145 | −0.147275 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.7943 | −0.980171 | −0.490086 | − | 0.871674i | \(-0.663034\pi\) | ||||
−0.490086 | + | 0.871674i | \(0.663034\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.0000 | 1.02003 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.8885 | −0.369794 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −47.9256 | −1.62577 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.9706 | −0.575026 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.9443 | −0.438097 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.3801 | −0.924561 | −0.462281 | − | 0.886734i | \(-0.652969\pi\) | ||||
−0.462281 | + | 0.886734i | \(0.652969\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 9.52786 | 0.320638 | 0.160319 | − | 0.987065i | \(-0.448748\pi\) | ||||
0.160319 | + | 0.987065i | \(0.448748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.2843 | 0.950765 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | 6.47214 | 0.216825 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.9473 | 1.26844 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.00000 | −0.267112 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.4164 | −0.780981 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.7943 | −0.959279 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.67080 | 0.0888788 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 49.1935 | 1.63525 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.1935 | 1.56703 | 0.783517 | − | 0.621370i | \(-0.213424\pi\) | ||||
0.783517 | + | 0.621370i | \(0.213424\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.333851 | 0.0110731 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.8098 | 0.490672 | 0.245336 | − | 0.969438i | \(-0.421102\pi\) | ||||
0.245336 | + | 0.969438i | \(0.421102\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.8885 | −1.38631 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.58359 | −0.217647 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.6197 | 0.978128 | ||||||||
\(918\) | 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 | ||||||||
\(923\) | 12.9443 | 0.426066 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −52.8360 | −1.73724 | ||||||||
\(926\) | 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 | ||||||||
\(931\) | 25.5279 | 0.836642 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.6414 | 0.643029 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 50.5964 | 1.65468 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0000 | 0.718709 | 0.359354 | − | 0.933201i | \(-0.382997\pi\) | ||||
0.359354 | + | 0.933201i | \(0.382997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.9443 | 0.683490 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.4465 | 1.02513 | 0.512564 | − | 0.858649i | \(-0.328696\pi\) | ||||
0.512564 | + | 0.858649i | \(0.328696\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.9845 | −0.455398 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.52786 | 0.179821 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.7771 | 0.772652 | 0.386326 | − | 0.922362i | \(-0.373744\pi\) | ||||
0.386326 | + | 0.922362i | \(0.373744\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.16383 | −0.135164 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.3044 | 0.561134 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.4721 | −0.598371 | −0.299186 | − | 0.954195i | \(-0.596715\pi\) | ||||
−0.299186 | + | 0.954195i | \(0.596715\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 46.8328 | 1.51547 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 38.7727 | 1.25334 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.32145 | 0.139547 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.7214 | −0.507141 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.944272 | −0.0304287 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.6352 | 0.503314 | ||||||||
\(966\) | 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 | ||||||||
\(971\) | 24.3607 | 0.781771 | 0.390886 | − | 0.920439i | \(-0.372169\pi\) | ||||
0.390886 | + | 0.920439i | \(0.372169\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.6197 | 0.949563 | ||||||||
\(974\) | 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 | ||||||||
\(979\) | −64.7214 | −2.06850 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.8918 | −0.539312 | ||||||||
\(982\) | 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 | ||||||||
\(989\) | 8.64290 | 0.274828 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.3972 | 0.457341 | 0.228671 | − | 0.973504i | \(-0.426562\pi\) | ||||
0.228671 | + | 0.973504i | \(0.426562\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.9443 | −0.537710 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.5836 | −0.525735 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.6799 | 1.32002 | 0.660008 | − | 0.751259i | \(-0.270553\pi\) | ||||
0.660008 | + | 0.751259i | \(0.270553\pi\) | |||||||
\(998\) | 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.a.q.1.3 | 4 | ||
3.2 | odd | 2 | 9216.2.a.bd.1.1 | 4 | |||
4.3 | odd | 2 | 3072.2.a.k.1.4 | 4 | |||
8.3 | odd | 2 | inner | 3072.2.a.q.1.2 | 4 | ||
8.5 | even | 2 | 3072.2.a.k.1.1 | 4 | |||
12.11 | even | 2 | 9216.2.a.bj.1.2 | 4 | |||
16.3 | odd | 4 | 3072.2.d.g.1537.1 | 8 | |||
16.5 | even | 4 | 3072.2.d.g.1537.4 | 8 | |||
16.11 | odd | 4 | 3072.2.d.g.1537.7 | 8 | |||
16.13 | even | 4 | 3072.2.d.g.1537.6 | 8 | |||
24.5 | odd | 2 | 9216.2.a.bj.1.3 | 4 | |||
24.11 | even | 2 | 9216.2.a.bd.1.4 | 4 | |||
32.3 | odd | 8 | 1536.2.j.h.1153.1 | yes | 8 | ||
32.5 | even | 8 | 1536.2.j.g.385.2 | ✓ | 8 | ||
32.11 | odd | 8 | 1536.2.j.h.385.1 | yes | 8 | ||
32.13 | even | 8 | 1536.2.j.g.1153.2 | yes | 8 | ||
32.19 | odd | 8 | 1536.2.j.g.1153.4 | yes | 8 | ||
32.21 | even | 8 | 1536.2.j.h.385.3 | yes | 8 | ||
32.27 | odd | 8 | 1536.2.j.g.385.4 | yes | 8 | ||
32.29 | even | 8 | 1536.2.j.h.1153.3 | yes | 8 | ||
96.5 | odd | 8 | 4608.2.k.bf.3457.2 | 8 | |||
96.11 | even | 8 | 4608.2.k.bg.3457.3 | 8 | |||
96.29 | odd | 8 | 4608.2.k.bg.1153.3 | 8 | |||
96.35 | even | 8 | 4608.2.k.bg.1153.4 | 8 | |||
96.53 | odd | 8 | 4608.2.k.bg.3457.4 | 8 | |||
96.59 | even | 8 | 4608.2.k.bf.3457.1 | 8 | |||
96.77 | odd | 8 | 4608.2.k.bf.1153.1 | 8 | |||
96.83 | even | 8 | 4608.2.k.bf.1153.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.j.g.385.2 | ✓ | 8 | 32.5 | even | 8 | ||
1536.2.j.g.385.4 | yes | 8 | 32.27 | odd | 8 | ||
1536.2.j.g.1153.2 | yes | 8 | 32.13 | even | 8 | ||
1536.2.j.g.1153.4 | yes | 8 | 32.19 | odd | 8 | ||
1536.2.j.h.385.1 | yes | 8 | 32.11 | odd | 8 | ||
1536.2.j.h.385.3 | yes | 8 | 32.21 | even | 8 | ||
1536.2.j.h.1153.1 | yes | 8 | 32.3 | odd | 8 | ||
1536.2.j.h.1153.3 | yes | 8 | 32.29 | even | 8 | ||
3072.2.a.k.1.1 | 4 | 8.5 | even | 2 | |||
3072.2.a.k.1.4 | 4 | 4.3 | odd | 2 | |||
3072.2.a.q.1.2 | 4 | 8.3 | odd | 2 | inner | ||
3072.2.a.q.1.3 | 4 | 1.1 | even | 1 | trivial | ||
3072.2.d.g.1537.1 | 8 | 16.3 | odd | 4 | |||
3072.2.d.g.1537.4 | 8 | 16.5 | even | 4 | |||
3072.2.d.g.1537.6 | 8 | 16.13 | even | 4 | |||
3072.2.d.g.1537.7 | 8 | 16.11 | odd | 4 | |||
4608.2.k.bf.1153.1 | 8 | 96.77 | odd | 8 | |||
4608.2.k.bf.1153.2 | 8 | 96.83 | even | 8 | |||
4608.2.k.bf.3457.1 | 8 | 96.59 | even | 8 | |||
4608.2.k.bf.3457.2 | 8 | 96.5 | odd | 8 | |||
4608.2.k.bg.1153.3 | 8 | 96.29 | odd | 8 | |||
4608.2.k.bg.1153.4 | 8 | 96.35 | even | 8 | |||
4608.2.k.bg.3457.3 | 8 | 96.11 | even | 8 | |||
4608.2.k.bg.3457.4 | 8 | 96.53 | odd | 8 | |||
9216.2.a.bd.1.1 | 4 | 3.2 | odd | 2 | |||
9216.2.a.bd.1.4 | 4 | 24.11 | even | 2 | |||
9216.2.a.bj.1.2 | 4 | 12.11 | even | 2 | |||
9216.2.a.bj.1.3 | 4 | 24.5 | odd | 2 |