Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | −1.52846 | −0.882458 | −0.441229 | − | 0.897395i | \(-0.645457\pi\) | ||||
−0.441229 | + | 0.897395i | \(0.645457\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.276340 | 0.123583 | 0.0617916 | − | 0.998089i | \(-0.480319\pi\) | ||||
0.0617916 | + | 0.998089i | \(0.480319\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.37933 | 0.899302 | 0.449651 | − | 0.893204i | \(-0.351548\pi\) | ||||
0.449651 | + | 0.893204i | \(0.351548\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.663805 | −0.221268 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.982619 | −0.296271 | −0.148135 | − | 0.988967i | \(-0.547327\pi\) | ||||
−0.148135 | + | 0.988967i | \(0.547327\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.12922 | −1.42259 | −0.711295 | − | 0.702894i | \(-0.751891\pi\) | ||||
−0.711295 | + | 0.702894i | \(0.751891\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.422376 | −0.109057 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.66490 | 1.85901 | 0.929505 | − | 0.368808i | \(-0.120234\pi\) | ||||
0.929505 | + | 0.368808i | \(0.120234\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.67902 | 1.07344 | 0.536721 | − | 0.843760i | \(-0.319663\pi\) | ||||
0.536721 | + | 0.843760i | \(0.319663\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.63671 | −0.793596 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.09647 | −1.47972 | −0.739858 | − | 0.672763i | \(-0.765107\pi\) | ||||
−0.739858 | + | 0.672763i | \(0.765107\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.92364 | −0.984727 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.59999 | 1.07772 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.66042 | 0.494027 | 0.247013 | − | 0.969012i | \(-0.420551\pi\) | ||||
0.247013 | + | 0.969012i | \(0.420551\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.74196 | −1.03129 | −0.515644 | − | 0.856803i | \(-0.672447\pi\) | ||||
−0.515644 | + | 0.856803i | \(0.672447\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.50189 | 0.261446 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.657504 | 0.111139 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.273473 | −0.0449587 | −0.0224793 | − | 0.999747i | \(-0.507156\pi\) | ||||
−0.0224793 | + | 0.999747i | \(0.507156\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.83981 | 1.25538 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.12965 | −0.644944 | −0.322472 | − | 0.946579i | \(-0.604514\pi\) | ||||
−0.322472 | + | 0.946579i | \(0.604514\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.07236 | 1.07852 | 0.539262 | − | 0.842138i | \(-0.318703\pi\) | ||||
0.539262 | + | 0.842138i | \(0.318703\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.183436 | −0.0273451 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.1984 | 1.77932 | 0.889659 | − | 0.456626i | \(-0.150942\pi\) | ||||
0.889659 | + | 0.456626i | \(0.150942\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.33880 | −0.191257 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.7155 | −1.64050 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.726931 | −0.0998516 | −0.0499258 | − | 0.998753i | \(-0.515898\pi\) | ||||
−0.0499258 | + | 0.998753i | \(0.515898\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.271537 | −0.0366141 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.15171 | −0.947267 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.80195 | −0.885538 | −0.442769 | − | 0.896636i | \(-0.646004\pi\) | ||||
−0.442769 | + | 0.896636i | \(0.646004\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.98444 | 0.766229 | 0.383114 | − | 0.923701i | \(-0.374851\pi\) | ||||
0.383114 | + | 0.923701i | \(0.374851\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.57941 | −0.198987 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.41741 | −0.175808 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.6673 | −1.30322 | −0.651611 | − | 0.758553i | \(-0.725907\pi\) | ||||
−0.651611 | + | 0.758553i | \(0.725907\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.8467 | 1.30579 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.23431 | −0.977232 | −0.488616 | − | 0.872499i | \(-0.662498\pi\) | ||||
−0.488616 | + | 0.872499i | \(0.662498\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.4776 | 1.81152 | 0.905758 | − | 0.423796i | \(-0.139303\pi\) | ||||
0.905758 | + | 0.423796i | \(0.139303\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.52559 | 0.868980 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.33797 | −0.266437 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.1624 | −1.36837 | −0.684187 | − | 0.729307i | \(-0.739843\pi\) | ||||
−0.684187 | + | 0.729307i | \(0.739843\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.56795 | −0.729772 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.56428 | −0.940052 | −0.470026 | − | 0.882653i | \(-0.655755\pi\) | ||||
−0.470026 | + | 0.882653i | \(0.655755\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.11812 | 0.229742 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.06634 | −0.435958 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.3251 | −1.73046 | −0.865230 | − | 0.501374i | \(-0.832828\pi\) | ||||
−0.865230 | + | 0.501374i | \(0.832828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.2041 | −1.27934 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.77637 | 0.910067 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.29300 | 0.132659 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.63657 | 0.673841 | 0.336921 | − | 0.941533i | \(-0.390615\pi\) | ||||
0.336921 | + | 0.941533i | \(0.390615\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.652267 | 0.0655553 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3406 | 1.02893 | 0.514466 | − | 0.857511i | \(-0.327990\pi\) | ||||
0.514466 | + | 0.857511i | \(0.327990\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.66191 | 0.262286 | 0.131143 | − | 0.991363i | \(-0.458135\pi\) | ||||
0.131143 | + | 0.991363i | \(0.458135\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00497 | −0.0980750 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.29618 | −0.898695 | −0.449348 | − | 0.893357i | \(-0.648344\pi\) | ||||
−0.449348 | + | 0.893357i | \(0.648344\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0187 | 1.05540 | 0.527698 | − | 0.849432i | \(-0.323055\pi\) | ||||
0.527698 | + | 0.849432i | \(0.323055\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.417993 | 0.0396741 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.38536 | 0.130324 | 0.0651621 | − | 0.997875i | \(-0.479244\pi\) | ||||
0.0651621 | + | 0.997875i | \(0.479244\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.96104 | −0.182868 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.40480 | 0.314774 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.2373 | 1.67181 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0345 | −0.912224 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.31202 | 0.569136 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.74230 | −0.245279 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.69029 | 0.149989 | 0.0749945 | − | 0.997184i | \(-0.476106\pi\) | ||||
0.0749945 | + | 0.997184i | \(0.476106\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.8098 | −0.951752 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3218 | 0.989186 | 0.494593 | − | 0.869125i | \(-0.335317\pi\) | ||||
0.494593 | + | 0.869125i | \(0.335317\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.1329 | 0.965347 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.54750 | 0.133188 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.67204 | −0.740902 | −0.370451 | − | 0.928852i | \(-0.620797\pi\) | ||||
−0.370451 | + | 0.928852i | \(0.620797\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.6663 | 1.24398 | 0.621988 | − | 0.783027i | \(-0.286325\pi\) | ||||
0.621988 | + | 0.783027i | \(0.286325\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.6448 | −1.57017 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.04007 | 0.421472 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.735180 | 0.0610534 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.04630 | 0.168776 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.9171 | −0.976291 | −0.488145 | − | 0.872762i | \(-0.662326\pi\) | ||||
−0.488145 | + | 0.872762i | \(0.662326\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.77060 | −0.632362 | −0.316181 | − | 0.948699i | \(-0.602401\pi\) | ||||
−0.316181 | + | 0.948699i | \(0.602401\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.08800 | −0.411340 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.58674 | −0.127450 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.9081 | −1.18980 | −0.594900 | − | 0.803800i | \(-0.702808\pi\) | ||||
−0.594900 | + | 0.803800i | \(0.702808\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.11109 | 0.0881148 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.8848 | −1.33071 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.2000 | −1.26889 | −0.634443 | − | 0.772970i | \(-0.718770\pi\) | ||||
−0.634443 | + | 0.772970i | \(0.718770\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.415034 | 0.0323104 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.0637168 | 0.00493055 | 0.00246528 | − | 0.999997i | \(-0.499215\pi\) | ||||
0.00246528 | + | 0.999997i | \(0.499215\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.3089 | 1.02376 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.10596 | −0.237519 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.8595 | 1.81401 | 0.907003 | − | 0.421124i | \(-0.138364\pi\) | ||||
0.907003 | + | 0.421124i | \(0.138364\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.7149 | −0.885567 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.3965 | 0.781450 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.2960 | −1.06853 | −0.534267 | − | 0.845316i | \(-0.679412\pi\) | ||||
−0.534267 | + | 0.845316i | \(0.679412\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7621 | 1.24592 | 0.622960 | − | 0.782254i | \(-0.285930\pi\) | ||||
0.622960 | + | 0.782254i | \(0.285930\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.14698 | −0.676165 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0755716 | −0.00555614 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.53167 | −0.550770 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.3242 | 0.969193 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.9060 | −1.07856 | −0.539279 | − | 0.842127i | \(-0.681303\pi\) | ||||
−0.539279 | + | 0.842127i | \(0.681303\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.51590 | −0.325062 | −0.162531 | − | 0.986703i | \(-0.551966\pi\) | ||||
−0.162531 | + | 0.986703i | \(0.551966\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.16646 | 0.155143 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.9542 | 1.27919 | 0.639593 | − | 0.768714i | \(-0.279103\pi\) | ||||
0.639593 | + | 0.768714i | \(0.279103\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5885 | 0.892378 | 0.446189 | − | 0.894939i | \(-0.352781\pi\) | ||||
0.446189 | + | 0.894939i | \(0.352781\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.3046 | 1.15004 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.33000 | 0.444279 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.14119 | −0.0797042 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.71068 | 0.327415 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.59769 | −0.318029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.10396 | −0.0760001 | −0.0380000 | − | 0.999278i | \(-0.512099\pi\) | ||||
−0.0380000 | + | 0.999278i | \(0.512099\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.5858 | 0.862366 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.95438 | 0.133287 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.6620 | −0.927438 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.6569 | −1.59859 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −39.3149 | −2.64461 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.8136 | −1.86254 | −0.931268 | − | 0.364335i | \(-0.881296\pi\) | ||||
−0.931268 | + | 0.364335i | \(0.881296\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.26834 | 0.217889 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.4401 | −1.02479 | −0.512397 | − | 0.858749i | \(-0.671242\pi\) | ||||
−0.512397 | + | 0.858749i | \(0.671242\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.73578 | 0.643359 | 0.321679 | − | 0.946849i | \(-0.395753\pi\) | ||||
0.321679 | + | 0.946849i | \(0.395753\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.57350 | 0.235119 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.8528 | −0.710988 | −0.355494 | − | 0.934679i | \(-0.615687\pi\) | ||||
−0.355494 | + | 0.934679i | \(0.615687\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.37091 | 0.219894 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.5897 | 1.20753 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.7278 | −1.66419 | −0.832095 | − | 0.554632i | \(-0.812859\pi\) | ||||
−0.832095 | + | 0.554632i | \(0.812859\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.19705 | −0.528018 | −0.264009 | − | 0.964520i | \(-0.585045\pi\) | ||||
−0.264009 | + | 0.964520i | \(0.585045\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.76110 | −0.433725 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.369964 | −0.0236361 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.9997 | −1.52707 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.0902 | 0.829556 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.07869 | 0.0680862 | 0.0340431 | − | 0.999420i | \(-0.489162\pi\) | ||||
0.0340431 | + | 0.999420i | \(0.489162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.97312 | 0.438397 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.23747 | −0.202738 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.7180 | −1.60425 | −0.802124 | − | 0.597158i | \(-0.796297\pi\) | ||||
−0.802124 | + | 0.597158i | \(0.796297\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.650682 | −0.0404314 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.76600 | −0.109313 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.0811 | 1.66990 | 0.834948 | − | 0.550330i | \(-0.185498\pi\) | ||||
0.834948 | + | 0.550330i | \(0.185498\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.200880 | −0.0123400 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.9523 | 1.52706 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.3997 | 1.12185 | 0.560923 | − | 0.827868i | \(-0.310446\pi\) | ||||
0.560923 | + | 0.827868i | \(0.310446\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.9111 | −1.08802 | −0.544010 | − | 0.839079i | \(-0.683095\pi\) | ||||
−0.544010 | + | 0.839079i | \(0.683095\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18.6535 | 1.12896 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.83806 | 0.291746 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.11279 | −0.427366 | −0.213683 | − | 0.976903i | \(-0.568546\pi\) | ||||
−0.213683 | + | 0.976903i | \(0.568546\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.81155 | 0.228191 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.9208 | −0.949758 | −0.474879 | − | 0.880051i | \(-0.657508\pi\) | ||||
−0.474879 | + | 0.880051i | \(0.657508\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.9716 | −0.949415 | −0.474708 | − | 0.880144i | \(-0.657446\pi\) | ||||
−0.474708 | + | 0.880144i | \(0.657446\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.97630 | −0.117066 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.82580 | −0.579999 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.7507 | 2.45592 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.1437 | −0.594636 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.1943 | −0.712399 | −0.356200 | − | 0.934410i | \(-0.615928\pi\) | ||||
−0.356200 | + | 0.934410i | \(0.615928\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.87965 | −0.109438 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.50265 | −0.319296 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 36.3994 | 2.10503 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.8275 | 0.969919 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.8053 | −0.907988 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.65374 | 0.0946930 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.9628 | −1.48178 | −0.740889 | − | 0.671628i | \(-0.765595\pi\) | ||||
−0.740889 | + | 0.671628i | \(0.765595\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.06863 | −0.231456 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.92858 | −0.562998 | −0.281499 | − | 0.959562i | \(-0.590832\pi\) | ||||
−0.281499 | + | 0.959562i | \(0.590832\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.4924 | 1.27135 | 0.635673 | − | 0.771958i | \(-0.280723\pi\) | ||||
0.635673 | + | 0.771958i | \(0.280723\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.436455 | −0.0245914 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.16889 | −0.346480 | −0.173240 | − | 0.984880i | \(-0.555424\pi\) | ||||
−0.173240 | + | 0.984880i | \(0.555424\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.61417 | −0.146366 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.2088 | 0.793061 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.8642 | 1.99554 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.2544 | 1.40086 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.8416 | −0.931343 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.0240 | 1.60014 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.3642 | −1.33918 | −0.669588 | − | 0.742733i | \(-0.733529\pi\) | ||||
−0.669588 | + | 0.742733i | \(0.733529\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.181533 | 0.00994794 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.94782 | −0.161056 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.5839 | −1.50259 | −0.751294 | − | 0.659967i | \(-0.770570\pi\) | ||||
−0.751294 | + | 0.659967i | \(0.770570\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.11748 | −0.115006 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.64216 | 0.305540 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.8407 | −1.07130 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.99738 | 0.161373 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.1313 | 0.865972 | 0.432986 | − | 0.901401i | \(-0.357460\pi\) | ||||
0.432986 | + | 0.901401i | \(0.357460\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.0145 | −0.536064 | −0.268032 | − | 0.963410i | \(-0.586373\pi\) | ||||
−0.268032 | + | 0.963410i | \(0.586373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −28.7236 | −1.53315 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.2704 | 0.972437 | 0.486218 | − | 0.873837i | \(-0.338376\pi\) | ||||
0.486218 | + | 0.873837i | \(0.338376\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.27547 | −0.120769 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −27.8750 | −1.47530 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.9280 | 1.94898 | 0.974492 | − | 0.224421i | \(-0.0720491\pi\) | ||||
0.974492 | + | 0.224421i | \(0.0720491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.89325 | 0.152276 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.3373 | 0.804999 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.27708 | 0.223873 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.0694 | −0.682219 | −0.341109 | − | 0.940024i | \(-0.610803\pi\) | ||||
−0.341109 | + | 0.940024i | \(0.610803\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.74129 | 0.142706 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.72961 | −0.0897967 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.5438 | 1.16728 | 0.583638 | − | 0.812014i | \(-0.301629\pi\) | ||||
0.583638 | + | 0.812014i | \(0.301629\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.19150 | 0.216448 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.6459 | −0.702797 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.21538 | 0.421996 | 0.210998 | − | 0.977487i | \(-0.432329\pi\) | ||||
0.210998 | + | 0.977487i | \(0.432329\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.58354 | −0.132359 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.7975 | 0.960508 | 0.480254 | − | 0.877129i | \(-0.340544\pi\) | ||||
0.480254 | + | 0.877129i | \(0.340544\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.646076 | −0.0329271 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.69467 | −0.238643 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.78801 | 0.344166 | 0.172083 | − | 0.985082i | \(-0.444950\pi\) | ||||
0.172083 | + | 0.985082i | \(0.444950\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −54.3937 | −2.75081 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.3049 | −0.872915 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.36095 | −0.169108 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.42103 | −0.322262 | −0.161131 | − | 0.986933i | \(-0.551514\pi\) | ||||
−0.161131 | + | 0.986933i | \(0.551514\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.0163 | −0.851878 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.42818 | −0.271070 | −0.135535 | − | 0.990773i | \(-0.543275\pi\) | ||||
−0.135535 | + | 0.990773i | \(0.543275\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.4518 | 1.46710 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.81499 | −0.0901875 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.268720 | 0.0133199 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.8163 | −1.57321 | −0.786607 | − | 0.617453i | \(-0.788164\pi\) | ||||
−0.786607 | + | 0.617453i | \(0.788164\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.2549 | 0.653815 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.1841 | −0.796366 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.36666 | −0.116175 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.4168 | −1.09776 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.8898 | −1.21594 | −0.607972 | − | 0.793958i | \(-0.708017\pi\) | ||||
−0.607972 | + | 0.793958i | \(0.708017\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.1147 | −1.07780 | −0.538902 | − | 0.842368i | \(-0.681161\pi\) | ||||
−0.538902 | + | 0.842368i | \(0.681161\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.09736 | −0.393707 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −37.7392 | −1.83062 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.2389 | 0.689071 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.70355 | −0.371931 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.2171 | −1.45551 | −0.727754 | − | 0.685839i | \(-0.759436\pi\) | ||||
−0.727754 | + | 0.685839i | \(0.759436\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.28105 | 0.301848 | 0.150924 | − | 0.988545i | \(-0.451775\pi\) | ||||
0.150924 | + | 0.988545i | \(0.451775\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.12369 | −0.0538770 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −33.2045 | −1.58839 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.6291 | −1.79594 | −0.897969 | − | 0.440058i | \(-0.854958\pi\) | ||||
−0.897969 | + | 0.440058i | \(0.854958\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.888701 | 0.0423191 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.5280 | −1.11785 | −0.558925 | − | 0.829219i | \(-0.688786\pi\) | ||||
−0.558925 | + | 0.829219i | \(0.688786\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.51129 | −0.213856 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.2149 | 0.861535 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.42606 | 0.303264 | 0.151632 | − | 0.988437i | \(-0.451547\pi\) | ||||
0.151632 | + | 0.988437i | \(0.451547\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.05787 | 0.191078 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.8771 | 0.558033 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.37248 | −0.158104 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.7818 | −1.62702 | −0.813511 | − | 0.581549i | \(-0.802447\pi\) | ||||
−0.813511 | + | 0.581549i | \(0.802447\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 42.9233 | 2.00349 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.7636 | 0.780761 | 0.390380 | − | 0.920654i | \(-0.372343\pi\) | ||||
0.390380 | + | 0.920654i | \(0.372343\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.1355 | −0.796356 | −0.398178 | − | 0.917308i | \(-0.630357\pi\) | ||||
−0.398178 | + | 0.917308i | \(0.630357\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.42527 | 0.112469 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.92161 | −0.181470 | −0.0907351 | − | 0.995875i | \(-0.528922\pi\) | ||||
−0.0907351 | + | 0.995875i | \(0.528922\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.3811 | −1.17199 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.7865 | 1.04995 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.94943 | −0.319535 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.0378 | −1.05705 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.482540 | 0.0220940 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.9032 | −0.589560 | −0.294780 | − | 0.955565i | \(-0.595246\pi\) | ||||
−0.294780 | + | 0.955565i | \(0.595246\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.40270 | 0.0639578 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 25.8078 | 1.17430 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.83395 | 0.0832754 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.9698 | −1.44869 | −0.724345 | − | 0.689438i | \(-0.757858\pi\) | ||||
−0.724345 | + | 0.689438i | \(0.757858\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.7611 | 1.11974 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.1637 | −0.819716 | −0.409858 | − | 0.912149i | \(-0.634422\pi\) | ||||
−0.409858 | + | 0.912149i | \(0.634422\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.3918 | 0.918401 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.180248 | 0.00810154 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.5921 | −0.878827 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.9820 | −1.07358 | −0.536791 | − | 0.843715i | \(-0.680363\pi\) | ||||
−0.536791 | + | 0.843715i | \(0.680363\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.0973887 | −0.00435100 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.0278 | −1.29429 | −0.647143 | − | 0.762368i | \(-0.724037\pi\) | ||||
−0.647143 | + | 0.762368i | \(0.724037\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.85753 | 0.127159 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.3421 | −0.903426 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.24316 | 0.143750 | 0.0718752 | − | 0.997414i | \(-0.477102\pi\) | ||||
0.0718752 | + | 0.997414i | \(0.477102\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.8263 | 1.62910 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 26.2025 | 1.15687 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.735593 | 0.0324141 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.9864 | −0.527160 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −36.4684 | −1.60078 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.00903 | 0.219450 | 0.109725 | − | 0.993962i | \(-0.465003\pi\) | ||||
0.109725 | + | 0.993962i | \(0.465003\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.7377 | 0.469525 | 0.234763 | − | 0.972053i | \(-0.424569\pi\) | ||||
0.234763 | + | 0.972053i | \(0.424569\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.9058 | 0.781475 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −44.0116 | −1.91717 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.3599 | 1.18956 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.51517 | 0.195942 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.1819 | 0.917490 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.56891 | −0.111064 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.8509 | 0.942936 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.31553 | 0.0566638 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.9617 | −0.729239 | −0.364619 | − | 0.931157i | \(-0.618801\pi\) | ||||
−0.364619 | + | 0.931157i | \(0.618801\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.6203 | −1.09947 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.04490 | 0.130429 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.5194 | −0.920105 | −0.460052 | − | 0.887892i | \(-0.652169\pi\) | ||||
−0.460052 | + | 0.887892i | \(0.652169\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.97250 | −0.169542 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.4481 | 0.530309 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.9383 | −1.23058 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.115508 | 0.00490306 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.5868 | 0.575689 | 0.287845 | − | 0.957677i | \(-0.407061\pi\) | ||||
0.287845 | + | 0.957677i | \(0.407061\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.2757 | −1.53430 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.5119 | 0.486032 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.9004 | 0.627978 | 0.313989 | − | 0.949427i | \(-0.398335\pi\) | ||||
0.313989 | + | 0.949427i | \(0.398335\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.382832 | 0.0161059 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.6273 | −0.656285 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.0502 | 1.51130 | 0.755651 | − | 0.654974i | \(-0.227320\pi\) | ||||
0.755651 | + | 0.654974i | \(0.227320\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.6936 | 1.70298 | 0.851488 | − | 0.524375i | \(-0.175701\pi\) | ||||
0.851488 | + | 0.524375i | \(0.175701\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.7832 | 0.951782 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.9404 | 1.45712 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −42.6151 | −1.77409 | −0.887046 | − | 0.461681i | \(-0.847246\pi\) | ||||
−0.887046 | + | 0.461681i | \(0.847246\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.90238 | 0.286853 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.3772 | −0.845390 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.714295 | 0.0295831 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.940884 | 0.0389008 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.7650 | 1.06343 | 0.531717 | − | 0.846922i | \(-0.321547\pi\) | ||||
0.531717 | + | 0.846922i | \(0.321547\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.8668 | −1.10703 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.4424 | −1.12883 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.5745 | −0.927025 | −0.463513 | − | 0.886090i | \(-0.653411\pi\) | ||||
−0.463513 | + | 0.886090i | \(0.653411\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.03970 | 0.206608 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.2411 | −0.787486 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.92050 | 0.364482 | 0.182241 | − | 0.983254i | \(-0.441665\pi\) | ||||
0.182241 | + | 0.983254i | \(0.441665\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.7007 | 0.599656 | 0.299828 | − | 0.953993i | \(-0.403071\pi\) | ||||
0.299828 | + | 0.953993i | \(0.403071\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.08104 | 0.288362 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.77293 | −0.112735 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.61731 | −0.227999 | −0.114000 | − | 0.993481i | \(-0.536366\pi\) | ||||
−0.114000 | + | 0.993481i | \(0.536366\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.67516 | −0.392057 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −62.5682 | −2.53124 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.0260 | −1.33391 | −0.666953 | − | 0.745100i | \(-0.732402\pi\) | ||||
−0.666953 | + | 0.745100i | \(0.732402\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.74427 | 0.0703356 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.6964 | 1.55786 | 0.778930 | − | 0.627111i | \(-0.215763\pi\) | ||||
0.778930 | + | 0.627111i | \(0.215763\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.27152 | 0.0511065 | 0.0255533 | − | 0.999673i | \(-0.491865\pi\) | ||||
0.0255533 | + | 0.999673i | \(0.491865\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −39.7401 | −1.59472 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −38.8429 | −1.55621 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.8604 | 0.954415 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.02740 | 0.280647 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.09614 | −0.0835787 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.6529 | −0.702750 | −0.351375 | − | 0.936235i | \(-0.614286\pi\) | ||||
−0.351375 | + | 0.936235i | \(0.614286\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.68737 | 0.0670668 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.467095 | 0.0185361 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.86699 | 0.272080 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.46598 | 0.216231 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.0368 | −0.949395 | −0.474697 | − | 0.880149i | \(-0.657442\pi\) | ||||
−0.474697 | + | 0.880149i | \(0.657442\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.27807 | 0.0898382 | 0.0449191 | − | 0.998991i | \(-0.485697\pi\) | ||||
0.0449191 | + | 0.998991i | \(0.485697\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.98719 | −0.117621 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.6344 | 0.575337 | 0.287668 | − | 0.957730i | \(-0.407120\pi\) | ||||
0.287668 | + | 0.957730i | \(0.407120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.68372 | 0.262359 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.8819 | 0.818425 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −45.3939 | −1.77640 | −0.888200 | − | 0.459456i | \(-0.848044\pi\) | ||||
−0.888200 | + | 0.459456i | \(0.848044\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.12866 | 0.122247 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.2741 | −0.400831 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.7090 | 0.650891 | 0.325446 | − | 0.945561i | \(-0.394486\pi\) | ||||
0.325446 | + | 0.945561i | \(0.394486\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.30234 | −0.0895505 | −0.0447752 | − | 0.998997i | \(-0.514257\pi\) | ||||
−0.0447752 | + | 0.998997i | \(0.514257\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 60.0914 | 2.33376 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.07648 | 0.119301 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.8796 | −0.731020 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 42.5120 | 1.64361 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.88042 | −0.227011 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.7779 | 0.646739 | 0.323369 | − | 0.946273i | \(-0.395184\pi\) | ||||
0.323369 | + | 0.946273i | \(0.395184\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −27.5723 | −1.06126 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.0279 | 1.15407 | 0.577033 | − | 0.816721i | \(-0.304210\pi\) | ||||
0.577033 | + | 0.816721i | \(0.304210\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.7906 | 0.605986 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.5996 | 0.904337 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.0981 | 1.22820 | 0.614099 | − | 0.789229i | \(-0.289519\pi\) | ||||
0.614099 | + | 0.789229i | \(0.289519\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.39643 | −0.0915631 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.8808 | −0.567737 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.72859 | 0.142048 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.4004 | −0.738027 | −0.369014 | − | 0.929424i | \(-0.620304\pi\) | ||||
−0.369014 | + | 0.929424i | \(0.620304\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.55196 | 0.0589540 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.05288 | 0.153734 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.6534 | −1.19896 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.5880 | 0.627417 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.9642 | −0.640730 | −0.320365 | − | 0.947294i | \(-0.603806\pi\) | ||||
−0.320365 | + | 0.947294i | \(0.603806\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.27959 | −0.0482605 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.15230 | −0.194047 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.6038 | 0.925319 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.7779 | 0.517440 | 0.258720 | − | 0.965952i | \(-0.416699\pi\) | ||||
0.258720 | + | 0.965952i | \(0.416699\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.07345 | 0.302778 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40.7477 | 1.52601 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.39277 | 0.0520868 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 39.3239 | 1.46858 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.1958 | 1.23800 | 0.618998 | − | 0.785393i | \(-0.287539\pi\) | ||||
0.618998 | + | 0.785393i | \(0.287539\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.33356 | 0.235874 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.5289 | 0.465954 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.0989 | −0.486482 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.4300 | 0.461004 | 0.230502 | − | 0.973072i | \(-0.425963\pi\) | ||||
0.230502 | + | 0.973072i | \(0.425963\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 30.0379 | 1.11252 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 54.2089 | 2.00499 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.0371 | 0.370727 | 0.185363 | − | 0.982670i | \(-0.440654\pi\) | ||||
0.185363 | + | 0.982670i | \(0.440654\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.565475 | 0.0208579 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.4819 | 0.386107 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.0083 | 1.43494 | 0.717471 | − | 0.696588i | \(-0.245299\pi\) | ||||
0.717471 | + | 0.696588i | \(0.245299\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.6827 | 1.34757 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.3362 | −1.00287 | −0.501433 | − | 0.865196i | \(-0.667194\pi\) | ||||
−0.501433 | + | 0.865196i | \(0.667194\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.29319 | −0.120653 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.68502 | 0.208004 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.1187 | −0.808198 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.64873 | −0.0600832 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.14733 | −0.0781493 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.9456 | 0.870317 | 0.435159 | − | 0.900354i | \(-0.356692\pi\) | ||||
0.435159 | + | 0.900354i | \(0.356692\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.6582 | −0.386866 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.7674 | 1.18782 | 0.593909 | − | 0.804533i | \(-0.297584\pi\) | ||||
0.593909 | + | 0.804533i | \(0.297584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.2170 | 0.949120 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.40602 | −0.0508347 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.8887 | 1.25976 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.43022 | −0.340063 | −0.170031 | − | 0.985439i | \(-0.554387\pi\) | ||||
−0.170031 | + | 0.985439i | \(0.554387\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 39.3090 | 1.41568 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.8115 | −0.856442 | −0.428221 | − | 0.903674i | \(-0.640859\pi\) | ||||
−0.428221 | + | 0.903674i | \(0.640859\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.2713 | 1.01554 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.994542 | 0.0356790 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.3227 | −0.692309 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.09118 | 0.289525 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.8983 | 0.532421 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.11972 | −0.147039 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.1542 | −0.825359 | −0.412679 | − | 0.910876i | \(-0.635407\pi\) | ||||
−0.412679 | + | 0.910876i | \(0.635407\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −41.3925 | −1.47361 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.29624 | 0.117201 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.6955 | −1.09003 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.307038 | 0.0108895 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.66856 | 0.0591035 | 0.0295517 | − | 0.999563i | \(-0.490592\pi\) | ||||
0.0295517 | + | 0.999563i | \(0.490592\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 93.4994 | 3.30777 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.8367 | 0.382896 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.2086 | −0.536699 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.66596 | −0.164453 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.1232 | −0.989982 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.91277 | −0.348515 | −0.174257 | − | 0.984700i | \(-0.555752\pi\) | ||||
−0.174257 | + | 0.984700i | \(0.555752\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.7942 | 1.46759 | 0.733797 | − | 0.679369i | \(-0.237747\pi\) | ||||
0.733797 | + | 0.679369i | \(0.237747\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.3764 | 0.960132 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.47673 | −0.156813 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.0917 | 1.15773 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.10114 | 0.283077 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.0792 | 1.60818 | 0.804088 | − | 0.594511i | \(-0.202654\pi\) | ||||
0.804088 | + | 0.594511i | \(0.202654\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.1828 | 0.982392 | 0.491196 | − | 0.871049i | \(-0.336560\pi\) | ||||
0.491196 | + | 0.871049i | \(0.336560\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.39478 | −0.257453 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.268104 | 0.00932290 | 0.00466145 | − | 0.999989i | \(-0.498516\pi\) | ||||
0.00466145 | + | 0.999989i | \(0.498516\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.1618 | −0.630787 | −0.315393 | − | 0.948961i | \(-0.602136\pi\) | ||||
−0.315393 | + | 0.948961i | \(0.602136\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.8716 | 0.377133 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.2617 | −0.355548 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.0176075 | 0.000609333 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32.1549 | −1.11144 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.35795 | 0.323072 | 0.161536 | − | 0.986867i | \(-0.448355\pi\) | ||||
0.161536 | + | 0.986867i | \(0.448355\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.9222 | −0.755938 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.3344 | 0.838121 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.67778 | 0.126520 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.8753 | −0.820364 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.4120 | 0.837819 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.94069 | 0.0665261 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.02773 | −0.206386 | −0.103193 | − | 0.994661i | \(-0.532906\pi\) | ||||
−0.103193 | + | 0.994661i | \(0.532906\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.858302 | −0.0293533 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.0052 | 0.341770 | 0.170885 | − | 0.985291i | \(-0.445337\pi\) | ||||
0.170885 | + | 0.985291i | \(0.445337\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −51.9917 | −1.77394 | −0.886968 | − | 0.461832i | \(-0.847192\pi\) | ||||
−0.886968 | + | 0.461832i | \(0.847192\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.0184 | 0.511824 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.4576 | 0.662344 | 0.331172 | − | 0.943570i | \(-0.392556\pi\) | ||||
0.331172 | + | 0.943570i | \(0.392556\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.59335 | 0.224181 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −63.8143 | −2.16725 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.9510 | 0.405409 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.7151 | 1.85395 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.40539 | −0.149100 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.52483 | −0.220580 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.0330 | 1.28428 | 0.642142 | − | 0.766586i | \(-0.278046\pi\) | ||||
0.642142 | + | 0.766586i | \(0.278046\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.6385 | 0.628662 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.3218 | 0.617277 | 0.308638 | − | 0.951179i | \(-0.400127\pi\) | ||||
0.308638 | + | 0.951179i | \(0.400127\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.2160 | −1.48799 | −0.743993 | − | 0.668187i | \(-0.767071\pi\) | ||||
−0.743993 | + | 0.668187i | \(0.767071\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.87298 | 0.0965740 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.6691 | 1.19765 | 0.598825 | − | 0.800880i | \(-0.295634\pi\) | ||||
0.598825 | + | 0.800880i | \(0.295634\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.02176 | 0.134885 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.45379 | 0.216210 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 57.0765 | 1.90999 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.95056 | −0.132053 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −55.6350 | −1.85760 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.2760 | −0.509483 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.57185 | −0.185625 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.7201 | −0.855912 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.63205 | 0.153975 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.6991 | −0.886530 | −0.443265 | − | 0.896391i | \(-0.646180\pi\) | ||||
−0.443265 | + | 0.896391i | \(0.646180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.86417 | −0.227670 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.9433 | 1.75409 | 0.877045 | − | 0.480408i | \(-0.159511\pi\) | ||||
0.877045 | + | 0.480408i | \(0.159511\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.41542 | 0.278510 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.52768 | −0.0835625 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.9382 | 0.889577 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.37609 | 0.210328 | 0.105164 | − | 0.994455i | \(-0.466463\pi\) | ||||
0.105164 | + | 0.994455i | \(0.466463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.6832 | 1.30761 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 42.2356 | 1.39020 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.34648 | 0.0442720 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.76699 | −0.0580356 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.7445 | 0.516559 | 0.258279 | − | 0.966070i | \(-0.416845\pi\) | ||||
0.258279 | + | 0.966070i | \(0.416845\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.26426 | −0.205303 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.1754 | 0.496822 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.08130 | −0.0680659 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.1060 | −0.558827 | −0.279414 | − | 0.960171i | \(-0.590140\pi\) | ||||
−0.279414 | + | 0.960171i | \(0.590140\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34.3788 | −1.12191 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.71609 | −0.0885421 | −0.0442710 | − | 0.999020i | \(-0.514097\pi\) | ||||
−0.0442710 | + | 0.999020i | \(0.514097\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.3060 | 0.954334 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.68201 | 0.119776 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.7796 | −1.45514 | −0.727571 | − | 0.686032i | \(-0.759351\pi\) | ||||
−0.727571 | + | 0.686032i | \(0.759351\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −79.3880 | −2.57704 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.42892 | 0.305754 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.3455 | −0.335123 | −0.167562 | − | 0.985862i | \(-0.553589\pi\) | ||||
−0.167562 | + | 0.985862i | \(0.553589\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.11912 | −0.133292 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.99566 | 0.129161 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.6336 | −0.666295 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.97015 | 0.0635533 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.17085 | 0.198853 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.24793 | −0.0401721 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.7745 | 0.700222 | 0.350111 | − | 0.936708i | \(-0.386144\pi\) | ||||
0.350111 | + | 0.936708i | \(0.386144\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −54.8171 | −1.76098 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.57418 | −0.0826093 | −0.0413046 | − | 0.999147i | \(-0.513151\pi\) | ||||
−0.0413046 | + | 0.999147i | \(0.513151\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.8958 | 1.11871 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −38.6004 | −1.23620 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.36961 | −0.0438178 | −0.0219089 | − | 0.999760i | \(-0.506974\pi\) | ||||
−0.0219089 | + | 0.999760i | \(0.506974\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.0414 | 0.512685 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.31425 | −0.233526 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.2147 | 0.325799 | 0.162899 | − | 0.986643i | \(-0.447915\pi\) | ||||
0.162899 | + | 0.986643i | \(0.447915\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.96148 | 0.158086 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −44.3620 | −1.41206 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −50.1888 | −1.59591 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.2800 | −0.580682 | −0.290341 | − | 0.956923i | \(-0.593769\pi\) | ||||
−0.290341 | + | 0.956923i | \(0.593769\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 37.2397 | 1.18177 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.47872 | 0.110283 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.3344 | −0.422304 | −0.211152 | − | 0.977453i | \(-0.567721\pi\) | ||||
−0.211152 | + | 0.977453i | \(0.567721\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.53144 | −0.0484528 |
(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 | 6008.2.a.b.1.16 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.16 | ✓ | 44 | 1.1 | even | 1 | trivial |