Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, 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("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 23x^{8} + 44x^{7} + 167x^{6} - 266x^{5} - 491x^{4} + 460x^{3} + 546x^{2} + 56x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 2432) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.719482\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | ||||||||
\(3\) | −2.46871 | −1.42531 | −0.712657 | − | 0.701513i | \(-0.752508\pi\) | ||||
−0.712657 | + | 0.701513i | \(0.752508\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.22672 | −1.44303 | −0.721516 | − | 0.692398i | \(-0.756554\pi\) | ||||
−0.721516 | + | 0.692398i | \(0.756554\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.04213 | −1.52778 | −0.763890 | − | 0.645346i | \(-0.776713\pi\) | ||||
−0.763890 | + | 0.645346i | \(0.776713\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.09455 | 1.03152 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.41171 | 1.93320 | 0.966601 | − | 0.256286i | \(-0.0824988\pi\) | ||||
0.966601 | + | 0.256286i | \(0.0824988\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.815411 | −0.226154 | −0.113077 | − | 0.993586i | \(-0.536071\pi\) | ||||
−0.113077 | + | 0.993586i | \(0.536071\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.96585 | 2.05677 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.62028 | −0.635510 | −0.317755 | − | 0.948173i | \(-0.602929\pi\) | ||||
−0.317755 | + | 0.948173i | \(0.602929\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.97886 | 2.17757 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.16717 | −1.28594 | −0.642972 | − | 0.765890i | \(-0.722299\pi\) | ||||
−0.642972 | + | 0.765890i | \(0.722299\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.41171 | 1.08234 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.233424 | −0.0449225 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.85818 | −0.716446 | −0.358223 | − | 0.933636i | \(-0.616617\pi\) | ||||
−0.358223 | + | 0.933636i | \(0.616617\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.43670 | −1.33567 | −0.667835 | − | 0.744309i | \(-0.732779\pi\) | ||||
−0.667835 | + | 0.744309i | \(0.732779\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15.8287 | −2.75542 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.0428 | 2.20464 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.13742 | −0.844586 | −0.422293 | − | 0.906459i | \(-0.638775\pi\) | ||||
−0.422293 | + | 0.906459i | \(0.638775\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.01302 | 0.322341 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.5007 | −1.79611 | −0.898054 | − | 0.439886i | \(-0.855019\pi\) | ||||
−0.898054 | + | 0.439886i | \(0.855019\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0837292 | −0.0127686 | −0.00638429 | − | 0.999980i | \(-0.502032\pi\) | ||||
−0.00638429 | + | 0.999980i | \(0.502032\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.98525 | −1.48851 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.99564 | −0.582824 | −0.291412 | − | 0.956598i | \(-0.594125\pi\) | ||||
−0.291412 | + | 0.956598i | \(0.594125\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.33880 | 1.33411 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.46871 | 0.905801 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.22608 | −0.580497 | −0.290248 | − | 0.956951i | \(-0.593738\pi\) | ||||
−0.290248 | + | 0.956951i | \(0.593738\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.6888 | −2.78967 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.46871 | −0.326989 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.53655 | 1.11136 | 0.555682 | − | 0.831395i | \(-0.312457\pi\) | ||||
0.555682 | + | 0.831395i | \(0.312457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.72239 | −0.732677 | −0.366339 | − | 0.930482i | \(-0.619389\pi\) | ||||
−0.366339 | + | 0.930482i | \(0.619389\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.5086 | −1.57593 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.63110 | 0.326348 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.4278 | −1.39613 | −0.698063 | − | 0.716036i | \(-0.745955\pi\) | ||||
−0.698063 | + | 0.716036i | \(0.745955\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.2250 | 1.83287 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.10168 | 0.130745 | 0.0653725 | − | 0.997861i | \(-0.479176\pi\) | ||||
0.0653725 | + | 0.997861i | \(0.479176\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.25458 | −0.849085 | −0.424542 | − | 0.905408i | \(-0.639565\pi\) | ||||
−0.424542 | + | 0.905408i | \(0.639565\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.3600 | −1.54268 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −25.9169 | −2.95351 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.9906 | 1.57407 | 0.787033 | − | 0.616911i | \(-0.211616\pi\) | ||||
0.787033 | + | 0.616911i | \(0.211616\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.70740 | −0.967489 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.51708 | −0.715343 | −0.357671 | − | 0.933848i | \(-0.616429\pi\) | ||||
−0.357671 | + | 0.933848i | \(0.616429\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.45489 | 0.917062 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.52474 | 1.02116 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.3867 | −1.63098 | −0.815492 | − | 0.578768i | \(-0.803534\pi\) | ||||
−0.815492 | + | 0.578768i | \(0.803534\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.29599 | 0.345514 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.3591 | 1.90375 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.22672 | −0.331054 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.2654 | −1.34690 | −0.673449 | − | 0.739234i | \(-0.735188\pi\) | ||||
−0.673449 | + | 0.739234i | \(0.735188\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.8414 | 1.99413 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.76311 | −0.274940 | −0.137470 | − | 0.990506i | \(-0.543897\pi\) | ||||
−0.137470 | + | 0.990506i | \(0.543897\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.529145 | −0.0521382 | −0.0260691 | − | 0.999660i | \(-0.508299\pi\) | ||||
−0.0260691 | + | 0.999660i | \(0.508299\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −32.1990 | −3.14230 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.211777 | 0.0204732 | 0.0102366 | − | 0.999948i | \(-0.496742\pi\) | ||||
0.0102366 | + | 0.999948i | \(0.496742\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.73908 | −0.932835 | −0.466417 | − | 0.884565i | \(-0.654456\pi\) | ||||
−0.466417 | + | 0.884565i | \(0.654456\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.6828 | 1.20380 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.09269 | −0.573152 | −0.286576 | − | 0.958058i | \(-0.592517\pi\) | ||||
−0.286576 | + | 0.958058i | \(0.592517\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.8997 | 1.85566 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.52333 | −0.233282 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.5915 | 0.970921 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.1100 | 2.73727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 28.3919 | 2.56002 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.32846 | −0.118821 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.64012 | 0.589215 | 0.294608 | − | 0.955618i | \(-0.404811\pi\) | ||||
0.294608 | + | 0.955618i | \(0.404811\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.206704 | 0.0181992 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.61315 | 0.315682 | 0.157841 | − | 0.987465i | \(-0.449547\pi\) | ||||
0.157841 | + | 0.987465i | \(0.449547\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.04213 | −0.350497 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.753194 | 0.0648246 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.7468 | −1.00360 | −0.501799 | − | 0.864984i | \(-0.667328\pi\) | ||||
−0.501799 | + | 0.864984i | \(0.667328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.4757 | −1.73672 | −0.868362 | − | 0.495931i | \(-0.834827\pi\) | ||||
−0.868362 | + | 0.495931i | \(0.834827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.86410 | 0.830707 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.22817 | −0.437202 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.4493 | 1.03385 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −23.0548 | −1.90153 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.4213 | 1.67298 | 0.836490 | − | 0.547982i | \(-0.184604\pi\) | ||||
0.836490 | + | 0.547982i | \(0.184604\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1686 | 1.07164 | 0.535822 | − | 0.844331i | \(-0.320002\pi\) | ||||
0.535822 | + | 0.844331i | \(0.320002\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.10858 | −0.655540 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.9961 | 1.92742 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.0668 | 1.20246 | 0.601232 | − | 0.799074i | \(-0.294677\pi\) | ||||
0.601232 | + | 0.799074i | \(0.294677\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.4330 | 0.827389 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.9285 | 1.96464 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.8860 | 0.930982 | 0.465491 | − | 0.885053i | \(-0.345878\pi\) | ||||
0.465491 | + | 0.885053i | \(0.345878\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 51.0747 | 3.97616 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.2419 | 1.48898 | 0.744491 | − | 0.667632i | \(-0.232692\pi\) | ||||
0.744491 | + | 0.667632i | \(0.232692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3351 | −0.948854 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.09455 | 0.236646 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.53489 | −0.116696 | −0.0583478 | − | 0.998296i | \(-0.518583\pi\) | ||||
−0.0583478 | + | 0.998296i | \(0.518583\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.8748 | −1.65358 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.0743 | −1.58404 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.82867 | −0.286169 | −0.143084 | − | 0.989711i | \(-0.545702\pi\) | ||||
−0.143084 | + | 0.989711i | \(0.545702\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.89663 | −0.438293 | −0.219147 | − | 0.975692i | \(-0.570327\pi\) | ||||
−0.219147 | + | 0.975692i | \(0.570327\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.1270 | 1.04429 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.5770 | 1.21877 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.8004 | −1.22857 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.943531 | 0.0686318 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.8427 | −1.43577 | −0.717885 | − | 0.696162i | \(-0.754890\pi\) | ||||
−0.717885 | + | 0.696162i | \(0.754890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.62263 | −0.260763 | −0.130381 | − | 0.991464i | \(-0.541620\pi\) | ||||
−0.130381 | + | 0.991464i | \(0.541620\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.49544 | −0.465148 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.1190 | 0.934690 | 0.467345 | − | 0.884075i | \(-0.345211\pi\) | ||||
0.467345 | + | 0.884075i | \(0.345211\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.9156 | −1.12823 | −0.564113 | − | 0.825697i | \(-0.690782\pi\) | ||||
−0.564113 | + | 0.825697i | \(0.690782\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 28.2120 | 1.98992 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.5953 | 1.09457 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 37.1095 | 2.59184 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −19.0846 | −1.32647 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.41171 | 0.443507 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.00713 | 0.344705 | 0.172352 | − | 0.985035i | \(-0.444863\pi\) | ||||
0.172352 | + | 0.985035i | \(0.444863\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.71973 | −0.186352 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.270170 | 0.0184255 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30.0601 | 2.04061 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.9095 | 1.21021 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.13660 | 0.143723 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.30156 | −0.555913 | −0.277957 | − | 0.960594i | \(-0.589657\pi\) | ||||
−0.277957 | + | 0.960594i | \(0.589657\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16.7468 | 1.11645 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.8177 | −1.77995 | −0.889976 | − | 0.456007i | \(-0.849279\pi\) | ||||
−0.889976 | + | 0.456007i | \(0.849279\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.15107 | −0.406474 | −0.203237 | − | 0.979130i | \(-0.565146\pi\) | ||||
−0.203237 | + | 0.979130i | \(0.565146\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 63.9815 | 4.20968 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.79905 | 0.510933 | 0.255466 | − | 0.966818i | \(-0.417771\pi\) | ||||
0.255466 | + | 0.966818i | \(0.417771\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.8928 | 0.841034 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −34.5388 | −2.24354 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.7964 | 1.79800 | 0.898999 | − | 0.437951i | \(-0.144296\pi\) | ||||
0.898999 | + | 0.437951i | \(0.144296\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.53347 | −0.356442 | −0.178221 | − | 0.983990i | \(-0.557034\pi\) | ||||
−0.178221 | + | 0.983990i | \(0.557034\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.1964 | 1.42390 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −30.1337 | −1.92517 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.815411 | −0.0518833 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.0888 | 1.01959 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.9928 | −0.946334 | −0.473167 | − | 0.880973i | \(-0.656889\pi\) | ||||
−0.473167 | + | 0.880973i | \(0.656889\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −39.5421 | −2.48599 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20.8727 | −1.30710 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.6003 | 0.848365 | 0.424182 | − | 0.905577i | \(-0.360562\pi\) | ||||
0.424182 | + | 0.905577i | \(0.360562\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.7661 | 1.29034 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.9393 | −0.739026 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.4415 | −1.63046 | −0.815228 | − | 0.579140i | \(-0.803388\pi\) | ||||
−0.815228 | + | 0.579140i | \(0.803388\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.6364 | 0.837675 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 37.9853 | 2.32466 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.6429 | −1.19765 | −0.598825 | − | 0.800880i | \(-0.704365\pi\) | ||||
−0.598825 | + | 0.800880i | \(0.704365\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0146 | 0.851327 | 0.425663 | − | 0.904882i | \(-0.360041\pi\) | ||||
0.425663 | + | 0.904882i | \(0.360041\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.13687 | −0.492466 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 34.6983 | 2.09238 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.92581 | −0.295963 | −0.147982 | − | 0.988990i | \(-0.547278\pi\) | ||||
−0.147982 | + | 0.988990i | \(0.547278\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.0133 | −1.37777 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.90466 | 0.292587 | 0.146294 | − | 0.989241i | \(-0.453266\pi\) | ||||
0.146294 | + | 0.989241i | \(0.453266\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.07261 | −0.123204 | −0.0616018 | − | 0.998101i | \(-0.519621\pi\) | ||||
−0.0616018 | + | 0.998101i | \(0.519621\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.96585 | 0.471856 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 46.4873 | 2.74406 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.1342 | −0.596127 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 32.7485 | 1.91975 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.4606 | 0.611117 | 0.305559 | − | 0.952173i | \(-0.401157\pi\) | ||||
0.305559 | + | 0.952173i | \(0.401157\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.5450 | −1.60373 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.49665 | −0.0868443 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.02878 | 0.290822 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.338444 | 0.0195076 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.82134 | 0.391875 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.4645 | 1.05728 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.87873 | 0.335517 | 0.167758 | − | 0.985828i | \(-0.446347\pi\) | ||||
0.167758 | + | 0.985828i | \(0.446347\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.30631 | 0.0743132 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.6861 | 0.719365 | 0.359683 | − | 0.933075i | \(-0.382885\pi\) | ||||
0.359683 | + | 0.933075i | \(0.382885\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.25089 | 0.353321 | 0.176661 | − | 0.984272i | \(-0.443471\pi\) | ||||
0.176661 | + | 0.984272i | \(0.443471\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 40.3617 | 2.27412 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.72978 | −0.265651 | −0.132826 | − | 0.991139i | \(-0.542405\pi\) | ||||
−0.132826 | + | 0.991139i | \(0.542405\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.7375 | −1.38503 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.522816 | −0.0291808 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.62028 | −0.145796 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.41276 | −0.244776 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.0430 | 1.32958 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.1509 | 0.890428 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.8060 | 1.08864 | 0.544318 | − | 0.838879i | \(-0.316788\pi\) | ||||
0.544318 | + | 0.838879i | \(0.316788\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.8980 | −0.871206 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 36.8743 | 2.01466 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.40107 | 0.512109 | 0.256054 | − | 0.966662i | \(-0.417577\pi\) | ||||
0.256054 | + | 0.966662i | \(0.417577\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.0411 | 0.816921 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −47.6819 | −2.58212 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.45373 | −0.510454 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −49.1267 | −2.64489 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.2991 | −1.35813 | −0.679063 | − | 0.734080i | \(-0.737614\pi\) | ||||
−0.679063 | + | 0.734080i | \(0.737614\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.9343 | 1.54882 | 0.774408 | − | 0.632687i | \(-0.218048\pi\) | ||||
0.774408 | + | 0.632687i | \(0.218048\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.190337 | 0.0101594 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.4897 | −1.19701 | −0.598503 | − | 0.801121i | \(-0.704238\pi\) | ||||
−0.598503 | + | 0.801121i | \(0.704238\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.55480 | −0.188669 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −26.1474 | −1.38387 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.7745 | −1.36033 | −0.680164 | − | 0.733060i | \(-0.738091\pi\) | ||||
−0.680164 | + | 0.733060i | \(0.738091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −74.3330 | −3.90147 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.4085 | 1.22526 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.91733 | 0.204483 | 0.102242 | − | 0.994760i | \(-0.467399\pi\) | ||||
0.102242 | + | 0.994760i | \(0.467399\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −35.5895 | −1.85272 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.0824 | 0.886871 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.17543 | −0.371530 | −0.185765 | − | 0.982594i | \(-0.559476\pi\) | ||||
−0.185765 | + | 0.982594i | \(0.559476\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.27959 | 0.169357 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.14600 | 0.162027 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.11028 | −0.467964 | −0.233982 | − | 0.972241i | \(-0.575176\pi\) | ||||
−0.233982 | + | 0.972241i | \(0.575176\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.3926 | −0.839816 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.4774 | 1.45513 | 0.727564 | − | 0.686040i | \(-0.240652\pi\) | ||||
0.727564 | + | 0.686040i | \(0.240652\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 83.6266 | 4.26201 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.259104 | −0.0131710 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.5101 | −1.39482 | −0.697409 | − | 0.716674i | \(-0.745664\pi\) | ||||
−0.697409 | + | 0.716674i | \(0.745664\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.1597 | 0.817231 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.91983 | −0.449946 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −45.1437 | −2.27143 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.7251 | 1.64242 | 0.821212 | − | 0.570624i | \(-0.193298\pi\) | ||||
0.821212 | + | 0.570624i | \(0.193298\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.97886 | 0.499568 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.5472 | 0.676515 | 0.338257 | − | 0.941054i | \(-0.390163\pi\) | ||||
0.338257 | + | 0.941054i | \(0.390163\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.06397 | 0.302068 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 28.0963 | 1.39612 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −32.9396 | −1.63276 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.0909 | 1.33956 | 0.669779 | − | 0.742561i | \(-0.266389\pi\) | ||||
0.669779 | + | 0.742561i | \(0.266389\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.9995 | 1.43044 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −34.5058 | −1.69792 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.0288 | 1.03226 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 50.5486 | 2.47538 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0175 | 0.587092 | 0.293546 | − | 0.955945i | \(-0.405165\pi\) | ||||
0.293546 | + | 0.955945i | \(0.405165\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.6253 | −1.05395 | −0.526977 | − | 0.849880i | \(-0.676675\pi\) | ||||
−0.526977 | + | 0.849880i | \(0.676675\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.3647 | −0.601194 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.1802 | −0.687839 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.1306 | 1.11937 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.9069 | 0.623150 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.466340 | 0.0224628 | 0.0112314 | − | 0.999937i | \(-0.496425\pi\) | ||||
0.0112314 | + | 0.999937i | \(0.496425\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.1789 | −0.585281 | −0.292640 | − | 0.956223i | \(-0.594534\pi\) | ||||
−0.292640 | + | 0.956223i | \(0.594534\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −30.7337 | −1.47357 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.16717 | −0.295016 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.9016 | −1.09303 | −0.546517 | − | 0.837448i | \(-0.684047\pi\) | ||||
−0.546517 | + | 0.837448i | \(0.684047\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 28.8994 | 1.37616 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.15864 | 0.197583 | 0.0987914 | − | 0.995108i | \(-0.468502\pi\) | ||||
0.0987914 | + | 0.995108i | \(0.468502\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 49.6485 | 2.35356 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −50.4144 | −2.38452 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.4154 | −0.633112 | −0.316556 | − | 0.948574i | \(-0.602527\pi\) | ||||
−0.316556 | + | 0.948574i | \(0.602527\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −73.7391 | −3.47224 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −32.5095 | −1.52743 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.6352 | −0.498588 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.9359 | −1.11968 | −0.559838 | − | 0.828602i | \(-0.689136\pi\) | ||||
−0.559838 | + | 0.828602i | \(0.689136\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.611636 | 0.0285487 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.0335 | 1.44537 | 0.722686 | − | 0.691176i | \(-0.242907\pi\) | ||||
0.722686 | + | 0.691176i | \(0.242907\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.3472 | −1.45683 | −0.728415 | − | 0.685136i | \(-0.759743\pi\) | ||||
−0.728415 | + | 0.685136i | \(0.759743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −59.2396 | −2.74717 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.14257 | 0.330519 | 0.165259 | − | 0.986250i | \(-0.447154\pi\) | ||||
0.165259 | + | 0.986250i | \(0.447154\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 46.1926 | 2.13298 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −37.1957 | −1.71389 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.536847 | −0.0246843 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.41171 | 0.248306 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.0778 | −0.598792 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.5447 | −1.21286 | −0.606430 | − | 0.795137i | \(-0.707399\pi\) | ||||
−0.606430 | + | 0.795137i | \(0.707399\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.18911 | 0.191007 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −61.5413 | −2.80023 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 42.8037 | 1.94362 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.74569 | 0.441619 | 0.220810 | − | 0.975317i | \(-0.429130\pi\) | ||||
0.220810 | + | 0.975317i | \(0.429130\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −29.3431 | −1.32694 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.6150 | 1.15599 | 0.577995 | − | 0.816040i | \(-0.303835\pi\) | ||||
0.577995 | + | 0.816040i | \(0.303835\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.1095 | 0.455309 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −64.0225 | −2.87760 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.45312 | −0.199750 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.48801 | −0.245677 | −0.122838 | − | 0.992427i | \(-0.539200\pi\) | ||||
−0.122838 | + | 0.992427i | \(0.539200\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −47.5028 | −2.12227 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.00013 | −0.401296 | −0.200648 | − | 0.979663i | \(-0.564305\pi\) | ||||
−0.200648 | + | 0.979663i | \(0.564305\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.91578 | 0.396747 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 30.4519 | 1.35241 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −28.2818 | −1.25357 | −0.626784 | − | 0.779193i | \(-0.715629\pi\) | ||||
−0.626784 | + | 0.779193i | \(0.715629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.3240 | 1.29722 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.233424 | −0.0103059 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.70740 | 0.0752371 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.6189 | −1.12672 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.78921 | 0.166328 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.19618 | −0.183838 | −0.0919190 | − | 0.995766i | \(-0.529300\pi\) | ||||
−0.0919190 | + | 0.995766i | \(0.529300\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.6631 | −1.47198 | −0.735992 | − | 0.676990i | \(-0.763284\pi\) | ||||
−0.735992 | + | 0.676990i | \(0.763284\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 54.0027 | 2.35687 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.4862 | 0.848833 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0340 | 0.653651 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26.4168 | 1.14639 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.37779 | 0.406197 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.683344 | −0.0295435 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.45191 | 0.407880 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 59.8776 | 2.57911 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.3995 | 0.791056 | 0.395528 | − | 0.918454i | \(-0.370562\pi\) | ||||
0.395528 | + | 0.918454i | \(0.370562\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.5571 | 0.624705 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 31.4253 | 1.34611 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.83156 | −0.249340 | −0.124670 | − | 0.992198i | \(-0.539787\pi\) | ||||
−0.124670 | + | 0.992198i | \(0.539787\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.7082 | −0.755770 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.85818 | −0.164364 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −56.5518 | −2.40483 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −40.9239 | −1.73712 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.9517 | 1.31146 | 0.655732 | − | 0.754993i | \(-0.272360\pi\) | ||||
0.655732 | + | 0.754993i | \(0.272360\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0682737 | 0.00288767 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 41.4755 | 1.75110 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.3007 | 1.82490 | 0.912452 | − | 0.409183i | \(-0.134186\pi\) | ||||
0.912452 | + | 0.409183i | \(0.134186\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.6594 | 0.827076 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 35.1964 | 1.47811 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.32798 | −0.349127 | −0.174563 | − | 0.984646i | \(-0.555851\pi\) | ||||
−0.174563 | + | 0.984646i | \(0.555851\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.5676 | 0.902574 | 0.451287 | − | 0.892379i | \(-0.350965\pi\) | ||||
0.451287 | + | 0.892379i | \(0.350965\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 48.9861 | 2.04642 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −33.3749 | −1.39183 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.5716 | −1.31434 | −0.657172 | − | 0.753741i | \(-0.728247\pi\) | ||||
−0.657172 | + | 0.753741i | \(0.728247\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.94324 | 0.371669 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.3429 | 1.09289 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.0964 | −1.12222 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.14208 | 0.336634 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.9679 | 1.19563 | 0.597817 | − | 0.801633i | \(-0.296035\pi\) | ||||
0.597817 | + | 0.801633i | \(0.296035\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.43670 | −0.306424 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32.3871 | −1.33223 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.8431 | 0.979117 | 0.489559 | − | 0.871970i | \(-0.337158\pi\) | ||||
0.489559 | + | 0.871970i | \(0.337158\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −34.1758 | −1.40107 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 39.2911 | 1.60808 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0716 | 0.983537 | 0.491769 | − | 0.870726i | \(-0.336351\pi\) | ||||
0.491769 | + | 0.870726i | \(0.336351\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.72226 | −0.0702523 | −0.0351262 | − | 0.999383i | \(-0.511183\pi\) | ||||
−0.0351262 | + | 0.999383i | \(0.511183\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −35.3639 | −1.44013 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −97.1564 | −3.94997 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.2198 | 0.698928 | 0.349464 | − | 0.936950i | \(-0.386364\pi\) | ||||
0.349464 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −38.5002 | −1.56011 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.25809 | 0.131808 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.5924 | −1.31639 | −0.658197 | − | 0.752845i | \(-0.728681\pi\) | ||||
−0.658197 | + | 0.752845i | \(0.728681\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −91.6128 | −3.69418 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.44448 | 0.259445 | 0.129722 | − | 0.991550i | \(-0.458591\pi\) | ||||
0.129722 | + | 0.991550i | \(0.458591\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.8637 | −1.28071 | −0.640356 | − | 0.768078i | \(-0.721213\pi\) | ||||
−0.640356 | + | 0.768078i | \(0.721213\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.43957 | 0.0577678 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 62.1949 | 2.49179 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.7720 | −0.910879 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.8287 | −0.632136 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.4615 | 0.536743 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.36348 | −0.293135 | −0.146568 | − | 0.989201i | \(-0.546823\pi\) | ||||
−0.146568 | + | 0.989201i | \(0.546823\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.3612 | −0.491312 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.4258 | −0.850257 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.61496 | −0.301716 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.40920 | 0.134866 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.4715 | 1.55903 | 0.779514 | − | 0.626384i | \(-0.215466\pi\) | ||||
0.779514 | + | 0.626384i | \(0.215466\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.7411 | 0.620768 | 0.310384 | − | 0.950611i | \(-0.399542\pi\) | ||||
0.310384 | + | 0.950611i | \(0.399542\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.666974 | −0.0262621 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.8689 | 0.702499 | 0.351250 | − | 0.936282i | \(-0.385757\pi\) | ||||
0.351250 | + | 0.936282i | \(0.385757\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 54.7338 | 2.14849 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −74.2098 | −2.90851 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.83114 | −0.0716581 | −0.0358291 | − | 0.999358i | \(-0.511407\pi\) | ||||
−0.0358291 | + | 0.999358i | \(0.511407\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.6586 | −0.455540 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.4497 | −0.875846 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.9446 | 0.699021 | 0.349510 | − | 0.936932i | \(-0.386348\pi\) | ||||
0.349510 | + | 0.936932i | \(0.386348\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.256100 | 0.00996114 | 0.00498057 | − | 0.999988i | \(-0.498415\pi\) | ||||
0.00498057 | + | 0.999988i | \(0.498415\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.27466 | −0.204851 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.0428 | 0.505778 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.7940 | 0.921309 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.4942 | 0.792350 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36.6903 | −1.41641 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.46127 | −0.133422 | −0.0667111 | − | 0.997772i | \(-0.521251\pi\) | ||||
−0.0667111 | + | 0.997772i | \(0.521251\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.26322 | −0.0486215 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.7402 | 0.528080 | 0.264040 | − | 0.964512i | \(-0.414945\pi\) | ||||
0.264040 | + | 0.964512i | \(0.414945\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 53.6205 | 2.05777 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 66.2052 | 2.53699 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.31127 | −0.203230 | −0.101615 | − | 0.994824i | \(-0.532401\pi\) | ||||
−0.101615 | + | 0.994824i | \(0.532401\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37.9036 | 1.44822 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.1852 | 0.579353 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.44599 | 0.131282 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.0583 | 0.534802 | 0.267401 | − | 0.963585i | \(-0.413835\pi\) | ||||
0.267401 | + | 0.963585i | \(0.413835\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −80.2013 | −3.04660 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 66.0692 | 2.50615 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.1350 | 1.14144 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.2536 | −0.728239 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.7193 | 1.80233 | 0.901167 | − | 0.433473i | \(-0.142712\pi\) | ||||
0.901167 | + | 0.433473i | \(0.142712\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.13742 | −0.193761 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31.8287 | −1.19874 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.1689 | 0.420048 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.8747 | −0.483519 | −0.241759 | − | 0.970336i | \(-0.577724\pi\) | ||||
−0.241759 | + | 0.970336i | \(0.577724\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 43.2947 | 1.62368 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.8634 | 1.71760 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.8698 | 0.630896 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −68.6213 | −2.56271 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.30671 | −0.235201 | −0.117600 | − | 0.993061i | \(-0.537520\pi\) | ||||
−0.117600 | + | 0.993061i | \(0.537520\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.13887 | 0.0796557 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.6606 | 0.508042 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.8793 | −0.775439 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.8092 | −0.920123 | −0.460061 | − | 0.887887i | \(-0.652173\pi\) | ||||
−0.460061 | + | 0.887887i | \(0.652173\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.6743 | −1.06201 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.219394 | 0.00811457 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.8961 | 0.771816 | 0.385908 | − | 0.922537i | \(-0.373888\pi\) | ||||
0.385908 | + | 0.922537i | \(0.373888\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 74.3914 | 2.74397 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −73.2716 | −2.69900 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.57101 | 0.352075 | 0.176038 | − | 0.984383i | \(-0.443672\pi\) | ||||
0.176038 | + | 0.984383i | \(0.443672\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.01302 | 0.0739500 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.3553 | −0.379900 | −0.189950 | − | 0.981794i | \(-0.560833\pi\) | ||||
−0.189950 | + | 0.981794i | \(0.560833\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −65.8939 | −2.41416 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.1675 | −0.737889 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.856029 | −0.0312786 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.4868 | −1.11248 | −0.556239 | − | 0.831022i | \(-0.687756\pi\) | ||||
−0.556239 | + | 0.831022i | \(0.687756\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 37.0128 | 1.34882 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −42.4913 | −1.54642 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.0841 | −0.475549 | −0.237774 | − | 0.971320i | \(-0.576418\pi\) | ||||
−0.237774 | + | 0.971320i | \(0.576418\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 97.6181 | 3.54331 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.3638 | 1.17319 | 0.586594 | − | 0.809881i | \(-0.300468\pi\) | ||||
0.586594 | + | 0.809881i | \(0.300468\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39.3666 | 1.42517 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 26.1641 | 0.945965 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.96079 | −0.251340 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.9234 | 0.393908 | 0.196954 | − | 0.980413i | \(-0.436895\pi\) | ||||
0.196954 | + | 0.980413i | \(0.436895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.5753 | −1.20919 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34.9008 | −1.25530 | −0.627648 | − | 0.778497i | \(-0.715982\pi\) | ||||
−0.627648 | + | 0.778497i | \(0.715982\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.2452 | −1.44565 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −51.2656 | −1.83914 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.5007 | −0.412055 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.06363 | 0.252756 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.900592 | 0.0321845 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.6164 | −1.73519 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.72739 | −0.204159 | −0.102080 | − | 0.994776i | \(-0.532550\pi\) | ||||
−0.102080 | + | 0.994776i | \(0.532550\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 65.2766 | 2.32391 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.6274 | 0.875650 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.66610 | 0.165698 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −33.6643 | −1.19395 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 45.1622 | 1.59973 | 0.799863 | − | 0.600183i | \(-0.204906\pi\) | ||||
0.799863 | + | 0.600183i | \(0.204906\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.4697 | 0.370391 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −47.6149 | −1.68239 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −46.5143 | −1.64145 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −80.4372 | −2.83504 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 48.4928 | 1.70703 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.4870 | 1.24766 | 0.623828 | − | 0.781562i | \(-0.285577\pi\) | ||||
0.623828 | + | 0.781562i | \(0.285577\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.2334 | −0.710492 | −0.355246 | − | 0.934773i | \(-0.615603\pi\) | ||||
−0.355246 | + | 0.934773i | \(0.615603\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34.5981 | −1.21341 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38.3527 | −1.34344 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.0837292 | −0.00292931 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.1996 | 0.356404 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.0305 | 1.81588 | 0.907938 | − | 0.419104i | \(-0.137656\pi\) | ||||
0.907938 | + | 0.419104i | \(0.137656\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.60310 | −0.195312 | −0.0976559 | − | 0.995220i | \(-0.531134\pi\) | ||||
−0.0976559 | + | 0.995220i | \(0.531134\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −85.6601 | −2.98230 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.3875 | 0.987129 | 0.493565 | − | 0.869709i | \(-0.335694\pi\) | ||||
0.493565 | + | 0.869709i | \(0.335694\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.5931 | 1.13201 | 0.566003 | − | 0.824403i | \(-0.308489\pi\) | ||||
0.566003 | + | 0.824403i | \(0.308489\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.1604 | 0.421841 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.4702 | −0.847844 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −62.0882 | −2.14865 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.73591 | 0.0600017 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.0055 | −1.55376 | −0.776881 | − | 0.629647i | \(-0.783199\pi\) | ||||
−0.776881 | + | 0.629647i | \(0.783199\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.1145 | −0.486706 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.1082 | −0.417029 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 39.8019 | 1.36923 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −121.708 | −4.18195 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.11667 | 0.175604 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.6833 | 1.08609 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.6381 | −0.740875 | −0.370438 | − | 0.928857i | \(-0.620792\pi\) | ||||
−0.370438 | + | 0.928857i | \(0.620792\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.98525 | −0.341488 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.4432 | −0.390892 | −0.195446 | − | 0.980714i | \(-0.562616\pi\) | ||||
−0.195446 | + | 0.980714i | \(0.562616\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.57422 | 0.258429 | 0.129215 | − | 0.991617i | \(-0.458754\pi\) | ||||
0.129215 | + | 0.991617i | \(0.458754\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −114.764 | −3.91114 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.6063 | 1.17801 | 0.589007 | − | 0.808128i | \(-0.299519\pi\) | ||||
0.589007 | + | 0.808128i | \(0.299519\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.95266 | 0.168396 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.0183 | 0.849667 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 89.7036 | 3.04299 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.31834 | 0.315740 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −41.0505 | −1.38935 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.36981 | 0.181533 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.4493 | −0.994434 | −0.497217 | − | 0.867626i | \(-0.665645\pi\) | ||||
−0.497217 | + | 0.867626i | \(0.665645\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.8243 | −0.871033 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.5583 | 1.73704 | 0.868522 | − | 0.495651i | \(-0.165070\pi\) | ||||
0.868522 | + | 0.495651i | \(0.165070\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.2991 | 0.851382 | 0.425691 | − | 0.904869i | \(-0.360031\pi\) | ||||
0.425691 | + | 0.904869i | \(0.360031\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 68.0008 | 2.28582 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.92340 | 0.0645815 | 0.0322908 | − | 0.999479i | \(-0.489720\pi\) | ||||
0.0322908 | + | 0.999479i | \(0.489720\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.8402 | −0.900192 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −55.8293 | −1.87035 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.99564 | −0.133709 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.3541 | 0.412950 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.4146 | −0.414512 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.6921 | 0.956936 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.0735 | 0.368912 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.835522 | −0.0278044 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.0268 | 0.632471 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.7093 | −0.920071 | −0.460036 | − | 0.887900i | \(-0.652163\pi\) | ||||
−0.460036 | + | 0.887900i | \(0.652163\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.55060 | −0.283605 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.4735 | −1.70539 | −0.852696 | − | 0.522407i | \(-0.825034\pi\) | ||||
−0.852696 | + | 0.522407i | \(0.825034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.7856 | −1.38290 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −45.5837 | −1.50695 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.6048 | −0.482293 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.4158 | 0.838390 | 0.419195 | − | 0.907896i | \(-0.362312\pi\) | ||||
0.419195 | + | 0.907896i | \(0.362312\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.5129 | −0.478216 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.898319 | −0.0295685 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.8022 | −0.914131 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.63747 | −0.0537815 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41.2485 | −1.35332 | −0.676661 | − | 0.736295i | \(-0.736574\pi\) | ||||
−0.676661 | + | 0.736295i | \(0.736574\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.33880 | 0.306067 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.3185 | −1.02532 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 54.2103 | 1.77287 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.1849 | −1.18211 | −0.591054 | − | 0.806632i | \(-0.701288\pi\) | ||||
−0.591054 | + | 0.806632i | \(0.701288\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.4317 | −0.503593 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.2262 | −0.561559 | −0.280779 | − | 0.959772i | \(-0.590593\pi\) | ||||
−0.280779 | + | 0.959772i | \(0.590593\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 70.9267 | 2.30969 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.04451 | −0.0990378 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.7823 | 0.577847 | 0.288924 | − | 0.957352i | \(-0.406703\pi\) | ||||
0.288924 | + | 0.957352i | \(0.406703\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.91546 | 0.192024 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.6765 | 0.378636 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.3478 | −1.53374 | −0.766872 | − | 0.641800i | \(-0.778188\pi\) | ||||
−0.766872 | + | 0.641800i | \(0.778188\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 64.0269 | 2.07186 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 61.0698 | 1.97411 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 47.4821 | 1.53328 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.3045 | 0.784017 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.655354 | 0.0211185 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.6892 | 0.376289 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.3504 | 0.815213 | 0.407606 | − | 0.913158i | \(-0.366364\pi\) | ||||
0.407606 | + | 0.913158i | \(0.366364\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.46871 | 0.207805 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.3901 | 1.45664 | 0.728319 | − | 0.685238i | \(-0.240302\pi\) | ||||
0.728319 | + | 0.685238i | \(0.240302\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 82.7653 | 2.65333 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.8939 | 0.348883 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.3398 | 0.874679 | 0.437339 | − | 0.899297i | \(-0.355921\pi\) | ||||
0.437339 | + | 0.899297i | \(0.355921\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −98.6549 | −3.15302 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.1381 | −0.962236 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.84750 | 0.154611 | 0.0773056 | − | 0.997007i | \(-0.475368\pi\) | ||||
0.0773056 | + | 0.997007i | \(0.475368\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42.3313 | −1.34879 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −39.8720 | −1.26914 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.516372 | 0.0164197 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.1022 | −0.892696 | −0.446348 | − | 0.894859i | \(-0.647276\pi\) | ||||
−0.446348 | + | 0.894859i | \(0.647276\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −48.8954 | −1.55165 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 51.3551 | 1.62807 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.99262 | −0.221458 | −0.110729 | − | 0.993851i | \(-0.535319\pi\) | ||||
−0.110729 | + | 0.993851i | \(0.535319\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.19920 | 0.0379409 |
(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 | 4864.2.a.bt.1.1 | 10 | ||
4.3 | odd | 2 | 4864.2.a.bs.1.9 | 10 | |||
8.3 | odd | 2 | inner | 4864.2.a.bt.1.2 | 10 | ||
8.5 | even | 2 | 4864.2.a.bs.1.10 | 10 | |||
16.3 | odd | 4 | 2432.2.c.j.1217.18 | yes | 20 | ||
16.5 | even | 4 | 2432.2.c.j.1217.17 | yes | 20 | ||
16.11 | odd | 4 | 2432.2.c.j.1217.3 | ✓ | 20 | ||
16.13 | even | 4 | 2432.2.c.j.1217.4 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.j.1217.3 | ✓ | 20 | 16.11 | odd | 4 | ||
2432.2.c.j.1217.4 | yes | 20 | 16.13 | even | 4 | ||
2432.2.c.j.1217.17 | yes | 20 | 16.5 | even | 4 | ||
2432.2.c.j.1217.18 | yes | 20 | 16.3 | odd | 4 | ||
4864.2.a.bs.1.9 | 10 | 4.3 | odd | 2 | |||
4864.2.a.bs.1.10 | 10 | 8.5 | even | 2 | |||
4864.2.a.bt.1.1 | 10 | 1.1 | even | 1 | trivial | ||
4864.2.a.bt.1.2 | 10 | 8.3 | odd | 2 | inner |