Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 9x^{7} + 25x^{6} + 29x^{5} - 58x^{4} - 43x^{3} + 34x^{2} + 25x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.836154\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.63508 | −0.731231 | −0.365615 | − | 0.930766i | \(-0.619141\pi\) | ||||
−0.365615 | + | 0.930766i | \(0.619141\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.18187 | 1.58060 | 0.790299 | − | 0.612721i | \(-0.209925\pi\) | ||||
0.790299 | + | 0.612721i | \(0.209925\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.63508 | −0.517058 | ||||||||
\(11\) | −0.197300 | −0.0594882 | −0.0297441 | − | 0.999558i | \(-0.509469\pi\) | ||||
−0.0297441 | + | 0.999558i | \(0.509469\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.53420 | −1.53491 | −0.767456 | − | 0.641101i | \(-0.778478\pi\) | ||||
−0.767456 | + | 0.641101i | \(0.778478\pi\) | |||||||
\(14\) | 4.18187 | 1.11765 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.24995 | 1.51584 | 0.757918 | − | 0.652350i | \(-0.226217\pi\) | ||||
0.757918 | + | 0.652350i | \(0.226217\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.76358 | −0.404593 | −0.202297 | − | 0.979324i | \(-0.564841\pi\) | ||||
−0.202297 | + | 0.979324i | \(0.564841\pi\) | |||||||
\(20\) | −1.63508 | −0.365615 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.197300 | −0.0420645 | ||||||||
\(23\) | −1.25693 | −0.262088 | −0.131044 | − | 0.991377i | \(-0.541833\pi\) | ||||
−0.131044 | + | 0.991377i | \(0.541833\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.32651 | −0.465302 | ||||||||
\(26\) | −5.53420 | −1.08535 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.18187 | 0.790299 | ||||||||
\(29\) | −6.46749 | −1.20098 | −0.600492 | − | 0.799631i | \(-0.705029\pi\) | ||||
−0.600492 | + | 0.799631i | \(0.705029\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.67005 | −1.73679 | −0.868396 | − | 0.495871i | \(-0.834849\pi\) | ||||
−0.868396 | + | 0.495871i | \(0.834849\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.24995 | 1.07186 | ||||||||
\(35\) | −6.83770 | −1.15578 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.61274 | −1.41593 | −0.707963 | − | 0.706250i | \(-0.750386\pi\) | ||||
−0.707963 | + | 0.706250i | \(0.750386\pi\) | |||||||
\(38\) | −1.76358 | −0.286091 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.63508 | −0.258529 | ||||||||
\(41\) | −7.00464 | −1.09394 | −0.546971 | − | 0.837152i | \(-0.684219\pi\) | ||||
−0.546971 | + | 0.837152i | \(0.684219\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.69520 | 0.716011 | 0.358006 | − | 0.933719i | \(-0.383457\pi\) | ||||
0.358006 | + | 0.933719i | \(0.383457\pi\) | |||||||
\(44\) | −0.197300 | −0.0297441 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.25693 | −0.185324 | ||||||||
\(47\) | −6.92211 | −1.00969 | −0.504847 | − | 0.863209i | \(-0.668451\pi\) | ||||
−0.504847 | + | 0.863209i | \(0.668451\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.4880 | 1.49829 | ||||||||
\(50\) | −2.32651 | −0.329018 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.53420 | −0.767456 | ||||||||
\(53\) | −5.96851 | −0.819838 | −0.409919 | − | 0.912122i | \(-0.634443\pi\) | ||||
−0.409919 | + | 0.912122i | \(0.634443\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.322602 | 0.0434996 | ||||||||
\(56\) | 4.18187 | 0.558826 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.46749 | −0.849224 | ||||||||
\(59\) | 4.41785 | 0.575155 | 0.287577 | − | 0.957757i | \(-0.407150\pi\) | ||||
0.287577 | + | 0.957757i | \(0.407150\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.34679 | 0.812623 | 0.406311 | − | 0.913735i | \(-0.366815\pi\) | ||||
0.406311 | + | 0.913735i | \(0.366815\pi\) | |||||||
\(62\) | −9.67005 | −1.22810 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.04888 | 1.12237 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.3102 | −1.87044 | −0.935222 | − | 0.354062i | \(-0.884800\pi\) | ||||
−0.935222 | + | 0.354062i | \(0.884800\pi\) | |||||||
\(68\) | 6.24995 | 0.757918 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.83770 | −0.817261 | ||||||||
\(71\) | 8.52896 | 1.01220 | 0.506100 | − | 0.862475i | \(-0.331087\pi\) | ||||
0.506100 | + | 0.862475i | \(0.331087\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.842454 | −0.0986018 | −0.0493009 | − | 0.998784i | \(-0.515699\pi\) | ||||
−0.0493009 | + | 0.998784i | \(0.515699\pi\) | |||||||
\(74\) | −8.61274 | −1.00121 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.76358 | −0.202297 | ||||||||
\(77\) | −0.825083 | −0.0940269 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.79367 | −0.314313 | −0.157156 | − | 0.987574i | \(-0.550233\pi\) | ||||
−0.157156 | + | 0.987574i | \(0.550233\pi\) | |||||||
\(80\) | −1.63508 | −0.182808 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.00464 | −0.773533 | ||||||||
\(83\) | 1.68295 | 0.184728 | 0.0923641 | − | 0.995725i | \(-0.470558\pi\) | ||||
0.0923641 | + | 0.995725i | \(0.470558\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.2192 | −1.10843 | ||||||||
\(86\) | 4.69520 | 0.506296 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.197300 | −0.0210323 | ||||||||
\(89\) | 0.518659 | 0.0549777 | 0.0274889 | − | 0.999622i | \(-0.491249\pi\) | ||||
0.0274889 | + | 0.999622i | \(0.491249\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −23.1433 | −2.42608 | ||||||||
\(92\) | −1.25693 | −0.131044 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.92211 | −0.713961 | ||||||||
\(95\) | 2.88360 | 0.295851 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.99290 | 0.303883 | 0.151941 | − | 0.988390i | \(-0.451447\pi\) | ||||
0.151941 | + | 0.988390i | \(0.451447\pi\) | |||||||
\(98\) | 10.4880 | 1.05945 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.32651 | −0.232651 | ||||||||
\(101\) | 4.86820 | 0.484404 | 0.242202 | − | 0.970226i | \(-0.422130\pi\) | ||||
0.242202 | + | 0.970226i | \(0.422130\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.84368 | 0.772860 | 0.386430 | − | 0.922319i | \(-0.373708\pi\) | ||||
0.386430 | + | 0.922319i | \(0.373708\pi\) | |||||||
\(104\) | −5.53420 | −0.542673 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.96851 | −0.579713 | ||||||||
\(107\) | −1.68404 | −0.162802 | −0.0814012 | − | 0.996681i | \(-0.525940\pi\) | ||||
−0.0814012 | + | 0.996681i | \(0.525940\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.7457 | −1.02925 | −0.514627 | − | 0.857414i | \(-0.672070\pi\) | ||||
−0.514627 | + | 0.857414i | \(0.672070\pi\) | |||||||
\(110\) | 0.322602 | 0.0307589 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.18187 | 0.395149 | ||||||||
\(113\) | 10.3413 | 0.972826 | 0.486413 | − | 0.873729i | \(-0.338305\pi\) | ||||
0.486413 | + | 0.873729i | \(0.338305\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.05519 | 0.191647 | ||||||||
\(116\) | −6.46749 | −0.600492 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.41785 | 0.406696 | ||||||||
\(119\) | 26.1365 | 2.39593 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9611 | −0.996461 | ||||||||
\(122\) | 6.34679 | 0.574611 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.67005 | −0.868396 | ||||||||
\(125\) | 11.9794 | 1.07147 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.37977 | 0.654849 | 0.327424 | − | 0.944877i | \(-0.393819\pi\) | ||||
0.327424 | + | 0.944877i | \(0.393819\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9.04888 | 0.793639 | ||||||||
\(131\) | −9.07961 | −0.793289 | −0.396645 | − | 0.917972i | \(-0.629825\pi\) | ||||
−0.396645 | + | 0.917972i | \(0.629825\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.37507 | −0.639499 | ||||||||
\(134\) | −15.3102 | −1.32260 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.24995 | 0.535929 | ||||||||
\(137\) | 12.7245 | 1.08713 | 0.543563 | − | 0.839368i | \(-0.317075\pi\) | ||||
0.543563 | + | 0.839368i | \(0.317075\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.66714 | 0.141405 | 0.0707026 | − | 0.997497i | \(-0.477476\pi\) | ||||
0.0707026 | + | 0.997497i | \(0.477476\pi\) | |||||||
\(140\) | −6.83770 | −0.577891 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.52896 | 0.715734 | ||||||||
\(143\) | 1.09190 | 0.0913092 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.5749 | 0.878196 | ||||||||
\(146\) | −0.842454 | −0.0697220 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.61274 | −0.707963 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.2820 | −1.40639 | −0.703193 | − | 0.710999i | \(-0.748243\pi\) | ||||
−0.703193 | + | 0.710999i | \(0.748243\pi\) | |||||||
\(152\) | −1.76358 | −0.143045 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.825083 | −0.0664871 | ||||||||
\(155\) | 15.8113 | 1.27000 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.9018 | −1.34891 | −0.674457 | − | 0.738314i | \(-0.735622\pi\) | ||||
−0.674457 | + | 0.738314i | \(0.735622\pi\) | |||||||
\(158\) | −2.79367 | −0.222253 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.63508 | −0.129265 | ||||||||
\(161\) | −5.25632 | −0.414256 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.9163 | 0.933355 | 0.466678 | − | 0.884428i | \(-0.345451\pi\) | ||||
0.466678 | + | 0.884428i | \(0.345451\pi\) | |||||||
\(164\) | −7.00464 | −0.546971 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.68295 | 0.130623 | ||||||||
\(167\) | 14.7560 | 1.14186 | 0.570929 | − | 0.821000i | \(-0.306583\pi\) | ||||
0.570929 | + | 0.821000i | \(0.306583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.6274 | 1.35596 | ||||||||
\(170\) | −10.2192 | −0.783775 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.69520 | 0.358006 | ||||||||
\(173\) | −24.6303 | −1.87260 | −0.936302 | − | 0.351195i | \(-0.885776\pi\) | ||||
−0.936302 | + | 0.351195i | \(0.885776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.72915 | −0.735455 | ||||||||
\(176\) | −0.197300 | −0.0148721 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.518659 | 0.0388751 | ||||||||
\(179\) | 20.1909 | 1.50914 | 0.754568 | − | 0.656221i | \(-0.227846\pi\) | ||||
0.754568 | + | 0.656221i | \(0.227846\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.5876 | −1.38160 | −0.690801 | − | 0.723045i | \(-0.742742\pi\) | ||||
−0.690801 | + | 0.723045i | \(0.742742\pi\) | |||||||
\(182\) | −23.1433 | −1.71550 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.25693 | −0.0926622 | ||||||||
\(185\) | 14.0825 | 1.03537 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.23312 | −0.0901743 | ||||||||
\(188\) | −6.92211 | −0.504847 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.88360 | 0.209198 | ||||||||
\(191\) | 22.5264 | 1.62995 | 0.814976 | − | 0.579495i | \(-0.196750\pi\) | ||||
0.814976 | + | 0.579495i | \(0.196750\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.61836 | −0.260455 | −0.130228 | − | 0.991484i | \(-0.541571\pi\) | ||||
−0.130228 | + | 0.991484i | \(0.541571\pi\) | |||||||
\(194\) | 2.99290 | 0.214878 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.4880 | 0.749145 | ||||||||
\(197\) | −22.2957 | −1.58851 | −0.794253 | − | 0.607587i | \(-0.792138\pi\) | ||||
−0.794253 | + | 0.607587i | \(0.792138\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0975 | −0.786680 | −0.393340 | − | 0.919393i | \(-0.628680\pi\) | ||||
−0.393340 | + | 0.919393i | \(0.628680\pi\) | |||||||
\(200\) | −2.32651 | −0.164509 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.86820 | 0.342525 | ||||||||
\(203\) | −27.0462 | −1.89827 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.4532 | 0.799923 | ||||||||
\(206\) | 7.84368 | 0.546495 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.53420 | −0.383728 | ||||||||
\(209\) | 0.347955 | 0.0240685 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.6815 | −0.873030 | −0.436515 | − | 0.899697i | \(-0.643787\pi\) | ||||
−0.436515 | + | 0.899697i | \(0.643787\pi\) | |||||||
\(212\) | −5.96851 | −0.409919 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.68404 | −0.115119 | ||||||||
\(215\) | −7.67703 | −0.523569 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −40.4389 | −2.74517 | ||||||||
\(218\) | −10.7457 | −0.727793 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.322602 | 0.0217498 | ||||||||
\(221\) | −34.5885 | −2.32667 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.65351 | −0.311622 | −0.155811 | − | 0.987787i | \(-0.549799\pi\) | ||||
−0.155811 | + | 0.987787i | \(0.549799\pi\) | |||||||
\(224\) | 4.18187 | 0.279413 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.3413 | 0.687892 | ||||||||
\(227\) | 13.2197 | 0.877425 | 0.438713 | − | 0.898627i | \(-0.355435\pi\) | ||||
0.438713 | + | 0.898627i | \(0.355435\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.02383 | −0.265902 | −0.132951 | − | 0.991123i | \(-0.542445\pi\) | ||||
−0.132951 | + | 0.991123i | \(0.542445\pi\) | |||||||
\(230\) | 2.05519 | 0.135515 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.46749 | −0.424612 | ||||||||
\(233\) | −7.44022 | −0.487425 | −0.243712 | − | 0.969848i | \(-0.578365\pi\) | ||||
−0.243712 | + | 0.969848i | \(0.578365\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.3182 | 0.738319 | ||||||||
\(236\) | 4.41785 | 0.287577 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 26.1365 | 1.69418 | ||||||||
\(239\) | −25.1146 | −1.62453 | −0.812263 | − | 0.583291i | \(-0.801765\pi\) | ||||
−0.812263 | + | 0.583291i | \(0.801765\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.39031 | −0.347220 | −0.173610 | − | 0.984814i | \(-0.555543\pi\) | ||||
−0.173610 | + | 0.984814i | \(0.555543\pi\) | |||||||
\(242\) | −10.9611 | −0.704604 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.34679 | 0.406311 | ||||||||
\(245\) | −17.1488 | −1.09560 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.76002 | 0.621015 | ||||||||
\(248\) | −9.67005 | −0.614049 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.9794 | 0.757646 | ||||||||
\(251\) | 27.5070 | 1.73623 | 0.868113 | − | 0.496366i | \(-0.165333\pi\) | ||||
0.868113 | + | 0.496366i | \(0.165333\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.247993 | 0.0155912 | ||||||||
\(254\) | 7.37977 | 0.463048 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.27868 | −0.516410 | −0.258205 | − | 0.966090i | \(-0.583131\pi\) | ||||
−0.258205 | + | 0.966090i | \(0.583131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −36.0173 | −2.23801 | ||||||||
\(260\) | 9.04888 | 0.561187 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.07961 | −0.560940 | ||||||||
\(263\) | 19.6577 | 1.21214 | 0.606072 | − | 0.795410i | \(-0.292744\pi\) | ||||
0.606072 | + | 0.795410i | \(0.292744\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.75900 | 0.599491 | ||||||||
\(266\) | −7.37507 | −0.452194 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −15.3102 | −0.935222 | ||||||||
\(269\) | 3.61876 | 0.220640 | 0.110320 | − | 0.993896i | \(-0.464812\pi\) | ||||
0.110320 | + | 0.993896i | \(0.464812\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.2770 | 0.988756 | 0.494378 | − | 0.869247i | \(-0.335396\pi\) | ||||
0.494378 | + | 0.869247i | \(0.335396\pi\) | |||||||
\(272\) | 6.24995 | 0.378959 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.7245 | 0.768714 | ||||||||
\(275\) | 0.459020 | 0.0276800 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.87391 | 0.593266 | 0.296633 | − | 0.954992i | \(-0.404136\pi\) | ||||
0.296633 | + | 0.954992i | \(0.404136\pi\) | |||||||
\(278\) | 1.66714 | 0.0999886 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.83770 | −0.408630 | ||||||||
\(281\) | −5.71542 | −0.340953 | −0.170477 | − | 0.985362i | \(-0.554531\pi\) | ||||
−0.170477 | + | 0.985362i | \(0.554531\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.6035 | −0.689754 | −0.344877 | − | 0.938648i | \(-0.612079\pi\) | ||||
−0.344877 | + | 0.938648i | \(0.612079\pi\) | |||||||
\(284\) | 8.52896 | 0.506100 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.09190 | 0.0645653 | ||||||||
\(287\) | −29.2925 | −1.72908 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.0619 | 1.29776 | ||||||||
\(290\) | 10.5749 | 0.620978 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.842454 | −0.0493009 | ||||||||
\(293\) | 1.62266 | 0.0947967 | 0.0473983 | − | 0.998876i | \(-0.484907\pi\) | ||||
0.0473983 | + | 0.998876i | \(0.484907\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.22354 | −0.420571 | ||||||||
\(296\) | −8.61274 | −0.500605 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | 6.95612 | 0.402283 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.6347 | 1.13173 | ||||||||
\(302\) | −17.2820 | −0.994465 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.76358 | −0.101148 | ||||||||
\(305\) | −10.3775 | −0.594215 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.46804 | −0.540369 | −0.270185 | − | 0.962809i | \(-0.587085\pi\) | ||||
−0.270185 | + | 0.962809i | \(0.587085\pi\) | |||||||
\(308\) | −0.825083 | −0.0470135 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.8113 | 0.898023 | ||||||||
\(311\) | −18.2503 | −1.03488 | −0.517440 | − | 0.855720i | \(-0.673115\pi\) | ||||
−0.517440 | + | 0.855720i | \(0.673115\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.6571 | 0.998037 | 0.499018 | − | 0.866591i | \(-0.333694\pi\) | ||||
0.499018 | + | 0.866591i | \(0.333694\pi\) | |||||||
\(314\) | −16.9018 | −0.953826 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.79367 | −0.157156 | ||||||||
\(317\) | −15.3212 | −0.860526 | −0.430263 | − | 0.902704i | \(-0.641579\pi\) | ||||
−0.430263 | + | 0.902704i | \(0.641579\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.27604 | 0.0714444 | ||||||||
\(320\) | −1.63508 | −0.0914038 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.25632 | −0.292923 | ||||||||
\(323\) | −11.0223 | −0.613297 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.8754 | 0.714197 | ||||||||
\(326\) | 11.9163 | 0.659982 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.00464 | −0.386767 | ||||||||
\(329\) | −28.9474 | −1.59592 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9330 | 0.600932 | 0.300466 | − | 0.953793i | \(-0.402858\pi\) | ||||
0.300466 | + | 0.953793i | \(0.402858\pi\) | |||||||
\(332\) | 1.68295 | 0.0923641 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.7560 | 0.807415 | ||||||||
\(335\) | 25.0335 | 1.36773 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.19251 | 0.119434 | 0.0597169 | − | 0.998215i | \(-0.480980\pi\) | ||||
0.0597169 | + | 0.998215i | \(0.480980\pi\) | |||||||
\(338\) | 17.6274 | 0.958806 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.2192 | −0.554213 | ||||||||
\(341\) | 1.90790 | 0.103319 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.5865 | 0.787595 | ||||||||
\(344\) | 4.69520 | 0.253148 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −24.6303 | −1.32413 | ||||||||
\(347\) | −22.7847 | −1.22315 | −0.611574 | − | 0.791187i | \(-0.709463\pi\) | ||||
−0.611574 | + | 0.791187i | \(0.709463\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.0409 | −1.01924 | −0.509618 | − | 0.860401i | \(-0.670213\pi\) | ||||
−0.509618 | + | 0.860401i | \(0.670213\pi\) | |||||||
\(350\) | −9.72915 | −0.520045 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.197300 | −0.0105161 | ||||||||
\(353\) | 15.2629 | 0.812365 | 0.406182 | − | 0.913792i | \(-0.366860\pi\) | ||||
0.406182 | + | 0.913792i | \(0.366860\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.9455 | −0.740152 | ||||||||
\(356\) | 0.518659 | 0.0274889 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.1909 | 1.06712 | ||||||||
\(359\) | −1.35972 | −0.0717635 | −0.0358817 | − | 0.999356i | \(-0.511424\pi\) | ||||
−0.0358817 | + | 0.999356i | \(0.511424\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.8898 | −0.836304 | ||||||||
\(362\) | −18.5876 | −0.976941 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −23.1433 | −1.21304 | ||||||||
\(365\) | 1.37748 | 0.0721006 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.15305 | 0.268987 | 0.134494 | − | 0.990914i | \(-0.457059\pi\) | ||||
0.134494 | + | 0.990914i | \(0.457059\pi\) | |||||||
\(368\) | −1.25693 | −0.0655221 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 14.0825 | 0.732116 | ||||||||
\(371\) | −24.9595 | −1.29583 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.71232 | 0.243995 | 0.121997 | − | 0.992530i | \(-0.461070\pi\) | ||||
0.121997 | + | 0.992530i | \(0.461070\pi\) | |||||||
\(374\) | −1.23312 | −0.0637629 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.92211 | −0.356981 | ||||||||
\(377\) | 35.7924 | 1.84340 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.9403 | 0.870166 | 0.435083 | − | 0.900390i | \(-0.356719\pi\) | ||||
0.435083 | + | 0.900390i | \(0.356719\pi\) | |||||||
\(380\) | 2.88360 | 0.147926 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.5264 | 1.15255 | ||||||||
\(383\) | −6.39895 | −0.326971 | −0.163486 | − | 0.986546i | \(-0.552274\pi\) | ||||
−0.163486 | + | 0.986546i | \(0.552274\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.34908 | 0.0687554 | ||||||||
\(386\) | −3.61836 | −0.184170 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.99290 | 0.151941 | ||||||||
\(389\) | 1.08628 | 0.0550767 | 0.0275384 | − | 0.999621i | \(-0.491233\pi\) | ||||
0.0275384 | + | 0.999621i | \(0.491233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.85576 | −0.397283 | ||||||||
\(392\) | 10.4880 | 0.529725 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.2957 | −1.12324 | ||||||||
\(395\) | 4.56789 | 0.229835 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.3461 | 1.27208 | 0.636042 | − | 0.771654i | \(-0.280570\pi\) | ||||
0.636042 | + | 0.771654i | \(0.280570\pi\) | |||||||
\(398\) | −11.0975 | −0.556267 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.32651 | −0.116325 | ||||||||
\(401\) | 2.08150 | 0.103945 | 0.0519725 | − | 0.998649i | \(-0.483449\pi\) | ||||
0.0519725 | + | 0.998649i | \(0.483449\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 53.5161 | 2.66582 | ||||||||
\(404\) | 4.86820 | 0.242202 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −27.0462 | −1.34228 | ||||||||
\(407\) | 1.69929 | 0.0842309 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.78094 | 0.0880617 | 0.0440309 | − | 0.999030i | \(-0.485980\pi\) | ||||
0.0440309 | + | 0.999030i | \(0.485980\pi\) | |||||||
\(410\) | 11.4532 | 0.565631 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.84368 | 0.386430 | ||||||||
\(413\) | 18.4749 | 0.909088 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.75177 | −0.135079 | ||||||||
\(416\) | −5.53420 | −0.271337 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.347955 | 0.0170190 | ||||||||
\(419\) | 20.4936 | 1.00118 | 0.500589 | − | 0.865685i | \(-0.333117\pi\) | ||||
0.500589 | + | 0.865685i | \(0.333117\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.6932 | −0.667364 | −0.333682 | − | 0.942686i | \(-0.608291\pi\) | ||||
−0.333682 | + | 0.942686i | \(0.608291\pi\) | |||||||
\(422\) | −12.6815 | −0.617326 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.96851 | −0.289857 | ||||||||
\(425\) | −14.5406 | −0.705321 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.5414 | 1.28443 | ||||||||
\(428\) | −1.68404 | −0.0814012 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.67703 | −0.370219 | ||||||||
\(431\) | 22.2846 | 1.07341 | 0.536707 | − | 0.843769i | \(-0.319668\pi\) | ||||
0.536707 | + | 0.843769i | \(0.319668\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.4806 | −1.08035 | −0.540175 | − | 0.841552i | \(-0.681642\pi\) | ||||
−0.540175 | + | 0.841552i | \(0.681642\pi\) | |||||||
\(434\) | −40.4389 | −1.94113 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.7457 | −0.514627 | ||||||||
\(437\) | 2.21670 | 0.106039 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.1239 | −1.15137 | −0.575686 | − | 0.817671i | \(-0.695265\pi\) | ||||
−0.575686 | + | 0.817671i | \(0.695265\pi\) | |||||||
\(440\) | 0.322602 | 0.0153794 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −34.5885 | −1.64521 | ||||||||
\(443\) | 29.6812 | 1.41020 | 0.705098 | − | 0.709110i | \(-0.250903\pi\) | ||||
0.705098 | + | 0.709110i | \(0.250903\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.848050 | −0.0402014 | ||||||||
\(446\) | −4.65351 | −0.220350 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.18187 | 0.197575 | ||||||||
\(449\) | −25.7344 | −1.21448 | −0.607240 | − | 0.794519i | \(-0.707723\pi\) | ||||
−0.607240 | + | 0.794519i | \(0.707723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.38202 | 0.0650766 | ||||||||
\(452\) | 10.3413 | 0.486413 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.2197 | 0.620433 | ||||||||
\(455\) | 37.8412 | 1.77402 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.610859 | 0.0285748 | 0.0142874 | − | 0.999898i | \(-0.495452\pi\) | ||||
0.0142874 | + | 0.999898i | \(0.495452\pi\) | |||||||
\(458\) | −4.02383 | −0.188021 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.05519 | 0.0958235 | ||||||||
\(461\) | 11.9751 | 0.557734 | 0.278867 | − | 0.960330i | \(-0.410041\pi\) | ||||
0.278867 | + | 0.960330i | \(0.410041\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.6330 | −0.587103 | −0.293552 | − | 0.955943i | \(-0.594837\pi\) | ||||
−0.293552 | + | 0.955943i | \(0.594837\pi\) | |||||||
\(464\) | −6.46749 | −0.300246 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.44022 | −0.344661 | ||||||||
\(467\) | −6.77417 | −0.313471 | −0.156736 | − | 0.987641i | \(-0.550097\pi\) | ||||
−0.156736 | + | 0.987641i | \(0.550097\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −64.0254 | −2.95642 | ||||||||
\(470\) | 11.3182 | 0.522070 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.41785 | 0.203348 | ||||||||
\(473\) | −0.926363 | −0.0425942 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.10299 | 0.188258 | ||||||||
\(476\) | 26.1365 | 1.19796 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −25.1146 | −1.14871 | ||||||||
\(479\) | 12.1625 | 0.555719 | 0.277859 | − | 0.960622i | \(-0.410375\pi\) | ||||
0.277859 | + | 0.960622i | \(0.410375\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 47.6647 | 2.17332 | ||||||||
\(482\) | −5.39031 | −0.245522 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9611 | −0.498231 | ||||||||
\(485\) | −4.89363 | −0.222208 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.0747 | −0.637783 | −0.318892 | − | 0.947791i | \(-0.603311\pi\) | ||||
−0.318892 | + | 0.947791i | \(0.603311\pi\) | |||||||
\(488\) | 6.34679 | 0.287306 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −17.1488 | −0.774703 | ||||||||
\(491\) | 19.2146 | 0.867141 | 0.433571 | − | 0.901120i | \(-0.357253\pi\) | ||||
0.433571 | + | 0.901120i | \(0.357253\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −40.4215 | −1.82049 | ||||||||
\(494\) | 9.76002 | 0.439124 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.67005 | −0.434198 | ||||||||
\(497\) | 35.6670 | 1.59988 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.5569 | 1.59175 | 0.795874 | − | 0.605463i | \(-0.207012\pi\) | ||||
0.795874 | + | 0.605463i | \(0.207012\pi\) | |||||||
\(500\) | 11.9794 | 0.535737 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 27.5070 | 1.22770 | ||||||||
\(503\) | 7.48503 | 0.333741 | 0.166871 | − | 0.985979i | \(-0.446634\pi\) | ||||
0.166871 | + | 0.985979i | \(0.446634\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.95990 | −0.354211 | ||||||||
\(506\) | 0.247993 | 0.0110246 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.37977 | 0.327424 | ||||||||
\(509\) | 6.17672 | 0.273778 | 0.136889 | − | 0.990586i | \(-0.456290\pi\) | ||||
0.136889 | + | 0.990586i | \(0.456290\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.52303 | −0.155850 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.27868 | −0.365157 | ||||||||
\(515\) | −12.8251 | −0.565139 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.36573 | 0.0600649 | ||||||||
\(518\) | −36.0173 | −1.58251 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.04888 | 0.396819 | ||||||||
\(521\) | 4.67763 | 0.204930 | 0.102465 | − | 0.994737i | \(-0.467327\pi\) | ||||
0.102465 | + | 0.994737i | \(0.467327\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.80751 | −0.297672 | −0.148836 | − | 0.988862i | \(-0.547553\pi\) | ||||
−0.148836 | + | 0.988862i | \(0.547553\pi\) | |||||||
\(524\) | −9.07961 | −0.396645 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.6577 | 0.857115 | ||||||||
\(527\) | −60.4373 | −2.63269 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.4201 | −0.931310 | ||||||||
\(530\) | 9.75900 | 0.423904 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.37507 | −0.319750 | ||||||||
\(533\) | 38.7651 | 1.67910 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.75354 | 0.119046 | ||||||||
\(536\) | −15.3102 | −0.661302 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.61876 | 0.156016 | ||||||||
\(539\) | −2.06929 | −0.0891306 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.6664 | −1.61940 | −0.809702 | − | 0.586841i | \(-0.800371\pi\) | ||||
−0.809702 | + | 0.586841i | \(0.800371\pi\) | |||||||
\(542\) | 16.2770 | 0.699156 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.24995 | 0.267964 | ||||||||
\(545\) | 17.5702 | 0.752623 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.8485 | −1.49001 | −0.745007 | − | 0.667056i | \(-0.767554\pi\) | ||||
−0.745007 | + | 0.667056i | \(0.767554\pi\) | |||||||
\(548\) | 12.7245 | 0.543563 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.459020 | 0.0195727 | ||||||||
\(551\) | 11.4060 | 0.485910 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.6828 | −0.496802 | ||||||||
\(554\) | 9.87391 | 0.419502 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.66714 | 0.0707026 | ||||||||
\(557\) | −11.6360 | −0.493034 | −0.246517 | − | 0.969138i | \(-0.579286\pi\) | ||||
−0.246517 | + | 0.969138i | \(0.579286\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.9842 | −1.09901 | ||||||||
\(560\) | −6.83770 | −0.288945 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.71542 | −0.241090 | ||||||||
\(563\) | −24.7461 | −1.04292 | −0.521462 | − | 0.853274i | \(-0.674613\pi\) | ||||
−0.521462 | + | 0.853274i | \(0.674613\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.9088 | −0.711360 | ||||||||
\(566\) | −11.6035 | −0.487730 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.52896 | 0.357867 | ||||||||
\(569\) | 8.14143 | 0.341306 | 0.170653 | − | 0.985331i | \(-0.445412\pi\) | ||||
0.170653 | + | 0.985331i | \(0.445412\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.63240 | 0.0683138 | 0.0341569 | − | 0.999416i | \(-0.489125\pi\) | ||||
0.0341569 | + | 0.999416i | \(0.489125\pi\) | |||||||
\(572\) | 1.09190 | 0.0456546 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −29.2925 | −1.22264 | ||||||||
\(575\) | 2.92426 | 0.121950 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.01805 | 0.375426 | 0.187713 | − | 0.982224i | \(-0.439892\pi\) | ||||
0.187713 | + | 0.982224i | \(0.439892\pi\) | |||||||
\(578\) | 22.0619 | 0.917652 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.5749 | 0.439098 | ||||||||
\(581\) | 7.03789 | 0.291981 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.17759 | 0.0487707 | ||||||||
\(584\) | −0.842454 | −0.0348610 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.62266 | 0.0670314 | ||||||||
\(587\) | −42.4374 | −1.75158 | −0.875789 | − | 0.482694i | \(-0.839658\pi\) | ||||
−0.875789 | + | 0.482694i | \(0.839658\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.0539 | 0.702695 | ||||||||
\(590\) | −7.22354 | −0.297388 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.61274 | −0.353981 | ||||||||
\(593\) | 40.5390 | 1.66474 | 0.832369 | − | 0.554222i | \(-0.186984\pi\) | ||||
0.832369 | + | 0.554222i | \(0.186984\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −42.7352 | −1.75197 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.95612 | 0.284457 | ||||||||
\(599\) | 11.4659 | 0.468484 | 0.234242 | − | 0.972178i | \(-0.424739\pi\) | ||||
0.234242 | + | 0.972178i | \(0.424739\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.0785 | 1.47167 | 0.735837 | − | 0.677159i | \(-0.236789\pi\) | ||||
0.735837 | + | 0.677159i | \(0.236789\pi\) | |||||||
\(602\) | 19.6347 | 0.800251 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17.2820 | −0.703193 | ||||||||
\(605\) | 17.9222 | 0.728643 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.2834 | −1.51329 | −0.756643 | − | 0.653828i | \(-0.773162\pi\) | ||||
−0.756643 | + | 0.653828i | \(0.773162\pi\) | |||||||
\(608\) | −1.76358 | −0.0715227 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.3775 | −0.420173 | ||||||||
\(611\) | 38.3084 | 1.54979 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.666270 | −0.0269104 | −0.0134552 | − | 0.999909i | \(-0.504283\pi\) | ||||
−0.0134552 | + | 0.999909i | \(0.504283\pi\) | |||||||
\(614\) | −9.46804 | −0.382099 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.825083 | −0.0332435 | ||||||||
\(617\) | −41.1430 | −1.65635 | −0.828177 | − | 0.560467i | \(-0.810622\pi\) | ||||
−0.828177 | + | 0.560467i | \(0.810622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.736346 | −0.0295962 | −0.0147981 | − | 0.999891i | \(-0.504711\pi\) | ||||
−0.0147981 | + | 0.999891i | \(0.504711\pi\) | |||||||
\(620\) | 15.8113 | 0.634998 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.2503 | −0.731770 | ||||||||
\(623\) | 2.16896 | 0.0868977 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.95481 | −0.318193 | ||||||||
\(626\) | 17.6571 | 0.705719 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.9018 | −0.674457 | ||||||||
\(629\) | −53.8292 | −2.14631 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.8071 | 1.86336 | 0.931681 | − | 0.363277i | \(-0.118342\pi\) | ||||
0.931681 | + | 0.363277i | \(0.118342\pi\) | |||||||
\(632\) | −2.79367 | −0.111126 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.3212 | −0.608483 | ||||||||
\(635\) | −12.0665 | −0.478845 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −58.0429 | −2.29974 | ||||||||
\(638\) | 1.27604 | 0.0505188 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.63508 | −0.0646323 | ||||||||
\(641\) | −20.0532 | −0.792052 | −0.396026 | − | 0.918239i | \(-0.629611\pi\) | ||||
−0.396026 | + | 0.918239i | \(0.629611\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 48.7277 | 1.92163 | 0.960817 | − | 0.277182i | \(-0.0894005\pi\) | ||||
0.960817 | + | 0.277182i | \(0.0894005\pi\) | |||||||
\(644\) | −5.25632 | −0.207128 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.0223 | −0.433666 | ||||||||
\(647\) | −21.8927 | −0.860692 | −0.430346 | − | 0.902664i | \(-0.641608\pi\) | ||||
−0.430346 | + | 0.902664i | \(0.641608\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.871641 | −0.0342149 | ||||||||
\(650\) | 12.8754 | 0.505014 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.9163 | 0.466678 | ||||||||
\(653\) | 29.9921 | 1.17368 | 0.586840 | − | 0.809703i | \(-0.300372\pi\) | ||||
0.586840 | + | 0.809703i | \(0.300372\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.8459 | 0.580077 | ||||||||
\(656\) | −7.00464 | −0.273485 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −28.9474 | −1.12849 | ||||||||
\(659\) | −42.8025 | −1.66735 | −0.833675 | − | 0.552255i | \(-0.813767\pi\) | ||||
−0.833675 | + | 0.552255i | \(0.813767\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.7037 | 1.46651 | 0.733253 | − | 0.679956i | \(-0.238001\pi\) | ||||
0.733253 | + | 0.679956i | \(0.238001\pi\) | |||||||
\(662\) | 10.9330 | 0.424923 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.68295 | 0.0653113 | ||||||||
\(665\) | 12.0588 | 0.467621 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.12920 | 0.314764 | ||||||||
\(668\) | 14.7560 | 0.570929 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 25.0335 | 0.967128 | ||||||||
\(671\) | −1.25222 | −0.0483415 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.65651 | −0.295137 | −0.147568 | − | 0.989052i | \(-0.547145\pi\) | ||||
−0.147568 | + | 0.989052i | \(0.547145\pi\) | |||||||
\(674\) | 2.19251 | 0.0844525 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.6274 | 0.677978 | ||||||||
\(677\) | −51.3670 | −1.97420 | −0.987098 | − | 0.160118i | \(-0.948812\pi\) | ||||
−0.987098 | + | 0.160118i | \(0.948812\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.5159 | 0.480317 | ||||||||
\(680\) | −10.2192 | −0.391887 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.90790 | 0.0730573 | ||||||||
\(683\) | 6.92554 | 0.264998 | 0.132499 | − | 0.991183i | \(-0.457700\pi\) | ||||
0.132499 | + | 0.991183i | \(0.457700\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.8056 | −0.794940 | ||||||||
\(686\) | 14.5865 | 0.556914 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.69520 | 0.179003 | ||||||||
\(689\) | 33.0310 | 1.25838 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.16011 | 0.348467 | 0.174233 | − | 0.984704i | \(-0.444255\pi\) | ||||
0.174233 | + | 0.984704i | \(0.444255\pi\) | |||||||
\(692\) | −24.6303 | −0.936302 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.7847 | −0.864896 | ||||||||
\(695\) | −2.72591 | −0.103400 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −43.7787 | −1.65823 | ||||||||
\(698\) | −19.0409 | −0.720709 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.72915 | −0.367727 | ||||||||
\(701\) | 14.6149 | 0.551995 | 0.275998 | − | 0.961158i | \(-0.410992\pi\) | ||||
0.275998 | + | 0.961158i | \(0.410992\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.1893 | 0.572874 | ||||||||
\(704\) | −0.197300 | −0.00743603 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.2629 | 0.574429 | ||||||||
\(707\) | 20.3582 | 0.765648 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.3835 | −1.59175 | −0.795873 | − | 0.605464i | \(-0.792988\pi\) | ||||
−0.795873 | + | 0.605464i | \(0.792988\pi\) | |||||||
\(710\) | −13.9455 | −0.523367 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.518659 | 0.0194376 | ||||||||
\(713\) | 12.1546 | 0.455193 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.78534 | −0.0667681 | ||||||||
\(716\) | 20.1909 | 0.754568 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.35972 | −0.0507444 | ||||||||
\(719\) | −20.0259 | −0.746841 | −0.373420 | − | 0.927662i | \(-0.621815\pi\) | ||||
−0.373420 | + | 0.927662i | \(0.621815\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.8012 | 1.22158 | ||||||||
\(722\) | −15.8898 | −0.591356 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.5876 | −0.690801 | ||||||||
\(725\) | 15.0467 | 0.558820 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.9223 | 0.405088 | 0.202544 | − | 0.979273i | \(-0.435079\pi\) | ||||
0.202544 | + | 0.979273i | \(0.435079\pi\) | |||||||
\(728\) | −23.1433 | −0.857748 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.37748 | 0.0509828 | ||||||||
\(731\) | 29.3448 | 1.08535 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.8316 | 1.24960 | 0.624799 | − | 0.780785i | \(-0.285181\pi\) | ||||
0.624799 | + | 0.780785i | \(0.285181\pi\) | |||||||
\(734\) | 5.15305 | 0.190203 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.25693 | −0.0463311 | ||||||||
\(737\) | 3.02071 | 0.111269 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.9760 | −0.698045 | −0.349023 | − | 0.937114i | \(-0.613486\pi\) | ||||
−0.349023 | + | 0.937114i | \(0.613486\pi\) | |||||||
\(740\) | 14.0825 | 0.517684 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −24.9595 | −0.916293 | ||||||||
\(743\) | −15.2042 | −0.557786 | −0.278893 | − | 0.960322i | \(-0.589968\pi\) | ||||
−0.278893 | + | 0.960322i | \(0.589968\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.63508 | 0.0599047 | ||||||||
\(746\) | 4.71232 | 0.172530 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.23312 | −0.0450872 | ||||||||
\(749\) | −7.04244 | −0.257325 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.34506 | −0.122063 | −0.0610316 | − | 0.998136i | \(-0.519439\pi\) | ||||
−0.0610316 | + | 0.998136i | \(0.519439\pi\) | |||||||
\(752\) | −6.92211 | −0.252423 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 35.7924 | 1.30348 | ||||||||
\(755\) | 28.2574 | 1.02839 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.2280 | −1.53480 | −0.767401 | − | 0.641167i | \(-0.778450\pi\) | ||||
−0.767401 | + | 0.641167i | \(0.778450\pi\) | |||||||
\(758\) | 16.9403 | 0.615301 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.88360 | 0.104599 | ||||||||
\(761\) | −27.8189 | −1.00844 | −0.504218 | − | 0.863577i | \(-0.668219\pi\) | ||||
−0.504218 | + | 0.863577i | \(0.668219\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −44.9373 | −1.62684 | ||||||||
\(764\) | 22.5264 | 0.814976 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.39895 | −0.231203 | ||||||||
\(767\) | −24.4493 | −0.882812 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.7072 | 1.28764 | 0.643818 | − | 0.765179i | \(-0.277349\pi\) | ||||
0.643818 | + | 0.765179i | \(0.277349\pi\) | |||||||
\(770\) | 1.34908 | 0.0486174 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.61836 | −0.130228 | ||||||||
\(773\) | −52.1349 | −1.87516 | −0.937580 | − | 0.347769i | \(-0.886939\pi\) | ||||
−0.937580 | + | 0.347769i | \(0.886939\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.4975 | 0.808133 | ||||||||
\(776\) | 2.99290 | 0.107439 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.08628 | 0.0389451 | ||||||||
\(779\) | 12.3533 | 0.442601 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.68276 | −0.0602140 | ||||||||
\(782\) | −7.85576 | −0.280921 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.4880 | 0.374572 | ||||||||
\(785\) | 27.6359 | 0.986367 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.2235 | −1.04170 | −0.520852 | − | 0.853647i | \(-0.674386\pi\) | ||||
−0.520852 | + | 0.853647i | \(0.674386\pi\) | |||||||
\(788\) | −22.2957 | −0.794253 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.56789 | 0.162518 | ||||||||
\(791\) | 43.2459 | 1.53765 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.1244 | −1.24730 | ||||||||
\(794\) | 25.3461 | 0.899500 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.0975 | −0.393340 | ||||||||
\(797\) | 16.9257 | 0.599538 | 0.299769 | − | 0.954012i | \(-0.403090\pi\) | ||||
0.299769 | + | 0.954012i | \(0.403090\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.2628 | −1.53053 | ||||||||
\(800\) | −2.32651 | −0.0822545 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.08150 | 0.0735002 | ||||||||
\(803\) | 0.166216 | 0.00586564 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.59452 | 0.302917 | ||||||||
\(806\) | 53.5161 | 1.88502 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.86820 | 0.171263 | ||||||||
\(809\) | −33.6153 | −1.18185 | −0.590926 | − | 0.806726i | \(-0.701237\pi\) | ||||
−0.590926 | + | 0.806726i | \(0.701237\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.8551 | 1.78577 | 0.892883 | − | 0.450289i | \(-0.148679\pi\) | ||||
0.892883 | + | 0.450289i | \(0.148679\pi\) | |||||||
\(812\) | −27.0462 | −0.949136 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.69929 | 0.0595602 | ||||||||
\(815\) | −19.4841 | −0.682498 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.28037 | −0.289693 | ||||||||
\(818\) | 1.78094 | 0.0622691 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.4532 | 0.399962 | ||||||||
\(821\) | 10.0302 | 0.350056 | 0.175028 | − | 0.984563i | \(-0.443998\pi\) | ||||
0.175028 | + | 0.984563i | \(0.443998\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.0828 | −0.595470 | −0.297735 | − | 0.954649i | \(-0.596231\pi\) | ||||
−0.297735 | + | 0.954649i | \(0.596231\pi\) | |||||||
\(824\) | 7.84368 | 0.273247 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.4749 | 0.642823 | ||||||||
\(827\) | 33.6331 | 1.16954 | 0.584768 | − | 0.811201i | \(-0.301186\pi\) | ||||
0.584768 | + | 0.811201i | \(0.301186\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.4770 | −1.02378 | −0.511889 | − | 0.859052i | \(-0.671054\pi\) | ||||
−0.511889 | + | 0.859052i | \(0.671054\pi\) | |||||||
\(830\) | −2.75177 | −0.0955152 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.53420 | −0.191864 | ||||||||
\(833\) | 65.5496 | 2.27116 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.1273 | −0.834961 | ||||||||
\(836\) | 0.347955 | 0.0120343 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20.4936 | 0.707940 | ||||||||
\(839\) | 22.2593 | 0.768476 | 0.384238 | − | 0.923234i | \(-0.374464\pi\) | ||||
0.384238 | + | 0.923234i | \(0.374464\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8285 | 0.442362 | ||||||||
\(842\) | −13.6932 | −0.471897 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.6815 | −0.436515 | ||||||||
\(845\) | −28.8223 | −0.991516 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −45.8378 | −1.57500 | ||||||||
\(848\) | −5.96851 | −0.204960 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −14.5406 | −0.498737 | ||||||||
\(851\) | 10.8256 | 0.371098 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.65495 | −0.227861 | −0.113931 | − | 0.993489i | \(-0.536344\pi\) | ||||
−0.113931 | + | 0.993489i | \(0.536344\pi\) | |||||||
\(854\) | 26.5414 | 0.908229 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.68404 | −0.0575593 | ||||||||
\(857\) | 47.2482 | 1.61397 | 0.806983 | − | 0.590574i | \(-0.201099\pi\) | ||||
0.806983 | + | 0.590574i | \(0.201099\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.1021 | 1.12943 | 0.564714 | − | 0.825287i | \(-0.308987\pi\) | ||||
0.564714 | + | 0.825287i | \(0.308987\pi\) | |||||||
\(860\) | −7.67703 | −0.261785 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22.2846 | 0.759018 | ||||||||
\(863\) | 5.50067 | 0.187245 | 0.0936225 | − | 0.995608i | \(-0.470155\pi\) | ||||
0.0936225 | + | 0.995608i | \(0.470155\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.2725 | 1.36931 | ||||||||
\(866\) | −22.4806 | −0.763923 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −40.4389 | −1.37259 | ||||||||
\(869\) | 0.551192 | 0.0186979 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 84.7300 | 2.87097 | ||||||||
\(872\) | −10.7457 | −0.363897 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.21670 | 0.0749810 | ||||||||
\(875\) | 50.0964 | 1.69357 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.7687 | 0.768844 | 0.384422 | − | 0.923157i | \(-0.374401\pi\) | ||||
0.384422 | + | 0.923157i | \(0.374401\pi\) | |||||||
\(878\) | −24.1239 | −0.814143 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.322602 | 0.0108749 | ||||||||
\(881\) | −35.0854 | −1.18206 | −0.591029 | − | 0.806650i | \(-0.701278\pi\) | ||||
−0.591029 | + | 0.806650i | \(0.701278\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.7453 | −0.462565 | −0.231283 | − | 0.972887i | \(-0.574292\pi\) | ||||
−0.231283 | + | 0.972887i | \(0.574292\pi\) | |||||||
\(884\) | −34.5885 | −1.16334 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 29.6812 | 0.997159 | ||||||||
\(887\) | −27.4555 | −0.921865 | −0.460932 | − | 0.887435i | \(-0.652485\pi\) | ||||
−0.460932 | + | 0.887435i | \(0.652485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.8612 | 1.03505 | ||||||||
\(890\) | −0.848050 | −0.0284267 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.65351 | −0.155811 | ||||||||
\(893\) | 12.2077 | 0.408515 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.0137 | −1.10353 | ||||||||
\(896\) | 4.18187 | 0.139706 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25.7344 | −0.858767 | ||||||||
\(899\) | 62.5410 | 2.08586 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.3029 | −1.24274 | ||||||||
\(902\) | 1.38202 | 0.0460161 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.3413 | 0.343946 | ||||||||
\(905\) | 30.3922 | 1.01027 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.38802 | 0.0792927 | 0.0396464 | − | 0.999214i | \(-0.487377\pi\) | ||||
0.0396464 | + | 0.999214i | \(0.487377\pi\) | |||||||
\(908\) | 13.2197 | 0.438713 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 37.8412 | 1.25442 | ||||||||
\(911\) | −27.0356 | −0.895729 | −0.447864 | − | 0.894101i | \(-0.647815\pi\) | ||||
−0.447864 | + | 0.894101i | \(0.647815\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.332047 | −0.0109891 | ||||||||
\(914\) | 0.610859 | 0.0202054 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.02383 | −0.132951 | ||||||||
\(917\) | −37.9697 | −1.25387 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.17380 | 0.104694 | 0.0523470 | − | 0.998629i | \(-0.483330\pi\) | ||||
0.0523470 | + | 0.998629i | \(0.483330\pi\) | |||||||
\(920\) | 2.05519 | 0.0677575 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.9751 | 0.394377 | ||||||||
\(923\) | −47.2010 | −1.55364 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.0376 | 0.658833 | ||||||||
\(926\) | −12.6330 | −0.415145 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.46749 | −0.212306 | ||||||||
\(929\) | 56.2318 | 1.84490 | 0.922452 | − | 0.386112i | \(-0.126182\pi\) | ||||
0.922452 | + | 0.386112i | \(0.126182\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.4965 | −0.606198 | ||||||||
\(932\) | −7.44022 | −0.243712 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.77417 | −0.221658 | ||||||||
\(935\) | 2.01624 | 0.0659382 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.0832 | −0.884770 | −0.442385 | − | 0.896825i | \(-0.645868\pi\) | ||||
−0.442385 | + | 0.896825i | \(0.645868\pi\) | |||||||
\(938\) | −64.0254 | −2.09050 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.3182 | 0.369159 | ||||||||
\(941\) | 37.6898 | 1.22865 | 0.614326 | − | 0.789052i | \(-0.289428\pi\) | ||||
0.614326 | + | 0.789052i | \(0.289428\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.80436 | 0.286709 | ||||||||
\(944\) | 4.41785 | 0.143789 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.926363 | −0.0301187 | ||||||||
\(947\) | −42.1198 | −1.36871 | −0.684354 | − | 0.729150i | \(-0.739916\pi\) | ||||
−0.684354 | + | 0.729150i | \(0.739916\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.66231 | 0.151345 | ||||||||
\(950\) | 4.10299 | 0.133118 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 26.1365 | 0.847088 | ||||||||
\(953\) | −6.25412 | −0.202591 | −0.101295 | − | 0.994856i | \(-0.532299\pi\) | ||||
−0.101295 | + | 0.994856i | \(0.532299\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.8325 | −1.19187 | ||||||||
\(956\) | −25.1146 | −0.812263 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.1625 | 0.392952 | ||||||||
\(959\) | 53.2121 | 1.71831 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62.5099 | 2.01645 | ||||||||
\(962\) | 47.6647 | 1.53677 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.39031 | −0.173610 | ||||||||
\(965\) | 5.91631 | 0.190453 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.9859 | 1.02860 | 0.514298 | − | 0.857611i | \(-0.328052\pi\) | ||||
0.514298 | + | 0.857611i | \(0.328052\pi\) | |||||||
\(968\) | −10.9611 | −0.352302 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.89363 | −0.157125 | ||||||||
\(971\) | 33.2640 | 1.06749 | 0.533747 | − | 0.845644i | \(-0.320783\pi\) | ||||
0.533747 | + | 0.845644i | \(0.320783\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.97177 | 0.223505 | ||||||||
\(974\) | −14.0747 | −0.450981 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.34679 | 0.203156 | ||||||||
\(977\) | 15.1642 | 0.485145 | 0.242573 | − | 0.970133i | \(-0.422009\pi\) | ||||
0.242573 | + | 0.970133i | \(0.422009\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.102331 | −0.00327053 | ||||||||
\(980\) | −17.1488 | −0.547798 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.2146 | 0.613162 | ||||||||
\(983\) | 20.6179 | 0.657609 | 0.328804 | − | 0.944398i | \(-0.393354\pi\) | ||||
0.328804 | + | 0.944398i | \(0.393354\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.4554 | 1.16156 | ||||||||
\(986\) | −40.4215 | −1.28728 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.76002 | 0.310508 | ||||||||
\(989\) | −5.90155 | −0.187658 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.9640 | 1.17420 | 0.587101 | − | 0.809514i | \(-0.300269\pi\) | ||||
0.587101 | + | 0.809514i | \(0.300269\pi\) | |||||||
\(992\) | −9.67005 | −0.307024 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 35.6670 | 1.13129 | ||||||||
\(995\) | 18.1453 | 0.575244 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.7817 | 1.16489 | 0.582444 | − | 0.812871i | \(-0.302096\pi\) | ||||
0.582444 | + | 0.812871i | \(0.302096\pi\) | |||||||
\(998\) | 35.5569 | 1.12554 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8046.2.a.h.1.4 | yes | 9 | |
3.2 | odd | 2 | 8046.2.a.g.1.6 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.g.1.6 | ✓ | 9 | 3.2 | odd | 2 | ||
8046.2.a.h.1.4 | yes | 9 | 1.1 | even | 1 | trivial |